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2 years ago

1250+27.50x=1400+20x

Mathematics

1 answer:

never [62]2 years ago

5 0

Answer:

x = 20

Step-by-step explanation:

Simplifying

1250 + 27.50x = 1400 + 20x

Solving

1250 + 27.50x = 1400 + 20x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-20x' to each side of the equation.

1250 + 27.50x + -20x = 1400 + 20x + -20x

Combine like terms: 27.50x + -20x = 7.5x

1250 + 7.5x = 1400 + 20x + -20x

Combine like terms: 20x + -20x = 0

1250 + 7.5x = 1400 + 0

1250 + 7.5x = 1400

Add '-1250' to each side of the equation.

1250 + -1250 + 7.5x = 1400 + -1250

Combine like terms: 1250 + -1250 = 0

0 + 7.5x = 1400 + -1250

7.5x = 1400 + -1250

Combine like terms: 1400 + -1250 = 150

7.5x = 150

Divide each side by '7.5'.

x = 20

Simplifying

x = 20

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The hypotenuse of a right triangle is 14 in. If the base

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Answer:

13.85

Step-by-step explanation:

U use the pythagorean theorem

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2 years ago

Evelyn has $524.96 in her checking account. She must maintain a $500 balance to avoid a fee. She wrote a check for $32.50 today.

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Answer:

524.96 − 32.50 + x ≥ 500

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Step-by-step explanation:

Given:

Amount in checking account = $524.96

Maintain amount = $500

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Find:

Amount need to deposit

Computation:

Assume, amount need to deposit = x

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524.96 − 32.50 + x ≥ 500

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Amount need to deposit = $7.54

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2 years ago

Evaluate the triple integral ∭ExydV where E is the solid tetrahedon with vertices (0,0,0),(5,0,0),(0,9,0),(0,0,4).

Elan Coil [88]

Answer: $\int\limits^a_E {\int\limits^a_E {\int\limits^a_E {xy} } \, dV$ = 1087.5

Step-by-step explanation: To evaluate the triple integral, first an equation of a plane is needed, since the tetrahedon is a geometric form that occupies a 3 dimensional plane. The region of the integral is in the attachment.

An equation of a plane is found with a point and a normal vector. Normal vector is a perpendicular vector on the plane.

Given the points, determine the vectors:

P = (5,0,0); Q = (0,9,0); R = (0,0,4)

vector PQ = (5,0,0) - (0,9,0) = (5,-9,0)

vector QR = (0,9,0) - (0,0,4) = (0,9,-4)

Knowing that cross product of two vectors will be perpendicular to these vectors, you can use the cross product as normal vector:

n = PQ × QR = $\left[\begin{array}{ccc}i&j&k\\5&-9&0\\0&9&-4\end{array}\right]$ $\left[\begin{array}{ccc}i&j\\5&-9\\0&9\end{array}\right]$

n = 36i + 0j + 45k - (0k + 0i - 20j)

n = 36i + 20j + 45k

Equation of a plane is generally given by:

$a(x-x_{0}) + b(y-y_{0}) + c(z-z_{0}) = 0$

Then, replacing with point P and normal vector n:

$36(x-5) + 20(y-0) + 45(z-0) = 0$

The equation is: 36x + 20y + 45z - 180 = 0

Second, in evaluating the triple integral, set limits:

In terms of z:

$z = \frac{180-36x-20y}{45}$

When z = 0:

$y = 9 + \frac{-9x}{5}$

When z=0 and y=0:

x = 5

Then, triple integral is:

$\int\limits^5_0 {\int\limits {\int\ {xy} \, dz } \, dy } \, dx$

Calculating:

$\int\limits^5_0 {\int\limits {\int\ {xyz} \, dy } \, dx$

$\int\limits^5_0 {\int\limits {\int\ {xy(\frac{180-36x-20y}{45} - 0 )} \, dy } \, dx$

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$\frac{1}{45} \int\limits^5_0 {2430x-1458x^{2}+\frac{94770}{125} x^{3}-\frac{23490}{375}x^{4} } \, dx$

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$\int\limits^5_0 {\int\limits {\int\ {xyz} \, dy } \, dx$ = 1087.5

The volume of the tetrahedon is 1087.5 cubic units.

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1 year ago

HELP 10 POINTS AND BRAINLIEST The triangles below are similar. In each traingle there is a 53°angle and a right angle. What is t

Mrrafil [7]

Answer:

Step-by-step explanation:

Since both triangles are similar, we know this because they have 2 angles in common, they both have the same third angle.

To find the third angle, we use the angle sum. The sum of angles in a triangle will always equal 180 degrees. We are given a right angle which is 90 degrees and another angle, which is 53 degrees. Knowing this:

90 + 53 + x = 180 (I have chosen to call the third angle x)

when rearranging this we get

180 - 90 - 53 = x

now we solve

x = 37 degrees

Hope this helps,

Cate

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2 years ago

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