Answer:
The vertex of [tex]y = 4\, (x - 3)^{2} - 8[/tex] is at [tex](3,\, -8)[/tex].
Step-by-step explanation:
Consider a quadratic function with the point [tex](h,\, k)[/tex] as the vertex (for some constants [tex]h[/tex] and [tex]k[/tex].) It would then be possible to express this function in the vertex form [tex]y = a\, (x - h)^{2} + k[/tex] for some constant [tex]a[/tex] where [tex]a \ne 0[/tex]. (Note the minus sign in front of [tex]h[/tex].)
For example, the quadratic function [tex]y = 4\, (x - 3)^{2} - 8[/tex] in this question is expressed in this vertex form:
[tex]y = 4\, (x - 3)^{2} + (-8)[/tex].
The values of [tex]h[/tex] and [tex]k[/tex] are [tex]h = 3[/tex] and [tex]k = (-8)[/tex], respectively. Thus, the vertex of this parabola would be at the point [tex](3,\, -8)[/tex].
Answer:
[tex]\displaystyle [3, -8][/tex]
Explanation:
First off, this equation came from the quadratic equation [tex]\displaystyle [y = Ax^2 + Bx + C],[/tex]in which it was [tex]\displaystyle y = 4x^2 - 24x + 28.[/tex]In the vertex equation [tex]\displaystyle [y = A(x - h)^2 + k],[/tex]the vertex is represented by [tex]\displaystyle [h, k],[/tex]in which −h gives you OPPOCITE TERMS OF WHAT THEY REALLY ARE, so be careful there.
I am joyous to assist you at any time.
Solve for x 64^x^2 = 256^x
Answer:
x = 0, 1.333333...
Step-by-step explanation:
1) Convert both sides to the same base.
[tex]16^{1.5x^{2} } =16^{2x}[/tex]
2) Cancel the base of 16 on both sides.
[tex]1.5x^{2} =2x[/tex]
3) Move all terms to one side.
[tex]1.5x^{2} -2x=0[/tex]
4) Factor out the common term x.
[tex]x(1.5x-2)=0[/tex]
5) Solve for x.
1 - Ask: When will x(1.5x-2) equal zero?
When x = 0 or 1.5x - 2 = 0
2 - Solve each of the 2 equations above.
x = 0, 1.333333...
About 20% of earths fresh water is stored in cracks and pores as _______.
Answer:
groundwater
Step-by-step explanation:
A triangle has an area of 66 in2. If the base is 11 inches, what is the height?
[tex] \Large{\boxed{\sf Height = 12 \ in}} [/tex]
[tex] \\ [/tex]
Explanation:The area of a triangle is given by the following formula:
[tex] \\ [/tex]
[tex] \left[ \begin{array}{c c c} \underline{\tt Area \ of \ a \ triangle \text{:}} \\ ~ \\ \tt A = \dfrac{B \cdot H}{2} \end{array} \right] [/tex]
Where:
A is the area of the triangle.B is the base.H is the height.[tex] \\ [/tex]
[tex] \Large{\boxed{\sf Given \text{:} } \ \begin{cases} \sf A &=\sf 66 \ in^2 \\ \sf B &=\sf 11 \ in \end{cases} } [/tex]
[tex] \\ [/tex]
Substitute these values into the formula and solve for H.
[tex] \sf A = \dfrac{B \cdot H}{2} \\ \\ \\ \longrightarrow \sf 66 \ in^2 = \dfrac{11 \ in \cdot H}{2} [/tex]
[tex] \\ [/tex]
Multiply both sides by 2:
[tex] \longrightarrow \sf 66 \ in^2 \cdot 2 = \dfrac{11 \ in \cdot H}{2} \cdot 2 \\ \\ \\ \longrightarrow \sf 132 \ in^2 = 11 \ in \cdot H [/tex]
[tex] \\ [/tex]
Divide both sides by 11in :
[tex] \longrightarrow \sf \dfrac{132 \ in^2 }{11 \ in } = H \\ \\ \\ \longrightarrow \boxed{\boxed{\sf H = 12 \ in}} [/tex]
[tex] \\ [/tex]
[tex] \hrulfill [/tex]
[tex] \\ [/tex]
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A triangle has an area of 66 in². If the base is 11 inches, what is the height?
