fine the equation of the line: slope = -2 y-intercept= 5

Answer:

62 32/39%

Step-by-step explanation:

\(\frac{49}{78}*\frac{100}{1}=\frac{4900}{78}=\frac{2450}{39}=62\frac{32}{39}%\)%

The percentage of Mrs. Rogers crafts sold is 62.82%.

Given that, Mrs. Rogers sold 49 out of 78 crafts at the fair.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Percent of crafts sold =Number of crafts sold/Total number of crafts ×100

= 49/78 ×100

= 0.6282×100

= 62.82%

Therefor, the percentage of Mrs. Rogers crafts sold is 62.82%.

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Answer:

a. C = 2(17)pi= 34pi

b. d/2= 5pi/2= 2.5pi

C= 2(2.5)pi= 5pi

\(~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{a~is~negative}{op ens~\cap}\qquad \stackrel{a~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\)

\(\begin{cases} h=3\\ k=-10\\ \end{cases}\implies y=a(~~x-3~~)^2 + (-10)\hspace{4em}\textit{we also know that} \begin{cases} x=0\\ y=8 \end{cases} \\\\\\ 8=a(~~0-3~~)^2 + (-10)\implies 8=9a-10\implies 18=9a\implies \cfrac{18}{9}=a \\\\\\ 2=a\hspace{7em}y=2(~~x-3~~)^2 + (-10)\implies \boxed{y=2(x-3)^2-10}\)

The extremas of the function f(x) = x³ - 7x² + 10x are given as follows:

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Answer:

the answer to your question is 5

Step-by-step explanation:

Mean - this is the average. Add up the numbers and divide by the count of the numbers in the data set.

11+13+14+16+17+18+20+20+21+24+25+29 = 228

There are 12 numbers, so divide by 12.

228/12 = 19. The mean is 19.

Median - - - this is the MIDDLE number. Your data is already in numerical order (hooray!) so there are 12 numbers. Since it's even, we'll take the average of the 2 middle numbers. The 6th number is 18 and the 7th number is 20. The average of these is 19. So the median is 19.

(Side note: yes, median and mean can be the same.)

Mode - - - this is repeat/most common numbers! 20 repeats. 20 is the mode.

Range - - - biggest number is 29, littlest is 11. The range is 29-11 = 18.

819 in base five is equal to 13134.

Base five is a positional numeral system used in mathematics, having 5 as its base or radix. This means that it represents any real number using five different symbols, often the digits 0, 1, 2, 3, and 4. The ones place is represented by the digit on the right, the place of the five by the digit to the left, the twenty-fives place by the digit after that, and so on. Each digit in base five represents a multiple of a power of five.

To write 819 in base five:

Repeat steps 1-3 with the remainder (194):

Repeat steps 1-3 with the remainder (69):

Repeat steps 1-3 with the remainder (19):

The remainder (4) is less than 5, so write it down in the 5^0 place (rightmost digit).

Combine all the digits: 13134.

Therefore, 819 in base five is equal to 13134.

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Answer:

7*7

Step-by-step explanation:

49 = 7*7

As 7 is a prime number ( a number that can only be written as a product of 1 and itself), we are finished

Factors of 49: 1 7 49

prime factorization: 49=7*7

which can also be written as 7²

hope this is helpful

Answer:

52 problems

Explanation:

8.13 hours

8.13 hours × 60 minutes = x minutes

487.8 minutes

487.8 minutes ÷ 9.3 minutes = 52.4516129 problems

The maximum height of the object is 15.4 m and occurs at 0.295 sec. The object touches ground at 2.06 seconds

An equation is an expression that shows the relationship between two or more variables and numbers.

A ball is thrown upward from the top of a building 15 meters high, at a velocity of 2.8m/sec. Hence:

s = -4.9t² + 2.8t + 15

The maximum height is at s'(t) = 0, hence:

-9.8t + 2.8 = 0

t = 0.295 s

s = -4.9(0.295)² + 2.8(0.295) + 15 = 15.4 m

The object reaches ground when s = 0, hence:

0 = -4.9t² + 2.8t + 15

t = 2.06 seconds

The maximum height of the object is 15.4 m and occurs at 0.295 sec. The object touches ground at 2.06 seconds

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Answer:

One share cost: $26.25.

