All categories

3 years ago

What is the y-intercept of the function, represented by the table of values

Mathematics

1 answer:

AleksandrR [38]3 years ago

6 0

Answer:

Step-by-step explanation:

The table is given below

$\left|\begin{array}{c|cc}x&y\\--&--\\-2&15\\1&6\\2&3\\4&-3\\7&-12\end{array}\right|$

We can see that the table represents a linear function since by checking its slope.

Using:

Points (-2,15) and (1,6)
Points (1,6) and (2,3)

$Slope =\dfrac{6-15}{1-(-2)} =\dfrac{3-6}{2-1}=-3$

Therefore, the values represent a linear function.

A linear equation is of the form y=mx+b

Therefore:

y=-3x+b

Using the points (7,-12)

$-12=-3(7)+b\\-12=-21+b\\b=-12+21\\b=9$

Therefore, the y-intercept of the function, represented by the table of values is 9.

You might be interested in

Evaluating algebraic expressions <br><br><br> B3 - 3a5

lutik1710 [3]

Answer:

3B-15a

Step-by-step explanation:

B3=3B

3a5=15a

3B-15a

8 0

3 years ago

Figure I and Figure II are similar figures,

ELEN [110]

The ratio of corresponding sides is same for all the sides for similar polygon. the correct proportion is,

$\frac{ST}{EF}=\frac{WR}{CD}$

Thus the option H is the correct option.

To find the correct proportion we need to know about the properties of slimier polygon.

<h3>What are the properties of similar polygon?</h3>

Two polygons are said to be similar or congruent pentagon-

The corresponding angle of two pentagons are congruent.

The ratio of corresponding sides is same for all the sides.

The figure given in the problem of similar two polygons with six sides.

Rearrange the second figure as shown in figure.

As for the similar polygons, the ratio of corresponding sides is same for all the sides.

Thus the sides shown in the two rearranged figure must be same. Therefore,

$\frac{ST}{EF}=\frac{WR}{CD}$

Hence the correct proportion is,

$\frac{ST}{EF}=\frac{WR}{CD}$

Thus the option H is the correct option.

Learn more about the similar polygon here;

brainly.com/question/771807

8 0

2 years ago

PLEASE HELP!!!!

Lunna [17]

NOTES:

Given a quadratic function in standard format (y = ax² + bx + c), the direction of the parabola is as follows:

if "a" is positive, then opens UP
if "a" is negative, then opens DOWN

Given a quadratic function in standard format (y = ax² + bx + c), the vertex can be found as follows:

the Axis Of Symmetry (x-value) is: x = $\frac{-b}{2a}$
y-value is found by plugging in the AOS for "x" in the equation

****************************************************************************************

1) y = x² + 11x + 24

a = +1 so the parabola opens UP

x = $\frac{-b}{2a}$ = $\frac{-11}{2(1)}$ = $-\frac{11}{2}$

y = $(-\frac{11}{2})^{2}$ + 11 $(-\frac{11}{2} )$ + 24 = $-\frac{25}{4}$

vertex $(-\frac{11}{2}$ , $-\frac{25}{4})$ is in Quadrant 3 and is below the x-axis

This COULD be the graph of the rain gauge.

The graph should contain the vertex, x-intercepts (-3, 0) and (-8, 0), and y-intercept (0, 24)

******************************************************************************************

2) y = -x² - 6x - 8

a = -1 so the parabola opens DOWN

x = $\frac{-b}{2a}$ = $\frac{-(-6)}{2(-1)}$ = $\frac{6}{-2}$ = -3

y = -(-3)² - 6(-3) - 8 = -9 + 18 - 8 = 1

vertex (-3, 1) is in Quadrant 2 and is above the x-axis

This could NOT be the graph of the rain gauge.

The graph should contain the vertex, x-intercepts (-2, 0) and (-4, 0), and y-intercept (0, -8)

******************************************************************************************

3) y = x² - 2x + 3

a = 1 so the parabola opens UP

x = $\frac{-b}{2a}$ = $\frac{-(-2)}{2(1)}$ = $\frac{2}{2}$ = 1

y = (1)² - 2(1) + 3 = 1 - 2 + 3 = 2

vertex (1, 2) is in Quadrant 1 and is above the x-axis

This could NOT be the graph of the rain gauge.

The graph should contain the vertex, y-intercept (0, 3), and its mirror image (2, 3). <em>There are no x-intercepts</em>

******************************************************************************************

4) y = x² + 4x + 4

a = 1 so the parabola opens UP

x = $\frac{-b}{2a}$ = $\frac{-4}{2(1)}$ = -2

y = (-2)² + 4(-2) + 4 = 4 - 8 + 4 = 0

vertex (-2, 0) is in Quadrant 2 and is on the x-axis

This COULD be the graph of the rain gauge.

The graph should contain the vertex, y-intercept (0, 4), and its mirror image (-4, 4). <em>The x-intercept is the vertex.</em>

Compared to the other four graphs, this is most likely the equation for the rain gauge!

******************************************************************************************

5) y = 3x² + 21x + 30

a = +3 so the parabola opens UP

x = $\frac{-b}{2a}$ = $\frac{-21}{2(3)}$ = $-\frac{7}{2}$

y = 3 $(-\frac{7}{2})^{2}$ + 21 $(-\frac{7}{2} )$ + 30 = $-\frac{27}{4}$

vertex $(-\frac{7}{2}$ , $-\frac{27}{4})$ is in Quadrant 3 and is below the x-axis

This COULD be the graph of the rain gauge.

The graph should contain the vertex, x-intercepts (-2, 0) and (-5, 0), and y-intercept (0, 30)

*******************************************************************************************

4 0

3 years ago

Read 2 more answers

Solve 765/14 and write your answer in terms of a mixed number (please use this format: 75 3/5). *

kozerog [31]

the answer is 54 9/14

because Divide using long division. The whole number portion will be the number of times the denominator of the original fraction divides evenly into the numerator of the original fraction, and the fraction portion of the mixed number will be the remainder of the original fraction division over the denominator of the original fraction.

6 0

3 years ago

Read 2 more answers

7. When dy/dx = (x -6)1/2, what does y equal?

Sergio039 [100]

The answer is below
$\frac{dy}{dx} = \frac{1}{2} (x - 6)$
multiply both sides by dx

$dy = \frac{1}{2} (x - 6)dx$
integrate both sides of the diffrential

$integral \: dy = integral \: \frac{1}{2} (x - 6)dx$
simplify and integrate to get y alone don't forget to tack on c with your indefinite integral

$y = \frac{x {}^{2} }{4} - 3x + c$

3 0

3 years ago