9.
The surface area of the right square pyramid shown is 129.5 cm. The base is 4.5 cm. Determine the slant height, s, of this
pyramid, rounded to the nearest tenth

Youssef lives 15 blocks away from his work

Solution:

Given that Youssef can either way from his home to his workplace or ride his bicycle

Let "x" be number of blocks away from work Youssef works

Case 1: walking

He walks at a pace of 1 block per min

Therefore,

1 block = 1 minute

Thus to cross "x" blocks he takes "x" minutes

Case 2: Bicycle

He can travel 1 block in 20 sec on his bicycle

We know that,

To convert seconds to minute, divide the time value by 60

[tex]\rightarrow 20 seconds = \frac{20}{60} minutes = \frac{1}{3} minutes[/tex]

Thus he takes 1/3 minutes for 1 block

So to cross "x" blocks he will take [tex]\frac{x}{3}[/tex] minutes

Given that it takes youssef 10 min longer to walk to work than to ride his bike

This means difference between time taken to cross "x" blocks by walking and ride by bicycle is 10 minutes

[tex]\rightarrow x - \frac{x}{3} = 10\\\\\rightarrow \frac{3x - x}{3} = 10\\\\\rightarrow \frac{2x}{3} = 10\\\\\rightarrow x = \frac{30}{2}\\\\\rightarrow x = 15[/tex]

Thus he lives 15 blocks away from his work

Final answer:

Youssef lives 15 blocks away from his workplace, which is determined by solving the equation x = x/3 + 10 after converting his biking speed to 3 blocks per minute.

Explanation:

To solve for how many blocks away Youssef lives from his workplace, we'll set up an equation using the information given. First, let's convert Youssef's bicycling speed to blocks per minute. Since he can travel 1 block in 20 seconds, and there are 3 sets of 20 seconds in a minute, he travels at a speed of 3 blocks per minute on his bicycle.

Let's denote the number of blocks to Youssef's workplace as 'x'. According to the question, walking there takes Youssef 10 minutes longer than biking. If he walks at the pace of 1 block per minute, walking to work takes 'x' minutes. Biking, at 3 blocks per minute, would take 'x/3' minutes. The relationship between the walking time and biking time is therefore 'x = x/3 + 10'.

We can solve the equation by multiplying each term by 3 to get rid of the fraction: '3x = x + 30'. Solving for 'x' gives us '2x = 30', and thus 'x = 15'. Youssef lives 15 blocks away from his workplace.

Answer:

Therefore

m∠ DCB is 55°

Step-by-step explanation:

Given:

ABCD is a parallelogram. The diagram is not drawn to scale.

m∠CDA = 125°,

To FInd

m∠DCB  = ?

Solution:

ABCD is a parallelogram.

AD || BC .......{opposite sides of a parallelogram are parallel}

∴∠CDA+∠DCB = 180°{SUM of the interior angles between parallel are supplementary}

substituting the values we get

[tex]125+m\angle DCB=180\\\\m\angle DCB =180-125=55\\\\m\angle DCB =55\°[/tex]

Therefore

m∠ DCB is 55°

Answer: OPTION B.

Step-by-step explanation:

Below are shown some transformations for a function f(x):

1) If [tex]f(x)+k[/tex], the function is shifted up "k" units.

2) If [tex]f(x)-k[/tex], the function is shifted down "k" units.

In this case you have the following function, which you can call f(x):

[tex]y =f(x)= x^2 + 2[/tex]

Based on the transformations explained before, if this function is shifted down 4 units, you know that function obtained g(x) is:

[tex]g(x)= x^2 + 2-4\\\\g(x)= x^2 -2[/tex]

Therefore, the equation that will shift the graph of the function down 4 units, is:

[tex]y= x^2 -2[/tex]

Hey Kim! :)

Glad to see you on Brainly.

Look below and watch how we solve this problem.

Ask any questions if you need it! I'll respond when you need it!

[tex]Remove \\parentheses. \\7+30-2=7 * 3\\\\7 + 30 - 2 = 161\\37 - 2 = 161\\\\35 = 161\\ \\ No solution.[/tex]

Answer:

Step-by-step explanation:

Answer:

Explanation:

1. Cost of each liter of yellow paint:

Yellow paint is sold in 5 litre tins and ach tin costs £26, thus the cost of one liter is £26 / 5 liters = £5.2 per liter.

2. Cost of each liter of blue paint:

Blue paint is sold in 10 litre tins and each tin costs £48, thus the cost of one liter of blue paint is £48 / 10 liters = £4.8 per liter

3. Cost of each liter of green paint.

Green paint is made by mixing yellow paint and blue paint in the ratio 2:3

Thus, 5 liters of green paint will cost:

2 liters yellow paint: 2 liter × £5.2 / liter = £10.4

3 liters blue paint:     3 liter × £4.8 / liter = £14.4

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

5 liters green paint:   5 liter                        £24.8

Cost of one liter of gree paint: £24.8 / 5 liter = £4.96 / liter

4. Profit

Price of each liter of green paint: £66.96 / 10 liters = £6.696 / liter = £6.70 / liter

Profit per liter = price per liter - cost per liter = £6.70/liter - £4.96 / liter = £1.74 / liter

Percentage profit = profit per liter / cost per liter × 100

Percentage profit = (£1.74 / liter) / (£4.96/liter) × 100 =  35.08% = 35%

Answer:

Smaller t = 2

Larger t = 5

Step-by-step explanation:

Given:

The given function is.

[tex]f(t)=-(t-2)(t-5)[/tex]

Find the zeros of the function.

Solution:

[tex]f(t)=-(t-2)(t-5)[/tex]

Simplify the equation above equation.

[tex]f(t)=-(t^{2}-5t-2t+10)[/tex]

[tex]f(t)=-(t^{2}-7t+10)[/tex]

[tex]f(t)=-t^{2}+7t-10[/tex]

Now, we first find the root of the above equation.

Use quadratic formula with [tex]a=-1, b=7, c=-10[/tex].

[tex]t=\frac{-b\pm \sqrt{(b)^{2}-4ac}}{2a}[/tex]

Put a, b and c value in above equation.

[tex]t=\frac{-7\pm \sqrt{(7)^{2}-4(-1)(-10)}}{2(-1)}[/tex]

[tex]t=\frac{-7\pm \sqrt{49-4\times 10}}{-2}[/tex]

[tex]t=\frac{-7\pm \sqrt{49-40}}{-2}[/tex]

[tex]t=\frac{-7\pm \sqrt{9}}{-2}[/tex]

[tex]t=\frac{-7\pm 3}{-2}[/tex]

For positive sign

[tex]t=\frac{-7 + 3}{-2}[/tex]

[tex]t=\frac{-4}{-2}[/tex]

t = 2

For negative sign

[tex]t=\frac{-7 - 3}{-2}[/tex]

[tex]t=\frac{-10}{-2}[/tex]

t = 5

Put t = 2 in given function.

[tex]f(t)=-(2-2)(2-5)=0[/tex]

Put t = 5 in given function.

[tex]f(t)=-(5-2)(5-5)=0[/tex]

So, the zeros of the function is t = 2 or 5

Therefore, the smaller value of t = 2 and larger value of t = 5.

Answer:

1/6

Step-by-step explanation:

2/3 x 1/4 is 2/12, which simplified is 1/6.

Answer: Marteen will paint 1/6 of her room today.

Step-by-step explanation:

In order to solve this equation, all you have to do is multiply how much of her room Marteen wants to paint today (2/3) by how much of that amount she wants to paint before lunch (1/4). because she wants to paint 1/4 of 2/3 of her room before lunch, you have to multiply 2/3 and 1/4. SO...

Multiply: 1/4 x 2/3 = 2/12

Simplify: 2/12 = 1/6

Answer: 1/6

Hope this helps!

Answer:

Step-by-step explanation:

Since the sale price is always less than the original, we take the original and subtract from it the percent off to give us the sale price.  Putting that into equation form:

s = r - .10r

which says, in words, that the sale price is equal to the regular price minus 10% of the regular price.

Answer:

25

Step-by-step explanation:

(4 + 6*3) + 3

(4+18) +3

25

18 km

Step-by-step explanation:

The vector appears as shown in the attached illustration. This is tantamount to finding the ? side of the right-angled triangle. The formulae is;

a² + b² = c²

24² + x² = 30²

x² = 30² – 24²

= 900 - 576

x² = 324

x = 18

Learn More:

For more on vectors check out;

https://brainly.com/question/10435343

https://brainly.com/question/12006588

#LearnWithBrainly

Final answer:

By using the Pythagorean theorem on the right triangle formed by the paths of the two airplanes, it is determined that the eastbound airplane has traveled 18 kilometers.

Explanation:

The question involves a geometrical problem that can be solved using the Pythagorean theorem. We are given that two airplanes leave the same airport, one heading north and the other heading east. After a certain time, the northbound airplane has traveled 24 kilometers. We are asked to find out how far the eastbound airplane has traveled, given that the two airplanes are now 30 kilometers apart.

To solve this, we can consider the path of the two airplanes as two sides of a right triangle, with the distance between the two airplanes being the hypotenuse. Using the Pythagorean theorem which states that in a right triangle the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b), or a2 + b2 = c2, we have:

Let x be the distance traveled by the eastbound airplane.

242 + x2 = 302

x2 = 302 - 242

x2 = 900 - 576

x2 = 324

x = √324

x = 18 kilometers

The eastbound airplane has traveled 18 kilometers.

Answer:

1. The option of spinning the chamber to make it random again gives you a probability of surviving of 67% (1 - Probability of having a bullet in the chamber). The option of taking the gun as it is for a second attempt gives you a probability of surviving of 60% (1- Probability of having a bullet in the chamber after a first non-bullet attempt). Therefore, spinning the chamber to make it random again gives you a better chance of surviving.

2. The option of spinning the chamber to make it random again gives you a probability of surviving of 83% (1 - Probability of having a bullet in the chamber). The option of taking the gun as it is for a second attempt gives you a probability of surviving of 80% (1- Probability of having a bullet in the chamber after a first non-bullet attempt). Therefore, spinning the chamber to make it random again also gives you a better chance of surviving with only one bullet.

Step-by-step explanation:

1. Which option gives you a better chance of surviving?

Let's assume the gun has six chambers, so the probabilities are:

Number of bullets remaining/Number of chambers

For the first attempt, probabilities are = 2/6 or 33%

For the second attempt of shooting the gun, the probability of having a bullet in the chamber would be = 2/5 or 40%

On the other hand, if you spin the chamber to make it random again, the probability of having a bullet in the chamber would be = 2/6 or 33%

The option of spinning the chamber to make it random again gives you a probability of surviving of 67% (1 - Probability of having a bullet in the chamber). The option of taking the gun as it is for a second attempt gives you a probability of surviving of 60% (1- Probability of having a bullet in the chamber after a first non-bullet attempt). Therefore, spinning the chamber to make it random again gives you a better chance of surviving.

2. What would the answer be if there was only 1 bullet instead?​

Number of bullets remaining/Number of chambers

For the first attempt, probabilities are = 1/6 or 17%

For the second attempt of shooting the gun, the probability of having a bullet in the chamber would be = 1/5 or 20%

On the other hand, if you spin the chamber to make it random again, the probability of having a bullet in the chamber would be = 1/6 or 17%

The option of spinning the chamber to make it random again gives you a probability of surviving of 83% (1 - Probability of having a bullet in the chamber). The option of taking the gun as it is for a second attempt gives you a probability of surviving of 80% (1- Probability of having a bullet in the chamber after a first non-bullet attempt). Therefore, spinning the chamber to make it random again also gives you a better chance of surviving with only one bullet.

Answer:

Step-by-step explanation:True

Answer:8.65

Step-by-step explanation:

87.5% of 64 is 0.875 • 64 = 56

Hope this helps.

Final answer:

To find 87.5% of 64, convert 87.5% to a decimal (0.875) and multiply by 64 to get 56.

Explanation:

To calculate 87.5% of 64, convert the percentage to a decimal and multiply by the number. Here's how you do it:

Calculating this, we get:

0.875 × 64 = 56

Answer:

p=40

w=l-8

40=w+l

40=2(l-8)+2l

40=2l-16+2l

40=4l-16

56=4l

14=l

length=14

w=14-8=6

l=14

w=6

Main equation:

2L + 2w = 40

We know that

w = L - 8

Substitute in known value

2L + 2(L - 8) = 40

Solve

2L + 2L - 16 = 40

4L = 24

L = 6

Length = 6 inches

Width =  14 inches

Hope this helps :)

Answer:

c

Step-by-step explanation:

got it right on app fuller l filler

Answer:

6.855

Step-by-step explanation:

I don't know how to explain that, you can use a calculator.

Answer:

39.95 × 3 = $119.85

Estimated at $40 each

3 pairs total $120

Option B

7569 number of people are going to vote for the other candidate

Solution:

Given that candidate took a phone poll of 110 people

Of the 110 people polled, 87 said they would vote for the other person

There are 9570 people in the district

You can set up this problem like a proportion

Let "x" be the number of people who would vote for the other candidate

[tex]\frac{87}{110} = \frac{x}{9570}[/tex]

To solve proportions, you cross-multiply. This means you multiply the numerator by the other denominator, and the denominator by the other numerator

[tex]87 \times 9570 = 110 \times x[/tex]

832590 = 110x

x = 7569

Thus 7569 number of people are going to vote for the other candidate

Answer:

Your answer is B. 7569 people hopefully this helps!

Answer:

The number of adults tickets sold is 165

The number of students tickets sold is 35

Step-by-step explanation:

Given as :

The total people that concert venue hold = 200 people

The price of adults tickets = $50

The price of students tickets = 50% less than adults tickets

I.e The price of students tickets = $50 - 50% of $50

Or, The price of students tickets = $25

The total revenue earn = $9125

Let The number of adults tickets sold = A

The number of students tickets sold = S

Now, According to question

The total people that concert venue hold = 200

Or, A + S = 200        ...........1

The total revenue earn = The number of adults tickets sold × The price of adults tickets +  The number of students tickets sold × The price of students tickets

Or, A × $50 + S × $25 = $9125

Or, 50 A + 25 S = 9125           ..........2

Solving both equations

(50 A + 25 S) - 25 × (A +S) = 9125 - 25 × 200

Or, (50 A - 25 A) + (25 S - 25 S) = 9125 - 5000

Or, 25 A + 0 = 4125

∴ A = [tex]\dfrac{4125}{25}[/tex]

I.e A = 165

So, The number of adults tickets sold = A = 165

Put the vale of A in eq 1

I.e A + S = 200

So, S = 200 - A

∴ S = 200 - 165

I.e S = 35

So. The number of students tickets sold = S = 35

Hence The number of adults tickets sold is 165 and

The number of students tickets sold is 35   Answer

Answer: x = 3

Step-by-step explanation: To solve for x in this equation, we must first isolate the term containing x which in this problem is -3x. Since 2 is being added to -3x, we subtract 2 from both sides of the equation to isolate the -3x.

On the left, the +2 and -2 cancel out and on the right -7 - 2 is -9 so we have -3x = -9. Now we can finish things off by just dividing both sides of the equation by -3. On the left the -3's cancel and on the right, -9 divided by -3 simplifies to 3. So we have x = 3.

Answer:

Options A, B, and D are correct.

Step-by-step explanation:

The given function is p(x) = x³ - 6x² - x + 30

Given that p(5) = 0, p(3) = 0 and p(-2) = 0

Therefore, putting x = 5, or x = 3, or x = -2, the function p(x) vanishes to zero.

Therefore, those are the roots of the given function p(x).

Hence, we can conclude that (x - 5), (x - 3) and (x + 2) are the factors of the function p(x) = x³ - 6x² - x + 30.

So, options A, B, and D are correct. (Answer)

Answer:

y= -2x + 7

Step-by-step explanation:

Answer:

Step-by-step explanation:

185,000[tex]\\\sqrt{x}[/tex]

Answer:

Step-by-step explanation:

∛108c¹⁷ =  ∛2*2*3*3*3*3*c¹⁵ *c²

= 3c⁵∛4c²

Hint: c¹⁵ = (c⁵)³ = c⁵ * c⁵ *c⁵

Answer:

The expression consists of two factors, and each factor contains three terms.

Step-by-step explanation:

Factors are numbers that multiply. The two brackets are written stuck to each other without any symbol between them, which means they are multiplying.

(a+b+c) is the first factor.

(d+e+f) is the second factor

Terms are numbers that separated by addition or subtraction.

Inside the first bracket, the terms are "a", "b", and "c".

Inside the second bracket, the terms are "d"", "e", and "f".

Answer:

1) The slope for the given points (6,7) and (-10,4) is [tex]m=\frac{3}{16}[/tex]

2) The slope for the given points (17,4) and (13,20) is [tex]m=-4[/tex]

3) The slope for the given points (12,19) and (14,18) is [tex]m=-\frac{1}{2}[/tex]

4) The slope for the given points (-11,0) and (18,13) is [tex]m=\frac{13}{29}[/tex]

5) The slope for the given points (3,6) and (-8,20) is [tex]m=-\frac{14}{11}[/tex]

6) The slope for the given points (-16,-20) and (12,5)  is [tex]m=\frac{25}{28}[/tex]

7) The slope for the given points (13,20) and (14,-14)  is [tex]m=-34[/tex]

8) The slope for the given points (18,15) and (3,0) is [tex]m=1[/tex]

