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3 years ago

Write the quadratic function 5x2 - 40x + 60 in its vertex form by completing the square. Then

Mathematics

2 answers:

aleksandr82 [10.1K]3 years ago

5 0

9514 1404 393

Answer:

5(x -4)² -20
turning point = (4, -20)

Step-by-step explanation:

It can work well to factor the leading coefficient from the x-terms.

5(x² -8x) +60

Now, add the square of half the x-coefficient inside parentheses, and subtract the same amount outside parentheses.

5(x² -8x +16) +60 -(5)(16)

5(x -4)² -20 . . . . write as a square, simplify the added constant

The vertex form is ...

5(x -4)² -20

It shows you the vertex is (4, -20). This is the turning point.

_____

Vertex form is a(x -h)² +k, where (h, k) is the vertex.

siniylev [52]3 years ago

3 0

There’s no turning point bc the multiplicity is one

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Rex runs one mile in 5 minutes, Stan runs one mile in 6 minutes, and Tim runs one mile in 7 minutes. There are 5280 feet in one

Brums [2.3K]

Answer:

$628.5ft$

Step-by-step explanation:

Find the velocity of Tim and Stan, by dividing the distance between the time:

$v_T=\frac{5280}{7} =754.3 ft/min$

$v_S=\frac{5280}{6} =880ft/min$

The distance that Stan and Tim travel in 5 minutes is equal to their respective velocity multiplied by the time.

$d_T=754.3\times5=3771.5ft\\$

$d_S=880\times5=4400ft$

The answer to the question is the difference in miles traveled by Stan minus those traveled by Tim.

$R=4400-3771.5=628.5ft$

4 0

3 years ago

Can someone help with this question

forsale [732]

11-15 Why: cause it’s beside 8 and 10

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3 years ago

Enny studied the characteristics of two species of bacteria. The number of bacteria of species A, A(t), after t hours is represe

fomenos

The number of bacteria in species A at time t is given by: $A(t)=5+(.25t) ^{3}$ .

The number of bacteria in species B at time t is given by $B(t)=2+8(1.06)t$

You are asked to find N(t) which is the difference in the species at time t. Difference refers to the answer is a subtraction problem. Thus, we are asked to find N(t) = A(t)-B(t)

We subtract and obtain: $N(t)=5+(.25t) ^{3}-(2+8(1.06)t )=5-2+(.25t) ^{3}-(8(1.06)t )$
That is, $N(t)=3+(.25t) ^{3}-(8(1.06)t )$ which is the last answer choice.

With respect to notation, it is common to denote an exponent using ^. So if we want to write $(.25t) ^{3}$ we can write "(.25t)^3"

5 0

4 years ago

Read 2 more answers

estimate the sum or difference. 4/5+3/7, round 4/5 to its closest benchmark. round 3/7 to its closest benchmark. add to find the

Ann [662]

Answer:

About 1.5

Step-by-step explanation:

We can round 4/5 to 1.

We can round 3/8 to 4/8 = 1/2.

So our estimate is

4/5 + 3/8 =

about 1 + 1/2 = 1.5

(Shh... let's check using the calculator... it's 1.2. We were pretty close!)

7 0

3 years ago

A piece of paper has an area of 93.5 square inches. How many times does it need to be folded in half before the area is less tha

borishaifa [10]

Answer:

7 times.

Step-by-step explanation:

Keep dividing 93.5 by 2 until it becomes less than 1.

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3 years ago

Read 2 more answers