I might not respond for a little while, please don’t end the session! Need help on #3 and 4

Answer:

C. 6 x 10^18
Step-by-step explanation:

This is the correct answer

Answer:

Step by step solution:

The

On simplifying the given expressions we get-

a) [tex]5^{12}[/tex]

b) [tex]5^{18}[/tex]

Here, we are given two expressions in exponential form. Let us solve them one by one.

Firstly, we look at a property of exponentials as follows-

[tex]x^{a} x^{b} = x^{a+b}[/tex]

Theoretically, this means that when the bases are equal, the powers can be added in case of multiplication of exponentials.

Now, we have-

a) [tex]5^{2} 5^{10}[/tex]

here, the base is equal, that is, 5. So we just add the powers to get-

[tex]5^{2+10}[/tex]

= [tex]5^{12}[/tex]

b) [tex]5^{2} 5^{7} 5^{9}[/tex]

Here, we have 3 exponents, but the property will still remain the same. Bases are all equal to 5, thus the expression will become-

[tex]5^{2+7+9}[/tex]

= [tex]5^{18}[/tex]

Thus, on simplifying the given expressions we get [tex]5^{12}[/tex] and [tex]5^{18}[/tex] respectively.

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7=- (1/5)x

Let the unknown surface area be x

The ratio of the surface area to volume in solid 1 must be equal to the ratio of the surface area to volume in solid 2.

Hence, the surface area of solid 2 is 54 cm^2

Answer:

12

Step-by-step explanation:

9/12 to y/16 (the ratio of the short side relative to the long side)

0.75 = y/16 (a ratio can be expressed as a decimal)

16(0.75) = y (multiply 16 to both sides, isolate y)

y = 12 (b/c three-quarters of 16 is 12)

Answer:

y = 12

Step-by-step explanation:

Δ RSQ and Δ ROP are similar ( AA postulate ) then the ratio of corresponding sides are in proportion, that is

[tex]\frac{SQ}{OP}[/tex] = [tex]\frac{RS}{RO}[/tex] ( substitute values )

[tex]\frac{y}{16}[/tex] = [tex]\frac{9}{12}[/tex] ( cross- multiply )

12y = 16 × 9 = 144 ( divide both sides by 12 )

y = 12

The plus sign is a composite of rectangles . The shape is comprised of:

1. 4 congruent rectangles with sides 20 in and 12 in

2. A square at the center with sides 20 in by 20in

The total area of Demi's Tester ca be found using the formula:

Substituting the given side lengths:

Hence, the total area of Demi's poster is 1360 square in

Multiplication of two real functions,  (f . g) (x) is  4/x - 8/x² and the correct domain for (f . g) (x) is (-∞,0) U (0,∞)

Let f(x) and g(x) are two real functions.

​f(x)= 4x -8

g(x)= 1/x²

then

(f . g)(x) = (4x -8 ) x (1/x²)

(f . g)(x) = 4/x - 8/x²

The set of all the initial elements in all the ordered pairs in a relation R is known as the domain of R.

we know that f(x) is undefined at x=0

so, domain will be

(-∞,0) U (0,∞)

Multiplication of two real functions,  (f . g) (x) is  4/x - 8/x² and the correct domain for (f . g) (x) is (-∞,0) U (0,∞)

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Answer:

• Vertex: (5,-2)

• Points to the left of the vertex: (3,2) and (4,-1)

• Points to the right of the vertex: (7,2) and (6, -1)

Explanation:

Given the equation of the parabola:

First, determine the vertex:

A table of values for the function is given below with the vertex identified:

Thus, we have the graph below:

• Vertex: (5,-2)

• Points to the left of the vertex: (3,2) and (4,-1)

• Points to the right of the vertex: (7,2) and (6, -1)

Given:

There are three terms in the given equation.

trinomial is the final answer.

The weights of the first and second alloys to be used are 23.707 and 30.293 pounds.

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(a) The initial cost that the shop spend is $56 and;

(b) The profit that the bike shop earned by selling the bicycle and helmet to you is $28.

The price of the bicycle is $63 in a shop.

The price of a helmet is $21.

