How many unique triangles can be drawn side lengths of 5 inches and 6 inches, with an angle of 45 degrees bewteen the given sides?

The calculated value of x at g(x) = 2 is x = 2.5

from the question, we have the following parameters that can be used in our computation:

f(x) = 3x - 1

Also, we have

g(x) = 2x - 3

When g(x) - 2, we have

2x - 3 = 2

So, we have

2x = 5

Divide by 2

x = 2.5

Hence, the value of x at g(x) = 2 is x = 2.5

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Answer:

105:175

Step-by-step explanation:

3+5 = 8

3/8 of 280 is 105.

5/8 of 280 is 175.

the ratio is 105:175

next we have to simplify it:

divide both sides by 5:

21:35 divide both sides by 7=

3:5

The value 280 in the ratio 3:5 will be 105 and 175.

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. The numerical relationship between two values demonstrates how frequently one value contains or is contained within another.

Given that the number 280 is divided in the ratio of 3:5. The number will be calculated as below,

3x + 5x = 280

8x = 280

x = 280 / 8

x = 35

The number will be distributed as,

3x = 3 x 35 = 105

5x = 5 x 35 = 175

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Answer:

(0, 7), (1, 11), (2, 15)

Step-by-step explanation:

to find the y values, plug in the given x values into the equation y= 4x+7

when x = 0

y = 4(0) + 7

y = 0 + 7

y = 7

so the y value that corresponds to the x value 0 is 7 which is also written as (0,7)

when x = 1

y = 4(1) + 7

y = 4 + 7

y = 11

so the y value that corresponds to the x value 1 is 11; also written as (1, 11)

when x = 2

y = 4(2) + 7

y = 8 + 7

y = 15

so the x value 2 corresponds to the y value 15; also written as (2 , 15)

hope this helps

Answer:(0, 7), (1, 11), (2, 15)

Step-by-step explanation:

Answer:

x = -3

Step-by-step explanation:

0.2x + 2 = 0.2(4 - x)

0.2x + 2 = 0.8 - 0.2x

0.4x = -1.2

x = -1.2/0.4

x = -3

The experimental probability that the card selected was a K or 6 is 17/100 or 0.17.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates that an event is impossible and 1 indicates that it is certain. The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. In other words, it is the ratio of the number of desired outcomes to the total number of outcomes.

The frequency of card 6 is 7 and the frequency of card K is 12. However, the card K is also counted in the total count for JQK, so we need to subtract 2 from the frequency of K to get the actual count of K.

Actual count of K = 12 - 2 = 10

Total count of 6 and K = 7 + 10 = 17

The experimental probability of drawing a K or 6 is the frequency of drawing K or 6 divided by the total number of draws:

Experimental probability = (frequency of K or 6) / (total number of draws)

Experimental probability = 17 / 100

Therefore, the experimental probability that the card selected was a K or 6 is 17/100 or 0.17.

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Answer:

439.32 (so 440)

Step-by-step explanation:

52% of people, and there are 846 people. what is 52% of 846? 439.32 and you round up.

Answer:

i think its

x^2 + (y + 2)^2 = 21.

Step-by-step explanation:

Answer:

x = 16

Step-by-step explanation:

Subtract x from both sides of the equation

\(\sqrt{x} = 20 - x\)

To remove the radical on the left side of the equation, square both sides of the equation.

\(\sqrt{x}^{2} = (20 - x)^{2}\)

Simplify each side of the equation.

\(x = (20 - x)^{2}\)

Solve for x.

\(x = 25, 16\)

Exclude the solutions that do not make \(x + \sqrt{x} = 20\) true.

x = 16

One would pay $5,232.96 in interest over the 5-year loan term.

To get interest paid on the loan, we will the formula for compound interest \(Interest = Principal * (1 + Annual Interest Rate)^{Number of Years} - Principal\)

The principal is the loan amount which is $9,000.

The annual interest rate is 9.6%

The number of years is 5.

Interest = $9,000 * (1 + 0.096)^(5) - $9,000

Interest = $9,000 * 1.58144018701 - $9,000

Interest = $5,232.96168

Interest = $5,232.96.

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Answer:

\(25\)

Step-by-step explanation:

\(2x-1=x+4\\2x=x+5\\x=5\\\text{Check:}\\2(5)-1=5+4\\10-1=9\\9=9\\9\cdot 2 +7=18+7=25\)

Answer:25 ft

Step-by-step explanation:

This triangle is an isosceles triangle (2 sides are congruent), we see this because is two angles of a triangle is congruent, then the two opposite sides are congruent.

From this information, we can say that 2x-1 = x+4

Add 1 on both sides to get 2x=x+5

Then minus x on both sides to get x=5

Next, plus x into the two equations separately.

1) 2 times 5-1

2 times 5 is 10

10-1=9

2) 5+4=9

Finally, add the sides together to get the answer.

9+9+7=25ft

Hope this helped!

1.57 meters of barbed wire are needed to fence the circular piece of land with a radius of 25 cm.

We have,

To calculate the amount of barbed wire needed to fence the circular piece of land, we need to find the circumference of the circle.

Given:

Radius (r) = 25 cm

The formula for the circumference (C) of a circle is:

C = 2πr

Substituting the given radius into the formula, we have:

C = 2π x 25 cm

Now, we can calculate the circumference in centimeters.

C = 2 x 3.14 x 25 cm

C ≈ 157 cm

Now,

To convert centimeters to meters, we divide the circumference by 100.

C (in meters) = 157 cm / 100

C (in meters) ≈ 1.57 meters

Therefore,

Approximately 1.57 meters of barbed wire are needed to fence the circular piece of land with a radius of 25 cm.

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The complete question.

A circular piece of land with a radius of 25 cm is going to be fenced. How many meters of barbed wire are needed?

As the margin of error decreases, the width of the confidence interval decreases.

So option B is correct option.

A confidence interval is a method used to estimate the population parameter of interest based on a random sample from the population. It is a range of values that contains the true population parameter with a certain degree of confidence.

To determine the accuracy of the estimate, the confidence interval is calculated as a range of values within which we are reasonably certain the true population parameter lies. The confidence interval is calculated based on the sample statistics (e.g. sample mean) and the sample size.

The margin of error (also known as the confidence interval half-width) determines the width of the confidence interval. It is the amount of uncertainty associated with the estimate. It is calculated as the product of the critical value (z*) and the standard error of the statistic.

The width of the confidence interval is inversely related to the margin of error. When the margin of error decreases, the width of the confidence interval decreases, and when the margin of error increases, the width of the confidence interval increases.

Therefore, the correct answer is b. Decreases.

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Answer:

Step-by-step explanation:

Putting value of x = 1/2 in the equation

8x - 3/x

8(1/2) - 3(1/2)

= 4 - 3/2

= 2.5 or 5/2

Answer: 803.84cm3

Step-by-step explanation:
The formula for finding the volume of a cylinder is πr2h.
In other words, the area of the top face's circle times the height.

To find the circle's area, we first find the radius of the circle. Since the diameter is 8cm, we divide by 2 to get the radius, which is 4cm.

4cm squared is 4cm x 4cm, which is 16cm. 16cm times 3.14 is 50.24cm squared.

Now, we have the area of the circle. 50.24cm squared!

The height is 16cm, so to find the cylinder, we times the area of the circle by the height of the cylinder! So,

16cm x 50.24cm squared = 803.84cm cubed.

The volume of the can of soup is 803.84cm cubed.

Answer:

108 inches²

Step-by-step explanation:

Rectangular prism = cuboid

To find how much paper is required to cover the box, we need to find the TSA of the cuboid.

TSA of cuboid = 2 [LB + LH + HB] = 2 [ (3×4) + (3×6) + (4×6) ] = 2 [ 12+18+24 ] = 2 × 54 = 108 inches²

Answer:

y=-2

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

7x - 2y = -52

7(-8) - 2y = -52

-56 - 2y = -52

-2y = 4

y = -2

Best of Luck!

Starting with the given equation: 2 sin x cos x = cos x

By dividing both sides by cos x, we may simplify: 2 sin x = 1

Dividing both sides by 2:

sin x = 1/2

The values of x that fulfil sin x = 1/2 must now be found, and they are:

x = π/6 + 2πn or x = 5π/6 + 2πn, where n is any integer.

Therefore, the general solution is:

x = π/6 + 2πn or

x = 5π/6 + 2πn, where n is any integer.

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The area of the square with a side length of 3.1 meters is 9.61 square meters.

To find the area of a square, we need to multiply the length of one side by itself. In this case, the square has a side length of 3.1 m.

Area of a square = side length × side length

Substituting the given side length into the formula:

Area = 3.1 m × 3.1 m

To perform the calculation:

Area = 9.61 m²

It's worth noting that when calculating the area, we are working with squared units. In this case, the side length is in meters, so the area is expressed in square meters (m²). The area represents the amount of space enclosed within the square.

Remember, to find the area of any square, you simply need to multiply the length of one side by itself.

The area of the square with a side length of 3.1 meters is 9.61 square meters.

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You have the following function:

y = (x + 4)²

consider that the associated pattern function is:

y = x²

you can notice that the given function is a translation of the patter function:

y(x) = x²

y(x + a) = (x + a)²

where a is any constant, in this case a = 4.

This kind of translation consist in a desplacement of the function to the left a units. In this case, you have a rigid translation to the left 4 units.

Hence, the graph is:

Blue curve is the pattern function and purple line is the translated function.

Answer:

It is balance she need to use. Answer is B.

Using the integers −9 to 9 at most one time each, place a digit in each box (1, 3) and (9, 3) or (-9, 3) to create endpoints for the longest possible line segment both numerically and graphically whose midpoint is (1, 3).

To find the endpoints of the longest possible line segment with midpoint (1, 3), we can use the midpoint formula, which states that the midpoint of a line segment with endpoints (x₁, y₁) and (x₂, y₂) is ((x₁+x₂)/2, (y₁+y₂)/2).

In this case, we know the midpoint is (1, 3), so we can set up two equations using the variables for the endpoints (x and y) and solve for them:

(x₁ + x₂)/2 = 1

(y₁ + y₂)/2 = 3

We also know that the line segment must be as long as possible, so the endpoints should be as far away from each other as possible. To maximize the distance between the endpoints, we can choose one endpoint to be -9 and the other endpoint to be 9. This gives us:

(x₁ + x₂)/2 = 1 => x₁ + x₂ = 2

(y₁ + y₂)/2 = 3 => y₁ + y₂ = 6

Now we can solve for x₁ and y₁, since x₂ and y₂ will be 2-x₁ and 6-y₁ respectively:

x₁ + (2-x₁) = 2 => x₁ = 1

y₁ + (6-y₁) = 6 => y₁ = 3

So the endpoints of the longest possible line segment with midpoint (1, 3) are (1, 3) and (9, 3) or (-9, 3), and its length is 8 units.

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The mass of the pipe is 254 grams.

First, The volume of the outer cylinder (V1) can be calculated using the formula for the volume of a cylinder:

V1 = π (radius_outer)² x  height

V1 = 3.14 (6)² (8)

and, the volume of inner cylinder

V2 = π(inner radius)² height

V2= 3.14 (5)² (8)

Now, let's calculate the volume of the plastic pipe:

Volume = V1 - V2

= 3.14 (6)² (8) - 3.14 (5)² (8)

= 3.14 x 8 (36- 25)

= 276.32 cm³

Now, Mass = Volume x density

Mass = 276.32 x 0.92

Mass = 254.19 grams

Thus, the mass of the pipe is 254 grams.

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The answer to the question is 4.5

Answer:

sin2x = √3/2.

Step-by-step explanation:

sin2x = 2 sinx cosx

So sinx cosx = 1/2 sin2x

So  1/2 sin2x = √3/4

sin2x = √3/4  * 2

sin2x = √3/2.