Find the product.

3(x + 4) (x - 5)

A.
3x2 − 20x
B.
3x2 − 11x − 20
C.
3x2 − 3x − 60
D.
3x2 − x − 20

Answer:

96 meatballs are required

Step-by-step explanation:

We know that the formula for he catering business is

[tex]m=4a+2c[/tex]

Where

c= the number of children, m=the number of meat balls, a= the number of adults

So if [tex]c = 8[/tex]  and [tex]a = 20[/tex] then

[tex]m = 4(20) + 2(8)[/tex]

[tex]m = 80 + 16[/tex]

[tex]m = 96[/tex]

Finally  96 meatballs are required for the party

[tex]

(2y-z)^5=(2y-z)^2\cdot(2y-z)^3 \\

(4y^2-4yz+z^2)\cdot(8y^3-12y^2+6yz-(-z)^3) \\

(4y^2-4yz+z^2)\cdot(8y^3-12y^2+6yz-z) \\

\boxed{32y^5-48y^4+24y^3z-4y^2z-32y^4z+48y^3z-24y^2z^2+4yz^2+8y^3z^2-12y^2z^2+6yz^3-z^3} \\

[/tex]

Answer:

Step-by-step explanation:

This shows step by step

Hope this helps <3

Answer:

D. [tex](x-2y)(x-y)(x+y)[/tex]

Step-by-step explanation:

In the polynomial [tex]x^3-2x^2y-xy^2+2y^3[/tex] group first two terms and second two terms:

[tex](x^3-2x^2y)+(-xy^2+2y^3)[/tex]

First two terms have common factor [tex]x^2[/tex] and last two terms have common factor [tex]y^2,[/tex] hence

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

In brackets you can see similar expressions that differ by sign, so

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

Now use formula

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

You get

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

Answer:

B

Step-by-step explanation:

A translation of 3 units up, means adding 3 to the y- coordinate of the original points while the x- coordinates remain unchanged, that is

S(1, 1) → S'(1, 1 + 3) → S'(1, 4)

T(2, - 3) → T'(2, - 3 + 3) → T'(2, 0)

U(4, 0) → U'(4, 0 + 3) → U'(4, 3)

Answer:

Square root of 21 + 4 = w

Step-by-step explanation:

Answer: [tex]x^2+4x-21=0[/tex]

Step-by-step explanation:

You need to remember that formula for calculate the area of a rectangle:

[tex]A=lw[/tex]

Where "l" is the lenght and "w" is the width.

You know that "x" represents the width of the doghouse, its rectangular base has an area of 21 square feet ([tex]A=21[/tex]) and its length is 4 feet more than its width ([tex]l=x+4[/tex])

Then, substituting into the formula, you get:

[tex]21=(x+4)(x)[/tex]

Simplifying, you get the following  that can be used to determine the possible dimensions of the base of the doghouse:

[tex]21=x^2+4x[/tex]

[tex]x^2+4x-21=0[/tex]

41° because it’s a right angle and if 90=2y+8, y=41

Answer:

41

Step-by-step explanation:

Answer:

two distinct real roots

Step-by-step explanation:

The coefficients of the equation are ...

a = 1

b = -5

c = -3

So, the discriminant, b^2-4ac, has the value ...

(-5)^2 -4(1)(-3) = 25 +12 = 37

This number is positive, so the square root of it is non-zero and real. This means the two roots are real and distinct.

Answer:

The error is: The solution shows the Sam's age and the problem asked for Micaela's age.

Solution fixed: [tex]m=17[/tex]

Micaela is 17 years old now.

Step-by-step explanation:

The error is: The solution shows the Sam's age and the problem asked for Micaela's age.

To fix the error, you can set up these equations based on the information given:

[tex]m=s+2[/tex]  

[tex](m+4)+(s+4)=40[/tex]  

Solve for "s" from the first equation:

[tex]s=m-2[/tex]

Substitute this equation into the second equation:

[tex](m+4)+((m-2)+4)=40[/tex]  

Now you need to solve for "m":

[tex]m+4+(m-2+4)=40\\m+4+m+2=40\\m+m=40-4-2\\2m=34\\m=\frac{34}{2}\\\\m=17[/tex]

Micaela is 17 years old now.

Answer:

The error is: The solution shows the Sam's age and the problem asked for Micaela's age.

Solution fixed: m=17

Micaela is 17 years old now.

Step-by-step explanation:

brainliest please?

For this case we have by definition, that the volume of a square base pyramid is given by:

[tex]V = \frac {1} {3} * L ^ 2 * h[/tex]

Where:

L: It's the side of the base (square side)

h: It's the height of the pyramid

Substituting:

[tex]L = 6 \ ft\\h = 10 \ ft[/tex]

[tex]V = \frac {1} {3} * (6) ^ 2 * 10\\V = \frac {1} {3} * 36 * 10\\V = 120 \ ft ^ 3[/tex]

Answer:

[tex]V = 120 \ ft ^ 3[/tex]

Hello!

Answer:

x = 7

Step-by-step explanation:

Substitute y = 4 into the equation and solve for x

8x - (2 × 4) = 48

8x - 8 = 48 ( add 8 to both sides )

8x = 56 ( divide both sides by 8 )

x = 7

Answer:

439cor.to 3 Sig. fig.

Step-by-step explanation:

(5+12)×6×14-(5÷2)²π×14

[tex]\bf \stackrel{\textit{using the exponential model}}{N=2^D}~\hspace{7em}\begin{array}{ccll} \stackrel{days}{D}&\stackrel{\$}{N}\\ \cline{1-2} 1&2^1\implies 2\\ 2&2^2\implies 4 \end{array}[/tex]

so, using that exponential model, the 1st output value works, but the second value of 2² does not give us 8 as output.

let's check the linear model using slopes to get the equation.

[tex]\bf (\stackrel{x_1}{1}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{8})\qquad \impliedby \begin{array}{|cc|ll} \cline{1-2} D&N\\ \cline{1-2} 1&2\\ 2&8\\ \cline{1-2} \end{array}[/tex]

[tex]\bf slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{8-2}{2-1}\implies \cfrac{6}{1}\implies 6 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-2=6(x-1) \\\\\\ y-2=6x-6\implies y=6x-4[/tex]

now, using that model, x = 6, then y = 6(6) - 4, or y = 32.

Answer:

[tex]\large\boxed{a=-\dfrac{1}{10}=0.1}[/tex]

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}3=10a+b\\2=20a+b&\text{change the signs}\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}3=10a+b\\-2=-20a-b\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad1=-10a\qquad\text{divide both sides by (-10)}\\.\qquad-\dfrac{1}{10}=a\Rightarrow a=-\dfrac{1}{10}[/tex]

Answer:

this is in copy and paste form a = - 1/10 - 1.0

Answer:

Part A)  Is a directly proportional

Part B) The constant of proportionality is [tex]k=0.25[/tex]

Part C) The equation is [tex]y=0.25x[/tex]

Part D) [tex]62.5[/tex]  acres of soybeans

Step-by-step explanation:

Part A) Are the number of acres of corn and the number of acres of soybeans directly proportional or inversely proportional?

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex]

Let

x-----> the number of acres of corn

y---->  the number of acres of soybeans

so

[tex]y/x=k[/tex]  

if the number of acres of corn increases then the number of acres of soybeans increases

if the number of acres of corn decreases then the number of acres of soybeans decreases

therefore

The relationship is a directly proportional

Part B) What is the constant of proportionality?

we have that

For x=200, y=50

substitute

[tex]y/x=k[/tex]

[tex]k=50/200[/tex]

[tex]k=0.25[/tex]

Part C) Let x equal the number of acres of corn and y equal the number of acres of soybeans. Write an equation to show this relationship.

The linear equation that represent the direct variation is equal to

[tex]y/x=k[/tex]

we have

[tex]k=0.25[/tex]

substitute

[tex]y/x=0.25[/tex]

[tex]y=0.25x[/tex]

Part D) How many acres of soybeans can the farmer plant this year if he plants 250 acres of corn?

For x=250

Find the value of y

substitute in the linear equation the value of x and solve for y

[tex]y=0.25(250)=62.5[/tex] -----> acres of soybeans

Answer:

Step-by-step explanation:

ΔNPM and ΔABM are similar (AAA). Therefore the corresponding sides are in proportion:

[tex]\dfrac{NM}{AM}=\dfrac{PM}{BM}[/tex]

We have

[tex]NM=67.2m,\ AM=67.2m-32m=35.2m,\ PM=81.9m,\ BM=x[/tex]

Substitute:

[tex]\dfrac{67.2}{35.2}=\dfrac{81.9}{x}[/tex]          cross multiply

[tex]67.2x=(35.2)(81.9)[\tex]

[tex]67.2x=2882.88[/tex]              divide both sides by 67.2

[tex]x=42.9\ m[/tex]

Check the picture below.

Answer:

It's a Right Triangle

After giving 93 centimeters (which is 0.93 meters) of his 214 meters of rope to his brother, Ravi has 213.07 meters of rope left.

This question involves the concept of subtraction in the measurement unit of meters and centimeters. Initially, Ravi has 214 meters of rope. If he gives 93 centimeters of rope to his brother, keep in mind that 1 meter equals 100 centimeters. So, 93 centimeters is equal to 0.93 meters.

So, to find out how much rope Ravi is left with, you subtract the amount he gave to his brother from the original amount he had: 214 meters - 0.93 meters = 213.07 meters. This is the amount of rope Ravi has left after giving some to his brother.

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x=3,y=2

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It's a system of linear equations; let me write it out more neatly for you:

[tex]\left \{ {x + 2y = 7} \atop {x - 2y = -1}} \right.[/tex]  

Good. In order to solve a system of equations with two variables, we can find one variable and then use that variable to find the other. This wouldn't be the case if we just had one equation, note.  

Let's work on the top one first. There's multiple ways of solving this one, but here's the most simple way: isolating a single variable. The goal is to get either just x or just y on one side.  

[tex]x + 2y=7\\x = 7-2y[/tex]  

Nice. Now that we have a value of x, we can just plug it into the other equation -- since we know that x is equal to another expression, we can replace x in the other equation with the expression.  

[tex]x - 2y = -1\\(7-2y)-2y = -1\\7 - 2y - 2y = -1\\7 - 4y = -1 \\-4y = -8\\y = 2[/tex]  

Now that we have y, we can do the same thing for x. This time, however, we have the actual value of y, meaning we can just plug that in.  

[tex]x = 7 - 2y\\x = 7 - 2(2)\\x = 7 - 4 \\x = 3[/tex]  

Our solution is  

[tex]\left \{ {{x=3} \atop {y=2}} \right.[/tex]  

We can check this by plugging the values back into the equation.  

[tex]3 + 2(2) = 7\\3 + 4 = 7[/tex]  

and  

[tex]3 - 2(2) = -1\\3 - 4 = -1\\[/tex]  

That's it. There's another (easier) way to handle this specific equation, but this is the simplest way to do it.

Answer: [tex]x=11[/tex]

Step-by-step explanation:

Remembert that, by definition:

[tex]log_b(x)=y[/tex] → [tex]b^y=x[/tex]

Then, you can rewrite [tex]log_4(2x-6)=2[/tex] in exponential form:

[tex]4^2=2x-6[/tex]

Now you can solve for the variable "x":

Add 6 to both sides of the equation:

[tex]4^2+6=2x-6+6[/tex]

[tex]22=2x[/tex]

And finally you must divide both sides of the equation by 2, then:

[tex]\frac{22}{2}=\frac{2x}{2}\\\\x=11[/tex]

Opposite of adding three is subtracting three or adding -3

Esther should save $125 each month to reach her goal of $3,000 in 2 years.

Esther wants to save $3,000 in 2 years and is determining the fixed monthly amount she should contribute to her savings. To find the monthly savings amount, we must divide the total savings goal by the total number of months in 2 years.

Total amount to save: $3,000
Total number of months: 2 years x 12 months/year = 24 months

Fixed monthly saving amount = Total savings goal / Total number of months
Fixed monthly saving amount = $3,000 / 24
Fixed monthly saving amount = $125

Step-by-step explanation:

3

√

2

2

⋅

2

Pull terms out from under the radical.

3

(

2

√

2

)

Multiply  

2

by  

3

.

6

√

2

The result can be shown in multiple forms.

