1. Kelly has a rock garden with a length of 6 feet. She constructs a scale model of the rock garden using the scale 1 inch:2 feet.
(a) What is the length of the garden in her model? Show your work, including your proportion.
(b) If the width is 5 inches for the scale model and the scale is still 1 inch to 2 feet, will her scale model drawing fit on a piece of paper that is 8.5 inches by 7 inches? Why or why not?

n(AxB) = 25

Step-by-step explanation:

AxB in sets is called Cartesian product. And is defined as a set of ordered pairs (a,b) where a belongs to A and b belongs to B.

Given

A = {a,b,c,d,e}

B = {1,2,3,4,5}

The number of elements for Cartesian product of two sets is determined by:

[tex]n(AxB) = n(A) * n(B)[/tex]

Here

[tex]n(A) = 5\\n(B) = 5[/tex]

So,

[tex]n(AxB) = 5*5 = 25[/tex]

Hence,

n(AxB) = 25

Keywords: Sets, Cartesian Product

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The value of n(AxB) is 25

Given the following sets

A= {a,b,c,d,e} and let B= {1,2,3,4,5}, we are to determine n(AxB)

n(A) = 5 (number of elements in the set)

n(B) = 5

Get the cardinality of n(AxB)

Hence the value of n(AxB) is 25

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Answer:

(-4,17)

Step-by-step explanation:

2x-3y=-11

2x+y=9

solve the equation

x=-4

2x+y=9

substitute the value of x into an equation

2×(-4)+y=9

solve the equation

y=17

A possible solution is

(-4,17)

check the solution

2×(-4)-3=-11

2×(-4)+17=9

simplify

-11=-11

9=9

the order pair is a solution

answer is (-4,17)

To solve the given system using the substitution method, solve the second equation for y, substitute into the first equation, and solve for x. Substituting x back into the expression for y gives the solution x = 2 and y = 5.

To solve the system of equations using the substitution method, we have to express one variable in terms of another from one of the equations and then substitute it into the other equation. For the given system of equations:

First, we solve the second equation for y:

y = 9 - 2x

Now we substitute this expression for y into the first equation:

2x - 3(9 - 2x) = -11

2x - 27 + 6x = -11

8x - 27 = -11

8x = 16

x = 2

After finding x, we can substitute x back into y = 9 - 2x to find the value of y:

y = 9 - 2(2)

y = 9 - 4

y = 5

The solution to the system of equations is x = 2 and y = 5.

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Answer:

1. a. 72/100 = 324/x

72x = 32,400

b. 450 students are in Math 6

2. a. o = 3b

b. o = 3 pounds

3. a. Most popular animals:

A. Dogs - 67%

B. Cats - 20%

C. Other - 8%

D. None - 4%

E. Horses - 1%

b.  20 students

c. If 75 students have cats, the estimate of 250 students isn't correct.

The actual number of students interviewed is 375.

Step-by-step explanation:

1. a. Let's use the following equation to solve the question:

x = Students that are in Math 6

72/100 = 324/x

72 * x = 324 * 100

72x = 32,400

b. Let's solve the equation, as follows:

x = 32,400/72

x = 450

450 students are in Math 6

2. a. The equation is:

o = 0.15 *20b

o = 3b

where, o = weight of oats in pounds and b = number of dog food bags

b. Let's find out the weight of the oats in one dog food bag, using our equation:

o = 0.15 *20b

o = 0.15 *20 * 1

o = 3 pounds

3. a. Most popular animals:

A. Dogs - 67%

B. Cats - 20%

C. Other - 8%

D. None - 4%

E. Horses - 1%

b. If 250 students were interviewed, the 8% who answered "other" are:

8% of 250 = 0.08 * 250 = 20 students

c. If 75 students have cats, the estimate of 250 students isn't correct.

The 20% of 250 is 50, not 75.

0.2 * 250 = 50

The actual number of students interviewed is:

x = Actual number of students interviewed

75/x = 20/100

20x = 7,500

x = 7,500/20

x = 375

The actual number of students interviewed is 375.

The right answer is Option 4.

Step-by-step explanation:

Given expression is;

-1.5w+7.5

To factorize this expression, we will first take -1.5 common to make w positive.

[tex]-1.5(w-5)[/tex]

Because 5 multiplied by 7.5 divided by -1.5 is -5.

Therefore;

The expression is factored form is -1.5(w-5).

The right answer is Option 4.

Keywords: subtraction, addition

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The factored form of the expression −1.5w+7.5 is −1.5(w-5), since −1.5 is the common factor for both terms in the expression.

The factored form of the expression −1.5w+7.5 can be found by factoring out a common factor. The common factor in this expression is −1.5, as both terms in the expression can be divided by −1.5.

Factoring out −1.5, we get:

−1.5w + 7.5
= −1.5 (w) + −1.5 (-5)
= −1.5 (w - 5)

Therefore, the factored form of −1.5w+7.5 is −1.5(w−5).

