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2 years ago

Wht is the value of a^3 - b^2 for a =3 and b = 1/2?

Mathematics

1 answer:

attashe74 [19]2 years ago

4 0

Answer:

a^3-b^2

3^3-1-2^2

3*3*3-1/2*1/2*1/2

3*3*3-0.5*0.5*0.5

27-0.125

=26.875

Step-by-step explanation:

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Rate of change on a graph.- I'll give brainly for the answer, thank you

Norma-Jean [14]

Answer:

The slope of graph is $\mathbf{\frac{3}{2}}$

Option C is correct option.

Step-by-step explanation:

We need to find the slope (rate of change) of the graph

The formula to calculate slope is: $Slope=\frac{y_2-y_1}{x_2-x_1}$

Taking two points from the graph: (You can take any two points from the graph)

Point 1 (-4,-3)

Point 2 (-2,0)

We have: $x_1=-4, y_1=-3, x_2=-2, y_2=0$

Putting values in the formula and finding slope

$Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{0-(-3)}{-2-(-4)} \\Slope=\frac{0+3}{-2+4} \\Slope=\frac{3}{2}$

So, the slope of graph is $\mathbf{\frac{3}{2}}$

Option C is correct option.

6 0

3 years ago

The monthly cost in dollars of a long distance phone plan is a linear function of the total calling time in minutes. The monthly

Deffense [45]

Answer:

The monthly cost for 45 minutes is $18.42

Step-by-step explanation:

Let

x -----> the total calling time in minutes

y ----> the monthly cost in dollars

we have the ordered pairs

(42,18.15) and (90,22.47)

step 1

Find the slope

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute the values

$m=\frac{22.47-18.15}{90-42}$

$m=\frac{4.32}{48}$

$m=\$0.09\ per\ minute$

step 2

Find the linear equation in point slope form

$y-y1=m(x-x1)$

we have

$m=0.09\\(x1,y1)=(42,18.15)$

substitute

$y-18.15=0.09(x-42)$

step 3

Find the monthly cost for 45 minutes of calls

For x=45 min

substitute the value of x in the linear equation and solve for y

$y-18.15=0.09(45-42)$

$y-18.15=0.09(3)$

$y-18.15=0.27$

$y=0.27+18.15$

$y=18.42$

therefore

The monthly cost for 45 minutes is $18.42

3 0

3 years ago

Kali had a total of 212121 balloons at her birthday party. The ratio of blue balloons to green balloons is shown in the tape dia

Misha Larkins [42]

Answer:

Blue balloons = 12

Step-by-step explanation:

Total no of balloons = 21

Let us assume that the ratio of blue balloons to green balloons is 4:3.

Let there are 4x blue balloons and 3x green balloons.

ATQ,

4x+3x = 21

7x = 21

x = 3

Blue balloons = 4x

= 4(3)

= 12

Hence, she will have 12 blue balloons at her party.

5 0

2 years ago

Find the measure of the missing angles in the triangle below round your answer to the nearest degree

navik [9.2K]

Answer:

a. 40°

b. 21°

Step-by-step explanation:

a. Reference angle = θ

Opposite = 5

Adjacent = 6

Apply TOA:

$Tan (\theta) = \frac{Opp}{Adj}$

$Tan (\theta) = \frac{5}{6}$

$\theta = Tan^{-1}(\frac{5}{6})$

$\theta = 40$ (nearest degree)

b. Reference angle = x

Opposite = 5

Hypotenuse = 14

Apply SOH:

$Sin (x) = \frac{Opp}{Hyp}$

$Sin (x) = \frac{5}{14}$

$x = Sin^{-1}(\frac{5}{14})$

$x = 21$ (nearest degree)

3 0

2 years ago

Given the general form of the sinusoidal function, y = AsinB(x - C) + D, match the following items.

Jet001 [13]

Answer:

$\Delta y = A$ (Amplitude) (Correct answer: 1)

$\omega = B$ (Angular frequency) (Correct answer: 2)

$x_{o} = C$ (Phase shift) (Correct answer: 3)

$y_{o} = D$ (Vertical shift) (Correct answer: 4)

$\frac{2\pi}{\omega} = \frac{2\pi}{B}$ (Period) (Correct answer: 5)

Step-by-step explanation:

The general form of a sinusoidal function is represented by the following characteristics:

$y = \Delta y \cdot \sin \omega\cdot (x- x_{o}) + y_{o}$ (1)

Where:

$\Delta y$ - Amplitude.

$\omega$ - Angular frequency.

$x_{o}$ - Phase shift.

$y_{o}$ - Vertical shift.

$x$ - Independent variable.

$y$ - Dependent variable.

In addition, we know that the period associated with the sinusoidal function ( $T$ ) is:

$T = \frac{2\pi}{\omega}$

By direct comparison, we get the following conclusions:

$\Delta y = A$ (Amplitude) (Correct answer: 1)

$\omega = B$ (Angular frequency) (Correct answer: 2)

$x_{o} = C$ (Phase shift) (Correct answer: 3)

$y_{o} = D$ (Vertical shift) (Correct answer: 4)

$\frac{2\pi}{\omega} = \frac{2\pi}{B}$ (Period) (Correct answer: 5)

6 0

2 years ago