Exact Form:

6

√

2

Decimal Form:

8.48528137

…

For this case we must simplify the following expression:

[tex]3 \sqrt {2} +3 \sqrt {8}[/tex]

We rewrite:

[tex]8 = 2 ^ 3 = 2 ^ 2 * 2\\3 \sqrt {2} +3 \sqrt {2 ^ 2 * 2} =[/tex]

For properties of potecnias and roots we have that:

[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]

Then, rewriting the expression:

[tex]3 \sqrt {2} + 2 * 3 \sqrt {2} =\\3 \sqrt {2} +6 \sqrt {2} =\\9 \sqrt {2}[/tex]

Answer:

[tex]9 \sqrt {2}[/tex]

Answer:

where is the questions

Step-by-step explanation:

1. The area of a circle is calculated using the formula:

[tex]Area = \frac{\pi \: {d}^{2} }{4} [/tex]

The diameter is d=11 feet.

This implies that,

[tex]Area = \frac{\pi \times {11}^{2} }{4} [/tex]

[tex]Area = \frac{121\pi}{4} = 95.03 {ft}^{2} [/tex]

2. For this second question the diameter is d=10.5 feet.

We substitute into the formula to get;

[tex]Area = \frac{\pi \times {10.5}^{2} }{4} [/tex]

[tex]Area = \frac{441\pi }{16} = 86.60 {in}^{2} [/tex]

3. The area of a circle is given by the formula,

[tex]Area =\pi \: {r}^{2} [/tex]

where the radius is r=6.3

This implies that,

[tex]Area =\pi \: {(6.3)}^{2} [/tex]

[tex]Area =36.69\pi = 124.69 {cm}^{2} [/tex]

4. The given circle has a radius of 3.25 yards.

[tex]Area =\pi \times {3.25}^{2} [/tex]

[tex]Area =10.5625 \pi = 33.18 {yd}^{2} [/tex]

5(0)-5y=4

-5y=4

y=-4/5

the answer is 4/5

i hope this could help!!

Answer:

Option b (1/2,1/3)

Step-by-step explanation:

we have

2x-3y=0 ------> equation A

4x+6y=4 -----> equation B

Solve the system by elimination

Multiply equation A by 2 both sides

2(2x-3y)=2(0)

4x-6y=0 ------> equation C

Adds eqution B and equation C

4x+6y=4

4x-6y=0

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

4x+4x=4+0

8x=4

x=1/2

Find the value of y

2x-3y=0

2(1/2)-3y=0

1-3y=0

3y=1

y=1/3

the solution is the point (1/2,1/3)

the answer is 3.5987

Answer:

Mindy uses more white beads

Step-by-step explanation:

For Mindy:

red : white = 4 : 5 = 12 : 15

For Daisy:

red : white = 6 : 7 = 12 : 14

When both use 12 red beads, Mindy uses 15 white beads and Daisy uses 14 white beads.

Mindy uses more white beads when both use 12 red beads.

When they each use 12 red beads, Mindy uses more white beads in her necklaces as per the given ratios. Mindy uses 15 white beads, while Daisy uses 14 white beads.

Mindy uses a ratio of 4 red beads to 5 white beads, and Daisy uses a ratio of 6 red beads to 7 white beads. If they each use 12 red beads, we can equate their ratios. For Mindy, the equivalent ratio would be 12 red beads to 15 white beads because 4 red beads go into 12 red beads three times and three times 5 gives 15 white beads. For Daisy, the equivalent ratio would be 12 red beads to 14 white beads as 6 red beads go into 12 red beads twice and twice 7 gives 14. Therefore, when they each use 12 red beads, Mindy uses more white beads in her necklaces using beads.

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Answer:

Final answer is 1/8.

Step-by-step explanation:

Total number cards in deck of cards = 52

Total number of cards with a letter = 16

Total number of cards with red King and letter both = 2

Then probability of getting card with letter P(L) = 16/52

Then probability of getting card with letter and king both  P(K and L) = 2/52

Then required compound probability P(K|L) is given by formula:

P(K and L)= P(L)*P(K|L)

2/52= 16/52*P(K|L)

(2/52)*(52/16)=P(K|L)

2/16=P(K|L)

1/8=P(K|L)

Hence final answer is 1/8.