Answer:

A rule of polygons is that the sum of the exterior angles always equals 360 degrees. Since it is a regular octagon, so each of the interior angles of octagon are equal. ((n-2)*180)/n where n is the number of sides of the polygon.for example in case n=8 for an octagon, so we get:

((8-2)*180)/8 => (6*180)/8 => 1080/8 = 135 degrees. This means that each interior angle of the regular octagon is equal to 135 degrees.  

Each exterior angle is the supplementary angle to the interior angle at the vertex of the polygon, so in this case each exterior angle is equal to 45 degrees. (180 - 135 = 45). Remember that supplementary angles add up to 180 degrees.  

And since there are 8 exterior angles, we multiply 45 degrees * 8 and we get 360 degrees.

This technique works for every polygon, as long as you are asked to take one exterior angle per vertex.

The sum of the exterior angles of any polygon, including an octagon, is always 360 degrees. This is true regardless of the polygon's number of sides, because when one traces around the polygon, the point will have made one full revolution, or 360 degrees.

In mathematics, the sum of the exterior angles of any polygon, not just an octagon, is always 360 degrees. This applies regardless of the number of sides the polygon has. The concept comes from observing how a point moves as one traces around the polygon: during the complete circuit, it will have made exactly one full revolution, which is 360 degrees in total. Just as a circle consists of 360 degrees, this concept applies to polygons and their exterior angles as well.

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Answer:

15-(6-3) = 12

Step-by-step explanation:

15 - (6-3) =

Solve inside the parenthesis

15-3=12

Answer:

answer is attached in the image below

Answer:

B. -3.

Step-by-step explanation:

If we take a look at the point (0, 1) in f(x), and compare it to the point (5, -2) in g(x), we can see that the point is simply moved to the right (translated horizontally) and moved down (translated vertically). Since k represents the vertical translation, the value must be -3.

1 -> -2

k = -3.

Answer:

B. -3

Step-by-step explanation:

Because I did the unit test

Answer:

The percent of the apartment that is unoccupied = (21/ 175) [tex]\times[/tex] 100 = 12%

Step-by-step explanation:

i.) the apartment complex has a total of 175 units.

ii.) 154 units are occupied.

iii.) therefore the number of unoccupied units is = 175 - 154 = 21 units.

iv.) the percent of the apartment that is unoccupied = (21/ 175) [tex]\times[/tex] 100 = 12%

Answer:

0.20

Step-by-step explanation:

0.20

Final answer:

Explaining how to create an equation for a specific scenario where 12 is subtracted from a certain number to equal 19.

Explanation:

An equation for 12 less than a number x is 19:

Define the variable: Let x be the number.

Set up the equation: x - 12 = 19.

Solve for x: x = 19 + 12 = 31.

Answer:

$50

Step-by-step explanation:

Simple math

Extended warranty don’t count so gotta take that out that’s be 20x18=360 1260-360=900 now divide 18 tvs from that and u get 900/18=50

To determine the fixed amount Gi earns for each television, a simple algebraic equation is set up and solved to find that he earns $ 50 per television without the extended warranty.

To solve for the fixed amount Gi earns for each television without the extended warranty, we can set up an equation.

Let's call the fixed amount $F. Each television with an extended warranty earns Gi an additional $ 20, so for each of those televisions, he earns $F + $20. If he sells 18 televisions with extended warranties,

the total amount he earns can be represented by 18($F + $ 20), which equals $ 1,260 according to the question.

We can create the following equation to find the fixed amount $F:

18($F + $ 20) = $ 1,260

To solve for $F, divide both sides of the equation by 18:

$F + $ 20 = $ 70

Then, subtract $ 20 from both sides to isolate $F:

$F = $ 50

So, the fixed amount Gi earns for each television is $ 50.

Answer:

C.

Step-by-step explanation:

recall that the point-slope form of a linear equation is given by

y = mx + c

Rearranging so that it is in the same form as the answer choices, we get

y = c + mx

where m is the slope and c is the y-intercept

we note the following observations

1) The line goes from top left to bottom right, this means that the slope is negative, hence m has to be negative. (in our case, all the choices have negative x)

2) The line crosses the y-axis at y = 4, this means the y-intercept is 4 and hence c = 4.

If we look at the choices, only choice B satisfies both observations (that m is negative and c = 4)

Answer:

B)

Step-by-step explanation:

Answer:

11x+50

Step-by-step explanation:

Answer:

15x - 24

Step-by-step explanation:

AnsWER:  22

Step-by-step explanation: (5+4)X 2+4

9X2+4

18+4

22

Answer:

-1

Step-by-step explanation:

Answer:

Step-by-step explanation:

(-1 - 4)/(2 + 3) = -5/5 = -1

answer is -1

Answer:

Step-by-step explanation:

i honestly dont even knw but i hope u get it right

Answer:

x=120°

Step-by-step explanation:

Let us draw a third horizontal line through x, parallel to the two parallel lines.

This line divides angle X into A and B as shown.

By alternate interior angle theorem, angle B=50°

and

angle A=70°

We know that: A+B=x

Therefore x=70°+50°=120°

Answer:

x=120 degrees

Step-by-step explanation:

1. 70+50=120

I get it its simple but its correct i do RSM

Answer: (3x-2)(x+5)

Hope this helps.

The correct answer for the factorization of   [tex]3x^{2} +13x -10[/tex]   is  [tex](3x-2)(x+5)[/tex].

Given expression:

[tex]3x^{2} +13x -10[/tex]

a: The coefficient  of [tex]x^{2}[/tex]

b: The coefficient of linear term variable.

c: The constant term.

In given question:

a= [tex]3x^{2}[/tex]  ,   b =[tex]13x[/tex]  ,   c = [tex]-10[/tex]

To factorize,
Split the middle term:

Find two numbers that multiply to ac (product of the coefficients of [tex]x^{2}[/tex] and the constant term) and add up to b (coefficient of [tex]x[/tex]).

ac = [tex]3*-10 = -30[/tex]

b = [tex]13[/tex]

The two numbers are:

[tex]15[/tex] and [tex]-2[/tex] because [tex]15 * -2[/tex] = [tex]-30[/tex] and [tex]15+(-2) = 13[/tex].

Rewrite the middle term using the two numbers found:

[tex]3x^{2} +15x-2x -10[/tex]

Simplify:

[tex]3x(x^{} + 5x)-2(x+5)[/tex]

[tex](x+5)(3x-2)[/tex]

The factored term of equation [tex]3x^{2} +13x -10[/tex]  is  [tex](3x-2)(x+5)[/tex].

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Answer: 722

Step-by-step explanation:

Add 700, 10, and 12. Your answer added altogether is 722.

Answer:

Period =½

Equation of midline, y=0

Maximum =2

Minimum=-2

Step-by-step explanation:

The given function is

[tex]f(x) = - 2 \cos(4 \pi \: x) [/tex]

The period is given by:

[tex] \frac{2\pi}{b} = \frac{2\pi}{4\pi} = \frac{1}{2} [/tex]

The equation of the midline is y=0 since there is no vertical shift

The amplitude of this function is 2 so the range is -2≤y≤2.

Hence the maximum value is 2 and minimum value is -2

Answer:

C. a 90° counterclockwise rotation about the origin and then a translation 10 units left.

Step-by-step explanation:

See the diagram attached to the question.

We have to select the sequence of transformations confirms congruence by mapping the shape I onto shape II.

The correct option is Option C.

C. a 90° counterclockwise rotation about the origin and then a translation 10 units left. (Answer)

Answer:11/12

Step-by-step explanation:

Answer:

Therefore the x-coordinate of the solution to this system is 2.4.

Step-by-step explanation:

Given system of equation is

      3x-y=6............(1)

and 2x+y=6...........(2)

Adding equation (1) and (2)

3x -y+2x-y=6+6

⇔5x =12

[tex]\Leftrightarrow x=\frac{12}{5}[/tex]

⇔x = 2.4

Putting the value of x in equation (1)

3×2.4 - y =6

⇔7.2 -y = 6

⇔y = 7.2-6

⇔y=1.2

Therefore the x-coordinate of the solution to this system is 2.4.

Step-by-step explanation:

Answer:

-8

Step-by-step explanation:

if its 2 more then [tex]-6-2=-8[/tex]

so if you think the opposite negative 8 plus 2 is -6

Step-by-step explanation:

The numbers which are multipe of 3:

3, 6, 9, 12, 15, 18, 21, 24, ......

The numbers which are multipe of 12:

12, 24, 36, 48, ......

The number is multiple of 12 is also multiple of 3 but the number is multiple of 3 the number may be multiple of 12 or may not be multople of 12.

Thus, If a number is a multiple of 3, it is not necessary to a multiple of 12.

Answer:

x < 21

Step-by-step explanation:

Given

12x < 252 ( divide both sides by 12 )

x < 21

Stephanie worked for 33 hours 20 minutes.

Explanation:

Step 1; Stephanie works and earns $4.50 an hour. Her last paycheck was for $150. So to find the number of hours she has worked we divide the total money earned by the money she earns every hour.

Total hours worked = Total money earned / Money earned for an hour

                                  = $150 / $4.50 = 33.33 hours.

Step 2; We need to convert the 33.33 hours into hours and minutes.

We multiply the 0.33 hours with 60 to convert it into minutes. 0.33 × 60 = 20 minutes. So Stephanie worked for 33 hours and 20 minutes to get her last paycheck.

Answer:

20 hours

Step-by-step explanation:

She receives $60 regardless of the number of hours she works for. Per hour, she earns $4.50. In t hours, she earns:

60 + 4.50t

For some t, the total is $150

150 = 60 + 4.50t

90 = 4.50t

t = 20