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4 years ago

5

Use the figure to answer the question that follows:

1 answer:

Olegator [25]4 years ago

3 0

Answer:

m∠SQV + m∠VQT = 180°

Step-by-step explanation:

<u> m∠SQT is substituted by 180° at step 5</u>

4 m∠SQV + m∠VQT = m∠SQT Angle Addition Postulate
5 m∠SQV + m∠VQT = 180° Substitution Property of Equality
6 m∠VQT + m∠ZRS = 180° Same-Side Interior Angles Theorem

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Solve for x ! problems attached please help!!

vampirchik [111]

Answer:

7. $x\le 8$

8. $x\le 1.7$

9. $-0.2\le x\le 2$

10. $3< x\le 4$

Step-by-step explanation:

7. Solve for x:

$4x+7-x\le 31$

Separate variable and numbers into different sides of inequality:

$4x-x\le 31-7\\ \\3x\le 24$

Divide the inequality by 3:

$x\le 8$

8. Solve for x:

$2(x-3)+8x\le 11$

Eliminate the brackets:

$2x-6+8x\le 11$

Separate variable and numbers into different sides of inequality:

$2x+8x\le 11+6\\ \\10x\le 17$

Divide the inequality by 10:

$x\le 1.7$

9. Solve for x:

$-7x\le 3x+2\le 8$

Solve two inequalities $-7x\le 3x+2$ and $3x+2\le 8$ separately:

$-7x\le 3x+2\\ \\3x+2\ge -7x\\ \\3x+7x\ge -2\\ \\10x\ge -2\\ \\x\ge -0.2$

and

$3x+2\le 8\\ \\3x\le 8-2\\ \\3x\le 6\\ \\x\le 2$

So,

$-0.2\le x\le 2$

10. Solve for x:

$8$

Add 1:

$8+1$

Divide by 3:

$3< x\le 4$

6 0

3 years ago

Read 2 more answers

The perimeter of the rectangle below is 112 units. Find the length of side VW . Write your answer without variables. Top YX: 4z

dimaraw [331]

Answer:

$VW = 33$

Step-by-step explanation:

<em>See attachment for complete question</em>

Given

$VY = 4x - 1$

$VW = 5x + 3$

$Perimeter = 112$

Required

Determine the length of VW

Perimeter is calculated as:

$Perimeter = 2 * (Width + Length)$

This gives:

$Perimeter = 2 * (VW + VY)$

Substitute values for VW, VY and Perimeter

$112 = 2 * (4x - 1 + 5x + 3)$

Collect Like Terms

$112 = 2 * (4x + 5x -1 +3)$

$112 = 2 * (9x +2)$

Divide through by 2

$56 = 9x + 2$

Collect Like Terms

$9x = 56 - 2$

$9x = 54$

$x = 54/9$

$x = 6$

Substitute 6 for x in $VW = 5x + 3$

$VW = 5 * 6 + 3$

$VW = 30 + 3$

$VW = 33$

4 0

3 years ago

Lcm of 1,2,12,30,84,165

cricket20 [7]

Answer:

$LCM(1,2,12,30,84,165)=2^2*3*5*7*11*1=4620$

Step-by-step explanation:

To find the LCM of 1,2,12,30,84,165 you must first find the prime factors of 12,30,84 and 165

12| 2 30| 2 84| 2 165| 3

6 | 2 15 | 3 42| 2 55 | 5

3 | 3 5 | 5 21 | 3 11 | 11

1 1 7 | 7 1

1

$12=2^2*3$ $30=2*3*5$ $84=2^2*3*7$ $165=3*5*11$

Now we look for common and uncommon factors with their greatest exponent

LCM(1,2,12,30,84,165)

Common factors with their greatest exponent: $2^2*3*5$

Uncommon factors with their greatest exponent: $7*11*1$

$LCM(1,2,12,30,84,165)=2^2*3*5*7*11*1=4620$

3 0

4 years ago

Convert 36000cm^2 to m^2

disa [49]

Answer:

its 3.6

Step-by-step explanation:

7 0

3 years ago

Given AG bisects CD, IJ bisects CE, and BH bisects ED. Prove KE = FD.

OverLord2011 [107]

When a line is bisected, the line is divided into equal halves.

See below for the proof of $\mathbf{KE \cong FD}$

The given parameters are:

<em>AC bisects CD</em>
<em>IJ bisects CE</em>
<em>BH bisects ED</em>

<em />

By definition of segment bisection, we have:

$\mathbf{CK \cong KE}$
$\mathbf{EF \cong FD}$
$\mathbf{CE \cong ED}$

By definition of congruent segments, the above congruence equations become:

$\mathbf{CK = KE}$
$\mathbf{EF = FD}$
$\mathbf{CE = ED}$

By segment addition postulate, we have:

$\mathbf{CE = CK + KE}$
$\mathbf{ED = EF + FD}$

Substitute $\mathbf{ED = EF + FD}$ in $\mathbf{CE = ED}$

$\mathbf{CK + KE = EF + FD}$

Substitute $\mathbf{CK = KE}$ and $\mathbf{EF = FD}$

$\mathbf{KE + KE = FD + FD}$

Simplify

$\mathbf{2KE = 2FD}$

Apply division property of equality

$\mathbf{KE = FD}$

By definition of congruent segments

$\mathbf{KE \cong FD}$

Read more about proofs of congruent segments at:

brainly.com/question/11494126

6 0

3 years ago