The length of a rectangle is 4.5 meters. The perimeter is 15.6 meters. What is the width?

Answer:

x = 10

Step-by-step explanation:

1st Divide both sides by 2: x2 ÷ 2 = 20 ÷ 2

2nd Simplify: x = 10

Hope I helped :)

Final answer:

The equation x² = 20 has two solutions: x = 2√5 and x = -2√5, as both positive and negative square roots are considered for the value of x.

Explanation:

To find the solutions for the equation x² = 20, we need to take the square root of both sides of the equation.

Generally, the square root of a variable squared, such as x², can be either positive or negative. This is because both a positive and a negative number, when squared, give the same positive result. Therefore, the equation has two solutions:

x = √20

x = -√20

Using a calculator or knowing that √4 ×√5 = 2 ×√5, we can simplify √20 to 2√5.

The final solutions are:

x = 2√5

x = -2√5

The domain of the function will be Domain: ( − ∞ , ∞ ) , { x | x  ∈  R }.

The entire range of independent variable values is the domain of a function. In algebra, a polynomial function with one or more variables in which the highest-degree term is of the second degree is known as a quadratic function, a quadratic polynomial, a polynomial of degree 2, or simply a quadratic.

The given quadratic function g(x) = 1 - 2x² will have a domain from negative infinity to positive infinity. The graph of the function is also attached with the answer below.

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Answer:

32 tanks

Step-by-step explanation:

since 562/18

is 31.222222...

You would have to round up because you the limit is 18 fish. You would need 32 tanks to fit all the fish

Answer:

32

Step-by-step explanation:

You have 562 gold fish and you need to have 18 in each tank, how many tanks do you need?

You first need to start with dividing the gold fish amount to the amount that can fit in each tank, (562 divided by 18 = 31.22222222222222). Then you multiply 18 by 31 and you get 558. This is obviously not as much goldfish as you had before, so to fix this you add another tank which makes 32 tanks, but you minus 562 from 558 and you have only 4 fish in the last tank.

Hope this helps! :)

720

91.2

=

c

0.513

Answer:

c

=

4.05

Answer:

c =  4.05  

Step-by-step explanation:

Given: 720/91.2 = c/0.513 .

To find: solve

Solution: We have given that  [tex]\frac{720}{91.2}[/tex]= [tex]\frac{c}{0.513}[/tex]    

 On cross multiplication

 [tex]\frac{720}{91.2}[/tex]= [tex]\frac{c}{0.513}[/tex]

91.2 * c = 0.513 * 720  

91.2 * c = 369.36

On dividing both side by 91.2

 c = [tex]\frac{369.36}{91.2}[/tex]

c =  4.05  

Therefore ,  c =  4.05  .

Answer:

Step-by-step explanation:

You need to know what prime factorization is.  Basically you split up a number into it's prime  factors.  Or in other words what prime numbers multiply to get this number.  So say you have 36, you can split it into 2*2*3*3.  This is the methodology we use.

For the fractions given we want to look at the prime factorization of  the denominators.  so for 4 = 2*2 and 6 = 2*3.  What do we have to do to make them equal.  Well, if we multiply 2*2 by 3 and 2*3 by 2 what do we get?  2*2*3 and 2*3*2 which are equal.  So there's another way to get common denominators.  You also have to multiply the numerators by the same numbers you multiply the denominators by.  So in total you do this.

1/4 + 1/6

1/(2*2) + 1/(2*3)

(1*3)/(2*2*3) + (1*2)/(2*3*2)

3/12 + 2/12

5/12

Final answer:

To add fractions with different denominators, find the Least Common Denominator (LCD) rather than multiplying the denominators. For 1/4 and 1/6, the LCD is 12. The resulting addition is 1/4 + 1/6 = 3/12 + 2/12 = 5/12.

Explanation:

Whitney, to add fractions with different denominators more efficiently, we can find a common denominator that is smaller than directly multiplying the two denominators. This is also known as the Least Common Denominator (LCD).

