3. The length of a rectangle is 3 times its width. The perimeter is 16 meters. Draw a picture to represent
this situation. Write an equation to represent the situation and solve it. What is the width?
4. Suppose you live near a park that has a bike trail you like to ride. The Park Department rents a bike with
safety equipment for $5 a day. If you provide your own safety equipment, the bike rental is $3 a day. You
could buy the equipment at a sports store for $28. How many times must you use the trail to justify
buying your own safety equipment? Support your answer mathematically or graphically.

Answer:

5

Step-by-step explanation:

If e = 7, you would replace e in the expression e - 2 with 7 so that the expression becomes 7 - 2 which results in 5.

Does that help?

Answer:

$114.17

Step-by-step explanation:

First we need to convert cubic yard to cubic feet.

One yard is equivalent to three feet, so one cubic yard is 3^3 = 27 cubic feet.

So the cost of one cubic feet is 64/27 = $2.3704

We also need to convert from inches to feet.

One inch is 1/12 feet, so 2 inches is 2/12 = 1/6 feet

Now we need to find the volume of the slab:

Volume = 17 * 17 * (1/6) = 48.1667 ft3

Now, to find the cost, we can use a rule of three:

1 cubic feet -> $2.3704

48.1667 cubic feet -> X

X = 48.1667 * 2.3704 = $114.1743

In one year, the Perseid meteor shower had a meteor appear every 1 1/5 minutes on average. That same year, the Leonid meteor shower had a meteor appear every 4 2/3 minutes on average. How many more meteors fell during the Perseid meteor shower?

Answer:

325,452 meteors

Step-by-step explanation:

We all know that :

We have 365 days in a year and in each day there are 24 hours, Likewise an hour has 60 minutes

SO, the total number of minutes in a year is :

365 × 24 × 60 = 525600 minutes

For Perseid  meteor:

[tex]1 + \frac{1}{5} \\ \\ = 1 + 0.2 \\ \\ = 1.2[/tex]

So one meteor fall at 1.2 minutes interval Thus, in a year, we will have :

1 meteor - 1.2 minutes.

x meteor - 525600 minutes.

1.2x = 525600

[tex]x = \frac{525600}{1.2}[/tex]

x = 438000

∴  438,000 meteors fell during the Perseid shower.

For  Leonid meteor shower:

[tex]4 + \frac{2}{3} = 4.67[/tex]

So one meteor fall at 4.67 minutes interval Thus, in a year, we will have :

1 meteor - 4.67 minutes.

x meteors - 525600 minutes.

[tex]4.67x = 525600[/tex]

[tex]x = \frac{525600}{4.67}[/tex]

x = 112548

112,548 meteors fell during the Leonid Shower.

Finally , the numbers of more meteors that  fell during the Perseid meteor shower is calculated by the difference in the number of Perseid meteor shower and Lenoid meteor shower. i.e

438,000 - 112,548 = 325,452

325,452 more meteors fell during the Perseid meteor shower

Answer:

For Leonid meteor shower: So one meteor fall at 4.67 minutes interval Thus, in a year, we will have : 1 meteor - 4.67 minutes. x meteors - 525600 minutes

Step-by-step explanation:

Answer: The base is a circle and you can use the formula (pi)r^2 the find the area of the base

Step-by-step explanation:

a soup can is a cylinder and the base of a cylinder is a circle. you can google "area of a circle calculator" on google to show you the formula

Answer:

Sample response: The soup can has a circular base. The radius measure is needed. If the diameter is given, find the radius, which is half the diameter. Square the radius and multiply that answer by pi for the base area.

Step-by-step explanation:

I just did it on edge

To increase £258 by 43%, convert the percentage to a decimal, calculate the increased amount, and add it to the original amount. The increased amount to the original amount is £368.94

To increase £258 by 43% using the multiplier method:

Convert the percentage to a decimal: 43% = 0.43

Calculate the increased amount: £258 x 0.43 = £110.94

Add the increased amount to the original amount: £258 + £110.94 = £368.94

Answer:

416 x 5 = 2080

721 x 8 = 5768

5768 + 2080 = 7848. Have a great day.

Answer:

The center of data is a single number that summarizes the entire data set.

Step-by-step explanation:

Answer:

x > -2

Step-by-step explanation:

-4x < 8

-8 < 4x

-2 < x

x > -2

Answer:

see below

Step-by-step explanation:

V = l*w*h for the rectangular  tank

V = 70* 40*40

  =112000 cm^3 = 1mL

The water is 84000

Make this a fraction

84000/112000  = 3/4

The water fills 3/4 of the tank

1-3/4 = 1/4

It is 1/4 from the top

Find the volume of the treasure chest

V = 12*10*8 =960

Tower

V = pi r^2

  3.14 * 10^2 *10

  =3140

Water + chest + tower

84000+960+3140 =88100

This is less than 112000 so the water will not overflow

Answer:

a) 10 cm

b) Will not overflow

Step-by-step explanation:

8400 = base area × height

84000 = 70 × 40 × h

h = 30

From the top: 40 - 30 = 10cm

b) Capacity of the tank:

70 × 40 × 40

112,000 cm³

Combined volume of the two vessels:

(12 × 10 × 8) + (3.14 × 10² × 10)

960 + 3140

4,100 cm³

4100 = 70 × 40 × rise

rise = 1.464285715 cm

Since 1.464285715 < 10

It will not overflow

Answer:

[tex]\dfrac{1}{3}[/tex]

Step-by-step explanation:

Given,

Total number of trial = 12

Total number of favorable event  = 4

Experimental probability of hitting home run is

[tex]P(home\ run)=\dfrac{Favorable\ event}{Total\ trial}[/tex]

[tex]P(home\ run)=\dfrac{4}{12}[/tex]

[tex]P(home\ run)=\dfrac{1}{3}[/tex]

Answer:1/3

Step-by-step explanation:Answer:

Step-by-step explanation:

Given,

Total number of trial = 12

Total number of favorable event  = 4

Experimental probability of hitting home run is

Answer:

21

Step-by-step explanation:

(9g+4)-55=

(72+4)-55=

76-55=

21

Final answer:

To find the answer, first multiply 9 by 8, then add 4, resulting in 76. Finally, subtract 55 to get the answer, which is 21.

Explanation:

To solve the problem, we need to first calculate the sum of 9g and 4 when g=8. This will be 9 × 8 + 4.

After calculating the sum, we will subtract 55 from this amount to get the final answer.

Following the steps:

Therefore, when g = 8, subtracting 55 from the sum of 9g and 4 results in  21.

Answer:

Arc KL = 30°

Arc JK = 90°

Step-by-step explanation:

Arc KL is a connected to a central angle with the measurement of 30°. Because it is a central angle, the arc's measurement will be the same as the central angle's measurement:

Arc KL = 30°

Arc JK is connected to a central angle that has a right angle measurement sign. A right angle = 90°. Because it is a central angle, the arc's measurement will be the same as the central angle's measurement:

Arc JK = 90°

~

Answer:

arc kl= 30

arc jk=90

Step-by-step explanation:

Answer:

30 ,345,986

Step-by-step explanation:

We have been given a sphere with radius 8.6 ft. We are asked to find the surface area of the given sphere.

We know that surface area of a sphere is equal to [tex]4\pi r^2[/tex].

[tex]A=4\pi r^2[/tex]

Upon substituting [tex]r=8.6\text{ ft}[/tex] in surface area formula, we will get:

[tex]A=4\pi (8.6\text{ ft})^2[/tex]

[tex]A=4\pi \cdot 73.96\text{ ft}^2[/tex]

[tex]A=295.84\pi\text{ ft}^2[/tex]

[tex]A=929.4087706\text{ ft}^2[/tex]

Upon rounding to nearest hundredth, we will get:

[tex]A\approx 929.41\text{ ft}^2[/tex]

Therefore, the surface of the given sphere would be approximately [tex]929.41\text{ ft}^2[/tex].

Answer:

B. Opposite angles add up to 180 degrees.

Step-by-step explanation:

Answer Choice B is incorrect because opposite angles are actually congruent. However, adjacent angles of a parallelogram do add up to 180 degrees.

