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3 years ago

Consider the diagram below. Which of the following statements is correct?

Mathematics

2 answers:

Nutka1998 [239]3 years ago

7 0

Answer:

Step-by-step explanation:

The diagram shows two parallel lines XY and WV.

1. Parallel lines XY and WV are cut by transversal XW, then angles YXZ and VWZ are congruent as alternate interior angles.

2. Parallel lines XY and WV are cut by transversal YV, then angles XYZ and WVZ are congruent as alternate interior angles.

AA similarity theorem states if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

So, $\triangle XYZ\sim \triangle WVZ$ by AA similarity

Mademuasel [1]3 years ago

3 0

Answer: AA similarity

Step-by-step explanation:

I tried it and it was right on math nation.

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Write an equation based on the table below

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Y= 15(x) should be your equation based on the table below

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3 years ago

What is the value of $x$ if $-\frac23(x-5) = \frac32(x+1)$?

Ipatiy [6.2K]

Answer:

x = (-29)/5

Step-by-step explanation:

Solve for x:

(2 (x - 5))/3 = (3 (x + 1))/2

Multiply both sides by 6:

(6×2 (x - 5))/3 = (6×3 (x + 1))/2

6/3 = (3×2)/3 = 2:

2×2 (x - 5) = (6×3 (x + 1))/2

6/2 = (2×3)/2 = 3:

2×2 (x - 5) = 3×3 (x + 1)

2×2 = 4:

4 (x - 5) = 3×3 (x + 1)

3×3 = 9:

4 (x - 5) = 9 (x + 1)

Expand out terms of the left hand side:

4 x - 20 = 9 (x + 1)

Expand out terms of the right hand side:

4 x - 20 = 9 x + 9

Subtract 9 x from both sides:

(4 x - 9 x) - 20 = (9 x - 9 x) + 9

4 x - 9 x = -5 x:

-5 x - 20 = (9 x - 9 x) + 9

9 x - 9 x = 0:

-5 x - 20 = 9

Add 20 to both sides:

(20 - 20) - 5 x = 20 + 9

20 - 20 = 0:

-5 x = 9 + 20

9 + 20 = 29:

-5 x = 29

Divide both sides of -5 x = 29 by -5:

(-5 x)/(-5) = 29/(-5)

(-5)/(-5) = 1:

x = 29/(-5)

Multiply numerator and denominator of 29/(-5) by -1:

Answer: x = (-29)/5

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3 years ago

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3 years ago

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A ratio comparing a number to 100

katen-ka-za [31]

"Percent" - For details read the explanation given below.

percentages compare numbers in the numerator to 100 and the ratio that compares a number to 100 is logically called percent.

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3 years ago

The function h(t) = -16t2 + 48t + 28 models the height (in feet) of a ball where t is the time (in seconds).

Alex17521 [72]

Answer:

Step-by-step explanation:

<em>[using calculus] </em>When the function h(t) reaches its maximum value, its first derivative will be equal to zero (the first derivative represents velocity of the ball, which is instantaneously zero). We have $h'(t) = -32t + 48$ , which equals zero when $t = 3/2 = 1.5$ . The ball therefore reaches its maximum height when t = 1.5. To find the maximum height, we need to find h(1.5), which is 64 feet.

<em>[without calculus] </em>This is a quadratic function, so its maximum value will occur at its vertex. The formula for the x-coordinate of the vertex is -b/2a, so the maximum value occurs when t = -48/(2*16), which is 1.5. The maximum height is h(1.5), which is 64 feet.

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3 years ago