8. In order to reach the top of a hill which is 250 feet high, one must travel 2000 feet straight up a road
which leads to the top. Find the number of degrees contained in the angle which the road makes with the
horizontal.

None of Ari's answer to the question is correct. The right application of the laws of exponents to get the correct answer is explained below.

Some of the laws of exponents can be summarized as follows.

Based on the above laws of exponents, none of Ari's answer is correct. Below are the correct way to solve the questions:

1. [tex]4^2 \times 4^5 = 4^{2 + 5} = 4^7[/tex]

2. [tex](2^{-5})^3 = 2^{-3 \times 5} = 2^{-15} = \frac{1}{2^{15}}[/tex]

3. [tex]\frac{(\frac{1}{4})^4 \times (\frac{1}{4})^5 }{(\frac{1}{4})^3} = \frac{(\frac{1}{4})^{4 + 5} }{(\frac{1}{4})^3} = \frac{(\frac{1}{4})^9 }{(\frac{1}{4})^3} = (\frac{1}{4})^{9 - 3}} = (\frac{1}{4})^6[/tex]

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Given:

Sum of the angle of any triangle is 180

So:

Then two sides are also equal.

So the value of x is 6.

Large point coordinates (original)= (1,-4)

To obtain the coordinates of the new point, add 4 to the y coordinate.

(1,-4+4) = (1,0)

Principal amount, P= $290.

Rate, r = 0.076

Time, t = 2

Therefore, the total amount in her account after 2 years is

Hence,

Therefore, the amount is 335.80 dollars.

That is, 335 dollars and 80 cents.

Answer: (x,y)= (-2/5,-43/5)

Step-by-step explanation:

It is given that the function is:

Therefore y=0 then the value of x will be:

Now at x=0, y will be:

at x=1, y will be:

These 3 points that is (-inf,0),(0,3/4),(1,3) are on graph D.

Hence option D is coreect.

Solution

We have the following function given:

f(x) = -3x+5

And we need to do the following:

5= -3x+5

And if we subtract 5 in both sides we got:

0 =-3x

Dividing both sides by -3 we got:

And finally we got:

x= 0

Problem 17

17) f(-2)= 3

18) f(0)= 3

19) f(1)= 0

20) f(-1)= 5.2

Length of y is 25.2.

Given:

The angle is given as 35 degree and a side is 36.

The objective is to find the length of the side y.

In a right angled traingle, the side opposite to the given angle is called oppotise side, the other smaller side is called adjacent side and the longer side is called hypotenuse.

Here, opposite side is y and adjacent side is 36.

Then, the relationship between oppsote and adjacent can be calculated using the trigonometric ratio of tan theta.

Hence, the length of y is 25.2.

Answer

Step-by-step explanation:

solve for b.

2x+14=10x+b

Step 1: Flip the equation.

b+10x=2x+14

Step 2: subtract 10x from both sides.

b+10x+−10x=2x+14+−10x

b=−8x+14

Answer:

b=−8x+14

The answer is NO, Marco is wrong.

The number 7.696696669.... has not a repeating decimal there is no a number that is repeating, like 0.6969696969... in the last number the 69 is repeating, in the Marco's number the decimal number change every time.

total money is 75$

protein cost = 47$

so the remaining money is

75 - 47 = 28 $

now she bought the protein bars of 28$

cost of one protein bar is 4$

so the number of protein bars that she bought is

so she bought 7 protein bars.

Given:

The point (0,0) lies on the graph f(x) and (4,-3) lies on the graph h(x).

To find:

We need to find the equation for the function h(x).

Explanation:

Consider the translation point which is translated horizontally a unit and vertically as b units.

The point (4,-3) can be written as follows.

We get the function h(x) after f(x) translated horizontally 4 units right and vertically 3 units down.

The function can be written as follows.

Final answer:

Given the functions:

You need to multiply them, in order to find:

Then, you get:

In order to find the Domain, you need to remember that the Domain of a Radical Function are those input values (x-values) for which the Radicand is positive. Then, in this case, you need to set up that:

Now you have to solve for "x":

Therefore:

Hence, the answer is:

Given:-

To find the graphical representation.

So the graph of y=2x-8 is,

Also the graph of y=-x+4 is,

Combining we get the graph

So the point is (4,0).

Length of the entire rectangle = 12 + 5 = 17

Width of the entire rectangle = 6+4 = 10

Part a

Area of rectangle = Length x width

Area of the entire rectangle = 17 x 10 = 170 square units

Part b

Perimeter of rectangle = 2( length + width )

Perimeter of the entire rectangle = 2(17 + 10 )

=2 (27) = 54

Perimeter of the entire rectangle = 54 units

Length of the entire rectangle = 12 + 5 = 17

Width of the entire rectangle = 6+4 = 10

Part a

Area of rectangle = Length x width

Area of the entire rectangle = 17 x 10 = 170 square units

Part b

Perimeter of rectangle = 2( length + width )

Perimeter of the entire rectangle = 2(17 + 10 )

=2 (27) = 54

Perimeter of the entire rectangle = 54 units

To calculate the distance between two points on the coordinate system you have to use the following formula:

Where

d represents the distance between both points.

