The width of a rectangle is 2/3 its length. The perimeter of the rectangle is 400 ft. What is the length, in feet, of the rectangle?

Answer:

y₂ = -3

x₁ = 2

x₂ = 2

Slope = ( 1 + 3) / 0 = undefined

y₁ = 1

y₂ = 4

x₁ = 2

x₂ = 5

Slope = ( 1-4) / (2-5) = 1

y₁ = 4

y₂ = 1

x₁ = 5

x₂ = 7

Slope = (4-1) / ( 5-7 ) = -1.5

y₁ = -3

y₂ = 1

x₁ = 2

x₂ = 7

slope = (-3-1) / ( 2-7) = 4/5

Answer:

c. 90 cm³

Step-by-step explanation:

Formula applied :

Volume (triangular prism) = Base × Height

Solving :

⇒ Volume = 9 cm² x 10 cm

⇒ Volume = 90 cm³

The answer option is c

Answer:

c.  90 cm³

Step-by-step explanation:

Formula

Volume of a right prism = area of base × height

Given:

Substitute the given values into the formula:

⇒ Volume = 9 cm² × 10 cm

                  = 90 cm³

Hey ! there

Answer:

Step-by-step explanation:

In this question we are given that the product of two integers is -160 and one of them is 8 . And we are asked to find the other integer .

For finding the other integer we are assuming ,

And now we can find other Integer by making equation and solving it .

SOLUTION : -

Equation is :

[tex] \quad \dashrightarrow \qquad \: 8 \times x = - 160[/tex]

or ,

[tex] \quad \dashrightarrow \qquad \: 8x = - 160[/tex]

To isolate the variable x , We are dividing both sides by 8 :

[tex] \quad \dashrightarrow \qquad \: \dfrac{ \cancel{8}x}{ \cancel{8}} = \cancel{ \dfrac{ - 160}{8} }[/tex]

On simplifying it , We get :

[tex] \quad \dashrightarrow \qquad \: \red{\underline{\boxed{\frak{x = - 20}}}} \quad \bigstar[/tex]

Verifying : -

Now we are verifying whether our answer is wrong or right by substituting value of x in the equation . So ,

Substituting value of x :

Multiplying 8 with - 20 :

Therefore , of answer is correct .

Answer:

[tex] \: [/tex]

Step-by-step explanation:

[tex] \: [/tex]

Given,

[tex] \: [/tex]

To Find,

[tex] \: [/tex]

Solution,

[tex] \: [/tex]

So, The equation will be :

[tex] \\ \longrightarrow \qquad{ \ {{ { \sf{x \times 8= - 160}}}}} \\ \: \: [/tex]

[tex] \longrightarrow \qquad{ \ {{ { \sf{8x= - 160}}}}} \\ \: \: [/tex]

Now, Let us divide both sides by 8 :

[tex] \\ \longrightarrow \qquad{ \ {{ { \sf{ \frac{8x}{8} = \frac{ - 160}{8} }}}}} \\ \: \: [/tex]

[tex] \longrightarrow \qquad{ \underline {\boxed{ \pmb{ \mathfrak{x= - 20}}}}} \: \: \bigstar \: \\ [/tex]

Therefore,

hope this helps :)

...........

Answer:

The volume of this composite figure is 312 cubic inches.

Step-by-step explanation:

Volume of pyramid:

[tex] \frac{1}{3} ( {6}^{2} )(5) = \frac{1}{3} (36)(5) = \frac{1}{3} (180) = 60[/tex]

Volume of rectangular prism:

[tex]12(3)(7) = 252[/tex]

Volume of composite figure:

[tex]60 + 252 = 312[/tex]

From the description of the function as we can see in the question, the function is a quadratic function.

The term quadratic function refers to a type of function that is obtained from the equation ax^2+ bx + c =0.

A function in which as the domain values approach infinity, the range values approach infinity and as the domain values approach negative infinity, the range values approach infinity is a quadratic function.

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Answer:

4^5

Step-by-step explanation:

When we are multiplying expressions with the same base, we add the exponents

a^b * a^c = a^(b+c)

4^2 * 4^3 = 4^(2+3) = 4^5

The value of the constant of variation is 3. The correct option is the third option- 3

From the question, we are to determine the constant of variation.

