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3 years ago

Please help solve the problem: (x+7)^2-7=25

Mathematics

2 answers:

Mila [183]3 years ago

6 0

Answer:

x = -7 ±4sqrt(2)

Step-by-step explanation:

(x+7)^2-7=25

Add 7 to each side

(x+7)^2-7+7=25+7

(x+7)^2=32

Take the square root of each side

sqrt((x+7)^2)=±sqrt(32)

x+7=±sqrt(32)

Subtract 7 from each side

x+7-7 = -7 ±sqrt(32)

x = -7 ±sqrt(32)

We can simplify the sqrt (32)

x = -7 ±sqrt(16*2)

x = -7 ±4sqrt(2)

frutty [35]3 years ago

3 0

Answer:

x=−7+4√2 or x=−7−4√2

Step-by-step explanation:

x^2+14x+42=25

x^2+14x+42−25=25−25

x^2+14x+17=0

For this equation: a=1, b=14, c=17

1x^2+14x+17=0

Step 3: Use quadratic formula with a=1, b=14, c=17.

−b±√b2−4ac

−(14)±√(14)2−4(1)(17)

2(1)

−14±√128

x=−7+4√2 or x=−7−4√2

pls give brainliest :))

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Answer:

GCF(2y²z , 8yz²) = 2yz

Step-by-step explanation:

2y²z = (2yz) × y

8yz² = (2yz) × 4z

then

GCF(2y²z , 8yz²) = 2yz

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2 years ago

Find area of the isosceles triangle formed by the vertex and the x-intercepts of parabola y=x2+4x−12.

xz_007 [3.2K]

The area of the isosceles triangle is 64 sq units.

Solution:

Part 1: x-intercepts

The x-intercepts occur at the points on the function where y=0

So, we need to solve

$x^2-4x-12=0$

The left side factors fairly easily into:

$(x-6)(x+2)=0$

So solution occur when

$x-6=0\rightarrow x=6$

and

$x+2=0\rightarrow x=(-2)$

So the x-intercepts are at (0,6) and (0,−2)

Part 2: vertex of the parabola

The vertex of a simple quadratic parabola occurs when the derivative of the quadratic is equal to 0.

The derivative of the given quadratic is

$\frac{dy}{dx}=2x-4$

By observation, this is equal to 0 when x=2

When x=2 the original equation becomes

$y=(2)^2-4(2)-12$

$y=-16$

Therefore the vertex of this parabola is at (2,−16)

The endpoints of the base of the isosceles triangle are (-6, 0) and (2, 0)

$\Rightarrow$ so its base is 8

The height of the triangle reaches from the midpoint of the base (-2, 0) and the vertex (2, -16)

$\Rightarrow$ so its height is 16

The area is $\frac{1}{2}\times \text { base }\times \text { height }=\frac{1}{2}\times8\times16=64 \text{ sq units }$

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3 years ago

What is the slope of (2,22) -(4,32) a.5 b.10 c.2 d.1

zhenek [66]

Use the formula for the slope of a line by substituting the given coordinates:
$\frac{ y_{2}-y_{1}}{ x_{2} - x_{1} }$
So for the coordinates (2,22) and (-4,-32)
So (-32-22)/(-4-2)= -54/-6= 9 is the slope of the line

6 0

3 years ago

Mr. Kim borrows $3,000 to pay for house repairs. The simple interest is 8% for one year.

Archy [21]

Answer:

3240

Step-by-step explanation:

If the simple interest is 8%, Mr. Kim will have to pay $3000, and the simple interest, which will be 8% of $3000.

You can write it in two ways:

3000+3000*0.08= 3240

3000*1.08= 3240

5 0

3 years ago

Read 2 more answers

Find the value of x (PICTURE LINKED)

yaroslaw [1]

Answer:

x=4

Step-by-step explanation:

the triangles are directly porportional.

if 2.5 is half of 5, to find x is just half of 8.

3 0

4 years ago