Carmen enters a painting in an art contest. The contest rules say that all paintings must be rectangular, with an area no greater that 3,003.04 cm2. Carmen painting is 16 cm wode. What is the greatest lenth the painting can have and still have an area within the contest rules?

Answer:

The even functions are options 2, 3, and 5

Step-by-step explanation:

Please, see the attached file.

Thanks.

Answer:

The rate of change of water in the pool is 400 gallons / hour

Step-by-step explanation:

We are given

At 6:00 AM:

there were 400 gallons of water in the pool

so,

[tex]N_1=400[/tex]

At 11:00 AM:

there were 2400 gallons of water in the pool

so,

[tex]N_2=2400[/tex]

now, we can find time between

t=11-6=5 hours

now, we can use formula

rate of change of water in pool is

=( change in water quantity)/( total time)

so, we get

[tex]=\frac{N_2-N_1}{t}[/tex]

now, we can plug values

[tex]=\frac{2400-400}{5}[/tex]

[tex]=\frac{2000}{5}[/tex]

[tex]=400[/tex]

So,

The rate of change of water in the pool is 400 gallons / hour

Answer:

49

Step-by-step explanation:

7^x

If x=2

7^2

49

Answer:

B. y = -1/2x

Step-by-step explanation:

Because the answer is in point-slope intercept form, we know -1/2 is m. Also, because the equation is setting y equal to x, we know it goes through the origin.

Answer:

The number of letters in the one street be 220 .

Step-by-step explanation:

As given

A postman has to deliver 450 letters .

The number of letters delivered in one street is twice the number delivered in other .

Let us assume that the number of letters delivered in second street be x.

Let us assume that the number of letters delivered in first street = 2x

As given

If he is left with 120 letters .

Thus

The number of letter delivered in one and other street  = 450 - 120

                                                                                            = 330

Than the equation becomes

x + 2x = 330

3x = 330

[tex]x = \frac{330}{3}[/tex]

x = 110

The number of letters in the one street = 2 × 110

                                                                  = 220

Therefore the number of letters delivered in first street be 220.

The postman delivered 110 letters to the first street and 220 letters to the second street

This is a problem of simple algebra where you have to solve for unknowns. We know the postman has 450 letters in total, and 120 are left after delivering to two streets. So, the total number of letters he delivered is 450 - 120 = 330 letters.

Let’s say the number of letters delivered in one street is x. Therefore, the number of letters delivered in the other street would be 2x because it's twice the number delivered in the first street.

Since the postman delivered all 330 letters in two streets, the equation becomes x + 2x = 330. Simplifying this we get 3x = 330. Then, solve for x by dividing both sides by 3, so x = 330 / 3 = 110.

Therefore, the number of letters delivered in the first street is x = 110, and in the second street it's 2x = 2*110 = 220.

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Ok so first of all, Why does rob need a mp3 player? we are in the new age, right?

Secondly, I will answer your question :P

Ok so we have some info here .... we know that Rob earns $15 and saves $6

We can assume that Rob earning's equation would be y = 15x-6x

We are also given that he earned $75 (My gosh Rob nice work man!)

we would plug in 75 for y >>>for now forget the fact that Rob saves<<<

Divide 75 by 15 which = 5

Now multiply 6 by 5 which = 30 (AnSWERR!)

We now also know that out of what Rob earned he used or donated to charity $75-30 = $ 45

We can double check our work here real quick

[tex]45=15x-6x\\45=(15*5)-(6*5)\\45= 75 - 30 \\45 = 45  true[/tex]

When x = 2, the expression evaluates to -442/3.

To evaluate the expression when x = 2, we substitute 2 for x in the expression:

x + 4/(3x) - 150

Now, we plug in the value of x:

2 + 4/(3 * 2) - 150

First, we simplify the denominator:

2 + 4/6 - 150

Now, simplify the fraction:

2 + 2/3 - 150

Next, we need to find a common denominator, which in this case is 3:

(3 * 2)/3 + 2/3 - 150

Now, add the fractions with the common denominator:

(6/3) + (2/3) - 150

Combine the fractions:

(6 + 2)/3 - 150

Now, perform the addition in the numerator:

8/3 - 150

To subtract a fraction from a whole number, we need a common denominator. In this case, it's 3:

(8/3) - (150 * 3/3)

Now, subtract:

8/3 - 450/3

Subtract the numerators:

(8 - 450)/3

Now, perform the subtraction in the numerator:

-442/3

So, when x = 2, the value of the expression x + 4/(3x) - 150 is -442/3.

To learn more about expression

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Answer:

B) 0.85

Step-by-step explanation:

By definition, complementary angles add to 90 degrees.

The given angle 58 degrees is complementary to 90-58 = 32 degrees. The two angles 58 and 32 add to 90.

Therefore, cos(32) = 0.848 = 0.85

The complementary angle to 58° is 42° and the cosine value of 42° is 0.74.

Given: angle 58°.

let the angle complementary to 58° be x.

By the definition of complementary angles, we can write:

⇒ x + 58° = 90°

⇒ x = 90° - 58°

⇒ x = 42°

Therefore, the angle complementary to 58° is 42°.

Now, we have to find the cosine value of 42°.

⇒ cos (42°) = 0.74

Therefore, the cosine value of 42° that is the complementary angle to 58° is 0.74.

Hence, the best answer will be option (A).

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Final answer:

40 child tickets and 95 adult tickets were sold.

Explanation:

Let's assume the number of child tickets sold is x.

According to the problem, the number of adult tickets sold is 15 more than twice the number of child tickets. So the number of adult tickets sold is 2x + 15.

The total income from ticket sales is $1,340. The income from child tickets is $5 times the number of child tickets and the income from adult tickets is $12 times the number of adult tickets.

Therefore, we can express the total income as the sum of the income from child tickets and adult tickets:

$5x + $12(2x + 15) = $1,340

Simplifying the equation:

$5x + $24x + $180 = $1,340

$29x = $1,340 - $180

$29x = $1,160

Dividing both sides by 29:

x = $1,160/$29

x = 40

So, the number of child tickets sold is 40, and the number of adult tickets sold is 2x + 15 = 2(40) + 15 = 80 + 15 = 95.

Therefore, 40 child tickets and 95 adult tickets were sold.

The total cost of the meal is $8. A 15% tip on this amount is $1.20.

The total cost of the meal is the cost of the cheeseburger ($5.50) plus the cost of the milkshake ($2.50), giving a total of $8. To calculate a 15% tip, we multiply the total cost by 0.15. So, JJ should leave a tip of $8 * 0.15 = $1.20.

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Answer:

A   $4025

B  $2415

C  $1610

Step-by-step explanation:

Part A

I=PRT

I = 23000* .035 * 5

 = 4025

You will pay $4025

Part B

I =PRT

= 23000 *.035 * 3

= 2415

You will pay $2415

Part C

Take the amount from Part A and subtract The amount from Part B and that is the amount you will save.

4025-2415=1610

A   $4025

B  $2415

C  $1610

Step-by-step explanation:

Part A

I=PRT

I = 23000* .035 * 5

= 4025

You will pay $4025

Part B

I =PRT

= 23000 *.035 * 3

= 2415

You will pay $2415

Part C

Take the amount from Part A and subtract The amount from Part B and that is the amount you will save.

4025-2415=1610

I'm really sorry that I took a long time. I got carried away. Hopefully my work was correct though.

A= about 354 square feet~ (rounded)

The stage can be split into two shapes. The first is a trapezoid and the formula to find the area for it would be A=(b₁+b₂)/2 and then multiple by the height. b₁ would be 17 and b₂ is 20 and the height is 13. 17+20 is 37. 37/2 is 18.5. 18.5 times 13 is 240.5. Area of the trapezoid is 240.5 square feet. Then we need to find the area of the semicircle. The formula is A=(πr²)2. r is the radius which is half of the diameter. The diameter is 17 so the radius is 8.5. π is about 3.14 if you don't have a calculator. 8.5 squared is 72.25. 72.25 times 3.14 is 226.865. 226.865/2 is 113.4325. The area of the half circle is 113.4325. Just add these two areas to get 353.9325. So I think the area is pretty much 353.9325 but might be slightly different because some values I said were rounded. Either way the answer should be similar.

I forgot you said you needed help fast and got carried away. Sorry if I wasn't fast enough and hopefully I did my math correctly.

[tex]\text{If k and l are the roots of a polynomial w(x), then}\ w(x)=a(x-k)(x-l).[/tex]

[tex](2-\sqrt3)-a\ root\ of\ a\ polynomial\\\\another\ root\ must\ be\ C.\ (2+\sqrt3),\ because\\\\\ [x-(2-\sqrt3)][x-(2+\sqrt3)]=(x-2+\sqrt3)(x-2-\sqrt3)\\\\=[(x-2)+\sqrt3][(x-2)-\sqrt3]\\\\\text{use}\ (a-b)(a+b)=a^2-b^2\\\\=(x-2)^2-(\sqrt3)^2\\\\\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\=x^2-2(x)(2)+2^2-3=x^2-4x+4-3=x^2-4x+1[/tex]

[tex]Answer:\ \boxed{C.\ (2+\sqrt3)}[/tex]

The correct answer to the question is therefore C. 2 + square root of 3.

If (2 - square root of 3) is a root of a polynomial with integer coefficients, the polynomial must have another root that is the conjugate of (2 - square root of 3), which is (2 + square root of 3). This is due to the Conjugate Root Theorem, which is a result of the fact that the coefficients of the polynomial are real numbers. When you have a non-real root in such a polynomial, its conjugate will also be a root.

The correct answer to the question is therefore C. 2 + square root of 3.

Answer: The answer to complete the sentence should be D).

Answer:

C

Step-by-step explanation:

3 times the quantity b squared  is 3b^2

Two more = 3b^2 + 2

Answer:

The zeros of a graph form the factors of the function. When we multiply the factors out and add the exponents up in the final function, we have the highest exponent known as the degree.

Step-by-step explanation:

A polynomial graph has several features we look for to determine the equations.

The rocket splashes down after 43 seconds.

The rocket peaks at 2400. meters above sea-level.

Step 1

We realise that the rocket will hit the ground when our function [tex]h(t)=0[/tex] , i.e [tex]-4.9t^2+202t+318=0.[/tex]

Step 2

Use the quadratic formula to solve for the time. For the general quadratic equation [tex]at^2+bt+c=0[/tex], the general solution to the equation is

[tex]t=\frac{-b\pm\sqrt{b^2-4ac}}{2a} .[/tex]

In our case, the quadratic equation [tex]h(t)=-4.9t^2+202t+318=0[/tex] has a solution

[tex]t=\frac{-202\pm\sqrt{202^2-4((-4.9)(318))}}{2(-4.9)} \\t=-1.52,t=42.74.[/tex]

Step 3

In this step we pick the value of [tex]t[/tex] that makes physical sense. Since the NASA team launced the rocket at [tex]t=0[/tex], the rocket reaches the bottom when [tex]t=42.74[/tex]. This can be rounded up to [tex]43[/tex] seconds.

Step 1

The first step is to realist that since the coefficient of the quadratic term is negative, the graph of this function will face downwards. From this we can gather that the maximum value of this function occurs at the vertex.

Step 2

In this step we calculate the t coordinate of the of the vertex of this function. For any quadratic equation [tex]h(t)=at^2+bt+c[/tex] , the vertex occurs when ,

[tex]t=-\frac{b}{2a}.[/tex]

For the equation [tex]h(t)=-4.9t^2+202t+318[/tex] , the vertex occurs when ,

[tex]t=-\frac{202}{2(-4.9)}=20.61.[/tex]

Step 3

We substitute the value of [tex]t[/tex] from step 2 above into [tex]h(t)[/tex] to get the maximum value of this function.  This calculation is shown below,

[tex]h(20.61)=-4.9(20.61)^2+202(20.61)+318=2399.84m.[/tex]

This can be rounded up to 2400m.

Answer:

Need the graph for final answer. Use the values of the graph to substitute into the slope formula and simplify.

Step-by-step explanation:

The average rate of change is the amount over an interval the outputs change in a ratio to the input change. In a linear function, this is constant and called slope. In all other function, it is called the average rate of change because the rate of change varies over the interval. We use the same formula for the average rate of change as we do slope. First we need both the input and output values of the function over the interval.

Slope:[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Substitute the values for your function into the slope formula and simplify.

Answer:

is there a graph

Step-by-step explanation:

Answer:

25 ounces.

Step-by-step explanation:

We have been given that a metal alloy is made by mixing 12 ounce of metal C with 13 ounce of metal D.

To find the total weight of the alloy we will add the weight of metal C and weight of metal D.

[tex]\text{The total weight of the alloy}=\text{Weight of metal C + Weight of metal D}[/tex]

[tex]\text{The total weight of the alloy}=12\text{ ounce}+13\text{ ounce}[/tex]

[tex]\text{The total weight of the alloy}=25\text{ ounce}[/tex]

Therefore, the total weight of alloy is 25 ounces.

Answer:

5/6 is your correct answer..

Step-by-step explanation:

Answer:

D) 120

Step-by-step explanation:

720- 135-115-110-140-100=120

Answer:

  y = 4x^2 -31x -8

Step-by-step explanation:

The roots tell you that (x +1/4) and (x -8) will be factors. We can eliminate the fraction by multiplying that factor by 4. Then our polynomial with integer coefficients is ...

  (4x +1)(x -8) = 4x^2 -31x -8

As an equation, this could be ...

  y = 4x^2 -31x -8

Answer: B) Adjacent interior angle

As the name implies, the angle is inside the triangle and it is adjacent (ie next to) the exterior angle. Contrast this with a remote interior angle, which is also inside the triangle, but it is not adjacent to the exterior angle in question. Alternate interior angles won't apply here because we don't have a set of parallel lines with a transversal cut.

Answer:

In 30 minutes:

The minute hand moves a distance of 25.13 inches

In 20 minutes:

The minute hand moves a distance of 16.76 inches

Step-by-step explanation:

When 60 minutes are completed, the minute hand of the relog makes a complete revolution. The distance s that the minute hand travels when making a complete revolution is:

[tex]s = 2\pi r[/tex] Where r is the radius of the circumference, and in this case, the radius of the minute hand.

So:

[tex]s = 16 \pi[/tex]

s = 50.27 inches.

In 30 minutes (which is half of 60) the minute hand covers only half a revolution. Then the distance traveled in 30 minutes is [tex]\frac{1}{2}(s) = 25.13[/tex] inches

In 20 minutes (which is one third of 60) the minute hand only travels a third of a complete revolution. Then the distance traveled in 20 minutes is [tex]\frac{1}{3}(s) = 16.76[/tex] inches

We calculate the distance traveled by the minute hand of a clock by using the arc length formula from geometry. Using the length of the hand as the radius and the angle covered as a fraction of 360 degrees (converted into radians), we can determine the distances for 30 and 20 minutes as 8π inches and 16/3 π inches respectively.

The subject of our question involves the calculation of arc lengths (distances) moved by a clock hand, an aspect of geometry. We'll be treating the minute hand of a clock as a line segment that sweeps out a circular path. The arc length formula will be utilized here, which is given by the equation L = rθ, where L is the arc length, r is the length of the minute hand (as the radius), and θ is the angle covered by the minute hand.

In a span of a whole hour or 60 minutes, the minute hand completes a full 360° circle. So, for 30 minutes, it covers half the circle which equates to 180°. This degree measure needs to be converted to radians because our formula uses radian measure. 180° equals π radians.

With r = 8 inches and θ = π, we substitute these values into our formula to get L = 8π inches for 30 minutes.

The same concept applies for 20 minutes. In this case, the hand covers a third of the circle which is (360/3)=120°, this is (2/3)π in radian. Substituting r = 8 inches and θ = (2/3)π into our formula, we get L = 16/3 π inches for 20 minutes.

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Answer:

8 sets of twenty sandwiches.

Step-by-step explanation:

first you find the answer to 3 x __ = __ lets make the answer 24. That makes the other blank 8. Now subtract 24 from 184 and you should get 160. Divide 160 by 20 and you'll get how many set the customer ordered of twenty sandwiches. Multiply by twenty and you will get the whole amount they ordered.

Answer:

Caterer males 3 extra sandwiches for every 20 sandwiches. That means Caterer makes 23 sandwiches for every 20 ordered sandwiches. Therefore is ratio form we can write it,

23:20

Now we need to check if Caterer makes total 184 sandwiches for a customer then ordered sandwiches will be,

[tex]23:20=184:x[/tex]

Where x represents the number of sandwiches ordered.

[tex]23:20=184:x\\\frac{23}{20}=\frac{184}{x}[/tex]

Now we need to solve it for x;

[tex]\frac{23}{20}=\frac{184}{x}\\x=\frac{184X20}{23}\\ x=160[/tex]

therefore ordered Sandwiches are 160.

Step-by-step explanation:

Answer: 345.9 ounces

Answer:

(A)

[tex]C_n=3+2n[/tex]

(B)

[tex]C_1_0=23[/tex]

Step-by-step explanation:

(A)

we are given

[tex]C_n_+_1=C_n+2[/tex]

[tex]C_1=5[/tex]

Firstly, we will find few terms

[tex]C_2=C_1+2[/tex]

[tex]C_2=5+2[/tex]

[tex]C_2=7[/tex]

[tex]C_3=C_2+2[/tex]

[tex]C_3=7+2[/tex]

[tex]C_3=9[/tex]

[tex]C_4=C_3+2[/tex]

[tex]C_4=9+2[/tex]

[tex]C_4=11[/tex]

so, we will get terms as

5, 7 , 9 , 11

we can see that this is arithematic sequence

First term =5

common difference =d=7-5=2

now, we can use nth term formula

[tex]C_n=C_1+(n-1)d[/tex]

now, we can plug values

[tex]C_n=5+2(n-1)[/tex]

[tex]C_n=5+2n-2[/tex]

[tex]C_n=3+2n[/tex]

(B)

we can plug n=10

[tex]C_1_0=3+2\times 10[/tex]

[tex]C_1_0=23[/tex]