The perimeter of a rectangle is 64m and it’s length is 3 times it’s width.what is the length of the rectangle?

Khalil uses the method of similar triangles to find the distance across the river, [tex]\overline{PR}[/tex]

Reasons:

The distances between the formed the sight-lines are;

[tex]\overline{RB}[/tex] = 185 feet

[tex]\overline{OC}[/tex] = 275 feet

The distance between the point close to the river and the next point further from the river [tex]\overline{RO}[/tex] = 150 feet

In triangles ΔPRB and ΔPOC, we have;

∠PRE = ∠POC = 90° Given

∠PER ≅ ∠PCO By corresponding angle formed between two parallel lines and a common transversal.

∴ ΔPRE is similar to ΔPOC by Angle-Angle, AA, similarity theorem

Which gives;

[tex]\displaystyle \frac{\overline {PR}}{\overline {PO}} = \mathbf{\frac{\overline {RE}}{\overline {OC}}}[/tex]

Let x represent the distance across the river, we have;

[tex]\overline{PR}[/tex] = x

[tex]\overline{PO}[/tex] = 150 + x

Which gives;

[tex]\displaystyle \frac{x}{150 + x} = \frac{185}{275}[/tex]

275·x = 185 × (150 + x) = 27,750 + 185·x

275·x - 185·x = 27,750

90·x = 27,750

[tex]\displaystyle x = \frac{27,750}{90} = \mathbf{308.\overline 3}[/tex]

Therefore, the distance across the river, x = [tex]\mathbf{\overline{PR}}[/tex] = [tex]\underline{308.\overline 3 \ feet}[/tex]

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The values of ||-10v|| is 51.96 units

Given the complex number v = 6i + 3j,

10v is expressed as 10(6i + 3j)

10(6i + 3j) = 60i + 30j

Take the modulus of the complex number:

[tex]|10v|=\sqrt{60^2+30^2}\\|10v|= \sqrt{1800+900}\\|10v|= \sqrt{2700} \\|10v|=51.96units[/tex]

Hence the values of ||-10v|| is 51.96 units

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Answer:

y = -2/3x-1

Step-by-step explanation:

Answer: 7/12 miles

Step-by-step explanation:

20mph = 20/60 miles per minute = 1/3 miles per minute

1 min 45s = 1 min + 3/4 min = 7/4 min

1/3 x 7/4 = 7/12 miles

The distance travelled by car with the given speed and time is 7/12 miles.

The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.

Given that, a car is traveling at 20 miles per hour during rush hour.

Time =1 minute and 45 seconds

= [tex]1\frac{45}{60}=1\frac{3}{4}[/tex]

= 7/4 minutes

Now, 20 miles per minute

= 20/60 miles per minute = 1/3 miles per minute

We know that, Distance =Speed×Time

= 1/3 ×7/4

= 7/12 miles

Therefore, distance travelled by car is 7/12 miles.

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I will set it up.

Let a = adults

Let s = seniors

The first equation is a + s = 325.

The second equation is 9a + 7s = 2504.

Here is your system of equations:

{a + s = 325

{9a + 7s = 2504

Take it from here.

Answer:

7s.

Step-by-step explanation:

2s - s + 6s (Given)

Rembember that - s is the same as - 1s because there is an invisible 1.

So, 2s - 1s =  1s or s.

1s + 6s = 7s.

2s - s + 6s (Given)

7s (Combine like terms)

Answer:

(i)= 45 KPH, (ii) = 251 miles

Step-by-step explanation:

'Per' essentially means divide. Thus, to find Kilometres per hour, divide 270 by 6= 45. The bus is travelling at 45 KPH.

Then, to see how far a nine hour trip would cover, distance = speed * time =  251 miles.

Answer:

Below.

Step-by-step explanation:

(i) Speed of the bus = 270/6 = 45 km/hour.

(ii) In 9 hours it travels 45 * 9 = 405 km.

B. 1, 3, 9, 27

Geometric Sequence is being multiplied by factor of 3.

Answer:

[tex]\left \{ {{y=-2} \atop {x=3}} \right.[/tex]

Step-by-step explanation:

[tex]\left \{ {{-6x - y = -16} \atop {-6x - 5y = -8}} \right. <=> \left \{ {{4y= -8} \atop {-6x-5y =-8}} \right. <=> \left \{ {{y=-2} \atop {-6x-5y=-8}} \right. <=> \left \{ {{y=-2} \atop {-6x-5*(-2)=-8}} \right. <=> \left \{ {{y=-2} \atop {-6x=-18}} \right. <=> \left \{ {{y=-2} \atop {x=3}} \right.[/tex]

Answer:

1231.50432021 cm³

Step-by-step explanation:

Use the formula:

[tex]\frac{1}{3} \pi r^{2} h[/tex]

And replace known values:

[tex]\frac{1}{3} \pi (7^{2})(24)[/tex]

Aaaand simplify:

[tex]\frac{1}{3}*1176 \pi[/tex]

Which gives approximately:

[tex]1231.50432021[/tex]

And don't forget to put the unit (cm³)!

