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Leno4ka [110]
2 years ago
12

What is the equation of the axis of symmetry for the parabola y equals start fraction one over three end fraction left parenthes

is x plus one right parenthesis squared minus three?
Mathematics
1 answer:
wariber [46]2 years ago
6 0
The correct axis of symmetry is x = -1.

Explanation:

Our equation is
y=\frac{1}{3}(x+1)^2-3.

This is in vertex form, which is 
y = a(x-h)² + k, where (h, k) is the vertex.

In our equation, h corresponds with -1 and k corresponds with -3, making the vertex (-1, -3).

The axis of symmetry is the x-coordinate of the vertex; this makes the axis of symmetry for this equation x = -1.
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Let the smallest of 4 consecutive odd numbers be 2 n + 1 , where n is an integer. Show, using algebra, that the sum of any 4 con
andrey2020 [161]

Answer:

Expression is 8(n+2)

Step-by-step explanation:

smallest of 4 consecutive odd numbers =2n + 1

consecutive odd integers are found by adding 2 to the any given odd numbers

Thus, 2nd consecutive odd integers  = 2n + 1 + 2 = 2n + 3

3rd consecutive odd integers  = 2n + 3 + 2 = 2n + 5

2nd consecutive odd integers  = 2n + 5 + 2 = 2n + 7

Thus, 4 consecutive odd integers are

2n + 1 ,2n + 3,2n + 5,2n + 7

sum of these numbers are = 2n + 1 +2n + 3 + 2n + 5+2n + 7 = 8n+16

sum of these numbers are = 8(n+2)

Thus, we see that the sum of numbers are 8(n+2)

As, 8 is common for n+2, whatever is value of n, the number will be multiple of 8 .

thus expression is 8(n+2)

7 0
3 years ago
How do you do this??<br> 14cents/oz = $__/Ib<br> ????????????????
yarga [219]

Answer:

$2.24 / lb

Step-by-step explanation:

$1 = 100 cents

16 oz = 1 lb

14 cents/oz *\frac{1 dollar}{100 cents}*\frac{16oz}{1lb}

Simplified,

\frac{14 *16}{100}

\frac{224}{100} = $2.24/ lb

6 0
3 years ago
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Jeff's math grade is based on two quizzes, two tests, and one project. The table shows Jeff’s scores on these items, as well as
vazorg [7]

Answer:

Step-by-step explanation:

If you can post the table then I'lI be happy to help

6 0
2 years ago
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A pom-pom manufacturer makes each of its pom-poms with 35% white strands (w), 25% blue strands (b), and 40% red strands (r). If
DIA [1.3K]

Answer:

28 white strands , 20 blue strands and 32 red strands are needed to make a pair of pom-poms

Step-by-step explanation:

Given :A pom-pom manufacturer makes each of its pom-poms with 35% white strands (w), 25% blue strands (b), and 40% red strands (r).

To Find : If each pom-pom has a total of 80 strands, how many of strands of each color are needed to make a pair of pom-poms?

Solution:

Total Strands = 80

White Strands = 35%

No. of white strands = 35\% \times 80 =\frac{35}{100} \times 80 =28

Blue Strands = 25%

No. of blue strands = 25\% \times 80 =\frac{25}{100} \times 80 =20

Red Strands = 40%

No. of Red strands = 40\% \times 80 =\frac{40}{100} \times 80 =32

Hence 28 white strands , 20 blue strands and 32 red strands are needed to make a pair of pom-poms

3 0
3 years ago
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Prove that the triangle EDF is isosceles. Give reasons for your answer.
Gekata [30.6K]

Answer:

\triangle EDF is isosceles.

Step-by-step explanation:

Please have a look at the attached figure.

We are <u>given</u> the following things:

\angle EDF = y

\text{External }\angle DFG = 90 +\dfrac{y}{2}

Let us try to find out \angle E and \angle DFE. After that we will compare them.

<u>Finding </u>\angle DFE<u>:</u>

Side EG is a straight line so \angle GFE = 180

\angle GFE is sum of internal \angle DFE and external \angle DFG

\angle GFE = 180 = \angle DFE  + \angle DFG\\\Rightarrow 180 = \angle DFE + (90+\dfrac{y}{2})\\\Rightarrow \angle DFE = 180 - 90 - \dfrac{y}{2}\\\Rightarrow \angle DFE = 90 - \dfrac{y}{2} ....... (1)

<u>Finding </u>\angle E<u>:</u>

<u>Property of external angle:</u> External angle in a triangle is equal to the sum of two opposite internal angles of a triangle.

i.e. external \angle DFG = \angle E + \angle EDF

\Rightarrow 90+\dfrac{y}{2} = \angle E + y\\\Rightarrow \angle E = 90+\dfrac{y}{2}  -y\\\Rightarrow \angle E = 90-\dfrac{y}{2} ....... (2)

Comparing equations (1) and (2):

It can be clearly seen that:

\angle DFE = \angle E =90-\dfrac{y}{2}

The two angles of \triangle EDF are equal hence \triangle EDF is isosceles.

8 0
3 years ago
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