Multiply and simplify the product (6 + 3i)(6 − 3i)

Answer:

7.5 pounds of muscles.

Step-by-step explanation:

Mr. Tan gained 5 pounds of solid fast twitching muscles during his last bulking phase lasting 24 days.

If this rate remains the same, then we can use the unitary method to calculate the amount of muscle he will gain in 36 days bulking phase.

Hence, within 24 days of the bulking phase, he gains 5 pounds of muscles.

So, within 36 days of the bulking phase, he will gain [tex]\frac{5}{24} \times 36 = 7.5[/tex] pounds of muscles. (Answer)

First, we calculated Mr. Tran's rate of muscle gain by dividing the total amount gained by the number of days. We then applied this rate to the asked time frame of 36 days. The result was approximately 7.48 lbs of muscle gain.

To solve this problem, we need to determine the rate of gain. Mr. Tran gained 5 lbs of solid fast twitching muscles in 24 days, so his rate of gain is 5 lbs / 24 days = 0.208 lbs/day. If Mr. Tran continues this rate for an extended period of 36 days, we can calculate the total gain by multiplying his daily rate by the number of days, i.e., 0.208 lbs/day * 36 days = 7.48 lbs. rounded to two decimal places.

So, if Mr. Tran’s bulking phase continues at the same rate for 36 days, he will gain approximately 7.48 lbs of muscle.

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Answer:

x=-5, y=-5. (-5, -5).

Step-by-step explanation:

-x-5y=30

10x+5y=-75

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

9x=-45

x=-45/9

x=-5

-(-5)-5y=30

5-5y=30

5y=5-30

5y=-25

y=-25/5

y=-5

Answer:

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

Step-by-step explanation:

[tex]using \: point \: slope \: form \\ y - y1 = m(x - x1) \\ y + 9= \frac{ - 4}{3} (x - 9) \\ y + 9= \frac{ - 4}{3}x + 12\\ y = \frac{ - 4}{3} x + 3[/tex]

The equation of the line in point-slope form passing through (9, -9) with a slope of -4/3 is y + 9 = -4/3 * (x - 9).

The point-slope form of a line's equation is expressed as y - y1 = m(x - x1). In this equation, 'm' represents the line's slope and (x1, y1) defines a particular point through which the line passes. In this scenario, the slope is given as '-4/3' and the point (9, -9). Consequently, by substituting these parameters into the point-slope form, we obtain the equation y - (-9) = (-4/3)(x - 9) or y + 9 = -4/3 * (x - 9).

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Answer:

A deck=52

Probability of selecting black cards 26/52

26/52*3/52

Step-by-step explanation:

Correct me if I am wrong.

Given expression is:

By substituting the value of "b" in the given expression, we get

→ [tex]a + \frac{3}{4} = 21[/tex]

→       [tex]a = 21 - \frac{3}{4}[/tex]

By taking L.C.M, we get

             [tex]= \frac{84-3}{4}[/tex]

             [tex]= \frac{81}{4}[/tex]

Thus the response above is correct.

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Answer:

9 tables

Step-by-step explanation:

Let x be the number of chairs sold and y be the number of tables sold.

Chairs are sold for $100 each, then x chairs cost $100x.

Tables are sold for $550 each, then y tables cost $550y.

Every day, the store can ship at most 21 pieces of furniture, then

[tex]x+y\le 21[/tex]

Store must sell no less than $5,700 worth of chairs and tables, then

[tex]100x+550y\ge 5,700[/tex]

If 10 chairs were sold, then [tex]x=10.[/tex] Substitute this value into both inequalities:

1. [tex]10+y\le 21\Rightarrow y\le 11[/tex]

2. [tex]100\cdot 10+550y\ge 5,700\Rightarrow 550y\ge 4,700\Rightarrow y\ge \dfrac{470}{55}=8\dfrac{6}{11}[/tex]

