Using the translation that maps (3,-4) to its image (1,0), what is the image of any point (x,y)?

Answer:

[tex]\large\boxed{\dfrac{1}{4}a^{-3}b^3=\dfrac{b^3}{4a^3}}[/tex]

Step-by-step explanation:

[tex]\dfrac{4a^2b^5}{16a^5b^2}\qquad\text{use}\ \dfrac{x^n}{x^m}=x^{n-m}\\\\=\dfrac{4}{16}a^{2-5}b^{5-2}=\dfrac{1}{4}a^{-3}b^3\qquad\text{use}\ x^{-n}=\dfrac{1}{x^n}\\\\=\dfrac{b^3}{4a^3}[/tex]

Step-by-step explanation:

[tex]\sqrt[n]{a^m}=a^\frac{m}{n}\\\\\large\huge\boxed{a^\frac{4}{9}=\sqrt[9]{a^4}}[/tex]

The radical expression which represents a to the four ninths power is:

         Ninth root of a to the fourth power.

We are asked to find the radical expression for the word phrase:

             a to the four ninths power.

i.e. mathematically it could be written as:

[tex]a^{\dfrac{4}{9}}[/tex]

Now, we know that:

[tex]a^{\dfrac{m}{n}}=(a^m)^{\dfrac{1}{n}}=\sqrt[n]{a^m}[/tex]

Here we have:

[tex]m=4\ \text{and}\ n=9[/tex]

Hence, the expression cold be written as:

[tex]a^{\dfrac{4}{9}}=\sqrt[9]{a^4}[/tex]

Answer:

12π

Step-by-step explanation:

The area of a circle is π*r^2, where r is the radius. Therefore, given that the area is π*36, the radius is 6.

The circumference of a circle is 2πr, which in this case is 2*6*π=12π.

Answer:

i will answer this in 5 mins

Step-by-step explanation:

Answer:

Option C is correct.

Step-by-step explanation:

[tex]\theta=\frac{5\pi }{6}[/tex]

We need to find reference angle and signs of sinФ, cosФ and tanФ

We know that [tex]\theta=\frac{5\pi }{6}radians[/tex] is equal to 150°

and 150° is in 2nd quadrant.

So, Ф is in 2nd quadrant.

And In 2nd quadrant sine is positive, while cos and tan are negative

The reference angle Ф' is found by: π - Ф

=> Ф = 5π/6

so, Reference angle Ф' = π - 5π/6

Ф' = 6π - 5π/6

Ф' = π/6

So, Option C Θ' = pi over 6; sine is positive, cosine and tangent are negative is correct.

Step-by-step explanation:

no it is not because if 3 maps on 2, then it cannot map on -2 at the same time

A relation is considered a function if each input has only one output. The given set contains the input '3' with two different outputs '2' and '-2', therefore, it is not a function.

In mathematics, a relationship is considered a function if for every input there is only one output. In other words, no two pairs should have the same first element yet different second elements.

If we look at the set of ordered pairs provided, we have {(3, 2), (3, -2), (1, -4), (-1, 2)}. We can see that the input '3' corresponds to both '2' and '-2'. Since there are two outputs for the same input, we can determine that this relation is not a function.

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Answer:

Step-by-step explanation:

Next time, please share the answer choices.

(4/5)^6 is equivalent to:

 4^6         4096

---------- = -----------

  5^6        15625

Answer:

4^6/5^6

Step-by-step explanation:

The value of sin n depends on the angle n and represents the ratio of the length of the side opposite an angle to the length of the hypotenuse in a right triangle.

The value of sin n depends on the angle n. In mathematics, sine is a trigonometric function that represents the ratio of the length of the side opposite an angle to the length of the hypotenuse in a right triangle. It is a periodic function that oscillates between -1 and 1 as the angle increases or decreases.

For example, if n is 0 degrees, then sin n is 0. If n is 90 degrees, then sin n is 1. If n is 180 degrees, then sin n is 0 again. The values of sin n for angles in between can be determined using a calculator or trigonometric tables.

It's important to note that in mathematics, the angle n is typically measured in radians rather than degrees. In radians, a full circle is equal to 2π, so an angle of 360 degrees is equal to 2π radians.

Answer:

x = 9

Step-by-step explanation:

When 2 chords intersect inside a circle then the product of the measures of the parts of one chord is equal to the product of the measures of the parts of the other chord, that is

2 × x = 3 × 6, that is

2x = 18 ( divide both sides by 2 )

x = 9

To answer your question the list price for Emily's vehicle would have a $23,655.91 list price

Hope this helped

Aaron

Answer:  The list price of the car was $ 23655.91.

Step-by-step explanation:  Given that Emily bought a new car for $22000 and she paid 93% of the list price.

