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Alex787 [66]
3 years ago
15

What’s the slope of the line?

Mathematics
1 answer:
Aleksandr [31]3 years ago
8 0

Answer: 2

Step-by-step explanation:

\frac{rise}{run} = \frac{2}{1}

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Which of the following is a solution to 2cos2x − cos x − 1 = 0?
Pavel [41]

Answer:

Option A is correct.

Solution for the given equation is, x = 0^{\circ}

Step-by-step explanation:

Given that : 2\cos^2x -\cos x -1 =0

Let \cos x =y

then our equation become;

2y^2-y-1= 0           .....[1]

A quadratic equation is of the form:

ax^2+bx+c =0.....[2] where a, b and c are coefficient and the solution is given by;

x = \frac{-b\pm \sqrt{b^2-4ac}}{2a}

Comparing equation [1] and [2] we get;

a = 2 b = -1 and c =-1

then;

y = \frac{-(-1)\pm \sqrt{(-1)^2-4(2)(-1)}}{2(2)}

Simplify:

y = \frac{ 1 \pm \sqrt{1+8}}{4}

or

y = \frac{ 1 \pm \sqrt{9}}{4}

y = \frac{ 1 \pm 3}{4}

or

y = \frac{1+3}{4} and y = \frac{1 -3}{4}

Simplify:

y = 1 and y = -\frac{1}{2}

Substitute y = cos x we have;

\cos x = 1

⇒x = 0^{\circ}

and

\cos x = -\frac{1}{2}

⇒ x = 120^{\circ} \text{and} x = 240^{\circ}

The solution set:  \{0^{\circ}, 120^{\circ} , 240^{\circ}\}

Therefore, the solution for the given equation  2\cos^2x -\cos x -1 =0 is, 0^{\circ}





8 0
4 years ago
Read 2 more answers
SIS<br> 2log(x + 86) = 4<br> EE<br> S<br> -
mina [271]

Answer:I think your Answer would be x=14 but I am not sure.

Step-by-step explanation:

2log 10 (x+86)=4

Determine the defined

2log 10 (x+86)=4,x >-86

Divide both sides by 2

log 10 (x+86)=2

Solve by converting the logarithm into exponential form

x+86=10 2

Evaluate the power

x+86=100

Move constant to the right

x=100-86

Subtract the numbers

x=14,x>-86

Check if the solution is in the defined range

SOLUTION

X=14

4 0
3 years ago
Pls pls help me pls help me
notka56 [123]

Answer:

68m squared or the first option

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
What is the surface area of a box with a height and width of 5 inches and a length of 8 inches ?
vodomira [7]

Answer:

210 sq in

Step-by-step explanation:

Box dimensions: 5 x 5 x 8

2 faces: 5 x 5 -> 2 * 5 * 5 = 50

4 faces: 5 x 8 -> 4 * 5 * 8 = 160

Total = 50 + 160 = 210 sq in

5 0
3 years ago
Find the sum of <br> -6 1/8+1 1/4
Vlad [161]

Answer:

\large\boxed{-4\dfrac{7}{8}=-4.875}

Step-by-step explanation:

To add two fractions, they must have the same denominator.

LCD = 8

1\dfrac{1}{4}=1\dfrac{1\cdot2}{4\cdot2}=1\dfrac{2}{8}

-6\dfrac{1}{8}+1\dfrac{1}{4}=-6\dfrac{1}{8}+1\dfrac{2}{8}=-\left(6\dfrac{1}{8}-1\dfrac{2}{8}\right)=(*)\\\\\text{We know}\ 1=\dfrac{8}{8},\ 6=5+1=5+\dfrac{8}{8}=5\dfrac{8}{8}.\\\\\text{Therefore}\ 6\dfrac{1}{8}=5\dfrac{8+1}{8}=5\dfrac{9}{8}\\\\(*)=-\left(5\dfrac{9}{8}-1\dfrac{2}{8}\right)=-\bigg((5-1)+\dfrac{9-2}{8}\bigg)=-\bigg(4+\dfrac{7}{8}\bigg)=-4\dfrac{7}{8}

You can convert the fractions to the decimals.

6\dfrac{1}{8}=8.125\\\\1\dfrac{1}{4}=1.25\\\\-6\dfrac{1}{8}+1\dfrac{1}{4}=-6.125+1.25=1.25-6.125=-4.875

5 0
4 years ago
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