In triangle FGH, we are given the following information: side f has a length of 8.8 inches, angle F measures 23 degrees, and angle G measures 107 degrees. The length of side g is 20.5 inches
To determine the length of side g, we can utilize the Law of Sines, which relates the lengths of the sides of a triangle to the sines of their opposite angles. The law states that the ratio of the length of a side to the sine of its opposite angle is constant for all sides and angles in a triangle.
Applying the Law of Sines to triangle FGH, we have:
[tex]sin(F) / f = sin(G) / g[/tex]
Substituting the given values:
[tex]sin(23°) / 8.8 = sin(107°) / g[/tex]
To solve for g, we can cross-multiply and rearrange the equation:
[tex]g = (8.8 * sin(107°)) / sin(23°)[/tex]
Using a calculator, we can evaluate the expression:
[tex]g = 20.53 inches[/tex]
Rounding to the nearest tenth of an inch, the length of side g is approximately 20.5 inches.
Therefore, in triangle FGH, the length of side g is 20.5 inches (rounded to the nearest tenth).
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Becca's car engine has a capacity of 3.6 quarts and
contains 1.2 quarts of engine oil. One bottle of engine oil is
0.5 quart. Approximately how many bottles of engine oil
does Becca need to completely fill her car engine?
Becca needs approximately 5 bottles of engine oil to completely fill her car engine.
How to determine the number of bottles of engine oil?Since Becca's car engine has a capacity of 3.6 quarts and contains 1.2 quarts of engine oil, the remaining space left in her car engine is given by:
Space = 3.6 - 1.2
Space = 2.4 quarts.
By applying direct proportion, we have:
1 bottle = 0.5 quart.
x bottles = 2.4 quarts.
Cross-multiplying, we have:
0.5x = 2.4
x = 2.4/0.5
x = 4.8 ≈ 5 bottles.
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Three schools have a chess tournament. Four players come from each school. Each player plays three games against each player from the other schools, and plays one game against each other player from his or her own school. How many games of chess are played
Using combinations, the number of games of chess played are 312 if each player plays three games against each player plays three games against each player from the other schools, and plays one game against each other.
According to the questions,
Three schools have a chess tournament and four players come from each school. Each player plays against each other from his/her own school.
Formula for Combinations [tex]nC_{r}[/tex] = [tex]\frac{(n-r)!}{r!}[/tex]
[tex]4C_{2}[/tex] = [tex]\frac{4*3}{1*2}[/tex]
= 6
They are 6 ways to select two schools. Given those 2 schools they are
[tex]4^{2}[/tex] = 16 ways to pair up players 1 from each school. They are 3 games played by each of those 3 pairs.
The total number of games played against other school.
6×16×3 = 288.
Similarly using combinations we can find the number of games played against schoolmates. To find this 4 combinations of 2 is 6 ways to select a pair from the 4 people at given school. They are four schools and they play one game each.
6×4×1 = 24
Thus using combinations, the number of games played against schoolmates is 24.
In order to find the number of games of chess are played only if we add the total number of games played against other school and the total number of games played against schoolmates.
288+24 = 312
Hence, using combinations, the number of games of chess played are 312 if each player plays three games against each player plays three games against each player from the other schools, and plays one game against each other.
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The edges of a cube increase at a rate of 3 cm/s. How fast is the volume changing when the length of each edge is 40 cm?
Answer:
14400 cm³/s
Step-by-step explanation:
Find the rate of change of volume in terms of edge length, and evaluate the expression for the given conditions.
