If the width of a rectangle is 8 less than the length and the perimeter is 32, find the dimensions of the rectangle

Final answer:

The expression equal to [tex]-x^2[/tex] - 4 is formed by multiplying two complex conjugates. Option C: (x+2i)(x-2i) correctly expands to [tex]-x^2[/tex] - 4, since the product of the imaginary parts (2i × -2i) equals -4. The correct option is C: (x+2i)(x-2i).

Explanation:

The expression [tex]-x^2[/tex] - 4 can be created by multiplying two complex numbers that, when multiplied, give a negative real part and a positive imaginary part squared. Using the fact that (i)(i) = -1, we can deduce that the product of complex conjugates will give us the desired expression because the imaginary parts will cancel each other out leaving us with a purely real number.

When we multiply two complex conjugates, the general form is (a+bi)(a-bi) = [tex]a^2 - (bi)^2 = a^2 + b^2[/tex], since [tex](bi)^2[/tex] equates to [tex]-b^2[/tex] because [tex]i^2[/tex] = -1. Applying this to our problem, we are looking for 2 numbers whose square equals 4. Since 2i × -2i = -4, we can construct the two factors as (x+2i) and (x-2i), which corresponds to option C: (x+2i)(x-2i).

Answer:

200

Step-by-step explanation:

200 × 33% = 66 so

200 is answer

Answer:

A) 200

Step-by-step explanation:

33% of x is 66

33/100 = 66/x

33x = 6600

x = 6600/33

x = 200

Answer:

Her weekly allowance is $8.

Step-by-step explanation:

Let the weekly allowance of Ming is $x.

If she spends half of her weekly allowance playing mini-golf and to earn more money her parents let her wash the car for $5, then the remaining amount of money that she has = [tex](\frac{x}{2} + 5)[/tex] dollars.

Now, given that [tex](\frac{x}{2} + 5) = 9[/tex]

⇒ [tex]\frac{x}{2} = 4[/tex]

⇒ x = $8

Therefore, her weekly allowance is $8. (Answer)

Answer:

2121.6 cubic inch

Step-by-step explanation:

Length of the box = 17 inches

Width of the box = 1.3 feet = 1.3 * 12 inches = 15.6 inches

Height of the box = 8 inches

Volume of the box is given by the product of its length , width and height.

Hence, Volume = {tex]\[length * width * height\][/tex]

= [tex]\[17 * 15.6 * 8\][/tex]

= 2121.6

Hence the volume of the box is 2121.6 cubic inch

This can also be expressed in cubic feet by dividing it by 1728.

In cubic feet the volume will be 1.23 cubic ft.

Answer:

C. x-intercepts: (-4,0), (-2,0)

E. Vertex: (-3,-1)

Step-by-step explanation:

Part 1) Find the x-intercepts

we have

[tex]y=(x+4)(x+2)[/tex]

This is a vertical parabola written in factored form

[tex]y=(x-x_1)(x-x_2)[/tex]

where

x_1 and X_2 are the roots or x-intercepts

so

[tex]x_1=-4\\x_2=-2[/tex]

Remember that the x-intercepts are the values of x when the value of y is equal to zero

therefore

The x-intercepts are

(-4,0) and (-2,0)

Part 2) Find the vertex

we have

[tex]y=(x+4)(x+2)[/tex]

This is a vertical parabola open upward (the leading coefficient is positive)

The vertex is a minimum

Applying distributive property

[tex]y=x^2+2x+4x+8\\y=x^2+6x+8[/tex]

Convert to vertex form

Complete the square. Remember to balance the equation by adding the same constants to each side.

[tex]y=(x^2+6x+3^2)+8-3^2[/tex]

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

Rewrite as perfect squares

[tex]y=(x+3)^2-1[/tex] ----> equation in vertex form

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

where

(h,k) is the vertex

therefore

The vertex is the point (-3,-1)

Answer:

Vertex: (-3,-1) X intercepts: (-4,0), (-2,0)

Step-by-step explanation:

A P E X ;)

Answer:

21 feet (20.977)

Step-by-step explanation:

1. Draw a picture, it makes it much easier. Draw a right triangle with the vertical labeled 25 and the horizontal labeled X, then label the angle adjacent to the horizontal and hypotenuse 40°

2. Use tangent because X is opposite of 40 and 25 is adjacent to angle 40. the equation would be Tan40/1 = X/25

3. You then cross multiply to get 25Tan(40) = X

4 You then plug it into a calculator and get the full answer of 20.97749078, but I always round up to either 20.98 or 21 feet, whatever your teacher allows

Answer:

35 lbs

Step-by-step explanation:

because 160-120=40-5=35. sorry if wrong

Maggie wants to the middle of the healthy range weight 130lbs should she gain.

Given that,

Maggie weighs for her height = 105lbs

Recommended weight = 120lbs

Limit for weighs not more than = 160lbs

We have to find ;

If she wanted to be in the middle of the healthy range how much weight should she gain.

According to the question,

If she wanted to be in the middle of the healthy range = Limit for weighs not more than - Recommended weight

= 160lbs - 120lbs

= 40lbs

Then,

Recommended weight - limit for weighs not more than

= 120lbs - 105lbs

= 15lbs

Difference between the weight = 40-15 = 25lbs

Therefore ,

Maggie weighs for her height + Difference between the weight = 105lbs + 25lbs = 130lbs

Hence , Maggie wants to the middle of the healthy range weight 130lbs should she gain.

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Answer:

Step-by-step explanation:

[tex]\frac{1}{4}*\frac{10}{9}=\frac{1*5}{2*9}=\frac{5}{18}[/tex]

The simplified fraction is 9/40.

To simplify the complex fraction 1/4 over 10/9, you can multiply both the numerator and the denominator by the reciprocal of the denominator of the complex fraction, which is 9/10. This is sometimes referred to as the skillfully chosen factor. By doing so, you are simplifying the expression by getting rid of the complex fraction structure.

Here's the step-by-step simplification:

Multiply both the numerator (1/4) and the denominator (10/9) by 9/10.

Simplifying the numerator: (1/4) * (9/10) = 9/40.

Simplifying the denominator: (10/9) * (9/10) = 1 because the nines and tens cancel out.

Now you have a simple fraction: 9/40 over 1, which is just 9/40.

The simplified fraction is 9/40. When multiplying fractions, you multiply the top numbers and divide by the bottom numbers in the fractions.

Answer:

18 servings each pint being 1/3 serving size that 3 servings per pint 3×6 =18

Answer:

300mb

Step-by-step explanation:

We can read the atmospheric pressure at an altitude of 22 kilometers can be read by tracing directly from the graph.

22 kilometers is half way between 20 kilometers and 24 kilometers on the vertical axis.

The reading is shown in the attachment.

From the reading the atmospheric pressure is about 300mb

The correct answer is A

Answer:

12x^2-15x

Step-by-step explanation:

PLATO

The expression 12x²-15x has the same GCF as 15x² - 21x.

An expression is combination of variables, numbers and operators.

The given expression is 15x²-21x

Let us find GCF of the given expression.

The GCF for a polynomial is the largest monomial that divides (is a factor of) each term of the polynomial

15x²-21x

3x(5x-7)

The GCF of 15x²-21x is 3x.

Now GCF of 18x²-24x,  6x(3x-4) is 6x

GCF of 12x²-15x, 3x(4x-4) is 3x

GCF of 15x²-21, 3(5x²-7) is 3

GCF of 12x²-18x, 6x(2x-3) is 6x

Hence, the expression 12x²-15x has the same GCF as 15x² - 21x.

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Answer: 7.6, 22/7, 1.01

Step-by-step explanation:

Answer:

B (-2, 0)

Step-by-step explanation:

put the first equation in for y in the second equation - watch the negative

2x - (x +2) = -4

2x - x -2 = -4

x = -2

plug this x back in to find y

y = -2 + 2 = 0

Answer:

B

Step-by-step explanation:

plug in the answers given into both equations to see if the statements true

y=x+2

0=(-2)+2

0=0

2x-y=-4

y=2x+4

0=2(-2)+4

0=0

Answer:

X=4 Hope it helps Lol

Step-by-step explanation:

  5*x-3-(21-x)=0

Step by step solution :

Step  1  :

Pulling out like terms :

1.1     Pull out like factors :

  6x - 24  =   6 • (x - 4)

Equation at the end of step  1  :

Step  2  :

Equations which are never true :

2.1      Solve :    6   =  0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation :

2.2      Solve  :    x-4 = 0

Add  4  to both sides of the equation :

                     x = 4

One solution was found :

                  x = 4

Answer:

X=4

Step-by-step explanation:

Answer:

NOTE: Standard form is Ax+By=C

Distribute -1

5a -a +3b

Rewrite

5a +3b = -a

Multiply every term by -1 so -a will be positive

-5a -3b = a

Answer:

Option D. y=4x+35

Step-by-step explanation:

From the graph take the points (5,50) and (50,250)

Find the slope

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

substitute the values

[tex]m=\frac{250-50}{50-5}[/tex]

[tex]m=\frac{200}{45}=4.4[/tex]

Find the equation of the line in slope intercept form

[tex]y=mx+b[/tex]

we have

[tex]m=4.4\\point\ (5,50)[/tex]

substitute

[tex]50=4.4(5)+b[/tex]

solve for b

[tex]b=50-22\\b=28[/tex]

substitute

[tex]y=4.4x+28[/tex]

therefore

The equation that BEST models the data is

[tex]y=4x+35[/tex]

Answer:

mean = -0.25

Step-by-step explanation:

Explanation:-

mean:- The sum of all the observations and then divided the number of observations and it is denoted by 'μ'

given data is -15 , -12 , 8 and 9

Given observations is '4' so n = 4

[tex]mean= \frac{-15-12+8+9 }{4}[/tex]

[tex]mean= \frac{-27+17}{4}[/tex]

[tex]mean = -0.25[/tex]

The mean of given data is - 0.25

The mean of -15, -12, 8, and 9 is calculated by summing the numbers to get -10 and then dividing by 4, leading to a mean of -2.5.

The mean of a set of numbers is calculated by summing up all the numbers and then dividing the total by the count of the numbers. In this case, to find the mean of -15, -12, 8, and 9, you would add these four numbers together and then divide by 4, because there are four numbers in this set.

The calculation would look like this:

(-15) + (-12) + 8 + 9 = -10

To find the mean, you would then divide -10 by the number of values in the set, which is 4:

Mean = -10 / 4 = -2.5

Therefore, the mean of the numbers -15, -12, 8, and 9 is -2.5.

x = 5

Solution:

Given equation is [tex]x+1=\sqrt{5x+11}[/tex].

[tex]\Rightarrow x+1=\sqrt{5x+11}[/tex]

Squaring on both sides of the equation to remove the square root.

[tex]\Rightarrow (x+1)^2=(\sqrt{5x+11})^2[/tex]

[tex]\Rightarrow (x+1)^2=5x+11[/tex]

Using algebraic identity: [tex](a+b)^2=a^2+2ab+b^2[/tex]

[tex]\Rightarrow x^2+2x(1)+1^2=5x+11[/tex]

[tex]\Rightarrow x^2+2x+1=5x+11[/tex]

Combine all terms in one side of the equation.

[tex]\Rightarrow x^2+2x+1-5x-11=0[/tex]

Arrange like terms together.

[tex]\Rightarrow x^2+2x-5x+1-11=0[/tex]

[tex]\Rightarrow x^2-3x-10=0[/tex]

Now solve by factorization.

[tex]\Rightarrow x^2-5x+2x-10=0[/tex]

[tex]\Rightarrow (x^2-5x)+(2x-10)=0[/tex]

Take common terms on left side of the term.

[tex]\Rightarrow x(x-5)+2(x-5)=0[/tex]

Now, take (x – 5) common on both terms.

[tex]\Rightarrow (x+2)(x-5)=0[/tex]

⇒ x + 2 = 0 (or) x – 5 = 0

⇒ x = –2 (or) x = 5

If we put x = –2 in the given equation,

[tex]-2+1=\sqrt{5(-2)+11}[/tex]

[tex]\Rightarrow-1=1[/tex]

It is false. So, x = –2 is not true.

If we put x = 5 in the given equation,

[tex]5+1=\sqrt{5\times5+11}[/tex]

[tex]5+1=\sqrt{36}[/tex]

[tex]\Rightarrow6=6[/tex]

It is true. So, x = 5 is true.

Hence x = 5 is the solution.

Answer:

5 pounds of shrimp and 5 pounds of crawfish were purchased in the mixture.                                          

Step-by-step explanation:

We are given the following in the question:

Bobby buys 10 pounds seafood for $30.

Let x pounds of shrimp be purchased and y pounds of crawfish.

Thus, we can write,

[tex]x + y =10[/tex]

Cost of shrimp = $5 per pound

Cost of crawfish = $1 per pound

Total money spent = $30

Thus, we can write the equation,

[tex]5x + y = 30[/tex]

Solving the two equation by elimination method,

[tex]5x + y-(x+y) = 30-10\\4x = 20\\x = 5\\y = 10 - x = 10 - 5 = 5[/tex]

Thus, 5 pounds of shrimp and 5 pounds of crawfish were purchased in the mixture.

Step-by-step explanation:

[tex]C = 2\pi \: r \\ = 2 \times 3.14 \times 4.5 \\ = 3.14 \times 9 \\ =28.26 \: units[/tex]

Answer:

b.

Step-by-step explanation:

Answer:

The sign of [tex]x[/tex] in [tex]g(x)[/tex] is opposite or negated. This is the only difference between [tex]f(x)[/tex] and  [tex]g(x)[/tex], meaning it is a reflection through the y-axis.

Therefore, [tex]g(x)[/tex]  will be the reflection of [tex]f(x)[/tex] through the y-axis.

Step-by-step explanation:

Considering the functions

We know that when we reflect a function through the y-axis, the x-coordinate gets opposite - negated.

Here, the sign of [tex]x[/tex] in [tex]g(x)[/tex] is opposite or negated. This is the only difference between [tex]f(x)[/tex] and  [tex]g(x)[/tex], meaning it is a reflection through the y-axis.

Therefore, [tex]g(x)[/tex]  will be the reflection of [tex]f(x)[/tex] through the y-axis.

Answer:

The sign of  in  is opposite or negated. This is the only difference between  and  , meaning it is a reflection through the y-axis.

Therefore,   will be the reflection of  through the y-axis.

Step-by-step explanation:

Considering the functions

f(x) = 0.7(6)x

g(x) = 0.7(6)–x

We know that when we reflect a function through the y-axis, the x-coordinate gets opposite - negated.

Here, the sign of  in  is opposite or negated. This is the only difference between  and  , meaning it is a reflection through the y-axis.

Therefore,   will be the reflection of  through the y-axis.

To calculate the remaining blueberries after using 1/5 for muffins, subtract 1/5 from the total, leaving you with 4/5 of the original amount in pounds.

To determine how many pounds of blueberries are left after using 1/5 of them to make muffins, we need to perform a subtraction based on the fraction used. Let's assume we start with a certain quantity 'X' pounds of blueberries. After using 1/5 of them, we have 4/5 of 'X' pounds left because we subtract the 1/5 that was used for muffins from the original amount. It's important to convert any measurement units if they are not consistent, as seen when comparing pounds and ounces for other items like yogurt or apples.

