The area of the triangle formed by points of intersection of parabola y=a(x−3)(x+2) with the coordinate axes is 10. Find a if it is known that parabola opens upward.

Answers

Answer 1

Answer: a = 4

Step-by-step explanation: Area of a triangle is calculated as: [tex]A_{t}=\frac{b.h}{2}[/tex].

The triangle formed by the parabola has base (b) equal to the distance between the points where the graph touches x-axis and height (h) is the point where graph touches the y-axis.

The points on the x-axis are the roots of the quadratic equation:

a(x-3)(x+2)=0

(x-3)(x+2)=0

x - 3 = 0

x = 3

or

x + 2 = 0

x = -2

So, base is the distance between (-2,0) and (3,0).

Since they are in the same coordinate, distance will be:

b = 3 - (-2)

b = 5

Area of the triangle is 10. So constant a is

[tex]10=\frac{5.a}{2}[/tex]

5a = 10.2

a = 4

The constant a of the function y = a(x-3)(x+2) is 4.

Answer 2

Answer: a = 2/3

Step-by-step explanation:

y-intercept: y=a(2)(-3) = -6a

x-intercepts: (-2,0) , (3,0)

height = -6a

base = 5

Area = 10 = 0.5 x 5 x -6a

10 = -15 a

a = -2/3

BUT a>0 since it opens upwards, so:

a = 2/3


Related Questions

SALARY Sondra just started a job with an annual salary of $30,000. Each year, her salary will increase by 6%. If Sondra continues to work at this job, what will be her total earnings in the first 5 years, rounded to the nearest dollar?
A. 31,915
B. 40,147
C. 169,113
D. 179,260

Answers

Answer:

C

Step-by-step explanation:

1st year-> 30000

2nd year-> 31800

3rd year ->33708

4th year->35730.48

5th year -> 37874.3088

37874.3088+35730.48+33708+31800+30000= 169112.7888

                                                                             ≈ 169113

The solution is Option C.

The total amount of earnings of Sondra after 5 years is $ 169,113

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the annual salary of Sandra be A = $ 30,000

Now , the percentage increase in salary = 6 %

So , the equation will be

First year :

The increase in first year =  annual salary of Sandra + percentage increase in salary x annual salary of Sandra

The increase in first year = 30000 + ( 6/100 ) x 30000

                                         = 30000 + 1800

                                         = $ 31,800

Second year :

The increase in second year =  increase in first year + percentage increase in salary x increase in first year

The increase in second year = 31800 + ( 6/100 ) x 31800

                                         = 31800 + 1908

                                         = $ 33,708

Third year :

The increase in third year =  increase in second year + percentage increase in salary x increase in second year

The increase in third year = 33708 + ( 6/100 ) x 33708

                                         = 33708 + 2022.48

                                         = $ 35,730.48

Fourth year :

The increase in fourth year =  increase in third year + percentage increase in salary x increase in third year

The increase in fourth year = 35730.48 + ( 6/100 ) x 35730.48

                                         = 35730.48 + 2143.8288

                                         = $ 37,874.3088

Now , the equation is

The total earnings of Sondra is = First year salary + second year salary + third year salary + fourth year salary

The total earnings of Sondra is = 30000 + 31,800 + 33,708 + 35,730.48 + 37,874.3088

The total amount earnings of Sondra is = $ 169,112.7888

Therefore , the total amount earnings = $ 169,113

Hence , The total amount of earnings of Sondra after 5 years is $ 169,113

To learn more about equations click :

https://brainly.com/question/10413253

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The figure is made up of a square and a rectangle. Find the area of the shaded region 16 by 3 by 7

Answers

Answer:

Go on Answers.com your welcome.

Solve for z.
2 + 8 - z = -24

Answers

Answer:

Z=34

Step-by-step explanation:

Answer:

z = 34

Step-by-step explanation:

Given

2 + 8 - z = -24

Combine Like Terms-

10 - z = -24

Rearrange Terms-

-z + 10 = -24

Subtract 10 from both sides

-z + 10 - 10 = -24 -10

Simplify

-z = -34

Divide -1 from both sides

-z/-1 = -34/-1

Answer-

z = 34

PLEASE HELP WITH BOTH!!! MARKING BRAINLIEST

Answers

Answer: The perpendicular distance between the two parallel sides of a trapezium is known as the height of a trapezoid. In simple words, the base and height of a trapezoid are perpendicular to each other. The trapezoids can be both right trapezoids (two 90-degree angles) and isosceles trapezoids (two sides of same length).

What is the diffrence between 7/8 and 1/2?

Answers

Answer:

3/8

Step-by-step explanation:

1. Find common denominators, which is 7/8 and 4/8

2. 7/8 - 4/8 = 3/8

Answer:

7/4 or 1 3/4

Step-by-step explanation:

Please help i need to help

Answers

Answer:

4.25

Step-by-step explanation:

Step 1: 23-(17-12)²+6.25

Step 2: 23-5²+6.25

Step 3: 23-25+6.25

66 > 58.5
True or False?

Answers

Answer:

66>58.5              true statement

Answer and Step-by-step explanation:

66 > 58.5 is true.

This is because 66 is a bigger number than 58.5.

The > sign means a number is greater than another number, and the < sign means a number is less than another number.

#teamtrees #PAW (Plant And Water)

HELP HELP ME PLEASEEEEEEE

Answers

It would be D because if you convert the fraction into a decimal it would be 6.2. Covert the square root of 36 which would be 6. And then the absolute value of -6.6 would be 6.6. Let’s put them together!

