Simplify the expression with distributive property: 8 ( x + 3 )

Answer: The answer is 5 and 3/5 hours

Step-by-step explanation:

Answer:

5 and 3/5 hours

Step-by-step explanation:

Answer:

Number of movies that can be shown = 2

Step-by-step explanation:

Given:

Movie night duration = 4 hours

Duration of each movie = 1.75 hours

Time given for eating popcorn = 0.5 hours

Time alloted for movies (excluding popcorn time) = 4 - 0.5 = 3.5 hours.

Number of movies that can be shown = [tex]\frac{Total\ time\ alloted\ for\ movie}{Time\ for\ 1\ movie}=\frac{3.5}{1.75}= 2[/tex]

To determine the number of movies that can be watched, an equation M*X <= T can be formulated where M is the length of the movie, X is the number of movies, and T is the total time available. To find X, divide T by M. This works when the time for each movie is the same.

Without the actual graphic novel frame, it's hard to provide a specific equation. However, I can give you an example on how to approach this situation. Let's assume each movie is of length 'M' minutes and you have a total of 'T' minutes available for watching movies.

,

Let 'X' be the number of movies you can watch. You would write this as a mathematical equation like this: M*X <= T. This equation states that the total time spent watching movies should be less than or equal to the total time available.

,

To solve the equation, you would divide both sides of the equation by 'M'. The result will be X <= T/M. If you know the values of 'M' and 'T', you can plug them in here to get the maximum number of movies you can watch.

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Answer:

To answer X and Y, all you need is a little common sense and a little bit of algebraic thinking. -x can equal: -x = 0? -6?, etc. Y could equal: 3?, 6?, 12?, etc. But the answer will always no matter what number will be 6.

The x-coordinate of the point that divides the  directed line segment from K to J into a ratio of 1:3 is 7

Step-by-step explanation:

The formula for x-cooridnate of a point that divides a line in ratio m:n is given by:

[tex]x = \frac{nx_1+mx_2}{m+n}[/tex]

Given

K(9,2) = (x1,y1)

J(1,-10) = (x2,y2)

m = 1

n = 3

Putting the values in the formula

[tex]x = \frac{(3)(9)+(1)(1)}{1+3}\\x = \frac{27+1}{4}\\x = \frac{28}{4}\\x = 7[/tex]

Hence,

The x-coordinate of the point that divides the  directed line segment from K to J into a ratio of 1:3 is 7

Keywords: Ratio, fraction

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By dividing 452 pictures of dogs by 4, we find that each of the 4 equal groups has 113 pictures. The division process involves using place value and the standard algorithm for long division.

To find out how many pictures of dogs are in each group, we need to divide the total number of pictures by the number of groups. The question states there are 452 pictures of dogs and these are divided into 4 equal groups. We can use long division to solve this.

Step-by-Step Solution:

Write down the division: 452 ÷ 4.

Start by looking at the hundreds place in 452. There are 4 hundreds in 452. Since 4 divided by 4 is 1, we put 1 in the hundreds place of the quotient.

Multiply the divisor (4) by the quotient (100) to get 400.

Subtract 400 from 452 to get 52.

Now, look at the tens place in 52. There are 5 tens in 52, and since 5 divided by 4 is 1 with a remainder, we put 1 in the tens place of the quotient and have a remainder of 12 after subtracting 40 (1 x 4 tens) from 52.

Next, look at the ones place in 12. There are 12 ones, and since 12 divided by 4 is 3, we put 3 in the ones place of the quotient.

After placing 3 in the ones place, we have no remainder, which means the division is complete and the quotient is 113.

Therefore, each group has 113 pictures of dogs.

Answer:

C = 6.75n + 50

Step-by-step explanation:

The equation for the cost of renting the party room can be written in the form;

C= mn+k ......i

Where C = cost

n = number of people

Substituting the 2 cases into the equation we have,

Case 1

117.5 = 10m + k ......1

Case 2

151.25 = 15m + k .....2

Subtracting eqn 1 from 2 we have

151.25 - 117.50 = 15m - 10m

5m = 33.75

m = 33.75/5 = 6.75

Substituting m = 6.75 into eqn 1, we have

117.50 = 10(6.75) + k

k = 117.5 - 67.50

k = 50

Therefore, rewriting the eqn i, we have

C = 6.75n + 50

Answer:

Yes, △ABC ∼ △FED by AA postulate.

