Essential: Solve the proportions
step by step ​

Answer:

Two Column Proofs. Two column proofs are organized into statement and reason columns. Each statement must be justified in the reason column. Before beginning a two column proof, start by working backwards from the "prove" or "show" statement. The reason column will typically include "given", vocabulary definitions, conjectures, and theorems.

Step-by-step explanation:

hope this helps :)

Answer:

0.04

Step-by-step explanation:

12^(-x) = 5   (taking log on both sides)

log [ 12^(-x)] = log 5

-x log 12 = log 5

-x = log 5 / log 12

x = - (log 5/log12)

x = -0.6477

12^(2x)

= 12^[2(-0.6477)]

= 12 ^ (-1.295)

= 0.04

The area of square flake of gold is [tex]53.29 \times 10^{-8} \mathrm{mm}[/tex]

Given that width of square flake of gold is [tex]7.3 \times 10^{-4}[/tex] millimeter

To find : Area of square flake

Since gold flake is in shape of square, we can use area of square formula

The formula for area of square is given as:

[tex]area = s^2[/tex]

where "s" is the length of one side

[tex]\begin{array}{l}{\text { Area of a square flake }=\left(7.3 \times 10^{-4}\right) \times\left(7.3 \times 10^{-4}\right)} \\\\ {\text { Area of a square flake }=53.29 \times 10^{8}}\end{array}[/tex]

Hence , the calculated area of flake is [tex]53.29 \times 10^{-8} \mathrm{mm}[/tex]

The smallest integer is 1 and middle integer is 2 and largest integer is 3

Given that , three times the largest increased by two is equal to five times the smallest increased by three times the middle integer.

We have to find the three consecutive integers

So, let the smallest integer be n, then the next two consecutive middle and largest integers will be n + 1, n + 2 respectively

Then, by the given statement,  

Three times the largest increased by two is equal to five times the smallest increased by three times the middle integer.

[tex]\begin{array}{l}{3 \times (n+2)+2=5 \times n+3 \times (n+1)} \\\\ {3 n+6+2=5 n+3 n+3} \\\\ {8=5 n+3} \\\\ {5 n=8-3} \\\\ {n=1}\end{array}[/tex]

Thus the smallest integer = n = 1

Middle integer = n + 1 = 1 + 1 = 2

Largest integer = n + 2 = 1 + 2 = 3

Final answer:

We defined three consecutive integers as x, x+1, and x+2. By setting up the equation based on the given condition and solving for x, we find that the three consecutive integers are 1, 2, and 3.

Explanation:

Let's define the three consecutive integers we are looking for as x, x+1, and x+2, where x is the smallest integer, x+1 is the middle integer, and x+2 is the largest integer.

The problem states that three times the largest increased by two is equal to five times the smallest increased by three times the middle integer. This gives us the equation:

3(x+2) + 2 = 5x + 3(x+1)

Now, simplify and solve for x:

3x + 6 + 2 = 5x + 3x + 3

6x + 8 = 8x + 3

Subtract 6x from both sides:

8 = 2x + 3

Subtract 3 from both sides to isolate the term with x:

5 = 2x

Divide both sides by 2 to solve for x:

x = 5/2 = 2.5

Since x has to be an integer, this approach shows that we've made a mistake in our calculation. Let's try again:

3x + 6 + 2 = 5x + 3x + 3

3x + 8 = 8x + 3

5 = 5x

x = 1

So the three consecutive integers are 1, 2, and 3.

Final answer:

To solve the system of equations -3x - 4y = 2 and 6x + 6y = -6, multiply the first equation by 2 to eliminate the coefficients of y, and then add the equations together. The solution is x = -2 and y = 1.

Explanation:

To solve the system of equations:

-3x - 4y = 2

6x + 6y = -6

First, multiply the first equation by 2 so that the coefficients of y will cancel when adding the equations together.

-6x - 8y = 4

Next, add the modified first equation to the second equation.

(-6x - 8y) + (6x + 6y) = 4 + (-6)

-8y + 6y = -2

-2y = -2

Divide both sides of the equation by -2 to solve for y.

y = 1

Substitute the value of y back into either equation to solve for x.

-3x - 4(1) = 2

-3x - 4 = 2

-3x = 6

x = -2

The solution to the system of equations is x = -2 and y = 1.

Answer:

13.  b.  4 + 5x = 29; $5.

14.  c.  74 + w = 3w + 6; 34 pounds.

15.  b.  $42.5.

Step-by-step explanation:

13. 4 + 5x = 29

5x = 29-4 = 25

x = 5.

14. 74 + w = 3w + 6

68 = 2w

w = 34.