Rate of change of volumeV = s³ . . . . volume in terms of edge length (s)
dV/dt = 3s²·ds/dt . . . . . . derivative of volume with respect to time
For the given values of s and ds/dt, this is ...
dV/dt = 3(40 cm)²(3 cm/s) = 14400 cm³/s
A square has an area of 49 square inches. how long are its sides
Answer:
Step-by-step explanation:
We know that,
Area of a square = l^2
so in this case, we form an equation:
l^2=49 square inches
Now taking square root on both sides
[tex]\sqrt{l}[/tex]^2=[tex]\sqrt{49}[/tex]
l=7 inches
so each side is 7 inches
Hope that helps
Answer:
7 inStep-by-step explanation:
A square has an area of 49 square inches. how long are its sides
A = l²
inverse formula
l = √A
l = √49
l = 7 in
Last-Minute Shopper #1 paid $102 for 3 gizmos and
6 thingamajigs. Last-Minute Shopper #2 paid $179
for 5 gizmos and 11 thingamajigs. Assume they both
shopped at the same store and bought the same
brands and model numbers, and then answer the
questions below.
a) How much did each gizmo cost?
b) How much did each thingamajig cost?
The cost of one gizmo is $18.
The cost of one thingamajigs is $9
What are the linear equations that represent the question?3g + 6t = 102 equation 1
5g + 11t = 179 equation 2
Where:
g = cost of one gizmo t = cost of one thingamajigs.What is the cost of one gizmo and thingamajigs?Multiply equation 1 by 5 and equation 2 by 3
15g + 30t = 510 equation 3
15g + 33t = 537 equation 4
Subtract equation 3 from equation 4
3t = 27
t = 27 / 3
t = $9
Substitute for t in equation 1
3g + 6(9) = 102
3g + 54 = 102
3g = 102 - 54
3g = 48
g = 48 / 3
g = $18
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Find the surface area of the prism. Round to the nearest tenth if necessary. please help!!
Answer:
72
Step-by-step explanation:
This shape is a prism; it's a 3-D shape with 6 sides. Basically, it's a box.
All 6 sides are rectangles.
Surface area means that we'll find the area of all 6 rectangles and add them up.
There's a front and back, left and right, and a top and bottom.
The area of a rectangle is length×width or base×height.
The front and back are identical.
Area = length×width
Area = 6×3 = 18
Since the front and back are the same, two of the rectangles have area = 18.
The left and right are the same:
Area = 3 × 2
Area = 6
Two faces have area = 6.
The top and bottom are the same.
Area = 6 × 2
Area = 12
Again, two faces have area = 12.
To find the total surface area, add up all 6 areas.
A =18+18+6+6+12+12
A = 72
The graph below shows the height of an object that has been launched off a 45 foot high wall. Approximately what is the maximum height this ball will reach?
A) 4.6 feet
B) 45 feet
C) 2 feet
D) 109 feet
The maximum height of the ball that is displayed by the graph is: D. 108 feet.
What is a Graph?A graph is a statistical diagram that displays the relation between two variables. One of the variables is plotted on the x-axis (horizontal axis) against the other variable on the y-axis (vertical axis).
The variable on the x-axis (horizontal axis) is the input, while the variable on the y-axis (vertical axis) is the output.
Considering the given graph in the image above, we have the following variables:
On the x-axis (horizontal axis): time which is the input
On the y-axis (vertical axis): height of the ball which is the output.
Thus, the peak of the line represents the maximum height the ball reaches. The maximum height which is the peak is approximately 109 feet.
Therefore, the maximum height is: D. 109 feet.
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Answer:
109 feet
Step-by-step explanation:
just took the lesson
( 1 ) 0.006 m (cm) =
( 2 ) 17, 605 mm (km) =
( 3 ) 1,001,00 dm (km) =
the value of the given figures in the other units can be found to be:
0.006 m = 0.6 cm17,605 mm (km) = 0.017605 km1,001,000 dm = 10.01 kmwhat are the converted values of the figures?A meter is 100 cm so:
= 0.006 x 100
= 0.6 cm
A kilometer is 1,000,000 mm so:
= 17,605 / 1,000,000
= 0.017605 km
A kilometer is 10,000 dm:
= 1,001,00 dm / 10,000
= 10.01 km
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help! what do i do
A square sandbox has sides of length 9 ft and a depth of 1 ft. If sand costs $5 / cubic foot, how much will it cost to fill the sandbox with sand?