Step-by-step explanation:

Given:

Two triangles ABC and FED.

m∠A = m∠B

m∠C = m∠A + 30°

m∠E = m∠F = [tex]x[/tex]

m∠D = [tex]2x-20[/tex]°.

Now, let m∠A = m∠B = [tex]y[/tex]

So, m∠C = m∠A + 30° = [tex]y+30[/tex]

Now, sum of all interior angles of a triangle is 180°. Therefore,

m∠A + m∠B +  m∠C = 180

[tex]y+y+y+30=180\\3y=180-30\\3y=150\\y=\frac{150}{3}=50[/tex]

Therefore, m∠A = 50°, m∠B = 50° and m∠C =  m∠A + 30° = 50 + 30 = 80°.

Now, consider triangle FED,

m∠D+ m∠E + m∠F = 180

[tex]2x-20+x+x=180\\4x=180+20\\4x=200\\x=\frac{200}{4}=50[/tex]

Therefore,  m∠F = 50°  

m∠E = 50° and  

m∠D =  [tex]2x-20=2(50)-20=100-20=80\°[/tex]

So, both the triangles have congruent corresponding angle measures.

m∠A = m∠F = 50°

m∠B = m∠E = 50°

m∠C = m∠D = 80°

Therefore, the two triangles are similar by AA postulate.

Answer:

[tex]AB=\dfrac{38}{3}\ units[/tex]

Step-by-step explanation:

ABCD is a rhombus, then

[tex]AB=BC=CD=DA[/tex]

Since

[tex]BC=2x+8\\ \\CD=5x+1,[/tex]

then

[tex]BC=CD\Rightarrow 2x+8=5x+1[/tex]

Solve this equation:

[tex]2x-5x=1-8\\ \\-3x=-7\\ \\3x=7\\ \\x=\dfrac{7}{3}[/tex]

Then

[tex]BC=2\cdot \dfrac{7}{3}+8=\dfrac{14}{3}+8=\dfrac{14+8\cdot 3}{3}=\dfrac{14+24}{3}=\dfrac{38}{3}\ units[/tex]

Therefore,

[tex]AB=\dfrac{38}{3}\ units[/tex]

(2/3)²+5×2-4

(4/9)+5×2-4

(4/9)+10-4

10 4/9 - 4

6 4/9

answer: second choice

Answer:

Use distributive property, add 3z to both sides, divide by -8 on both sides

Step-by-step explanation:

You have to do parenthesis first, then equal both sides, then divide

Answer:

[tex](2x+5)(4x^{2} -10x+25)=0[/tex]

Step-by-step explanation:

Given:

The given equation is.

[tex]8x^{3} +125=0[/tex]

Find the some of cube.

Solution:

[tex]8x^{3} +125=0[/tex]

[tex]2^{3}x^{3} +5^{3}=0[/tex]

[tex](2x)^{3} +5^{3}=0[/tex]----------(1)

The sum of the cube formula is given below.

[tex](a^{3} +b^{3})=(a+b)(a^{2} -ab+b^{2} )[/tex]-----------(2)

By comparing equation 1 and equation 2

[tex]a=2x, b=5[/tex]

substitute a and b value in equation 2

[tex]((2x)^{3} +5^{3})=(2x+5)((2x)^{2} -(2x)(5)+5^{2})[/tex]

[tex]((2x)^{3} +5^{3})=(2x+5)(4x^{2} -(10x)+25)[/tex]

[tex]((2x)^{3} +5^{3})=(2x+5)(4x^{2} -10x+25)[/tex]

Therefore the sum of the cube [tex](2x+5)(4x^{2} -10x+25)=0[/tex]

Answer: 44

Step-by-step explanation:

we will find RN and NQ, then add together to give us RQ.

To find RN;

RP= 17 PN = 15 and RN =?

using pythagoras theorem,

adj^2 = hyp^2 - opp^2

RN^2 = RP^2 - PN^2

?^2 = 17^2 - 15^2

?^2 = 17^2 - 15^2

?^2 = 289 - 225

?^2 = 64

? = √64

? = 8

RN=8

To find NQ,

PN = 15 PQ=39 and NQ=?

using pythagoras theorem

NQ^2 = PQ^2 - PN^2

?^2 = 39^2 - 15^2

?^2 = 1521 - 225

?^2 = 1296

? = √1296

? = 36

NQ= 36

RQ = RN + NQ

RQ= 8 + 36

RQ=44

Answer: none

Step-by-step explanation: since -6x+3y can't equal to -7−6x+3y

Find base and height of the triangle to find area.