15. Let x be the money he got last year. Then:

2x + 5 = 90

2x = 85

x = $42.5.

Answer:

I would say you're right, 2 + 2

Step-by-step explanation:

Final answer:

The mathematics optimization problem involves finding the maximum sum of the square of one non-negative number and the cube of the other, with their total being 4. Calculus is applied by taking the derivative of the function representing the sum, setting it to zero to find critical points, and checking the second derivative to ensure a maximum is found. The optimized numbers are x and 4-x, based on the critical point found.

Explanation:

To solve the optimization problem, we need to use calculus to find the maximum value of the sum of the square of one number and the cube of the other, given that the sum of the two numbers is 4. Let's call these numbers x and y, with x + y = 4. We want to maximize S = x^2 + y^3.

Since x + y = 4, we can express y as y = 4 - x. Substituting this into S, we have S = x^2 + (4-x)^3. This becomes a function of one variable.

To find the maximum value, we differentiate S with respect to x, set the derivative equal to zero, and solve for x. We can check the second derivative to ensure it is a maximum. The function S' will have a maximum when the first derivative is zero (S'(x) = 0) and the second derivative is negative (S''(x) < 0).

Therefore, the two non-negative numbers that maximize S are x and 4-x, with x being the value at which S' equals zero with S'' negative.

Direct variation equation is y=kx . Your k is your variation or you could look at it as your slope.  y=kx Plug in what you know, 4=k12 Divide both sides by 12 to cancel out your 12 that is being multiplied by k.

4(/12)=k12(/12) Simplify

1/3=k

y=1/3x This is your direct variation equation.

Answer:

Step-by-step explanation:

1) y=kx

plug in the #s

(0.9)=k(0.1)

divide both sides by 0.1

k=9

plug in k and that is your equation (y=9x)

Answer:  4!

Step-by-step explanation:

You can turn 4 2/3 into improper fraction as 14/3. Then you have 14/3 and 6/7. You multiply both tops, then both bottoms. 6x14 is 84 and 3x7 is 21. You get 84/21 or 4. -viridiancat4, an 8th grader.

Answer: 16/7

Step-by-step explanation:

6/7 times 4 2/3 equals 16/7

W=L+2

A=48=L*W

48=L*(L+2)

48=L^2+L*2

0=L^2+L*2-48

L1=6

L2=-8 (can't be used since it's negative)

Lenght=6

Width=8

Answer: C) 19%

Step-by-step explanation:250 +200 + 150 + 125 + 50 = 775 total complaints.  150 rude sales clerks out of 775 total complaints equals 150/775 = 0.1935 which is a 19 percent. So 19 percent of the complaints are about rude sales clerks.

Answer:

6cd+10c

Step-by-step explanation:

(c+c)(3d+5)

2c(3d+5)=6cd+10c

Answer:

The third number line

Step-by-step explanation:

first, make each fraction a complex fraction

47/10 = 4 7/10, so you know its the 7th dash from the left.

for 4 2/5 you need to make the denominator 10 by multiplying the numerator and denominator by 2 to get 4 4/10; this should be the 4th dash.

divide 24/5 to get 4 4/5. Multiply the numerator and denominator of the fraction part to get a denominator of 10. you should get 4 8/10; this is on the 8th dash from the last

You would have a dot on the 4th 7th and 8th dash altogether

They must sell 18 small pizzas, 12 medium pizzas and 6 large pizzas

Step-by-step explanation:

A Pizzeria sells pizza according to size:

We need to find how many of each size pizza they must sell to get $600

Assume that the number of small pizza is x, the number of medium pizza is y and the number of large pizza is z

∵ The Pizzeria sells x small pizzas, y medium pizzas and

   z large pizzas

∵ The small pizzas cost $10, medium pizzas cost $15, and

   large pizzas cost $40

∵ They get $600

∴ 10x + 15y + 40z = 600 ⇒ (1)

∵ They sell as many small pizzas as medium and large pizzas

   combined

∴ x = y + z ⇒ (2)

∵ The number of medium pizzas sold is twice as many as large ones

∴ y = 2z ⇒ (3)

Substitute equation (3) in equation (2) to find x in terms of z only

∵ x = (2z) + z

∴ x = 3z ⇒ (4)

Substitute x in equation (1) by equation (4), and substitute y in equation (1) by equation (3)

∵ 10(3z) + 15(2z) + 40z = 600

- Simplify the left hand side

∴ 30z + 30z + 40z = 600

- Add like terms

∴ 100z = 600

- Divide both sides by 100

∴ z = 6

Substitute the value of z in equations (3) and (4) to find y and x

∵ y = 2(6)

∴ y = 12

∵ x = 3(6)

∴ x = 18

They must sell 18 small pizzas, 12 medium pizzas and 6 large pizzas

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Answer:

25

Step-by-step explanation:

0.25/0.01

=25

Answer:

the answer will be 48

Step-by-step explanation:

The answer 48 because 12 times 3 is 36 and then you add Jose's score and you get 48

Answer:

Formula - y=mx+b

You have $100  and you're increasing it by $20 each month.

m=slope, b= initial value.

