Answer:
Part AWhen graphing the function y = f(x+3), all of the x values would be shifted to the right by 3 because the transformation is a shift right by 3 units.
Mistake: This is not a shift rightCorrection: ... all of the x values would be shifted to the left by 3 because the transformation is a shift left by 3 unitsPart BWhen graphing the function y=−f(x), there is a reflection over the y-axis
Mistake: This is not a reflection over the y-axisCorrection: ...there is a reflection over the x-axisPart CWhen graphing the function y=2f(x), all of the y-values would be multiplied by 2 because the transformation is a vertical compression by a factor of 2.
Mistake: This is not a vertical compressionCorrection: ... a horizontal compression by a factor of 2Note: "multiplied by 12" considered as typo otherwise this is to be included as correction
Answer:
the answer is A When graphing the function
y=f(x+3)
, all of the
x
values would be shifted to the right by 3 because the transformation is a shift right by 3 units.
Following the steps below, what is the next step in constructing a line perpendicular to a segment? Start with a line and point K on that line. Set the compass's width to a medium setting. The actual width does not matter. Without changing the compass's width, mark a short arc on the line at each side of the point K, forming the points P and Q. These two points are the same distance from K because you did not change the width of the compass. ? Using the straight edge, draw a line from K to where the arcs cross. Without changing the compass's width, repeat from the point Q so that the two arcs cross each other, creating the point R. From P, mark off a short arc above K. Increase the compass to almost double the width (the exact setting is not important).
''Start with a line and point K on that line'' is the next step in constructing a line perpendicular to a segment
What is perpendicular line?
Whenever two lines cross at a right angle, they are perpendicular or orthogonal. All four of the angles created by two perpendicular lines are 90 degrees.
If and only if the slope product of two non-vertical lines is negative one, those lines are perpendicular. In other words, two perpendicular lines' slopes are the negative reciprocals of one another. A vertical line is perpendicular to only horizontal lines and has an infinite slope (which have slope 0).
This provides a way to determine if two lines are parallel by using their equations. Additionally, this enables us to discover the equations of lines that are perpendicular to another line.
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Computer the lower Riemann sum for the given function f(x) = 4 - x^3 over the interval x E [0,1] with respect to the partition P = [0, 1/2, 3/4, 1]
Answer:
[tex]\dfrac{917}{256}=3.58203125[/tex]
Step-by-step explanation:
The Riemann sum is a method by which we can approximate the area under a curve using a series of rectangles.
The Lower Riemann Sum uses the minimum height of the rectangle on each subinterval.
As the Lower Riemann Sum is entirely below the curve, it is an underestimation of the area under the curve.
The number of partitions is the number of rectangles used.
Partitions can be of equal length or not of equal length.
Given:
Function: f(x) = 4 - x³Interval: [0, 1]Partition, P = [0, 1/2, 3/4, 1]The given partition divides the interval [0, 1] into 3 subintervals:
[0, 1/2], [1/2, 3/4] and [3/4, 1]To calculate the areas of the rectangles, multiply the width of each rectangle by its height.
The width is the difference between the x-values of each subinterval.
The height is the minimum value of the function across the subinterval. For the given function, this is the value of the function for the right side of the subinterval.
First rectangle [0, 1/2]:
[tex]\begin{aligned}\implies \left(\dfrac{1}{2}-0\right) \cdot f\left(\dfrac{1}{2}\right)&=\dfrac{1}{2} \cdot \left(4-\left(\dfrac{1}{2}\right)^3\right)\\\\&=\dfrac{1}{2} \cdot \dfrac{31}{8}\\\\&=\dfrac{31}{16}\end{aligned}[/tex]
Second rectangle [1/2, 3/4]:
[tex]\begin{aligned}\implies \left(\dfrac{3}{4}-\dfrac{1}{2}\right) \cdot f\left(\dfrac{3}{4}\right)&=\dfrac{1}{4} \cdot \left(4-\left(\dfrac{3}{4}\right)^3\right)\\\\&=\dfrac{1}{4} \cdot \dfrac{229}{64}\\\\&=\dfrac{229}{256}\end{aligned}[/tex]
Third rectangle [3/4, 1]:
[tex]\begin{aligned}\implies \left(1-\dfrac{3}{4}\right) \cdot f\left(1\right)&=\dfrac{1}{4} \cdot \left(4-\left(1\right)^3\right)\\\\&=\dfrac{1}{4} \cdot 3\\\\&=\dfrac{3}{4}\end{aligned}[/tex]
Therefore, the Lower Reimann Sum for the given function over the given interval and partitions is the sum of the area of the rectangles:
[tex]\implies \dfrac{31}{16}+\dfrac{229}{256}+\dfrac{3}{4}=\dfrac{917}{256}=3.58203125[/tex]
A baker has three banana muffin recipes. Recipe A uses 3 bananas to make 12 muffins. Recipe B uses 5 bananas to make 24 muffins. Recipe C uses 11 bananas to make 48 muffins.
