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3 years ago

Which congruence theorems can be used to prove EFG congruent to JHG

Mathematics

1 answer:

MatroZZZ [7]3 years ago

3 0

SAS you have two pairs of parallel sides

you have another pair of side congruent to one another

and angle G is the same to itself.

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A circle has area 2251 m2. What is its diameter?

Gemiola [76]

Answer:

53.54m

Step-by-step explanation:

Using the formulas

A=πr2

d=2r

Solving for d

d=2A

π=2·2251

π≈53.53562m

8 0

3 years ago

Five decreased by twice a number is same as five less than<br> three times the number.

sergejj [24]

Answer: If you are suppose to write an algebraic expression it is: 5 - 2x = 3x - 5
If you are suppose to solve the answer is:
5-2x=3x-5
-2x=3x-10
-5x=-10
x=2

8 0

2 years ago

A ladder 16 feet long is leaning against the wall of a tall building. The base of the ladder is moving away from the wall at a r

svet-max [94.6K]

Answer:

a. 0.588

b. 0.0722

c. 4.576 sqft/sec

Step-by-step explanation:

Let b and h denote the base and height as indicated in the diagram. By pythagoras theorem, $h^2 + b^2 = 16^2 = 256 \dotsc\;(1)$ because it is a right angle triangle.

It is given that $\frac{db}{dt} = 1$

Now differentiate (1) with respect to t (time) :

$\displaystyle{2h\frac{dh}{dt} + 2b\frac{db}{dt} = 0 \implies \frac{dh}{dt} = -\frac{b}{h} \frac{db}{dt}}$

$\displaystyle{=-\frac{b}{\sqrt{256 - b^2}} \frac{db}{dt} = -\frac{8}{13.856} \times 1 = -0.588}$

The minus sign indicates that the value of h is actually decreasing. The required answer is 0.588.

b. From the diagram, infer that $16 \sin{\theta} = b$ . When b = 8, then $\theta = \arcsin{0.5} = \ang{30}$ .

Differentiate the above equation w.r.t t

$\displaystyle{16 \cos{\theta} \frac{d\theta}{dt} = \frac{db}{dt} \implies \frac{d\theta}{dt} = \frac{1}{16 \cos{\theta}} = \frac{1}{13.856} = \mathbf{0.0722}}$

c. The area of the triangle is given by $A = 0.5\times h \times b$ . Differentiating w.r.t t,

$\displatstyle{\frac{dA}{dt} = 0.5 b \frac{dh}{dt} + 0.5 h \frac{db}{dt}}$

Plugging in b = 8, h = 13.856, $\frac{dh}{dt} = -0.588$ ,

$\frac{dA}{dt} = -2.352 + 6.928 = \mathbf{4.576 ft^2/sec}$

8 0

3 years ago

Please do the agree or disagree part and justification

Jlenok [28]

Answer:

<em>We disagree with Zach and Delia and agree with Alicia</em>

Step-by-step explanation:

The domain of a function is the set of values of the independent variable that the function can take according to given rules or restrictions.

The range is the set of values the dependent variable can take for every possible value of the domain.

The graph shows a continuous line representing the values of the function. We must take a careful look to the values of x (horizontal axis) where the function exists. It can be done by drawing an imaginary vertical line passing through the value of x. If that line touches the graph of the function, it belongs to the domain. It's clear that every value of x between -5 and 3 (both inclusive because there are solid dots in the extremes) belong to the domain:

Domain: $-5\leq x \leq 3$

The range is obtained in a similar way as the domain, but the imaginary lines must be horizontal. That gives us the values of y range from -7 to 5 both inclusive:

Range:

$-7\leq y \leq 5$

Thus we disagree with Zach and Delia and agree with Alicia

8 0

3 years ago

What linear function equation can be represented by the set of ordered pairs?

BaLLatris [955]

Y = (3/4)x - 3
Use two of the ordered points to find the slope.
Then use the slope and one of the ordered pairs to find the y-intercept.

3 0

3 years ago

Read 2 more answers