Hannah simplified the radical below and wants someone to check the work (view image)

When the points are (2, 6), (2, -2), and (8 units), the polygon's or triangle's area is 8. ( 4 , -2)

A triangle, which is a polygon, has three sides and three vertices. One of geometry's basic shapes is it. A triangle with the vertices A, B, and C is referred to as Triangle ABC. A unique plane and triangle are discovered in Euclidean geometry when the three points are not collinear. Having three sides and three corners, a triangle is a polygon. The triangle's corners are defined as where the three sides meet one another end to end. 180 degrees is the sum of the angles in a triangle.

given

area of the polygon ( triangle ) = 1/2 * b * h

= 1/2 * 4 * 4

= 8 units

so When the points are (2, 6), (2, -2), and (8 units), the polygon's or triangle's area is 8. ( 4 , -2)

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Answers to ratios are first one is option B, second one is option A and third one is option C.

Ratio is defined as the relationship between two quantities where it tells how much one quantity is contained in the other.

1. Ratio of smoothie size to mangos used for Kim = 8 : 1

Ratio of smoothie size to mangos used for Bri = 24 : 3

                                                                             = 8 × 3 : 1 × 3

                                                                             = 8 : 1

Ratio of smoothie size to mangos used for Angela = 32 : 4

                                                                                    = 8 × 4 : 1 × 4

                                                                                    = 8 : 1

So the ratio of smoothie size to mangos used for Bri is the same as the ratio of smoothie size to mangos used for Angela.

So the answer is option B.

2. Ratio of width to length of larger canvas = 4 : 6 = 2 : 3

Ratio of width to length of smaller canvas = 2 : 3

So the painting's width to length ratios are equal because the ratio 4 to 6 is equal to the ratio 2 to 3.

So the answer is option A.

3. Ratio of students who prefer free time at the beginning of the class to students who prefer free time at the end of the class is 12/19

Total students = 12 + 19 = 31

Out of 31 students, 12 students prefer free time at the beginning of the class and 19 students prefer free time at the end of the class.

So the answer is option C.

Hence the answers on ratios are done.

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The value of x = -7 and y = 9 from the system of equations .

A finite collection of equations for which common solutions are sought is referred to as a set of simultaneous equations, often known as a system of equations or an equation system.

simultaneous equations, system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.

To create an equation in one variable using the elimination approach, you may either add or subtract the equations. To remove a variable, add the equations when the coefficients of one variable are in opposition, and subtract the equations when the coefficients of one variable are in equality.

The equations are :

-x - y = -2          (i)

and

5x + 7y = 28        (ii)

multipling eqation (i) with 5 and then adding both equations we get,

-5x - 5y +5x + 7y = -10 + 28

⇒ 2y = 18

⇒ y = 9

Again, -x -9 = -2

or, x = -7

The value of x = -7 and y = 9 from the system of equations

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On solving the question, 5 topping would pay the same amount for Pizza A and Pizza B,  the value of equation 0.50x=2.50=>   x=5

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

let x be the number of toppings,the total cost of a pizza is given by:

pizza cost+topping cost

for pizza a =10+1.50x

for pizza b=12.50+1.00x

we solve for when cost are same and for how many toppings

   10+1.50x=12.50+1.00x

   10+0.50x=12.50

   0.50x=2.50

        x=5

would pay the same amount for Pizza A and Pizza B. are 5 toppings,

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Tracy gets $1299.375 interest after 8 years and 3 months for an investment of  $3,500 at a 4.5% annual interest rate.

What is Simple Interest?

Simple interest is calculated based on a loan's principal or the initial deposit into a savings account. Simple interest doesn't compound, therefore a creditor will only charge interest on the principal sum, and a borrower will never be required to pay further interest on the interest that has already accrued.

The formula for calculating Simple Interest is -

S.I. = (P×R×T)/100

where, P = initial principal balance, R = annual interest rate and T = time (in years)

So, the principal rate, P = $3,500, the interest value, R = 4.5%, and the Time is T= 8.25 years.

Applying the formula for Simple Interest -

S.I. = (P×R×T)/100

S.I. = (3500×4.5×8.25)/100

S.I. = 1299.375

Therefore, the interest amount obtained is $1299.375.

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Using formula of midpoint of a line, the coordinate of the midpoint is (-3, 0)

The midpoint of a line is a point that is equidistant from both endpoints of the line. It can be found by taking the average of the x-coordinates of the two endpoints, and then taking the average of the y-coordinates of the two endpoints. For example, if the two endpoints of a line are (x₁, y₁) and (x₂, y₂), then the midpoint of the line is:

Midpoint = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)

The formula of midpoint of a line is given as;

M(x, y) = (x₂ + x₁) / 2, (y₂ + y₁) / 2

Substituting the values into the formula;

M(x, y) = (-7 + 1) / 2, (-5 + 5) / 2

M(x , y) = -6/2, 0/2

M(x, y) = -3, 0

The coordinate of midpoint is (-3, 0)

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According to the information the amount of insurance would be $66,160, the amount of coverage for personal property would be $41,350, the amount of coverage for loss of use would be $16,540 and the amount of coverage for garage would be $8,270.

To calculate the amount of each insurance we have to take into account the main value ($82,700) and the percentage of each insurance. Then, we have to calculate every percentage value as shown.

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Answer:

The graph of the cube root function is a continuous and smooth curve that starts at the point (0,0) and extends indefinitely in both the positive and negative directions on the x-axis. The graph increases as x increases from negative infinity to 0, and then decreases as x increases from 0 to positive infinity.

The graph has a vertical asymptote at x = 0, meaning that as x approaches 0 from either direction, the y-values of the points on the graph become very large. However, since the function is defined as the cube root of x, the function is not actually defined at x = 0, so the asymptote is not part of the graph.

The function is an odd function, which means that it is symmetrical about the y-axis. This means that if we were to reflect the part of the graph that is to the right of the y-axis over the y-axis, the resulting graph would exactly match the part of the graph that is to the left of the y-axis.

Overall, the graph of the cube root function is a smooth curve that starts at (0,0) and extends indefinitely in both directions on the x-axis, with a vertical asymptote at x = 0 and symmetry about the y-axis.

a cubic function whose graph passes through the points (-3, 0), (1, 0), (4, 0), and (0,8) is: f(x) = - 2 (x + 3) (x - 1) (x - 4)

A cubic function is a function whose expression contains the cube of the x variable. A function is referred to as a cubic function if its formula is f(x) = ax³ + bx² + cx + d. a, b, c, and d can all be constants in this case, but make sure that a 0. The b, c, or d might all be zeros.

A cubic function has 3 roots.

Let, assume α, β and γ.

So, f(x) = K (x - α). (x - β). (x - γ)

f(x) is defined by values of x where f(x) = 0

0 = K (x - α). (x - β). (x - γ)

x = α, β, γ

The given cubic function graph is cutting x - axis at 3 points: (-3, 1 ,4)

Now, f(x) = K (x - (-3). (x - 1). (x - 4)

f(x) = K (x + 3) (x - 1) (x - 4)

Next, f(x) passes through point (0,8) which means:

f(0) = 8

so, 8 = K (0 + 3) (0 - 1) (0 - 4)

or, k = - 2

Now, f(x) = - 2 (x + 3) (x - 1) (x - 4)

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By adding the weight of the triangle, the weight of the circle heavier than that of the square.

The linear equation that results from examining the weights will contain the following parameters.

Let t stand for the triangle.

Let c stand for the circle.

Let's use the shape square.

left side of the equation = 6s + 3t

right side of the equation = 3s + 3c

equating both sides

6s + 3t = 3s + 3c

6s - 3s + 3t = 3s + 3c

3s + 3t = 3c

3(s + t) = 3c

dividing all through by 3

s + t = c

10 + t = c

Because of the resulting equation, we can conclude that the the circle is weightier than the square by the weight of the triangle

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The table is given below.

The graph is given below.

The linear model that represents lucky's current weight in pounds as a function of his age in months is

f(x) = 9x - 15.

Lucky's weight in one year is 93 pounds.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

Lucky current age and weight = 2 months and 3 pounds.

The growth rate of lucky per month = 9 pounds.

Table of age and weight of lucky.

Age (months)        Weight (pounds)

2                              3

3                              12

4                              21

5                              30

6                              39

7                              48

8                              57

Now,

The coordinates on the graph from the table are:

(2, 3), (3, 12), (4, 21), (5, 30), (6, 39), (7, 48), and (8, 57).

The graph of the table is given below.

Now,

The function for the weight of the lucky in x months.

f(x) = mx + c

m = 9

(2, 3) = (x, f(x))

So,

3 = 9 x 2 + c

c = 3 - 18

c = -15

So,

f(x) = 9x - 15

Where x is the number of months.

Now,

The weight of lucky in one year i.e 12 months.

This means,

x = 12 months

f(12) = 9 x 12 - 15 = 108 - 15 = 93

Thus,

The table is given above.

The graph is given below.

The function for lucky weight in x months is f(x) = 9x - 15.

The weight of lucky in one year is 93 pounds.

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The correct comparison between two function is

Both functions are increasing, but function g increases at a faster average rate.

The Correct option is (B).

If the slope of a function is continuously increasing or constant in an interval, the function is known as an increasing function.

Let us assume

f(x) = [tex]ab^x[/tex]+ c

so, at x=0, f(0)=-10

a +c = -10

Similarly, by satisfying the above table in the f(x)

f(x) = -33/5 [tex](1/11)^x[/tex] - 17/5

and, f'(x) > 0

Thus, f(x) is an increasing function.

Now, g(x) = -18 [tex](1/3)^x[/tex] +2

g'(x) = -18 [tex](1/3)^x[/tex] log(1/3)

as log 1/3 <0

So, g'(x) > 0

Thus, g(x) is an increasing function.

For any x ∈ f(x) and x ∈ g(x), g'(x) > f'(x).

Hence, Both functions are increasing, but function g increases at a faster average rate.

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The total amount of interest you will have to pay is $21,849.92. As a result, choice A is accurate.

Compound monthly is the term used to describe a loan's interest rate, which is added to the principle each month and charged in installments. For instance, a $1,000 loan with a 12% annual interest rate compounded monthly would become $1,010 after the first month if the interest rate was 1%.

Monthly compounding is calculated by multiplying the principal amount by one plus the interest rate by the number of periods, raised to the power of the number of periods. This quantity is subtracted from the principal amount to determine the interest amount.

Thus;

[tex]Interest = 44,500(1 + 0.1311/100)^{6.5} \\= $21,849.92[/tex]

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The gross monthly earnings for February will be $1012.2

It should be noted that gross monthly earnings simply means the earnings that an individual makes for a particular month.

In this case, Dave earns $200 per week plus 4.1 commission. He sold $5175.50 in the month of February. His gross monthly earnings for February will be:

= ($200 × 4) + (4.1% × $5175.50)

= $1012.2

Therefore, $1012.2 will be the earnings.

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Yes. Coupon B gives the lower price.

The price of coupon B is less than the price with Coupon A

Discount is defined as a deduction from the usual cost of something

Since there is a $16 rebate on a $55 jacket using Coupon A. The price when Coupon A is used will be:

price using Coupon A = $55 - $16 = $39

Since Coupon B gives a 35% discount on the price of the jacket. The price when Coupon B is used will be:

price using Coupon B = $55 - (0.35×55) = $35.75

Thus, the price of coupon B is less than the price with Coupon A

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Answer:

[tex]y1 = 4 \\ x1 = 3[/tex]

[tex]y - y1 = m(x - x1)[/tex]

[tex]y - 4 = 0(x - 3)[/tex]

[tex]y - 4 = 0[/tex]

[tex]y = 4[/tex]

Answer:

To find Q1, Q2, Q3, and the interquartile range (IQR) of a data set, we need to first arrange the data in numerical order. For the given data set, the ordered data is:

7, 8, 10, 12, 12, 14, 15, 15, 16, 19, 21, 23, 24

To find Q1, we need to find the median (Q2) of the lower half of the data. The lower half of the data is:

7, 8, 10, 12, 12, 14

There are 6 values in the lower half of the data, so the median (Q2) is the average of the 3rd and 4th values, which is (10 + 12) / 2 = 11. Therefore, Q1 = 11.

