Solve the formula for the specified variable. V=CMU for C

A Conjuncture and the paragraph proof used to prove the conjecture are shown

Finger [1]

Answer:

Given

This is our initial premise.

2) Linear pairs of angles are supplementary

This one is a little questionable, as some definitions of linear pairs require supplementary angles, whereas others only require the intersection of two lines. Check your book or notes for any given theorems regarding supplementary angles.

3)

m

∠

A

B

C

+

m

∠

C

B

D

=

180

∘

The definition of supplementary angles is that two angles are supplementary if their measures sum to

180

∘

.

4) Substitution of 1. into 3.

As with 2), this may differ based on the teacher or book. Some may prefer that you write out the equation, whereas others may be satisfied with the references as given. Check for similar examples.

5)

m

∠

A

B

C

=

90

∘

Subtracting

90

∘

from each side of 4. gives us the above result.

6) Definition of right angle

Step-by-step explanation:

3 0

3 years ago

The function y = x 2 - 10x + 31 has a ____

katrin [286]

Answer:

Option B. minimum is correct for the first blank

Option C. 6 is correct for second blank.

Step-by-step explanation:

In order to find the maxima or minima of a function, we have to take the first derivative and then put it equal to zero to find the critical values.

Given function is:

$f(x) = x^2-10x+31$

Taking first derivative

$f'(x) = 2x-10$

Now the first derivative has to be put equal to zero to find the critical value

$2x-10 = 0\\2x = 10\\x = \frac{10}{2} = 5$

The function has only one critical value which is 5.

Taking 2nd derivative

$f''(x) =2$

$f''(5) = 2$

As the value of 2nd derivative is positive for the critical value 5, this means that the function has a minimum value at x = 5

The value can be found out by putting x=5 in the function

$f(5) = (5)^2-10(5)+31\\=25-50+31\\=6$

Hence,

<u>The function y = x 2 - 10x + 31 has a minimum value of 6</u>

Hence,

Option B. minimum is correct for the first blank

Option C. 6 is correct for second blank.

8 0

3 years ago

Rewrite the following linear equation in slope intercept form.<br> Y-5=3(x+1)

jarptica [38.1K]

Y=3x+8

Step-by-step explanation:

The slope is 3

Slope Intercept form is Y=Mx=b

5 0

3 years ago

Read 2 more answers

Use the value of the first integral I to evaluate the two given integrals. I = integral^3_0 (x^3 - 4x)dx = 9/4 A. integral^3_0 (

Troyanec [42]

Answer:

A) -9/2

B) 9/4

C) -9/2, same as A)

Step-by-step explanation:

We are given that $I=\int_0^3 x^3-4x dx=9/4$ . We use the properties of integrals to write the new integrals in terms of I.

A) $\int_0^3 8x-2x^3 dx=\int_0^3 -2(x^3-4x) dx=-2\int_0^3 x^3-4x dx=-2I=-9/2$ . We have used that ∫cf dx=c∫f dx.

B) $\int_3^0 4x - x^3 dx=-\int_0^3 (4x-x^3) dx=\int_0^3-(4x-x^3) dx=\int_0^3 x^3-4x dx=I=9/4$ . Here we used that reversing the limits of integration changes the sign of the integral.