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3 years ago

The sum of 5 times a number and 24 is 79

Mathematics

1 answer:

Thepotemich [5.8K]3 years ago

6 0

You can make an equation for this

5x+24=79
-24=-24
5/5 = 55/5
x=11

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The population is everyone that lives in the city.

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3 years ago

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What is the nth term?

kumpel [21]

Let $a_k$ denote the kth term of the sequence. Then

$a_k=a_1+d(k-1)$

where d is the common difference between consecutive terms in the sequence and a₁ is the first term.

The sum of the first n terms is

$S_n=\displaystyle\sum_{k=1}^na_k=a_1+a_2+\cdots+a_{n-1}+a_n$

From the formula for $a_k$ , we get

$S_n=\displaystyle\sum_{k=1}^n(a_1+d(k-1))=a_1\sum_{k=1}^n1+d\sum_{k=1}^n(k-1)$

$S_n=\displaystyle na_1+d\sum_{k=0}^{n-1}k$

$S_n=na_1+\dfrac{d(n-1)n}2$

$S_n=\dfrac n2(2a_1-d+dn)$

So we have $d=-5$ , and $2a_1-d=16$ so that $a_1=\frac{11}2$ .

Then the nth term in the sequence is

$a_n=\dfrac{11}2-5(n-1)=\boxed{\dfrac{21-10n}2}$

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4 years ago

An air traffic controller spots two airplanes at the same altitude converging to a point as they fly at right angles to each oth

dedylja [7]

Answer:

(a) D(t) = 250t -500 miles

(b) Controller has 2 hours, but including time for pilots to divert course or altitude.

Step-by-step explanation:

Given:

two planes at same altitude heading in a collision course.

Plane A at 400 miles from collision point at 200 mph

Plane B at 300 miles from collision point at 150 mph.

Theoretical collision happens in

t = 400/200 = 300/150 = 2 hours

Distance ya of plane A from collision point as a function of time in hours

ya(t) = 400 -200t

Distance yb of plane B from collision point as a function of time in hours

yb(t) = 300-150t

(a) Distance between two planes,

Since the two planes are on courses perpendicular to each other, will need using pythagorean theorem

D(t) = sqrt(ya(t)^2+yb(t)^2)

= sqrt((400-200t)^2+(300-150t)^2)

= 250(t-2)

D(t) = 250t -500 miles

b. time available

Time until D(t) = 0

solve D(t) = 0

D(t) = 0

250(t-2) = 0

t = 2 (two hours)

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3 years ago

Find the sales tax on a $36.89 radio if the tax rate s 7 percent

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4 years ago

Please I need the answer

Vedmedyk [2.9K]

Answer:

x=4

Step-by-step explanation:

Simplifying

2(6x + 4) + -6 + 2x = 3(4x + 3) + 1

Reorder the terms:

2(4 + 6x) + -6 + 2x = 3(4x + 3) + 1

(4 * 2 + 6x * 2) + -6 + 2x = 3(4x + 3) + 1

(8 + 12x) + -6 + 2x = 3(4x + 3) + 1

Reorder the terms:

8 + -6 + 12x + 2x = 3(4x + 3) + 1

Combine like terms: 8 + -6 = 2

2 + 12x + 2x = 3(4x + 3) + 1

Combine like terms: 12x + 2x = 14x

2 + 14x = 3(4x + 3) + 1

Reorder the terms:

2 + 14x = 3(3 + 4x) + 1

2 + 14x = (3 * 3 + 4x * 3) + 1

2 + 14x = (9 + 12x) + 1

Reorder the terms:

2 + 14x = 9 + 1 + 12x

Combine like terms: 9 + 1 = 10

2 + 14x = 10 + 12x

Solving

2 + 14x = 10 + 12x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-12x' to each side of the equation.

2 + 14x + -12x = 10 + 12x + -12x

Combine like terms: 14x + -12x = 2x

2 + 2x = 10 + 12x + -12x

Combine like terms: 12x + -12x = 0

2 + 2x = 10 + 0

2 + 2x = 10

Add '-2' to each side of the equation.

2 + -2 + 2x = 10 + -2

Combine like terms: 2 + -2 = 0

0 + 2x = 10 + -2

2x = 10 + -2

Combine like terms: 10 + -2 = 8

2x = 8

Divide each side by '2'.

x = 4

Simplifying

x = 4

Hope it helps!

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3 years ago

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