Answers
Take into account that in a general way, a parabola can be written as follow:
y = a(x - h)^2 + k
where,
a: is the leadding coefficient
(h,k): vertex of the parabola
In order to graph the parabola, first calculate the value of a, by using the following information:
(h,k) = (0,-2)
(x,y) = (5,8)
Replace the previous values into the equation of the parabola and solve for a:
[tex]\begin{gathered} 8=a(5-0)^2-2 \\ 8=25a-2 \\ a=\frac{8+2}{25}=\frac{10}{25}=\frac{2}{5} \end{gathered}[/tex]Then, the equation of the given parabola is:
[tex]\begin{gathered} y=\frac{2}{5}(x-0)^2-2 \\ y=\frac{2}{5}x^2-2 \end{gathered}[/tex]Another point could be:
x = -2
[tex]\begin{gathered} y=\frac{2}{5}(-2)^2-2 \\ y=\frac{2}{5}(4)-2 \\ y=\frac{8}{5}-2 \\ y=-\frac{2}{5} \end{gathered}[/tex]the point is (-2,-2/5).
Then, the graph is:
Related Questions
How can you find the next digit in the quotient?
Bring down the ? to show there are 2 tens
? ones that still need to be divided.
Answers
Bring down the next digit 6 to show there are 2 tens and 6 ones that still need to be divided.
This method of dividing is called the long division method.
In this, we divide the dividend with the divisor and get a quotient and a remainder.
The steps involved are given below :
1. Take the dividend's first digit from the left. Determine whether this digit is bigger than or equal to the divisor.
2. Then divide it by the divisor and write the result as the quotient on top.
3. Subtract the result from the digit and record the difference in the box below.
4. Reduce the dividend by the following digit (if present).
5. Repeat the above steps.
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A laptop computer consumes about 40 watts of electricity per hour when operating. At $0.20 per kilowatt-hour, how much does a laptop cost to operate for 10 hours?A )8 centsB )800 centsC )40 centsD) 200 cents
Answers
A) 8 cents
Explanation
Step 1
find the rate
[tex]\begin{gathered} \text{rate}=\text{ 40 }\frac{\text{w}}{h} \\ \end{gathered}[/tex]cost
[tex]\begin{gathered} \text{ Cost= 0.20 per 1000 wats hour} \\ \end{gathered}[/tex]hence
total cost = time*rate*consume
[tex]\begin{gathered} \text{ Total cost = 10 hours}\cdot40\frac{w}{h}\cdot0.2\frac{\text{ \$}}{1000\text{ w}} \\ \text{ Total cost =}0.08\text{ dollars} \end{gathered}[/tex]now, to convert from dollars to cents, multply by 100
[tex]\text{ Total cost =}0.08\text{ dollars}\cdot(\frac{100\text{ cents}}{1\text{ dollar}})=8\text{ cents}[/tex]I hope this helps you
Which of the following graphs represents the reflection of the point ( -3, 5) over the x-axis? I have to send you the other 2. It’s 4 altogether.
Answers
We have to identify the graph that represents the reflection of the point (-3,5) over the x-axis.
A reflection over the x-axis can be defined by the following rule: if we have a point (x,y), the image point after the reflection will have the same x-coordinate but the opposite of the y-coordinate.
It can be expressed as:
[tex]P=(x,y)\longrightarrow P^{\prime}=(x,-y)[/tex]Then, the image point for (-3,5) will be:
[tex](-3,5)\longrightarrow(-3,-5)[/tex]Then, this can be represented in a graph as:
This matches the following graph:
Out of a group of 120 students, 28 said they ski and 52 said they snowboard. Sixteen of thestudents said they do both. If a student is chosen at random, find the probability that theysnowboard given they ski (Hint: Draw a Venn Diagram).
Answers
Given:
The total number of students = 128 students.
The number of students who play ski, N(S)= 28 students.
The number of students who play snowboard, N(B)= 52 students.
The number of students who play both ski and snowboard, N(S and B)= 16 students.
[tex]N(S\cap B)=16[/tex]Required:
We need to find the probability that they snowboard given they ski.
Explanation:
The ven diagram.
Consider the Conditional probability formula.
[tex]P(\frac{S}{B})=\frac{N(S\cap B)}{N(B)}[/tex][tex]Substitue\text{ }N(S\cap B)=16\text{ and N\lparen B\rparen=52 in the formula.}[/tex][tex]P(\frac{S}{B})=\frac{16}{52}[/tex][tex]P(\frac{S}{B})=\frac{4}{13}[/tex]Final answer:
The probability that they snowboard given they ski is 4/13.
4 years ago Lena won some money in the lottery and put it in a bank account that earns 6% interest compounded annually if Lena currently has $5,000 00 in the bank account how much interest has she earned round your answer to the nearest cent
Answers
Solution
For this case we can use the compound interest formula given by:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]and for this case A= 5000, r = 0.06, t= 4 and n = 1 ( compounded yearly)
[tex]A=5000(1+\frac{0.06}{1})^{1\cdot4}=6312.38[/tex]and the interest would be:
[tex]i=6312.38-5000=1312.38[/tex]An ice cream store has the pricing shown below. You want to determine the best value. The height of the cone is 4.5 in and the diameter is 2 in. The diameter of each scoop is 3 in. Assume the cone is stuffed full with ice cream.Question: Which size is the best value? Explain your reasoning using complete sentences.
Answers
Solution:
Step 1:
We will calculate the volume of ice cream in the single scoop
The volume of the ice cream will be
[tex]\begin{gathered} V=\frac{1}{3}\pi r^2h+\frac{2}{3}\pi r^3 \\ r=\frac{2in}{2}=1in(cone) \\ h=4.5in \\ r=\frac{3in}{2}=1.5in(radius\text{ of the hemisphere\rparen} \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} V=\frac{1}{3}\pi r^{2}h+\frac{2}{3}\pi r^{3} \\ V=\frac{1}{3}\times\frac{22}{7}\times1^2\times4.5+\frac{2}{3}\times\frac{22}{7}\times1.5^3 \\ V=\frac{33}{7}+\frac{99}{14} \\ V=\frac{165}{14} \\ V=11.79in^3 \end{gathered}[/tex]Step 2:
We will use the formula below to calculate the volume of the two scoops of ic cream
[tex]\begin{gathered} V=\frac{1}{3}\pi r^2h+\frac{4}{3}\pi r^3 \\ V=\frac{1}{3}\times\frac{22}{7}\times1^2\times4.5in+\frac{4}{3}\times\frac{22}{7}\times1.5^3 \\ V=\frac{33}{7}+\frac{99}{7} \\ V=\frac{132}{7} \\ V=18.86in^3 \end{gathered}[/tex]Step 3:
We will use the formula below to calculate the volume of the three scoops of ic cream
[tex]\begin{gathered} V=\frac{1}{3}\pi r^2h+\frac{6}{3}\pi r^3 \\ V=\frac{1}{3}\times\frac{22}{7}\times1^2\times4.5+2\times\frac{22}{7}\times1.5^3 \\ V=\frac{33}{7}+\frac{297}{14} \\ V=\frac{363}{14} \\ V=25.93in^3 \end{gathered}[/tex]For the first ice cream with one scoop
[tex]\begin{gathered} 1in^3=\frac{3.50}{11.79} \\ 1in^3=\text{ \$}0.30 \end{gathered}[/tex]For the second ice cream with two scoops
[tex]\begin{gathered} 1in^3=\frac{4.50}{18.86} \\ 1in^3=\text{ \$}0.24 \end{gathered}[/tex]For the third ice cream with three scoops
[tex]\begin{gathered} 1in^3=\frac{5.50}{25.93} \\ 1in^3=\text{ \$}0.21 \end{gathered}[/tex]Hence,
The final answer is
The triple sold at $5.50 has the best value because it has the lowest price of $0.21 per cubic inch of the ice cream
need help with this problem.
Answers
[tex]\cfrac{6^3\cdot 15^3}{(7^0)^3}\implies \cfrac{(6\cdot 15)^3}{(1)^3}\implies \cfrac{90^3}{1}\implies 729000[/tex]
Pythagorean TheoremFor the following right triangle, find the side length x. Round your answer to the nearest hundredth.18Х11
Answers
Solution
For this case we can use the Pythagoras theorem and we have:
[tex]18^2=11^2+x^2[/tex]And solving for x we got:
[tex]x=\sqrt[]{18^2-11^2}=\sqrt[]{324-121}=\sqrt[]{203}=14.25[/tex]Then the answer is:
14.25
Need help w whole paper
Answers
Answer:
it is 1+1=2 and 8+x(1230+8723)=27t9230
Step-by-step explanation:
its easy for me
I need to factor this expression (7th grade math):26x + 18
Answers
SOLUTION:
Required: To factorize the expression:
Solving:
[tex]\begin{gathered} 26x\text{ + 18} \\ \text{First we find the GCF of each terms of the binomial. The greatest co}mmon\text{ factor betwe}en\text{ 26x and 18} \\ 2(13x\text{ + 9)} \end{gathered}[/tex]Final answer:
The final answer is 2(13x + 9)
use nPr formula 11P0=
Answers
we know that
the formula is equal to
P(n,r) = n! / (n-r)!
we have that
nPr = n!/(n-r)!
we have
11P0
so
n=11
r=0
= 11!/(11-0)!
=11!/11!
=1
answer is 1What is the inverse of the function y = 2(x + 1)³?
Answers
Answer:
[tex]\sqrt{x}[/tex][tex]\sqrt[3]{1/2(x)}[/tex] - 1 = y
Step-by-step explanation:
Inverse: swap x and y
y =2(x+1)^3
x = 2(y + 1)^3
now put it in a y = mx + b form
x = 2(y + 1)^3
1/2(X) = (y+1)^3
[tex]\sqrt{x}[/tex][tex]\sqrt[3]{1/2(x)}[/tex]= y + 1
[tex]\sqrt{x}[/tex][tex]\sqrt[3]{1/2(x)}[/tex] - 1 = y
Dude I need help so if anyone can answer this for me that would be great!
5/6 ÷ -2/3
A -5/4
B -5/9
C 5/9
D 5/4
Answers
A fraction is written in the form of a numerator and a denominator where the denominator is greater than the numerator.
The final expression for this division of fraction 5/6 ÷ (-2/3) is -5/4.
What is a fraction?A fraction is written in the form of a numerator and a denominator where the denominator is greater than the numerator.
Example: 1/2, 1/3 is a fraction.
We have,
The division of two fraction:
5/6 ÷ (-2/3)
= (5/6) / (-2/3)
= 5/6 x (-3/2)
= (5 x (-3)) / (6 x 2)
= -5 x 3 / 6 x 2
= -5 / 4
Thus,
The final expression for this division of fraction 5/6 ÷ (-2/3) is -5/4.
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The quadratic equation d = -t2 + 4t + 33 models the depth of water, d, in feet
in a flood channel t hours after a rainstorm.
a. Solve the equation -t2 + 4t+ 33 = 0.
b. Approximate the positive solution found in part (a) to two decimal
places.
c. Interpret the answer to part (b) in terms of the problem.
Answers
a. The solution of the equation is t = 2 ± √37.
b. The approximation of the positive solution is 8.08.
c. The interpretation is that the depth of the water is 0 feet after 8.08 hours of the rainstorm.
We are given a quadratic equation. The equation is given below :
d = -t² + 4t + 33
The equation models the depth of the water "d" in a flood channel "t" hours after a rainstorm.
a. We have to solve the equation :
-t² + 4t + 33 = 0
t² - 4t - 33 = 0
t = 2 ± √37
b. We need to approximate the positive solution found in part (a) to two decimal places. The positive solution is t = 2 + √37.
t = 2 + 6.08
t = 8.08
c. The depth of the water is 0 feet after 8.08 hours of the rainstorm.
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Find the area of the shadedSector in terms of π12 90
Answers
Consider the following figure:
I bought a suit that was on sale for 40% off the original price the original price of the suit was 260. How much did I save? and how much did I pay for the suit not including tax to the nearest dollar?
Answers
I saved 104
I payed 156
Explanations:% Discount = 40%
Original Price = 260
The amount I saved is the discount given
[tex]\begin{gathered} \text{Discount = }\frac{\%\text{ Discount}}{100}\times\text{ 260} \\ \text{Discount = }\frac{40}{100}\times260 \\ \text{Discount = 0.4}\times260 \\ \text{Discount = }104 \end{gathered}[/tex]Therefore, I saved 104
The amount payed = Original Price - Amount saved
Amount payed = 260 - 104
Amount payed = 156
The water level in a lake was monitored and was noted to have changed −213 inches in one year. The next year it was noted to have changed −116 inches. What was the total change in the water level over the two years? Enter your answer as a simplified mixed number by filling in the boxes.
Answers
are those fractions??
Solve the equation. Justify each step using the word bank provided. *Properties may be used more than once!
Given
Addition Property of Equality
Subtraction Property of Equality
Multiplication Property of Equality
Division Property of Equality
Distributive Property
Combine
Like Terms
Justifications for each step:
2(x − 4) − 9 = 3(2x + 1) + 4
HELP PLEASE
Answers
The result of the equation 2(x − 4) − 9 = 3(2x + 1) + 4 by using the distributive property is x = -6
The equation is
2(x − 4) − 9 = 3(2x + 1) + 4
The distributive property states that multiplying the sum of two or more variables by a number will provide the same result as multiplying each variable individually by the number and then adding the products together.
The distributive property of the addition
A(B + C) = AB + AC
The distributive property of the subtraction
A(B - C) = AB - AC
The equation is
2(x − 4) − 9 = 3(2x + 1) + 4
Apply the distributive property
2x-8-9 = 6x+3+4
2x-17 = 6x+7
Rearrange the like terms and combine it
2x-6x = 7+17
-4x = 24
x = -6
Hence, the result of the equation 2(x − 4) − 9 = 3(2x + 1) + 4 by using the distributive property is x = -6
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If f(x) = 4x - 1 and g(x)=2x-4, what is (fog)(x)?
Answers
The value of the composite function (f o g)(x) is 8x - 17
How to evaluate the function?The definition of the functions are given as
f(x) = 4x - 1
g(x) = 2x - 4
The composite function definition is given as
(f o g)(x)
This composite function is calculated using the following composite function formula
(f o g)(x)= f(g(x))
Substitute the known values in the above equation
So, we have the following equation
(f o g)(x) = 4(g(x)) - 1
So, we have the following equation
(f o g)(x) = 4(2x - 4) - 1
Open the brackets
(f o g)(x) = 8x - 16 - 1
Evaluate
(f o g)(x) = 8x - 17
Hence, the composite function is (f o g)(x) = 8x - 17
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Will someone please help me with this? I tried getting help but it didn’t work
Answers
What is the mean absolute deviation of 10,4,12,4,2,10,10,6
Answers
3.25 is the mean absolute deviation of 10,4,12,4,2,10,10,6
What is Mean absolute Deviation?Mean absolute deviation (MAD) of a data set is the average distance between each data value and the mean. Mean absolute deviation is a way to describe variation in a data set.
Given data:
10,4,12,4,2,10,10,6
Using the formula
Mean Absolute deviation = ∑(xi - x)/n
Mean = (10+ 4+ 12 +4+ 2+ 10 + 10+6)/8
= 58 / 8
= 7.25
Now,
10-7.25 = 2.75
4-7.25= -3.25
12-7.25=4.75
4-7.25=-3.25
2-7.25=-5.25
10-7.25=2.75
10-7.25=2.75
6-7.25=-1.25
mean absolute deviation=(2.75+3.25+4.75+3.25+5.25+2.75+2.75+1.25)/8
=26/8
=3.25
Hence 3.25 is the mean absolute deviation of 10,4,12,4,2,10,10,6.
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what is the probability that Glenn will get a yellow marble
Answers
The bag has 5 marbles
3 yellow marbles
2 red marbles
"Glen chooses a marble first and then Kris chooses one" You have to determine the probability of Kris choosing a yellow marble if Glen chooses a yellow one first.
1. First you have to determine the probability that Glen choose a yellow marble first.
To do so, you have to calculate the quotient between the number of yellow marbles on the bag and the total number of marbles on the bag:
[tex]\begin{gathered} P(Y_1)=\frac{nº\text{yellow}}{\text{total}} \\ P(Y_1)=\frac{3}{5} \end{gathered}[/tex]2. and 3.
After Glen takes the first yellow marble from the bag, the total number of marbles is reduced by one and so is the number of yellow marbles on the bag, so:
New total: 4 marbles
Number of yellow marbles: 2
4.
To determine the probability of Kris choosing a yellow marble, you have to use the data on the remaining marbles on the bag. And calculate the quotient between the remaining number of yellow marbles and the remaining number of marbles:
[tex]\begin{gathered} P(Y_2)=\frac{2}{4} \\ P(Y_2)=\frac{1}{2} \end{gathered}[/tex]You invest $1000 in an account that has an annual interest rate of 4%, compounded quarterly for 12 years. How much money will you have after the 12 years? $3138.43 O $3237.27 O $1601.03 O $1612.23
Answers
The compound interest formula is given by
[tex]A=P(1+\frac{r}{n})^{n\times t}[/tex]where A is the resulting amount after t years, P is the present value (or principal amount) , r is the annual interest rate and n is the number of compounding periods per year.
From the given information, we have that
[tex]\begin{gathered} P=1000 \\ r=0.04 \\ n=4\text{ (quaterly=4 times per year)} \\ t=12\text{ years} \end{gathered}[/tex]By substituting these values into the formula, we have
[tex]A=1000(1+\frac{0.04}{4})^{4\times12}[/tex]which gives
[tex]\begin{gathered} A=1000(1.01)^{48} \\ A=1000(1.6122) \\ A=1612.226 \end{gathered}[/tex]Therefore, by rounding to the nearest thousandth, the answer is $1612.23, which corresponds to the last option.
Two-digit natural numbers are formed, with replacement, from the digits 0 through 9.
How many numbers are greater than 64?
Answers
There are 35 natural numbers that are greater than 64.
Natural numbers:
Natural number are the numbers that start from 1 and end at infinity. In other words, they are counting numbers and they do not include 0 or any negative values.
Given,
Two-digit natural numbers are formed, with replacement, from the digits 0 through 9.
Here we need to find the numbers that satisfied the given condition and that is also greater than 64.
We know that, two digit natural numbers range from 10 to 99.
Since there are replacement take place, then each number formed from 10 to 99 is valid in this exercise.
Now, we have to move on to the other thing that is, those number are greater than 64,
Then we have to calculate it as,
=> 99-64 = 35 are greater than 64.
And those number are 65,66,67,68,69,...,98,99.
Finally, we have identified that there are 35 number are greater than 64.
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Use the long division method to find the result when 8x3 + 14x2 11x - 8 is divided by 2x + 1. If there is a remainder, express the result in the form q(a) +
Answers
Let's develop a synthetic division
As you can observe, the division is exact because its reminder is zero.
Hence, the answer is-
[tex]\frac{8x^3+14x^2-11x-8}{2x+1}=4x^2+5x-8[/tex]The slope of the line is given by the variable m. Slowly drag the m slider to the right. How does this changethe line?
Answers
2.
As you can see:
Rise = 2
Run = 2
Slope = 2
Write an phrase that would translate into the following mathematical expression: 8z- 2 ?
Answers
The mathematical expression 8z - 2 can be phrased as:
The difference between 8 times the variable z and 2.
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
Any mathematical object has a symbol, and that symbol is called a variable. A variable can specifically represent a number, a vector, a matrix, a function, its argument, a set, or one of its elements.
Consider the mathematical expression,
8z - 2
The expression can be defined as 2 less than the product of 8 and variable z.
The expression can also be rephrased as:
The difference between 8 times the variable z and 2.
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Pattern A Step 0 Step 1 pattern A or pattern B) shows a quadratic relationship?Step 2 Step 3 8 Pattern B Step 0 Step 1 Step 2 Step 3 2 a. How many dots will there be in Step 4 of each pattern? Pattern A = 16 dots Pattern B = 16 dots b. Which pattern (
Answers
Looking at pattern A, the rate at which the number of dots in increasing is linear. The common difference between the number of dots in consecutive steps is 2. The sequence formed is
4, 8, 12.......
The common difference is 8 - 4 = 12 - 8 = 4
Thus, the number of dots in step 4 is
12 + 4 = 16
Looking at pattern B, the sequence formed is
2, 3, 6, 11
3 - 1 = 1
6 - 3 = 3
11 - 6 = 5
We can see that the difference between consecutive terms is increasing by a constant value, 2. This means that the difference between the fourth term and the third term is 5 + 2 = 7
Thus, the number of dots in step 4 is
11 + 7 = 18
b) A quadratic sequence is one in which the second difference between any two consecutive terms is constant. The constant value for the second difference in pattern B is 2
Thus, pattern B is shows a quadratic relationship
Solve the following inequality for n. Write your answer in the simplest form.9n + 4 ≤ 6n - 6
Answers
Given,
The expression is,
[tex]9n+4\le6n-6[/tex]Substracting 4 from both sides then,
[tex]\begin{gathered} 9n+4-4\le6n-6-4 \\ 9n\le6n-10 \end{gathered}[/tex]Substracting 6n from both sides then,
[tex]\begin{gathered} 9n\le6n-10 \\ 9n-6n\le6n-6n-10 \\ 3n\le-10 \end{gathered}[/tex]Multiplying both sides by 1/3 then,
[tex]\begin{gathered} 3n\le-10 \\ 3n\times\frac{1}{3}\le-10\times\frac{1}{3} \\ n\le-\frac{10}{3} \end{gathered}[/tex]Hence, the solution for n is n<= (-10/3).
what is the least common multiple of 62 and 31?
Answers
Answer:
there is none so it would be 62
Step-by-step explanation:
