Answer:
Part A
The equation of the parabola in standard form is f(x) = 0.5·x² + x - 7.5
Part B
The equation of the parabola in factored form is f(x) = 0.5·(x + 5)·(x - 3)
Step-by-step explanation:
The coordinates of the vertex of the parabola, (h, k) = (-1, -8)
The zeros of the parabola = -5, 3
Part A
The quadratic equation representing the parabola can be written as follows;
y = a·(x - h)² + k
The standard form of the equation is f(x) = a·x² + b·x + c
k = c - b²/(4·a)
h = -b/(2·a)
c = k + a·h² = -8 + a
From the zeros of the parabola, we have;
f(-5) = a × (-5)² + b×(-5) + c = 25·a - 5·b + c = 0
f(3) = a × (3)² + b×(3) + c = 9·a + 3·b + c = 0
Therefore, we have;
25·a - 5·b + c = 0...(1)
9·a + 3·b + c = 0...(2)
From which we have;
25·a - 5·b + c = 25·a - 5·b - 8 + a = 26·a - 5·b - 8 = 0
9·a + 3·b + c = 9·a + 3·b - 8 + a = 10·a + 3·b - 8 = 0
We then have;
26·a - 5·b = 8...(3)
10·a + 3·b = 8...(4)
Making 'b', the subject of both equations (3) and (4), equating the values, we find the value of 'a' as follows;
From equation (3), we have;
26·a - 5·b = 8
∴ b = (26·a - 8)/5
From equation (4), we have;
10·a + 3·b = 8
∴ b = (8 - 10·a)/3
From b = b, by transitive property, we have;
(26·a - 8)/5 = (8 - 10·a)/3
3 × (26·a - 8) = 5 × (8 - 10·a)
78·a - 24 = 40 - 50·a
∴ 128·a = 64
a = 64/128 = 1/2 = 0.5
a = 0.5
∴ b = (26·a - 8)/5 = (26 × 0.5 - 8)/5 = (13 - 8)/5 = 1
b = 1
c = -8 + a
∴ c = -8 + 0.5 = -7.5
c = -7.5
The equation of the parabola in standard form is therefore presented as follows;
f(x) = 0.5·x² + x - 7.5
Part B
The equation of the parabola in factored form is given as follows;
With the aid of a graphing calculator, we have;
f(x) = 0.5·x² + x - 7.5 = 0.5×(x² + 2·x - 15) = 0.5·(x + 5)·(x - 3)
The equation of the parabola in factored form is f(x) = 0.5·(x + 5)·(x - 3)
Jada walks up to a tank of water than can hold up to 10 gallons. When it is active, a drain empties water from the tank at a constant rate. When Jada first sees the tank, it contains 7 gallons of water. Three minutes later, the tank contains 5 gallons of water.
a. At what rate is the amount of water in the tank changing? Use a signed number, and include the unit of measurement in your answer.
b. How many more minutes will it take for the tank to drain completely? Explain or show your reasoning.
c. How many minutes before Jada arrived was the water tank completely full? Explain or show your reasoning.
Answer:
a. rate to empty the tank = - 2/3 gal/min
b, 7.5 min to empty the tank
c. 4.5 min.
Step-by-step explanation:
I use the formula that the work done = rate of work times the time working = W = rt
The work in this problem is emptying the tank.
a. The rate to empty the tank is -2 gal/3 min or - 2/3 gal/min
b. 5/(2/3) = 15/2 = 7.5 min to empty the tank
c. Since 3 gal. had already drained, 3/(2/3) = 9/2 = 4.5 min.
4. Are the triangles below similar? Explain
your reasoning.
Answer:
No, the triangles are not the same because the angles within in the triangle are different making the sides different lengths making the triangle a different type
A sandbox is 5 feet long and 5 feet wide. If you dig 1 foot deep in it. How much does it take to fill the sandbox to the nearest cubic foot?
Answer:
25 I think
Step-by-step explanation:
A square has a side length of x inches. Each side of the square will be increased by 8 inches to create a larger square. If the larger square has a perimeter of 40 inches, what is the side length, in
inches of the original square?
What is the domain of y=/x+7 +5?
x>=0
x>=7
X>=-7
all real numbers
DONE
Step-by-step explanation:
when x >0
y=/0+7 +5
y=8
(0,8)
when x>7
y= /7+7 +5
y= 9
(7,9)
when x >-7
y = /7-7 +5
y=5
(-7, 5)
Answer: c
Step-by-step explanation: the next one is b
can u help me
the question is: find the value of x for each equation below and the numbers is
-x+3=3x-2
1.5x-3=2.25x
-1/3x+2=3x-1
Answer:
1. x=5/4
2. x=-4
3. x= 9/10
Step-by-step explanation:
Let's solve your equation step-by-step.
−x+3=3x−2
Step 1: Subtract 3x from both sides.
−x+3−3x=3x−2−3x
−4x+3=−2
Step 2: Subtract 3 from both sides.
−4x+3−3=−2−3
−4x=−5
Step 3: Divide both sides by -4.
−4x/−4 = −5/ −4
x= 5/4
Answer:
x= 5/4 (5 over 4)
Let's solve your equation step-by-step.
1.5x−3=2.25x
Step 1: Subtract 2.25x from both sides.
1.5x−3−2.25x=2.25x−2.25x
−0.75x−3=0
Step 2: Add 3 to both sides.
−0.75x−3+3=0+3
−0.75x=3
Step 3: Divide both sides by -0.75.
−0.75x/−0.75=3/−0.75
x=−4
Answer:
x=−4
Let's solve your equation step-by-step.
−1/3x+2=3x−1
Step 1: Subtract 3x from both sides.
−1/3x+2−3x=3x−1−3x
−10/3x+2=−1
Step 2: Subtract 2 from both sides.
−10/3x+2−2=−1−2
−10/3x=−3
Step 3: Multiply both sides by 3/(-10).
(3/−10)*(−10/3x)=(3/−10)*(−3)
x=9/10
Answer:
x=9/10 (9 over 10)
Find the distance between -6 and 8.
What is an expression that represents the distance
Answer:
14
Step-by-step explanation:
8 - |-6| = 14
|| means absolute value, or the distance the number has from 0 on the number line. ex. |-92| = 92 |8| = 8
Which equation matches the given graph?
A. f(x) = x^2 - 2x - 4
B. f(x) = x^2 - 3x + 16
C. f(x) = 2x^2 - 4x - 2
D. f(x) = 2x^2 + 12x + 16
Answer:
B
Step-by-step explanation:
f(x) = x ^ 2 What is g(x)?
Answer:
A ; g(x) = (1/2 x)^2
Step-by-step explanation:
Here, we want to get g(x)
we have a point on the curve g(x)
The point is represented by (2,1)
What this mean here is that, when x = 2, y = 1
Looking at the first option;
Substitute 1 for y and 2 for x
1 = (1/2 * 2)^2
1 = 1
This means this is our answer
The equation for g(x) is;
g(x) = (1/2 x)^2
Help me pleaseeeeeee it would mean the world to me! .
Multiple choice answers:
A)14.7%
B)1187.5%
C)11.7%
D)26.4%
Answer:
I believe your answer is b
15/3 = 45/x
solve for x
Answer:
15/3=45/x
We move all terms to the left:
15/3-(45/x)=0
Domain of the equation: x)!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
-(+45/x)+15/3=0
We add all the numbers together, and all the variables
-(+45/x)+5=0
We get rid of parentheses
-45/x+5=0
We multiply all the terms by the denominator
5*x-45=0
We add all the numbers together, and all the variables
5x-45=0
We move all terms containing x to the left, all other terms to the right
5x=45
x=45/5
x=9
Step-by-step explanation:
write the set in builder form. A{2,4,6,8}
Answer:A=2,4,6,8
One way of writing this in set builder notation could be:
A={x|2≤x≤8|x2∈N}
Which can be interpreted as:
The set A is the set of any x such that 2≤x≤8 such that half of x is a natural number ( N ).
There are many ways of writing sets in set builder notation. Which is why it can be a little confusing to learn (the syntax) at first. Once you understand what all these new mathematical symbols mean (i.e. ∈ , | , N ), it becomes much easier to “read as a sentence”.
Here are a few more ways of writing the set A=2,4,6,8 in set builder notation:
A={x|2≤x≤8|x∈2⋅N}
A={x|(x−2)(x−4)(x−6)(x−8)=0}
A={x|x=2p|p∈{1,2,3,4}}
A={x∈N|mod(x,2)=0|x≤8}
Step-by-step explanation:
Answer: Answer:A=2,4,6,8
Step-by-step explanation:
Can anyone help please with 6 and 7 I’m in desperate need of can someone help please and God bless
What is the value of m in the m + 3/4 = − 3/8
Answer:
M=-9/8
Step-by-step explanation:
-3/8-3/4=-3/8-6/8=-9/8
Answer:
m = -9/8
Step-by-step explanation:
First, let's get m by itself by subtracting 3/4 from both sides:
m = -3/8 - 3/4
The least common denonimator between our two fractions is 8, so we can turn 3/4 into the equivalent fraction 6/8 to subtract our two fractions:
m = -3/8 - 6/8 = -9/8
Saul makes trail mix with peanuts, raisins, and pretzels. The ratio of cups of raisins to cup of peanut is 1 to 6. The ratio of cups of pretzels to cups of raisin is 3 to 1. Decide if the statement is true or false. "Saul uses 6 times as many cups of peanuts as cups of raisin." *
1 point
True
False
Answer:
true
Step-by-step explanation:
Answer:
true
Step-by-step explanation:
Jose paid $1.12 for a dozen eggs at Target. How much would Jose have to pay for 18 eggs?
Answer:
56.16
Step-by-step explanation: All you do is just multiply
Answer:
$1.67
Step-by-step explanation:
Given it's $1.12 for 12 eggs, we divide 1.12 by 12 to see how much it cost for 1 egg
1.12/12 = 0.093
so 0.093 cents for 1 egg
0.093x18 eggs = 1.674 = $1.67
Hope this helps, have a nice day :)
Benny bought a laptop for work. The screen measures 9 inches in height and 12 inches in width.
