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2 years ago

The opposite angles of a parallelogram are (3x + 5)° and (61 – x)°. Find the measure of four angles.

Mathematics

1 answer:

DanielleElmas [232]2 years ago

5 0

Answer:

47°;47°;113°;113°

Step-by-step explanation:

3x+5=61-x

4x=56

X=14

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A polynomial function upper P left parenthesis x right parenthesis with rational coefficients has the given roots. Find two addi

mylen [45]

Given that a polynomial function P(x) has rational coefficients.

Two roots are already given which are i and 7+8i,

Now we have to find two additional roots of P(x)=0

Given roots i and 7+8i are complex roots and we know that complex roots always occur in conjugate pairs so that means conjugate of given roots will also be the roots.

conjugate of a+bi is given by a-bi

So using that logic, conjugate of i is i

also conjugate of 7+8i is 7-8i

Hence final answer for the remaining roots are (-i) and (7-8i).

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2 years ago

A bag contains 50 blue marbles and 66 red marbles. If 88 more red marbles are added to the bag, how many more blue marbles must

vaieri [72.5K]

Answer:

Step-by-step explanation:

After adding 88 red marbles, there are 50 blue marbles out of the 204 marbles total.

Let the number of blue marbles to be added be x.

$\frac{50+x}{204+x}=\frac{5}{12} \\ \\ 600+12x=1020+5x \\ \\ 420=7x \\ \\ x=60$

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1 year ago

(HELP PLEASE) It costs $68 for 16 square feet of flooding. How much does it cost for 12 square feet of flooring?

FromTheMoon [43]

Answer:

12 feet of flooring cost $51

Step-by-step explanation:

68/16 = 4.25

4.25 x 12 = 51

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3 years ago

Read 2 more answers

Divide line segments

ser-zykov [4K]

tis noteworthy that the segment contains endpoints of A and C and the point B is in between A and C cutting the segment in a 1:2 ratio,

$\bf \textit{internal division of a line segment using ratios} \\\\\\ A(-9,-7)\qquad C(x,y)\qquad \qquad \stackrel{\textit{ratio from A to C}}{1:2} \\\\\\ \cfrac{A\underline{B}}{\underline{B} C} = \cfrac{1}{2}\implies \cfrac{A}{C}=\cfrac{1}{2}\implies 2A=1C\implies 2(-9,-7)=1(x,y)\\\\[-0.35em] ~\dotfill\\\\ B=\left(\frac{\textit{sum of "x" values}}{\textit{sum of ratios}}\quad ,\quad \frac{\textit{sum of "y" values}}{\textit{sum of ratios}}\right)\\\\[-0.35em] ~\dotfill$

$\bf B=\left(\cfrac{(2\cdot -9)+(1\cdot x)}{1+2}\quad ,\quad \cfrac{(2\cdot -7)+(1\cdot y)}{1+2}\right)~~=~~(-4,-6) \\\\[-0.35em] ~\dotfill\\\\ \cfrac{(2\cdot -9)+(1\cdot x)}{1+2}=-4\implies \cfrac{-18+x}{3}=-4 \\\\\\ -18+x=-12\implies \boxed{x=6} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{(2\cdot -7)+(1\cdot y)}{1+2}=-6\implies \cfrac{-14+y}{3}=-6 \\\\\\ -14+y=-18\implies \boxed{y=-4}$

6 0

3 years ago

A movie theater sends out a coupon for 85% off the price of a ticket. Write an equation for the situation, where y is the pri

ra1l [238]

Answer:

$y=0.15x$

Step-by-step explanation:

Given:

Original price of the ticket is $x$

Price after using the coupon is $y$

Coupon discount is 85% of $x=0.85x$

Therefore, the price after applying coupon is given as the difference of the original price and the coupon discount. That is,

$y=x-0.85x=x(1-0.85)=0.15x\\\therefore y=0.15x$

The graph is shown below. The graph passes through the origin as the above relationship is a proportional relationship.

The line $y=0.15x$ strictly remains in the first quadrant as both $x$ and $y$ can't be negative as they represent price of tickets and price can never have negative values. Hence, only the first quadrant has both the values of $x$ and $y$ positive.

3 0

3 years ago