Solve the following equation by completing the square. x2-18x+78=0

Answer:

B. 12/13

Step-by-step explanation:

Hypotenuse= [tex]\sqrt{(5)^{2}+12^{2} } \\[/tex]

hypotenuse=13

opposite= 5

adjacent= 12

Cosine= adjacent/hypotenuse

cosine= 12/13

1 = 61° because it is a corresponding angle to angle 6  

2 = 119° because it is an alternate exterior angle to angle 7  

3 = 61° because it is an alternate angle to angle 1  

4 = 119° because it is an alternate angle to angle 2  

5 = 119° because it is an alternate angle to angle 7  

6 = 61° because is is an alternate angle to 61°  

7 = 119° because it and 61° are supplementary angles (total 180° together)

Answer:

1 = 61° because it is a corresponding angle to angle 6

2 = 119° because it is an alternate exterior angle to angle 7

3 = 61° because it is an alternate angle to angle 1

4 = 119° because it is an alternate angle to angle 2

5 = 119° because it is an alternate angle to angle 7

6 = 61° because is is an alternate angle to 61°

7 = 119° because it and 61° are supplementary angles (total 180° together)

Step-by-step explanation:

Answer:

ans is 13/25

Step-by-step explanation:

hope it helps!!!

Answer:

8

Step-by-step explanation:

-4x+8+2x

2x+8

compare both sides

2x+__= 2x+8

it is 8

Answer:

AC = 20

Step-by-step explanation:

Δ BDE and Δ BAC are similar, so the ratios of corresponding sides are equal, that is

[tex]\frac{AC}{DE}[/tex] = [tex]\frac{BA}{BD}[/tex] , substitute values

[tex]\frac{AC}{8}[/tex] = [tex]\frac{10}{4}[/tex] ( cross- multiply )

4AC = 80 ( divide both sides by 4 )

AC = 20

In the triangle ABC if  DE is parallel to AC then the length of AC is 12 units.

A triangle is a three-sided polygon that consists of three edges and three vertices.

Given that the triangles ABC and BDE are similar triangles.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

Let us form a proportional equation by comparing the proportional sides.

AC/DE=AD/BD

AC/8= 6/4

Apply cross multiplication

AC=48/4

Divide numerator and denominator by 4.

AC=12

Hence, in the triangle ABC if  DE is parallel to AC then the length of AC is 12 units.

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Answer:

oh wait i got it! those are oppisite from eachother so theyre angle is the same. the answer would be 59°

Answer:

b=59º

Step-by-step explanation:

Vertical angle theorem states that if angles are vertical, they are congruent.

Answer:

i am pretty sure it's a.

Step-by-step explanation:

i hope this helps :)

Answer:

it's -2sqrt7

the first answer

Step-by-step explanation:

pls mark me brainliest!

Answer:

5.4 units

Step-by-step explanation:

The diagonal AC has length

|AC|  =  √(2² + 5²) = √29 ≈ 5.4 units.

The horizontal distance from A to C is 2 units; the vertical distance is 5 units.  That's where the 2² and 5² come from.  

Answer:

z = -2.13

Therefore, the standardized z score for the state of Colorado means the score is below the mean.

Step-by-step explanation:

The formula for z score is given as:

z = (x-μ)/σ,

where

x is the raw score = 9.7%

μ is the population mean = 13.26%

σ is the population standard deviation = 1.67%

z = z score or standardize score

Hence,

z = 9.7 - 13.26/1.67

z = -2.13174

Approximately z = -2.13

Therefore, the standardized z score for the state of Colorado means the score is below the mean

Answer:

Where is the image to the equations?

Step-by-step explanation:

Answer:

there's no picture???

Step-by-step explanation:

Hello!

This is a problem about relating values of the Unit Circle.

First, we need to figure out the specific "points" of each angle measure of 30 and 60.

For the angle measure 30, the point will be [tex](\frac{\sqrt{3}}{2},\frac{1}{2})[/tex].

For the angle measure 60, the point will be [tex](\frac{1}{2},\frac{\sqrt{3}}{2})[/tex].

The tangent value of a point will be its [tex]y[/tex] value over its [tex]x[/tex] value.

[tex]\frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}}=\frac{1}{2}*\frac{2}{\sqrt{3}}=\frac{1}{\sqrt{3}}=\frac{\sqrt{3}}{3}[/tex]

The cotangent value of a point will be the reciprocal of the tangent value, which we found previously.

[tex]\frac{3}{\sqrt{3}}=\frac{3\sqrt{3}}{3}=\sqrt{3}[/tex]

The sine value of a point will be the [tex]y[/tex] value of the point.

[tex]\frac{\sqrt{3}}{2}[/tex]

So the values we have so far are [tex]\frac{\sqrt{3}}{3}+\sqrt{3}+\frac{\sqrt{3}}{2}[/tex]

Now we have to find the LCD to add these together, which in this case would be 6.

[tex]\frac{2\sqrt{3}}{6}+\frac{6\sqrt{3}}{6}+\frac{3\sqrt{3}}{6}[/tex]

Which adds up to [tex]\frac{11\sqrt{3}}{6}[/tex], which is in simplest radical form.

Hope this helps!

Answer:

yellow box

Step-by-step explanation:

Answer:

c or the orange option. m^2n/2

Step-by-step explanation:

i hope this helps :)

Answer:

28

Step-by-step explanation:

Answer:

wow that hard even i dont know how to do that

Step-by-step explanation:

sorry

Answer:

200 in2

Step-by-step explanation:

diameter= 15 in. so raduis = 15/2

area of circle = πr2

= 22/7 * 15/2 *15/2

= 176.79

rounding to the nearest 100, its 200 in2

Answer:

Step-by-step explanation:

speed=distance /time=0.9/2.5=90/25=3.6 m/s

Answer:

The distance around a circle on the other hand is called the circumference (c).

Step-by-step explanation:

A straight line that passes from one side of a circle to the other through the center is called the diameter. The distance around the outside of a circle is called the circumference. All points on the edge of a circle are the same distance to the center.

The length of the outside of a circle is called the "circumference."

The circumference is the total distance around the outer boundary of the circle.

The distance cover while completing one full lap around the track is equivalent to the circumference of the circle.

The formula to calculate the circumference (C) of a circle is:

C = πd

where π (pi) is a mathematical constant equal to 3.14159, and d represents the diameter of the circle.

The formula for circumference in terms of the radius is:

C = 2πr

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Answer:

z=19

Step-by-step explanation:

3(5)=15

15+4=19

Mark me Brainliest?

Answer: z = 5/7

Step-by-step explanation:

Step-by-step explanation:

You can use this app is call symbols and it's completely free.

Hope this helps

Answer:

a) growing

b) 5% per year

c) $11819.64

The graph of  y=-x^2-12x-35 is attached and it has x intercepts at x=-7 and x=-5 and vertex is at (6, -107).

A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .

To graph the equation y=-x^2-12x-35, we can start by finding the x-intercepts (or roots) and the vertex of the parabola.

To find the x-intercepts, we can set y=0 and solve for x:

0 = -x² - 12x - 35

Using the quadratic formula, we get:

x=-b±√b²-4ac/2a

x=12±√144-140/2(-1)

x=12±√144-140/(-2)

x=12±2/(-2)

The x-intercepts are approximately x=-7 and x=-5

To find the vertex, we can use the formula x=-b/2a to get the x-coordinate, and then substitute it into the equation to get the y-coordinate:

x = -b / 2a = -(-12) / 2(-1) = 6

y = -x² - 12x - 35 = -(6)^2 - 12(6) - 35 = -107

So the vertex is at (6, -107).

Hence, the graph of  y=-x^2-12x-35 is attached and it has x intercepts at x=-7 and x=-5 and vertex is at (6, -107).

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Answer:

Its C

Step-by-step explanation:

23 times 34 is 782 and since its a square you add the 2

Here is a video to help you with your question:

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Answer:

the third option

Step-by-step explanation:

when X is negative f(x) is positive. and when f(x) is negative x is positive

Answer:

[tex]p(11)=626[/tex]

Step-by-step explanation:

Substitute the value (p(11)) into the function and evaluate by solving. Do not forget to follow the order of operations. The order of operations is the steps one must do operations in an equation in order to get a valid result, they are the following,

1. Parenthesis

2.Exponent/Radicals

3.Multiplication/Division

4.Addition/Subtraction

[tex]p(x)=5(x^2+1)+16[/tex]

Substitute,

[tex]p(11)=5((11)^2+1)+16[/tex]

Simplify,

[tex]p(11)=5(121+1)+16[/tex]

[tex]p(11)=5(122)+16[/tex]

[tex]p(11)=610+16[/tex]

[tex]p(11)=626[/tex]

Answer:

Im not sure if you have to provide an exact or estimated answer so here's both:

314.16 cm3     or   100pi

Answer:

100π

Step-by-step explanation:

[tex]V=\frac{pi r^{2} h}{3} \\ =\frac{pi*5^{2}*12 }{3} \\ =pi*5^{2} *4\\ =pi*25*4\\ =pi*100[/tex]

Sorry I had to write pi instead of π in the equation

Image of figure is missing so i have attached it.

Answer:

The total length of three sides of the square = 36 in

Side length of square = 12 in

A_triangle = 48 in²

Area of square = 144 in²

Total area of figure = 192 in²

Step-by-step explanation:

Total perimeter = 56 inches

Let the side of the square be s.

Thus, perimeter of the 3 sides of the square = 3s

Therefore, adding all the external sides of the figure, we have;

3s + 10 + 10 = 56

3s + 20 = 56

3s = 56 - 20

3s = 36

s = 36/3

s = 12

Area of triangle is given by the formula;

A_triangle = ½bh

Where;

b is base

h is height

Thus;

A_triangle = ½ × 12 × 8

A_triangle = 48 in²

Area of square = 12 × 12 = 144 in²

Total area of figure = 144 + 48 = 192 in²

Answer:

onomatopoeia

Step-by-step explanation Onomatopia is when the author uses sounds in their writing. In this case ooohing and ahhing were the sounds.