Write a proportion relating the side lengths of the triangle to any other triangle that has the line as a hypotenuse, a horizontal length of x units, and a vertical length of y units.

Answer:

1) x = 55°

2) x = 30°

3) x = 68°

Step-by-step explanation:

In the given set of questions where it requires to find the unknown value of x to prove that v ||w:

The Consecutive Interior Angles Theorem states that for any given two parallel lines cut by a transversal, the measures of a pair of consecutive interior angles have a sum of 180°. Hence, the pair of consecutive interior angles are supplementary.

1.)  In the given diagram, the two consective interior angles are m ∠70° and m ∠ 2x°.  As defined by the Consecutive Interior Angles Theorem:

m ∠70° + m ∠ 2x° = 180°

Solve for x algebraically:

70° + 2x° =  180°

Subtract 70° from both sides:

70° - 70° + 2x° =  180° - 70°

2x° =  110°

Divide both sides by 2 to solve for x:

[tex]\LARGE\mathsf{\frac {2x^{\circ}}{2}\:=\:\frac{110^{\circ}}{2}}[/tex]

x = 55°

Verify whether the value for x is valid:

70° + 2x° =  180°

70° + 2(55)° =  180°

70° + 110° =  180°

180° =  180° (True statement).

2) In the given diagram, the two consective interior angles are m ∠2x° and m ∠ 4x°.  As defined by the Consecutive Interior Angles Theorem:

m ∠2x° + m ∠ 4x° = 180°

Solve for x algebraically:

2x° + 4x° =  180°

Add like terms:

6x° = 180°

Divide both sides by 6 to solve for x:

[tex]\LARGE\mathsf{\frac {6x^{\circ}}{6}\:=\:\frac{180^{\circ}}{6}}[/tex]

x = 30°

The Consecutive Interior Angles Theorem still applies in this question. The two consective interior angles are m ∠90° and m ∠ (x + 22)°.  As defined by the Consecutive Interior Angles Theorem:

m ∠90° + m ∠ (x + 22)° = 180°

Solve for x algebraically:

90° + x° + 22 =  180°

Combine like terms:

112° + x° = 180°

Subtract 112° from both sides to isolate x:

112° - 112° + x° = 180° - 112°

x = 68°

Verify whether the value for x is valid:

90° + x° + 22 =  180°

90° + 68° + 22 =  180°

180° =  180° (True statement).

Answer:

x = 69

Step-by-step explanation:

2x - 3 = 135

2x = 135 + 3

2x = 138

2x/2 = 138/2

x = 69

Answer:

When you use a debit card, the funds for the amount of your purchase are taken from your checking account in almost real time. When you use a credit card, the amount will be charged to your line of credit, meaning you will pay the bill at a later date, which also gives you more time to pay.

Answer:

x+27

Step-by-step explanation:

Let's simplify step-by-step.

4(x+3)+3(5−x)

Distribute:

=(4)(x)+(4)(3)+(3)(5)+(3)(−x)

=4x+12+15+−3x

Combine Like Terms:

=4x+12+15+−3x

=(4x+−3x)+(12+15)

=x+27

Hope you find this Useful!

Answer:

x+27

Step-by-step explanation:

Distribute

4(+3)+3(5−)

4+12+3(5−)

Rearrange terms

4x+12+3(5−x)

4+12+3(−+5)

Distribute

4x+12+3(−x+5)

4+12−3+15

Add the numbers

4x+12−3x+15

4+27−3

Combine like terms

4x+27−3x

1+27

Multiply by 1

1x+27

+27

Answer:

see explanation

Step-by-step explanation:

Using the rules of exponents

[tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex]

[tex]a^{m}[/tex] ÷ [tex]a^{n}[/tex] = [tex]a^{(m-n)}[/tex]

(a)

3² × 3² = [tex]3^{(2+2)}[/tex] = [tex]3^{4}[/tex]

(b)

7 × [tex]7^{4}[/tex] = [tex]7^{(1+4)}[/tex] = [tex]7^{5}[/tex]

c)

[tex]10^{9}[/tex] ÷ [tex]10^{7}[/tex] = [tex]10^{(9-7)}[/tex] = 10²

(d)

[tex]5^{8}[/tex] ÷ 5 = [tex]5^{(8-1)}[/tex] = [tex]5^{7}[/tex]

Answer:

The first option you have selected should be correct. if any doubt comment.

Answer:

= 215008. 21 in²

Step-by-step explanation:

Answer:

x-intercept(s): (-2, 0), (6, 0)

y-intercept(s): (0, -6)

Step-by-step explanation:

An x-intercept represents the point(s) at which the parabola intersects the x axis.  A parabola can have 0, 1, or 2 x-intercepts.  

