find the volume of the prism.
a) 1728 cu. in.
b) 864 cu. in.
c) 288 cu. in.

ANSWER

[tex]34 {units}^{2} [/tex]

EXPLANATION

The width of the rectangle is |AB|

A(-1,4) and B(3,3)

We use the distance formula,

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

This implies that,.

[tex]d = \sqrt{ {(3- - 1)}^{2} + {(3 - 4)}^{2} } [/tex]

[tex]d = \sqrt{ {(4)}^{2} + {( - 1)}^{2} } [/tex]

[tex]d = \sqrt{ 16+ 1 } [/tex]

[tex]d = \sqrt{17} [/tex]

The length is BC

C(1,-5) and B(3,3)

[tex]d = \sqrt{ {(3- 1)}^{2} + {(3 - - 5)}^{2} } [/tex]

[tex]d = \sqrt{ {2}^{2} + {(8)}^{2} } [/tex]

[tex]d = \sqrt{4 + 64 } [/tex]

[tex]d = \sqrt{68} [/tex]

[tex]d = 2 \sqrt{17} [/tex]

The area is

[tex] = l \times w[/tex]

[tex] = 2 \sqrt{17} \times \sqrt{17} [/tex]

[tex]2 \times 17 = 34 {units}^{2} [/tex]

Answer:

The amount in the account at the end of the 2nd quarter is $1537.73 ⇒ 2nd answer

Step-by-step explanation:

* Lets revise the compound interest

- Compound interest can be calculated using the formula

 A = P (1 + r/n)^(nt)

Where:

• A = the future value of the investment, including interest

• P = the principal investment amount (the initial amount)

• r = the annual interest rate (decimal)

• n = the number of times that interest is compounded per unit t

• t = the time the money is invested for

* Now lets solve the problem

# P = $1500

# r = 5/100 = 0.05

# n = 4 ⇒ quarterly compound

# t = 1/2 ⇒ two quarters means 1/2 year

∴ A = 1500(1 + 0.05/4)^(4 × 1/2) = $1537.73

* The amount in the account at the end of the 2nd quarter is $1537.73

Answer:

R= q+c over 5y

Step-by-step explanation: Good luck sweetie!!

[tex]

d=295

t=120

s=d\div t= 295\div120\approx2.46\frac{\text{ft}}{\text{s}}

[/tex]

Answer:

[tex](x+3)^2 + (y-4)^2 = 1[/tex]

Step-by-step explanation:

Equation of a circle can be found by

[tex](x-a)^2 + (y-b)^2 = r^2[/tex]

Given center 3,-4 i.e

a= 3 and b=-4

and radius r = 1

Putting the values of a,b and r in the equation we get:

[tex](x-(-3))^2 + (y-4)^2 =(1)^2\\(x+3)^2 + (y-4)^2 = 1[/tex]

Answer:

27.6

Step-by-step explanation:

https://brainly.com/question/12181840

credit to Calculista

You need to multiply the amount she makes per hour by the number of hours (t) she works.

The equation would be y = 16.8t

Here is a table that will help you understand. And the answer.

Answer:

FIGURE IT OUT THIS IS SUPER BASIC YOU REALLY NEED TO DO THIS BY YOURSELF

Step-by-step explanation:

girl slope intercept form is just when you isolate y and whatever you do to one side you do to the other you just minus the extra term which isn't y and then you divide whatever is multiplied to y on each term and it's that easy

Answer:

2. y = -8x + 9

3. y = -1/6x - 1/3

4. y = -4/3x + 3

Step-by-step explanation:

the goal for 2, 3, and 4 is to get them into y = mx + b form. to do this, we need to isolate y on one side of the equation