To find Q3, we need to find the median (Q2) of the upper half of the data. The upper half of the data is:

15, 15, 16, 19, 21, 23, 24

There are 7 values in the upper half of the data, so the median (Q2) is the fourth value, which is 19. Therefore, Q3 = 19.

To find the IQR, we need to subtract Q1 from Q3. The IQR is equal to Q3 - Q1 = 19 - 11 = 8.

The correct answers are:

1.  Interquartile Range = 8

2.  Q3 = 19

3.  Q2 = 11

4.  Q1 = 8

Therefore, the correct answer choices are:

a. 15 (incorrect)

b. 9 (incorrect)

c. 20 (incorrect)

d. 11 (correct)

Answer:

[tex]4x^2+4vx + v^2[/tex]

Step-by-step explanation:

[tex](2x+v)^2 \\(2x)^2+2(2x)(v)+(v)^2\\4x^2+4vx + v^2[/tex]

The model lies between 0 and 1 on the number line.We can find by dividing number and then add both of number.

The real number line is a horizontal line with arrows on both sides. It consists of the origin “0”. All the positive numbers are represented on the right side of the origin and all the negative numbers are represented on the left side of the origin, with a definite scale.

A number line model is a representation of numbers plotted on an infinite line that extends at both ends.It is a visual representation of numbers on a straight line. This line is used to compare numbers that are placed at equal intervals on an infinite line that extends on both sides horizontally or vertically.

Now we find

-2/4 =-0.5

3/4= 0.75

0.75- 0.5=0.25

which is lies between 0 and 1 on the number line.

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It's difficult to determine exactly how much interest Timothy will pay over 30 years without more information about the terms of his mortgage. However, we can use the following formula to calculate his monthly mortgage payment, which includes both the principal and the interest:

Monthly payment = P * (r/12) / (1 - (1 + r/12)^(-n))

Where:

P is the principal amount (the total cost of the house minus the down payment)

r is the monthly interest rate (we need to convert the annual interest rate to a monthly rate by dividing it by 12)

n is the number of payments (in this case, the number of months over which Timothy will pay off the mortgage, which is 30 years * 12 months/year = 360 months)

We can plug in the given values to find Timothy's monthly payment:

Monthly payment = $360,000 * (0.04/12) / (1 - (1 + 0.04/12)^(-360)) = $1,375.69

To find the total amount of interest Timothy will pay over 30 years, we would need to know the interest rate on his mortgage and the length of the loan in months. With this information, we could calculate the total amount of interest Timothy will pay by multiplying his monthly payment by the number of payments he makes (360 payments in this case) and subtracting the principal amount ($360,000).

Answer:

far   t more far     t

Step-by-step explanation:

so, if we take 40(origin amount) to be the 100%, what is 26 off of it in percentage anyway?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 40 & 100\\ 26& x \end{array} \implies \cfrac{40}{26}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{ 20 }{ 13 } ~~=~~ \cfrac{ 100 }{ x }\implies 20x=1300\implies x=\cfrac{1300}{20}\implies x=65[/tex]

Answer:

8

Step-by-step explanation:

Since it's an equilateral triangle, as you can tell from the red lines, m∠2 = 60. You can substitute to get:

⇒ 60 = 6x + 12

Subtract 12 from both sides

⇒ 48 = 6x

Divide by 6

⇒ x = 8

Therefore, the answer is 8.

Let C be the number of children who used the public swimming pool and A be the number of adults.

The total number of people at the pool is given by the equation: C + A = 660

The total cost of admission for all the people at the pool is given by the equation: 1.5C + 2.5A = 1279

Solving the system of equations using substitution, we get:

A = 289 and C = 371

There were 371 children and 289 adults at the public pool on the hot summer's day.

The volume of the parallelopiped is 14 cubic units

The volume of a parallelopiped with vector sides a, b and c is given by

V = (a × b).c

Given that the parallelopiped has sides

So, we have that

(a × b) = (2, 1, 0) × (3, -1, 2) = (2 × 3)i × i + (2 × -1)i × j + (2 × 2)i × k + (1 × 3)j × i + (1 × -1)j × j + (1 × 2)j × k + (0 × 3)k × i + (0 × -1)k × j + (0 × 2)k × k

Since

So,

(a × b) = (2, 1, 0) × (3, -1, 2) = (6) × 0 + (-2)k + -(4)j + 3i + (-1) × 0 + (2)i + -(3)j + -(0)i + (0) × 0

= 0 -2k - 4j + 3i + 2i - 3j - 0 + 0

= 5i  -7j - 2k

= (5, -7, -2).

Since (a × b) = (5, -7, -2)

So, the volume of the parallelopiped is

V = (a × b).c

= (5, -7, -2).(4, 0, 3)

= 5 × 4 + (-7 × 0) + (-2 × 3)

= 20 - 0 - 6

= 14.

So, the volume is 14 cubic units.

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So we're trying to find the equation of a line using the provided x and y values in the chart. We should start by finding the slope of the line, since that's easiest!

We know that the equation for slope is [tex]m=\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}[/tex]

All we need to do is pick two points (two x and y coordinates) and respectively plug them into the equation! I want to note that it does not matter which two points you choose! You will always get the same slope!

Alright, so using the two points (-2, -17) and (0, 23) I'll calculate the slope!

[tex]m=\frac{y_2-y_1}{x_2-x_1}\\m=\frac{23-(-17)}{0-(-2)}\\m=\frac{23+17}{0+2}\\m=\frac{40}{2}\\m=20[/tex]

(Just to prove that you can use any two points I'm going to do another example. The only thing you need to keep in mind is that y values are always on top and x values are always on the bottom! In this example I'm using (-6, -97) and (2,63)!)

[tex]m=\frac{63-(-97)}{2-(-6)}\\m=\frac{160}{8}\\m=20[/tex]

As we can see, no matter which points you use, it will always simplify to the same slope!

Now that we have the slope, we need to find the x and y intercepts! An x intercept is the point where y = 0 on the x-axis. A y intercept is the pint where x = 0 on the y-axis!

We already have a y intercept given to us, as you can see in the table there is a point (0, 23). This point is where x = 0! This will be our value next to the y in the equation. So so far, our equation looks like this:

[tex]y-23=20(x-x_1)[/tex]

And how do we know what the x intercept (x1) is? Well, we have a table full of values, so we can use those to plug in for y and x! I want to note again, you do not need to worry about which values you use! Just make sure you have your x and y straight and plug in whichever pair of coordinates you want! I will use the point (-2, -17).

[tex](-17)-23=20((-2)-x_1)\\-40=20(-2-x_1)\\-2=-2-x_1\\x_1=0[/tex]

So it looks like this line goes straight through the origin! If you want to confirm your findings, you can just use another point. This time I'll just use (2, 63)!

[tex](63)-23=20(2-x_1)\\40=20(2-x_1)\\2=2-x_1\\x_1=0[/tex]

This also makes sense to be our x-intercept value since if it was any other number, our y intercept would not be (0, 23) and the given values wouldn't be true anymore! (This is just another way to confirm that it's right!)

Therefore, our final equation is:

y - 23 = 20 (x - 0)

y = 20x + 23 (same answer, just in a different form)

the blank space must be 2 or x must be zero, I don't know what you mean by one solution

the blank must equal 2 because on the right side the coefficient of x is 2 so it must be same

Answer:

Perimeter = 9x + 6

Step-by-step explanation:

Perimeter = x+14 + x-1 + x+5 + 3x + 2x-10 + x-2

Perimeter = 9x + 14 + 5 - 1 - 10 - 2

Perimeter = 9x + 19 - 13

Perimeter = 9x + 6