Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.


Polygon ABCD, shown in the figure, is dilated by a scale factor of 8 with the origin as the center of dilation, resulting in the image A′B′C′D′.

The slope of is
.

Answer:

Any quotient of polynomials a(x)/b(x) can be written as q(x)+r(x)/b(x), where the degree of r(x) is less than the degree of b(x). For example, (x²-3x+5)/(x-1) can be written as x-2+3/(x-1). This latter form can be more useful for many problems that involve polynomials.

Step-by-step explanation:

The quotient in polynomial division refers to the result of dividing one polynomial by another. When a polynomial S is divided by a polynomial P, the result is a quotient Q of a degree less than P. The quotient Q represents a rational function when it is derived from the division of two polynomials.

In terms of algebra, let's consider a polynomial P of degree n, and we divide another polynomial S with a degree less than 2n by P. The result is a quotient Q and a remainder R, both of which are polynomials and Q has a degree less than n. If P(x) has a degree higher than Q(x), one can use the method of long division to find the quotient. This quotient, Q, alongside the remainder, R, conforms to the relation S(x) = P(x)\Q(x) + R, where Q and R are of lesser degrees than P.

When dealing with rational functions, we often find ourselves in positions of evaluating expressions formed by dividing polynomials. These functions are called rational functions, which are essentially the quotient of two polynomials. Applying the quotient rule can simplify differentiable polynomial functions and is useful when finding limits or derivatives in calculus.

Answer:

637

Step-by-step explanation:

Ticket ending 00= £12 * 7 = £84  

Tickets ending 5 = £1.5 * 75 = £112.5  

£84+£112.5=£196.5  

Price money + Profit: £196.5+£163= 356

356/£0.5 = 719 total tickets sold

719- 82 (WINNING TICKETS) = 637 losing tickets sold

Tomas made £232.5 from the winning tickets. Subtracting his profit of £163, we see he made £69.5 from the losing tickets. At a price of £0.5 per ticket, that means he sold 139 losing tickets.

First, calculate the total amount Tomas made by selling all the winning tickets. There are ten tickets that end in '00' between 1 and 750, each valued at £12, i.e., £120. There are 75 tickets that end in '5' between 1 and 750, each valued at £1.50, i.e., total of £112.50. So, the total income from these tickets is £120 + £112.50 = £232.5.

Then, subtract Tomas's profit from the total income of the winning tickets to get the total revenue from the losing tickets. So, £232.5 - £163 = £69.5. Given each ticket costs 50p or £0.5, divide £69.5 by £0.5 to find the number of losing tickets sold. That is, £69.5/£0.5 = 139. Thus, Tomas sold 139 losing tickets.

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A. f(-3) = -11

If the function is f(x) = 2x - 5, then just replace x with -3 to find f(-3).

f(-3) = 2(-3) - 5

Multiply 2 times -3.

f(-3) = -6 - 5

Subtract -6 minus 5.

f(-3) = 11

There’s the answer.

Answer:

-11

Step-by-step explanation:

If you substitute x with -3 in the equation then you will get -11. Have a good night/day!

=)

The value of the expression is 14.

Answer:

1)no

2)no

Fractions are rational numbers

Step-by-step explanation:

irrational numbers are numbers which can't be written as ratios, fractions, or rational decimals

hope this helps!

Answer:

The probability is 1/15 or 6.67%

Step-by-step explanation:

step 1

Find the probability that when she shakes the piggy bank a half-dollar fall out

P=2/15

step 2

Find the probability that when she shakes the piggy bank a dime fall out

P=7/14

step 3

Find he probability that when she shakes the piggy bank a half-dollar and then a dime fall out

P=(2/15)(7/14)=1/15

Convert to percentage

(1/15)*100=6.67%

The complete factorization of the polynomial [tex]x^3 + x^2 + 9x + 9[/tex] is [tex]x + 1)(x^2 + 9)[/tex] using real coefficients, and [tex](x + 1)(x + 3i)(x - 3i)[/tex] using complex coefficients.

The complete factorization of the polynomial [tex]x^3 + x^2 + 9x + 9[/tex] can be found by grouping and factoring terms with common factors.

