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3 years ago

Simplify the expression: 12g + 9g 11x + 9 - 7 8s - 11s + 6s

Mathematics

1 answer:

Serggg [28]3 years ago

8 0

Step-by-step explanation:

12g+9g= 21 g

11x+9-7= 11x+2

8s-11s+6s= 3s

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Two parrallel lines may have 1 intersection point.<br> A.) True<br> B.) False

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B. False

parallel never intersects

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3 years ago

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Solution to 34x-80=10x-8

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A 13-ft ladder is leaning against a house when its base starts to slide away. By the time the base is 5 ft from the house, the

lord [1]

Answer:

a. -5 ft per sec

b. 59.5 ft² per sec

Step-by-step explanation:

a. Suppose l represents the ladder, x represents the height of the top of ladder from the base of house and y represents the distance of base of ladder from the base of house.

By the Pythagoras theorem,

$l^2 = x^2 + y^2------(1)$

Differentiating with respect to t ( time ),

$2l\frac{dl}{dt} = 2x \frac{dx}{dt}+2y\frac{dy}{dt}$

But, height of ladder, l = 13 ft = constant,

$\implies \frac{dl}{dt}=0$

$\implies 0= 2x \frac{dx}{dt}+2y\frac{dy}{dt}-----(2)$

We have,

y = 5, $\frac{dy}{dt}=12\text{ ft per sec}$ ,

Again by equation (1),

$13^2 = x^2 + 5^2\implies 169 = x^2 + 25\implies 169 - 25 = x^2\implies 144 = x^2\implies x = 12\text{ ft}$

From equation (2),

$0 = 2(12) \frac{dx}{dt} + 2(12)(5)$

$0= 24\frac{dx}{dt}+120$

$-120 =24\frac{dx}{dt}$

$\implies \frac{dx}{dt}=-\frac{120}{24}=-5\text{ ft per sec}$

Hence, the rate of change of the height of the top of the ladder is -5 ft per sec.

b. Now area of the triangle = 1/2 × base × height

$\implies A = \frac{1}{2}\times y\times x$

Differentiating with r. t. t,

$\frac{dA}{dt}=\frac{1}{2}(y\frac{dx}{dt}+x\frac{dy}{dt})$

$= \frac{1}{2}(5(-5) + 12(12))$

$=\frac{1}{2}(-25 + 144)$

$=\frac{119}{2}$

= 59.5 ft² per sec

Hence, area of the triangle is changing with the rate of 59.5 ft per sec.

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4 years ago

A triangle has angle measurements of 61°, 84°, and 35°. is this triangle isosceles?

ch4aika [34]

Answer: No

Step-by-step explanation:

This is not an isosceles triangle because there are different angle measurements. The rule of an isosceles triangle is that it must always have two equal sides and angles.

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2 years ago

Lynne was making cookies and she

fomenos

Answer:

11/2is the answer hope it helps

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3 years ago