1/5(4x-2.5)=5(0.4+10)+3 1/3

The value of x in both case is 17 and 10.

If the sum of two angles is 180 degrees then they are said to be b angles, which form a linear angle together. Whereas if the sum of two angles is 90 degrees, then they are said to be complementary angles, and they form a right angle together.

1. As the given angle is 90 degree i.e., complementary angle.

So,

 22+4x=90

  4x= 90-22

  4x= 68

    x= 17

2. As the figure for the linear pair i.e., supplementary angle

So,

110+7x=180

7x=70

x=10

Hence the value of x in both case is 17 and 10.

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Answer:

80 mm

Step-by-step explanation:

Pythagorean theorm can be applied here to solve for the length of the last leg, \(a^{2}\) + \(b^{2}\) = \(c^{2}\), where (a) and (b) are the legs of the triangle and (c) is the hypotenuse. We can rearrange the pythagorean theorm for our purposes like the following:

b = √c^2 - √a^2

  = √(82)^2 - √(18)^2

  = √6724 - √324

  = √6400

  = 80 mm

Answer:

the basic family of this right- angled triangle is generally 6 , 8 , 10.

this units have been derived from 3, 4, 5 by multiplying each unit by 2.

So, the answer to the length of one of its legs can either be 6 units or 8 units.

HOPE THIS HELPS.

Answer:

a. h = A/w = 2 ³/₄ ft

b. A'/A = 2/3

Step-by-step explanation:

a. What is the total height of the wall? Write an equation to represent the situation. Then solve.

The wall is a rectangle and its area is A = wh where w = width and h = height of wall.

Making h subject of the formula,

h = A/w

Now, Since the area of the retaining wall, A is 23 ³/₈ ft² and its width is the length of the portion of the wall which is brick w is 8 ¹/₂ ft, then

h = A/w

= 23 ³/₈ ft² ÷ 8 ¹/₂ ft

= 187/8 ft² ÷ 17/2 ft

= 187/8 ft² × 2/17 ft

= 187/4 ft² × 1/17 ft

= 187/68 ft

= 2 ³/₄ ft

b. If the area of the brick portion of the wall is 15(7/12), what fraction of the wall is brick? Write an equation to show your work.

Since the area of the brick portion of the wall is A' = 15 ⁷/₁₂ ft²  and the total are of the retaining wall is A =  23 ³/₈ ft²

The fraction of the wall that is brick = A'/A

= 15 ⁷/₁₂ ft² ÷ 23 ³/₈ ft²

= 187/12 ÷ 187/8

= 187/12 × 8/187

= 8/12

= 2/3

Answer with Step-by-step explanation:

a) 2 3/4 ÷ 3 = 11/12 feet

11/12 + 11/12 = 1 5/6

Or, you could write an algebraic equation:

2 3/4 ÷ 3 = x.  (3x = 2 3/4)

x = 11/12

The height of the brick proportion of the wall is 1 5/6

b)

You know that 8 x 2 is 16. Well, you already know that the whole total of fractions, multiplied together, would probably be less that 1 and less than 1/2.

So, your rounded answer should be 16. Or 16 1/2

c)  

Area = 8 1/2 x 2 3/4.

Use Distributive Property to solve the area.

(8 x 2) + (3/4 x 1/2) = x

8 x 2 = 16

3/4 x 1/2 = 3/8

16 + 3/8 = 16 3/8

x = 16 3/8

I think my answer is reasonable because I estimated 16, and 1/2. 3/8 is close to 1/2. That's why my answer is reasonable.

-kiniwih426

Answer:

16. 1 miles

Step-by-step explanation:

Using Pythagorean Theorem,

a^2 + b^2 = c^2

Since the road that goes from his home to work directly is c^2...

Plug in the rest of the numbers

16^2 + 2^2 = c^2

256 + 4 = c^2

260 = c^2

The reverse square of 260 is

16. 1 miles

Answer:

$720

Step-by-step explanation:

Add them and divide by 2 to find the middle between 480 and 960

480 + 960 = 1440 / 2 = 720

Answer:

$720

Step-by-step explanation:

$180 + $960 then ÷ it by 2 that equals your answer

the image above is the shows the steps

The percentage increase in Total GDP in 1999 over 1998 was b.14.8%.

This can be calculated by using the formula for percentage increase:
Percentage Increase = [(New Value - Old Value) / Old Value] x 100

In this case, the New Value is the Total GDP in 1999 and the Old Value is the Total GDP in 1998. Plugging in the values and solving for the percentage increase, we get:

Percentage Increase = [(Total GDP in 1999 - Total GDP in 1998) / Total GDP in 1998] x 100

Percentage Increase = [(14.8 - 12.9) / 12.9] x 100

Percentage Increase = [1.9 / 12.9] x 100

Percentage Increase = 0.147 x 100

Percentage Increase = 14.7%


Therefore, the correct answer is b. 14.8%.

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The c = 1/9 satisfies the conclusion of the Mean Value Theorem for the function f(x) = sqrt(x) on the interval [4,16].

We can apply the Mean Value Theorem to the function f(x) = sqrt(x) on the interval [4,16]. The Mean Value Theorem states that if f(x) is continuous on the closed interval [a,b] and differentiable on the open interval (a,b), then there exists a point c in (a,b) such that

\(f'(c) = (f(b) - f(a))/(b - a).\)

Using this theorem, we can find a point c in (4,16) such that

\(f'(c) = (f(16) - f(4))/(16 - 4):\)

\(f(16) = sqrt(16) = 4\)

\(f(4) = sqrt(4) = 2\)

So, \((f(16) - f(4))/(16 - 4) = (4 - 2)/12 = 1/6.\)

Now, we need to find a point c in (4,16) such that f'(c) = 1/6. The derivative

of f(x) is \(f'(x) = 1/(2*sqrt(x))\), so we need to solve the equation

f'(c) = 1/6:

\(1/(2*sqrt(c)) = 1/6\)

Multiplying both sides by 2*sqrt(c), we get:

\(1 = (2*sqrt(c))/6\)

Simplifying, we get:

\(sqrt(c) = 1/3\)

Squaring both sides, we get:

\(c = 1/9\)

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The optimal solution for the given linear programming model is:

max z = 38

when x1 = 5, x2 = 10, x3 = 0

To solve the given linear programming model using the simplex algorithm, we start by converting the inequalities into equations and introducing slack variables. The initial tableau is constructed with the coefficients of the decision variables and the right-hand side constants.

Next, we apply the simplex algorithm to iteratively improve the solution. By performing pivot operations, we move towards the optimal solution. In each iteration, we select the pivot column based on the most negative coefficient in the objective row and the pivot row based on the minimum ratio test.

After several iterations, we reach the optimal tableau, where all the coefficients in the objective row are non-negative. The optimal solution is obtained by reading the values of the decision variables from the tableau.

In this case, the optimal solution is z = 38 when x1 = 5, x2 = 10, and x3 = 0. This means that to maximize the objective function, the decision variables x1 and x2 should be set to 5 and 10 respectively, while x3 is set to 0.

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Answer:

20

Step-by-step explanation:

180 - 90 - 70  = 20

The sum of all angles in a triangle equals 180.

Triangle Sum Theory

Answer:

do you still need help this was 20 hours ago lol

Step-by-step explanation:

The trains will be 380 miles apart at 3:00 PM, which is 4 hours after the freight train leaves the station at 12 noon.

We can use the formula d = rt (distance = rate x time) to calculate the distance each train has traveled during this time:

Let's call the time elapsed from 12 noon until the trains meet as t hours.

During this time, the freight train has traveled at a rate of 50 mph for t hours and the passenger train has traveled at a rate of 60 mph for (t-1) hours (since it started one hour after the freight train).

Distance traveled by freight train = 50t

Distance traveled by passenger train = 60(t-1)

The total distance between the two trains at time t is the sum of these distances, which we can write as:

Total distance = 50t + 60(t-1)

We want to find the time t at which the total distance is 380 miles. So we can set up the equation:

50t + 60(t-1) = 380

Simplifying this equation, we get:

110t - 60 = 380

110t = 440

t = 4

Therefore, the time elapsed from 12 noon until the trains meet is 4 hours. Since the passenger train left one hour after the freight train, it has been traveling for 3 hours.

So the time at which the trains are 380 miles apart is 3:00 PM (12 noon + 4 hours).

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Answer: The length of the path along the longest side of the park would be 35 yds.

