1. What is the total cost of a $95.00 item with a sales tax of 6%?

Answer: y = x - 9

Step-by-step explanation:

The equation of line slope - point form is given as :

y - [tex]y_{1}[/tex] = m ( x -[tex]x_{1}[/tex]

From the question

m = 1

[tex]x_{1}[/tex] = 9

[tex]y_{1}[/tex] = 0

Substituting into the formula , we have

y - 0 = 1 (x - 9)

y = x - 9

Therefore , the equation of the line in slope - intercept form is given as

y = x - 9

The equation of the line in slope-intercept form is y = x - 9.

The equation of a line in slope-intercept form is y = mx + b, where m represents the slope and b represents the y-intercept. Given that the slope of the line is 1 and it passes through the point (9, 0), we can substitute the values into the equation.

Let's substitute the slope m = 1 and the x-coordinate of the point x = 9:

y = 1(9) + b

Since the point (9, 0) lies on the line, we can substitute the y-coordinate y = 0:

0 = 9 + b

Solving for b, we subtract 9 from both sides:

b = -9

Therefore, the equation of the line in slope-intercept form is y = x - 9.

Answer:

It's B.

Step-by-step explanation:

Have a good day.

The bug's speed is approximately 5.33 meters per minute, which is closest to option (2).

To find the bug's speed in meters per minute, we need to convert its speed from inches per second to meters per minute.

First, let's convert the bug's speed from inches per second to inches per minute:

[tex]\[3.5 \text{ inches per second} \times 60 \text{ seconds per minute} = 210 \text{ inches per minute}\][/tex]

Now, let's convert inches to meters:

[tex]\[210 \text{ inches} \times \frac{2.54 \text{ centimeters}}{1 \text{ inch}} \times \frac{1 \text{ meter}}{100 \text{ centimeters}} = 5.33 \text{ meters per minute}\][/tex]

So, the bug's speed is closest to option (2) 5.33.

Complete Question:

There are 2.54 centimeters in every inch. If a bug moves at a rate of 3.5 inches per second, then which of the following is closest to its speed in meters per minute?

(1) 3.86

(3) 6.25

(2) 5.33

(4) 7.19

Answer:

6 1/2

Step-by-step explanation:

So basically 8 2/3 is equally to 26/3 so 45 minutes is 45/60.

45/60=3/4

26/3*3/4=6 1/2

Jordan, with a speed of 8 2/3 miles per hour, will cover a distance of 6.5 miles in a 45 minute bike ride.

First, we need to understand that Jordan is biking at a speed of 8 2/3 miles per hour. This means in 1 hour, or 60 minutes, he covers that distance. If we want to know how much he covers in a different timeframe - 45 minutes in this case - we have to adjust proportionally.

As a step-by-step calculation, first change 8 2/3 to a decimal, which equal to 8.67.

To find out how far Jordan bikes in 45 minutes, you need to multiply his speed (8.67 mph) by the time in hours. Since 45 minutes is 0.75 of an hour (45/60), the mathematical calculation will be:

Distance = Speed x Time = 8.67 miles/hour x 0.75 hour = 6.5 miles

Therefore, Jordan will bike 6.5 miles in 45 minutes.

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Answer:

$87200

Step-by-step explanation:

Here is the complete question:

At the beginning of the period, the Cutting Department budgeted direct labor of $46,300 and supervisor salaries of $37,200 for 4,630 hours of production. The department actually completed 5,000 hours of production.

Determine the budget of the department assuming that it uses flexible budgeting?

Given: Budget for direct labour= $46300

           Supervisor salaries= $37200

           Expected production hours= 4630 hours

           Completed production hours= 5000 hours

Now, we know that company budget include both fixed and variable cost.

∴ Direct labour cost is a variable cost and Supervisor salaries are fixed cost.

Using flexible budgeting for determining the budget of department, we will pro rate the direct labour cost on the basis of production hours.

Direct labour= [tex]Budget\times \frac{completed\ production\ hours}{expected\ production\ hours}[/tex]

Direct labour= [tex]46300\times \frac{5000}{4630}[/tex]

∴ Direct labour= $50000

we know the department budget = Fixed cost+variable cost

∴ Department budget= [tex]\$ 37200+\$ 50000 = \$ 87200[/tex]

∴ The department budget is $87200.

Answer: 12 small candles and 16 large candles.

Step-by-step explanation:

Notice that an small candle costs $4 and a large candle costs $6.