Let the constant of variation be k

From the give information,

A quantity h varies directly with w and inversely with p

That is,

[tex]h \propto \frac{w}{p}[/tex]

Introducing the constant of variation, k, we get

[tex]h = k\frac{w}{p}[/tex]

Also, from the give information,

w = 4

p = 6

h = 2

Putting the parameters into the relation, we get

[tex]2 = k \times \frac{4}{6}[/tex]

[tex]6\times 2 = 4k[/tex]

[tex]k = \frac{6\times 2}{4}[/tex]

k = 3

Hence, the value of the constant of variation is 3. The correct option is the third option- 3

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Answer:

Answer is 3

Step-by-step explanation:

~Hope this helps!

Considering the definition of probability,  the probability that the first movie selected is an comedy movie and the second movie is a action film is 30%.

Probability is the greater or lesser chance that a given event will occur.

In other words, the probability establishes a relationship between the number of favorable events and the total number of possible events.

Then, the probability of any event A is defined as the ratio between the number of favorable cases (number of cases in which event A may or may not occur) and the total number of possible cases. This is called Laplace's Law.

[tex]P(A)=\frac{number of favorable cases}{number of possible cases}[/tex]

The multiplication rule or product rule allows you to find the probability that event A and event B occur at the same time.

Two events A and B are dependent if the occurrence of one affects the occurrence of the other. For dependent events, the multiplication rule states that:

P(A∩B)= P(A)× P(B|A) (where P(B|A) indicates “the probability of ‘B’ having occurred ‘A’)

In this case, you know:

The probability that the first movie selected is an comedy movie and the second movie is a action film.

Once the first movie is selected, there are no longer 6 movies available. There are only 5, because one of the options is eliminated. So the occurrence of the first event affects the second event and the events are dependent.

Then, the probabilty can be calculated A:

Probability= [tex]\frac{3}{6}[/tex]× [tex]\frac{3}{5}[/tex]

Probability= 0.3= 30%

Finally, the probability that the first movie selected is an comedy movie and the second movie is a action film is 30%.

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Answer:

x= 3

x= -2

Step-by-step explanation:

x^2-x=6

x^2-x-6=0

find which 2 numbers when multiplied give -6 and

when added give -1

they are -3 and 2

(x-3)(x+2)

x= 3

x= -2

Answer:

₹165.79

Step-by-step explanation:

Given:-

No. of electric bulbs = 1000

cost of each electric bulb = ₹ 150

No. of bulbs broken = 50

Selling price of each bulb = x

Profit percentage = 5%

To Find:-

The selling price of each bulb.

Solution:-

Cost price of 1000 electric bulbs,

= 1000 × ₹150

= ₹1,50,000

5% profit on the total cost price,

= {5}/{100}× ₹150000

= ₹7500

Total selling price = ₹157500

No. of bulbs remaining = 950

Therefore, selling price of each bulb,

= {₹157500}/{950}

= ₹165.79

Therefore,

Selling price of each bulb = ₹165.79

The length of the third side is [tex]≈15.7[/tex]

Note:

Phitagors theorem:

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

[tex]c: hypotenuse[/tex]

[tex]a: altitude[/tex]

[tex]b: base[/tex]

1) Using Phitagors theorem

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

[tex]c^{2}=14^{2}+7^{2}[/tex]

2) Calculate

[tex]c^{2}=245[/tex]

3) Take the square root of both sides of the equation

[tex]\sqrt {c^{2}}=\sqrt{245}[/tex]

[tex]c=\sqrt{245}[/tex]

[tex]c≈15.7[/tex]

Answer:

Yes, the sequence is an arithmetic sequence

Step-by-step explanation:

Notice that each consecutive number is being added by the next odd number up:

0+3=3

3+5=8

8+7=15

15+9=24

24+11=35

We can represent this as the arithmetic sequence [tex]a_n=n(n+2)[/tex]

the scientific notation is just another mumble jumble way to write the same thing without so many repetitive zeros, so hmmm 780000 has 4 zeros, so what we do is we can say

78 and 4 zeros following it

or we can say

78 * 10⁴, if we get that product, is 780000

in scientific notation, we only leave one digit to the left of the decimal point

so the same thing above can be written as

78 * 10000, can be written as 78.0 * 10000

or as

7.8 * 100000

or as

0.78 * 1000000

check their product

7.8 * 100000, is really just 780000

because we moved the decimal to the left one more slot, it

became 7.8 * 100000

or in

Answer:

780,000 [tex]=7.8 * 10^5[/tex]

Step-by-step explanation:

Don't worry! I hope you do great on your finals, goodluck<3.

