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REY [17]
2 years ago
9

100 POINTS!!!!!!!!!!!!!!!!!!!!!!!!!!! PLEASE SHOW STEPS TO ALL PARTS

Mathematics
2 answers:
goldfiish [28.3K]2 years ago
8 0

Answer:

Step-by-step explanation:

<u>Part A: the x-intercepts are -3/2 and 5/2 </u>

  • 4x^{2} - 7x - 15 -----> (2x + 3) (2x - 5)

2x + 3 = 0 --------> 2x = -3 ----------> x = \frac{-3}{2}

2x - 5 = 0 ---------> 2x = 5 -----------> x = \frac{5}{2}

<u>Part B: the parabola is a minimum, the vertex is (7/8,-289/16) </u>

f(x)=ax^2+bx+c

if a>0, then the parabola opens up and the vertex is a minimum

a<0 then the parabola opens down and the vertex is a max

  • a = 4, it is a minimum

the x value of  the vertex in f(x)=ax^2+bx+c= is -b/(2a)

the y value of the vertex is f(-b/(2a))  

f(x) = 4x^{2} - 7x - 15

a = 4

b = -7

-b/2a=-(7)/(2*4)=7/8

f(7/8) = 4(7/8)^{2} - 7(7/8) - 15

f(7/8) = 49/16 - 49/8 - 15

f(7/8) = -289/16

  • the vertex is (7/8,-289/16)

<u>Part C: </u>

  1. the vertex is minimum and the graph goes through the x intercepts
  2. plug in x values to get the y value (EX: choose 0 for x, and you'll get -15 for y, so you would plot the point at (0, -15). you could plug in 1 for x, and get -18 for y, plotting the point (1, -18) )

ANTONII [103]2 years ago
4 0

Answer: I can Confirm that the guy above me is correct!!

Step-by-step explanation:

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DedPeter [7]

Answer:

Step-by-step explanation:

midline: y = -2 (take the average of the min and max)

amplitude = 1.5 (distance from min or max to midline. Always a positive number)

period = 4pi

4 0
3 years ago
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7. Two people enter a whispering gallery t want to know where they should stand so they can hear other people whisper. The galle
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Answer: Just get closer

Step-by-step explanation:

Walk next to someone to hear them left foot right foot towards them.

6 0
3 years ago
A store decreases the price of an item from 120 to 90. what is the percent decrease
vampirchik [111]

There is a 25% decrease because the decrease is 30, which is 25% of 120.

8 0
3 years ago
A quadrilateral has vertices at A(-5,5), B(1,8), C(4,2), and D(-2,-2). Use slope to determine if the quadrilateral is a rectangl
AysviL [449]

Answer:

The quadrilateral is not a rectangle

Step-by-step explanation:

we know that

If a quadrilateral ABCD is a rectangle

then

Opposite sides are congruent and parallel and adjacent sides are perpendicular

Remember that

If two lines are parallel, then their slopes are the same

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

The formula to calculate the slope between two points is equal to

m=\frac{y2-y1}{x2-x1}

we have

A(-5,5), B(1,8), C(4,2), and D(-2,-2)

Plot the figure to better understand the problem

see the attached figure

Find the slope of the four sides and then compare

step 1

Find slope AB

A(-5,5), B(1,8)

substitute in the formula

m=\frac{8-5}{1+5}

m=\frac{3}{6}

m_A_B=\frac{1}{2}

step 2

Find slope BC

B(1,8), C(4,2)

substitute in the formula

m=\frac{2-8}{4-1}

m=\frac{-6}{3}

m_B_C=-2

step 3

Find slope CD

C(4,2), and D(-2,-2)

substitute in the formula

m=\frac{-2-2}{-2-4}

m=\frac{-4}{-6}

m_C_D=\frac{2}{3}

step 4

Find slope AD

A(-5,5), D(-2,-2)

substitute in the formula

m=\frac{-2-5}{-2+5}

m=\frac{-7}{3}

m_A_D=-\frac{7}{3}

step 5

Verify if the opposites are parallel

Remember that

If two lines are parallel, then their slopes are the same

The opposite sides are

AB and CD

BC and AD

we have

m_A_B=\frac{1}{2}

m_C_D=\frac{2}{3}

so

m_A_B \neq m_C_D

It is not necessary to continue verifying, because two of the opposite sides are not parallel

therefore

The quadrilateral is not a rectangle

4 0
3 years ago
I need help please ??
Genrish500 [490]

Answer with step-by-step explanation:

Equation: x × 4 = y

This equation is true because if you look at the graph, multiply 4 by each x length and you will get the y length.

Hope this helped!

8 0
3 years ago
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