2. Find the measure of eº.

Step-by-step explanation:

perpendicular bisector

AB= 17

Answer:

y = 4/5x - 18/5

Step-by-step explanation:

y = mx + b

m = 4/5

(2, -2)

-2 = 8/5 + b

b = -10/5 - 8/5 = -18/5

y = 4/5x - 18/5

Answer:

(х + 1)(х - 2)

Step-by-step explanation:

х²-х-2=(х + 1)(х - 2)

Answer:

= 4/15

Step-by-step explanation:

=4 . 2/5  /6

= 4/15

Answer:

0.26

Step-by-step explanation:

4 (2/5) /6

2/5 = 0.4

4 × 0.4 = 1.6

1.6 / 6 = 0.26

The answer is 0.26

Answer:

x = 0, π/3, 2π/3,  π,  4π/3,  5π/3

Step-by-step explanation:

4cos^4(x) – 5cos^2(x) + 1 = 0

(4cos^2(x) - 1)(cos^2(x) - 1) = 0

When 4cos^2(x) - 1 = 0

cos^2(x) = 1/4

cos x = +/-1/2

so x = π/3, 2π/3, 4π/3, 5π/3.

When cos^2x - 1 = 0

cos x = +/- 1

x =  0, π.

x

The solution is : x = 0, π/3, 2π/3,  π,  4π/3,  5π/3

Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.

here, we have,

given that,

4cos^4(x) – 5cos^2(x) + 1 = 0 from [0, 2π)

so, we get,

4cos^4(x) – 5cos^2(x) + 1 = 0

(4cos^2(x) - 1)(cos^2(x) - 1) = 0

When 4cos^2(x) - 1 = 0

cos^2(x) = 1/4

cos x = +/-1/2

so x = π/3, 2π/3, 4π/3, 5π/3.

When cos^2x - 1 = 0

cos x = +/- 1

x =  0, π.

Hence, The solution is : x = 0, π/3, 2π/3,  π,  4π/3,  5π/3.

To learn more on simplification click:

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Answer:

6[tex]\sqrt{3}[/tex]

Step-by-step explanation:

we use Euclidian theorem to find n

n^2 = 6*18

n^2 = 108

n = 6[tex]\sqrt{3}[/tex]

Answer:

f+g = 11x-8

f*g = 28x^2 - 47x+15

Step-by-step explanation:

f(x) = 4x - 5 and g(x) = 7x -3

(f+g)(x) = 4x - 5  + 7x -3

Combine like terms

         = 4x+7x -5-3

        = 11x-8

(f * g) (x) = ( 4x - 5) (7x -3)

FOIL

          = 4x*7x + 4x(-3) + (-5)(7x) + (-5)(-3)

            =28x^2 -12x-35x+15

Combine like terms

            =28x^2 - 47x+15

Step-by-step explanation:

Step 1:  Find (f + g)(x)

The definition of (f + g)(x) is f(x) + g(x).  Basically add the two functions together.  

[tex]f(x) + g(x)[/tex]

[tex](4x - 5) + (7x - 3)[/tex]

[tex]11x - 8[/tex]

Answer:  [tex]11x - 8[/tex]

Step 2:  Find (f * g)(x)

The definition of (f * g)(x) is f(x) * g(x).  Basically multiply the two functions together.  

[tex]f(x) * g(x)[/tex]

[tex](4x - 5) * (7x - 3)[/tex]

[tex](4x * 7x) + (4x * -3) + (-5 * 7x) + (-5 * -3)[/tex]

[tex](28x^{2}) + (-12x) + (-35x) + (15)[/tex]

[tex]28x^{2} - 47x + 15[/tex]

Answer:  [tex]28x^{2} - 47x + 15[/tex]

To find the indicated angle, we can use one of the three main trigonometric functions: sine, cosine, or tangent.

Remember: SOH-CAH-TOA

Looking from the angle, we know the adjacent side and the hypotenuse. Therefore, we should use cosine to solve.

cos(x) = 12/36

x = cos^-1(12/36)

x = 71 degrees

Hope this helps!

Answer:

is it 2/5 I could be wrong

Answer:

∠9 and ∠12

Step-by-step explanation:

Supplementary angles are two angles that add up to 180. Looking at all the answer choices, A, C, and D have either Big-Big angle or Small-Small angle. What we need is Big-Small angle that is next to eachother, which is ∠9 and ∠12.

Hope this helped.

(Also sorry!)

A and B

I hoped it helped you

Answer:

[tex]a\cdot b\cdot c=\frac{15}{4}[/tex]

Step-by-step explanation:

Vertex is the minimum or maximum point of parabola

Vertex of parabola is (h,k)

Therefore, from given graph (-3,-2) is the lowest point.

Vertex of parabola is at (-3,-2).

Standard equation of parabola

[tex]y-k=a(x-h)^2[/tex]

Substitute the values

[tex]y-(-2)=a(x-(-3))^2=a(x+3)^2[/tex]

[tex]y+2=a(x+3)^2[/tex]

(-1,0) lies on the parabola.

Therefore, it satisfied the equation of parabola.

[tex]0+2=a(-1+3)^2=4a[/tex]

[tex]a=2/4=1/2[/tex]

Now, using the value of a

[tex]y+2=1/2(x+3)^2=1/2(x^2+6x+9)[/tex]

[tex]y+2=\frac{1}{2}x^2+3x+\frac{9}{2}[/tex]

[tex]y=\frac{1}{2}x^2+3x+\frac{9}{2}-2[/tex]

[tex]y=\frac{1}{2}x^2+3x+\frac{9-4}{2}[/tex]

[tex]y=\frac{1}{2}x^2+3x+\frac{5}{2}[/tex]

By comparing with

[tex]y=ax^2+bx+c[/tex]

We get

[tex]a=\frac{1}{2}, b=3, c=5/2[/tex]

[tex]a\cdot b\cdot c=\frac{1}{2}\times 3\times \frac{5}{2}[/tex]

[tex]a\cdot b\cdot c=\frac{15}{4}[/tex]

Answer:

Percentage error in the student measurement = 2%

Step-by-step explanation:

Percentage error = (change in length) / actual length × 100

Approximate length =294 feet

Actual length = 300 feet

Percentage error = (change in length) / actual length × 100

= (300 feet - 294 feet) / 300 feet × 100

= 6/300 × 100

= 0.02 × 100

= 2%

Percentage error in the student measurement = 2%

Answer:

4%

Step-by-step explanation:

Yearly salary = 9600 * 12 = Rs. 115200

Tax = Rs . 4530

[tex]Tax \ percent = \frac{4530}{115200}*100[/tex]

                    = 3.93 = 4%

Answer: 20

Step-by-step explanation:

X - 8 = 12

+ 8 +8

X = 20

20 gallons were in the tub to start with

Step-by-step explanation:

sqrt(x+4)

the answer is in the image above

Answer:

Every parabola has a turning point called the axis of symmetry,so for this question you just have to find the turning points

x turning point= -b/2a,and the y turning point is gotten by replacing the value of x in the equation

y=(x+1)(x-4)

=x^2-3x-4

a is 1,b is -3 and c is -4

x= -(-3)/2(1)

=1.5

and y=x^2-3x-4

=1.5^2-3(1.5)-4

= -6.25

therefore the axis of symmetry is (1.5,-6.25)

I hope this helps

Answer:

A

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

(4x)²=x+15

Answer:

78

Correct term:60

Step-by-step explanation:

We are given that

[tex]\frac{4x^4-6x^3+6x+3}{x-3}[/tex]

The quotient of this expression is given by

[tex]4x^3+6x^2+18x+78+\frac{183}{x-3}[/tex]

We have to find the term in this expression  which contains an error.

[tex]\frac{4x^4-6x^3+6x+3}{x-3}[/tex]

The quotient of this expression is given by

[tex]=4x^3+6x^2+18x+60[/tex]

[tex]Dividend=Divisor\times quotient+ remainder[/tex]

Using the formula

[tex]4x^4-6x^3+6x+3=(x-3)(4x^3+6x^2+18x+60)+\frac{183}{x-3}[/tex]

We can see that in the given expression there is 60 in place of 78.

The error in the expression of quotient is 78.

Correct term is 60.

Answer:

Step-by-step explanation:

Answer:

12.496

Step-by-step explanation:

a=10 (first term)

r= 1/5 (common ratio)

sum of first five terms

[tex] s_{5} = \frac{a( 1 - {r}^{n} ) }{1- r} [/tex]

=10{1-⅕⁵} ÷ 1-⅕

=10{1 - 1/3125} ÷ 4/5

=10{3124/3125} ÷ 4/5

=9.9968÷0.8

=12.496.

OR

a+ar+ar²+ar³+ar⁴

=10+(10x⅕)+(10x⅕²)+(10x⅕³)+(10x⅕⁴)

=10+2+0.4+0.08+0.016

=12+0.48+0.016

=12.496

Answer:

(-6, 0) and  (0, 1.5)

Step-by-step explanation:

The equation of the line in pint slope form is expressed as;

y-y0= m(x-x0)

m is the slope

(x0, y0) is the point on the line

Given

m = 1/4

(x0, y0) = (6,3)

Substitute into the formula;

y - 3 =  1/4(x-6)

4(y-3) = x - 6

4y - 12 = x-6

4y - x = -6+12

4y - x = 6

x = 4y - 6

To get the points to plot, we will find the x and y-intercept of the resulting expression.

For the x-intercept,

at y = 0

x = 4(0) - 6

x = -6

Hence the x-intercept is at (-6, 0)

For the y-intercept,

at x = 0

0 = 4y - 6

4y = 6

y = 6/4

y = 3/2

y = 1.5

Hence the y-intercept is at (0, 1.5)

Hence the required points to plot to get the required line are  (-6, 0) and  (0, 1.5)

Answer:

2cm

Step-by-step explanation:

The volume of water displaced by the rod is

v = πr^2 h = π * 3^2 * 8 = 72π cm^3

The drop in water level is the rod volume divided by the cross-section area of the tin, or

72π/(π*6^2) = 2 cm

Answer:

The answer is 100:40:50

Answer:

131 plums

Step-by-step explanation:

The fraction of plums = 10/(10+4.5)

= 10/14.5

= 100/145

So the required number of plums = 100 * 190 /145

= 131.

Answer:

D

Step-by-step explanation:

(5√2 - 4√3)^2 =

50 + 48 - 40√6 = 98 - 40√6

here's the answer to your question

Answer:

16%

Step-by-step explanation:

Use the percentage formula:

P × V1 = V2

Example:

EX: P × 30 = 1.5

P =  

1.5

30

= 0.05 × 100 = 5%