A line passes through the point (6,1) and has a slope of -3.

Write an equation in point-slope form for this line

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:

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:

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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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:

Step-by-step explanation:

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

The sales tax rate is 5%.

Step-by-step explanation:

Given,

Amount of sales tax = $49

Price of dining room set = $980

Sales tax rate = [tex]\frac{Amount\ of\ sales\ tax}{Price\ of\ dining\ room\ set}*100[/tex]

Sales taxa rate = [tex]\frac{49}{980}*100[/tex]

[tex]Sales\ tax\ rate=\frac{4900}{980}\\Sales\ tax\ rate=5\%[/tex]

The sales tax rate is 5%.

Keywords: percentage, division

Learn more about percentages at:

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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:

Part 1) [tex]c=\sqrt{146}\ cm[/tex]

Part 2) [tex]c=8\sqrt{2}\ in[/tex]

Part 3) The diagonal of rectangle is [tex]d=3\sqrt{29}\ cm[/tex]

Part 4) The length of the diagonal of computer monitor is [tex]d=15\ in[/tex]

Part 5) The ramp is [tex]10.59\ ft[/tex] long

Part 6) The distance between their houses is [tex]=4\sqrt{2}\ mi[/tex]

Part 7) [tex]234.31\ mi[/tex]

Part 8) 120 feet of wire is required

Step-by-step explanation:

Part 1) we know that

To find the length of the hypotenuse in a right triangle apply the Pythagorean Theorem

[tex]c^2=a^2+b^2[/tex]

where

c is the hypotenuse (the greater side)

a and b are the legs

we have

[tex]a=11\ cm\\b=5\ cm[/tex]

substitute

[tex]c^2=11^2+5^2[/tex]

[tex]c^2=146[/tex]

[tex]c=\sqrt{146}\ cm[/tex]

Part 2) we know that

To find the length of the hypotenuse in a right triangle apply the Pythagorean Theorem

[tex]c^2=a^2+b^2[/tex]

where

c is the hypotenuse (the greater side)

a and b are the legs

we have

[tex]a=8\ in\\b=8\ in[/tex]

substitute

[tex]c^2=8^2+8^2[/tex]

[tex]c^2=128[/tex]

[tex]c=\sqrt{128}\ in[/tex]

simplify

[tex]c=8\sqrt{2}\ in[/tex]

Part 3) we know that

To find the length of the diagonal in a rectangle apply the Pythagorean Theorem

[tex]d^2=b^2+h^2[/tex]

where

d is the diagonal of rectangle

b and h are the base and the height of rectangle

we have

[tex]b=15\ cm\\hb=6\ cm[/tex]

substitute

[tex]d^2=15^2+6^2[/tex]

[tex]d^2=261[/tex]

[tex]d=\sqrt{261}\ cm[/tex]

simplify

[tex]d=3\sqrt{29}\ cm[/tex]

Part 4) we know that

To find the length of the diagonal of a computer monitor apply the Pythagorean Theorem

[tex]d^2=w^2+h^2[/tex]

where

d is the diagonal of computer monitor

w and h are the wide and the high of computer monitor

we have

[tex]w=12\ in\\h=9\ in[/tex]

substitute

[tex]d^2=12^2+9^2[/tex]

[tex]d^2=225[/tex]

[tex]d=\sqrt{225}\ in[/tex]

simplify

[tex]d=15\ in[/tex]

Part 5) we know that

To find out the length of the ramp apply the Pythagorean Theorem

[tex]L^2=x^2+y^2[/tex]

where

L is the length of the ramp

x  is the horizontal distance of the ramp

y  is the vertical distance of the ramp

we have

[tex]x=10\ ft\\y=3.5\ ft[/tex]

substitute

[tex]L^2=10^2+3.5y^2[/tex]

[tex]L^2=112.25[/tex]

[tex]L=10.59\ ft[/tex]

Part 6) we know that

To find the distance between their houses apply the Pythagorean Theorem

[tex]c^2=a^2+b^2[/tex]

where

c is the hypotenuse (distance between their houses)

a and b are the legs

we have

[tex]a=4\ mi\\b=4\ mi[/tex]

substitute

[tex]c^2=4^2+4^2[/tex]

[tex]c^2=32[/tex]

[tex]c=4\sqrt{2}\ mi[/tex]

Part 7) we know that

The speed is equal to divide the distance by the time

[tex]speed=distance/time[/tex]

so

the distance is equal to multiply the speed by the time

[tex]distance=speed*time[/tex]

First train

speed=60 mph

time=3 hours

distance=60(3)=180 miles

Second train

speed=50 mph

time=3 hours

distance=50(3)=150 miles

To find out how far apart are the trains at the end of 3 hours apply the Pythagorean Theorem

[tex]c^2=a^2+b^2[/tex]

where

c is the hypotenuse (distance between the trains)

a and b are the legs

we have

[tex]a=180\ mi\\b=150\ mi[/tex]

substitute

[tex]c^2=180^2+150^2[/tex]

[tex]c^2=54,900[/tex]

[tex]c=234.31\ mi[/tex]

Part 8)  we know that

For one tree is needed three wire

To find out the length of one wire apply the Pythagorean Theorem

[tex]c^2=a^2+b^2[/tex]

where

c is the hypotenuse (length of one wire)

a and b are the distance above the ground and the distance from the base

we have

[tex]a=3\ ft\\b=4\ ft[/tex]

substitute

[tex]c^2=3^2+4^2[/tex]

[tex]c^2=25[/tex]

[tex]c=5\ ft[/tex]

so

For one tree is required ----> (5)3=15 ft

therefore

For 8 trees is required

Multiply by 8

15(8)=120 ft

We can use the points (2, -2) and (4, -1) to solve.

Slope formula: y2-y1/x2-x1

= -1-2/4-(-2)

= -3/6

= -1/2

Point slope form: y - y1 = m(x - x1)

y - 2 = -1/2(x + 2)

______

Best Regards,

Wolfyy :)

Answer:

The number is 50.

Step-by-step explanation:

1.12x=56

x=56/1.12

x=50

Answer:

1809

Step-by-step explanation:

Answer:

67 x 27 = 1,809 have a good day

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

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.

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.

Answer:

Step-by-step explanation:

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

Answer:

Joel will save $145.

Step-by-step explanation:

1125-980=145

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:

250 students

Step-by-step explanation:

Another way of saying this is:

40% of all six-grade students are 100 of them.

So,

40% of total is equal to 100

We can translate this into an algebraic equation and solve for the total number of students.

Let total number of students be "t"

Also, note "of" means "multiplication" and "is" means "equal"

Lets translate word equation to algebraic:

"40% of total is equal to 100"

40% * t = 100

Converting percentage to decimal by dividing by 100, we have:

40% = 40/100 = 0.4

Now, we have:

0.4 * t = 100

We can now solve for t:

[tex]0.4 * t = 100\\t=\frac{100}{0.4}\\t=250[/tex]

Hence,

the total number of students is 250

Answer:

250 students

Step-by-step explanation:

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:

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:

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:

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.

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:

D

Step-by-step explanation:

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

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:

I would say the answer is 90 degrees

Answer:

360-48-42-90-48-42=90°

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 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:

less

Step-by-step explanation:

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