Simplify the following leave the answer in radical notation:

Please explain!!

1. Square root of (125x^2y^7)

2. Cubed root of (24x^3y8)

Answer:

22.5

Step-by-step explanation:

cause

Answer:

It is 22.5

Step-by-step explanation:

add up all they shaded parts:

22.5 x 4 = 90 degrees

as each unshaded part is three times more then you do 22.5 x 3 for one part

22.5 x 3 = 67.5 degrees

then times by four because there is four unshaded sections.

67.5 x 4 = 270 degrees

270 + 90 = 360 degrees and there is 360 degrees in a circle so 22.5 degrees is the correct answer.

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Explanation:

Let's square both sides and do a bit of algebra to get the following.

[tex]\sin(x) + \cos(x) = 1/5\\\\\left(\sin(x) + \cos(x)\right)^2 = \left(1/5\right)^2\\\\\sin^2(x) + 2\sin(x)\cos(x) + \cos^2(x) = 1/25\\\\\sin^2(x) + \cos^2(x) + 2\sin(x)\cos(x) = 1/25\\\\1 + 2\sin(x)\cos(x) = 1/25\\\\\sin(2x) = 1/25 - 1\\\\\sin(2x) = 1/25 - 25/25\\\\\sin(2x) = -24/25\\\\[/tex]

Now apply the pythagorean trig identity to determine cos(2x) based on this. You should find that cos(2x) = -7/25

This then means tan(2x) = sin(2x)/cos(2x) = 24/7.

From here, you'll use this trig identity

[tex]\tan(2x) = \frac{2\tan(x)}{1-\tan^2(x)}\\\\[/tex]

which is the same as solving

[tex]\tan(2x) = \frac{2w}{1-w^2}\\\\[/tex]

where w = tan(x)

Plug in tan(2x) = 24/7 and solve for w to get w = -4/3 or w = 3/4

So either tan(x) = -4/3 or tan(x) = 3/4.

If we were to numerically solve the original equation for x, then we'd get roughly x = 2.21; then notice how tan(2.21) = -1.345 approximately when your calculator is in radian mode.

Since tan(x) < 0 in this case, we go for tan(x) = -4/3

Answer:

(n^(2)+6n-4)(2n-4)

5 cm or 29 cm

Step-by-step explanation:

Let x length is cut off from each measurements.

Thus, the new measurements would be: 20 - x, 41 - x, 44 - x, which forms the sides of a right triangle.

Here, (44 - x) will be hypotenuse and (20 - x) and (41 - x) will be perpendicular legs of the triangle.

Therefore, by Pythagoras theorem:

[tex] {(41 - x)}^{2} + {(20 - x)}^{2} = {(44 - x)}^{2} \\ \\ \therefore \: {(41)}^{2} - 82x + {x}^{2} + {(20)}^{2} - 40x + {x}^{2} \\ = {(44)}^{2} - 88x + {x}^{2} \\ \\ \therefore \: 1681 - 122x + 2 {x}^{2} + 400 \\ = 1936 - 88x + {x}^{2} \\ \\ \therefore \: 2081 - 122x + {x}^{2} = 1936 - 88x \\ \\ \therefore \: {x}^{2} - 122x + 88x + 2081 - 1936 = 0 \\ \\ \therefore \: {x}^{2} - 34x + 145 = 0 \\ \\ \therefore \: {x}^{2} - 29x - 5x+ 145 = 0 \\ \\ \therefore \: x(x - 29) - 5(x - 29) = 0 \\ (x - 5)(x - 29) = 0 \\ x - 5 = 0 \: or \: x - 29 = 0 \\ \\ \therefore \: x = 5, \: 29[/tex]

So, the length that is cut off will be either 5 cm or 29 cm.

Answer:

C. 4

Step-by-step explanation:

The graph seems to start at y=4, and decreases.

Answer:

sin(theta)=-2/3 and cos(theta)=-sqrt(5)/3

Step-by-step explanation:

First of all, as the theta is in 3rd quadrant, all the other ratios will be negative. Second tan(theta)=P/B. So, 2=P and B=sqrt(5), H=sqrt(P^2+H^2)=sqrt(4+5)=3. sin(theta) will be P/H=-2/3 and cos(theta) will be B/H=-sqrt(5)/3

Answer:

Step-by-step explanation:

Hello, please consider the following.

Option A. First week we got $200.

Week 2, we got $200+$50=$250

Week 3, we got $250+$50=$300

Week 4, we got $300+$50=$350

Week 5, we got $350+$50=$400

Week 6, we got $400+$50=$450

[tex]\begin{array}{c |c |c |c |c |c |c|}Week & 1 & 2 & 3 & 4 & 5 & 6\\----&---&---&---&---&---&---\\Amount &200 &250 &300 &350 & 400 &450\end{array}[/tex]

Option B. First week we got $200.

Week 2, we got $200+$200*10%=$200+$20=$220

Week 3, we got $220(1+10%)=$220(1.10)=$242

Week 4, we got $242(1.10)=$266.2

Week 5, we got $266.2(1.10)=$292.82

Week 6, we got $292.82(1.10)=$322.102

[tex]\begin{array}{c |c |c |c |c |c |c|}Week & 1 & 2 & 3 & 4 & 5 & 6\\----&---&---&---&---&---&---\\Amount &200 &220 &242 &266.2 & 292.82 &322.102\end{array}[/tex]

Thank you.

Answer:

25 ( 5 width times 5 length)

Step-by-step explanation:

Answer:

y = -x +57

Step-by-step explanation:

y=3x +38 -4x +19

Combine like terms

y = 3x-4x   + 38 +19

y = -x +57

Answer:

y= -x+57

Step-by-step explanation:

[tex]\sf{}[/tex]

♛┈⛧┈┈•༶♛┈⛧┈┈•༶

✌️

Answer:

Hey there!

