Please help with this quiz question!
Using the parallelogram pictured, find the length of the shorter diagonal. Round your answer to the nearest inch.
A) 32.1 in
B) 31.0 in
C) 22.3 in
D) 21.0 in

Step-by-step explanation:

"Of" means multiplication, and percent means out of 100.

25/100 × 150 = 700/100 × n

75/2 = 7n

n = 75/14

n ≈ 5.357

The number n is equal to  [tex]\frac{75}{14}[/tex] .

Percentage is a ratio of output to total that can be expressed as a fraction of 100.

We have,

According to the question,

25% of 150 = 700 % of n,

Here,

n = number

Now,

Solving,

25% of 150 = 700 % of n

i.e.

[tex]\frac{25}{100} *150=\frac{700}{100} n[/tex]

On solving we get,

[tex]\frac{75}{2} =7n[/tex]

⇒

[tex]n=\frac{75}{14}[/tex]

So, the value of n is  [tex]\frac{75}{14}[/tex],

Hence, we can say that the number n is equal to  [tex]\frac{75}{14}[/tex] .

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Answer:

4. 120

5. 13

6. 70

7. 115

8. 28

9. I'm not sure for this one

10. 22

11. 45

Step-by-step explanation:

If you need me to explain how I got any of these just ask :)

The answer is 1 and 3/4

Final answer:

Yasmine needs 1 1/4 cups of water to make 3 3/4 servings of spaghetti sauce.

Explanation:

Yasmine uses 1/3 cup of water for 1 serving of spaghetti sauce. She plans to make 3 3/4 servings of the sauce. To find out the total amount of water she will need, we first convert 3 3/4 servings to an improper fraction which is 15/4 servings. We then multiply this by the amount of water needed for one serving (1/3 cup).

Here's the calculation:

(15/4) servings × (1/3) cup/serving = (15/4) × (1/3) = 15/12 cups

Simplify 15/12 cups to get 5/4 cups or 1 1/4 cups.

Therefore, Yasmine needs 1 1/4 cups of water for 3 3/4 servings of spaghetti sauce.

Answer:

A

Step-by-step explanation:

The equation of a parabola is y = ax² + bx + c : a ≠ 0

Given

y = 2 (x + 4)² - 7 ← expand the squared factor

y = 2(x² + 8x + 16) - 7 ← distribute the parenthesis by 2

y = 2x² + 16x + 32 - 7 ← collect constant terms

y = 2x² + 16x + 25 → A

ANSWER

x=27

EXPLANATION

The two triangles are similar so the corresponding sides are equal.

[tex] \frac{x}{x +1 8} = \frac{39}{39 + 26} [/tex]

[tex]\frac{x}{x +1 8} = \frac{39}{65} [/tex]

Cross multiply to get;

[tex]65x = 39(x + 18)[/tex]

Expand:

65x=39x+702

Group similar terms:

65x-39x=702

Simplify

26x=102

Divide both sides by 26,

x=702/26

x=27

Answer:

Step-by-step explanation:

We need to find the graph of the following function:

Y - 4 = 4/3(x-2)

Solving for Y we have:

Y = 4/3(x-2) + 4

The graph is similar to the graph of f(x) = 1/x. But, with the following differences:

1. The graph is translated vertically upwards by 4 units.

2. The graph is translated horizontally to the right 2 units.

3. The graph is enlarged by a factor of 4/3.

Then, considering all these facts. The graph of f(x) = 1/x and the new graph according to all the characteristics stated before are attached.

The correct function to represent the transformation of the parent function f(x) = 5x, after being vertically compressed by a factor of one-fourth, shifted to the right three units, and up two units, is g(x) = 1.25(x - 3) + 2.

To find the transformed function of the parent function f(x) = 5x after a series of transformations, we must apply the following transformations step by step:

Vertically compress by a factor of one-fourth, which means we multiply the output by 1/4 or 0.25. Therefore, f(x) becomes f(x) = (1/4) * 5x = 1.25x.

Shift to the right three units, which means we replace x with (x - 3). Therefore, our function becomes f(x - 3) = 1.25(x - 3).

Shift up two units, which means we add 2 to the function's output. Our function now becomes f(x - 3) + 2 = 1.25(x - 3) + 2.

Putting it all together, the function that represents the transformation is g(x) = 1.25(x - 3) + 2.

Answer:

[tex]\large\boxed{x>\dfrac{1}{2}}[/tex]

Step-by-step explanation:

[tex]3(2x-1)>4x-2\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\(3)(2x)+(3)(-1)>4x-2\\\\6x-3>4x-2\qquad\text{subtract 4x from both sides}\\\\2x-3>-2\qquad\text{add 3 to both sides}\\\\2x>1\qquad\text{divide both sides by 2}\\\\x>\dfrac{1}{2}[/tex]

• P is the principal amount, $3000.00.

• r is the interest rate, 6% per year, or in decimal form, 6/100=0.06.

• t is the time involved, 8 years time periods.

• So, t is 8 year time periods.

