Please help 20 POINTS. Problem below

Distance covered in 12 gallons tank of gas = 420 miles

So, distance covered in 1 gallon tank of gas = [tex]\frac{420}{12}[/tex] miles

Now, distance covered in 8 gallons will be =

[tex]8*\frac{420}{12}[/tex] =280 miles

Hence, distance covered by Mr.Fink's economy car in 8 gallons tank of gas is 280 miles.

The weight of the body when the distance is 750 miles if it is inversely proportional is 3,920 pounds.

w = k/d²

Where,

k = constant of proportionality

w = 180 pound

d = 3,500 miles

w = k/d²

180 = k/3500²

180 = k/12,250,000

cross product

k = 180 × 12,250,000

k = 2,205,000,000

Therefore, when d = 750 miles

w = k/d²

w = 2,205,000,000 / 750²

= 2,205,000,000 / 562,500

= 3,920 pounds

Hence, the weight of the body is 3,920 pounds.

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Answer:  

There will be 213 songs in each group.

Step-by-step explanation:

Suppose, the number of songs in each group is  [tex]x[/tex]

As he has 4 different groups of songs, so the total number of songs in all 4 groups will be:  [tex](4*x)= 4x[/tex]

Given that, the mp3 player has a total of 852 songs. So, the equation will be........

[tex]4x=852\\ \\ x=\frac{852}{4}=213[/tex]

So, there will be 213 songs in each group.

i THINK its 2 1/2 ?????

Answer : (-∞,-1) U  (-1, 1)

We need to find  the interval(s) over which the function is increasing

We look at the intervals of x  where the graph is increasing

Increasing interval of the graph is the part where the graph goes up.

At first  the graph starts increasing and it increases till x=-1

So the first increasing interval is -infinity to -1 . We write it as (-∞,1)

Now, we look at the part where the graph changes direction

In the middle  inverted U shaped graph , the graph starts increasing at x=-1  and increases till it changes direction. The graph is increasing till x=1

so second increasing interval is x=-1  to 1. we write it as (-1,1)

Now combine both intervals by a 'U' union

(-∞,-1) U  (-1, 1)

The  interval(s) over which the function that is increasing is  (-∞,-1) U  (-1, 1)

From the question, One need to find  the interval(s) over which the function is increasing

Since intervals of x  where the graph is increasing Increasing interval of the graph is the part where the graph goes up.

At first  the graph starts increasing and it increases till x=-1, So the first increasing interval is -infinity to -1 . We write it as (-∞,1). So, one look at the part where the graph changes direction

In the middle  inverted U shaped graph , the graph starts increasing at x=-1  and increases till it changes direction. The graph is increasing till x=1

Since the  increasing interval is x=-1  to 1. one then need to write it as (-1,1)

So, The function is increasing for all values of x in the open interval from negative infinity to negative 1, excluding -1, and also in the open interval from -1 to 1, excluding both -1 and 1."

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Answer:

Only one solution

Step-by-step explanation:

Given that there is a coordinate plane (say xy)

Two lines are given.

One line crosses the y axis at 3 and has a slope of negative 1.

hence equation of I line is y = -x+3

The other line crosses the y axis at 3 and has a slope of two thirds.

So equation is y = 2x/3 +3

Since the two lines lie in the same plane and are having different slopes, they intersect at one point.

Eliminate y to get

-x+3=2x/3+3

Or x=0

y=3

Hence solutionis (0,3) for the system.

Answer:

One solution

Step-by-step explanation:

we know that

The solution of the system of equations  is equal to the intersection point both graphs

we have

[tex]y=-x+3[/tex] ------> equation A

[tex]y=-(2/3)x+3[/tex] ------> equation B

Using a graphing tool

see the attached figure to better understand the problem

In this problem the intersection point is only one

therefore

The system of equations has one solution

The solution is the point [tex](0,3)[/tex]

Answer:

Sali's speed was 18.75 km/h.

Step-by-step explanation:

Jane took 3.5 hours to cycle the 63 km.

As,  [tex]Speed= \frac{Distance}{Time}[/tex] , so the speed of Jane will be:  [tex]\frac{63}{3.5} km/h = 18 km/h[/tex]

Suppose, the speed of Sali is  [tex]x[/tex] km/h

Sali caught up with Jane when they had both cycled 30 km.

So, the time required for Jane to cycle 30 km [tex]= \frac{30}{18}=\frac{5}{3} hours[/tex] and the time required for Sali to cycle 30 km  [tex]=\frac{30}{x} hours[/tex]

Given that, Sali started to cycle 4 minutes or [tex](\frac{4}{60}) or (\frac{1}{15}) hours[/tex] after Jane started to cycle. So, the equation will be.......