To add 1/4 and 1/6, rather than multiplying the denominators to get 24, we can look for the least common multiple (LCM) of 4 and 6. The LCM of 4 and 6 is 12, because 12 is the smallest number that both 4 and 6 can divide evenly into.

Now we can write each fraction with a denominator of 12:

Now the fractions have the same denominator:

1/4 + 1/6 = 3/12 + 2/12 = 5/12

By using the LCD, the fractions are now easy to add, and the added result of 5/12 is in simplified form.

Answer:

3.2 gallons

Step-by-step explanation:

Write a proportion:

1 gallon / 825 square feet = x / 2640 square feet

Solve:

x = 3.2 gallons

Answer:

The integer he wrote could be between -3.4 to -2.1, you could just say -3

Answer:

x=-2

Step-by-step explanation:

-3(x+5)=-9

x+5 = 3

x=-2

Answer:

Step-by-step explanation:

95 degrees farighite

Answer:

Students ticket = $4

Child ticket = $1

Adult ticket = $5

Step-by-step explanation:

Let the price of the student ticket be $x and the price of a child ticket be $y.  An adult ticket costs as much as the combined cost of a student ticket and a child ticket, so the price of one adult ticket is $(x+y).

1. A movie theater advertises that a family of two adults, one student, and one child between the ages of 3 and 8 can attend a movie for $15. Then

[tex]2(x+y)+x+y=15[/tex]

2. If you purchase 1 adult ticket, 4 student tickets, and 2 child tickets for $23, then

[tex](x+y)+4x+2y=23[/tex]

Now, solve the system of two equations:

[tex]\left\{\begin{array}{l}2(x+y)+x+y=15\\ \\(x+y)+4x+2y=23\end{array}\right.\Rightarrow \left\{\begin{array}{l}3(x+y)=15\\ \\5x+3y=23\end{array}\right.\\ \\\left\{\begin{array}{l}x+y=5\\ \\5x+3y=23\end{array}\right.\\ \\\left\{\begin{array}{l}y=5-x\\ \\5x+3(5-x)=23\end{array}\right.[/tex]

Solve the last equation

[tex]5x+15-3x=23\\ \\2x=23-15\\ \\2x=8\\ \\x=4\\ \\y=5-x=5-4=1[/tex]

Students ticket = $4

Child ticket = $1

Adult ticket = $5

Answer:

The ticket prices will as follows:

Students ticket = $4

Child ticket = $1

Adult ticket = $5

Step-by-step explanation:

Thinking process:

Let the price of the student ticket be $x and the price of a child ticket be $y.  An adult ticket costs as much as the combined cost of a student ticket and a child ticket, so the price of one adult ticket is $(x+y).

1. A movie theater advertises that a family of two adults, one student, and one child between the ages of 3 and 8 can attend a movie for $15. Then

2. If you purchase 1 adult ticket, 4 student tickets, and 2 child tickets for $23, then

Now, solve the system of two equations:

Solve the last equation

Students ticket = $4

Child ticket = $1

Adult ticket = $5

Answer:

It is called a gerund

Step-by-step explanation:

Answer:

Gary

Step-by-step explanation:

Edward more than Gabby

So Edward>Gabby

But Edward swam fewer laps than Noelle

So Noelle>Edward>Gabby

Gabby swam more than Gary

So Noelle>Edward>Gabby>Gary

Answer:

x=-1

Step-by-step explanation:

-2(x+4)+8=2

1) Use the Distributive property:

-2x-8+8=2

2) Combine alike terms:

-2x=2

3) Divide both sides by -2:

x=-1

Let R = total revenue the year before

R = 45,000 x 0.25 + 45,000

R = 11,250 + 45,000

R = $56,250

Answer:

$14.63

Step-by-step explanation:

175 × $5.60 ÷ 100 = 9.8

$5.60 + 9.8 = $15.40

5 × $15.40 ÷ 100 = $0.77

$15.40 - 0.77 = $14.63

The answer 67.6 and in fraction form it is 203/3

Answer:  The required length of DE is 29.