Find the diagonal length of the screen.
A 4.5 in
В 10 in
C 15 in
D 225 in
Answer:
Step-by-step explanation:
Which of the following are not perfect squares? Select all that apply.
16
44
81
6
49
24
Answer and Step-by-step explanation:
44, 6, and 24 do not have perfect squares.
To be a perfect square, they have to be able to have a number that, when it multiplies itself by itself (needs to be a whole number), it turns into the bigger number.
44, 6, and 24 can't do this when being square rooted.
16 turns into 4.
81 turns into 9.
49 turns into 7.
#teamtrees #PAW (Plant And Water)
Answer:
44, 6, and 24
Step-by-step explanation:
4²=16 so it's a perfect square
9²=81 so it's a prefect square
7²=49 so it's a perfect square
44, 6, and 24 all result in decimals so it's not a perfect square.
What is the domain of the function below? {(1,6), (2, 6), (3,7) plzzzzzzzz
Answer:
the domin{1,2,3}
the range{6,7}
and its a function
Step-by-step explanation:
What's another way to define absolute value?
The opposite of a number
The multiplicative inverse of a number
The distance of a number from zero
a. n
The value of a number
Answer:
the distance of a number from zero
Step-by-step explanation:
in other words, it is the positive value of the number.
if the number is negative then the absolute value is the positive of it.
if the value is positive, then it is still positive.
i need help to solve for x
Answer: 15°
Step-by-step explanation:
Find the function h(x) = f(x) + g(x) if f(x) = 4^x + 2 and g(x) = x - 4.
h( x) = 4 x + 1 -2
h( x) = 4 x + x + 6
h( x) = 4 x - 4
h( x) = 4 x + x - 2
Answer:
h( x) = 4^x + x - 2
Step-by-step explanation:
h(x)=f(x)+g(x)=4^x+2+x-4=4^x+x-2
What is the input value when the output value is 31.5?
HELP PLEASE ASAP
Answer:
The correct Answer is 9 my good sir ( or ma'am )
Step-by-step explanation:
Simple, just flip the equation around and change the multiplication sign to a division sign.
So basically with all planks filled in its 9 times 3.5 which is equal to 31.5
Brianliest? :/
Hope I helped
given f(x)=-x+2 find f(-6)
Answer:
8
Step-by-step explanation:
Substitute -6 for every x in the equation:
f(-6) = -(-6) + 2
Solve the right side of the equation:
6 + 2
=8
Hello, Earthlings! Martian here! Need help with math, I'm new to this subject! You'll get 50 (B) coins for answering!
100³ = ______
Thanks for your help! I award brainliest!!!
Answer:
answer is 10000
Step-by-step explanation:
THANK U AGAIN <33ewiudhuids
Sally bought 4 chocolate bars and 8 lollipops and paid $8.00. Josh bought 3 chocolate bars and 10 lollipops and paid $7.00.
What is the cost of a lollipop? Enter your answer as a decimal
Answer:
Lollipops cost $0.25
Step-by-step explanation:
4C + 8L = $8.00
3C + 10L = $7.00. We need to cancel out chocolate bars
-12C - 24L = $-24.00 Mulitply by -3
12 C + 40L = $28.00 Muliply by 4 Next simplify
16L = $4.00 Divide both sides by 16
L = $0.25
WE CAN EVEN CHECK OUR WORK
4C + 8(0.25) = $8.00
4C = $6.00
C = 1.5
3(1.5) + 10(.25) = $7.00
4.5 + 2.5 = 7
0.36 x 20 = x10
14 divided by 50 = +100
need ASAP please help
Answer:
0.36 × 20 = 7.2
7.2 × 10 = 72
14 ÷ 50 = 0.28
0.28 + 100 = 100.28
Lucius sells jellyfish jam part-time. He is paid a monthly commission. He receives 30% of his first $900 in sales and 25% of the rest of his sales. Last month he sold $2,600 worth of jam. How much commission did he earn last month?
Answer:
695
Step-by-step explanation:
First I would septate the 900 from the 2600
2600-900=1700
Then I'll take both %s and turn them to decimal 25%-0.25 30%-0.30
I take the 900 times the 0.30 and the 0.25 times 1700
900x0.30=270
1700x0.25=425
then add them both together
270+425=695
John called a plumber to fix a leak in his bathroom. The plumber charged $30 to come to the house and $25 an hour while fixing the leak. If the final bill
was $105. how many hours was the plumber at John's house?
Answer:
30 subtracted from 105 leaves u with 75 so divide that with 25 & he took abt 3 hrs
Triangle Congruency please help!!
Answer:
A
Step-by-step explanation:
the nice thing about triangle is that the smallest angle is always opposite the smallest side, etc. also, we can get the remaining angle because we have 2 angles already and there are always 180 degrees in a triangle.
50+ 63= 113
180-113 =67
so, 50 is the smallest angle and thus the side opposite of it is the smallest. next is side bc because 63 is the next biggest angle measure. lastly, side ac is the largest because it's opposite of the largest angle measure
Answer:
a
Step-by-step explanation: