Amy studied 3- hours for her Biology test. She studied half as long for her math test as she did for her biology test. How long did she study for her math test?

For any given point, the transformation that occurs is

Transformations are mathematical operations that are performed on a function or object to change is shape or orientation or value.

The types of transformations that can be performed on an object or function include

Given the transformation rule (x,y) --> (x - 4, y + 8), we see that both the x and y coordinated are shifted or translated.

So, for any given point, the transformation that occurs is

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By solving the equations, We get

[tex](\frac{34}{31} ,\frac{10}{31} )[/tex]

A unique solution to a set of linear simultaneous equations exists if and only if,

(A) There are the same number of equations and unknowns.

(b) Each equation is valid.

(c) All equations are independent and there is no linear connection between any two or more equations.

Given:

[tex]2(3x+y)=y-x+8[/tex]

[tex]x-\frac{4}{3}\;y=\frac{2}{3}[/tex]

Solving the equations,

[tex]2(3x+y)=y-x+8[/tex]

[tex]6x+2y=y-x+8[/tex]

[tex]7x+y=8\;\;\;\;\;------equation(1)[/tex]

[tex]x-\frac{4}{3}\;y=\frac{2}{3}[/tex]

[tex]\frac{3x-4y}{3}=\frac{2}{3}[/tex]

[tex]3x-4y=2 \;\;\;\;\;------equation(2)[/tex]

By solving equation(1) and (2), We get

[tex]x=\frac{34}{31}[/tex]

Substitute the value of x in equation(1),

[tex]7\;(\frac{34}{31}) +y=8[/tex]

[tex]y=8-7(\frac{34}{31} )[/tex]

[tex]y=8-\frac{238}{31}[/tex]

[tex]y=\frac{248-238}{31}[/tex]

[tex]y=\frac{10}{31}[/tex]

Therefore, The points (x, y) is,

[tex](\frac{34}{31} ,\;\frac{10}{31} )[/tex]

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Answer: 15

Step-by-step explanation:

n=number

8*n=120

n=120/8

n=15

Answer:

The water required to pump all the water to a platform 2 feet above the top of the pool is  is 6061310.32 foot-pound.

Step-by-step explanation:

Answer: x = 7

Step-by-step explanation:

1. Set line PS equal to QR

2x - 3 = 11

2. Add 3 to both sides:

2x = 14

3. Divide both sides by two:

2x/2 = 14/2

4. Simplify

x = 7

if 10 customers show up between 9:00 am and 10:00 am and 25 customers show up between 10:00 am and 11:00 am, then there is a variability in customer Arrivals.

The term "variability" (also known as "spread" or "dispersion") describes how dispersed a set of data is. You may use statistics to compare your data to other sets of data by using the term "variability" to indicate how much the data sets differ from one another.

In a data collection, there are four major approaches to describe variability:

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Answer: 8 weeks

Step-by-step explanation: 25x4 =100 double it that makes 25x8=200 then 500 - 200 = 300

Answer:

12

Step-by-step explanation:

500 is what we are starting with and 300 is the endpoint.

if he spends 25 a week, we can multiply 25 12 times and we get 300

25•12= 300

The cost of ten pack of stylus pen is $(50/3).

This problem can be solved by unitary method and can be understood by the following process.

In this method we have to determine the cost of a unit of product and then the total amount by multiplying the unit cost by the desired quantity what we want.

Here, it is given that three packs of stylus pen costs $5.

Cost of one pack of stylus pen = $ 5/3

Therefore cost of 10 packs of stylus pen = $(5/3)*10

                                                                    = $(50/3)

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The simplified forms of the given expressions are

From the question, we are to evaluate the given radical expressions

The given radical expressions are

[tex]\sqrt{40+9}[/tex]

and

[tex]\frac{\sqrt[3]{125+3} }{2}[/tex]

Evaluating [tex]\sqrt{40+9}[/tex]

[tex]\sqrt{40+9}[/tex]

= [tex]\sqrt{49}[/tex]

= 7

Evaluating [tex]\frac{\sqrt[3]{125+3} }{2}[/tex]

[tex]\frac{\sqrt[3]{125+3} }{2}[/tex]

= [tex]\frac{\sqrt[3]{128} }{2}[/tex]

= [tex]\frac{\sqrt[3]{64 \times 2} }{2}[/tex]

= [tex]\frac{\sqrt[3]{64 } \times \sqrt[3]{2} }{2}[/tex]

= [tex]\frac{4\times \sqrt[3]{2} }{2}[/tex]

= [tex]\frac{4 }{2} \times \sqrt[3]{2}[/tex]

= [tex]2\times \sqrt[3]{2}[/tex]

= [tex]2\sqrt[3]{2}[/tex]

Hence, the simplified forms of the given expressions are

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Answer:

Hello.

