Lines A and B are parallel.


What is the measure of angle B?


Enter your answer is the box.


B = __

Answer:

Step-by-step explanation:

Area of rectangle: L x B.

Conclusion:

Hence, 3 yards² is your area.

Hoped this helped.

\(GeniusUser\)

Answer:

3 square yards

Step-by-step explanation:

You multiply the length by the width (one side multiplied by the other side that does not have the same size)

1x3=3

The given expression is cos(tan⁻¹ 5). Let y = tan⁻¹ 5. Then, tan y = 5. Therefore, we have a right triangle where opposite side = 5 and adjacent side = 1. Then, hypotenuse = √(5² + 1²) = √26

3. a. cos (tan-¹5)

The given expression is cos(tan⁻¹ 5). Let y = tan⁻¹ 5. Then, tan y = 5

Therefore, we have a right triangle where opposite side = 5 and adjacent side = 1.

Then, hypotenuse = √(5² + 1²) = √26

Then, cos y = adjacent/hypotenuse= 1/√26

Therefore, cos (tan⁻¹ 5) = cos y = 1/√26b. cot(sin-¹-)

The given expression is cot(sin⁻¹ x).

Let y = sin⁻¹ x

Then, sin y = x

Therefore, we have a right triangle where opposite side = x and hypotenuse = 1. Then, adjacent side = √(1 - x²)

Then, cot y = adjacent/opposite = √(1 - x²)/x

Therefore, cot(sin⁻¹ x) = cot y = √(1 - x²)/x4.

a. π+3cos¹¹(x + 1) = 0

Let cos⁻¹(x + 1) = y

Then, cos y = x + 1

Therefore, we have cos⁻¹(x + 1) = y = π - 3y/3So, y = π/4

Then, cos y = x + 1 = √2/2 + 1 = (2 + √2)/2π + 3(π/4) = (7π/4) ≠ 0

There is no solution to the given equation.

b. 2tan⁻¹(2) = cos⁻¹x

Let y = tan⁻¹(2)

Then, tan y = 2

Therefore, we have a right triangle where opposite side = 2 and adjacent side = 1. Then, hypotenuse = √(1² + 2²) = √5

Therefore, sin y = 2/√5 and cos y = 1/√5

Hence, cos⁻¹x = 2tan⁻¹(2) = 2y

So, x = cos(2y) = cos[2tan⁻¹(2)] = 3/5

c. sin⁻¹ x = cos⁻¹(2x)

Let sin⁻¹ x = y

Then, sin y = x

Therefore, we have a right triangle where opposite side = x and hypotenuse = 1.

Then, adjacent side = √(1 - x²)

Then, cos⁻¹(2x) = z

So, cos z = 2x

Therefore, we have a right triangle where adjacent side = 2x and hypotenuse = 1.

Then, opposite side = √(1 - 4x²)

Then, tan y = x/√(1 - x²) and tan z = √(1 - 4x²)/2x

Hence, x/√(1 - x²) = √(1 - 4x²)/2x

Solving this, we get x = ±√2/2

Therefore, sin⁻¹ x = π/4 and cos⁻¹(2x) = π/4

Therefore, the given equation is true for x = √2/2.5.

Proof Given: tan x + cos x = sin x (sec x + cot x)

We know that sec x = 1/cos x and cot x = cos x/sin x

Therefore, the given equation can be written as tan x + cos x = sin x (1/cos x + cos x/sin x)

Multiplying both sides by sin x cos x, we get sin x cos x tan x + cos² x = sin² x + cos² x

Multiplying both sides by 1/sin x cos x, we get tan x + sec² x = 1

This is true. Hence, proved.

To know more about right triangle visit: https://brainly.com/question/22215992

#SPJ11

Answer:

90

Step-by-step explanation:

The symbol represented in the angle is the right angle symbol ∟

This means that the angle would be 90

Have a lovely day :)

Answer:

There's no m so I'm assuming you meant b.

The angle of b is 121

Step-by-step explanation:

The shape here is a heptagon. The formula for calculating the sum of interior angles is ( n − 2 ) × 180. *n represents the number of sides.

(7-2) × 180               There are 7 sides so plug that in.

(5) × 180 = 900       This means the shape's interior angles add up to 900.

Now, all we have to do is add up all the sides known and set it equal to 900.

c + d + e + f + g + a = 900

148 + 90 + 142 + 130 + 139 + 130 + b = 900

779 + b = 900              

now subtract 779 from both sides to isolate b.

b = 121

Answer:

$4.76

Step-by-step explanation:

It costs $2.80 to make a sandwich at the local deli shop and the deli sells it at a price that is 170% of the cost.

We have to find 170% of the cost of making each sandwich ($2.80):

170/100 * 2.80 = $4.76

The sandwich sells for $4.76

Answer:

ben

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

To solve this place an imaginary decimal point right before the 8 now going one number value at a time move it to where its original place was and count the number of time you had to move it.

The directional derivative of z = x^3 – 5y^3 in the direction of θ = π/4 at the point (5, 2) is sqrt(2) * (75 – 20sqrt(2)).

To find the directional derivative, we need to compute the dot product of the gradient vector (∇z) and the unit vector in the direction of θ. First, we find the gradient of z by taking the partial derivatives with respect to x and y: ∂z/∂x = 3x^2 and ∂z/∂y = -15y^2.
At the point (5, 2), we substitute these values to get ∂z/∂x = 75 and ∂z/∂y = -60.

Next, we construct the unit vector in the direction of θ = π/4, which is (cos(π/4), sin(π/4)) = (sqrt(2)/2, sqrt(2)/2).
Taking the dot product of the gradient vector (∇z) = (75, -60) and the unit vector (sqrt(2)/2, sqrt(2)/2), we get sqrt(2) * (75 – 20sqrt(2)). Hence, the directional derivative is sqrt(2) * (75 – 20sqrt(2)).

Learn more about Dot product here: brainly.com/question/23477017
#SPJ11

Answer:

Step-by-step explanation:

B

Answer:

1    x4 – 6x2 – 27 = 0

4    6(2x + 4)2 = (2x + 4) + 2

5   6x4 = -x2 + 5

Step-by-step explanation:

Answer:

I think the person with the greatest debt is Marcus cause he has -25 dollars in his bank account.

Step-by-step explanation:

Sara and Maria both have positive numbers as their bank amount.  Samuel have to deposit 10 dollars into his bank account to not be in debt while Marcus has to deposit 25 dollars. 

To find a quadratic equation with the y-intercept and vertex, follow these steps: identify the coordinates of the y-intercept and vertex, substitute them into the general form of the quadratic equation, solve for the coefficients, and substitute the coefficients back into the equation. For example, if the y-intercept is (0, 3) and the vertex is (-2, 1), the quadratic equation would be y = x^2 + x + 3.

To find a quadratic equation with the y-intercept and vertex, we can follow these steps:

For example, let's say the y-intercept is (0, 3) and the vertex is (-2, 1). We can substitute these coordinates into the general form of the quadratic equation:

3 = a(0)^2 + b(0) + c

1 = a(-2)^2 + b(-2) + c

Simplifying these equations, we get:

c = 3

4a - 2b + c = 1

By substituting c = 3 into the second equation, we can solve for a and b:

4a - 2b + 3 = 1

4a - 2b = -2

2a - b = -1

By solving this system of equations, we find a = 1 and b = 1. Substituting these values back into the general form of the quadratic equation, we obtain the final equation:

y = x^2 + x + 3

About quadratic equation here:

https://brainly.com/question/30098550

#SPJ11

To find a quadratic equation with a given y-intercept and vertex, you need the coordinates of the vertex and one additional point on the curve.

Example:

Suppose we want to find a quadratic equation with a y-intercept of (0, 4) and a vertex at (2, -1).

To find a quadratic equation with a given y-intercept and vertex, you can use the vertex form of a quadratic equation and substitute the coordinates to obtain the equation. Then, use the y-intercept to find an additional point on the curve and solve a system of equations to determine the coefficients. Finally, substitute the coefficients into the standard form of the quadratic equation to get the final equation.

To know more about quadratic equation visit:

https://brainly.com/question/30164833

#SPJ11

Answer:

2128

Step-by-step explanation:

T=wma T=76 X 7 X 4=2128

Answer:

T = 2128

Step-by-step explanation:

Step 1: Define equation

T = wma

w = 76

m = 7

a = 4

Step 2: Substitute

T = 76(7)(4)

Step 3: Evaluate

T = 2128

Let's denote the unknown number as 'x'. The equation can be set up as x + (1/2)x = 45. Solving this equation, we find that the number is 30.

The problem states that the sum of a number and its half is equal to 45. To find the number, we can set up an equation and solve for it.

Let's represent the number as "x". The problem states that the sum of the number and its half is equal to 45. Mathematically, this can be written as:

x + (1/2)x = 45

To simplify the equation, we can combine the like terms:

(3/2)x = 45

To isolate the variable x, we can multiply both sides of the equation by the reciprocal of (3/2), which is (2/3):

x = 45 * (2/3)

Simplifying the right side of the equation:

x = 30

Therefore, the number is 30.

for such more question on number

https://brainly.com/question/859564

#SPJ8

The value of x is -7.

An equation is an expression that shows the relationship between two or more numbers and variables. A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

We are given the equation as

\(8^{x + 3} = 2 ^{x - 5}\)

Solving the equation as;

\(8^{x + 3} = 2 ^{x - 5}\\\\2^{3(x + 3)} = 2 ^{x - 5}\)

Then we have;

3x + 9 = x - 5

2x = -14

x = -7

The value of x is -7.

Learn more about equations here;

brainly.com/question/25180086

#SPJ1

Answer:

x = 5

Step-by-step explanation:

the whole equation is

2log(x) - 3log(2) + log(32) = 2

converting the first 2 expressions by using standard logarithm laws

2log(x) = log(x²)

3log(2) = log(2³) = log(8)

the combining these converted expressions again by using standard logarithm laws

log(x²) - log(8) = log(x²/8)

log(x²/8) + log(32) = log(32×x²/8) = log(4x²)

log(4x²) = 2

now dissolving the logarithm by converting every side to the power of 10.

4x² = 10² = 100

x² = 25

x = 5

Answer:

Mean 140 grams

Standard deviation 22.4 grams

Step-by-step explanation:

What would the mean and standard deviation of these apples' weights be as determined by this scale? (Note: 1 ounce ≈ 28 grams).

Mean = 5.2 ounces.

First step would be to convert from ounces to grams

1 ounce = 28 grams

5.2 ounces =

5.2 ounces × 28 grams

= 145.6 grams

He underweighs by 0.2 ounces

We convert this too

1 ounce = 28 grams

0.2 ounce =

0.2 ounce × 28 grams

= 5.6 grams.

The new mean weight of the Fuji apples is grams = 145.6 grams - 5.6 grams = 140 grams.

Standard Deviation = 0.8 ounces.

Even though he underweighed that apples by 0.2 ounces, there has minimal effect on the standard deviation of the apples.

Hence, the standard deviation if the apples in grams =

1 ounce = 28 grams

0.8 ounce =

0.8 ounce × 28 grams

= 22.4 grams

Answer:

a. 1120

Step-by-step explanation:

15 years

each year 4%

or 60% decrease in 15 years

so 2800×60%=1680

2800-1680=1120

Answer:

788878

Step-by-step explanation:

789879

Answer:

Step-by-step explanation:

275

Hi!

-4(x - 5) + 8x = 9x - 3

-4x + 20 + 8x = 9x - 3

-4x + 8x - 9x = -3 - 20

-5x = -23

Answer: B

Answer:

B

Step-by-step explanation:

-4x +20 +8x = 9x -3. That's equall to 4x+20=9x-3. subtract 9x both sides, -5x+20=-3. subtract 20 both sides, -5x=-23.

Note that this is still a rectangle, and the length of the fencing is still 600 ft.

So the sum of the sides NOT along the river x + x + y = 600, and the area equals xy.

This makes the two equations: 2x + y = 600, and A = xy.

To find the largest area, we need to find A as a function of x or y. I suggest solving the first equation for y and replacing that in the second equation.

y = 600 - 2x. and A(x) = x(600-2x)

We now need to maximize A(x) = 600x - 2x2.

Remember, if x = -b/(2a), we find the x value of the vertex, the y value can be found by substitution.

So, since a = -2, and b = 600, x = -600/(-4) = 150 ft. If x = 150, y = 600 - 2(150) = 300.

So, the dimensions are 150 x 300 and the maximum area = 300(150) = 45,000 ft2

I hope this helps. By the way, there are many variations of this, and they are all similar. For example, you might want to make several pens with two lengths parallel and have three parallel withs inside.

Answer:

1

2,3,4

Step-by-step explanation: to

when the number of football is 1 is less expensive than basketball

Answer:

I can't see ;-; show close up

See the two pictures, explanation and solution ^_^

In order to check your answer is true or false. We check the two analyzes whether the number from the equation becomes 19x. First you multiply the first number in the first bracket by the second number in the second bracket 2x by 3 to get 6x. Secondly, you multiply the second number of the first bracket by the first number of the second bracket -5 by 4x to get -20x. The sum of the two numbers that you extracted from multiplying the numbers in parentheses (6x) + (-20x) equals - 14x, so this number is not the number 19x, so the first analysis error . Try it for the second analysis .

You can multiply the parentheses together and check the solution too.

\((2x - 5)(4x + 3) \\ (2x)(4x) + (2x)(3) + ( - 5)(4x) + ( - 5)(3) \\ = 8 {x}^{2} + 6x - 20x - 15 \\ = 8 {x}^{2} - 14x - 15\)

\((8x - 5)(x + 3) \\ (8x)(x) + (8x)(3) + ( - 5)(x) + ( - 5)(3) \\ = 8 {x}^{2} + 24x - 5x - 15 \\ = 8 {x}^{2} + 19x - 15\)

Using the Pythagorean theorem:

47 ^2 = 11^2 + x^2

2209 = 121 + x^2

Subtract 131 from both sides

2088 = x^2

Take the square root of both sides

X = sqrt(2088)

Simplify

X = 6sqrt(58)

Answer:

671.96 or 214\(\pi\)

Step-by-step explanation:

C=2\(\pi\)*r

C=2\(\pi\)*107

C=2*3.14*107

C=671.96

107*2=214

The value of the constant m for which the area between the parabolas is 1/2 is m = 1/(12a^2), where a represents the x-coordinate of the point where the two curves intersect.

To find the value of the constant m for which the area between the parabolas y = 2x^2 and y = -x^2 + 6mx is 1/2, we need to set up an integral and solve for m.

The area between the two curves can be found by integrating the difference between the upper and lower curves with respect to x over the interval where they intersect.

First, let's find the x-values where the two curves intersect:

2x^2 = -x^2 + 6mx

Combining like terms:

3x^2 = 6mx

Dividing both sides by 3x^2 (assuming x ≠ 0):

1 = 2m

Therefore, the two curves intersect at m = 1/2.

Now, we can set up the integral to find the area between the curves:

A = ∫[a, b] [(upper curve) - (lower curve)] dx

Using the x-values where the curves intersect, the integral becomes:

A = ∫[-a, a] [(-x^2 + 6mx) - 2x^2] dx

Simplifying:

A = ∫[-a, a] [-3x^2 + 6mx] dx

Integrating:

A = [-x^3 + 3mx^2] |[-a, a]

Substituting the limits of integration:

A = [-(a)^3 + 3ma^2] - [-(−a)^3 + 3m(−a)^2]

Simplifying further:

A = -a^3 + 3ma^2 + a^3 - 3ma^2

A = 6ma^2

We want this area to be equal to 1/2, so we can set up the equation:

6ma^2 = 1/2

Simplifying and solving for m:

m = 1/(12a^2)

Therefore, the value of the constant m for which the area between the parabolas is 1/2 is m = 1/(12a^2), where a represents the x-coordinate of the point where the two curves intersect.

Learn more about area  from

https://brainly.com/question/25292087

#SPJ11

since the powers are same, ignore 'em , and let's calculate the bases.

-16.(1/2)

-8.1 (upon cancellation)

ans = -8

hope it helps...!!!

All the correct fractions are,

⇒ 2 yd / 8 ft = 3 / 4

⇒ 24 in / 3 ft = 2 / 3

⇒ 4 ft / 4 yd = 1 / 3

⇒ 32 in / 2 ft = 4 / 3

A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y. Where, x and y are individual amount of two quantities. And, Total quantity gives after combine as x + y.

We have to given that;

All the fractions are,

⇒ 2 yd / 8 ft

⇒ 24 in / 3 ft

⇒ 4 ft / 4 yd

⇒ 32 in / 2 ft

Now, We know that;

⇒ 1 yard = 3 feet

⇒ 1 feet = 12 inches

So, By the fractions we get;

⇒ 2 yd / 8 ft

⇒ 6 ft / 8 ft

⇒ 6 / 8

⇒ 3 / 4

⇒ 24 in / 3 ft

⇒ 24 in / 36 in

⇒ 12 / 18

⇒ 2 / 3

⇒ 4 ft / 4 yd

⇒ 4 ft / 12 ft

⇒ 1 / 3

⇒ 32 in / 2 ft

⇒ 32 in / 24 in

⇒ 4 / 3

Learn more about the fraction visit:

https://brainly.com/question/5454147

#SPJ1

Answer:

523.6 ft

Step-by-step explanation:

Answer:

523.6 ft

Step-by-step explanation:

The equation of circle centered at the origin and has a radius of 7 is,

⇒ x² + y² = 49

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Given that;

Radius of circle = 7

Centre of circle = (0, 0)

Now, The equation of circle centered at the origin and has a radius of 7 is,

⇒ (x - 0)² + (y - 0)² = 7²

⇒ x² + y² = 49

Thus, The equation of circle centered at the origin and has a radius of 7 is,

⇒ x² + y² = 49

Learn more about the circle visit:

https://brainly.com/question/24810873

#SPJ1

The total number of starting lineups (of 5 players) can coach yells lot make, if the starting lineup can't contain both bob and yogi is 672.

An official list of the players who will take part in the event when the game starts is known as a starting lineup in sports. The players who are in the starting lineup are frequently referred to as starters, while the rest are known as bench players or replacements.

Case 1: Bob starts (and Yogi doesn't). In this case, the coach must choose 4 more players from the 10 remaining players (remember that Yogi won't play, so there are only 10 players left to select from). Thus there are 10C4 lineups that the coach can choose.

⇒ ¹⁰C₄ = 10!/4!(10-4)! = 10!/4!6!

⇒ ¹⁰C₄ = (10*8*9*7)/(4*3*2*1)

⇒ ¹⁰C₄ = 210

Case 2: Yogi starts (and Bob doesn't). As in Case 1, the coach must choose 4 more players from the 10 remaining players. So there are 10C4 lineups in this case.

⇒ ¹⁰C₄ = 210

Case 3: Neither Bob nor Yogi starts. In this case, the coach must choose all 5 players in the lineup from the 10 remaining players. Hence there are 10C5 lineups in this case.

⇒ ¹⁰C₅ = 10!/5!(10-5)! = 10!/5!5!

⇒ ¹⁰C₅ = (10*8*9*7*6)/(5*4*3*2*1)

⇒ ¹⁰C₅ = 252

To get the total number of starting lineups, we add the number of lineups in each of the cases:

Case 1 + Case 2 + Case 3

= 210 + 210 + 252 = 672

The total number of starting lineups (of 5 players) can coach yells lot make, if the starting lineup can't contain both bob and yogi is 672.

To learn more about starting lineups visit:

brainly.com/question/28140396

#SPJ4