If cde is a straight angle, de bisects gdh, m gde = (8x-1), m edh = (6x-15), and m cdf= 43, find each measure.

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Short explanation:

Plug z = 2 into the equation and you'll find that

z^3 + 8 = 2^3 + 8 = 8+8 = 16

but the result should be 0 since the original equation has 0 on the right side. Therefore, z = 2 is not a solution.

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Longer explanation:

Solve the equation for z to find the three roots.

z^3 + 8 = 0

(z+2)(z^2 - 2z + 4) = 0 ... sum of cubes factoring rule

z+2 = 0 or z^2 - 2z + 4 = 0

z = -2 or z^2 - 2z + 4 = 0

We see that z = -2 is one root. To find the other two roots, use the quadratic formula to solve z^2 - 2z + 4 = 0 for z

[tex]z = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\z = \frac{-(-2)\pm\sqrt{(-2)^2-4(1)(4)}}{2(1)}\\\\z = \frac{2\pm\sqrt{-12}}{2}\\\\z = \frac{2\pm\sqrt{-1*4*3}}{2}\\\\z = \frac{2\pm\sqrt{-1}*\sqrt{4}*\sqrt{3}}{2}\\\\z = \frac{2\pm i*2*\sqrt{3}}{2}\\\\z = \frac{2\pm 2i*\sqrt{3}}{2}\\\\z = \frac{2(1\pm i*\sqrt{3})}{2}\\\\z = 1\pm i\sqrt{3}\\\\z = 1+ i\sqrt{3} \ \text{ or } \ z = 1- i\sqrt{3}\\\\[/tex]

Therefore, the three roots of z^3+8=0 are [tex]z = -2, \ z = 1+i\sqrt{3}, \ z=1-i\sqrt{3}[/tex]

The value z = 2 is not part of the list of solutions.

We can verify each solution by plugging it back into the original equation. For instance, with z = -2, we get

z^3 + 8 = 0

(-2)^3+8 = 0

-8+8 = 0

0 = 0 ... solution is confirmed.

I'll let you check the other solutions.

Answer: x= 40

Step-by-step explanation:

x + 4x -20=180

5x -20=180

    +20   +20

5x= 200

x= 40

Answer:

A) x=32

Step-by-step explanation:

To work out the value of x you would first need to minus 20° from 180°, this gives you 160°. This is because the total angle in a straight line is 180° and that by subtracting 20 from 180 you are isolating the value of the x's.

The next step is to add up the number of x's in that angle. You can do this by adding the values of 4 and 1, this gives you 5.

The final step is to divide the angle 160 by the total number of x's of 5, this gives you 32°. This si because we had previously isolated the value of the 5x and so by dividing it by 5 so we would work out the value of x.

1) Minus 20 from 180.

[tex]180-20=160[/tex]

2) Add 4 and 1.

[tex]4+1=5[/tex]

3) Divide 160 by 5.

[tex]160/5=32[/tex]

Answer:

100

Step-by-step explanation: It is 100 because they are dividing by 2 each time, so it is 100.

Answer:

100

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer: The answer is 4.

log5 (625) can be interpreted as, "5to what power is equal to 625?

"Since 54=625,log5(625)=4

The value of the logarithm of 625 to base 5, log₅(625), obtained from the definition of logarithms is 4

The logarithm function logₐ(x) is the inverse of the exponential function, bˣ, which indicates that where, y = logₐ(x), then [tex]a^y[/tex] = x. Therefore, the logarithm function gives the power to which the base a must be raised to produce x.

With regards to log₅(625), the power to which the base, 5, should raised to produce 625 is required.

Whereby 5⁴ = 625, it can be concluded that log₅(625) = 4

Therefore, the value of log₅(625) is 4

Learn more on the logarithm of a number here: https://brainly.com/question/28845183

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Answer:

11x2-y=

Step-by-step explanation:

well it's easy simplifying 10+1=11

Answer:

(-6, -5).

Step-by-step explanation:

If there is a zero between the integers there will be a change of sign of f(x).

x^3 + 5x^2 - x - 6

f(1) = 1 + 5 - 1 - 6 = -1

f(-1) = -1 + 5 + 1 - 6 = -1

f(2) = 8 + 20 - 2  -6 = 20

There' a change of sign between f(1) and f(2) so there is a zero between (1, 2).

f(-2) = -8 + 20 + 2 - 6= 6

So there is also a zero between -1 and -2. (-2, -1)

F(-4) = 14,  f(-5) = -1  = change of sign so there is also a zero  in (-5,-4)

f(-6) = -36 - no change in sign between -5 and -6.

Answer:A  

+9

Step-by-step explan                                                                                    ation:

2020

Answer:

i say C

Step-by-step explanation:

pi is 3.14 so you have to find either 3.13 or 3.15

Answer:

21.75 km/h

Step-by-step explanation:

Let's call the aircraft carrier speed 'x', so the speed of the container ship is 'x+8'

The distance travelled can be found with the product of the speed and the time travelled: d = v * t

The aircraft carrier travelled five hours, so the distance travelled is:

d1 = x * 5 = 5x

Then, the container ship travelled seven hours, so the distance travelled is:

d2 = (x+8)*7 = 7x + 42

As they travelled in opposite directions, the distance between then is the sum of these distances, and it is equal 303 km, so we have that:

d1 + d2 = 303

5x + 7x + 42 = 303

12x = 261

x = 21.75 km/h

Answer:

The aircraft carrier's speed was 13 km/h

Step-by-step explanation:

The parameters given in the question are;

Time of departure of the aircraft carrier = 5 hours before the container ship

Speed of the container ship = 8 km/h faster than the aircraft carrier

Distance between the two ships after 7 hours = 303 km

Let the speed of the aircraft carrier be Z

∴ The speed of the container ship = Z + 8

Since the aircraft carrier left port 35 travelling North 5 hours earlier we have;

Total time of travel of the aircraft carrier at the time of measurement of the distance between the two ships = 5 + 7 = 12 hours

Therefore, since both ships are moving in opposite direction on the same line path, we have;

303 = 12×Z + 7 × (Z + 8) = 12·Z + 7·Z + 56

19·Z = 303 - 56 = 247

∴ Z = 247/19 = 13 km/h

Hence, the aircraft carrier's speed was 13 km/h.

Answer:

greater than

Step-by-step explanation:

half the times the cube was rolled it landed on six the theoretical probability is only eight, 48 > 8

Answer:

54 degrees

Step-by-step explanation:

180- 72 = 108

108 divided by 2 = 54

Answer:

54°

Step-by-step explanation:

There is 180° is a triangle. We have 72° given already

180 - 72 = 108

Since there are two y's we divide by two

108 ÷ 2 = 54°

I hope this helps! ^_^

Answer:

f(3) = 71

Step-by-step explanation:

f(x) = 10(x + 5) − 9

f(3) = 10(3 + 5) - 9

f(3) = 10(8) - 9

f(3) = 80 - 9

f(3) = 71

Answer:

The chair travels approximately 4,394.924 feet.

Step-by-step explanation:

We need to use trigonometric functions to solve this problem. You are given the opposite side of an angle and asked to find the hypotenuse. This means you must use sine, because sine is the ratio between opposite and hypotenuse.

Set up the equation as so:

sin(21) = 1575/x

(x being the hypotenuse). Solve for x by multiplying both sides by x and then dividing both sides by sin(21). Solve 1575/(sin(21)), and you get 4,394.924273, or 4,394.92

Answer:

45%

Step-by-step explanation:

100%=36+26+18= 80 36/80 as a fraction is 45%

Answer:

D i think

Step-by-step explanation:

Answer

D. -(-300/5 meters per hour

Step-by-step explanation:

I took the quiz, and I got it right on time4learning 2022 I hope I helped and more importantly I hope you pass byee!!!

Answer:

1209.06 cubic feet

Step-by-step explanation:

use the formula for the volume of a cylinder and the volume of a rectangular prism, and then plug the values into that

The volume of the composite figure consisting of a cylinder and a rectangular prisms to the nearest tenth is 1209.1ft³.

A cylinder is simply a 3-dimensional shape having two parallel circular bases joined by a curved surface.

The volume of a cylinder is expressed as;

V = π × r² × h

Where r is radius of the circular base, h is height and π is constant pi ( π = 3.1415 )

A rectangular prism is simply a three-dimensional solid shape which has six faces that are rectangles.

The volume of a rectangular prism is expressed as;

V = w × h × l

Where w is width, l is length and h is the height

From the diagram, the figure consist of a cylinder and a rectangular prism.

For the cylinder;

For the rectangular prism;

Volume of the cylinder.

V_c = π × r² × h

V_c = 3.1415 × (4ft)² × 4ft

V_c = 3.1415 × 16ft² × 4ft

V_c = 201.1ft³

Volume of the rectangular prism.

V_r = w × h × l

V_r = 14ft × 6ft × 12ft

V_r = 1008ft³

Now, the volume of the composite figure will be;

V = V_c + V_r

V = 201.1ft³ + 1008ft³

V = 1209.1ft³

Therefore, the volume of the composite figure consisting of a cylinder and a rectangular prisms to the nearest tenth is 1209.1ft³.

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Answer:

B and D

Step-by-step explanation:

Answer: 1,253

Step-by-step explanation:

Just multiply length, width, and height of both boxes and add them together. So 7x5x5= 175 and 11x14x7=1,078. 1,078+175=1,253

Answer: 9.19 ft

Step-by-step explanation:

Hi, since the situation forms a right triangle (see attachment) we have to apply the next trigonometric function.  

Sin α = opposite side / hypotenuse  

Where α is the angle of elevation of the ladder to the ground, the hypotenuse is the longest side of the triangle (in this case is the length of the ladder), and the opposite side (x) is distance between the top of the ladder and the ground.

Replacing with the values given:  

Sin 45 = x/ 13

Solving for x  

sin45 (13) =x  

x= 9.19 ft

Feel free to ask for more if needed or if you did not understand something.  

Answer: Look at explanation, and hope it helps. Please mark as brainliest! Take care during these hard time.

Step-by-step explanation:

a.

A diagonal of a square inscribed in a circle is the diameter.

So, to find the diameter we know if we separate the square into two different 45-45-90 degree triangles where a and b is 8[tex]\sqrt{2}[/tex]. Use the 45-45-90 degree theorem shown in picture to find that the diagonal 8[tex]\sqrt{2}[/tex] times [tex]\sqrt{2}[/tex] equals 16.

So, the diagonal is 16, thus the diameter is 16.

b.

Multiply 8[tex]\sqrt{2}[/tex] times 4 to get 32[tex]\sqrt{2}[/tex] as the perimeter as there are 4 sides which are equal to RS

c.

The circumference of a circle is the diameter times [tex]\pi[/tex]. The diameter we know from a, which is 16. So, it is 16[tex]\pi[/tex]

Answer:

the whole

Step-by-step explanation:

i may be wrong

sorry

Answer:

Definitely percent

Step-by-step explanation:

Answer:

Correct option: second one -> Andy and Donald do not collide.

Step-by-step explanation:

To find if the boys collide, we need to find if there is a common value of t where the their x position are equal and their y position are equal. To do this, we make x(t) of Andy equal to x(t) of Donald, , then if there is a value for t, we do the same for y(t) and check if the values of t are equal:

24 + 23t = 12 + t

22t = -12

t = -0.5455 seconds

As the time is negative, it will not occur, so the boys will never collide.

Correct option: second one

Isolate the variable by dividing each side by factors that don't contain the variable.

Inequality Form:

x<4

The solution to the given inequality 3x - 3 < 9 is;

x < 4

We are given the inequality;

3x - 3 < 9

Using addition property of equality, add 3 to both sides to get;

3x - 3 + 3 < 9 + 3

3x < 12

Using division property of equality, divide both sides by 3 to get;

3x/3 < 12/3

x < 4

Read more at; https://brainly.com/question/21644280

Answer:

The answer is 6

Step-by-step explanation:

2+4

Answer:

2 cans to cover the room but she will have a lot of paint left over

Step-by-step explanation:

12*18=216

the area of her room is 216 square ft.

216*2=432

she will need 2 cans

Answer:

Lyana will need 4 cans of paint to paint her whole room or only 3 if she doesn't paint the floor.

Step-by-step explanation:

Firstly we need to know how much paint she will need to use.

The area of her room is given by 2(ac+bc), where a is the length, b is the width and c is the height.

Applying that we get that the area of her room is 2*12*18+2*18*8=720.

This applies if we assume that she also paints the floor. If she doesn't we need to subtract the area of the floor which is 12*18=216. So 720-216=504

She will paint her room twice she the amount of paint she needs is twice the area:

720*2=1440

or if she does not paint the floor

504*2=1008

Now we answer how many cans is that by dividing by 400 and rounding up.

1440/400=3.6 she needs, therefore, 4 cans

1008/400=2.52 she needs 3 cans

Answer:

volume of empty space is 1307.245in

Step-by-step explanation:

I'm pretty sure this is right because I found the volume of the cube which came out to be 2744 and the volume of the sphere which came out to 1436.755 and subtracted them.

Answer: BRAINLIEST PLEASE

her supply has 18 pounds

Explanation:

Assume that the number of pounds in her supply is x.

We are given that:

She uses 1/3 x in salted mix and 2/9 x in unsalted mix.

This means that:

Total amount used = 1/3 x + 2/9 x = 5/9 x of her supply

Now, we are also given that:

She used 10 pounds of her supply.

This means that:

5/9 x = 10

5x = 9*10 = 90

x = 18 pounds

Hope this helps :)

The number of pounds of seeds in her supply is 18

Given:

let

her total supply = x

Supply of salted snack = 1/3x

Supply of unsalted snack = 2/9x

Total pounds of sunflower seed = 10

Total supply of sunflower seeds = salted snack + unsalted snack

10 = 1/3x + 2/9x

10 = (3x + 2x) / 9

10 = 5/9x

divide both sides by 5/9

x = 10 ÷ 5/9

x = 10 × 9/5

= (10 × 9) / 5

= 90/5

= 18

x = 18

Therefore, number of pounds of seeds in her supply is 18

Read more:

https://brainly.com/question/2261275

Answer:

Since a and b are constant the answer is 6.5

Step-by-step explanation:

g(x) = 2x + 5

g(x) = y

y = 2x + 5

y - 5 = 2x

[tex]\frac{y-5}{2}[/tex] = x

[tex]g^{-1}[/tex](x) = [tex]\frac{x-5}{2}[/tex]

8 = h(1) and h(3) = 26

26 = a(3) + b

a = b

6.5 = 6.5

26 = 6.5(3) + 6.5

26 = 19.5 + 6.5

26 = 26