Answer: When dividing two fractions you simply multiply the first one by the reciprocal of the second:
1
4
3
5
=
1
4
⋅
5
3
=
5
12
The function f(x) = –x2 – 4x + 5 is shown on the graph. On a coordinate plane, a parabola opens down. It goes through (negative 5, 0), has a vertex at (negative 2, 9), and goes through (1, 0). Which statement about the function is true? The domain of the function is all real numbers less than or equal to −2. The domain of the function is all real numbers less than or equal to 9. The range of the function is all real numbers less than or equal to −2. The range of the function is all real numbers less than or equal to 9.
Considering the vertex of the parabola, the correct statement is given by:
The range of the function is all real numbers less than or equal to 9.
What is the vertex of a quadratic equation?A quadratic equation is modeled by:
[tex]y = ax^2 + bx + c[/tex]
The vertex is given by:
[tex](x_v, y_v)[/tex]
In which:
[tex]x_v = -\frac{b}{2a}[/tex][tex]y_v = -\frac{b^2 - 4ac}{4a}[/tex]Considering the coefficient a, we have that:
If a < 0, the vertex is a maximum point, which means that the range is all real numbers less than or equal to [tex]y_v[/tex].If a > 0, the vertex is a minimum point, which means that the range is all real numbers greater than or equal to [tex]y_v[/tex].In this problem, we have that:
a = -1 < 0, hence the vertex is a maximum point.The vertex is (-2,9).Hence the range is described by:
The range of the function is all real numbers less than or equal to 9.
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Which number has a repeating decimal form?
A. √15
B. 11/25
C. 30
D. 2/6
Write -3/12 as a mixed number in reduced form.
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation:}[/tex]
[tex]\mathsf{-\dfrac{3}{12}}[/tex]
[tex]\huge\textbf{Simplify:}[/tex]
[tex]\mathsf{-\dfrac{3}{12}}[/tex]
[tex]\mathsf{= \dfrac{-3\div 3}{-12\div3}}[/tex]
[tex]\mathsf{= -\dfrac{1}{4}}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\frak{- \dfrac{1}{4}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Suppose we want to choose objects, without replacement, from the objects pencil, eraser, desk, and chair.
(a) How many ways can this be done, if the order of the choices is relevant?
(b) How many ways can this be done, if the order of the choices is not relevant?
The number of ways when the choice is not relevant is 10
How to determine the number of ways?The number of objects are:
Object, n = 5
The object to choose are:
r = 3
Relevant choice
When the choice is relevant, we have:
[tex]Ways = ^nP_r[/tex]
This gives
[tex]Ways = ^{5}P_3[/tex]
Evaluate
Ways = 60
Hence, the number of ways when the choice is relevant is 60
Not relevant choice
When the choice is not relevant, we have:
[tex]Ways = ^nC_r[/tex]
This gives
[tex]Ways = ^{5}C_3[/tex]
Evaluate
Ways = 10
Hence, the number of ways when the choice is not relevant is 10
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The length of a rectangle is two more than double the width. If the perimeter is 100 inches, find the
dimensions.
Answer:
width = 34 inches
length = 16 inches
Step-by-step explanation:
Given:
1.)The length of a rectangle is two more than double the width
2.)The perimeter is 100 inches
Let's analyze the first part,
The length is 2 more than double the width so if we let x represent the length the width would be 2x + 2
Now the second part,
the perimeter is calculated by the following formula:
2*(w+l)
(w: width, l: length)
2*(x+2x+2) first do inside the parenthesis by adding like terms
x+2x+2 = 3x + 2 now multiply both terms with 2
2*(3x+2) = 6x + 4 this is the perimeter of the rectangle, now write another equation using this
6x + 4 = 100 subtract 4 from both sides
6x = 96 divide both sides by 6
x = 16 this the length and the width would be
2x + 2 = 2*16 + 2 = 34
TV and RI intersect at E. If the measure of IVE=50, the measure of VIE=70 and the measure of RET=2X-10 , find the value of x
Answer:
x = 35
Step-by-step explanation:
The angle sum theorem can be used to find the congruent vertical angles RET and IEV. The equation relating these can be solved for x.
