The ways in which the graph of f(x) = (x + 7)^3 − 8 compare to the parent function g(x) = x^3 are as follows:
Shifted 7 units to the left.Shifted 8 units down. What is a translation?In Mathematics, the translation a geometric figure to the left simply means subtracting a digit from the value on the x-coordinate of the pre-image while translating a geometric figure down simply means subtracting a digit from the value on the y-coordinate (y-axis) of the pre-image.
In Geometry, g(x + 7) simply means shifting a graph 7 units to the left while subtracting 8 from the function simply means moving the graph down.
In this context, we can reasonably infer and logically deduce that the parent function g(x) was shifted 7 units to the left and 8 units down.
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Sarah needs to lease out a music studio to record her new album. The studio chargesan initial studio-use fee plus an hourly fee for each hour in the studio. The fixed fee touse the studio is $150 and the total cost charged for 2 hours is $300. Write anequation for P, in terms of t, representing the amount of money Sarah would have topay to use the studio for t hours.
Fixed fee is 150
Total cost for 2 hours is 300
If the fixed fee is 150, and Sarah paid 300, then she paid 150 for the fixed fee and anohter 150 for the two hours, that means that each hour is 75
Then we can write the equation:
P = 75t + 150
Answer:
P = 75t + 150
24 miles is to 1 gallon of gas as 60 miles is to 2.5 gallons of gas Choose the correct letter
Since 24 miles is to 1 gallon of gas as 60 miles is to 2.5 gallons of gas
These are 2 equal ratios, then
They will be 2 equal fractions
[tex]\frac{24\text{ miles}}{1\text{ gallon}}=\frac{60\text{ miles}}{2.5\text{ gallons}}[/tex]The correct answer is D
Lloyd is standing near a telephone pole. When his head touches the support wire, he is 25 feet from where the wire meets the ground. Lloydis 5 ft tall. Hon tallis the pole?1-8f feetO A 20 ft.B. 15 ftC. 80 ft.D. 17 ft
We will use the pythagorean theorem to figure the answer out.
Applying the Pythagorean Theorem, we have (let unknown side be x):
[tex]\begin{gathered} 6^2+x^2=10^2 \\ 36+x^2=100 \\ x^2=100-36 \\ x^2=64 \\ x=\sqrt[]{64} \\ x=8 \end{gathered}[/tex]Answer 8 feet (B)Rewrite the polynomial expression using the GCF: 4x^2+8x+24 ?What is the new polynomial expression
GCF of 4,8 and 24
is. = 4
Then new expression is
y = 4• (x^2 + 2x + 6)
Tom Blasting invested $4,500 in an investment paying 10% compounded quarterly for 3 years. Find the interest
Given that Tom invested $4500 in an investment paying 10% compounded quarterly for 3 years.
We have to find the interest for the given time period.
We know that the formula of amount on a principal P, rate r per annum, time t years where interest is compounding quarterly is:
[tex]A=P(1+\frac{r}{4})^{4t}[/tex]Here, P = 4500, r = 0.1 and t = 3. So,
[tex]\begin{gathered} A=4500(1+\frac{0.1}{4})^{4(3)} \\ =4500(1+0.025)^{12} \\ =4500(1.025)^{12} \\ =4500(1.3448) \\ =6051.6 \end{gathered}[/tex]So, the amount we get is $6051.6.
Now, it is known that the interest is the difference between the amount and the principal. So,
[tex]\begin{gathered} \text{ interest}=\text{ amount-principal} \\ =6051.6-4500 \\ =1551.6 \end{gathered}[/tex]Thus, the interest is $1551.6.
How do you decide which rational number operations to use to solve problems
One can decide which rational number operations to use to solve problems based on the context of the information.
What is a rational number?Studying rational numbers is significant because they illustrate how the world is so complex that we will never be able to comprehend it.
A rational number is defined as the ratio or fraction p/q of two numbers, where p and q are the numerator and denominator, respectively. Every integer and 3/7, for example, are rational numbers.
A rational number is defined as the quotient of the fraction p/q of two integers, a numerator p and a non-zero denominator q. Every integer is a rational number since q might be equal to 1.
In this case, the operation include addition, subtraction, division, etc. This will be based on the context.
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Miscavage Corporation has two divisions: the Beta Division and the Alpha Division.
The Beta Division has:
sales of $320,000,
variable expenses of $158,100,
and traceable fixed expenses of $72,300.
The Alpha Division has:
sales of $630,000,
variable expenses of $343,800,
and traceable fixed expenses of $135,100.
The total amount of common fixed expenses not traceable to the individual divisions is $137,200.
What is the total company's net operating income?
The total company's net operating income (NOI) is $103,500.
What is a Net operating income?In accounting, a Net operating income refers to the figure that equals to all revenue from the property minus all reasonably necessary operating expenses.
The computation of the Net operating income is as follows:
= Gross Income - Operating Expenses
= (Sales+Sales) - [(variable expenses + variable expenses) + (fixed expenses + fixed expenses) + 137,200]
= (320,000+630,000) - [(158,100 + 343,800) + (72,300 + 135,100) + 137,200]
= 950,000 - (5,01,900 + 2,07,400 + 137,200)
= 950,000 - 8,46,500
= $1,03,500
In conclusion, the total company's net operating income (NOI) is $103,500.
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Select the similarity transformation(s) that make ABCD similar to EFGH.
Answer:
D
F
Explanation:
We would compare the coordinates of the corresponding vertices of rectangles ABCD and EFGH. We would compare vertices A and E. From the information given,
A = (1, - 2)
E = (- 2, 4)
If we apply (x, y)---(- x, - y) to A, it becomes (- 1, - - 2) = (- 1, 2)
If we apply (x, y)---(2x, 2y) to (- 1, 2), it becomes (2 * - 1, 2 * 2) = (- 2, 4)
Thus, the correct similarity transformation(s) that make ABCD similar to EFGH are
D
F
A shellfish absorbed 40% of the heavy metals in the water in and just the concentration of heavy metals is 0.0002 mg/m³ .The shellfish ingests 4 L of water per hour. How many heavy metal does it absorb in 3 months? (Assume there are 30 days in a month there are 1000 L in one cubic meter)
Answer:
Step-by-step explanation:
For the function f(x)5x – 2, what does the x represent?
The given function is
f(x) = 5x - 2
If we are given a function f(x), the x is called argument of the function.
You just have to pass argument x to get the value of f(x).
Brody spent $260 on 4 chairs. To find out how much he spent on each chair, he did the following work in long division. 65 4) 260 -24 20 -20 0 Did he do the problem correctly? Why or why not? O A. No, because there is a remainder of o. B. No, because the first digit in the quotient should be 4, not 6. O C. No, because the problem should be 260 14. O D. Yes, he worked the problem correctly.
He spend $260 on 4 chairs:
To know how much he spent on each chair he must:
Divide 260 into 4You first pick the firt digit of the dividend (260) and look if you can divide that digit into the divider (4) as in this case the firt digit 2 cannot be divided into 4 you take the first and secon digit (26) and divide it into 4 (how many times fix 4 in 26), this is equal to 6 times (this is the first digit of the quotient), then you multiply the 6 by 4 (6*4=24)and put the result under the 26 to substract it:
Now you lower the zero (of the 260) next to the result of the previous subtraction:
And divide 20 into 4 (how many times fix 4 in 20) this is equal to 5 times (this is the second digit of the quotient ) then you multiply the 5 by 4 (5/4 =20) and put the result under the 20 to substract it:
The remainder of 0 means the division has not decimal result, the result of 260 into 4 is an interger number (65)
The firt digit of the quotient is 6 because 26 into 4 is 6.
So the division he did is the correct form to find how much cost each chair ($65)Point A is shown on the complex plane.What is the standard form of the complex number that point A represents?
Hello there. To solve this question, we have to remember some properties about the representation of a complex number in the complex or Argand-Gauss plane.
Given the complex plane with the point A representing a complex number:
We have to remember that in the complex plane, a complex number z:
[tex]z=a+ib[/tex]has coordinates
[tex](a,\,b)[/tex]And it is more commonly represented by a vector starting at the origin and with the tip on this point.
In this case, we find that the coordinates of the point A are:
[tex]A=(-5,\,3)[/tex]Which means that the complex number is
[tex]-5+3i[/tex]And this is the answer contained in the last option.
You are researching the speed of sound waves in dry air
at 86°F. The linear function d = 0.217t represents the distances d (in miles) sound waves
travel in t seconds.
A. Represent the situation using a table and a graph.
B. Which of the three representations would you use to find how long it takes sound waves to travel 0.1 mile in dry air at 86°F? Explain.