Step-by-step explanation:  We are given that DF = 42 in the figure shown.

We are to find the length of DE.

From the figure, we note that

[tex]DE=7x+1,~~EF=4x-3.[/tex]

According to the given information, we have

[tex]DF=42\\\\\Rightarrow DE+EF=42\\\\\Rightarrow 7x+1+4x-3=42\\\\\Rightarrow 11x=42+2\\\\\Rightarrow 11x=44\\\\\Rightarrow x=\dfrac{44}{11}\\\\\Rightarrow x=4.[/tex]

Therefore, we get

[tex]DE=7x+1=7\times4+1=28+1=29.[/tex]

Thus, the required length of DE is 29.

The length of DE using the measurements DF = 42, DE = 7x + 1 and EF = 4x - 3 is 29 unit.

given that,

the length of DF = 42

length of DE = 7x + 1

and, length of EF = 4x - 3

Now, from the figure

DE + EF = DF

Plugging the values back to the formula as

7x + 1 + 4x - 3= 42

Combine like terms

11x - 2 = 42

add 2 both side

11x = 42 + 2

11x = 44

Divide both side by 11

x= 44/11

x= 4

So, the length of DE is

= 7x + 1

= 28 + 1

= 29

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Answer:

Option 2) 300

Uranus has a mass that is approximately 300 times greater than Mercury's

Step-by-step explanation:

Let

x ----> Uranus's mass

y ---->  Mercury's mass

we have

[tex]x=8.61*10^28\ units[/tex]

[tex]y=3.302*10^26\ units[/tex]

Divide Uranus's mass by Mercury's mass

[tex]\frac{x}{y}[/tex]

substitute the values

[tex]\frac{8.61*10^28}{3.302*10^26}=260.75[/tex]

Round to the nearest hundred

therefore

Uranus has a mass that is approximately 300 times greater than Mercury's

Answer:

The answer is 300

Step-by-step explanation:

Answer:

10 units.

Step-by-step explanation:

That would be the difference in the x coordinates as the y coordinates are both -8.

So it's 10 - 0 = 10 units.

Answer:

[tex]\large\boxed{x=-3}[/tex]

Step-by-step explanation:

[tex]-14=3x+x-2\qquad\text{add 2 to both sides}\\\\-14+2=3x+x-2+2\qquad\text{combine like terms}\\\\-12=4x\qquad\text{divide both sides by 4}\\\\\dfrac{-12}{4}=\dfrac{4x}{4}\\\\-3=x\to x=-3[/tex]

Answer:

24 Kids per group

Step-by-step explanation:

14 x 12 = 168

168 / 7 = 24

24 kids

Answer:

24 Students

Step-by-step explanation:

Answer:

y = -3

Step-by-step explanation:

First, subtract 2y from both sides, (3y - 2y) and that should give you the equation, -3 = y. And that's your final answer.

2y-3=3y

Move 2y to the other side

Sign changes from +2y to -2y

2y-2y-3=3y-2y

-3=y

Answer: y=-3

Answer:

what I don't understand

Step-by-step explanation:

what exactly is the question

Answer:

Step-by-step explanation:

[tex]16x-4+5x=-67\qquad\text{add 4 to both sides}\\\\16x+5x-4+4=-67+4\qquad\text{combine like terms}\\\\21x=-63\qquad\text{divide both sides by 21}\\\\\dfrac{21x}{21}=\dfrac{-63}{21}\\\\x=-3[/tex]

The solution for x in the equation is -3

Given equation is, 16x-4+5x = -67

The given equation is a linear equation, so we will get only one value of x.

