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raketka [301]
2 years ago
5

Only Question #5! If JKLM is a rectangle, find Measure NML

Mathematics
1 answer:
Allushta [10]2 years ago
8 0

Answer;

5. 22°

6. 74°

Step-by-step explanation:

5. Since rectangle JKLM has two equal diagonals that intersect each other, therefore JN = MN.

If JN = MN therefore:

m<NMJ = m<NJM

Thus:

3x + 38 = 7x - 2

Solve for x. Collect like terms

3x - 7x = -38 - 2

-4x = - 40

Divide both sides by -4

x = 10

✔️Find m<NMJ

m<NMJ = 7x - 2

Plug in the value of x

m<NMJ = 7(10) - 2 = 70 - 2

m<NMJ = 68°

✔️Find m<NML;

m<NML = 90 - 68° (Complimentary angles)

m<NML = 22°

6. Diagonal of a rhombus bisects teach vertex angle, this means that <U is divided into two equal parts. Therefore:

10x - 23 = 3x + 19

Solve for x. Collect like terms

10x - 3x = 23 + 19

7x = 42

Divide both sides by 7

x = 6

✔️Find m<RST:

m<SUT = m<RST (opposite angles of a rhombus are congruent)

Thus,

m<SUT = (10x - 23) + (3x + 19)

Plug in the value of x

m<SUT = (10(6) - 23) + (3(6) + 19)

= (60 - 23) + (18 + 19)

= 37 + 37

m<SUT = 74°

Also, m<RST = 74°

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3 0
3 years ago
Perry is buying an I phone that is a sale for 40% off the original price.after he uses a $25 gift card.the total cost before tax
marta [7]

Answer:

$599

Step-by-step explanation:

Given: Discount- 40% off on original price.

           Gift card= $25

           Total cost before taxes is $334.40

Lets assume the original price be "x".

We know there is 40% on original price and Perry uses $25 gift card.

Remember; Total cost= Original\ price- discount- gift\ card

Now, finding the original price of Iphone.

⇒ x-0.40x-25= 334.40

⇒ 0.60x-25= 334.40

Adding both side by 25

⇒0.60x= 334.40+25

⇒0.60x= 359.4

Dividing both side by 0.60

⇒ x= \frac{359.4}{0.60}

∴ x= 599

Hence, the original price of iphone is $599

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3 years ago
Anita Read 24 Pages Of Her Book In 12 Minutes . How Long Will It Take Her To Read 34 Pages ?
Digiron [165]
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7 0
3 years ago
PLEASE HELP FAST!!!!!!!!!
Lana71 [14]

Answer:

132 degrees

Step-by-step explanation:

To solve this problem, you need to know a couple of rules

1) Inscribed angle theroem: when an angle is inscribed in a circle and touches the other end (as opposed to ending at the diameter of the circle), the measure of this angle is half of the measure of the arc.

2)Angles of a quadrilateral shape add up to 360 degrees.

3) The angles inside a circle and the angles of the circles arclength adds up to 360 degrees.

So first, solve angle S with inscribed angle theorem. 126/2 = 63

Then, use the rule that all arc angles in a circle add up to 360 degrees to find the arc angle from Q to S. 360-90-126 = 144. Now find angle P with inscribed angle theorem by doing 144/2 = 72.

Now, use the rule that all angles in a quadrilateral add up to 360 to find R. 360-93-72-63 = 132.  

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7 0
2 years ago
Here is an equilateral triangle. The length of each side is units. A height is drawn. In an equilateral triangle, a line drawn f
Temka [501]

1. Height of the equilateral triangle is: √3 units

2. Area of the equilateral triangle = √3 units²

3. Area = √3/4 x², when each side is x.

<h3>What is an Equilateral Triangle?</h3>

A triangle that has all its three sides equal in length, is referred to as an equilateral triangle.

1. Given the each side measures 2 units, and h is the height, applying the Pythagorean theorem, we would have:

h = √(2² - 1²)

h = √(4 - 1)

h = √3

2. Area of the equilateral triangle = 1/2bh = 1/2(2)(√3)

Area of the equilateral triangle = √3 units²

3. If x is the side length of the equilateral triangle, we would have:

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Area = 1/2bh = 1/2(x)(√3/2x) = √3/4 x²

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