A y-intercept represents the point at which the parabola intersects the y axis.  A parabola always has exactly 1 y-intercept.

Hope it helps :) and let me know if you're still confused.

Answer:

18

Step-by-step explanation:

Total=70.

Last week she posted= 2/5 of 70= She posted 28 last week

So, 42 left

then, she posted 4/7 of remaining (42)

4/7 of 42 is 24

42-24= 18

She still needs to post 18 flyers

HOPE THIS HELPS!

Answer:

OK, so she started with 70 fliers.

Last week, she posted 2/5 of them. 2/5 of 70 is equal to 28, so she has 28 fliers less than she started with. 70-28=42.

This week, she posted 4/7 of the remaining fliers (42). 4/7 of 42 is equal to 24. So, she has 24 less than 42, so 42-24=18.

She still needs to post 18 fliers.

Hope this helps!!!

Answer:

Hi freind just it

Step-by-step explanation:

Answer:

1280 is the answer. hope it helps you

Answer:

If three sides of one triangle are congruent to three corresponding sides of another triangle, then the triangles re congruent.  SSS

Step-by-step explanation:

or If two sides and the included angle of one triangle are congruent to the corresponding sides and the included angle of another triangle, then the triangles are congruent.  SAS

Answer:

2.5i

Step-by-step explanation:

-5/2 = 2.5

+i = 2.5i

Answer:

add

subtract

multiply

Step-by-step explanation:

Answer:

I think the greater fraction is 27/5

Answer:

Step-by-step explanation:

what is greater: 19/5, 27/5, 10/3, 14/5​

fractions are divisions, we divide to see the greater

19/5= 3.8

27/5= 5.4

10/3= 3.33

14/5= 2.8

Answer:

0.16

Step-by-step explanation:

Percent means 'per 100'. So, 16% means 16 per 100 or simply 16/100.

The answer is 0.16

Answer:

0.16

Step-by-step explanation:

Answer:

129º

Step-by-step explanation:

This is just a guess since you didn't include the diagram

b is supplemetary to a

therefor

b = 180 - a

b = 180 - 51

b = 129º

Answer:

yes it's a function, but not a relation.

Step-by-step explanation:

Because it is a polynomial function

Answer:

y=-3x-9

Step-by-step explanation:

Let's find the slope of the line

m=-2-10/3--1

m=-12/4=-3

The equation is given as

y-y1=m(x-x1)

y--2=-3(x-3)

y+2=-3x+9-2

y=-3x-7-2

y=-3x-9

Answer:

3 square miles

Step-by-step explanation:

Answer:

Step-by-step explanation:

- 4x^3 / (- 4) = 32 / (- 4)

x should and cannot be negative or it shouldn't be for example (- x) = 90

cubic root (x^3) = cubic root (- 8)

x = cubic root (- 8)

x = 2i

what is "i"?

It is an imaginary number as you cannot square, cubic, or whatever root with a negative in it. so instead you must add "i" to remove the negative as a replacement and indicator that it was a negative number.

I don't know what you mean by this but you'll just get a value larger than the two sums that you added

5 + 7 = 12

3 + 4 = 7

Answer:

The sum will always be even

Step-by-step explanation:

Answer:

I believe it is d

Step-by-step explanation:

it is the only option where every combination of two sides is larger than the third

Answer:

d

Step-by-step explanation:

if you add up 2 sides it is larger than the third, which is what we are looking for :))

Step-by-step explanation:

how many cups of water do you need to fill in one jar maths

Answer:

15 in i am guessing

Step-by-step explanation:

i need to know the height of the can first

The height of a can of fruit juice used as a prop, if its actual height is 7 inches, should be of 3.85 inches.

A proportional relationship is a linear function that has an intercept of zero and hence it has the output variable y as the multiplication of the input variable x and the constant of proportionality k, as follows:y = kx.

Given that, the input and the output variables in this problem are as follows:

Input variable: Actual height = 80 in

Output variable: Height on set = 44 in

k = 44/80

k = 0.55.

Therefore, the equation is:

y = 0.55x.

Then the height on the set when the actual height is of 7 inches is given by:

y = 0.55(7) = 3.85 inches.

More can be learned about proportional relationships at brainly.com/question/10424180

#SPJ1

Answer:

D

Step-by-step explanation:

My gut tells me D because I don't understand your language

Answer:2 1/2

Step-by-step explanation:

Answer:

Length of three sides=3(25)=75ft

Cost per metre=15.00

Total cost:-

[tex]\\ \sf\longmapsto 15(15)=225.00[/tex]