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2 years ago

Find the value of x by filling in the blanks in the provided statement- reason solution

Mathematics

1 answer:

fgiga [73]2 years ago

3 0

Answer/Step-by-step explanation:

Given:

m<MNQ = 132°

m<Q = 54°

m<P = 3x

1. m<MNQ = m<P + m<Q

Reason: exterior angle theorem of a triangle

Plug in the values

2. 132° = 3x + 54°

Reason: Substitution

3. x = 26

Reason: Algebra

132 - 54 = 3x (substraction property of equality)

78 = 3x

78/3 = x (division property of equality)

26 = x

x = 26

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Perform the indicated operations. Write the answer in standard form, a+bi. 5-3i / -2-9i

Vsevolod [243]

$\huge \boxed{\mathfrak{Answer} \downarrow}$

$\large \bf\frac { 5 - 3 i } { - 2 - 9 i } \\$

Multiply both numerator and denominator of $\sf \frac{5-3i}{-2-9i} \\$ by the complex conjugate of the denominator, -2+9i.

$\large \bf \: Re(\frac{\left(5-3i\right)\left(-2+9i\right)}{\left(-2-9i\right)\left(-2+9i\right)}) \\$

Multiplication can be transformed into difference of squares using the rule: $\sf\left(a-b\right)\left(a+b\right)=a^{2}-b^{2}$ .

$\large \bf \: Re(\frac{\left(5-3i\right)\left(-2+9i\right)}{\left(-2\right)^{2}-9^{2}i^{2}}) \\$

By definition, i² is -1. Calculate the denominator.

$\large \bf \: Re(\frac{\left(5-3i\right)\left(-2+9i\right)}{85}) \\$

Multiply complex numbers 5-3i and -2+9i in the same way as you multiply binomials.

$\large \bf \: Re(\frac{5\left(-2\right)+5\times \left(9i\right)-3i\left(-2\right)-3\times 9i^{2}}{85}) \\$

Do the multiplications in $\sf5\left(-2\right)+5\times \left(9i\right)-3i\left(-2\right)-3\times 9\left(-1\right)$ .

$\large \bf \: Re(\frac{-10+45i+6i+27}{85}) \\$

Combine the real and imaginary parts in -10+45i+6i+27.

$\large \bf \: Re(\frac{-10+27+\left(45+6\right)i}{85}) \\$

Do the additions in $\sf-10+27+\left(45+6\right)i$ .

$\large \bf Re(\frac{17+51i}{85}) \\$

Divide 17+51i by 85 to get $\sf\frac{1}{5}+\frac{3}{5}i \\$ .

$\large \bf \: Re(\frac{1}{5}+\frac{3}{5}i) \\$

The real part of $\sf \frac{1}{5}+\frac{3}{5}i \\$ is $\sf \frac{1}{5} \\$ .

$\large \boxed{\bf\frac{1}{5} = 0.2} \\$

3 0

2 years ago

A coordinate map of the local grocery store is shown below. Ice cream is located at the point (-8,0)(−8,0)left parenthesis, minu

Alona [7]

Answer:

Step-by-step explanation:

If on the coordinate map, ice cream is located at the point (-8,0) and sprinkles are located at the point (-8,6), we can find the distance between the coordinate points using the formula;

D = √(x2-x1)²+(y2-y1)²

Given

x1 = -8, y1 = 0, x2 = -8 and y2 = 6

Substitute

D = √(x2-x1)²+(y2-y1)²

D = √(-8-(-8))²+(6-0)²

D = √0²+6²

D = √36

D = 6units

Hence the distance between the coordinate points is 6units

7 0

3 years ago

What’s is 17 subtract 75

Taya2010 [7]

-58 is your answer.
17 - 75 = -58
I hope this helps!

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2 years ago

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The vertices of a triangle are p(3,7) Q(7,-6) R(-8,7). Name the vertices of the image reflected across the x axis

pantera1 [17]

Answer:

P'(3,-7) Q'(7,6) R'(-8,-7).

Step-by-step explanation:

Reflection across the x-axis

Given a point P(x,y), its reflection across the x-axis will map to point P'(x,-y), i.e., the y-coordinate gets inverted.

We are given the vertices of a triangle P(3,7) Q(7,-6) R(-8,7). The vertices of the image reflected across the x-axis are:

P'(3,-7) Q'(7,6) R'(-8,-7).

The new triangle has vertices P'Q'R'.

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2 years ago

Which graph represents the function? f(x) = ∛x+2

Gnoma [55]

Answer:

graph shown in image below

Step-by-step explanation:

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3 years ago

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