Answer:The height of the triangle is 12 inches.
Step-by-step explanation:As per the provided information in the given problem, we know that the area of a triangle is given by 66 inches². The base of the triangle is given by 11 inches. In this problem, we are tasked to find the height of the triangle.
To do this, we will use the formula below:
[tex]\Large\begin{aligned}\rm\qquad\dashrightarrow{Area_{(Triangle)} = \dfrac{1}{2}bh}\end{aligned}[/tex]
Where:
The base is denoted as b.The height is denoted as h.Substitute the given values into the formula given earlier and solve for h:
[tex]\Large\begin{aligned}\rm\dashrightarrow{Area_{(Triangle)}}& = \rm{\dfrac{1}{2}bh}\\\rm\dashrightarrow{66\: in^2}& = \rm{0.5(11\: in)(h)} \\\rm\dashrightarrow{66\: in^2}& = \rm{(5.5\: in)(h)} \\\rm\dashrightarrow{\dfrac{66\: in^{\cancel{2}}}{5.5\: \cancel{in}}}& = \rm{\dfrac{(\cancel{5.5\: in})(h)}{\cancel{5.5\: in}}} \\\rm\dashrightarrow{12\: in}& = \rm{h}\end{aligned}[/tex]
Hence, the height of the triangle is 12 inches.
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Melanie invested $63,000 in an account paying an interest rate of 7\tfrac{1}{8}7
8
1
% compounded quarterly. Lillian invested $63,000 in an account paying an interest rate of 7\tfrac{3}{8}7
8
3
% compounded continuously. After 15 years, how much more money would Lillian have in her account than Melanie, to the nearest dollar?
Answer:
$8727
Step-by-step explanation:
The difference in investment values can be found by computing the value of each investment, then finding the difference. Here, we're concerned with investments compounded quarterly and compounded continuously.
a)Melanie's investment value is computed using the formula ...
FV = P(1 +r/n)^(nt) . . . . where P is the principal, r is the annual rate, t is the number of years
FV = $63,000(1 +0.07125/4)^(4×15) = $63,000(1.0178125^60)
FV = $181,721.94
__
b)Lillian's investment value is computed using the formula ...
FV = Pe^(rt)
FV = $63,000·e^(0.07375×15)
FV = $190,449.05
__
c)The amount more that Lillian has is ...
$190,449.05 -181,721.94 = $8,727.11
Lillian has about $8727 more than Melanie.
_____
Additional comment
The interest rates expressed as decimal values are ...
7 1/8% = 0.07125
7 3/8% = 0.07375
As part of a science experiment, Sam recorded the four values shown in the table, but one of them got smudged on his paper. He remembers that the sum of the trials was −1. What was the value that was smudged?
Trials
−9
12
(smudged)
−8
A) 2
B) −2
C) −4
D) 4
Answer:
C
Step-by-step explanation:
ok so sam started with 0 and got -9 then he got 12 then the next known number is -8 so those three numbers together are -5 and the end result was -1 so -1 minus -5 is -4 therefore the anser is C
How do you graph the function y=1/5x+4
You substitute x or y values and then plot the solution point that you find. You should plot at least three solution points. For example, here is a solution table that can be used to graph this function.
x | y
___
5 | 5
10 | 6
15 | 7
Please Help
Which expressions are equivalent to 7(-4/3 x -3)? Select two options.
Answer:
Step-by-step explanation:
7(-3/4x-3) is the same as
7(-3/4x)-7(3) and
-5 1/4x-21
Let me explain this a little bit more.
If you take the 7 times the first part or -3/4x you get 7(-3/4x) You take 7 times the second part you get -7(3)
When you actually solve them:
7(-3/4x) = -5 1/4x and -7(3) = -21.
hope this helps.
In which number is the digit 8 ten times larger than it is in the number 18?
Answer:
387 contains 80 and 8 x 10 = 80
Two adults and one child go to a movie and pay $26. One adult and 3 children pay
$28. How much would it cost for one adult and one child to see the movie?