Step-by-step explanation: Area of triangle = (1/2) x base x height294 = (1/2) x 21 x heightMultiplying both sides by 2 and dividing by 21, we get:height = 28So the other leg of the triangle is 28 yds.Now we can use the Pythagorean theorem to find the length of the hypotenuse:hypotenuse² = shortest side² + other leg²hypotenuse² = 21² + 28²hypotenuse² = 441 + 784hypotenuse² = 1225Taking the square root of both sides, we get:hypotenuse = 35Therefore, the length of the path along the longest side of the park would be 35 yds.

The triangle transitive congruent is proved by considering that if one triangle is congruent to second triangle and second triangle is congruent to third one, then the first triangle is congruent to third triangle.

The transitive property states that if one geometry is congruent with another, and the second is congruent with a third, then the first is also congruent with the third.

Statement : If triangle ABC is similar to triangle PQR and triangle PQR is similar to triangle EFG , then triangle ABC is similar to triangle EFG.

Given, ∆ABC ≅ ∆PQR and ∆PQR ≅ ∆EFG

RTP -> ∆ABC ≅ ∆EFG.

Proof : ∆ABC ≅ ∆PQR, SSA Congruence which implies, AB = PQ --(1)

PR = AC --(2)

and angle ABC = angle PQR --(3)

∆PQR ≅ ∆EFG, AAS Congruence which gives

Angle PQR = Angle EFG --(4)

PQ = EF --(5)

Angle PRQ = Angle EGF --(6)

from (3) and (4) we get,

angle ABC = Angle EFG --(7)

from (1) and (5) we get , AB = EF --(8)

angle BAC = angle FEG = 40° --(9)

Now, from (7) , (8), (9) we conclude that the triangle ABC is Congruent to triangle EFG by ASA Congrauance postulate i.e ∆ABC ≅ ∆EFG.

Hence proved.

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The original price of the coat was $130. In this case, we worked with the dollar sign ($) to represent the currency.

To find the original price of the coat, we can set up an equation based on the given information.

Let's assume that the original price of the coat is represented by "x" dollars.

According to the problem, the price of the coat decreased by $40, so we can express the new price as:

x - $40

We are also given that the new price of the coat is $90. Therefore, we can set up the equation:

x - $40 = $90

To find the original price, we need to isolate the variable "x" on one side of the equation. We can do this by adding $40 to both sides:

x - $40 + $40 = $90 + $40

This simplifies to:

x = $130

It's important to note that when solving equations involving prices or monetary values, it's crucial to pay attention to the units and keep them consistent throughout the calculation.

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Answer:

50th

Step-by-step explanation:

10 multiply by 5 is 50

And 25 multiply by 2 is 50

50 is the first to appear on both sides

We get the consecutive numbers as 257 and 258 from the equation 2 x + 1 = 515.

We are given that,

The sum of 2 consecutive numbers is 515.

Consecutive numbers:

Numbers that follow each other continuously in the order from smallest to largest are called consecutive numbers. For example: 1 and 2 are consecutive numbers, 34 and 35 are also consecutive numbers.

Here let the first number be x

Second number will be:

x + 1

We need to find their sum:

x + x + 1 = 515

2 x + 1 = 515

2 x = 515 - 1

2 x = 514

x = 514 / 2

x = 257

x + 1 = 257 + 1 = 258

Therefore, we get the consecutive numbers as 257 and 258 from the equation 2 x + 1 = 515.

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Both the degree 2 and degree 3 Taylor polynomials centered at a = 2 for the function f(x) = 4x - 7 are given by P_2(x) = 4x - 7 and P_3(x) = 4x - 7, respectively.

To calculate the Taylor polynomials of degree 2 and 3 centered at a = 2 for the function f(x) = 4x - 7, we will use the Taylor series expansion formula:

P_n(x) = f(a) + f'(a)(x - a) + (1/2!)f''(a)(x - a)^2 + ... + (1/n!)f^n(a)(x - a)^n

where P_n(x) is the Taylor polynomial of degree n, f'(x) represents the first derivative of f(x), f''(x) represents the second derivative, and f^n(x) represents the nth derivative of f(x).

First, let's calculate the derivatives of f(x):

f'(x) = 4

f''(x) = 0

f'''(x) = 0

Now, we can evaluate the Taylor polynomials of degree 2 and 3 centered at a = 2.

