you own a pet store that sells fish tank you brought a fish tank for $35 and are going to mark it up 20% what is the selling price going to be on the fish tank

we have the equation

7x - 7 = 13 + 12x​

solve for x

Group terms

12x-7x=-7-13

Combine like terms

5x=-20

x=-20/5

Verify

substitute the value of x=-4 in the original expression

7(-4)-7=13+12(-4)

-28-7=13-48

-35=-35 -------> is ok

519 people smoked

Explanation

to figure out this we need to find teh 13.2 % of 3932

so

Step 1

Convert 13.2% to a decimal by removing the percent sign and dividing by 100

then

Step 2

now, multyply the number by the percentage ( in decimal form),so

therefore, the answer is

519 people smoked

I hope this helps you

If the bees are working at the same rate, the number of years taken to make 70 jars is 4 years.

The rate at which a bee makes a jar is calculated as follows;

rate = 2000 bees / 7 Jars

rate = 285.71 b/J

The later of rate of the bees is calculated as follows;

rate = 5000 bees / 70 jars

rate = 71.42 b/J

If the bees were to maintain the first rate, the number of years taken to make 70 jars is calculated as follows;

number of years = (285.71) / (71.42) = 4 years

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Solution

A polynomial is a function in the form of ; where n is non- negative integers which is known as the degree of polynomial. from this definition, it is clear that only option (2) √2 x -1 , is polynomial. because coefficient of variables ; √2, -1 are real number and also power of variable is non-negative integer.

I have selected the options , the ones I have ticked are polynomials, while the one cancelled are none polynomials:

Answer:

The first option is correct

Explanation:

Two negatives makes a positive.

Given data:

The given sets of equations.

The polynomial in which degree of the variable is 1 is said to be linear expression.

The first option 2x+3y=6 is only linear function.

Thus, the option (A) is correct.

EXPLANATION

Given the parallel lines that are cutted by two non-parallel lines, m and n, the supplementary angle to 102 degrees is by the supplementary angles theorem 180-102= 78 degrees.

By the alternate interior angles theorem, the value of x is 78 degrees.

Also, by the corresponding angles theorem, the value of y is 115 degrees.

We have the following:

The questions can be found thanks to the graph of the statement

A)what height was the basketball thrown from?

The graph starts at the point (0, 6) therefore the basketball was thrown from 6 feet height

B)what is the maximum height the basketball went ?

The highest point of the graph is (2, 10), therefore the maximum height is 10 ft

C)after how many seconds did the basketball reach its maximum height?

The highest point of the graph is (2, 10), therefore the time it reached this height was 2 seconds

D)how many seconds did it take for the basketball to hit the ground ? make sure you look at the exact value in the graph?

The ground would be when the value of y is equal to 0, therefore according to the point (5.162, 0) the time was 5.162 seconds

Given,

The initial height of H feet.

The initial velocity of the object is Vo.

The equation of the path of projectile is,

This is the expression of the projectle path.

Hence, the path of the projectile object is y = h + xtan(theta) - x²/2V₀²cos²(theta)

Answer:

Angle C = 40 degrees

angle D = 75 degrees

Explanation:

From the information given,

Angle A = 75 degrees

Angle B = 40 degrees

AB is parallel to CD. This means that AD and BC are transversals.

Angles A and D have similar positions but they are opposite sides of the transversal. This means that they are alternate angles. Alternate angles are congruent. Thus,

angle D = 75 degrees

Angles B and C have similar positions but they are opposite sides of the transversal. This means that they are alternate angles. Alternate angles are congruent. Thus,

Angle C = 40 degrees

The expression (-1)^n means the number -1 multiplies itself n times.

So for example if n = 2, we have that:

For n = 3, we have:

For n = 4:

We can see that the result alternates from -1 and 1, and when n is odd, the result is -1, and when n is even, the result is 1.

So for any even number n, the result will be 1.

the area of the rectangular garden is 289 square ft

so

so the value of y is 289/x

the outer perimeter of the garden is 2(x+y)

now perimeter is 2(x+289/x)

it is given that the outer wall cost 22 $ per linear foot

so the total cost is

it is given that the cost of an interior wall is 9 $

and the length of the interior wall is x

the total cost of the interior wall is 9x

so the total cost of the wall is 9x +22 (2x + 578/x).

and the correct answer is 9x +22 (2x + 578/x). option B.

the sum of angles in a triangle is 180

missing angle + 90 + 51 = 180

missing angle = 180 - 141

missing angle = 39 degrees.

in the triangle,

x = 200 tan51

x = 200 * 1.234

x = 246.97 ft apporx 247 ft

'so the length x = 247 ft

that is greater than 200

so the answer is

x > 200 ft

To identify the slope and y-intercept, we will take the given equation to its slope-intercept form:

where m is the slope and b is the y-intercept.

To take the equation to its slope-intercept form, we add 3y to the given equation:

Now, we subtract 9, and get:

Finally, dividing by 3, we get:

Therefore, the slope and y-intercept are:

correspondingly.

Answer:

Slope:

Y-intercept:

Equations

We are given the following equation:

a/5 = 8+ 9

Adding 9 to both sides of the equation we have:

a/5 + 9 = 8 + 9 + 9

It's evident that a/5 + 9 is not equal to 8 + 9, but to 8+9+9 instead.

Answer: No

Number of sandwiches = 80p

Given:

Laura produces 80 sandwiches per day

To find:

The number of sandwiches that will be produced in p days

1 day = 80 sandwiches

p days = 80 × p

p days = 80p

This means that she will produce 80p number of sandwiches in p days

Answer:

The estimated crowd is of 380160 people.

Step-by-step explanation:

We solve this question applying a proportion on the following format:

People divided by area.

Let's do the drawing:

12 people fit comfortably in a 5 feet by 5 feet area.

So

12 people fitting in an area of 5*5 = 25 ft².

Area of the street:

3 miles = 3*5280 ft = 15840 ft

25 feet on both sides. So, the total area in which the crowd is sparsed is:

A = 15840*25*2= 792000 ft².

Now we apply the ratio:

People over area.

Applying cross multiplication:

25x = 12*792000

x = (12*792000)/25

x = 380160

The estimated crowd is of 380160 people.

Remember that we can get the mean of a dataset by adding up each datum and dividing such sum by the number of data.

Now, let's call the number of puppets Marco made M

This way, we would have that:

Solving for M :

Therefore, we can conclude that Marco made 4 puppets.

y varies directly with x

y=kx

y=12, x=9

12=k9

Solve for k:

12/9 =k

y= 12/9x

For y=36

36 = 12/9 x

Solve for x:

36 /(12/9)= x

27=x

x=27

The radius of the circle is r = 5 units.

The formula for the arc length of RQ is,

Substitute the values in the formula to obatin the arc length RQ.

So arc length of RQ is 12.39 units.

1 5/8 + 2 1/3

= 3 23/24

1 5/8 + 2 1/3

= 1 + 2 + 5/8 + 1/3

= 3 + 23/24

= 3 23/24

Given:

Vender sold a combined total of 249 sodas and hot dogs.

The number of sodas sold was 55 more than the number of hot dogs sold.

Let x and y be the number of sodas and hot dogs sold.

Substitute equation (2) in (1)

Number of sodas sold is 152.

Number of hot dogs sold is 97.

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data:

diagram:

circle and chords

Step 02:

congruent chords:

Congruent chords are equidistant from the center of a circle.

x = 7 + 7

x = 14

The answer is:

x = 14

Answer

Age of Car in years is represented as x

Avg. Miles per Gallon is represented as y

y = 0.97x + 1.214

Correlation Coefficient = 0.673

Explanation

Age of Car in years is represented as x

Avg. Miles per Gallon is represented as y

The datapoints are fed into a calculator and plotted with the datapoints also processed according to some formulas that'll be provided here

The first figure contains the data points and the regression data processed to be used to calaculate the required parameters.

The second attached image shows the plotted data and the line of best fit and the equation that best represents the relationship between the two parameters.

Then the last image shows the parameters used to calculate the equation of correlation and the correlation coefficient.

Hope this Helps!!!

Answer:

P(x) = 1.3x² + 0.1x + 2.8

Explanation:

We need to find an equation that satisfies the relationship shown in the table. So, let's replace x by 2 and then compare whether the value of p(x) is 8.2 or not

P(x) = 1.3x³ + 0.1x² + 2.8x

P(2) = 1.3(2)³ + 0.1(2)² + 2.8(2)

P(2) = 16.4

Since P(2) is 16.4 instead of 8.2, this is not a correct option

P(x) = 1.3x² + 0.2x - 2.8

P(2) = 1.3(2)² + 0.2(2) - 2.8

P(2) = 2.8

Since 2.8 and 8.2 are distinct, this is not the correct option

P(x) = 2.3x² + 0.2x + 1.8

P(x) = 2.3(2)² + 0.2(2) + 1.8

P(x) = 11.4

Since 11.4 and 8.2 are distinct, this is not the correct option

P(x) = 1.3x² + 0.1x + 2.8

P(2) = 1.3(2)² + 0.1(2) + 2.8

P(2) = 8.2

Therefore, this is the polynomial function for the data in the table.

So, the answer is P(x) = 1.3x² + 0.1x + 2.8

Answer:

seven less than the quotient of two and a number squared increased by six

7 -  (2/n²)  + 6

nine times the difference of a number cubed and three; 9(n³-3)

eight more than the quotient of a number squared and four, decreased by seven; 8 + (4 /n²) - 7

twice the difference of a number cubed and eight;  2 n³- 8

Step-by-step explanation:

From properties of linear equation, 1036 students attend east high school.

What is linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

Let east high school have x students

West high school have 2x - 250

Total count of students from both the schools are 2858 students.

Then we get

x + 2x-250 = 2858

=> 3x - 250 = 2858

=> 3x = 2858 + 250

=> 3x = 3108

=> x = 3108/3

=> x = 1036

Therefore, 1036 students attend east high school.

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Well we just need to do the analise of the function h, so for the first question we need to know what is the value of h when x=0, so if we evaluate we see that

So the first answer is that the start heigth of the rocket is 20.

Now for the second we need to do the derivate and see the critical ponit to know the maximum, we are going to calculate first the derivate, so

now we need to find the critical ponits so for this, we are going to see when h'(x) = 0, this meand when the derivate is equal to zero, so h'(x) = 0 when

to see if this critical poni is a maximum we need to calculate the secon derivate and see that the second derivate valued in 300/32 is smaller than 0, so

now when x= 300/32 we have that h''(x) is -32 because the second derivate is constant, in this case h''(300/32) < 0, because of this the answer is that 300/32 is the maximum, bur 300/32 = 75/8.

Now for the third question, we need to see the roots of h, so we need to see when h is zero, so for wich values of x we have that h(x) = 0, then

we can solve this with the quadratic equation to solve this kind of equations. This equation is

so we have that

the answer is x = (-300 - v/ 91280)/(-32) or x = (-300 + v/ 91280)/(-32) and this is equal to x = (300 + v/ 91280)/(32) or x = (300 - v/ 91280)/(32) if you prefer. We can also write the answer in a simpler way: x = (75 + v/ 5705)/(8) or x = (75 - v/ 5705)/(8), this is

Well we just need to do the analise of the function h, so for the first question we need to know what is the value of h when x=0, so if we evaluate we see that

So the first answer is that the start heigth of the rocket is 20.

Now for the second we need to do the derivate and see the critical ponit to know the maximum, we are going to calculate first the derivate, so

now we need to find the critical ponits so for this, we are going to see when h'(x) = 0, this meand when the derivate is equal to zero, so h'(x) = 0 when

to see if this critical poni is a maximum we need to calculate the secon derivate and see that the second derivate valued in 300/32 is smaller than 0, so

now when x= 300/32 we have that h''(x) is -32 because the second derivate is constant, in this case h''(300/32) < 0, because of this the answer is that 300/32 is the maximum, bur 300/32 = 75/8.

Now for the third question, we need to see the roots of h, so we need to see when h is zero, so for wich values of x we have that h(x) = 0, then

we can solve this with the quadratic equation to solve this kind of equations. This equation is

so we have that

the answer is x = (-300 - v/ 91280)/(-32) or x = (-300 + v/ 91280)/(-32) and this is equal to x = (300 + v/ 91280)/(32) or x = (300 - v/ 91280)/(32) if you prefer. We can also write the answer in a simpler way: x = (75 + v/ 5705)/(8) or x = (75 - v/ 5705)/(8), this is

Answer:

Step-by-step explanation:

This question can be solved using a rule of three.

For each configuration, we need the perimeter and the amount of bags of mulch.

For a square of side s, the perimeter is P = 4s

If the 10 x 10 garden took 3 1/2 bags of mulch:

10x10 means that s = 10.

So the perimeter is:

P = 4*10 = 40

The number of bags of mulch is:

3 1/2 = 3 + (1/2) = 3 + 0.5 = 3.5

15 x 15 garden

15x15 means that s = 15.

The perimeter is: P = 4*s = 4*15 = 60.

The number of bags is X.

Now applying the rule of three:

With the number of bags and the perimeter.

3.5 bags - 40'

X bags - 60'

Now we apply cross multiplication: