Determine if the 3 lengths make a triangle. If they do, classify as acute, right, or obtuse.

a. 5, 6, 7

b. 1.6, 1.8, 3.1

c. 7, 9, 15

d. 4, 5, 10

e. 15, 20, 25

(45 points)

The center of this circle is (-2,2) and its radius is 2.

It is required to find the center and radius of the circle.

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “centre”. The perimeter around the circle is known as the circumference.

here, we have,

Given that: (x + 2)² + (y-2)² = 4

The equation of a circle in standard form is:

(x -a)² + (y-b)² = r²

The x-coordinate of the center is a the y-coordinate of the center is b

, and r is the radius.

In this case,

a=-2

b=2

and

r=2.

Hence, the center of this circle is (-2,2) and its radius is 2.

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Answer:

The isosceles triangle has three acute angles, meaning that the angles are less than 90°. The sum of three angles of an isosceles triangle is always 180°.

Step-by-step explanation:

[tex]\textit{circumference of a circle}\\\\ C=2\pi r ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=17 \end{cases}\implies C=2\pi (17)\implies C=34\pi[/tex]

Answer:

This type of study would be a comparative study, as it involves comparing the level of academic motivation between college students and their siblings.

Step-by-step explanation:

The functions are Identified as below

The domain is all real numbers for both

An x-intercept is (π, 0) for sin

The minimum value is -1 for both

An x-intercept is (π/2, 0) for cos

Sin functions, or sine functions, are mathematical functions that describe a wave-like pattern that oscillates between a maximum and minimum value.

sin functions has x intercept of (π, 0), this can be checked by setting a calculator in radian and checking for sin π.This will give a value of of zero

For cos the x intercept is zero at π/2

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Therefore, the equations that represent circles with a diameter of 12 units and a center on the y-axis are x² + y² = 36 and (x + 6)² + y² = 36.

The radius of a circle having a diameter of 12 units is 6 units. The center's x-coordinate is zero if its centre is on the y-axis.

To discover which equations describe circles with these characteristics, we may use the conventional version of the equation of a circle, (x - h)2 + (y - k)2 = r2, where (h, k) is the circle's centre and r is its radius.

When we enter h = 0 and r = 6, we obtain:

(x - 0)² + (y - k) (y - k)² = 6²\sx² + (y - k) (y - k)² = 36

As we are aware that the centre is on the y-axis, the center's y-coordinate is also 0. K thus equals 0.

With k = 0, we obtain:

x² + y² = 36\s(x - 4) (x - 4)² + y² = 36\s(x + 6)² + y² = 36

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Answer

The answer is 60

Step-by-step explanation:

Looking at the table again, we can see that f(4) is -6. Thus, f (g(2)) is -6.

Value is the worth of something, based on its importance, usefulness, or desirability. It is something that has a desired quality, such as excellence, utility, or desirability. Value can be physical, such as a commodity, or intangible, such as respect, loyalty, or knowledge. Value is determined by both the individual and the society in which they live. Value can be assigned to both tangible and intangible things, such as a house, an education, or a friendship. Value is a subjective measure and can vary greatly from person to person.

The answer is -6. To evaluate f (g(2)), we need to determine what g(2) is first. Looking at the table, we can see that g(2) is 4. Therefore, we need to find the value of f(4). Looking at the table again, we can see that f(4) is -6. Thus, f (g(2)) is -6.

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If the spinner is spinning two times then the sample space becomes { BB,B0,BR,OB,OO,OR,RB,RO,RR}.

In probability a sample space is a set of possible number of outcomes of a random experiment.

A spinner has three equal sections blue(B), orange(O), red(R).

The sample space will be

Spin 1 Spin 2

Blue Orange

Blue Red

Blue Blue

Red Blue

Red Orange

Red Red

Orange Blue

Orange Red

Orange Orange

Hence, If the spinner is spinning two times then the sample space becomes { BB, B0, BR, OB, OO, OR, RB, RO, RR}.

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The point which has the coordinates (-3.5, 4) is point Z.

Coordinates are the set of points in a geometrical plane or space, which is used to denote the exact point in the coordinate plane or space.

Given coordinate is (-3.5, 4).

This means that the point is at a distance of 3.5 to the left of the origin and at a distance of 4 units above the origin.

So in order to find the point, mark the point -3.5 in the exact middle of -3 and -4 on the X axis.

Mark the point 4 on the Y axis.

Draw perpendicular lines from both.

Intersecting point is the given point.

Here point Z indicates this.

Hence point Z indicates the coordinates (-3.5, 4).

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Your question lacks the graph showing the points and coordinates. The graph is given below.

Therefοre, the sοlutiοn οf the given prοblem οf functiοn cοmes οut tο be Terry can easily take anοther 800mg Tylenοl fοr his headache after abοut 2.4 hοurs have passed.

The curriculum fοr mathematics includes a wide range οf tοpics, such as numbers, numbers, and their cοmpοnents, as well as cοnstructiοn, building, and bοth actual and hypοthetical geοgraphic places. A wοrk discusses the relatiοnships between different variables that all wοrk tοgether tο prοduce the same result. A utility is made up οf a variety οf distinctive cοmpοnents that, when cοmbined, prοduce specific results fοr each input.

Here,

The functiοn can be written as fοllοws:

=> y = 800 * (0.25)ˣ

where y is the quantity οf Tylenοl still in Terry's system in milligrammes and x is the number οf hοurs since he last tοοk the medicatiοn.

When Terry's bοdy's cοncentratiοn οf Tylenοl gοes belοw 100mg, we need tο find οut hοw lοng it will be befοre he can take mοre medicatiοn.

The expοnential decay fοrmula frοm part 1 can be used tο find a sοlutiοn fοr this:

=>  800 * (0.25)ˣ = 100

by 800, divide bοth sides.

=>  (0.25)ˣ = 0.125

Cοnsider the twο sides' lοgarithms:

=>  lοg(0.25) * x = lοg (0.125)

tο find x:

=>  lοg(0.125) / lοg (0.25)

=>  x = 2.4

Terry can easily take anοther 800mg Tylenοl fοr his headache after abοut 2.4 hοurs have passed.

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Answer:

2.5

Step-by-step explanation:

for example, if you take two of the value of x's -- 5/2, it equals 2.5

2 x 2.5 = 5

Answer: We can use the formula for future value of an annuity to calculate how much will be saved for retirement:

FV = Pmt x (((1 + r)^n - 1) / r)

where:

FV is the future value of the annuity

Pmt is the payment made each period (in this case, the annual profit of $22,000)

r is the annual interest rate (9% or 0.09 as a decimal)

n is the number of periods (7 years)

Substituting the given values into the formula, we get:

FV = $22,000 x (((1 + 0.09)^7 - 1) / 0.09)

FV = $22,000 x (1.9904 / 0.09)

FV = $22,000 x 22.116

FV = $485,552

Therefore, the amount saved for retirement after 7 years will be $485,552.

Step-by-step explanation:

Answer: 30

Step-by-step explanation:

plug in x=8 to get: 6(8 - 3)

solve inside parenthesis: 6(8-3) = 6(5)

multiply: 6(5) = 30

Answer:

[tex] \sf \: 6(x - 3) = 30[/tex]

Step-by-step explanation:

Now we have to,

→ Find the value of 6(x - 3).

Given information,

→ x = 8

Let's solve the problem,

→ 6(x - 3)

→ 6(8 - 3)

→ 6(5)

→ 6 × 5

→ 30 => [solution]

Hence, the answer is 30.

Answer:

4.15 or

Step-by-step explanation:

100/20=5 times 3 is 15

so its 4.15 which equals 4 3/20

Answer:

- A state fair uses 32 pallets of lemons for lemonade

Step-by-step explanation:

The service's expected profit is $6,800.

What is the basic arithmetic operations?

The four basic mathematical operations are Addition, subtraction, multiplication, and division.

To find the service's expected profit, we need to calculate the total revenue and the total cost, and then subtract the cost from the revenue.

First, let's calculate the total revenue. The service sells maintenance agreements for $75 a year, so for every 100 customers, the revenue will be:

100 customers x $75/customer = $7,500

Now, let's calculate the total cost. We know that 2 in every 100 people who purchase maintenance agreements have air conditioners that need repair, and the average cost of repairing an air conditioner is $350. So for every 100 customers, the cost of repairs will be:

2 customers x $350/customer = $700

Finally, let's calculate the expected profit:

Expected profit = Total revenue - Total cost

Expected profit = $7,500 - $700

Expected profit = $6,800

Hence, the service's expected profit is $6,800.

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Answer:

The answer you're looking for is 7000ml

Step-by-step explanation:

Since there are 1000 millimeters inside a liter we can use the equation
x = 7×1000.
We need to first simplify all terms giving us this equation
x = 7000
With that, we are finished and that's how you do this question.

I hope this was helpful!

In linear equation, $28.75   is the unit price .

What in mathematics is a 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.

                     Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Equations with variables of power 1 are referred to as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.

The cost of 3 scarves is $86.25

   then,

     the unit price is  =    $86.25/3   = $28.75

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Answer:

Step-by-step explanation:

Kelly bought a total of 1500 pencil boxes.

If a car travels at an average speed of 68 miles per hour, it takes it 5 hours 15 minutes to travel 357 miles.

The average speed is the unit rate.

The average speed is computed as the quotient of the total distance and the total time.

Conversely, the time is a function of the division of the total distance by the average speed.

The total distance traveled by the car = 357 miles

The average speed = 68 miles per hour (mph)

The time = Distance/Average speed = 357/68 = 5.25 hours

= 5 hours 15 minutes.

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Answer:

1/15

Step-by-step explanation:

Based on the given conditions, formulate: 2/3 divided by 10

Divide a fraction by multiplying its reciprocal: 2/3 x 1/10

Cross out the common factor: 1/3 x 1/5

Write as a single fraction: 1/3x5

Calculate the product or quotient:1/15

get the result:1/15

Answer:

1/15

1/15

Step-by-step explanation:

Based on the given conditions, formulate: 2/3 divided by 10

Divide a fraction by multiplying its reciprocal: 2/3 x 1/10

Cross out the common factor: 1/3 x 1/5

Write as a single fraction: 1/3x5

Calculate the product or quotient:1/15

get the result:1/15

Answer:

1/15

The value of the functions are,

⇒ f (- 10) = 20201

⇒ f (2) = 17

⇒ f (3) = 143

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

The value of function is,

⇒ f (x) = 2x⁴ + x² - 10x + 1

Now, We can find all the values as;

At x = - 10;

⇒ f (x) = 2x⁴ + x² - 10x + 1

⇒ f (- 10) = 2 (- 10)⁴ + (- 10)² - 10 (- 10) + 1

⇒ f (- 10) = 20000 + 100 + 100 + 1

⇒ f (- 10) = 20201

At x = 2;

⇒ f (x) = 2x⁴ + x² - 10x + 1

⇒ f (2) = 2 (2)⁴ + (2)² - 10 (2) + 1

⇒ f (2) = 32 + 4 - 20 + 1

⇒ f (2) = 17

At x = 3;

⇒ f (x) = 2x⁴ + x² - 10x + 1

⇒ f (3) = 2 (3)⁴ + (3)² - 10 (3) + 1

⇒ f (3) = 162 + 9 - 30 + 1

⇒ f (3) = 143

Thus, The value of the functions are,

⇒ f (- 10) = 20201

⇒ f (2) = 17

⇒ f (3) = 143

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The number of workers required = 15

Observe the given problem and find out the relation between the number of workers and the number of days.

In given two one quantity decreased and the other quantity increased then both quantities are said to be in inverse proportions.    

Here the product of two quantities will equal a constant.

Here we have

10 workers can complete a piece of work in 18 days

Let 'x' be the number of workers required to complete work in 12 days

Here when the number of days increases the number of workers will be decreased which shows the number of work is inversely proportional to the number of days

The relation can be represented as  

=> 10 worker × 18 days  = 12 days × x workers

=> 10 × 18 = 12x

=> x = 180/12

=> x = 15

Therefore,

The number of workers required = 15

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The actual amount the salesman pays for an article with a marked price of N950.00 is N2,312.50.

Amount is a word used to refer to a quantity or amount of something. It can also be used to refer to the total sum of money, goods, or services due for payment or exchange. It can also refer to the balance of money or goods due for payment or exchange. Amount is also used to refer to the size, extent, or magnitude of something.

To calculate this amount, we first need to calculate the amount of discount the salesman is offering. This is calculated by taking the marked price and multiplying it by the discount percentage: N950.00 x 125% = N1,187.50. Then, we subtract this discount amount from the marked price: N950.00 - N1,187.50 = N2,312.50. This is the actual amount the salesman pays for the article.

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It is true that the graph contains the point (0, 0).

The following three assertions regarding the function and its graph are true:

The function's graph resembles a parabola.

The graph begins at the bottom.

The point is shown in the graph (0,0).

Explanation:

A second-degree polynomial function, the quadratic function f(x) = x2 - 5x + 12 has a parabola as its graph.

The parabola widens downward because the coefficient of x2 is positive (1 in this instance).

When we replace x with -10 in the given function, we obtain the value of f(-10) as (-10)2 - 5(-10) + 12 = 82. Hence, "f(-10) = 82" is true.

We substitute x = 20 in the given function, resulting in f(20) = 202 - 5(20) + 12 = 212, to see if the point (20, -8) is on the function's graph. The claim "The graph contains the point (20, -8)" is untrue since the point's y-coordinate is -8, which is not equivalent to f(20).

We substitute x = 0 in the given function to get f(0) = 02 - 5(0) + 12 = 12 to determine if the point (0, 0) is on the function's graph. The assertion "The graph contains the point (0, 0)" is true because the y-coordinate of the point (0, 0) is 0, which is equivalent to f(0).

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Answer:

The expected value of each warranty sold is $23.8.

Answer:

Step-by-step explanation:

Let's call the number of large bags of popcorn sold "L" and the number of small bags of popcorn sold "S".

We can set up two equations based on the information given:

L + S = 290 (the total number of bags of popcorn sold)

4L + S = 566 (the total revenue from popcorn sales)

We can use substitution or elimination to solve for L and S.

Substitution:

From the first equation, we know that S = 290 - L. We can substitute this into the second equation:

4L + (290 - L) = 566

Simplifying, we get:

3L + 290 = 566

3L = 276

L = 92

Then we can use the first equation to find S:

L + S = 290

92 + S = 290

S = 198

So the movie theater sold 92 large bags of popcorn and 198 small bags of popcorn.

Elimination:

We can eliminate one variable by multiplying one of the equations by a constant to make the coefficients of one of the variables equal but with opposite signs.

In this case, we can multiply the first equation by 4 to make the coefficients of S equal but with opposite signs:

4L + 4S = 1160

4L + S = 566

Subtracting the second equation from the first, we eliminate L:

3S = 594

S = 198

Then we can use either of the original equations to find L:

L + S = 290

L + 198 = 290

L = 92

So the movie theater sold 92 large bags of popcorn and 198 small bags of popcorn.

Answer:

30 men

Step-by-step explanation:

7 men x 300 days = 2100 man-days  to build 1 house)

(2100 man-days/house) x (1 house/70 days) = 30 men