Missing angleThe missing angle in triangle IVE is found using the angle sum theorem:
∠IVE +∠VIE +∠IEV = 180°
∠IEV = 180° -50° -70° = 60°
Vertical angleVertical angles RET and IEV are congruent:
∠RET = ∠IEV
2x -10 = 60
2x = 70 . . . . . . . . add 10
x = 35 . . . . . . . . divide by 2
The value of x from the given conditions is 35.
The line TV and RI intersect at E.
The measure of IVE=50° and the measure of VIE=70°.
Since, the points V, I and E makes a triangle.
Therefore, the total angle inside the triangle is 180°.
Hence,
∠IVE + ∠VIE + ∠VEI = 180°
50°+70°+ ∠VEI = 180°
∠VEI = 180°-50°-70°
∠VEI = 60°
Also the angles ∠VEI and the angle ∠RET are congruent.
Therefore, ∠VEI = ∠RET
60° = 2x-10
2x = 70
x = 70/2
x = 35.
The lines TV and RI intersect at E. If the measure of IVE=50, the measure of VIE=70 and the measure of RET=2X-10. Then the value of x = 35.
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Suppose a line has a slope of −5.
What is the slope of a line parallel to this line?
What is the slope of a line perpendicular to this line?
The slope of a line parallel to this line is -5 and the slope of a line perpendicular to this line is 1/5
How to determine the slopes?The slope is given as:
m = -5
Parallel line have the same slope.
So, the slope of a line parallel to this line is -5
However, perpendicular lines have their slopes to be opposite reciprocal
This means that:
Perpendicular slope = -1/-5Perpendicular slope = 1/5The slope of a line perpendicular to this line is 1/5
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how do I find the value of x?
Answer: x = 15
Step-by-step explanation:
The formula for calculating the sum of the interior angles of a regular polygon is: (n - 2) × 180°. Where n is number of sides.
sum of angles = (n - 2) × 180
sum of angles = (7 - 2) × 180
sum of angles = 5 × 180
sum of angles = 900°
Now to find the value of x, we have to set each of the interior angles, added up, equal to 900°:
7x + 1 + 10x + 6x + 7 + 10x - 9 + 9x + 4 + 8x + 10 + 9x + 2 = 900
Combine like terms:
(7x + 10x + 6x + 10x + 9x + 8x + 9x) + (1 + 7 - 9 + 4 + 10 + 2) = 900
59x + 15 = 900
59x + 15 - 15 = 900 - 15 subtract 15 from both sides
59x = 885
59x/59 = 885/59 divide by 59 on both sides
x = 15
Which equation is an integer?
5-3 =
6-10 =
11.6 - 3 =
63 - 4 x 5 =
[tex]5-3=2\\\\6-10=-4\\\\11.6-3=8.6\\\\63-4\times 5=63-20=43[/tex]
So, the first, second, and fourth equations are integers.
The first and last are positive integer and second is negative integer.
What are integers?Integers come in three types:
Zero (0)Positive Integers (Natural numbers)Negative Integers (Additive inverse of Natural Numbers)Given:
a) 5-3 =2
b) 6-10 = -4
c) 11.6 - 3 =8.6
d) 63 - 4 x 5 =63- 20 = 43
So, among the above first and last are positive integer and second is negative integer.
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What is the total length of all meteors that are 1 6/8 inches?
A line plot with the title, length of meteors. The data is measurement in inches. The line plot goes from two eighths to one and seven eighths, with fourteen tick marks in all. The first tick mark is two eighths and has one data point. The second tick mark is three eighths and has three data points. The third tick mark is four eighths and has two data points. The fourth tick mark is five eighths and has no data points. The fifth tick mark is six eighths and has two data points. The sixth tick mark is seven eighths and has no data points. The seventh tick mark is one and has no data points. The eighth tick mark is one and one eighth and has no data points. The ninth tick mark is one and two eighths and has one data point. The tenth tick mark is one and three eighths and has two data points. The eleventh tick mark is one and four eighths and has no data points. The twelfth tick mark is one and five eighths and has no data points. The thirteenth tick mark is one and six eighths and has two data points. The fourteenth tick mark is one and seven eighths and has one data point.