6, is the smallest.
6.2 is the middle
6.6 is the biggest


Answer is D

Square tiles of side 30 cm were
used to cover a floor which is 9 m
long and 6 m wide. How many
square tiles were used?​

Answers

The answer would be 600 I think

If 1 meter= 100 cm then you would convert 9 and 6 to 900 and 600. Then if each tile is 30 centimeters then you would do 900/30= 30 and 600/30= 20. Then to find the amount for the whole area you have to do 20 x 30= 600.

I hope this helps :)

~!!!! PLEASE HELP I HAVE AN HOUR TO DO THIS !!!!~ im a 7th grader in honors learning 9th and 8th grade math please help me
QUESTION~~
How the graph of f(x) = |x| compare with the graph of g(x) = −1/2|x|
ANSWERS CHOICES~
(A):The graph of g is a vertical compression and reflection over the x-axis of the graph
of f.
(B):The graph of g is a vertical stretch and reflection over the y-axis of the graph of f.
(C):The graph of g is a vertical stretch and reflection over the x-axis of the graph of f.
(D):The graph of g is a vertical compression and reflection over the y-axis of the graph of f.

Answers

Answer:

A.

Step-by-step explanation:

the blue is f(x) and red is g(x) as you can see the numbers and it reflects over the x-axis.

Calculate and write your answer in standard form.

(7x10^-4) divided by(4x10^4)
I
Enter your math answer

Answers

1.75 x 10^-3
hope that helps

Witch triangle o be an acute angle

Answers

Answer:

An acute triangle

Step-by-step explanation:

A triangle that is 47°

28 orders in 4 days = orders per day

Answers

Answer:

7 orders per day

Step-by-step explanation:

28/4=7

Answer:

7

Step-by-step explanation:

divide 28 / 4  = orders per day

Pls help I will give points

Answers

Answer:

60

Step-by-step explanation:

someone help solve this! f + 1 1/2 = 4 1/4

f= ?

Answers

- 1 and 1/4
Because -1 and 1/4 + 11/2= 4 and 1/4

Answer:

2 1/4

Step-by-step explanation:

I need help immediately

Answers

45 degrees. In a straight line, its angle is 180 degrees. That means you subtract 135 from 180, which gives you 45.

Answer:

<DEC= 45

Step-by-step explanation:

those two lines are parallel which means they are cross by the diagonal line at the same angle

180-135= 45

A preschool teacher gave out a total of 65 cookies to her class during snack ... She allowed each of her 25 students to choose either 3 small cookies or 2 large cookies. Assuming all the children in the class choose one of these two options at snack time, how many of the students in her class choose to have 3 small cookies

Answers

Answer:

25

Step-by-step explanation:

Create a function that has all of the following:

- A vertical asymptote at 3, 6, and -2

- A hole at -2 and 1

- A zero at 5 and 4

- A horizontal asymptote at y=7

You may need to add more zeros or more asymptotes

(I’m in highschool, I don’t know why it said college sorry)

Answers

The answer is the first one Which is A

Consider the equation y=−4x+3. What are the slope and y-intercept?

Answers

Answer:

m=-4, b=3

Step-by-step explanation:

Answer:

Slope = -4

Y-intercept = 3

Step-by-step explanation:

Solve for C
-1.3 = -0.8+c/3.4

Answers

i think its c= -1.69

!! HELP IM IN 7TH GRADE AND M LEARNING 9TH AND 8TH GRADE MATH!!
QUESTION~
If f(x) = 2|x| is graphed on a regular
coordinate grid, does the graph
form an acute, right, or obtuse
angle at its vertex?

Answers

Answer:

The vertex forms an acute angle.


What is the area of a rectangle whose length is 36 inches and whose width is 42 inches?

Answers

Answer:

1512

Step-by-step explanation:

L x W = Area

8^1/6 x 2^x = 32^1/2
Work out the exact value of x.

Answers

Answer:

I think 2

Step-by-step explanation:

It depends on whether 8^1/6 really actually means (1/6) the fraction... or (8^1)/6

I took it as 8^(1/6) meaning to the power of a fraction

Calcul
A train travels 60 miles in 90 minute
Calculate the train's average speed.

Answers

Answer:

Step-by-step explanation:

Speed per min = 60 ÷ 90 = 0.66 miles

Answer:

0.66 miles/1 min

Step-by-step explanation:

60/90=0.66/1

The difference of five times a number and 11 is 39

Answers

Answer:

no

Step-by-step explanation:

I mean the point s is hi

Find the value of x and y in the diagram below.

A. X= 9/2, y = 9
B. x = 18, y = 9-13
C. X= 9/3, y = 4.5
D. = 6/3, y = 3/5

Answers

Answer:

D) x=6√3, y=3√3

Step-by-step explanation:

Given both triangles are 30-60-90 triangles, this means that the length of y will be 9/√3=√81/√3=√(81/3)=√27=3√3

This also means that x will be twice the length of y which means x=2y=2(3√3)=6√3

This means that the correct answer is D) x=6√3, y=3√3

Refer to the diagram below to understand where I got these lengths.

During his first vet visit, Pedro's puppy weighed
6 pounds. On his second visit, he weighed
91 pounds. How much weight did he gain
between visits?

Answers

You would subtract 91 from 6
91-6=85
He gained 85 pounds between visits

Answer:

85 pounds

Step-by-step explanation:

did the dog not go to the vet in like 2 years??? anyways its 91-6

determine how (if possible) the triangles can be proved similar​

Answers

Answer: sas

Step-by-step explanation:

Pls I need help for my grade

Answers

Answer:

C

Step-by-step explanation:

cuz when he replace x with all numbers, it matches the graph

What is the measure of the angle

Protractor tool

Answers

Youve gotta actually measure it with a protractor
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