2. 8x + y = 9 < subtract both sides by 8x

y = -8x + 9

3. x + 6y = -2 < subtract x from both sides

6y = -x - 2 < divide both sides by 6 to get y alone

6y/6 = y

-x - 2 / 6 = -1/6 - 1/3

y = -1/6x - 1/3

4. 4x + 3y = 9 < subtract 4x from both sides

3y = -4x + 9 < divide both sides by 3 to get y isolated

3y/3 = y

-4x + 9/3 = -4/3x + 3

y = -4/3x + 3

[tex]\bf \textit{Sum and Difference Identities} \\\\ sin(\alpha + \beta)=sin(\alpha)cos(\beta) + cos(\alpha)sin(\beta) \\\\ sin(\alpha - \beta)=sin(\alpha)cos(\beta)- cos(\alpha)sin(\beta) \\\\ cos(\alpha + \beta)= cos(\alpha)cos(\beta)- sin(\alpha)sin(\beta) \\\\ cos(\alpha - \beta)= cos(\alpha)cos(\beta) + sin(\alpha)sin(\beta) \\\\[-0.35em] ~\dotfill\\\\[/tex]

[tex]\bf cos(x)cos\left( \cfrac{\pi }{7} \right)+sin(x)sin\left( \cfrac{\pi }{7} \right)=-\cfrac{\sqrt{2}}{2}\implies cos\left( x-\cfrac{\pi }{7} \right)=-\cfrac{\sqrt{2}}{2} \\\\\\ x-\cfrac{\pi }{7}=cos^{-1}\left( -\cfrac{\sqrt{2}}{2} \right)\implies x-\cfrac{\pi }{7}= \begin{cases} \frac{3\pi }{4}\\\\ \frac{5\pi }{4} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf x-\cfrac{\pi }{7}=\cfrac{3\pi }{4}\implies x=\cfrac{3\pi }{4}+\cfrac{\pi }{7}~\hfill \stackrel{n ~\in~ \mathbb{Z}}{x=\cfrac{3\pi }{4}+\cfrac{\pi }{7}~~~~+2\pi n} \\\\[-0.35em] ~\dotfill\\\\ x-\cfrac{\pi }{7}=\cfrac{5\pi }{4}\implies x=\cfrac{5\pi }{4}+\cfrac{\pi }{7}~\hfill \stackrel{n ~\in~ \mathbb{Z}}{x=\cfrac{5\pi }{4}+\cfrac{\pi }{7}~~~~+2\pi n}[/tex]

Slope=5

Y-intercept=-7

Answer:

[tex] {3}^{7} \times \frac{1}{ {3}^{4} } [/tex]

Answer:

DDDDDDDDDDD for sure...

D it might look as if it were B but if it was you would cross multiply so it’s definitely D

Answer:

[tex]+2n^5 - 9n^2 + 5n[/tex]

Step-by-step explanation:

To solve the expression

[tex]-n(-2n^4+9n-5)[/tex]

first we will multiply -n with each term and then find their products.

When doing multiplication the powers will be added and co-efficient will be multiplied.

[tex]-n(-2n^4+9n-5)​\\-n(-2n^4) -n(+9n) -n(-5)\\+2n^5 - 9n^2 + 5n[/tex]

Answer:

1.5 pound of beans are in each bag

Step-by-step explanation:

12/8=1.5

1.5 pounds of beans are in each bag.

Diving 12 by 8 will give you 1.5, the total number of pounds in any given cup. You can check this by multiplying 8 by 1.5, which gives you one-and-a-half pounds.

The answer is negative 96

The answer to 8(-12) is - 96

Answer:

The correct option is B.

Step-by-step explanation:

It is given that Alondra took out a car loan for $22,500 that has a 0% APR for the first 24  months and will be paid off with monthly payments over 5 years.

We know that

1 year = 12 months

Using this conversion we get

5 year = 60 months

It means total number of months in 5 years is 60. For first 24  months the APR is 0%. So, the number of months will Alondra be charged interest is

[tex]60-24=36[/tex]

Therefore the correct option is B.

Answer:

B: 3z-4

Step-by-step explanation:

First you start with PEMDAS. Parenthesis first.

Distribute 4 to (2z-1)

You get 8z-4

Next combine like terms such as 8z and -5z.

You get 3z because 8-5 is 3.

then you add on the negative four and get 3z-4.

Answer:

b

Step-by-step explanation:

i got it right on edge :)

ANSWER: 60 female lions

In the ratio there are 21 male lions and 20 female lions, in total 41 lions. Create a proportion relating the total number of lions in the ratio (41) and in the problem (123), and the number of female lions in the ratio (20) and in the problem (unknown).