Answer:

1230

Step-by-step explanation:

1/3*pi*7^2*24

1/3*pi*49*24

=1230

Answer:Mmm

Step-by-step explanation:

I am doing the work I will thell you the answer

The domain and the range of the function describes the possible profit or

loss from the sale of popcorn and the number of popcorn units.

The correct responses are;

Reasons:

The question parameters are;

The price of a popcorn = $1.5

Number of popcorn he purchases = 150

Total profit made = $5.50

The number of containers sold = 25

Therefore;

C. Given that the number of containers sole is countable, the function will be discrete.

D. Cost of the containers = Revenue - Profit

Which gives;

Cost of the containers = 1.5 × 25 - 5.5 = 32

The given function is therefore;

y = 1.5·x - 32

E. The domain is the 150 containers which gives;

The domain = 0 ≤ x ≤ 150

F. When no popcorn is sold, we have;

x = 0, which gives;

y = 1.5 × 0 - 32 = -32

If he does not sell any popcorn, the loss is $32

G. If all the popcorn are sold, we have;

x = 150

Therefore;

y = 1.5 × 150 - 32 = 193

The profit if all the popcorn are sold = $193

H. The range of the function are the possible y values, which is the possible profit or loss, which gives;

The range = -32 ≤ y ≤ 193

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Hey there! :-)

First, let's find the slope of the line.

We can do that by using this formula:

Slope=Rise/Run

Where

Rise=how many units we move up

Run=how many units we move left or right.

We move 5 units up and 8 units to the right.

Therefore, the slope is 5/8.

The y-intercept (where the line touches the graph) is -9/8.=

Therefore, the equation of the line is y=5/8x-9/8.

Hope this helps you daughter. Use the comment section to clarify any doubts.

Answered by

~A felicitous teen who helps others with a smile on her face

Good luck.

Answer:

a - y=5/8x - 9/8

Step-by-step explanation:

firstly, work out the gradient between those two coordinates

[tex]gradient = \frac{change \: in \: y}{change \: in \: x} [/tex]

[tex]gradient \: = \frac{ - 3 - 2}{ - 3 - 5} = \frac{ - 5}{ - 8} = \frac{5}{8} [/tex]

now, use formula y=mx+c where y is the y coordinate, m is the gradient, x is the x coordinate and c is the y intercept

use any of the two coordinates in the graph. I'll use (5,2)

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

[tex]2 = \frac{5}{8} (5) + c[/tex]

[tex]2 = \frac{25}{8} + c[/tex]

[tex]therefore \: c \: is \: - \frac{9}{8} from \: doing \: 2 - \frac{25}{8} [/tex]

now we have the gradient and y intercept

so the equation is

[tex]y = \frac{5}{8} x - \frac{9}{8} [/tex]

Answer:

x=5

Step-by-step explanation:

[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ V=\stackrel{cm^3}{648\pi }\\ h=8 \end{cases}\implies 648\pi =\pi r^2(8) \\\\\\ \cfrac{648\pi }{8\pi }=r^2\implies 81=r^2\implies \sqrt{81}=r\implies \boxed{9=r}[/tex]

Answer:

16

Step-by-step explanation:

1) Plug x=1 into equation

f(x) = -2(1)²+4(1)+6

f(x) = -2²+4+6

f(x) = 4+4+6

y = 14

(1,14)

2) Plug in x=2 into equation

f(x) = -2(2)²+4(2)+6

f(x) = -4²+8+6

f(x) = 16+8+6

y = 30

(2,30)

3) Use slope formula ([tex]\frac{y2-y1}{x2-x1}[/tex])

[tex]\frac{30-14}{2-1}[/tex]

[tex]\frac{16}{1}[/tex]

16

Answer:

  35°

Step-by-step explanation:

The base angles of an isosceles triangle are congruent. The sum of angles in a triangle is 180°, so we have ...

  2M +110 = 180

  2M = 70

  M = 35

The measure of angle M is 35°.

Answer:

.6 miles

Step-by-step explanation:

Answer:

0.6 miles

Step-by-step explanation:

6 × t = 4 × (15 - t)

6t = 60 - 4t

6t + 4t = 60 - 4t + 4t

10t = 60

t = 6

6 × [tex]\frac{1}{10}[/tex] = 0.6

Answer:

3/7

Step-by-step explanation:

The first black marble is 10/15 and the second is 9/14. Multiply them together to get 3/7 after you simplify it.

Answer:

20+20=40

they have 40 apples altogether.

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

(-5,-7)

Step-by-step explanation:

Set functions equal to each other.

2x+3= -4x-27

2x+4x = -3-27

6x=-30

x= -5

f(-5) = 2(-5) +3

f(-5) =-10+3 y= - 7

g(-5) = -4(-5) -27

g(-5) =20-27 y= -7

x=-5 y=-7

(-5,-7)

Answer:

(-5,-7)

Step-by-step explanation:

Answer:

1. <  2. < 3. > 4. = 5. >

Step-by-step explanation: