Which Line is longer?
A.——————————
B.—————

Answer:

Part 1) [tex]\frac{\sqrt{2}}{2}\ sec[/tex] or [tex]0.7\ sec[/tex]

Part 2) The side length of each piece Trinette used to make the pillow covers is [tex]30 in[/tex]

Part 3) Elton's hourly wage is [tex]\$6.50[/tex]

Step-by-step explanation:

Part 1)

Let

x------> the time in seconds

we have

[tex]f(x)=-16x^{2}+c[/tex]

In this problem the initial height is 8 ft

so

[tex]f(x)=-16x^{2}+8[/tex]

To find how long does it take the apple to reach the ground, equate the function to zero and solve for x

[tex]0=-16x^{2}+8[/tex]

[tex]16x^{2}=8[/tex]

[tex]x^{2}=1/2[/tex]

[tex]x=\frac{\sqrt{2}}{2}\ sec[/tex]

[tex]x=0.7\ sec[/tex]

Part 2)

step 1

The area of a square tablecloth is

[tex]A=3,600\ in^{2}[/tex]

Divided by 4

[tex]3,600/4=900\ in^{2}[/tex]

step 2

Find the length of each piece

[tex]A=b^{2}[/tex]

so

[tex]900=b^{2}[/tex]

[tex]b=30 in[/tex]

Part 3)

we know that

[tex]2x^{2} =84.50[/tex]

solve for x

[tex]x^{2} =42.25[/tex]

[tex]x=\sqrt{42.25}[/tex]

[tex]x=\$6.50[/tex]

question 1 is congruent. 2 is not congruent and 3 is congruent

Answer: 1) Congruent

2) Not congruent

3) Congruent

Step-by-step explanation:

We know that a rigid transformations preserves side-lengths and angle measures of a figure in such a way that the figure doesn't shrink or get enlarger. It creates congruent figures.

    a) reflections, b) rotations, c) translations

On the other hand a dilation changes the size of the image when the scale factor is not equal to 1. It does not produces congruent images.

Answer:

to make 1000 gallons with 10% alcohol, we need 714.3 gallons of mixture that contains 5% alcohol and 285,7 gallons of mixture that contains 12% alcohol.

Step-by-step explanation:

According to the statement, there are two mixtures. One mixture contains 5% alcohol and the other contains 12% alcohol.

We want to make 1000 gallons with 10% alcohol, so we have the following system of equations:

A + B = 1000 gallons. [1]

0.05A + 0.12B = 0.1(1000) ⇒ 0.05A + 0.12B = 100 [2]

(Where 'A' represents the mixture that contains 5% alcohol and 'B' the one that contains 12% alcohol).

Solving the system of equations:

A + B = 1000 ⇒ A = 1000 - B [3]

[3] → [2]

0.05(1000 - B) + 0.12B = 100 ⇒ 50 - 0.05B + 0.12B = 100

⇒ 0.07B = 50 ⇒ B = 714.28 ≈ B=714.3 [4]

[4] → [1]

A + B = 1000 ⇒ A + 714.3 = 1000 ⇒ A = 285,7

Therefore, to make 1000 gallons with 10% alcohol, we need 714.3 gallons of mixture 'A' and 285,7 gallons of mixture 'B'

Answer:

Step-by-step explanation:

In 8 hours 30m Corner earns $80.75

In how many hours Zoey earns $118.75

Hours Zoey works= 510*118.75/80.75(converted 8hours into minutes by multiplying with 60)

Solving we get 12 hours 30m.

Answer:

x = - 2 ± [tex]\sqrt{5}[/tex]

Step-by-step explanation:

Given

x² + 4x - 1 = 0 ( add 1 to both sides )

x² + 4x = 1

To complete the square

add (half the coefficient of the x- term )² to both sides

x² + 2(2)x + 2² = 1 + 2² ← complete the square on the left side

(x + 2)² = 5 ← take the square root of both sides

x + 2 = ± [tex]\sqrt{5}[/tex] ← subtract 2 from both sides

x = - 2 ± [tex]\sqrt{5}[/tex]

roots are x = - 2 - [tex]\sqrt{5}[/tex] or x = - 2 + [tex]\sqrt{5}[/tex]

Final answer:

To find the roots of the quadratic function x² + 4x - 1 = 0, the equation is rearranged, a perfect square is formed by adding (b/2)² to both sides, and the square root is taken to obtain the solutions x = √{5} - 2 and x = -√sqrt{5} - 2.

Explanation:

To find the roots of the quadratic function x² + 4x - 1 = 0 by completing the square, we need to follow a series of steps:

First, we'll arrange the equation so that the x-squared and x terms are on one side, leaving the constant on the other side. In this case, we add 1 to both sides to obtain x² + 4x = 1.

Next, we find the number that needs to be added to x^2 + 4x to make it a perfect square trinomial. This number is (b/2)², where b is the coefficient of x. Here, b is 4, so we need to add (4/2)² = 4 to both sides.

Our equation now reads x² + 4x + 4 = 5. Notice that the left-hand side is a perfect square, as it can be written as (x+2)².

Finally, we take the square root of both sides, giving us x + 2 = √{5} or x + 2 = -√{5}. Therefore, the solutions are x = √{5} - 2 and x = -√{5} - 2.

To check our solutions, we could substitute them back into the original equation and ensure that the left side equals zero.

Answer:

(x/7) = actual time

Step-by-step explanation:

D, 196,608.

The sequence is multiplying by -4 every time.

Answer:  The correct option is (D) 196608.

Step-by-step explanation:  We are given to find the 9th term of the following sequence :

3,    -12,    48,    -192,    .    .    .

Let a(n) denote the n-th term of the given sequence.

Then, a(1) = 3,  a(2) = -12,  a(3) = 48,  a(4) = -192,   .   .   .

We see that

[tex]\dfrac{a(2)}{a(1)}=\dfrac{-12}{3}=-4,\\\\\\\dfrac{a(3)}{a(2)}=\dfrac{48}{-12}=-4,\\\\\\\dfrac{a(4)}{a(3)}=\dfrac{-192}{48}=-4,~~.~~.~~.[/tex]

So, we get

[tex]\dfrac{a(2)}{a(1)}=\dfrac{a(3)}{a(2)}=\dfrac{a(4)}{a(3)}=~~.~~.~~.~~=-4.[/tex]

That is, the given sequence is a GEOMETRIC one with first term a = 3  and common ratio d= -4.

We know that

the n-th term of an geometric  sequence with first term a and common ratio r is given by

[tex]a(n)=ar^{n-1}.[/tex]

Therefore, the 9th term of the given sequence is

[tex]a(9)=ar^{9-1}=3\times(-4)^8=3\times 65536=196608.[/tex]

Thus, the 9th term of the given sequence is 196608.

Option (D) is CORRECT.

It would be 83.

Reason it 83 units away from 0.

I hope this helps :)

Answer:

83

Step-by-step explanation:

Answer:

I believe it is C

Step-by-step explanation:

since x+y=4 that could mean, 2+2=4 which means x and y has the same value, that is 2.

so if we make the equation

6(2)+6(2)= it WOULD equal to 24, and for that reason I think it is C.

(24,4)

Answer:

[tex]m<1=92\°[/tex]

Step-by-step explanation:

we know that

The sum of the interior angles in a quadrilateral must be equal to 360 degrees

so

[tex]62\°+92\°+114\°+m<1\°=360\°[/tex]

solve for the measure of angle 1

[tex]268\°+m<1\°=360\°[/tex]

[tex]m<1=360\°-268\°=92\°[/tex]

Answer:

The answer is

B. 92 degrees.

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

7 * 12 = 84

And 1/4 hours which is 7/4 which is $1.25 more.

So she got 85.25 dollars in total, which is a little less than $90.

Simplify

5 - 2i + 3 + 4i - (-6 + 2i)

Simplify brackets

5 - 2i + 3 + 4i + 6 - 2i

Collect like terms

(5 + 3 + 6) + (-2i + 4i - 2i)

Simplify

= 14

The equation (5-2i)+(3+4i)-(-6+2i) simplifies to 14 after adding real parts and imaginary parts separately, resulting in the complex number 14+0i which simplifies to 14.

The student's question involves complex number addition and subtraction. To solve the equation (5-2i)+(3+4i)-(-6+2i), we combine like terms, which means separately adding the real parts and the imaginary parts of the complex numbers. The real parts are 5, 3, and 6 (because we subtract a negative, which becomes plus), which add up to 14. The imaginary parts are -2i, 4i, and -2i (again, subtraction of a negative becomes addition), which add up to 0i. Therefore, the final answer is 14+0i, which simplifies to 14.