Hence, [tex]8\dfrac{6}{11}\le y\le 11[/tex]

The minimum number of tables that the the store must sell in order to meet the requirements is 9 tables

Answer:{ 9, 10, 11 }

Step-by-step explanation:

Correct option:

[tex]2x^2+3x-13x-1[/tex]

A quadratic function is given by the form:

[tex]f(x)=ax^2+bx+c \\ \\ Being \ a,b,c \ any \ real \ constants[/tex]

On the other hand, a quadratic equation is given by the form:

[tex]ax^2+bx+c=0 \\ \\ Being \ a,b,c \ any \ real \ constants[/tex]

And a quadratic expression is given by the form:

[tex]ax^2+bx+c \\ \\ Being \ a,b,c \ any \ real \ constants[/tex]

As you can see, when talking about the term quadratic the higher degree of the polynomial is 2. The options are:

[tex]1. \ 6x^4-5x^3+3x^2-7x-8 \\ \\ 2. \ 5x^3+3x^2-7x-8 \\ \\ 3. \ 2x^2+3x-13x-1[/tex]

So the only option that meets our requirement is:

[tex]2x^2+3x-13x-1[/tex]

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Answer:

2x^2+3x-13x-1

Step-by-step explanation:

Answer:

$1.95 is 15% of 13 dollars

Answer:

13 - 15% (1.90) = 11.10

Step-by-step explanation:

13 - 15% (1.90) = 11.10

Answer: B

Step-by-step explanation:

The common factor missing from both sets of parentheses in the polynomial 10x^3 + 35x^2 - 4x - 14 when factored by grouping is (2x + 7).

To factor the polynomial 10x3 + 35x2 - 4x - 14 by grouping, we must first split the polynomial into two pairs that have a common factor. We can pair the terms as follows: (10x3 + 35x2) and (-4x - 14).

Factoring out the greatest common factor from each pair, we get:

5x2(2x + 7)

-2(2x + 7)

Now, we can observe that both pairs contain the common factor (2x + 7). So, the polynomial can be re-written using this common factor:

5x2(2x + 7) - 2(2x + 7)

Drawn out completely, the factored form of the polynomial using the distributive property (also known as factoring by grouping) thus becomes:

(5x2 - 2)(2x + 7)

Answer:

See explanation

Step-by-step explanation:

    Statement                              Reason

1. [tex]\overline{PS}\perp \overline{SQ}[/tex]                           Given

2. [tex]m\angle PSQ = 90^{\circ}[/tex]          Definition of perpendicular lines

3. [tex]\triangle PSQ[/tex] is right triangle   Definition of right triangle

4. [tex]\overline{RQ}\perp \overline{SQ}[/tex]                          Given

5. [tex]m\angle RQS = 90^{\circ}[/tex]          Definition of perpendicular lines

6. [tex]\triangle RQS[/tex] is right triangle   Definition of right triangle

7. [tex]m\angle PSQ=m\angle RQS[/tex]       Substitution property of equality

8. [tex]\overline {SQ}\cong \overline {QS}[/tex]    Reflexive property

9. [tex]\overline {PQ}\cong \overline {RS}[/tex]                        Given

10. [tex]\triangle PSQ\cong \triangle RQS[/tex]               HL postulate

Step-by-step explanation:

A box of cereal states that there are 93 calories in a three fourths-cup serving. What is the unit rate for calories per cup?

126.7 ~= 127 calories

How many calories are there in 2 cups of the cereal?

127 *2 = 254 calories.

The unit rate for calories per​ cup is 124 calories and 2 cups of the​ cereal contain 248 calories.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given is a box of cereal which states that there are 93 calories in a

(3/4)th of a cup serving.

We can write -

3/4 cup serving contain → 93 calories

1 cup serving will contain → (93 x 4)/3 which is equivalent to 124 calories

Similarly, we can calculate for 2 cups of serving as -

1 cup → 124 calories

2 cups → (2 x 124) = 248 calories

Therefore, the unit rate for calories per​ cup is 124 calories and 2 cups of the​ cereal contain 248 calories.