The total price is 150% more than what the shop originally paid for these times:

The total cost, C = $63 + $21 = $84

The cost is 150% of the initial cost let's say K;

C = 150% of K

C = 150/100 × K

C = 1.5K

Hence, the initial cost will be:

K = C/1.5 = $84/1.5

K = $56

The difference between the two costs will be the profit:

P = C - K

P = $84 - $56 = $28

Hence, the amount the shop spend is $56 and the profit the bike shop earns by selling the bicycle and helmet is $28.

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Answer:12+27= 39.

Step-by-step explanation: You would do 6x4 first due to PEMDAS. Then you would do 24 divided by 2 which is 12. Then, you add it to 3 to the power of 3, which is 39. The simplified equation would be be 12+27.

Let's use the variable x to represent the shortest side of the triangle.

If one side is 4 times longer than the shortest side, it measures "4x".

If the third side is 3 cm less than twice the length of the shortest side, it measures "2x - 3".

So, if the perimeter is 46 cm, we have:

So the shortest side measures 7 cm.

Exponential functions have the form:

The initial value of the function f(x) is given by the value of f(x) when x = 0:

For an exponential function:

we have:

Answer:

x = 7

y = 8

Step-by-step explanation:

Create two equations.

Equation 1

Both triangles are isosceles triangles since two of their sides are congruent.  Therefore, the base angles of the top triangle are equal:

[tex]\implies y^2-8=x^2+x[/tex]

Equation 2

According to the Vertical Angles Theorem, when two straight lines intersect, the opposite vertical angles are congruent.  Therefore, the apexes of the triangles are equal.  This means the sum of the base angles are equal:

[tex]\implies (y^2-8)+(x^2+x)=8x+8x[/tex]

[tex]\implies y^2-8+x^2+x=16x[/tex]

[tex]\implies y^2-8+x^2+x-x^2=-x^2+16x[/tex]

[tex]\implies y^2-8+x=-x^2+16x[/tex]

[tex]\implies y^2-8+x-x=-x^2+16x-x[/tex]

[tex]\implies y^2-8=-x^2+15x[/tex]

Substitute the first equation into the second equation and solve for x:

[tex]\implies x^2+x=-x^2+15x[/tex]

[tex]\implies x^2+x+x^2=-x^2+15x+x^2[/tex]

[tex]\implies 2x^2+x=15x[/tex]

[tex]\implies 2x^2+x-15x=15x-15x[/tex]

[tex]\implies 2x^2-14x=0[/tex]

[tex]\implies 2(x^2-7x)=0[/tex]

[tex]\implies x^2-7x=0[/tex]

[tex]\implies x(x-7)=0[/tex]

Therefore:

[tex]\implies x=0, \quad x=7[/tex]

If x was zero, some of the angles would be zero, which is impossible.

Therefore, the only valid solution is x = 7.

Substitute the found value of x into the first equation and solve for y:

[tex]\implies y^2-8=(7)^2+7[/tex]

[tex]\implies y^2-8=49+7[/tex]

[tex]\implies y^2-8=56[/tex]

[tex]\implies y^2=64[/tex]

[tex]\implies y=8[/tex]

Solution

The given expression is

To find the equivalent expression, we use the formula for the difference of perfect cubes.

But, we have to express the numbers 8 and 27 as cubic powers.

Then, we know that a and b are

So, the difference would be

Once we have the difference expressed in cubes, we apply the formula using the a and b values we determined before.

Therefore, the factors are

Answer:  [tex]0 < h \le 107[/tex]

This is the same as writing [tex]h \le 107[/tex] where h is positive

======================================================

Work Shown:

1 foot = 12 inches

8*(1 foot) = 8*(12 inches)

8 feet = 96 inches

8 feet + 11 inches = 96 inches + 11 inches

8 feet + 11 inches = 107 inches

The tallest person is 107 inches tall.

If h is someone's height in inches only, then [tex]0 < h \le 107[/tex] is the inequality that describes all possible values of h.

We can simplify that into writing [tex]h \le 107[/tex] and write off to the side somewhere that h must be positive.

Answer: 0 < h < 107 inches

Step-by-step explanation:

     First, we see this question asks us to represent in inches, so we will convert 8'11" into inches.

           8 feet * 12 inches in a foot = 96 inches

           96 inches + 11 inches = 107 inches

     Next, we will write our inequality. If this person was the tallest, then everyone else will be less tall. We assume that nobody will be less than 0 inches tall, so that is the left side of our inequality.

