The diagram shows a circular pond, of radius r metres, surrounded by a circular path.The circular path has a constant width of 1.5 metres.The area of the path is the area of the pond.(a) Show that 2r2 − 60r − 45 = 0

The answers to all the equations are:

So, f(x):

(A) f(x) = x + 3 when f(4)

(B) f(x) = 2x - 9 when f(5)

(C) f(x) = -6x + 2 when f(-3)

Therefore, the answers to all the equations are:

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the correct inequality that shows Annika's spending in terms of h is 35h + 180 ≤ 400.To express Annika's spending in terms of h, the number of hours the DJ can be at the party, we can set up an inequality by considering the total cost.

Let's represent Annika's spending on the DJ as 35h, where h is the number of hours. Additionally, we know Annika plans to spend $180 on decorations. Therefore, the total cost should be no more than $400.

The inequality can be written as:

35h + 180 ≤ 400

This inequality states that the cost of hiring the DJ (35h) plus the cost of decorations ($180) should be less than or equal to $400.

Therefore, the correct inequality that shows Annika's spending in terms of h is 35h + 180 ≤ 400.

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CosA is negative for the largest angle in an obtuse triangle. Using the law of cosines, a²>b²+c², a>b, and a>c are derived.

Step 1: As the obtuse triangle has the largest angle A (more than 90 degrees), the cosine function's value is negative.

Step 2: By applying the Law of Cosines in the triangle, a²>b²+c², which is derived from a²=b²+c²-2bccosA, and hence a>b and a>c can be derived.

Step 3: From the previously derived inequality a²>b²+c², we can conclude that a>b and a>c as a²-b²>c². The value of a² is greater than both b² and c² when a>b and a>c.

Therefore, the largest angle of an obtuse triangle is opposite the longest side.

Step 4: In triangle ABC, A=103°, a=25, and c=30.

a² = b² + c² - 2bccos(A),

a² = b² + 900 - 900 cos(103),

a² = b² + 900 + 900 cos(77),

a² > b² + 900, so a > b.

Similarly, a² > c² + 900, so a > c.

Therefore, triangle ABC satisfies a>b and a>c.

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Answer: true

Step-by-step explanation:

Answer:

The expression cannot be factored

Step-by-step explanation:

got it correct

Hey there! The answer to your problem is:

6 square units: rectangle PQRS, triangle TUV

8 square units: rectangle ABCD, triangle EFG

Answer:

what he said it right

Step-by-step explanation:

Answer:

x = 8

Step-by-step explanation:

Vertically opposite angles are congruent.

          5x + 9 = 57 - x

 Add x to both sides,

      5x +x + 9 = 57

           6x + 9 = 57

Subtract 9 from both sides,

                  6x = 57 - 9

                  6x = 48

Divide both sides by 6,

                 x = 48 ÷ 6

                x = 8

Answer:

4/3

Step-by-step explanation:

To find the slope from two points, we need to label these coordinates.

(1, 3) will be coordinates 1, and (4, 7) will be coordinates 2.

(Basically 1 = x1, 3 = y1, 4 = x2, 7 = y2)

To find slope, we need to solve this equation:

\(\frac{y_2-y_1}{x_2-x_1}\)

Plug the numbers into the equation.

\(\frac{7-3}{4-1}\)

Solve. 4/3

Slope = 4/3

Answer:

1.59

Step-by-step explanation:

Divide 2,787 by 1,750

Answer:

x=1

Step-by-step explanation:

It will be x=1 because once it is at x=1, the parobola is split into 2 EQUAL parts. For example, if you graph this on paper and try to guess the middle and place a line where you want to split it, the line will go at x=1

Thank you :)

The value of k could be 48, 49, 50, 51, or 52, as these all result in the fractions being in lowest terms.

To further explain, let's look at each of the possible values of k and see how they result in the fractions being in lowest terms:

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A parabola is a U-shaped curve that is symmetrical about a specific axis. It is a conic section defined by a quadratic equation and has applications in various fields, including mathematics, physics, and engineering.

