A group of 8 students are painting a mural at the local library. Each student uses 1/4

of the paint in their bucket. How many total buckets of paint did the students use?

8 buckets each with 1 of 4 sections shaded.

Answer:

(x - 6)² + y² = 36 and x2 + (y + 6)2 = 36.

Step-by-step explanation:

The equation of a circle with center (h, k) and radius r is given by:

(x - h)² + (y - k)² = r².

So, for a circle with a diameter of 12 units, the radius is 6 units.

For the center of the circle to lie on the y-axis, the x-coordinate, h, is 0.

So, the equation for a circle with center (0, k) and radius 6 units is:

(x - 0)² + (y - k)² = 6²

x² + (y - k)² = 36

Two possible values for the y-coordinate of the center, k, that would give us two different circles are k = 6 and k = -6.

So, the two equations are:

x² + (y - 6)² = 36

and

x² + (y + 6)² = 36.

Answer: [tex]8[/tex] and [tex]8[/tex]

Step-by-step explanation:

Let the numbers be [tex]x[/tex] and [tex]y[/tex].

[tex]x+y=16 \implies y=16-x\\\\xy=64 \longrightarrow x(16-x)=64\\\\16x-x^2 =64\\\\x^2 -16x+64=0\\\\(x-8)^2=0\\\\x=8 \implies y=8[/tex]

Answer:

Step-by-step explanation:

yes

Answer:

yes

Step-by-step explanation:

each 'x-value' maps to a unique 'y-value'

A wheelchair ramp is too steep, it may be difficult to use so we need to choose correct slope to design wheel chair.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

Slope is also important to people who use wheelchairs. If a wheelchair ramp is too steep, it may be difficult to use. Constructing a ramp with the right slope is especially important for people who use manual wheelchairs instead of power wheelchairs. If a ramp is too steep, the user may not have the upper arm strength necessary to power a manual chair up the ramp.

Therefore, a wheelchair ramp is too steep, it may be difficult to use so we need to choose correct slope to design wheel chair.

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The equation that represents the total amount the fan paid is

32 x (P + 25) = 3,232.

The amount spent by the friend is $909.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 8 is an equation.

We have,

Amount spend for 32 tickets = $3,232

Cost of parking = $25

Let p represent the amount the fan paid for each ticket.

The cost of each ticket.

32 x (P + 25) = 3,232

Solve for P.

32 x (P + 25) = 3,232

P + 25 = 3,232/32

P = 101 - 25

P = $76

Now,

The amount spent by the friend.

= 9 x (76 + 25)

= 9 x 101

= $909

Thus,

32 x (P + 25) = 3,232 represents the total amount the fan paid is

The amount spent by the friend is $909.

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The amount invested in savings with annual interest rate of 6% and 10% is $398200 and $199100.

Simple Interest (S.I.) is a way for figuring out how much interest will accrue on a specific principal sum of money at a certain rate of interest. For instance, if someone borrows Rs. 5000 at a rate of 10 p.a. for two years, they will pay S.I. on the borrowed money for those two years.

Let S be his savings.

He divided S into x that goes at 6% and y at 10%

As he put twice as much at the lower-yielding one, x = 2y.....(1)

Simple interest is given by: Amount x interest x time

Thus,

SI₁ = x . 0.06 . 1 = 0.06x

S I₂ = y. 0.10 . 1 = 0.10y

As x = 2y, I₁ = = 0.06 . 2y = 0.12y

As we know that the annual interest was $3982

SI₁ + SI₂ = 3982

0.12y + 0.10y = 3982

0.22y = 3982

y = 3982/0.22

y = 18100

As x = 2y, x = 36200

Hence, the amount invested is $36200 and $18100.

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There are 4 kilograms of type B in one bag of the blend.

What is a linear equation in one variable?

A linear equation in one variable is an equation that can be written in the form ax + b = 0, where a and b are constants and x is the variable. This equation represents a straight line in a coordinate plane and the solution to the equation corresponds to the x-coordinate of the point where the line intersects the x-axis.

Let's call the amount of type B in one bag of the blend "x".

Since one bag of the blend is 4 kilograms of type A, we know that one bag is 4 + x kilograms of coffee.

And since 6 bags of the blend is a total of 48 kilograms, we can write an equation:

6 * (4 + x) = 48

Expanding the left-side of the equation:

24 + 6x = 48

Subtracting 24 from both sides:

6x = 24

Dividing both sides by 6:

x = 4

Hence, there are 4 kilograms of type B in one bag of the blend.

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The system of equations that models the situation is given as follows:

The system of equations is constructed by linear functions in slope-intercept format, which are explained as follows:

y = mx + b.

In which:

Hence the two functions are given as follows:

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The solution to the equation -1/5 = -2y + 8/5 is y = 9/10

Given the equation in the question;

-1/5 = -2y + 8/5

First, rewrite the equation as;

-2y + 8/5 = -1/5

Move all terms not containing y to the right side of the equation

-2y + 8/5 - 8/5 = -1/5 - 8/5

-2y = -1/5 - 8/5

Add  -1/5 and -8/5

-2y = ( -1 - 8) / 5

-2y = -9 / 5

Divide both sides by -2

-2y / -2 = -9/5 ÷ -2

y = -9/5 × -1/2

y = 9/10

Therefore, the value of y is 9/10.

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Answer: second blank for x= 2, fifth blank for x= 9. First blank for y= 0, third blank for y= 4, fourth blank for y= 36.

Step-by-step explanation:

plug in x and y values to equation and solve.

The total commission the realtor earns is given by the equation A = $ 9375

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 total commission amount the realtor earns be represented as A

Now , the equation will be

The percentage of commission = 1.25 %

The total amount for the 2 homes = $ 750,000

So , the amount of commission A = percentage of commission x total amount for the 2 homes

Substituting the values in the equation , we get

The amount of commission A = ( 1.25 / 100 ) x 750,000

On simplifying the equation , we get

The amount of commission A = 0.0125 x 750,000

The amount of commission A = $ 9375

Hence , the amount of commission is $ 9375

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The required number of ice blocks that fit in the storage box is 80 ice blocks.

The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.

The volume of the storage box is,
= 7.5 feet × 6 feet × 6 feet
= 270 cubic feet.

Each ice block has a volume,

= 1.5 feet × 1.5 feet × 1.5 feet
= 3.375 cubic feet.

Therefore, the number of ice blocks that fit in the storage box is,
= 270 / 3.375
= 80 ice blocks.

Thus, the required number of ice blocks that fit in the storage box is 80 ice blocks.

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Answer:

(x - 1)² + (y - 1)² = 25

Step-by-step explanation:

the distance from the center of the circle to any point on the edge (or arc) of the circle is the radius of the circle.

per the distance formula (= Pythagoras for the right-angled triangle of the coordinate differences between the 2 points) we know

AB² = (xb - xa)² + (yb - ya)² = (5 - 1)² + (4 - 1)² =

= 4² + 3² = 16 + 9 = 25

AB = radius = 5

the standard form of a circle is

(x - h)² + (y - k)² = r²

(h, k) being the coordinates of the center of the circle, r being the radius.

(x - 1)² + (y - 1)² = 25

is the correct equation.

By solving a system of equations, wewill see that they sold 325hamburgers.

Let's define the variables:

h = number of hamburgers.

c = number of cheeseburgers.

We know that the total combined number is 588, then we can write:

h +c = 588

And there were 62 fewer cheeseburers than hamburgers, then:

c = h - 62

Now we have a system of equations:

h +c = 588

c = h - 62

c is already isolated on the second equation, so we can replace that on the first equation to get:

h + (h - 62) = 588

2h = 588 + 62

2h = 650

h = 650/2 = 325

They sold 325 hamburgers.

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Answer:

1:20

Step-by-step explanation:

Let's review the ratio of meters:centimeters

1:100 (1 meter to 100 centimeters)

Thus, our answer will be in meters:centimeters

Let's plug this in

5:100

Let's simplify by dividing both sides by 5, now!

5 / 5 = 1

100 / 5 = 20

So, our final ratio is 1:20

Answer:

Step-by-step explanation:

The place value of the 5 in the number 2.35 x 104 is ten thousand.

