Factor Pairs (HIGH POINTS!)

What does the letter "L" stand for in the simulation?

Answer: d

Step-by-step explanation: ion know man but i looked it up and got it right

Let l be the length of the rectangle and w its width.

Then its area is given by:

a = l*w

Its perimeter is given by:

p = 2l + 2w

We also know that, for this specific triangle, we have:

2w = l - 4

l = 2w + 4

a = 126 m²

Applying this result in the area formula, we have:

w*l = 126

w(2w + 4) = 126

2w² +4w = 126

2w + 4w - 126 = 0

Therefore, w = 7 m and l = 2*7 + 4 = 10 m

Then, the perimeter is given by:

p = 2*18 + 2*7 = 36 + 14 = 50 m

The person must buy 10 gumballs so that she gets 4 gumballs that are the same color.

Given, gumball machine contains 9 red gumballs

7 white gumballs and

8 blue gumballs.

we are asked to determine the least number of gumball a person must buy to be sure that she gets 4 gumballs that are the same color.

If a person gets three gumballs of each of the three colors, that is, 9 gumballs, then the 10th gumball must be the fourth one for one of the colors. Therefore, the person must buy 10 gumballs.

Hence 10 gumballs should be purchased.

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The error term, which refers to the sum of the deviations within the regression line and explains the discrepancy between the theoretical value of the model and the actual observed results, denotes the margin of error inside a statistical model.

Y=αX+βρ+ϵ

where:

α,β=Constant parameters

X,ρ=Independent variables

ϵ=Error term

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x = 17

Step-by-step explanation:

5x = 85

x = 85/5

x = 17.

Hence, option (b) is correct answer

Answer: x=17 the answer is B

Hope this helped

Step-by-step explanation:

30

Given the expression for the instantaneous voltage expressed as:

Given the following parameter:

θ = 30⁰

Substitute the given parameter into the formula to have:

Therefore the instantaneous voltage when θ = 30⁰ is 30.

144 yards of string will need to use balloons for the party.

Given,

The length of balloon string Orlando wanted = 6 feet

Number of balloons = 72

We have to find the total length of strings wanted for 72 balloons in yards.

1 yard = 3 feet

Now,

Total length of strings Orlando needs = length of one string x number of balloons = 6 x 72 = 432 feet

Now convert 432 feet into yard

That is,

432 / 3 = 144 yards

So,

144 yards of string will need to use balloons for the party.

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The most appropriate choice for percentage will be given by -

Total salary of Marques in a week = $825

If Marques makes $x in sales, his total salary in a week = $([tex]750 + \frac{x}{10}[/tex])

What is Percentage?

Suppose there is a number and that number has to be expressed as a fraction of 100. The fraction is called percentage. For example 2% means [tex]\frac{2}{100}[/tex]

Here,

Guarantee salary of Marques = $200

Sales made by Marques in a week= $750

Percentage commission on total sales = 10 %

Commission received by Marques = [tex]\frac{10}{100} \times 750\\[/tex]

                                                          = $75

Total salary of Marques in a week = $(750 + 75)

                                                         = $825

If Marques makes $x in sales, his total salary in a week = $([tex]750 + \frac{10}{100}\times x[/tex])

                                                                                            = $([tex]750[/tex] + [tex]\frac{x}{10}[/tex])

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Answer:

0.14 meters, or 140 mm

Step-by-step explanation:

(1/40) means that the model car will have dimensions that are (1/40) the original car.

Real car = 5.5 meters.

Model car = (1/40)*(5.5 m) = 0.14 meters, or 140 mm

The Total cost of x small and y large greeting cards is; 1.25x + 4.50y.

An equation is an expression that shows the relationship between two or more numbers and variables.

Given that the Cost of the small greeting card = is $1.25 .

The Cost of the large greeting card =$4.50.

We need to determine the Total cost of 5 small and 4 large greeting cards and the total cost of x small and y large greeting cards.

The Cost of 5 small greeting cards = 6.25

The Cost of 4 large greeting cards = 18

Then the Total cost = $6.25+ $18 =$24.25

Therefore, the Total cost of 5 small and 4 large greeting cards is; $24.25.