[tex]\frac{5}{3}-\frac{30}{x}= \frac{1}{15}\\ \\ \frac{30}{x}= \frac{5}{3}-\frac{1}{15}\\ \\ \frac{30}{x}= \frac{24}{15}\\ \\ 24x=450\\ \\ x= \frac{450}{24}= 18.75[/tex]

Thus, the speed of Sali was 18.75 km/h.

Answer:Thus, the speed of Sali was 18.75 km/h.

Step-by-step explanation:

Sali's speed was 18.75 km/h.

Answer:

Option B) 5    

Step-by-step explanation:

We are given the following information:

A scatter plot is given which shows the number of hats and scarves each knitter sold at a knitting show.

In the scatter plot the x-axis shows the number of hats sold and the y-axis shows the number of scarves sold.

We have to find the number of hats sold by the knitter when he sold 8 scarves.

In order to find this we have to find the x-values corresponding to the y-values of 8 scarves in the scatter plot.

Corresponding to 8 on y-axis we have a point that have a corresponding value of 5.

Hence, 5 hats were sold by the knitter when he sold 8 scarves.

Option B) 5 is the correct answer.

The scatter plot that shows the number of hats and scarves each knitter sold at a knitting show is Option B) 5    

To find the number of hats sold when 8 scarves were sold, you can look at the scatter plot and observe that there is a data point on the plot where the y-value (number of scarves) is 8, and the corresponding x-value (number of hats) is 5.

In the scatter plot the x-axis shows the number of hats sold and the y-axis shows the number of scarves sold. In order to find this we have to find the x-values corresponding to the y-values of 8 scarves in the scatter plot.

Hence, 5 hats were sold by the knitter when he sold 8 scarves.

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Yes, there was a mistake in applying the distributive property. If you have to perform

[tex] 3(2x-5) [/tex]

you have to multiply both terms in the parenthesis by 3, not just the first one.

So, the correct expansion would be

[tex] 3(2x-5) = 3\cdot 2x - 3 \cdot (-5) = 6x-15 [/tex]

Leeza made an error she did not multiply 3 into the bracket correctly. Therefore, the solution to an equation is 4.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation is 4x=7+3(2x-5).

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

Now, 4x=7+6x-15

4x=6x-8

4x-6x= -8

-2x=-8

x=4

Leeza made an error she did not multiply 3 into the bracket correctly. Therefore, the solution to an equation is 4.

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Answer:

Domain = R

Range =(0,infinity)

Step-by-step explanation:

Given a function as

y = 4(1/3)^x

The function does not have x or y in the denominator or any square root sign.

Hence we can assign any values to x.

Domain = R = Set of all real numbers = (-infinity, infinity)

Let us consider range.

We find that 4(1/3)^x is a multiple of 4 and powers of 1/3

Since power of 1/3 is always positive, y cannot take any negative value.

When x=0 y =4.

When x tends to -infinity, y tends to 0

So y cannot take the value 0 except at -infinity.

Range =(0,infinity)

answer is equal to2:1/2=4:1

4 cups are required

Final answer:

For every cup of butter in the recipe, 4 cups of flour are needed. This is found by analyzing the ratio of flour to butter given in the recipe, which is 2 cups flour to 0.5 cup butter.

Explanation:

The question asks how many cups of flour are needed to mix with each cup of butter according to a given recipe. To determine this, we look at the provided ratios and find that the recipe calls for 2 cups of flour and 0.5 cup of butter. This results in the ratio of 4 cups of flour for every 1 cup of butter.

To calculate the amount of flour required for each cup of butter, we use a simple proportion:

0.5 cup butter : 2 cups flour
1 cup butter : x cups flour

To solve for x (the amount of flour needed for 1 cup of butter), we cross-multiply and get:

0.5x = 2
x = 2 / 0.5
x = 4

So, for every cup of butter, 4 cups of flour are needed.

The value of the expression 2d + 32 is 48 when d equals 8.

The student has provided an expression 2d + 32 and the value for d is given as 8. In order to evaluate the expression, we simply need to substitute the value of d into the expression.

Evaluating the expression:
2d + 32
= 2(8) + 32
= 16 + 32
= 48.

So, the value of the expression when d = 8 is 48.

Given rate is = 7% or 0.07

Total amount needed = $12000

Time = 4 years

Here, the  deposit is  compounded semiannually, means twice per year and this gives 8 annual compounding periods in 4 years.

The equation becomes:

P= [tex]\frac{12000}{(1+\frac{0.07}{2})^{2.4}}[/tex]

P = [tex]\frac{12000}{1.035^{8}}[/tex]

Solving it, we get P = $ 9112.93

Hence $9112.93 should be deposited today.

To accumulate $12,000 in four years in an account earning 7% compounded semiannually, approximately $8,289.64 should be deposited today.

