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sergey [27]
3 years ago
14

1. Circles and segments create the many relationships addressed in the theorems throughout this unit. Use those theorems and the

information given for the following diagram to find each indicated measure. Show all your work. Note that the importance of justifications for your answers is equal to or greater than the importance of simply the answers in the earning of points.

Mathematics
1 answer:
jeyben [28]3 years ago
8 0
(a) m<IJK = 90 since segment IK is a diameter
(b) KI = 10 since since LM = KM = KI = 5. The 3 segments are radii.
(c) EP * PL = OP * PF; EP = 2
(d) m<OFH = 178/2 = 89; inscribed angle is half measure of intercepted arc
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Write an<br> explicit formula for An, the nth term of the sequence 7, -42, 252, ....
erik [133]

Answer:

A_n = 7(-6)^{n-1}

Step-by-step explanation:

<u>Key skills needed: Explicit formula, Geometric sequence</u>

1) This is a geometric sequence, meaning a constant (like 6 or 3.5) is being multiplied to every term. First we need to find the constant.

This can be done by doing -42 ÷ 7   or   252 ÷ -42

-42 ÷ 7 equals -6.

252 ÷ -42 also equals -6.

2) This means that constant is -6.

3) The general form for an explicit formula of a geometric sequence is:

a_n = a_1(r)^{n-1}

--> r means the constant (or common ratio) that is being multiplied.

--> a_1 means the first term

--> a_n means the "nth" numbered term (so a_3 is the 3rd term, a_{10} is the 10th term and so on).

--> n-1 is just the "n" in a_n minus 1.

4) We can use this formula to create an explicit formula for the geometric sequence in the problem.

--> r = -6 (Since we got -6 as the constant/common ratio).

--> a_1  = 7 (Since 7 is the 1st term)

This means that our formula would be --> A_n = 7(-6)^{n-1}

<em>Hope you understood and have a nice day!! :D</em>

8 0
3 years ago
A man realizes he lost the detailed receipt from the store and only has the credit card receipt with the after-tax total. If the
Ilia_Sergeevich [38]

$972.00/1.08 = Total pre-tax was $900

5 0
3 years ago
Find the slope of a line parallel to a line that contains the points (8, -3) and (2, 5).
Illusion [34]

Answer:

-\frac{4}{3}(Your answer choices were really confusing, so I just put the plain answer)

Step-by-step explanation:

To find the slope of a line with just two points, we can use the formula \frac{y2-y1}{x2-x1}. In this case, \frac{5-(-3)}{2-8}. This is \frac{8}{-6}. This reduces to -\frac{4}{3}

8 0
2 years ago
Help me look at photo below
arsen [322]
The photo is above.... lol
5 0
3 years ago
Fleece vests regularly priced at $15.99 are on sale for $13.99. If the sales tax is 5%, how much can you save by buying the vest
Marysya12 [62]

Saving of $2.10 is made by buying fleece vest on sale.

<u>Solution:</u>

Given that regular price of fleece vest = $15.99

And sale price of fleece vest = $13.99

Sales tax = 5%

When we buy at regular price, total amount including sales tax which needs to be paid is:

\mathrm{A}_{\mathrm{R}} = 15.99 + 5% of 15.99

\begin{array}{l}{\mathrm{A}_{\mathrm{R}}=15.99+5 \times \frac{15.99}{100}} \\\\ {\mathrm{A}_{\mathrm{R}}=15.99\left(\frac{105}{100}\right)=15.99 \times 1.05}\end{array}

When buy at sales price, total amount including sales tax which needs to be paid that is

\begin{array}{l}{\mathrm{A}_{\mathrm{S}}=13.99+5 \% \text { of } 13.99} \\\\ {\mathrm{A}_{\mathrm{S}}=13.99+5 \times \frac{13.99}{100}} \\\\ {\mathrm{A}_{\mathrm{S}}=13.99\left(1+\frac{5}{100}\right)} \\\\ {\mathrm{A}_{\mathrm{S}}=13.99\left(\frac{105}{100}\right)=13.99 \times 1.05}\end{array}

\text { Saving made }=\mathrm{A}_{\mathrm{R}}-\mathrm{A}_{\mathrm{S}}

\begin{array}{l}{=(15.99 \times 1.05)-(13.99 \times 1.05)} \\\\ {=1.05(15.99-13.99)} \\\\ {=1.05 \times 2=\$ 2.10}\end{array}

Hence saving of $2.10 is made by buying fleece vest on sale.

7 0
3 years ago
Read 2 more answers
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