Graph the polygon with the given vertices and its image after a dilation with scale factor k.
A(0, 5), B( 10,-5), C(5,-5); k= 120%

In the function, f(x) = a(b)ˣ the value of a and b is

The function defined by f(x) = a(b)ˣ is a exponential function

Where

a is the starting function

b is the base function

The starting function from (0,24)

24 = a(b)ˣ

a = 24

using (1, 18), we solve for the base

18 = 24(b)

b = 0.75

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The probability both get a 3 is 1/60

From the question, we have the following parameters that can be used in our computation:

Jim = 1 to 10

Lyn = 1 to 6

Using the above as a guide, we have the following:

P(Jim = 3) = 1/10

P(Lyn= 3) = 1/6

Using the above as a guide, we have the following:

Required probability = 1/10 * 1/6

Evaluate the product

Required probability = 1/60

Hence, the probabilty is 1/60

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[tex] \large \blue{ \large\tt{C ) \$500}}[/tex]

_____________

[tex] \: [/tex]

Given:-

[tex] \: [/tex]

By using formula:-

[tex] \boxed{ \rm{ \pink{Simple \: interest= \frac{Principal × Time × Rate}{100}}}}[/tex]

[tex] \: [/tex]

Solution:-

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

hope it helps!:)

Answer: the answer is c.$500 hope that helps !

Step-by-step explanation: I took the test

The measure of other sides of a triangle are 15.11 units and 10.76 units.

Law of Sines In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles.

The formula for sine rule is sinA/a=sinB/b=sinC/c

In the given triangle, ∠B=45°, ∠C=52° and AB=12 units.

By using angle sum property of a triangle,

∠A+∠B+∠C=180°

∠A+45°+52°=180°

∠A+97°=180°

∠A=83°

Now, by using sine rule, we get

sin83°/a=sin45°/b=sin52°/12

0.9925/a=0.7071/b=0.788/12

0.9925/a=0.788/12 and 0.7071/b=0.788/12

0.788a=11.91 and 0.788b=8.4852

a=11.91/0.788 and b=8.4852/0.788

a=15.11 units and b=10.76 units

Therefore, the measure of other sides of a triangle are 15.11 units and 10.76 units.

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Answer:

Step-by-step explanation:

You just need to remember to first convert percentages to decimal form by dividing the percent by 100. Then you can work out the calculations.

Also, remember that if the problem is asking you to find a percentage, you need to turn your decimal answer to a percentage by multiplying by 100.

I used x to represent what we are looking for:

6.5% of $400 = x

0.065 * 400 = $26

12.5% of 100 = x

0.125 * 100 = $12.5

x of 650 = 130

130/650 = 0.2 which equals 20%

x of $4.50 = $5.40

5.40/4.50 = 1.2 which equals 120%

x of $28 = $8.40

8.40/28 = 0.3 which equals 30%

56% of x = $21.84

21.84/0.56 = 39

55% of x = $495

495/0.55 = 900

x of 400 = 120

120/400 = 0.3 which equals 30%

4% of 975 = x

0.04 * 975 = 39

Answer:

See below

Step-by-step explanation:

a. 6.5% of $400:

[tex]= \frac{65}{100}[/tex]× ($400)

= $260

b. 12.5% of $100:

[tex]= \frac{12.5}{100}[/tex] × ($100)

= $12.5

c. 130 is what percent of 650:

[tex]=\frac{130}{650}[/tex]×100%
= 20%

d. $5.40 is what percent of $4.50:

[tex]= \frac{5.40}{4.50}[/tex]×100%
= 120%

e. $8.40 is what percent of $28:

[tex]= \frac{8.40}{28}[/tex]× 100%
= 30%

f. 56% of what number is $21.84:

=[tex]\frac{56}{100}[/tex]× number = $21.84

∴ Number = [tex]\frac{100}{56}[/tex]×$21.84

                 = $39

g. $495 is 55% of what number:

= $495 = [tex]\frac{55}{100}[/tex]× Number

∴Number = [tex]\frac{100}{55}[/tex]×($495)

                 = $900

h. 120 is what percent of 400:

= [tex]\frac{120}{400}[/tex]×100%
= 30%

i. 4% of 975 is what number:

= [tex]\frac{4}{100}[/tex]×975

= 39

The solution for x in the triangle is x = 52.5

The bisector of an angle in a triangle divides the opposite side in the ratio of the sides containing the angle. That is:

PQ/QR = PS/SR

PQ = x, QR = 35, PS = 42 and SR = 70 - 42 = 28.

