type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Consider the given function.

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Adam earned approximately 12.48% interest on his savings account over 10 years.

To find the rate of interest (r) earned by Adam, we can use the formula for compound interest:

A = P * (1 + r[tex])^{t}[/tex]

where:

A = ending amount ($1649 in this case)

P = principal (initial amount) ($100 in this case)

r = interest rate (what we want to find)

t = time (in years) (10 years in this case)

We know the values of A, P, and t, so we can plug them into the formula and solve for r:

1649 = 100 * (1 + r)¹⁰

Divide both sides of the equation by 100:

16.49 = (1 + r)¹⁰

Now, let's isolate (1 + r) by taking the 10th root of both sides:

(1 + r) = √(16.49)

(1 + r) ≈ 1.12479

Now, subtract 1 from both sides to find the value of r:

r ≈ 1.12479 - 1

r ≈ 0.12479

Finally, convert the decimal to a percentage to get the interest rate:

r ≈ 0.12479 * 100

r ≈ 12.48%

So, Adam earned approximately 12.48% interest on his savings account over 10 years.

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Answer:

f(x)  = ax + b;

f(0) = -5;

a·0 + b = -5;

b = -5;

f(1) = -3;

a·1 + (-5) = -3;

a - 5 = -3;

a = 5 - 3;

a = 2;

f(x) = 2x - 5;

Step-by-step explanation:

The linear function with the values f(0)=−5 and f(1)=−3 is f(x) = 2x - 5

The linear function can be represented as follows:

y = mx + b

where

m = slope

b = y-intercept

The y-intercept is the value of y when x = 0

Since,

f(0) = -5

Therefore,

b = -5

The equation will be as follows

f(x) = mx - 5

lets find the slope(m) using the f(1)=−3

-3 = m - 5

m = -3 + 5

m = 2

Therefore,

f(x) = 2x - 5

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Answer:

3 and 9

Step-by-step explanation:

The factors of 18 can be listed as

1, 2, 3, 6, 9, 18

The two which sum to 12 are 3 and 9

Answer:

B. $0.30

Step-by-step explanation:

1 bar of candy = $0.20

3 bars of candy = $0.50

To solve, multiply for both:

If you pay for each candy bar individually, they each cost $0.20. Multiply 9 with 0.20:

9 x 0.20 = $1.80

If you pay for the candy bars by 3's, they cost $0.50 each pack. Divide 9 with 3, then multiply by 0.50:

9/3 = 3

3 x 0.50 = $1.50

Subtract the total cost of the individual from the pack:

$1.80 - $1.50 = $0.30

B. $0.30 is your answer.

~

Answer:

7

Step-by-step explanation:

2x² - 28x + 98 = 0

x² - 14x + 49 = 0

(x - 7)² = 0

x = 7

To solve the equation 2x^2 - 28x + 98 = 0, we can use the quadratic formula. After substituting the values into the formula, we simplify the equation and solve for x. The solution is x = 7.

To solve the equation 2x2 - 28x + 98 = 0, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 2, b = -28, and c = 98. Substituting these values into the formula:

x = (-(-28) ± √((-28)^2 - 4(2)(98))) / (2(2))

Simplifying the equation gives:

x = (28 ± √(784-784)) / 4

Since the term inside the square root is zero, we have:

x = (28 ± √0) / 4

The square root of zero is zero, so:

x = (28 ± 0) / 4

Simplifying further:

x = 28 / 4

x = 7

Therefore, the solution to the equation 2x2 - 28x + 98 = 0 is x = 7.

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Final answer:

Using the sum of the interior angles formula for a polygon, S = (n - 2) x 180 degrees, and substituting the provided sum of 2280 degrees, it is calculated that the polygon has 14 sides.

Explanation:

To solve for the number of sides n in a polygon given the sum of the interior angles, we use the formula:

S = (n - 2) × 180°

where S is the sum of the interior angles in degrees. Given that the sum of the interior angles S is 2280 degrees, we can set up the equation:

2280 = (n - 2) × 180

Divide both sides of the equation by 180:

2280 ÷ 180 = n - 2

12 = n - 2

Now, add 2 to both sides of the equation to find n:

n = 12 + 2

n = 14

So, the polygon has 14 sides.

Answer:

$2

Step-by-step explanation:

Step 1: Subtract the amount he had left from the amount he had to spend. 24 - 18 is 6. That's the amount spent on pencils.

Step 2: Divide the amount spent on pencils by 3. 6/3 is 2. That's the total cost of each pencil.

Answer:

A. [tex]y = \frac{4}{3} x - \frac{3}{2}[/tex]

Step-by-step explanation:

First, we have to turn 4x - 3y = -12 into slope-intercept form (y = mx + b). To do this, we first have to isolate 3y.

4x - 3y = -12

    +3y    +12     Add 3y to both sides and add 12 to both sides

4x + 12 = 3y

3y = 4x + 12

Isolate y by dividing 3 from both sides.

y = [tex]\frac{4}{3}[/tex]x + 4

The graph that is parallel will have the same slope as this equation, which is [tex]\frac{4}{3}[/tex].

Therefore, A. [tex]y = \frac{4}{3} x - \frac{3}{2}[/tex] would be the correct answer.

Answer:

A

Step-by-step explanation:

Solve for y.

4x – 3y = -12

4x + 12 = 3y

y = 4/3 x + 4

The slope of the line is 4/3.  So you need another line with the same slope.  So the answer is A.

Answer:

supplementary

Step-by-step explanation:

Consecutive angles in a parallelogram sum to 180°

That is they are supplementary.

Answer:

The answer to this question is the first option:

Line segment TU is parallel to line segment RS because 32/36=40/45

Answer:

The correct option is 1.

Step-by-step explanation:

From the given figure it is clear that QT=32, TR=36, QU=40 and US=45.

The converse of side splitter theorem states that if a line divides two sides proportionally, then that line is parallel to the third side.

The ratio in which TU divides the two sides is

[tex]\frac{QT}{TR}=\frac{32}{36}=\frac{8}{9}[/tex]

[tex]\frac{QU}{US}=\frac{40}{45}=\frac{8}{9}[/tex]

[tex]\frac{QT}{TR}=\frac{QU}{US}=\frac{8}{9}[/tex]

It means the line TU divides two sides proportionally.

Using converse of side splitter theorem, Line segment TU is parallel to line segment RS because

[tex]\frac{32}{36}=\frac{40}{45}[/tex]

Therefore the correct option is 1.

Answer:

70

Step-by-step explanation:

70 combinations of four books can be made from eight different books.

Answer:

your answer should be 45

Step-by-step explanation:

Answer:

15 to the third power would be 3375

Step-by-step explanation:

You start by multiplying

15 X 15 X 15

First you would get

225 X 15

Then you do the final multiplication

3375

Answer:

12x+6

Step-by-step explanation:

Multiply the like terms.

4x • 3x=12x

-1 • -6= 6

put it back into equation form

12x + 6

Answer:

Step-by-step explanation:

Look at the picture.

Coordinates of a point (x, y)

x - from x-axis

y - from y-axis

Answer:

The Answer is 1111

Step-by-step explanation:

15 = 2(7)+1

7=2(3)+1

3=2(1)+1

1=2(0)+1

look the remainder of division by 2 : 1111 in binary system​

verify : 15 = 1(2^0)+ 1(2^1)+ 1(2^2)+ 1(2^3 = 1+2+4+8=15 .....right

Answer:

12 cm.

Step-by-step explanation:

The distance between the opposite sides is a perpendicular line so we can form a right angled triangle by drawing a perpendicular line from one corner of the parallelogram  to the opposite 24 cm side.

So  one angle of the parallelogram will have a sine of 8/16 = 1/2 so this angle =  30 degrees.

In a similar way to the above we form a right angled triangle  from the same corner by drawing a perpendicular line to the opposite 16 cm side.

This has an angle of 30 degrees (  opposite angles in a parallelogram are congruent).

So sine 30 = x / 24

1/2 = x /24

x = 12 feet.