Base=Perimeter/3

Base=36/3=12 cm

Height²=12²-6²

Height²=108

Height=(6√3) cm

area=base×height

area=1/2×12×6√3=62 cm² approx.

answer: 3rd choice

Answer:

Find base and height of the triangle to find area.

Base=Perimeter/3

Base=36/3=12 cm

Height²=12²-6²

Height²=108

Height=(6√3) cm

area=base×height

area=1/2×12×6√3=62 cm² approx.

answer: 3rd choice

Step-by-step explanation:

Answer:9

Step-by-step explanation:4

1. The reciprocal of 5 plus the reciprocal of 7 is the reciprocal of what number?

The reciprocal of 5 plus the reciprocal of 7 is the reciprocal of [tex]\frac{12}{35}[/tex]

1. The reciprocal of 5 plus the reciprocal of 7 is the reciprocal of what number?

From given question,

[tex]\text{ reciprocal of 5} = \frac{1}{5}[/tex]

[tex]\text{ reciprocal of 7} = \frac{1}{7}[/tex]

Given that,

reciprocal of 5 + reciprocal of 7 = ?

[tex]\frac{1}{5} + \frac{1}{7} = x[/tex]

On cross-multiplying we get,

[tex]\frac{1}{5} + \frac{1}{7} = \frac{7+5}{5 \times 7} = \frac{12}{35}[/tex]

Thus reciprocal is [tex]\frac{35}{12}[/tex]

So the reciprocal of 5 plus the reciprocal of 7 is the reciprocal of [tex]\frac{12}{35}[/tex]

2. The reciprocal of the product of two consecutive integers is 1/72

The value of two consecutive numbers are 8 and 9

Let the two consecutive integers be x and x + 1

Given that reciprocal of product of two consecutive integers is [tex]\frac{1}{72}[/tex]

product of two consecutive integers = x(x + 1) = [tex]x^2 + x[/tex]

reciprocal of the product of two consecutive integers = [tex]\frac{1}{72}[/tex]

[tex]\frac{1}{x^2 + x} = \frac{1}{72}\\\\x^2 + x = 72\\\\x^2 + x - 72 = 0[/tex]

Solve the above quadratic equation by grouping method

[tex]x^2 + x - 72 = 0\\\\x^2 -8x + 9x - 72 = 0\\\\x^2 + 9x + (-8x - 72) = 0\\\\x(x + 9) -8(x + 9) = 0\\\\(x + 9)(x - 8) = 0[/tex]

Thus x = -9 or 8

Ignoring negative value,

x = 8

Thus two consecutive integers are x = 8 and x + 1 = 8 + 1 = 9

8 and 9 are two consecutive integers

Answer:

A = π/6 + kπ, or A = 2π/3 + kπ

Step-by-step explanation:

tan A / (1 − tan² A) = √3 / 2

Cross multiply and simplify:

√3 (1 − tan² A) = 2 tan A

√3 − √3 tan² A = 2 tan A

3 − 3 tan² A = 2√3 tan A

0 = 3 tan² A + 2√3 tan A − 3

Solve with quadratic formula:

tan A = [ -2√3 ± √((2√3)² − 4(3)(-3)) ] / 2(3)

tan A = [ -2√3 ± √(12 + 36) ] / 6

tan A = (-2√3 ± √48) / 6

tan A = (-2√3 ± 4√3) / 6

tan A = -√3 or √3/3

Solve for A:

A = 2π/3 + kπ, or A = π/6 + kπ

Answer:

the slope, m, is -6

Step-by-step explanation:

One of the most commonly used equations for a straight line is y = mx + b, where m is the slope and b is the y-intercept.

Comparing  y=4-6x to y = b + mx, we see that the slope, m, is -6 and the y-intercept, b, is 4.

The slope of the line y = 4 - 6x is -6, which shows that for every increase of 1 in the x-coordinate, the y-coordinate decreases by 6.

The equation is given as follows:

y = 4 - 6x

As we know that the equation is in slope-intercept form, y=mx+b.

Here, m is the slope and b is the y-intercept.

As per the question, the y-intercept is 4, which means the line crosses the y-axis at (0,4).

The slope, -6, tells us that for every increase of 1 in the x-coordinate, the y-coordinate decreases by 6.

Thus, the slope of the line y = 4 - 6x is -6.

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1. Set up a ratio:

7 tagged / 350 fish = 250 tagged / x fish

Solve for x:

x = (350 * 250) / 7

x = 12,500 fish

2. Divide number of boys by the population ratio:

450 / 2/5 =  (450 *5) /2 = 2250 / 2 = 1125 total students.

3.  4 quarters = $1, so they have 24 quarters total.

The ratio 3:5 means for every 3 quarters there are 5 dimes.

24 quarters / 3 = 8

8 x 5 = 40 dimes.

(1)  The population of fish in the False river is 12500.

(2) There are 1125  total number of students in the school .

(3) There are 40 dimes in the bag.

(1) Number of fish tagged by Louisiana biologists =  250

On the next day a sample was collected from the False river

The number of fish in the sample = 350

Number of tagged fish in the sample =  7

Let the population of fish in the False river  = P

Takin the ratio we can

[tex]\rm \dfrac{7}{350}= \dfrac{250}{P} \\\\P = (250)(350)/(7)\\P = 12500[/tex]

So the population of fish in the False river = 12500

(2) The number of boys in the school = 450

Let the total number of students in the  school be B

According to the given condition

[tex]\rm \dfrac{2}{5}\times B = 450\\\\B = (450\times 5) /2 \\B = 2250/2 =1125[/tex]

So the total number of students in the school = 1125

(3) Let the number of dimes in the bag be x

According to the given condition we can write

[tex]\rm \dfrac{Number\; of\; quarters }{Number\; of\; dimes } = \dfrac{3}{5} ........(1)[/tex]

Also  it is given that there are $6 in quarters in the bag.

$1 = 4 quarters

So $6 has  [tex]\rm 4\times 6 = 24 \; quarters[/tex]

So we can put this value in equation (1)

[tex]\dfrac{24}{x} =\dfrac{3}{5} \\\\x = 40 dimes[/tex]

So we can conclude that there are 40 dimes in the bag.

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Answer:

190.02

Step-by-step explanation:

Trust

The ending balance of the account after 8 years is approximately $184.16.

To find the ending balance of the account after 8 years, we can use the equation t=log1.03(E/150), where t is the time in years and E is the ending balance. Since the account was open for 8 years, we can substitute t=8 into the equation.

8=log1.03(E/150)

To solve for E, we can isolate it by first multiplying both sides of the equation by 150 and then raising both sides to the power of 1.03.

E/150=1.03⁸

E=150*1.03⁸

Using a calculator, we can find that E is approximately $184.16.

3.25 x 10^-6 written in decimal notation  is 0.00000325

Solution:

Decimal notation is simply a form of a number using a decimal point

Given number : [tex]3.25 \times 10^{-6}[/tex]

Steps to follow:

In order to convert a number written in scientific notation to one written in standard or decinal notation, follow these steps:

To convert to decimal notation:

Multiply the decimal number by 10 raised to the power indicated.

[tex]\rightarrow 3.25 \times 10^{-6}[/tex]

Here the exponent of 10 is -6

So the decimal point is moved 6 places to right

[tex]\rightarrow 3.25 \times 10^{-6} = 0.00000325[/tex]

Final answer:

To convert the scientific notation 3.25 x 10^-6 into decimal form, you move the decimal point six places to the left, resulting in 0.00000325.

Explanation:

To convert 3.25 x 10^-6 into decimal notation, you need to move the decimal point 6 places to the left because it is a negative exponent. Start with 3.25 and move the decimal:

The decimal notation of 3.25 x 10^-6 is 0.00000325.

Answer:

The equation of the required line is: 2x + y = 8

Step-by-step explanation:

When a point on the line and the slope of the line are given, we use the slope - one - point form to determine the equation of the line.

Say, [tex]$ (x_1, y_1) $[/tex] is the point passing through the line and the slope of the line is say, [tex]m[/tex]. Then the equation would be:

                      [tex]$ (y - y_1) = m(x - x_1) $[/tex]

Here [tex]$ (x_1, y_1) = (7, -6) $[/tex] and slope, [tex]$ m = - 2 $[/tex].

Therefore, the equation of the line becomes:

[tex]$ y - (-6) = -2(x - 7) $[/tex]

[tex]$ \implies y + 6 = -2x + 14 $[/tex]

Rearranging we get:

[tex]$ 2x + y - 8 = 0 $[/tex] which is the required equation of the line.

Answer: 2√3

Step-by-step explanation: To divide √60 by √5, we simply divide the numbers that are inside the radicals.

Since the quotient of 60 divided by 5 is 12,

the square root of 60 divided by the square root of 5 is √12.

However, we can simplify the square root of 12.