By observing the pace at which this compressed region moves through the medium, we may determine the sound speed.The speed of sound is roughly 343 meters per second or 767 miles per hour in dry air at 20 degrees Celsius.
Calculate speed of sound wave?
The formula for the airborne sound speedThe equation for the speed of sound in air as a function of absolute temperature is given by the simplification of v=RTM:v=√γRTM=√γRTM(273K273K)=√(273K)γRM√T273K≈331m 2) Time required for 1620m to be traveled at that speed: t = d / v 0.217m / 0.1 m/s) = 2.17m/ s from the beginning of the sound wave.Since you were watching the lightning, you might have wanted to know the time.Then, using the speed of light, you can determine how long it was between the lights being generated o.217 meters distant from you and Light travels at a speed of3*108 m/s, hence t = 0.217m / (3*108 m/s) = 0.000669 s.
The answer is o.000669 s, as determined in step 2, even though this time is entirely negligible.
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Question 2 A recipe for homemade modeling clay requires 4 parts plain flour to 1 part cornstarch. Indicate whether each set of ingredients below is proportional to the recipe. Proportional Not Proportional 8 cups plain flour and 2 cups cornstarch 20 cups plain flour and 5 cups cornstarch 2 cups plain flour and 1 cup cornstarch Next Question Check Answer Privacy and Cookies | Terms of Use | Minimum Frequirements | Platform Status 2021 McGraw-HI Education. All Rights Reserved
The given ratio is 4 parts of plain flour to 1 part of cornstarch.
So, each recipe with the same ratio will be the answer.
As you can observe, the first choice is proportional because the plain flour is 4 times the cornstarch.
The second choice is proportional too because the plain flour is 4 times the cornstarch.
However, the last choice is not proportional because it has a ratio of double, which is not correct.
A car drove 300 miles in four hours. How fast was the car traveling in miles per hour?
Given that,
A car drove 300 miles in four hours.
We can simply put it in this way.
In 4 hours, a total distance covered by the car = 300 miles
In 1 hour, a total distance covered by the car = 300/4 miles = 75 miles.
Hence, the car was traveling at a speed of 75 miles per hour.
1 litre=1000cm³. About how many test tubes, each holding 24cm³ of water, can be filled from a
1 litre flask?
Answer: 125/3 or about 41.667
Note that you can't have 2/3 of a test tube, so the expected answer may be 42 test tubes.
Step-by-step explanation:
Write a simple algebra equation using the word problem
24x = 1000
x represents the number of test-tubes, each of which hold 24cm^3 of water.
divide both sides by 24
x = 125/3 or about 41.667
Add these fractions using fraction bars after choosing a common denominator Use the fraction bar inactivate to find the difference
The fractions you have to add are 1/3 and -5/6
[tex]\frac{1}{3}+(-\frac{5}{6})[/tex]The denominators are "3" and "6"
The common denominator between both numbers is 6.
6*1=6
3*2=6
Multiply 1/3 by factor 2 so that both fractions will have the same denominator
[tex]\frac{1}{3}\cdot2=\frac{1\cdot2}{3\cdot2}=\frac{2}{6}[/tex]Now you can add both fractions
[tex]\frac{2}{6}+(-\frac{5}{6})=\frac{2}{6}-\frac{5}{6}=\frac{2-5}{6}=-\frac{3}{6}[/tex]The result is not in its most reduced form, to siplify the fraction divide both the numerator and denominator by 3
[tex]-\frac{3}{6}\div3=-\frac{1}{2}[/tex]The result is -1/2, in the number line:
35% of the employees in a company receive an incentive in the month of April. What is theprobability that among 4 employees chosen at random, all 4 do not receive the incentive inApril?
ANSWER :
0.1785
EXPLANATION :
35% will receive an incentive and (100% - 35% = 65%) will NOT receive an incentive.
So an employee has 65% chance of NOT receiving an incentive.
The probability that among 4 employees do not receive the incentive is :
[tex](0.65)^4=0.1785[/tex]Find the exact values of the six trigonometric functions of the real number t
In a unit circle, given the (x,y) coordinate, x corresponds to cosine, and y corresponds to sine.
Then use the trigonometric identity to solve for tangent.
We therefore have the following ratios for sin, cos, and tan.
[tex]\begin{gathered} \sin t=\frac{15}{17} \\ \cos t=-\frac{8}{17} \\ \tan t=\frac{\sin t}{\cos t}=\frac{\frac{15}{17}}{-\frac{8}{17}}=-\frac{15}{8} \\ \\ \text{Therefore,} \\ \sin t=\frac{15}{17} \\ \cos t=-\frac{8}{17} \\ \tan t=-\frac{15}{8} \end{gathered}[/tex]Solving for the reciprocal of sin, cos, and tan we have
[tex]\begin{gathered} \csc t=\Big(\sin t\Big)^{-1}=\Big(\frac{15}{17}\Big)^{-1}=\frac{17}{15} \\ \sec t=\Big(\cos t\Big)^{-1}=\Big(-\frac{8}{17}\Big)^{-1}=-\frac{17}{8} \\ \cot t=\Big(\tan t\Big)^{-1}=\Big(-\frac{15}{8}\Big)^{-1}=-\frac{8}{15} \\ \\ \text{Therefore,} \\ \csc t=\frac{17}{15} \\ \sec t=-\frac{17}{8} \\ \cot t=-\frac{8}{15} \end{gathered}[/tex]The science class is taking a trip to the science center. there are 20 students and an unknown number of adult chaperones going. the bus holds at most 35 people.what is the greatest number of adults who can chaperone? I know the answer is 15. however, what they want us to do is create an equation using inequalities (<, >, etc..) That's what I don't know how to do with this problem. I'm trying to explain it to my daughter but I don't know how to do it myself.
We are given that there are 20 students and an unknown number of adult chaperones.
Let x denotes the unknown number of adult chaperones.
The bus holds at most 35 people
We know that 20 students plus x number of adult chaperones should be at most 35
at most 35 means equal or less than 35
So we can write
[tex]20+x\le35[/tex]Now we can easily solve for x
[tex]\begin{gathered} 20+x\le35 \\ x\le35-20 \\ x\le15 \end{gathered}[/tex]Trying to figure out this for my home work assignment
Given:
Choosing a even number from the numbers between 1 and 10.
The sample space is
[tex]\mleft\lbrace2,3,4,5,6,7,8,9\mright\rbrace[/tex]Let A be the event of choosing a even number.
There are 4 out comes in the experiment.
given that the measure of arc AD=(17×+2), measure of arc AC=(7×-10),and measure of angle ABC=(4×+15) find the measure of angle ABC
In the given figure, angle ABC is formed by a tangent and a secant.
The angle formed by tangent and secant is given by
[tex]m\angle ABC=\frac{1}{2}(m\bar{AD}-m\bar{AC})[/tex]Where mAD and mAC are the intercepted arcs.
For the given case,
[tex]\begin{gathered} m\angle ABC=(4x+15)\degree \\ m\bar{AD}=(17x+2)\degree \\ m\bar{AC}=(7x-10)\degree \end{gathered}[/tex]Let us substitute the given values into the above formula and solve for x
[tex]\begin{gathered} m\angle ABC=\frac{1}{2}(m\bar{AD}-m\bar{AC}) \\ (4x+15)\degree=\frac{1}{2}\lbrack(17x+2)\degree-(7x-10)\degree\rbrack \\ 2\cdot(4x+15)\degree=(17x+2)\degree-(7x-10)\degree \\ 8x+30=17x+2-7x+10 \\ 8x-17x+7x=2+10-30 \\ -2x=-18 \\ x=\frac{-18}{-2} \\ x=9 \end{gathered}[/tex]The value of x is 9
So, the measure of angle ABC is
[tex]\begin{gathered} m\angle ABC=4x+15 \\ m\angle ABC=4(9)+15 \\ m\angle ABC=36+15 \\ m\angle ABC=51\degree \end{gathered}[/tex]Therefore, the measure of angle ABC is 51°
according to recent study 7 out of every 500 Americans aged 13-17, years are vegetarian.in a group of 350 13 to 17- years old about how many would you expect to he vegetarian
7 out of every 500 Americans aged 13 -17 years are vegetarians
This implies that in a group of 500 Americans , 7 Americans that are within the age range of 13 - 17 years are vegetarians
7 ======== 500
x ======== 350
Introduce cross multiplication
7 x 350 = x * 500
2450 = 500x
Divide both sides by 500
2450/500 = 500x/ 500
x = 4.9
Approximately, 5
5 vegetarians aged 13 - 17 years will be present is in a group of 350 Americans
The answer is 5
which of the following would be an acceptable first step in simplifying the expression?
Solution:
Given:
[tex]\frac{cos\text{ }x}{1-sin\text{ }x}[/tex]The only acceptable first step in simplifying the expression from the options that would not change or alter the values of the expression is by multiplying (1 + sin x) to both the numerator and the denominator.
Therefore, the correct answer is OPTION B.
write three things you used to do but don't do anymore
Answer:
Trusting peoples
Be happy
make friends
Jacob is constructing a pentagonal tent for his school carnival. The tent has a side length of 5.13 meters. What is the area of the tent? What is the perimeter of the tent? What is the sum of three of the interior angles in the tent once Jacob obtains the value of its area and perimeter?
The tent is pentagonal , this means it has 5 sides. The tent have a side length of 5.13 meters.
The area of the pentagon can be calculated below
[tex]\begin{gathered} \text{area of the tent=}\frac{perimeter\times apothem}{2} \\ \tan \text{ 36=}\frac{2.565}{a} \\ a=\frac{2.565}{\tan \text{ 36}} \\ a=\frac{2.565}{0.726542528} \\ a=3.53041962601 \\ \text{perimeter}=\text{ 5.13}\times5=25.65\text{ meters} \\ \text{area =}\frac{25.65\times3.53041962601}{2} \\ \text{area}=\frac{90.5445}{2} \\ \text{area}=45.27225 \\ \text{area}\approx45.27meter^2 \end{gathered}[/tex]Each interior angle of a pentagon is
[tex]\begin{gathered} \text{ interior angle=}\frac{180\times3}{5}=\frac{540}{5}=108^{\circ} \\ \text{ Sum of thr}ee\text{ interior angles = 108}\times3=\text{ }324\text{ degre}e \end{gathered}[/tex]The graph of F(x), shown below, resembles the graph of G(X) = x2, but it hasbeen changed somewhat. Which of the following could be the equation ofF(x)?600 = x2FUO = ?O. A. F(x) = 0.272 - 3B. F(x) = -x2 - 3C. F(x) = 2x2 - 3D. F(X) = 32 - 3
You have G(x) = x².
take into account that G(x) can be considered as an streched of the F(X), moreover, F(x) is a translation of G(x) downward 3 units. If G(x) is an strech of F(x), then, G(x) is multipled by a constant lower than 1.
Then, based on the previous considerations, you have that the form of F(x) is:
F(x) = 0.2x² - 3
Karen is planning to drive 870 miles on a road trip. If she wants to complete the trip in 6 days, how many miles will she need to drive each day??
Answer:
145 miles
Step-by-step explanation:
870 ÷ 6 = 145
A can contains 24 fluid ounces of fruit juice. How many pints of fruit juice does the can contain?A 12 ptB 3 pt C 1 1/2 ptD 1/3 pt
In order to convert from fluid ounce to pint, we need to know that 16 fluid ounces is equivalent to 1 pint.
Then, to find how many pints is 24 fluid ounces, we can use a rule of three:
[tex]\begin{gathered} 16\text{ fluid ounces}\to1\text{ pint} \\ 24\text{ fluid ounces}\to x\text{ pints} \\ \\ \frac{16}{24}=\frac{1}{x} \\ x=\frac{24}{16}=\frac{3}{2}=1\frac{1}{2} \end{gathered}[/tex]So 24 fluid ounces is equivalent to 1 1/2 pints, therefore the correct answer is C.
Write the equation for a circle with the following informationcenter: (5,-3) radius: 7
Step 1: Problem
To determine the equation of a circle with centre (5, -3) and radius 7
Step 2: Substitute the centre value and radius to the equation
[tex]\begin{gathered} \text{Equation of a circle} \\ (x-a)^2+(y-b)^2=r^2 \\ \text{centre (5,-3) , radius =7} \\ a=5,\text{ b=-3, r=7} \\ (x-5)^2+(y-(-3))^2=7^2 \end{gathered}[/tex]Step 3: Simplify the above equation
[tex]\begin{gathered} (x-5)(x-5)\text{ + (y+3)(y+3) = 49} \\ x^2-5x-5x+25+y^2+3y+3y+9=49 \\ x^2-10x+25+y^2+6y+9=49 \\ x^2+y^2-10x+6y=49-25-9 \\ x^2+y^2-10x+6y=15 \\ x^2+y^2-10x+6y-15=0 \end{gathered}[/tex]Hence the equation of the circle is
[tex]x^2+y^2-10x+6y-15=0[/tex]