Venn diagram ( attached image )

1.

Answer:

<B ≅ <F

<C ≅ <G

<D ≅ <H

<A ≅ <E

Explanation:

Little tick marks are used to show that two sides are the same length (congruent).  You can use just one tick mark, two or three, or more -- just as long as you use the same number on sides that are equal.

You make the little rounded sweep in the angle and then use tick marks to show which angles are the same size (have the same measure -- are congruent).

2.

Answer: x = 8 and y = 19

Explanation:

Triangle MLN ≅Triangle SRT

Therefore, each angle and side measure of one triangle are equal to the corresponding angle and side of the other triangle.

<M ≅ <S

<S= 93 (Given)

<M=93

<N=63 (Given)

Line segment ML ≅ Line segment SR

Line segment ML = 43

Line segment SR = 3x + y

Now, we need to find the values of x and y.

43 = 3x + y

<M+<N+<L=180 (Interior angles measure of a triangle is always 180)

93+63+z=180

156+z=180

z= 24

24 is the measure of <R.

<R=3x

24=3x

x=8

Now if we plug in the 8, the value of x, into our equation above,

43=3x+y

43=3(8)+y

43=24+y

43-24=y

19=y

3.

Answer:

<K ≅ <M

<J ≅ <N

<Q ≅ <P

<L≅ <L

Explanation:

Because all four interior angles are congruent to each other, these two quadrilaterals are equal to each other. Additionally, the side measurements of one shape are equal to the corresponding measurements of the other shape.

4.

Answer: What must be true about these two triangles is that triangle ABC and triangle DEF are equilateral triangles.

Explanation: This means that the measurement of all sides is equal and the measurement of all angles is also equal.

The box plot first represents the data set option first is correct the third quartile lies between 52 to 54.

A box and whisker plot is a method of abstracting a set of data that is approximated using an interval scale. It's also known as a box plot. These are primarily used to interpret data.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have data set:

30, 35, 35, 45, 46, 46, 52, 55, 57

We can find below details from the data set:

Population size = 9

Minimum: 30

First quartile: 35

Median = 46

Third quartile = 53.5

Interquartile Range = 18.5

Maximum = 57

Outliers = none

Thus, the box plot first represents the data set option first is correct.

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Answer:

[tex]\huge\boxed{\sf L = 78\°}[/tex]

Step-by-step explanation:

Exterior angle of L = 5x + 12

M = 3x - 2

N = 50

So, the exterior angle that is adjacent to L is equal to the sum of non-adjacent sides (M and N) of the triangle.

Here,

Exterior angle of L = M + N

5x + 12 = 3x - 2 + 50

5x + 12 = 3x + 48

Subtract 12 to both sides

5x = 3x + 48 - 12

5x - 3x = 36

2x = 36

Divide 2 to both sides

x = 18

So,

= 3x - 2

= 3 (18) - 2

= 54 - 2

= 52°

Now,

We know that,

L + M + N = 180°

L + 52 + 50 = 180

L + 102 = 180

Subtract 102 to both sides

L = 180 - 102

L = 78°

[tex]\rule[225]{225}{2}[/tex]

Answer:

Assuming the gas tank was filled to the maximum of 13 gallons, the car motorcycle achieves 39 miles per gallon.

Step-by-step explanation:

507/13 = 39

Answer:

[-3, 5)

Step-by-step explanation:

At x = -3, the circle is filled in, so -3 is part of the domain. At x = 5, the circle is not filled in, so 5 is not part of the domain. So the domain is [-3, 5).

Answer:

409

Step-by-step explanation:

296 = 200 + 90 + 6
The value of the 9 is 90 in 296.
1/10 of 90 is 9. The only number that has a 9 in the units digit is 409.

Answer:

y = 139

Step-by-step explanation:

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

110° is an exterior angle of the triangle , then

3x + 2x - 5 = 110

5x - 5 = 110 ( add 5 to both sides )

5x = 115 ( divide both sides by 5 )

x = 23

then

2x - 5 = 2(23) - 5 = 46 - 5 = 41

y and 2x - 5 are a linear pair and sum to 180° , so

y = 180 - 41 = 139

Answer:

I got 139

Someone correct me if I'm wrong.

Step-by-step explanation:

(2x-5) + 3x + 70 = 180

Collect liketerms. Take away 70 from both sides and add 5.

5x=115

x=23

2(23) -5 = 41

180-41 = 139

y = 139

An equation is formed of two equal expressions. The correct option is B.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The complete option is:

Which values of a and b make the equation true?

[tex]\dfrac{(2xy)^4}{4xy}=4x^ay^b[/tex]

A)a = 0, b = 0

B)a = 3, b = 3

C)a = 4, b = 4

D)a = 5, b = 5

The given equation can be simplified as shown below,

[tex]\dfrac{(2xy)^4}{4xy}=4x^ay^b\\\\\dfrac{2^4 \times x^4 \times y^4}{4xy}=4x^ay^b\\\\\dfrac{16x^4y^4}{4xy} = 4x^ay^b\\\\4x^{(4-1)}y^{(4-1)} = 4x^ay^b\\\\4x^3y^3 = 4x^ay^b[/tex]

Now, comparing the two sides of the equation, the value of a and b should 3 for the equation to be satisfied.

Hence, the correct option is B.

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Answer:

I'm pretty sure its a since if the exponints negite they drop the the bottom and non of the others look right

Hope This Helps!!!

Answer:

1/r^7  + 1/s^12

Step-by-step explanation:

See attached image.

Step-by-step explanation:

b l think so

Answer:

y = 10x + 422

Step-by-step explanation:

Answer:

-11 < x < 7

(first option listed)

Step-by-step explanation:

we know that x² + 4x < 77

first, we should rewrite our expression in standard

x² + 4x - 77 < 0

factor {find two numbers that multiply to c (77) and add to b (4)  }

(x - 7) (x + 11) < 0

set both roots to 0:

x - 7 < 0

  + 7  + 7

x < 7

x + 11 < 0

x > -11

so, x will be < 7 and > -11

which can be expressed as

-11 < x < 7

So, -11 < x < 7

Answer:

-11 < x < 7

Step-by-step explanation:

1st option;

Answer:

B. (4, -2)

Step-by-step explanation:

Please see attachment.

Hope this helps!

If not, I am sorry.

1. In terms of x and y, the height of the tree is [tex]h = y \times tan \ t^\circ[/tex] and[tex]h = x \times tan \ s^\circ[/tex]

2. The height of the tree is 6.71 meters

From the question, we are to determine the height of the tree in terms of x and y

Using SOH CAH TOA, we can write that

[tex]tan \ t^\circ =\frac{h}{y}[/tex]

∴ [tex]h = y \times tan \ t^\circ[/tex]

Also,

[tex]tan \ s^\circ =\frac{h}{x}[/tex]

∴ [tex]h = x \times tan \ s^\circ[/tex]

2. If m∠t = 40° and y = 8 meters,

Then, the height of the tree

h = 8 × tan40°

h = 6.71 meters

Hence, the height of the tree is 6.71 meters

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Answer: Yes.

Step-by-step explanation: No number in the map is paired to two different, distinct numbers.

The probability that Alex takes out three red apples is 1/30.

The probability that Alex takes out one green apple and two red apples is 1/10.

The probability that Alex takes out three red apples = (number of red apples / total number of apples) x (number of red apples - 1 / total number of apples - 1) x (number of red apples - 2 / total number of apples - 2)

4/10 x 3/9 x 2 /8 = 1 / 30

The probability that Alex takes out one green apple and two red apples = (number of green apples / total number of apples) x (number of red apples / total number of apples - 1) x (number of red apples - 1 / total number of apples - 2)

6/10 x 4/9 x 3/8 = 1 / 10

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You buy 3 shirts and 1 pair of pants for $32. Your friend buys 2 shirts and 3 pairs of pants for $40. How much did each item cost?

First let’s define a shirt as X and pants as Y!

In the first scenario, the equation will be 3X + Y =$32

In the second scenario, the equation will be 2X + 3Y = $40  

Now because we have two different variables (X & Y) let’s solve for one of them (Ex: Y) to simplify the equations!

3X + Y= $32—> subtract 3X on both sides of the equation  

-3X.        - 3X

Net result: Y= 32- 3X

Now we can insert this into the second equation 2X + 3Y = $40 in order to solve for X variable  

2X + 3(32-3X) = $40

2X + 96 - 9X = $40 —> simplify the equation  

-7X + 96 = $40 —> substrate 96 from both sides  

-7X = -56 —> divide both sides by -7  

X= 8  

Now reinsert 8= X into 3X + Y = $32

3(8) + Y = $32

24+ Y = $32 —> substract 24 from both sides

y = 8

ANSWER: X= 8, Y= 8

Answer:

x+5 (under assumption you meant to do -3x

Step-by-step explanation:

you can use long division.

Take the leading coefficient x^4 and divide it by x^3. This results in x which is going to be the first part of you quotient. Now take that x and multiply it by the divisor (x^3 - 3). This gives you x(x^3 - 3) = x^4 - 3x. Now subtract that x^4 - 3x from the original polynomial and repeat this until you can't divide anymore

[tex]x^4+5x^3-3x-15 - (x^4-3x) = 5x^3-15\\x^3/5x^3=5\\5(x^3-3) = 5x^3-15\\5x^3-15-(5x^3-15) = 0\\\\x+5[/tex]

Using the slope concept, it is found that the thundercloud is 6.43 miles above the ground.

The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.

In this problem, we have that:

Hence:

tan(65º) = h/3.

h = 3 x tan(65º)

h = 6.43 miles.

The thundercloud is 6.43 miles above the ground.

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Answer:

4.2 pints

Step-by-step explanation:

3.5 × 1.2 = 4.2

Answer: 4.2 pints

If the height of the triangle will be 6.28 meters. Then the value of x will be 8.46 meters.

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

In the diagram shown, the area of the triangle is 44.3 m².

If b = 14.1 m and the angle at C = 48°.

Then the value of x will be

The height of the triangle will be

    A = 1/2 × B × H

44.3 = 1/2 × 14.1 × h

    h = 6.28 m

Then the value of x will be

sin 48° = 6.28 / x

x = 8.455 ≈ 8.46 m

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Answer:

Yes it is what is the question you are answering and it's 90 degree

Answer:

yes line is a tangent to the circle

Step-by-step explanation:

the angle between a tangent and the radius of a circle is 90°

If the triangle is right then the line touching the circle is a tangent.

using the converse of Pythagoras' identity

if the square on the longest side is equal to the sum of the squares on the other 2 sides then the triangle is right

longest side = 65 and 65² = 4225

56² + 33² = 3136 + 1089 = 4225

then the triangle is right and the line touching the circle is a tangent

If the statement is "The difference of four times a number and seven is ten times the number." then an algebraic equation is 4x-7= 10+x and the solution is -7/6.

Given the statement "The difference of four times a number and seven is ten times the number." We have to translate the statement in an algebraic equation and then solve it.

Let, the number be x.

This difference of four times a number and seven is 4x-7 and ten times the number is 10x

According to the question, the equation is,4x-7= 10x

4x-7=10x

6x=-7

x=-7/6

x=-7/6

Hence the value of the x is -7/6.

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The amount of the investment at the end of the 10 years period if compounded quarterly is $2,649.6.

A = P(1 + r/n)^nt

= 1200(1 + 0.08/4)^(4×10)

= 1200(1 + 0.02)^40

= 1200(1.02)^40

= 1200(2.208)

= $2,649.6

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