A soup pot will hold 14 cups or water. How many quarts will the pot hold?

(Set up as a proportion and solve)

Answer: A=jack

Step-by-step explanation:

Answer:

Choice A (Jack)

Step-by-step explanation:

Hope this helps!

Answer:

(w + 11)(w + 7)

Step-by-step explanation:

Consider the factors of the constant term ( + 77) which sum to give the coefficient of the w- term ( + 18)

The factors are + 11 and + 7, since

11 × 7 = 77 and + 11 + 7 = + 18

w² + 18w + 77 = (w + 11)(w + 7)

Answer:

[tex]\large\boxed{w^2+18w+77=(w+11)(w+7)}[/tex]

Step-by-step explanation:

[tex]w^2+18w+77\\\\77=7\cdot11\\18=7+11\\\\w^2+18w+77=w^2+11w+7w+77=w(w+11)+7(w+11)\\\\=(w+11)(w+7)[/tex]

[tex]\text{Use:}\ (a+b)^2=a^2+2ab+b^2\\\\w^2+18w+77=0\qquad\text{subtract 77 from both sides}\\\\w^2+18w=-77\\\\w^2+2(w)(9)=-77\qquad\text{add}\ 9^2\ \text{to both sides}\\\\w^2+2(x)(9)+9^2=-77+9^2\\\\(w+9)^2=-77+81\\\\(w+9)^2=4\to w+9=\pm\sqrt4\\\\w+9=-2\ \vee\ w+9=2\qquad\text{subtract 9 from both sides}\\\\w=-11\ \vee\ w=-7\\\\(w-(-11))(w-(-7))=(w+11)(w+7)[/tex]

Answer:

Step-by-step explanation:

The slope-intercept form of an equation of a line:

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

m - slope

b - y-intercept

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

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

From the table we have :

x = 1 → y = 6

x = 2 → y = 9

x = 3 → y = 12

x = 4 → y = 15

Calculate the slope (choice any two pairs, and calculate the slope):

(1, 6), (2, 9)

[tex]m=\dfrac{9-6}{2-1}=\dfrac{3}{1}=3[/tex]

We have the equation:

[tex]y=3x+b[/tex]

Put the coordinates of the point (1, 6) to the equation, and solve it for b:

[tex]6=3(1)+b[/tex]

[tex]6=3+b[/tex]              subtract 3 from both sides

[tex]3=b\to b=3[/tex]

Finally:

[tex]y=3x+3[/tex]

Answer:

f(- 2) = 1

Step-by-step explanation:

Evaluate f(- 2) by substituting x = - 2 into f(x)

f(- 2) = - 2(- 2) - 3 = 4 - 3 = 1

Answer:

6(7 - 3y) + 6(y + 1) = 42 - 18y + 6y + 6 =

-12y + 48 = 12(4 - y)

The expression 6(7-3y)+6(y+1) simplifies to 48-12y by distributing the 6 and combining like terms.

To simplify the expression 6(7-3y)+6(y+1), we need to apply the distributive property and then combine like terms.

The simplified equivalent expression is 48 - 12y.

To check that the expression is reasonable, you can substitute values for y and see if the original and the simplified expressions yield the same result.

Thus, for the given equation, the result is obtained as: 48 - 12y.

Answer:

43 and 41

Step-by-step explanation:

2n-1+2n-3=84

4n-4=84

4n=88

n=22

2(22)-1 and 2(22)-3

44-1 and 44-3

43 and 41

write these numbers according to the directions (in least to greatest form) and you get the numbers 41 and 43.

.

Odd integers can be written in as 2n-1, 2n+1, 2n+3 and so on. Basically, by writing 2n, you guarantee an even integer and when you add an odd integer to an even integer, you get an odd integer. Try using 2n-1 and 2n+1 as your consecutive odd integers and you will get the same solution.

Answer:

19 bears, 38 boxes of candy.

Step-by-step explanation:

We can use a system of equations (b = # of bears, c = # of candy boxes):

b + c = 57, 8b + 6c = 380.

We can use substitution by isolating b in the first eq.: b = 57 - c, then substitution b with 57 - c in the second eq.: 8(57 - c) + 6c = 380.

Then, we solve: 456 - 8c + 6c = 380, 76 = 2c, c = 38 candy boxes.