The cost spent on fill the box with sand is 405$.
According to the statement
we have given a square sandbox with length 9 ft and depth of 1 ft.
and the rupees of sand per cubic ft is $5
then
Now, we have to find the volume of sandbox with the given length and depth.
So, for this purpose we use Volume formula
V = (a)^3
V = 9*9*1
V = 81 cubic feet
And the cost of sand per cubic feet is $5.
then
The cost of sand for 81 cubic per feet is calculate by multiplication formula then
Total cost of sand = 81*5
Total cost of sand = 405$
So, The cost spent on fill the box with sand is 405$.
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can someone explain?
Answer: K
Step-by-step explanation:
I. Correct. When t=0, h=c, so if you alter the value of c, the h-intercept changes.
II. Correct, the maximum value of [tex]-at^2 +bt[/tex] will stay the same, but you are changing c, which is the amount you are always adding to it, meaning the maximum will change.
III. Correct. If you plug into the quadratic formula setting h=0, it is easy to see changing the value of c will change the solutions.
The correct statement regarding the quadratic function is:
K. I, II and III.
What is a quadratic function?A quadratic function is given according to the following rule:
[tex]y = ax^2 + bx + c[/tex]
If a > 0, it has a maximum value, and if a < 0, it has a minimum value.
The extreme value is [tex](x_v,y_v)[/tex], in which:
[tex]x_v = -\frac{b}{2a}[/tex][tex]y_v = -\frac{\Delta}{4a}[/tex][tex]\Delta = b^2 - 4ac[/tex]The solutions are:
[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a}[/tex][tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a}[/tex]In this problem, we have a function h(t). Changing the coefficient c, the h-intercept h(0) changes. Looking at the formulas in the bullet point, the value of [tex]\Delta[/tex] changes, meaning that both the maximum value [tex]y_v[/tex] and the t-intercepts [tex]t_1[/tex] and [tex]t_2[/tex] will change, so option K is correct.
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according to the graph, what is the value of the constant in the equation below?
Answer:
3
Step-by-step explanation:
height = constant * width
let's rearrange this equation
constant = height/width
let's pick several points as a proof
15/5 =3
6/2 =3
1.5/0.5 = 3
hope this helps you!!
Create a coordinate proof to show that the two triangles are congruent by the SSS Triangle Congruence Theorem.
For a person to be able to create a coordinate proof to show that the two triangles are congruent by the SSS Triangle Congruence Theorem one can simply use the distance formula.
How can the distance formula prove SSS Triangle Congruence Theorem?Given that the distance formula =
[tex]\sqrt{(x_{2} -x_{1})^{2} + (y_{2} - y_{1}^{2} )}[/tex]
Let say that Angle ABC has the vertices of A (-4, -2), B (-5,1). C (0,2) and Angle DEF has the vertices of D (7, -4), E (4,-5), F (3,0)
So lets prove it:
AC = [tex]\sqrt{(x_{2} -x_{1})^{2} + (y_{2} - y_{1}^{2} )}[/tex]
=[tex]\sqrt{(-4-0)^2 + (-2-2)^2}[/tex]
=[tex]\sqrt{32}[/tex]
= 4[tex]\sqrt{2}[/tex]
Do the same for DF:
DF = [tex]\sqrt{(x_{2} -x_{1})^{2} + (y_{2} - y_{1}^{2} )}[/tex]
= [tex]\sqrt{(7-3)^2 + (-4-0)^2}[/tex]
=[tex]\sqrt{32}[/tex]
= 4[tex]\sqrt{2}[/tex]
Looking at the above, one can see the values are the same and as such this proves that AC is the same to DF. If you do the same for the other part of the angles, you will see that they are congruent.
Therefore, For a person to be able to create a coordinate proof to show that the two triangles are congruent by the SSS Triangle Congruence Theorem one can simply use the distance formula.
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The sum, s, of 4 consecutive odd integers can be represented by the equation s = 4n â 12. what does n represent?
The variable n represents the smallest of the four integers.
How to interpret what n represents?The given parameters are
Number of consecutive odd integers = 4
Sum of consecutive odd integers= s
Where
S = 4n - 12
The variable n represents the smallest of the four integers.
In the sense that, the consecutive odd integers are
n, n + 2, n + 4 and n + 6
Hence, the variable n represents the smallest of the four integers.
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Zoe keeps track of the miles per gallon her car gets per week. she has accumulated the following data: (1,24), (2,24,38), (3,24,76) (4,25,14) what is the common difference or ratio?
The common difference is (1,0.38).
An arithmetic progression (AP) is a sequence where the differences between every two consecutive terms are the same. In this type of progression, there is a possibility to derive a formula for the nth term of the AP. For example, the sequence 2, 6, 10, 14, … is an arithmetic progression (AP) because it follows a pattern where each number is obtained by adding 4 to the previous term.
x1 = 1 , y1 = 24
x2 = 2, y2 = 24.38
x3 = 3 , y3 = 24.76
x4 = 4 , y4 = 25.14
Thus the common difference equals :-
x2 - x1 = x3 - x2 = x4 - x3 = 1
y2 - y1 = y3 - y2 = y4 - y3 = 0.38.
Thus the common difference is (1,0.38).
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For a moving object, the force acting on the object varies directly with the object's acceleration. When a force of 10 N acts on a certain object, the acceleration of the object is 5 meters per second². If the acceleration of the object becomes 4 meters per second², what is the force?
Answer:
8
Step-by-step explanation:
F=ma
10=5m
4m=10*4/5
4m=8
So the answer is 8
slope and y intercept?
Answer:
slope: -1/3
Y-intercept: 0
Step-by-step explanation:
The line crosses the y-axis at 0, and the pibe decreases by 1 down and goes to the side by 3, using rise over tu it would be -1/3
I hope it helps! Have a great day!
Pan~
Answer:
Slope: -1/3
Y-intercept: 0
Step-by-step explanation:
I hope it helps! Have a great day!
bren~
Can someone help me on this pls? It’s urgent, so ASAP (it’s geometry)
Write formal proofs using LA Theorem.
Given the parameters in the diagrams, we have;
4. ∆ABC ≈ ∆DEF by ASA
5. UW ≈ XZ by CPCTC
6. QR ≈ TR by CPCTC
How can the relationship between the triangles be proven?4. The given parameters are;
<B = <E = 90°
AB = DE Definition of congruency
<A = <D Definition of congruency
Therefore;
∆ABC ≈ ∆DEF by Angle-Side-Angle, ASA, congruency postulate5. Given;
XY is perpendicular to WZ
UV is perpendicular to WZ
VW = YZ
<Z = <W
Therefore;
∆UVW ≈ ∆XYZ by Angle-Side-Angle, ASA, congruency postulate
Which gives;
UW is congruent to XZ, UW ≈ XZ, by Corresponding Parts of Congruent Triangles are Congruent, CPCTC6. Given;
PQ is perpendicular to QT
ST is perpendicular to QT
PQ ≈ ST
From the diagram, we have;
<SRR ≈ <PRQ by vertical angles theorem;
Therefore;
∆QRP ≈ ∆TRS by Side-Angle-Angle, SAA, congruency postulate
Which gives;
QR ≈ TR by Corresponding Parts of Congruent Triangles are Congruent, CPCTCLearn more about congruency postulates here:
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help!
Find the missing side lengths. Leave the answers as radicals in simplest form.
Answer:
b = 3.5
a = 7
Step-by-step explanation:
Hello!
This triangle is a 30°-60°-90° triangle, as the missing angle is 30° and the other two angles are 60° and 90°.
There are some important Rules:
The leg that is opposite to the 30° angle is half of the hypotenuse. The leg that is opposite to the 60° angle is the length of the leg opposite to the 30° multiplied by [tex]\sqrt3[/tex].We can first solve for the leg that is opposite to the 30° angle.
Since [tex]\frac{7\sqrt3}{2}[/tex] is [tex]b\sqrt3[/tex]:
[tex]\frac{7\sqrt3}{2} = b\sqrt3[/tex][tex]\frac72 = b[/tex]The length of b is 3.5.
We can multiply 3.5 by 2 to find the length of a.
[tex]\frac a2 = b[/tex][tex]\frac a2 = \frac72[/tex][tex]a = 7[/tex]The length of a is 7.
Use the drop-down menus to complete the proof. by the unique line postulate, you can draw only one segment,
The reflection of BC over I is shown below.
What is reflection?A reflection is a mapping from a Euclidean space to itself that is an isometry with a hyperplane as a set of fixed points; this set is known as the reflection's axis (in dimension 2) or plane (in dimension 3). A figure's mirror image in the axis or plane of reflection is its image by reflection.See the attached figure for a better explanation:
1. By the unique line postulate, you can draw only one line segment: BC
Since only one line can be drawn between two distinct points.2. Using the definition of reflection, reflect BC over l.
To find the line segment which reflects BC over l, we will use the definition of reflection.3. By the definition of reflection, C is the image of itself and A is the image of B.
Definition of reflection says the figure about a line is transformed to form the mirror image. Now, the CD is the perpendicular bisector of AB so A and B are equidistant from D forming a mirror image of each other.4. Since reflections preserve length, AC = BC
In Reflection the figure is transformed to form a mirror image.Hence the length will be preserved in case of reflection.Therefore, the reflection of BC over I is shown.
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The question you are looking for is here:
C is a point on the perpendicular bisector, l, of AB. Prove: AC = BC Use the drop-down menus to complete the proof. By the unique line postulate, you can draw only one segment, Using the definition of, reflect BC over l. By the definition of reflection, C is the image of itself and is the image of B. Since reflections preserve , AC = BC.
FIND THE SURFACE AREA PLSS
Answer:
BrainlyMidIsBusy Sucks
In algebra, we transfer these same skills to expressions involving variables. what elementary skills have you used so far in this course, and how have you extended them?
For every 5 employees there must be 3 supervisors. if there are a total company size of 160 people how many supervisors are needed
Answer:
Step-by-step explanation:
x - 3y = 9, complete the ordered pair (12, ).
Answer:
(12,1)
Step-by-step explanation:
We know that ordered pairs are in the format of (x,y).
This means in that (12, __) 12 is our x coordinate. Plugging 12 into the equation as x we get:
[tex]12-3y=9\\-3y=9-12\\-3y=-3\\y=1[/tex]
Therefore our answer is (12,1) as we plug y back into our coordinate (x,y).
Answer:
(12,1)
Step-by-step explanation:
In the ordered pair, x=12
plug 12 back in the equation
12-3y=9
-3y=-3
3y=3
y=1
In quadrilateral LMNO, LO ∥ MN.
Quadrilateral L M N O is shown.
What additional information would be sufficient, along with the given, to conclude that LMNO is a parallelogram? Check all that apply.
ML ∥ NO
ML ⊥ LO
LO ≅ MN
ML ≅ LO
MN ⊥ NO
The additional information which would be sufficient to conclude that LMNO is a parallelogram is; ML ∥ NO, LO ≅ MN, and ML ≅ LO.
What information renders LMNO a parallelogram?The condition for a quadrilateral to be a parallelogram is that; the opposite pairs must be parallel and consequently opposite pairs are congruent as they have equal length measures.
On this note, it can be concluded that the additional information which would be sufficient are; ML ∥ NO, LO ≅ MN, and ML ≅ LO.
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(A.) ML ∥ NO,
(C.) LO ≅ MN.
