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spin [16.1K]
3 years ago
7

If two angles of a triangle measure 39° and 56°, what is the measure of the third angle? A. 85° B. 55° C. 105° D. 265°

Mathematics
1 answer:
yarga [219]3 years ago
8 0

Answer:

A

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

Subtract the sum of the 2 given angles from 180 for third angle

third angle = 180° - (39 + 56)° = 180° - 95° = 85° → A

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Enter the correct answer in the box. solve the equation x2 − 16x 54 = 0 by completing the square. fill in the values of a and b
poizon [28]

The roots of the given polynomials exist  $x=8+\sqrt{10}$, and $x=8-\sqrt{10}$.

<h3>What is the formula of the quadratic equation?</h3>

For a quadratic equation of the form $a x^{2}+b x+c=0$ the solutions are

$x_{1,2}=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

Therefore by using the formula we have

$x^{2}-16 x+54=0$$

Let, a = 1, b = -16 and c = 54

Substitute the values in the above equation, and we get

$x_{1,2}=\frac{-(-16) \pm \sqrt{(-16)^{2}-4 \cdot 1 \cdot 54}}{2 \cdot 1}$$

simplifying the equation, we get

$&x_{1,2}=\frac{-(-16) \pm 2 \sqrt{10}}{2 \cdot 1} \\

$&x_{1}=\frac{-(-16)+2 \sqrt{10}}{2 \cdot 1}, x_{2}=\frac{-(-16)-2 \sqrt{10}}{2 \cdot 1} \\

$&x=8+\sqrt{10}, x=8-\sqrt{10}

Therefore, the roots of the given polynomials are $x=8+\sqrt{10}$, and

$x=8-\sqrt{10}$.

To learn more about quadratic equations refer to:

brainly.com/question/1214333

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3 0
1 year ago
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Please help using the picture below I need the surface area I also need an explanation
Taya2010 [7]

Answer:

155

Step-by-step explanation:

5*5=25

((5*13)/2)*4=130

130+25=155

6 0
2 years ago
1. Identify the DEPENDENT VARIABLE in the testable
MAVERICK [17]

To identify the dependent variable in the testable, look out for the variable that is affected by the other. The variable that changes as a result of another variable is the dependent variable.

In a research study, there are typically two main variables that direct the scientific enquiry. They are:

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The independent variable causes a change in the dependent variable, i.e. the dependent variable receives the <em>effect</em>, the independent variable is the <em>cause </em>of the change.

It is very easy to identify the dependent variable in any testable hypothesis once you are able to pick out which variable is causing a change in the other.

For example, let's say the topic of a research is: <em>The Impact of Sunlight on Germination Rate of Seedlings.</em>

Here, <em>Sunlight </em>is the independent variable affecting <em>Germination Rate</em>.

The dependent variable here would be: <u><em>Germination Rate.</em></u>

Therefore, to identify the dependent variable in the testable, look out for the variable that is affected by the other. The variable that changes as a result of another variable is the dependent variable.

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5 0
2 years ago
Find the 2th term of the expansion of (a-b)^4.​
vladimir1956 [14]

The second term of the expansion is -4a^3b.

Solution:

Given expression:

(a-b)^4

To find the second term of the expansion.

(a-b)^4

Using Binomial theorem,

(a+b)^{n}=\sum_{i=0}^{n}\left(\begin{array}{l}n \\i\end{array}\right) a^{(n-i)} b^{i}

Here, a = a and b = –b

$(a-b)^4=\sum_{i=0}^{4}\left(\begin{array}{l}4 \\i\end{array}\right) a^{(4-i)}(-b)^{i}

Substitute i = 0, we get

$\frac{4 !}{0 !(4-0) !} a^{4}(-b)^{0}=1 \cdot \frac{4 !}{0 !(4-0) !} a^{4}=a^4

Substitute i = 1, we get

$\frac{4 !}{1 !(4-1) !} a^{3}(-b)^{1}=\frac{4 !}{3!} a^{3}(-b)=-4 a^{3} b

Substitute i = 2, we get

$\frac{4 !}{2 !(4-2) !} a^{2}(-b)^{2}=\frac{12}{2 !} a^{2}(-b)^{2}=6 a^{2} b^{2}

Substitute i = 3, we get

$\frac{4 !}{3 !(4-3) !} a^{1}(-b)^{3}=\frac{4}{1 !} a(-b)^{3}=-4 a b^{3}

Substitute i = 4, we get

$\frac{4 !}{4 !(4-4) !} a^{0}(-b)^{4}=1 \cdot \frac{(-b)^{4}}{(4-4) !}=b^{4}

Therefore,

$(a-b)^4=\sum_{i=0}^{4}\left(\begin{array}{l}4 \\i\end{array}\right) a^{(4-i)}(-b)^{i}

=\frac{4 !}{0 !(4-0) !} a^{4}(-b)^{0}+\frac{4 !}{1 !(4-1) !} a^{3}(-b)^{1}+\frac{4 !}{2 !(4-2) !} a^{2}(-b)^{2}+\frac{4 !}{3 !(4-3) !} a^{1}(-b)^{3}+\frac{4 !}{4 !(4-4) !} a^{0}(-b)^{4}=a^{4}-4 a^{3} b+6 a^{2} b^{2}-4 a b^{3}+b^{4}

Hence the second term of the expansion is -4a^3b.

3 0
3 years ago
Find the midpoint of MN M=-24 N=1
LekaFEV [45]
Midpoint=12.5 let me know if this helps
4 0
3 years ago
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