Let be "s" the number of small candles you sold and "l" the number of large candles you sold.

Set up a System of equations:

[tex]\left \{ {{4s+6l=144} \atop {s+l=28}} \right.[/tex]

Use the Elimination Method to solve it:

- Multiply the second equation by -4.

- Add the equations.

- Solve for "l".

Then:

[tex]\left \{ {{4s+6l=144} \atop {-4s-4l=-112}} \right.\\.......................\\2l=32\\\\l=16[/tex]

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

[tex]s+16=28\\\\s=12[/tex]

The equation which is equivalent to [tex]\log _{x} 36=2[/tex] is [tex]x^{2}=36[/tex] or x = 6 ([tex]\log _{6} 36=2[/tex]).

Step-by-step explanation:

Given Equation:

           [tex]\log _{x} 36=2[/tex]

As we know, in terms of logarithmic rules, when b is raised to the power of y is equal x:

           [tex]b^{y}=a[/tex]

Then, the base b logarithm of x is equal to y

           [tex]\log _{b}(x)=y[/tex]

Now, use the logarithmic rule for the given equation by comparing with above equation. We get b = x, y = 2, and x = 36. Apply this in equation,

            [tex]b^{y}=a[/tex]

            [tex]x^{2}=36[/tex]

When taking out the squares on both sides, we get x = 6. Hence, the given equation can be written as [tex]\log _{6} 36=2[/tex]

Answer:D

Step-by-step explanation:

i got it right

Answer:

[tex]105.84\ cm^2[/tex]

Step-by-step explanation:

step 1

Find the area of the circle

The area of the circle is

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

we have

[tex]r=21.2/2=10.6\ cm[/tex] ----> the radius is half the diameter

substitute

[tex]A=\pi (10.6)^{2}[/tex]

[tex]A=112.36\pi\ cm^2[/tex]

step 2

Find the area of a sector

Remember that

The area of the circle subtends a central angle of 360 degrees

so

using proportion

Find out the area of a sector with a central angle of 108 degrees

[tex]\frac{112.36\pi}{360^o}=\frac{x}{108^o}\\\\x=112.36\pi(108)/360\\\\x=33.708\pi\ cm^2[/tex]

assume

[tex]\pi=3.14[/tex]

substitute

[tex]33.708(3.14)=105.84\ cm^2[/tex]

Answer:

Part a) The solution is the ordered pair (6,10)

Part b) The solutions are the ordered pairs (7,3) and (15,1.4)

Step-by-step explanation:

Part a) we have

[tex]\frac{x}{2}-\frac{y}{5}=1[/tex] ----> equation A

[tex]y-\frac{x}{3}=8[/tex] ----> equation B

Multiply equation A by 10 both sides to remove the fractions

[tex]5x-2y=10[/tex] ----> equation C

isolate the variable y in equation B

[tex]y=\frac{x}{3}+8[/tex] ----> equation D

we have the system of equations

[tex]5x-2y=10[/tex] ----> equation C

[tex]y=\frac{x}{3}+8[/tex] ----> equation D

Solve the system by substitution

substitute equation D in equation C

[tex]5x-2(\frac{x}{3}+8)=10[/tex]

solve for x

[tex]5x-\frac{2x}{3}-16=10[/tex]

Multiply by 3 both sides

[tex]15x-2x-48=30[/tex]

[tex]15x-2x=48+30[/tex]

Combine like terms

[tex]13x=78[/tex]

[tex]x=6[/tex]

Find the value of y

[tex]y=\frac{x}{3}+8[/tex]

[tex]y=\frac{6}{3}+8[/tex]

[tex]y=10[/tex]

The solution is the ordered pair (6,10)

Part b) we have

[tex]xy=21[/tex] ---> equation A

[tex]x+5y=22[/tex] ----> equation B

isolate the variable x in the equation B

[tex]x=22-5y[/tex] ----> equation C

substitute equation C in equation A

[tex](22-5y)y=21[/tex]

solve for y

[tex]22y-5y^2=21[/tex]

[tex]5y^2-22y+21=0[/tex]

Solve the quadratic equation by graphing

The solutions are y=1.4, y=3

see the attached figure

Find the values of x

For y=1.4

[tex]x=22-5(1.4)=15[/tex]

For y=3

[tex]x=22-5(3)=7[/tex]

therefore

The solutions are the ordered pairs (7,3) and (15,1.4)

Answer:

b

Step-by-step explanation:

Answer:

y=1/2x-5/4

Step-by-step explanation:

y=2x+5/2

x=2y+5/2

2y=x-5/2

y=1/2x-(5/2)/2

y=1/2x-(5/2)(1/2)

y=1/2x-5/4

Answer:

The food at the fast food restaurant of chicken nuggets is  having higher unit price.