(x₁,y₁) are the coordinates of one of the points.

(x₂,y₂) are the coordinates of the second point.

To determine the length of CD, the first step is to determine the coordinates of both endpoints from the graph

C(2,-1)

D(-1,-2)

Replace the coordinates on the formula using C(2,-1) as (x₁,y₁) and D(-1,-2) as (x₂,y₂)

The length of CD is √10 units ≈ 3.16 units

A.

x^2 and 2x^2 means:

3 x^2 tiles

3x - 4x = -x

ONE -x tiles

5 - 1 is "4"

B.

2x^2 - 4x - 1

This is just an expression

so there are 2 x^2 tiles, 4 -x tiles and one 1-tiles

Given:

The resistance

Given the sentence;

Subtracting 3 from both sides;

Given the absolute value of x to be greater than zero, the range of value of x is;

Therefore, the correct graph of the solution is;

For exponential functions, it is found that:

An exponential function is modeled according to the rule presented as follows:

[tex]y = ab^x + c[/tex]

In which the coefficients of the rule are given as follows:

To graph the function, along with the coefficients of the function, the end behavior of the function is needed, as follows:

They are compared by their rate of changes, if they are increasing/decreasing, and which one increases faster.

The transformations are as follows:

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Answer

(x - 2)² + (y - 2)² = 8

Step-by-step explanation

The equation of the circle centered at (h, k) with radius r is:

In this case, the center of the circle is the point (2, 2), then h = 2 and k = 2, that is,

Given that the circle passes through the center, then the point (0, 0) satisfies the above equation. Substituting x = 0 and y = 0 into the equation and solving for r²:

Substituting r² = 8 into the equations, we get:

The science club had more sixth graders.

The math club has 18 members and 50% are sixth graders. The number of sixth graders will be:

= Percentage × Number of members

= 50% × 18

= 0.5 × 18

= 9

The science club has 25 members and 40% are sixth graders. The number of sixth graders will be:

= Percentage × Number of members

= 40% × 25

= 0.4 × 25

= 10

Since 10 is more than 5, the science class has higher number.

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Answer:

The length of the parallelogram is 20 meters.

The width of the parallelogram is 18 meters.

Explanation:

The perimter of a parallelogram is calculated by addition of the lengths of all the enclosed sides.

⇒ x + (x - 2) + x + (x -2) = 76

Remove the brackets

x + x - 2 + x + x - 2 = 76

Collecting the like terms, we have

4x - 4 = 76

4x = 80

x = 80/4

x = 20 meters, which is the length of the parallelogram.

For width, we have,

20 - 2 = 18 meters.

Answer:

The length of the parallelogram is 20 meters.

The width of the parallelogram is 18 meters.

Explanation:

The perimter of a parallelogram is calculated by addition of the lengths of all the enclosed sides.

⇒ x + (x - 2) + x + (x -2) = 76

Remove the brackets

x + x - 2 + x + x - 2 = 76

Collecting the like terms, we have

4x - 4 = 76

4x = 80

x = 80/4

x = 20 meters, which is the length of the parallelogram.

For width, we have,

20 - 2 = 18 meters.

SOLUTION

Write out the original equation

Then, Apply the distributive property on the left hand side of the equation

Then combine trhe like terms subtracting 6x from both side

Subtract 8 from both sides of the last equation

hence

Divide both sides by -4, we have

Therefore, the solution is x=0

Hence

When we divide both sides of the equation by x, we have

While the solution is x=0

Therefore

When we divide the equation by 2x=6x by x it could lead us to think that there is no solution while the solution is x=0

Answer; The second option is right

Consider drawing a card at random from a standard deck of cards,

Part A: Determine the probability that the card is a spade, given that it is black,

Part B: Determine the probability that the card is red, given that it is a heart,

Part C: Determine the probability that the card is an ace, given that it is black.

Part D: Determine the probability that the card is a queen given that it is a face card,

we have 52 cards

A standard 52-card deck comprises 13 ranks in each of the four French suits: clubs (♣), diamonds (♦), hearts (♥) and spades (♠)

so

Part A: Determine the probability that the card is a spade, given that it is black,

If the card is black, that means the possible outcomes are 26 cards

so

P=13/26

Part B: Determine the probability that the card is red, given that it is a heart,

if the card is a heart, that means, the possible outcomes are 13

so

P=13/13

because all the cards that are heart are red

Part C: Determine the probability that the card is an ace, given that it is black.

if the card is black the possible outcomes are 26

therefore

P=2/26

Part D: Determine the probability that the card is a queen given that it is a face card

Solution

In interval notation, we have

The answer is

120

Explanation:

total colours = 10

number of colours to be chosen = 7

We apply combination

The different color combinations possible:

The different color combinations possible is 120