Sam wants to buy 100, which means that the total price of the shares is:

100*$26.25=$2625.

There is also commission of 5% of the total amount:

5% of $2625, which is:

(5/100)*$2625=0.05*$2625=$131.25

So, Sam's total cost will be: the total price of the shares + the commission

$2625+$131.25=$2756.25

Step-by-step explanation:

Answer:

$2756.25

Step-by-step explanation:
Trust

Answer:

its x=-3

Step-by-step explanation:

Answer:

The family will pay 34722 cents more if they take the van

Step-by-step explanation:

Given

Van = 12 miles per gallon

Sedan = 36 miles per gallon

Distance = 2500 miles

Gas = $2.50 per gallon

First, we need to determine the number of gallons that'll be used by both vehicles

This  is done by dividing total distance by number of miles per gallon

\(Van = \frac{2500}{12} \ gallon\)

\(Sedan = \frac{2500}{36}\ gallon\)

Next, is to multiply this by the cost of gas per gallon;

This gives the total spendable amount on both vehicles

\(Van = \frac{2500}{12} * \$2.50\)

\(Van = \frac{\$6250}{12}\)

\(Van = \$520.833\)

\(Sedan = \frac{2500}{36}* \$2.50\)

\(Sedan = \frac{\$6250}{36}\)

\(Sedan = \$173.611\)

Next is to get the difference between these amounts

\(Difference = \$520.833 - \$173.611\)

\(Difference = \$347.222\)

Multiply by 100 to convert to cents

\(Difference = 347.222 * 100 cents\)

\(Difference = 34722.2 \ cents\)

\(Difference = 34722\ cents\) (Approximated)

Hence;

The family will pay 34722 cents more if they take the van

The adjusting journal entry will include a debit to the allowance for credit losses of R4,400.

the correct answer is C. debit to allowance for credit losses of R4,400.

To determine the adjusting journal entry for J&L Electrical Services, we need to calculate the ending balance of accounts receivable and the necessary adjustment for the allowance for credit losses.

Beginning balance of accounts receivable: R200,000

Services delivered on credit: R660,000

Collections from debtors: R640,000

To find the ending balance of accounts receivable, we subtract the collections from the sum of the beginning balance and services delivered on credit:

Ending accounts receivable = (Beginning balance + Services delivered) - Collections

Ending accounts receivable = (R200,000 + R660,000) - R640,000

Ending accounts receivable = R220,000

Now, we need to calculate the adjustment for the allowance for credit losses. J&L Electrical Services estimates that 2% of the ending accounts receivable will not be collected:

Allowance for credit losses adjustment = Ending accounts receivable * Estimated uncollectible percentage

Allowance for credit losses adjustment = R220,000 * 2% = R4,400

Since the allowance for credit losses has a beginning balance of R4,000, we need to increase it by R4,400 to match the estimated uncollectible amount:

the correct answer is C. debit to allowance for credit losses of R4,400.

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The equation of the perpendicular line passing through (0, -1) is y = -9x - 1.

To find the equation of a line that is perpendicular to the given line y = (1/9)x + 2 and passes through the point (0, -1), we can use the fact that perpendicular lines have slopes that are negative reciprocals of each other.

The given line has a slope of 1/9. To find the slope of the perpendicular line, we take the negative reciprocal of 1/9, which is -9.

Using the slope-intercept form of a linear equation, y = mx + b, where m represents the slope and b represents the y-intercept, we can substitute the slope and the coordinates of the given point (0, -1) into the equation.

y = -9x + b

Since the line passes through the point (0, -1), we can substitute the x-coordinate as 0 and the y-coordinate as -1 into the equation:

-1 = -9(0) + b

-1 = b

Therefore, the y-intercept (b) of the perpendicular line is -1.

Putting it all together, the equation of the line that passes through (0, -1) and is perpendicular to y = (1/9)x + 2 is:

y = -9x - 1

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Answer:
V = 180 (vans)

S = 90 (small trucks)

L = 40 (large trucks)

Step-by-step explanation:

Set up the variables: Let V represent the number of vans, S represent the number of small trucks, and L represent the number of large trucks.