Answer:

The answer would be D because both ordered pair that was substituted in the equation didn't equal to each other.

Explanation:

All you do is substitute the x and y numbers. (x,y)

A:

Substitute the x and y number

7(2) - 5 = 4(4) - 6

Multiply the number in the parentheses by the outside number on both sides.

14 - 5 = 16 - 6

Subtract both sides to get your solution.

9 = 10

Doesn't equal so that means it's not the solution.

B:

Substitute

7(3) - 5 = 4(6) - 6

Multiply the number in the parentheses by the outside number on both sides.

21 - 5 = 24 - 6

Subtract both sides to get your solution.

16 = 18

It also doesn't equal so that means that it's not the solution either.

C:

Both ordered pair didn't equal to each other so this is not the answer.

Hope this helps!

Answer: OPTION D.

Step-by-step explanation:

The formula for calculate the circumference of a circle is:

[tex]C=2r\pi[/tex]

Where r is the radius.

The formula for calculate the area of a circle is:

[tex]A=r^2\pi[/tex]

Where r is the radius.

Solve for r from [tex]A=r^2\pi[/tex] to calculate it:

[tex]r=\sqrt{\frac{A}{\pi}}\\r=\sqrt{\frac{58ft^2}{\pi}}\\r=4.296ft[/tex]

Subsitute the radius into [tex]C=2r\pi[/tex]. Then:

[tex]C=(2)(4.296ft)\pi=26.99ft[/tex]

Answer:

D. 26.99 ft

Step-by-step explanation:

The formula for area of a circle is

A = πr², where r is the radius. We are given A = 58, so plug that in to find r...

58 = πr²    solve for r...

   58/π = r²           (divide both sides by π)

       √(58/π) = r       (take the square root of both sides)

now simplify...

           (√58)/(√π) = r

               [(√58)(√π)]/[(√π)(√π)] = r

                       [√(58π)]/π = r  

The formula for circumference is C = 2πr,  where r is the radius....so we have

  C = 2π([√(58π)]/π)      now simplify...

        C = 2√(58π)             (the 2 pi's cancel out)

          C = 26.9972124    (crunch in your calculator)

Answer: [tex]x\geq6[/tex]

Step-by-step explanation:

g°h indicates that you must plug the function h(x) into the function g(x) as you can see below:

[tex]g\°h=\sqrt{(2x-8)-4}[/tex]

Now you must simplify by adding like terms, as following:

[tex]g\°h=\sqrt{2x-12}[/tex]

By definition you have that:

[tex]2x-12\geq0[/tex]

Theen you must solve for x:

[tex]2x\geq12\\x\geq6[/tex]

Therefore, the domain is:

{[tex]x[/tex] ∈R:[tex]x\geq6[/tex]}

Then the answer is [tex]x\geq6[/tex]

Answer:

Restriction on the domain is x ≥ 6.

Step-by-step explanation:

We have given two functions.

g(x) = √x-4 and h(x) = 2x-8

We have to find the restrictions on the domain of (g o f).

(g o h)(x) = g(h(x))

(g o h)(x) = g(2x-8)

(g o h)(x) = √2x-8-4

(g o h)(x) = √2x-12

Hence, 2x-12 ≥ 0

2x ≥ 12

x ≥ 6

Hence, restriction on the domain is x ≥ 6.

Answer: [tex]s = \sqrt{81}[/tex]

Step-by-step explanation: A= s^2, A = 81

81 = s^2

[tex]\sqrt{81} = \sqrt{s^{2} }[/tex]

s = [tex]\sqrt{81}[/tex]

Answer:

Option 2nd is correct

[tex]s = \sqrt{81}[/tex] inches

Step-by-step explanation:

The area of a square can be found using the equation:

[tex]A=s^2[/tex]               ....[1]

where,

A is the area of square

s is the measure of one side of the square.

Given that:

A square has an area of 81 square inches.

⇒A = 81

Substitute in [1] we have;

[tex]s^2 = 81[/tex]

⇒[tex]s =\pm \sqrt{81}[/tex]

∵Side of square cannot be in negative.

⇒[tex]s = \sqrt{81}[/tex] inches

Therefore:

A square has an area of 81 square inches →[tex]s = \sqrt{81}[/tex] in

Answer: The first option.

Step-by-step explanation:

The function is:

θ(r) = 45°

so we have a constant function (because r does not apear in the right side of the equation), this means that for every value of r, we have that θ(r) is equal to 45 degrees.

then the correct answer is the first table, because for every value of r we have that the value of theta is the same.

Table 1 best represents the graph of the equation θ(r)= 45°.

It is given that

θ(r)= 45°, which is a constant function.

For a constant function, the value of the dependent variable is the same for each value of the independent variable.

So, θ will remain constant for all values of r.

r =1, θ=45°

r =2,  θ=45°

r=3, θ=45°

r=4,θ=45°

Therefore, Table 1 best represents the graph of the equation θ= 45°.

To get more about function visit:

https://brainly.com/question/2292795

Answer:

x = 2

Step-by-step explanation:

Similar triangles are triangles which have the same shape but not the same size. This means their angle measures are equal but their side lengths are not instead they are proportional. To solve, we will set up a proportion and solve.

A proportion is two equal ratios set equal to each other. We form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). Out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

[tex]\frac{little}{big} =\frac{little}{big}[/tex].

[tex]\frac{36}{36 + 12}=\frac{24}{24 + 6x - 4}[/tex]

To solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.

[tex]36(24 + 6x - 4)=(36+12)(24)\\36(6x + 20)=48(24)\\216x + 720 = 1152 \\216x = 432\\\frac{216x}{216}=\frac{432}{216} \\x = 2[/tex]

Answer:

2

Step-by-step explanation:

8 ( 4 - x ) = 7x + 2

(Expand brackets

32 - 8x = 7x + 2

(-7x from both sides)

-15x = -30

(Divide by -15 from both sides)

x=2

Answer:

x = 2

Step-by-step explanation:

8(4 - x) = 7x + 2

Distribute the 8 on the left side.

32 - 8x = 7x + 2

Subtract 7x from both sides.

32 - 15x = 2

Subtract 32 from both sides.

-15x = -30

Divide both sides by -15.

x = 2

Answer:explanation:

The answer is B because Nathan will use more cups

Answer:

D

Step-by-step explanation:

Nathan uses 3 cups of water for every 8 cups of flour. Cody uses 4 cups of water for every 12 cups of flour. Create tables of equivalent ratios for Nathan and Cody to find who uses more cups of water when each use 48 cups of flour.

When they each use 48 cups of flour, Nathan will use 18 cups of water and Cody will only use 16 cups of water, so Nathan will use more cups of water.

Answer:

Part 1: Find (f/g)(4) = 3

Part 2: Find (f+g)(4) = 28

Step-by-step explanation:

Part 1: Find (f/g)(4):

(f/g)(4) means divide f function by g function and simplify it. Then plug in 4 into x of that simplified function.

Let's do this:

[tex]\frac{x^2+2x-3}{x^2-9}\\=\frac{(x+3)(x-1)}{(x-3)(x+3)}\\=\frac{x-1}{x-3}[/tex]

Plugging in 4 into x gives us:

[tex]\frac{x-1}{x-3}\\=\frac{4-1}{4-3}\\=\frac{3}{1}\\=3[/tex]

The answer is 3

Part 2: Find (f+g)(4):

(f+g)(4) means add f function and g function and simplify it. Then plug in 4 into x of that simplified function.

Let's do this:

[tex](x^2+2x-3)+(x^2-9)\\=2x^2+2x-12[/tex]

Plugging in 4 into x gives us:

[tex]2x^2+2x-12\\=2(4)^2+2(4)-12\\=28[/tex]

The answer is 28

Answer: the first one is -11 and the second one is 0

step-by-step explanation:

someone answered your question but it was wrong so i had too guess and got the real answers since you know ... i ended up getting it wrong lol so yea

Answer:

V =20.4 in^3

Step-by-step explanation:

The formula for volume of a triangular prism is

V = B *h

B is the area of the triangle which is 1/2 b*h

B = 1/2 (2.5) (3.4)

The height is 4.8 in

V = 1/2 (2.5) (3.4) * 4.8

V =20.4 in^3

Answer:

V =20.4 in^3 is your answer

Step-by-step explanation:

Answer:

10oz:1lb

Step-by-step explanation:

divide by two

Answer:

Answer:

B.

Explanation:

If you want to multiply a parenthesis by a number, you simply distribute the number to all the terms in the parenthesis.

Step-by-step explanation:

Answer:

B. [tex]15x-35[/tex]

Step-by-step explanation:

We are asked to simplify the expression [tex]5(3x-7)[/tex] using distributive property.

Distributive property states that we can multiply a quantity to sum by multiplying each addend separately and then add the products as:

[tex]a(b+c)=a\cdot b+a\cdot c[/tex]

Using distributive property, we will multiply 5 by [tex]3x[/tex] and [tex]-7[/tex] as:

[tex]5\cdot 3x-5\cdot 7[/tex]

[tex]15x-35[/tex]

Therefore, the simplified form of the given expression would be [tex]15x-35[/tex] and option B is the correct choice.

Find the slope or the y-intercept.

The approximate volume of the sphere is 4188.79 cubic units.

Calculating the volume of a sphere.

A sphere is a three-dimensional round object. The volume of a sphere can be calculated by using the formula [tex]\dfrac{4}{3} \pi r^3[/tex].

In the given question, the radius of the sphere is stated to be 10 units. So, the volume of the sphere can be determined by replacing the value of the radius into the equation. i.e.

[tex]V= \dfrac{4}{3}\pi r^3[/tex]

[tex]V= \dfrac{4}{3} \times \pi \times (10)^3[/tex]

V = 4188.79 cubic units.

Therefore, the approximate volume of the sphere is 4188.79 cubic units.

Answer:

wrong its 5gallons

Step-by-step explanation:

Answer:

[tex]x^2+y^2=16[/tex]

Step-by-step explanation:

The equation of a circle with center (h,k) and radius r is given by the formula;

[tex](x-h)^2+(y-k)^2=r^2[/tex]

Given (h,k)=(0,0) and r=4, we substitute the values to obtain;

[tex](x-0)^2+(y-0)^2=4^2[/tex]

The required equation is

[tex]x^2+y^2=16[/tex]

The standard form of the equation for a circle centered at the origin with a radius of 4 is x2 + y2 = 16.

The equation of a circle in standard form with the center at the origin (0, 0) and a radius of 4 is given by x2 + y2 = r2, where x and y are the coordinates of any point on the circle, and r is the radius.

Plugging the given radius into the equation, we have x2 + y2 = 42. Simplifying this, we get the equation x2 + y2 = 16. This is the standard form of the equation for the given circle.

Answer:

Part A) The volume of the ice cream scoop is [tex]36\pi\ in^{3}[/tex]

Part B) The melted ice cream won't fill the cup

Part C) The melted ice cream exceeds the volume  of Anna's cup

Part D) The height of the smallest cylindrical cup is [tex]h=8\ in[/tex]

Step-by-step explanation:

Part A) Find the volume of the ice cream scoop

we know that

The volume of the sphere (ice cream scoop) is equal to

[tex]V=\frac{4}{3}\pi r^{3}[/tex]

we have

[tex]r=3\ in[/tex]

substitute

[tex]V=\frac{4}{3}\pi (3)^{3}=36\pi\ in^{3}[/tex]

Part B) Find the volume of Anna's cylindrical cup

we know that

The volume of a cylinder is equal to

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

we have

[tex]r=3\ in[/tex]

[tex]h=6\ in[/tex]

substitute

[tex]V=\pi (3)^{2}(6)=54\pi\ in^{3}[/tex]

[tex]54\pi\ in^{3}> 36\pi\ in^{3}[/tex]

The volume of Anna's cup (cylinder) is greater than the volume of melted ice cream scoop

therefore

The melted ice cream won't fill the cup.

Part C) Will two scoop of melted ice cream fit in Anna's cup?

Multiply the volume of ice cream scoop by 2 and compare with the volume of Anna's cup

so

[tex](2)36\pi\ in^{3}=72\pi\ in^{3}[/tex]

[tex]72\pi\ in^{3}> 54\pi\ in^{3}[/tex]

The volume of Anna's cup (cylinder) is less than the volume of two melted ice cream scoop

therefore

The melted ice cream exceeds the volume  of Anna's cup

Part D) Find the smallest cylindrical cup that will hold two scoops of melted ice cream

we know that

The volume of a cylinder is equal to

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

we have

[tex]V=72\pi\ in^{3}[/tex] ------> volume of two scoops of melted ice cream

[tex]r=3\ in[/tex]

substitute in the formula and solve for h

[tex]72\pi=\pi (3)^{2}h[/tex]

simplify

[tex]72=(9)h[/tex]

[tex]h=8\ in[/tex]