Translate the sentence into an equation. Two less than the product of 5 and a number is equal to 6 . Use the variable w for the unknown number.

Answer:

[tex]\dfrac{12}{x-7},[/tex]

[tex]x\neq 7,\ x\neq -3.[/tex]

Step-by-step explanation:

Consider the expression

[tex]\dfrac{12x+36}{x^2-4x-21}.[/tex]

1. The numerator can be factored as

[tex]12x+36=12(x+3).[/tex]

2. The denominator [tex]x^2-4x-21[/tex] has the discriminant

[tex]D=(-4)^2-4\cdot (-21)\cdot 1=16+84=100.[/tex]

Then

[tex]x_{1,2}=\dfrac{-(-4)\pm \sqrt{100}}{2\cdot 1}=\dfrac{4\pm 10}{2}=7,\ -3.[/tex]

Then

[tex]x^2-4x-21=(x-7)(x+3).[/tex]

Note that restrictions on the variable x are [tex]x\neq 7,\ x\neq -3.[/tex]

3. Simplify the fraction:

[tex]\dfrac{12x+36}{x^2-4x-21}=\dfrac{12(x+3)}{(x-7)(x+3)}=\dfrac{12}{x-7}.[/tex]

Answer:

y-determinant = 2

Step-by-step explanation:

Given the following system of equation:

Let's represent it using a matrix:

[tex]\left[\begin{array}{ccc}1&2\\1&-3\end{array}\right] = \left[\begin{array}{ccc}5\\7\end{array}\right][/tex]

The y‐numerator determinant is formed by taking the constant terms from the system and placing them in the y‐coefficient positions and retaining the x‐coefficients. Then:

[tex]\left[\begin{array}{ccc}1&5\\1&7\end{array}\right] [/tex]

y-determinant = (1)(7) - (5)(1) = 2.

Therefore, the y-determinant = 2

Answer:

f(x)·g(x) = -6x² -x +77

Step-by-step explanation:

Given:

f(x) = 3x + 11

g(x) = -2x+7

f(x) * g(x) = (3x+11)*(-2x+7)

              = -6x²+21x-22x+77

              = -6x² -x +77

Answer: 81, 27, 9, 3, 1, 1/3

There are six terms listed. The first five are whole numbers and the sixth term is a fraction.

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

Explanation:

The equation t1 = 81 means that the first term "t" is 81. The second term is t2 = 27 because we multiply 1/3 by 81, or divide 81 over 3, and we end up with 81/3 = 27 as the second term.

We know to multiply by 1/3 because of the equation tn = (1/3)*t_(n-1) where the "n-1" portion is smaller than 't'. We can write it like this[tex]t_n = \frac{1}{3}*t_{n-1}[/tex]

To get the next term, we multiply by 1/3 again: 27*(1/3) = 27/3 = 9 giving us the third term

And repeat until we have six terms

9*(1/3) = 9/3 = 3 is the fourth term

3*(1/3) = 3/3 = 1 is the fifth term

1*(1/3) = 1/3 is the sixth term

So that is how I got the first six terms to be 81, 27, 9, 3, 1, 1/3

Answer:

$16

Step-by-step explanation:

A dozen is equal to 12 eggs. In order to find the amount for 50 eggs, we need to find the unit rate. In this problem, we can assume that each of the eggs cost the same amount.  Therefore, we can divide 3.84 by 12 to get the amount of one egg.

3.84/12= 0.32

Now that we have found the unit rate, we simply have to multiply it by 50 to get the cost. To explain why we do this, I will set it up as a proportion.

3.84/1 = ?/50

In order to get the equivalent amount you must multiply by 50.  

0.32 x 50= 16

Therefore, the answer is $16

The cost of 50 eggs is $16.

Given that, a dozen eggs cost $3.84.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Here, the cost of one egg = 3.84/12

= $0.32

Now, the cost of 50 eggs

= 50 × 0.32

= 16

Therefore, the cost of 50 eggs is $16.

To learn more about the unitary method visit:

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Answer:

The answer is $61.20

Step-by-step explanation:

First you multiply 72 by .15 (which is 15% converted to a decimal), which gives you 10.8. You then subtract 10.8 from 72.

Julie's salary started at $25,000. t is the number of years since her original $25,000 salary started. Each year she gets a 4% raise. The expression gives her salary at year t.

Answer:

b.

Step-by-step explanation:

Interpret the meaning of the expression.

A.  

Julia's initial salary is $4,000, and the growth rate is 25% per year.

B.  

Julia's initial salary is $25,000, and the growth rate is 4% per year.

C.  

Julia's initial salary is $4,000, and the growth rate is 2.5% per year.

D.  

Julia's initial salary is $25,000, and the growth rate is 40% per year.

[tex]i=1i\\\\i+6i=1i+6i=(1+6)i=\boxed{7i}[/tex]

Substitution method

y = x + 3   (*)

y = 3x + 1  (**)

Substitute (*) to (**):

3x + 1 = x + 3      subtract 1 from both sides

3x = x + 2       subtract x from both sides

2x = 2        divide both sides by 2

Put the value of x to (*):

y = 1 + 3

the answer to the question is 7-3x.

Answer:

7 - 3x

Step-by-step explanation:

let "some number" = x

"3 times x" = 3(x)

"seven decreased by" 7 -

Put together the phrases.

"seven decreased by 3 times x" is 7 - 3x

7 - 3x is your answer

~

Answer:

40 cm

Step-by-step explanation:

Using the conversion

1 litre = 1000 cm³, then

40 litres = 40 × 1000 = 40000 cm³

The volume ( V) of a cuboid is

V = lbh ( divide both sides by bh )

l = [tex]\frac{V}{bh}[/tex] = [tex]\frac{40000}{50(20)}[/tex] = [tex]\frac{40000}{1000}[/tex] = 40 cm

Length of water tank is 40 cm

Given that;

Capacity of tank = 40 liters

Dimensions of tank = 50cm × 20cm

Find:

Length of water tank

Computation:

Capacity of tank = 40 liters

Capacity of tank = 40 × 1000

Capacity of tank = 40,000 cm³

Length of water tank = 40,000 / [50cm × 20cm]

Length of water tank = 40,000 / 1,000

Length of water tank = 40 cm

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A. Negative Association

C. Strong Association

E. Linear

Answer:

1. Negative Correlation

3. Strong Correlation

5. Linear

Step-by-step explanation:

We have been given a scatter-plot. We are asked to choose the characteristics of the given scatter-plot.

Upon looking at our given scatter-plot, we can see that as the values of x are increasing values of y are decreasing.

We know that the relationship between two variables in which one variable increases as the other decreases is known as negative correlation. Therefore, the given scatter-plot represents negative correlation and 1st option is a correct choice.

We can also see that the slope of the line connecting all data points is approximately [tex]-1[/tex], which represents a strong negative correlation, therefore, 3rd option is correct as well.

If we draw a line on our given scatter-plot, it will connect all the data points. Therefore, the given scatter-plot has a linear correlation and 5th option is correct as well.

Answer:

9W + 72

Step-by-step explanation:

using the distributive property, you would multiply both the w and the 8 by 9 to obtain 9*w and 9*8. 9*w + 9*8 = 9w + 72.

This works because if you have 9 of (w+8), you have 9 w's and 9 8's. Adding these up is simply multiplying 9 by w (since there are 9 w's) and 9 by 8 (since there are 9 8's).

Answer:

I’m patty’s urge in 9W + 8

Step-by-step explanation:

I just got the question right on Edge!

Answer:

2A/b =h

Step-by-step explanation:

A = 1/2bh

Multiply each side by 2

2*A = 2*1/2bh

2A = bh

Divide each side by b

2A/b = bh/b

2A/b =h

Answer:

3/1

Step-by-step explanation:

think in this question we have to find the ratio .

Question:

There are 9 tennis balls in 3 cans. What is the RATIO of number of tennis balls to number of cans?

Solution:

Given:

Number of tennis ball= 9

Number of cans = 3

Ratio of number of tennis balls to number of cans= tennis ball : cans

= 9/3 = 3/1

Hence, Ratio of number of tennis balls to number of cans= tennis ball : cans= 3:1

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

Hope this will help you....

Answer:

21100%

Step-by-step explanation:

Move the decimal point two places to the right.

Answer: p = 6

Step-by-step explanation:

HI !

 px + 3y - ( p-3)=0

a₁ = p , b₁ = 3 , c₁ = - (p-3)

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

12x + py - p=0

a₂ = 12  , b₂ = p , c₂ = -p

since , the equations have infinite solutions , 

a₁/a₂ = b₁/b₂ = c₁/c₂

p/12 = 3/p =  p-3/p

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

p/12 = 3/p

cross multiply ,

p² = 36

p = √36

 p = 6

for the value of p = 6 , the equations will have infinitely many solutions

Answer:

x =56.4 degrees

Step-by-step explanation:

For right triangles, we know that the sin x = opposite/ hypotenuse

sin x = 20/24

Taking the arcsin of each side

arcsin (sin x) = arcsin (20/24)

x = 56.44269024 degrees

To the nearest tenth

x =56.4 degrees

Answer:

B = 2

Step-by-step explanation:

using the rule of exponents

• [tex]a^{\frac{m}{n} }[/tex] = [tex]\sqrt[n]{a^{m} }[/tex]

consider [tex]83^{\frac{2}{3} }[/tex] = [tex]\sqrt[3]{83^{2} }[/tex]

⇒ B = 2

Answer:

The maximum amount of money that should be spent on housing each month is $522.

The maximum amount of money that should be spent on transportation each month is $290.

The maximum amount of money that should be spent on food each month is $246.50.

The maximum amount of money that should be spent on entertainment each month is $116.

Answer:

$522

Step-by-step explanation:

The maximum amount of money that should be spent on housing each month is $522.

The maximum amount of money that should be spent on transportation each month is $290.

The maximum amount of money that should be spent on food each month is $246.50.

The maximum amount of money that should be spent on entertainment each month is $116.

Answer: Her total bill including tip is $51.75

Step-by-step explanation:

Hi, first, we have to multiply the cost of the meal by the tip percentage in decimal form (percentage divided by 100).

Mathematically speaking:

45 x (15/100) = 45 x 0.15 = 6.75 tip amount

Finally, add the amount of the tip to the meal's cost.

45 +6.75 = $51.75

Her total bill including tip is $51.75

Feel free to ask for more if needed or if you did not understand something.

Answer:

7(x + 2)

Step-by-step explanation:

7x + 14 =

7 can be factored out of each term.

= 7 * x + 7 * 2

= 7(x + 2)

Answer:

You are going to line up the decimal points to each other and add a zero to the end of the shortest decimal.

3.99+39.9=43.89

Step-by-step explanation:

You are going to take the 3.99 and add that to the 39.9 like normal but you are first going to line up the decimals.

The side measure of the largest-sized square tile will be 4 in.

The greatest common factor (GCF) of a set of numbers is the largest factor that all the numbers share.

Given that, The top of a stepping stone  is 24 inches by 20 inches.

GCF of 24 and 20 = 4

Hence, The side measure of the largest-sized square tile will be 4 in.

For more references on GCF, click;

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Answer:

[tex]y = 140000(1.04)^{x}[/tex]; 262 000

Step-by-step explanation:

The general formula for an exponential function is

[tex]y = a(b)^{x}[/tex]

a = 140 000; b = 1.04; x = 16

[tex]y = 140000(1.04)^{x}[/tex]

y = 140 000(1.04)¹⁶

y = 140 000 × 1.873

y = 262 000

The graph below shows the population growth over time.

Final answer:

An exponential function to model the population growth is P(t) = P_0 * e^{rt}, where the initial population P_0 is 140,000, the rate of growth r is 0.04, and the time t is 16 years. The population after 16 years is calculated by P(16) = 140,000 * e^{0.64}.

Explanation:

To model the population growth, we can use the formula for exponential growth which is P(t) = P_0 e^{rt}, where:

P(t) is the future population after time t,

P_0 is the initial population size,

e is the base of natural logarithms (approximately equal to 2.71828),

r is the rate of growth (expressed as a decimal), and

t is the time in years.

In the given situation, the initial population P_0 is 140,000, the growth rate r is 4% per year which is 0.04 when expressed as a decimal, and the time period t is 16 years. Plugging these values into the formula:

P(16) = 140,000 * e^{0.04 * 16}

To calculate the future population after 16 years, solve the equation:

P(16) = 140,000 * e^{0.64}

Using a calculator to compute e^{0.64}, and then multiplying by 140,000, we obtain the future population.

Look at the picture.

[tex]A(3,\ 2)\to A'(2,\ 3)\\\\B(-4,\ 1)\to B(1,\ -4)\\\\C(-3,\ -2)\to C'(-2,\ -3)[/tex]

1. The answer is A.

Based on the line plot, we can see that Sandy drank 12 juice boxes on October 12th. Each X on the plot represents 2 juice boxes, and there are 6 of them, meaning she drank 12. October 2nd has 1 X, meaning she drank 2 that day.

2. The answer is A.

On a graph, the point (1, 3) would mean that 1 is on the x-axis, and 3 is on the y-axis. Therefore, point B is correct because it is 1 space to the right, and 3 spaces up from the origin.

3. The answer is C.

If the coordinate we're looking for is (4, 0) then on a graph you would move 4 spaces to the right, and 0 spaces up or down. Therefore, point B is the correct choice.

Answer: u = -4w + 9

Step-by-step explanation:

u - 5 = -4(w - 1)

u - 5 = -4w + 4

  +5           +5  

u         = -4w + 9

The proper formula to solve the equation u - 5 = -4(w - 1) for w is w = (u + 9) / 4, after rearranging and simplifying the terms of the equation.

The question involves solving a linear equation with variables u and w. Initially, we have the equation u - 5 = -4(w - 1). To solve for w, we need to isolate w on one side of the equation. A statement in the information provided seems to mistakenly give the result of w, which probably arises from a typo or error, stating w = -40 - 5. However, this is incorrect given the initial equation.

Let's start by expanding the right side of the initial equation:

And then rearranging to solve for w:

From this process, we see that the correct formula to isolate and solve for w is w = (u + 9) / 4.

Answer:

840 kg of bamboo in 6 weeks

Step-by-step explanation:

if a panda eats 20 kg of bamboo per day he eats 140 kg of bamboo every week. multiply the amount he eats per week (140) by the amount of weeks (6) and you get 840 kg of bamboo

Answer:

1,848

Step-by-step explanation:

The panda eats 20kg of bamboo per day, and 1 L = 2.2 Ib, so multiplying 20 x 2.2 = 44, and there is 42 days in 6 weeks, so you multiply 44 x 22 = 1,848. I hope this is the correct answer, you're welcome!