We are to find the list price of the car.

Let $ x denote the list price of the car.

Then, according to the given information, we have

[tex]93\%\times x=22000\\\\\\\Rightarrow \dfrac{93}{100}\times x=22000\\\\\Rightarrow 93x=22000\times100\\\\\Rightarrow 93x=2200000\\\\\Rightarrow x=\dfrac{2200000}{93}\\\\\Rightarrow x=23655.91.[/tex]

Thus, the list price of the car was $ 23655.91.

To find the total quarts of liquid ingredients for the muffin recipe, add together 1/2 quart of buttermilk, 1/3 quart of skim milk, and 1/16 quart of oil, resulting in 43/48 quarts in total after converting to a common denominator and summing up.

The question asks how many total quarts of liquid ingredients are called for in a muffin recipe, which includes 1/2 quart of buttermilk, 1/3 quart of skim milk, and 1/16 quart of oil. To find the total, you need to add these measurements together.

Adding the fractions:

First, find a common denominator, which would be 48 in this case. Converting each fraction:

Adding these fractions together gives us 43/48 quarts as the total amount of liquid ingredients needed for the recipe.

Answer:

5.2

Step-by-step explanation:

Since you have a linear function, asking for derivative is equivalent to asking for the slope.

The slope of y=5.2x+2.3 is 5.2 so the derivative is 5.2 .

However, if you really want to use the definition of derivative, you may.

That is, [tex]\lim_{h \rightarrow 0} \frac{f(x+h)-f(x)}{h}[/tex].

We know [tex]f(x)=5.2x+2.3[/tex] so [tex]f(x+h)=5.2(x+h)+2.3[/tex].  All I did was replace any x in the 5.2x+2.3 with (x+h) to obtain f(x+h).

Let's plug it into our definition:

[tex]\lim_{h \rightarrow 0} \frac{f(x+h)-f(x)}{h}[/tex]

[tex]\lim_{h \rightarrow 0} \frac{[5.2(x+h)+2.3]-[5.2x+2.3]}{h}[/tex]

Now we need to do some distributing.  I see I need this distributive property both for the 5.2(x+h) and the -[5.2x+2.3].

[tex]\lim_{h \rightarrow 0} \frac{5.2x+5.2h+2.3-5.2x-2.3}{h}[/tex]

There are some like terms to combine in the numerator.  The cool thing is they are opposites and when you add opposites you get 0.

[tex]\lim_{h \rightarrow 0} \frac{5.2h}{h}[/tex]

There is a common factor in the numerator and denominator. h/h=1.

[tex]\lim_{h \rightarrow 0}5.2[/tex]

5.2

[tex]f(x)=5.2x+2.3\\f'(x)=5.2[/tex]

Answer:

The equation is (x+9)^2 + (y-3)^2 = 5

Step-by-step explanation:

The standard form for the equation of a circle is:

(x−h)^2+(y−k)^2=r2

The center of the circle is the midpoint of the diameter.

So the midpoint of the diameter at  (-10, 1) and (-8, 5) can be determined as:

(-10 +(-8))/2 , (1+5)/2

= -10-8/2, 1+5/2

= -18/2 , 6/2

= -9 , 3

Thus(-9,3) is the center of the circle.

Now we will use the distance formula to find the radius of the circle.

r^2=(-10-(-9))^2 + (1-3)^2

r^2=(-10+9)^2 +(-2)^2

r^2=(-1)^2 + (-2)^2

r^2=1 + 4

r^2= 5

Take square root at both sides.

√r^2= √5

r=√5

Now put the values in the 1st equation.

(x−h)^2+(y−k)^2=r2

where h = -9, k =3 and r = √5

(x-(-9))^2 + (y-3)^2= (√5)^2

(x+9)^2 + (y-3)^2 = 5

Thus the equation is (x+9)^2 + (y-3)^2 = 5 ....

Answer:

439.7.

Step-by-step explanation:

The mean of these number is

(500+372+536+ 328 +369+412+561) / 7

=439.7.

Final answer:

To determine the mean of the numbers 500, 372, 536, 369, 328, 412, and 561, you add them together and divide by the total count, which results in a mean of approximately 439.71.

Explanation:

To find the mean of a set of numbers, you add up all the numbers and then divide by the number of values in the set. The numbers given are 500, 372, 536, 369, 328, 412, and 561. Let's calculate the mean step by step:

The mean (average) of the numbers is approximately 439.71.

Answer:

[tex]\large\boxed{6.\ x=-\dfrac{12}{7}}\\\boxed{7.\ p=0}[/tex]

Step-by-step explanation:

[tex]6.\\\\1-7x+4=18\\(1+4)-7x=18\\5-7x=18\qquad\text{subtract 5 from both sides}\\-7x=12\qquad\text{divide both sides by (-7)}\\x=-\dfrac{12}{7}\\\\7.\\\\5p+10=10\qquad\text{subtract 10 from both sides}\\5p=0\qquad\text{divide both sides by 5}\\p=0[/tex]

Answer:

60% growth, 40% decay, 20% decay, 80% decay, 40% growth. In that order :)

Step-by-step explanation:

The number inside the parenthesis is always 1+a number. So for every .1 up or down, that's 10% growth or decay(up being growth, down being decay).

Answer:

Step-by-step explanation:

A). In exponential equation [tex]80(1.6)^{t}=20[/tex], 1.6 is the common ratio which represents [(1 + 60% of 1) = 1.6] a growth of 60%.

B). In [tex]20(0.6)^{t}=1.2[/tex] common ratio is 0.6 [(1 - 40% of 1)] which represents 40% decay.

C). In [tex]60(0.8)^{t}=1.4[/tex] common ratio is 0.8 [(1 - 20% of 1)] which represents 20% decay.

D). In [tex]40(0.2)^{t}=1.6[/tex] common ratio is 0.2 [(1 - 80% of 1)] which represents 80% decay.

E). In [tex]1.2(1.4)^{t}=80[/tex] common ratio is 1.4 [(1 + 40% of 1)] which represents 40% growth.

Answer:

The correct option is C

Step-by-step explanation:

x2 - 12x + 36

The coefficient of 1st term will be multiplied by the constant:

1*36 = 36

Now find two numbers whose product is 36 and whose addition is 12.

6*6 = 36

6+6 =12

Now break the middle term:

x^2-6x-6x+36 = 0

Now group the terms:

(x^2-6x) - (6x-36) = 0

Now take common of each group:

x(x-6)-6(x-6) = 0

(x-6) (x-6) =0

(x-6)=0    ,  (x-6) =0

x-6=0       , x-6=0

x=0+6      , x=0+6

x=6        ,   x=6

Thus the correct option is C. x=6 only....

Answer:

  15

Step-by-step explanation:

To find the x-intercept, set y=0 and solve for x:

  6x -0 = 90

  x = 90/6 = 15

The x-intercept is the point (15, 0).

Answer:

a. _ √20 , about 4.472136

b - (-3, 8)

c- Slope of 2

Step-by-step explanation:

Calculator

Answer:

a. [tex]AB=2\sqrt{5}[/tex]

b. [tex](-3,8)[/tex]

c. [tex]2[/tex]

Step-by-step explanation:

You have the points:

A(-2,10)

where i will call: [tex]x_{1}=-2[/tex] and [tex]y_{1}=10[/tex]

B(-4,6)

where i will call: [tex]x_{2}=-4[/tex] and [tex]y_{2}=6[/tex]

for our calculations we are going to need the distance in x between the points ([tex]\Delta x[/tex] )and the distance in y between the points ([tex]\Delta y[/tex]):

[tex]\Delta x =|x_{2}-x_{1}|=|-4-(-2)|=|-4+2|=|-2|=2\\\Delta y =|y_{2}-y_{1}|=|6-10|=|-4|=4[/tex]

a. To find AB (the distance between point A and point B) you need The Pythagorean Theorem:

[tex](AB)^2=(\Delta x)^2+(\Delta y)^2\\(AB)^2=(2)^2+(4)^2\\(AB)^2=4+16\\\\AB=\sqrt{20}\\ AB=2\sqrt{5}[/tex]

b. to find the coordinates of the midpoint we average the x-coordinates and the y coordinates

[tex]x_{mid}=\frac{x_{1}+x_{2}}{2} =\frac{-2-4}{2}=\frac{-6}{2} =-3\\y_{mid}=\frac{y_{1}+y_{2}}{2} =\frac{10+6}{2}=\frac{16}{2} =8\\[/tex]

so the midpoint [tex](x_{mid},y_{mid})[/tex] is at: [tex](-3,8)[/tex]

c. For the slope we use the slope formula:

[tex]slope=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{6-10}{-4-(-2)}=\frac{-4}{-2}=2[/tex]

The slope is equal to 2.

Answer:

-4

Step-by-step explanation:

plug 2 into the equation.

f(2)=4(2)-12

    = 8-12

    = -4

I hope this helped!

Answer:

f(2) =-4

Step-by-step explanation:

f(x)=4x-12

Let x=2

f(2) = 4(2) -12

      =8-12

       =-4

Answer: The total cost would be 37.95

Step-by-step explanation:

The total cost for the night, including a 15% tip on a $33 meal, is $37.95.

