Step-by-step explanation:
The graph of the cube root parent function y = RootIndex 3 StartRoot x EndRoot is translated to form f(x) shown on the graph.
On a coordinate plane, a cube root function goes through (negative 7, 0), has an inflection point at (negative 6, 1), and goes through (2, 3).
Which equation represents f(x)?
f(x) = RootIndex 3 StartRoot x + 6 EndRoot + 1
f(x) = RootIndex 3 StartRoot x minus 6 EndRoot + 1
f(x) = RootIndex 3 StartRoot x + 6 EndRoot minus 1
f(x) = RootIndex 3 StartRoot x minus 6 EndRoot minus 1
Answer:
Step-by-step explanation:
The translation of the parent function is:
g(x) = ∛(x + 6) + 1
How do translations work?
There are two types of translations, these are:
Horizontal translation:
For a function f(x), a horizontal translation of N units is written as:
g(x) = f(x + N)
If N is positive, the translation is to the left.
If N is negative, the translation is to the right.
Vertical translation:
For a function f(x), a vertical translation of N units is written as:
g(x) = f(x) + N
If N is positive the translation is upwards.
If N is negative the translation is downwards.
Here we start with the parent function:
f(x) = ∛x
And we apply two translations such that:
g(x) = ∛(x + a) + b
Such that:
g(-7) = 0
g(2) = 3
Then we have the system of equations:
∛(-7 + a) + b = 0
∛(2 + a) + b = 3
From the options, the only ones that make the first option true are:
g(x) = ∛(x + 6) + 1
Such that when evaluated in x = -7 we get:
g(-7) = ∛(-7 + 6) + 1 = ∛(-1) + 1 = 0
When evaluated in x = 2 it gives:
∛(2 + 6) + 1 = ∛(8) + 1 = 2+ 1 = 3
So the only option that meets these conditions is:
g(x) = ∛(x + 6) + 1
Which is a translation to the left of 6 units and up 1 unit.
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What is the length of each leg of the triangle below?
45°
90⁰
22
OA. 15
B. √22
C. 11
45°
D. 11/2
E. VIT
F. 1
Answer:
A. 15
Step-by-step explanation:
Hypotenuse = 22
Since the two angles other than the 90° are both
45° , it means that the two legs of the right triangle are of equal length.
So, (x)²+ (x)² = 22²
2x² = 22²
x² = 484/2
x² = 242
x = √242
x = 15.55
x ≈ 15
What is the value of 6¹?
6° = 1
6 = 6
6 = 36
6 = 216
A.220
B.240
C.864
D.1,296
Answer: D
Step-by-step explanation:
6^4 = 6 x 6 x 6 x 6 = 1,296
6^4 = 1,296
A tea shop owner is mixing a blend of two teas, one of which costs $6.50 per pound, the other costing $4.00 per pound. The owner wants to have 20 pounds of a mixture that will sell for $5.50 per pound. How much of each type of teach should be used?
Answer:
12 pounds of tea-1 and 8 pounds of tea-2 should be used.
Step-by-step explanation:
find the slope for the given equation: - 3x-5y=11
Answer:
K=-3/5
Step-by-step explanation:
y= -3x/5 - 11/5
PLEASE HELP
In a softball diamond, each of the bases, including home plate, are equidistant from each other. Although the name implies differently, a softball diamond is in the shape of a square. Given that the distance between the bases is unknown, determine an expression for the straight line distance between first and third bases.
So far I know that the equation is
x² + x² = c²
But i dont know how to simplify that
The expression for the distance from the 1st base to the 3rd base in terms of side length will be c=x√2
Given that the softball diamond is square in shape.
Let the side of the square i.e. distance between consecutive bases is x
The distance from the 1st base to the 3rd base creates the hypotenuse of a right triangle, where each side is equal to x i.e. x is the side length of the square formed by the baseball diamond.
Using the Pythagorean theorem we have:
x² +x²= c²,
where c is the distance from the 1st base to the 3rd base.
Combining similar terms gives us
2x²=c²
Taking the square root of both sides we have
√2x²= √c²
⇒x√2=c
⇒c=x√2
This is the expression for the distance from the 1st base to the 3rd base in terms of side length.
Therefore the expression for the distance from the 1st base to the 3rd base in terms of side length will be c=x√2.
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Parallel lines m and n are cut by a transversal t. Which pair of angles is a pair of alternate interior angles?
A. 2 and 5
B. 1 and 5
C. 4 and 6
D. 2 and 6
Step-by-step explanation:
2and5 is 7
1and 5 is 6
4and 6 is 10
2and 6is 8
Which of the following is the best buy?
a 6 oz box of rice for $0.90
a 12 oz box of rice for $1.93
a 16 oz bag of rice for $2.42
a 9 oz box of rice $1.25
The best buy is (d) a 9 oz box of rice $1.25
How to determine the best buy?The best buy is the product that has the least unit rate.
The unit rate is calculated as:
Unit = Price/Weight
So, we have:
Box 1:
Unit rate = $0.90/6 oz = $0.150 per oz
Box 2:
Unit rate = $1.93/12 oz = $0.161 per oz
Box 3:
Unit rate = $2.42/16 oz = $0.151 per oz
Box 4:
Unit rate = $1.25/9 oz = $0.139 per oz
The least unit price is $0.139 per oz for box 4
Hence, the best buy is (d) a 9 oz box of rice $1.25
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Find the acute x given that tan x=2sinx
The measure of the acute angle is 60 degrees
Trigonometry identityGiven the following trigonometry equation
tan x=2sinx
This can also be written as;
sinx/cosx=2sinx
Simplify to have:
1/cosx =2
2cosx = 1
cosx = 1/2
x = arccos(1/2)
x = 60 degrees
Hence the measure of the acute angle is 60 degrees
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Can someone tell me why this wrong please
Answer:
4,051,500
Step-by-step explanation:
You have 7.3 % that are one native one foreign
Multiply that by the number of households
.073 * 55,500,000
4,051,500
A survey asked 20 mobile phone dealers how many mobile phones were sold during the previous week. Their answers are displayed in the Box-and-Whisker Plot and the Stem-and-Leaf Plot shown. Which graph can be used to find the mean? What is the mean of the data set?
A. Stem-and-Leaf Plot, Mean: 41.95
B. Stem-and-Leaf Plot, Mean: 42.55
C. Box-and-Whisker Plot, Mean: 43.65
D. Box-and-Whisker Plot, Mean: 38.80
Answer:
= B
Step-by-step explanation:
1 If the population of a town increases by 280 people per year, then the growth is LINEAR (or constant). If the population in 2022 is 120,500, then what will the population be in 2023?
The population in the year 2023 is 120,780.
The growth is linear hence, the equation of the growth is
y=ax+b where b represents the initial population and a is the number of people growing yearly.
So, according to the question statement, we have that
y=280x+b where x is the number of years past and y is the population in the xth year.
According to the given problem population in 2022 will be 120,500.
Suppose that the initial population is taken at 2000.
Hence, 120,500=280×(2022-2000)+b
⇒b=120,500-280×22
⇒b=120,500-6,160
=114,340
So, the Linear equation becomes
y=280x+114,340
⇒y=280×(2023-2000)+114,340
⇒y=120,780
Hence, the population in the year 2023 is 120,780.
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A greedy hamster hoarded two piles of sunflower seeds. Yesterday the ratio of seeds in these piles was 3:4, but today the greedy hamster placed another 2 pounds of seeds in the bigger pile. He also ate 1/4 pound from the smaller pile and now the quantities of seeds in those piles is in the ratio of 5:16. What was the weight of each pile yesterday?
The weight of the each pile yesterday would be 6 and 8 pounds.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Given;
Yesterday the ratio of seeds in these piles was 3:4.
Let it be 3x and 4x.
If the 2 pounds of seeds is added in the bigger pile, then it become
4x + 2
He also ate 1/4 pound from the smaller pile, then
3x - 1/4
Now the quantities of seeds in those piles is in the ratio of 5:16.
So, 4x + 2 = 5x
3x - 1/4 = 16x
Solve;
So, 4x + 2 = 5x
2 = 5x - 4x
x = 2
The weight of the each pie would be
3x = 6 pound
4x = 8 pound
Hence, The weight of the each pile yesterday would be 6 and 8 pounds.
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the stream frontage is 800 feet in length and the property line is 3900 feet in length
The lot has an area of about ___ acres
Using the Pythagorean Theorem, it is found that the lot has an area of about 35 acres.
What is the Pythagorean Theorem?The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, according to the following equation:
[tex]h^2 = l_1^2 + l_2^2[/tex]
Researching the problem on the internet, the lot has one leg of 800 feet and the hypotenuse is of 3900 feet, hence the other leg is found as follows:
[tex]800^2 + l^2 = 3900^2[/tex]
[tex]l = \sqrt{3900^2 - 800^2}[/tex]
l = 3817 feet.
What is the area of a right triangle?The area of a right triangle is given by half the multiplication of it's legs. Hence, the area of the lot, in square feet, is given by:
A = 0.5 x 800 x 3817 = 1,526,800 square feet.
Each square feet is equivalent to 0.000029568 acres, hence the area in acres is given by:
Aa = 0.000029568 x 1,526,800 = 35 acres.
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Please help! I don't know how to do slopes.
The slope of the given line in the image is -4 , Option A is the answer.
What is the equation of a straight line ?The equation of the straight line is given by
y =mx +c ,
Where m is the slope , C is the intercept
The line is passing through the point
(-1,8) ,(2,-4)
The slope is given by
m = (y₂-y₁) /(x₂-x₁)
m = (-4 - 8 )/(2 +1)
m = -12/3
m = -4
Therefore the slope of the given line in the image is -4 , Option A is the answer.
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The graph shows a relationship between x and y.
What are the zeros of the function?
Answer:
x = -3
x = -1
x = 2
Step-by-step explanation:
The zeros of a function are the x-values of the points at which the curve crosses the x-axis.
From inspection of the given graph, the curve crosses the x-axis at:
x = -3x = -1x = 2Therefore, these are the zeros of the function.
Generalize A system of linear equations has exactly one solution. What can you say about the slopes of the lines when the equations are graphed? How do you know? Generalize A system of linear equations has exactly one solution . What can you say about the slopes of the lines when the equations are graphed ? How do you know ?
If a system of linear equations has exactly one solution then the slopes of both the lines should be different.
Given A system of linear equations has exactly one solution.
Linear equation is a type of equation when when plotted on the graph gives a straight line. The slope is the ratio of the vertical change to the horizontal change between two distinct points on a line.
let two equations be who have one solution
2x+3y=7
5x+6y=1
solving them
x=7-3y/2
put the value of x in second equation
5(7-3y)/2+6y=1
35-15y/2+6y=1
35-15y+12y=2
-3y=-33
y=11
put the value of y in x=7-3y/2
x=7-3*11/2
x=7-33/2
x=-26/2
x=-13.
There is only one solution which is (-13,11)
Taking equations and convert them into standard form
first
y=7/3-2/3x
second
y=1/6-5/6x
The standard form is y=a+bx where b is slope
from the above equations we can find that the slope of first equation is -2/3 and the slope of second equation is -5/6. In this way we are able to conclude that slopes should be different for one solution.
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5m³ into cm³
Show the answer step by step
Answer: So you want to convert 5 cubic meters into cubic centimeters? If you're in a rush and just need the answer, the calculator below is all you need. The answer is 5000000 cubic centimeters.
Step-by-step explanation:
Two dice are rolled. What is the probability of getting a sum equals 5?
Probability = (Round to 4 decimal places)
A study of the amount of time it takes a mechanic to rebuild the transmission for a 1992 Chevrolet Cavalier shows that the mean is 8.4 hours and the standard deviation is 1.77 hours. Assume that a random sample of 40 mechanics is selected and the mean rebuild time of the sample is computed. Assuming the rebuilding times are normally distributed, what percentage of sample means are greater than 8.8 hours? Express your answer as a percent rounded to hundredths of a percent.
Answer:
40.9 %
Step-by-step explanation:
8.8 is .4 hours above the mean this is .4/1.77 = .226 standard deviations above the mean
Using z-score table this corresponds to ~ .5910 (59.10%)
this percentage is LESS than 8.8 hours
the percentage ABOVE this is 40.9%
(Not asked, but this is 40.9 (40 ) = ~ 16 of the 40 mechanics sampled)
Isabella is making a scrapbook each page of the scrapbook is a square with a length of 11 in if each page holds three pictures that each have an area of 15 in squared what is the remaining area on each page and square inches that can be used for decoration
The remaining area of the page will be 80 square inches.
The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the square in a two-dimensional plane is called the area of the square.
The area of the remaining part will be calculated as;-
Area of the square page will be = 11 x 11 = 121 square inches.
Area of three pictures will be = 15 x 3 = 45 square inches.
So the remaining area will be = 121 - 45 = 80 square inches.
Therefore the remaining area of the page will be 80 square inches.
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can someone please help me
Answer: C
Step-by-step explanation:
The slope is positive, so m>0.
The y-intercept is negative, so b<0.
Drag each tile to the correct box.
Using the order of operations, what are the steps for solving this expression?
Step-by-step explanation/Answer:
PE(MD)(AS) (a good way to remember how to solve order of operations)
Start:
P: Parenthesis
E: Exponent
M: Multiplication & D: Division
A: Addition & S: Subtraction
:End
*Multiplication and Division are grouped together because they are on the same level, you decide which to do first depending on which comes first in the equation. The same applies for addition and subtraction.
So:
first thing we can look is the parenthesis, but before we can solve the whole thing we must notice the exponent only on the four. Since it is inside the parenthesis we must solve it first.
1. 4^2 = 16
now we will solve the addition inside the parenthesis
2. 16-13 = 3
now lets continue with pemdas, no more parenthesis so we tackle exponents
3. 5^2 = 25
Lets rewrite our equation with the changes we have made
8 × 3 ÷ 3 + 25 + 4 × 3
Now we solve multiplication and division
Equations is worked left to right, like english is read, so we will start on the left side and continue to the right, only solving multiplication and division.
4. 8 x 3 = 24
5. 24 ÷ 3 = 8
6. 4 x 3 = 12
new equation: 8 + 25 + 12
now we can use addition and subtraction (no subtraction luckily!)
7. 8 + 25 = 33
8. 33 + 12 = 45
Sam wants to measure the height of a tree. She walks 100 feet from the base of the tree and looks up. The angle of elevation from the ground to the top of the tree is 33°. How tall is the tree? Round your answer to the nearest hundredth.
The height of the tree from which Sam is standing 100 feet away from the base is 64.94 feet.
What is angle of elevation?The angle of elevation is an angle that is formed between the horizontal line and the line of sight.
To calculate the height of the tree , we use the formula below.
Formula:
tan∅ = H/B.............Equation 1Where:
∅ = Angle of elevation from the ground to the top of the treeH = Height of the treeB = Distance of the base of the tree to the point where Sam looks upFrom the question,
Given:
∅ = 33°B = 100 feetSubstitute these values into equation 1 and solve for H
tan33° = H/100H = tan33°×100H = 64.94 feetHence, the height of the tree is 64.94 feet.
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Math Problem...can you help? (Functions)
Step-by-step explanation:
[tex]h(x) = \frac{3}{x}\\h(h(x)) = \frac{3}{\frac{3}{x}}\\\\h(h(x)) = \frac{3}{1} * \frac{x}{3}\\h(h(x)) = \frac{3x}{3}\\h(h(x)) = x\\\\\\f(f(x)) = (x^2-3)^2-3\\f(f(x)) = x^4+2(x^2)(-3)+(-3)^2-3\\f(f(x)) =x^4-6x^2+9-3\\f(f(x)) = x^4-6x^2+6\\[/tex]
in need of assistance
Answer:
60
Step-by-step explanation:
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It is 6 kilometers from Linda's house to the nearest mailbox. How far is it in meters?
Answer:
6000 meters
Step-by-step explanation:
Each kilometer is 1000 meters so 1000 x 6 is 6000
22. A 1 m high pole is fixed vertically on the ground at a point 50√3 m far from the foot of a building. If the angle of elevation from the top of the pole to the top of the building is 30°, what is the height of the building? A. 150 m B. 51 m C. 151 m D. 50m
Answer:
This is my answer↓:
Step-by-step explanation:
A company finds that there is a linear relationship between the amount of money that it spends on advertising and the number of units it sells. If it spends no money on advertising, it sells 250 units. For each additional $4000 spent, an additional 25 units are sold. If x is the amount of money that the company spends on advertising, find a formula for y, the number of units sold as a function of x.
The formula for the equation of y, the number of units sold as a function of x is y = 0.00625x + 250
How to illustrate the equation?From the information given, when the company spends no money on advertising, it sells 250 units and for each additional $4000 spent, an additional 25 units are sold.
The formula for y will be:
y = (25/4000)x + 250
y = 0.00625x + 250
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Match the scatter plot with its description
weak and positive
moderate and negative
strong and negative
strong and positive
weak and negative
moderate and positive
good morning i need help very fast
Step-by-step explanation:
all the details You can find in the attachment.
