What is the image of (-4,12) after a dilation by a scale factor of 1/4 centered at the origin

Answer:

-23

Step-by-step explanation:

13-4(3+6)

13-4x9

13-36

-23

The zeros of the function defined by

h(x) = x³ – 4x² – 5x are x = 0, x = 5 and x = -1

The zeros of a function, also referred to as roots or x-intercepts, occur at x-values where the value of the function is 0. It is simply the values of x when f(x) is equal to 0.

For x = 0, we substitute 0 for x in the function h(x);

h(0) = (0)³ - 4(0)² - 5(0)

h(0) = 0

For x = 1, we substitute 1 for x in the function h(x);

h(1) = (1)³ - 4(1)² - 5(1)

h(1) = 1 - 4 - 5

h(1) = -8

For x = -5, we substitute -5 for x in the function h(x);

h(-5) = (-5)³ - 4(-5)² - 5(-5)

h(-5) = -125 - 100 +25

h(-5) = -200

For x = 5, we substitute 5 for x in the function h(x);

h(5) = (5)³ - 4(5)² - 5(5)

h(5) = 125 - 100 - 25

h(5) = 0

For x = -1, we substitute -1 for x in the function h(x);

h(-1) = (-1)³ - 4(-1)² - 5(-1)

h(-1) = -1 - 4 + 5

h(-1) = 0

Therefore, the values of x that makes the function h(x) = x³ – 4x² – 5x equal to zero are; 0, 5, and -1, they are the zeros of the function h(x).

Know more about zeros of a function here: https://brainly.com/question/16550963

#SPJ1

The total cost of the pita bread and hummus dips will be $305.00.

To determine the cost of the pita bread and hummus dips, Toula can use the following expressions:

Cost of pita bread:

Number of crates needed = (150 bags) / (50 bags/crate) = 3 crates

Cost of each crate = $15.00

Total cost of pita bread = (Number of crates needed) × (Cost of each crate) = 3 crates × $15.00/crate = $45.00

Cost of hummus dips:

Number of boxes needed = (65 containers) / (5 containers/box) = 13 boxes

Cost of each box = $20.00

Total cost of hummus dips = (Number of boxes needed) × (Cost of each box) = 13 boxes × $20.00/box = $260.00

Therefore, the expressions Toula can use to determine the costs are:

Cost of pita bread = 3 crates × $15.00/crate

Cost of hummus dips = 13 boxes × $20.00/box

The total cost will be the sum of the costs of pita bread and hummus dips:

Total cost = Cost of pita bread + Cost of hummus dips

Total cost = $45.00 + $260.00

Total cost = $305.00

Therefore, the total cost of the pita bread and hummus dips will be $305.00.

for such more question on cost

https://brainly.com/question/8993267

#SPJ8

Answer:

Let us set up a ratio to find the relationship between side lengths of the two triangles.

25:10

5:2

We can divide both sides by two, but there's no need as the smaller triangle has multiples of two.

So, if XZ is 6, let's place it into the ratio and find what "x" is.

5(3) : 2(3)

15 : 6

x = 15

Answer:

56 people

Step-by-step explanation:

49 times 8= 392

392 divided 7= 56

The value of 'n' for which the division of x^(2n-1) by x + 3 leaves a remainder of -80 is n = 1.

To find the value of 'n' for which the division of x^(2n-1) by x + 3 leaves a remainder of -80, we can use polynomial long division. Let's perform the division step by step:

Write the dividend and divisor in polynomial long division format:

_________________________

x + 3 │ x^(2n-1) + 0x^(2n-2) + 0x^(2n-3) + ...

Divide the leading term of the dividend (x^(2n-1)) by the leading term of the divisor (x). The result is x^(2n-1)/x = x^(2n-2).

Multiply the divisor (x + 3) by the quotient obtained in the previous step (x^(2n-2)). The result is x^(2n-2) * (x + 3) = x^(2n-1) + 3x^(2n-2).

Subtract the result obtained in step 3 from the original dividend:

x^(2n-1) + 0x^(2n-2) + 0x^(2n-3) + ... - (x^(2n-1) + 3x^(2n-2)) = -3x^(2n-2) + 0x^(2n-3) + ...

Bring down the next term of the dividend (which is 0x^(2n-3)) and repeat steps 2-4 until the remainder is constant.