To find the coefficient b, we need to use the given points to form a system of equations. Substituting (0,3), (1,4), and (2,3) into the equation y=ax²+bx+c, we get:

3=c
4=a+b+c
3=4a+2b+c

Substituting c=3 into the second equation, we get:

4=a+b+3

Substituting c=3 into the third equation, we get:

3=4a+2b+3

Simplifying the third equation, we get:

1=2a+b

Now we have two equations:

4=a+b+3
1=2a+b

Solving for b, we get:

b=1-2a

Substituting b=1-2a into the first equation, we get:

4=a+(1-2a)+3

Solving for a, we get:

a=0

Substituting a=0 into b=1-2a, we get:

b=1

Therefore, the coefficient b is 1.

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Answer:

5.28

Step-by-step explanation:

we use the formula

H²=B²+P²

and we will get the answer

branliest if it is helpful

Answer:

Angle BXY

using pythogoras theory which is

hyp*2= opp*2 +adj*2

hypothenus being the longest part of the angle BX=?

Step-by-step explanation:

hyp= 4.2*2+ 3.2*2

hyp*2 =17.64 + 10.24

hyp*2 = 27.88

hyp =√27.88

hyp=5.28...Ans

note *2...square

Answer:

64 servings

Step-by-step explanation:

The computation is shown below:

As dog eats 8 ounces of dog food each day

And, he purchased 32 pound bag of dog food

We know that

1 pound = 16 ounces

So for 32 pounds, the ounces would be

= 16 ×32

= 512 ounces

So, the number of 8 ounces servings would be

= 512 ÷ 8

= 64 servings

Answer:

Answer:

64 servings

Step-by-step explanation:

The computation is shown below:

As a dog eats 8 ounces of dog food each day

And, he purchased a 32-pound bag of dog food

We know that

1 pound = 16 ounces

So for 32 pounds, the ounces would be

= 16 ×32

= 512 ounces

So, the number of 8 ounces servings would be

= 512 ÷ 8

= 64 servings

Answer:

gsyshehejejeijsjejekwkwkwkwkwkwk

Answer:

this dude is a loser

Step-by-step explanation:

this person is a fat loser

answered

There are 50 deer in a particular forest. The population is increasing at a rate of 15% per year. Which exponential growth function represents

the number of deer y in that forest after x months? Round to the nearest thousandth.

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Answer:

The expression that represents the number of deer in the forest is

y(x) = 50*(1.013)^x

Step-by-step explanation:

Assuming that the number of deer is "y" and the number of months is "x", then after the first month the number of deer is:

y(1) = 50*(1+ 0.15/12) = 50*(1.0125) = 50.625

y(2) = y(1)*(1.0125) = y(0)*(1.0125)² =51.258

y(3) = y(2)*(1.0125) = y(0)*(1.0125)³ = 51.898

This keeps going as the time goes on, so we can model this growth with the equation:

y(x) = 50*(1 - 0.15/12)^(x)

y(x) = 50*(1.013)^x

The exponential growth function that represents the number y of deer in that forest after x months is 50 × \((1.013)^{x}\).

An exponential function is a nonlinear function that has the form of

y=\(ab^{x}\),wherea≠0,b>0. An exponential function with a > 0 and b > 1, like the one above, represents an exponential growth and the graph of an exponential growth function rises from left to right.

There are 50 deer in a particular forest.

The population is  increasing at a rate of 15% per year.

Assuming that the number of deer is 'y' and the number of month is 'x' then after the first month the number of deer is

y(x) = 50 × \(1+(\frac{0.15}{12} )\)

= 50 × 1.0125

= 50.625

y(2) = y(1) × (1.0125)

= y(0) × \((1.0125)^{2}\)

= 51.258

y(3) = y(2) × (1.0125)

= y(0) × \((1.0125)^{2}\)

= 51.898

y(x) = 50 × \((1-\frac{0.15}{12} )^{x}\)

= 50 × \((1.013)^{x}\)

Hence, the exponential growth function that represents the number y of deer in that forest after x months is 50 × \((1.013)^{x}\).

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Answer:

\(m = \frac{2.90 - 2.50}{20 - 0} = \frac{.40}{20} = .02\)

\(f(x) = .02x + 2.50\)

\(f(30) = .02(30) + 2.50 \)

\(f(30) = 3.10\)

In 2030, the price of oil would be $3.10.

The volume of the solid generated by revolving the region bounded by the given curve and lines about the x-axis is V = 8π/3

The volume of a solid, given by the function f(x), over an interval between a and b, is given by:

\(V = \pi \int\limits^a_b {f(x)^2} \, dx\)

To find the area, integrate around that area. We're revolving around the x-axis so the area will be a circle;

V = ∫A(x)dx =  ∫(πr²)dr

Then we subtract them from each others.

∫(πr₂² - πr₁²)dr

Now substitute the value and integrate;

∫(π(2)² - π(2x)²)dr

∫(4π - 4πx²)dr

4π∫(1 - x²)dr

Now integrate from 0 to 1 since that's where our boundary is.

V = 4π∫(1 - x²)dr = 8π/3

Therefore, The volume of the solid generated by revolving the region bounded by the given curve and lines about the x-axis is V = 8π/3

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The name of the relationship is b. Alternate interior angles.

Alternate interior angles are two angles that are located on opposite sides of a transversal line, but within the same two lines. When two lines are cut by a transversal line, the alternate interior angles are always congruent, meaning that they have the same measure.

In this case, angles ∠1 and ∠4 are alternate interior angles. Alternate interior angles are formed when two parallel lines are cut by a transversal line. When this happens, corresponding angles are formed on the same side of the transversal.

The alternate interior angles are the two angles that are on opposite sides of the transversal. These angles are also congruent, meaning that they have the same measure.

To summarize, alternate interior angles are two angles that are located on opposite sides of a transversal line and within the same two lines. In this case, angles ∠1 and ∠4 are alternate interior angles, meaning that they have the same measure.

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If the length of the model airplane is 12 inches, then the length of the actual airplane is 18 feet.

Rob collects model planes. One of his planes uses a scale in which 1 inch represents 1. 5 feet.

We will use unitary method to find the length of airplane in inches.

This means according to the model,

1 inch in the model = 1.5 feet of the actual

Therefore, if the length of the model airplane is 12 feet

12 inches of the model airplane = 1.5 × 12

                                                     = 18 feet

so, the actual length of airplane is 18 feet.

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Inverse distance weighting is a useful tool for estimating values at unsampled locations in geostatistics. Another advantage of inverse distance weighting is that it allows for the incorporation of multiple variables into the estimation process.

Inverse distance weighting is a method used in geostatistics to estimate values at unsampled locations based on values at surrounding sample locations. It works by assigning weights to the sample points based on their proximity to the unsampled point. The closer a sample point is to the unsampled point, the higher its weight. The weights are then used to calculate a weighted average of the sample values, which is used as the estimate for the unsampled location.
The benefit of inverse distance weighting over a simple average is that it takes into account the spatial variability of the data. A simple average treats all sample points equally, regardless of their distance from the unsampled point. This can lead to inaccurate estimates if there is a high degree of spatial variability in the data. In contrast, inverse distance weighting gives more weight to sample points that are closer to the unsampled point, which is likely to provide a more accurate estimate.
Another advantage of inverse distance weighting is that it allows for the incorporation of multiple variables into the estimation process. For example, if there are two variables of interest (e.g., temperature and precipitation), inverse distance weighting can be used to estimate values for both variables simultaneously. This is not possible with a simple average.
Overall, inverse distance weighting is a useful tool for estimating values at unsampled locations in geostatistics. Its ability to account for spatial variability and incorporate multiple variables makes it a powerful technique for analyzing spatial data.

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The expression for Total discount for 20 group tickets is 5 m, Amount of discount per ticket is 0.25 m, Number of tickets is 20 and Cost of buying 20 single ticket is 20 m.

We have:

a discount of 25% per ticket if a group buys 20 or more tickets.

The expression 20 m - 20 (0.25 m) describes the total cost of buying 20 tickets for a group.

Total discount for 20 group tickets will be:

Total discount = 20 × 0.25 m = 5 m

Amount of discount per ticket = 5 m / 20 = 0.25 m

Number of tickets = 20

Cost of buying 20 single ticket = 20 m

where m = cost of buying 1 ticket.

Therefore, the expression for Total discount for 20 group tickets is 5 m, Amount of discount per ticket is 0.25 m, Number of tickets is 20 and Cost of buying 20 single ticket is 20 m.

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a + b = 7

Finding the area between two curves is an essential application of integration. By using integration, we have learned to find the area under the curve, similarly, we can also find the area between two intersecting curves using integration. It is the portion of the space that falls between two linear or non-linear curves within the given limits.

\(g(x) = y = -\frac{1}{2} (x+2)^{2}+2 \\\textup{Now area of region R =} \int_{-4}^{0} [-\frac{1}{2} (x+2)^{2}+2] dx\)

\(\textup{ the x-axis are rectangles with height 1/4}\\\therefore volume=\frac{1}{4} \int_{-4}^{0} [-\frac{1}{2} (x+2)^{2}+2] dx ( \because volume = area*height)\\\)

\(volume=\frac{1}{4} \int_{-4}^{0} [2-\frac{1}{2} (x^2+4x+4] dx\\\\volume=\frac{1}{4} \int_{-4}^{0} [2-\frac{1}{2} x^2-2x-2] dx\\\\volume=-\frac{1}{4} \int_{-4}^{0} [\frac{1}{2} x^2+2x] dx\\\\volume=-\frac{1}{4} [\frac{x^3}{6} +x^2 ]^0_-7\\\\volume=-\frac{1}{4} (0-(-\frac{64}{6}+16 ))\\\\volume=\frac{4}{3} =\frac{a}{b} \\\\\therefore a=4 ,b=3\\\\Hence, a+b=7\)

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Answer: 340

Step-by-step explanation:

100 - 74 = 26%

26% = .26

x * .26 = 88.4

  /.26    /.26

x = 340

check

340 * .74 = 251.6

340 - 251.6 = 88.4

Answer:

A ÷ (WH)

Step-by-step explanation:

The given expressions are equivalent.

What is equivalent expression?

Expressions that function identically despite having different appearances are called equivalent expressions. If two algebraic expressions are equivalent, then when we enter the same value(s) for the variable, the two expressions have the same value (s).

Consider the given expressions,

-(-3m + 6 - 12 + 15m) and 2(1 - 2m)

First simplify the expression -(-3m + 6 - 12 + 15m)

= 3m - 6 + 12 - 15m

= -12m + 6

Divide the expression by 3,

= -4m + 2

= 2 + 4m            ..(1)

Now, consider the expression,  2(1 - 2m)

Simplifying this,

2(1 - 2m) = 2 - 4m         ..(2)

From (1) and (2) we can see that the expressions are equivalent.

Hence, the given expressions are equivalent.

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Answer:

Its C, the answer with the link is a virus so don't click that !

Step-by-step explanation:

Answer: Calculating a bowling score involves adding up the total number of pins knocked down over a series of frames. The basic scoring system in bowling is as follows:

- Each game is made up of 10 frames.

- In each frame, the bowler gets two chances to knock down all 10 pins.

- If the bowler knocks down all 10 pins on the first roll (called a strike), the frame is over, and the bowler is awarded 10 points plus the total number of pins knocked down on the next two rolls.

- If the bowler knocks down all 10 pins on the second roll (called a spare), the frame is over, and the bowler is awarded 10 points plus the total number of pins knocked down on the next roll.

- If the bowler does not knock down all 10 pins in a frame, the score for that frame is simply the total number of pins knocked down.

- To calculate the score for each frame, you add up the total number of pins knocked down in the two rolls. If the bowler gets a strike or a spare, you need to take into account the bonus points for the next rolls as described above.

To calculate the total score for the game, you add up the scores for all 10 frames, including any bonus points earned from strikes or spares.

For example, if a bowler knocked down 7 pins on the first roll, and 3 pins on the second roll (a spare) in the first frame, they would receive 10 points for that frame, plus the number of pins knocked down on the next roll (let's say 6). So the score for the first frame would be 10 + 6 = 16.

If in the second frame, the bowler gets a strike, then the score for that frame would be 10 plus the total number of pins knocked down on the next two rolls. Let's say they knock down 8 and 1 on the next two rolls. Then, the score for the second frame would be 10 + 8 + 1 = 19.

This process continues for all 10 frames, with bonus points being added for strikes and spares, until a total score for the game is obtained.

Step-by-step explanation: