MATHEMATICS COLLEGE

If m_2= x, m/3=40, and m24=5x + 14, what is mZ1?
A. 80
B. 121
C. 21
D. 61

Answers

Answer 1

Answer:

Answer:

D. 61

Step-by-step explanation:

find x from the given triangle.

first step is to get x

add all inside angles = 180

∠2 + ∠3 + ∠4 = 180

x + 40 + 5x + 14 = 180

x + 5x = 180 - 40 - 14

6x = 126

x = 126 / 6

x = 21

substitute x=21 into angle 4

∠4 = 5x + 14

∠4 = 5(21) + 14

∠4 = 119

lastly, add ∠1 + ∠4 = 180

∠1 + 119 = 180

∠1 = 180 - 119

∠1 = 61°

therefore, the answer is D. 61

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A student is trying to solve the set of two equations given below:Equation A: x + z = 6Equation B: 3x + 2z = 1Which of the following is a possible step used in eliminating the z-term?Multiply equation A by −2.Multiply equation B by 2.Multiply equation A by 3.Multiply equation B by 3.

How do I find the lateral and total surface area of the prism.Please give a step by step. Thanks.

Answers

Explanation:

Lateral Area

The lateral area is the area of the sides of the prism. If the faces are perpendicular to the bases, then each face is a rectangle. The area of each rectangle is the product of its length and width, generally the product of the height of the prism and the length of one edge of the base.

The total lateral area will then be the product of the height of the prism and the perimeter of the base.

Total Area

The total area is the sum of the lateral area (computed as above) and the area of the two bases of the prism. The formula for that area depends on the shape of the prism. (You have already seen formulas for the areas of triangles, rectangles, and other plane shapes. If not, they are readily available in your text or using a web search.)

The magnitude of an earthquake depending on the energy it produces can be modeled using the equationM = 0.6666 log x - 3.2. Complete the sentences about the model.
The curve representing the relationship includes the point
The growth factor is
An earthquake with an energy level of has a magnitude of

Answers

Final answer:

The equation 'M = 0.6666 log x - 3.2' describes the relationship between the energy produced by an earthquake (x) and its resulting magnitude (M). The 0.6666 in the formula is the growth factor. To get a magnitude for a specific energy level, we plug the energy value into the formula, and solve.

Explanation:

The equation given represents the relationship between the magnitude of an earthquake (M) and the energy it produces (x), with M being the earthquake's magnitude and x being the energy produced by the earthquake. This equation is a logarithmic model with a base of 10 (without the base explicitly stated, we assume it to be 10).

The curve representing the relationship includes the point: To identify a point, we need a specific x-value for the energy level. For instance, for x=1000, we can plug it into the equation to get the magnitude M = 0.6666 log(1000) - 3.2.
The growth factor is: In this context, the growth factor refers to the constant 0.6666 which is multiplied by the logarithm. This factor impacts the rate at which the magnitude of the earthquake grows for a given increase in energy.
An earthquake with an energy level of (an x-value should be inserted here) has a magnitude of: We would again plug the energy value (x-value) into the formula, compute the expression to determine the corresponding magnitude.

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Answer:

Step-by-step explanation:

3 times the sum of one third of a number and 8 is 11

Answers

Answer:

3( $(1)/(3)$ x+8)=11

Step-by-step explanation:

It says 3 times the sum of one third of a number and 8, so we group that expression into the parentheses. Since there is a key word is, we need to put an equal sign.

Who'd be better at speed answering? Datguy323 or some Helping Hand? (Not a serious question) Solve for the variables: $x^3+y^7=28\nx^3=27$

Answers

Answer:

x = 3

y = 1

Step-by-step explanation:

The equations are:

$x^3+y^7 = 28$

and

$x^3 = 27$

Putting second equation in the first one:

=> $27+y^7 = 28$

Subtracting 27 to both sides

=> $y^7 = 28-27$

=> $y^7 = 1$

Taking power 7 to both sides

=> y = 1

Now,

$x^3 = 27$

Taking cube root on the both sides

x = 3

Answer: (3,1)

Step-by-step explanation:

First, to find x, simply take the cube root of 27, or 3. Thus, x = 3.

Then, simply plug it in:

$27+y^7=28\nSubtract(27)\ny^7=1\ny=1$

Thus, y = 1

Hope it helps <3

p.s. for some reason, in a graphing calculator, it shows no solutions

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2 in a row!

George Mendel is examining peas to try to understand how traits are passed from parents to offspring. Today Gregor has 228 peas to examine . The pods have 6 peas per pod. How many pods of peas are there?

Answers

The answer is 38 peas per pod

228÷6 = 38

Glad to help you :)

Final answer:

By dividing the total number of peas (228) by the number of peas per pod (6), we find that Gregor Mendel has 38 pods of peas.

Explanation:

This question is asking how many pods of peas Gregor Mendel has if he has a total of 228 peas and each pod contains 6 peas. To find out this, you can divide the total number of peas by the number of peas per pod.

So, 228 peas ÷ 6 peas/pod = 38 pods.

Therefore, Gregor Mendel has 38 pods of peas that he is examining for his research.

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What can you say about a solution of the equation y' = - y2 just by looking at the differential equation? The function y must be decreasing (or equal to 0) on any interval on which it is defined. The function y must be increasing (or equal to 0) on any interval on which it is defined.

Answers

Answer:

The function y must be decreasing (or equal to 0) on any interval on which it is defined.

Step-by-step explanation:

The derivative of a function gives us the rate at which that function is changing. In this case, -y^2, yields a negative value for every possible value of y, thus, the rate of change is always negative and the function y is decreasing (or equal to 0) on any interval on which it is defined.

Final answer:

The differential equation y' = - $y^2$ implies that y is either decreasing or constant wherever it is defined, because the derivative y' is non-positive.

Explanation:

By examining the differential equation y' = - $y^2$ , we can infer some characteristics about the solutions without solving it. If y is a solution to this equation, then y' represents the derivative of y with respect to x. This derivative tells us about the rate of change of the function y.

Since the right side of the equation is - $y^2$ , and a square of a real number is always non-negative, multiplying by -1 makes it non-positive. This implies that the derivative y' is either less than or equal to zero. Therefore, wherever the function y is defined, it must be either decreasing or constant (equal to zero). If y is positive, y will decrease because of the negative sign in front of the square. If y is negative, squaring it results in a positive number, but the negative sign still ensures that the rate of change is non-positive.

Conclusion: the function y is decreasing or remains constant on any interval it is defined; it cannot be increasing.