is abc = dce? justify your answer below, please explain why! please help :)

Answer:

[tex]y =  \frac{22-x}{2}[/tex]

For width = 2 ft, the length of the flower bed = 10 ft.

For width = 3 ft, the length of the flower bed = 9.5 ft.

For width = 4 ft, the length of the flower bed = 9 ft.

Step-by-step explanation:

Here, the Perimeter of the flower garden is given as

22 = 2 y + x

: where, y : Length of the garden

and x : Width of the garden .

Now, solving for y in the above expression,we get

22 = 2 y + x  ⇒    22 - x = 2 y

or, [tex]y =  \frac{22-x}{2}[/tex]

Now, when the width (x) = 2 feet

Length of the flower  bed [tex]y =  \frac{22-x}{2}  = \frac{22-2}{2}  = \frac{20}{2}  = 10[/tex]

or, x = 10 ft

⇒For, the width = 2 ft, the length of the flower bed = 10 ft.

when the width (x) = 3 feet

Length of the flower  bed [tex]y =  \frac{22-x}{2}  = \frac{22-3}{2}  = \frac{19}{2}  = 9.5[/tex]

or, x = 9.5 ft

⇒For, the width = 3 ft, the length of the flower bed = 9.5 ft.

when the width (x) = 4 feet

Length of the flower  bed [tex]y =  \frac{22-x}{2}  = \frac{22-4}{2}  = \frac{18}{2}  = 9[/tex]

or, x = 9 ft

⇒For, the width = 4 ft, the length of the flower bed = 9 ft.

A waterfall has a height of 1400 feet. A pebble is thrown upward from the top of the falls with an initial velocity of 16 feet per second. The​ height, h, of the pebble after t seconds is given by the equation h equals negative 16 t squared plus 16 t plus 1400

h=−16t2+16t+1400. How long after the pebble is thrown will it hit the​ ground?

Answer

The pebble hits the ground after 9.8675 s

Step-by-step explanation:

Given

waterfall height = 1400 feet

initial velocity =  16 feet per second

The height, h, of the pebble after t  seconds is given by the equation.

[tex]h(t) = -16t^{2}+16t+1400[/tex]

The pebble hits the ground when  [tex]h = 0[/tex]

[tex]h=-16t^{2}+16t+1400[/tex] ---------------(1)

put [tex]h=0[/tex] in equation (1)

[tex]0=-16t^{2}+16t+1400[/tex]

[tex]-16t^{2}+16t+1400=0[/tex]

Divide by -4 to simplify this equation

[tex]4t^{2}-4t-350=0[/tex]

using the Quadratic Formula where

a = 4, b = -4, and c = -350

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

[tex]t=\frac{-(-4)\pm\sqrt{(-4)^{2}-4(4)(-350) } }{2(4)}[/tex]

[tex]t=\frac{4\pm\sqrt{16-(-5600) } }{8}[/tex]

[tex]t=\frac{4\pm\sqrt{16+5600 } }{8}[/tex]

[tex]t=\frac{4\pm\sqrt{16+5616 } }{8}[/tex]

The discriminant [tex]b^{2}-4ac>0[/tex]

so, there are two real roots.

[tex]t=\frac{4\pm12\sqrt{39 } }{8}[/tex]

[tex]t=\frac{4}{8}\pm\frac{12\sqrt{39 }}{8}[/tex]

[tex]t=\frac{1}{2}\pm\frac{3\sqrt{39 }}{2}[/tex]

Use the positive square root to get a positive time.

[tex]t=9.8675 s[/tex]

The pebble hits the ground after 9.8675 second

Answer:

4

Step-by-step explanation:

If we were to work backwards, 4 would be the 2 part in the equation, already done. 2x2=4. so that means that the other number must also be multiplied by 2, making the number 6. 6+4 is 10, meaning ten gallons. message me with any remaining questions!

There are 4 gallons of yellow paint are needed to mixed with the ten gallons of green paint.

To calculate how many gallons of yellow paint must be used to mix with blue paint in order to make ten gallons of green paint, using a ratio of 3 parts blue to 2 parts yellow, we first need to understand the total ratio parts. The ratio given is 3:2, which means there are 3 + 2 = 5 parts in total. Since we want to mix ten gallons of green paint, we need to split these ten gallons according to the ratio.

First, we calculate the value of one part by dividing the total gallons of green paint by the total number of parts:

10 gallons / 5 parts = 2 gallons per part

Now, since we have 2 parts yellow, we need:

2 parts  imes 2 gallons per part = 4 gallons

Therefore, to make ten gallons of green paint with the given ratio, 4 gallons of yellow paint must be used.

Final answer:

The sale price of the television, after a 35% discount on the original price of $1,800, is $1,170.

Explanation:

To calculate the sale price of the television that was originally priced at $1,800 and now has a 35% discount, we need to determine what 35% of the original price is and subtract it from the original price.

Step-by-Step Calculation

Find 35% of $1,800:
(35/100) × $1,800 = $630.

Subtract the discount from the original price:
$1,800 - $630 = $1,170.

