Bill is building a sand box for his son to play in. The length is 2 feet more than the width. He has 20
feet of boards. What are the dimensions of his sand box?

Answer:

c=4

Step-by-step explanation:

Answer:

C=4

Step-by-step explanation:

when solving these equations you have to get the letter by itself and in this case the 4 is being multiplied by the c so you have to do the opposite and divide the 4 from the c and divide 16 by 4 because what you do to one side of the equal sign you have to do to the other side.

Your answer is A. $485

200 – 130 = 70

70 – 25 = 45

45 + 240 = 285

285 + 225 = 510

510 – 100 = 410

410 + 75 = 485

Answer:

Step-by-step explanation:

3x+4y=5

6x+8y=10

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

-2(3x+4y)=-2(5)

6x+8y=10

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

-6x-8y=-10

6x+8y=10

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

0=0

Answer: Infinitely many solutions.

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

7x-2y=9

7x-2y=13

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

-1(7x-2y)=-1(9)

7x-2y=13

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

-7x+2y=-9

7x-2y=13

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

0=4

Answer: NO Solution.

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

2x-y=-11

-2x+y=11

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

0=0

Answer: Infinitely many solutions.

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

3x+6y=1

x+y=0

x=0-y=-y

3(-y)+6y=1

-3y+6y=1

3y=1

y=1/3

x=-y=-1/3

Answer: x=-1/3, y=1/3. (-1/3, 1/3).

Answer:69

Step-by-step explanation:

69

Rena's answer is correct.

To evaluate whether Rena's answer is correct, we need to perform the division of the two fractions 3/4 and 2/5. To divide one fraction by another, you multiply the first fraction by the reciprocal of the second fraction. The reciprocal of a fraction is obtained by flipping its numerator and denominator.
Here is a step-by-step solution:
Step 1: Write down the problem.
\[ \frac{3}{4} \div \frac{2}{5} \]
Step 2: Find the reciprocal of the second fraction.
The reciprocal of \( \frac{2}{5} \) is \( \frac{5}{2} \).
Step 3: Multiply the first fraction by the reciprocal of the second.
\[ \frac{3}{4} \times \frac{5}{2} \]
Step 4: Multiply the numerators together and the denominators together.
\[ \frac{3 \times 5}{4 \times 2} \]
\[ \frac{15}{8} \]
Step 5: Simplify the fraction if necessary.
In this case, \( \frac{15}{8} \) is an improper fraction because the numerator is larger than the denominator. We can convert it into a mixed number.
The whole number part of the mixed number is obtained by dividing the numerator by the denominator:
\[ 15 \div 8 = 1 \text{ with a remainder of } 7 \]
So, the mixed number is \( 1 \frac{7}{8} \).
Conclusion:
Rena's answer of \( 1 \frac{7}{8} \) is correct. The statement about her answer is true; she correctly evaluated the division of \( \frac{3}{4} \) by \( \frac{2}{5} \).

Answer:

x=0.8, y=2.2 (0.8, 2.2).

Step-by-step explanation:

y+x=3

y=1.5x+1

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

1.5x+1+x=3

2.5x=3-1

2.5x=2

x=2/2.5

x=0.8

y+0.8=3

y=3-0.8

y=2.2

To solve the given system of equations by substitution, we substitute the second equation into the first, solve for x, and then substitute x back into the second equation to solve for y, which yields x=0.8 and y=2.2 as the solution.

To solve the system of equations using substitution, we start by isolating one variable in one of the equations. Here, the second equation already gives us y in terms of x: y = 1.5x + 1.

Next, we substitute this expression for y into the first equation y + x = 3. This gives us:

Combine like terms to solve for x:

Now that we have the value of x, we can find the value of y by substituting x back into the equation y = 1.5x + 1:

Hence, the solution to the system of equations is x = 0.8 and y = 2.2.

As a final step, you may want to check your solution by plugging the values back into the original equations to confirm that they satisfy both equations.

The expression in terms of "n" for how much of the fire they will extinguish in 1 minute when both hoses are turned on together is [tex]\frac{n + 14}{7n + 49}[/tex]

Solution:

Given that,

Hose A, when turned on alone, can extinguish the fire in 7 minutes

Hose B takes "n" minutes more time than hose A

Hose takes (n + 7) minutes to extinguish the fire

STEP 1: Calculate how much work (here work is to extinguish the fire) each person does in one minute

[tex]Hose A = \frac{1}{7}th \text{ of the work }\\\\Hose B = \frac{1}{n+7}th \text{ of the work }[/tex]

STEP 2: Add up the amount of work done by each person in one minute

Work done in one minute when both are working together:

[tex]\rightarrow \frac{1}{7} + \frac{1}{n + 7}\\\\\rightarrow \frac{n + 7 + 7}{7n + 49}\\\\\rightarrow \frac{n + 14}{7n + 49}[/tex]

Therefore, the expression in terms of "n" for how much of the fire they will extinguish in 1 minute when both hoses are turned on together is:

[tex]\frac{n + 14}{7n + 49}[/tex]

The total rate in 1 minute is [tex]\frac{1}{7} + \frac{1}{7+n}[/tex].