Step-by-step explanation:

The resulting coordinate points after translation is (4, -4), (0, -2) and -6,-2)

The triangle is a shape that has three sides and angles. Given the coordinate points of the triangle given as:

A(-2, 3)

B (-2, 5)

C (-4, 5)

If the coordinate points is translated by the vector (2, -7), hence the resulting coordinate points will be:

A' = (2+2, 3-7) = (4, -4)

B' = (-2+2, 5-7) = (0, -2)

C' = (-4-2, 5-7) = (-6,-2)

Hence the resulting coordinate points after translation is (4, -4), (0, -2) and -6,-2)

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Answer:

linear algebra, an n-by-n square matrix A is called invertible, if there exists an n-by-n square matrix B such that \mathbf {AB} =\mathbf {BA} =\mathbf {I} _{n}\ where Iₙ denotes the n-by-n identity matrix and the multiplication used is ordinary matrix multiplication.

Answer:

Brainliest pls

Step-by-step explanation:

The inverse of a square matrix A, denoted by A-1, is the matrix so that the product of A and A-1 is the Identity matrix.

The significant benefit of a cumulative frequency polygon above a histogram and frequency polygon is that it can demonstrate the total number of observations that are less than the upper limit of a specific class.

A line segment-joined plot of a cumulative frequency against by the upper class boundary. An ogive would be any continuous cumulative frequency curve, along with a cumulative frequency polygon.

Some main points related to cumulative frequency polygon are-

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Step-by-step explanation:

4x^2 +10+ 2(2x+4)

4x^2 + 10x+4x+8

4x^2 +14x+8

4x^2+16x-2x -8

4(x+4)+2(x+4)

4+2(x+4)

6(x+4)

When Angelo drove home from college with an average speed of 71.7 mph and back to college with an average speed of 64.1 mph, she took 5 hours for full trip then the time taken to travel from home to college is 2.63 hours

Given,

The average speed from college to home = 71.7 mph

The average speed from home to college = 64.1 mph

We know,

Speed =  Distance / Time

Consider the total distance as x

Time taken = Distance / Speed

Then the time taken to travel from college to home  = [tex]\frac{x}{71.7}[/tex] hours

time taken to travel from home to college = [tex]\frac{x}{64.1}[/tex] hours

Total time taken = 5 hours

Then the equation will become

[tex]\frac{x}{71.7}+\frac{x}{64.1}=5[/tex]

Cross multiply the terms

[tex]\frac{64.1x+71.7x}{(71.7)(64.1)}=5\\ \frac{135.8x}{4595.97}=5[/tex]

135.8x= 5×4595.97

135.8x=22979.85

x=169.21

Time taken to travel from home to college =[tex]\frac{169.21}{64.1}[/tex]

=2.63 hours

Hence, When Angelo drove home from college with an average speed of 71.7 mph and back to college with an average speed of 64.1 mph, she took 5 hours for full trip, then the time taken to travel from home to college is 2.63 hours

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The expression when Bryar gathered 10 eggs from the chickens is 10 - x = 0.

Let the eggs that are broken be represented by x.

Therefore, from the information, Bryar gathered 10 eggs from the chickens. When he got to the house, he discovered all of the eggs were broken.

Therefore, the expression will be:

10 - x = 0

This illustrates that there are zero left.

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Answer: y = 7x

Step-by-step explanation:

11x + y = 18x

-11x        -11x

       y =   7x

Answer:

Step-by-step explanation:

If you make a list of factors for 18 you will get 1, 2, 3, 6, 9 and 18.

If you make a list of divisors you will get 1, 2, 3, 6, 9 and 18.

yes the factors of the numbers are also divisors because factors are numbers that go into 18, and we can use those same numbers for dividing with the number 18.