Now, the total cost of x small and y large greeting cards will be;

Cost of x small greeting cards = 1.25x

Cost of y large greeting cards = 4.50y

Total cost = 1.25x + 4.50y

Therefore, the Total cost of x small and y large greeting cards is; 1.25x + 4.50y.

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Answer:4 sodas

Step-by-step explanation:

1.75 x 2 = 3.5

10- 3.5 = 6.5

6.5 Divided by 1.50 =  4.33333333

(Round that to 4 and he will be left with cents)

to get the slope of any straight line, we simply need two points off of it, let's use the ones from the picture below.

[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{20}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{20}-\stackrel{y1}{0}}}{\underset{run} {\underset{x_2}{5}-\underset{x_1}{0}}} \implies \cfrac{ 20 }{ 5 } \implies \text{\LARGE 4}[/tex]

Answer:

The answer is d) 22.4

Step-by-step explanation:

I attached a file below if you want to see the process!

The general form of an equation in intercetp form is:

Where m is the change of y in function of x and b is the value of b when x is 0

In this situation you have:

y=C

x=r

m= 1.75 ( C increase 1.75 each r)

b= 7 (When there is not ride r=0 the admission fee is 7)

It will take 15 days for Akash to complete the entire work if he is assisted by Sunil and Rakesh every third day.

To determine the number of days, we first represent the number of days to do a piece of work by each one of them in fractions as follows;

Fraction of work completed by Akash in 1 day = 1/20

Fraction of work completed by Sunil in 1 day = 1/30

Fraction of work completed by Rakesh in 1 day = 1/60

The total work done in 1 day can be given as;

Total work done by the three in one day = [(1/20) + (1/30) + (1/60)] = 1/10

Work done by Akash in two days = 2 × (1/20) = 2/20 = 1/10

The work done in three days (1 day of all three together + Work done by Akash in two days) = (1/10) + (1/10) = 1/5

Therefore; the total work done in 3 days = 1/5

At this rate, the total number of cycles required to finish the work =

(1) ÷ (1/5) = 5

Since each cycle has three days, the total number of days required to finish the work can be calculated as follows;

5 × 3 = 15 days

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The number of soda bottles = 4

The number of sugar bottles = 7

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Weight of each bottle of soda = 45 grams

Weight of each bottle of sugar = 15 grams

Total weight of sugar and soda = 285 grams

Let the number of soda bottle = x

And, The number of sugar bottle = y

Since, Total number of bottles = 11

So, We can formulate;

⇒ x + y = 11    .... (i)

And, Weight of each bottle of soda = 45 grams

Weight of each bottle of sugar = 15 grams

Total weight of sugar and soda = 285 grams

So, We can formulate;

⇒ 45x + 15y = 285   ... (ii)

Multiply by 15 in equation (i) and subtract from (ii), we get;

⇒ 45x + 15y - 15x - 15y = 285 - 165

⇒ 30x = 120

Divide by 30;

⇒ x = 4

Hence,  x + y = 11    

4 + y = 11

y = 11 - 4

y = 7

So, The number of soda bottles = 4

The number of sugar bottles = 7.

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w=L+15

p=(L+w)

150cm=L+L+15

150cm=2L+15

2L=150cm-15

2L=135cm

2L÷2=135cm÷2

L=67.5

w=67.5+15

w=82.5

The graph of g and f have equal intercepts while the slope of the graph of f is 5 times larger than the slope of the graph of g

Given: f(x) = 2x-5 and g(x)=2(0.2x)-5

To compare the two graphs, we can make use of the equation of a line:

The general form of the equation of a line is y = mx + c

Where m is the slope and c is the intercept

So we will compare two the functions with the equation of a line:

Comparing f(x) = (2x-5) with y = mx + c

The slope(m) of the line = 2 and the intercept(c) = -5

Also, comparing g(x) = 2(0.2x)-5 with y = mx + c

The slope(m) of the line = 2(0.2) = 0.4 and the intercept(c) = -5

Since the slope of f(x) = 2 and the slope of g(x) = 0.4. Thus:

slope of f(x) / slope of g(x)  = 2/0.4 = 5

So we can say the slope of  f(x) is  5 times the slope of g(x)