To find the simple interest, we multiply 3000 × 0.06 × 8 to get that:

The interest is: $1440.00

Answer:6

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

Answer:

2, but it can be 4 if the perpendicular line goes through the other line.

Step-by-step explanation:

Answer:

14 1/8 inches of molding

Step-by-step explanation:

In order to find the solution, we'll have to do 2 fractions subtractions.

To be able to subtract fractions, we have to make sure they are placed in the same denominator.  So, the first thing we'll do is to convert all the numbers in 8th, because that's the greatest denominator.

[tex]48 \frac{1}{2}  = 48 \frac{4}{8} = \frac{(48 * 8) + 4}{8}  = \frac{388}{8}[/tex]

[tex]10 \frac{1}{4} = 10 \frac{2}{8} = \frac{(10 * 8) + 2}{8} = \frac{82}{8}[/tex]

For the last one, we'll first convert the 2 feet into 24 inches.

[tex]24 \frac{1}{8} = \frac{(24 * 8) + 1}{8} = \frac{193}{8}[/tex]

Now, we'll subtract each of the two pieces cut from the original molding's length, first the 10 1/4 inches piece

[tex]\frac{388}{8} - \frac{82}{8} = \frac{388 - 82}{8} = \frac{306}{8}[/tex]

then the 2 feet 1/8 piece

[tex]\frac{306}{8} -  \frac{193}{8} = \frac{306 - 193}{8} = \frac{113}{8} = 14 \frac{1}{8}[/tex]

So,  the contractor is left with 14 1/8 inches of molding.

Answer:

8

Step-by-step explanation:

When you divide by a fraction, you can also say that you are multiplying by the reciprocal.

So [tex]6/\frac{3}{4}=6*\frac{4}{3}[/tex]

[tex]6=\frac{6}{1}[/tex]

[tex]\frac{6}{1}*\frac{4}{3}=\frac{24}{3}=8[/tex]

ANSWER

A.

[tex]P(x)=6x^2 +75x +200[/tex]

EXPLANATION

The given revenue function is:

[tex]R(x)=6x^2 +100x+300[/tex]

The cost function is

[tex]C(x)=25x+100[/tex]

The profit function can be obtained by subtracting the cost function from the revenue function.

[tex]P(x)=R(x)-C(x)[/tex]

This implies that:

[tex]P(x)=6x^2 +100x+300 - (25x + 100)[/tex]

Expand the parenthesis to get:

[tex]P(x)=6x^2 +100x+300 - 25x - 100[/tex]

Group similar terms:

[tex]P(x)=6x^2 +100x - 25x - 100+300[/tex]

Combine the similar terms to get:

[tex]P(x)=6x^2 +75x +200[/tex]

The cot answer is A

Answer:

To quickly solve this problem, we can use a graphing tool or a calculator to plot the equation.

Please see the attached images below, to find more information about the graph

The equation is:

f(x) = x^4 – 2x^3 + 5x^2 – 7x + 9

The equation has only complex roots.

Answer:

+1,+3,+9

Step-by-step explanation:

Factors of the constant term

Answer:

2

Step-by-step explanation:

Because 1 ball + 1 Ball = 2 Ball

Answer:

I believe the answer is 129.3mm.

Hope this helps!

Length of the chain without beads = 377.58 m

The total length of the chain = 400 m

Note that:

1 inch = 0.0254 m

Forty 17 inches beads = 40  x  17

Forty 17 inches beads = 680 inches

Forty 17 inches beads = 680  x  0.0254

Forty 17 inches beads = 17.272 m

Twenty-seven 6 1/2 'll beads = 27 x 6.5 x 0.0254

Twenty-seven 6 1/2 'll beads = 4.4577 m

Eight 3.4 inches beads on the chain = 8 x 3.4 x 0.0254

Eight 3.4 inches beads on the chain = 0.69088 m

Total length of the chain with beads = 17.272 m + 4.4577 m + 0.69088 m

Total length of the chain with beads =22.42 m

Length of the chain without beads = 400 m - 22.42 m

Length of the chain without beads = 377.58 m

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Answer:

The area of the park is [tex]108\ m^{2}[/tex]

Step-by-step explanation:

we know that

The scale drawing is [tex]\frac{5}{3}\frac{cm}{m}[/tex]

step 1

Find the actual length of the rectangular park

Divide the length in the drawing by the scale drawing

[tex]20/(5/3)=12\ m[/tex]

step 2

Find the actual width of the rectangular park

Divide the width in the drawing by the scale drawing

[tex]15/(5/3)=9\ m[/tex]

step 3

Find the area of the park

[tex]A=(12)(9)=108\ m^{2}[/tex]

Answer:

16

Step-by-step explanation:

3/1 divided by 3/4 = 3/1 times 4/3. Multiply across to get 12/3 which = 4. It dripped for 4 hours.

Answer:

hold up i know it

Step-by-step explanation:

50, because 4÷5=.80 or 80%.

So 40÷50=.80 or 80%

Answer:

8568

Step-by-step explanation:

You have to choose 5 out of 18, and the order does not matter. So you're looking for the number of combinations, not permutations.

So you have to find 18C5.

nCr = n!/(n-r)!r!

so 18C5 = 18!/13!5!

              = (18 * 17 * 16 * 15 * 14 * 13!)/ 13!5!

              = 18*17*16*15*14/5*4*3*2*1

              = 8568

Hope it helps :)

The total number of ways to select a committee of 5 people from a group of 18 is 8568.

The question is asking for the total number of ways to select 5 people from 18. This is a commonly encountered problem in combinatorics, a mathematic field that deals with countable structures. To solve this, we use the combination formula, usually denoted as nCr where n is total items and r is number of items to choose. In this case, we use the combination formula C(18,5) where 18 is the total number of people and 5 is the committee size.

The formula for combination (nCr) is:

n! / (r!(n - r)!)

where '!' signifies a factorial which is the product of an integer and all the integers below it.

Inserting the numbers into the formula gives us:

18! / (5!(18 - 5)!) = 8568

So, there are 8568 different ways to choose a committee of 5 people from a group of 18.

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[tex]\bf ((5^{-2})(9^5))^{-6}\implies ((5^{-2\cdot -6})(9^{5\cdot -6}))\implies 5^{\stackrel{\stackrel{n}{\downarrow }}{12}}\times 9^{\stackrel{\stackrel{m}{\downarrow }}{-30}}[/tex]

Answer:

Drawing a picture  = 1 and 2

Making a Table  = 5 and 8

Working Backwards  = 3 and 4

Looking for a Pattern =6 and 7

Step-by-step explanation:

Answer:

its 18

Step-by-step explanation:

b/c 6 times 3 is 18

It’s 2 because 6 divided by 3 is 2

Answer:

(1, - 4 )

Step-by-step explanation:

To find the y- coordinate, substitute x = 1 into the equation

y = (3 × 1) - 7 = 3 - 7 = - 4

The missing value is -4.

Since you already know that x = 1, substitute that into the equation and simplify. y = 3(1) - 7

Anything times 1 equals itself. y = 3 - 7

Subtract. y = -4

Answer:

C. [tex]f(x) = (x-2.5)^{2}-3.25[/tex]

Step-by-step explanation:

The vertex form for a quadratic function is:

[tex]f(x) = a(x-h)^2+k[/tex]

[tex]f(x) = a(x^2-2hx +h^2) + k[/tex]

[tex]f(x) = ax^2-2ahx +ah^2 + k[/tex]

[tex]f(x) = ax^2+bx+c, Second\ form[/tex]

[tex]ax^2+2ahx +ah^2 + k = ax^2+bx+c[/tex]

[tex]-2ah = b[/tex]

[tex]h = -\frac{b}{2a}[/tex]

from the quadratic function given you know that a = 1 , b = -5 and c = 3, thus:

[tex]h = -\frac{(-5)}{2(1)}=2.5[/tex]

[tex]ah^2+k = c[/tex]

[tex]Isolate\ k =>\ k = c-ah^2[/tex]

You know c,a and h, so replace the values:

[tex]k = 3-(1)(2.5)^2 \\ k = 3-6.25\\ k = -3.25\\[/tex]

• Finally replace the values for a, h and k in the vertex form:

[tex]f(x) = a(x-h)^2+k\\ f(x) = (1)(x-2.5)^2+(-3.25)\\ f(x) = (x-2.5)^2-3.25[/tex]

So answer is C. [tex]f(x) = (x-2.5)^2-3.25[/tex]

The markup would be $1.81 I hope this helps! : )

Answer:

120 divided by 1/6= 720

Step-by-step explanation:

120 divided by 1/6

When we divide by a fraction , we change the division to multiplication .

To divide 120 by a fraction 1/6.

We take reciprocal of 1/6 and multiply with 120

Reciprocal of 1/6 is 6/1

[tex]\frac{120}{\frac{1}{6} } = 120 * \frac{6}{1} = 720[/tex]

120 divided by 1/6 equals 720, which is found by multiplying 120 by the reciprocal of 1/6.

To find what 120 divided by 1/6 is, you use the principle of division of fractions.

In this case, you multiply 120 by the reciprocal of 1/6. The reciprocal of 1/6 is 6/1, or simply 6.

Therefore, the calculation you need to perform is:

120 × 6 = 720

This means that 120 divided by 1/6 equals 720.

Your answer is A.

y = -1/2x + 9

Answer:

Option A is correct.

Step-by-step explanation:

Given Two points on line are ( 2 , 8 )  &  ( 8 , 5 )

We have to find A line of best fit for the graph using these two points.

We find the equation of line using two point form,

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

So,

[tex]y-8=\frac{5-8}{8-2}(x-2)[/tex]

[tex]y-8=\frac{-3}{6}(x-2)[/tex]

[tex]y-8=\frac{-1}{2}(x-2)[/tex]

[tex]y-8=\frac{-1}{2}x-\frac{-1}{2}\times2[/tex]

[tex]y-8=\frac{-1}{2}x+1[/tex]

[tex]y=\frac{-1}{2}x+1+8[/tex]

[tex]y=\frac{-1}{2}x+9[/tex]

Therefore, Option A is correct.