Scientists believe that there is an extremely massive black hole at the center of the Milky Way. How many times more massive than the Sun would a black hole with a mass of 7.36 x 10^36 kg be? The mass of the Sun is approximately 1.99 x 10^30 kg.

A. 3.7 x 10^8
B. 3.7 x 10^6
C. 3.7 x 10^4
D. 3.7 x 10^3

To find the area of rectangles, use the formula A = b * h. Each problem was solved using this formula, leading to areas of 299 sq yards, 71,142 sq inches, 212.79 sq meters, 10,530 sq feet, and 24.96 sq yards respectively.

Let's solve each of the given problems step-by-step using the formula for the area of a rectangle, which is A = b * h where A is the area, b is the base (or length), and h is the height (or width).

For the rectangle with a length of 13 yards and a width of 23 yards, the area is:

A = 13 * 23 = 299 square yards

For the name tag with dimensions 334 inches by 213 inches, the area is:

A = 334 * 213 = 71,142 square inches

For the rectangle with a length of 24.6 meters and a width of 8.65 meters, the area is:

A = 24.6 * 8.65 = 212.79 square meters

Thus, the correct choice is C 212.79 m².

For the rectangular print with dimensions 78 feet by 135 feet, the area is:

A = 78 * 135 = 10,530 square feet

For the living room that is 4.8 yards wide and 5.2 yards long, the area is:

A = 4.8 * 5.2 = 24.96 square yards

Summary of Answers:

Answer:

(2,3)

Step-by-step explanation:

Multiplying the first equation by 5 and the second equation by $-2$ gives

\begin{align*}

10x-15y&=-25,\\

-10x + 4y &=-8.\\

\end{align*}Adding the two equations gives $-11y = -33$, so $y=3$. Substituting $y=3$ in the first original equation gives $2x - 9 = -5$, so $2x = 4$ and $x = 2$. Therefore, the solution is $(x,y) = \boxed{(2,3)}$

Answer:

(B)

Step-by-step explanation:

In the given graph,   it is shown the number of cups of mango juice are mixed with different numbers o cups of lemon juice.

Then, From the graph, at Point(10,1),

Ratio of the cups of mango juice to the number of cups of lemon juice soda=[tex]\frac{10}{1}[/tex]

=10:1

At point (20,2)

Ratio of the cups of mango juice to the number of cups of lemon juice soda=[tex]\frac{20}{2}=\frac{10}{1}[/tex]

=10:1

At point (30,3)

Ratio of the cups of mango juice to the number of cups of lemon juice soda=[tex]\frac{30}{3}=\frac{10}{1}[/tex]

=10:1

At point (40,4)

Ratio of the cups of mango juice to the number of cups of lemon juice soda=[tex]\frac{40}{4}=\frac{10}{1}[/tex]

=10:1

Thus, Option B is correct.

Answer:

B

Step-by-step explanation:

In the given graph,   it is shown the number of cups of mango juice are mixed with different numbers o cups of lemon juice.

Then, From the graph, at Point(10,1),

Ratio of the cups of mango juice to the number of cups of lemon juice soda=

=10:1

At point (20,2)

Ratio of the cups of mango juice to the number of cups of lemon juice soda=

=10:1

At point (30,3)

Ratio of the cups of mango juice to the number of cups of lemon juice soda=

=10:1

At point (40,4)

Ratio of the cups of mango juice to the number of cups of lemon juice soda=

=10:1

Thus, Option B is correct.

To solve for z, add the equations for VC and CW (z + 13 and z + 8 respectively) and set them equal to VW (61). Solve the resulting equation to get z = 20.

To solve for z when point C is between V and W on line w, with VW = 61, VC = z + 13, and CW = z + 8, you need to set up an equation knowing that VC + CW is equal to VW.

Therefore, the value of z is 20.

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Answer:

k-n

Step-by-step explanation:

Answer:

k-n-1

Step-by-step explanation:

This is what I think based on other formulas

Answer:

In the park's pool there are 7 less chlorine tablets as compared to safety standards.

Step-by-step explanation:

Number of chlorine tablets in 2,000 gallons water = 3 tablets

Number of tablets in 1 gallon of water = [tex]\frac{3}{2,000} tablets[/tex]

Number of tablet to be added in 10,000 gallons of water :

[tex]\frac{3}{2,000}\times 10,000 tablets=15 tablets[/tex]

Number of chlorine tablets added by lifeguard in 10,000 gallon water=8 tablets

Tablets of chlorine to be more added =

=15 tablets - 8 tablets = 7 tablets

In the park's pool there are 7 less chlorine tablets as compared to safety standards.

Answer:

C. y-2=2(x-4)

Step-by-step explanation:

The football team scored 43 times this season, comprising solely of touchdowns worth 7 points each, totalling to 301 points. The team did not score any field goals worth 3 points.

This problem can be solved using systems of linear equations. We have two equations here: 1. The total number of times the team scored, which is touchdowns(T) plus field goals(F) equals 43 (T+F=43). 2. The total points the team made, each touchdown being 7 points and each field goal being 3 points, equals 301 (7T + 3F = 301). By solving this system of equations, we can find the number of touchdowns and field goals.

Thus, the team scored 43 touchdowns and 0 field goals.