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Answer:

about $2,557

Actual cost : $2556.97

Step-by-step explanation:

well since all of them are .99 if you round to the hundreths it make another dollar cause it will force the .9 to become 1.0

so it be 1450 for the refrigerator, 490 for the dishwasher, and 617 for the electric range.

add those numbers to get about $2,557

Answer:

B

Step-by-step explanation:

The circumference (C) of a circle is calculated as

C = 2πr ( isolate r by dividing both sides by 2π )

C ÷ 2π = r → B

Answer:

b=[tex]\frac{c}{2\pi }[/tex]

Step-by-step explanation:

Answer:

[tex]AB=DC=32\ units[/tex]

[tex]AD=BC=24\ units[/tex]

Step-by-step explanation:

we know that

In a parallelogram, opposite sides are parallel and congruent

In this problem we have a parallelogram

so

[tex]DC=AB[/tex]

[tex]AD=BC[/tex]

substitute the given values

[tex]5x-18=2x+12[/tex]

[tex]5x-2x=12+18[/tex]

[tex]3x=30[/tex]

[tex]x=10[/tex]

Find the length of side AB

[tex]AB=2x+12[/tex]

substitute the value of x

[tex]AB=2(10)+12=32\ units[/tex]

Find the length of side CB

[tex]BC=3x-6[/tex]

substitute the value of x

[tex]BC=3(10)-6=24\ units[/tex]

therefore

[tex]AB=DC=32\ units[/tex]

[tex]AD=BC=24\ units[/tex]

Answer:

x=1/2

Step-by-step explanation:

4x-5(x-2)=12x+4-x

4x-5x+10=12x-x+4

-x+10=11x+4

-x-11x+10=4

-12x+10=4

-12x=4-10

-12x=-6

12x=6

x=6/12

simplify

x=1/2

Answer: x = 1/2

Explanation :

First write the equation as you see it:

4x-5(x-2)=12x+4-x

Next do the math in the parentheses:

4x-5x+10=12x-x+4

Combine the x’s:

-12x+10=4

Switch the 10 and put it on the other side:

-12x=4-10

Change to negative to positive:

12x=6

Divide:

x=6/12

Simplify

x=1/2

Thus, you answer is x = 1/2

Hope this helps! :)

The equation for Louis's purchase is: [tex]x+y=8[/tex]

The equation for Kate's purchase is: [tex]y+z=9[/tex]

The equation for Biff's purchase is: [tex]x+y+z=13.50[/tex]

Step-by-step explanation:

First of all we have to define variables for each item involved in the purchase

Let x represent burger

y represent soda

z be the slice of pizza

Then

"Louis bought a burger and soda for $8"

[tex]x+y=8[/tex]

"Kate purchased a slice of pizza and soda for $9"

[tex]y+z=9[/tex]

"Biff purchased a burger, a slice of pizza and a soda for $13.50"

[tex]x+y+z=13.50[/tex]

The equation for Louis's purchase is: [tex]x+y=8[/tex]

The equation for Kate's purchase is: [tex]y+z=9[/tex]

The equation for Biff's purchase is: [tex]x+y+z=13.50[/tex]

Keywords: Linear Equations, Variables

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[tex]\bf \left( \cfrac{1}{~~\begin{matrix} 2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~} \right)(~~\begin{matrix} 2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~x)(x+8)\implies x(x+8)\implies x^2+8x[/tex]

Answer:

[tex]x^{2} +8x[/tex]

Answer:

3/6 or 1/2 or 50:50 there all right

Step-by-step explanation:

I am guessing that by simple dice you mean a 6 sided die and we know that 6 sided dice goes up to 6 and there are 3 prime number up to 6 which are 2 3 5 so if 3 out of 6 numbers are prime it is half of the dice so there is a 50/50 chance you role a prime number

Answer:

-1

Step-by-step explanation:

if x = 0...