To calculate the total cost for the night, we need to add the meal cost and the tip. For a $33 meal, a 15% tip would be calculated using the formula tip = meal cost x tip percentage/ 100. In this case, tip = $33 x 15/100= $4.95. Therefore, the total cost for the night (meal cost + tip) would be $33 + $4.95 = $37.95.

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Answer:

A

Step-by-step explanation:

One and three hundred and four thousand

1+                             3/100+          4/1000

Answer:

D

Step-by-step explanation:

It crosses the y-axis at y=1 so the y-intercept is b=1.

The slope is count straight up from (-5,-2) to you are on the same horizontal level as (5,4).  The rise is 6

Once you get the same horizontal level as (5,4), you will count straight over to you get to (5,4). The run is 10.

Slope=rise/run=6/10=3/5.

Or you could find slope by using the slope formula.  I like to line up two pairs of points and subtract then put 2nd difference over first difference. Like so,

  (5,4)

-(-5,-2)

----------

 10   6

So the slope is 6/10 or 3/5 after reducing.

Slope-intercept form of a line is y=mx+b

Plug in m=3/5 and b=1

y=3/5 x +1

So the answer is D.

Answer:

5 large frames

16 small frames

Step-by-step explanation:

$13 times 5 large frames = $65

$9 times 16 small frames = $144

144+65=209

Answer:

The number of calories in a peanut treat is 30.

The number of calories in a coconut treat is 25.

Step-by-step explanation:

So we have Ben ate 2 peanut treats (let p represent the calories in each peanut treat) and 4 coconut treats (let c represent the calories in each coconut treat).  The sum of those calories is 160.

This is the equation for Ben:

2p+4c=160

I'm going to use the same representation here.  p for the number of calories in each peanut treat and c for the number of calories in each coconut treat.

Arnold ate 3 p's and 2 c's for a sum of 140 calories:

Alrnoldo's equation is:

3p+2c=140

So we have the system:

2p+4c=160

3p+2c=140

I'm going to divide the first equation by 2 because each term is divisible by 2:

p+2c=80

3p+2c=140

This system is setup for elimination because the equations are in the same form and the second column have the same variable expression, 2c.  So we are going to subtract to eliminate the variable c, that is 2c-2c=0.

p+2c=80

3p+2c=140

---------------------Subtract!

-2p+0=-60

-2p    =-60

Divide both sides by -2:

  p      =30

So if p=30 and p+2c=80 , then 30+2c=80.

So let's solve:

30+2c=80 for c

Subtract 30 on both sides:

     2c=50

Divide both sides by 2:

     c=25

The number of calories in a peanut treat is 30.

The number of calories in a coconut treat is 25.

Answer:

≈ 545.42 cm²

Step-by-step explanation:

The area (A) of sector EOG is calculated as

A = area of circle × fraction of circle

   = πr² × [tex]\frac{100}{360}[/tex]

   = π × 25² × [tex]\frac{10}{36}[/tex]

   = 625π × [tex]\frac{10}{36}[/tex]

   = [tex]\frac{625(10)\pi }{36}[/tex] ≈ 545.42 ( to 2 dec. places )

To solve the student's question, we calculated the time period from the initial amount and interest rate, then used that to determine the amount that Rs 600 would become at an 11% interest rate over the same period, which is Rs 930.

The essence of the question revolves around the concept of calculating the future amount of money based on the principal, the rate of interest, and the time for which the money is lent or invested. In the given scenario, we have a principal of Rs 500 which, at a 9% simple interest rate, amounts to Rs 725 over a certain period.

To find the equivalent amount for Rs 600 at an 11% interest rate over the same period, we need to first understand the amount of interest accrued in the first situation and use its proportion to calculate the second.

The formula for simple interest is Interest = Principal × rate × time.

First, let's calculate the interest earned on the initial Rs 500:

Now, we can calculate the time period using the simple interest formula:

Knowing the time period, we can find the amount that Rs 600 would amount to at an 11% interest rate over the same period:

So, Rs 600 will amount to Rs 930 at an 11% simple interest rate over the same time period of 5 years.

Answer:

-4/3

Step-by-step explanation:

because the line are perpendicular, so the slope of re line is -1/(3/4)=-4/3

Answer

The answer after you divide one number by another

dividend ÷ divisor = quotient

Example: in 12 ÷ 3 = 4, 4 is the quotient

The answer is 675 units²

The surface area of the rectangular pyramid is 675 units².

The area is the space occupied by a two-dimensional flat surface. It is expressed in square units. The surface area of a three-dimensional object is the area occupied by its outer surface.

We have to find the surface area of the rectangular pyramid.

So, to find the surface we need to find SA of each face

= (15 x 15) + (15 x 15)/2 x 4

= 225 + 225 x 2

= 225 + 450

= 675 units²

Learn more about Surface Area here:

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