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The solutions are:

           [tex]x=-5.372\ and\ x=0.372[/tex]

The equation is given by:

              [tex]2x(x+5)=4[/tex]

on using the distributive property of multiplication in the left hand side of the equation we have:

[tex]2x\times x+2x\times 5=4\\\\i.e.\\\\2x^2+10x=4\\\\i.e.\\\\2x^2+10x-4=0\\\\i.e.\\\\2(x^2+5x-2)=0\\\\i.e.\\\\x^2+5x-2=0[/tex]

Now, we know that the solution of the quadratic equation:

[tex]ax^2+bx+c=0[/tex] is given by:

[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

Here we have:

[tex]a=1,\ b=5\ and\ c=-2[/tex]

Hence, the solution is:

[tex]x=\dfrac{-5\pm \sqrt{5^2-4\times 1\times (-2)}}{2\times 1}\\\\i.e.\\\\x=\dfrac{-5\pm \sqrt{25+8}}{2}\\\\i.e.\\\\x=\dfrac{-5\pm \sqrt{33}}{2}\\\\x=\dfrac{-5+\sqrt{33}}{2},\ x=\dfrac{-5-\sqrt{33}}{2}[/tex]

Hence, in decimal for the solution is:

[tex]x=-5.372\ and\ x=0.372[/tex]

Answer:

25+3=28 - 28=j or j=28

Step-by-step explanation:

just add 25 and 3 and you will get 28.

Answer:153.9

Step-by-step explanations equation A=pi×r^2

A=pi×7^2

A=pi×79

A=153.9 i round

To convert the bike wheel diameter from inches to millimeters, multiply 26 inches by the conversion factor of 25.4 mm/inch, resulting in a diameter of 660.4 mm.

To convert the diameter of a bike wheel from inches to millimeters, we use the conversion factor that 1 inch is equal to 25.4 millimeters. Hence, we multiply the diameter in inches by this conversion factor.

The calculation will be:

Therefore, the diameter of the bike wheel is 660.4 millimeters.

Final answer:

To factor the expression y^3 - 9y^2 + y - 9 by grouping, divide it into two groups, factor out common factors, and note that (y - 9) is common to both, yielding the final factored form (y^2 + 1)(y - 9).

Explanation:

To factor by grouping the expression y3 − 9y2 + y − 9, we first split it into two parts where common factors are apparent:

(y3 − 9y2) and (y − 9)

Next, we factor out the common factors from each group:

y2(y − 9) + 1(y − 9)

Now, we notice that (y − 9) is a common factor in both terms. So, we factor (y − 9) out of the entire expression:

(y2 + 1)(y − 9)

This gives us the final factored form of y3 − 9y2 + y − 9, which is (y2 + 1)(y − 9).

The width of the rectangle is 6 inches and the length is 12 inches.

To find the dimensions of the rectangle, we can use the fact that the length is 2 times the width. Let's define the width as 'w' inches. According to the problem, the length is 2 times the width, so the length would be '2w' inches. The area of a rectangle is calculated by multiplying the length and the width, so we can set up the equation: 'w * 2w = 72'. Solving this equation, we find that 'w' equals 6 inches. Therefore, the width of the rectangle is 6 inches and the length is 2 times that, which is 12 inches.

Final answer:

The width is 11 feet and the length is 17 feet.

Explanation:

The question asks us to find the length and width of a rectangle where the length is 6 feet longer than the width and the perimeter is 56 feet. To solve this, let's denote the width of the rectangle as w feet.

Since the length is 6 feet longer, the length will be w + 6 feet.

The formula for the perimeter (P) of a rectangle is P = 2(length + width). We can plug in our expressions for length and width into this formula:

P = 2(w + 6 + w)

Given that the perimeter is 56 feet, we have:

56 = 2(2w + 6)

Dividing both sides by 2, we get:

28 = 2w + 6

Subtract 6 from both sides:

22 = 2w

Divide both sides by 2:

11 = w

Therefore, the width of the rectangle is 11 feet and the length is w + 6 = 11 + 6 = 17 feet.

To find the exponential model for Ashmore's population, rewrite the linear model as p = a(b)^t and solve for a and b. In this case, a is equal to 925 and b is approximately 1.111.

To find the exponential model for Ashmore's population, we need to express it in the form P = a(b)^t. We know that in the linear model, p = 103t + 925. To convert this to an exponential model, we need to rewrite it in the form p = a(b)^t. To do this, we need to find the values of a and b.

From the linear model, we can see that when t = 0 (in the year 2000), p = 925. This gives us the equation 925 = a(b)^0. Since any number raised to the power of 0 is 1, we can simplify this equation to a = 925.

Next, we need to find the value of b. We can do this by substituting the given values of p and t from the year 2001 (p = 1028 and t = 1) into the exponential model. This gives us the equation 1028 = 925(b)^1. Dividing both sides by 925, we get b ≈ 1.11.

Therefore, the exponential model for Ashmore's population is P = 925(1.11)^t. Rounded to the nearest thousandth, b ≈ 1.111.

The exponential model for the population of Ashmore t years after 2000 is P=925(1.111)^t, where a is the initial population 925, and b is the growth rate rounded to the nearest thousandth, which is 1.111.

To find an exponential model for Ashmore's population in the form P=a(b)^t, where P is the population t years after 2000, we need to use the given data points: 925 in 2000 and 1028 in 2001.

First, let's establish our initial population a as the population at t=0, which is 925. Now we need to find the growth rate b. Since the population in 2001 is 1028, we have one growth period, which is t=1. We can write the equation for 2001 as 1028 = 925b. Dividing both sides by 925 gives us b = 1028 / 925 ≈ 1.111.

For simplicity and to follow instructions, we will round b to the nearest thousandth, giving us b ≈ 1.111. Therefore, the exponential model is P=925(1.111)^t.