Which function is increasing?

Answer:

Step 1 is justified by the Distributive Property.

Step 4 is justified by the Symmetric Property

Step-by-step explanation:

Given the equation solved by Nigel expressed as

4(5x−12)−7x=5x.

First, we need to expand the bracket using the distributive property

4(5x−12)−7x=5x.

4(5x)-4(12) -7x = 5x

20x - 48 - 7x = 5x

Hence Step 1 is justified by the Distributive Property.

Next is to collect the like terms;

20x - 7x - 48 = 5x

Take the difference

13x - 48 = 5x

Next is to subtract 13x from both sides according to the symmetric property

13x - 48 - 13x = 5x - 13x

Hence Step 4 is justified by the Symmetric Property

The resulting equation will be

0-48 = -8x

Divide both sides by -8

-48/-8 = -8x/-8

6 = x

Hence the correct justifications are Step 1 is justified by the Distributive Property AND Step 4 is justified by the Symmetric Property

Answer:

x = 65 degrees

Step-by-step explanation:

x° + x° + 50° = 180°

2x + 50° = 180°

2x = 180° - 50°

2x = 130°

x = 130°/2

x = 65°

Answer:

Step-by-step explanation:

1) The smaller sticks will range in length from almost 0 unit up to a maximum of 0.5 unit, with each length equally possible.

Therefore, the average length will be about (0 + 0.5)/2 = 0.25 unit

2)If you assume that each break in the stick is uniformly distributed along the length of the stick and is independent of the location of the other break, then the odds are 25% that you will be able to form a triangle with the 3 pieces.

We'll call the length of the stick 1, so each break can occur at a position in the interval [0,1]. Let x and y represent the two breaks. Then we can look at the area of the region in the square bounded x=0, x=1, y=0, y=1, which represents combinations of x and y, for which we can form a triangle. Since the area of the whole square is 1, the area of the region inside is our probability.

If y>x, then the lengths of the pieces are x, y-x, and 1-y.

The triangle inequality must hold for each combination of edges.

for y>x ...

x+y−x≥1−y

x+1−y≥y−x

y−x+1−y≥x

these simplify to...

for y>x ...

y≥1/2

x+1/2≥y

x≤1/2

If we cut our 1x1 square into two triangles along the line x=y,

then the region in the upper triangle which satisfies the inequalities above forms a smaller triangle which connects the midpoints of the upper triangle.

The lower triangle (x>y), is just a reflection about x=y of the upper triangle, so together, the entire region looks like a bow-tie at a 45 degree angle.

This region takes up 25% of the square, so the probability that you can form a triangle is 25%

Answer:

(0.5,3)

Hope this helps..Have a good day!!

Answer:

[tex]\displaystyle \displaystyle \cos A = \frac{a^2-b^2}{a^2 + b^2}\text{ and } \sin A = \frac{2ab}{a^2 + b^2}[/tex]

Step-by-step explanation:

We are given that:

[tex]\displaystyle \tan A = \frac{2ab}{a^2 - b^2}[/tex]

And we want to find the value of cos(A) and sin(A).

Recall that tangent is the ratio of the opposite side to the adjacent side.

Therefore, the opposite side measures 2ab, and the adjacent side measures a² - b².

Using the Pythagorean Theorem, solve for the hypotenuse:

[tex]\displaystyle \begin{aligned} c^2 &= a^2 + b^2 \\ \\ c&= \sqrt{(2ab)^2 + (a^2-b^2)} \\ \\ &= \sqrt{(4a^2b^2)+(a^4-2a^2b^2+b^4)} \\ \\ &= \sqrt{a^4 + 2a^2b^2 + b^4 } \\ \\ &= \sqrt{(a^2 +b^2)^2} \\ \\ &= a^2 + b^2\end{aligned}[/tex]

Thus, our hypotenuse is given by a² + b².

Cosine is the ratio between the adjacent side and the hypotenuse. Thus:

[tex]\displaystyle \cos A = \frac{a^2-b^2}{a^2 + b^2}[/tex]

And sine is the ratio between the opposite side and the hypotenuse. Thus:

[tex]\displaystyle \sin A = \frac{2ab}{a^2 + b^2}[/tex]

In conclusion:

[tex]\displaystyle \displaystyle \cos A = \frac{a^2-b^2}{a^2 + b^2}\text{ and } \sin A = \frac{2ab}{a^2 + b^2}[/tex]

Answer:

Step-by-step explanation:

[tex]sec^2A-tan^2A=1\\sec^2A=1+tan^2A=1+\frac{4a^2b^2}{(a^2-b^2)^2} =\frac{(a^2-b^2)^2+4a^2b^2}{(a^2-b^2)^2} =\frac{(a^2+b^2)^2}{(a^2-b^2)^2} \\cos^2A=\frac{(a^2-b^2)^2}{(a^2+b^2)^2} \\cos A=\frac{a^2-b^2}{a^2+b^2} \\sin A=\sqrt{1-cos^2A} =\sqrt{1-(\frac{a^2-b^2}{a^2+b^2} )^2} =\sqrt{\frac{(a^2+b^2)^2-(a^2-b^2)^2}{(a^2+b^2)^2} } =\sqrt{\frac{4a^2b^2}{(a^2+b^2)^2} }=\frac{2ab}{a^2+b^2}[/tex]

Answer:

(1/21)(21×5^(x+2)-4×5^2x)

Step-by-step explanation:

5^(x+2)-4×5^x÷21×5^x

= 5^(x+2)-4×5^2x/21

= 1/21(21×5^(x+2)-4×5^2x)

Answer:

I think E

Step-by-step explanation:

You know the shortest building is 25 m.

to find the rest, use trigo so Tan(20)=opposite/adjacent.

Adjacent is 50. Do the math and add the answer with 25.

Answer:

The answer would be E. 43.2

According to TOA, The opposite side is tan(20) x adjacent side( 50m)

the answer is 18.2( to 1 dp). Add the height of the second building together with 18.2 and you will get ur answer. HOpe this helps:)

Answer:

285

Step-by-step explanation:

B+A=360, B=360-75=285

An angle whose measure is greater than 180° but less than 360° is termed a reflex angle.

[tex]\large{\textrm{{{\color{navy}{∠A \: + \: ∠B \: = \: 360°}}}}}[/tex]

[tex] \bf \large \longrightarrow \: \:75 \degree \: + \: ∠ B \: = \: 360°[/tex]

[tex] \bf \large \longrightarrow \: \: \angle B \: = \: 360° \: - \: 75 \degree[/tex]

[tex] \bf \large \longrightarrow \: \: \angle B \: = \:285 \degree[/tex]

Answer: a = -8

Step-by-step explanation:

Given

-8a - 5 = -7a + 3

Subtract 3 on both sides

-8a - 5 - 3 = -7a + 3 - 3

-8a - 8 = -7a

Add 8a on both sides

-8a - 8 + 8a = -7a + 8a

a = -8

Hope this helps!! :)

Please let me know if you have any questions

Answer:

a = -8

Step-by-step explanation:

-8a-5=-7a+3                    Add 5 to both sides.

- 8a = - 7a + 3 + 5           Combine

-8a = - 7a + 8                  Add 7a to both sides

-8a + 7a = 8                    Combine

-a = 8                              Multiply by - 1

a = - 8                          

When you get a weird number like this, you should check it.

LHS = -8(-8) - 5

LHS = 64 - 5

LHS = 59

RHS = -(7*-8) + 3

RHS = -(-56) + 3

RHS = 56 + 3

RHS = 59

So a = - 8 must be right.

Answer:

[tex]\frac{dy}{dx} = \frac{13}{8} [/tex]

Step-by-step explanation:

[tex] y = 2x + 6 {x}^{ - \frac{1}{2} } \\ \frac{dy}{dx} = 2 + 6( - \frac{1}{2}) {x}^{ - \frac{1}{2} - 1 } \\ \frac{dy}{dx} = 2 - 3 {x}^{ - \frac{3}{2} } \\ \frac{dy}{dx} = 2 - \frac{3}{ \sqrt{ {x}^{3} } } [/tex]

When x = 4,

[tex]\frac{dy}{dx} = 2 - \frac{3}{ \sqrt{ {4}^{3} } } \\ = \frac{13}{8} [/tex]

Answer:

Hello,

Answer 13/8

Step-by-step explanation:

[tex]y=2x+\dfrac{3}{\sqrt{x} } \\\\y'=2+6*\dfrac{-1}{2} x^{\frac{-3}{2} }\\\\y'=3-\frac{3}{\sqrt{x^3}} \\\\\\For x=4, \\\\y'(4)=2-\dfrac{3}{8} =\dfrac{13}{8}[/tex]

Answer:

The answer is the last one, (X^2-2)/3!

Step-by-step explanation:

To get the inverse of a function, you switch the variables and solve for y. Doing this produces the last choice.

Step-by-step explanation:

(+4)+(-7)

=4-7

=-3

Hope it will help you..

Answer:

Option 4. All real numbers greater than or equal to 2.

I hope this will help.

Answer:

see explanation

Step-by-step explanation:

Under a reflection in the x- axis

a point (x, y ) → (x, - y ) , then

A (2, 0 ) → A' (2, 0 )

B (4, 1 ) → B' (4, - 1 )

C (6, - 4 ) → C' (6, 4 )

Under a reflection in the y- axis

a point (x, y ) → (- x, y ) , then

A' (2, 0 ) → A'' (- 2, 0 )

B' (4, - 1 ) → B'' (- 4, - 1 )

C' (6, 4 ) → C'' (- 6, 4 )

Part (a)

This is the empty set

------------------

Explanation:

It doesn't matter what set A is composed of. Intersecting any set with the empty set Ø will always result in the empty set.

This is because we're asking the question: "What does some set A and the empty set have in common?". The answer of course being "nothing" because there's nothing in Ø. Not even the value zero is in this set.

We can write Ø as { } which is a set of curly braces with nothing inside it.

=========================================================

Part (b)

-----------------

Explanation:

When you union the universal set with any other set, you'll get the universal set.

The rule is [tex]A \cup B = B[/tex] where I've made B the universal set to avoid confusion of the letter U and the union symbol [tex]\cup[/tex] which looks nearly identical.

Why does this rule work? Well if an item is in set [tex]\overline{A}[/tex], then it's automatically in set U (everything is in set U; it's the universe). So we're not adding anything to the universe when applying a union involving this largest set.

It's like saying

we can see that [tex]\overline{A} \cup U[/tex] will basically form the set of every item, aka the universal set.

Answer:

ES LA NUME  C                                        R

Step-by-step explanation:

होय साहेब!!!!!!!!!!

Answer: x = 74.3

Step-by-step explanation:

Let 22 be reference angle

so

tan 22 = p/b

tan 22 = 30/x

or, x= 30/tan22

so, x = 74.252

so, x = 74.3

Answer:

A) 2 cm

Step-by-step explanation:

By definition, regular polygons have equal sides and angles. Therefore, each side of the regular hexagon must be equal. Since one side is marked as 2 cm, the length of PQ must also be 2 cm.

Answer:

B. $28

Step-by-step explanation:

Find the sales tax by finding 4% of 711:

711(0.04)

= 28.44

This is closest to 28.

So, the correct answer is B. $28

Some additional context would be helpful in providing a complete answer. But the basic idea is this:

• Object ABC has a price X set on it.

• Hey, ABC is on sale! Let's say there's a 20% discount. That means 20% of the price X is subtracted from X.

• Boo, there's a 15% sales tax! This means whatever you would pay for ABC, discount included, you will ultimately have to pay an additional 15% of, or 0.15 times, that amount in tax.

Suppose you're looking to buy a T-shirt. The price tag on says it costs $25, but there's a 20% discount and a 15% sales tax.

• The discount has a value of 0.2 ($25) = $5. Subtract this from the original price, and its discounted price is $20.

• The sales tax is applied to this discounted price, and comes out to 0.15 ($20) = $3. This gets added to the discounted price, so you end up paying $23.

Answer:

the first difference are all 20.

since the first differences of this relation are constant, it is a linear relation

Answer:

Linear because the account balance increases by a constant 20.

Step-by-step explanation:

→ The first difference is 20 for all values because :

20 - 0 = 20

40 - 20 = 20

60 - 40 = 20

80 - 60 = 20

100 - 80 = 20

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Number cube:

Coin:

Required probability:

Answer: Probability of rolling a number more than one: 5/6

Probability of heads: 1/2

Probability of both: 1/2 + 5/6 = 4/3

Step-by-step explanation:

Answer:

The answer would be -a

Step-by-step explanation:

In the examples,

5 + (-5) = 0

-1.33 + 1.33 = 0

THat means there will be a negative then a positive, or a positive then a negative.

INVERSE is the key word in this problem.

Answer:

Me = no it doesn't....

you = why tho

me = becoz function not given .....

so lame joke ik...

Answer:

x=5

y=2

w= -5

Step-by-step explanation:

We have that the two matrix are equal, so all corresponding elements are equal.

X-Y=3

From the second row and second column, we have y=2

so x-2=3

x=5

From the third row and the first column, we have w= - 5

the value of 4 tenths x hundreds.

4000

Answer:

40

Step-by-step explanation:

4/10 x 100 = 40