Thus, y=20x+100, is your linear equation.

Hope This Helps! :D

Answer:

.

Step-by-step explanation:

Answer:

117/78

Step-by-step explanation:

(-50-67)/(-12-56)=-117/-78=117/78

Answer:

x will be number of pounds

.5x is less than or equal to 6.50

She can afford 13 pounds of potatoes

You would solve the inequality by dividing each side by .5 to isolate x then write it as x is less than or equal to 13.

Part A:

You are given the amount of money Madison can spend and the price per pound for the potatoes. To find how many pounds Madison can buy, you would need to divide the amount of money she has by the price per pound.

The equation would be Pounds of potatoes = 6.50 / 0.50

Part B:

The only step required to solve the equation from part A is division.

Dividing 6.50 by 0.50 = 13. This means Madison can buy 13 pounds of potatoes.

The slope of line perpendicular to given line is is 3/2 and y-intercept is: -1/2

Step-by-step explanation:

Given equation of line:

[tex]y = -\frac{2}{3}x+5[/tex]

The given equation of line is in slope-intercept form so the co-efficient of x will be the slope of the line

Let m_1 be the slope of given line

[tex]m_1 = -\frac{2}{3}[/tex]

As we know that the product of slopes of perpendicular lines is -1

Let m_2 be the slope of required line

So,

[tex]m_1.m_2= -1\\-\frac{2}{3} . m_2 = -1\\m_2 = -1 * -\frac{3}{2}\\m_2 =\frac{3}{2}[/tex]

The lope-intercept form is:

[tex]y =m_2x+b[/tex]

Putting the value of m2

[tex]y = \frac{3}{2}x+b[/tex]

To find the value of y-intercept, putting (5,7) in the equation

[tex]7 = \frac{3}{2}(5) + b\\7 = \frac{15}{2} + b\\7 - \frac{15}{2} = b\\b =\frac{14-15}{2}\\b = -\frac{1}{2}[/tex]

Putting the values of slope and y-intercept

[tex]y = \frac{3}{2}x - \frac{1}{2}[/tex]

Hence,

the slope is 3/2 and y-intercept is: -1/2

Keywords: Slope, y-intercept

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Answer:

Here is the complete question (in attachment).

The least price is for Water Spring brand and the greatest price is of Clear Mountain brand.

Step-by-step explanation:

To find the unit price we have to divide the full price with the whole of the quantity.

From least to greatest unit prices are arranged below.

In ascending order the number are.

[tex]0.416 < 0.423< 0.437< 0.457< 0.499[/tex]

So the least price is for Water Spring brand,and the greatest price is for Clear Mountain brand.

Carla bought one package each of Blue and Red pens. These are the only two packages that when combined bring the total number of pens to 49.

This problem revolves around simple arithmetic and logical reasoning. What we need to do is to figure out which combination of pen packages adds up to make 49 pens.

By looking at the numbers given, we can see that the only combination that adds up to 49 would be one package of Blue pens (25 pens) and one package of Red pens (24 pens). There is no other combination of two packages which would result in a total of 49.

Therefore, Carla would have bought one package of Blue pens and one package of Red pens to have a total of 49 pens.

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Answer:

154.34%

Step-by-step explanation:

We are asked to determine what percentage of 357 is 551.

Let us assume that x% of 357 is 551.

So, [tex]\frac{357 \times x}{100} = 551[/tex]

⇒ [tex]\frac{x}{100} = \frac{551}{357}[/tex]

⇒ [tex]x = \frac{551}{357} \times 100[/tex] ......... (1)

⇒ x = 154.34%

So, it is clear from the step (1) that when we take the basic ratio then multiply with 100, then we will get the percentage. (Answer)

Final answer:

To determine what percent 551 is of 357, divide 551 by 357, multiply by 100, and round to the nearest hundredth. The answer is 154.34%.

Explanation:

To find what percent 551 is of 357, we use the formula for calculating percentages: 'part over total, times one hundred, equals percent'. The 'part' in this case is 551, and the 'total' is 357.

The calculation is as follows:

Divide the part (551) by the total (357) which equals approximately 1.5434.