To find out how much money should be deposited today in an account that earns 7% compounded semiannually to accumulate to $12,000 in four years, we can use the formula for calculating compound interest:

A = P(1 + r/n)^(nt)

Where A is the final amount, P is the principal (initial deposit), r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

Hence, approximately $8,289.64 should be deposited today in the account.

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Answer: c. ;]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]

6. vertical

7. LSM and MSN are vertical angles

8. MSN

Answer:

6. Which type of angle pair are LSM and OSN?

Answer - D. Vertical angles

Vertical angles are pairs of opposite angles made by two intersecting lines.

7. Which of the following statements are false?

Answer - C. LSM and MSN are vertical angles.

Vertical angles are pairs of opposite angles made by two intersecting lines.

8. Which angle is supplementary to LSM?

Answer - D. MSN

Two angles are supplementary when they add up to become 180 degrees.

Here adding both we will get angle S as 180 degrees.

ANSWER

[tex]x=4[/tex]

EXPLANATION

We have[tex]6x-8=16[/tex]

We add 8 to both sides of the equation

[tex]6x-8+8=16+8[/tex]

We simplify

[tex]6x=24[/tex]

We divide both sides by 6

[tex]x=\frac{24}{6}[/tex]

[tex]x=4[/tex]

Remark

You are dealing with a right angle triangle. You can use one of Sin(x) Cos(x) or Tan(x). Since the Hypotenuse is involved and since you are given the adjacent side, Cos(71) is what you will need.

Solution

H = BC

Cos(x) = adjactent / hypotenuse

Cos(71) = 6.3 / H            Multiply both sides by H

H * Cos(71) = 6.3            Divide by Cos(71)

H = 6.3 / cos(71)             Cos(71) = 0.32557

H = 6.3 / 0.32557          Divide

H = BC = 19.351                       Answer

The sum of the measures of the angles of a hexagon is equal 720°.

Therefore we have the equation:

[tex]160^o+75^o+132^o+113^o+108^o+x^o=720^o\\\\588^o+x^o=720^o\ \ \ \ |-588^o\\\\x^o=132^o[/tex]

Answer: x = 132

Oh this is easy.I completed the table. C) 40%

THE ANSWER IS C (◡ ‿ ◡ ✿)

Number of Horses in Avery's farm, after t years from now is given by function H(t); where  [tex]H(t) = 25(2)^{t}[/tex]

The amount of hay, in tons, that is produced on her farm t years from now is given by function A(t); where  [tex]A(t) = 150(1.5)^{t}[/tex]

The predicted yearly supply of hay, in tons, available to each horse in Avery's farm t years from now is given by function F(t); where F(t) = A(t)/H(t)

So, F(t) = [tex]\frac{150(1.5)^{t}}{25(2)^{t}}[/tex] = [tex]6 (\frac{1.5}{2}) ^{t}[/tex] = [tex]6 (0.75)^{t}[/tex] tons/horse

The formula for F(t) in terms of H(t) and A(t) is F(t) = (150(1.5)^t) / (25(2)^t).

To find the formula for F(t), we need to divide the amount of hay produced, A(t), by the number of horses, H(t). So, the formula for F(t) is F(t) = A(t) / H(t). Substituting the given functions, we have F(t) = (150(1.5)^t) / (25(2)^t).

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Point slope form says the line through (a,b) with slope m is

y - b = m(x - a)

Here that's

y - - 1 = -2(x - -4)

Answer: y + 1 = -2(x + 4)

Point-Slope equation: y - y₁ = m(x - x₁)  ; m is slope and (x₁ ,y₁) is the coordinate

y - (-1) = -2(x - (-4)

y + 1 = -2(x + 4)     simplified (two negatives make a positive)

6 on the sq rt 5 - 4 on the sq rt 7

To simplify the given expression, substitute the values of each square root and simplify the expression to get the final result of 1.416.

To simplify the given expression:
3 times the square root of 5 - 2 times the square root of 7 + the square root of 45 - the square root of 28

We can simplify each square root separately:

√5 = 2.236 (approx.)

√7 = 2.646 (approx.)

√45 = 6.708 (approx.)

√28 = 5.292 (approx.)

Substituting these values in the expression:

3(2.236) - 2(2.646) + 6.708 - 5.292

This simplifies to:
6.708 - 5.292 = 1.416

Therefore, the simplified expression is 1.416.

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Answer:

9i(2+3i) = -27+18i

Step-by-step explanation:

Distribute to get → 9i·2+9i(3i)

Multiply 2 and 9 → 18i+9i(3i)

Simplify → 18i+27i²

Simplify → 18i-27

Reorder → -27+18i

675 : 5 = 135

135 : 5 = 27

27 : 3 = 9

9 : 3 = 3

3 : 3 = 1

675 = 5 · 5 · 3 · 3 · 3 = 5² · 3³