Type SSS, SAS, ASA, SAA, or HL to
justify why the two larger triangles are
congruent.
A
B
F
D
C
E AC = BC
ZAZB

Answer:

[tex]\dfrac{991}{40\sqrt{2}}[/tex]

Step-by-step explanation:

Given expression:

[tex]\sqrt{72}-\dfrac{48}{\sqrt{50}}-\dfrac{45}{\sqrt{128}}+2\sqrt{98}[/tex]

Rewrite 72 as 36·2, 50 as 25·2, 128 as 64·2 and 98 as 49·2:

[tex]\implies \sqrt{36 \cdot 2}-\dfrac{48}{\sqrt{25 \cdot 2}}-\dfrac{45}{\sqrt{64 \cdot 2}}+2\sqrt{49 \cdot 2}[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}:[/tex]

[tex]\implies \sqrt{36}\sqrt{2}-\dfrac{48}{\sqrt{25}\sqrt{2}}-\dfrac{45}{\sqrt{64}\sqrt{ 2}}+2\sqrt{49}\sqrt{2}[/tex]

Rewrite 36 as 6², 25 as 5², 64 as 8² and 49 as 7²:

[tex]\implies \sqrt{6^2}\sqrt{2}-\dfrac{48}{\sqrt{5^2}\sqrt{2}}-\dfrac{45}{\sqrt{8^2}\sqrt{ 2}}+2\sqrt{7^2}\sqrt{2}[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{a^2}=a, \quad a \geq 0[/tex]

[tex]\implies 6\sqrt{2}-\dfrac{48}{5\sqrt{2}}-\dfrac{45}{8\sqrt{ 2}}+2\cdot 7\sqrt{2}[/tex]

Simplify:

[tex]\implies 6\sqrt{2}-\dfrac{48}{5\sqrt{2}}-\dfrac{45}{8\sqrt{ 2}}+14\sqrt{2}[/tex]

Combine like terms:

[tex]\implies 20\sqrt{2}-\dfrac{48}{5\sqrt{2}}-\dfrac{45}{8\sqrt{ 2}}[/tex]

Make the denominators of the two fractions the same:

[tex]\implies 20\sqrt{2}-\dfrac{384}{40\sqrt{2}}-\dfrac{225}{40\sqrt{ 2}}[/tex]

Rewrite 20√2 as a fraction with denominator 40√2:

[tex]\implies 20\sqrt{2}\cdot\dfrac{40\sqrt{2}}{40\sqrt{2}}-\dfrac{384}{40\sqrt{2}}-\dfrac{225}{40\sqrt{ 2}}[/tex]

[tex]\implies \dfrac{1600}{40\sqrt{2}}-\dfrac{384}{40\sqrt{2}}-\dfrac{225}{40\sqrt{ 2}}[/tex]

Combine fractions:

[tex]\implies \dfrac{991}{40\sqrt{2}}[/tex]

The value of N is 28.

A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation. To determine the value of an unknown variable that represents an unknown quantity, equations can be solved.

According to the question,

a+b+c=60

a-7=N

b+7=N

7c=N

From the above three equations,

a=N+7

b=N-7

c=N/7

So, N+7+N-7+N/7=60

2N+N/7=60

14N+N=420

15N=420

N=28

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The volume of the oblique prism is 16261 cubic units

The given parameters are:

Height = 23

Base area = 707

The volume is calculated as:

V = base area * height

So, we have:

V = 707 * 23

Evaluate

V = 16261

Hence, the volume of the oblique prism is 16261 cubic units

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Answer:

sin a = -3/5

Step-by-step explanation:

sin^2(a)+cos^2(a)=1

sin^2(a)+ (4/5)^2 = 1

sin^2(a) = 1 - 16/25 = 9/25

sin a = 3/5 ( in Quadrant 1)

In quadrat IV the sine is negative

so sin a = -3/5

Answer:

26.1 to the nearest  tenth.

Step-by-step explanation:

tan 43 = x / 28

x = 28 tan 43

  = 26.1102

Answer:

Min: 32

Lower Quartile: 36

Median: 42

Upper Quartile: 47

Max: 53

Interquartile: 11

Step-by-step explanation:

The min. is just the lowest number.  The lower quartile is the number in the middle of the numbers below 42, the median is the number in the very middle, the upper quartile is the middle number above 41 and the interquartile is the upper quartile minus the lower quartile.  

If the base angles of a trapezoid are congruent, the diagonals are congruent.

A trapezium is a quadrilateral and the sum of the interior angles is 360 degrees. Therefore, the properties of a trapezium includes the following:

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Step-by-step explanation:

Since there is 2 unknown variable ,

so we need 2 equation to find their values.

17.49 is the magnitude of the resultant vector. This can be obtained by adding the vectors and finding magnitude.

Resultant vector: vector that gives the combined effect of all the vectors. When we add two or more vectors, the outcome is the resultant vector.

