Write an absolute value equation that represents these heights 10 and 15

Mathematics

1 answer:

djverab [1.8K]3 years ago

6 0

Answer:

An equation for the absolute value that represents the midpoint of 10 and 15 would be (10 + 15)/2 = 12.5

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If the second term of a geometric sequence of real numbers is -2 and the fifth term is 16 then what is the fourteenth term?

Agata [3.3K]

<h3>Given</h3>

A geometric sequence such that ...

$a_2=-2\quad\text{and}\quad a_5=16$

$a_{14}$

<h3>Solution</h3>

We can use the ratio of the given terms to find the common ratio of the sequence, then use that to find the desired term from one of the given terms. We don't actually need the common ratio (-2). All we need is its cube (-8).

$a_2=a_1r^{(2-1)}=a_1r^1\\a_5=a_1r^{(5-1)}=a_1r^4\\a_{14}=a_1r^{(14-1)}=a_1r^13=a_5r^9\\\\\dfrac{a_5}{a_2}=\dfrac{a_1r^4}{a_1r^1}=r^3=\dfrac{16}{-2}=-8\\\\r^9=\left(r^3\right)^3=(-8)^3=-512\\a_{14}=a_5(-512)\\\\a_{14}=-8192$

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3 years ago

In the football game between NM and JL. It's the end of the second half and the cougars are attempting a miraculous 50 yard fiel

Yanka [14]

Answer:

88.02 ft/s

Step-by-step explanation:

Angle with the horizontal, θ =25°

Initial velocity, v = 60 mph

1 mph = 1.467 ft/s

60 mph = 60 × 1.467 ft/s = 88.02 ft/s

Vertical component, v sin θ = 88.02 sin 25° = 37.2 ft/s

Horizontal component, v cos θ = 88.02 cos 25°= 79.8 ft/s

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3 years ago

Which graph shows the solution to the system of linear inequalities?<br> y< 2x-5<br> y>-3x + 1

trapecia [35]

Answer:

See explanation

Step-by-step explanation:

Plot the solution sets to both inequalities.

1. For the inequality $y$ First, plot the dotted line $y=2x+5$ (dotted because sign is without notion "or equal to"), then choose correct part by substitution coordinates of the origin.

$2\cdot 0-5=-5$

so the origin does not belong to the needed part. Shade the part, which does not include origin.

2. For the inequality $y>-3x+1.$ First, plot the dotted line $y=-3x+1$ (dotted because sign is without notion "or equal to"), then choose correct part by substitution coordinates of the origin.