Another way to do this is by noting that the 2 triangles are similar (because  2 corresponding angles are equal).

So  8/ 16 = x/24

16x = 192

x = 12 feet.

Final answer:

The distance between the 16 cm sides of the parallelogram is 12 cm, determined by calculating the area of the parallelogram and then using it to find the missing dimension.

Explanation:

The student in the question is dealing with a geometrical problem involving the calculation of the distance between sides of a parallelogram. To solve the problem, we must understand that the opposite sides of a parallelogram are equal in length, and the area can be calculated as the product of the base and the height (the distance between the parallel sides). The question is analogous to finding the height of a parallelogram when the area and the base are known and can be approached in a similar way to finding dimensions of scaled geometric figures.

Therefore, the distance between the 16 cm sides of the parallelogram is 12 cm.

Answer:

The answer is A. (3,5,8)

[tex]\bf (\stackrel{x_1}{8}~,~\stackrel{y_1}{17})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{4}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{4-17}{1-8}\implies \cfrac{-13}{-7}\implies \cfrac{13}{7} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \cfrac{17-4}{1-8}\stackrel{\leftarrow \textit{atop she used }y_1-y_2}{\frac{}{}}~\hfill[/tex]

For this case we have that by definition, the slope of a line is given by:

[tex]m = \frac {y_ {2} -y_ {1}} {x_{2} -x_ {1}}[/tex]

According to the data we have the following points:

[tex](x_ {1}, y_ {1}) :( 1,4)\\(x_ {2}, y_ {2}) :( 8,17)[/tex]

Substituting we have:

[tex]m = \frac {17-4} {8-1}\\m = \frac {13} {7}[/tex]

So, the slope is [tex]\frac {13} {7}[/tex]

ANswer:

The student's mistake was to erroneously subtract the "x" coordinates from the points

Answer:

The answer is B. the diameter of the base

Step-by-step explanation:

Just got it right on edg! Have a great day!

Answer:

The correct answer option is D. (-2, 1).

Step-by-step explanation:

We are given the coordinates of the square A"B"C"D" after the rule is applied and we are to find the coordinates of the vertex A.

For that, we will reverse the rule.

A" = (-5, -3)

x: - 5 + 4 = -1

y: - 3 + 1 = -2

Now we will reverse the 90 degrees counter in counter clockwise rotation:

(x, y) ---> (y, -x)

(-1. -2) ---> (-2, -(-1)) = (-2, 1)

Answer:

[tex](x-6)(x+1)[/tex]

Step-by-step explanation:

Factoring is usually just a bit of guess and check.  [tex]x^2-5x-6[/tex] is written in the form [tex]a^2+b+c[/tex], where [tex]a=1[/tex], [tex]b=-5[/tex], and [tex]c=-6[/tex].

You need to find the two numbers that multiply together to equal [tex]-6[/tex] and can be added together to get [tex]-5[/tex].  These are [tex]-6[/tex] and [tex]1[/tex] in this case.

Now, put them together in the form [tex](x-6)(x+1)[/tex].  We will now check this answer using the FOIL method.

First term in each parentheses: [tex]x * x = x^2[/tex]

Outside terms: [tex]x * 1 = x[/tex]

Inside terms: [tex]-6 * x = -6x[/tex]

Last term in each parentheses: [tex]-6 * 1 = -6[/tex]

Now, add these together: [tex]x^2 + x - 6x - 6 = x^2 - 5x - 6[/tex]

Since we get the original expression, this is correct.

Answer:

Option C : y = -4x+10

Step-by-step explanation:

Given equation of line is:

[tex]y = -4x-1[/tex]

Comparing it with standard form

y=mx+b

m = -4

As the slopes of parallel lines are equal, the slop of other line will also be -4.

Now, to find the value of b

[tex]2 = -4(2) + b\\2 = -8 + b\\2+8=b\\b=10[/tex]

Putting the values of b and m in standard form

[tex]y=mx+b\\y = (-4)x+10\\y= -4x+10[/tex]

Hence,

Option C is the correct answer ..

For this case we have that the equation of a line of the slope-intersection form is given by:

[tex]y = mx + b[/tex]

Where:

m: It's the slope

b: It is the cut point with the y axis.

By definition, if two straight lines are parallel then their slopes are equal.

So, if we have:

[tex]y = -4x-1[/tex]

A parallel line has slope [tex]m = -4[/tex]

y = -4x + b

We substitute the point (2,2) to find "b":

[tex]2 = -4 (2) + b\\2 = -8 + b\\b = 2 + 8\\b = 10[/tex]

Finally we have:

[tex]y = -4x + 10[/tex]

Answer:

Option C

Answer:

20°

Step-by-step explanation:

They are Vertically Opposite angles and hence are equal.

So, x + 40 = 3x.

Answer:

a. 20

Step-by-step explanation:

You are solving vertical angles. Put the measurements equal to each other:

x + 40 = 3x

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Subtract x from both sides.

x (-x) + 40 = 3x (-x)

40 = 3x - x

40 = 2x

Isolate the variable x. Divide 2 from both sides:

(2x)/2 = (40)/2

x = 40/2

x = 20

a. 20 is your answer.

~

Answer:

D. 12

Step-by-step explanation:  

We have been given a diagram of a triangle. We are asked to find the value of y for our given triangle.

First of all, we will find 3rd side of larger triangle using Pythagoras theorem.

[tex]\text{3rd side}^2=16^2-8^2[/tex]

[tex]\text{3rd side}^2=256-64[/tex]

[tex]\text{3rd side}^2=192[/tex]

[tex]\text{3rd side}^2=192[/tex]  

We will use geometric mean (leg) theorem to solve our given problem.

[tex]\text{3rd side}^2=y\times 16[/tex]  

[tex]192=y\times 16[/tex]  

[tex]\frac{192}{16}=\frac{y\times 16}{16}[/tex]  

[tex]y=12[/tex]  

Therefore, the value of y is 12 and option D is the correct choice.

The percentage decrease(loss) of selling sweatshirts is 28%.

To find the percentage change of any value we need to divide by that change to the original value and then multiply by 100.

Percentage change = (change in value × 100)÷(riginal value).

Given that the selling cost of sweatshirts is $18.

The cost of the sweatshirt was $25.

Change of value

$25 - $18 = $7

By the formula

Percentage decrease = ($7)×100÷ ($25) %

Percentage decrease = 28% Hence,the percentage decreases is 28$.

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Answer:

x = 98°

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

x is an exterior angle and 53° and 45° are the opposite interior angles, hence

x = 53° + 45° = 98°

Answer:

Answers: 46, 23, and 111

Step-by-step explanation:

To answer, we need to know the angles. Therefore, give each angle a name. Angle 1 will be x, 2 will be y, 3 will be z. So, using this system of equations:

x=2y

z=y+88

x+y+z=180

Substituting, z = 1/2(x)+88, now plug z into the third equation:

x+1/2(x)+1/2(x)+88=180

this simplifies to 2x+88=180

subtracting 88 from both sides leaves 2x=92

x=46

plug this in to the first equation: 46 = 2y, so y = 23

plug this into the third one leaves z = 111

Hope this helps!

Answer:

d)  1

Step-by-step explanation:

3a = –2b – 7

We have the point (a, -5) so b = -5

Substituting in

3a = -2(-5) -7

3a = 10-7

3a = 3

Divide each side by 3

3a/3 = 3/3

a =1

To find the value of a in the equation 3a = -2b - 7, substitute the coordinates of the given point and solve for a. The value of a is -5.

In this given equation 3a = -2b - 7, o find the value of a, we can substitute the coordinates of the given point into the equation and solve for a. Let's substitute the value of a as -5:

3(-5) = -2b - 7

Simplifying the equation:

-15 = -2b - 7

Adding 7 to both sides:

-8 = -2b

Dividing both sides by -2:

b = 4

So, the value of a is -5.

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Hello There!

.84 ÷ .02 ≈ 42

WORK SHOWN IN IMAGE ATTACHED