2(0) + 8(0) - 1 =

0 + 0 - 1 =

0 - 1 =

-1

Answer:

The kinetic energy of the roller coaster is 1600000 J.

Step-by-step explanation:

Given:

Mass of the roller coaster is 8000 Newton's and speed 20.0 meters/seconds.

Now, we need to find the kinetic energy [tex]E_{k}[/tex] of the roller coaster.

So, Mass of roller coaster (m) = 8000 N.

Velocity of roller coaster (v) = 20.0 m/s.

Now, putting the formula of kinetic energy:

[tex]E_{k} = \frac{1}{2}\times m\times v^{2}[/tex]

[tex]E_{k}=\frac{1}{2} \times 8000\times 20^{2}[/tex]

[tex]E_{k}=\frac{1}{2} \times 8000\times 400[/tex]

[tex]E_{k}=\frac{1}{2} \times 3200000[/tex]

[tex]E_{k}=1600000[/tex]

Therefore, the kinetic energy of the roller coaster is 1600000 J.

Answer:

Step-by-step explanation:

5/10 and 1/2 are both equivalent ratios resulting in half of themselves you can multiply these by any numbers but they will stay as half ratios such as 1:2 x 6 it would be 6:12 divide it by 6 and you have a half

Equivalent ratios have a multiplicative relationship, where multiplying both terms of a ratio by the same number results in another equivalent ratio. For example, multiplying the ratio 1:2 by 2 gives the equivalent ratio 2:4, showing that the ratios are proportional to each other.

Understanding Equivalent Ratios through Multiplication

We can explore the concept of equivalent ratios by looking at their multiplicative relationship. For instance, let's consider the ratios 1:2 and 2:4. These two ratios are equivalent because if we multiply both terms of the first ratio by 2, we get the second ratio. Mathematically, this can be expressed as 1x2/2x2 = 2/4, which is the same as the second ratio. Hence, the multiplication of both the numerator and the denominator of the first ratio by the same number (in this case, 2) maintains the ratio's equivalence to the second ratio.

This concept is crucial when dealing with proportions, unit rates, and unit scales. For example, if a map uses a unit scale of 1 inch = 100 feet, doubling the distance on the map to 2 inches would also double the actual distance to 200 feet, showing a direct multiplicative relationship between the two equivalent ratios.

Understanding how to use multiplication to find equivalent ratios is fundamental in solving problems that involve scaling, such as converting units or working with maps and models.

Answer:

[tex]\frac{11}{36}[/tex] yard

Step-by-step explanation:

Length of string Mrs. Ruiz has = [tex]\frac{11}{12}[/tex] yard

Mrs. Ruiz needs to hang 3 banners using the string.

Having known that each banner uses same length of string to be hung we can divide total length of sting into 3 equal parts.

So, we can divide [tex]\frac{11}{12}[/tex] yard by 3 as

⇒ [tex]\frac{11}{12}\div 3[/tex]

Changing the division sing to multiplication by taking reciprocal of divisor.

⇒ [tex]\frac{11}{12}\times \frac{1}{3}[/tex]

We can now multiply numerators and denominators.

⇒ [tex]\frac{11}{36}[/tex] yard

∴  Mrs. Ruiz must used  [tex]\frac{11}{36}[/tex] yard of string for each banner.

