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blsea [12.9K]
1 year ago
9

Solve the following question

Mathematics
1 answer:
Svetach [21]1 year ago
4 0

Answer:

x=-1

Step-by-step explanation:

First we can square both sides to remove the square roots:

(\sqrt{x+7})^{2}  +(\sqrt{x+2})^{2} = (\sqrt{6x+13})^{2}

Simplify:

x+7+x+2=6x+13

Now we simplify further:

2x+9=6x+13

Now we subtract 13 from both sides:

2x+9-13=6x+13-13

Simplify:

2x-4=6x

Subtract 2x from both sides:

2x-4-2x=6x-2x

Simplify:

-4=4x

Divide both sides by 4:

\frac{-4}{4} = \frac{4x}{4}

Simplify:

-1=x

x=-1

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3 years ago
Sketch three possible rectangle of perimeter 20 feet
mina [271]
1. L1= 7 L2=7 W1= 3 W2=3   2. L1= 5 L2=5 W2=5 W2=5   3. L1= 6 L2=6 W1=4 W2=4  


4 0
3 years ago
The face of the triangular concrete panel shown has an area of 22 square meters, and its base is 3 meters longer than twice its
Elodia [21]

Answer:

The length of the base is 11 meters.

Step-by-step explanation:

The diagram of the triangle is not shown; However, the given details are enough to solve this question.

Given

<em>Shape: Triangle</em>

<em>Represent the height with h and the base with b</em>

b = 3 + 2h

Area = 22

Required

Find the length of the base

The area of a triangle is calculated as thus;

Area = \frac{1}{2} * b * h

Substitute 22 for Area and 3 + 2h for b

The formula becomes

22 = \frac{1}{2} * (3 + 2h) * h

Multiply both sides by 2

2 * 22 = 2 * \frac{1}{2} * (3 + 2h) * h

44 = (3 + 2h) * h

Open the bracket

44 = 3 * h + 2h * h

44 = 3h + 2h^2

Subtract 44 from both sides

44 - 44 = 3h + 2h^2 - 44

0 = 3h + 2h^2 - 44

Rearrange

0 = 2h^2 +3h - 44

2h^2 +3h - 44 = 0

At this point, we have a quadratic equation; which is solved as follows:

2h^2 +3h - 44 = 0

2h^2 + 11h - 8h - 44 = 0

h(2h + 11) - 4(2h + 11) = 0

(h - 4)(2h + 11) = 0

Split the above

(h - 4) = 0\ or\ (2h + 11) = 0

h - 4 = 0\ or\ 2h + 11 = 0

Solve the above linear equations separately

h - 4 = 0

Add 4 to both sides

h - 4 + 4 = 0 + 4

h = 0 + 4

h = 4 ---- <em>First value of h</em>

2h + 11 = 0

Subtract 11 from both sides

2h + 11 - 11 = 0 - 11

2h  = 0 - 11

2h = -11

Divide both sides by 2

\frac{2h}{2} = -\frac{11}{2}

h = -\frac{11}{2}<em> ------ Second value of h</em>

Since height can be negative, we'll discard h = -\frac{11}{2}

Hence, the usable value of height is h = 4

Recall that b = 3 + 2h

Substitute 4 for h

b = 3 + 2(4)

b = 3 + 8

b = 11

Hence, the length of the base is 11 meters

3 0
3 years ago
The volume of a cylinder is 47x3 cubic units and its height is x units.
allochka39001 [22]

Answer:

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Step-by-step explanation:

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3 years ago
What is the value of x
aivan3 [116]

Answer:

x=14√3 and y=28

Step-by-step explanation:

This is a 30, 60, 90 triangle. We have to multiply 14 by 2 to get the hypotenuse. In this case, the hypotenuse is y. 14x2 is equal to 28. Therefore, y=18. The long side is equal to the small side times the √3. Therefore, x is equal to 14√3. Therefore, x=14√3 and y=28.

If this has helped you please mark as brainliest

4 0
2 years ago
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