Therefore, we have:

PQ/QR = PS/SR

x/35 = 42/28

28*x = 42*35

28x = 1470

x = 1470/28

x = 52.5

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The term that best describes the point W in the triangle is given by the following option:

B. Orthocenter.

The orthocenter is the point where all three altitudes of a triangle will intersect.

An altitude is a line which passing through one of the three vertices of the triangle and is perpendicular to the opposite side relative to this vertex.

Hence point W is the orthocenter of triangle XYZ.

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Answer:

17

Step-by-step explanation:

5 x 3 = 15

15 - (-2) = 17

Sarah goes first, James goes second, and Matthew goes third.

Answer:

C) 175.

Step-by-step explanation:

Sure, here's a step-by-step solution:

Let's call the number of employees at the agency "x".

If 80% of the employees have more than 12 days of unused sick leave, that means 0.8 * x employees have more than 12 days of unused sick leave.

We know that 0.8 * x = 140, so we can solve for x by dividing both sides of the equation by 0.8:

x = 140 / 0.8

Simplifying, we get:

x = 175

So there are 175 employees who work at the agency, and the answer is C) 175.

Answer: Let's call the ratio of the perimeters of the two similar figures "k". That means that for every unit of length in RSTU, there are k units of length in ABCD.

Since UR = 18 and DA = 24, k = 24/18 = 4/3.

So for every length in RSTU, there are 4/3 times that length in ABCD. We can use this ratio to find the corresponding lengths in ABCD. For example, SR = 36, so BS = 36 * (4/3) = 48.

Now that we have the lengths of all sides of ABCD, we can find its perimeter:

Perimeter of ABCD = 24 + 48 + BC + 24 = 120 + BC

Perimeter of RSTU = 18 + 36 + 18 + 36 = 108

So the ratio of their perimeters is:

Perimeter of ABCD / Perimeter of RSTU = (120 + BC) / 108 = (120 / 108) + (BC / 108) = 20/18 + BC/108

Since the perimeters of the two figures are similar, the ratio of their perimeters is equal to the ratio of their corresponding side lengths:

20/18 + BC/108 = 4/3

Solving for BC:

BC = (4/3 - 20/18) * 108 = 36

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

1.4 m = .42     divide both sides of the equation by   1.4 to get

 m = .3     Done.

The amount of money that would be paid for rent each year for the spa would be = $37,800

The area of the potential space for the opening of your first spa = 1,800 square feet.

The price for each square feet per year = $21

That is; = 1800× 21 = $37,800

Therefore, annual rent fees for the space which will be used for spa = $37,800.

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Answer:

= -1+12h.

Step-by-step explanation:

I guess my answer is correct

The tables of x- and y-values that represents a function include the following: C. table C.

In Mathematics, a function is a mathematical expression which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair in tables or relations.

This ultimately implies that, a function is typically used in mathematics for uniquely mapping an input variable (domain) to an output variable (range) representing a given scenario or situation such as the following:

x  1   3   7   5   2  4

y  6  6   6   6   6  6

In conclusion, we can reasonably infer and logically deduce that only table C represent a function.

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Answer:

f(2) = 18

Step-by-step explanation:

If f(x) = 3 * (x + 4)

Than f(2) = 3 * (2 + 4) (coz x is an argument)

f(2) = 3 * (2 + 4)

f(2) = 3 * 6

f(2) = 18

The correct options are sample more families, sample families having children who are not in seventh grade.

Sample families that do not have children. Sample families living in every third house in neighborhood.

To increase the validity of the results of Kai's survey, he could make the following improvements to his sample:

Sample more families: Increasing the sample size would make the results more representative of the neighborhood as a whole, reducing the impact of random variation and making the estimates more precise.

Sample families that have children who are not in seventh grade: This would make the sample more diverse and representative of families with children of different ages.

Sample families that do not have children: Including families without children would make the sample more diverse and representative of the entire neighborhood.

Sample families living in every third house in the neighborhood: This would help to ensure that the sample is geographically representative of the neighborhood, reducing the chance of

sampling bias.

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7 nickels is 7/5, thus 7 nickels to 47 dime is 1.4 dime to 47 dime.

When both terms are multiplied by their biggest common factor, 1.4 dime, the ratio can be simplified to its simplest form: 47 dimes = 14: 470

The ratio of quantity, amount, or size of two or more items is known as proportion. It is the indicated quotient of two mathematical expressions.

"1 to 2" is the way to write the ratio 1: 2. Accordingly, of the total of 3, there is one component that is worth 1 and another part that is worth 2. Changing a part-to-part ratio to a fraction To get the whole, add the ratio terms. The denominator should be this.

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Answer:

  C.  Solve for the variable y.

Step-by-step explanation:

You want to know what needs to be done to an equation to find the slope and y-intercept.

The slope-intercept form of the equation for a line is ...

  y = mx + b

This is a polynomial equation written in standard form with the terms in decreasing order of the power of the variable. In this equation, the coefficient 'm' is the slope of the line, and the constant 'b' is the y-intercept on the graph.

This equation can be obtained from other forms of the equation for a line by solving for y and arranging the terms to match this form. That is, to find the slope and y-intercept, what needs to be done is ...

  C.  Solve for the variable y.

__

Additional comment

The description "standard form" as used above applies to polynomials in general. Specific polynomial equations, as for lines, circles, ellipses, hyperbolas, have their own "standard form."

The form called "standard form" for a linear equation is ...

  ax +by = c

where a, b, c are mutually prime integers with a > 0. In the case of a horizontal line, b > 0.

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Answer:

Step-by-step explanation:

To calculate the compound interest on Mary's savings account, we can use the formula:

A = P * (1 + r/n)^(nt)

Where:

A is the amount after t years

P is the initial principal (£12000)

r is the interest rate (1.5%)

n is the number of times the interest is compounded in a year (let's assume it's compounded annually)

t is the number of years (2)

So, plugging in the values, we get:

A = £12000 * (1 + 0.015/1)^(1 * 2)

A = £12000 * (1.015)^2

A = £12000 * 1.0302

A = £12363.84

So, after 2 years, Mary's £12000 investment would be worth £12363.84, including the compound interest.

The functions f(x) = x³ + x² - 2x + 3 and g(x) = log(x) + 2 have same range as (-∞,∞) or {y : y∈R}.

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

The given functions are -

f(x) = x³ + x² - 2x + 3

g(x) = log(x) + 2

The graph for function f(x) is plotted.

The function f(x) is a cubic function.

The domain for the function is (-∞,∞) or {x : x∈R}.

The range for the function is (-∞,∞) or {y : y∈R}.

The x-intercept for the function is (-2.37442376,0).

The y-intercept for the function is (0,3).

The graph for function g(x) is plotted.

The function g(x) is a logarithmic function.

The domain for the function is (0,∞) or {x : x>0}.

The range for the function is (-∞,∞) or {y : y∈R}.

The x-intercept for the function is (0.01,0).

The y-intercept for the function is not available.

Therefore, both functions have same range,

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Answer:

Below

Step-by-step explanation:

One leg would be    hyp * cos 30   and one would be  hyp cos 60

                   hyp cos 30 : hyp cos 60

                           cos 30 : cos 60

                      =   ratio     sqrt (3) /2  :  1/2     or     sqrt 3  : 1

A reasonable exponent is one that is fractional. For instance, 412 4 1 2 can be used to represent the number 4.

Given,

[tex]$\left(\frac{4 y^2}{5}\right)^2[/tex]

Apply exponent rule: [tex]$\left(\frac{a}{b}\right)^c=\frac{a^c}{b^c}$[/tex]

[tex]$=\frac{\left(4 y^2\right)^2}{5^2}[/tex]

Simplify [tex]$\left(4 y^2\right)^2: 16 y^4$[/tex]

[tex]$=\frac{16 y^4}{5^2}[/tex]

The we get,

[tex]$& =\frac{16 y^4}{25}[/tex]

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Answer:

Let's call the number of students at the college "x". Then, the number of faculty/staff is 3 times that number, or 3x. The total number of people at the college is the sum of the students and faculty/staff, which is x + 3x = 4x.

According to the problem, the ratio of faculty/staff to students is 3 to 13, so we can write an equation:

3x / x = 3 / 13

To find the number of students, we can solve for x:

4x = 4000

x = 1000

So, there are 1000 students at the college.

Answer:

140

Step-by-step explanation:

(5*7*8)/2= 280/2 =140

To volume to fill the rectangular garden is 8.99 cubic yard

To determine the volume of amount of sand required to fill the garden, we can simply convert the dimensions from inches and feet into yard.

inch to yard

6 inch = 0.17 yard

Feet to yard

28 feet = 9.33 yard

17 feet = 5.67 yard

The volume of the rectangular garden is given as;

v = l * w * h

Substituting the values;

V = 0.17 * 9.33 * 5.67

v = 8.99 cubic yard

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