Answer:

132 inches

Step-by-step explanation:

first convert yards(yd) to feet(ft)

3yd* (3ft / 1 yd)  (yds cancel)

3 * 3ft = 9ft

9ft + 2ft = 11ft

11ft * (12in / 1ft) (ft cancel)

11 * 12in = 132in

Answer:

110 inches

Step-by-step explanation:

1 yard = 36 * 3 = 108 + 2 = 110

Answer:

[tex](x-2)(8x+4)[/tex]

Step-by-step explanation:

we have

[tex]8x^{2} -12x-8[/tex]

Equate to zero and find the roots of the quadratic equation

The formula to solve a quadratic equation of the form

[tex]ax^{2} +bx+c=0[/tex]

is equal to

[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]

in this problem we have

[tex]8x^{2} -12x-8=0[/tex]

so

[tex]a=8\\b=-12\\c=-8[/tex]

substitute in the formula

[tex]x=\frac{-(-12)(+/-)\sqrt{-12^{2}-4(8)(-8)}} {2(8)}[/tex]

[tex]x=\frac{12(+/-)\sqrt{400}} {16}[/tex]

[tex]x=\frac{12(+/-)20} {16}[/tex]

[tex]x_1=\frac{12(+)20} {16}=2[/tex]

[tex]x_2=\frac{12(-)20} {16}=-\frac{1}{2}[/tex]

therefore

[tex]8x^{2} -12x-8=8(x-2)(x+\frac{1}{2})=(x-2)(8x+4)[/tex]

Answer:

x = 7,y = 8

Step-by-step explanation:

(20 + x + y )/ 5 = x

4x = 20 + y

x ≥ 6

y ≥ 6

if x = 6, y = 4 No

if x = 7, y = 8 Yes!

Answer:

-1 1/2

The drawing will help

Answer:

-15

Step-by-step explanation:

9 divided by 10 is 0.9 and -3 divided by 5 is -0.06

and 0.9 divided by -0.06 is

We can see here that the cost of the food bill and tip before sales tax was approximately $253.20.

To find the cost of the food bill and tip before sales tax, you first need to calculate the tip amount and then add it to the food bill.

Given:

Food bill = $214.58

Tip rate = 0.18 (18% expressed as a decimal)

First, calculate the tip amount:

Tip = Food bill × Tip rate

Tip = $214.58 × 0.18

Tip = $38.6244 (rounded to two decimal places)

Tip ≈ $38.62

Now, add the food bill and the tip to find the total cost before sales tax:

Total cost = Food bill + Tip

Total cost = $214.58 + $38.62

Total cost = $253.20

Therefore, the cost of the food bill and tip before sales tax was approximately $253.20.

Answer:

60°

Step-by-step explanation:

Jenny drew a figure in art school and the figure is shown in the attached diagram.  

The diagram is a regular hexagon and it has rotational symmetry.  

Two of its sides is placed parallel to the x-axis.

Therefore, by rotating 60° the adjacent sides will become parallel to the x-axis and the figure remains the same and symmetric with respect to the coordinate axes. (Answer)

Answer:

Step-by-step explanation:

The fiven figure is a hexagon, which is a regular polygon with six equal sides.

Now, the symmetry of a hexagon is based on a 60° rotation, because each symmetrical portion of the figure enclosed a 60° angle.

Therefore, the right answer is 60°.

x equals 22

____________________________________________

The Segment Postulate states the following:

Given two end points A and B, a third point C lines on the segment AB if and only if the distances between the points satisfy the equation:

[tex]\overline{AB}=\overline{AC}+\overline{CB}[/tex]

____________________________________________

From the figure:

[tex]\overline{AC}=8+x \\ \\ \overline{CB}=10 \\ \\ \overline{AB}=40[/tex]

Our goal is to find x:

[tex]\overline{AB}=\overline{AC}+\overline{CB} \\ \\ Substituting \ values: \\ \\ 40=(8+x)+10 \\ \\ 18+x=40 \\ \\ Subtracting \ 18 \ from \ both \ sides: \\ \\ 18-18+x=40-18 \\ \\ \boxed{x=22}[/tex]

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Answer:

If by bi-weekly you mean once every two weeks, then the friend who is payed bi-weekly has a higher annual salary. The same for if he is payed twice a week.

Step-by-step explanation:

1458 x 24 = 34992

1346 x 26 =34996