1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
julia-pushkina [17]
3 years ago
7

What is the factor tree for 68

Mathematics
1 answer:
alexira [117]3 years ago
4 0
The answer to your question is... 68 / \ 32(times)2 / \ 17(times)2
You might be interested in
point b on the ground is 5 cm from point E at the entrance to Ollie's house. He is 1.8 m tall and is standing at Point D, below
enot [183]

Point B on the ground is 5 cm from point E at the entrance to Ollie's house.

Ollie is at a distance of 2.45 m from the entrance to his house when he first activates the sensor.

The complete question is as follows:

Ollie has installed security lights on the side of his house that is activated by a  sensor. The sensor is located at point C directly above point D. The area covered by the sensor is shown by the shaded region enclosed by triangle ABC. The distance from A to B is 4.5 m, and the distance from B to C is 6m. Angle ACB is 15°.

The objective of this information is:

  • To find angle CAB and;
  • Find the distance Ollie is from the entrance to his house when he first activates the sensor.

The diagrammatic representation of the information given is shown in the image attached below.

Using  cosine rule to determine angle CAB, we have:

\mathbf{\dfrac{AB}{Sin \hat {ACB}} = \dfrac{BC}{Sin \hat {CAB}}= \dfrac{CA}{Sin \hat {ABC}}}

Here:

\mathbf{\dfrac{AB}{Sin \hat {ACB}} = \dfrac{BC}{Sin \hat {CAB}}}

\mathbf{\dfrac{4.5}{Sin \hat {15^0}} = \dfrac{6}{Sin \hat {CAB}}}

\mathbf{Sin \hat {CAB} = \dfrac{Sin 15 \times 6}{4.5}}

\mathbf{Sin \hat {CAB} = \dfrac{0.2588 \times 6}{4.5}}

\mathbf{Sin \hat {CAB} = 0.3451}

∠CAB = Sin⁻¹ (0.3451)

∠CAB = 20.19⁰

From the diagram attached;

  • assuming we have an imaginary position at the base of Ollie Standing point called point F when Ollie first activates the sensor;          

Then, we can say:

∠CBD = ∠GBF

∠GBF = (CAB + ACB)      

(because the exterior angles of a Δ is the sum of the two interior angles.

∠GBF = 15° + 20.19°

∠GBF = 35.19°

Using the trigonometric function for the tangent of an angle.

\mathbf{Tan \theta = \dfrac{GF}{BF}}

\mathbf{Tan \ 35.19  = \dfrac{1.8 \ m }{BF}}

\mathbf{BF  = \dfrac{1.8 \ m }{Tan \ 35.19}}

\mathbf{BF  = \dfrac{1.8 \ m }{0.7052}}

BF = 2.55 m

Finally, the distance of Ollie║FE║ from the entrance of his bouse is:

= 5 - 2.55 m

= 2.45 m

Therefore, we can conclude that Ollie is at a distance of 2.45 m from the entrance to his house when he first activates the sensor.

Learn more about exterior angles here:

8 0
3 years ago
Solve for y. -5(6+7y)= -5(6+y)​
Keith_Richards [23]
Simplify to -30-35y=-30-5y
Move all ys to the right and move constants left, -30y= 0
Divide by -30
y=0
7 0
2 years ago
Read 2 more answers
Could I get help with this ?
Leokris [45]

Answer:

top is -2,4 and bottom is 3,-2 ??

hope that what u need

Step-by-step explanation:

???

7 0
3 years ago
A man gave half of his welfare allowance to his wife,1/5 to each of his two sons the rest to his daughter. Find the fraction giv
vichka [17]

Answer:

1/10.

Step-by-step explanation:

Total allowance=1

Half to wife so 1-1/2=1/2(Left from total)

1/5 to each son so 2/5 to both(Total for sons).

Left for daughter 1/2-2/5=1/10(Ans)

8 0
2 years ago
A family buys a studio apartment for 240,000. They pay for a down payment of 72,000.
swat32

Answer:

A. 30% B. 45%

Step-by-step explanation:

A. 72,000/240,000 = x/100

(72,000)(100) = (240,000)x

7,200,000 = 240,000x

30 = x

B. 108,000/240,000 = x/100

10,800,000 = 240,000x

45 = x

7 0
2 years ago
Other questions:
  • F(x) = 3x-7 and g(x) = -2x-6. Find (f o g)(4)
    5·1 answer
  • the most a bowling ball can weigh is 7,258 grams. what is the most it can weigh when measured in pounds? explains plz
    5·1 answer
  • Describe the angles of an obtuse triangle?
    5·2 answers
  • Write a expression that is equivalent of 4+3(5+x)
    5·1 answer
  • What is the answer I’m not sure I’m right
    6·1 answer
  • What is the equation of the line that passes through the point (−4,−8) and has an undefined slope?
    13·1 answer
  • Some one PLEASE help me
    7·1 answer
  • Someone plz help asap
    8·2 answers
  • In right triangle PQR , PQ=12 cm and QR=5cm .What is cos R?
    7·1 answer
  • Terrance made a list of his expenses. He is creating a check-off matrix to organize when his bills are due. A check-off matrix i
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!