To proceed, let's group the terms as follows: [tex](x^3 + x^2) + (9x + 9).[/tex]

Factoring out the common factors in each group gives us [tex]x^2(x + 1) + 9(x + 1).[/tex]

Now, we notice that (x + 1) is a common factor in both terms, so we can factor it out to get our complete factorization: [tex](x + 1)(x^2 + 9).[/tex]

As [tex]x^2 + 9[/tex] can't be factored further using real coefficients, this is the fullest factorization in the realm of real numbers.

However, if complex numbers are considered, [tex]x^2 + 9[/tex] can be expressed as [tex](x + 3i)(x - 3i)[/tex], where i is the imaginary unit.

So, the complete factorization using complex coefficients is [tex](x + 3i)(x - 3i)[/tex]

Answer:

r = 6

Step-by-step explanation:

Given that M is directly proportional to r³ then the equation relating them is

M = kr³ ← k is the constant of proportionality

To find k use the condition r = 4 when M = 160

k = [tex]\frac{M}{r^3}[/tex] = [tex]\frac{160}{64}[/tex] = 2.5, so

M = 2.5r³ ← equation of proportionality

When M = 540, then

540 = 2.5 r³ ( divide both sides by 2.5 )

216 = r³ ( take the cube root of both sides )

r = [tex]\sqrt[3]{216}[/tex] = 6

Answer:

[tex]7.7n=112.42[/tex]

[tex]n=14.6[/tex]

Step-by-step explanation:

The product is the result obtained by multiplying two factors. Then, the sentence ""The product of a number n and 7.7 equals 112.42" can be expressed with the following equation:

[tex]7.7n=112.42[/tex]

To solve for the variable "n", you has two apply the Division property of equality and divide both sides of the equation by 7.7

Therefore, the value of "n" is:

[tex]\frac{7.7n}{7.7}=\frac{112.42}{7.7}\\\\n=14.6[/tex]

Answer:

The domain = (-∞ , -1/4) ∪ (-1/4 , ∞)

The range = (-∞ , 21/4)∪(21/4 , ∞)

The answer is not in the choices

Step-by-step explanation:

* Lets revise how to find the inverse function

- At first write the function as y = f(x)

- Then switch x and y

- Then solve for y

- The domain of f(x) will be the range of f^-1(x)

- The range of f(x) will be the domain of f^-1(x)

* Now lets solve the problem

- At first find the domain and the range of f(x)

∵ f(x) = (x - 9)/(21 - 4x)

- The domain is all real numbers except the value which

  makes the denominator = 0

- To find this value put the denominator = 0

∴ 21 - 4x = 0 ⇒ subtract 21 from both sides

∴ -4x = -21 ⇒ ÷ -4 both sides

∴ x = 21/4

∴ The domain = R - {21/4} OR the domain = (-∞ , 21/4)∪(21/4 , ∞)

* Now lets find the range

- The range will be all the values of real numbers except -1/4

 because the horizontal asymptote equation is y = -1/4

- To find the horizontal asymptote we find the equation y = a/b

 where a is the coefficient of x up and b is the coefficient of x down

∵ The coefficient of x up is 1 and down is -4

∴ The equation y = 1/-4

∴ The value of y = -1/4 does not exist

∴ The range = R - {-1/4} OR the range = (-∞ , -1/4) ∪ (-1/4 , ∞)

* Switch the domain and the range for the f^-1(x)

∴ The domain = (-∞ , -1/4) ∪ (-1/4 , ∞)

∴ The range = (-∞ , 21/4)∪(21/4 , ∞)

Answer:

Step-by-step explanation:

[tex]\left(\dfrac{4}{7}\right)^r=\dfrac{s}{343}\\\\\dfrac{4^r}{7^r}=\dfrac{s}{7^3}\to r=3\ and\ 4^r=s\\\\4^r=4^3=64\to  s=64[/tex]

Answer:

m∠8 = 4x

Step-by-step explanation:

Angle 8 is the same angle measure of angle 1, which is m∠1 = 4x

Answer:

B

Step-by-step explanation:

Find all probabilities:

A. False

[tex]Pr(\text{red shirt}|\text{large shirt})=\dfrac{\text{number red large shirts}}{\text{number large shirts}}=\dfrac{42}{77}=\dfrac{6}{11}\\ \\Pr(\text{large shirt})=\dfrac{\text{number large shirts}}{\text{number shirts}}=\dfrac{77}{165}=\dfrac{7}{15}[/tex]

