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s2008m [1.1K]
3 years ago
15

Can someone help me solve this please. I forgot how to so if you could explain please.

Mathematics
2 answers:
Licemer1 [7]3 years ago
8 0

So for this, I will be using the quadratic formula, which is x=\frac{-b\pm \sqrt{b^2-4ac}}{2a} , with a = x^2 coefficient, b = x coefficient, and c = constant. Using our equation, plug the numbers in their appropriate spots:

x=\frac{-10\pm \sqrt{10^2-4*1*(-2)}}{2*1}

Next, solve the exponent and the multiplications:

x=\frac{-10\pm \sqrt{100-(-8)}}{2}\\\\x=\frac{-10\pm \sqrt{100+8}}{2}

Next, solve the addition:

x=\frac{-10\pm \sqrt{108}}{2}

Next, apply the product rule of radicals here and simplify the radical:

  • Product rule of radicals: √ab = √a × √b

\sqrt{108}=\sqrt{6}\times \sqrt{18}=\sqrt{3} \times \sqrt{2} \times \sqrt{9} \times \sqrt{2} =3\times 2\times \sqrt{3}=6\sqrt{3}\\\\x=\frac{-10\pm 6\sqrt{3}}{2}

Next, divide:

x=-5\pm 3\sqrt{3}}

*<u>The above is your exact solution. Approximates (rounded to the hundreths) are below:</u>

Next, solve the equation twice, once with the + symbol and once with the - symbol:

x=-5\pm 3\sqrt{3}}\\x=0.20, -10.20

Luba_88 [7]3 years ago
5 0

Hi,

Let's solve the equation step-by-step.

x2+10x−2=0

Step 1: Use quadratic formula with a=1, b=10, c=-2.

x= −b±√b2−4ac  / 2a

x=  −(10)±√(10)2−4(1)(−2)  / 2(1)

x=  −10±√108  / 2

x=−5+3√3 or x=−5−3√3

Answer:

x=−5+3√3 or x=−5−3√3

Have a great day!

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In the △ABC, the height AN = 24 in, BN = 18 in, AC = 40 in. Find AB and BC. Consider all possible cases. Case 1 : N∈BC, AB = __,
aivan3 [116]

Answer:

Case 1:

AB = 30

BC = 50

Case 2:

AB = 15.9

BC = 36.7

Case 3: Not possible

Step-by-step explanation:

Given

See attachment for illustration of each case

Required

Find AB and BC

Case 1:

Using Pythagoras theorem in ANB, we have:

AB^2 = AN^2 + BN^2

This gives:

AB^2 = 24^2 + 18^2

AB^2 = 576 + 324

AB^2 = 900

Take square roots of both sides

AB = \sqrt{900

AB = 30

To calculate BC, we consider ANC, where:

AC^2 = AN^2 + NC^2

40^2 = 24^2 + NC^2

1600 = 576 + NC^2

Collect like terms

NC^2 = 1600 - 576

NC^2 = 1024

Take square roots

NC = \sqrt{1024

NC = 32

So:

BC = NC + BN

BC = 32 + 18

BC = 50

Case 2:

Using Pythagoras theorem in ANB, we have:

AN^2 = AB^2 + BN^2

This gives:

24^2 = AB^2 + 18^2

576 = AB^2 + 324

Collect like terms

AB^2 = 576 - 324

AB^2 = 252

Take square roots of both sides

AB = \sqrt{252

AB = 15.9

To calculate BC, we consider ABC, where:

AC^2 = AB^2 + BC^2

40^2 = 252 + BC^2

1600 = 252 + BC^2

Collect like terms

BC^2 = 1600 - 252

BC^2 = 1348

Take square roots

BC = \sqrt{1348

BC = 36.7

Case 3:

This is not possible because in ANC

The hypotenuse AN (24) is less than AC (40)

3 0
2 years ago
Find an expression that is equivalent to 1 - 1/3 + 1/5 . Use denominator of 15 . plz help
love history [14]
1 - 5/15 + 3/15
Just use common denominators!
Hope that helped. :)
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3 years ago
The number of Calories c that are burned by walking depends on t, the number of hours spent walking. If you burn 300 Cal/h, how
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300/2.5= 120 Calories

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3 years ago
A<br> Write the equation for<br> line that<br> passes through (1, 1) and (-1,7)
KengaRu [80]

Answer:y=-3x+4

Step-by-step explanation:

You want to find the equation for a line that passes through the two points:

(1,1) and (-1,7).

First of all, remember what the equation of a line is:

y = mx+b

Where:

m is the slope, and

b is the y-intercept

First, let's find what m is, the slope of the line...

The slope of a line is a measure of how fast the line "goes up" or "goes down". A large slope means the line goes up or down really fast (a very steep line). Small slopes means the line isn't very steep. A slope of zero means the line has no steepness at all; it is perfectly horizontal.

For lines like these, the slope is always defined as "the change in y over the change in x" or, in equation form:

So what we need now are the two points you gave that the line passes through. Let's call the first point you gave, (1,1), point #1, so the x and y numbers given will be called x1 and y1. Or, x1=1 and y1=1.

Also, let's call the second point you gave, (-1,7), point #2, so the x and y numbers here will be called x2 and y2. Or, x2=-1 and y2=7.

Now, just plug the numbers into the formula for m above, like this:

m=

7 - 1

-1 - 1

or...

m=

6

-2

or...

m=-3

So, we have the first piece to finding the equation of this line, and we can fill it into y=mx+b like this:

y=-3x+b

Now, what about b, the y-intercept?

To find b, think about what your (x,y) points mean:

(1,1). When x of the line is 1, y of the line must be 1.

(-1,7). When x of the line is -1, y of the line must be 7.

Because you said the line passes through each one of these two points, right?

Now, look at our line's equation so far: y=-3x+b. b is what we want, the -3 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the two points (1,1) and (-1,7).

So, why not plug in for x and y from one of our (x,y) points that we know the line passes through? This will allow us to solve for b for the particular line that passes through the two points you gave!.

You can use either (x,y) point you want..the answer will be the same:

(1,1). y=mx+b or 1=-3 × 1+b, or solving for b: b=1-(-3)(1). b=4.

(-1,7). y=mx+b or 7=-3 × -1+b, or solving for b: b=7-(-3)(-1). b=4.

See! In both cases we got the same value for b. And this completes our problem.

The equation of the line that passes through the points

(1,1) and (-1,7)

is

y=-3x+4

8 0
3 years ago
For the given triangles select the lengths of the sides.
aivan3 [116]

Answer:

v=3

u=6

x=2√2

y=2√2

Step-by-step explanation:

First triangle :

tanΦ=v/3√3

tan30=v/3√3

(√3)/3=v/(3√3)

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9/3=v

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0.5xu=3

0.5u=3

Divide both sides by 0.5

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Second triangle :

sin45=x/4

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x=4 x sin45

x=4 x (√2)/2

x=2√2

Cos45=y/4

Cross multiply

4 x Cos45=y

4 x (√2)/2=y

(4√2)/2=y

2√2=y

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5 0
3 years ago
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