Solve using the FOIL method



1. (x - 2)(x + 8)


2. (x + 6)(x - 12)


3. (x + 9)(x + 4)


4. (x + 6)(x + 2)


5. (x + 6)(x + 9)


6. (x - 4)(x + 5)


7. (x + 3)(x - 3)


8. (x + 10)(x + 10)


9. (x - 3)(x + 12)


10. (x + 4)(x - 3)


11. (x + 5)(x + 2)


12. (x - 3)(x - 4)


13. (x + 8)(x - 8)


14. (x -6)(x+3)


15. (x + 1)(x - 5)

Answer:

25%

Step-by-step explanation:

To find the percentage discount for the cost of the cell phone, we need to first find the difference between the original price and the discounted price:

$120 - $90 = $30

Then we need to divide this amount by the original price and multiply by 100% to express the result as a percentage:

($30 / $120) * 100% = 25%

Therefore, the percentage discount for the cost of the cell phone is 25%.

Answer:

x = 1.28

Step-by-step explanation:

Given equation:

[tex]3 \frac{1}{2}x-6=2-2\frac{3}{4}x[/tex]

Add 2³/₄x to both sides of the equation:

[tex]\implies 3 \frac{1}{2}x+2\frac{3}{4}x-6=2-2\frac{3}{4}x+2\frac{3}{4}x[/tex]

[tex]\implies 3 \frac{1}{2}x+2\frac{3}{4}x-6=2[/tex]

Add 6 to both sides of the equation:

[tex]\implies 3 \frac{1}{2}x+2\frac{3}{4}x-6+6=2+6[/tex]

[tex]\implies 3 \frac{1}{2}x+2\frac{3}{4}x=8[/tex]

Rewrite the mixed numbers as improper fractions:

[tex]\implies \dfrac{3 \cdot 2+1}{2}x+\dfrac{2 \cdot 4+3}{4}x=8[/tex]

[tex]\implies \dfrac{7}{2}x+\dfrac{11}{4}x=8[/tex]

Make the denominators of the fractions the same:

[tex]\implies \dfrac{7 \cdot 2}{2 \cdot 2}x+\dfrac{11}{4}x=8[/tex]

[tex]\implies \dfrac{14}{4}x+\dfrac{11}{4}x=8[/tex]

[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}+\dfrac{b}{c}=\dfrac{a+b}{c}:[/tex]

[tex]\implies \dfrac{14+11}{4}x=8[/tex]

[tex]\implies \dfrac{25}{4}x=8[/tex]

Multiply both sides by 4:

[tex]\implies 4 \cdot \dfrac{25}{4}x=4 \cdot8[/tex]

[tex]\implies 25x=32[/tex]

Divide both sides by 25:

[tex]\implies \dfrac{25x}{25}=\dfrac{32}{25}[/tex]

[tex]\implies x=\dfrac{32}{25}[/tex]

Convert the improper fraction to a mixed number:

[tex]\implies x=1 \frac{7}{25}[/tex]

The value of x as a decimal:

[tex]\implies x=1.28[/tex]

The expected profit, in cents, for a player who plays 1 game is 5.25 cents.

The distribution that models the profit of a player for a single game is given as follows:

P(X = -4 cents) = 0.25. -> pays 5 cents, wins 1 cent, loses 4 cents.

P(X = 0 cents) = 0.25. -> pays 5 cents, wins 5 cents.

P(X = 5 cents) = 0.25. -> pays 5 cents, wins 10 cents.

P(X = 20 cents) = 0.25. -> pays 5 cents, wins 25 cents.

The expected value of a discrete distribution is computed by adding the total of each outcome and multiplying it by its probability, as follows:

E(X) = -4 x 0.25 + 0 x 0.25 + 5 x 0.25 + 20 x 0.25

E(X) = 5.25 cents.