To find the expression for how much of the fire they will extinguish in 1 minute when both Hose A and Hose B are turned on together, we need to determine their individual rates first.

Hose A can extinguish the fire in 7 minutes, so its rate is:

⇒ Rate of Hose A = 1 fire ÷ 7 minutes = [tex]\frac{1}{7}[/tex].

Hose B takes 'n' minutes more than Hose A. Therefore, it takes (7 + n) minutes to extinguish the fire, so its rate is:

⇒ Rate of Hose B = 1 fire ÷ (7 + n) minutes = [tex]\frac{1}{7+n}[/tex].

When both hoses are operating together, their combined rate is the sum of their individual rates:

⇒ Combined Rate = [tex]\frac{1}{7} + \frac{1}{7+n}[/tex]

We need the combined rate per minute:

⇒ Combined Rate per Minute = [tex]\frac{1}{7} + \frac{1}{7+n}[/tex]

This fraction represents the portion of the fire they will extinguish in 1 minute when both hoses are used together.

Step-by-step explanation:

2x²-4x=0

2x²=4x

[tex] \frac{2x {}^{2} }{x} = 4[/tex]

2x=4

x=2

Answer:

a. true

b. false

c. true

d. false

Step-by-step explanation:

a. A product raised to a power is equivalent to each of the multiplicand raised to that power as well. Example:

  (xyz)ⁿ = xⁿyⁿzⁿ

  (1·3·7)² = 1²(3²)(7²)

b. Is wrong. When you have addition/subtraction inside a parentheses, you have to foil. Example:

  (a + b)² = (a + b)(a + b)

               = a² + 2ab + b²

  (1 + 3)² = (1 + 3)(1 + 3)

               = 1² + 2(1)(3) + 3²

               = 16

c. Numbers with the same root can be merged when you're multiplying/dividing them. Example:

  √(a)√(b) = √(ab)

  √(2)√(3) = √(2·3) = √(6)

d. You can only merge or split the root when multiplying/dividing.

You CANNOT merge the root when adding/subtracting.

  √(a ± b) ≠ √(a) + √(b),    this is NOT allowed

e. I already gave examples in the previous parts.

Answer:

D

Step-by-step explanation:

For a function to be true, there cannot be the same x used for two different ys. D is the only table that follows this rule.

Answer: B. Adjacent

Step-by-step explanation: They share a common side and vertex

Answer:

4.37%

Step-by-step explanation:

Given: Value of object in 1997 is $5000

            Value of object in 2012 is $4500.

             Number of years (2012-1997)= 15 years

∵We know that there is growth in value of object over multiple years.

∴Compound annual growth rate (CAGR)= [tex][(\frac{end\ value}{initial\ value} )^{\frac{1}{n} } ] -1[/tex]

Remember, n = number of years

∴ Growth rate=  [tex][(\frac{9500}{5000} )^{\frac{1}{15} } ]-1[/tex]

⇒Growth rate= [tex][(1.9)^{\frac{1}{15} } -1][/tex]

⇒Growth rate= [tex](1.9)^{0.0667} -1= 1.0437-1[/tex]

⇒ Growth rate= 0.0437

Now, finding percentage of growth rate

∴ [tex]0.0437\times 100= 4.37\%[/tex]

∴ Annual growth percent over the period of time is 4.37%

Answer:

[tex]g(x)=\frac{1}{4}x-3[/tex]

Step-by-step explanation:

we have

[tex]f(x)=4x+12[/tex]

Find the inverse

step 1

Let

y=f(x)

[tex]y=4x+12[/tex]

step 2

Exchange the variables  (x for y and y for x)

[tex]x=4y+12[/tex]

step 3

Isolate the variable y

we have

[tex]x=4y+12[/tex]

Subtract 12 both sides

[tex]x-12=4y[/tex]

Divide by 4 both sides

[tex]y=\frac{x-12}{4}[/tex]

simplify

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

step 4

Let

[tex]f^{-1}(x)=y[/tex]

[tex]f^{-1}(x)=\frac{1}{4}x-3[/tex]

we have that

[tex]g(x)=f^{-1}(x)[/tex]

therefore

[tex]g(x)=\frac{1}{4}x-3[/tex]

Answer: 18%

Step-by-step explanation:

The percentage spent on book = cost of books / total cost x 100

% spent on book = 504/2800 x 100

= 18

Therefore , the percentage spent on book is 18

Answer:

No, we can't.