Rutendo tried to order the recipes from least to greatest by bananas per muffin, but he made a mistake. Here's his work:
\begin{aligned} \dfrac{12}{3}&=4\\\\ \dfrac{24}{5}&=4.8\\\\ \dfrac{48}{11}&\approx 4.36\\\\ \stackrel{\text{Least}}{\underbrace{4}_\text{Recipe A}} &< \underbrace{4.36}_\text{Recipe C} < \stackrel{\text{Greatest}}{\underbrace{4.8}_\text{Recipe B}} \end{aligned}
3
12
5
24
11
48
Recipe A
4
Least
=4
=4.8
≈4.36
<
Recipe C
4.36
<
Recipe B
4.8
Greatest
What was Rutendo's mistake?
Choose 1 answer:
Answer: Rutendo's mistake was ordering the recipes from least to greatest by bananas per muffin by comparing the number of bananas in each recipe rather than the number of bananas per muffin. ✅
Step-by-step explanation:
By dividing the number of bananas used in each recipe by the number of muffins, he would have been able to determine which recipe uses the least amount of bananas per muffin.
Recipe A: 3/12 = 0.25 bananas per muffin
Recipe B: 5/24 = 0.208 bananas per muffin
Recipe C: 11/48 = 0.229 bananas per muffin
So Recipe A uses the least amount of bananas per muffin, Recipe C uses the next least amount of bananas per muffin, and Recipe B uses the most amount of bananas per muffin.
Answer: The answer is C
Step-by-step explanation:
Because it is
Given m∠ABC=37°m∠ABC=37°and m∠CBD=165°m∠CBD=165°. According to the Angle Addition Postulate, what is the measure of ∠ABD∠ABD, that contains −−→BCBC→?
According to the Angle Addition Postulate, the measure of m∠ABD = 202°.
What is an angle addition postulate?According to the Angle Addition Postulate, an angle's measure is equal to the sum of the measures of any two adjacent angles. The Angle Addition Postulate can be used to determine the measurement of a missing angle or to determine the angle produced by two or more other angles.
Given:
The angle measures:
m∠ABC=37°,
and m∠CBD= 165°.
So, according to the angle addition postulate;
m∠ABD = m∠ABC + m∠CBD
Substituting the values,
m∠ABD = 37° + 165°
m∠ABD = 202°
Therefore, the angle measure of m∠ABD = 202°.
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What does it look like on a graph line
A horizontal x-axis and a vertical y-axis make up the line graph.
What does a graph line look like? These axes often cross around the bottom of the y-axis and the left end of the x-axis because the majority of line graphs only deal with positive numerical values. The intersection of the axes is always at (0, 0). To draw a graph line the following steps containStep 1: Identify the variables. Step 2: Determine the variable range. Step 3: Determine the scale of the graph.Step 4: Number and label each axis and title the graph.Step 5: Determine the data points and plot on the graph.Step 6: Draw the graph.To learn more about graph line refer to:
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need a bit help, im stuck on these.
Answer:
7. VS = 17
8. QR = 6
9. UT = 17
Step-by-step explanation:
You have trapezoid QRTU with midsegment VS parallel to bases QR and TU. Given dimensions for two of these parallel lines, you want the measure of the third.
Segment relationshipsThe markings on the parts of segments QU and RT indicate that points V and S are their midpoints, respectively. This makes segment VS a "midsegment", one that joins the midpoints of opposite sides. As such, its length is the average of the lengths of QR and TU:
VS = (QR +TU)/2
This is the relation that is used for problem 7.
For problems 8 and 9, this is rearranged to give the values of QR and UT:
QR = 2VS -UT
UT = 2VS -QR
7. VSFrom above, ...
VS = (QR +UT)/2 = (12 +22)/2
VS = 17
8. QRFrom above, ...
QR = 2VS -UT = 2(9) -12
QR = 6
9. UTFrom above, ...
UT = 2VS -QR = 2(11) -5
UT = 17
__
Additional comment
You will note that the line segments form an arithmetic sequence: the difference in length between adjacent segments is the same.
