the perimeter of a rectangular garden is 62 feet. The length is 1 foot more than twice the width find the dimension of the garden.

Answer:

B, C D

Step-by-step explanation:

Inequalities are the "alligators"  <   or >  or the "alligators" with lines  ≤  or ≥

<  less than

>greater than

≤  less than or equal to

≥  greater than or equal to

ANSWERS:

B) 11 > (w - 4)^2 & C) y < 3^4 & D) 5 + 9 < 5 x 9

About this > inequality sign:

About this < inequality sign:

About this > inequality sign:

About this < inequality sign:

Answer:

Option B is correct.

Reason:It is an argument

Step-by-step explanation:

Given: [tex]AB \cong BC[/tex]  and [tex]BC \cong EF[/tex]

By transitive property:  a = b  and b = c then, a =c

⇒[tex]AB \cong EF[/tex]

AB = EF                                [def of [tex]\cong[/tex] segment]

By Segment Addition Postulate states that given  two points A and C, and a third point B lies on the line segment AC if and only if the distances between the  points satisfy the equation

AB + BC = AC.

Since, the line segment EG , F lies on the line segment;

then, by segment addition postulates we have;

EG = EF + FG

By substitution AB=EF

⇒ EG = AB + FG                     hence proved!

Since, in the fourth statement reason is:  It is an argument

Answer:

B, it is an argument

Step-by-step explanation:

A you earn 3 percent more money

Step-by-step explanation:

4-1

Answer:

If you are given a 4% raise and inflation is 1%, you are making 3% more.

Step-by-step explanation:

If you are given a 4% raise and inflation is 1%, you are making 3% more.

[tex]4-1=3[/tex]

Or we can say you are making more money.

This is because you are given high percent of raise as compared to the low rate or percent of inflation, that shows you are on the positive side.

Answer:

[tex]k=2[/tex]

Step-by-step explanation:

1) Rewriting:

[tex]f(x+k)=f(x)+2[/tex]

2) Suppose f(x)= ax (Linear function with b=0)

[tex]a(x+k)=ax+2\\a(x+k)=x+2\\ax+ak=x+2 \Rightarrow a=1\\x+k=x+2\\k=2[/tex]

3) Check the graph below

The correct option is D) 2.

Step-by-step explanation:

Given :

f(x) +2 and f(x +k)

Solution :

let, [tex]f(x) = ax[/tex] (linear function with b = 0)

so,   [tex]f(x+k)=a(x + k)\;\;\;at,\; x=x+k[/tex]

Rewriting,

[tex]f(x+k)=f(x) + 2[/tex]

[tex]a(x + k) = ax +2[/tex]

[tex]k = 2 \;\;\;(at,\;a=1)[/tex]

Therefore, the correct option is D) 2.

For more information, refer the link given below

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Answer:

Step-by-step explanation:

Commutative property: 3x+12-2x = 3x-2x+12

Substitution property: 3x-2x+12 = x+12

x+12 = x+12

Subtraction property: x-x+12 = x-x+12

Substitution property: 12 = 12

Answer:

5 2/3 hours  

Step-by-step explanation:

We can use a ratio to solve this problem

hours over money

4.5 hours         x hours

-------------    =  ------------

27 dollars        34 dollars

Using cross products

4.5 * 34 = 27 * x

153 =27x

Divide each side by 27

153/27 = 27x/27

5.666666 hours

Answer:

$206.54

Step-by-step explanation:

Divide the number of officials by the total days pay to get the pay for each official working the race

Answer:

72,220 inches per  minute

Step-by-step explanation:

A car's wheels spins at 1000 revolutions per minute. The diameter of the wheels is 23 inches.

1 revolution = [tex]2\pi[/tex] radians

[tex]\frac{theta}{tome}=\frac{1000 \ revolution}{1 \ minuite} = \frac{1000* 2\pi }{1} =\frac{2000\pi}{1 \ minute}[/tex]

Speed [tex]V= \frac{r*theta}{t}[/tex]

r is the radius , theta is the angle and t is the time

We know diameter = 23  , then radius = 23/2

Speed [tex]V= \frac{23}{2}*\frac{2000\pi}{1}[/tex]

Value of pi = 3.14

speed = 23000* 3.14= 72220 inches/ minute

Answer:

72,220 inches per minute

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

Let x = tootsie rolls

y = lollipops

Toosie rolls are 3 dollars and lollipops are $5 and you only have 30 dollars.

3x+5y =30

To find the x intercept, set y=0 and solve for x

3x +0 = 30

3x = 30

Divide by 3

3x/3 = 30/3

x = 10

The x intercept is 10.  This means if you get no lollipops, you can have ten tootsie rolls.

To find the y intercept, set x=0 and solve for y

0 +5y = 30

5y = 30

Divide by 5

5y/5 = 30/5

x = 6

The y intercept is 6.  This means if you get no tootsie rolls you can have 6 lollipops.

To find the slope, solve the equation for y

3x+5y =30

Subtract 3x from each side

3x-3x+5y = -3x+30

5y = -3x+30

Divide by 5

y = -3/5 x +30/5

y = -3/5 x +6

The slope is -3/5.  For every three less lollipops you get, you can have 5 more tootsie rolls.

If you have $45 dollars instead of 30,  this will change the x and y intercepts, but not the slope.  

3x+5y =45

To find the x intercept, set y=0 and solve for x

3x +0 = 45

3x = 45

Divide by 3

3x/3 = 45/3

x = 15

The x intercept is 15.  This means if you get no lollipops, you can have 15 tootsie rolls.

To find the y intercept, set x=0 and solve for y

0 +5y = 45

5y = 45

Divide by 5

5y/5 = 45/5

x = 9

The y intercept is 9.  This means if you get no tootsie rolls you can have 9 lollipops.

To find the slope, solve the equation for y

3x+5y =45

Subtract 3x from each side

3x-3x+5y = -3x+45

5y = -3x+45

Divide by 5

y = -3/5 x +45/5

y = -3/5 x +9

The slope is -3/5.  For every three less lollipops you get, you can have 5 more tootsie rolls.

[tex]25=12+r\\r=25-12\\r=13[/tex]

12 + r = 25      subtract 12 from both sides

12 - 12 + r = 25 - 12

Answer:

Option C.

Step-by-step explanation:

System of the equation consists of two equations

2x + y - 4 = 0

2x + y - 4 + 4 = 0 + 4

2x + y = 4--------(1)

and 2x - y - 4 = 0

2x - y + 4 - 4 = 0 + 4

2x - y = 4------(2)

Now we will add these equations to eliminate y.

(2x + y) + (2x - y) = (4 + 4)

(2x + 2x) + (y - y) = 8

4x = 8

Therefore, resulting equation will be 4x = 8

Option C. will be the answer.

Easy, just do 60 seconds which equals a minute. Since we know that now simply use 60 minutes to get you to an hour. If your doing minutes to hours make sure there is a 0 at the end.

6(9)-8(-2)

6*9=54

8*(-2)=-16

54-16=38

38<-----

Answer:

70

Step-by-step explanation:

x=9 and y=−2, evaluate the following expression : 6x−8y

plug in

6(9) - 8(-2)

= 54 + 16

= 70

Answer:

If two events are mutually exclusive then they cannot occur at the same time.

Step-by-step explanation:

If two events are mutually exclusive then they cannot occur at the same time.

For example: If you take a coin, the two possible outcomes on flipping a coin will be mutually exclusive as when you flip a coin, it cannot give both heads and tails at the same time.

Hence, the two mutually exclusive events cannot occur at the same time.

Answer:

c =1.50n +2.50

Step-by-step explanation:

c=1.50(n-2)+5.50

The first step is to distribute the 1.5

c= 1.50*n -1.50*2 + 5.50

c = 1.50n - 3.0 +5.50

Now we need to combine like terms

c =1.50n +2.50

Answer:

30 miles per 1 day

Step-by-step explanation:

so 30 miles for each day and if you add 30 eight times which is the same as 30 times 8 you will get 240 miles hope it helps

Answer:

$12.50

Step-by-step explanation:

1) Mutliply 6 with 2

6*2= 12

2) multiply 1/4 with 2

1/4 * 2 =1/2

3) add 12 and 1/2

12+1/2 = 12.50

By converting the mixed number of pizzas sold to an improper fraction and multiplying by the price per whole pizza, we find the food booth made $100 in one hour from selling pizzas.

