What is the surface area of a cone that has a radius of 8 feet and a slant height of 12 feet? (Use 3.14 for π.)

301.44 ft 2

502.4 ft 2

200.96 ft 2

803.84 ft 2

​

Answer:

The exponential function is [tex]C(t)=y(b)^t\ Or\ C(t)=1800(1.15)^1[/tex]

Step-by-step explanation:

Given

[tex]t[/tex] be the number of hours.

[tex]y[/tex] number of bacteria cells.

And we know that an exponential function is [tex]C(t)=y(b)^t[/tex],where [tex]b[/tex] is a positive real number, and in which the argument [tex]t[/tex] occurs as an exponent

The petri dish has [tex]1800[/tex] bacteria cells we can say that [tex]y=1800[/tex]

In the equation as [tex]C[/tex] is function of  time and [tex](t)[/tex] will vary as [tex]1,2,3[/tex] for respective hours.

To find the value of [tex]b[/tex] we have to understand that it is dependent on percent increase if there is increment of [tex]15\%[/tex] then [tex]b=1+15\%=1+\frac{15}{100}=1+0.15=1.15[/tex]

So the exponential function will be [tex]C(t)=y(b)^t[/tex] ,plugging the values it will be equivalent to [tex]C(t)=1800(1+0.15)^1[/tex]

Check:

[tex]15\% of 1800 =0.15\times 1800=270[/tex]

So in first hour the cells will increased by a quantity of [tex]270[/tex] cells.

The number of cells after an hour in the petri dish [tex]=(1800+270)=2070[/tex]

That can also be from the formula.

[tex]C(t)=1800(1.15)^1=2070[/tex]

So the exponential function is [tex]C(t)=y(b)^t\ Or\ C(t)=1800(1.15)^1[/tex]

[tex]y[/tex] will increase exponentially as the value of [tex]t[/tex] increase.

Final answer:

The exponential function to represent the growth of bacteria cells, y, after t hours with an initial amount of 1800 cells and a 15% hourly growth rate is y = 1800(1 + 0.15)^t.

Explanation:

To write an exponential function showing the relationship between the number of bacteria cells, y, and the time in hours, t, we begin by using the initial value of 1800 bacteria cells and apply a 15% increase each hour. The exponential growth formula is given by y = P(1 + r)^t, where P is the initial amount, r is the growth rate (expressed as a decimal), and t is the time.

Since the growth rate is 15%, we convert this to a decimal by dividing by 100, resulting in 0.15. The formula to model this bacterial growth would be y = 1800(1 + 0.15)^t. Therefore, for any given number of hours t, you can calculate the number of bacteria cells y.

Answer:

x=0

Step-by-step explanation:

4(x+1)=2x+4

4x+4=2x+4

4x-2x+4=4

2x+4=4

2x=4-4

2x=0

x=0/2

x=0

Answer:

yes it's a solution

Step-by-step explanation:

the guy before me explained it well

Answer:

6

Step-by-step explanation:

4 divided by 2/3 is 6, because 4 x 2 = 8, and 8/3 is 6.

Answer:

The two numbers are -419 and -2095.

Step-by-step explanation:

5x=y

x-y=1676

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

x-5x=1676

-4x=1676

x=1676/-4

x=-419

5(-419)=y

y=-2095

Answer:

4000

Step-by-step explanation:

Answer: 4,000.

Hope this helps!

By proving that triangles DEA and EFB are congruent due to the Side-Angle-Side postulate and demonstrating that AE is parallel to FB as well as AD parallel to BC, we can conclude that EABC is a parallelogram.

To prove that quadrilateral EABC is a parallelogram, we can use the properties of triangles and the definition of a parallelogram. According to the given information, E is the midpoint of DA and F is the midpoint of DB. Additionally, we know that E, F, and C are collinear and that FC is congruent to EF.

Leveraging these pieces of information, we observe that triangle DEA is congruent to triangle EFB because they have a side (EF or DE), an angle (at point E, since DE is an extension of EF), and another side (EA or FB, which are halves of DA and DB, respectively) in common (Side-Angle-Side postulate).

Since the two triangles are congruent, angle DEA is congruent to angle EFB, and angle DAE is congruent to angle FEB. These congruent angles imply that line AE is parallel to line BF. Since E and F are midpoints, AE is half of DA and BF is half of DB. If we continue the line AE to meet CD at point A and the line BF to meet CD at point B, EA will be parallel to FB, and AD will be parallel to BC, meeting the definition of a parallelogram.

EABC is a parallelogram because opposite sides are parallel and equal due to the Midpoint Theorem.

Given:

E - midpoint of DA

F - midpoint of DB

E, F, C collinear, FC ≅ EF

To Prove: EABC is a parallelogram.

Proof:

1. By the Midpoint Theorem, EF || AB and EF = 1/2 * AB. (Midpoint Theorem)

2. Since E, F, C are collinear and FC ≅ EF, EC bisects EF at C. Therefore, AB || EC. (Definition of a parallelogram)

3. Since E is the midpoint of DA and C is the midpoint of EF, EC = 1/2 * DA. Since DA = AB, EC = 1/2 * AB. Similarly, EF = 1/2 * AB. Hence, EC = EF. Therefore, EA || BC. (Midpoint Theorem)

4. Since E is the midpoint of DA and C is the midpoint of EF, EC = 1/2 * DA. Since DA = BC, EC = 1/2 * BC. Similarly, EF = 1/2 * BC. Hence, EC = EF. Therefore, EB ≅ AC. (Midpoint Theorem)

Therefore, EABC is a parallelogram.

Answer:20592

Step-by-step explanation:

Because you multiply 5 times 2288

Leo has 2574 red marbles.

Let's say that the number of blue marbles Leo has is x. According to the given information, Leo has 9 times as many red marbles as blue marbles. So the number of red marbles Leo has is 9x.

It is also given that he has 2288 more red marbles than blue marbles, which means 9x = x + 2288.

Simplifying the equation, we can subtract x from both sides: 8x = 2288. Dividing both sides by 8, we find that x = 286.

Therefore, Leo has 9 times 286 red marbles, which equals 2574 red marbles.

Answer:

$240

Step-by-step explanation:

The amount in the account after 3 years will be 16171.45701

What is a deposit?

It is a financial term that means money held at bank. It is a sum of  money which you pay when you start renting something. The deposit is a money which we put in our bank account. It is made for funds and we can withdraw that money anytime. If you take a loan the money can be deposited is in the form of collateral amount. Demand and time are two types of deposits made by businesses or individuals. The amount of money that is paid to an account is known as deposit. The sum of money that is given in advance as a part of a total payment is termed as deposit. It is a transaction involving the transfer of money to a bank account. It is an another way for safekeeping.

Given p=periodic payment=$100/week

r= interest rate=2.4%, compounded weekly

t=3 years

n=52 weeks

b= future value= P([tex](1+r/n)^{nt}[/tex]-1)/(r/n)

=100([tex](1+2.4/5200)^{156}[/tex]-1)/(2.4/100×52)

=16171.45701

After 3 years the amount in the account will be 16171.45701.

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The number of people who can still have a hot dog is 82 people

Given:

Total hot dogs bought = 8 dozens

Total hot dogs bought = 8 × 12

= 96

Number of hot dogs his pet ate = 14

Number of guests who are hotdog = Total hot dogs bought - Number of hot dogs his pet ate

= 96 - 14

= 82

Therefore, the number of people who can still have a hot dog is 82 people

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Answer:

Three zeros [tex]x=-4,\ x=1,\ x=6[/tex]

x-intercepts: (-4,0), (1,0), (6,0)

Step-by-step explanation:

Plot the graph of the function [tex]y=x^3-3x^2-22x+24[/tex] on the coordinate plane. This graph intersects the x-axis at three different points (see attached diagram):

This means [tex]x=-4,\ x=1,\ x=6[/tex] are zeros of the function [tex]y=x^3-3x^2-22x+24[/tex]

Answer:

D

because i think

Answer:

C. Sea level

zero represent in this situation is Sea level.

