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kkurt [141]
3 years ago
15

Solve the quadratic equation: 2(x-3)^2-24-0

Mathematics
1 answer:
Keith_Richards [23]3 years ago
7 0

Answer:

x=3+2×sqrt(3)

x=3-2×sqrt(3)

Step-by-step explanation:

2(x-3)²-24=0

2(x-3)²=24

(x-3)²=12

Case 1:

x-3=sqrt(12)=2×sqrt(3)

x=3+2×sqrt(3)

Case 2:

x-3=-sqrt(12)=-2×sqrt(3)

x=3-2×sqrt(3)

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A bag contains 150 marbles. Some are blue, and the rest are white. There are 21 blue marbles for every 4 white marbles. How many
Olin [163]

Given:

Total number of marbles in the bag = 150

There are 21 blue marbles for every 4 white marbles.

To find:

The number of blue marbles in the bag.

Solution:

Since, there are 21 blue marbles for every 4 white marbles, therefore the ratio of blue marble to white marbles is 21:4.

Let the number of blue marbles be 21x and white marbles be 4x.

Total number of marbles in the bag = 150

21x+4x=150

25x=150

Divide both sides by 25.

x=\dfrac{150}{25}

x=6

Now,

\text{Blue marbles}=21x

\text{Blue marbles}=21(6)

\text{Blue marbles}=126

Therefore, the number of blue marbles is 126.

8 0
3 years ago
The height of a tree, y, is related to the length of its shadow, x, by the equation y = kx. If a tree's height is 24 feet and it
Marta_Voda [28]

Answer:

The value of k is 8/3

Step-by-step explanation:

To find this, start with the base equation and input the values. Then solve for k.

y = kx

24 = k9

24/9 = k

8/3 = k

6 0
3 years ago
To steam rice, Paul uses m cups of water for every p
GenaCL600 [577]

Answer:

\frac{(p + 2)m}{p}

Step-by-step explanation:

Given

m cups of water = p cups of rice

Required

Cups of water required for p + 2 cups of rice

<em>The question shows a direct proportion between cups of rice and cups of water.</em>

<em>So, the first step is to get the proportionality constant (k)</em>

<em />

This is calculated using the following expression;

m = k * p

Where k represents cups of water and p represents cups of rice

Make k the subject of formula

k = \frac{m}{p}

Let x represents cups of water when cups of rice becomes p + 2;

k becomes:

k = \frac{x}{p + 2}

Equate both expressions of k; to give

\frac{m}{p} = \frac{x}{p + 2}

Multiply both sides by p + 2

(p + 2) * \frac{m}{p} =(p + 2) *  \frac{x}{p + 2}

(p + 2) * \frac{m}{p} =x

x = (p + 2) * \frac{m}{p}

x =  \frac{(p + 2)m}{p}

<em>Hence, the expression that represents the cups of water needed is </em>\frac{(p + 2)m}{p}<em></em>

4 0
3 years ago
(( all - Same )) ----- Quadrilaterals are polygons
Marina CMI [18]

Answer:

yes

Step-by-step explanation:

6 0
4 years ago
The difference between the water levels for high and low tide was 3.6 feet. The low is .2 foot. Write an equation to find the wa
serg [7]
.2+3.6=3.8 because all you do is add the .2 feet with 3.6 feet
6 0
3 years ago
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