Answer:

20 pages

Step-by-step explanation:

Answer:

20 pages

Step-by-step explanation:

3/5 minute =36sec

if 36=12

.·.60= 60×12÷36=20

Answer:

x= [tex]2-\sqrt{3}[/tex]          and          x=[tex]2+\sqrt{3}[/tex]

Step-by-step explanation:

- transfer the -1 to the other side so that the equation reads as [tex]x^{2} -4x+1[/tex]

- factor! think about what numbers add -4 but also multiply to be 1

- you may then realize that there are no numbers with those characteristics

- since that is the case, we have to use the quadratic formula, which is:

               [tex]\frac{-b+\sqrt{b^{2}-4ac }}{y}[/tex]        and         [tex]\frac{-b-\sqrt{b^{2}-4ac }}{y}[/tex]

- the equation is shown as [tex]a^{2}+b^{2}=c^{2}[/tex]

- using the numbers that correspond with those lettered values, plug it in the quadratic formulas

the solutions to the equation [tex]\( x^2 - 4x = -1 \) are \( x = 2 + \sqrt{3} \) and \( x = 2 - \sqrt{3} \)[/tex].

To find the solutions to the equation [tex]\( x^2 - 4x = -1 \)[/tex], we can follow these steps:

1. Move all terms to one side of the equation to set it equal to zero:

 [tex]\[ x^2 - 4x + 1 = 0 \][/tex]

2. We can solve this quadratic equation using the quadratic formula:

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

  where [tex]\( a = 1 \), \( b = -4 \), and \( c = 1 \).[/tex]

3. Plug in the values and simplify:

  [tex]\[ x = \frac{-(-4) \pm \sqrt{(-4)^2 - 4(1)(1)}}{2(1)} \] \[ x = \frac{4 \pm \sqrt{16 - 4}}{2} \] \[ x = \frac{4 \pm \sqrt{12}}{2} \] \[ x = \frac{4 \pm 2\sqrt{3}}{2} \] \[ x = 2 \pm \sqrt{3} \][/tex]

So, the solutions to the equation [tex]\( x^2 - 4x = -1 \) are \( x = 2 + \sqrt{3} \) and \( x = 2 - \sqrt{3} \)[/tex].

Answer:

8

Step-by-step explanation:

3m + 9 -9m = 2m + 25

3m + 9 = 11m + 25

9 = 8m + 25

16/2 = 8m/2

M = 8

Answer:

im not sure

Step-by-step explanation:

so sorry i didnt know the answer.

Answer:

the perimeter of the rectangle is 23.75 feet.

Step-by-step explanation:

5 5/8 × 2 = 11 1/4.

6 1/4 × 2 = 12 1/2

11 1/4 + 12 1/2 = 23 3/4 or 23.75

Answer:

the sum of B and C is negative

A + D = B

The quotient of C and B is equivelent to -2/3

Step-by-step explanation:

The quotient of C and B is equivalent to -2/3. Therefore, the correct option is option D among all the given options.

A picture of numbers along a straight line is called a number line. It serves as a guide for contrasting and arranging numbers. Any real number, including all whole numbers and natural numbers, can be represented by it. Just to refresh your memory, a whole number is a collection of numbers that contains all counting numbers.

Comparing numbers is made simpler by writing them on a number line. As seen in the aforementioned graphic, the integers to the left are smaller compared to the integers for the right. As an illustration, the numbers 0 and 1 are less than each other, as are the numbers -1 and -2. The sum of B and C is negative.

Therefore, the correct option is option D.

To know more about number line, here:

https://brainly.com/question/16191404

#SPJ3

Answer:

[tex]y = 66.25(1.11)^x[/tex]

Step-by-step explanation:

Let's plug in 9 for x and 171 for y into the given exponential equation:

y = [tex]ab^x[/tex]

171 = [tex]ab^9[/tex]

Now do the same with (10, 190):

190 = [tex]ab^{10}[/tex]

Write them both in terms of a and set them equal:

a = 171/[tex]b^9[/tex]

a = 190/[tex]b^{10}[/tex]

171/[tex]b^9[/tex] = 190/[tex]b^{10}[/tex]

Multiply both sides by [tex]b^{10}[/tex]:

171b = 190

b = 190/171 = 10/9 ≈ 1.11

Plug this in to find a:

a = 171 / (10/9)^9 ≈ 66.25

So, the exponential model is:

[tex]y = 66.25(1.11)^x[/tex]

Answer:

y = 66.25[(10/9)^x]

Step-by-step explanation:

171 = a(b⁹)

b⁹ = 171/a

190 = a(b¹⁰)

190 = a(171/a) × b

b = 190/171

b = 10/9

(10/9)⁹ = 171/a

a = 66.24890362

Answer: 2713 cubic centimeter

Step-by-step explanation:

Answer:

339 cubic centimeters

Step-by-step explanation:

The formula for the volume of a sphere is [tex]\frac{4}{3}\pi r^3[/tex]. In this case, a ball with the radius of 3 centimeters would have a volume of [tex]\frac{4}{3}\pi \cdot 3^3=113.04[/tex] cubic centimeters. Multiplying this by the three soccer balls, you get about 339 cubic centimeters, or the third option. Hope this helps!

Answer:

x=2 x=-2

Step-by-step explanation:

f(x)=4x^2−16

f(x)=4(x^2-4)

f(x)=4(x-2)(x+2)

x=2 x=-2

Hope this helps! Please mark brainliest :)

The zeros of the function f(x) = 4x2 − 16 are found by factoring the quadratic equation, which results in two solutions x = -2 and x = 2.

To find the zeros of the function f(x) = 4x2 − 16, we need to set the function equal to zero and solve for x:

0 = 4x2 - 16

To solve this quadratic equation, you can factor out the common factor of 4:

0 = 4(x2 - 4)

We now have a difference of squares, which can be factored further:

0 = 4(x + 2)(x - 2)

Set each factor in the parentheses equal to zero:

So the zeros of the function are x = -2 and x = 2.

Answer:

5940 y

Step-by-step explanation:

Simplify the following:

-11 (-9)×5×3×4 y

-9×3 = -27:

-11×5×-27×4 y

-27×4 = -108:

-11×5×-108 y

-11×5 = -55:

-108-55 y

-55 (-108) = 5940:

Answer: 5940 y

Final answer:

The new cost of houses after a 25% increase from the original price of £100,000 is £125,000. You calculate this by finding 25% of £100,000, which is £25,000, and then add it to the original price.

Explanation:

The student is asking how to calculate the new cost of houses after a 25% price increase from the previous year when the houses cost
£100,000. To find the new price, we need to calculate 25% of £100,000 and then add that to the original price.

First, find 25% of £100,000:

0.25
(multiplier for 25%)
× £100,000
(original cost)
= £25,000
(the increase).

Next, add the increase to the original cost:

£100,000
+ £25,000
= £125,000.

Therefore, the new cost of the houses after a 25% increase is £125,000.

Answer:

18 is for the top

6 is for the bottom

Answer:

1. C

2. D

Step-by-step explanation:

Let r represent the radius of cylinder.

We have been given that the height of a right circular cylinder is 1.5 times the radius of the base. So the height of the cylinder would be [tex]1.5r[/tex].

We will use lateral surface area of pyramid to solve our given problem.

[tex]LSA=2\pi r h[/tex], where,

LSA = Lateral surface area of pyramid,

r = Radius,

h = height.

Upon substituting our given values in above formula, we will get:

[tex]LSA=2\pi r\cdot (1.5)r[/tex]  

Now we will find the total surface area of cylinder.

[tex]TSA=2\pi r(r+h)[/tex]

[tex]TSA=2\pi r(r+1.5r)[/tex]

[tex]TSA=2\pi r(2.5r)[/tex]

[tex]\frac{TSA}{LSA}=\frac{2\pi r(2.5r)}{2\pi r(1.5r)}[/tex]

[tex]\frac{TSA}{LSA}=\frac{2.5r}{1.5r}[/tex]

[tex]\frac{TSA}{LSA}=\frac{25}{15}[/tex]

[tex]\frac{TSA}{LSA}=\frac{5}{3}[/tex]

Therefore, the ratio of total surface area to lateral surface area is [tex]5:3[/tex].

Answer:

The answer is 41>6t+7

Step-by-step explanation:

It said that he wants to earn "more than" $41 so the inequality sign is more than. Then it says $6 per hour so 6t. Then you add $7

Answer:

Step-by-step explanation:

[tex](\frac{a^{4}}{-7b^{3}})^{2}=\frac{(a^{4})^{2}}{(-7b^{3})^[2}}\\\\=\frac{a^{4*2}}{(-7)^{2}b^{3*2}}\\\\=\frac{a^{8}}{49b^{6}}[/tex]