Answer:
y = |x -4|
Step-by-step explanation:
You want the new function after the absolute value function is moved 4 units to the right.
Horizontal translationWhen the function f(x) is translated to the right by h units, the new function is f(x -h).
ApplicationWhen the function ...
y = |x|
is translated right 4 units, the new function is ...
y = |x -4| . . . . . . . x is replaced by x-4.
Pls help answer fast rapidly is of khan academy:
Answer:
expanded: 7+0.08
standard: 7.08
Step-by-step explanation:
The hundredths place is the second digit after the decimal, so 8 hundredths is 0.08.
Solve for x
2 1/2x - 3/4 ( 2x + 5 ) = 3/8
Please explain step by step on how I get this answer to solve x!
Answer:
4 [tex]\frac{1}{8}[/tex]
Step-by-step explanation:
How do you prove a trapezoid is isosceles?
Answer:
A trapezoid is isosceles if and only if its diagonals are congruent. So if we can prove that the bases are parallel and the diagonals are congruent, then we know the quadrilateral is an isosceles trapezoid, as Cool Math accurately states.
Step-by-step explanation:
←
Diana has available 280 yards of fencing and wishes to enclose a rectangular area.
(a) Express the area A of the rectangle as a function of the width W of the rectangle.
(b) For what value of W is the area largest?
(c) What is the maximum area?
Answer:
(a) A = W(140 -W)
(b) W = 70
(c) 4900 square yards
Step-by-step explanation:
You want an expression for the rectangular area that can be enclosed by 280 yards of fence, if that area has width W. Further, you want the value of W that maximizes the area, and the size of that maximum area.
Perimeter expressionThe perimeter of the rectangle with length L and width W is ...
P = 2(L +W)
Then the length can be found from the width as ...
L = P/2 -W
For P=280, this is ...
L = 140 -W
(a) Area expressionThe area is the product of length and width:
A = LW
A = (140 -W)(W)
(b) Maximum areaThe area expression describes a downward-opening parabola with zeros at W=0 and W=140. The vertex (maximum) of the parabola is on the line of symmetry, halfway between these zeros. The value of W there is ...
W = (0 +140)/2 = 70
The area is largest for W = 70.
(c) AreaFor that value of W, the area is ...
A = (140 -70)(70) = 70² = 4900 . . . . . square yards
__
Additional comment
The generic solution to the area problem when fence is on all sides is that the shape is a square.
If the cost of fence is different for the different sides, the total cost in the east-west direction is equal to the total cost in the north-south direction when cost is minimized.
Can you prove triangle congruence by Asa?
Based on the concept of ASA, when two angles and the included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent.
Congruent triangle:
Congruent triangle means all three corresponding sides are equal and all the three corresponding angles are equal in measure.
Given,
Here we need to prove that triangle congruence by ASA.
In order to prove this one, we have to know that definition of ASA,
ASA also known as Angle-side-angle is a rule used to prove whether a given set of triangles are congruent.
In geometry, ASA rule states that "If two angles and the included side of one triangle are equal to two angles and included side of another triangle, then the triangles are congruent."
When we compare the given triangle to this rule then we clearly identify whether the triangle is congruent or not.
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tic is an isosceles triangle with a vertex angle i if the measure of i90
Applying the definition of an Isosceles triangle, given that isosceles triangle TIC has a vertex angle I of 90 degrees, the measure of angle T is 45 degrees.
In geometry, an isosceles triangle is a triangle that has at least two sides of equal length. Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal length, the latter version thus including the equilateral triangle as a special case. Examples of isosceles triangles include the isosceles right triangle, the golden triangle, and the faces of bipyramids and certain Catalan solids.
The two equal sides are called the legs and the third side is called the base of the triangle. The other dimensions of the triangle, such as its height, area, and perimeter, can be calculated by simple formulas from the lengths of the legs and base. Every isosceles triangle has an axis of symmetry along the perpendicular bisector of its base. The two angles opposite the legs are equal and are always acute, so the classification of the triangle as acute, right, or obtuse depends only on the angle between its two legs.
An Isosceles triangle has a vertex angle and two equal base angles.
