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3 years ago

In an arithmetic sequence a17=-40 and a28=-73 write the first 5 terms

Mathematics

1 answer:

Alla [95]3 years ago

5 0

Answer:

First 5 terms: 8, 5, 2, -1, -4

Step-by-step explanation:

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Work varies directly with the

irinina [24]

Answer:

yes

Step-by-step explanation:

6 0

3 years ago

In a right triangle ABC, CD is an altitude, such that AD=BC. Find AC, if AB=3 cm, and CD= 2 cm.

konstantin123 [22]

Consider right triangle ΔABC with legs AC and BC and hypotenuse AB. Draw the altitude CD.

1. Theorem: The length of each leg of a right triangle is the geometric mean of the length of the hypotenuse and the length of the segment of the hypotenuse adjacent to that leg.

According to this theorem,

$BC^2=BD\cdot AB.$

Let BC=x cm, then AD=BC=x cm and BD=AB-AD=3-x cm. Then

$x^2=(3-x)\cdot 3,\\ \\x^2=9-3x,\\ \\x^2+3x-9=0,\\ \\D=3^2-4\cdot (-9)=9+36=45,\\ \\\sqrt{D}=\sqrt{45}=3\sqrt{5},\\ \\x_1=\dfrac{-3-3\sqrt{5} }{2}0.$

Take positive value x. You get

$AD=BC=\dfrac{-3+3\sqrt{5} }{2}\ cm.$

2. According to the previous theorem,

$AC^2=AD\cdot AB.$

Then

$AC^2=\dfrac{-3+3\sqrt{5} }{2}\cdot 3=\dfrac{-9+9\sqrt{5} }{2},\\ \\AC=\sqrt{\dfrac{-9+9\sqrt{5} }{2}}\ cm.$

Answer: $AC=\sqrt{\dfrac{-9+9\sqrt{5} }{2}}\ cm.$

This solution doesn't need CD=2 cm. Note that if AB=3cm and CD=2cm, then

$CD^2=AD\cdot DB,\\ \\2^2=AD\cdot (3-AD),\\ \\AD^2-3AD+4=0,\\ \\D$

This means that you cannot find solutions of this equation. Then CD≠2 cm.

8 0

3 years ago

Read 2 more answers

Nicole and adam are each saving money for a car. the total amount of money nicole will save is represented by the function f (x)

Yakvenalex [24]

For this case we have the following functions:
f (x) = 36 + 4x
g (x) = x2 + 15
By matching both functions we have:
f (x) = g (x)
36 + 4x = x2 + 15
Rewriting we have:
x2 + 15 - 4x - 36 = 0
x2 - 4x - 21 = 0
Solving the polynomial we have:
(x-7) (x + 3) = 0
x = -3
x = 7
Taking the positive root we have:
x = 7
Answer:
They will have the same amount of money saved after:
x = 7 weeks

8 0

3 years ago

Read 2 more answers

What is the answer to this question?

saul85 [17]

B is the correct answer

8 0

3 years ago

Read 2 more answers

Need help pls answer asap. Sorry the photo quality is bad.

castortr0y [4]

Answer:

Step-by-step explanation:

1 + 3 = 4

so find the point 1/4 of the way from (-1, 2) to (7, 8)

x coordinate

Δx = ¼(7 - (-1)) = 2

x = x₀ + Δx

x = -1 + 2 = 1

y coordinate

Δy = ¼(8 - 2) = 1½

y = y₀ + Δy

y = 2 + 1½ = 3½

(1, 3½)

4 0

3 years ago