What’s the approximate length of an arc with radius 3 miles and central angle of 45°?

Answer Options:
3.2 miles
2.4 miles
1.4 miles
1.2 miles

Answer:

x = - 9

Step-by-step explanation:

2x + 7 = - 11 ( subtract 7 from both sides )

2x = - 18 ( divide both sides by 2 )

x = - 9

The answer is:

x = -9

Work/explanation:

The point of equations is to find the variable's value by isolating it step-by-step.

For this equation, the variable is x.

To isolate it, I will perform a few operations.

First, I will subtract 7 from each side:

\(\sf{2x+7=-11}\)

\(\sf{2x=-11-7}\)

\(\sf{2x=-18}\)

Divide each side by 2

\(\sf{x=-9}\)

Hence, x = -9.

\(\rule{350}{4}\)

Answer:

ASA

Step-by-step explanation:

they share the side in the middle (reflexive property) and have two congruent angles

Answer:

x = -7

x = 5

Step-by-step explanation:

The standard form of quadratic equations is

Ax^2 + Bx + C = 0

The factors need to multiply together to be C and add together to be B.

The two numbers that will multiply together to be -35 and add together to be 2 are -5 & 7.

The factor pairs are (x+7)(x-5). Zero product property means we set each of those factor pairs = 0 and solve.

x + 7 = 0

-7 -7 Subtract 7 from each side to solve

x = -7

x - 5 = 0

+5 +5 Add 5 to each side to solve

x = 5

To solve the equation, factor x²+2x−35 use the formula x² +(a + b) x + ab = (x + a)(x + b). To find a and b, set up a system to be solved.

a + b = 2

ab = −35

Since ab is negative, a and b have opposite signs. Since a+b is positive, the positive number has a greater absolute value than the negative. Show all pairs of integers whose product is −35.

Calculate the sum of each pair.

The solution is the pair that gives sum 2.

Rewrite the factored expression (x + a)(x + b) with the values obtained.

To find solutions to equations, solve x−5=0 and x+7=0.

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Answer:

2.1087

Step-by-step explanation:

0.297

7.1 +

2.1087

Given the Complex Number:

You can identify that it is written in Rectangular Form:

By definition, the coordinates in Rectangular Form are:

And in Polar Form:

In this case, you can identify that:

In order to convert them to Polar Form, you need to use these formulas:

Use this formula to find "r":

Then, this is:

You need to find the angle. You can use this formula:

Therefore the angle is:

Then:

Hence, the answer is: Last option.

The distance to second base is approximately 127.28 feet. Round to the nearest hundredth

Since the angle is 45 degrees, the other side of the right triangle are equal, hence we have two sides of 90 ft to be used to find the hypotenuse

Using Pythagoras theorem given by the  the formula

hypotenuse² = opposite² + adjacent²

plugging the values as in the problem

let x be the required distance

x² = 90² + 90²

x² = 16200

x = √16200

x = 90√2

x = 127.28 ft (to the nearest hundredth)

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Answer:

the area is 50

Step-by-step explanation:

Answer:

its 0.09637 but round it by urself . please like my answer and brainliest me hshsshhs

Answer:

1 Is A

2 is B

3 is A

4a is D

4b is -53 but that's not an answer choice

4c is C

4d is D

Charles should hire 20 workers for each hour.

To determine the optimal number of workers to hire, Charles needs to compare the marginal cost and marginal benefit of each additional worker.

The marginal benefit of each worker is the additional number of drinks they can produce multiplied by the average selling price per drink. The marginal cost is the hourly wage of each worker multiplied by the number of hours they work.

Initially, the marginal benefit of the first worker is 20 drinks * $3/drink = $60.

The marginal cost is $15/worker * 8 hours = $120.

The second worker has a marginal benefit of 18 drinks * $3/drink = $54.

The marginal cost is still $120.

For each additional worker hired, the marginal benefit decreases by 2 drinks * $3/drink = $6, while the marginal cost remains constant at $120.

Charles should hire workers as long as the marginal benefit is greater than the marginal cost.

Once the marginal benefit is equal to or less than the marginal cost, it is no longer profitable to hire more workers.

Therefore, Charles should hire workers until the marginal benefit is equal to the marginal cost, which occurs when the marginal benefit is $120.

To find out how many workers will provide a marginal benefit of $120, we set the marginal benefit equal to $120 and solve for the number of workers:

$6 * n = $120

$n = 20

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Answer:B. Yes; the triangles are congruent by ASA.

Step-by-step explanation:

In triangle ACD and CAB, AB || CD and AC ≅ BD, B. Yes; the triangles are congruent by ASA.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know two similar planer figures are congruent when we have sides or angles or both that are the same as the corresponding sides or angles or both.

Given,

In triangle ACD and CAB, AB || CD and AC ≅ BD.

Therefore, The triangles ACD and CAB are congruent by ASA as ∠A is congruent to ∠C, Side AB is congruent to side CD and ∠B is congruent to ∠B.

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Answer:

Step-by-step explanation:

I think it 5

Answer:

Step-by-step explanation:

The number that goes under the radical sign in 17.

The answer is \(\sqrt{17}\)

use the distance formula to calculate the distance between to two points.

Distance (d) = √(3 - -1)² + (-1 - -2)²

= √(4)² + (1)²

= √17

Answer:

First answer: 7x+19x+18+9

Second answer: 26x+27

The child who is 4 feet tall can walk under the tent without bending over, as the height of the tent at that point is greater than 4 feet.

1. Given equation: y = -0.1\(8x^2\) + 1.6x, where y represents the height of the tent and x represents the distance from the center of the tent.

2. We want to find the maximum height of the tent to determine if a 4-foot tall child can walk under it without bending over.

3. To find the maximum height, we need to determine the vertex of the parabolic equation.

4. The vertex of a parabola in the form y = a\(x^2\) + bx + c is given by the formula x = -b / (2a).

5. In our equation, a = -0.18 and b = 1.6. Plugging these values into the formula, we get x = -1.6 / (2 * -0.18).

6. Simplifying the expression, we find x = 4.44.

7. Now, substitute this value back into the equation to find the maximum height: y = -0.18 * (4.4\(4)^2\) + 1.6 * 4.44.

8. Evaluating the expression, we find y ≈ 4.32.

9. The maximum height of the tent is approximately 4.32 feet.

10. Since the child's height is 4 feet, the child can comfortably walk under the tent without bending over, as the height is greater than 4 feet.

11. Therefore, the child who is 4 feet tall can walk under the tent without bending over.

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Answer: What is the commutative property of addition? To “commute” means to move around or travel. According to the commutative property of addition, changing the order of the numbers we are adding, does not change the sum. Here's an example of how the sum does NOT change, even if the order of the addends is changed and The commutative property of multiplication

states that when two numbers are being multiplied, their order can be changed without affecting the product.

Step-by-step explanation: Have a blessed day hopefully this helped!

Answer:

(-5, 2)

Step-by-step explanation:

We can see that the g(x) is a translated form of f(x) using the formula:

y = (x - h)³ + k,

where (h, k) is the origin of the graph's translation.

We can assign the following h and k values based on the given g(x):

g(x) = (x + 5)³ + 2

h = -5

k = 2

Finally, we can form an ordered pair (h, k):

(-5, 2)

Step-by-step explanation:

This is a geometric series where our common ratio is -1/2, and a is -4

Since r is less than -1, this series converges so

The sun is

\( \frac{ - 4}{1 + 0.5} \)

\( \frac{ - 4}{1.5} = - \frac{8}{3} \)

The sum is -8)3

Answer:

  6.515 < 6 11/20 < 6.56 < 53/8

Step-by-step explanation:

You want the sorted order of 6.56, 6.515, 6 11/20, 53/8.

The decimal value of the mixed number is ...

  6 11/20 = 6 (5·11)/(5·20) = 6 55/100 = 6.55

The decimal value of the improper fraction is ...

  53/8 = 6 +5/8 = 6.625

All of the numbers have 6 as their most-significant digit, so we need to compare 10th digits. The highest number has 6 as a 10th digit, so 6.625 will be last on the list

Comparing hundredths digits, we have 6, 1, and 5, so the first of these will be last among this group. The least-to-greatest order is ...

  6.515 < 6.55 < 6.56 < 6.625

Using the original numbers, this ordering is ...

  6.515 < 6 11/20 < 6.56 < 53/8

Answer:

y= -2x + 4

Step-by-step explanation:

Answer:

y = -2x + 4

Explanation:

Pick two points from the line: (1, 2), (0, 4)

Slope intercept form: y = mx + b

Find 'm': 2 - 4 = -2

Find 'b': 4

Insert numbers into equation: y = -2x + 4

Answer: I hope this helps!

Step-by-step explanation:

The volume of cone having diameter 18 units and height 8 units is 678.85 cubic units which is nearest to 648.17 cubic units which is option C.

Volume is basically amount of substance a container can hold in its capacity. Volume of cone is 1/3 *π\(R^{2}H\) in which R is the radius and H is height of cone.

We know that volume of cone is 1/3 *π*\(R^{2} H\)

We have to put the value of radius and height in the formula to get the value of volume of cone.

Radius=diameter/2

=18/2

=9 units.

Volume=1/3 * 3.14*9*9*8

=2034.72/3

=678.24 cubic units

Nearest option is 648.17 cubic units.

Hence the volume of the cone is 648.17 units.

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Answer:

Below

Step-by-step explanation:

Let T be triangle, C the circle and S the square.

● T + T + T = 30

● 3T = 30

Divide both sides by 3

● 3T/3 = 30/3

● T = 10

So the triangle has a value of 10.

●30 T + C + C = 20C + S + S = 13T +C ×S/2

Add like terms together

●30 T + 2C = 20C +2S= 13T + C×S/2

Replace T by its value (T=10)

● 300 + 2C = 20C + 2S = 130 + C×S/2

Take only this part 20C + 2S = 130 + C × S/2

● 20C + 2S = 130 + C×S/2 (1)

Take this part (300+2C = 20C+2S) and express S in function of C

● 20C + 2S = 300 + 2C

Divide everything by 2 to make easier

● 10 C + S = 150+ C

● S = 150+C-10C

● S = 150-9C

Replace S by (5-9C) in (1)

● 20C + 2S = 130 + C×S/2

● 20C + 2(150-9C) = 130 +C× (150-9C)/2

● 20C + 300-18C= 130 + C×(75-4.5C)

● 2C + 300 = 130 + 75 -4.5C^2

● 2C +300-130 = 75C - 4.5C^2

● 2C -75C + 170 = -4.5C^2

● -73C + 170 = -4.5C^2

Multiply all the expression by -1

● -4.5C^2 +73C+ 170= 0

This is a quadratic equation, so we will use the discriminant method.

Let Y be the discriminant

● Y = b^2-4ac

● b = 73

● a = -4.5

● c = 170

● Y = 73^2 - 4×(-4.5)×170= 8389

So the equation has two solutions:

● C = (-b +/- √Y) /2a

√Y is approximatively 92

● C = (-73 + / - 92 )/ -9

● C = 18.34 or C = -2.11

Approximatively

● C = 18 or C = -2

■■■■■■■■■■■■■■■■■■■■■■■■■

● if C = 18

30T + 2C = 300 + 36 = 336

● if C = -2

30T + 2C = 300-4 = 296

Answer:

$239.68

Step-by-step explanation:

Given

Solving

Answer: I believe the answer is C. All of the other options dont have anything to do with lee and her construction

Answer:

slope 3/4

y intercept -1

Step-by-step explanation:

y=mx+b

m=slope

b=y intercept

Answer:

Slope-3/4

Intercept-(0,-1)

Step-by-step explanation:

Answer:

Step-by-step explanation:

r:=interest rate =7%

p = unknown

Principle + interest = 4280

t = 1 year

Formula

Total = p*r*t + p

4280 = p*(1 + r*t)

4280 = p*(1 + 7/100 * 1)

4280 = p (1.07)

4280 / 1.07 = p

P = 4000

===================

What this means is that if you loan out 4000 dollars for a year at 7%, you will get 280 dollars in return (plus of course your 4000). However in this day and age, try getting 7%.

The 100 dollar problem is the same thing. This time you have P and you want the total.

Total = p(1 + r*t)

Total = 100 (1 + 7/100 * 1

Total = 100 ( 1 + 0.07)

Total = 107

So the principle is given and the value of the investment after 1 year is 107 dollars.

Parent function f(x) = 1/2ˣ will be translated Vertically compress by a factor of 1/3, which gives a function f(x) = 1/2ˣ - 1/3.

A translation is a geometric change in Euclidean geometry that involves moving each point in a figure, shape, or space by the same amount in one direction. A translation can also be thought of as moving the origin of the coordinate system or as adding a constant vector to each point. Each point in a figure is moved the same distance in the same direction using a type of transformation known as translation. For instance, this transformation shifts the parallelogram 3 units upward and 5 units to the right. The formula is (x, y) (x + 5, y + 3).

Given

Parent function

f(x) = 1/2ˣ

Vertically compress by a factor of 1/3

Translation

f(x) = x - k

f(x) = 1/2ˣ - 1/3

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