The remaining amount of blueberries in the container is [tex]\( \frac{4}{5} \)[/tex] of the initial amount.

To determine how many pounds of blueberries are left in the container, we need to set up the problem and solve it step-by-step.

Let's denote the initial amount of blueberries as [tex]\( x \)[/tex] pounds.

1. Define the amount used for muffins:

If [tex]\( \frac{1}{5} \)[/tex] of the remaining blueberries is used to make muffins, it means that [tex]\( \frac{1}{5} \)[/tex] of the total blueberries is used.

Therefore, the amount of blueberries used for muffins is [tex]\( \frac{1}{5} x \)[/tex].

2. Calculate the remaining blueberries:

The remaining blueberries will be the total amount minus the amount used for muffins.

Thus, the remaining blueberries are:

[tex]\[ x - \frac{1}{5} x \][/tex]

3. Simplify the expression:

[tex]\[ x - \frac{1}{5} x = \frac{5}{5} x - \frac{1}{5} x = \frac{4}{5} x \][/tex]

Answer:

160+192+144=496

Step-by-step explanation:

120% of 160=Friday

75% of (1.2*160)=Sat

160=Thursday

Answer:

160+192+144=496

Step-by-step explanation:

120% of 160=Friday

75% of (1.2*160)=Sat

160=Thursday

Step-by-step explanation:

Answer:

Cost per Apple is $0.75

Step-by-step explanation:

Step 1:  Divide cost by the apples

$6.00 / 8 = x

$0.75 = x

Cost per Apple is $0.75

Answer:

0.75

Step-by-step explanation:

Just divide $8.00 by $6.00

Mega Moving truck is 632.102 cubic feet greater than 2-bedroom  moving truck.

Solution:

Volume of the mega moving truck = length × width × height

                                                          [tex]$=22 \frac{1}{4}\times7 \frac{7}{12}\times 8 \frac{5}{12}[/tex]

Convert mixed fraction into improper fraction.

                                                          [tex]$= \frac{22\times4+1}{4}\times \frac{7\times12+7}{12}\times \frac{8\times12+5}{12}[/tex]

                                                          [tex]$= \frac{89}{4}\times \frac{91}{12}\times \frac{101}{12}[/tex]

Volume of the mega moving truck = 1420.137 cubic ft

Volume of the 2-bedroom  moving truck = length × width × height

                                                          [tex]$=14 \frac{1}{2}\times7 \frac{7}{12}\times 7\frac{1}{6}[/tex]

Convert mixed fraction into improper fraction.

                                                          [tex]$= \frac{14\times2+1}{2}\times \frac{7\times12+7}{12}\times \frac{7\times6+1}{6}[/tex]

                                                          [tex]$= \frac{29}{2}\times \frac{91}{12}\times \frac{43}{6}[/tex]

Volume of the 2-bedroom  moving truck = 788.035 cubic ft

Difference between them = 1420.137 – 788.035

                                           = 632.102 cubic ft

Hence Mega Moving truck is 632.102 cubic feet greater than 2-bedroom  moving truck.

Answer:

3(2s + 6t + w)

Step-by-step explanation:

Since the highest GCF is 3, I divided 6s, 18t, and 3w. This equals to 3(2s + 6t + w)

Answer:

3(2s+6t+w)

Step-by-step explanation:

Answer:

43.7 ft

Step-by-step explanation:

Radius of the semicircular garden is 8.5 ft .

Diameter = 8.5 × 2 = 17 ft

Circumference of the garden = [tex]\frac{1}{2}[/tex] × π × diameter = [tex]\frac{1}{2}[/tex] × π × 17 = 26.7 ft (rounded up to the nearest tenth of a foot)

Distance around the gardent = Circumference + diameter = 26.7 ft + 17 ft =  43.7 ft

Answer:

answer is a

Step-by-step explanation:

look at picture