How many minutes does it take to put 42 gallons of water in the tub at a rate of 5 1/4 gallons per minute?

Taking square root on both sides, that becomes 2x - 5 = (+/-) √11

Then:

2x = (+/-)√11 + 5

x = [5 +/- √11 ] / 2

x = 5/2 +/- (√11)/2

That is, x = 5/2 +(√11)/2 and x = 5/2 - (√11)/2

Answer:

Sorry that I’m late, answer is C. y=7x

Step-by-step explanation:

14/2 = 7

28/ = 7

Answer:

24 miles per hour.

Step-by-step explanation:

So in order to calculate this you just need to use the formula for the speed:

Speed=Distance/time

Speed= 2 miles/ 5 minutes

Speed= 2 miles/,083 hours

Speed= 24

So the speed at the final 5 minutes will be 24 miles per hour.

Quotients are used to represent the division of  numbers

The number is -0.52

Let the number be represented with x.

So, the quotient of a number (x) and 0.2 is -2.6 is represented as:

[tex]\frac x{0.2} = -2.6[/tex]

Multiply both sides of the equation by 0.2

[tex]0.2 * \frac x{0.2} = -2.6 * 0.2[/tex]

Evaluate the quotient, on the left hand side

x = -2.6 * 0.2

Evaluate the product on the right hand side

x = -0.52

Hence, the number is -0.52

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The final mark you can get by substitute the 6 to the x  which you get the total of 38 because you have to calculate the perimeter of the isosceles triangle. You both literally helped me to get the full marks on Mathswatch Thank you!

Answer:

C. $25

Step-by-step explanation:

We will find,

The slope of the function using [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex].

Taking the points (1,40) and (2,55).

Slope = [tex]\frac{55-40}{2-1}[/tex]

i.e. Slope = [tex]\frac{15}{1}[/tex]

i.e. Slope = 15

Substituting the slope and point (1,40) in the equation [tex]y=mx+b[/tex],

We have, [tex]40=15\times 1+b[/tex]

i.e. [tex]b=40-15[/tex]

i.e. b= 25

Thus, the equation of the linear function is [tex]y=15x+25[/tex].

This linear function represents the cost of the comic book since Lucy purchased it, where x= years.

So, the initial value of the comic book is when x= 0.

So, [tex]y=15\times 0+25[/tex] i.e. y= 25

Hence, the cost of the book when Lucy purchased it was $25.

Answer:

The answer be 25

Step-by-step explanation:

The diameter of the field is 83 yards.

To find the diameter of a circular field, we can use the formula for the circumference of a circle, which is C = 2πr, where C is the circumference and r is the radius. Given that the circumference of the field is 260.62 yards, we can solve for the radius by dividing the circumference by 2π.

Using the value of π as 3.14, we can calculate:

260.62 / (2 * 3.14) = 41.50 yards

Since the diameter of a circle is twice the radius, the diameter of the field is 2 * 41.50 = 83 yards.

The domain of the function is [tex][0,3.5][/tex] and the range of the function is [tex][0,1750][/tex].

Speed [tex]= 500[/tex] mph

Distance [tex]= 1750[/tex] miles

Distance [tex]=[/tex] Speed [tex]\times[/tex] Time

The distance Jackson has traveled in miles is a function of time in hours he has been flying.

[tex]f(t)=500t.[/tex]

For maximum distance, [tex]f(t)=1750[/tex] miles.

[tex]1750=500t.[/tex]

[tex]t=\frac{1750}{500}[/tex]

[tex]t=3.5[/tex] hours

So, domain [tex]= [0,3.5][/tex]

Range [tex]= [0,1750][/tex]

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Answer:

D. x + 15 ≤ 60

Step-by-step explanation:

Let x be the amount you have left to spend after you purchase the shirt.

We must add to x the cost of the shirt, $15.  This gives us x+15.

We only have $60 to spend; this means we can spend anything up to and including $60.  This means we want "less than or equal to."  This gives us the inequality

x+15 ≤ 60

The inequality of the form x + 15 ≤ 60 is the correct choice.

An inequality is a comparison between two non equal expression or terms or numbers.

According to the given question You have a gift card for your favorite clothing store for the amount of $60.

You have found a shirt you want to buy that costs $15 but you don't want to spend more than the amount of the gift card.

Assuming the amount you will have is x dollars.

∴ x + 15 ≤ 60

As x ≤ 60 - 15

x ≤ 45.

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Answer: 8.

Step-by-step explanation: since the y coordinates are the same number and they are both positive you move to the x coordinates and you subtract them since they are both negative and you'd get a positive 8. Have a Blessed Day! :D

To find the distance between two points in a coordinate plane, you can use the distance formula. In this case, the distance between point G (-4, 1) and point H (-12, 1) is 8 units.

To find the distance between two points in a coordinate plane, you can use the distance formula. The distance formula is derived from the Pythagorean theorem and is given by:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

In this case, the coordinates of point G are (-4, 1) and the coordinates of point H are (-12, 1).

So, substituting the values into the distance formula:

distance = sqrt((-12-(-4))^2 + (1-1)^2)

Simplifying that expression, the distance between point G and point H is 8 units.

Answer:

Option C. 12 years

Step-by-step explanation:

Let principal amount taken = x

We know the formula of compound interest

Final amount = Principal amount×[tex](1+\frac{r}{n})^{nt}[/tex]

Where r = rate of interest (per year)

n = number of times compounded (annually)

t = time in years (years)

Here we have to find the time in which principal amount is doubled.

From the question r = 6% = .06

n = 1

Principal amount = P

Final amount = 2P

Now we put these values in the formula

[tex]2P=P(1+.06)^{t}[/tex]

[tex]2=(1.06)^{t}[/tex]

Now we take log on both the sides

[tex]log(2)=log(1.06)^{t}[/tex]

0.301 = tlog(1.06)

0.301 = t×(.025)

[tex]\frac{0.301}{0.25}=t[/tex]

t = 12 years.

Option C. 12 years is the answer.

Answer:18.75 gallons

Step-by-step explanation:

The solution is Option B.

The value of x = 2

The value of y = -2

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the first equation be represented as A

The value of A is

5x + 2y = 6   be equation (1)

Let the second equation be B

The value of B is

3x + y = 4   be equation (2)

Now , on simplifying the equations , we get

Multiply equation (2) by 2 , we get

6x + 2y = 8   be equation (3)

Subtracting equation (1) from equation (3) , we get

x = 8 - 6

x = 2

So , the value of x = 2

Substituting the value of x in equation (2) , we get

3x + y = 4

3 ( 2 ) + y = 4

6 + y = 4

Subtracting 6 on both sides of the equation , we get

y = -2

So , the value of y = -2

Hence , the solution to the system of equations is x = 2 and y = -2

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Answer:

C. [tex](0,-5)[/tex]

Step-by-step explanation:

We have been given a graph of system of equation on coordinate plane. We are asked to find the solution for the system of equations.

We know that we can find solution of a system of linear equations by graphing. The solution of the system is the point, where both lines intersect.

Upon looking at our given graph, we can see that both lines intersect at point [tex](0,-5)[/tex] that is at y-axis.

Therefore, the solution to the system of equations is [tex](0,-5)[/tex] and option C is the correct choice.

To find the number of hours Carla worked, we'll set up and solve equations based on the information given.

To solve this problem, we'll set up an equation based on the information given.

Let x be the number of hours Carla worked last week and y be the number of hours she worked this week.

According to the problem, 15 more than twice the hours Carla worked last week is the same as three times the hours she worked this week decreased by 15:

2x + 15 = 3y - 15

Next, we'll set up another equation based on the fact that Carla worked the same number of hours each week:

x = y

We can now solve this system of equations to find the value of y, which represents the number of hours Carla worked this week:

Substituting y for x in the first equation: 2y + 15 = 3y - 15

Combining like terms: 15 = y - 15

Adding 15 to both sides: 30 = y

So, Carla worked 30 hours this week.

Answer:

5040

Step-by-step explanation:

To Find : How many different 4-digit personal identification numbers are possible if no digit can be used twice?

Solution :

Since we are given that no digit can be used twice

SO, when one digit is used so next digit will be chosen from the remaining digit an so on .

the digits can be 0,1,2,3,4,5,6,7,8,9

Since these are 10 in number

out of these 10 we need to choose 4 but no digit can be used twice

⇒[tex]_{10}\textrm{C}_1 *_{9}\textrm{C}_1 *_{8}\textrm{C}_1*_{7}\textrm{C}_1  [/tex]

Formula : [tex]_{n}\textrm{C}_r=\frac{n!}{r!(n-r)!}[/tex]

thus using this formula

⇒[tex]\frac{10!}{1!(10-1)!} *\frac{9!}{1!(9-1)!}*\frac{8!}{1!(8-1)!}*\frac{7!}{1!(7-1)!}[/tex]

⇒[tex]\frac{10!}{9!} *\frac{9!}{8!}*\frac{8!}{7!}*\frac{7!}{6!}[/tex]

⇒[tex]10*9*8*7[/tex]

⇒[tex]5040[/tex]

Thus  different 5040 number of 4-digit personal identification numbers are possible if no digit can be used twice

The monthly interest rate on this annuity is approximately 0.4318%.

To find the monthly interest rate on the annuity, we need to use the present value formula for an annuity:

PV = A * (1 -[tex](1+r)^{(-n)[/tex]) / r

Where PV is the present value, A is the monthly payment, r is the monthly interest rate, and n is the total number of payments. In this case, PV = $90,000, A = $850, and n = 15 (since the professor's remaining life expectancy is 15 years).

By plugging in these values and solving for r, we can find the monthly interest rate on the annuity.

$90,000 = $850 * (1 - [tex](1+r)^{-15)[/tex] / r

After solving this equation, we find that the monthly interest rate on this annuity is approximately 0.4318%.

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The monthly interest rate is approximately 0.58%.

To determine the monthly interest rate on the annuity, we need to solve for the rate that equates the present value of the annuity payments to the initial payment of $90,000. The payments of $850 are made for the expected life of 15 years, which translates to 180 monthly payments.

The present value (PV) of an annuity can be calculated using the formula:

[tex]PV = Pmt * [(1 - (1 + r)^{-n}) / r][/tex]

Where:
Pmt = $850 (monthly payment)
r = monthly interest rate
n = 180 (total number of payments)

Given PV = $90,000, we need to solve for r:

$90,000 = $850 × [(1 - (1 + r)^-180) / r]

This requires solving the equation iteratively or using a financial calculator, as it's a non-linear equation. By trial and error or using a financial calculator or spreadsheet:

We find that r ≈ 0.0058 or 0.58%

Thus, the monthly interest rate on this annuity is approximately 0.58%.

Answer:

The slope of the function is 5.

Step-by-step explanation:

Remember that to calculate the slope of any function you just need the equation of the function on slope form: y=mx+c or any two points in the graph that are result of the function, in this case we have a table, and we will use the first two points:

(-4,-16)

(-2.-6)

So the formula for slope is:

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

We insert the values of our two points:

[tex]\frac{y2-y1}{x2-x1} \\\frac{-6-(-16)}{-2-(-4)}\\\frac{10}{2}\\  Slope=5[/tex]

So the slope of the function is 5.

-6 -(-4) = -6 +4 = -2

 So answer is:

A number line is shown from negative 10 to 0 to positive 10. There are increments of 2 on either side of the number line. The even numbers are labeled on either side of the number line. An arrow pointing from 0 to negative 6 is shown. Above this, another arrow pointing from negative 6 to negative 2 is shown. A vertical bar is shown at the tip of the arrowhead of the top arrow.

Answer:

The correct option is B) A number line is shown from negative 10 to 0 to positive 10. There are increments of 2 on either side of the number line. The even numbers are labeled on either side of the number line. An arrow pointing from 0 to negative 6 is shown. Above this, another arrow pointing from negative 6 to negative 2 is shown. A vertical bar is shown at the tip of the arrowhead of the top arrow.

Step-by-step explanation:

Consider the provided expression.

−6 − (−4)

Open the parentheses and change the sign.

−6 − (−4)

−6 + 4

Subtract the numbers.

−2

Now draw this on number line.

First draw a number line is shown from −10 to 0 to 10. with scale of 2 unit on either side of the number line. Draw an arrow pointing from 0 to −6 Which show −6. Above this, another arrow pointing from −6 to −2 which shows −6 − (−4) = −2. A vertical bar is shown at the tip of the arrowhead of the top arrow.

The required number line is shown in the figure 1.

Hence, the correct option is B) A number line is shown from negative 10 to 0 to positive 10. There are increments of 2 on either side of the number line. The even numbers are labeled on either side of the number line. An arrow pointing from 0 to negative 6 is shown. Above this, another arrow pointing from negative 6 to negative 2 is shown. A vertical bar is shown at the tip of the arrowhead of the top arrow.