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3 years ago

Which of the following best describes the graph of this system of equations ? y=-2x+3 and 5y=-10x +15

Mathematics

1 answer:

ELEN [110]3 years ago

6 0

Remark

When talking about straight lines, D is never true. Never.

C is possible, but in this case not true. Read on.

B. Might be true but in this case it is not. The lines (to be parallel) have to have the same number in front of the x. These two lines do when you divide through by 5. But the y intercept has to be different. That is not so in this case. So B is incorrect.

A is your answer. If you divide through by 5 on the second one, you get the first one. They are identical.

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What's 5 to the first power

shusha [124]

The correct answer is 5.

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3 years ago

Triangle PQR is transformed to triangle P′Q′R′. Triangle PQR has vertices P(4, −8), Q(0, 12), and R(−4, 0). Triangle P′Q′R′ has

Tom [10]

Part A:

The scale factor is 1/4, because you obtain the coordinates of points P', Q', R' by dividing the coordinates of P, Q and R respectively by 4.

Part B:

Reflecting about the y axis causes a sign swap in the x coordinate. So, the new point will be

$P''(-1, -2),\quad Q''(0, 3),\quad R''(1, 0)$

Part C:

The triangles are similar, but not congruent. When you transform PQR into P'Q'R', you get a scaled version of the original triangle. This means that the angles and the proportion between sizes will be the same, but the length are scaled by 1/4, and the area is consequentially scaled by 1/16.

Triangles P'Q'R' and P''Q''R'' are congruent, so they are both similar but not congruent to the original triangle.

6 0

3 years ago

Help!!! Brainliest to 1 or 2 answer!!

lyudmila [28]

Answer:

35-17=3y

Step-by-step explanation:

3y+17=35

-17 -17

3y=35-17

7 0

1 year ago

What is the surface area of this cone?

DanielleElmas [232]

surface area of this cone?

Use A= 3.14 and round your answer to the nearest hundredth

9 ft

6 ft

8 0

3 years ago

Write the integral in one variable to find the volume of the solid obtained by rotating the first-quadrant region bounded by y =

Dovator [93]

Answer:

V = π ∫₀² (y² − 8y + 6√(2y)) dy

V = π ∫₀² (6x − 5x² + x³) dx

Step-by-step explanation:

y₁ = 0.5x²

y₂ = x

First, find the intersections of the curves.

0.5x² = x

x² = 2x

x² − 2x = 0

x (x − 2) = 0

x = 0 or x = 2

So the points of intersection are (0, 0) and (2, 2).

When we revolve this region about the line x = 3, we get a hollow shape that looks like an upside-down funnel, or a volcano.

One option is to use washer method to find the volume, by cutting a thin horizontal slice of thickness dy, inner radius 3−x₁ = 3−√(2y), and outer radius of 3−x₂ = 3−y.

V = ∫₀² π [(3−y)² − (3−√(2y))²] dy

V = ∫₀² π (9 − 6y + y² − 9 + 6√(2y) − 2y) dy

V = π ∫₀² (y² − 8y + 6√(2y)) dy

Another option is to use shell method to find the volume, by cutting a thin vertical slice of thickness dx, radius 3−x, and height y₂−y₁ = x−0.5x².

V = ∫₀² 2π (3 − x) (x − 0.5x²) dx

V = ∫₀² 2π (3x − 1.5x² − x² + 0.5x³) dx

V = ∫₀² 2π (3x − 2.5x² + 0.5x³) dx

V = π ∫₀² (6x − 5x² + x³) dx

The second option is arguably easier to evaluate, but either one will get you the same answer (V = 8π/3).

7 0

4 years ago