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2 years ago

What is the measure of the vertex angle of an isosceles triangle if one of its base angles measures 42°?

Mathematics

1 answer:

blsea [12.9K]2 years ago

3 0

Answer:

96 degrees

Step-by-step explanation:

you have two angles that each measure 42 degrees, giving you 84 degrees combined

there are 180 degrees in a triangle, therefore the vertex angle is equal to 180 minus 84, or 96 degrees

check:

42 + 42 + 96 = 180

180 = 180

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Which expression represents the number 2i4−5i3+3i2+−81‾‾‾‾√ rewritten in a+bi form?

vichka [17]

Answer:

The expression $-1+14i$ represents the number $2i^4-5i^3+3i^2+\sqrt{-81}$ rewritten in a+bi form.

Step-by-step explanation:

The value of $i$ is $i=\sqrt{-1}[tex] or [tex]i^{2}=-1[\tex].Now [tex]i^{4}$ in term of $i^{2}[\tex] can be written as, [tex]i^{4}=i^{2}\times i^{2}$

Substituting the value,

$i^{4}=\left(-1\right)\times \left(-1\right)$

Product of two negative numbers is always positive.

$\therefore i^{4}=1$

Now $i^{3}$ in term of $i^{2}[\tex] can be written as, [tex]i^{3}=i^{2}\times i$

Substituting the value,

$i^{3}=\left(-1\right)\times i$

Product of one negative and one positive numbers is always negative.

$\therefore i^{3}=-i$

Now $\sqrt{-81}$ can be written as follows,

$\sqrt{-81}=\sqrt{\left(81\right)\times\left(-1\right)}$

Applying radical multiplication rule,

$\sqrt{ab}={\sqrt{a}}\sqrt{b}$

$\sqrt{\left(81\right)\times\left(-1\right)}={\sqrt{81}}\sqrt{-1}$

Now, $\sqrt{\left(81\right)=9$ and $\sqrt{-1}}=i$

$\therefore \sqrt{\left(81\right)\times\left(-1\right)}=9i$

Now substituting the above values in given expression,

$2i^4-5i^3+3i^2+\sqrt{-81}=2\left(1\right)-5\left(-i\right)+3\left(-1\right)+9i$

Simplifying,

$2+5i-3+9i$

Collecting similar terms,

$2-3+5i+9i$

Combining similar terms,

$-1+14i$

The above expression is in the form of a+bi which is the required expression.

Hence, option number 4 is correct.

5 0

3 years ago

Please answer this correctly

olasank [31]

Answer:

12 days

Step-by-step explanation:

8 0

3 years ago

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Find the x and y intercepts of the graph of the equation y=x^2-5

mr_godi [17]

Answer:

x intercepts -sqrt(5), + sqrt(5)

y intercept -5

Step-by-step explanation:

y = x^2 -5

to find the x intercept set y=0 and solve for x

0 = x^2-5

add 5 to each side

5 = x^2

take the square root of each side

+- sqrt(5) = sqrt(x^2)

x = +-sqrt(5) there are 2 x intercepts since it is a quadratic

to find the y intercept set x=0 and solve for y

y = 0-5

y = -5

8 0

2 years ago

What is the length of the line segment BC

Blizzard [7]

I don't know you have to use a measuring tool to figure it out ruler helps sorry try a ruler of a angle scale

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2 years ago

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What is the value of x

motikmotik

Answer:

x = 4

Step-by-step explanation:

<u>All triangles add up to 180 degrees</u>

76 + 17x + 9x = 180

76 + 17x + 9x - 76 = 180 - 76

26x / 26 = 104 / 26

x = 4

Answer: x = 4

3 0

2 years ago