The shorter leg of a right triangle is 6 feet shorter than the longer leg. The hypotenuse is 6 feet longer than the longer leg. Find the side lengths of the triangle.

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:

1809

Step-by-step explanation:

Answer:

67 x 27 = 1,809 have a good day

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.

The formula can be used to describe the sequence is [tex]a_{n}=\frac{-2}{3}(6)^{n-1}[/tex]

Step-by-step explanation:

The formula of the nth term of the geometric sequence is [tex]a_{n}=a(r)^{n-1}[/tex] , where

∵ The sequence is [tex]\frac{-2}{3}[/tex] , -4 , -24 , -144 , .......

∵ The 1st term is [tex]\frac{-2}{3}[/tex]

∵ The 2nd term is -4

∴ [tex]\frac{-4}{\frac{-2}{3}}=6[/tex]

∵ The 3rd term is -24

∴ [tex]\frac{-24}{-4}=6[/tex]

∵ The 4th term is -144

∴ [tex]\frac{-144}{-24}=6[/tex]

∵  [tex]\frac{a_{2}}{a_{1}}[/tex] = [tex]\frac{a_{3}}{a_{2}}[/tex] =  [tex]\frac{a_{4}}{a_{3}}[/tex] = 6

∴ There is a constant ratio between each two consecutive terms

∴ The sequence is a geometric sequence

∵ The formula of the nth term of the geometric sequence is [tex]a_{n}=a(r)^{n-1}[/tex]

∵ a = [tex]\frac{-2}{3}[/tex]

∵ r = 6

∴ The formula of the sequence is [tex]a_{n}=\frac{-2}{3}(6)^{n-1}[/tex]

The formula can be used to describe the sequence is [tex]a_{n}=\frac{-2}{3}(6)^{n-1}[/tex]

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Answer:

c - f(x) = -2/3(6)^x − 1

Step-by-step explanation:

Edge 2020

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:

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.

[tex]\( \cos(2x) = \frac{1}{2} \).[/tex]

Given that [tex]\( \sin(x) = -\frac{1}{2} \) and \( \tan(x) \)[/tex] is negative, we can find \[tex]( \cos(2x) \)[/tex]using the trigonometric identities.

First, let's find the value of [tex]\( \cos(x) \)[/tex] using the Pythagorean identity:

[tex]\[ \cos^2(x) = 1 - \sin^2(x) \][/tex]

Given [tex]\( \sin(x) = -\frac{1}{2} \),[/tex] we have:

[tex]\[ \cos^2(x) = 1 - \left(-\frac{1}{2}\right)^2 \][/tex]

[tex]\[ \cos^2(x) = 1 - \frac{1}{4} \][/tex]

[tex]\[ \cos^2(x) = \frac{3}{4} \][/tex]

Taking the square root of both sides, since [tex]\( \cos(x) \)[/tex] is positive in the first and fourth quadrants:

[tex]\[ \cos(x) = \pm \frac{\sqrt{3}}{2} \][/tex]

Given that [tex]\( \tan(x) \)[/tex] is negative, we know that ( x ) lies in either the second or fourth quadrant. In the second quadrant, both [tex]\( \sin(x) \) and \( \cos(x) \)[/tex] are negative. In the fourth quadrant, [tex]\( \sin(x) \)[/tex] is negative but [tex]\( \cos(x) \) i[/tex]s positive.

Since [tex]\( \cos(x) = \pm \frac{\sqrt{3}}{2} \),[/tex] we conclude that [tex]\( \cos(x) = -\frac{\sqrt{3}}{2} \)[/tex]  (since [tex]\( \cos(x) \)[/tex] is negative in the second quadrant).

Now, using the double angle identity for cosine:

[tex]\[ \cos(2x) = 2\cos^2(x) - 1 \][/tex]

Substituting [tex]\( \cos(x) = -\frac{\sqrt{3}}{2} \):[/tex]

[tex]\[ \cos(2x) = 2\left(-\frac{\sqrt{3}}{2}\right)^2 - 1 \][/tex]

[tex]\[ \cos(2x) = 2\left(\frac{3}{4}\right) - 1 \][/tex]

[tex]\[ \cos(2x) = \frac{3}{2} - 1 \][/tex]

[tex]\[ \cos(2x) = \frac{3}{2} - \frac{2}{2} \][/tex]

[tex]\[ \cos(2x) = \frac{1}{2} \][/tex]

So, [tex]\( \cos(2x) = \frac{1}{2} \).[/tex]

Answer: 40 000

Step-by-step explanation:

Population doubles in first 55 years =

5000 * 2 = 10 000

In 220 years from now, 220/55 = 4

Hence, 10 000 * 4 = 40 000 population

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:

x-intercept = 1 and y-intercept = -3

Step-by-step explanation:

The graph of the function is attached with this answer.

I have used some computer program to draw graph but you can draw a rough graph manually on a graph sheet. For that

To Calculate Some Important Points :

These are the points where the the first derivative of the function becomes zero. This means that at these points the graph takes turn, if it was increasing behind this point then it will start decreasing after this point or the other way. The second derivative of the function at these points are either positive or negative (positive for local minima and negative for local maxima).

To calculate the x-intercept, first you need to analyse the graph to know how many x-intercepts are there. According to this graph only one intercept is there, it means that only one real root of this cubic equation is there (a cubic equation has 3 roots in which either one is real and two are imaginary or all the three are real). To calculate roots of a cubic equation there is no specific way. Generally, the first root is through hit and trial method. So, let's start with the simplest number which is x=0

[tex](0)^{3}+2(0)^{2}-3 \neq 0[/tex]

∴ 0 is not a root.

Now, let x=1

[tex](1)^{3}+2(1)^{2}-3=0[/tex]

∴ 1 is a root.

Since 1 is the only real root of the equation, therefore (1,0) is the only x-intercept of the graph.

To calculate y-intercept, simply put x=0 in the equation which is

[tex]f(0)=(0)^{3}+2(0)^{2}-3=-3\\\therefore f(0)=-3[/tex]

Therefore the y intercept is (0,-3).

* Cubic Polynomial : Polynomials which have a degree (highest power of the variable) of 3 are called cubic polynomials.

** Local Maxima : Points at which the left and right neighbours have less function value are called local maxima.

*** Local Minima : Points at which the left and right neighbours have more function value are called local minima.

Answer:

x = 1 and the y = -3

Step-by-step explanation:

here below hope this helps

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:

Step-by-step explanation:

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

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:

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:

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

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.

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Answer:

Step-by-step explanation:

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

Answer:

81

Step-by-step explanation:

Answer:

4/7

Step-by-step explanation:

32/56=4/7

Answer:

The number of boys = 32

The number of girls = 56

therefore, to fine the possible ratio, you divided 32 and 56 to their lowest terms.

i.e 32: 56. 32÷8 : 56÷8 = 4:7

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:

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.

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:

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:

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:

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:

D

Step-by-step explanation:

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

Answer:

The number is 50.

Step-by-step explanation:

1.12x=56

x=56/1.12

x=50

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.