The √12 breaks down into 4 · 3 and 4 breaks down into 2 · 2.

The 2's match up, so a 2 comes outside of the radical.

Since the 3 doesn't pair up, it stays inside.

So our answer is 2√3.

Final answer:

The simplification of [tex]\sqrt{60}/\sqrt{5[/tex] results in [tex]2\sqrt{3,[/tex] by combining the square roots into one and then simplifying the inner value.

Explanation:

The question asks for the simplification of the expression which is the square root of 60 divided by the square root of 5. To simplify this expression, one can utilize the property of square roots that allows the division within a single square root function. Here’s a step-by-step explanation:

Write the expression as [tex]\sqrt{60}/\sqrt{5[/tex]

Combine the square roots using the property[tex]\sqrt{(a)}/\sqrt{(b)} = \sqrt{(a/b),[/tex] giving[tex]\sqrt{60}/\sqrt{5[/tex]

Simplify 60/5 to get 12.

Now take the square root of 12, which is not a perfect square. However, we can express 12 as the product of 4 (which is a perfect square) and 3 (4 * 3 = 12).

Finally, we write the expression  [tex]\sqrt{4} * \sqrt{3,[/tex] which simplifies to [tex]2\sqrt{3,[/tex]

Thus, the simplified form of [tex]\sqrt{60}/\sqrt{5[/tex] is [tex]2\sqrt{3,[/tex], which cannot be simplified any further as [tex]\sqrt{3[/tex] is an irrational number and does not have a precise decimal representation.

It is always important to remember that when rounding is necessary, you should round the result up if the digit following the last significant digit is 5 or greater, and round it down if it is less than 5.

Answer:

9

Step-by-step explanation:

9 times 5 =45

Answer:

9

Step-by-step explanation:

When you do the math, 9 multiplied by 5 will get you 45

Answer:

About $0.10 per ounce

Step-by-step explanation:

12 pound costs $18.75. Lets find the cost per pound first:

Cost Per Pound = [tex]\frac{18.75}{12}=1.5625[/tex]

We know, there are 16 ounces in 1 pound.

We know 1 pound costs 1.5625

To find cost per ounce, we have to divide this by 16.

So,

Cost Per Ounce = [tex]\frac{1.5625}{16}=0.097[/tex]

Rounded to nearest cent, that would be 10 cents per ounce

Answer:

12x+25

Step-by-step explanation:

7x+7+5x+15+3

12x+25

Answer:

48 inches

Step-by-step explanation:

Dagne can jump 13.2 inches that is 27.5% of her height. Let x inches be Dagne's height.

Then

x inches - 100%

13.2 inches - 27.5%

Write a proportion:

[tex]\dfrac{x}{13.2}=\dfrac{100}{27.5}[/tex]

Cross multiply:

[tex]27.5x=13.2\cdot 100\\ \\27.5x=1,320\\ \\x=\dfrac{1,320}{27.5}\\ \\x=48\ inches[/tex]

Answer:

(x - 2)(x + 2).

Step-by-step explanation:

This is the difference of 2 squares:

a^2 - b^2 = (a - b)(a + b)

So

x^2 - 4 = (x - 2)(x + 2).

Final answer:

To find the area of the clock face with a 4-meter radius, use the area formula for a circle, which gives approximately 50.265482 m². Rounded to the nearest square meter, the clock face area is about 50 m².

Explanation:

The clock face in a famous clock tower has a radius of 4 meters, and we want to find the area of the clock face to the nearest square meter. To do this, we use the formula for the area of a circle, which is A = πr², where A is the area and r is the radius of the circle.

Plugging in the radius of the clock face:

A = π(4 m)² = π(16 m²) ≈ 50.265482 m²

However, since we want the answer to the nearest square meter, we round this to:

A ≈ 50 m²

Final answer:

The area of the clock face with a radius of 4 meters is approximately 50 square meters when rounded to the nearest square meter.

Explanation:

The area of a clock face in a famous clock tower, given its radius is 4 meters, can be calculated using the formula for the area of a circle, which is [tex]A = πr^2[/tex] where A is the area and r is the radius of the circle. In this case, substituting the radius of 4 meters into the formula gives us[tex]A = π(4m)^2 = π16πm^2.[/tex] To give an answer to the nearest square meter, we use the value π = 3.14, resulting in [tex]A = 16(3.14)m^2 = 50.24m^2[/tex], which rounds to 50 m².

Answer:

square root of 72 is approximately 8.49

i hope that right!

Step-by-step explanation: