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egoroff_w [7]
3 years ago
10

ASAP!!!! 10 POINTS!!!!

Mathematics
1 answer:
S_A_V [24]3 years ago
3 0

Completing the Square

2. Solve the equation by completing the square. Show your work.

x^2 – 30x = –125

Step 1: Add to both sides of the equation. (2 points)

Add 225 both sides of the equation

x^2 – 30x + 225 = –125 + 225

x^2 - 30x + 225 = 100

Step 2: Factor the left side of the equation. Show your work. (2 points)

Hint: It is a perfect square trinomial.


x^2 - 30x + 225 = 100


Factor the left side of the equation:

(x - 15)^2 = 100

Step 3: Take the square root of both sides of the equation from Step 2. (1 point)

√(x - 15)^2 = √100


Step 4: Simplify the radical and solve for x. Show your work. (1 point)

x - 15 = + - 10


x - 15 = 10

x = 25


x - 15 = -10

x = 5


Solutions x = 25, 5

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The product of two consecutive odd integers is 1 less than four times their some. find the two integers.
nignag [31]
2 consecutive odd integers.....x and x + 2.....the product means multiply....the sum means add.

x(x + 2) = 4(x + x + 2) - 1
x^2 + 2x = 4(2x + 2) - 1
x^2 + 2x = 8x + 8 - 1
x^2 + 2x = 8x + 7
x^2 + 2x - 8x - 7 = 0
x^2 - 6x - 7 = 0
(x - 7)(x + 1) = 0

x - 7 = 0            x + 2 = 7 + 2 = 9
x = 7
 
x + 1 = 0           x + 2 = -1 + 2 = 1
x = -1

there can be 2 answers for this....
(1) 7 and 9
(2) -1 and 1
7 0
3 years ago
HELP!!!! it’s due by 10 am and it’s 9:30am!!!!!!
Mashutka [201]

Answer:

2010.62

Step-by-step explanation:

the formula to find a cylinders volume is r and h so you just divide 14 and get 8, then you get the 10 and you solve for how you would usually get your cylinder volume. which is  V=πr2h=π·82·10≈2010.62

6 0
2 years ago
Read 2 more answers
A log raft is moving downstream at a speed of 3 km/h. To insure that there are no river jams a supervisor travels along the raft
skad [1K]

Answer:

2000 meters

Step-by-step explanation:

When the motorboat is moving downstream, its speed relative to the ground is 18 km/h, so its speed relative to the raft is 15 km/h.

When the motorboat is moving upstream, its speed relative to the ground is 12 km/h, so its speed relative to the raft is again 15 km/h.

Converted to m/min, the relative speed is:

15 km/h × (1000 m/km) × (1 h / 60 min) = 250 m/min

It takes the motorboat 16 minutes to travel to the front of the raft and back.  Since the speed is the same in both directions, the motorboat takes 8 minutes to travel the length of the raft.

So the length of the raft is 250×8 = 2000 meters.

8 0
3 years ago
Which fraction is equal to one third
KIM [24]

Answer:

2/6, 3/9, 4/12 ...

Step-by-step explanation:

We can find equivalent fractions to 1/3 by multiplying the numerator, or top number, and the denominator, or bottom number, by the same factor.

7 0
3 years ago
Calculate the average (arithmetic mean) of the list of numbers shown in the table. (rounded to the nearest tenth) A) 35.2 B) 39.
jenyasd209 [6]
<h3><u>Given Numbers:-</u></h3>
  • 23, 33 ,33 ,27 ,25 ,68 ,27 ,44 ,72

<h3><u>To Find:-</u></h3>
  • average of this set of numbers

<h3><u>Solution</u>:-</h3>

\green{ \underline { \boxed{ \sf{Average = \frac{Sum \:of \: observation}{Number \:of \: observation}}}}}

\longrightarrow Here, no of observation are 9

Now,

\begin{gathered}\implies \small \sf Average =\frac{23+33+33+27+25+68+27+44+72}{9}\\\end{gathered}

\begin{gathered}\\\implies \small \sf Average =\frac{56+60+93+71+72}{9}\\\end{gathered}

\begin{gathered}\\\implies \sf Average =\frac{116+164+72}{9}\\\end{gathered}

\begin{gathered}\\\implies \sf Average =\frac{352}{9}\\\end{gathered}

\begin{gathered}\\\implies \sf Average = 39.1 \\\end{gathered}

\longrightarrowThe Average of given set of numbers is 39.1 .

∴ Option C) is correct ✔️

3 0
2 years ago
Read 2 more answers
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