Since we are given that the remainder is -80, we can set the remainder equal to -80 and solve for 'n'.

-3x^(2n-2) + 0x^(2n-3) + ... = -80

Since the remainder is constant (-80), it means that all the terms with x have been canceled out in the division process. Therefore, we can deduce that the highest power of x in the divisor (x + 3) is 0.

This implies that x^(2n-2) = 0, and for any value of 'n', the exponent 2n-2 should be equal to zero. Solving this equation:

2n-2 = 0

2n = 2

n = 1

Therefore, the value of 'n' for which the division of x^(2n-1) by x + 3 leaves a remainder of -80 is n = 1.

for such more question on remainder

https://brainly.com/question/825875

#SPJ8

People at the concession stand as input Cost of their order's output.

(1) The relation in question is a function.

(II) This function is not constant. (Each category of concession has a different order cost.)

Not a 1-1 function (iii). (Several persons arrived seeking the same sort of concession. So they all pay the same price for their order.)

A function describes the relationship between patrons' inputs at the concession stand and the cost of their order as an output. A function is a relationship between a set of possible inputs and outputs, where each input is associated to exactly one output.

The quantity of patrons at the concession stand serves as the input in this scenario, while the cost of their order serves as the output.

Learn more about on concession, here:

https://brainly.com/question/32140051

#SPJ1

9514 1404 393

Answer:

  (b)  h(x) ≤ 5

Step-by-step explanation:

The maximum vertical extent of the graph is h(x) = 5 at x = 3. The range is all values of h(x) less than or equal to that:

  h(x) ≤ 5

Answer:  Choice B

The range is \(h(x) \le 5\)

==============================================================

Explanation:

If we graph y = x+2, but only draw the line for x values smaller than 3, then we'll end up with the red line shown in the diagram below.

The blue line is the graph of y = -x+8, but it's only drawn when \(x \ge 3\)

The two lines form an upside down V shape. This is an absolute value graph.

The highest point is at the vertex (3,5). The y coordinate is y = 5. This tells us that the largest h(x) can get is h(x) = 5.

Therefore, the range is \(h(x) \le 5\)

This is the same as saying \(y\le 5\) since y and h(x) are both outputs of a function.

The orthogonal projection of vector v onto vector w in R^3 is (-54/14, -159/70, -159/35).

To find the orthogonal projection of v onto w, we need to calculate the scalar projection of v onto w and multiply it by the unit vector of w. The scalar projection of v onto w is given by the formula:

proj_w(v) = (v⋅w) / (w⋅w) * w

where ⋅ denotes the dot product.

Calculating the dot product of v and w:

v⋅w = (-7)(-5) + (6)(-3) + (-6)(-6) = 35 + (-18) + 36 = 53

Calculating the dot product of w with itself:

w⋅w = (-5)(-5) + (-3)(-3) + (-6)(-6) = 25 + 9 + 36 = 70

Now, substituting these values into the formula, we have:

proj_w(v) = (53/70) * (-5,-3,-6) = (-54/14, -159/70, -159/35)

Therefore, the orthogonal projection of v onto w is (-54/14, -159/70, -159/35).

In simpler terms, the orthogonal projection of v onto w can be thought of as the vector that represents the shadow of v when it is cast onto the line defined by w. It is calculated by finding the component of v that aligns with w and multiplying it by the direction of w. The resulting vector (-54/14, -159/70, -159/35) lies on the line defined by w and represents the closest point to v along that line.

for such more questions on vector

https://brainly.com/question/15519257

#SPJ8

Answer:

12

Step-by-step explanation:

Solution:

To solve the inequality, isolate the variable on either side. Then graph it.

Simplifying the inequality:

Graphing the line:

The value of the expression a(b + c) when a = 2, b = 3, and c = 4 is 14.

Given the expression in the question:

a( b + c )

Also, a = 2, b = 3, and c = 4

To evaluate the expression a( b + c ) when a = 2, b = 3, and c = 4, we substitute these values into the expression:

Hence:

a( b + c )

Plug in a = 2, b = 3, and c = 4

2( 3 + 4 )

First, we simplify the parentheses by adding 3 and 4:

2( 7 )

Next, we multiply 2 and 7:

14

Therefore, the value of a(b + c) is 14 .