Hence, the expected profit is 5.25 cents

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Answer:

To simplify the expression -3x + 6 - 3x - 24 + 2y, you can start by combining like terms.

-3x and -3x are both negative, so they can be combined to give -6x.

6 and -24 are both constants, so they can be combined to give -18.

So the simplified expression is: -6x - 18 + 2y

If you want to write the expression in standard form, you can rearrange the terms to give: 2y - 6x - 18

The two equations can you use to find the adult and child admission fees for a puppet show are 45a + 30c = 315 and 50a + 40c = 370

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that, two equations can you use to find the adult and child admission fees for a puppet show

Let a represent the fee for adults

Let c represent the fee for children.

On day 1 number of adults = 45

So, fees of 45 adults = 45a

On day 1 number of children= 30

So, fees of 30 children = 30c

Total collection on day 1 = 315

Therefore, equation is 45a + 30c = 315

On day 2 number of adults = 50

So, fees of 50 adults = 50a

On day 2 number of children = 40

So, fees of 40 children = 40c

Total collection on day 2 = 370

So, equation = 50a + 40c = 370

Hence, The two equations can you use to find the adult and child admission fees for a puppet show are 45a + 30c = 315 and 50a + 40c = 370

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If the customer purchases every pack of 12 which the shop has 192 plates in stock.

Total number of  packs of plates = 54.

The set are either sets of 8 or sets of 12.

Let x represent the overall number of 12-plate packets.

There will therefore be in total packs of 8 plates: 54 - x.

Thus,

8(54−x) + 12x = 496

432 − 8x + 12x = 496

4x = 64

x = 16

Thus, there are 16 packs of 12 plates in the store.

So, if a consumer purchases all of the 12-packs of plates, he will ultimately purchase 1216 = 192 plates.

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Answer: $72.96

Step-by-step explanation:

7.6% = 0.076

Take 960.00 times 0.076 = $72.96

Answer:

(x + 6)^2 + (y - 8)^2 = 81

Step-by-step explanation:

Here every 50th candy bar is tested . It is a sampling interval .

What does "systematic sampling" mean?

Systematic sampling is a probability sampling technique where researchers choose individuals from the population at regular intervals, such as every 15th person on a population list.

                       The advantages of simple random sampling can be imitated if the population is arranged randomly.

Systematic sampling is a type of probability sampling method in which sample members from a larger population are selected according to a random starting point but with a fixed, periodic interval. This interval, called the sampling interval.

Here every 50th candy bar is tested . It is a sampling interval .

Therefore he use systematic sampling plan.

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Answer:

hypotenuse is 17cm

Step-by-step explanation:

According to Pythagoras theorem,

AC²=AB²+BC²

AC² = 8²+15²

AC = √64+225

AC =√ 289

AC =17cm

If Mark’s mother borrows the money of $25,000 from company 2 which offers a rate of 8.5% for 3 years, she needs to pay the charge of $6375.

Interest is the cost of borrowing or saving money. Simple interest is an easy method to calculate the interest charge on a loan.

As its name, calculating the simple interest is simple and quick. We only multiply the money we borrow or deposit, by the period, then multiply them by the interest rate applied by the bank or any financial institution chosen.

The formula for calculating the simple interest is

P x R x T

P means principal or how much money we borrow or save

R means rate or how many percentages of interest applied

T means time or how long we borrow or save the money

By using the formula mentioned before, the simple interest would be

$25,000 x 8.5% x 3  = $6375

Thus, the amount of simple interest paid is $6375 and the total amount paid is $25000 + $6375 = $31,375

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Points on a perpendicular bisector of a line segment are equidistant from the segment’s endpoints is the meaning of perpendicular bisector theorem

The perpendicular bisector theorem states that if a point is on the perpendicular bisector of a segment ,then it is equidistant from the segment's endpoints.

The perpendicular bisector of a triangle is the line segment that is drawn from a vertex to the opposite side bisecting the side at a right angle. The perpendicular of a triangle is perpendicular to the sides drawn from the opposite vertices and divides the sides into two equal parts. The point at which all the three perpendicular bisectors of a triangle meets is called the circumcenter of a triangle.

It is the meaning of perpendicular bisector theorem.

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The number is the standard from is given by the equation A = 8.254 x 10⁶

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

A = 8.254 x 10⁶

On simplifying the equation , we get

A = 8.254 x 1000000

Multiplying the number , we get

A = 8,254,000

Now , the number can also be written as

A = 8254000

So , the standard form of the number A is given by the equation

A = 8.254 x 10⁶

Hence , the number is A = 8.254 x 10⁶

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a) The percentile rank of a score of 71 on this test is given as follows: 33rd percentile.

b) Victor's score, which is the 60th percentile, is given as follows: 84.

A measure is said to be in the xth percentile of the data-set if it the bottom separator of the bottom x% of measures of the data-set and the top (100 - x)% of measures, that is, it is greater than x% of the measures of the data-set.

The ordered data-set in this problem is given as follows:

58, 64, 66, 70, 71, 75, 77, 80, 84, 85, 87, 90, 93, 95, 96.

The data-set is composed by 15 scores, and 5 is the 5th score in the data-set, hence the percentile rank of a score of 71 on this test is calculated as follows:

5/15 = 0.33 = 33rd percentile.

The 60th percentile is the score at the position given as follows:

0.6 x 15 = 9th score = 84.

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Exact Form: 87/14

Decimal Form: 6.21428571... or 6.21

Answer: 6.21

Step-by-step explanation:

80085

For the data  12, 14, 21, 19, 25, 29, 26, 21, 15, and 18.

the mean is 20

the standard deviation is 3.7

the interquartile is 10

For the data  12, 14, 21, 19, 25, 29, 26, 21, 15, and 18. the mean is calculated as follows

= sum of data / number of data

sum = 200

number of data = 10

mean (x bar)  = 200 / 10

= 20

standard deviation

standard deviation is the square root of  the ratio of sum of squares to number of samples

sum of squares = (x - x bar)²

= (12 - 20)² + (14 - 20)² + (21 - 20)² + ......+(21 - 20)² + (15 - 20)² + (18 - 20)²

= 274

standard deviation = √(274 / 20) = 3.7

Interquartile range = upper quartile - lower quartile

raw data = 12, 14, 21, 19, 25, 29, 26, 21, 15, and 18

arranged data =  12, 14, 15, 18, 19, 21, 21, 25, 26, 29,

upper quartile = 25

lower quartile = 15

Interquartile range = 25 - 15 = 10

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Answer:

Hey, answer is attached.

Step-by-step explanation:

Hope this helps.

Answer:

El valor de la variable b se corresponde con:

  a) b = 0,25

  b) b = 9

  c) b = 125

The two possible solutions for the given equation are -

[x] = 0.696 and [x] = 3.054.

Given is the equation as follows -

6(x - 3).2(4x - 3) = 6

We have the equation as -

6(x - 3).2(4x - 3) = 6

12(x - 3)(4x - 3) = 6

(x - 3)(4x - 3) = 6/12

(x - 3)(4x - 3) = 1/2

x(4x - 3) - 3(4x - 3) = 1/2

4x² - 3x - 12x + 9 = 1/2

4x² - 15x + 9 = 1/2

2(4x² - 15x + 9) = 1

8x² - 30x + 18 = 1

8x² - 30x + 17 = 0

(x - 0.696)(x - 3.054) = 0

(x - 0.696) = 0     and     (x - 3.054) = 0

x = 0.696     and    x = 3.054

Therefore, the two possible solutions for the given equation are -

[x] = 0.696 and [x] = 3.054.

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Answer:

it is 3

Step-by-step explanation:

I don't know I would

Answer:

it is 3

Step-by-step explanation:

It Basile 9 divide by 4

Option A is the correct answer. All the eigenvalues of a real symmetric matrix are always real.