Integers come in three types:

Given:

An eagle is flying 30 feet above sea level = +30 feet

and, spots a fish swimming 2 feet below sea level. = -2 feet

So, using integers the zero represent the Sea Surface,

Hence, zero represent in this situation is Sea level.

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Answer:

-2y+6 or -2(y-3)

Step-by-step explanation:

-3y+6+y=-2y+6

Answer:

13.406

The drawing will help

Answer:

13.406

Step-by-step explanation:

Answer: In general, a solution of a system in two variables is an ordered pair that makes BOTH equations true. In other words, it is where the two graphs intersect, what they have in common. So if an ordered pair is a solution to one equation, but not the other, then it is NOT a solution to the system

Answer:

B.6 inches

Step-by-step explanation:

Given: Three boards with measurement  24, 36, and 42 inches.

For the longest length of board we have to find out the H.C.F.

And for H.C.F. we will find out the factors,

[tex]24=2\times2\times2\times3\\36=2\times2\times3\times3\\42=2\times3\times7[/tex]

Here 2 and 3 is the common factor of given length of boards.

So the H.C.F. is 6.

Hence the longest length of board that carpenter can cut is 6 inches.

Answer:

4/9

Step-by-step explanation:

(4/9)/(7/9) is equal to (4/9)*(9/7) because "keep change flip." So we keep the first number, change division into multiplication, and flip 4/9 (basically find the reciprocal) and that is 9/4. Thus,  (4/9)*(9/7) is equal to 4/9 because the 7's cancel.

I hope this helped!

Answer: 4/7

Step-by-step explanation: In this problem, we have 4/9 ÷ 7/9. Dividing by a fraction is the same as multiplying by its reciprocal. In other words, we can change the division to multiplication and flip the second fraction.

So here, 4/9 divided by 7/9 can be rewritten as 4/9 × 9/7.

Now we are simply multiplying fractions.

To multiply fractions, we multiply across the numerators and multiply across the denominators.

Image provided.

Notice however that 36/63 is not in lowest terms so we divide both the numerator and denominator by 9 and we get the equivalent fraction 4/7.

Therefore, 4/9 divided by 7/9 = 4/7.    

Answer:

Step-by-step explanation:

The formula of a distance between two points:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

We have two points (-4, -4) and (-1, 0).

Substitute:

[tex]d=\sqrt{(-1-(-4))^2+(0-(-4))^2}=\sqrt{(-1+4)^2+(0+4)^2}\\\\=\sqrt{3^2+4^2}=\sqrt{9+16}=\sqrt{25}=5[/tex]

F(n) = 5n

You are being told n is the number of tables, and there are 15 tables:

f(15) = 5(15)

F(n) = 75

You need 75 candles.

Answer:

C) y+6=3/2(x-2)

Step-by-step explanation:

y-y1=m(x-x1)

m=slope & (x1, y1) is a point on the line

m=(y2-y1)/(x2-x1)

m=(-3-(-6))/(4-2)

m=(-3+6)/2

m=3/2

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

y+6=3/2(x-2)

Option 3

The point slope form of the given points (2, -6) and (4, -3) is [tex]y+6=\frac{3}{2}(x-2)[/tex]

Given that two points are (2, -6) and (4, -3)

We have to find the point slope form

The point-slope of the line is given as:

[tex]y - y_1 = m(x - x_1)[/tex]

Where m is the slope of the given line.

So now to write the given points in point intercept form we need to find the slope, m

The slope of line is given as:

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

[tex]\text { Here } x_{1}=2 ; y_{1}=-6 ; x_{2}=4 ; y_{2}=-3[/tex]

Plugging in the values, we get

[tex]m=\frac{-3-(-6)}{4-2}=\frac{3}{2}[/tex]

So, the slope of the given line is [tex]\frac{3}{2}[/tex]

Now, we need to find the point slope form. For that purpose we can use either of the points, but since in the answer options they have used the 1st point we will do so too.

Therefore, the point slope form is:

[tex]\begin{array}{l}{y-(-6)=\frac{3}{2}(x-2)} \\\\ {y+6=\frac{3}{2}(x-2)}\end{array}[/tex]

From the given options we can see that the correct answer is option 3.

Answer:

63 miles left

Step-by-step explanation:

253+157=410

473-410=63

Answer:

11 yards

Step-by-step explanation:

The volume of a cone formula is:

[tex]V=\frac{1}{3}\pi r^2 h[/tex]

Where V is the volume,

r is the radius (half of diameter)

h is the height

Given,

h = 15

V = 475.17

We find the radius (r) first by substituting given values:

[tex]V=\frac{1}{3}\pi r^2 h\\475.17=\frac{1}{3}\pi r^2 (15)\\475.17=5\pi r^2\\r^2=30.25\\r=5.5[/tex]

The radius (r) is 5.5 yards

We need the diameter, which is DOUBLE THE RADIUS, so diameter would be:

Diameter = 5.5 * 2 = 11 yards

Answer:

A. x + 4

Step-by-step explanation:

f(x) = 4x⁴ − 21x³ − 46x² + 219x + 180

Plug in the zero of each binomial.  If it's also a zero of f(x), then that binomial is a factor of f(x).

f(-4) = 936

f(-3) = 0

f(5) = 0

f(-3/4) = 0

The binomial (x + 4) is not the factor of the polynomial. Then the correct option is A.

The algebraic factors with exactly two terms are known as binomial components. Although binomials are simple to solve and their roots are identical to those of polynomials, binomial factors are intriguing.

The polynomial is given below.

⇒ 4x⁴ – 21x³ – 46x² + 219x + 180

Let's check all the factors.

If the factor does not satisfy the polynomial, then the binomial is a factor of the polynomial.

For x + 4 = 0, then we have

The value of the polynomial at x = -4, will be

⇒ 4(-4)⁴ – 21(-4)³ – 46(-4)² + 219(-4) + 180

⇒ 4(256) – 21(-64) – 46(16) + 219(-4) + 180

⇒ 1024 + 1344 – 736 – 876 + 180

⇒ 2548 – 1612

⇒ 936

Thus, the binomial (x + 4) is not the factor of the polynomial.

Then the correct option is A.

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Answer:

the solution is, x=2

Step-by-step explanation:

we have

y= 3x

y=2x+2

so we can write,

3x=2x+2

3x-2x=2

x=2

Dustin spends $13.6125 on going to work daily. It is 0.11 dollars per mile

Step-by-step explanation:

we have to caalculate the distance between Dustin's home and work

So

Given

Speed =s = 55 miles per hour

Time = t = 2 hours and 15 minutes

Converting time into fraction

Time = 2.25 hours

We know that

[tex]s = \frac{d}{t}\\d = s * t\\d = 55 * 2.25\\d = 123.75\ miles[/tex]

So the distance is 123.75 miles

The car travels 25 miles per gallon

We have to calculate the total number of gallon first

So,

[tex]No.\ of\ gallons = \frac{Miles}{Miles\ per\ gallon}\\=\frac{123.75}{25}\\=4.95\ gallons[/tex]

So the total amount is:

[tex]2.75*4.95\\= 13.6125\ dollars[/tex]

Total amount is $13.6125. Dividing it by total distance will give us the cost of each mile

So,[tex]Cost\ of\ mile = \frac{Total\ amount}{Distance}\\= \frac{13.6125}{123.75}\\=0.11\ dollars[/tex]

Hence,

Dustin spends $13.6125 on going to work daily. It is 0.11 dollars per mile

Keywords: Speed, Distance

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Answer:

A

Step-by-step explanation:

It's A because in order to have an equation, you need a equal sign and a variable and an expression is a base of algebra and i see your in middle school and have you ever seen a inequality sign in a algebraic expression?

