Find two supplementary angles if the measure of the first is four times the second. Helpful hint: supplementary angles have a sun of 180 degrees

The cost of renting the mower for 3 hours is $16.

Formula:

Where:

c= total cost in dollars

h= number of hours the mower is rented.

So, we simply have to substitute h=3 ( mower rented for 3 hours) and solve:

Given that:

- Marc sold 500 tickets for the school play.

- Student tickets cost $2.

- Adult tickets cost $5.

- The total amount of money from the sale was $1,789.

a.) Let be "x" the number of student tickets Marc sold for the school play, and "y" the number of adult tickets Marc sold for the school play.

You can represent the total number of tickets he sold with this equation:

You can represent the total amount of money from the sale with this equation:

Now you can set up this System of Equations that can be used to determine how many of each type of ticket Marc sold:

b.) You can solve the System of Equations using the Elimination Method:

1. Multiply the first equation by -2:

2. Add the equations:

3. Solve for "y":

4. Substitute the value of "y" into the first original equation and solve for "x":

Hence, the answers are:

a.)

b.)

Answer:

Step-by-step explanation:

14-7=7

7-1=6

6=12x

x=0.5

Given the quadratic equation

we want to solve for the vertex and its axis of symmetry.

To easily identify these properties of quadratic equation, we must put the equation first into its vertex form. The first step to write it in its vertex form is to move the constant on the right-hand side of the equation

After that, we add the square of b/2 on the equation above. The value of b on the quadratic equation is -16. We have

Simplify the equation above

We write the expression on the left-hand side as perfect square, which is (x-4)^2.

Transfer 4 to left-hand side to write the vertex form of the quadratic equation

The vertex form has the general equation

where (h,k) is the vertex of the parabola.

Based on the vertex form of the quadratic formula, the vertex exists at (4,-4). Also, the axis of symmetry is equal to h, which is in this case, equal to 4.

The representation of a vertex and axis of symmetry in a quadratic plot will be

Answer: Vertex = (4,-4)

Axis of symmetry = 4

The student's estimate is off by 4%.

The total points possible for each task are added. A student's semester average is the total points earned divided by the total points available. A method of testing hypotheses about the mean of a small sample drawn from a normally distributed population when the standard deviation of the population is unknown.

Calculation:-

A container with a volume of 2.5 Liters.

Estimates volume = 2.6 L

The student's estimates off by percent = 2.6 - 2.5 = 0.1

percentage = 0.1/2.5 =100

= 4%.

Student's t-test is used when comparing two independent groups but ANOVA extends the t-test to more than two groups. Both methods are parametric and assume the normality of the data and equal variance between comparison groups.

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Step-by-step explanation:

what is the basic unit of length ? m or meter ?

a cube is like a 3-dimensional square : all side lengths are equal.

the volume of a cube =

side³

side³ = 343 m³

side = cubic root(343) = 7 m

a cube has 6 sides (look at dice). the surface of a cube is therefore 6 times the area of a side² square.

so, for side = 7 the surface area of the cube is

6 × 7² = 6 × 49 = 294 m²

and in the other direction, when we have the surface area (216 m²) :

216 m² = 6 × side²

36 = side²

side = sqrt(36) = 6 m

the volume of that cube is then

6³ = 216 m³

The given information is:

- The function of decay is:

Where A0 is the initial amount of strontium-90, A is the amount present at time t (in years).

- The initial amount is 800 grams.

a. What is the decay rate of strontium-90?

The given formula is written in the form:

Where r is the decay rate in decimal form, so:

The decay rate is -2.44%.

b. How much strontium-90 is left after 30 years?

Replace t=30 and solve:

There is 384.8 grams after 30 years.

c. When will only 200 g of strontium-90 be left?

A(t)=200g, then replace it and solve for t:

There will be 200 g left after 56.8 years.

d. What is the half-life of strontium-90?

The half-life is when A(t)=A0/2, then if we replace this into the decay formula we obtain:

The half-life of strontium-90 is 28.4 years.

The money owed by the cashier after selling three shirts and two sweatshirts for $203.75 and 6% clothing tax is $215.975.

The percentage tax is the tax amount charged for the item. The tax amount is given by dividing the per cent by 100 and multiplying it by the total amount of the item.

The total cost of three shirts and two sweatshirts is $203.75 and the tax is 6%.

The tax amount will be,

Tax amount = [tex]\frac{6}{100}\times203.75[/tex]

[tex]=12.225[/tex]

So, the total money owed by the cashier will be,

Total money owed by cashier [tex]=203.75+12.225[/tex]

= $215.975

Therefore, the money owed by the cashier after selling three shirts and two sweatshirts is $215.975.

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Scale factor is given by the formula below:

Using the right-hand side

new length = 1

old length= 3

substitute the values into the formular

ANSWER:

1.8176 * 10^-20 m^3

STEP-BY-STEP EXPLANATION:

Given:

Wide = 0.000000284 m

Long = 0.000000025 m

High = 0.00000256 m

Because it is rectangular in shape, the volume is the product of the three measurements, just like this:

The volume is 1.8176 * 10^-20 cubic meters

The inequality that can be used to determine x, the number of outfits Indigo can purchase will be; 367.39 + 68.49x ≤ 700

Inequality is defined as the relation which makes a non-equal comparison between two given functions.

The given parameters are:

Budget = $700

New bicycle = $296.71

Three bicycle reflectors = $12.34 each

Pair of a bike gloves = $33.66.

New biking outfits = $68.49 each.

Let the number of new biking outfits be x

So, we have the inequality;

New bicycle + 3 times price of bicycle reflectors + Pair of a bike gloves + New biking outfits ≤ Budget

This gives;

296.71 + 3( 12.34) + 33.66+ 68.49x ≤ 700

296.71 + 68.49x ≤ 700

Solve the inequality

367.39 + 68.49x ≤ 700

Hence, the inequality that can be used to determine x, the number of outfits Indigo can purchase will be; 367.39 + 68.49x ≤ 700

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Answer:

True

Step-by-step explanation:

to determine if the point is a solution, substitute x = - 0.6 and y = 1 into the left side of the inequality and compare resul with right side.

2y + 5x + 7

= 2(1) + 5(- 0.6) + 7

= 2 - 3 + 7

= - 1 + 7

= 6 > 3 ← True

then (- 0.6, 1 ) is a solution of the inequality

The values of the area of the shaded region are;

1. Area = 36, perimeter = 28

2. Area = 16, perimeter = 16

3. Area = 22, perimeter = 30

4. Area = 29, perimeter = 28

6. Area = 53.9

The area of a figure is the area bounded by the line that serves as the boundary of the figure.

The areas and perimeters of the figures are found as follows;

1. The figure consists of two rectangles

The dimension of the small rectangle at the top are;

Length = 4, Width = 3

Area = 3 × 4 = 12

Dimensions of the larger rectangle are;

Width = 4, Length = 6

Area = 4 × 6 = 12

The area of the composite figure is therefore; A = 3 × 4 + 6 × 4 = 36

The sum of the length of the sides, which is the perimeter, P = 8 + 3 + 4 + 3 + 4 + 6 = 28

2. The figure consists of a right triangle at the top rectangle;

The leg lengths of the right triangle are; 3 and 4

The area of the right triangle = 0.5 × 3 × 4 = 6

The dimension of the rectangle are; Length = 5, width = 2

Area of the rectangle = 5 × 2 = 10

Area of the composite figure is therefore, A = 0.5 × 4 × 3 + 2 × 5 = 16

The perimeter of the composite figure, P = 4 + 3 + 2 + 5 + 2 = 16

3. The figure is a composite figure that is found by subtracting the area of a rectangle from the area of a right triangle as follows;

The dimensions of the triangle are;

Leg lengths; (8 + 4) = 12 and (3 + 2) = 5

Area of the right triangle = 0.5 × (8 + 4) × (3 + 2) = 30

Dimensions of the rectangle left blank are;

Length = 4, width = 2

Area of the rectangle = 4 × 2 = 8

Therefore;

Area of the composite figure = 0.5 × (8 + 4) × (3 + 2) - 4 × 2 = 22

Length of the hypotenuse side = √((8 + 4)² + (3 + 2)²) = 13

The perimeter of the composite figure = 3 + 13 + 8 + 2 + 4 = 30

4. The figure is a composite figure that consist a large rectangle and small rectangle.

Dimensions of the large rectangle are;

Length = 2 + 2 + 3 = 7

Width = 5

Area of the large rectangle = 7 × 5 = 35

Dimensions of small rectangle are;

Length = 3, width = 2

Area of the small rectangle = 3 × 2 = 6

Area of the composite figure = 35 - 6 = 29

The perimeter = 2 × (2 × 2 + 3) + 2 × 5 + 2 × 2 = 28

6. Area of the circle = π × 14²/4

Area of the square = 10 × 10 = 100

The area of the shaded region = π × 14²/4 - 100 ≈ 53.9

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Fruit punch is served during the reception in 154-ounce cups using division.

Repetitive subtraction is the process of division. It is the multiplication operation's opposite. It is described as the process of creating equitable groupings. When dividing numbers, we divide a bigger number down into smaller ones such that the larger number obtained will be equal to the multiplication of the smaller numbers.

For instance, 4 2 Equals 2. As a multiplication fact, this can be expressed as 2 + 2 = 4.

The division is represented mathematically by a symbol consisting of a tiny horizontal line with dots above and below the line. The division of two integers is represented by one of two fundamental division symbols.

Total fruit punch foe prepared = 3696 ounces

Number of punch balls = 4

Each serving has = 6 ounces of punch

So, 4 servings will have

4 × 6 = 24

The number of servings of fruit punch available at reception is given by

3696÷24

= 154

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Answer

Angle PST = 80°

Explanation

Opposite angles of a parallelogram are equal.

Angle R = 130° = Angle QPS

The sum of angles on a straight line is 180°.

Angle QPS + Angle SPT = 180°

130° + Angle SPT = 180°

Angle SPT = 180° - 130° = 50°

Then, we were told that ST = SP, so, the the base angles of triangle PST are equal.

Angle SPT = Angle STP = 50°

Sum of angles in a triangle = 180°

Angle SPT + Angle STP + Angle PST = 180°

50° + 50° + Angle PST = 180°

100° + Angle PST = 180°

Angle PST = 180° - 100°

Angle PST = 80°

Hope this Helps!!!

We need to check if y=8 and x = -1 are perpendicular or parallel.

The line y=8, is a straight line for which the y-values within it are equal to 8, therefore it is parallel to the x-axis.

The line x=-1, is a straight line for which all the values have the same value of x, which is -1, therefore it is parallel to the y-axis.

The lines are, therefore, perpendicular.

Step 01:

Data

total math problems = 60

problems solved = 1/4

problems

Step 02:

Answer:

equation and fraction addition and subtraction

The line y = 2x + 6 shown in the data is the line of best fit of the data

What is line of best fit?

There are many points of the data and by plotting the points on the graph, a single line cannot pass through all the points.

Line of best fit minimize the distance between the line and the points of the data

The points which are plotted on the graph in red are the points of the data and y = 2x + 6 is the line of best fit of the data.

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The first step you have to follow is to find k(1) by replacing each x in k(x) for 1:

Now, find g(k(1)), it means, g(-7):

(g°k)(1)=573.

[tex]\cfrac{2}{3}\div 8\implies \cfrac{2}{3}\div \cfrac{8}{1}\implies \cfrac{2}{3}\times \cfrac{1}{8}\implies \cfrac{2}{8}\times \cfrac{1}{3}\implies \cfrac{1}{4}\cdot \cfrac{1}{3}\implies \cfrac{1}{12}[/tex]

The equation that represents the same line as the points in the table is  y = - 1 / 3 x - 2

The equation of a line in slope intercept form can be represented as follows:

y = mx + b

where

Using the table let's find the slope of the line as follows:

(-6, 0)(0, -2)

slope = m = -2 - 0  / 0 + 6

slope = - 2 / 6

slope = - 1 / 3

Therefore, let's find the y-intercept of the line using (0, -2).

y = - 1 / 3x + b

-2 = - 1 / 3 (0) + b

b = -2

Therefore, the equation of the table is y = - 1 / 3 x - 2

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If 40% of 95 is 38, what is 4% of 95?

Answer: 3.8

Answer:

  $900

Step-by-step explanation:

You want to know Lauren's average daily balance if she was charged a $13.50 finance charge on a card with an APR of 18%.

The finance charge is the product of the monthly interest rate and the average daily balance. The monthly rate is 1/12 of the annual rate. This tells us ...

  finance charge = ADB × 18%/12

  $13.50 = ADB × 0.015

  ADB = $13.50/0.015 = $900

Lauren's average daily balance was $900.

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Solution:

Given the composite figure below;

The figure is made up of a triangle and a trapezoid of the following side measures,

To find the total area, A, of the figure, the formula is

Substituting the values of the variables into the formula above

Hence, the total area, A, of the figure is 141 square inches.

The perimeter of the triangle is 12 in.

What is perimeter of similar triangle?

The perimeter of similar triangle is equal to the ratio of the similar sides of the triangle.  The ratio of two similar perimeters of two similar shapes is equal to the  ratio of the lengths of their corresponding sides.

Here, perimeter of triangle PQR = sum of all the side

=12+20+16

=48

The ratio of the corresponding side = 12/3

=4/1

Hence, the perimeter of triangle xyz = ?

perimeter of triangle PQR /perimeter of triangle xyz =4/1

48/x =4/1

x = 48/4

=12

Hence, the perimeter of triangle xyz = 12

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Answer: 196 miles

Step-by-step explanation: speed = 56 = distance / time

time = 3.5 hours

distance = speed x time = 56 x 3.5 = 196 miles

Answer:

196 miles

Step-by-step explanation:

If it drove for 56 miles per hour and rod for 3 1/2 hours the if we multiply 56 by 3 we have 168 miles and 1/2 of 56 is 28.

So the bus drove 196 miles

Answer:

13,307 years

Step-by-step explanation:

The expression for the decay of a radiactive material is:

A = B*(1/2)^(t/HL),

where A is the amount remaining, B is the initial amount, t is time (in years), and HL is the half life (in years).

We learn that A is 20% of B, so let's rewrite for that:

0.20B = B*(1/2)^(t/HL)

and we can divide both sides by B to leave us:

0.20 = (1/2)^(t/HL)

The HL is 5730 years:

0.20 = (1/2)^(t/5730)

We need to solve this expression for t, the time (in years) that is required before we have 20% of the carbon remaining.

The answer I get, by graphing, is 13,305 years,  The closest to this is A) 13,307 years.  An algebraic solution might result in a slightly different number.

Answer:

1.75

Step-by-step explanation:

1/4 (5 - -2)

1/4(5 + 2)

1/4(7)

7/4

1 3/4

We could state an exponential model.

Number of bateria will be given by:

where k=growth constant and t=time in minutes.

We're given that N0 is the initial population, which is:

We also know that, when t=236 min, N=2(9,085) = 18,170:

We're going to solve this equation to find the value of k:

Then, our expression is:

To find the population of bacteria after 708 minutes, we replace t by 708:

Therefore, the population of bacteria 708 minutes from now, is 72680.