B. True

[tex]Pr(\text{blue shirt}|\text{large shirt})=\dfrac{\text{number blue large shirts}}{\text{number large shirts}}=\dfrac{35}{77}=\dfrac{5}{11}\\ \\Pr(\text{blue shirt})=\dfrac{\text{number blue shirts}}{\text{number shirts}}=\dfrac{75}{165}=\dfrac{5}{11}[/tex]

C. False

[tex]Pr(\text{shirt is medium and blue})=\dfrac{\text{number medium and blue shirts}}{\text{number shirts}}=\dfrac{48}{165}=\dfrac{16}{55}\\ \\Pr(\text{medium shirt})=\dfrac{\text{number medium shirts}}{\text{number shirts}}=\dfrac{88}{165}=\dfrac{8}{15}[/tex]

D. False

[tex]Pr(\text{large shirt}|\text{red shirt})=\dfrac{\text{number red large shirts}}{\text{number red shirts}}=\dfrac{42}{90}=\dfrac{7}{15}\\ \\Pr(\text{red shirt})=\dfrac{\text{number red shirts}}{\text{number shirts}}=\dfrac{90}{165}=\dfrac{6}{11}[/tex]

Answer:

[tex]x_1=-4\\\\x_2=\frac{1}{3}[/tex]

Step-by-step explanation:

Given the quadratic equation:

[tex]2x^2+14x-4=-x^2+3x[/tex]

You can follow these steps in order to solve it:

- Make the equation equal to 0:

[tex]2x^2+14x-4+x^2-3x=0[/tex]

- Now, add the like terms:

[tex]3x^2+11x-4=0[/tex]

- Finally, apply the Quadratic formula ([tex]x=\frac{-b\±\sqrt{b^2-4ac} }{2a}[/tex]):

In this case we know that:

[tex]a=3\\b=11\\c=-4[/tex]

Therefore, substituting values into the Quadratic formula and evaluating, we get:

[tex]x=\frac{-11\±\sqrt{11^2-4(3)(-4)} }{2(3)}\\\\x_1=-4\\\\x_2=\frac{1}{3}[/tex]

To find the solutions to the quadratic equation 2x^2+14x-4=-x^2+3x, we need to rearrange the equation and use the quadratic formula.

The quadratic equation is 2x^2+14x-4=-x^2+3x. To find the solutions, we need to rearrange the equation in the form ax^2 + bx + c = 0. Combining like terms, we get 3x^2 + 11x - 4 = 0. Now we can use the quadratic formula to find the solutions:

x = (-b ± √(b^2 - 4ac)) / 2a

Plugging in the values a = 3, b = 11, and c = -4 into the formula, we can calculate the solutions.

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Answer:

Step-by-step explanation:

Just use the slope equation.

y = 4x - 10. The linear functions y = 4x - 10 represent the line given by the point-slope equation y - 2 = 4(x - 3).

In order to solve this problem, we have to take the point-slope equation y - 2 = 4(x - 3) and convert it to the linear function form y = mx + b as follow:

y - 2 = 4(x - 3)

y - 2 = 4(x) - (4)(3)

y - 2 = 4x - 12

y - 2 + 2 = 4x -12 +2

y = 4x - 10 (Linear function)

Answer: 4 + (-1)^10 = 4+ 1 = 5

The tenth term of the sequence is 5.

Given to us,

Sequence, [tex]\bold{a_n=4+(-1)^n}[/tex]

For tenth term,

n = 10,

Subsituting the value of n we get,

[tex]{a_n=4+(-1)^n}\\a_{10}=4+(-1)^{10}\\a_{10} = 4 + 1\\a_{10} = 5[/tex]

Hence, the tenth term of the sequence is 5.

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Answer:

option A

f(x) = (x – 1)2 + 3

Step-by-step explanation:

Given in the question a function,

f(x) = 4 + x² – 2x

f(x) = 4 + x² – 2x

here a = 1

        b = -2

        c = 4

x = -b/2a

h = -(-2)/2(1)

h = 2/2

h = 1

Step 3

Find k

k = 4 + 1² – 2(1)

k = 3

Step 4

To convert a quadratic from y = ax² + bx + c form to vertex form,

y = a(x - h)²+ k

y = 1(x - 1)² + 3

y = (x - 1)² + 3

ANSWER

The vertex form is

[tex]f(x) = {(x - 1)}^{2} + 3[/tex]

EXPLANATION

The given function is

[tex]f(x) = 4 + {x}^{2} - 2x[/tex]

This is the same as:

[tex]f(x) = {x}^{2} - 2x + 4[/tex]

We add and subtract the square of half the coefficient of x.

[tex]f(x) = {x}^{2} - 2x + {( -1 )}^{2} - {( -1 )}^{2} + 4[/tex]

[tex]f(x) = {x}^{2} - 2x + 1 - 1 + 4[/tex]

The first three term is a perfect square trinomial:

[tex]f(x) = {(x - 1)}^{2} + 3[/tex]

The vertex form is

[tex]f(x) = {(x - 1)}^{2} + 3[/tex]

The answer is I. 8

Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84.

By buying 9 packs of 4 cartons and 2 single cartons, Lewis was able to spend the least amount of money to get the 38 cartons he needed. The total cost was £14.94.

The subject of this question is mathematics, specifically cost optimization and arithmetic. Lewis can buy single carton of juice for 45p or a pack of 4 cartons for £1.56. The goal is to minimize the cost. First, Lewis can start by buying packs of 4. The number of 4-carton packs he can buy is 38 divided by 4 which gives you 9 packs that include 36 cartons. He then needs to buy 2 more single cartons to reach 38. So, the total cost is 9 packs times £1.56/pack plus 2 single cartons times 45p/carton. Doing the arithmetic:

Convert 90p to pounds that is £0.90. Adding both gives £14.94. Therefore, Lewis spent a total of £14.94 on juice cartons.

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Answer:

Final answer is [tex]x=9[/tex].

Step-by-step explanation:

we know that if BD is angle bisector of angle B in triangle ABC then

[tex]\frac{AB}{BC}=\frac{AD}{DC}[/tex]

[tex]\frac{36}{28}=\frac{x}{DC}[/tex]

[tex]\frac{36}{28}=\frac{x}{16-x}[/tex]

[tex]\frac{9}{7}=\frac{x}{16-x}[/tex]

cross multiply

[tex]7x=9(16-x)[/tex]

[tex]7x=144-9x[/tex]

[tex]7x+9x=144[/tex]

[tex]16x=144[/tex]

[tex]x=\frac{144}{9}[/tex]

[tex]x=9[/tex]

Hence final answer is [tex]x=9[/tex].

Answer:

i believe it would be 1/27 or 0.037 depending on the form you need it in

Step-by-step explanation:

[tex] \bf \underline{Solution-} \\ [/tex]

[tex]\textsf{Given}\\[/tex]

[tex] \sf{ {9}^{ \frac{3}{2} } } \\ [/tex]

[tex] \longrightarrow{ \: ( {3}^{2} {)}^{ \frac{3}{2} } } \\ [/tex]

[tex] \longrightarrow{ \: {3}^ { \cancel2 \times \frac{3}{ \cancel2} } } \\ [/tex]

[tex] \longrightarrow{ {3}^{3} } \\ [/tex]

[tex] \longrightarrow{ \: 3 \times 3 \times 3} \\ [/tex]

[tex] \sf \longrightarrow{ \: 27 \: ans.} \\ [/tex]

[tex]\textsf{Hope this helps!!}\\[/tex]

Answer:

∛4²

Step-by-step explanation:

A fraction exponent can be represented using a radical. The base number is the number in the radical. The numerator of the fraction is the exponent inside the radical. The denominator is the type of radical.

To write an exponent in radical form , the denominator, or index goes in front of the radical, and the numerator goes inside of the radical. We raise the base to the power of the numerator

4 2/3

∛4².

The radical form of 4 2/3 is the cube root of 4 squared, denoted as √(4^2).

The radical form of the expression 4 2/3 means expressing the number as a radical, which refers to roots of numbers. In this case, the number 2/3 is the exponent in fractional form. To convert this into a radical, the numerator indicates the power and the denominator indicates the root. Therefore, 42/3 can be expressed as the cube root of 4 squared. The cube root is denoted by the radical symbol √ with a small three above or to the left of the radical. Thus, 42/3 = √(42).

This is the answer (I believe): 18 + x = 29

Answer:

11

Step-by-step explanation:

29-18 is 11

Answer:

77 inches

Step-by-step explanation:

Given

1 inch = 3 miles in map

We are also given the actual distance between City A and City B = 231 miles.

In order to get the distance in inches = Distance between City A and City B in miles/ 3

We are dividing the distance by 3 to get the distance in inches.

So,

Distance on map = 231/3

= 77 inches

Answer: 77 inches.

Step-by-step explanation:

You know that this map uses this scale:

[tex]1in=3mi[/tex]

This means that 1 inch in the map represents 3 miles.

In this case, you know that the actual distance between City A and City B is 231 miles, then, to find the distance between the cities on the map, you can set up de following proportion:

[tex]\frac{1in}{3mi}=\frac{x}{231mi}[/tex]

Now, you need to solve for "x":

[tex](231mi)(\frac{1in}{3mi})=x\\\\x=77in[/tex]

Answer:

the first one is 23

the second one is 70-79

the third one is 11

Step-by-step explanation:

this is because frequency refers to the amount of people who got the scores on the x-axis.

so for the first one you would count up how many people participated i.e. 2+9+7+5 = 23

the second one is asking for the mode test score and mode refers to the most common, so the most common test score is the 70-79 bar

the third one is asking for how many people scored below 80, which is 11 as 2 people scored 60-69 and 9 scored 70-79 on the test (2+9=11)

Hope this helps :)

the answer is 23

hope this helps

Answer:

Step-by-step explanation:

[tex]x^o\ \text{and}\ \left(\dfrac{2}{3}x\right)^o\ \text{are suplementary angles, therefore}\\\\x^2+\left(\dfrac{2}{3}x\right)^o=180^o\\\\x+\dfrac{2}{3}x=180\qquad\text{multiply both sides by 3}\\\\3x+2x=540\\\\5x=540\qquad\text{divide both sides by 5}\\\\x=108[/tex]

Answer:

First of all, let's find the area of the upper rectangle. We have side lengths 5 and 6, so its area is 30.

Now to find the bottom. If we add our ten, and the five on top, we get a length of 15. We multiply this by 6, giving us 90.

Now we add.

90+30=120

Therefore, our answer is A) 120 square units.

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Step-by-step explanation:

Answer:

B. 1.47*10^18

Step-by-step explanation:

Given

Distance of largest start from earth in light years = 250000

1 light year = 5880000000000 miles

So,

Distance of largest star from earth in miles = 250000 * 5880000000000

= 1470000000000000000 miles

In order to convert in scientific notation, point will be moved 18 places to the left, so the number will become:

1.47* 10^18 miles

So option B is correct..

Answer: OPTION B

Step-by-step explanation:

Scientific notation has the form:

[tex]a10^n[/tex]

Where "a" is a number between 1 and 10 but is not less than 10 and "n" is an integer.

If a light-year is about 5,880,000,000,000 miles and the large star is 250,000 light-years from Earth, then this distance in miles is:

[tex]d=(250,000)(5,880,000,000,000)\\d=1,470,000,000,000,000,000.0\ mi[/tex]

To express this distance in scientific notation, the decimal point must be after the first digit. You can observe that the decimal point must be moved 18 places, then:

[tex]a=1.47[/tex] and  [tex]n=18[/tex]

Therefore, you get that the distance of the large star from Earth in scientific notation is:

[tex]d=1.47*10^{18}\ mi[/tex]

Answer:

Part 1) The equation for the monthly charges for Runfast is [tex]y=8x+8[/tex] and for BA&D is [tex]y=4x+15[/tex]

Part 2) The solution of the system of equations is the point  (1.75.22)

Step-by-step explanation:

Let

x -----> the number of gig of data

y -----> the total monthly charges

we know that

Runfast Company

[tex]y=8x+8[/tex] -----> equation A

BA&D Company

[tex]y=4x+15[/tex] -----> equation B

Part 2) Use your mathematical skill to solve this system of equations using the substitution method

we have

[tex]y=8x+8[/tex] -----> equation A

[tex]y=4x+15[/tex] -----> equation B

Substitute equation B in equation A and solve for x

[tex]4x+15=8x+8[/tex]

[tex]8x-4x=15-8[/tex]

[tex]4x=7[/tex]

[tex]x=1.75\ Gb[/tex]

Find the value of y

[tex]y=8(1.75)+8=\$22[/tex]

so

The solution is the point (1.75.22)

That means

For the number of gig equal to 1.75 the monthly charge is equal to $22 in both company's

therefore

For a number of gigs less than 1.75 the company Runfast has the better pricing, while for a number of gigs greater than 1.75 the company BA&D has the better pricing