Solving the equation we get,

16x-4+5x = -67

⇒ 16x-4+4+5x = -67+4  (adding 4 in both sides)

⇒ 16x+5x = -63

⇒ 21x = -63

⇒ x = -63/21

⇒ x = -3

The required value of x = -3

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The formula for midpoint is

([tex]\frac{x_{1}+x_{2}}{2}[/tex], [tex]\frac{y_{1}+y_{2}}{2}[/tex])

Look at the image below to see the line segment of Estefani's (A), Jasmin's (M), and Preston's (B) houses. Keep in mind that the segment shown below is not accurate in regards to how the line segment formed by Estefani's, Jasmin's, and Preston's houses. It is simply there so you can picture the segment better.

In this case:

[tex]x_{1} =3\\x_{2} =unknown\\y_{1} =-2\\y_{2} =unknown[/tex]

^^^Plug in these number into the formula given above...

([tex]\frac{3+x}{2}[/tex], [tex]\frac{-2 + y}{2}[/tex])

To find what x is (a coordinate of Preston's house) you must take the x-value part of the midpoint equation ([tex]\frac{3+x}{2}[/tex]) and set it equal to the x-value of the midpoint (-5). Then you must solve for x:

[tex]\frac{3+x}{2}[/tex] = -5

3 + x = -5 * 2

3 + x = -10

x = -10 - 3

x = -13

To find what y is (a coordinate of Preston's house) you must take the  y-value part of the midpoint equation([tex]\frac{-2 + y}{2}[/tex]) and set it equal to the y-value of the midpoint (3). Then you must solve for y:

[tex]\frac{-2 + y}{2}[/tex] = 3

-2 + y = 3 * 2

-2 + y = 6

y = 6 + 2

y = 8

The coordinate of Preston's house is:

(-13, 8)

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

The dimensions of rectangle whose perimeter is 70 inches and width is five less than three times the length of worktable is  length = 10 and width = 25

Solution:

Consider ‘P’ as perimeter and ‘L’ as length and ‘W’ as width  

P = 70 inches

W = 5 less than thrice of length  

Therefore, [tex]\mathrm{W}=3 L-5 \quad(\text {equation } 1)[/tex]

Using perimeter formula for rectangle,

[tex]\begin{array}{l}{P=2(L+W)} \\ {70=2(L+3 L-5)} \\ {70=2(4 L-5)} \\ {70=8 L-10} \\ {8 L=80} \\ {L=10}\end{array}[/tex]

Substitute L= 10 in equation 1

[tex]\begin{aligned} W &=3 \times 10-5 \\ W &=30-5 \\ W &=25 \end{aligned}[/tex]

Answer: 6√35

Step-by-step explanation:

since the √ 210 cannot come out into an equal number then you have to try to get two numbers closest to answering 210 to get it except you have to do 6 square root of 35. I hope this helps you!!!

The two whole numbers between which the square root of 210 lie are 14 and 15.

The square root of 210 is approximately 14.49. Since you are looking for the two whole numbers between which this value lies, you need to find the next higher and lower whole numbers from this value. These would be 14 and 15, as 14.49 is more than 14 and less than 15.

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Answer:

B. Figure B is congruent to figure C.

Step-by-step explanation:

Figure D is dilated about a quarter of the other two, and Figure A is out of the question because it is dilated about twice their size, so with that being said, you have your answer.

I am joyous to assist you anytime.

Answer:

b

Step-by-step explanation:

[tex]\bf 3^2\cdot 3^3\implies 3^{2+3}\implies 3^5\implies 243[/tex]

Final answer:

To simplify 3 to the 2nd power times 3 to the third power, we add the exponents because the base is the same, resulting in 3 to the 5th power, which equals 243.

Explanation:

To simplify 3 to the 2nd power times 3 to the third power, we need to apply the rule of multiplying exponential terms with the same base. When multiplying terms like 32 and 33, we simply add the exponents together because the base (the number 3 in this case) remains the same. So this simplification process looks like:

32 × 33 = 3(2+3) = 35

The next step is to calculate the value of 3 raised to the 5th power:

35 = 3 × 3 × 3 × 3 × 3 = 243

Therefore, the simplified expression is 243.