Finally we plug in 38 for c in the first eq.: b + 38 = 57, b = 19 bears.

Parallel streets are roads that run alongside each other without intersecting. An example of this can be seen with 7th Avenue and 8th Avenue in New York City.

In the realm of Geography, the concept of parallel streets refers to streets that run concurrently to each other without ever intersecting. Imagine two streets in your town or city that never meet regardless of how far they stretch - they maintain the same distance apart. For example, in New York City, 7th Avenue and 8th Avenue run parallel to each other on the west side of Manhattan.

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Answer:

A 120

Step-by-step explanation:

3x^2 - 36 ÷ y - (5 + 16)

Let x = 7 and y =6

3(7)^2 - 36 ÷ 6 - (5 + 16)

PEMDAS

Parentheses first

3(7)^2 - 36 ÷ 6 - (21)

Exponents

3*49 - 36 ÷ 6 - (21)

Multiplication and division from left to right

147 - 6 -21

Addition and subtraction from left to right

120

Answer:

7/6

Step-by-step explanation:

The sequence is an AP the rule is common difference  it's called arithmetic progression.

Answer:

7 is the number of how many days are in a week. So 7 x 3 is 21. That is less than 24 days. 24 days is 3 weeks and 3 days.

Step-by-step explanation:

Well, there is 7 days in a week.

So, in 3 weeks, there are 3 times more days than 7 days.

Therefore, there are 21 days in three weeks, and 24 days are more than 21 days, or three weeks.

To simplify the expression 7√5-3√80, the second term is broken down and then subtracted from the first term, resulting in the final simplified answer of √5.

To simplify the expression 7√5-3√80, we should first break down the second term, 3√80, into simpler terms.

The second term can be rewritten as 3√(4*20), since 4*20 = 80. Then this can be further broken down into 3√(4*4*5) which equals 3*2√5. In other words, 3√80 equals 6√5.

So, the original expression, 7√5-3√80, can now be rewritten as 7√5 - 6√5.

Since these two terms share the same radical, √5, you can subtract them just like you would subtract regular numbers. So, 7√5 - 6√5 equals 1√5, which simplifies further to √5.

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To simplify the given expression, we simplify the square roots and combine like terms. The expression simplifies to -5√5.

To simplify the expression 7√5-3√80, we need to simplify the square roots.

The square root of 5 cannot be simplified further, but the square root of 80 can be simplified as the square root of 16 times the square root of 5.

Therefore, the expression becomes 7√5 - 3√16√5.

The square root of 16 is 4, so the expression simplifies to 7√5 - 3(4)√5. Continuing to simplify, we get 7√5 - 12√5.

Combining the like terms, we have (7-12)√5, which simplifies to -5√5.

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Area = r^2 x PI

to find r take the square root of the area:

r = √100 = 10

The circumference of a circle is the diameter times PI.

The diameter is 2 times r = 2 x 10 = 20

The circumference = 20PI m

The answer is C.

-3 because below is less and 3 less than zero is -3

6 because sea level would be zero and 6 above is 6

-5 cause your losing 5 pounds which means its 5 less so -5

4 because say you have zero dollars then you find 4 you now have positive 4

Answer:

The answer is 672.

Step-by-step explanation:

To solve this problem, first let's find the surface area of the rectangular prism. To do that, multiply each dimension with each (times 2 | just in case you don't understand [what I'm talking about is down below]).

8 x 8 x 2 = 128

8 x 11 x 2 = 176

8 x 11 x 2 = 176

Then, add of the products together to find the surface area of the rectangular prism.

176 + 176 + 128 = 480

Now, let's find the surface area of the square pyramid. Now, for this particular pyramid, let's deal with the triangles first, then the square. Like we did with the rectangular prism above, multiply each dimension with each other (but dividing the product by 2 | in case you don't understand [what i'm talking about is down below]).

8 x 8 = 64.

64 ÷ 2 = 32.

SInce there are 4 triangles, multiply the quotient by 4 to find the surface area of the total number of triangles (what i'm talking about is down below).

32 x 4 = 128.

Now, let's tackle the square. All you have to do is find the area of the square.

8 x 8 = 64.

To find the surface area of the total square pyramid, add both surface areas.

128 + 64 = 192.

Finally, add both surface areas of the two 3-D shapes to find the surface area of the composite figure.

192 + 480 = 672.

Therefore, 672 is the answer.

Answer:

Yes The triangles are similar by SAS Similarity Theorem

Step-by-step explanation:

we know that

Side-Angle-Side Similarity, states that If an angle of a triangle is congruent to an angle of another triangle and if the included sides of these angles are proportional, then the two triangles are similar

In this problem

Angle  L is congruent with Angle Z

so

Verify if the included sides are proportional

so

[tex]\frac{LJ}{ZY}=\frac{KL}{XZ}[/tex]

substitute the values

[tex]\frac{3}{1.5}=\frac{4}{2}[/tex]

[tex]2=2[/tex] -----> is true

therefore

The triangles are similar by SAS

Answer:

y = 3

Step-by-step explanation:

The side labeled 'y' is the 'adjacent side' of the 30° angle.  The hypotenuse of this right triangle is 2√3.

The trig function relating this 30° angle, the 2√3 hypotenuse and the adj. side labeled 'y' is the cosine:

                 adjacent side          y

cos 30° = ---------------------- = --------- , and the value of cos 30° is (√3)/2.

                        2√3                2√3

Solving for y, we get 2√3 (√3)/2, or y = 2(3)/2, or y = 3

Answer:

x + 2

Step-by-step explanation:

3x^3 - 12x

=3x(x^2 - 4)

= 3x(x + 2)(x - 2)

so (x+2), (x - 2) and 3x are the factors of 3x^3 - 12x

answer:

x + 2

Answer:

x + 2

Step-by-step explanation:

given

3x³ - 12x ← factor out 3x from each term

= 3x(x² - 4) ← x² - 4 is a difference of squares, hence

= 3x(x - 2)(x + 2) ← fully factorised

hence x + 2 is a factor of the polynomial

Answer:

[tex]\large\boxed{(1,\ 7)}[/tex]

Step-by-step explanation:

[tex]|a|=a\ \text{for}\ a\geq0\\\\|a|=-a\ \text{for}\ a<0\\\\\text{Examples}\\\\|3|=3,\ |1.6|=1.6\\|-3|=-(-3)=3,\ |-1.6|=1.6\\===================[/tex]

[tex]y>|x|+5\\\\\text{Put the values of x and y from the coordinates of the points and check inequality}\\\\(0,\ 5)\to x=0,\ y=5\\5>|0|+5=0+5=5\qquad\text{FALSE\ :(}\\\\(1,\ 7)\to x=1,\ y=7\\7>|1|+5=1+5=6\qquad\text{CORRECT\ :)}\\\\(7,\ 1)\to x=7,\ y=1\\1>|7|+5=7+5=12\qquad\text{FALSE :(}[/tex]

Answer:

53 divided by 12 is 4.4167

Step-by-step explanation:

The option (D) the range is 70 and the midrange is 35 is correct option (D) would be correct.

It is defined as the difference between the maximum value in the data set to the minimum value in the data set.

The range is a quick yet effective technique to understand the distribution of the numbers in the data collection. Furthermore, since it simply calls for a simple arithmetic operation, it is simple to calculate. The standard deviation, a different measure of spread, can also be estimated using the range.

Range = max value - min value

Range = 85 - 15

Range = 70

Mid range = 70/2 = 35

Thus, the option (D) the range is 70 and the midrange is 35 is correct option (D) would be correct.

Learn more about the range here:

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Without specific statements to evaluate, we can't determine which is true for the set of numbers given. These numbers could represent heights in inches, and more context is needed to provide an accurate answer.

The student may be asking which statement regarding the listed set of numbers is true. These numbers are 20, 15, 50, 85, 75, 60. Without knowing the specific statements, we cannot definitively say which one is true or false. However, we can examine the statistics provided for a different data set of students' heights and base our answer on typical statistical questions.

A true statement about this set could be related to trends, averages, medians, modes, ranges, or any other statistical measure. For example, if asked whether this set of numbers could represent a set of heights, the answer could be true, assuming these numbers are in inches since all fall within a plausible range of human heights.

More context or specific questions about the data set would be needed for a more precise answer. The reference information about the heights of students, percentile data, and uniform distributions provide examples of typical problems in a statistics class.

Answer:

[tex]\large\boxed{x-intercepts:-2\ and\ 4}[/tex]

Step-by-step explanation:

[tex]m(x)=\dfrac{x^2-2x-8}{x^2-x-2}\\\\\text{At the beginning we de}\text{fine the domain:}\\\\D:x^2-x-2\neq0\\\\x^2-2x+x-2\neq0\\x(x-2)+1(x-2)\neq0\\(x-2)(x+1)\neq0\iff x-2\neq0\ \wedge\ x+1\neq0\\\boxed{x\neq2\ \wedge\ x\neq-1}\\================================\\\text{The x-intercept is for}\ m(x)=0.\ \text{Therefore we have the equation:}\\\\\dfrac{x^2-2x-8}{x^2-x-2}=0\iff x^2-2x-8=0\\\\x^2+2x-4x-8=0\\x(x+2)-4(x+2)=0\\(x+2)(x-4)=0\iff x+2=0\ \vee\ x-4=0\\\\x=-2\in D\ \vee\ x=4\in D[/tex]

Answer:

28.35

Step-by-step explanation:

10 percent of 31.5 = 3.15

31.5

-3.15

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

28.35

Answer:

34.45 minute or 34 and 9/20 minutes

Step-by-step explanation:

10 percent of 31.5 is 3.15

And 31.5+3.15=34.45

We add because it is 10% longer.

Answer:

V = 490 cm^3

Step-by-step explanation:

V = l*w*h

V = 7*10*7

V = 490 cm^3

To find the volume of a rectangular prism, we use the formula

Volume = length × width × height.

Since the rectangular prism has a length of 10 cm, a width of 7 cm, and a height of 7 cm we can plug this information into the formula.

(10 cm) (7 cm) (7 cm)

10 × 7 = 70

70 × 7 = 490 cm³

Answer:

Step-by-step explanation:

The first thing to do is get a graph of the function if you can.

The graph helps you see the following.

Answer:

Increasing:  on the interval of x: (-∞, 0)

Decreasing: on the interval of x: (0, ∞)

Step-by-step explanation:

See attached photos, one is done using calculus, the other is done using the graph.  (I'm not sure which level of math you are in)

*For the graph, you can see that f(x) is always increasing from  (-∞, 0), and always decreasing from (0, ∞)

The new coordinations would be (6,8)

Answer:

(6, 8)

Step-by-step explanation:

The y- axis (the vertical axis) acts as a mirror point.  When reflecting over the y axis, the y value will stay the same.  Think about looking into a mirror on your wall, your height is the same on both sides of the vertical reflecting object

The x-value will change and be the other side of the y-axis.  It will be the same distance away from the y-axis that is was, but will have an opposite sign.

Here is was 6 units to the left of the y-axis (where x values are negative), now it is 6 units to the right of the y-axis (where x values are positive)

Answer:

∠MNO = 51°

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

Sum the 3 given angles and equate to 180, that is

3x + 15 + 2x + 25 + 5x + 10 = 180 ← simplify left side

10x + 50 = 180 ( subtract 50 from both sides )

10x = 130 ( divide both sides by 10 )

x = 13

∠MNO = 2x + 25 = (2 × 13) + 25 = 26 + 25 = 51°

Answer:

y=-x+2

Step-by-step explanation:

Take two points and solve for the slope using: (y2-y1)/(x2-x1)=m

Then take the slope and plug it into the slope-intercept equation, y=mx+b.

Finally, take a xy pair and plug it into your equation to solve for b.

Answer:

DC = 6

Step-by-step explanation:

Given in the question,

radius = 3x

tangents to the circle = 12 + 5x and 8 + 7x

If you draw line from A to D, two right angle triangle will be form ADC and ADB

having radius  = 3x

Since, both triangle share same hypotenuse AD

so,

3x² + (8 + 7x)² = 3x²  + (12 + 5x)²

3x² will be cancel out

(8 + 7x)² =  (12 + 5x)²

64 + 112x + 49x² = 144 + 120x + 25x²

rearranging like terms

49x²-25x² +112x - 120x + 64 -144 = 0

24x² - 8x - 80 = 0

(x- 2)(x + 5/3)

x = 2

x = -5/3 rejected as radius can't be negative

So,

length of radius = 3x = 6