Symmetrix matrix: A matrix is said to be a Symmetrix matrix if A=A^T the matrix should be equal to the transpose of A.

All the eigenvalues of the Symmetric matrix are real. Eigenvectors corresponding to distinct eigenvalues are orthogonal.

Skew-Symmetrix matrix: A matrix 'A' is said to be a Skew-Symmetrix matrix if A=-A^T

Eigenvalues of the skew-symmetric matrix are zero or purely imaginary.

Skew-Hermitian matrix: A square matrix is said to be a Skew-Hermitian matrix if it is equal to the negotiation of its complex conjugate transpose.

A=-(A)^T

Eigenvalues of the Skew-Hermitian matrices are zero or imaginary.

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The vector field F = [tex](3x^2y + z^3, x^3 + 2yz, y^2 + 3xz^2)[/tex] has a nonzero divergence and a nonzero curl, indicating that it is not a conservative vector field. F cannot be expressed as the curl of another vector field.

To compute the divergence of F, we take the partial derivatives of each component with respect to their corresponding variables and sum them up. The divergence of F is given by div(F) = ∇·F = (∂/∂x)[tex](3x^2y + z^3)[/tex] + (∂/∂y)[tex](x^3 + 2yz)[/tex] + (∂/∂z)[tex](y^2 + 3xz^2)[/tex]. Evaluating these partial derivatives, we find div(F) = 6xy + 3z^2 + 2yz + 6xz.

To compute the curl of F, we take the curl operator (cross product of the del operator with F) and expand the determinant. The curl of F is given by curl(F) = ∇×F = (∂/∂y)[tex](y^2 + 3xz^2)[/tex] - (∂/∂z)[tex](x^3 + 2yz)[/tex], (∂/∂z)[tex](3x^2y + z^3)[/tex] - (∂/∂x)[tex](y^2 + 3xz^2)[/tex], (∂/∂x)[tex](x^3 + 2yz)[/tex] - (∂/∂y)[tex](3x^2y + z^3)[/tex]. Simplifying these expressions, we obtain curl(F) = [tex](-2xz, -3z^2, -6xy)[/tex].

The divergence of F is nonzero, indicating that F does not satisfy the divergence theorem, which states that a vector field with zero divergence is conservative. Additionally, the curl of F is nonzero, indicating that F does not satisfy the curl theorem, which states that a vector field with zero curl is conservative. Therefore, F is not conservative and cannot be expressed as the curl of another vector field.

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The numbers of hours taken to fill the order if the number of working machines decreased by a factor of 2 is; 44 hours

We are given;

Numbers of hours a work is complete by 6 machines = 22 hours

Now, we know that the number of hours required to complete a work is inversely proportional to the number of machines used.

Therefore, If the number of working machines decreased by a factor of 2, then the number of hours will be increased twice.

Therefore, we can say that;

The numbers of hours taken to fill the order = (22 * 6)/3

= 44 hours

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Percent changes are measured by (the change in amount) divided by (the starting amount).

In this case, you'd have

        [tex]\dfrac{6116-1951}{6116}=\dfrac{4165}{6116}\approx 0.6810[/tex]

This is about a 68% discount.

Answer:

the answer is yes because angles 5 and 2 are same side interior angles and same side interior angles add up to 180*.

Step-by-step explanation:

Make sure not to be fooled by the "it looks like it" theorem.  Teachers will try to trick you by making the lines look not parallel.  All you need to look at are if the angles are congruent or supplementary based on the theorems you hopefully were taught in class.  Wow what has brainly done I sound like a teacher lol.

Answer:

(d) 73
- and - are plus so 45+28

Step-by-step explanation:

Answer:

D) 73

Step-by-step explanation:

-)- basically means plus so 45 + 28 is ... 73,so that's your answer!

Answer:

x degrees, 14x degrees, x degrees, 14x degrees, x degrees, 14x degrees, 2x degrees, and 28x degrees.

Step-by-step explanation:

The ratio of the same side interior angles of two parallel lines is 1:14, which means that for every one degree of the first angle, the second angle measures 14 degrees. If the first angle is x degrees, then the second angle is 14x degrees.

Since the lines are parallel and the angles are on the same side of the transversal, the alternate interior angles are congruent, so the measure of the third angle is also x degrees, and the measure of the fourth angle is also 14x degrees.

Since the lines are parallel, the alternate exterior angles are also congruent, so the measure of the fifth angle is also x degrees, and the measure of the sixth angle is also 14x degrees.

Finally, the measures of the seventh and eighth angles can be found by adding the measures of the adjacent angles. The seventh angle is adjacent to the third and fifth angles, so its measure is x + x = 2x degrees. The eighth angle is adjacent to the fourth and sixth angles, so its measure is 14x + 14x = 28x degrees.

In summary, the measures of the eight angles formed by the parallel lines and transversal are x degrees, 14x degrees, x degrees, 14x degrees, x degrees, 14x degrees, 2x degrees, and 28x degrees. The value of x can be determined by knowing the measure of one of the angles, or by using other information about the angles or the parallel lines.

Answer:

I believe that the answer is 2/5 because all of the other answers equal 10 (for b and c) or 20 (for a)

Step-by-step explanation:

The work is done in pumping a full tank of water up to ground level is 470400πNm.

Tank sizes variety from 6 ft. to one hundred twenty ft. in diameter with a roof, and as much as two hundred toes in diameter as an open pinnacle tank. Tanks with a roof have capacities starting from seven-hundred gallons to 500,000 gallons at the same time as the open pinnacle tanks may be constructed with even large capacities

The radius of the layer = 2m

V= pi (2)^2 (Delta y) m^3 = four pi Delta y m^3V=π(2) 2 (Δy)m 3 =4πΔym 3

Weight of the layer =9800 (four pi Delta y)=9800(4πΔy)

Weight of the water = 9800 frac=9800 m 3 N

So, weight of the layer = 39200 pi Delta y=39200πΔy

distance layer is moved =5-y=5−y

W=int_^{four} (5-y)(39200 pi dyW=∫ 04 (5−y)(39200πdy

=39200 pi int_^{four} (5-y) dy=39200π∫ 04 (5−y)dy

=39200 pi left[ 5y - frac y^2 right]_^{four}=39200π[5y− 21 y 2 ] 04

=-39200 pi (12) = 470400 pi Nm=−39200π(12)= 470400πNm.

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The solution is Option A.

The amount after 9 years with an investment of $ 7000 at a simple interest calculated quarterly at rate 2.05 is $ 7,322.88

What is Simple Interest?

Simple interest is a method of calculating interest that ignores the impact of compounding. While interest frequently compounds throughout the course of a loan's set periods, simple interest does not. Simple interest is calculated by multiplying the principal amount by the interest rate, times the number of periods.

Simple Interest = ( Principal Amount x Rate x Time Period ) / 100

Given data ,

Let the simple interest be represented as I

Now , the amount invested P = $ 7,000

The rate of interest R = 2.05 %

The time period t = 9 years

Since the interest is calculated quarterly , t= T/4

Now , the simple interest is calculated by the formula

Simple Interest = ( Principal Amount x Rate x Time Period ) 100

Substituting the values in the equation , we get

Simple Interest I = [ ( 7000 x 2.05 x 9 ) / 4 ] / 100

On simplifying the equation , we get

Simple Interest I = ( 129150 ) / 400

Simple Interest I = $ 322.875

I = $ 322.88

Now , the amount after 9 years = initial amount P + Interest I

Amount after 9 years = 7,000 + 322.88

Amount after 9 years = $ 7,322.88

Hence , the amount after 9 years is $ 7,322.88

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