Step-by-step explanation:

Given:

A fast food restaurant had 5 boxes of chicken nuggets for $33.95.

A competing restaurant had 4 boxes of chicken fingers for $26.96.

Now, to get the food which has a higher unit price.

So, to get the unit price we use unitary method:

In, a fast food restaurant:

5 boxes of chicken nuggets cost for = $33.95.

Thus, 1 box of chicken nuggets cost for = [tex]\$33.95\div 5 = \$6.79.[/tex]

In a competing restaurant:

4 boxes of chicken fingers cost for = $26.96.

Thus, 1 box of chicken fingers cost for = [tex]\$26.96 \div 4 = \$6.74.[/tex]

Now, as comparing the prices of both restaurant the price of chicken nugget in fast food restaurant is $6.79 per box which is higher than the price of chicken fingers cost of $6.74 per box in competition restaurant.

Therefore, the food at the fast food restaurant of chicken nuggets is  having higher unit price.

Answer:

The coordinates of point D are (7,11)

Step-by-step explanation:

we know that

The formula to calculate the midpoint between two points is equal to

[tex]M(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]

In this problem we have

[tex]M=(3,5)\\C(x1,y1)=(-1,-1)\\D(x2,y2)=?[/tex]

substitute the given values

[tex](3,5)=(\frac{-1+x2}{2},\frac{-1+y2}{2})[/tex]

Solve for x2

[tex]\frac{-1+x2}{2}=3[/tex] ---> [tex]-1+x2=6[/tex] --->[tex]x2=6+1=7[/tex]

Solve for y2

[tex]\frac{-1+y2}{2}=5[/tex] ---> [tex]-1+y2=10[/tex] ---> [tex]y2=10+1=11[/tex]

therefore

The coordinates of point D are (7,11)

Answer:

[tex]a=36.87\ units[/tex]

[tex]B=57.47^o[/tex]

[tex]C=71.53^o[/tex]

Step-by-step explanation:

step 1

Find the length side a

Applying the law of cosines

[tex]a^2=b^2+c^2-2(b)(c)cos(A)[/tex]

substitute the given values

[tex]a^2=40^2+45^2-2(40)(45)cos(51^o)[/tex]

[tex]a^2=1,359.4466[/tex]

[tex]a=36.87\ units[/tex]

step 2

Find the measure of angle B

Applying the law of sines

[tex]\frac{a}{sin(A)} =\frac{b}{sin(B)}[/tex]

substitute the given values

[tex]\frac{36.87}{sin(51^o)} =\frac{40}{sin(B)}[/tex]

[tex]sin(B)=\frac{sin(51^o)}{36.87}{40}[/tex]

[tex]B=sin^{-1}(\frac{sin(51^o)}{36.87}{40})=57.47^o[/tex]

step 3

Find the measure of angle C

Remember that the sum of the interior angles in any triangle must be equal to 180 degrees

so

[tex]A+B+C=180^o[/tex]

substitute the given values

[tex]51^o+57.47^o+C=180^o[/tex]

[tex]108.47^o+C=180^o[/tex]

[tex]C=180^o-108.47^o=71.53^o[/tex]

The solution for y in 2x − 5y ≤ 15  is [tex]y \geq \frac{2x}{5} - 3[/tex]

Solution:

Given that we have to find solution for given inequality for y

2x − 5y ≤ 15

Let us solve above equation for "y"

[tex]2x - 5y \leq 15[/tex]

Add -2x on both sides

[tex]-2x + 2x - 5y\leq 15 - 2x\\\\-5y \leq 15 - 2x[/tex]

Divide by -5 on both sides

Remember that You can perform on operations on both sides of inequality, and have its truth value unchanged

But if we multiply or divide by a negative number, we must flip the sign

[tex]\frac{-5y}{-5} \geq \frac{15}{-5} - \frac{2x}{-5}\\\\y \geq -3 + \frac{2x}{5}\\\\y \geq \frac{2x}{5} - 3[/tex]

Thus solution for "y" is found

Answer:

The number of each coin she have are 17 dimes and 14 nickels.

Step-by-step explanation:

Given:

A coin collector has 31 dimes and nickels with a total face value of $2.40.

Now, to find each does she have.

Let the number of dimes be [tex]x[/tex].

Let the number of nickels be [tex]y[/tex].

So, total number of coins are:

[tex]x+y=31[/tex]

[tex]x=31-y.............(1)[/tex]

Value of a dime = 10 cents

Value of a nickel = 5 cents

Total face value = 240 cents

(1$ = 100 cents.  $2.40×100 =240 cents)

Now, total value of coins:

[tex]10x+5y=240[/tex]

Putting the equation (1) in the place of [tex]x[/tex]:

[tex]10(31-y)+5y=240[/tex]

[tex]310-10y+5y=240[/tex]

[tex]310-5y=240[/tex]

Moving variables on one side and the numbers on other:

[tex]310-240=5y[/tex]

[tex]70=5y[/tex]

Dividing both sides by 5 we get:

[tex]14=y[/tex]

The number of nickels = 14.

Now, putting the value of [tex]y[/tex] in equation (1) we get:

[tex]x+y=31[/tex]

[tex]x+14=31[/tex]

Subtracting both sides by 14 we get:

[tex]x=17.[/tex]

The number of dimes = 17.

Therefore, the number of each coin she have are 17 dimes and 14 nickels.

Answer:

The net pay of her will be $4702.21

Step-by-step explanation:

The State Tax plus Social Security Taxes plus Medicare takes (3 + 6.2 + 1.45) = 10.65% from Jessica's monthly gross pay.

If the gross pay is $5660 then the after the above deduction the remaining pay will be [tex]5660(1 - \frac{10.65}{100}) = 5057.21[/tex] dollars.

Now, again there is a deduction of $355 from her payment each month.

Therefore, the net pay of her will be = $(5057.21 - 355) = $4702.21 (Answer)

Answer:

75%

Step-by-step explanation:

2 x 1.75 = 3.5

The required percentage increase in the distance she can run is 75%.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,
Shelby could run 2 miles.
she can run 3.5 miles.
percentage increase = 3.5 - 2 / 2 × 100%
percentage increase = 75%

Thus, the required percentage increase in the distance she can run is 75%.

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Answer:

x-intercept - x = 1/2y - 3.15

y-intercept - y = 2x + 6.3

Step-by-step explanation:

For x,

-6x + 3y = 18.9

-6x = -3y + 18.9

x = -3y/-6 + 18.9/-6

x = 1/2y - 3.15

For y,

-6x + 3y = 18.9

3y = 6x + 18.9

y = 6x/3 + 18.9/3

y = 2x + 6.3

Option B

The choice has a value that is closest to the value of the following expression 17/12 - 49/40 is [tex]\frac{1}{5}[/tex]

Solution:

Given that we have to find the value that is closest to the value of following expression

[tex]\frac{17}{12} - \frac{49}{40}[/tex]

Let us take L.C.M of denominators and solve the sum

L.C.M of 12 and 40

List all prime factors for each number

prime factorization of 12 = 2 x 2 x 3

prime factorization of 40 = 2 x 2 x 2 x 5

For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.

The new superset list is

2, 2, 2, 3, 5

Multiply these factors together to find the LCM.

LCM = 2 x 2 x 2 x 3 x 5 = 120

Thus the given expression becomes:

[tex]\rightarrow \frac{17 \times 10}{12 \times 10} - \frac{49 \times 3}{40 \times 3}\\\\\rightarrow \frac{170}{120} - \frac{147}{120}\\\\\rightarrow \frac{170-147}{120}\\\\\rightarrow \frac{23}{120} = 0.1916 \approx 0.2[/tex]

[tex]0.2 = \frac{1}{5}[/tex]

Thus correct answer is option B

Answer:

B

Step-by-step explanation:

Answer:

Step-by-step explanation:

1) 1/5 + 1/7 = 1*7/5*7 + 1*5/7*5

=7/35 + 5/35 = 7+5/35 = 12/35

2) Let the number be x

x +6*1/x = -5

x + 6/x = -5

(x² + 6 ) / x = -5

x² + 6 = -5x

x² +5x + 6 = 0

x² + 3x +2x + 2*3 = 0

x(x+3) + 2(x+3)= 0

(x+3)(x+2) = 0

x + 3 = 0  or x +2 = 0

x = -3    or x = -2

the number is (-3)   or (-2)

Answe 72

Step-by-step explanation:

360 divided by 5 is 72

A circle is a curve sketched out by a point moving in a plane. The measure of the angle is 72°.

A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.

Let the angle that turns through 1/5 of the circle be x.

We know that the measure of the centre of a circle is 360°, while it is given that the angle turns through 1/5 of the circle. Therefore, the angle will turn 1/5 of 360°.

[tex]x = \dfrac15 \times 360^o = 72^o[/tex]

Thus, the measure of the angle is 72°.

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Answer:

  (x, y) = (6, 1) is the solution

Step-by-step explanation:

Each of the equations is written in "slope-intercept" form:

  y = mx + b . . . . . . . . where m is the slope and b is the y-intercept

First equation

  The y-intercept is +7 and the slope is -1. That means the line goes down 1 unit for each unit it goes to the right. It will go through the points (0, 7) and (7, 0).

Second equation

  The y-intercept is -2 and the slope is 1/2. That means the line goes up 1 unit for each 2 units it goes to the right. It will go through the points (0, -2) and (4, 0).

The lines will intersect at the point (6, 1), which is the solution found by graphing.

The student is probably asking about the cube root function multiplied by 3, which is an increasing function and is defined for all real numbers, including negative values.

The phrase 'f(x)=3 square root x' seems to be a typo. Assuming this refers to the cube root function, such as 'f(x) = 3 √x,' then this function represents the cube root of 'x' multiplied by 3. To graph this function, start by plotting points, taking the cube root of various values of 'x' and scaling these by 3.

The graph will pass through the origin and rise less steeply than a linear function; it will be an increasing function for all 'x' as the cube root of a real number is always real. This also means that the function will be defined for all real numbers, including negatives, as cubing can produce both positive and negative results.

Ashley sold 98 small cups and 57 large cups of lemonade.

Step-by-step explanation:

Given,

Price of small cup of lemonade = $1.25

Price of large cup of lemonade = $2.50

Total cups sold = 155

Total worth of cups = $265

Let,

x represent the number of small cups sold

y represent the number of large cups sold

According to given statement;

x+y=155    Eqn 1

1.25x+2.50y=265    Eqn 2

Multiplying Eqn 1 by 1.25

[tex]1.25(x+y=155)\\1.25x+1.25y=193.75\ \ \ Eqn\ 3[/tex]

Subtracting Eqn 3 from Eqn 2

[tex](1.25x+2.50y)-(1.25x+1.25y)=265-193.75\\1.25x+2.50y-1.25x-1.25y=71.25\\1.25y=71.25[/tex]

Dividing both sides by 1.25

[tex]\frac{1.25y}{1.25}=\frac{71.25}{1.25}\\y=57[/tex]

Putting y=57 in Eqn 1

[tex]x+57=155\\x=155-57\\x=98[/tex]

Ashley sold 98 small cups and 57 large cups of lemonade.

Keywords: linear equation, elimination method

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Answer:

32 cars

Step-by-step explanation:

we know that he can paint 12 cars in 3 weeks.

that means that he can paint 4 cars per week.

4cars x 8weeks = 32 cars in 8 weeks

Answer:

Step-by-step explanation:

12 cars in 3weeks

Then in 1week he will paint= 12/3 car

= 4 cars

so in 8weeks = 4 × 8 cars

= 32cars

Answer:

11%

Step-by-step explanation:

To fine the percentage decrease, we use the formula change/original x 100. In this case, the change is $11000-$9799=$1201 while the original is $11000. So 1201/11000 x 100 = 10.9% ≈ 11%

Answer:

y-5=4(x+3)

Step-by-step explanation:

y-y1=m(x-x1)

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

y-5=4(x+3)

Answer: 700 adults and 1500 children

Step-by-step explanation:

Let the number of adults be x and the number of children be y , then

x + y = 2200 ........................... equation 1

4x + 1.5y = 5050 ............................ equation 2

solving the system of linear equation by substitution method , from equation 1 make x the subject of the formula , that is

x = 2200 - y ....................... equation 3

substitute x = 2200 - y into equation 2 , that is

4 ( 2200 - y ) + 1.5y = 5050

8800 - 4y + 1.5y = 5050

8800 - 2.5y = 5050

2.5y = 8800 - 5050

2.5y = 3750

y = 3750/2.5

y = 1500

substitute y = 1500 into equation 3 , we have

x = 2200 - y

x = 2200 - 1500

x = 700

Therefore , 700 adults and 1500 children entered