Step-by-step explanation:

To find the slope of the line through each pair of points:

1) Given points are (6,7) and (-10,4)

The slope formula is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Let [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] be the given points (6,7) and (-10,4) respectively

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

[tex]m=\frac{4-7}{-10-6}[/tex]

[tex]m=\frac{-3}{-16}[/tex]

[tex]m=\frac{3}{16}[/tex]

Therefore the slope for the given points (6,7) and (-10,4) is [tex]m=\frac{3}{16}[/tex]

2) Given points are (17,4) and (13,20)

The slope formula is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Let [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] be the given points (17,4) and (13,20) respectively

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

[tex]m=\frac{20-4}{13-17}[/tex]

[tex]m=\frac{16}{-4}[/tex]

[tex]m=-4[/tex]

Therefore the slope for the given points (17,4) and (13,20) is [tex]m=-4[/tex]

3) Given points are (12,19) and (14,18)

The slope formula is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Let [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] be the given points (12,19) and (14,18) respectively

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

[tex]m=\frac{18-19}{14-12}[/tex]

[tex]m=\frac{-1}{2}[/tex]

Therefore the slope for the given points (12,19) and (14,18) is [tex]m=-\frac{1}{2}[/tex]

4) Given points are (-11,0) and (18,13)

The slope formula is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Let [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] be the given points (-11,0) and (18,13) respectively

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

[tex]m=\frac{13-0}{18-(-11)}[/tex]

[tex]m=\frac{13}{29}[/tex]

Therefore the slope for the given points (-11,0) and (18,13) is [tex]m=\frac{13}{29}[/tex]

5) Given points are (3,6) and (-8,20)

The slope formula is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Let [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] be the given points (3,6) and (-8,20) respectively

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

[tex]m=\frac{20-6}{-8-3}[/tex]

[tex]m=\frac{14}{-11}[/tex]

[tex]m=-\frac{14}{11}[/tex]

Therefore the slope for the given points (3,6) and (-8,20) is [tex]m=-\frac{14}{11}[/tex]

6) Given points are (-16,-20) and (12,5)

The slope formula is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Let [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] be the given points (-16,-20) and (12,5) respectively

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

[tex]m=\frac{5-(-20)}{12-(-16)}[/tex]

[tex]m=\frac{5+20}{12+16}[/tex]

[tex]m=\frac{25}{28}[/tex]

Therefore the slope for the given points (-16,-20) and (12,5)  is [tex]m=frac{25}{28}[/tex]

7) Given points are (13,20) and (14,-14)

The slope formula is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Let [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] be the given points (13,20) and (14,-14) respectively

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

[tex]m=\frac{-14-20)}{14-13}[/tex]

[tex]m=\frac{-34}{1}[/tex]

[tex]m=-34[/tex]

Therefore the slope for the given points (13,20) and (14,-14)  is [tex]m=-34[/tex]

8) Given points are (18,15) and (3,0)

The slope formula is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Let [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] be the given points  (18,15) and (3,0) respectively

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

[tex]m=\frac{0-15}{3-18}[/tex]

[tex]m=\frac{-15}{-15}[/tex]

[tex]m=1[/tex]

Therefore the slope for the given points  (18,15) and (3,0) is [tex]m=1[/tex]

Answer: 2/3

Step-by-step explanation: We can rewrite the ratio 6 out of 9 as the fraction 6/9 by putting 6 in the position of the numerator and 9 in the position of the denominator.

Notice however, 6/9 is not in lowest terms so we need to divide the numerator and the denominator by the greatest common factor of 6 and 9 which is 3 to get the equivalent fraction 2/3.

Therefore, the ratio 6 out of 9 can be rewritten as the fraction 2/3.

Answer:

4 1/2

Step-by-step explanation:

Answer:

4 1/2

Step-by-step explanation:

He made the recipe 3 times. 1 1/2*3=4 1/2

Answer:

  -1 ± i√3

Step-by-step explanation:

You can rearrange the expression to vertex form:

  x^2 +2x +1 +3

  (x +1)^2 +3

You want to find the values of x that make this zero:

  (x +1)^2 +3 = 0 . . . . . . . set the expression equal to zero

  (x +1)^2 = -3 . . . . . . . . . subtract 3 to get the square alone

  x +1 = ±√(-3) = ±i√3 . . .take the square root

  x = -1 ±i√3 . . . . . . . . . . subtract 1

The zeros are the complex numbers -1+i√3 and -1-i√3.