Which is the correct standard notation for 9.3 × 105?

The parent function f(x) = x3 is transformed to g(x) = (x – 1)3 + 4. Identify the graph of g(x).

Dominik [7]

we have $f(x)=x^3$ which is a cubic function.

and $=(x-1)^3+4$ .

from f(x) and g(x) we know that both are cubic and g(x) has shrink of 1 and up by 4 units in x axis .

4 0

2 years ago

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Abraham throws a ball from a point 40 m above the ground. The height of the ball from the ground level after ‘t' seconds is defi

Minchanka [31]

Answer:

8.899s

Solve: -5t^+40t+40

7 0

2 years ago

Marty is asked to draw triangles with side lengths of 4 units and 2 units, and a non-included angle of 30°. Select all the trian

777dan777 [17]

Answer:

The drawn in the attached figure

see the explanation

Step-by-step explanation:

<em>First case</em>

In the triangle ABC

Let

$a=4\ units\\b=2/ units\\B=30^o$

Applying the law of sines

Find the measure of angle A

$\frac{a}{sin(A)}=\frac{b}{sin(B)}$

substitute the given values

$\frac{4}{sin(A)}=\frac{2}{sin(30^o)}$

$sin(A)=1$

so

$A=90^o$

Find the measure of angle C

In a right triangle

we know that

$B+C=90^o$ ----> by complementary angles

$B=30^o$

therefore

$C=60^o$

Find the length side c

Applying the law of sines

$\frac{c}{sin(C)}=\frac{b}{sin(B)}$

substitute the given values

$\frac{c}{sin(60^o)}=\frac{2}{sin(30^o)}$

$c=2\sqrt{3}\ units$

therefore

The dimensions of the triangle are

$A=90^o$

$B=30^o$

$C=60^o$

$a=4\ units\\b=2\ units\\c=2\sqrt{3}=3.46\ units$

<em>Second case</em>

In the triangle ABC

Let

$a=4\ units\\b=2/ units\\A=30^o$

Applying the law of sines

Find the measure of angle B

$\frac{a}{sin(A)}=\frac{b}{sin(B)}$

substitute the given values

$\frac{4}{sin(30^o)}=\frac{2}{sin(B)}$

$sin(B)=0.25$

so

using a calculator

$B=14.48^o$

Find the measure of angle C

we know that

The sum of the interior angles in any triangle must be equal to 180 degrees

so

$A+B+C=180^o$

$A=30^o\\B=14.48^o$

therefore

$30^o+14.48^o+C=180^o$

$C=135.52^o$

Find the length side c

Applying the law of sines

$\frac{c}{sin(C)}=\frac{a}{sin(A)}$

substitute the given values

$\frac{c}{sin(135.52^o)}=\frac{4}{sin(30^o)}$

$c=5.61\ units$

therefore

The dimensions of the triangle are

$A=30^o$

$B=14.48^o$

$C=135.52^o$

$a=4\ units\\b=2\ units\\c=5.61\ units$

see the attached figure to better understand the problem

4 0

2 years ago

What are the possible steps involved in solving the equation shown? Select three options.

e-lub [12.9K]

Answer:

Option B, C and D are correct choices.

Step-by-step explanation:

We have been given an equation $3.5+1.2(6.3-7x)=9.38$ . We are asked to choose the steps that are involved in solving the equation.

Let us solve the equation.

Using distributive property $a(b+c)=ab+ac$ , we will distribute 1.2 to 6.3 and $-7x$ .

$3.5+1.2*6.3-1.2*7x=9.38$

$3.5+7.56-8.4x=9.38$

Therefore, option B is the correct choice.

Now, we will combine like terms.

$11.06-8.4x=9.38$

Therefore, option C is the correct choice.

Now, we will subtract 11.06 from both sides of our equation.

$11.06-11.06-8.4x=9.38-11.06$

$-8.4x=-1.68$

Therefore, option D is the correct choice.

Now, to solve for x, we need to divide both sides of our equation by $-8.4$

$\frac{-8.4x}{-8.4}=\frac{-1.68}{-8.4}$

$x=0.2$

3 0

2 years ago

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Rachel is bowling with her friends. her bowling ball has a radius of 4 inches. as she bowls she tracks the location of the finge

Goshia [24]

Question Continuation

The finger hole changes by 45 degrees.

Define a function, f, that gives the height of the finger hole above the ground (in inches) in terms of the angle of rotation (measured in radians) it has swept out from the 12 o'clock position.

Answer:

f(θ) = r(1 + cos(θ)) for 0 ≤ θ ≤ π/4

Step-by-step explanation:

Given

Let represent radius

r = 4 inches

Considering that she starts tracking the location when the finger hole is at the 12 o'clock; this means that the angle measurement at this point is 0°.

Let θ represent the angle

At 12 o'clock mark

θ = 0

When the finger hole changes by 45 degrees

θ = 45°

Convert 45° to radians

θ = 45° * π/180

θ = π/4

So, angle θ is such that θ∈[0, π/4]

This can be represented as

0 ≤ θ ≤ π/4

Calculating the measure of f(θ) in polar coordinates

When θ = 0, f(θ) = r (i.e. the current position of the bowl)

When θ = π/2, f(θ) = rcosθ

This is so because f(θ), being the function of the height is a measure of the radius* cos(θ)

Taking measurement of f(θ) from 0 to π/2

f(θ) = r + rcosθ

f(θ) = r(1 + cos(θ))

So, f(θ) = r(1 + cos(θ)) for 0 ≤ θ ≤ π/4

7 0

2 years ago