7: 12, 17, 22
8: 6, 9, 12
9: 5, 11, 17
Determine if each equation has one solution, no solution, or infinite solutions.
1. -4g + 8 = 20
2. -3b = 2b - 5b
3. -3f = 2 - 3f
4. 2n - 12 = -12 + 2n
5. 7c - 4 = 3 + 7c
6. 3 - 5y = 2y + 24
7. 22 + w = 2(4w - 3)
8. 6h - 8 + 4h = 12 + 10h
9. 12j = 4(3j - 8)
10. 5(u-9) = -2u - 45 + 7u
11. 2 (4a - 7) - 3a = 19 - 6a
12. 3 - 11d = -6d + 3 - 5d
Answer:
Step-by-step explanation:
1. One solution. Solving for g gives g=2.
2. No solution. The equation is equivalent to -3b = -3b, which is always false.
3. One solution. Solving for f gives f=2/5.
4. Infinite solutions. The equation is equivalent to 2n-12 = 2n-12, which is always true for any value of n.
5. Infinite solutions. The equation is equivalent to 7c-4 = 7c+3, which is always true for any value of c.
6. One solution. Solving for y gives y = -3/7.
7. One solution. Solving for w gives w = -22
8. One solution. Solving for h gives h = 2
9. One solution. Solving for j gives j = -2
10. One solution. Solving for u gives u = -5
11. One solution. Solving for a gives a = -1/2
12. No solution. The equation is equivalent to 3-11d = -11d+3, which is always false.
explain how you know which number 1 15/16 17/8 63/32 is closest to 2
The closest number of 2 is 63/32. By using the subtraction operation, we can compute it.
What are numbers?
A number is a mathematical object that can be used to count, measure, and name things. The natural numbers 1, 2, 3, 4, and so on are the original examples. Number words can be used to represent numbers in language.
Given numbers are [tex]1\frac{15}{16}[/tex], 17/8, 63/32
Now find the difference between the given numbers from 2.
The difference of [tex]1\frac{15}{16}[/tex] from 2 is
2 - [tex]1\frac{15}{16}[/tex]
= 2 - 31/16
= 1/16.
The difference of 17/8 from 2 is
|2 - 17/8|
= |(16 - 17)/8|
=| -1/8|
= 1/8
The difference of 63/32 from 2 is
2 - 63/32
= (64 - 63)/32
= 1/32
The numerator of the difference is the same. The greater denominator represents a less number.
Thus 63/32 is close to 2.
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please write an equation for each line.
By analytic geometry, the equations for lines represented by figure are:
Red line: y = 2 · x + 5 Yellow line: y = - 3.333 · x + 5 Black line: y = 2 · x - 6 Green line: y = - 2 Blue line: x = 5How to derive the equations of lines seen in a picture
In this problem we find the representation of five lines (red - yellow - green - blue - black). There is a horizontal line (green), a vertical line (blue) and three oblique lines (red - yellow - black). According to analytic geometry, we find the following definitions:
Horizontal lines: y = aVertical lines: x = bOblique lines: y = m · x + b (m - Slope, b - Intercept).The slope for oblique lines is determined by secant line formula:
m = Δy / Δx
Where:
Δx - Change in independent variable.Δy - Change in dependent variable.From picture we get the following hints:
Red line crosses the y-axis at (x, y) = (0, 5).Yellow line crosses the y-axis at (x, y) = (0, 5).Black line crosses the y-axis at (x, y) = (0, - 6).Green line crosses the y-axis at (x, y) = (0, - 2).Blue line crosses the x-axis at (x, y) = (5, 0).Finally, we proceed to find the equations for each line:
Red line
Slope
m = 5 / 2.5
m = 2
Intercept
b = y - m · x
b = 5 - 2 · 0
b = 5
The equation for the red line is y = 2 · x + 5.
Yellow line
Slope
m = - 5 / 1.5
m = - 3.333
Intercept
b = y - m · x
b = 5 - (- 3.333) · 0
b = 5
The equation for the yellow line is y = - 3.333 · x + 5.
Black line
Slope
m = 6 / 3
m = 2
Intercept
b = y - m · x
b = - 6 - 2 · 0
b = - 6
The equation for the black line is y = 2 · x - 6.
