Brandon bought a 5-gallon container of paint to paint his house. After he finished painting, he had 2 quarts of paint left over. How many quarts of paint did Brandon use?

Answer:

  0 + 5i

Step-by-step explanation:

Multiply these the way you would any binomials, then replace i² with -1.

  (1 +2i)(2 +i) = 1·2 +1·i +(2i)·2 +(2i)·i

  = 2 + i + 4i + 2i² . . . . . the partial products

  = 2 +5i -2 . . . . . . . . . . after replacement of i² = -1

  = 0 +5i

Answer:

(x-2)²+(y--2)²=9

Step-by-step explanation:

The center moves to the right by 2 so its x-2

The center moved down 2 so its y+2 or y--2

The radius is 3 so we square that to get what it equals (9)

Answer:

[tex]2\sqrt[4]{5}[/tex]

Step-by-step explanation:

First, you calculate the quotient which is [tex]\sqrt[4]{80}[/tex]

Then you simplify the radical which is [tex]2\sqrt[4]{5}[/tex]

Inputting this in a calculator will give you 2.99 which is also correct.

Answer:

B. 28.26

Step-by-step explanation:

First you have to find the circumference:

R²= 3²=9

Then you multiply your circumference by 3.14 to get you answer:

9·3.14=28.26

Answer:

y=3(0.8)x

Step-by-step explanation:

An exponential function is a function of the form;

[tex]y=ab^{x}[/tex]

The explanatory variable x is the exponent, a is the initial value and b the base of the exponential function.

The function is said to be an exponential decay function if the base is between 0 and 1;

0<b<1

Therefore, y=3(0.8)^x is the required function. The values of y become smaller as x increases.

Answer:

Statements (1) and (2) TOGETHER are NOT sufficient.

Step-by-step explanation:

If the point order is DCAB or CDAB (or the reverse of either of these), then the BD distance will be 36±8 units. It cannot be determined.

__

If the point order is AD(BC) or A(BC)D, then the BD distance is the same as the CD distance, which is given as 8. In this scenario, point B and C lie at the same place on the number line.

__

So, we have 3 possible values of BD, even when both statements are used together. TOGETHER, the statements aren NOT sufficient.

Answer:

240.3

Step-by-step explanation:

       Tan(31) = y/400ft

400 tan (31) = y

                 y = 240,3

Answer:

20,944 years

Step-by-step explanation:

The formula you use for this type of decay problem is the one that uses the decay constant as opposed to the half life in years.  We are given the k value of .00012.  If we don't know how much carbon was in the bones when the person was alive, it would be safer to say that when he was alive he had 100% of his carbon.  What's left then is 8.1%.  Because the 8.1% is left over from 100% after t years, we don't need to worry about converting that percent into a decimal.  We can use the 8.1.  Here's the formula:

[tex]N(t)=N_{0} e^{-kt}[/tex]

where N(t) is the amount left over after the decay occurs, [tex]N_{0}[/tex] is the initial amount, -k is the constant of decay (it's negative cuz decay is a taking away from as opposed to a giving to) and t is the time in years.  Filling in accordingly,

[tex]8.1=100e^{-.00012t}[/tex]

Begin by dividing the 100 on both sides to get

[tex].081=e^{-.00012t}[/tex]

Now take the natural log of both sides.  Since the base of a natual log is e, natural logs and e "undo" each other, much like taking the square root of a squared number.

ln(.081)= -.00012t

Take the natual log of .081 on your calculator to get

-2.513306124 = -.00012t

Now divide both sides by -.00012 to get t = 20,944 years

Answer:

250/3π cubic inches

Step-by-step explanation:

we know that

The volume of the space between the cylinder and the sphere is equal to the volume of the cylinder minus the volume of the sphere

step 1

Find the volume of the cylinder

The volume of the cylinder is equal to

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

we have

[tex]h=10\ in[/tex]

[tex]r=5\ in[/tex]

substitute

[tex]V=\pi (5)^{2} (10)[/tex]

[tex]V=250\pi\ in^{3}[/tex]

step 2

Find the volume of the sphere

The volume of the sphere is equal to

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

we have

[tex]r=5\ in[/tex]

substitute

[tex]V=\frac{4}{3}\pi (5)^{3}[/tex]

[tex]V=(500/3)\pi\ in^{3}[/tex]

step 3

Find the difference

[tex]250\pi\ in^{3}-(500/3)\pi\ in^{3}=(250/3)\pi\ in^{3}[/tex]

The domain is the X values and the range is the y values.

