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2 years ago

he heights of △ABC are drawn from vertices A and C. These heights intersect at point M. Find m∠AMC, if m∠A=70° and m∠C=80°.

Mathematics

1 answer:

raketka [301]2 years ago

3 0

Answer: 150°

Step-by-step explanation:

In the given triangle ABC ∠A=70°, ∠C=80°

therefore ∠B=180-(∠A+∠C)=180-(70+80) [sum angle property of triangle]

⇒∠B=30°

Now, heights(altitude) are drawn from vertices A and C on respective bases

they intersect at a point M. Also, we know that heights are perpendicular on the bases.

Also, point of intersection of altitudes is called orthocenter.

Now since M is orthocenter, ∠ABC+∠AMC=180° (property of orthocenter in a triangle)

⇒30°+∠AMC=180°

⇒∠AMC=180°-30°=150°

<u>Hence in the triangle ABC, ∠AMC=150°</u>

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luda_lava [24]

Answer:

The standard deviation of the data set is $\sigma = 12.7906$ .

Step-by-step explanation:

The Standard Deviation is a measure of how spread out numbers are. Its symbol is σ (the greek letter sigma)

To find the standard deviation of the following data set

$\begin{array}{cccccccc}83&87&90&92&93&100&104&111\\115&121&&&&&&\end{array}$

we use the following formula

$\sigma = \sqrt{ \frac{ \sum{\left(x_i - \overline{X}\right)^2 }}{n-1} }$

Step 1: Find the mean $\left( \overline{X} \right)$ .

The mean of a data set is the sum of the terms divided by the total number of terms. Using math notation we have:

$Mean = \frac{Sum ~ of ~ terms}{Number ~ of ~ terms}$

$Mean = \frac{Sum ~ of ~ terms}{Number ~ of ~ terms}=\frac{83+87+90+92+93+100+104+111+115+121}{10} \\\\Mean = \frac{996}{10} =\frac{498}{5}=99.6$

Step 2: Create the below table.

Step 3: Find the sum of numbers in the last column to get.

$\sum{\left(x_i - \overline{X}\right)^2} = 1472.4$

Step 4: Calculate σ using the above formula.

$\sigma = \sqrt{ \frac{ \sum{\left(x_i - \overline{X}\right)^2 }}{n-1} } = \sqrt{ \frac{ 1472.4 }{ 10 - 1} } \approx 12.7906$

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2 years ago

Jaleel and Lisa are simplifying the expression 2 (x minus 2) + 2 as shown. Jaleel’s Method 2 (x minus 2) + 2 = 2 x minus 4 + 2 =

Art [367]

Answer:

(D)Jaleel's method is correct because 2(x-2)=2x-4.

Step-by-step explanation:

Jaleel and Lisa are simplifying the expression 2(x-2)+2 as shown.

$J$aleel's Method: \left\{\begin{array}{ccc}2 (x -2) + 2 \\= 2 x - 4 + 2 \\= 2 x - 2\end{array}\right$

$L$isa's Method: \left\{\begin{array}{ccc}2 (x-2) + 2 \\= 2 x -2 + 2 \\= 2 x\end{array}\right$

We can see that Jaleel's method is correct because:

2(x-2)=2x-4.

When you expand, you must multiply the term outside by all the terms inside the bracket.

The correct option is D.

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2 years ago

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Liza's cousin Marie bought her a ring for 250 euros in France. Liza wants to pay Marie for it in U.S. dollars. If the foreign ex

EleoNora [17]

Answer:

416.67 dollars

Step-by-step explanation:

the exchange rate between U.S. dollar and euro is given as

Exchange rate = 1:0.6

1 U.S. dollar /1 euro = 0.6

cross-multiplying both side

1 x 1 U.S. dollar = 0.6 x 1 euro

1 U.S. dollar = 0.6 euro

multiplying both side by 10

10 U.S. dollar = 0.6 x 10 euro

10 U.S. dollar = 6 euro

dividing both side by "6"

10 U.S. dollar/6 = 6 euro/6

(10/6) U.S. dollar = 1 euro

1 euro = (10/6) U.S. dollar

the ring was bought for 250 euros , we need to convert 250 euros in dollars.

multiplying both side by 250

250 x 1 euro = (250 x 10/6) U.S. dollar

250 euro = 416.67 U.S. dollar

so liza should pay 416.67 U.S. dollar to marie.

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gladu [14]

Answer:

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2 years ago

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Dmitrij [34]

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2 years ago