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77julia77 [94]
2 years ago
8

Solve each of these equations. Explain or show your reasoning.

Mathematics
1 answer:
Svetlanka [38]2 years ago
4 0

1.

2(x+5)=3x+1 \\2x+10=3x+1 \\-x=-9 \\x=9

2.

3y-4=6-2y \\5y=10 \\y=2

3.

3(n+2)=9(6-n) \\3n+6=54-9n \\12n=48 \\n=\frac{48}{12}=4

Hope this helps.

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What are the domain and range of the function
atroni [7]

Answer:

Domain (-∞,∞)

Range (0, ∞)

Step-by-step explanation:

The domain of a function is always the set of all real numbers therefore the domain is going to be (-∞,∞). The range is (0, ∞) because 0 is one of the outputs for the function

3 0
3 years ago
Determine the rate: 6,000 miles in 3 hours
zmey [24]

Answer:

6,000:3

Step-by-step explanation:

6 0
1 year ago
What value of x makes this equation true? 15-7x=5x-21​
belka [17]

Answer:

x=3

Step-by-step explanation:

15-7x=5x-21

12x=36

x=3

4 0
2 years ago
On the 1st January 2014 Carol invested some money in a bank account.
Ghella [55]

Answer:

\large \boxed{\text{\pounds 23 360.00}}

Step-by-step explanation:

The formula for the accrued amount from compound interest is

A = P \left(1 + \dfrac{r}{n}\right)^{nt}

1. Amount in account on 1 Jan 2015

(a) Data:

a = £23 517.60

r = 2.5 %

n = 1

t = 1 yr

(b) Calculations:  

r = 0.025

\begin{array}{rcl}23517.60 & = & P\left (1 + \dfrac{r}{n}\right)^{nt}\\\\& = & P\left (1 + \dfrac{0.025}{1}\right)^{1\times1}\\\\& = & P (1 + 0.025)\\ & = & 1.025 P\\P & = & \dfrac{23517.60 }{1.025} \\\\& = & 22 944.00 \\\end{array}

The amount that gathered interest was £22 944.00 but, before the interest started accruing, Carol had withdrawn £1000 from the account.

She must have had £23 944 in her account on 1 Jan 2015.

(2) Amount originally invested

(a) Data

A = £23 944.00

\begin{array}{rcl}23 944.00 & = & 1.025 P\\P & = & \dfrac{23 944.00 }{1.025} \\\\& = & \mathbf{23 360.00} \\\end{array}\\\text{Carol originally invested $\large \boxed{\textbf{\pounds23 360.00}}$ in her account.}

3. Summary

1 Jan 2014      P = £23 360.00

1 Jan 2015     A =    23 944.00

     Withdrawal = <u>    -1  000.00 </u>

                     P =     22 944.00

1 Jan 2016    A =    £23 517.60

5 0
3 years ago
To the nearest tenth, what is the area of the figure shown in the image? Segment BF is a line of symmetry of the pentagon ABCDE.
Sidana [21]

Answer:

C, 39.3 in²

Step-by-step explanation:

Lets first find the area of the rectangle part of the house.

To find the area of a rectangle its base × height.

So its 6×4=24 in².

Now lets find the area of the top triangle.

Area for a triangle is (base × height)/2.

The height is 3 inches, because its 7-4. While the base is 6 inches.

(6×3)/2=9 in².

To find the area of the half circle the formula, (piR²)/2.

The radius of the circle is 2 because its half of the diamter which is 4.

(pi2²)/2=6.283 in².

Now we just need to add up the area of every part,

24+9+6.283=39.283in²

5 0
3 years ago
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