Have a great day and hydrate!! <3
The average age of 4 children is 15 yrs . if the ages of their parents are added , their average age is 25 .find the age of their father if he is 4 yrs older than is wife
The age of the father is 57 years old
Calculating mean of a populationTotal age = Average age x Population
Average of the four children = 15
Population = 4
Total age of the four children = 15 x 4
Total age of the four children = 60 years
If the parents are added:
Population = 6
Average age = 25
Total age = 25 x 6
Total age = 150 years
Total age of the parents = 150 - 60
Total age of the parents = 110 years
The father is 4 years older than his wife
Let the age of the father be x
The age of the wife = x - 4
x + x - 4 = 110
2x = 114
x = 114/2
x = 57
Therefore, the age of the father is 57 years old
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PLEASE HELP ME AS SOON AS POSSIBLE
The parent function of g(x) = |x - 7| +6 is f(x) = |x|
How to determine the parent function?The function is given as:
g(x) = |x - 7| +6
The above function is an absolute function, and the parent function is f(x) = |x|
Hence, the parent function of g(x) = |x - 7| +6 is f(x) = |x|
The reflectionWhen f(x) is reflected across the x-axis, we have:
f'(x) = -|x|
When f(x) is reflected across the y-axis, we have:
f'(x) = |x|
Stretching and CompressionWhen f(x) is stretched horizontally by a factor k
g'(x) = |kx|
When f(x) is stretched vertically by a factor k
g'(x) = k|x|
Horizontal ShiftWhen f(x) is shifted horizontally by k units
f'(x) = |x ± k|
Vertical ShiftWhen f(x) is shifted vertical by k units
f'(x) = |x| ± k
See attachment for the graph of g(x)
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Solve the equation below by factorising.
2m? - 11m + 5 = 0
Answer:
m = [tex]\frac{1}{2}[/tex] , m = 5
Step-by-step explanation:
assuming you mean
2m² - 11m + 5 = 0
consider the product of the factors of the m² term and the constant term which sum to give the coefficient of the m- term
product = 2 × 5 = 10 and sum = - 11
the factors are - 10 and - 1
use these factors to split the m- term
2m² - 10m - m + 5 = 0 ( factor the first/second and third/fourth terms )
2m(m - 5) - 1(m - 5) = 0 ← factor out (m - 5) from each term
(m - 5)(2m - 1) = 0 ← in factored form
equate each factor to zero and solve for m
2m - 1 = 0 ⇒ 2m = 1 ⇒ m = [tex]\frac{1}{2}[/tex]
m - 5 = 0 ⇒ m = 5
When calculating correlation and regression both sets of data must be __________
When calculating correlation and regression both sets of data must be Statistical.
According to the statement
we have to find the type of data when we calculate the correlation and regression both sets.
so, The difference between these two statistical measurements is that correlation measures the degree of a relationship between two variables (x and y), whereas regression is how one variable affects another.
And when we calculate both then data sets must be a statistical data. because correlation summarizing direct relationship between two variables and regression predict or explain numeric response. So, without statistical data this is not possible to calculate correlation and regression both sets.
so, When calculating correlation and regression both sets of data must be Statistical.
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Determine the value of x that would make quadrilateral lmno a parallelogram. 3 9 11 18
The correct answer is x = 9
What is a parallelogram in math?
A parallelogram is a quadrilateral with opposite sides parallel (and therefore opposite angles equal). A quadrilateral with equal sides is called a rhombus, and a parallelogram whose angles are all right angles is called a rectangle.Diagonals of a parallelogram bisect each other.
For quadrilateral LMNO to be a parallelogram, LP must equal PN, and OP must equal PM.
Set OP equal to PM and solve for x.
PM = OP
3x - 9 = 18
Add 9 to both sides.
3x = 27
Divide both sides by 3.
x = 9
Therefore, the value of x = 9
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The complete question is -
Determine the value of x that would make quadrilateral LMNO a parallelogram.
3
9
11
18
Answer: x=9
Step-by-step explanation: