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3 years ago

Two numbers total 43 and have a difference of 11 Find the two numbers.

Mathematics

1 answer:

OverLord2011 [107]3 years ago

6 0

Answer:

27 and 16

27 + 16 = 43

And the difference between them ( 27-16) = 11

Step-by-step explanation:

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3 years ago

Part of the graph of the function f(x) = (x – 1)(x + 7) is shown below. Which statements about the function are true? Select thr

devlian [24]

Answer:

The vertex of the function is at (–3,–16)

The graph is increasing on the interval x > –3

The graph is positive only on the intervals where x < –7 and where x > 1

Step-by-step explanation:

The roots of this function are the values that make f(x) = 0. As the equation is already factored, we can see that the roots are x1 = 1 and x2 = -7

The x-coordinate of the vertix can be calculated as:

x_v = (x1 + x2)/2 = -6/2 = -3

So the first statement: "The vertex of the function is at (–4,–15)" is wrong.

The y_coordinate of the vertex is:

f(x_v) = (x_v - 1)*(x_v + 7) = (-3 -1) * (-3 +7) = (-4) * (4) = -16

So the second statemente: "The vertex of the function is at (–3,–16)" is correct.

for values of x greater than x_v = -3, the graph increases, as the equation represents a parabola with concavity upwards. So the third statement is correct.

As the roots are 1 and -7 and the concavity is upwards, the parabola have positive values for x<-7 and x>1. So the fourth statement is correct.

For values of x< -4, the parabola can have both positive or negative values (it has positive values for x < -7) so the fifth statement is wrong.

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4 years ago

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3 years ago

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Is the relationship shown by the data linear? If so, model the data with an equation.

Harrizon [31]

The correct answer is:

The relationship is linear, and the equation is
y-5 = 2(x+7).

Explanation:

To determine if the relationship is linear, we find the slope between each pair of points. Slope is given by the formula:

$m=\frac{y_2-y_1}{x_2-x_1}$

The slope between the first two points is given by:

$m=\frac{9-5}{-5--7}=\frac{9-5}{-5+7}=\frac{4}{2}=2$

The slope between the second pair of points is given by:

$m=\frac{13-9}{-3--5}=\frac{13-9}{-3+5}=\frac{4}{2}=2$

The slope between the third pair of points is given by:

$m=\frac{17-13}{-1--3}=\frac{17-13}{-1+3}=\frac{4}{2}=2$

Since the slope is the same throughout the data, the relationship is linear and the slope is 2.

To write the equation, we use point-slope form, which is:

y-y₁ = m(x-x₁)

Using the first point, we have:

y-5 = 2(x--7)
y-5 = 2(x+7)

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