Answer:
adults pay $10
children pay $6
Step-by-step explanation:
x = adult
y = child
2x + y = 26
x + 3y = 28
you want to cancel out x or y
multiply -2 with (x + 3y = 28) which is -2x -6y = -56
2x + y = 26
-2x -6y = -56
-5y = -30
y = 6
put y back into an equation
2x + y = 26 is
2x + 6 = 26
x = 10
check the answer
Two adults and one child go to a movie and pay $26
20 + 6 = 26 : checks
One adult and 3 children pay $28
10 + 18 = 28 : checks
Aunt Jane weighs 45 newtons. What is her mass in kilograms?
Answer:
45 newtons = 10.1164024 pounds/force
Step-by-step explanation:
Hope this helps!!!
The required mass of Aunt jane is given as 4.5 kilograms.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
Given that, Aunt Jane weighs 45 newtons.
So,
F = 45
Since F = Mg,
Mg = 45
M(10) = 45
N = 4.5 kilograms,
Thus, the required mass of Aunt jane is given as 4.5 kilograms.
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1/8 expressed as a percentage is
Answer:
The answer is 12.5%
Step-by-step explanation:
Hope this helped!
Answer:
12.5%
Step-by-step explanation:
Divide 1 by . Therefore, the fraction 18 is equivalent to 12.5% .
What the answer to number 3 is
Answer:
is proof an option?
Step-by-step explanation:
WILL GET MARKED BRAINLIEST FOR BEST ANSWER
Come up with an example of a game other than chess that uses the concept coordinate plane. Explain how the game uses a coordinate plane.
Answer:
Draughts
Step-by-step explanation:
It still counts
BRAINLIEST AND 100 POINTS, I NEED THIS ANSWER IMMEDIATLY.
Please, tell me the answer, AND what to shade.
Answer:
10 centimeters = 0.1 meters
Step-by-step explanation:
Question
How many meters are in 10 centimeters?
There are 100 centimeters in 1 meter.
Therefore, 1 centimeter = 1 ÷ 100 meters
= 0.01 meters
So if 1 centimeter = 0.01 meters
Then 10 centimeters = 0.01 × 10 = 0.1 meters
Factor the trinomial.
x² - 2- 8
can you multiply whole number by a number with a variable?
Answer: Definitely Yes.
Step-by-step explanation:
Answer: YES, YOU CAN
Step-by-step explanation:
The function is defined as follows for the domain given.
f(x)=3x+2, domain = (-2,-1,0, 1}
What is the range?
Answer:
just go to Khan academy, they explain how to get it there. that way you'll learn how to do it while also getting the answer
Area of a circle
You might need: Calculator
Find the area of a circle with a radius of 2.
Either enter an exact answer in terms of IT or use 3.14 for TT and enter your answer as a decimal.
units
2
Show Calculator
Report a problem
Stuck? Review related articles/videos or use a hint.
Answer:
12.56
Step-by-step explanation:
π x 2² = π x 4 = 3.14 x 4 = 12.56
Regina currently makes $15 an hour. Her boss decided to give her a 7% raise. Write the expression she would use to determine how much more she will make per hour.
Answer:
[tex]\frac{7\times15}{100}[/tex]
Step-by-step explanation:
Given the following question:
7% of 15
To find the answer we need to use the formula to calculate percentages in which we multiply the percentage by the whole number and then divide that answer by 100, of course rounding to the nearest cent if needed.
[tex]\frac{p\times n}{100}[/tex]
[tex]\frac{7\times15}{100}[/tex]
[tex]7\times15=105[/tex]
[tex]105\div=1.05[/tex]
[tex]=1.05[/tex]
7% of 15 is "1.05" which means Regina receives a $1.05 raise.
Hope this helps.
Twice the sum of a number and 7
Answer:
2 · (n + 7)Step-by-step explanation:
The sum of a number n and 7 → n + 7
Twice the sum of a number n and 7 → 2 · (n + 7)
Need help with this only 25 minutes
-31.25 + 19.70
explanation:
change in account = withdraw amount + amount deposited
change in account:
-31.25 + 19.70
note: withdrawal will be negative and deposited positive
Combine like terms. 5y - 8 - y
hence the combination=
[tex] \bold {4y - 8}[/tex]
All the best !
Answer:
4(y-8)
Step-by-step explanation:
5y-y (1) = 4y-8
4 (y-8)
How do signs of factors affect their product?
Answer:
If a negative number is multiplied with a positive number, the result will be negative. If two positive numbers are multiplied, the result will be positive. If two negative numbers are multiplied, the result will also be positive.
Step-by-step explanation:
Which number line represents the solution set for the inequality 3x < -9?
Answer:
i think 5 might be the correct answer
Step-by-step explanation:
Answer:
the third option or c
Step-by-step explanation:
hope this helps!
Karen started painting the walls at 9:25 am, and she said that she would finish the job at 2:35 pm. Her mother said that three fourths of that time was enough to paint the walls. However, when Karen finished the job, they noticed that it actually took her 2/3 of an hour longer than the time predicted by the mother. How much longer did Karen predict it would take then the time it actually took her to complete the job (what part of an hour)?
Answer:
She predicted it would take her 2/3 of an hour less than it actually took her.
Step-by-step explanation:
Answer:
2/3 of an hour less than it actually took her.
Step-by-step:
Not the Karen's hahahaha
Moving to another question will save this response.
Question 1
Solve the equation for X.
4(3x + 2) = 68
Answer:
x=5
Step-by-step explanation:
1. Open the parenthesis:
12x+8=68
2. Subtract 8 from both sides
12x=60
3. Solve for x:
x=60/12
x=5
Answer:
x=5
Step-by-step explanation:
4(3x+2=68
x=5
this is the answer
In the picture at right, lines l and m are parallel. The measure of angle
Answer:
Angle APB is 95∘
Step-by-step explanation:
180 - 54 = 126
126 - 31 = 95
Answer:
145 Degree
Step-by-step explanation:
it is a reflex angle and all reflex angle measures at 145 Degrees
Last year, 15 dogs entered the local dog show. This year, 20 entered. What is the percent increase?
Answer: 0.75?
Step-by-step explanation:
This might be wrong but, you cross multiply and then divid by one hundred.
5 x. 100x 75 / 100
100. 15
Answer:
the answer is 33 1/3%
Step-by-step explanation:
I took the test
A net has a square at the center and 4 triangles on the sides. The square has side lengths of 2 yards. The triangles have a base of 2 yards and height of 3 yards.
What is the surface area of the square pyramid?
The surface area is
yd2.
Answer:
16 yd²
Step-by-step explanation:
The total surface area is the sum of the area of the square base and the 4 triangular sides.
SA = s² + 4 × bh/2
SA = (2 yd)² + 4 × (2 yd)(3 yd)/2
SA = 4 yd² + 12 yd²
SA = 16 yd²
Answer:
16
Step-by-step explanation:
You have 12 coins. Some quarters and dimes. You have a total of $2.40, how many of each coin do you have?
Answer:
8 quarters and 4 dimes
Step-by-step explanation:
4 quarters = 1 dollars
4 quarters = 1 dollars
4 dimes = 40 cents
2.40$
============================================
Work Shown:
d = number of dimes
q = number of quarters
1 dime = 10 cents
d dimes = 10d cents
1 quarter = 25 cents
q quarters = 25q cents
d+q = 12 since we have 12 coins total
q = -d+12 after solving for q
10d+25q = total value in cents
10d+25q = 240
10d+25(-d+12) = 240 ... plug in q = -d+12
10d-25d+300 = 240
-15d+300 = 240
-15d = 240-300
-15d = -60
d = -60/(-15)
d = 4
q = -d+12
q = -4+12
q = 8
Since d = 4 and q = 8, this means we have 4 dimes and 8 quarters
-----------------------------
Check:
4 dimes = 4*10 = 40 cents
8 quarters = 8*25 = 200 cents
(4 dimes) + (8 quarters) = (40 cents) + (200 cents) = 240 cents
240 cents = 240/100 = $2.40
We have 4+8 = 12 coins total
The answers are confirmed