If the students that stated they would be going to Camp Redwood, 20 percentage did not go to camp and the students that stated they would be going to Camp Kern, 15 percentage  did not go to camp, then 51 more students went to camp kern than camp redwood

The total number of students in Camp redwood =170

Number of students who didn't  attend the camp redwood = 170×(20/100)

=34 students

Number of students who went to camp redwood =170-34

=136  students

Total number of students in Kern camp = 220

Number of students who didn't  attend the camp Kern=220×(15/100)

=33 students

Number of students who went to camp kern =220-33

=187 students

How many more students went camp Kern than Camp Redwood= 187-136

=51

Hence, 51 more students went to camp kern than camp redwood

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The value of the arcsin of 3 is 90 - 100.998i

From the question, we are to determine the inverse sine or arcsine of the given number

The given number is 3

All the values for the sine of angles are less than or equal to 1

That is,

Given an angle θ,

sinθ ≤ 1

From this, we can infer that the arcsine of 3 will be an imaginary number.

The arcsine of 3 is

sin⁻¹(3) = 90 - 100.998i

Hence, the value of the arcsin of 3 is 90 - 100.998i

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An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable. If f(x)=7/3x -9 then f(-3) is -88/9.

An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

Given function is

f(x)=7/3x -9

where x=-3.

Subtract x=-3 in the above function.

f(-3)=7/3(-3) - 9

f(-3)=7/-9 - 9

f(-3)=-7/9-9

f(-3)=(-7-81)/9

f(-3)=-88/9

Therefore f(-3) is -88/9.

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Answer:

The triangle has sides lengths 28, 56, 48

Step-by-step explanation:

Let x = the shortest side

So then the longest side will be 2x, because the question said that "the longest side... is twice the length of the shortest side" Then the third side would be x + 20.

The perimeter was given so add all the sides and set it equal to 132.

x + 2x + x + 20 = 132

Combine like terms.

4x + 20 = 132

Subtract 20

4x = 112

Divide by 4.

x = 28

Then use x = 28 to find the lengths of all the sides.

Shortest Side:

x = 28

Longest Side:

2x

= 2(28)

= 56

Third Side:

x + 20

= 28 + 20

= 48

The percent of population in the situation is 20 %.

Percentage means a number or a ratio represented in the form of fractions of 100. It is represented using the percentage sign ‘%’.  In other words, the percentage is defined as how much of one quantity is made by another quantity and it is evaluated in terms of 100.

We have to find the percentage of population 90 out of a population of 450 people represents.

We know that, the formula for percentage will be:-

(Given people/ Total people)*100

Here,

Given people = 90

Total people = 450

Hence, the percentage will be :-

= (90/450)*100 = (1/5)*100 = 20 % .

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√x+7 The solution to the equation is x=-3.

Square root: If we take the square root of a number and then take the square of the outcome, we get the original number back again.

   e.g.  4 = 2 and 22 = 4.

We can say that the square root and the square cancel each other out. They are the inverse of each other.

If we have a number written with the index 2 ( squared) then taking the square root simply means that we leave out the 2 ( this only applies to positive numbers ).

We can therefore take any squared numbers that are under the square root sign out from under the root sign by leaving out the power 2.

The solution to the equation√x+7= -2.

√x+7= -2

First we take Squaring on both sides

(√x+7)2= (-2)2

x+7 = 4

x=-3.

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Answer:

A

Step-by-step explanation:

31 divided by 31 is 1 (Since fractions are basically division)

The GCF of [tex]12w^{2} - 4w^{3}[/tex] is [tex]4w^{2}[/tex].

The Greatest Common Factor (GCF) of two or more numbers is defined as the factors which is common and highest .

For Example The GCF of 6 and 8

express 6=2*3

             8=2*2*2.    since 2 is common in both the GCF is 2.

In the given question

we need to factor out gcf from [tex]12w^{2} - 4w^{3}[/tex]

first express both terms in prime factors

[tex]12w^{2} =3*4*w*w[/tex]

and

[tex]4w^{3} =4*w*w*w[/tex]

the equation becomes

[tex](3*4*w*w-4*w*w*w)[/tex]

we can see that [tex]4*w*w[/tex] is common in both the terms .

So we can write [tex]4w^{2} (3-w)[/tex]

Therefore [tex]4w^{2}[/tex] is the gcf by factoring of [tex]12w^{2} - 4w^{3}[/tex].

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The solution of the quadratic equation is x=5±√35 .

A quadratic equation is given by the equation which can be written in the form ax²+bx +c.

the given quadratic equation is :

x²-10x+25=35

Simplifying the equation we get:

or, x²-10x+25-35=0

or, x²-10x-10=0

Now we will solve the equation by completion squares method:

x²-10x-10=0

or, x²-2×x×5+5²-5²-10=0

or, (x-5)²=35

or, x-5=±√35

or, x= 5±√35

Therefore the solution of the quadratic equation is 5+√35 and 5-√35 .

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