The blue line starts at X 0 and Y 0 and moves up and to the right.

This means the range and domain are equal to or greater than 0.

The 3rd choice is the correct one.

Answer:

[tex]\boxed{\text{Year 17}}[/tex]

Step-by-step explanation:

[tex]a(t) = 100e^{0.024t}[/tex]

Data:

a(t) = 150

a(0) = 100

Calculations :

[tex]\begin{array}{rcll}150 & = & 100e^{0.024t} & \\\\1.50 & = & e^{0.024t} & \text{Divided each side by 100}\\0.4055 & = & 0.024t & \text{Took the ln of each side}\\t & \approx & \mathbf{17} & \text{Divided each side by 0.024}\\\end{array}[/tex]

[tex]\text{The consumer price index will be 50 \% higher in } \boxed{\textbf{year 17}}[/tex]

Answer:

  3/4

Step-by-step explanation:

1/2 the deck is red cards.

1/4 of the deck is spades.

There are no spades that are red cards, so the probability of drawing a red card or a spade at random from a well-shuffled deck is ...

  1/2 + 1/4 = 3/4

Answer:

[tex]\boxed{x = 8}[/tex]

Step-by-step explanation:

1. Jump discontinuity

In the graph, you can see that the left-hand limit of g(x) as x⟶ 8 is 3 and the right-hand limit is -3.

When the left- and right-hand limits at x = 8 exist but are different, we say that g(x) has a jump discontinuity at [tex]\boxed{\textbf{x = 8}}[/tex].

2. Other discontinuities

At x = 10, the left-hand limit is ∞ and the right-hand limit is -∞. Both one-sided limits are infinite, so this is an infinite discontinuity.

At x= 1, both one-sided limits are equal, but g(1) does not exist,

At x= 4, the limits are equal, and g(4) = 3.

In each case, the holes can be removed by redefining g(x), so the holes are removable discontinuities.

Answer:

B

Step-by-step explanation:

The domain is all possible values of x.  Here, x is the number of $5 nontaxable items.  So x must be an integer, and it can't be negative.  It is possible for x to be 0.  So x is all whole numbers.

The practical domain for the function f(x) which represents the total amount spent at a store is all whole numbers. Option B is correct.

Domain of a function is the set of all the possible input values which are valid for that function.

The function ​f(x) represents the total amount spent at a store.  The purchasing number of x items which are $5 each and the items which are not taxable is represented by x.

Thus, this function can be given as,

f(x)=5x

Now the domain of a function is the set of all the possible input values which are valid for that function. Thus, for this case the domain is,

-∞<x<∞

(-∞,∞)

For the practical domain, the numbers should be whole number to avoid negative amount value and integer amount.

Hence, the practical domain for the function f(x) which represents the total amount spent at a store is all whole numbers. Option B is correct.

Learn more about the domain of the function here;

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Answer:

6 y² - 20 y + 6

Step-by-step explanation:

Multiply step by step the terms inside the brackets:

3y * y

3y * -3

-1 * y

-1 * -3

add those up to get 3y² - 10 y + 3

multiply all terms of the result by 2

Answer:

6y^2 - 20y + 6.

Step-by-step explanation:

2(3y − 1)(y − 3)

= 2 [ 3y(y - 3) - 1(y - 3)]

= 2 (3y^2 - 9y - y + 3)

= 2(3y^2 - 10y + 3)

= 6y^2 - 20y + 6.

Answer:

position: (-6, -4)

range: 6

Step-by-step explanation:

The equation is that of a circle centered at (-6, -4) with a radius of √36 = 6. We presume that the "position" is that of the circle's center, and the "range" is the radius of the circle.

___

The standard form equation of a circle with center (h, k) and radius r is ...

(x -h)^2 +(y -k)^2 = r^2

Matching parts of the equation, we find ...

h = -6, k = -4, r = √36 = 6.

The source of the radio signal is at the point (-6, -4), and the range of the signals is within a circular area with a radius of 6 units.