Learn more about algebraic expressions here: https://brainly.com/question/28959918

#SPJ1

Answer: D

Step-by-step explanation:

2x-36=0                                                

+36     +36

___________

2x=36

x=18

Even if one equation, -18 was not solved, you can easily cross out the ones without 18 and get the answer.

Answer:

(2+n)-3

That's how you write if that is what you want.

Answer:

A. y<-3

Step-by-step explanation:

(A) Triangle ABC, and triangle QPR are similar based on side-side-side (SSS) similarity.

(B) Triangle ABC and triangle DEF are similar based on side-side-side (SSS) similarity.

(C) ) Triangle STU and triangle JPM are similar based on side-angle-side (SAS) similarity.

(D) ) Triangle SMK and triangle QTR are similar based on angle-angle (AA) similarity.

Similar triangles have the same corresponding angle measures and proportional side lengths.

The triangle similarity criteria are:

(A) Triangle ABC, and triangle QPR are similar based on side-side-side similarity.

12/8 = 9/6

1.5 = 1.5

(B) Triangle ABC and triangle DEF are similar base on side-side-side similarity as shown in the side lengths.

(C) ) Triangle STU and triangle JPM are similar base on side-angle-side similarity.

14/10 = 21/15

1.4 =

(D) ) Triangle SMK and triangle QTR are similar base on angle-angle similarity.

SMK = 90⁰, 60⁰, 30⁰

QTR =  90⁰, 30⁰, 60⁰

Learn more about similar triangles here: brainly.com/question/27996834

#SPJ1

Answer:

a) p=0.154

b) P(X≤2)=0.019

c) He can argue that the proportion of minority jurors is not representative of the proportion of that minority in the population.

Step-by-step explanation:

a) The proportion can be calculated dividing the number of jurors that are from the minority race by the total number of jurors:

\(p=X/N=2/13=0.154\)

b) We can model this with a binomial random variable, with sample size n=13 and probability of success p=0.47.

The probability of k minority jurors in the sample is:

\(P(x=k)=\dbinom{n}{k}p^k(1-p)^{n-k}=\dbinom{13}{k}\cdot0.47^k\cdot0.53^{13-k}\)

We have to calculate the probability that 2 or less minority jurors. This can be calculated as:

\(P(x\leq2)=P(x=0)+P(x=1)+P(x=2)\\\\\\P(x=0)=\dbinom{13}{0}\cdot0.47^{0}\cdot0.53^{13}=1\cdot1\cdot0.0003=0.000\\\\\\P(x=1)=\dbinom{13}{1}\cdot0.47^{1}\cdot0.53^{12}=13\cdot0.47\cdot0=0.003\\\\\\P(x=2)=\dbinom{13}{2}\cdot0.47^{2}\cdot0.53^{11}=78\cdot0.221\cdot0.001=0.016\\\\\\\\P(x\leq2)=0.000+0.003+0.016\\\\P(x\leq2)=0.019\)

The probability that 2 or less minority jurors is 0.019.

Peter makes $25000 working as an Administrator per year.

Let's assume that Peter's salary is "S" dollars. We know that his expenses are 52.0% of his salary or 0.52S dollars per year. We also know that his expenses amount to $13000. Therefore, we can set up the following equation:

0.52S = $13000

To solve for S, we can divide both sides by 0.52:

S = $13000 / 0.52

S = $25000

Therefore, Peter makes $25000 working as an administrator per year.

To know more about Administrator .

https://brainly.com/question/31156967

#SPJ11

Answer:

50 cent

Step-by-step explanation:

Answer:

.50¢

Step-by-step explanation:

50 cents = 1 pound

$1.00 = 2 pound

$1.50 = 3 pounds

$2.00 = 4 pounds

basically adding 50 cents equals to $2

The 10th term of the geometric sequence is given as follows:

\(a_{10} = a_5\left(\sqrt{\frac{a_5}{a_3}}\right)^{n-5}\)

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

The nth term of a geometric sequence is given by:

\(a_n = a_1q^{n-1}\)

In which \(a_1\) is the first term.