For example,

(3,4) + (5,7) = (3+5,4+7) = (8,11)

(8,11) is the resultant vector of vector (3,4) and vector (5,7)

Magnitude of a vector: the length of the vector. The magnitude of the vector a is denoted as ∥a∥.

Magnitude of a = (a₁, a₂)

∥a∥=[tex]\sqrt{a_{1}^{2} +a_{2}^{2} }[/tex]

In the given question,

v (8,10) and w (7, -1)

Adding the vectors,

resultant vector = (8,10) + (7, -1) = (15, 9)

Magnitude of a vector (a,b) = √a²+b²

Here, magnitude = √15²+9² = √225+81 = √306 ≈ 17.49

Hence 17.49 is the magnitude of the resultant vector.

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Answer:

z = 5

Step-by-step explanation:

To solve for z, means to get z all by itself on one side of the equation. In your equation z has had two things done to it. First, z has been times by 4, then 10 is subtracted. So, you "un-do" that in reverse order.

FIRST, add 10. To reverse or "un-do" subtracting.

4z - 10 = 10

4z -10+10 = 10+10

4z = 20

Then, divide by 4 to reverse the multiplying.

4z/4 = 20/4

z = 5

see image.

Also, you can check you answer.

put in 5 in place of z and be sure that you get a true statement.

4(5) - 10 = 10

20 - 10 = 10

10 = 10 Checked!

Answer:

[tex]z=5[/tex]

Step-by-step explanation:

First, substitute in 5 for z: [tex]4(5) -10=10[/tex]

Since [tex]4*5=20[/tex], we can now simplify the equation to [tex]20-10=10[/tex].

Now, check the equation to make sure that the value of z is correct. Do this by subtracting [tex]20-10[/tex] to see if it results in a solution of 10.

Since the equation [tex]20-10=10[/tex] is equal/true, we can conclude that [tex]z=5[/tex].

The equations that are true for x = –2 and x = 2 are x^2 - 4 = 0 and 4x^2 = 16

Given the solution to a quadratic equation to be -2 and 2, the equation is expressed as:

(x-(-2))(x -2) = 0
(x+2)(x - 2) = 0

Expand

x^2 - 2x + 2x - 4 = 0

x^2 - 4 = 0

Hence the equations that are true for x = –2 and x = 2 are x^2 - 4 = 0 and 4x^2 = 16

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Answer:

D.  d = √(V/5)

E.  A = √(b/c).

Step-by-step explanation:

V = 5d^2

Divide both sides by 5:

V/5 = d^2

Now take the square root of both sides:

d = √(V/5)

Note - it's the square root of the whole term (V/5).

b = cA^2

A^2 = b/c

A = √(b/c).

Answer:

the third : x + x + x + 2 = 10

Step-by-step explanation:

x = the length of the first 2 pieces.

the third piece will be x+2 ft long.

so, the total length of the original board is the sum of all 3 pieces and must be all in all 10 ft.

10 = x + x + (x + 2) = x + x + x + 2

so, it is the third answer option.

Using proportions, it is found that there are 5 cups of milk in each bowl of chocolate pudding.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The cafeteria used 10 quarts for 8 bowls, hence the number of quarts per bowl is:

10/8 = 1.25

Each quart has 4 cups, hence the number of cups is:

4 x 1.25 = 5 cups.

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Each van carries 13 students and each bus carries 25 students.

Given that the senior class at High School A and the senior class at High School B both planned trips to Yellowstone, and the senior class at High School A rented and filled 5 vans and 2 buses with 115 students, while High School B rented and filled 1 van and 6 buses with 163 students, and each van carried the same number of students and each bus carried the same number of students, to determine the number of students in each van and in each bus, the following calculation must be made:

Therefore, each van carries 13 students and each bus carries 25 students.

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Answer:

Each van carries 13 students and each bus carries 25 students.

Step-by-step explanation:

The perimeter of the new rectangular piece of glass is 80m.

Here, a rectangular piece of glass has a perimeter of 20 meters.

As we know the perimeter P of a rectangle is given by the formula,

P = 2l+2w...(1)

Therefore,

20 = 2l + 2w

20 = 2(l + w)

20/2 = l + w

10 = l + w ....(2)

Now, both the length and width of the rectangle are multiplied by 4,

That is,

The new length of the rectangle is, l = 4l

The new width of the rectangle is, w = 4w

Therefore by substituting this in the equation(1) we get,

P = 2(4l) + 2(4w)

P = 8l + 8w

P = 8(l+w)....(3)

Substitute equation (2) in (3),

That is,

P = 8*10

P = 80m

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The standard deviation is approximately 3.84

Step 1: Find the mean
Find the sum of the values, and divide by number of terms.
Mean (average) = (36+32+38+28)/4 = 134/4 = 33.5

We must use Standard Deviation formula which is attached as an image below.

X is the mean here, so lets plug in 33.5

Step 2. Distance from the mean squared |x-mean∣²

For each data point, we will plug in the numbers.
|36-33.5|²=2.5²=6.25

|32-33.5|²=1.5²=2.25

|38-33.5|²=4.5²=20.25

|28-33.5|²=5.5²=30.25
Step 3: Find the sum (∑)
We find the sum here by adding all the distances from the mean squared
∑|x-mean|²=59

Step 4: Divide the sum by the amount of points, 4
59/4=14.75
Step 5: Take the square root of step 4
[tex]\sqrt{14.75}[/tex] is about 3.84

The standard deviation is approximately 3.84

Answer:

Hector makes a tent shaped like a rectangular pyramid the volume is 56 cubic feet and the area is 24 square feet how tall is the tent

Step-by-step explanation:

When the current mortgage rates are high and expected to drop in the near future, the loans that will be gotten is one that has C. variable rate.

It should be noted that a mortgage simply means a loan that's made by a bank to purchase a house.

In this case, the current mortgage rates are high and expected to drop in the near future, the loans that will be gotten is one that has a variable rate. This is because once the mortgage rate decreases, one will pay a lesser amount.

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The design of the experiment above will center around:

The aim of this study is to know  and compare student's level of satisfaction with school cafeteria food services so as to improve the quality of food served at school meal service.

Hence The design of the experiment above will center around:

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The total mass of Adrian and Chang at birth is 7.41 kilograms

Total mass of the babies = Adrian weight + Chang weight

= 2.87 kilograms + 4.54 kilograms

= 7.41 kilograms

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The vector AB is not related with the vector CD as k is not the same for each pair of components.

In this question we must prove if the vector AB is a multiple of the vector CD, that is:

[tex]\overrightarrow{AB} = k \cdot \overrightarrow {CD}[/tex]

[tex]\vec B - \vec A = k \cdot [\vec D - \vec C][/tex]

(1, 4) - (2, 3) = k · [(- 2, 2) - (1, 3)]

(- 1, 1) = k · (- 3, - 1)

Hence, the vector AB is not related with the vector CD as k is not the same for each pair of components.

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the trick being, you flip the ratio as needed, hmmm in this case we want 750 oz converted to lbs, so hmmm we'd want to cancel out the "oz" part and only leave the "lbs" part,

[tex]750~~~\begin{matrix} oz \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~\cfrac{1lbs}{16~~\begin{matrix} oz \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies \cfrac{750}{16}lbs\implies 46.875lbs[/tex]

notice, to cancel out the "oz", we placed the 16 at the bottom.

Answer:

A. x=5 is a solution, but x=3 is not

Step-by-step explanation:

When x=5, 11-5<7, 6<7, this is a solution

When x=3, 11-3<3l, 8<7, this is not a solution

The values of x is 1 and 6.

According to the statement

we have two tangents which are represented by x+5 and x+1 then

we have to find the value of x to get the perfect value of tangent

so, due to interior values of tangent they are equal to each other but in opposite sign.

But here we have to find the value of x one by one.

It means

Here we take interior value of tangent and exterior value of tangent equal to each other

So, the equations become are written below

X+5= 6 then x = 1

X+1= 7 then x = 6

So, The values of x is 1 and 6.

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The average speed is 50 meters per second

The given parameters are:

Laps = 4

Time = 2 minutes

1 lap = 25 meters

Start by calculating the total distance

Distance = Laps * Meters

Distance = 4 * 25 meters

Distance = 100 meters

The average speed is then calculated as:

Speed = Distance/Time

This gives

Speed = 100 meters/2 minutes

Evaluate

Speed = 50 meters per second

Hence, the average speed is 50 meters per second

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Answer:

The translation rule is: (x,y) → (x-3, y+3)

Step-by-step explanation:

A translation rule in geometry is basically asking you what was done to move the shape to its new location on a graph.

In this particular problem, visualizing the graph isn't actually necessary. You only need to figure out what was added or subtracted to get the new numbers from the old ones.

In the beginning, point D was at the x coordinate 1. To make 1 into -2, you subtract three. The points E and F were also changed from their old numbers to the new ones by subtracting 3.

So, we know that the first half of our rule is x-3.

In the beginning, point D was at the y coordinate 3, but it changed to a 6. To get from 3 to 6, you add three more. Points E and F can also be made into their new numbers by adding 3.

So, we know that the second half of the rule is y+3.

I hope this helped. Please let me know if you have any questions :)

The vertex form of the function is f(x) = -2(x-4)^2 + 2

The standard vertex form of a function is expressed according to the expression;

f(x) = a(x-h)^2+k

where

a is a constant = -2

(h, k) is the vertex = (4, 2)

Substitute

f(x) = -2(x-4))^2+2

f(x) = -2(x-4)^2 + 2

Hence the vertex form of the function is f(x) = -2(x-4)^2 + 2

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