The equation given, (x + 6)² + (y + 4)² = 36, is a mathematical representation of a circle in a Cartesian plane. This equation indicates that the source of the radio signal is at the center of the circle, which is the point (-6, -4).

The number 36 on the right side of the equation is the square of the radius of the circle, which implies that the radius of the circle is 6 units. Hence, the range of the signals emitted from the source is limited to a circular area with a radius of 6 units around the point (-6, -4).

Answer:

B

Hope this helps!

Answer:

B

Step-by-step explanation:

The rate of change is the slope.  Function 1 has a slope of 4.  Function 2 has a slope of:

m = Δy / Δx

m = (10 - 6) / (3 - 1)

m = 4 / 2

m = 2

So function 1 has the greater rate of change.  Answer B.

Answer:

  36

Step-by-step explanation:

The total number of options is the product of the numbers of independent options: 3×3×4 = 36.

__

For each of the bedroom options, she can choose any parking option, so can have ...

  1 br, street parking

  2 br, street parking

  3 br, street parking

  1 br, assigned parking

  2 br, assigned parking

  3 br, assigned parking

  1 br, garage spots

  2 br, garage spots

  3 br, garage spots

That is, 3×3 = 9 options. Any of these can be put with any of the four lease options, for a total of 9×4 = 36 options altogether.

The answer would be 36

The lengths of the legs of a similar triangle to the one Juan drew, which has leg lengths 6cm and 8cm, could be 12 cm and 16 cm because the sides of similar triangles are proportional.

Juan's right triangle has leg lengths of 6 centimeters and 8 centimeters. To find a similar right triangle, we need ratios of corresponding sides to be equivalent or proportional. As these are right triangles, we can use the Pythagorean theorem which states that a² + b² = c². If the original triangle has sides 6 cm and 8 cm, then triangle with proportional sides could have sides that are multiple of these dimensions, such as 12 cm (which is 6cm x 2) and 16 cm (which is 8cm x 2). So, one example of a similar triangle could have leg lengths of 12 cm and 16 cm.

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Answer:

[tex]200in^3[/tex]

Step-by-step explanation:

To solve this, we are using the formula for the volume of a rectangular prism:

[tex]V=whl[/tex]

where

[tex]w[/tex] is the width of the base

[tex]l[/tex] is the length of the base

[tex]h[/tex] is the height of the prism

We know from our problem that the height is 10 inches. The length of the base is 6 inches. The width of the base is 5 inches.

Replacing values

[tex]V=(5in)(10in)(6in)[/tex]

[tex]V=300in^3[/tex]

Now, to find 2/3 of that volume, we just need to multiply it by 2/3

[tex]\frac{2}{3} V=\frac{2}{3} 300in^3[/tex]

[tex]\frac{2}{3} V=200in^3[/tex]

We can conclude that 2/3 of the volume of the vase is 200 cubic inches.

Answer:

55cm

Step-by-step explanation:

11 x 5 = 55, so the area of the pyrmid is 55cm.

Answer:You will have to multiply 55 x 5 because if the base if 5 cm and the height is 11 cm which equals to 55 and a pyramid has 5 faces, so the answer will be 220. I hoped this helped! :)

Step-by-step explanation:

Answer:

Step-by-step explanation:

X has a binomial distribution when the probability of X is the same for each spin.

When the spinner is spun four times, X is the number of times the spinner does not land on an odd number.

When the spinner is spun five times, X is the number of times the spinner lands on 1.

Answer with explanation:

Total number of sections in the spinner = 1 to 5=5 in all

For, a Distribution to be a Binomial Distribution,

Number of trials  should be fixed.

All trials should be Independent of one another.

Only two outcomes  are Possible one is called Success and Other is failure.

Probability of each Outcome should remain constant irrespective of number of trials.

Probability of getting either of 1,2,3,4,or 5 when the spinner is spun once

    [tex]=\frac{1}{5}[/tex]

Option C

When the spinner is spun four times, X is the number of times the spinner does not land on an odd number.

Probability of Failure ={1,3,5}=Getting odd number on spinner

          [tex]=\frac{3}{5}[/tex]

Probability of Success={2,4}=Getting even number on spinner

       [tex]=\frac{2}{5}[/tex]

Number of trials is fixed and each trial is independent of another.