           0 < h < 107 inches

      Since this question asks about every other person who has ever lived, we do not use ≤ (greater than or equal to) since the tallest person is the only height equivalent to 107 inches.

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Based on the information in the provided table, the elk population for the first month is 11, the second month is 16, and the third month is 30.

Using the information in the give table, we need to calculate the elk population size for each month.

For first month,

elk population = tagged elk + total elk

                        = 4 + 7

                        = 11

For second month,

elk population = tagged elk + total elk

                        = 6 + 10

                        = 16

For third month,

elk population = tagged elk + total elk

                        = 12 + 18

                        = 30

Therefore, the elk population for first month is 11, second month is 16 and third month is 30 which is calculated from the given table data.

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The coefficient 3 represents that the numbers of blueberry muffins sold by Jake is 3.

For the given question;

Total amount = chocolate muffins's amount + blueberry muffins's amount

Jake's total sell = $38.

Mia's total sell = $20.

Let 'x' be the price of each chocolate muffins.

Let 'y' be the price of each blueberry muffins.

The system of linear equation is;

8x + 3y = 38

2x + 6y = 20

Thus, the coefficient 3 represents that the numbers of blueberry muffins sold by Jake is 3.

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we have the following:

therefore, the answer is 82.5%

so the answer is B

(C.) The two right angles in the diagram are NOJ and JOL.

A right angle is formed when two straight lines intersect each other at 90˚ or are perpendicular to each other at the intersection.

A right angle is denoted by angle 90 degrees.

The symbol between NOJ indicates right angle because the measure of the angle is 90 degrees.

Since the sum of angles on a straight line is 180 degrees, and we know angle NOJ, angle JOL can be calculated as follows;

NOJ + JOL = 180

JOL = 180 - NOJ

JOL = 180 - 90

JOL = 90

Thus, the two right angles in the diagram are NOJ and JOL.

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EXPLANATION

We can get the solution by calculating the frequency on the Histogram as shown as follows:

Hours Frequency

4.5-5.5 7

5.5-6.5 4

------------

Total Frequency ----------------------> 11

The number of people that average greater than 4.5 and less than 6.5 hours of sleep per night are 11 persons.

Let z(t) be the function:

Then, to find z(-1), we evaluate directly into the function like this:

and we do the same thing for z(2):

therefore, z(-1)=-9 and z(2)=18

Explanation

Step 1

a)nearest ten

If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.

so,In this case, the digit to the right (7) is 5 or above. So, we add 1 to the tens place (2). The digit(s) at the right (7) becomes 0, thus we get 2230 as answer.

b)Nearest hundred

Remember that the hundreds place is three moves from the left of the decimal point (if it exists). To round to the nearest hundred (nearest 100), we use the tens place to determine whether the hundreds place rounds up or stays the same,so

in this case: 27

c)nearest thousand

Remember that the thousand place is four moves from the left of the decimal point (if it exists). To round to the nearest thousand (nearest 10000), we use the hundreds place to determine whether the thousands place rounds up or stays the same

so,in this case:227

Step 2

now, for :

a) nearest ten

b)nearest hundred

c)nearest thousand

I hope this helps you

The width of the rectangle is twice its length.

So lets assume the width to be------ 2x feet

Then the length will be ------ x feet

The perimeter is given as ---- 78 feet

The formula for perimeter of a rectangle is ; 2[ l+w ] where l is length and w is width

Use the assumed measurements in the equation for perimeter as;

2[ l+w ] =78

2{x +2x] =78

2x +4x =78

6x = 78

x=13 feet

Length = x = 13 feet

Width = 2x = 2*13 = 26 feet

We know that the man loses 16% of his weight, to find how much was that we just have to multiply his total weight by 0.16, like this:

lost weight = 0.16 * total weight, by replacing 200 lbs for total weight, we get:

lost weight = 0.16 * 200 = 32

Now we need to express 32 lbs in ounces, we can do this by multiplying the weight in pounds by 16, since 1 pound is equivalent to 16 ounces, then we get:

lost weight in ounces = 32 * 16 = 512

Then, the man lost 512 ounces

The pattern consists of adding a new square on the right, and then adding a new square below previous squares.