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2 years ago

What's the hinge theorem and it's converse?

1 answer:

7 0

The converse of the hinge theorem is also true: If the two sides of one triangle are congruent<span> to two sides of another triangle, and the third side of the first triangle is greater than the third side of the second triangle, then the included angle of the first triangle is larger than the included angle of the second .</span>

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Question Please help. Alina spent no more than $45 on gas for a road trip. The first gas station she used charged $3.50 per gall

Nadusha1986 [10]

3.5x + 4y = 45 x=6, y= 6 is the most likely answer. Non whole number variations would be: x=8, y=4.25 x=4, y=7.75

4 0

2 years ago

Sides AB and DC of the rectangle are increased in length by 50% and sides AD and BC are decreased in length by 50%. What is the

emmainna [20.7K]

The percentage of change in the area of the rectangle is -25% ⇒ B

Step-by-step explanation:

The given is:

Sides AB and DC of the rectangle are increased in length by 50%
Sides AD and BC are decreased in length by 50%

We need to find the percentage change in the <em>AREA</em> of the rectangle

Assume that the length of AB ans DC is x units, and the length of AD and BC is y units

∵ The length of the sides AB and DC increased by 50%

∵ The length of AB and CD = x

- That means x will increase by 50% of x

∵ 50% of x = (50 ÷ 100) × x = 0.5 x

∴ The length is increased by 0.5 x

∴ The new length of AB and CD = x + 0.5 x = 1.5 x units

∵ The length of the sides BC and AD decreased by 50%

∵ The length of BC and AD = y

- That means y will decrease by 50% of y

∵ 50% of y = (50 ÷ 100) × y = 0.5 y

∴ The length is decreased by 0.5 y

∴ The new length of BC and AD = y - 0.5 y = 0.5 y units

∵ The area before the change = x × y = xy units²

∵ The area after the change = 1.5 x × 0.5 y = 0.75 xy units²

∵ The new area is less than the old area

∴ The area is decreased

- To find the the percentage of change in the area subtract the

new area from the old area and divide the difference by the

old area and then multiply the quotient by 100%

∴ The percentage of the change = $\frac{xy-0.75xy}{xy}$ × 100%

∴ The percentage of the change = $\frac{0.25xy}{xy}$ × 100%

∴ The percentage of the change = 0.25 × 100%

∴ The percentage of the change = 25%

∴ The area of the rectangle is decreased by 25% ⇒ (-25%)

The percentage of change in the area of the rectangle is -25%

Learn more:

You can learn more about the percentage in brainly.com/question/12960754

#LearnwithBrainly

7 0

2 years ago

Find the given limit lim(x,y)→(a,a)x4−y4x2−y2=lim(x,y)→(a,a) (x^4−y^4)/(x2−y2)= here aa is a constant. (find the limit assuming

Aliun [14]

If $x\neq y$ , then we can write

$\dfrac{x^4-y^4}{x^2-y^2}=\dfrac{(x^2-y^2)(x^2+y^2)}{x^2-y^2}=x^2+y^2$

and since this is continuous for all $x\neq y$ , the limit as $(x,y)\to(a,a)$ will be

$\displaystyle\lim_{(x,y)\to(a,a)}\frac{x^4-y^4}{x^2-y^2}=\lim_{(x,y)\to(a,a)}(x^2+y^2)=2a^2$

7 0

2 years ago

A picture frame holds 3 same-sized photos as shown. The distance between the photos is 1 inch. The distance from the edge of eac

Valentin [98]

Answer:48

Step-by-step explanation: 4+4+4+2 inch border+2 inch separators 16

6+2 inch border. 16+16+8+8

6 0

2 years ago

Read 2 more answers

1,250 an 15% sale an 6.5 sales tax

eimsori [14]

Given:
price = 1,250
sales discount = 15%
sales tax = 6.5%

The problem is unclear whether the price is the original price or the discounted price. I am assuming that the price is the original price.

Original price times sales discount rate is the value of sales discount
1,250 x 15% = 187.50

Original price less the value of sales discount is the discounted price.
1,250 - 187.50 = 1,062.50

Discounted price times sales tax rate is the value of the sales tax
1,062.50 x 6.5% = 69.06

Discounted price plus sales tax is the total cost of the purchase
1,062.50 + 69.06 = 1,131.56

4 0

2 years ago