Therefore, the sale price of the television is $1,170.

Answer:

The circumference of the pipe can be derived by 2(pi) r = 2 (3.14) (2.5)= 15.7. Hence the steel ring needs to be 15.7 cm. (option A).

The length of the steel ring necessary to fit around a pipe with a diameter of 5 cm is 15.7 cm, found using the formula for the circumference of a circle. This formula is Circumference = Pi * Diameter.

The student wants to find out how long a steel ring needs to be to fit around a pipe with a diameter of 5 centimeters. This involves finding the circumference of a circle, which uses the formula Circumference = Pi* Diameter. So, to find the needed length of the steel ring, we substitute the given diameter into the formula.

Step 1: Write down the formula: Circumference = Pi*Diameter.

Step 2: Substitute the given diameter of 5 cm into the formula: Circumference = 3.14 * 5 cm.

Step 3: Calculate the circumference: Circumference = 15.7 cm.

Therefore, the steel ring needs to be 15.7 cm long to fit perfectly around the pipe. So, the answer is A. 15.7 cm.

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Answer:

1/15 of a kilogram

Step-by-step explanation:

Answer:1/15 of a kilograms

Step-by-step explanation:

1/5 divided by three is the same as 1/5*1/3. 1*1 =1 and 5*3 =15

Answer:

45

Step-by-step explanation:

45 is constant, because no mater how many miles you drive, you will always be charged $45. It stays the same

Answer:

45

Step-by-step explanation:

your equation would be y= 45+22x and no matter what x equals, you will always have the set $45, so that is your constant.

Final answer:

To solve the problem, we set up an equation with 'x' representing adult tickets and concluded that 375 adult tickets were sold for the school play.

Explanation:

The question involves solving a numerical problem related to ticket sales. To find the number of adult tickets sold for the school play, we can set up an algebraic equation. Let x represent the number of adult tickets and x + 64 represent the number of student tickets (since there were 64 more student tickets sold than adult tickets). The total tickets sold were 814, so we can write the equation as follows:

x + (x + 64) = 814

Combining like terms, we have:

2x + 64 = 814

Subtracting 64 from both sides, we get:

2x = 750

Dividing both sides by 2, we obtain:

x = 375

Therefore, 375 adult tickets were sold for the school play.

Answer:

Henry: 21

Latoya: 28

Manuel = 63

Step-by-step explanation:

x = orders henry served

x + 7 = orders latoya served

3x = orders manuel served

x + (x + 7) + 3x = 112

5x + 7 = 112

5x = 105

x = 21

x + 7 = 21 + 7 = 28

3x = 3 * 21 = 63

Answer:

The number is 50.

Step-by-step explanation:

1.12x=56

x=56/1.12

x=50

Answer:

Joel will save $145.

Step-by-step explanation:

1125-980=145

Answer:

The width of the given rectangle  =  6 m

The width of the rectangle  = 14 m

Step-by-step explanation:

Let us assume the width of the rectangle  = k

So, the length of the rectangle  =  2 + 2 ( The width)  = 2 +  2 k

Perimeter of the rectangle  = 40 meters

Now, PERIMETER OF THE RECTANGLE = 2(LENGTH + WIDTH)

or, 40 =  2 ( k + (2 +  2 k))

⇒ 2( 3  k + 2) = 40

or, 2(3 k) +  2(2) = 40

or, 6 k = 40 - 4  =  36

⇒ k = 36 / 6 = 6, or  k = 6

Hence, the width of the given rectangle  = k = 6 m

The width of the rectangle = 2 + 2 k =  2 + 2(6)  = 14 m

Answer:

D

Step-by-step explanation:

its like going from point A to point B and then back to point A

Answer:

They eat 125lbs of food a day

Step-by-step explanation:

You do 875 divide by 7 for the days of the week and you get 125

Answer:

125 pounds

Step-by-step explanation:

One week is equivalent to 7 days

If the bears eat 875 pounds each week all we have to do to get the answer is divide 875 by 7.

875 ÷ 7 = 125

Hope I helped!

Answer:

less

Step-by-step explanation:

5/10 is equal to one half, but 4/10 is less than one half

Answer:

x=2

Step-by-step explanation:

x/6=3/9

simplify 3/9 into 1/3

x/6=1/3

cross product

6*1=3x

6=3x

x=6/3=2

x=2

Answer:

x=2, y=4. (2, 4).

Step-by-step explanation:

x+y=6

3x-2y=-2

---------------

y=6-x

3x-2(6-x)=-2

3x-12+2x=-2

5x-12=-2

5x=-2+12

5x=10

x=10/5

x=2

y=6-(2)=6-2=4

Answer:

1809

Step-by-step explanation:

Answer:

67 x 27 = 1,809 have a good day

Answer:

Step-by-step explanation:

[tex]5+3w+3-w\qquad\text{combine like terms}\\\\=(3w-w)+(5+3)\\\\=2w+8[/tex]

Answer:

The speed of the boat in still water is 12 km/hour.

Step-by-step explanation:

Given:

Boat goes 50 km downstream and 30 km upstream. The speed of the stream 3 km/hour.

Now, to find the speed of the boat in still water:

Let the speed of boat in still water be [tex]x km/hour[/tex].

The speed of the downstream be [tex]x+3[/tex]

And, the speed of the upstream be [tex]x-3[/tex]

And, now we find the time by putting the formula:

[tex]Time = \frac{Distance}{Rate}[/tex]

So, downstream time is:

[tex]downstream\ time = \frac{50}{x+3}[/tex]

So, upstream time is:

[tex]upstream\ time = \frac{30}{x-3}[/tex]

According to question:

Time upstream = Time downstream

[tex]\frac{30}{x-3} = \frac{50}{x+3}[/tex]

By cross multiplication:

[tex]30\times (x+3)= 50\times (x-3)[/tex]

[tex]30x+90=50x-150[/tex]

By taking variables in one side and taking numbers on the other side we get:

[tex]90+150=50x-30x[/tex]

[tex]240=20x[/tex]

Dividing both sides by 20 we get :

[tex]12=x[/tex]

Therefore, the speed of the boat in still water is 12 km/hour.

Answer:

Part 1) The rate of change of the linear function is [tex]\frac{1}{3}[/tex]

Part 2) The initial value is -4

Step-by-step explanation:

Part 1) Find the rate of change

we know that

The rate of change of the linear function is the same that the slope of the linear function

To determine the slope we need two points

Looking at the graph

take the points (0,-4) and (3,-3)

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

substitute the values

[tex]m=\frac{-3+4}{3-0}[/tex]

[tex]m=\frac{1}{3}[/tex]

therefore

The rate of change of the linear function is [tex]\frac{1}{3}[/tex]

Part 2) Find the initial value

we know that

The initial value or y-intercept is the value of y when the value of x is equal to zero

Looking at the graph

when the value of x is equal to zero

The value of y is equal to -4

so

The y-intercept is the point (0,-4)

therefore

The initial value is -4

The slope of the given line with points (0, -3) and (-2, 5) is -4.

The slope is the rate of change of the y-axis with respect to the x-axis. We can also think of slope as the rise over run. The slope of a line also describes the amount of angle a line forms from the positive x-axis.

From the given graph we can determine two points when x = 0 , y = -3 and when x = -2 , y = 5.

∴ The points of the given line are (0, -3) and (-2, 5).

We know the slope of a line is rise over run which is (y₂ - y₁)/(x₂ -x₁).

Therefore the slope of the given line is,

= (5 + 3)/(-2 - 0).

= 8/-2.

= -4.

learn more about slope here ;

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Answer:

81

Step-by-step explanation:

Answer:

Total cost for a day=246 dollars

Hourly rate=10 dollars

Step-by-step explanation:

Let the Total cost be a function of 't' (time),i.e. total cost=R(t)

let R(t)=at+b where a and b are some constants belonging to real numbers

Now substitute t=1 in above equation

R(1)=a+b⇒16=a+b

substitute t=2,

R(2)=2a+b⇒26=2a+b

Now solving a+b=16 and 2a+b=26,

we get a=10 dollars/hour and b=6 dollars

Therefore the cost function is, R(t)=10t+6

where 10 dollars/hour is the hourly rate and 6 dollars is the base charge.

To get the Total charge for one day substitute t=24 in R(t)

⇒R(24)=10*24+6=246 dollars

Answer:

Step-by-step explanation:

You need to divide 74308 divided by 52 which equals 1429.

Answer:

R+T=24

2t+9=R

(2t+9)+t=24

3t+9=24

3t=15

t=5

r+5=24

r=19

Teo is 5 and Richard is 19

Richard is 19 years old and Teo is 5 years old.

To solve this problem, we'll start by assigning variables to Richard's age (R) and Teo's age (T).

From the given information, we can form the following equations:

We can solve this system of equations by substituting the second equation into the first equation, which gives us:

(2T + 9) + T = 24

Combining like terms, we get 3T + 9 = 24. Subtracting 9 from both sides gives 3T = 15. Dividing by 3, we find T = 5.

Substituting this value back into the first equation, we get R + 5 = 24. Subtracting 5 from both sides gives R = 19.

Therefore, Richard is 19 years old and Teo is 5 years old.

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Answer:

40/7

Step-by-step explanation:

Answer: y=5.7 approx.

Step-by-step explanation:

2y÷8-2y=-10

follow order of operations and simplify a bit first

2y÷8-2y=-10 becomes 1/4y-2y=-10

you can keep on going

so 1/4y-2y=-10 becomes -7/4y=10

y=5.7 approx.

Answer:

25

Step-by-step explanation:

To calculate rate, divide the number of cans by the time to get "Cans per minute".

300/15min = 20/min

Let m represent minutes and c for cans.

We write an equation for the problem:

c = 20m

We want to know the time for 500 cans, so substitute 500 for c.

500 = 20m

Isolate m and solve:

m = 500/20

m = 25

It will take 25 minutes to put 500 labels.