Math Skills Integer Practice 1 Find each sum. 1) (-6)+6

Which of these scales are equivalent to 3 cm to 4 km? select all that apply. recall that 1 inch is 2.54 cm

AlladinOne [14]

Answer:

1. 0.75 cm to 1 km

4. 0.3 mm to 40 m

Step-by-step explanation:

we have the scale

$\frac{3}{4}\frac{cm}{km}=0.75\frac{cm}{km}$

Verify each case

case 1) 0.75 cm to 1 km

$\frac{0.75}{1}\frac{cm}{km}=0.75\frac{cm}{km}$

therefore

The scale is equivalent to the given value

case 2) 1 cm to 12 km

$\frac{1}{12}\frac{cm}{km}=0.08\frac{cm}{km}$

$0.08\frac{cm}{km} \neq 0.75\frac{cm}{km}$

therefore

The scale is not equivalent to the given value

case 3) 6 mm to 2 km

Remember that

1 cm= 10 mm

1 mm=0.1 cm

we have

$\frac{6}{2}\frac{mm}{km}=\frac{0.6}{2}\frac{cm}{km}=0.30\frac{cm}{km}$

$0.30\frac{cm}{km} \neq 0.75\frac{cm}{km}$

therefore

The scale is not equivalent to the given value

case 4) 0.3 mm to 40 m

Remember that

1 cm= 10 mm -----> 1 mm=0.1 cm

1 km=1,000 m ----> 1 m=0.001 km

we have

$\frac{0.3}{40}\frac{mm}{m}=\frac{0.03}{0.04}\frac{cm}{km}=0.75\frac{cm}{km}$

$0.75\frac{cm}{km}=0.75\frac{cm}{km}$

therefore

The scale is equivalent to the given value

case 4) 1 inch to 7.62 km

Remember that

1 in= 2.54 cm

we have

$\frac{1}{7.62}\frac{in}{km}=\frac{2.54}{7.62}\frac{cm}{km}=0.33\frac{cm}{km}$

$0.33\frac{cm}{km} \neq 0.75\frac{cm}{km}$

therefore

The scale is not equivalent to the given value

6 0

3 years ago

6=2-8 is this equation correct?

nirvana33 [79]

Answer:

8-2=6

Step-by-step explanation:

:)

8 0

2 years ago

Read 2 more answers

Which graph represents this system of inequalities? y> x+3 Y> 5x-1 pls need help

Cerrena [4.2K]

Answer:

5x

Step-by-step explanation:

It’s 5x

4 0

3 years ago

For which inequality is x = 5 a solution? A x<2 B. x>9 C x<18 D. x> 42

marishachu [46]

Answer:

c

Step-by-step explanation:

because 5 is smaller then 18

7 0

3 years ago

A sine function has the following key features: Period = 4 Amplitude = 3 Midline: y=−1 y-intercept: (0,-1) The function is not a

mezya [45]

Answer:

See the graphs attached and the explanation below

Explanation:

The most simple sine function, considered the parent function, is:

$y=sin(x)$

That function has:

Midline, also known as rest or equilibrium position: y = 0
Minimum: - 1
Maximum: 1
Amplitude: the distance between a minimum or a maximum and the midline = 1
period: the interval of repetition of the function = 2π

The more general sine function is:

$y=Asin(Bx+C)+D$

That function has:

Midline: y = D (it is a vertical shift from the parent function)
Minimum: - A + D
Maximum: A + D
Amplitude: A
period: 2π/B
phase shift: C (it is a horizontal shift of the from the parent function)

Now, you have to draw the sine function with the given key features:

Period = 4 ⇒ 2π/B = 4 ⇒ B = π/2

Amplitude, A = 3

midline y = - 1 ⇒ D = - 1

y-intercept = (0, -1)

Substitute the know values and use the y-intercept to find C:

$y=3sin(2x/\pi+C)-1$

Substitute (0, -1)

$-1=3sin(0+C)-1\\ \\ 3sin(C)=0\\ \\ sin(C)=0\\ \\ C=0$

Hence, the function to graph is:

$y=3sin(\pi x/2)-1$

To draw that function use this:

Maxima: 3(1) - 1 = 3 - 1 = 2, at x = 1 ± 4n (n = 0, 1, 2, 3, ...)
Minima: 3(-1) - 1 = - 3 - 1 = -4
y-intercept: (0, - 1)
x-intercepts: the solutions to 0 = 3sin(πx/2) = - 1
first point of the midline: (0, -1) it is the same y-intercept

With that you can understand the graphs attached.

4 0

3 years ago