what is the measure of angle EXF

Answer:

For right angle triangle,

we use Pythagoras theorem that is:

[tex]c^{2} =a^{2} +b^{2}[/tex]

c = [tex]\sqrt{a^{2} +b^{2} }[/tex]

For question 1:

c = ?

a = 40

b = 9

putting them in formula,

c = [tex]\sqrt{40^{2} + 9^{2} }[/tex]

c = 41

For question 2:

c = ?

a = 12

b = 13

putting them in formula,

c = [tex]\sqrt{12^{2} + 13^{2} }[/tex]

c = approximately 17.69181

For question 3:

c = 35

a = 20

b = ?

putting them in formula,

[tex]c^{2} =a^{2} +b^{2}[/tex]

[tex]35^{2} = 20^{2} + b^{2}[/tex]

1225 = 400 + [tex]b^{2}[/tex]

[tex]b^{2}[/tex] = 1225 - 400

[tex]b^{2}[/tex] = 825

[tex]\sqrt{b^{2} } = \sqrt{825}[/tex]

b = 5 [tex]\sqrt{33}[/tex]

For question 4:

c = 37

a = 20

b = ?

putting them in formula,

[tex]c^{2} =a^{2} +b^{2}[/tex]

[tex]37^{2} = 20^{2} + b^{2}[/tex]

1369 = 400 + [tex]b^{2}[/tex]

[tex]b^{2}[/tex] = 1369 - 400

[tex]b^{2}[/tex] = 969

Taking square root on both sides

b = 31.12

Hope it helps.

Answer:

1. The similar triangles are ΔXYZ and ΔPQR

The triangles are similar by the AA rule of similarity

2. The similar triangles ΔXYZ and ΔPQR cannot be assumed as being congruent because more information are required about the length of a pair of corresponding sides of both triangles

3. x = 17.5

4. x = 20

Step-by-step explanation:

1. The angles of triangle ΔXYZ are;

∠X  = 32°, ∠Y = 84° and ∠Z = 180° - (84° + 32°) = 64°

The angles of triangle ΔPQR are;

∠P  = 64°, ∠R = 32° and ∠Q = 180° - (64° + 32°) = 84°

The angles of triangle ΔABC are;

∠A  = 64°, ∠C = 92° and ∠B = 180 - (92 + 64) = 24°

Therefore, the two similar triangles are ΔXYZ and ΔPQR

The triangles are similar based on Angle-Angle (AA) rule of similarity

2. The similar triangles ΔXYZ and ΔPQR cannot be assumed as being congruent because more information are required about the length of a pair of corresponding sides of both triangles

3. We have by corresponding triangles formed by the tree and Enzo as follows;

5 ft./(6 ft.)= x/(21 ft.)

∴ x = 21 ft.× (5 ft./6 ft.) = 17.5 ft.

x = 17.5 feet

4. By corresponding triangles, we have;

(35 ft.)/(40.5 ft.+ 54 ft.) = x ft./(54 ft.)

∴ x ft. = (54 ft.) × (35 ft.)/(40.5 ft.+ 54 ft.) = 54 ft. × (35 ft.)/(94.5 ft.) = 20 ft.

x ft. = 20 ft.

∴ x = 20

Answer:

Opposite

Step-by-step explanation:

Opposite sides are parallel is the statement which is a property of parallelogram.

A quadrilateral is defined as a two-dimensional shape with four sides, four vertices, and four angles.

A parallelogram is a special type of quadrilateral that has both pairs of opposite sides parallel and equal.

There are six important properties of parallelograms to know:

Opposite sides are congruent .

Opposite angels are congruent .

Consecutive angles are supplementary.

If one angle is right, then all angles are right.

The diagonals of a parallelogram bisect each other.

In the given options Opposite sides are parallel is the statement which is a property of parallelograms.

Hence, Opposite sides are parallel is the statement which is a property of parallelogram.

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Answer:

its d

Step-by-step explanation:

The  equations that are correct are:

0.02(750) + 0.03(x - 750) = 37.5

0.03(750 - x) = 37.5 - 15

Given:

Melissa earns a 2% commission on the first $750 of sales.

She earns a 3% commission on greater than $750 each week.

1. Sales up to $750:

Melissa earns a 2% commission on the first $750 of sales.

=0.02(750)

= 15

2. Sales exceeding $750:

Melissa earns a 3% commission on the amount of sales that exceed $750.

0.03(x - 750) = 37.5 - 15

Combining both equations, we have:

0.02(750) + 0.03(x - 750) = 15 + 37.5 - 15

15 + 0.03x - 22.5 = 37.5

0.03x - 7.5 = 37.5

Adding 7.5 to both sides

0.03x = 45

Dividing both sides by 0.03

x = 1500

Therefore, the correct equations that calculate the amount of money Melissa made in sales last week are:

Equation 1: 0.02(750) + 0.03(x - 750) = 37.5

Equation 2: 0.03(750 - x) = 37.5 - 15

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I hope it helps you ❤️❤️❤️❤️

The solution to the inequality, 4x^2 - 25 < 0 is determined as x < 5/2.

The solution to the inequality is obtained by solving the inequality as shown below;

4x^2 - 25 < 0

add 25 to both sides of the equation;

4x² < 25

divide both sides by 4

x² < 25/4

take square root of both sides

x < 5/2

Thus, the solution to the inequality, 4x^2 - 25 < 0 is determined as x < 5/2.

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Answer: 69

Step-by-step explanation:

First, you add the 34 with the 35.

You can check your answer by subtracting the answer 69 with 35 and if the answer comes out as 34 it is correct.

Answer: 69 lol

Step-by-step explanation: i got it by adding 34 + 35 lol

Given:

The variable y varies directly as x and inversely as z. When x = 4 and z= 14, y=2.