Write the equations:

V + S + L = 310 (total number of vehicles)

V = 2S (twice as many vans as small trucks)

35,000V + 70,000S + 60,000L = 15,000,000 (total cost of the vehicles)

Substitute equation 2) into equation 1):

2S + S + L = 310

3S + L = 310

Simplify equation 3) by substituting V = 2S:

70,000S + 70,000S + 60,000L = 15,000,000

140,000S + 60,000L = 15,000,000

Set up a system of equations:

3S + L = 310

140,000S + 60,000L = 15,000,000

Eliminate L by multiplying equation 1) by 60,000:

60,000(3S + L) = 60,000(310)

180,000S + 60,000L = 18,600,000

Subtract equation 2) from the new equation:

(180,000S + 60,000L) - (140,000S + 60,000L) = 18,600,000 - 15,000,000

40,000S = 3,600,000

Solve for S:

S = 90

Substitute the value of S into equation 1) to solve for L:

3(90) + L = 310

270 + L = 310

L = 40

Substitute the values of S and L into equation 2) to solve for V:

V = 2S

V = 2(90)

V = 180

The final answer is:

V = 180 (vans)

S = 90 (small trucks)

L = 40 (large trucks)

Answer:

180 Vans 90 Small trucks and 40 Large trucks

Step-by-step explanation:

Answer:

Longer side = 145ft

Shorter side = 135ft

Step-by-step explanation:

Here we have a rectangle.

Let's define L as the longest side (the one that is perpendicular to the wall of the house) and S as the shorter side.

We know that the perimeter of a rectangle is:

P = 2*L + 2*S

So if we wanted to fence this rectangle, we would need fencing equal to the perimeter.

But in this case, one of the shorter sides does not need to be fenced, so we only need:

2*L + S of fencing.

And we know that we will use 425ft of fencing, then:

2*L + S = 425 ft

We also know that The length of the fence opposite the house is 10 ft less than  either of the other two sides, then:

S = L - 10ft

Then we have two equations:

2*L + S = 425 ft

S = L - 10ft

Here we can just replace the second equation into the first one to get:

2*L + (L - 10ft) = 425 ft

Now we can solve this for L

2*L + L - 10ft = 425ft

3*L = 425ft + 10ft

3*L = 435ft

L = 435ft/3 = 145ft

This means that the longer side is 145ft long.

And by the equation:

S = L - 10ft

S = 145ft - 10ft = 135ft

S = 135ft

We know that the shorter side is 135ft long.

Answer:

\(5800 \times 9 \times 5 \div 100\)

Distance traveled after toll payment is 1.2 miles on highway 40.

The distance may be calculated using a curved route. Displacement measurements can only be made along straight lines. Distance is path-dependent, meaning it varies depending on the direction followed. Displacement simply depends on the body's beginning and ending positions; it is independent of the route.

Distance is the sum of an object's movements, regardless of direction. Distance may be defined as the amount of space an item has covered, regardless of its beginning or finishing position.

The size or extent of the displacement between two points is referred to as distance. Keep in mind that the distance between two points and the distance traveled between them are not the same. The entire length of the journey taken between two points is known as the distance traveled. Travel distance is not a vector.

Distance traveled before toll payment =3/5 miles on highway 40

Distance traveled after toll payment =2*3/5  = 6/5 =

1.2 miles on highway 40.

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48 minutes is equivalent to 1/5 of 4 hours.

We have,

To express 48 minutes as a fraction of 4 hours, we need to convert both the minutes and hours into a common unit of time.

Since there are 60 minutes in an hour, we can convert 4 hours to minutes:

4 hours = 4 x 60 minutes = 240 minutes

Now, we can express 48 minutes as a fraction of 240 minutes:

48 minutes / 240 minutes

To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 48:

= 48 minutes / 240 minutes

= 1/5

Therefore,

48 minutes is equivalent to 1/5 of 4 hours.

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To achieve a comparable rate of return, Hank would need to earn an interest rate of approximately 0.86% per month, compounded monthly on his ordinary annuity.

To find the interest rate, compounded monthly, that Hank would need to earn on an ordinary annuity for a comparable rate of return, we can use the present value formula for an ordinary annuity.

