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skelet666 [1.2K]
3 years ago
11

2. Solve each given equation and show your work. Tell whether each equation has one solution, an infinite number of solutions, o

r no solution. Explain your answers. (a) 4 + 2( − 1) = 10 + 2 (b) 30 − = 10 − (6 + 10) (c) 8x = 4x + 4x + 10(x − x)
Mathematics
1 answer:
Brut [27]3 years ago
7 0

Hello!

To solve algebraic equations, we need to use SADMEP. SADMEP is an acronym used only solve for x in algebraic equations. SADMEP is expanded to be: subtraction, addition, division, multiplication, exponents, and parentheses.

(a) 4 + 2(-1) = 10 + 2 (multiply)

4 + -2 = 10 + 2 (add)

2 = 12

This equation has no solutions because <u>2 is never equal to 12</u>.

(b) 30 = 10 - (6 + 10) (simplify the parentheses)

30 = 10 + -1(16) (multiply)

30 = 10 - 16 (simplify)

30 = -6

This equation has no solutions because<u> 30 and -6 is never equal to each other</u>.

(c) 8x = 4x + 4x + 10(x - x)

8x = 4x + 4x + 10(x - x) (simplify [add and subtract])

8x = 8x + 10(0) (multiply)

8x = 8x  

This equation has an infinite number of solutions because if you <u>substitute any value into the original equation</u>, <u>both sides of the equation</u> will be <u>always equal</u>.

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your friend says that the volume of a sphere with a radius r is four times the volume of a cone with radius r. when is this true
Ierofanga [76]
Volume of a sphere is given by the formula: V_{\circ}=\frac43\pi r^3

If we pull the 4 out front we have, V_{\circ}=4\left(\frac13\pi r^3\right).

Volume of a cone is given by the formula: V_{\triangle}=\frac{1}{3}\pi r^2\cdot h

Notice that if the height of the cone is equal to the radius, V_{\triangle}=\frac13\pi r^2\cdot r

then it's exactly what we see in our volume formula without the 4!
7 0
2 years ago
. What is the solution to the equation –3.5(x + 12) = –2x + 18?
kotegsom [21]

Answer:

x=-4.36

     

Step-by-step explanation:

4 0
2 years ago
A cookie company packages its cookies in rectangular prism boxes designed with square bases that have both a length and width of
Verdich [7]

Answer:

length and width=4

height=8

Step-by-step explanation:

Hello to solve this problem we must propose a system of equations of 3x3, that is to say 3 variables and 3 equations.

Ecuation 1

Leght=Width

.L=W

Ecuation 2

To raise the second equation we consider that the length and width of 4 inches less than the height of the box

H-4=W

Ecuation 3

To establish equation number 3, we find the volume of a prism that is the result of multiplying length, width, and height

LxWxH=128

From ecuation 1(w=h)

HW^2=128

solving for  H

H=\frac{128}{W^2}

<em />

<em>Using ecuation 2</em>

H-4=W

\frac{128}{W^2}-4=W\\W^3+4W^2-128=0

Now we find the roots of the equation, 2 of them are imaginary, and only one results in 4

W=4in

L=4in

to find  the height we use the ecuation 2

H-4=W

H=4+W

H=4+4=8

H=8IN

7 0
3 years ago
If t= 14,what is the value of 3t?
Goryan [66]
42 bro it’s pretty simple just multiplication
7 0
3 years ago
Formulate the indicated conclusion in nontechnical terms. Be sure to address the original claim.The owner of a football team cla
nydimaria [60]

Answer:

Option D is correct.

Failure to reject the null hypothesis means that there is not sufficient evidence to support the claim that the mean attendance is greater than 694.

Step-by-step explanation:

For hypothesis testing, the first thing to define is the null and alternative hypothesis.

The null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.

It usually maintains that random chance is responsible for the outcome or results of any experimental study/hypothesis testing.

While, the alternative hypothesis usually confirms the the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test.

It usually maintains that other than random chance, there are significant factors affecting the outcome or results of the experimental study/hypothesis testing.

For this question, the owner of a football team claims that the average attendance at games is over 694, and he is therefore justified in moving the team to a city with a larger stadium.

So, the null hypothesis would be that there isn't enough evidence to support the claim that the mean attendance is greater than 694.

That is, the mean isn't greater than 694; the mean is less than or equal to 694.

While the alternative hypothesis would be that there is sufficient evidence to support the claim that the mean attendance is greater than 694.

Mathematically,

The null hypothesis is represented as

H₀: μ₀ ≤ 694

The alternative hypothesis is represented as

Hₐ: μ₀ > 694

Failure to reject the null hypothesis means that the null hypothesis is true. Hence, the answer choice picked is the obvious correct answer.

Hope this Helps!!!

6 0
2 years ago
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