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
WINSTONCH [101]
2 years ago
5

Which expression is equivalent to the given expression?

Mathematics
1 answer:
DochEvi [55]2 years ago
3 0

Answer:

8(34a-1)

Step-by-step explanation:

Hope this helps :)

You might be interested in
If a circle has a diameter of 4 inches, what is the area?
gulaghasi [49]
The formula for area of a circle is π × radius^2, and to find the radius we can just divided the diameter by 2 and get 2 inches. You don't need to use a calculator here, because π is approximately equal to 3.14, so 3.14 × 2^2 = 12.56, which is answer B. I hope this helps!
7 0
3 years ago
Read 2 more answers
The cost to take a taxi includes a flat rate, plus a charge for the number of miles the taxi travels.
Alenkasestr [34]

Answer:

412$

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Is 2,750 a reasonable answer for 917 x 33? Explain.
vovangra [49]

No, 2750 is a sadly unreasonable estimate. 917 is almost 1,000 . 33 times as much is around 30,000 . 2,750 is less than 3,000 .

Step-by-step explanation:

so it will be 3,0261

4 0
3 years ago
Find MZP. The diagram is not to scale.
Ad libitum [116K]

Answer:

p= 50

Step-by-step explanation:

the angle that measures 130 is supplementary to the angle below, meaning the other angle must equal 50 degrees. This angle is an alternate interior angle with angle p, making them congruent.

3 0
2 years ago
You work at a pioneer historical site. On this site you have handcarts. One cart has a handle that connects to the center of the
Gelneren [198K]

Answer:

a)  see below

b)  radius = 16.4 in (1 d.p.)

c)  18°. Yes contents will remain. No, handle will not rest on the ground.

d)  Yes contents would spill.  Max height of handle = 32.8 in (1 d.p.)

Step-by-step explanation:

<u>Part a</u>

A chord is a <u>line segment</u> with endpoints on the <u>circumference</u> of the circle.  

The diameter is a <u>chord</u> that passes through the center of a circle.

Therefore, the spokes passing through the center of the wheel are congruent chords.

The spokes on the wheel represent the radii of the circle.  Spokes on a wheel are usually evenly spaced, therefore the congruent central angles are the angles formed when two spokes meet at the center of the wheel.

<u>Part b</u>

The <u>tangent</u> of a circle is always <u>perpendicular</u> to the <u>radius</u>.

The tangent to the wheel touches the wheel at point B on the diagram.  The radius is at a right angle to this tangent.  Therefore, we can model this as a right triangle and use the <u>tan trigonometric ratio</u> to calculate the radius of the wheel (see attached diagram 1).

\sf \tan(\theta)=\dfrac{O}{A}

where:

  • \theta is the angle
  • O is the side opposite the angle
  • A is the side adjacent the angle

Given:

  • \theta = 20°
  • O = radius (r)
  • A = 45 in

Substituting the given values into the tan trig ratio:

\implies \sf \tan(20^{\circ})=\dfrac{r}{45}

\implies \sf r=45\tan(20^{\circ})

\implies \sf r=16.37866054...

Therefore, the radius is 16.4 in (1 d.p.).

<u>Part c</u>

The measure of an angle formed by a secant and a tangent from a point outside the circle is <u>half the difference</u> of the measures of the <u>intercepted arcs</u>.

If the measure of the arc AB was changed to 72°, then the other intercepted arc would be 180° - 72° = 108° (since AC is the diameter).

\implies \sf new\: angle=\dfrac{108^{\circ}-72^{\circ}}{2}=18^{\circ}

As the handle of the cart needs to be no more than 20° with the ground for the contents not to spill out, the contents will remain in the handcart at an angle of 18°.

The handle will not rest of the ground (see attached diagram 2).

<u>Part d</u>

This can be modeled as a right triangle (see diagram 3), with:

  • height = (48 - r) in
  • hypotenuse ≈ 48 in

Use the sin trig ratio to find the angle the handle makes with the horizontal:

\implies \sf \sin (\theta)=\dfrac{O}{H}

\implies \sf \sin (\theta)=\dfrac{48-r}{48}

\implies \sf \sin (\theta)=\dfrac{48-45\tan(20^{\circ})}{48}

\implies \theta = 41.2^{\circ}\:\sf(1\:d.p.)

As 41.2° > 20° the contents will spill out the back.

To find the <u>maximum height</u> of the handle from the ground before the contents start spilling out, find the <u>height from center of the wheel</u> (setting the angle to its maximum of 20°):

\implies \sin(20^{\circ})=\dfrac{h}{48}

\implies h=48\sin(20^{\circ})

Then add it to the radius:

\implies \sf max\:height=48\sin(20^{\circ})+45\tan(20^{\circ})=32.8\:in\:(1\:d.p.)

(see diagram 4)

------------------------------------------------------------------------------------------

<u>Circle Theorem vocabulary</u>

<u>Secant</u>: a straight line that intersects a circle at two points.

<u>Arc</u>: the curve between two points on the circumference of a circle

<u>Intercepted arc</u>: the curve between the two points where two chords or line segments (that meet at one point on the other side of the circle) intercept the circumference of a circle.

<u>Tangent</u>: a straight line that touches a circle at only one point.

7 0
2 years ago
Other questions:
  • What is the correct answer?
    11·1 answer
  • Ariana completed 6/7 of her math problems before dinner and the rest after dinner. How many problems did she have if she complet
    12·1 answer
  • Use the net to find the surface area of the prism
    15·1 answer
  • Gloria went to the mall and spent 50 minutes shopping
    8·1 answer
  • Someone anyone Help pleeeaassse! Will give Brainliest!
    8·1 answer
  • lydia wants to purchase guitar lessons she sees a sign that gives the price is 47 guitar lessons and 11 guitar lessons write a l
    8·1 answer
  • What is Algebra really about and what is it the study of? XXADDICTEDXX please respond.
    13·2 answers
  • Celeste wants to have her hair cut and permed and also go to lunch. She knows she will need $68. The perm costs twice as much as
    14·2 answers
  • What’s the answer to this math question?
    14·1 answer
  • Please give a full explanation and I will give you brainlest
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!