The total length of all meteors that are 1 6/8 inches is three and four-eighths inches.
What is the total length of all meteors?Given :
Tick 1 exists 2/8 (1 data point)
Tick 2 exists 3/8 (3 data points)
Tick 3 exists 4/8 (2 data points)
Tick 4 exists 5/8 (no points)
Tick 5 exists 6/8 (2 data points)
Tick 6 exists 7/8 (no data points)
Tick 2 exists 3/8 (3 data points)
....
Tick 13 exists [tex]$1\frac{6}{8}[/tex] (2 data points)
Therefore, total length of all meteors that exist [tex]$1\frac{6}{8}[/tex] inches :
Length of meteor = [tex]$1\frac{6}{8}[/tex]
Number of meteors = 2
[tex]$(2 * 1\frac{6}{8}) = 2 * 1\frac{4}{8} = \frac{28}{8} = 3 \frac{3}{8} = 3 \frac{1}{2}[/tex]
Therefore, the correct answer is option A. three and four-eighths inches
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The complete question is :
What is the total length of all meteors that are 1 6/8 inches? A line plot with the title, length of meteors. The data is a measurement in inches. The line plot goes from two eighths to one and seven eighths, with fourteen tick marks in all. The first tick mark is two eighths and has one data point. The second tick mark is three eighths and has three data points. The third tick mark is four eighths and has two data points. The fourth tick mark is five eighths and has no data points. The fifth tick mark is six eighths and has two data points. The sixth tick mark is seven eighths and has no data points. The seventh tick mark is one and has no data points. The eighth tick mark is one and one eighth and has no data points. The ninth tick mark is one and two eighths and has one data point. The tenth tick mark is one and three-eighths and has two data points. The eleventh tick mark is one and four eighths and has no data points. The twelfth tick mark is one and five-eighths and has no data points. The thirteenth tick mark is one and six eighths and has two data points. The fourteenth tick mark is one and seven eighths and has one data point.
A) three and four-eighths inches
B) three and five-eighths inches
C) four and seven-eighths inches
D) three and seven-eighths inches
If x is a real number, what is the smallest possible value of x^2+8 ?
hi,
smallest value is 8.
x^2 will always be a positive number regardless of the value of x.
the smallest value for a positive number is 0, therefore x^2 +8 will never be smaller than 8
1. Which of the following results in the difference of two squares?
O (3r-5y) (3x - 5y)
O (5x+3y) (5x-3y)
O 4r²(3r-9)
O (2r-3y)2
The difference of two squares is (5x+3y) (5x-3y)
How to determine the difference of two squares?The difference of two squares of variables a and b is represented as:
(a + b)(a - b) = a^2 - b^2
By comparing the list of options, we have:
(5x+3y) (5x-3y)
This means that
a = 5x and b = 3y
Hence, the difference of two squares is (5x+3y) (5x-3y)
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In △ OPQ, OP ≅ QO and m∠O=65∘. Find m∠Q
Answer:
65°
Step-by-step explanation:
Angles opposite congruent sides in a triangle are congruent, so both angle Q and angle P are congruent.
Since angles in a triangle add to 180°, angle Q measures (180-50)/2 = 65°
convert this into a standard number
[tex]10^{6}[/tex]
Answer:
1,000,000
Step-by-step explanation:
The attached place value chart shows the power of ten associated with each number place in a decimal number.
ApplicationYou have ...
1 × 10⁶ = 1,000,000
(Put the multiplier digit in the appropriate number place, and fill the remaining spaces with zeros. The digits 32,465 on the chart can be ignored.)
__
Additional comment
For powers of 10, the exponent (6 in this case) tells you the number of zeros to the right of the digit 1. That is, 10^6 is 1 followed by 6 zeros:
1,000,000
Identify the compositions performed on ΔXYZ to map onto ΔX″Y″Z″.
Triangle XYZ was translated 2 units left and 1 unit up to form triangle X'Y'Z'. It was then rotated 180° about the origin to form triangle X''Y''Z''
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, rotation, translation and dilation.
Translation is the movement of a point either up, left, right or down in the coordinate plane.
Triangle XYZ was translated 2 units left and 1 unit up to form triangle X'Y'Z'. It was then rotated 180° about the origin to form triangle X''Y''Z''
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A rectangular vegetable patch is 5 meters long and 4 meters wide. what is the area?
Answer:
20
Step-by-step explanation:
Area of a rectangle = l*w
5*4 = 20
Assume a firm reports net income of 84,000 prior to making adjusting entries for expired rent $6400, depreciation 7600 and supplies used 3,000
Assume that the entries have not been made What effect do these errors have on the reported net income
Assume that the entries have not been made. The effect that these errors have on the reported net income is: Net income will be overstated by $17,000.
Net incomeUsing this formula
Net income=Expired rent+Depreciation+Supplies
Let plug in the formula
Net income=$6400+$7600+$3000
Net income=$17,000 (Overstated)
Therefore the net income will be overstated by $17,000.
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A line has the equation 32 - 2y = 1 What is the equation of
parallel line going through the point (-6,
- 10)?
The equation is given by Ar + By = C where
Answer:
A = 3; B = -2; C = 2
Step-by-step explanation:
Original line:
3x - 2y = 1
Slope of original line:
-2y = -3x + 1
y = 3/2 x - 1/2
slope = m = 3/2
Parallel lines have equal slopes, so we need the equation of the line with slope 3/2 that passes through the point (-6, -10)
y = mx + b
y = (3/2)x + b
Substitute -6 for x and -10 for y and solve for b.
-10 = (3/2)(-6) + b
-10 + 9 = b
b = -1
Equation: y = (3/2)x - 1
2y = 3x - 2
3x - 2y = 2
would appreciate the help ty!!!
By using the concept of linear progression and some algebraic handling, we conclude that Joe will earn an amount of $ 31 700 in the 14th year.
How to determine the future income of a worker
According to the statement, we have a case of linear progression as income increases at same rate in time. Linear progressions are described by this formula:
c' = c + r · t (1)
Where:
c - Initial amountc' - Current amountr - Increase ratet - TimeFirst, we calculate the increase rate:
r = (29 600 - 22 600)/10
r = 700
Now we proceed to find when Joe will earn an annual income of $ 31 700:
31 700 = 22 600 + 700 · t
t = 13
By using the concept of linear progression and some algebraic handling, we conclude that Joe will earn an amount of $ 31 700 in the 14th year.
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i need the answer to this.
Answer:
56:49 = 8.7 36:48 = 3:448:42 = 8:724:36 = 2:320:30 = 2:324:32 = 3:418:27 = 2:316:14 = 8:79:12 = 3:4hope this helps
sin0=7/25 and cos0=-24/25. find tan0.
A. -7/24
B. 24/7
C. -24/7
D. 7/24
The answer is A
sin0 = p/h = 7/25
cos0 = b/h = -24/25
Therefore , p = 7 , b = -24
tan0 = p/b = 7 / -24 = -7/24
Please help me with this, going to take an exam on these tomorrow, wish me luck.
The Cartesian equation of the parametric formulae is x² - y² = 1. Please see the image attached below for further details of the behavior of the function.
How to analyze and to graph a hyperbolic parametric function
In this question we have an hyperbolic function, a kind of transcendent function based on exponential functions. The parametric equations can be rewritten in rectangular coordinates by the using the following property:
sinh² t - cosh² t = 1 (1)
x² - y² = 1
The graph of the Cartesian equation is present in the figure attached below, in which the directions are shown in detail.
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A pendant is formed using a cylinder and cone. Once assembled, as shown below, the pendant is painted.
How many square millimeters are covered with paint? Express the answer in terms of π.
336π square millimeters
400π square millimeters
416π square millimeters
464π square millimeters
336π square millimeter answer
Step-by-step explanation:
Answer:
336pi square millimeters
Step-by-step explanation:
E2020 Geometry B :3 !!
. Trevor mows 5 times as
many lawns in the
summer as he does in
the fall. If he mows 20
lawns in the summer,
how many does he mow
in the fall?
Answer:
4 lawns
Step-by-step explanation:
20/5
Select the correct answer. Which chart best represents the following information about student results from a class assignment? Frequency 10 Score Frequency Chart 1 23 2 Frequency 10 24 8 25 4 Chart 2 26 3 27 5 28 4 29 5
The chart that best represents the student results from a class assignment is B. Histogram or bar graph.
What is a histogram or bar graph?Both histograms and bar charts are graphic vertical and horizontal bars that visually display frequencies with columns plotted on a graph.
The frequencies are depicted on the Y-axis (vertical axis).
The X-axis (horizontal axis) represents the measured variable.
Question Completion with Answer Options:A. Frequency table
B. Histogram or bar graph
C. Pareto chart
D. Pictogram
E. Pie chart
Thus, the best chart to represent the student results from a class assignment is B. Histogram or bar graph.
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If you vertically compress the exponential function f(x)=2^x by a factor of 5, what is the equation of the new function?
The equation of the new function is:
[tex]g(x) = \frac{2^x}{5}[/tex]
What is the equation of the compressed function?Here we have the function:
[tex]f(x) = 2^x[/tex]
A vertical compression by a factor of 5 is written as:
[tex]g(x) = f(x)/5[/tex]
Replacing the function f(x) we get:
[tex]g(x) = \frac{2^x}{5}[/tex]
That is the equation of the new function.
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the chairs in a hall are about to be arranged in a row. if i put 6 chairs in a row there will be 4 left if i put 7 chairs in a row there will be 3 short how many chairs are there
Step-by-step explanation:
THERE WILL BE
6+4+3+7= 23
Triangles L M N and P O N connect at point N. Angles L M N and N O P are congruent.
Why is the information in the diagram enough to determine that △LMN ~ △PON using a rotation about point N and a dilation?
because both triangles appear to be equilateral
because∠MNL and ∠ONP are congruent angles
because one pair of congruent corresponding angles is sufficient to determine similar triangles
because both triangles appear to be isosceles, ∠MLN ≅ ∠LMN, and ∠NOP ≅ ∠OPN
The information is enough because: C. because one pair of congruent corresponding angles is sufficient to determine similar triangles.
What are Similar Triangles?Similar triangles can be formed during dilation. All corresponding angles of similar triangles are usually congruent to each other.
From the image given, the using rotation about point N and then dilation by a scale factor will make both triangles similar. Thus, with the given information, we can determine both triangles are similar because: C. because one pair of congruent corresponding angles is sufficient to determine similar triangles.
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Answer:
C
Step-by-step explanation:
Took the test
3x/2y=11 x+y/2=7 igualacion
Alguien me puede ayudar
La solución del sistema de ecuaciones es igual a (x, y) = (308/47, 42/47).
¿Cómo resolver un sistema de ecuaciones linear por igualación?
Los sistemas de ecuaciones basadas en entidades algebraicas se resuelven mediante procedimientos algebraicos. Grosso modo, el método de resolución por igualación consiste en despejar una variable en dos ecuaciones del sistema para eliminarla y reducir el número de ecuaciones lineales y el número de variables.
A continuación, presentamos una aplicación del método de eliminación:
[tex]\frac{3\cdot x}{2\cdot y} = 11[/tex]
[tex]x = \frac{22\cdot y}{3}[/tex]
[tex]x + \frac{y}{2} = 7[/tex]
[tex]x = 7 - \frac{y}{2}[/tex]
[tex]\frac{22\cdot y}{3} = 7 - \frac{y}{2}[/tex]
[tex]\frac{47\cdot y}{6} = 7[/tex]
y = 42/47
[tex]x = 7 - \frac{y}{2}[/tex]
x = 308/47
La solución del sistema de ecuaciones es igual a (x, y) = (308/47, 42/47).
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What is the area of this parallelogram?
h = 2 in.
A
b= 10 in.
in.
in²
The area of a parallelogram is 20 inches square
What is the area of a parallelogram?
The area of a parallelogram is the base of the shape multiplied by the height
Area of parallelogram = b × h
Where h = height = 2 In
base = 10 in
Area = 2 × 10
Area = 20 Inches square
Thus, the area of a parallelogram is 20 inches square
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