First, let's calculate the present value of Hank's payments. He made payments of $219 per month for 30 years, so the total payments amount to $219 * 12 * 30 = $78840.

Now, we need to find the interest rate that would make this present value equal to the selling price of the property, which is $195,258.

Using the formula for the present value of an ordinary annuity, we have:

PV = P * (1 - (1+r)\(^{(-n)})\)/r,
where PV is the present value, P is the payment per period, r is the interest rate per period, and n is the number of periods.

Plugging in the values we have, we get:
$78840 = $219 * (1 - (1+r)\({(-360)}\))/r.

Solving this equation for r, we find that Hank would need to earn an interest rate of approximately 0.86% per month, compounded monthly, in order to have a comparable rate of return.

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We have

scale factor

The largest side 10 in

Then we need to obtain the shortest side

Therefore the dimensions of the largest possible map are

6 2/3 in by 10 in

The PEMDAS method gives us the order of solving operations like this:

1)Parenthesis

2)Exponents

3)Multiply or Divide

4)Add or Substract

Therefore, we have the following:

6^2-2(5+1-3)=6^2-2(3)=36-2(3)=36-6=30

We get the cost of the system and cost of the games  as $126 and $378 respectively.

Given, the price of the video game and several games are sold for $504.

The cost of the game is 3 times as much as the cost of the system.

we need to determine the cost of the system and the cost of the game = ?

Let x = the cost of the games.

Let y = the cost of the system.

therefore, x+y=504

and y = 3x

substitute the value of y.

⇒ x + y = 504

⇒ x + 3x = 504

combine like terms.

⇒ 4x = 504

Divide both sides by 4.

⇒ x = 504/4

⇒ x = 126

The cost of the system is $126.

Use y = 3x substituting 126 for x.

g = 3(126)

g = 378

The cost of the games is $378.

Hence we get the cost of the system and cost of the games as $126 and $378 respectively.

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The graph of the inverse function is added as an attchment

From the question, we have the following parameters that can be used in our computation:

f(x) = -∛x + 3

Express as an equation

So, we have

y = -∛x + 3

Swap the variables x and y

This gives

x  = -∛y + 3

So, we have

∛y = 3 - x

Take the cube of both sides

y = (3 - x)³

This represents the inverse function

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Answer: anything between -3 and 3, inclusive (meaning-3 and 3 are answers)

Step-by-step explanation:

6≤-x+9≤12(-x is just x times 1)

Answer:

A.

Step-by-step explanation:

The figure moves to the right 8 units which is positive and then up 7 units which is also positive.

Answer:

the answer is                                                 b

Step-by-step explanation:

Total area = 63 cm² + 33 cm² + 4 cm² + 4 cm² = 104 cm²

The area of a trapezoid is given by the formula:

A = (a + b)h/2

where a and b are the lengths of the parallel sides of the trapezoid and h is the height (the perpendicular distance between the parallel sides).

To use this formula, simply plug in the values of a, b, and h and then solve for A. Note that all measurements must be in the same unit (such as centimeters or inches) for the formula to work correctly.

First, we can find the area of the rectangle with sides 7 cm and 9 cm:

Area of rectangle = length × width = 7 cm × 9 cm = 63 cm²

Next, we can find the area of the trapezoid with bases 2 cm and 5 cm and height 11 cm:

Area of trapezoid = (sum of bases × height) / 2 = ((2 cm + 5 cm) × 11 cm) / 2 = 33 cm²

Finally, we can find the area of the two squares with side lengths 2 cm and 2 cm:

Area of square 1 = side × side = 2 cm × 2 cm = 4 cm²

Area of square 2 = side × side = 2 cm × 2 cm = 4 cm²

Adding up the areas of all the shapes, we get:

Total area = 63 cm² + 33 cm² + 4 cm² + 4 cm² = 104 cm²

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We can write k(x) as the composition of g(x) and f(x).

k(x) = g(f(x))

A composition of two functions means that we need to evaluate one function in the other one.

Here we have the functions:

f(x)=  x²

g(x) = √(x - 1)

h(x) = 2x + 3

And we know that:

k(x) = √(x² - 1)

So we have a square root, then we need to evaluate g(x), and the argument is a square, then we need to evaluate in f(x), the composition is:

k(x) = g(f(x))

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