Step-by-step explanation:

Let x be the amount of time it takes each machine to make 1 cockpit, and y be the amount of time it takes each machine to make 1 propulsion system.

For machine A: 22 hours to produce 3 cockpits and 5 propulsion system.

For machine B: 44 hours to produce 6 cockpits and 10 propulsion system.

So, this will produce the following system of equations:

3x + 5y = 22  ⇒(1)

6x + 10y = 44  ⇒(2)

We can note that the second equation is two times the first equation.

So, the two equation are actually represent one equation.

OR, by another way the two equation have the same slope and y-intercept

So, the two equation are identical, therefore, we can't solve one equation with two variables.

Also, see the attached figure.

equation (1) with blue color and the second equation with red color.

Answer:

x  =    1

   ----------

     82V

Step-by-step explanation:

Answer:

2.15

×

10

−

3

Step-by-step explanation:

Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the

10

. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.

Answer:

The answer is 2.15 * 10^-3

Step-by-step explanation:

I got this answer from Khan Academy.

Hope this helps! :)

Answer:

46 and 47.

Step-by-step explanation:

If x is one of the integers then the other is x+1.

x + x + 1 = 93

2x = 92

x = 46.

Answer: One small box of oranges costs $7 and one large box of oranges costs $13.

Step-by-step explanation:

Let be "s" the cost in dollars of one small box of oranges and "l"  the cost in dollars of one small box of oranges.

Based on the data given in the exercise, you can set up the following System of equations:

[tex]\left \{ {{3s+14l=203} \atop {11s+11l=220}} \right.[/tex]

Use the Elimination Method to solve it:

- Multiply the first equation by 11 and the second one by -3.

- Add the equations.

- Solve for "l".

Then:

[tex]\left \{ {{33s+154l=2233} \atop {-33s-33l=-660}} \right.\\...............................\\\\121l=1573\\\\l=13[/tex]

- Substitute the value of "l" into any original equation and solve for "s":

[tex]3s+14(13)=203\\\\3s=203-182\\\\s=\frac{21}{3}\\\\s=7[/tex]

Answer:

2 times

Step-by-step explanation:

Mai biked [tex]7\frac{1}{4} = \frac{29}{4}[/tex] miles today and Noah biked [tex]3\frac{5}{8} = \frac{29}{8}[/tex] miles  today.

We are asked how many times the length of Noah's bike ride was Mai's bike ride.

Therefore, the length of Mai's bike ride was [tex](\frac{29}{4} \div \frac{29}{8})  = 2[/tex] times the length of Noah's bike ride.  

Therefore, we will take option B will be correct. ( Answer )

the answer is c

Step-by-step explanation:

12

23

34

56

512

the answer is c

Step-by-step explanation:

12

23

34

56

Answer:

Dimensions of printed area

x   =  7.58     the length

y   =  31.40  cm   the height

Step-by-step explanation:

Printed region    P(a)  =  238 cm²

Let call x  and y dimensions of printed area then:

A  =  238  =  x*y       ⇒    y  = 238/x

And the area of the advertisement   is

A(a)  =  L *  W        where     L  =  x  + 6       and   W  =  y  + 5

A(x)  =  (x  +  6  ) * (  y  +  5 )

Area as a function of x                         y  =  238/ x

A(x)  =  (x  +  6  ) * ( 238/x  +  5 )

A(x)  = 238  + 5x  + 1428/x  +  30

A(x)   =  268  +   5x    + 1428/x

Taking derivatives on both sides of the equation

A´(x)   =   5  -  1428/x²

A´(x)   =  0         ⇒   5x²   =  1428       ⇒ x²   =  57.12

x  = 7.58 cm         and         y  =  238/ 7.58       y  =  31.40 cm

Answer:

If you wanted the intersecting points there is only one and It's (12, 14)

Hope that could help.

Answer:

The estimated population in 2025 will be 22261221.

Step-by-step explanation:

Let us assume that the annual growth rate is compounded annually on the population.

Now, in 2000, the population was 19169000 and the annual growth rate is 0.6%, the the population in the year 2025 will be given by  

[tex] 19169000(1 + \frac{0.6}{100} )^{25} = 22261220.7[/tex] ≈ 22261221

Therefore, the estimated population in 2025 will be 22261221. ( Answer )

Answer:

16. Disagree because 0.1 0f 0.1 is 0.01

17. the whale swam for 19 to 21.7 hours. Because 152/8=19 and 152/7=21.7

18. Meg can use 15,000 / 50 because 14,270 rounded up to by the thousand will be 15,000.

19. 61.5 because 3016/7 = 430.8   430.8/7=61.5

Step-by-step explanation:

Final answer:

To find the product, multiply 400 by 9.460730473, then multiply the result by 2/3.

Explanation:

To find the product of 400 and 9.460730473 times 10/15, we need to multiply the three numbers together. First, let's simplify 10/15 to 2/3. Then, multiply 400 by 9.460730473 to get the product. Finally, multiply the result by 2/3 to find the final answer.

400 x 9.460730473 = 3784.2921892

3784.2921892 x 2/3 = 2522.8614595

The product of 400, 9.460730473, and 10/15 is approximately 2522.8614595.

Answer:

36 more students of grade 7 went on a trip than students of grade 6

Step-by-step explanation:

60 % of 110 students= 60/100*110= 66 students

85 % of 120 students= 85/100 * 120= 102 students

No of students of grade 7th more than 6th grade students= 102-66= 36

60% of the 6th grade band members and 85% of the 7th grade band members went on a trip Disney World trip. Then 36 more 7th graders went on the trip than 6th graders

percentage, a relative value indicating hundredth parts of any quantity.

Given,

The number of students in 6th grade=100

The number of students in 7th grade=120

60% of the 6th grade band members

60%×110

60/100×110=0.6×110=66

85% of the 7th grade band members

85%×120=85/100×120

=0.85×120=102

We need to find how many more 7th graders went on the trip than 6th graders

For this we need to find difference of 7th and 6th grade

102-66=36

Hence 36 more 7th graders went on the trip than 6th graders

To learn more on Percentage click:

https://brainly.com/question/28269290

#SPJ6

Answer:

1) [tex]9\frac{1}{6}-8\frac{5}{6}=\frac{1}{3}[/tex]

2) [tex]10\frac{3}{4}-6\frac{4}{4}=3\frac{3}{4}[/tex]

Step-by-step explanation:

You can convert he mixed numbers to improper fractions:

1. Multiply the whole number part by the denominator of the fraction.

2. Add the product obtained to the numerator.

3. The denominator does not change.

Then:

[tex]9\frac{1}{6}=\frac{54+1}{6}=\frac{55}{6}\\\\8\frac{5}{6}=\frac{48+5}{6}=\frac{53}{6}\\\\10\frac{3}{4}=\frac{40+3}{4}=\frac{43}{4}\\\\6\frac{4}{4}=\frac{24+4}{4}=\frac{28}{4}[/tex]

Observe that, in each subtraction, the denominators are equal, then you can rewrite the denominator and subtract the numerators:

[tex]1)\ \frac{55}{6}-\frac{53}{6}=\frac{55-53}{6}= \frac{2}{6}=\frac{1}{3} \\\\2)\ \frac{43}{4}-\frac{28}{4}=\frac{43-28}{4}= \frac{15}{4}[/tex]

Divide 15 by 4. The quotient will be 3 and the remainder 3.

Then:

[tex]\frac{15}{4}=3\frac{3}{4}[/tex]

Answer:

△JKL ≅ △XYZ by HL congruency for right triangles

Step-by-step explanation:

If only given two sides and an uncontained angle, the triangles may not necessarily be congruent. However, since the given angle is a right angle, they are congruent.

When given that the hypotenuse and any "leg" of the right triangles are equal, the triangles are congruent.

Since one angle is 90°, the other two angles must be acute. This is unlike the ambiguous case when given an uncontained acute angle, where two possible triangles can be made by making another angle obtuse.

Imagine an isosceles triangle cut in half at the altitude, creating two right triangles (JKL and XYZ). They have the same angle measures. Each with a right angle, the angle that had an equal measure in the isosceles, and the unequal angle bisected. For the triangles' sides, the isosceles base was bisected by the altitude, and they have the same altitude.

Answer:

2.3 × [tex]10^{-4}[/tex] is 20,000 times greater than 1.15 × [tex]10^{-8}[/tex]

Step-by-step explanation:

Given as :

The first number= x = 2.3 × [tex]10^{-4}[/tex]

The second number= y = 1.15 × [tex]10^{-8}[/tex]

Let The first number is z times greater than second number

i.e x = z × y

Or, z = [tex]\dfrac{x}{y}[/tex]

Or, z = [tex]\dfrac{2.3\times 10^{-4}}{1.15\times 10^{-8}}[/tex]

Or, z = 2 × [tex]10^{4}[/tex]

∴  z = 20,000

So,The first number is 20,000 times greater than second number

Hence, 2.3 × [tex]10^{-4}[/tex] is 20,000 times greater than 1.15 × [tex]10^{-8}[/tex] . Answer