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3 years ago

Given: m∠A + m∠B = m∠B + m∠C Prove: m∠C = m∠A Write a paragraph proof to prove the statement.

Answer is: We are given that the sum of the measures of angles A and B is equal to the sum of the measures of angles B and C. The measure of angle B is equal to itself by the reflexive property, so you can subtract that measure from both sides of the equation. Now the measure of angle A equals the measure of angle C. By the symmetric property, this means the measure of angle C equals the measure of angle A. Correct: Egde

Mathematics

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What is the range of the function f(x)= 2 + 4 when the domain is {-2, 0, 3}?

Orlov [11]

The domain is the possible input values "x" .. in this case [-4, -2, 0, 2, 4]

The range are the possible output values of f(x)

We need to solve f(x) = 3.2x for each value in our domain

f(-4) = 3.2(-4) = -12.8

f(-2) = 3.2(-2) = -6.4

f(0) = 3.2(0) = 0

f(2) = 3.2(2) = 6.4

f(4) = 3.2(4) = 12.8

4 0

3 years ago

The surface area of this rectangular solid is? (it does contain a top)

LiRa [457]

Answer:

Step-by-step explanation:

surface area=2(l+w)×h+2×l×w

=2(14+5)×8+2×14×5

=2×19×8+140

=304+140

=444 inches²

7 0

3 years ago

A person is standing close to the edge on a 56 foot building and throws the ball vertically upward. The quadratic function h(t)=

Romashka [77]

Answer:

Part 1)

225 feet.

Part 2)

7 seconds.

Step-by-step explanation:

The height h(t) of the ball above the ground after t seconds is modeled by the function:

$h(t)=-16t^2+104t+56$

Part 1)

We want to determine the maximum height of the ball.

Notice that the function is a quadratic with a negative leading coefficient, so its maximum will be at its vertex point.

The vertex of a parabola is given by:

$\displaystyle \text{Vertex} = \left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)$

In this case, a = -16, b = 104, and c = 56.

Find the x- (or rather t-) coordinate of the vertex. So:

$\displaystyle t=-\frac{(104)}{2(-16)}=\frac{104}{32}=\frac{13}{4}=3.25\text{ seconds}$

In other words, the ball reaches its maximum height after 3.25 seconds.

To find the maximum height, substitute this value back into the function. Hence:

$\displaystyle h(3.25)=-16(3.25)^2+104(3.25)+56=225\text{ feet}$

The maximum height of the ball is 225 feet in the air.

Part 2)

We want to find the amount of time it took for the ball to hit the ground.

When the ball hit the ground, its height above the ground is zero. Therefore, we can set h(t) to 0 and solve for t:

$0=-16t^2+104t+56$

We can simplify a bit. Divide both sides by -8:

$0=2t^2-13t-7$

We can factor. Find two numbers that multiply to 2(-7) = -14 and add to -13.

-14 and 1 works! Therefore, split the second term into -14 and 1:

$\displaystyle 0=2t^2-14t+t-7$

Factor out a 2t from the first two terms and group the last two terms:

$0=2t(t-7)+(t-7)$

Factor by grouping:

$0=(2t+1)(t-7)$

Zero Product Property:

$2t+1=0\text{ or } t-7=0$

Solve for each case:

$\displaystyle t=-0.5\text{ or } t=7$

Since time cannot be negative, we can ignore the first case.

Therefore, it takes seven seconds for the ball to hit the ground.

6 0

3 years ago

If ab = 9 and a² + b² = 81, then (a+b)² = ?

Andre45 [30]

Answer:

Step-by-step explanation:

Through some clever algebra, we can combine our first two equations using the fact that

$(a+b)^2=a^2+2ab+b^2$

We have the a² and the b² in the equation $a^2+b^2=81$ , and we almost have a 2ab in the equation $ab=9$ . To get that 2ab, we can simply double both sides of the first equation to get $2ab=18$ . From there, we'll add the first two equations together, giving us the summed equation