An inequality sign is not part of an algebraic equation

Option A

Explanation :

Any algebraic equation will have an equal sign

For example , Algebraic equation is

[tex]y=3x+2[/tex]

This algebraic equation have = sign

The above algebraic equation have expression 3x+2

Also the above algebraic equation have variable 'x'  and 'y'

So , an algebraic equation have = sign , variables and expression

If we have inequality sign then we call it as inequality not an equation

An inequality sign is not part of an algebraic equation

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Answer:

-12 feet per second

Step-by-step explanation:

average rate of change over [0.75, 1.25] = [tex]\frac{f(1.25) - f(0.75)}{1.25 - 0.75}[/tex]

f(1.25) - f(0.75) = 4 - 10 = -6

1.25 - 0.75 = 0.5

[tex]\frac{f(1.25) - f(0.75)}{1.25 - 0.75}[/tex] = [tex]\frac{-6}{0.5}[/tex] = -12

The average rate of change of the function f(t) over the interval [0.75, 1.25] is -12 feet per second.

We have,

To find the average rate of change of the function f(t) over the interval [0.75, 1.25], you can use the following formula:

Average Rate of Change = [f(1.25) - f(0.75)] / (1.25 - 0.75)

Calculate f(1.25):

f(1.25) = -16(1.25)^2 + 20(1.25) + 4

Calculate f(0.75):

f(0.75) = -16(0.75)^2 + 20(0.75) + 4

Plug these values into the formula:

Average Rate of Change = [f(1.25) - f(0.75)] / (1.25 - 0.75)

Calculate the numerator:

Average Rate of Change = [(-16(1.25)^2 + 20(1.25) + 4) - (-16(0.75)^2 + 20(0.75) + 4)] / (1.25 - 0.75)

Simplify the numerator:

Average Rate of Change = [-25 + 25 + 4 - (-9 + 15 + 4)] / (1.25 - 0.75)

Further, simplify:

Average Rate of Change = (4 - (-9 + 15 + 4)) / (1.25 - 0.75)

Continue simplifying:

Average Rate of Change = (4 - 10) / (1.25 - 0.75)

Calculate the final result:

Average Rate of Change = (-6) / (0.5)

Average Rate of Change = -12 feet per second

Thus,

The average rate of change of the function f(t) over the interval [0.75, 1.25] is -12 feet per second.

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Answer:

Katherine invested $12,000

Step-by-step explanation:

Use formula

[tex]I=P\cdot r\cdot t,[/tex]

where

I = interest,

P = principal,

r = rate (as decimal),

t = time (in years).

In your case,

t = 1 year,

r = 0.06 (or 6%)

P + I =$12,720, thus

[tex]12,720-P=P\cdot 0.06\cdot 1\\ \\12,720-P=0.06P\\ \\12,720=P+0.06P\\ \\1.06P=12,720\\ \\P=\dfrac{12,720}{1.06}\\ \\P=\$12,000\\ \\I=\$12,720-\$12,000=\$720[/tex]

The price of less expensive equipment is $1575.

Step-by-step explanation:

Let,

Price of one equipment = x

Price of other equipment = y

According to given statement;

x+y=4000   Eqn 1

x = y+850    Eqn 2

Putting Eqn 2 in Eqn 1

[tex](y+850)+y=4000\\y+850+y=4000\\2y=4000-850\\2y=3150[/tex]

Dividing both sides by 2;

[tex]\frac{2y}{2}=\frac{3150}{2}\\y=1575[/tex]

Putting y=1575 in Eqn 2;

[tex]x=1575+850\\x=2425[/tex]

The price of less expensive equipment is $1575.

Keywords: linear equation, substitution method

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Final answer:

The price of the less expensive piece of equipment is $1575. This was calculated by setting up an equation based on the total cost and the difference in price between the two pieces of equipment and then solving for the unknown price.

Explanation:

To find the price of the less expensive piece of equipment, we will first assign variables to the two pieces of equipment. Let's call the cost of the less expensive piece of equipment x dollars. Since the other piece cost $850 more, the cost of the second piece would then be x + $850. We are given that the total cost of both pieces is $4000, so we can set up the following equation to represent this relationship:

x + (x + $850) = $4000

To solve for x, we combine like terms and get:

2x + $850 = $4000

Subtracting $850 from both sides gives us:

2x = $3150

Dividing both sides by 2, we find the value of x:

x = $1575

Therefore, the price of the less expensive piece of equipment is $1575.