In scientific notation, the number 2.35 x 104 represents 2.35 times 10 to the power of 4. The number 10 to the power of 4 is 10,000, so the digit 5 is in the ten thousand place. The ten thousand place has a value of 10,000, so the 5 in 2.35 x 104 has a place value of 10,000.

So, the place value of the 5 in 2.35 x 104 is ten thousand.

The Angle C is 83.2°

The Law of Cosines, also known as the Cosine Formula, is a mathematical relationship that relates the lengths of the sides of a triangle to the cosine of one of its angles. The law states that in a triangle ABC with sides a, b, and c opposite to angles A, B, and C, respectively, the following equation holds:

c^2 = a^2 + b^2 - 2ab cos(C)

where "cos" represents the cosine function. The Law of Cosines can be used to find missing sides or angles in a triangle when given sufficient information. It is widely used in geometry, trigonometry, and engineering. The Law of Cosines is an extension of the Pythagorean theorem and can be used when the triangle is not a right triangle. It is a powerful tool for solving a variety of problems in a wide range of fields.

To find the angle C in triangle ABC, you can use the Law of Cosines. The Law of Cosines states that in a triangle ABC with sides a, b, and c and opposite angles A, B, and C, the following equation holds:

c² = a² + b² - 2abcos(C)

In this case, a = 20 cm, b = 29 cm, and c = 24 cm, and we are given that angle BAC = 82 degrees. Using this information, we can calculate cos(C) as follows:

cos(C) = (a² + b² - c²)/(2ab) = (20² + 29² - 24²)/(2×20×29) = 0.2618

Finally, we can use the inverse cosine function (arccos) to find angle C:

C = arccos(cos(C)) = arccos(0.2618) = 83.2 degrees (rounded to one decimal place).

So, angle C in triangle ABC is approximately 83.2 degrees.

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35?

I just subtracted 39 from 52 and i got 14 so i added 13 to 22 and i got 35 so i assume thats it

Answer:

  (a)  y = x/3 -1

Step-by-step explanation:

You want the equation of the line graphed showing points (3, 0) and (6, 1).

The slope of the line is its "rise" divided by its "run." Here, the points are 3 units apart horizontally, and 1 unit vertically, with the line going up to the right. That means ...

  slope = rise/run = +1/+3 = 1/3

The slope-intercept form of the equation for a line is ...

  y = mx +b . . . . line with slope m and y-intercept b

The slope of 1/3 means the coefficient of x will be 1/3. There is only one answer choice like that:

  y = x/3 -1

The maximum amount of weight, a human being could lift is  0.0002 kilograms.

Since an average ant can lift a maximum of 50 times its own body weight, and it weighs 4 milligrams,

The maximum weight it can lift is

50 * 4 milligrams = 200 milligrams.

To convert milligrams to kilograms, we divide by 10^6:

200 milligrams / 10^6 = 0.0002 kilograms

So, the maximum amount of weight a human being could lift if it could lift as much as an average ant is 0.0002 kilograms.

Therefore, the answer is 0.0002 kilograms or 0.2 grams

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Answer:

The inequality to compare the number of pictures taken during school to the number of pictures taken after school is: 19 < 24.

Step-by-step explanation:

Here's a step-by-step explanation of the inequality comparison:

Start with the two values being compared: 19 pictures taken during school and 24 pictures taken after school.

Use the inequality symbol (<) to compare the two values: 19 < 24.

Read the inequality as "19 is less than 24". This means that there were fewer pictures taken during school (19) than after school (24).

So the inequality comparison between the number of pictures taken during school and after school is: 19 < 24.

Therefore , the solution of the given problem of speed comes out to be

speed of freight train is 10 mi/h.

We can determine how fast that anything is traveling by looking at it from a distance. The amount of distance an object can go in a given length of time depends on its speed. Velocity is calculated using the formula velocity = distance/time. The three most used units of speed are meters per second (m/s), kilometers per hour (km/h), and miles per hour (mph) (mph).

Here,

Given :

passenger train covers a distance of 175 mi.

freight train covers a distance of 125 mi.

Speed of passenger train is 14 mi /h

Using formula of time -distance,

=> 175/14 = 12.5 hour

So, speed of freight train is :

=> speed = 125/12.5 = 10 mi/h

Therefore , the solution of the given problem of speed comes out to be

speed of freight train is 10 mi/h.

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It took 3 hours to travel 150 miles with a speed of 50 miles per hour.

The speed of an object tells how fast or slow an object will cover a distance in the time period. The speed of an object is directly proportional to the distance covered by the object and will be inversely proportional to time.

Here we have

A drive of 50 miles per hour between Seattle and Portland
which are 150 miles apart  

Given speed = 50 miles per hour

Distance covered = 150 miles  

The time is taken to travel the distance, Time = Distance / Speed  

= (150/50) =  3 hrs

Therefore,

It took 3 hours to travel 150 miles with a speed of 50 miles per hour.  

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Answer:

y= -(x)-2

Step-by-step explanation:

if you want to find  an equation passing through the point that is perpendicular to an y=mx +c type equation. all you have to do is to change sign of the gradient. it's simple.

Sorry for the inconvenience.

Answer:

(-infinity,-1)U(-1,infinity)

Step-by-step explanation:

plug in the number where the piecewise function changes which is -1 and 1

(-1)^2-(-1)-2 =0

(-1)=-1

These aren't equal so the function  is discontinuous at x = -1 because of a jump

(1) = 1

-2(1) + 3 = 1

These are equal so the function is continuous at x = 1

So from negative infinity to -1 the function is continuous and from -1 to infinity

(-infinity,-1)U(-1,infinity)

[tex]\displaystyle \lim_{x\to 16} ~~ \cfrac{4-\sqrt{x}}{16x-x^2} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{4-\sqrt{x}}{16x-x^2}\implies \cfrac{4-\sqrt{x}}{x(16-x)}\implies \cfrac{4-\sqrt{x}}{x( ~~ 4^2-(\sqrt{x})^2 ~~ )} \\\\\\ \cfrac{4-\sqrt{x}}{x( ~~ [4-(\sqrt{x})][4+(\sqrt{x})] ~~ )}\implies \cfrac{1}{x( ~~ 4+\sqrt{x} ~~ )} \\\\[-0.35em] ~\dotfill\\\\ \displaystyle \lim_{x\to 16} ~~ \cfrac{1}{x( ~~ 4+\sqrt{x} ~~ )}\implies \cfrac{1}{16( ~~ 4+\sqrt{16} ~~ )}\implies \cfrac{1}{16(4+4)}\implies \cfrac{1}{128}[/tex]

Answer: To find the limit as x approaches 16, we can substitute x = 16 into the expression:

lim (4-√X)/16X-X² = (4 - √16)/16 * 16 - 16^2 = (4 - 4)/16 * 16 - 256 = 0/256 - 256 = -256.

So the limit as x approaches 16 is -256.

Step-by-step explanation:

The total surface area painted black = 90.5 square feet to the nearest tenth.

A cone is a three-dimensional geometric form with a flat base and a smooth, tapering apex or vertex. A cone is made up of a collection of line segments, half-lines, or lines that link the base's points to the apex, which is a common point on a plane that does not include the base.

Given:

Three large cones hang from the ceiling in an office building in front of a bank of windows.

The height of each cone is 12 feet, and the circumference of the base of each cone is 8π feet.

The base and 40% of the lateral surface of each cone is painted red, and the rest of each cone is painted black.

Circumference of the base of the cone = 8π feet.

2πr = 8π

πr = 4π

The surface area of the cone = πr x height

The surface area of the cone = 12 x 4π

The surface area of the cone = 48π.

The total surface area painted black = 60% of 48π.

The total surface area painted black = 90.5 square feet to the nearest tenth.

Therefore, the result is 90.5 square feet to the nearest tenth.

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The graph of the function is given by the image presented at the end of the answer.

The minimum value on the interval [-2,0] is given as follows:

y = -1 at x = -2.

The maximum value on the interval [-2,0] is given as follows:

y = 1 at x = 1.

The minimum value of a function in an interval is the lowest value of y assumed by the function.

The maximum value of a function in an interval is the lowest value of y assumed by the function.

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Answer: 2 1/2 or 2.5

Step-by-step explanation: 3/1 * 5/6= 15/6

divide 15/6 which equals 2.5 or 2 1/2