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Tems11 [23]
3 years ago
6

Can someone help me with #18 & #20?​

Mathematics
1 answer:
Nuetrik [128]3 years ago
4 0

Answer:

\large\boxed{18)\ x=13\ and\ y=9}\\\boxed{20)\ AO=8}

Step-by-step explanation:

18)

If a quadrilateral is inscribed in a circle, the opposite angles add up to 180°.

Therefore we have the system of equations:

\left\{\begin{array}{ccc}(6x+23)+(8y+7)=180\\(6x-4)+(12y-2)=180\end{array}\right\\\\\left\{\begin{array}{ccc}6x+8y+(23+7)=180\\6x+12y+(-4-2)=180\end{array}\right\\\left\{\begin{array}{ccc}6x+8y+30=180&|\text{subtract 30 from both sides}\\6x+12y-6=180&|\text{add 6 to both sides}\end{array}\right\\\left\{\begin{array}{ccc}6x+8y=150\\6x+12y=186&|\text{multiply both sides by (-1)}\end{array}\right

\underline{+\\\left\{\begin{array}{ccc}6x+8y=150\\-6x-12y=-186\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad-4y=-36\qquad|\text{divide both sides by (-4)}\\.\qquad\qquad\boxed{y=9}\\\\\text{Put the value of y to the first equation and solve them for x:}\\\\6x+8(9)=150\\6x+72=150\qquad\text{subtract 72 from both sides}\\6x=78\qquad\text{divide both sides by 6}\\\boxed{x=13}

20)

If line AB is tangent to the circle, then the angle A is a right angle

m\angle A=90^o

Therefore the triangle is a right triangle. We can use the Pythagorean theorem:

Let O - center of the circle. Therefoe OA is the radius of a circle.

From a Pythagorean theorem:

AO^2+15^2=(9+8)^2\\\\AO^2+225=17^2\\\\AO^2+225=289\qquad\text{subtract 225 from both sides}\\\\AO^2=64\to AO=\sqrt{64}\\\\AO=8

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Leroi and Sylvia both put $200 in a savings account. Leroi decides he will put in an additional $40 each week. Sylvia decides to
Arlecino [84]

Answer:

First deposit - Same amount

Second deposit - Sylvia

Third deposit - Sylvia

Step-by-step explanation:

Leroi put $200 in their account. They will add $40 every week.

Deposit 1: $240

Deposit 2: $280

Deposit 3: $320

Sylvia put $200 in their account. They will add 20% of the amount in the account each week.

Deposit 1: $240 (20% of $200 is $40)

Deposit 2: $288 (20% of $240 is $48)

Deposit 3: $345.60 (20% of $288 is $57.60)

So, Sylvia and Leroi have the same amount of money in their accounts after the first deposit. After the second and third deposit, Sylvia has more money.

4 0
3 years ago
Triangle ABC contains side lengths b=3 inches and c= 5 inches in two or more sentences describe whether or not it is possible fo
Scrat [10]

Answer:

Since sine of all angles are always less than one, this shows there is no possible way to have an angle C. Thus it is impossible to have a triangle ABC with the given properties of side lengths b=3 inches and c= 5 inches to have angle B =45 degrees.

Step-by-step explanation:

In the attached  drawing, each of the tic-marks are equal and

represent 1 inch each.  The angle B has measure 45.  We can

see by the arc that the line AC, which equals 3 inches, is

not long enough to reach the slanted side of the 45 angle.

Therefore triangle ABC is not possible.  We can also show

by the law of sines that no triangle ABC with the given

properties in possible.

5 0
3 years ago
If sin²∅ + sin∅ = 1 , then what is the value of sin²∅ + sin⁴∅.​
Yakvenalex [24]

Answer:

Step-by-step explanation:

Given  sin²∅ + sin∅ = 1, we are to find the value of  sin²∅ + sin⁴∅. ... 2

From  sin²∅ + sin∅. = 1;  sin²∅ = 1 - sin∅. ... 3

Substitute equation 3 into 1

sin²∅ + sin⁴∅

=  sin²∅ + (sin²∅)²

=  (1 - sin∅)+( 1 - sin∅)²

open the parenthesis

= 1 - sin∅+ (1-2sin∅+ sin²∅)

= 1 - sin∅+ 1-2sin∅+ sin²∅

= 1+1-sin∅-2sin∅+sin²∅

= 2 - 3sin∅+sin²∅

Since sin²∅ = 1 - sin∅, the resulting equation becomes;

= 2 - 3sin∅+(1 - sin∅)

= 2 - 3sin∅+1-sin∅

= 3-4sin∅

7 0
4 years ago
Picture of the question below.
mylen [45]
The correct answer is c I believe so
3 0
3 years ago
Square A and rectangle B have the same width. The length of rectangle B is 4 cm greater than its width. The area of rectangle B
andre [41]
Noting that square A is a square, this is what we have:
A = B
A^2 = B x (B + 4) + 20

I can try subbing in A to B
since A = B:

A^2 = A x (A + 4) + 20
20 = A^2 - (A x (A + 4))
20 = A^2 - (A^2 + 4A)
20 = 4A
A = 5

By the way, A is width of square A and B is the width of rectangle B in my solution,
3 0
3 years ago
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