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Nutka1998 [239]
2 years ago
13

Find the 89th term of the arithmetic sequence 25, 35, 45, ...

Mathematics
1 answer:
Eddi Din [679]2 years ago
8 0

Answer:

905

Step-by-step explanation:

arithmetic sequence are in form

a(n)=a(0)+d(n-1)

a(0)=25

common difference: d=35-25=10

a(n)=25+10(n-1)

a(89)=25+10(88)=905

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The reasons as well as the answer
Radda [10]

Answer:

x = 46, y = 67

Step-by-step explanation:

x = ∠ AEC = 46 ( alternate angles )

Since Δ ACE is isosceles then the base angles are congruent, then

y = \frac{180-46}{2} = \frac{134}{2} = 67

4 0
3 years ago
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Last week at the park Haeather ran 4 miles in 48 minutes when she runs her next race she Hope's to improve her time by 2 minutes
Korvikt [17]

Answer:

Haeather ran at a speed of 5 miles per hour.

Step-by-step explanation:

Given that last week at the park Haeather ran 4 miles in 48 minutes, to determine what was Haeather rate of speed in miles per hour the following mathematical calculation must be performed:

48/4 = 12

Thus, Haeather ran 1 mile every 12 minutes.

60/12 = 5

1 x 5 = 5

Therefore, Haeather ran at a speed of 5 miles per hour.

3 0
3 years ago
Find the two intersection points
bogdanovich [222]

Answer:

Our two intersection points are:

\displaystyle (3, -2) \text{ and } \left(-\frac{53}{25}, \frac{46}{25}\right)

Step-by-step explanation:

We want to find where the two graphs given by the equations:

\displaystyle (x+1)^2+(y+2)^2 = 16\text{ and } 3x+4y=1

Intersect.

When they intersect, their <em>x-</em> and <em>y-</em>values are equivalent. So, we can solve one equation for <em>y</em> and substitute it into the other and solve for <em>x</em>.

Since the linear equation is easier to solve, solve it for <em>y: </em>

<em />\displaystyle y = -\frac{3}{4} x + \frac{1}{4}<em />

<em />

Substitute this into the first equation:

\displaystyle (x+1)^2 + \left(\left(-\frac{3}{4}x + \frac{1}{4}\right) +2\right)^2 = 16

Simplify:

\displaystyle (x+1)^2 + \left(-\frac{3}{4} x  + \frac{9}{4}\right)^2 = 16

Square. We can use the perfect square trinomial pattern:

\displaystyle \underbrace{(x^2 + 2x+1)}_{(a+b)^2=a^2+2ab+b^2} + \underbrace{\left(\frac{9}{16}x^2-\frac{27}{8}x+\frac{81}{16}\right)}_{(a+b)^2=a^2+2ab+b^2} = 16

Multiply both sides by 16:

(16x^2+32x+16)+(9x^2-54x+81) = 256

Combine like terms:

25x^2+-22x+97=256

Isolate the equation:

\displaystyle 25x^2 - 22x -159=0

We can use the quadratic formula:

\displaystyle x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}

In this case, <em>a</em> = 25, <em>b</em> = -22, and <em>c</em> = -159. Substitute:

\displaystyle x = \frac{-(-22)\pm\sqrt{(-22)^2-4(25)(-159)}}{2(25)}

Evaluate:

\displaystyle \begin{aligned} x &= \frac{22\pm\sqrt{16384}}{50} \\ \\ &= \frac{22\pm 128}{50}\\ \\ &=\frac{11\pm 64}{25}\end{aligned}

Hence, our two solutions are:

\displaystyle x_1 = \frac{11+64}{25} = 3\text{ and } x_2 = \frac{11-64}{25} =-\frac{53}{25}

We have our two <em>x-</em>coordinates.

To find the <em>y-</em>coordinates, we can simply substitute it into the linear equation and evaluate. Thus:

\displaystyle y_1 = -\frac{3}{4}(3)+\frac{1}{4} = -2

And:

\displaystyle y _2 = -\frac{3}{4}\left(-\frac{53}{25}\right) +\frac{1}{4} = \frac{46}{25}

Thus, our two intersection points are:

\displaystyle (3, -2) \text{ and } \left(-\frac{53}{25}, \frac{46}{25}\right)

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3 years ago
Please help!! <br><br><br> Find the inverse of y=7x-10. Is the inverse a function?
kolezko [41]

Answer: f^{-1} (x) = \frac{x+10}{7}

Step-by-step explanation:

To find the inverse , all we need do is to make x the subject of the formula.

y = 7x - 10

Add 10 to both sides

y + 10 = 7x

divide both sides by 7

Therefore:

x = y + 10 / 7 , that is

f^{-1} (x) = \frac{x+10}{7}

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Nitella [24]
1 can go into anything so that is the mystery number sorry if not right first time on here
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