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3 years ago

A^2+14a-51=0 solve the quadratic by completing the square.

2 answers:

8 0

A^2+14a-51=0
Add 51 to both sides
a^2+14a-51+51=0+51
a^2+14a=51
add (14/2)^2
a^2+14a+(14/2)^2=100
Solve a+7=+sqrt 100: a=3
Solve a-7 = -sqrt 100: a=-17
a=3 a=-17

ehidna [41]3 years ago

7 0

Steps if you have ax^2+bx+c=0
1. put vairable on other side (-c from both sides)
2. make sure that leading term is 1 (ax^2+bx+c=0 where a=1)
3. take half of b and square it

so
a^2+14a-51=0
move c to other side
add 51 to both sides
a^2+14a=51
leading term is 1
take 1/2 of b and square
14/2=7, 7^2=49
add that to both sides
a^2+14a+49=51+49
factor perfect square
(a+7)^2=100
square root both sides
a+7=+/-10

a+7=10
a+7=-10

a+7=10
minus 7
a=3

a+7=-10
subtract 7
a=-17

a=3 or -17

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Find the difference between 6/7 and 2/3 in lowest terms.

kramer

As per the problem,

we have been asked to find the difference of the given fractions.

The given fractions are $\frac{6}{7} \ and \ \frac{2}{3}$

$\frac{6}{7}-\frac{2}{3}$

Make denominator equal and simplify we get

$\Rightarrow \frac{6}{7}-\frac{2}{3} =\frac{6}{7}*\frac{3}{3}-\frac{2}{3}*\frac{7}{7} \\\\\Rightarrow \frac{6}{7}-\frac{2}{3} =\frac{18}{21}-\frac{14}{21} \\\\\Rightarrow \frac{6}{7}-\frac{2}{3} =\frac{18-14}{21}\\\\\Rightarrow \frac{6}{7}-\frac{2}{3} =\frac{4}{21}$

The difference of the given fractions=4/21

8 0

3 years ago

Read 2 more answers

Elisa has 10 gold colored coins and 6 silver colored coins. She selects 2 coins with replacement. What is the probability she se

amm1812

Answer: $\frac{9}{64}$

Step-by-step explanation:

n(gold colored coins) = 10

n(silver colored coins) = 6

Total number of coins = 16

since there is replacement , the probability she selects 2 silver colored coins will be :

$\frac{6}{16}$ x $\frac{6}{16}$

= $\frac{3}{8}$ x $\frac{3}{8}$

= $\frac{9}{64}$

Therefore : the probability she selects 2 silver colored coins is $\frac{9}{64}$

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4 years ago

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There are 4 pizzas and 3 people. How much would each person get if each person had the same amount?

julia-pushkina [17]

Each person would have 4/3 of a pizza, or C.

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3 years ago

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In Which Quadrant is this true

34kurt

Given:

$\sin \theta$

$\tan \theta$

To find:

The quadrant in which $\theta$ lie.

Solution:

Quadrant concept:

In Quadrant I, all trigonometric ratios are positive.

In Quadrant II, only $\sin\theta$ and $\csc\theta$ are positive.

In Quadrant III, only $\tan\theta$ and $\cot\theta$ are positive.

In Quadrant IV, only $\cos\theta$ and $\sec\theta$ are positive.

We have,

$\sin \theta$

$\tan \theta$

Here, $\sin\theta$ is negative and $\tan\theta$ is also negative. It is possible, if $\theta$ lies in the Quadrant IV.

Therefore, the correct option is D.

5 0

3 years ago

Order the values of the differences from least to greatest. First, write the fractions as decimals. StartFraction 4 Over 5 EndFr

ddd [48]

Complete Question:

Ms. Perez's biology class grew sunflowers to learn about plants. During the first week, the average sunflower grew 3 inches. The table shows the difference from the average for three students.

Order the values of the differences from least to greatest.

Student: Raj. Difference (in.): 4/5

Student: Clara. Difference (in.): -1 1/2

Student: Jacob. Difference (in.): 0.9

Answer:

$-1.5$ , $0.8$ and $0.9$