Degree 2 Taylor Polynomial:

P_2(x) = f(a) + f'(a)(x - a) + (1/2!)f''(a)(x - a)^2

= f(2) + f'(2)(x - 2) + (1/2!)f''(2)(x - 2)^2

First, let's find the values of f(2), f'(2), and f''(2):

f(2) = 4(2) - 7 = 1

f'(2) = 4

f''(2) = 0

Now we substitute these values into the degree 2 Taylor polynomial:

P_2(x) = 1 + 4(x - 2) + (1/2!)(0)(x - 2)^2

= 1 + 4(x - 2)

= 1 + 4x - 8

= 4x - 7

Therefore, the degree 2 Taylor polynomial centered at a = 2 for the function f(x) = 4x - 7 is P_2(x) = 4x - 7.

Degree 3 Taylor Polynomial:

P_3(x) = f(a) + f'(a)(x - a) + (1/2!)f''(a)(x - a)^2 + (1/3!)f'''(a)(x - a)^3

Again, let's find the values of f(2), f'(2), f''(2), and f'''(2):

f(2) = 4(2) - 7 = 1

f'(2) = 4

f''(2) = 0

f'''(2) = 0

Now we substitute these values into the degree 3 Taylor polynomial:

P_3(x) = 1 + 4(x - 2) + (1/2!)(0)(x - 2)^2 + (1/3!)(0)(x - 2)^3

= 1 + 4(x - 2)

Therefore, the degree 3 Taylor polynomial centered at a = 2 for the function f(x) = 4x - 7 is also P_3(x) = 4x - 7.

In summary, both the degree 2 and degree 3 Taylor polynomials centered at a = 2 for the function f(x) = 4x - 7 are given by P_2(x) = 4x - 7 and P_3(x) = 4x - 7, respectively.

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2+1/6y=3x+4

3/6y=3x+4

3=3x+4×6y

3-4=3x×6y

-1=18xy

-1/18=xy

HOPE ITS RIGHT!! GIVE BRAINLIEST PLS

Answer:

Y would have to equal 1 over 2(3x+4) in order for this equation to even work properly. 2+1 over 6 would actually equal 1/2y which is basically 3/6y. And since 3 and 6 are like terms 3 divided by 3 is 1 and 6y divided by 3 is 2y

Hope this helps

Answer:7

Step-by-step explanation:

21=42-3r

21-42=3r

-21=3r

r=7

Answer:

-7

Step-by-step explanation:

The solution of the given initial value problem is: \(y = y0e6t\) where y0 is the initial condition that is

y(0) = 6. Placing this value in the equation above, we get:

\(y = 6e6t\)

Given that the initial condition is y0 = 6,

the differential equation is\(dy/dt = 6y.\)

As we know that the solution of this differential equation is:\(y = y0e^(6t)\)

where y0 is the initial condition that is y(0) = 6.

Placing this value in the equation above, we get :\(y = 6e^(6t)\)

Hence, the solution of the given initial value problem is\(y = 6e^(6t).\)

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The solution to (11cis61.5 ∘ )(5cis159.5 ∘ ) is approximately 55.6158 + 34.1628i in rectangular form.

Explanation:

To multiply complex numbers in polar form, we multiply their magnitudes and add their angles. In this case, we have (11cis61.5 ∘ )(5cis159.5 ∘ ).

First, we multiply the magnitudes: 11 * 5 = 55.

Then, we add the angles: 61.5 ∘ + 159.5 ∘ = 221 ∘.

Now we have the product in polar form, which is 55cis221 ∘.

To convert it to rectangular form, we use Euler's formula: z = r(cosθ + isinθ).

The rectangular form of 55cis221 ∘ is 55(cos221 ∘ + isin221 ∘).

Using a calculator to evaluate cos221 ∘ and sin221 ∘, we find that cos221 ∘ ≈ 0.616 and sin221 ∘ ≈ -0.787.

Finally, we multiply the magnitude (55) by the real part (cos221 ∘) and the imaginary part (sin221 ∘) to obtain the rectangular form of the product:

55 * 0.616 ≈ 33.880 and 55 * (-0.787) ≈ -34.283.

So, the solution in rectangular form is approximately 33.880 - 34.283i, which can be rounded to 55.6158 + 34.1628i to four decimal places.

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Answer:

The answer would be C. An obtuse equilateral triangle :)

Answer:

the 3rd doesnt have a relationship and the 4th one is positive relationship

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

option B is correct(ASA)because the S in the middle of the two A(s) makes it congruent