The formula for the function obtained when the graph is shifted is f(x)=(x+7)^3+3.
How do we make graph of a function?Suppose the considered function whose graph is to be made is function f(x). The values of 'x' (also called input variable, or independent variable) are usually plotted on horizontal axis, and the output values f(x) are plotted on the vertical axis.
They are together plotted on the point
(x,y) = (x, f(x))
This is why we usually write the functions as:
y = f(x)
Given;
f(x)=x^3 is shifted up 3 unit and to the left 7 units.
Now,
To shift upwards, we will add outside of the argument
To shift to the left, we will add inside of the argument
Therefore, the function will be f(x)=(x+7)^3+3
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Can you help me with this?
The vertices of triangle J'K'L' after a reflection of the triangle JKL over the x-axis is given as follows:
J'(-5, -5).K'(5, -7).L'(2,-3).How to model the reflection over the x-axis?The original vertices of the figure are given as follows:
J(-5,5), K(5,7) and L(2,3).
For a reflection over the x-axis, the reflection rule is defined as follows:
(x,y) -> (x,-y).
Meaning that the x-coordinate remains constant while the y-coordinate has the sign exchanged.
Then the vertices of the reflected figure are given as follows:
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5 divided by 206 Using long division
Solution is in the attachment!!
Correct
The perimeter of a square must be greater than 96 inches but less than 124 inches. Find the range of possible side lengths that satisfy these conditions. (Hint: The
perimeter of a square is given by P= 4s, where a represents the length of a side).
Express your answer in interval notation. Use decimal form for numerical values.
The range of the side of the square is 24 to 31. The interval notation is (24,31).
What is interval notation?
An interval on a number line can be represented using interval notation. It is a method of representing subsets of the real number line, in other words.
Given that, the perimeter of a square must be greater than 96 inches but less than 124 inches.
Inequality form is
96 < P < 124
Where P is the perimeter.
The perimeter of a square is P = 4s, where s is the length of the side.
Putting P = 4s in 96 < P < 124
96 < 4s < 124
Divide by 4:
24 < s < 31
The interval notation is (24,31).
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PLEASE HELP!!
solve the inequality
a. x > 8 and < -4
b. x > -30 and x < 2
c. x < -30 and x < 18
d. x > -30 and x < 18
The absolute inequality 3/4 * |(1/3)x + 2| < 6 has a solution of (d) x > -30 and x < 18
How to determine the solution to the inequalityTo solve the inequality, we'll start by isolating the absolute value expression on one side of the inequality.
3/4 * |(1/3)x + 2| < 6
We'll first distribute the 3/4 across the absolute value:
|(1/3)x + 2| < 8
To simplify this, we'll split the inequality into two cases:
(1/3)x + 2 < 8
(1/3)x + 2 > -8
First, let's consider the case where (1/3)x + 2 < 8
(1/3)x < 6
x < 18
Now let's consider the case where (1/3)x + 2 > -8
(1/3)x > -10
x > -30
So, the solution set is x > -30 and x < 18
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Complete question
Solve the inequality three-fourths times the absolute value of the quantity one third times x plus 2 end quantity is less than 6. x > −8 and x < −4 x > −30 and x < 2 x < −30 and x < 18 x > −30 and x < 18
The number of eggs in the refrigerator e decreased by 3 equals 18. enter an equation to represent the situation
The situation can be described by the equation x - 3 = 13 = x = 13 + 3 = x = 16.
How Do Equations Work?A mathematical phrase with two equal sides and an equal sign is called an equation. An example of an equation is 4 + 6 = 10. 4 + 6 can be seen on the equal sign's left side, and 10 can be seen on the equal sign's right side. A relationship between two terms on either side of an equal sign is represented by a simple equation. The four mathematical operations of addition, subtraction, multiplication, and division are also used in simple equations, either singly or in combination.
no of egg is decreased e= x - 3
equation to represent the situation
x - 3 = 13
x = 13 + 3
x = 16
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Sally buys 5 dolls and 1 purse for $21.
Donna buys 7 dolls and 1  purse for 27$
Answer:
1. The unit price for a doll is three dollars. The unit price for a purse is six dollars.
2. One doll costs three. One purse costs six.
3. Polly spends $24 on the 2 dolls and 3 purses.
Step-by-step explanation:
Doing some calculations, 1 doll costs three dollars and 1 purse costs six dollars.
5 x 3 + 6 = 21
7 x 3 + 1 = 27
If Polly buys 2 dolls and 3 purses, that means she spends six dollars on the dolls and eighteen dollars on the purses.
(2 x 3) + (3 x 6) = $24
Polly spends $24 on 2 dolls and 3 purses.
Hope This Helps!The volume of a cone with radius r and height h is given by the 1 expression 3 -Tr^2h. Write an expression for the volume of a cone in terms of the height h if the radius is equal to one half the height.
Answer:If the radius of the cone is equal to one half the height, we can write the radius as r = h/2. Substituting this expression into the formula for the volume of a cone, we get:
V = 1/3 * (h/2)^2 * h = 1/3 * h^3 / 4
So, the volume of a cone in terms of the height, if the radius is equal to one half the height, is V = 1/3 * h^3 / 4.
Step-by-step explanation:
If the radius of the cone is equal to one half the height, we can write the radius as r = h/2. Substituting this expression into the formula for the volume of a cone, we get:
V = 1/3 * (h/2)^2 * h = 1/3 * h^3 / 4
So, the volume of a cone in terms of the height, if the radius is equal to one half the height, is V = 1/3 * h^3 / 4.
If v = 2i- ¡ and w = xi + 31, find all numbers * for which Iv + w= 5.
Answe
Step-by-step explanation:
answer is 9
1/2[(x+4)(x+7)] find the area
The area of the triangle in terms of 'x' will be (x² + 13x + 28) / 2.
What is the area of the triangle?Assume 'h' is the height of the triangle and 'b' be the base of the triangle. Then the area of the triangle is given as,
A = (1/2) × h·b
The area of the triangle is given as,
A = 1/2 [(x + 4)(x + 7)]
Simplify the equation, then we have
A = [(x + 4)(x + 7)] / 2
A = (x² + 7x + 4x + 28) / 2
A = (x² + 13x + 28) / 2
The area of the triangle in terms of 'x' will be (x² + 13x + 28) / 2.
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Solve for X round to the nearest tenth. Trigonometry For 2,3,5,6,9
The value of x are:
2) x = 18.87
3) x = 26.68
5) x = 35.52
6) x = 13.75
9) x = 3.69
What are trigonometric identities?There are three commonly used trigonometric identities.
Sin x = 1/ cosec x
Cos x = 1/ sec x
Tan x = 1/ cot x or sin x / cos x
Cot x = cos x / sin x
We have,
2)
Tan 48 = x / 17
1.11 = x / 17
x = 17 x 1.11
x = 18.87
3)
Sin 67 = x / 29
0.92 = x / 29
x = 0.92 x 29
x = 26.68
5)
Cos 16 = x / 37
0.96 = x / 37
x = 0.96 x 37
x = 35.52
6)
Tan 58 = 22/x
1.6 = 22 / x
x = 22/1.6
x = 13.75
9)
Sin 24 = x / 9
0.41 = x / 9
x = 0.41 x 9
x = 3.69
Thus,
The value of x is given above.
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For a moving object, the force acting on the object varies directly with the object's acceleration. When a force of 20 N acts on a certain object, the acceleration of the object is 5 /ms2. If the force is changed to 16 N, what will be the acceleration of the object? /ms2
The acceleration of the object when the force on the object changes to 16 N is 4 m/s²
What is the basic formula for force?The second law of motion by Newton says that the force is equal to the change in momentum per change in the time. For a constant mass, force equals the mass times acceleration, i.e. F = m x a.
Given here: A force acting on an object.
We know, The formula for force states that the force is equal to mass that is multiplied by the acceleration.
Thus we have the equation as F=m.a
Now in case 1 we have
20=m×5
m=4 kg
Again in case 2 we have
16 = 4×a
a=4 ms⁻²
Hence, The acceleration of the object when the force on the object changes to 16 N is 4 m/s²
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I am a number. If the area of each squer below is 4 squer unite. I am the perimeter ot the figure. What number I am
Calculate the volume of the cylinders.
Answer: 588π = 1846.32
Step-by-step explanation:
Volume of cylinder = πr²h
Volume = (7)²*12*π = 588π = 1846.32
At an educational district's office, three types of employee wages are incorporated into the budget specialists, managers, and directors. Employees of each type have the same salary across districts. One district employs five specialists, two managers, and a director with total annual budgeted salaries of $550,000
. Another district employs six specialists three managers, and two directors with an annual salary budget of $777,000
A third district has eight specialists, no managers, and two directors with an annual salary budget of $676,000
The salary of each of specialist, manager and director are $62,000, $75,000 and $90,000.
What are Linear Equations?Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.
Linear equations may include one or more variables.
Let x, y and z be the salary of specialist, manager and director respectively.
From the given information, we have three linear equations.
5x + 2y + z = 550,000
6x + 3y + 2z = 777,000
8x + 0y + 2z = 676,000
From the third equation,
2z = 676,000 - 8x
z = 338,000 - 4x
Substituting the value of z in the first equation,
5x + 2y + 338,000 - 4x = 550,000
x + 2y = 212,000
2y = 212,000 - x
y = 106,000 - (1/2) x
Substituting z = 338,000 - 4x and y = 106,000 - (1/2) x in the second equation 6x + 3y + 2z = 777,000,
6x + 3(106,000 - (1/2) x) + 2(338,000 - 4x) = 777,000
6x + 318,000 - (3/2)x + 676,000 - 8x = 777,000
(6x - 3/2 x - 8x) + (318,000 + 676,000) = 777,000
-(7/2) x = -217,000
x = 62,000
y = 106,000 - (1/2) x = 75,000
z = 338,000 - 4x = 90,000
Hence the salary of each specialist is $62,000, each manager is $75,000 and each director is $90,000.
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At the market,grapes cost 0.85 per pound.Clarissa buys grapes and pays a total of 2.55.How many pounds of grapes does she buy.
3 pounds of grapes she buy grapes in the market.
What is Division?A division is a process of splitting a specific amount into equal parts.
Given that each pound of grapes cost 0.85.
Clarissa buys grapes and pays a total of 2.55.
We have to find the number of pounds of grapes does she buy.
To find this we have to divide 2.55 by 0.85.
Two point five five by zero point eight five.
2.55/0.85
3 pounds of grapes.
Hence, 3 pounds of grapes she buy grapes in the market.
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Robert and Tony love to read. Robert reads 30 pages the first day and 20 pages each day after that. Tony reads 40 pages the first day and 15 pages each day after that. Which graph represents the total number of pages each has read after each day?
The solution graph is given in the attached image.
The solution is x = 2 and y = 70.
What is the system of equations?One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.
Given:
Robert and Tony love to read.
Robert reads 30 pages the first day and 20 pages each day after that.
Tony reads 40 pages the first day and 15 pages each day after that.
We have a system of equations,
y = 20x + 30
y = 15x + 40
Subtracting the equations, we get,
5x = 10
x = 2
And y = 70.
And the graph is given in the attached image.
Therefore, the solution is x = 2 and y = 70.
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A store specializing in mountain bikes is to open in one of 2 miles if the first mall selected the store anticipates a yearly profit of $300,000 if successful and yearly loss of $100,000 otherwise. The probability of success is 1/2 if the second most selected it is estimated that the yearly profit will be $200,000 if successful otherwise the annual loss will be $60,000. The probability of success at the second mall is 3/4 which mall should be chosen in order to maximize the expected profit?
The probability of success at the second mall is 3/4 which mall should be chosen in order to maximize the expected profit $135,000.
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
Given:
First mall:
Profit if successful = $300,000
Loss if otherwise = $100,000
Probability of success = 1/2
Second mall:
Profit if successful = $200,000
Loss if otherwise = $60,000
Probability of success = 3/4
If probability of profit 'P(profit)' = 3/4
Then,
Probability of loss P(loss) = 1 - P(profit)
P(loss) = 1 - 3/4 = 1/4
Expected profit:
= [P(profit) x profit] + [P(loss) x loss])
= (0.75 x $200,000) + (0.25 x (-$60,000))
= 150,000 - 15000
= $135,000
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What is x in this equation
Answer:
x = 3 rounded to the nearest whole number (actually 2.735)
Step-by-step explanation:
The triangle formed by the sides of length 7x, 12x and 32 form a right triangle with the side of length 32 as they hypotenuse
By the Pythagorean theorem
c² = a² + b² where c = hypotenuse, a and b being the other two sides
Plugging in values we get
38² = (7x)² + (12x)²
1,444 = 49x² + 144x² = 193x²
Switching sides:
193x² = 1444
x² = 1444/193 = 7.48
x = √7.48= 2.735 = 3 rounded to the nearest whole number
The measures of the exterior angles of a heptagon are
x°, 2x°, 3x°, 4x°, 5x°, 7x°, and 8x°.
Find the measure of the largest exterior angle.
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The measure of the largest exterior angle is 96°.
What is heptagon?Heptagon is a two-dimensional shape with seven angles, seven vertices, and seven edges. This seven-sided polygon “heptagon” is made up of two words ‘Hepta’ and ‘Gonia’, which means seven angles. Another name given to it is septagon or 7-gon.
In heptagon, the sum of the interior angles is equal to 900 degrees. The sum of exterior angles of a heptagon is 360 degrees.
Here, x°+2x°+3x°+4x°+5x°+7x°+8x°=360°
30x°=360°
x°=12°
So, 8x°= 96°
Therefore, the measure of the largest exterior angle is 96°.
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If you would like to make $2483 in 8 years, how much would you have to deposit in an account that pays simple interest of 8%? I really need help and would also seriously benefit if you could explain formula for it as well
Answer:
2483 in 8yrs means you multiply the two first
2483
× 8
_____
19864
so 8% of 19864
you have to divide the number by the percentage
o. 8÷ 19864= 2483
Two different workers are producing a specialized part for a machine. The number of parts produced per hour by the workers are as follows:
Worker A: 5, 4, 4, 6, 7, 5, 6, 3
Worker B: 4, 8, 1, 9, 2, 9, 4, 3
Both workers averaged 5 parts per hour. Which worker has the higher variance and standard deviation?
Worker B has the higher variance and standard deviation than Worker A.
What is standard deviation?Standard deviation in statistics, typically denoted by σ, is a measure of variation or dispersion (refers to a distribution's extent of stretching or squeezing) between values in a set of data. The lower the standard deviation, the closer the data points tend to be to the mean (or expected value), μ.
Given,
The number of parts produced per hour by the workers are as follows:
Worker A: 5, 4, 4, 6, 7, 5, 6, 3
Worker B: 4, 8, 1, 9, 2, 9, 4, 3
Average μ = 5
Variance = σ² = Σ(xi - μ)²/N
Variance for first worker
= [(5 - 5)² + (4 - 5)² + (4 - 5)² + (6 - 5)² + (7 - 5)² + (5 - 5)² + (6 - 5)² + (3 - 5)²]/8
= [0² + -1² + -1² + 1² + 2² + 0² + 1² + -2²]/8
= [1 + 1 + 1 + 4 + 1 + 4]/8
= 12/8
= 1.5
Standard deviation σ = √1.5
= 1.2247448713916
Variance for second worker
= [(4 - 5)² + (8 - 5)² + (1 - 5)² + (9 - 5)² + (2 - 5)² + (9 - 5)² + (4 - 5)² + (3 - 5)²]/8
= [-1² + 3² + -4² + 4² + -3² + 4² + -1² + -2²]/8
= [1 + 9 + 16 + 16 + 9 + 16 + 1 + 4]/8
= 72/8
= 9
Standard deviation σ = √9
= 3
Hence, Variance and Standard deviation of worker B are higher than worker A.
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What is the sum of the series sum from n equals 1 to infinity of negative 3 times three eighths to the n power question mark
negative nine fifths
nine fifths
negative nine eighths
nine elevenths
The solution is Option A.
The sum of the infinite geometric progression is S = -( 9/5 )
What is Geometric Progression?A geometric progression is a sequence in which each term is derived by multiplying or dividing the preceding term by a fixed number called the common ratio.
The nth term of a GP is aₙ = arⁿ⁻¹
The general form of a GP is a, ar, ar2, ar3 and so on
Sum of first n terms of a GP is Sₙ = a(rⁿ-1) / ( r - 1 )
Given data ,
Let the sum of the geometric progression be represented as S
Now , the equation will be
∑ n = 1 to ∝ ( -3 ( 3/8 )ⁿ ) be equation (1)
The sum of the infinite GP is S = a / ( 1 - r ) , where r is the common ratio
Substituting the values in the equation , we get
when n = 1
a₁ = -3 ( 3/8 )
a₁ = -9/8
when n = 2
a₂ = -3 ( 3/8 )²
a₂ = -27/64
So , the common ratio r = a₂ / a₁
The common ratio r = 3/8
Substituting the values in the equation , we get
The sum of the infinite GP is S = a / ( 1 - r )
The sum of the infinite GP is S = ( -9/8 ) / ( 1 - 3/8 )
The sum of the infinite GP is S = ( -9/8 ) / ( 5/8 )
The sum of the infinite GP is S = - ( 9/5 )
Hence , the sum of GP is - ( 9/5 )
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Find the possible formula for the linear function h(x) if h (-30) = 90 and h (20) = -160.
H(x) =
Answer:
The possible formula for the linear function h(x) is h(x) = -7x + 190. This can be determined by using the information from numerade.com, which states that the formula for a linear function is y = mx + b. Applying this formula to the given values of h(-30) = 90 and h(20) = -160 gives a formula of h(x) = -7x + 190.
Step-by-step explanation:
which number line shows the solution to the inequality -2x-3>-11
Answer:-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
Step-by-step explanation:
The movie Brayden and his friends went to see started at 2:05 P.M. and ended at
3:40 P.M. Use the number line to find how long the movie was.
Start
End
What is the sum of 5 of the interior angles of a regular octagon?
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The sum of 5 of the interior angles of a regular octagon is 675°.
What is interior angle?Angles inside a polygon are referred to as interior angles. A triangle, for instance, has three internal angles. Interior angles are sometimes defined as "angles confined in the interior area of two parallel lines when they are crossed by a transversal."
A regular octagon has equal interior angles.
And one interior angle is equal to 135°.
The sum of 5 of the interior angles of a regular octagon,
= 135 x 5
= 675°
Therefore, the sum is 675°.
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how do u count by 5's.
its 5,10,15,20,25,30,45,50,55,60,65,70,75,80,85,90,95,100!!!!
I hope this helps! BYEE!!!
Counting of numbers by 5's end with 0, 5, 0, 5, 0, .....
What is Counting?Counting in mathematics is defined as the process of finding the number of objects in a set which is finite.
Counting numbers are the natural numbers.
The question is how to count by 5's.
In order to count by 5's, we have to add 5 to each of the preceding number to get the next number.
So the pattern will be,
5, 10, 15, 20, 25, 30, 35, ........
So the numbers end either in 0 or 5.
Hence the pattern of counting by 5's are the numbers which ends in either 0 or 5.
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help pls .............................
a) The measure of angle 3 is given as follows: m < 3 = 3x + 105.
b) The value of x is given as follows: x = 10.
c) It is not possible for a triangle to have side lengths 5, 8 and 14, as the sum of the lengths of the two smaller sides would be less than the length of the larger side.
How to obtain the angle measures?The measure of angle 1 is given as follows:
m<1 = 3x + 15.
As the sum of the measures of the internal angles of a triangle is of 180º, and there is a right triangle, we have that angles 1 and 2 are complementary, hence:
m < 1 + m < 2 = 90
3x + 15 + m < 2 = 90
m < 2 = 75 - 3x.
An angle is always supplementary with it's exterior angle, hence the measure of angle 3 is obtained as follows:
m < 2 + m < 3 = 180
75 - 3x + m < 3 = 180
m < 3 = 180 - 75 + 3x
m < 3 = 3x + 105.
For an isosceles right triangle, the two non-right angles measure 45º, hence the value of x is obtained as follows:
3x + 15 = 45
3x = 30
x = 30/3
x = 10.
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Higher order thinking Akira asked 20 friends what their favorite
The circle graph for the given table is as mentioned.
What is circle graph?In graph theory, a circle graph is the intersection graph of a chord diagram. That is, it is an undirected graph whose vertices can be associated with a finite system of chords of a circle such that two vertices are adjacent if and only if the corresponding chords cross each other.
Given is a data as shown in the table.
The circle graph for the given table is attached with the answer.
Therefore, the circle graph for the given table is as mentioned.
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0.000549 in scientific notation
Answer: 5.49 × 10-4
Step-by-step explanation:
When you move the decimal over move it over to the right by 4 units.
When you move right it is (-) negative. So you get 5.49 x 10-4.