Answer:
-26
Step-by-step explanation:
Answer:
The answer to this problem is -26
What is the inverse of the function y = 2(x + 1)³?
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
Which letrero Best represents √27 on the number line.
You have the following number
√27
In order to determine which letter best represent the previous number, you take into account the following square roots:
√25 = 5
√36 = 6
Then, you can consider that √27 is a number in between 5 and 6, because √27 in anumber in between √25 and √36.
The only letter that is in between 5 and 6 on the number line, is the letter C.
Hence, letter C best represents √27
Solve -4x + 3 > 23 or 7x - 6 > 22
Answer:
-4x + 3 > 23 Answer is x<-5
Step-by-step explanation:
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
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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A rocket is launched straight up with a velocity of 8.36. What would be the velocity when it lands?
If the rocket is launched straight up with a velocity of 8.36 then at the velocity of landing the speed of the rocket will also be 8.36.
Given that the rocket is launched straight up with a velocity of 8.36.
We are required to find the velocity when the rocket lands.
Velocity is basically the directional speed of a object in motion as an indication of its rate of change in position as observed from a particular frame of reference.
When the velocity of rocket while it goes up is 8.36 then the velocity when it lands is also 8.36 because if the velocity will increase then the rocket will crash also.
Hence if the rocket is launched straight up with a velocity of 8.36 then at the velocity of landing the speed of the rocket will also be 8.36.
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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?
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
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.
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:
The slope of the line is given by the variable m. Slowly drag the m slider to the right. How does this changethe line?
2.
As you can see:
Rise = 2
Run = 2
Slope = 2
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.
are those fractions??
you invest 1,000 in an account that pays simple interest of 3% for 10 years. what is the amount of money you'll have at the end of the 10 years?
Given data:
The given principal is P=1,000.
The given rate of interest is r=3%.
The given time is t=10 years.
The expression for the final amount after 10 years is,
[tex]A=P+\frac{P\times r\times t}{100}[/tex]Substitute the given values in the above expression.
[tex]\begin{gathered} A=1,000+\frac{1,000\times3\times10}{100} \\ =1,300 \end{gathered}[/tex]Thus, the final amount after 10 years is 1,300.
I need to factor this expression (7th grade math):26x + 18
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)
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.
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 vehicle factory manufactures cars. The unit cost C (the cost in dollars to make each car) depends on the number of cars made. If x cars are made, then theunit cost is given by the function C (x) = 0,3x2 -96x+14,848. How many cars must be made to minimize the unit cost?Do not round your answer
Answer:
[tex]160\text{ cars}[/tex]Explanation:
Here, we want to get the number of cars to be made so as to minimize the unit cost
What we have to do here is to find the first derivative of the given cost function
Mathematically, we have that as:
[tex]C^{\prime}(x)\text{ = 0.6x -96}[/tex]To get the minimum x value, we simply set the first derivative to zero and solve for x
Mathematically, that would be:
[tex]\begin{gathered} 0\text{ = 0.6x-96} \\ 0.6x\text{ = 96} \\ x\text{ = }\frac{96}{0.6} \\ x\text{ = 160 } \end{gathered}[/tex]Need help w whole paper
Answer:
it is 1+1=2 and 8+x(1230+8723)=27t9230
Step-by-step explanation:
its easy for me
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.
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
j
knjfjfjfjfjfjf help me solve this thanks !!
Answer:
132 degrees
Step-by-step explanation:
102+30 = 132
Find the area of the shadedSector in terms of π12 90
Consider the following figure:
od 2 - 7th Grade Math) Simplify the following expressions: (9x + 3) - (5x - 7) (1 Point) Enter your answer
Simplifying the expression, we have:
[tex]\begin{gathered} (9x+3)-(5x-7) \\ =9x+3-5x+7 \\ =(9x-5x)+(3+7) \\ =4x+10 \end{gathered}[/tex]So the simplified expression is 4x + 10.
Will someone please help me with this? I tried getting help but it didn’t work
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
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.
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
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]Find the equation of the line with the following:slope = 2/5; passes through (-3, 1)
Answer:
[tex]y=\frac{2}{5}x+\frac{11}{5}[/tex]Explanation:
Given the slope and a point on the line, we use the point-slope form to find the equation of the line:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ m=\frac{2}{5} \\ (x_1,y_1)=(-3,1) \end{gathered}[/tex]Substitute the given values:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-1=\frac{2}{5}(x-(-3)) \\ y-1=\frac{2}{5}(x+3) \\ y=\frac{2}{5}(x+3)+1 \\ y=\frac{2}{5}x+\frac{6}{5}+1 \\ y=\frac{2}{5}x+\frac{11}{5} \end{gathered}[/tex]The equation of the line in slope-intercept form is:
[tex]y=\frac{2}{5}x+\frac{11}{5}[/tex]What is the mean absolute deviation of 10,4,12,4,2,10,10,6
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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Select the equations below that are equivalent to -6 = -20 - v
Given
[tex]-6=-20-v[/tex]- For -72 = 9(-20 - v):
[tex]\begin{gathered} -\frac{72}{9}=\frac{9(-20-v)}{9} \\ -8=-20-v \end{gathered}[/tex]The equation is not equivalent
- For -90 = 15(-20 - v):
[tex]\begin{gathered} \frac{-90}{15}=\frac{15(-20-v)}{15} \\ -6=-20-v \end{gathered}[/tex]The equation is equivalent
- For 5 * -6 = -100 - 5v:
Common factor 5
[tex]\begin{gathered} -30=5(-20-v) \\ \frac{-30}{5}=\frac{5(-20-v)}{5} \\ -6=-20-v \end{gathered}[/tex]The equation is equivalent
- For 3 * -6 = -60 - 3v:
Common factor 3
[tex]\begin{gathered} -18=3(-20-v) \\ \frac{-18}{3}=\frac{3(-20-v)}{3} \\ -6=-20-v \end{gathered}[/tex]The equation is equivalent
Answer:
-90 = 15(-20 - v)
5 * -6 = -100 - 5v
3 * -6 = -60 - 3v
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
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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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.
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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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 (
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
A jeweler has found that the monthly revenue received from selling a pair of earrings at a cost of d dollars each is given by the polynomial −7d2+180d. Find the monthly revenue received when d=17 dollars.
The monthly revenue is $1037
What is a linear equation in one variable?
A linear equation in one variable is equation whose degree is one and there is only one variable present.
We are given the monthly revenue received from selling a pair of earrings at a cost of d dollars is given by equation [tex]-7d^{2}+180d[/tex]
We have to find the monthly revenue received when the cost is $17
That is d=17
Now we substitute d=17 in the given equation to find the monthly revenue
We get,
[tex]-7d^{2}+180d\\[/tex]
⇒[tex]-7(17^{2})+180(17)\\[/tex]
⇒ -2023+3060
⇒1037
Hence the monthly revenue earned is $1037
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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).
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.
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) +
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]