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: 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
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
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
#SPJ2
The figure is made up of a square and a rectangle. Find the area of the shaded region 16 by 3 by 7
Answer:
Go on Answers.com your welcome.
Solve for z.
2 + 8 - z = -24
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
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?
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
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?
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
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?
~!!!! 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.
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
Witch triangle o be an acute angle
Answer:
An acute triangle
Step-by-step explanation:
A triangle that is 47°
28 orders in 4 days = orders per day
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
Answer:
60
Step-by-step explanation:
someone help solve this! f + 1 1/2 = 4 1/4
f= ?
Answer:
2 1/4
Step-by-step explanation:
I need help immediately
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
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)
Consider the equation y=−4x+3. What are the slope and y-intercept?
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
!! 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?
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?
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.
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.
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
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
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?
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
Answer: sas
Step-by-step explanation:
Pls I need help for my grade
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