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Ann [662]
1 year ago
5

A line, y mx + b, passes through the point (2, 3) and is parallel to y 2x + 5. What is the value of b?​

Mathematics
1 answer:
Vitek1552 [10]1 year ago
3 0

Answer:

Step-by-step explanation:

If a line is parallel to another it must have the same slope

The slope/intercept form of a line is y = mx + b where m is the slope and b the y intercept

The line y = 2x + 5 has slope 2

So the slope of the line that passes through (2,3) must also have the slope 2

We have
y = 2x + b; Substituting x =2, y =3 in this equation gives us
3 = 2 (2) + b or b = -1

Hence the equation of the line is
y = 2x -1

Cross-check

Substitute for x = 2 ==> y = 2(2) - 1 = 3 which is consistent

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so the answer is A
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Cutting her time by 50% means reducing her time by half. Half of 45 seconds is 22.5 seconds. Therefore, to make the team, she must run a lap in 22.5 seconds.
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Simplify (9 + 8 – 6)(4 – 5).
Temka [501]

Answer:

The answer would be - 11.

Step-by-step explanation:

9 + 8 = 17

17 - 6 = 11.

4 - 5 = 4 + - 5 = - 1

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Find the length of CD shown in red below. Show all work.
PIT_PIT [208]

By definition of circumference, the length of the arc EF (radius: 6 in, central angle: 308°) shown in red is approximately equal to 32.254 inches.

<h3>How to calculate the length of an arc</h3>

The figure presents a circle, the arc of a circle (s), in inches, is equal to the product of the <em>central</em> angle (θ), in radians, and the radius (r), in inches. Please notice that a complete circle has a central angle of 360°.

If we know that θ = 52π/180 and r = 6 inches, then the length of the arc CD is:

s = [(360π/180) - (52π/180)] · (6 in)

s ≈ 32.254 in

By definition of circumference, the length of the arc EF (radius: 6 in, central angle: 308°) shown in red is approximately equal to 32.254 inches.

<h3>Remark</h3>

The statement has typing mistakes, correct form is shown below:

<em>Find the length of the arc EF shown in red below. Show all the work.</em>

To learn more on arcs: brainly.com/question/16765779

#SPJ1

4 0
2 years ago
How do you do this question?
r-ruslan [8.4K]

Step-by-step explanation:

y = 3 + 8x^(³/₂), 0 ≤ x ≤ 1

dy/dx = 12√x

Arc length is:

s = ∫ ds

s = ∫₀¹ √(1 + (dy/dx)²) dx

s = ∫₀¹ √(1 + (12√x)²) dx

s = ∫₀¹ √(1 + 144x) dx

If u = 1 + 144x, then du = 144 dx.

s = 1/144 ∫ √u du

s = 1/144 (⅔ u^(³/₂))

s = 1/216 u^(³/₂)

Substitute back:

s = 1/216 (1 + 144x)^(³/₂)

Evaluate between x=0 and x=1.

s = [1/216 (1 + 144)^(³/₂)] − [1/216 (1 + 0)^(³/₂)]

s = 1/216 (145)^(³/₂) − 1/216

s = (145√145 − 1) / 216

5 0
3 years ago
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