To determine how much money was made at the food booth in the given hour, we need to calculate the total sale of pizzas. Since 1/8 of a pizza costs $2, an entire pizza would cost 8 times that amount, which is $16 per pizza. It was stated that 6 1/4 pizzas were sold in that hour. To find the total, we multiply the price per pizza by the number of pizzas sold.

First, convert the mixed number 6 1/4 to an improper fraction to simplify the calculation: 6 1/4 is the same as (6 × 4 + 1) / 4, which is 25/4. Then, multiply the cost per pizza, which is $16, by the number of pizzas sold, which is represented by the fraction 25/4.

The equation for total money made is then $16 ×  {25}/ {4} = $100.

So, the food booth made $100 in that hour from selling pizzas.

Answer:

Part a) The area of the figure is [tex]\frac{9}{2}(4+\pi )\ cm^{2}[/tex]

Part b) The perimeter of the figure is [tex]3(2+2\sqrt{2}+ \pi)\ cm[/tex]

Step-by-step explanation:

Step 1

Find the area of the figure

In this problem we have that

The figure ABC is the half of a square and the other figure is a semicircle

Find the area of the figure ABC

we have

[tex]AB=6\ cm, BC=6\ cm[/tex]

The area of the half square ABC is equal to find the area of triangle ABC

so

[tex]A1=\frac{1}{2}*6*6=18\ cm^{2}[/tex]

Find the area of the semicircle

The area of the semicircle is equal to

[tex]A2=\pi r^{2}/2[/tex]

we have that

[tex]r=6/2=3\ cm[/tex]

substitute

[tex]A2=\pi (3)^{2}/2[/tex]

[tex]A2=(9/2) \pi\ cm^{2}[/tex]

The area of the figure is equal to

[tex]18\ cm^{2}+(9/2) \pi\ cm^{2}= \frac{9}{2}(4+\pi )\ cm^{2}[/tex]

Step 2

Find the perimeter of the figure

The perimeter of the figure is equal to

[tex]P=AB+AC+length\ CB[/tex]

we have

[tex]AB=6\ cm[/tex]

Applying Pythagoras theorem

[tex]AC=\sqrt{6^{2}+6^{2}}\\AC=6\sqrt{2}\ cm[/tex]

Remember that

the circumference of a semicircle is equal to

[tex]C=\frac{1}{2}2\pi r=\pi r[/tex]

[tex]r=6/2=3\ cm[/tex]

[tex]C=\pi(3)[/tex]

[tex]C=3 \pi\ cm[/tex]

The perimeter of the figure is equal to

[tex]P=6\ cm+6\sqrt{2}\ cm+3 \pi\ cm[/tex]

Simplify

[tex]P=3(2+2\sqrt{2}+ \pi)\ cm[/tex]

Answer:

the correct answer is 14.29%

Step-by-step explanation:

Answer:

a= 14

b= 111

just took it

Answer: 11(y+15)

Step-by-step explanation:

−

42

6

=

x

+

15

−

7

=

x

+

15

−

7

−

15

=

x

−

22

=

x

Answer:

The bill total is $27.32

Step-by-step explanation:

how to figure out tax amount: 25.30 x .08 = $2.024

add tax to cost of meal : 25.30 + 2.024 = $27.32

To calculate the total cost of the meal including an 8% tax, multiply the cost of the meal by the tax rate and add this to the original meal cost. The tax comes to $2.02. So, the total cost of the meal, including tax, is $27.32.

The question asks how much the total bill is for Michael and Imani when they go out to eat for lunch. The food and beverages cost $25.30 and there is an 8% meal tax. To calculate the total cost of the meal including the tax, we can multiply the cost of the meal ($25.30) by the tax rate (8%) and add this to the original cost for the meal.

First, let's convert the tax rate from a percentage to a decimal. 8% is equivalent to 0.08 as a decimal. Then, we multiply $25.30 by 0.08:

$25.30 * 0.08 = $2.02

This amount ($2.02) is the tax on the meal. To get the total cost, add this tax amount to the cost of the meal:

$25.30 + $2.02 = $27.32

So, Michael and Imani's bill, including the 8% meals tax, will be $27.32.

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Answer:

2 6/15, 2 4/9, 2 3/5, 2 2/3

Step-by-step explanation:

Make all the fractions improper fractions. So 2 2/3= 8/3, 2 6/15= 13/15, etc.

Then make all the denominators 45 and then order them from there.

Answer:

1,500 rotations

Step-by-step explanation:

To answer this, divide 2.2 m into 3300 m.  This results in 1500.

The wheels made 1,500 rotations each.

Answer:

Step-by-step explanation:

So if p is the total amount paid, and h is the amount of time spent working, it'll be worked out something like this.

The amount of money she makes per hour   x    the amount of time spent working = the amount she is paid.

Thus making it...

8 x h = p

but in algebra expressions, we don't normally use arithmetic symbols. So if we get rid of that, we get the answer of 8h = p.

:)

The solution in scientific notation si:

Option D: 6.8 * 10⁵

How to give the answer in scientific notation?

Scientific notation is a way of expressing very large or very small numbers. It involves writing a number as a product of a number between 1 and 10 and a power of 10.

For example, 800,000,000 can be written in scientific notation as 8 × 10⁸.

We are given the expression:

(3.4 * 10²) * (2 * 10³)

= (3.4 * 2) * 10² ⁺ ³

= 6.8 * 10⁵

Answer:

Step-by-step explanation:

1. When you replace f(x) by x and x by y, you have

... x = 2^y + 6

The first thing you do is subtract 6; then you take the base-2 logarithm:

... (x -6) = 2^y

... log2(x -6) = y = f^-1(x)

You know that to get the y-term by itself, you must subtract 6. Anything else you do will operate on (x-6). Only answer choice D has that sort of construction.

2. When you swap x and y and solve for y, you have ...

... x = -1/2√(y+3)

... -2x = √(y +3) . . . . . . multiply by -2

... (-2x)^2 = y +3 . . . . . square

... 4x^2 - 3 = y = f^-1(x) . . . . subtract 3

The range of f(x) is (-∞, 0], so that is the domain of f^-1(x). That is, f^-1(x) is defined for x ≤ 0.

3. The product of the two functions is ...

... (x -6)(√x)(x +3) = (√x)(x^2 -3x -18)

Every term will have a factor of √x, and the coefficients will be 1, -3, -18. Only selection B matches those conditions.

Answer:

Question One: log_2(x - 6) = y

Question Two: First blank: 4 Second blank 0

Question Three: B

Step-by-step explanation:

f(x) = 2^x + 6

y = 2^x + 6                 Interchange the x and y

x = 2^y + 6                Subtract 6 from both sides

x - 6 = 2^y                 Take the log of both sides

log(x - 6) = log 2^y    The power can be multiplied by the log of 2

log(x - 6) = y log(2)    Divide by the log of 2

log(x - 6)/log(2) = y    This to me is the preferred answer. It allows you to calculate what the actual number is or graph it on Desmos

The answer I have given is equivalent to using base 2 as your log, but calculating that is not always easy.

log_2(x - 6) = y

Answer: D

Problem Two

You want the inverse of y = - 1/2 sqrt(x + 3)   x ≥ - 3

Note: you cannot have any number less than -3 because if you do, you will be taking the square root of -x which involves complex numbers. In addition x ≥ -3 is a domain. You have to keep that in mind when doing this question.

The domain and range of this is a little harder to figure out. The range of f(x) becomes the domain of f-1(x)

The range of f(x) is 0 <=y < - infinity

So the domain of f-1(x) <= 0

Answer: The first blank is 4 and the second one is 0

Graph: the graph is given you below the question. What it shows is the f(x) and f^-1(x) are symmetrical about y = x. Most inverses are. If you want to check your work, it is best to include a graph when doing inverses.

Problem Three

The best way to begin this problem is to apply the associative property of multiplication and start by rewriting the givens as x^(1/2)[(x - 6)(x + 3)]. Do what is in the square brackets first.

Now deal with the x^(1/2) which must be multiplied by all three terms in the square brackets.

Result: x^(5/2) - 3x^(3/2) - 18x^(1/2)

Answer: √(x^5) - 3√x^3 - 18√x

Answer: B