Multiply the result by 100 to find the percentage.

1.5434 × 100 = 154.34%

To round the final answer to the nearest hundredth, we look at the digit in the thousandths place. Since the third decimal place is 4, which is less than 5, we do not need to round up, so the rounded percentage is 154.34%.

Answer:

C) -19w-3

Step-by-step explanation:

(-14w-3)-5w

-14w-3-5w

-19w-3

Answer: Original price $184

Step-by-step explanation:

(X/2) - 6 = 86

X/2 = 86+6

X/2 = 92

X = 92*2

X = 184

keeping in mind that standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

[tex]\bf (\stackrel{x_1}{2}~,~\stackrel{y_1}{-4})~\hspace{10em} \stackrel{slope}{m}\implies \cfrac{3}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{\cfrac{3}{5}}(x-\stackrel{x_1}{2})\implies y+4=\cfrac{3}{5}x-\cfrac{6}{5}[/tex]

[tex]\bf \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{5}}{5(y+4)=5\left( \cfrac{3}{5}x-\cfrac{6}{5} \right)}\implies 5y+20=3x-6\implies 5y=3x-26 \\\\\\ -3x+5y=-26\implies 3x-5y=26[/tex]

The value of k is -6

Step-by-step explanation:

The general form of the quadratic equation is y = ax² + bx + c

∵ 2x² + 11x = -k

- Add k to both sides

∴ 2x² + 11x + k = 0

∵ The roots of the quadratic equations is the values of x when y = 0

∵ [tex]\frac{1}{2}[/tex] is a root of the equation

- Substitute x by [tex]\frac{1}{2}[/tex] in the equation above to find k

∵ 2( [tex]\frac{1}{2}[/tex] )² + 11( [tex]\frac{1}{2}[/tex] ) + k = 0

∴ 2( [tex]\frac{1}{4}[/tex] ) + [tex]\frac{11}{2}[/tex] + k = 0

∴ [tex]\frac{1}{2}[/tex] + [tex]\frac{11}{2}[/tex] + k = 0

- Add the like terms

∵ [tex]\frac{1}{2}[/tex] + [tex]\frac{11}{2}[/tex] = [tex]\frac{12}{2}[/tex] = 6

∴ 6 + k = 0

- Subtract 6 from both sides

∴ k = -6

The value of k is -6

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Final answer:

By substituting x = 1/2 into the equation [tex]2x^2 + 11x = -k[/tex] and simplifying, we find that k must equal -6 for 1/2 to be a root of the equation.

Explanation:

To find the value of k such that 1/2 is a root of the quadratic equation [tex]2x^2 + 11x = -k[/tex], we can substitute x = 1/2 into the equation and solve for k.

First, substitute x = 1/2:

[tex]2(1/2)^2 + 11(1/2) = -k[/tex]

Then, simplify the equation:

2(1/4) + 11/2 = -k

1/2 + 11/2 = -k

Now, combine the terms:

(1 + 11)/2 = -k

12/2 = -k

6 = -k

Finally, multiply both sides by -1 to find k:

k = -6

Answer:

[tex]9 {x}^{2} - 49[/tex]

Step-by-step explanation:

Do FOIL, first outside inside last

3x × 3x = 9x^2

3x × -7 = -21x

7 × 3x = 21x

7 × -7 = -49

[tex]9 {x}^{2} - 21x + 21x - 49 \: midde \: cancels \: each \: other \: out[/tex]

So it would just be 9x^2 - 49

(3x + 7)(3x - 7) =

= 9x² + 21x - 21x - 49

= 9x² - 49

For this case we have that by definition, the equation of the line in the slope-intersection form is given by:

[tex]y = mx + b[/tex]

Where:

m: It's the slope

b: It is the cut-off point with the y axis

According to the statement we have two points through which the line passes:

[tex](x_ {1}, y_ {1}): (- 3,4)\\(x_ {2}, y_ {2}) :( 1,0)[/tex]

We found the slope:

[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {0-4} {1 - (- 3)} = \frac {-4} { 1 + 3} = \frac {-4} {4} = - 1[/tex]

By definition, if two lines are perpendicular then the product of their slopes is -1.

Thus, a perpendicular line will have a slope: [tex]m_ {2} = \frac {-1} {- 1} = 1[/tex]

Thus, the equation will be of the form:

[tex]y = x + b[/tex]

We substitute the given point and find "b":

[tex]6 = -2 + b\\6 + 2 = b\\b = 8[/tex]

Finally, the equation is:

[tex]y = x + 8[/tex]

Answer:

[tex]y = x + 8[/tex]

Answer:

They are arranged greatest to least