Therefore, the graph of g and f have the same intercept. But the slope of f(x) is  5 times the slope of g(x)

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Answer:

x = 40

Step-by-step explanation:

x = 8 x 5

x = 40

that's it

Answer:

x=5,−5

Step-by-step explanation:

The slope-intercept form of the linear equation is

y = m x + b, where

m is the slope

b is the y-intercept

If the x-coordinates of the two points are equal, that means the line is vertical

A vertical line has no slope

Its equation is x = a, where a is the x-coordinate of any point on the line

13) The two points are (5, 3) and (5, 4)

They have the same x-coordinates, then its equation is

x = 5

The rule of the slope is

(x1, y1) and (x2, y2) are two points on the line

The line passes through points (0, 4) and (2, 3)

x1 = 0 and y1 = 4

x2 = 2 and y2 = 3

Substitute them in the rule above to find m

The equation is

b is the value of y at x = 0

at x = 0 y = 4

b = 4

The equation of the line is

Answer:

x=23

Step-by-step explanation:

The amount of degrees in a triangle is 180 degrees.

line AC and line DF are straight angles meaning that the opposite angles are equal to each other. That means that angle FBC is also equal to x. Because line AC and EF are parallel we know that FBC and BFE are equal. Therefore, BFE is equal to x. The sum of the values of each angle of the triangle should add up to 180. 5x+65=180

5x=115

x=23

Answer:

second answer

Step-by-step explanation:

The distance between the two points in simplest radical form(−2,−7) and (5,0) is 9.8995

Distance can be described as the differences that exist between two points and this can be expressed i different form such as the radical form.

We can calculate the distance between the two points by firstly expressed them as :

(−2) - (5) = -7

(-7) - 0 = -7

Then the distance between them can be found as :

Distance = (-7)^2 + (-7)^2 = 49 +49 = 98

Then we will find the square root of the the figure as

= [tex]\sqrt{98}[/tex] = 9.8995

The formula can as well be used to find this by substituting the values of x and y into the formula as :

x1=-2

y1=-7

x2=5

y2=0

[tex]d = \sqrt{ ( x_{2} - x_{1} )^{2} + ( y_{2} - y_{1} )^{2}}[/tex]

then [tex]d = \sqrt{ ( 5 - (-2 )^{2} + ( 0 - (-7) )^{2}}[/tex]

= [tex]\sqrt{ 49^{2} + 49^{2} }[/tex]

= [tex]\sqrt{98}[/tex]

=9.8995

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The two equations that are true when x = -2 and x = 2 are x^2 - 4 = 0 and 4x^2 = 16.

We have given x = 2 and x = -2

Substitute the values in the given equations

Equation 1

x^2 - 4 = 0

Substitute x = 2 in LHS, we get

2^2-4 = 4 - 4 = 0 = RHS

Substitute x = -2 in LHS, we get

(-2)^2-4 = 4 - 4 = 0 = RHS

Equation 2

x^2 = -4

Substitute x = 2 in LHS, we get

2^2 = 4 ≠ RHS

Substitute x = -2 in LHS, we get

(-2)^2 = 4 ≠ RHS

Equation 3

3x^2 + 12 = 0

Substitute x = 2 in LHS, we get

3(2)^2 + 12 = 12 + 12 = 24 ≠ RHS

Substitute x = -2 in LHS, we get

3(-2)^2 + 12 = 12 + 12 = 24 ≠ RHS

Equation 4

4x^2 = 16

Substitute x = 2 in LHS, we get

4(2)^2 = 4(4) = 16 = RHS

Substitute x = -2 in LHS, we get

4(-2)^2 = 4(4) = 16 = RHS

Equation 5

2(x-2)2 = 0

Substitute x = 2 in LHS, we get

2(2-2)2 = 2(0)(2) = 0 = RHS

Substitute x = -2 in LHS, we get

2(-2-2)2 = 2(-4)(2) = 16

Hence, we find that Equation 1 and Equation 2 are true for x = 2 and x = -2

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Given:

The series is 1/3−2/21+4/147−8/1029+··

Explanation:

For the given series, the first term is,

The common ratio is,

The formula for the sum of infinite series is,

Substitute the values in the formula to determine the sum of infinite series.

Answer: 7/27