Given that triangle TIC is an isosceles triangle:
angle I is the vertex angle = 90 degrees
angle T is a base angle
angle C is also a base angle
Thus:
angle C and angle T are congruent or equal to each other.
Therefore,
Angle T = (180 - 90)/2
⇒ Angle T = 90/2
⇒ Angle T = 45 degrees.
applying the definition of an isosceles triangle, given that isosceles triangle TIC has a vertex angle I of 90 degrees, the measure of angle T is 45 degrees.
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12. A factory needs to package 2,835 cartons
of orange juice in boxes. How many
more small boxes than large boxes are
needed to package the cartons of orange
juice?
Box Size
Small 15 number of cartons
Large. 35 number of cartons
The total number of cartons needed more to pack small 15 cartons than 35 large cartons is108 cartons.
What is the number of cartons needed?Division is defined as one of the four basic operations of arithmetic in mathematics.
The parameters for this question are:
Total number of cartons =2835
Number of small cartons needed = 15 cartons
Number of large cartons needed = 35 cartons
To package the orange juice in large cartons we need [tex]\frac{2835}{35} =81 cartons[/tex]
Also, to package 15 small cartons we need [tex]\frac{2835}{15} =189 cartons[/tex]
Number of more small cartons than large cartons is
Small cartons -large cartons
=189-81=108 more cartons.
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Does an isosceles triangle have 3 acute angles?
Answer:
some do but not all
Step-by-step explanation:
some do but there is a right isosceles triangle where there is 45 45 and 90 degrees
hopes this helps please mark brainliest
Is a cubic graph exponential?
Yes, a cubic graph is an exponential.
What is Cubic Graph?
A cubic graph in the study of graph theory is a graph with all of its vertices having degree three. A cubic graph is a 3-regular graph, to put it another way. Trivalent graphs are another name for cubic graphs. A cubic bipartite graph is known as a bicubic graph.
What is Exponential?
The mathematical expression f(x)=exp or ex denotes the exponential function. Unless otherwise stated, the phrase usually refers to the positive-valued function of a real variable, though it can also be applied to complex numbers or extrapolated to other mathematical objects like matrices or Lie algebras.
Graphs of Exponential Functions if;
When the base is greater than 1, the exponential function has the following characteristics and you can easly understand from this :
The point is traversed by the graph (0,1)The domain only uses actual integers.It is between y>0.The graph is going up.The graph approaches negative infinity and becomes asymptotic to the x-axis.As x gets closer to positive infinity, the graph grows without bound.The chart is non-stop.The graph is rounded.Learn more about cubic graph exponential click here:
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Round 0.799 to the nearest hundredth
Answer:
0.80
Step-by-step explanation:
The hundredth is 2 digits after the decimal.
Rounding 0.799, we want 0.xx
Look at the third digit, 9, meaning we round up.
However, since the second digit after the decimal is also a 9, we can make that a 0 by adding 1 to the first digit after the decimal.
We get 0.80
what is the equation of yx3 with the given transformations vertical compression by a factor of 17
The transformed equation of is y = x³ is y =-1/7(x+8)³
Given that :
The equation of y=x^3 and Vertical compression by a factor of 1/7 ,horizontal shift 8 units to the left, reflection across the x axis
Applying the given transformations, we have:
To have a vertical compression by a factor of 1/7, we need to multiply the function by 1/7. So, we have:
y=1/7x³
We must add 8 to x in order to have a horizontal shift of 8 units to the left. We thus have:
y=1/7(x+8)³
A reflection over the x-axis would be the final step, we need to multiply the function by −1. So, we have:
y= -1/7(x+8)³
Therefore, the transformed equation is y= -1/7(x+8)³
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is x^2+x+1=0 linear?
Answer:
No.
Step-by-step explanation:
Because the equation has an exponent, it is quadratic, and not linear.
Answer:1
Step-by-step explanation:
david performed the following mathematical operation
1 must be the root of the polynomial [tex]$3 x^2+x-4$[/tex].
We are given that polynomial [tex]$3 x^2+x-4$[/tex] is being divided by factor [tex]$(\mathrm{x}-1)$[/tex]
It is also said that when David perform the mathematical operation it gives remainder 0 .
Remainder 0 represents that divisor [tex]$(\mathrm{x}-1)$[/tex] is a factor polynomial [tex]$3 x^2+x-4$[/tex].
As x-1 is a factor of the given ploynomial, we can get one of the root of by setting it equal to 0 and solve for x.
Therefore,
x-1=0
Adding 1 on both sides, we get
[tex]$$\begin{aligned}& x-1+1=0+1 \\& x=1 .\end{aligned}$$[/tex]
Therefore, 1 must be the root of the polynomial [tex]$3 x^2+x-4$[/tex].
Polynomials are sums of terms of the form k⋅xⁿ, where k is any number and n is a positive integer. For example, 3x+2x-5 is a polynomial. Introduction to polynomials. This video covers common terminology like terms, degree, standard form, monomial, binomial and trinomial.
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find the inverse of the function fx 2x 4
The inverse function of the function f(x) = 2x - 4 will be x/2 +2.
What is inverse function?
A function that returns the initial value for which a function has produced output is called an inverse function. If f(x) is a function that produces the value y, then f-1(y), which is the inverse function of y, will produce the value x. Inverse and reciprocal functions should not be confused. The output's original value is returned by the function's inverse, which is represented by the symbol f-1 (x). While the reciprocal of a function is represented by 1/f(x) or f(x)-1
Those that do are referred to as invertible. For a function f: X Y to have an inverse, it must possess the characteristic that there is exactly one x in X such that f(x) = y for every y in Y. This characteristic guarantees the existence of a function g: Y X that has the required connection to f.
f(x) = 2x - 4
y = 2x - 4
So x = y +4 /2
x = y/2 +2
Now to get the inverse of the function put the x value in y
So [tex]f^{-1}[/tex](x) = x/2 +2
Hence, inverse function will be x/2 +2.
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A ball is dropped from a height of 20 feet. Each time the ball bounces it returns to 7/9 of the height it fell from. Let an represent the maximum height of the ball on the nth bounce.
A) Find a formula that describes an. Express the common ratio as a fraction. Hint: Use an = a1r^n-1 and place r in parentheses!
an = _____________
B) What is the maximum height of the ball on the 6th bounce? Round your answer to three decimal places.
_______________ feet
(A) The formula for nth bounce is [tex]a_n = 20 (7/9)^{n}[/tex].
(B) 4.43 feet is the maximum height of the ball on the 6th bounce.
What is an algebraic expression?An algebraic expression is consists of variables, numbers with various mathematical operations,
Given that,
The height from where the ball is dropped = 20 feet.
Also, the ball bounces and returns to 7/9 to its original height.
(A)
The representation of the maximum height of the ball on the nth bounce can be given as
[tex]a_n = 20 (7/9)^{n}[/tex]
(B)
The maximum height of the ball on the 6th bounce = 20 (7/9)⁶ = 4.43 feet
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A college student has budgeted $25 a month for phone services. If the telephone
company charges $17 a month for basic service and $0.05 a minute for each long
distance call, how many minutes can be spent on long distance calls each month?
(Define a variable, create an equation, solve using algebra, and answer in a sentence.)
Answer:
160 minutes can be spent on long distance calls each month.
Step-by-step explanation:
first we know that there is standard charge of $17 for basic service, $0.05 cost per minute with a budget of $25.
let's write that into an equation to solve for (a) which will be number of minutes.
17 + a(0.05) = 25
solving:
17 + a(0.05) = 25
carry across the 17 whilst changing the sign, or some people is also thought to minus on both sides to get rid of a certain variable.
a(0.05) = 25 - 17
a(0.05) = 8
carry across the multiplication of 0.05 which will then turn into division, or divide by 0.05 on both sides to remove it.
[tex]a = \frac{8}{0.05} [/tex]
a = 160
therefore 160 minutes can be spent on long distance calls each month.
You can redefine your answer more simply to hours by dividing by 60, which gives 2 hours and 40 minutes
A line with a slope of 1 passes through the point (5, 3). What is its equation in slope "-intercept" form?
Answer: y=x−2 y = x − 2
Step-by-step explanation:
Write this ratio as a fraction in simplest form without any units.
Answer:
change 5 weeks to days(5*7)-35days
then convert the days to seconds
35*86400/10*86400
answer 7/2
Find the value of x. Then find the measure of each angle and write the answers in ascending order.
The value of x and the unknown angles of the triangle are as follows;
x = 1180 degrees117 degreesHow to find angles in a triangle?The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle.
Therefore, let's find the value of x using the exterior angle theorem.
Hence,
37 + 3x + 47 = 5x + 62
3x - 5x + 37 + 47 = 62
-2x = 62 - 37 - 47
-2x = -22
x = -22 / -2
x = 11
Therefore, the angles are as follows:
3x + 47 = 3(11) + 47 = 33 + 47 = 80 degrees
5x + 62 = 5(11) + 62 = 55 + 62 = 117 degrees
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One integer is 2 times another. If the product of the two integers is 32, then find the integers
Answer:
The integers could be 8 and 4, just checked with a calculator
Write the following using algebraic notation, using the letter x for any unknown numbers:
I think of a number, multiply it by two, then subtract nine.
Answer:
2x - 9
Step-by-step explanation:
x = unknown number
2 * x -9
2x - 9
CAN SOMEONE HELP WITH THIS QUESTION?✨
The equation that models the function is P(t) = 20400(1,09)⁺ and the fox population in 2008 is 40648
The equation of the functionFrom the question, we have the following parameters that can be used in our computation:
Initial population of fox = 20400
Rate of growth = 9 percent per year
These parameters can be presented as
Initial population of fox, a = 20400
Rate of growth, r = 9%
An exponential function is represented as
P(t) = a(1 + r)⁺
So, we have:
P(t) = 20400(1 + 9%)⁺
Evaluate
P(t) = 20400(1,09)⁺
The population in 2008Recall that
t = 0 in 2000
So, the value of t in 2008 is
t = 2008 - 2000
t = 8
Substitute t = 8 in P(t) = 20400(1,09)⁺
So, we have
P(8) = 20400(1.09)⁸
Evaluate
P(8) = 40648
So, the population is 40648
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Nathan is building a toolshed with a rectangular floor. The area of a rectangle is given by the formula 1 w, where I represents
the length, and w represents the width. The floor of the shed will have measurements of either / = 9 and w =
= 7 or/= 8 and
w = 8. What is the area of the larger floor?
O63
O 64
O 56
O 72
The area of the larger floor is 64 square units when w = 8 and l = 8. which is the correct answer would be an option (B).
To compare the values, we must first calculate each given situation. The area of any given rectangle is length times width.
If w = 7 and l = 9
A = l × w = 8 × 6 = 48
If w = 8 and l = 8
A = l × w = 8 × 8 = 64
So, the second case would obtain a larger area.
Therefore, the area of the larger floor is 64 square units when w = 8 and l = 8.
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How do you find the degree of a polynomial in precalculus?
Answer:
add up the exponents of each term and select the highest sum.
A toy maker is putting multicolored sand in transparent cubes. Each cube measures 10 millimeters on each side. A coworker remarks that, for the cubes to be completely filled, each cube will need no more than 30 cubic millimeters of sand. Is the coworker correct? The coworker is correct. The volume of each cube is 20 cubic millimeters. The coworker is correct. The volume of each cube is 30 cubic millimeters. The coworker is not correct. The volume of each cube is 100 cubic millimeters. The coworker is not correct. The volume of each cube is 400 cubic millimeters. The coworker is not correct. The volume of each cube is 1,000 cubic millimeters.
The true statements are
The co-worker is not correct. The volume of each cube is 1,000 cubic millimetresHow to determine the true statement about the volume?The side length of the transparent cube is given as
Length = 10 millimetres
The volume of the cube is calculated as
Volume = Length³
Substitute the known values in the above equation, so, we have the following representation
Volume =10³
Evaluate
Volume = 1000 cubic millimetres
1000 cubic millimetres and 30 cubic millimetres do not have the same value
So, the co-worker is incorrect.
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Joseph has $1.45 worth of nickels and dimes. He has a total of 17 nickels and dimes altogether. Determine the number of nickels and the number of dimes that Joseph has.
The number of nickels and the number of dimes that Joseph has are 12 and 5 respectively.
What is a linear equation?An equation of degree one is known as a linear equation.
A linear equation of two variables can be represented by ax + by = c.
Let the no. of nickels be N and no. of dimes be D.
∴ N + D = 17...(i) and 0.05N + 0.1D = 1.45...(ii)
Multiplying (ii) by 100 we get 5N + 10D = 145...(iii)
Now multiply (i) by 5 we get 5N + 5D = 85...(iv)
Now subtracting (iv) from (iii) we get,
5D = 60.
D = 12 hence N = 5.
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What is a paragraph proof of Theorem 3 8?
We prooved the paragraph proof of Theorem 3.8 that if two lines are perpendicular to the same line, then they are parallel to each other.
In the given question we have to explain the a paragraph proof of Theorem 3.8.
Let the lines that cross line a be m and n. Let m be parallel to a. As a result, the intersection of m and a produces four 90° angles.
Let n be parallel to a. This indicates that each of the four angles created by the intersection of n and an is 90 degrees.
The same-side internal angles (between lines m and n) are also congruent because all of the angles are congruent. The lines are parallel if two internal angles on the same side are congruent.
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The right question is:
Write a paragraph proof of theorem 3-8: in a plane, if two lines are perpendicular to the same line, then they are parallel to each other.
Before painting a picture on canvas, an artist must stretch the canvas on a rectangular wooden frame. To be sure the angles are true right angles, the artist can measure the diagonals of the stretched canvas. What should be the diagonal measure of a canvas whose sides are 12 inches and 16 inches in length?
The diagonal measure of a canvas whose sides are 12 inches and 16 inches in length is 20 inches.
How can this be calculated?The Pythagorean theorem can be used in the solving of the question since the square of the diagonal can be regarded as the sum of the squares of the sides:
Pythagorean theorem can as well be regarded as one that have fundamental relation in Euclidean geometry between the three sides of a right triangle.
The sides are be given as : 12 inches and 16 inches in length
Then this can be expressed as ;
d^2 = (16^2 +12^2 )
= 256 +144 = 400
d = √400 = 20
Therefore the diagonal measure is 20 inches.
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Ted is not particularly creative. He uses the pickup line ""If I could rearrange the alphabet, I'd put U and I together."" The random variable x is the number of women Ted approaches before encountering one who reacts positively. Determine whether a probability distribution is given. If a probability distribution is given, find its mean and standard deviation. If a probability distribution is not given, identify the requirements that are not satisfied.
Does the table show a probability distribution? Select all that apply.
A. Yes, the table shows a probability distribution.
B. No, the sum of all the probabilities is not equal to 1 .
C. No, the random variable x is categorical instead of numerical.
D. No, the random variable X 's number values are not associated with probabilities.
E. No, not every probability is between 0 and 1 inclusive.
Option B, The table does not show a probability distribution. the sum of all the probabilities is not equal to 1 .
What is a probability distribution?A statistical function called a probability distribution explains the range of values and probabilities that a random variable might have. A statistical function known as a probability distribution explains the possibility of obtaining each potential value that a random variable can have.
The sum of the values is given as 0.001 + 0.008 + 0.034 + 0.057
= 0.1
Due to the fact that this is not a probability distribution.
We must choose the standard deviation as well. There is no probability distribution displayed in the table. These exist because sum = 1, which is not present here, is required for a probability distribution.
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A rectangular yard measuring 40 ft by 70 ft is bordered (and surrounded) by a fence. Inside, a walk that is 4 ft wide goes all the way along the fence. Find the area of this walk. Be sure to include the correct unit in your answer.
The area of the path is 456 square feet
How to determine the areaThe formula for determining area of a rectangle is given as;
A = lw
Where;
l is the length of the rectanglew is the width of the rectangleNow, substitute the values into the formula, we have;
Area of the rectangle = 40 × 70
Area of the rectangle = 2800 square feet (1)
Bordered fence with a 4 ft path so dimensions 44 ft by 74 ft
Area of rectangular garden with Path = 44 × 74
= 3256 square feet (2)
Area of the walk = (2) - (1) = 3256 - 2800 = 456 square feet
Hence, the value is 456 square feet
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