Option D

Total Number of Trials= 5

Probability of Success = When the Spinner is spun and it Lands on 1

Probability of Failure = When the Spinner is spun and it does not Land on 1

When the Spinner is spun five times ,Probability of each Outcome,that is either of 1,2,3,4,or 5 is constant which is [tex]\frac{1}{5}[/tex]

⇒⇒When the spinner is spun five times, X is the number of times the spinner lands on 1.

→≡Option C and D

Here,

the initial point of vector u(x1,y1)=(-7,2)

the final point of vector u (x2,y2)=(11,5)

so the component of vector u(x,y)=(x2,y2)-(x1,y1)

=(11+7,5-2)=(18,3)

according to the question, the magnitude of vector is thrice the magnitute of vector u and is opposite ot the ditecrion of vector u.

so the component of vector v is -3(x,y)

=-3(18,3)=(-54,-9)

Answer:

Step 1: Multiply 1x5 Step 2: Multiply 2x3 Step 3: Add the two products

d=v*t

d=distance

v=velocity(speed)

t=time

distance is equal to the product of velocity and time, equation form;

d=vt

Any questions please feel free to ask. Thanks!

Answer: brianna rode for 54 minutes and maddie rode for 108 minutes.

Step-by-step explanation:

let the time for which brianna rode be = x

(since maddie rode twice as brianna then,)

let the time for which maddie rode be = 2x

(together they rode for 162 minutes. so,)

x + 2x = 162

3x = 162

x = 162/3

=>x = 54

=>2x = 54*2 = 108

hope it helps

Answer:

Step-by-step explanation:

If the sides form a right triangle, the sum of the squares of the shorter two sides will equal the square of the longest side.

1. 10.5^2 + 20.8^2 = 23.3^2 . . . . . true algebraic statement; right triangle

__

2. 6^2 +20.1^2 = 440.01 ≠ 22.9^2 = 524.41 . . . . . this is an obtuse triangle

here the centre of circle(h,k) is (-2,4)

and its radius(r) is 6 uints.

now the equation of circle is,

(x-h)^2 +(y-k)^2 =r^2

or, (x+2)^2 + (y-4)^2=6^2

or, x^2 + 4x + 4+y^2 -8y+16=36

or, x^2 +y^2 + 4x -8y -16=o

Answer:

Part A) The system has one solution

Part B) The solution is the point (4,4)

Step-by-step explanation:

step 1

Find the equation of the line A

we have

(0,6) and (6,3)

Find the slope

m=(3-6)/(6-0)

m=-0.5

Find the equation of the line into slope intercept form

y=mx+b

we have

m=-0.5

b=6 -----> the point (0,6) is the y-intercept

substitute

y=-0.5x+6 ------> equation A

step 2

Find the equation of the line B

we have

(0,0) and (6,6)

Find the slope

m=(6-0)/(6-0)

m=1

Find the equation of the line into slope intercept form

y=mx+b

we have

m=1

b=0 -----> the line represent a direct variation

substitute

y=x ------> equation B

step 3

Find how  many solutions does the pair of equations for lines A and B have

we have

y=-0.5x+6 ------> equation A

y=x ------> equation B

Solve the system of equations by graphing

Remember that the solution of the system of equations is the intersection point both lines

using a graphing tool

There is one point of intersection

therefore

The system has one solution

see the attached figure

step 4

What is the solution to the equations of lines A and B?

we know that

The solution of the system of equations is the intersection point both lines

The intersection point is (4,4)

therefore

The solution is the point (4,4)

so

x=4,y=4

well, the movie lasted 1:38   so.... and she finished it at 1:10pm.

1:10pm minus 1 hour?  12:10pm.

12:10 pm minus 10 and minus 28 minutes?   12:10 - 00:10 = 12:00pm, 12:00 - 00:28 minutes = 11:32am.

Answer: 11:32

Step-by-step explanation:

Answer:

y ≈ - 3.8

Step-by-step explanation:

Given the 2 equations

5x + 2y = 21 → (1)

- 2x + 6y = - 34 → (2)

To eliminate the terms in x , multiply (1) by 2 and (2) by 5

10x + 4y = 42 → (3)

- 10x + 30y = - 170 → (4)

Add (3) and (4) term by term

(10x - 10x) + (4y + 30y) = (42 - 170)

34y = - 128 ( divide both sides by 34 )

y ≈ - 3.8 ( to the nearest tenth )