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
sergejj [24]
2 years ago
11

Help me please ...........with this work

Mathematics
1 answer:
Zolol [24]2 years ago
7 0

Answer:

Vertex form is: y = ( x + 1 )^2 − 2

Step-by-step explanation:

I'm not sure about the substitution part.

You might be interested in
If 2/3 of a certain number is subtracted from twice the number, the result is 20. Find the number.​
sleet_krkn [62]

Let x be the number.

Set up an equation:

2x - 2/3x = 20

Simplify:

1 1/3x = 20

Divide both sides by 1 1/3

X = 15

The number is 15

3 0
3 years ago
Read 2 more answers
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
What is 100,789,388,369,012 times 479,000,000
8_murik_8 [283]

Answer:

4.8278117e+22

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Which fractions are equivalent to -30/48 ?
Vedmedyk [2.9K]

The answer is D

Because

-35/65 = -0.53


I hope that's help:)

6 0
3 years ago
Which graph best represents a quadratic function that has only one zero?
GenaCL600 [577]

Answer:

B

Step-by-step explanation:

A has 2 it crosses the x axis 2x

B Has 1.

C has 2

D has none since it never touched the x axis

8 0
2 years ago
Read 2 more answers
Other questions:
  • You have $39 to spend at the music store. Each cassette tape costs $5 and each CD costs $11. Write a linear inequality that repr
    12·2 answers
  • Find the length of the diagonal of a square with perimeter of 24
    10·1 answer
  • Find the distance between A(-2,3) and B(11,-15)
    11·1 answer
  • Help I don't get the question.
    15·1 answer
  • What is 856 divided by 82
    8·2 answers
  • A detergent company periodically tests its products for variations in the fill weight. To do this, the company uses x-bar and R
    8·1 answer
  • Simplify the expression (3x^2y^-3)^3/27(xy)^-9 . The simplified expression is________ . PLEASE HELP
    15·1 answer
  • The base of a triangle is 18 cm and its height is 7w-1 cm. Find the expression for the triangles area
    6·1 answer
  • Jamaal bounces on a trampoline. His height, as a function of time, is modeled y y=-16x^2+20x+4
    10·1 answer
  • Through (-4,5) and parallel to y = -3/2x-5
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!