Give the dimensions of the small prisms that can be used to pack the larger prism

Given: mAngleEDF = 120°; mAngleADB = (3x)°; mAngleBDC = (2x)° Prove: x = 24 3 lines are shown. A line with points E, D, C inters

N76 [4]

Answer:

" Vertical angles are congruent " ⇒ 2nd answer

Step-by-step explanation:

* <em>Look to the attached figure </em>

- There are three lines intersected at point D

- We need to find the missing in step 3

∵ Line FA intersects line EC at point D

- The angles formed when two lines cross each other are called

vertical angles

- Vertical angles are congruent (vertical angles theorem)

∴ ∠ADC and ∠FDE are vertical angles

∵ Vertical angles are congruent

∴ ∠EDF ≅ ∠ADC

∴ m∠EDF ≅ m∠ADC

∵ m∠EDF = 120° ⇒ given

∵ m∠ADC = m∠ADB + m∠BDC

∴ m∠ADB + m∠BDC = 120°

∵ m∠ADB = (3x)° ⇒ given

∵ m∠BDC = (2x)° ⇒ given

∴ 3x + 2x = 120 ⇒ add like terms

∴ 5x = 120 ⇒ divide both sides by 5

∴ x = 24

Column (1) Column (2)

m∠EDF = 120° given

m∠ADB = 3 x given

m∠BDC = 2 x given

∠EDF and ∠ADC are vertical angles defin. of vert. ∠s

∠EDF is congruent to ∠ADC vertical angles are

congruent

m∠ADC = m∠ADB + m∠BDC angle add. post.

m∠EDF = m∠ADC defin. of cong.

m∠EDF = m∠ADB + m∠BDC substitution

120° = 3 x + 2 x substitution

120 = 5 x addition

x = 24 division

∴ The missing reason is " vertical angles are congruent "

- From the explanation above ∠ADC and ∠FDE are vertical

angles then they are congruent according to vertical angle

theorem

6 0

3 years ago

Read 2 more answers

Evaluate the expression, when x = 3.2x + 4(x - 2)a910ObocOd118

love history [14]

The initial expression is:

2x + 4(x - 2)

Replacing x by 3, we get:

2(3) + 4(3 - 2)

6 + 4(1)

6 + 4

10

The value of the expression is 10

4 0

1 year ago

beaus recipefor granola bars calls for 3 1/2 cups of oatmeal. he only have 1/6 cup scoop.how many scoops of oatmeal will he need

Stells [14]

<h2>Answer:</h2>

The number of scoops of oatmeal he will need for the recipe is:

21 scoops.

<h2>Step-by-step explanation:</h2>

It is given that:

Beaus recipe for granola bars calls for 3 1/2 cups of oatmeal.

i.e. the cups of oatmeal required is:

$3\dfrac{1}{2}\ cups=\dfrac{3\times 2+1}{2}\ cups$

i.e.

$\dfrac{7}{2}\ \text{cups\ of\ oatmeal\ is\ required}$

Also, he has:

$\dfrac{1}{6}\ \text{cup scoop}$

This means that:

$\text{Number of scoops of oatmeal he need}=\dfrac{\text{Number of cups of oatmeal}}{\text{Number of cup scoop he has}}\\\\i.e.\\\\\text{Number of scoops of oatmeal he need}=\dfrac{\dfrac{7}{2}}{\dfrac{1}{6}}\\\\i.e.\\\\\text{Number of scoops of oatmeal he need}=\dfrac{7\times 6}{1\times 2}\\\\i.e.\\\\\text{Number of scoops of oatmeal he need}=21\ \text{scoops}$

7 0

3 years ago

Read 2 more answers

Can someone please help with this trig question?

atroni [7]

First we must understand how to write a logarithmic function:

$log_{b}a=x$

In the equation above, b is the base, x is the exponent, and a is the answer. These same variables can be rearranged to be expressed as an exponential equation as followed:

$b^x=a$

Next, we need to understand basic logarithm rules.

1. When a value is raised to a power, we can move the exponent to the front of the logarithm. Example:

log(a^2) = 2log(a)

2. When two variables are multiplied together, we can add the logarithms of the individual variables together. Example:

log(ab) = log(a) + log(b)

3. When a variable is divided by another variable, we can subtract the logarithms of the individual variables. Example:

log(a/b) = log(a) - log(b)

Now we can use these rules to solve the problem.

$log(r)=log( \sqrt[3]{ \frac{A^2B}{C} } )$

We can rewrite the cube root as:

$log(r) = log( (\frac{A^2B}{C})^ \frac{1}{3} )$

Now we can move the one-third to the front:

$log(r) = \frac{1}{3} log( \frac{A^2B}{C} )$

Now we can split up the logarithm:

$log(r) = \frac{1}{3} (log(A^2)+log(B)-log(C))$

Finally, we can move the exponent to the front of the log of A:

$log(r) = \frac{1}{3} (2log(A)+log(B)-log(C))$

Distribute the one-third to get the answer:

$log(r) = \frac{2}{3} log(A) + \frac{1}{3} log(B) - \frac{1}{3} log(C)$

The answer is (4).

3 0

3 years ago

PLEASE HELP I HAVE SOME POINTS THAT I'M GIVING OUT IF YOU ANSWER THIS QUESTION CORRECTLY. PLEASE HELP For each value of x , dete

Zigmanuir [339]

Answer:

8: yes

14: no

6: yes

9: yes

Step-by-step explanation:

Hope this helps!

(P.S.I changed the answer)

3 0

3 years ago