[tex]a * 10^{b}[/tex]

Variable A represents a number thats absolute value has to be greater than or equal to 1 and less than 10. This is represented below

1 ≤ | a | < 10

Therefore we know that 780,000 will be 7.8, because it is greater than 1 and less than 10 as well can still represent our original number.

[tex]7.8 * 10^b[/tex]

Assuming you know how powers work, if not I'll go over them very quickly.

For example 8² = 8 * 8, 8³ = 8 * 8 * 8.

what I mean by this is if its in, tenths, hundreths, thousands, 10 thousands..

It's pretty obvious that our number is in the 100 thousands place.

Now if you know you're powers pretty well, this will be easy, although let me try to walk you through it if not.

remember the equation:

[tex]7.8 * 10^b[/tex]

We are trying to find b.

10 to what power is equal to 100,000

[tex]10^{1} = 10, 10^{2} = 100, 10^3 = 100, 10^{3} = 1,000, 10^4 = 10,000, 10^5 = 100,000[/tex]

How I like to remember what a power equals is counting the 0's :)

How we know if our answer is correct is plugging it into our equation and solve:

[tex]7.8 * 10^5[/tex]

We know that 10 to the power of 5 equals 100,000.

[tex]7.8 * 100,000[/tex]

and using a calculator, or mental math, or doing it the old fashion way, we know that 7.8 * 100,000 is equal to 780,000

Answer:

The answer is option C

Step-by-step explanation:

The solution is in the image

Answer:

1/2 - 1/8= 4/8 - 1/8= 3/8

Step-by-step explanation:

hope this helps

Answer:

8 times larger than original

Step-by-step explanation:

the volume (V) of a sphere is calculated as

V = [tex]\frac{4}{3}[/tex]πr³

when r = 2 , then

V = [tex]\frac{4}{3}[/tex]π × 2³ = [tex]\frac{4}{3}[/tex]π × 8

when r is doubled , that is r = 4 , then

V = [tex]\frac{4}{3}[/tex]π × 4³ = [tex]\frac{4}{3}[/tex]π × 64

64 is 8 times larger than 8

then new sphere is 8 times larger than original sphere

Answer:

8 times

Step-by-step explanation:

Answer: [tex]\frac{7}{16}[/tex]

Step-by-step explanation: Distance to school = [tex]\frac{7}{10}[/tex] mile

Distance covered = [tex]\frac{5}{8}[/tex] of [tex]\frac{7}{10}[/tex]

                      = [tex]\frac{5}{8}[/tex] x [tex]\frac{7}{10}[/tex]

                       = [tex]\frac{35}{80}[/tex]

                      = [tex]\frac{7}{16}[/tex]

The equation of the circle is given as (x-h)² + (y-k)² = r². Then the value of y will be ± √5/3.

A circle can be characterized by its center's location and its radius's length.

Let the center of the considered circle be at (h, k) coordinate.

Let the radius of the circle be 'r' units.

Then, the equation of that circle would be:

(x-h)² + (y-k)² = r²

The equation of the circle has the center at the origin and the radius is one unit. Then we have

x² + y² = 1

The point P = (-2/3, y) lies on the unit circle. Then the value of y will be

(-2/3)² + y² = 1

y² = 1 - 4/9

y² = 5/9

y = ± √5 / 9

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Travis cuts 125 whole 2/5 inches wide strip if the percent of error was 10% the actual length of the strips he needs to cut was 114 inches

It is defined as the ratio of two numbers expressed in the fraction of 100 parts. It is the measure to compare two data, the % sign is used to express the percentage.

We have:

The length Travis needs to cut = 114 inches

Percent of error = 10%

Let's assume he cuts x inches wide strip

So from the percent of error formula:

[tex]\rm \dfrac{x-114}{114} = \dfrac{10}{100}[/tex]

[tex]\rm x = \dfrac{114}{10}+114[/tex]

[tex]\rm x = \dfrac{1254}{10}\Rightarrow \dfrac {627}{5}[/tex]  or

[tex]\rm x = 125\dfrac{2}{5} \ inches[/tex]  

Thus, Travis cuts 125 whole 2/5 inches wide strip if the percent of error was 10% the actual length of the strips he needs to cut was 114 inches

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Answer:

it’s 1 3/8 I don’t know what dude it’s talking about

Step-by-step explanation:

Answer:

240

Step-by-step explanation:

see photo for solution

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

Let's solve ~

[tex]\qquad \sf  \dashrightarrow \: \dfrac{3 {x}^{2} y {}^{ - 1}}{27x {}^{ - 3} {y}^{8} } [/tex]

Now, let's get the common terms out :

[tex]\qquad \sf  \dashrightarrow \: \dfrac{3 {x}^{2} y {}^{ - 1}}{3 {x}^{2} {y}^{ - 1}(9 {x}^{ - 5} {y}^{9} )} [/tex]

cancel out the common terms in numerator and denominator

[tex]\qquad \sf  \dashrightarrow \: \dfrac{1}{9 x {}^{ - 5} {y}^{9} } [/tex]

[tex]\qquad \sf  \dashrightarrow \: \dfrac{ {x}^{5} }{9 {}^{ } {y}^{9} } [/tex]

So, the correct choice is C

Answer: 68850

Step-by-step explanation:

interest = 765000(3/100x3)

= 68850

if your finding total cost add 765000 + 68850 = 833850

Divide through the limand by the highest power of t :

[tex]\displaystyle \lim_{t\to\infty} \frac{t^3-t+2}{(2t-1)(t^2+t+1)} = \lim_{t\to\infty} \frac{1 - \frac1{t^2} + \frac2{t^3}}{\left(2-\frac1t\right) \left(1+\frac1t + \frac1{t^2}\right)}[/tex]

(I distributed 1/t³ in the denominator as 1/t (2t - 1) and 1/t² (t² + t + 1).)

As to goes to infinity, these 1/tⁿ terms will converge to 0, and you're left with

[tex]\displaystyle \lim_{t\to\infty} \frac{1 - \frac1{t^2} + \frac2{t^3}}{\left(2-\frac1t\right) \left(1+\frac1t + \frac1{t^2}\right)} = \frac{1 - 0 + 0}{(2-0)(1+0+0)} = \boxed{\frac12}[/tex]

The rate of change of the linear function whose graph passes through points (-5, -2) and (-2, 6) is: 2.7.

The rate of change of a linear function is given as change in y over change in x.

Given the points:

(-5, -2) and (-2, 6)

Change in y = 6 -(-2) = 8 units

Change in x = -2 -(-5) = 3 units

Rate of change = 8/3 = 2.7.

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Answer:

Based on hint and given formula, we can complete the problem. The question asks for square feet of grass so we know that we are solving for the area, A. It also tells us the height (looking downward) of the field is 75 ft,h, while the two bases are 125 ft and 81 ft (b1 and b2). So we can solve the equation. A = 75((125+81)/2) A = 75(206/2) A = 75(103) A = 7725 The area of the field is 7725 square feet.

Step-by-step explanation:

The equivalent equations of the trapezoid are:

h = 2A / (b₁ + b₂)

b₁ = 2A / h - b₂

b₂ = 2A / h - b₁

A = (b₁ + b₂) x h / 2

It is a quadrilateral that has one pair of parallel sides and a height.

The area is calculated as 1/2 x the sum of the parallel sides x height.

Examples:

Area of a trapezium that has the parallel sides as 3 cm and 4 cm and a heght o 5 cm.

Area = 1/2 x (3 + 4) x 5

Area = 1/2 x 7 x 5

Area = 35/2 = 17.5 cm^2

We have,

The formula for the area of a trapezoid can be rearranged in different ways to express the same relationship between the height, the bases, and the area.

Here are a few equivalent equations:

h = 2A / (b₁ + b₂) (solve for h)

b₁ = 2A / h - b₂ (solve for b₁)

b₂ = 2A / h - b₁ (solve for b₂)

A = (b₁ + b₂) x h / 2 (multiply both sides by 2 and divide by h)

These equations can be used interchangeably to calculate the area, height, or base of a trapezoid, depending on which variables are known or given.

Thus,

The equivalent equations are:

h = 2A / (b₁ + b₂)

b₁ = 2A / h - b₂

b₂ = 2A / h - b₁

A = (b₁ + b₂) x h / 2

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Explanation:

The diameter is 64 yards

Divide it in half to get 64/2 = 32 yards as the radius.

Plug it into the formula below to get the area of the circle.

A = pi*r^2

A = 3.14*32^2

A = 3215.36

The area of the circle is approximately 3215.36 square yards.

The area is approximate since pi = 3.14 is approximate.

Answer:

they are congruent

Step-by-step explanation:

b because a same size