To find:

The combined variation equation and find y when x = 6 and z= 3.

Solution:

The variable y varies directly as x and inversely as z.

[tex]y\propto \dfrac{x}{z}[/tex]

[tex]y=k\dfrac{x}{z}[/tex]           ...(i)

Where, k is the constant of proportionality.

Putting x=4, y=2 and z=14, we get

[tex]2=k\dfrac{4}{14}[/tex]

[tex]2=k\dfrac{2}{7}[/tex]

[tex]2\times \dfrac{7}{2}=k\dfrac{2}{7}\times \dfrac{7}{2}[/tex]

[tex]7=k[/tex]

Putting k=7 in (i), we get

[tex]y=7\dfrac{x}{z}[/tex]

Putting x=6 and z=3, we get

[tex]y=7\times \dfrac{6}{3}[/tex]

[tex]y=7\times 2[/tex]

[tex]y=14[/tex]

Therefore, the required equation is [tex]y=7\dfrac{x}{z}[/tex] and the value of y is 14 when x = 6 and z= 3.

Answer:

-4/5

Step-by-step explanation:

y=mx+c

m=gradient=-4/5

Answer:

It is 19

Step-by-step explanation:

Hope this helps.

Answer:

56 cards

Step-by-step explanation:

If 5 baseball cards multiplied by 8 is 40, then you multiply the 7 football cards by 8 as well.

7x8=56

56 is the answer because if 5 baseball cards multiplied by 8 is 40, then you multiply the 7 football cards by 8 as well.

Answer:

[tex]\frac{1}{3}[/tex]

Step-by-step explanation:

[tex]\frac{1}{6}[/tex] +  [tex]\frac{1}{6}[/tex]

This is because there is only one "5" and one "6" in a dice. Moreover the total number of numbers in a dice are 6 so the denominator will be 6. Then when the word 'or' is present it means that both the probabilities must be added.

P (of rolling a 5 or 6 on a fair dice) = [tex]\frac{1}{6}[/tex] +  [tex]\frac{1}{6}[/tex]

[tex]\frac{2}{6}[/tex] can be simplified further. Both 2 and 6 are factors of 2 so..

[tex]\frac{2}{6}[/tex] = [tex]\frac{1}{3}[/tex]

P (of rolling a 5 or 6 on a fair dice) = [tex]\frac{1}{3}[/tex]

Answer:

545.5%

Step-by-step explanation:

Answer:

Step-by-step explanation:

Multiply both numerator and denominator by 100. We do this to find an equivalent fraction having 100 as the denominator.

5.545 ×

100

100

= (5.545 × 100) ×

1

100

=

554.5

100

Write in percentage notation: 554.5%

Answer:

2nd one: amelia has 7 muffins left after filling 42 boxes

Step-by-step explanation:

Answer:

100

Step-by-step explanation:

hopes this helps

Answer:

100

Step-by-step explanation:

Answer:

$17.85

1 ten

1 five

2 ones

3 quarters

1 nickel

4 pennies

Hope I helped! <3 :)

$24.96

1 twenty

4 ones

3 quarters

2 dimes

1 penny

Step-by-step explanation:

(x+20)=9x

4x=20

x= 5°

because GEF AND DEG ARE EQUAL

THEN DEF= 2 * GEF

DEF = (9*5)*2=90

DEF= 90°

Answer:

The unit price is the price of a single unit.

To find it, you need to find the quotient between the total price and the number of objects you get for that price.

Brand A:

You get 25 spoons for $1.97

Then the unit price is:

unit price of brand A = $1.97/25 = $0.079

Brand B:

You get 48 spoons for $2.98

Then the unit price is:

unit price of brand B: $2.98/48 = $0.062

Here we can see that the unit price for brand B is smaller, then the better buy is brand B.

Answer:

Step-by-step explanation:

Hope this helps

Answer:

2(9r) and 18r are equivalent

Answer:

67.5 mm²

Step-by-step explanation:

Alright, we're going to make 3 different smaller shapes

Shape (triangle)

Shape (skinny rectangle)

Shape (bigger rectangle)

Add them all together

42+18+7.5= 67.5

Answer:

100

Step-by-step explanation:

Answer:

The answer is

[tex] \frac{30}{48} = \frac{15}{24} [/tex]

Answer:

Hello! You can Simplify 30/48 to 5/8

I do not think you can make a whole with 30/48

Answer:

32.5 km

Step-by-step explanation:

6.5 / 2 = 3.25

3.25 x 10 = 32.5 km

Hope that helps!

Answer:

32.5 km

Step-by-step explanation:

Our ratio is 2cm: 10km

We can also write a ratio to look like a fraction. I'm attaching a picture. Sometimes it's easier to see that way.

We cross-multiply, then divide.

Ask any questions in the comments.

Answer:

c

Step-by-step explanation:

Answer:

75000000

Step-by-step explanation:

se multiplica

45×70= 3150 metros

luego multiplica

60×50= 3000 metros

luego se divide

78750000/ 3150 = 25000

y por último multiplica

25000×3000

conclusiones

el metro cuadrado de tierra vale 25000 por lo que los 3000 metros cuadrados que son del terreno de 60x50 estan valorados en 750000000

Answer: quadratic

Step-by-step explanation:

The given polynomial is a quadratic polynomial with two terms.

The given expression is:

[tex]2p^{2} -2p[/tex]

A quadratic polynomial is a single variable polynomial with the maximum power of the variable as 2.

Maximum power of p in the given expression =2

So, the given polynomial is a quadratic polynomial.

Hence, the given polynomial is a quadratic polynomial with two terms.

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