Select the correct answer.
Consider the piecewise function shown on the graph.
Over which interval of the domain does the graph represent an exponential function?

A. x ≥ 6

B. -3 ≤ x ≤6

C. x ≥ 1

D. -4 < x ≤ 1

[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:

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:

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:

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

Answer:

240

Step-by-step explanation:

see photo for solution

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,

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.

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 probability that exactly four of the students were been born on a weekday (i.e. Monday through Friday) is 0.2125.

To determine the probability, we need to first find the probability of having a student being born on a weekday.

[tex]=\mathbf{\dfrac{5}{7}}[/tex]

The probability of having 4 students born on a weekday is:

[tex]=\mathbf{(\dfrac{5}{7})^4}[/tex]

Since we have 4 students, we also need to find the probability of the students that are not being born, which is:

[tex]=\mathbf{(\dfrac{2}{7})^3}[/tex]

Also, there are [tex](^7_4)[/tex] = 35 ways to get four students out of seven students.

Therefore, we have the probability as:

[tex]\mathbf{P = 35 \times (\dfrac{5}{7})^4 \times (\dfrac{2}{7})^3}[/tex]

P = 0.2125  

Therefore, we can conclude that the probability that exactly four of the students were born on a weekday is 0.2125.

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Answer:

[tex]\boxed{\sf x = 11.57}[/tex]

Step-by-step explanation:

[tex] \sf {x}^{2} = {3.6}^{2} + {11}^{2} [/tex]

Calculate 3.6 to the power of 2 to get 12.96, and 11 to the power of 2 which will give you 121.

[tex] \sf {x}^{2} = 12.96 + 121[/tex]

Add 12.96 and 121.

[tex]\sf {x}^{2} = 133.96[/tex]

Now, we'll take the square root of both sides of the equation.

[tex] \sf \sqrt{ {x}^{2} } = \sqrt{133.96} [/tex]

[tex]\sf x = 11.57[/tex]

Answer:

they are congruent

Step-by-step explanation:

b because a same size

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

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

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: [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 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:

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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Answer:

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

Step-by-step explanation:

hope this helps

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!

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

The height of the cylinder is 19 meters if the volume of 475pie cubic meters and the radius is 5 meters.

In geometry, it is defined as the three-dimensional shape having two circular shapes at a distance called the height of the cylinder.

We know the volume of the cylinder is given by:

[tex]\rm V = \pi r^2 h[/tex]

We have a volume of the cylinder:

V = 475π cubic meter

The radius r = 5 meters

475π = π(5)²h

h = 19 meters

Thus, the height of the cylinder is 19 meters if the volume of 475pie cubic meters and the radius is 5 meters.

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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:

See below ~

Step-by-step explanation:

Kindly note the 2nd equation in the above question formed will be :

2x + 4y = 20

The plotted graph is correct and it shows that the intersection of the lines (the solution) is at (2, 6), which means :

Answer:

1. x=37

2. x= 50

Step-by-step explanation:

Add up the two angles you already have, 43+100 and then subtract from 180.

180-143= 37

Do the same thing for number 2.

Add up 99+31, which is 130

The subtract from 180

180-130=50

The equation for triangles is x + (the angle measures) = 180

Hope this helps <3

Answer:

more than what i have

Step-by-step explanation:

Answer:

polynomial

Step-by-step explanation:

because poly=more than 1

mono=1

bi= 2

tri=3