Green line
The equation for the green line is y = - 2.
Blue line
The equation for blue line is x = 5.
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y=x^2+9x+8 in vertex form
The vertex form of parabola y = x² + 9 · x + 8 is the quadratic equation y + 49 / 4 = (x + 9 / 2)².
How to determine the equation of a parabola in vertex form
Herein we find the equation of a parabola in standard form, that is, a quadratic equation of the form:
y = a · x² + b · x + c
Where:
a, b, c - Real coefficientsx - Independent variable.y - Dependent variable.And we are asked to transform this expression into vertex form, that is, a quadratic equation of the form:
y - k = C · (x - h)²
Where:
(h, k) - Coordinates of the vertex.C - Vertex constant.This can be done by means of algebra properties. First, write the quadratic equation:
y = x² + 9 · x + 8
Second, use algebra properties until a perfect square trinomial is found:
y = x² + 9 · x + 8
y + 49 / 4 = x² + 9 · x + 81 / 4
Third, factor the perfect square trinomial:
y + 49 / 4 = (x + 9 / 2)²
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Exit Slip: (5) The 6th grade class is competing in Field Day. There
are 32 girls and 40 boys. If each team must have the same
number of girls and boys, what's the greatest number of teams
that can be formed?
We shall see that a maximum of 8 teams can be created, with 3 boys and 4 girls on each team.
what is common factors ?The largest factor that will divide into two or more numbers is known as the highest common factor (HCF). The smallest multiple shared by two or more numbers is known as the lowest common multiple (LCM). A number that divides two or more numbers precisely is referred to as a common factor. For instance, because they are both even, 10 and 20 share a common factor of 2. The largest number that precisely divides two or more numbers is known as the greatest common factor (GCF).
given
32 girls and 24 boys
Additionally, we must divide them into groups in order to determine the number of groups that can be formed. To do this, we must determine the highest common factor between 24 and 32.
To obtain that, we can express both of these as a prime number product as follows:
24 = 2*2*2*3
32 = 2*2*2*2*2
The highest common factor between 24 and 32 is 2*2*2 = 8 since in all of these we have three times the factor 2.
Each squad will have the following number of boys 24/8 = 3
Each team will have four girls, or 32/8, total.
We shall see that a maximum of 8 teams can be created, with 3 boys and 4 girls on each team.
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Choose the better buy.
5 qt.: $2.25
5 liters: $2.35
There are 1.057 quarts in a liter, and there are 0.946 liters in a quart.
How to calculate the value?5 Quarts =4.7317647 Liters
5 Liters =5.2834410 Quarts
The cost is In liter calculate
5 qt.: $2.25=4.7317647 liter
5 liters: $2.35=1000×5=5000
=5000-4.731
= 4,995.269 litter difference from 5 liter
5000 liter in liter $2.35 so each value 2,127.65957447
4.731 liter in of quarts $2.25 each value 2,102.66666667
1 qt = 2pt For every quart there are 5 qts = 10 pts two pints. So, multiply 5 x 2 = 10 pints. Example: If a pot has a capacity of 16 cups, how many quarts can it hold? 1 qt = 4c For every quart, there are 4 cups. The quart (symbol: qt) is an English unit of volume equal to a quarter gallon. Three kinds of quarts are currently used: the liquid quart and dry quart of the US customary system and the imperial quart of the British imperial system. All are roughly equal to one liter.
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Share £32 in the ratio 1 : 5 : 2.
Step-by-step explanation:
In order to share the money equally
We take the variables as 'x'
This is because the given values are in the form of a ratio
So to do this we plug these values into a equation which is,
[tex]x + 5x + 2x = 32[/tex]
Adding the values we get,
[tex]8x = 32[/tex]
Dividing both sides by 8 we get,
[tex]\frac{8x}{8}= \frac{32}{8}[/tex]
[tex]x = 4[/tex]
Now we multiply the given values by x which is 4 in order to find how much money each ratio get
[tex]x = 4[/tex]
[tex]5x = 5X4 = 20[/tex]
[tex]2x = 2X4 = 8[/tex]
4 + 20 + 8 = £ 32 (Proving)
(25 points) find x and y of the heptagon more info in the picture above
Answer:
x = 128.57°
y = 51.43°
Step-by-step explanation:
x = (n - 2) × 180°/n = (7 - 2) × 180°/7 = 900/7° = 128.57°
x + y = 180
y = 180° - 128.57°
y = 51.43°
A container can hold a maximum of 17.75 pounds. There are two objects in the container. The first object weighs 6.53 pounds and the second weighs 10.1 pounds. How many more pounds can the container hold? Write your answer as a decimal.
The container can hold 1.12 pounds
How to calculate the number of pounds that the container can hold?
A container can hold a maximum of 17.75 pounds
There are two objects in the container
The first object weights 6.53 pounds
The second object weight 10.1 pounds
The amounts of pounds that the container can hold is
6.53+10.1
= 16.63
17.75-16.63
= 1.12
Hence the container can hold 1.12 pounds
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Bart found 20 quadrilaterals in his classroom. He made a Venn diagram using the properties of the quadrilaterals, comparing those with four equal side lengths. (E) and those with four right angles (R). Given that a randomly chosen quadrilateral has four right angles, what is the probability that the quadrilateral also has four equal side lengths? Express your answer in percent form, rounded to the nearest whole percent.
The probability that a randomly chosen quadrilateral with four right angles will also have four equal side lengths is 25%.
What is probability?Probability is a branch of mathematics that deals with the likelihood of an event occurring. It is the measure of how likely it is that something will happen or be the case. Probability is expressed as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty. Probability can be used to calculate the chances of a certain outcome based on a set of conditions or data. Probability can also be used to make decisions and predictions about the future.
This is because of the Venn diagram that Bart created. If a quadrilateral has four right angles, then it can either have four equal side lengths (which makes it a square) or it can have four unequal side lengths. Since there are 8 quadrilaterals in the set with four equal side lengths (E) and 16 quadrilaterals in the set with four right angles (R), the probability that a randomly chosen quadrilateral with four right angles will also have four equal side lengths is 8/16, which is equivalent to 25%. Therefore, the probability that a randomly chosen quadrilateral with four right angles will also have four equal side lengths is 25%, rounded to the nearest whole percent.
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14. Point B(4, -16) is dilated by a scale factor
3
of to create B'.
a. Write a rule for the transformation.
The rule for the transformation that dilates point B(4, -16) by a scale factor of 3 is: (x, y) --> (3x, 3y)
What is transformation?A transformation is a function that maps points in a given space to points in a different space. There are many types of transformations, including translations, rotations, dilations, and reflections.
What is coordinate?A coordinate is a set of numerical values that are used to specify the position of a point in a specific space. In two-dimensional space, a point is typically defined by an ordered pair of numbers (x, y), where x is the horizontal position and y is the vertical position. In three-dimensional space, a point is typically defined by an ordered triple of numbers (x, y, z), where x, y, and z are the positions in the three dimensions.
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A ball is rolled at a speed of 12m/sec after 40 seconds it comes to a stop . What is the acceleration of the ball ? Answer to nearest hundredth
Therefore , the solution of the given problem of speed comes out to be
the ball accelerates at 0.33 m/s2.
What is speed?Speed is a pace that is measured in terms of how far an object travels in a given amount of time. Speed can be measured in a wide range of ways, including in miles an hour, laps every minute, and meters a second. There are connections between the units of time, distance, and speed. Three ways of expressing the relationship are
d = rt, r = dt, and t = dr.
Given -
The ball's initial speed is 0 meters per second.
v = 12 m/s is the ball's final speed.
36 seconds were used.
Determine the ball's acceleration.
Solution:
=> A = (v-u)/t
=>A = (12-0)/36
=> A = 12/36
=> A =1 /3
=> A = 0.33 m/s²
Consequently, the ball accelerates at 0.33 m/s2.
Therefore , the solution of the given problem of speed comes out to be
the ball accelerates at 0.33 m/s2.
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I need help
Find the length of the segment with the given endpoints.
(-3, -12.5), (-3, 16.5)
Answer:
The length would be 29.
Step-by-step explanation:
Follow the distance formula in the image.
-Hope this Helped
HEL Two students created paintings for their art class. The canvas size used for each is shown.
2 rectangles: Rectangle 1 has a length of 6 feet and width of 4 feet. Rectangle 2 has a length of 3 feet and width of 2 feet.
Which statement is true about the ratios comparing the width and length of each painting?
The paintings' width to length ratios are equal because the ratio 4 to 6 is equal to the ratio 2 to 3.
The paintings' width to length ratios are equal because the ratio 6 to 4 is equal to the ratio 2 to 3.
The paintings' width to length ratios are different because the ratio 3 to 2 is not equal to 6 to 4.
The paintings' width to length ratios are different because the ratio 4 to 6 is not equal to 3 to 2.P ASAP
The statement that is true about the ratios comparing the width and length of each painting is:
The paintings' width to length ratios are equal because the ratio 4 to 6 is equal to the ratio 2 to 3.
Ratio of numbers.A ratio is a fraction which compares the values of two numbers. Such that they can be expressed as a ratio of one to the other. Example is the ratio of a to b which can be expressed as; a:b or a/ b.
From the first dimension of the canvas size, we have;
length = 6 feet
width = 4 feet
So that,
the ratio comparing the width and length = 4/ 6
= 0.6667
From the second dimensions of the canvas size, we have;
length = 3 feet
width = 2 feet
the ratio comparing the width and length = 2/ 3
= 0.6667
Therefore, the statement that is true about the ratios comparing the width and length of each panting is; The paintings' width to length ratios are equal because the ratio 4 to 6 is equal to the ratio 2 to 3.
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Mason had 30 minutes to do a three-problem quiz. He spent 9 1/4 minutes on question A and 3 4/5 minutes on question B. How much time did he have left for question C?
Answer:
16 57/60 mins
Step-by-step explanation:
9 1/4 = 555 secs
3 4/5 = 228 secs
30.mins = 1800 secs
time for C = 1800 - 555 - 228
= 1017 sec
16 57/60 mins
Drag each symbol to the correct location on the equation. Not all symbols will be used.
A group of third-grade and fourth-grade students are taking a field trip. The group will fill a total of 4va
Each van seats 8students.
• There are 27third-grade students in the group.
• The rest of the students in the group are fourth-graders.
Complete the equation to show how to find f, the number fourth-grade students in the group.
X
4
+
8
27 = f
Answer:
The equation to find the number of fourth-grade students in the group (f) is:
(number of vans) x (number of students per van) + (number of third-grade students) = (number of fourth-grade students)
So, the equation would be:
4v x 8s + 27s = f
Where "v" stands for vans, "s" stands for students, and "f" stands for fourth-grade students.
To find the number of fourth-grade students, you would need to substitute in the given information:
4 x 8 + 27 = f
32 + 27 = f
So, there are 59 fourth-grade students in the group.
Step-by-step explanation:
2. If we want to find the volume of the child's toy shown below, what will the units be on our answer?
A cm^3
B cm
C cm^4
If we want to find the volume of the given toy, then the units of our answer will be (A) cm³.
What is volume?Volume is the amount of space a thing takes up, whereas capacity is the amount of solid, liquid, or gas that it can hold.
Volume is measured in cubic units, although capacity can be expressed in almost any other unit, such as liters, gallons, pounds, etc.
The capacity of an object is measured by its volume.
For instance, a cup's capacity is stated to be 100 ml if it can hold 100 ml of water in its brim.
The quantity of space occupied by a three-dimensional object can also be used to describe volume.
So, in the description, it is stated that the value is measured in cubic units.
Therefore, if we want to find the volume of the given toy, then the units of our answer will be (A) cm³.
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Determine the ratio adjacent over hypotenuse using
8. The ratio of the adjacent over the hypotenuse is 8:17
10. The ratio of the adjacent over the hypotenuse is 1:√2
Calculating the ratio of adjacent over hypotenuseFrom the question, we are to calculate the ratio of the adjacent over the hypotenuse in the given triangles
8.
Using angle A as the reference angle
Adjacent = 16
Hypotenuse = 34
Thus,
The ratio of the adjacent over the hypotenuse = 16/34
The ratio of the adjacent over the hypotenuse = 8/17
Hence, the ratio is 8:17
10.
First,
We will calculate the hypotenuse, H
From the Pythagorean theorem, we can write that
H² = 4² + 4²
H² = 16 + 16
H² = 32
H = √32
H = 4√2
Now,
Using angle A as the reference angle
Adjacent = 4
Hypotenuse = 4√2
Thus,
The ratio of the adjacent over the hypotenuse = 4/4√2
The ratio of the adjacent over the hypotenuse = 1/√2
Hence, the ratio is 1:√2
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Problem 5.1
A publisher wants to know the thickness of a new book.
The book has a front cover and a back cover, each with a
thickness of of an inch.
The paper has a thickness of
inch per 100 pages.
Write an equation that represents the total width of the
book, y, for every 100 pages of paper, x.
Given that for every hundred pages a thickness of 1/4 inch is added to the book, then the equation is: y = 1/2 + 1/4*x
How to find the Solution?Considering that the book's front and back covers each have a thickness of 1/4 inch, adding them together results in a thickness of 1/2 inch for the book, regardless of how many pages it has.
Given that a book's thickness increases by a quarter of an inch for every hundred pages, the equation is:
y = 1/2 + 1/4*x
where y denotes the book's width and x is the number of bond paper pages printed every 100 pages. Y has a length of inches.
Equations that have the same roots or solutions are said to be equivalent.
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Need this please !!!!!
Answer:
m∠H = 53°m∠I = 74°m∠J = 53°----------------------------------
Since the triangle is isosceles, the two angles opposite to equal sides are congruent:
m∠J = m∠H = (3x + 11)°The sum of the three angles is 180°:
2(3x + 11) + 4x + 18 = 1806x + 22 + 4x + 18 = 18010x + 40 = 18010x = 140x = 14The angle measures are:
m∠J = m∠H = (3*14 + 11)° = 53°m∠I = (4*14 + 18)° = 74°write -40.425 as a mixed number
Answer:
-40 17/40
Step-by-step explanation:
Answer: -40 7/40
Step-by-step explanation:
Rewrite the decimal number as a fraction with 1 in the denominator
40.425=40.4251/1
Multiply to remove 3 decimal places. Here, you multiply top and bottom by 103 = 1000
40.4251×1000/1000=40425/1000
Find the Greatest Common Factor (GCF) of 40425 and 1000 and reduce the fraction by dividing both numerator and denominator by GCF = 25
40425÷25
1000÷25
=1617/40
Simplify the improper fraction
in conclusion
-40 17/40
you must not forget the minus/negative sign :)
Considering both dividends paid and capital gains, Dylan's pretax profit from his investment is $
Dylan's pretax return on investment (ROI) is
Type the correct answer in each box. Use numerals instead of words.
The pretax rate of return is the profit or loss on an investment before taxes are subtracted.
What is the difference between taxable income and pretax income?Pretax financial income, on the other hand, is the amount a firm earns before taxes are taken into account. Taxable income is the amount of income that a corporation must pay taxes on.
Generally speaking, investment income includes, but is not limited to: interest, dividends, capital gains, rental and royalty income, non-qualified annuities, income from firms engaged in trading financial instruments or commodities, and enterprises that are passive for the taxpayer.
The profit or loss on an investment prior to deducting taxes is known as the pretax rate of return. Taxes on investment income are levied by the government on any additional income derived from purchasing or disposing of investments. Securities that are profitably sold are subject to capital gains taxes.
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Answer: Considering both dividends paid and capital gains, Dylan’s pretax profit from his investment is $30. Dylan’s pretax return on investment (ROI) is 24%.
Step-by-step explanation: To determine Dylan’s profit from his investment, add his dividends of $5 and his capital gains of $25.total profit = $25 + $5= $30Before taxes are applied, Dylan can calculate his return on investment (ROI) by dividing his profit by the cost of his investment:30125 = 0.24, or 24%.
Simplify
8!/(8-2)
A. 720
b. 0.018
C. 8
d. 56
e. 40320
f. 1.333
Answer:
D) 56
Step-by-step explanation:
[tex]\displaystyle \frac{8!}{(8-2)!}=\frac{8!}{6!}=\frac{8*7*6*5*4*3*2*1}{6*5*4*3*2*1}=8*7=56[/tex]
From midnight until 8:00 AM, the temperature tripled and then rose 5 degrees. The temperature at 8:00 AM was –7 degrees Celsius. Write and solve an equation to find the temperature at midnight.
The equation for the temperature at midnight and the solution are Tm = 3T + 5 and -16 degrees Celsius respectively
How to write and solve an equation?
An equation is a mathematical statement that is made up of two expressions joined by an equal sign.
Let T represent the temperature
The temperature tripled and then rose 5 degrees can be written as:
Tm = 3T + 5
where Tm is the temperature at midnight.
If the temperature at 8:00 AM was –7 degrees Celsius, we have:
Tm = 3(-7) + 5
Tm = -21 + 5
Tm = -16 degrees Celsius
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