In parallelogram ABCD , diagonals AC ? ? ? ? ? and BD ? ? ? ? ? intersect at point E, AE= x 2 ?16 , and CE=6x . What is AC ? Enter your answer in the box.

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: 345.9 ounces

Answer:

the answer is C

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:

  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:

D) 120

Step-by-step explanation:

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

Answer:

25 capsules.

Step-by-step explanation:

We are told that Joan has a prescription for 100 Theophylline capsules. Joan informs the pharmacist that she only has enough money to purchase ¼ of the prescription today.

To find the number of capsules that Joan will pay for today, we will find 1/4 of 100.

[tex]\text{The number of capsules that Joan will pay for today}=\frac{1}{4}\times 100[/tex]

[tex]\text{The number of capsules that Joan will pay for today}=25[/tex]

Therefore, Joan will pay for 25 capsules today.

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.

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:

-2744/405

Step-by-step explanation:

Answer:

-6 314/405

Step-by-step explanation:

( -2 1/3)^3 / (1 7/8)

I am going to change the mixed numbers to improper fractions

2 1/3 = (3*2 +1)/3 = 7/3

1 7/8 = (8*1+7)/8 = 15/8

( -7/3)^3 / (15/8)

I will use copy dot flip

( -7/3)^3 * (8/15)

Now I can split the first term into parts (a/b)^x = a^x/ b^x

(-7)^3/ 3^3 *8/15

-343/27 * 8/15

-2744/405

Now we need to change it back to a mixed number

405 goes into 2744  6 times

6*405 =2430  2744-2430 = 314  

-6 314/405

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:

(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]

Answer:

The even functions are options 2, 3, and 5

Step-by-step explanation:

Please, see the attached file.

Thanks.

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:

The second choice.

Step-by-step explanation:

f(x) = -(x + 1)^2 + 4

This is a parabola which opens downwards ( because the coefficient of x is negative).

This is the vertex form of a parabola:  f(x) = a(x - b)^2 + c where the vertex is at (b, c). So in this case:-

The vertex is at (-1, 4).

The domain is  All Real Numbers and the Range is (-∞, 4]  (or y ≤ 4)

Answer:

The vertex is (-1, 4), the domain is all real numbers, and the range is y ≤ 4.

We have

[tex]81-49n^4=9^2-(7n^2)^2[/tex]

so this is indeed a difference of squares. Factorizing would give

[tex]81-49n^4=(9-7n^2)(9+7n^2)[/tex]

making the answer D.

We can further factor the first term here and write

[tex]9-7n^2=3^2-(\sqrt 7\,n)^2=(3-\sqrt7\,n)(3+\sqrt7\,n)[/tex]

but that's clearly out of the scope of this question.

Answer:

D is the answer

Answer:

- 2 - 3i

Step-by-step explanation:

given a complex number a + bi

then the conjugate is a - bi

The real part a remains unchanged while the sign of the imaginary part is reversed.

the conjugate of - 2 + 3i is - 2 - 3i

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:

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.

Answer:

Local max is .5

Step-by-step explanation:

The local maximum is for x values between 2 and 4

It looks like the x value is 2.5 and the y value is .5

Adam's cleats cost $65 and the sales tax is 5.5%. The sales tax amount is calculated by multiplying the price by the tax rate. The total cost is the sum of the initial price and the sales tax which is approximately $68.58.

Adam is buying a new pair of baseball cleats for $65 and the sales tax is 5.5%. To find the total cost, we must find out the cost of the sales tax first. The sales tax can be calculated by multiplying the cost of the cleats by the sales tax percentage (in decimal form).

So, $65 * 0.055 = $3.575 is the tax amount. This means the sales tax on the cleats is $3.575.

The total cost Adam needs to pay is the sum of the cost of the cleats and the sales tax. Hence, $65 + $3.575 = $68.575. Therefore, the total cost that Adam will pay is approximately $68.58, because we usually round the money amount to the nearest cent.

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[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:

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

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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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.

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]

Answer:

49

Step-by-step explanation:

7^x

If x=2

7^2

49