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andrey2020 [161]
3 years ago
10

Which of the following pairs are not equivalent statements?

Mathematics
1 answer:
lesya692 [45]3 years ago
4 0

Answer:

sorry but what is this I don't understand?

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What is the result of isolating x^2 in the equation below 10x^2-36y^2=100
aniked [119]
For the answer to the question above,
<span>10x^2-36y^2=100
Then isolate x^2, first add 36y^2 to both sides: 10x^2 = 100 + 36y^2 divide both sides by 10:
x^2 = 10 + 3.6y^2 or
10 + 36/10 * y^2 = 10 + 18/5 * y^2
</span>
So the answer to this question is
<span><span>x2</span>=10 + (<span>18/5)</span><span>y2

I hope my answer helped you. Have a nice day!</span></span>
5 0
3 years ago
Read 2 more answers
You deposit $650 in a savings account. How long does it take an account with an annual interest rate of 5% to earn $178.25 in in
laiz [17]

Answer:

It takes an account 5.4 years  to earn $178.25 in interest with an annual interest rate of 5%.

Step-by-step explanation:

You can use the following formula to calculate the time it takes an account to earn a certain amount in interest:

t=(1/r)*((F/P)-1), where:

t= time

r= rate of interest= 5%

F= future value= 650+178.25=828.25

P= present value= 650

Now, you can replace the values on the formula:

t=(1/0.05)*((828.25/650)-1)

t=20*0.27

t=5.4

According to this, the answer is that it takes an account 5.4 years  to earn $178.25 in interest with an annual interest rate of 5%.

3 0
3 years ago
Find all the missing sides or angles in each right triangles
astra-53 [7]
In previous lessons, we used the parallel postulate to learn new theorems that enabled us to solve a variety of problems about parallel lines:

Parallel Postulate: Given: line l and a point P not on l. There is exactly one line through P that is parallel to l.

In this lesson we extend these results to learn about special line segments within triangles. For example, the following triangle contains such a configuration:

Triangle <span>△XYZ</span> is cut by <span><span>AB</span><span>¯¯¯¯¯¯¯¯</span></span> where A and B are midpoints of sides <span><span>XZ</span><span>¯¯¯¯¯¯¯¯</span></span> and <span><span>YZ</span><span>¯¯¯¯¯¯¯</span></span> respectively. <span><span>AB</span><span>¯¯¯¯¯¯¯¯</span></span> is called a midsegment of <span>△XYZ</span>. Note that <span>△XYZ</span> has other midsegments in addition to <span><span>AB</span><span>¯¯¯¯¯¯¯¯</span></span>. Can you see where they are in the figure above?

If we construct the midpoint of side <span><span>XY</span><span>¯¯¯¯¯¯¯¯</span></span> at point C and construct <span><span>CA</span><span>¯¯¯¯¯¯¯¯</span></span> and <span><span>CB</span><span>¯¯¯¯¯¯¯¯</span></span> respectively, we have the following figure and see that segments <span><span>CA</span><span>¯¯¯¯¯¯¯¯</span></span> and <span><span>CB</span><span>¯¯¯¯¯¯¯¯</span></span> are midsegments of <span>△XYZ</span>.

In this lesson we will investigate properties of these segments and solve a variety of problems.

Properties of midsegments within triangles

We start with a theorem that we will use to solve problems that involve midsegments of triangles.

Midsegment Theorem: The segment that joins the midpoints of a pair of sides of a triangle is:

<span>parallel to the third side. half as long as the third side. </span>

Proof of 1. We need to show that a midsegment is parallel to the third side. We will do this using the Parallel Postulate.

Consider the following triangle <span>△XYZ</span>. Construct the midpoint A of side <span><span>XZ</span><span>¯¯¯¯¯¯¯¯</span></span>.

By the Parallel Postulate, there is exactly one line though A that is parallel to side <span><span>XY</span><span>¯¯¯¯¯¯¯¯</span></span>. Let’s say that it intersects side <span><span>YZ</span><span>¯¯¯¯¯¯¯</span></span> at point B. We will show that B must be the midpoint of <span><span>XY</span><span>¯¯¯¯¯¯¯¯</span></span> and then we can conclude that <span><span>AB</span><span>¯¯¯¯¯¯¯¯</span></span> is a midsegment of the triangle and is parallel to <span><span>XY</span><span>¯¯¯¯¯¯¯¯</span></span>.

We must show that the line through A and parallel to side <span><span>XY</span><span>¯¯¯¯¯¯¯¯</span></span> will intersect side <span><span>YZ</span><span>¯¯¯¯¯¯¯</span></span> at its midpoint. If a parallel line cuts off congruent segments on one transversal, then it cuts off congruent segments on every transversal. This ensures that point B is the midpoint of side <span><span>YZ</span><span>¯¯¯¯¯¯¯</span></span>.

Since <span><span><span>XA</span><span>¯¯¯¯¯¯¯¯</span></span>≅<span><span>AZ</span><span>¯¯¯¯¯¯¯</span></span></span>, we have <span><span><span>BZ</span><span>¯¯¯¯¯¯¯</span></span>≅<span><span>BY</span><span>¯¯¯¯¯¯¯¯</span></span></span>. Hence, by the definition of midpoint, point B is the midpoint of side <span><span>YZ</span><span>¯¯¯¯¯¯¯</span></span>. <span><span>AB</span><span>¯¯¯¯¯¯¯¯</span></span> is a midsegment of the triangle and is also parallel to <span><span>XY</span><span>¯¯¯¯¯¯¯¯</span></span>.

Proof of 2. We must show that <span>AB=<span>12</span>XY</span>.

In <span>△XYZ</span>, construct the midpoint of side <span><span>XY</span><span>¯¯¯¯¯¯¯¯</span></span> at point C and midsegments <span><span>CA</span><span>¯¯¯¯¯¯¯¯</span></span> and <span><span>CB</span><span>¯¯¯¯¯¯¯¯</span></span> as follows:

First note that <span><span><span>CB</span><span>¯¯¯¯¯¯¯¯</span></span>∥<span><span>XZ</span><span>¯¯¯¯¯¯¯¯</span></span></span> by part one of the theorem. Since <span><span><span>CB</span><span>¯¯¯¯¯¯¯¯</span></span>∥<span><span>XZ</span><span>¯¯¯¯¯¯¯¯</span></span></span> and <span><span><span>AB</span><span>¯¯¯¯¯¯¯¯</span></span>∥<span><span>XY</span><span>¯¯¯¯¯¯¯¯</span></span></span>, then <span>∠<span>XAC</span>≅∠<span>BCA</span></span> and <span>∠<span>CAB</span>≅∠<span>ACX</span></span> since alternate interior angles are congruent. In addition, <span><span><span>AC</span><span>¯¯¯¯¯¯¯¯</span></span>≅<span><span>CA</span><span>¯¯¯¯¯¯¯¯</span></span></span>.

Hence, <span>△<span>AXC</span>≅△<span>CBA</span></span> by The ASA Congruence Postulate. <span><span><span>AB</span><span>¯¯¯¯¯¯¯¯</span></span>≅<span><span>XC</span><span>¯¯¯¯¯¯¯¯</span></span></span> since corresponding parts of congruent triangles are congruent. Since C is the midpoint of <span><span>XY</span><span>¯¯¯¯¯¯¯¯</span></span>, we have <span>XC=CY</span> and <span>XY=XC+CY=XC+XC=2AB</span> by segment addition and substitution.

So, <span>2AB=XY</span> and <span>AB=<span>12</span>XY</span>. ⧫

Example 1

Use the Midsegment Theorem to solve for the lengths of the midsegments given in the following figure.

M, N and O are midpoints of the sides of the triangle with lengths as indicated. Use the Midsegment Theorem to find

<span><span> A. <span>MN</span>. </span><span> B. The perimeter of the triangle <span>△XYZ</span>. </span></span><span><span> A. Since O is a midpoint, we have <span>XO=5</span> and <span>XY=10</span>. By the theorem, we must have <span>MN=5</span>. </span><span> B. By the Midsegment Theorem, <span>OM=3</span> implies that <span>ZY=6</span>; similarly, <span>XZ=8</span>, and <span>XY=10</span>. Hence, the perimeter is <span>6+8+10=24.</span> </span></span>

We can also examine triangles where one or more of the sides are unknown.

Example 2

<span>Use the Midsegment Theorem to find the value of x in the following triangle having lengths as indicated and midsegment</span> <span><span>XY</span><span>¯¯¯¯¯¯¯¯</span></span>.

By the Midsegment Theorem we have <span>2x−6=<span>12</span>(18)</span>. Solving for x, we have <span>x=<span>152</span></span>.

<span> Lesson Summary </span>
8 0
3 years ago
A quality control inspector has determined that 0.25% of all parts manufactured by a particular machine are defective. If 50 par
Arlecino [84]

Answer:

9.941*10^-6

Step-by-step explanation:

Probability of at most 1 means not more than 1 defective= probability of 1 or probability of 0

Probability of 1 = 50C1(0.25)(0.75)^49

Probability= 50(0.25)*7.55*10^-7

Probability= 9.375*10^-6

Probability of 0

= 50C0(0.25)^0(0.75)^50

= 1(1)(0.566*10^-6)

= 0.566*10^-6

Total probability

= 9.375*10^-6+ 0.566*10^-6

= 9.941*10^-6

4 0
3 years ago
I’m pretty sure the answer is 50.3 but could someone please tell me if it’s square yards or yards?
olchik [2.2K]

Answer:

yards because it can't be squared if its a circle

Step-by-step explanation:

3 0
3 years ago
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