20/41 = x/123

Cross multiply and solve

20(123)=41x

2460=41x

60=x

The volume of each sample is 0.10 liters of water from each water sample

Answer:

Step-by-step explanation:

Put the coordinates of the points to the inequalities:

y ≤ x - 5; y ≥ -x - 4

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

(-5, 2) → x = -5, y = 2

2 ≤ -5 - 5

2 ≤ -10   FALSE

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

(5, -2) → x = 5, y = -2

-2 ≤ 5 - 5

-2 ≤ 0   TRUE

-2 ≥ -5 - 4

-2 ≥ -9   TRUE

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

(-5, -2) → x = -5, y = -2

-2 ≤ - 5 - 5

-2 ≤ -10   FALSE

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

(5, 2) → x = 5, y = 2

2 ≤ 5 - 5

2 ≤ 0    FALSE

Final answer:

Option b) (5, -2) is the only point that satisfies both inequalities, y ≤ x − 5 and y ≥ −x − 4, making it the correct answer.

Explanation:

The goal is to determine which point lies in the solution set of the given system of inequalities:

y ≤ x − 5

y ≥ −x − 4

Let's evaluate each option given for the system of inequalities:

(−5, 2): Plugging into the inequalities, y = 2 is not less than or equal to x − 5, because 2 is not ≤ (−5 − 5).

(5, −2): y = −2 is less than or equal to 5 − 5, and is also greater than or equal to −5 − 4. Therefore, (5, −2) satisfies both inequalities.

(−5, −2): y = −2 is not less than or equal to −5 − 5, thus not in the solution set.

(5, 2): y = 2 is not less than or equal to 5 − 5, hence it does not satisfy the first inequality.

The only point that satisfies both inequalities is option b) (5, −2).

Answer:

1/3

Step-by-step explanation:

There are 2 u's in August and there are 6 total letters if you divide 2/6. you get 1/3

The probability of selecting a 'u' is 1/3.

The Probability in mathematics is the possibility of an event in time. In simple words, how many times that incident is happening in any given time interval.

Given:

The letters in the word August are placed into a bag.

There are two 'u' in the word August.

And the total letters are 6.

So, the probability of selecting one u,

= 2 / 6

= 1 / 3

Therefore, 1/3 is the probability.

To learn more about the probability;

brainly.com/question/11234923

#SPJ6

Answer:

61.2

Step-by-step explanation:

The product of 918.642 and 1/10 is 91.8642.

Dividing this by 1.5 yields 61.2, which has been rounded off from 61.2428.

Answer:

4 packages of fruits, 5 packages of chocolate

Step-by-step explanation:

We need to find the lowest common multiple of 12 and 15.

12 is ( 2 * 2 * 3) and 15 is (5 * 3).

The lowest common multiple would be three.

Then we can multiply 12 by 5 and 15 by 2 * 2.

The are both equal to 60.

Then we divide:

60 / 15 = 4, which is the amount of packages for the fruits

60/ 12 = 5, the packages of chocolates.

IF THIS WAS NOT THE ANSWER YOU WERE LOOKING FOR, PLEASE COMMENT.

To find the smallest number of packages needed to have the same amount of both fruit and chocolate pastries, calculate the LCM of 15 and 12, which is 60. Thus, one needs 4 fruit pastry packages and 5 chocolate pastry packages.

The student's question relates to finding the least common multiple (LCM) of two numbers, in this case, the number of pastries in each package. Mrs. Patterson's bakery sells fruit pastries in packages of 15, and chocolate pastries come in packages of 12. To find how many of each type of package one needs to buy to get the same number of both types of pastries, we need to calculate the LCM of 15 and 12.

The LCM of 15 and 12 is 60. This means the smallest number of fruit pastry packages (of 15) needed is 60 / 15, which equals 4. Similarly, the smallest number of chocolate pastry packages (of 12) needed is 60 / 12, which equals 5. Therefore, the person would need to buy 4 fruit pastry packages and 5 chocolate pastry packages to have an equal number of pastries.

Answer:

The name of the polygon is rectangle

Step-by-step explanation:

* Lets find the slope of the four sides and the length of two adjacent

 side to know what is the name of the figure

∵ The vertices are (1 , 3) , (3 , 4) , (5 , 0) , (3 , -1)

∵ The rule of the slope of a line which passes through the points

  (x1 , y1) and (x2 , y2) is m = (y2 - y1)/(x2 - x1)

- Let (x1 , y1) is (1 , 3) and (x2 , y2) is (3 , 4)

∴ m1 = (4 - 3)/(3 - 1) = 1/2

- Let (x1 , y1) is (3 , 4) and (x2 , y2) is (5 , 0)

∴ m2 = (0 - 4)/(5 - 3) = -4/2 = -2

- Let (x1 , y1) is (5 , 0) and (x2 , y2) is (3 , -1)

∴ m3 = (-1 - 0)/(3 - 5) = -1/-2 = 1/2

- Let (x1 , y1) is (3 , -1) and (x2 , y2) is (1 , 3)

∴ m4 = (3 - -1)/(1 - 3) = 4/-2 = -2

- The parallel lines have equal slopes

- The product of the slopes of the perpendicular lines is -1

∵ m1 = m3 and m2 = m4

∴ The sides contains points (1 , 3) , (3 , 4) and (5 , 0) , (3 , -1) are parallel

  and the sides contain points (3 , 4) , (5 , 0) and (3 , -1) , (1 , 3) are

  parallel

∵ m1 × m2 = 1/2 × -2 = -1

∴ The side contains points (1 , 3) , (3 , 4) is ⊥ to the line contains points

  (3 , 4) , (5 , 0)

∵ m3 × m4 = 1/2 × -2 = -1

∴ The side contains points (5 , 0) , (3 , -1) is ⊥ to the line contains points

  (3 , -1) , (1 , 3)

- Now lets find the length of the four sides by using the rule

 of the distance

- If a segment has two endpoints (x1 , y1) and (x2 , y2), then the length

 of the distance is √[(x2 - x1)² + (y2 - y1)²]

∵ The length of the side which contains points (1 , 3) and (3 , 4) is

 √[(3 - 1)² + (4 - 3)²] = √[4 + 1] = √5

∵ The length of the side which contains points (3 , 4) and (5 , 0) is

 √[(5 - 3)² + (0 - 4)²] = √[4 + 16] = √20 = 2√5

∵ The length of the side which contains points (5 , 0) and (3 , -1) is

 √[(3 - 5)² + (-1 - 0)²] = √[4 + 1] = √5

∵ The length of the side which contains points (3 , -1) and (1 , 3) is

 √[(1 - 3)² + (3 - -1)²] = √[4 + 16] = √20 = 2√5

∴ The four sides are not equal but each two opposite sides are equal

- From all above

# Each two opposite sides are parallel and equal

# Each two adjacent sides are perpendicular

∴ The name of the polygon is rectangle

Answer:

rectangle

Step-by-step explanation:

well I know for a fact that the equation for a parabola is

[tex]ax^{2} + bx + c[/tex]

so obviously it is an equation for an ellipse, sadly I am not exactly sure whether the answer is b or c.(I'm leaning towards b)

hopefully I helped out by eliminating 2 options.

Brainliest people comment what the answer is!!!!

Have a great day

Answer:

Option d)

[tex]3x^2+y^2+6x-6y+3=0[/tex]

Step-by-step explanation:

we are given with the equation

[tex]3x^2+y^2=9[/tex]

Dividing both sides by 9 and simplifying we get

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

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

Which represents an ellipse. Hence we have an ellipse in our problem. And also  it is obvious that any translation or rotation of this ellipse will again result into en ellipse.

If we see the first two options , they are the equations of the parabolas hence they can not be answer to the problem.

Let us see the third equation.

It is

[tex]3x^2+y^2+3x-3y+3=0[/tex]

Let us transform this equation in perfect square form.

[tex]3x^2+3x+y^2-3y+3=0[/tex]

[tex]3(x^2+x)+y^2-3y+\frac{9}{4}-\frac{9}{4}+3=0[/tex]

[tex]3(x^2+x+\frac{1}{4}-\frac{1}{4})+y^2-3y+\frac{9}{4}-\frac{9}{4}+3=0[/tex]

[tex]3(x^2+x+\frac{1}{4})-3\times\frac{1}{4}+y^2-3y+\frac{9}{4}-\frac{9}{4}+3=0[/tex]

[tex]3(x+\frac{1}{2})^{2}+(y+\frac{3}{2})^{2}-3\times\frac{1}{4}-\frac{9}{4}+3=0[/tex]

[tex]3(x+\frac{1}{2})^{2}+(y+\frac{3}{2})^{2}=0[/tex]

Which represents the equation of an circle , Although Circle also comes in the category of an ellipse but it clearly not the same as we have in the problem in which the minor and major axis are different.

Hence this is also not our answer. So we have a clue that as the first three options are not correct , the right answer must be the forth one. Let us confirm it by converting it into a perfect square.

The equation given is

[tex]3x^2+y^2+6x-6y+3=0[/tex]

[tex]3x^2+6x+y^2-6y+3=0[/tex]

[tex]3(x^2+2x)+y^2-6y+9-9+3=0[/tex]

[tex]3(x^2+x+1-1)+y^2-6y+9-9+3=0[/tex]

[tex]3(x^2+x+1)-3+y^2-6y+9-9+3=0[/tex]

[tex]3(x+1)^{2}+(y-3)^{2}-3-9+3=0[/tex]

[tex]3(x+1)^{2}+(y-3)^{2}-9=0[/tex]

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

Which certainly represents an ellipse. hence this is our correct answer.

Answer: Option B

No solutions

Step-by-step explanation:

We have the following system of equations

[tex]2x - y = -6[/tex]    (1)

[tex]-4x + 2y = -9[/tex]   (2)

To solve the system using the substitution method, solve the first equation for the variable y

[tex]y=2x+6[/tex]

Now substitute the value of y in the second equation

[tex]-4x + 2(2x +6) = -9[/tex]

[tex]-4x + 4x +12=-9[/tex]

[tex]12=-9[/tex]

2 is not equal to -9, the system is inconsistent. The system has no solution

Answer:

No solution

Step-by-step explanation:

Given equations are 2x-y=-6 and -4x+2y=-9.

Now we need to solve that system of equation using substitution method.

solve 2x-y=-6 for y

2x-y=-6

-y=-6-2x

y=6+2x

Plug this value of y into other equation -4x+2y=-9

-4x+2(6+2x)=-9

-4x+12+4x=-9

12=-9

Which is a false equation.

Hence there is no solution to the given system.

For this case we have the following functions:

[tex]m (x) = \frac {x + 5} {x-1}\\n (x) = x-3[/tex]

By definition we have to:

[tex](f * g) (x) = f (x) * g (x)[/tex]

So:

[tex](m * n) (x) = m (x) * n (x)\\(m * n) (x) = \frac {x + 5} {x-1} (x-3)\\(m * n) (x) = \frac {(x + 5) (x-3)} {x-1}[/tex]

By definition, the domain of a function is given by the values for which the function is defined.

The domain of m(x) is given by all reals except 1.

The domain of n(x) is given by all reals.

While the domain of [tex](m * n) (x)[/tex] is given by:

All reals, except the 1. With [tex]x = 1[/tex], the denominator is 0 and the function is no longer defined.

Answer:

Domain of[tex](m * n) (x)[/tex] is given by all reals except 1.

Answer:

w = 21.4 ft

Step-by-step explanation:

Area of Trapezoid = Area = (a+b)/2 * h

Where a and b are the bases of trapezoid, and h is the height.

In the figure we are given:

a= 32.3 ft

b=w=?

h= 22.9 ft

Area = 614.865 ft²

Putting values in formula

Area = (a+b)/2 * h

614.865 = (32.3 + w) / 2 * 22.9

1229.73 = 32.3 + w * 22.9

1229.73 / 22.9 = 32.3 +w

53.7 -32.3 = w

=> w = 21.4 ft