Using the mth term as the reference, we have that:

\(a_n = a_mq^{n-m}\)

Hence:

\(a_5 = a_3q^2\)

\(q = \sqrt{\frac{a_5}{a_3}}\)

And then the 10th term is given as follows:

\(a_{10} = a_5\left(\sqrt{\frac{a_5}{a_3}}\right)^{n-5}\)

More can be learned about geometric sequences at https://brainly.com/question/11847927

#SPJ1

Answer:

1 83/200

Step-by-step explanation:

You need to make the 2/3 a decimal which is 0.66 repeating. Then you do 5.66 divided by 4 which equals 1.415 then you need to simplify.

Hope this helps.

9514 1404 393

Answer:

Step-by-step explanation:

The area is the product of length and width:

  A = LW

  144 = (w+10)(w)

  w^2 +10w -144 = 0 . . . . . . subtract 144 and put in standard form

  (w +18)(w -8) = 0 . . . . . . . . factor

  w = -18 or 8 . . . . . . . values that make the factors zero, -18 is extraneous

The width of the wall is 8 ft; the length is 18 ft.

_____

Additional comment

The equation is factored by looking for factors of -144 that have a sum of 10. We can choose from the different ways 144 can be factored:

  -144 = -1(144) = -2(72) = -3(48) = -4(36) = -6(24) = -8(18) = -9(16) = -12(12)

The respective sums are 143, 70, 45, 32, 18, 10, 7, 0.

So, the factors of -144 that have a sum of 10 are {-8, 18}. These are the constants that go into the binomial factors.

Answer: 117.2%

Step-by-step explanation:

Multiply both numerator and denominator by 100. We do this to find an equivalent fraction having 100 as the denominator.

Multiply both numerator and denominator by 100. We do this to find an equivalent fraction having 100 as the denominator.

= (1.172 × 100) × 1/100=117.2/100

Write in percentage notation: 117.2%

Answer:

1.172 as a percent is 117.2%

Step-by-step explanation:

To turn a decimal into a percent just move the decimal point(.) 2 spaces back.

To turn a Percent to a decimal move the move the decimal (.) two spaces up.

(If you dont see the decimal in the Percent it is alway behind the the last number) EX: 70% would be .70 as a decimal.

The steps which you would take to determine if these figures are similar include the following:

2. Multiply the vertices of polygon ABCD by 1/2.

5. Reflect the intermediate image.

In Mathematics and Geometry, a dilation is a type of transformation which typically transforms the dimension (size) or side lengths of a geometric object, without affecting its shape.

Therefore, the dimension or side lengths of the dilated geometric object would be stretched or compressed (shrunk) depending on the scale factor that is applied.

By critically observing the graph representing polygon ABCD, we can logically deduce that a sequence of transformations that would polygon ABCD (pre-image) onto polygon A"B"C"D" (image) is a dilation by a scale factor of 1/2 and a reflection of intermediate image.

Read more on dilation and scale factor here: brainly.com/question/4421026

#SPJ1

Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer: the number is 12.

Step-by-step explanation:

Let's call the two-digit number "x". We know that the sum of its digits is 7, so we can represent the number as 10a + b, where a and b are the digits of the number and a is the tens digit and b is the units digit.

The statement that "reversing its digits increases the number by 9" means that the number obtained by reversing the digits is x + 9. We can represent this reversed number as 10b + a.

So, we have two equations:

10a + b = x

10b + a = x + 9

Now, we can substitute the value of x from the first equation into the second equation:

10b + a = 10a + b + 9

Expanding both sides, we get:

10b + a = 10a + b + 9

9b = 9a + 9

b = a + 1

We know that 0 < a < 9, since the number is a two-digit number. So, we can conclude that 0 < b < 10.

We can now substitute the value of b into the first equation:

10a + (a + 1) = x

11a + 1 = x

11a = x - 1

a = (x - 1) / 11

Since a is the tens digit of the number, it must be an integer. We can test different values of x to find the value that satisfies this condition.

If x = 20, then a = (20 - 1) / 11 = 1. This gives us b = a + 1 = 2. The original number is 10a + b = 10 + 2 = 12, which satisfies all the conditions.

So, the number is 12.

Answer:

[6, 8).

Step-by-step explanation:

When we are looking for the range of a function by just looking at the graph, we have to define from what point to what point the graph move vertically. On the other hand, if we were looking for the domain, we would state from where to where the graph moves horizontally.

In this case we have to analyze the graph vertically, since we are looking for the range of the function. Therefore, if we take a look at the line we can notice that it goes from y=6 to y=8. Therefore the range should be from 6 to 8.

Now, this result must be expressed in interval notation, meaning that we have to state whether the values of each end are contained or not by the function. The graph already tells us about it., because it marks it with the closed or open dots. In the case of the number 6, we have a closed dot, means that the function contains the number 6. For the other end we have an open dot, means that the function doesn't contain the number 8.

Applying internal notation, the range of this function is:

[6, 8).

Learn more about interval notation here:

1. https://web.nmsu.edu/~kberver/Unit1/Unit18.html#:~:text=An%20interval%20is%20closed%20if,used%20for%20an%20open%20endpoint.

2. https://brilliant.org/wiki/interval-notation/#:~:text=Interval%20notation%20is%20a%20way,inequality%20or%20system%20of%20inequalities.

The population of North Carolina will reach 12 million in the year 2028.

Population growth is defined as the increase in the number of people which is calculated using population growth rate.

Given that,

Population in 2010 = 9.5 million

Population is increasing to 1.3% per year.

Annual growth rate = 1.3% = 1.3/100 = 0.013

We have the population growth formula,

P = P₀ e^(r t)

Here, P₀ = 9.5 million = 9,500,000

and P = 12 million = 12,000,000

r = 0.013

We have to find t.

12,000,000 = 9,500,000 e^(0.013t)

120 / 95 = e^(0.013t)

Taking natural logarithm on both sides and also ㏑(e^m) = m ㏑ e, we get,

㏑(12/9.5) = 0.013t × ㏑e

[㏑(12/9.5) ÷ 0.013] = t  [since ln e = 1]

t = 17.97 ≈ 18 years

The year is 2010 + 18 = 2028

Hence in the year 2028, the population will be 12 million.

Learn more about Population Growth here :

https://brainly.com/question/29885709

#SPJ1

Answer:

x = 10^34

Step-by-step explanation:

length × width = area

area/length = width

width = (1.12 × 10^45 ft²)/(7 × 10^11 ft)

width = 1.12/7 × (10^45)/(10^11)   ft

width = 0.16 × 10^34  ft

width = 1.6 × 10^34  ft

width = 1.6 × x  ft

x = 10^34

The value of x is \(10^3^2\)  or \(\rm x =10^3^2\)

It is given that the area of a rectangular field is  \(\rm 1.12\times10^4^5 \ feet^2\)

It is required to find the value of x

It is defined as the space occupied by the rectangle which is planner 2-dimensional geometry.

The formula for finding the area of a rectangle is given by:

Area of rectangle = length × width

We have:

Area of rectangle = \(\rm 1.12\times10^4^5 \ feet^2\)

The length of the rectangle = \(7\times 10^1^1\) feet

The width of the rectangle = \(\rm 1.6\times 10x\) feet

After putting the values in the formula, we get:

\(\rm 1.12\times10^4^5 =7\times 10^1^1\times\rm 1.6\times 10x\)

\(\rm x =\frac{1.12\times10^4^5}{7\times 10^1^1\times\rm 1.6\times 10} \\\)

\(\rm x =\frac{1.12\times10^4^5}{7\times 10^1^1\times\rm 1.6\times 10} \\\\\rm x = 0.1\times 10^3^3\)

\(\rm x =10^3^2\)

Thus, the value of x is \(10^3^2\)

Learn more about the area here:

https://brainly.com/question/14383947

Answer:

60 problems

Step-by-step explanation:

Find how many he got correct by multiplying 80 by 0.75:

80(0.75)

= 60

So, Bill got 60 problems correct

Answer:

−135z

2

−2z
The 2 is representing Square

Step-by-step explanation:

(3z)
2

−4z+11−(12z)
2

+2z−11

Expand (3z)

2

.

3

2

z

2

−4z+11−(12z)

2

+2z−11

Calculate 3 to the power of 2 and get 9.

9z

2

−4z+11−(12z)

2

+2z−11

Expand (12z)

2

.

9z

2

−4z+11−12

2

z

2

+2z−11

Calculate 12 to the power of 2 and get 144.

9z

2

−4z+11−144z

2

+2z−11

Combine 9z

2

 and −144z

2

 to get −135z

2

.

−135z

2

−4z+11+2z−11

Combine −4z and 2z to get −2z.

−135z

2

−2z+11−11

Subtract 11 from 11 to get 0.

−135z

2

−2z