2/3 of 90 cm would be 60 cm.

Hope this helps :)

Answer

[tex] \boxed{60}[/tex]

Step by step explanation

To multiply one fraction by another, multiply the numerators for the numerator and multiply the denominators for its denominator and reduce the fraction obtained after multiplication into lowest term :

[tex] \mathsf{ \frac{2}{3} \times 90}[/tex]

⇒[tex] \mathsf{ \frac{2 \times 90}{3 \times 1} }[/tex]

⇒[tex] \mathsf{ \frac{180}{3} }[/tex]

⇒[tex]60[/tex]

Hope I helped!

Best regards!!

Answer:

1

5

4

2

3

Step-by-step explanation:

1 combines the sets A and B. that symbol there stands for U like "union". so, all values of x, where x is either < 1 or >= 5.

2 is again a union. A and C are combined. C contains only one element : x=5.

3 is again a union. B and C are combined. but the element of C (x=5) is already part of B (x>=5), so the union does not change anything, the result is simply B again.

4 is doing a "cross section" between the sets A and B. only elements that are in both sets are in the result. but x < 1 and x >= 5 don't have any elements in common. so, the result is an empty set.

5 is again a cross section. the only shared element between B and C is x=5.

Hey there! I'm happy to help!

SYSTEM #1

-4x+2y=22

-y=-3x-9

We can multiply both sides of the second equation by -1 to see what y equals.

y=3x+9

We can substitute this value for y into the first equation and solve for x.

-4x+2(3x+9)=22

We use distributive property to undo the parentheses.

-4x+6x+18=22

We combine like terms.

2x+18=22

Subtract 18 from both sides.

2x=4

Divide both sides by 2.

x=2

Our x has to be -4 to be the correct answer, so this option is incorrect.

SYSTEM #2

-4x+2y=22

y=-3x-9

We plug this y value into the first equation to solve for x.

-4x+2(-3x-9)=22

We use distributive property to undo the parentheses.

-4x-6x-18=22

We combine like terms.

-10x-18=22

Add 18 to both sides.

-10x=40

x=-4

We have the correct x-value to be the answer, so let's find the y-value by plugging our x-value into one of the equations.

y=-3(-4)-9

y=12-9

y=3

So, the solution of this system of equations is (-4,3), so the correct answer is 2. -4x+2y=22, y=-3x-9

Have a wonderful day! :D

Step-by-step explanation:

the measure of the segment YZ

[tex] \sin(30) = \frac{yz}{50} \\ yz = 50 \times \sin(30) = 25[/tex]

YZ= 25 m

Answer:

g(5) = -1

Step-by-step explanation:

Let x = 5.

[tex]g(5)=-(5)+4\\g(5)=-5+4\\g(5)=-1[/tex]

Answer:

-1

Step-by-step explanation:

g(x)= -x+4

then substitute 5 on x

=-(5)+4=-1

Answer:

The 4th term = a+3d = 0,

or a = -3d.

The 25th term = a+24d = -3d+24d = 21d. ...

the 25th term is 3 times the 11th term. Proved.

Answer:

a^25 = 3 x a^11 .

Step-by-step explanation:

Given a^4 = 0

That is (a + 3d) = 0

⇒ a = - 3d ........... (1)

nth term of AP is given by an = a + (n – 1)d

a^11 = a + 10d = – 3d + 10d = 7d  [From (1)]

a^25 = a+ 24d = – 3d + 24d = 21d  [From (1)]

Hence

The answer is a^25=3 x a^11

Answer:

-4 -5x

Step-by-step explanation:

4(1 – 3x) + 7x – 8.

Distribute

4 -12x +7x -8

Combine like terms

-4 -5x

Answer:

The simplified answer of this expression is -5x - 4

Step-by-step explanation:

4(1 - 3x) + 7x - 8

Distribute 4 to (1 - 3x)

4 - 12x + 7x - 8

Rearrange the terms so it'll be easier to combine them.

4 - 8 - 12x + 7x

Combine like terms.

-4 - 5x

Put the equation in standard form.

-5x - 4

If [tex]x-a[/tex] is a factor of a polynomial [tex]P(x)[/tex] then, [tex]a[/tex] is its root.

So [tex]-2[/tex] is a root of [tex]x^3-19x-p[/tex]

[tex](-2)^3-19\cdot(-2)-p=0\\-8+38-p=0\\p=30[/tex]

Answer:

x = s/2

Step-by-step explanation:

● s states have joined the union in 1788

● half of s have joined in 1889

Let x be the number of states that have joined in 1889

● x = (1/2)× s

● x = s/2

Answer:

625

Step-by-step explanation:

250 × X = 2

X = 5

250 × 5 = 2

1250 = 2 after this step u divided it by 2

1250 ÷ 2

= 625

Answer:

increasing spread epidemics your outlook

sine and cosecant.

you can see the graph or on unit circle, as the for these ratios, (which depend on y coordinate) 1st and 2nd quadrant have positive y coordinate

Answer:

1.) (2,1) is a solution

2.) (4,3) is NOT a solution

Step-by-step explanation:

1.) (2,1)

These are these mean (x,y)

2=x and 1=y

You want to substitute the numbers for the letters in the equation.

so.

2(2)+1=5

4+1=5

5=5, This statement is true so (2,1) is a solution.

2.) Same as above. 4=x and 3=y

4(4)-3(3)=10

16-9=10

7 Does Not Equal 10, Therefore, (4,3) is Not a solution to the equation.

Answer:  (2, 1)

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Explanation:

Let's add the equations straight down

After those three things happen, we're left with 3x = 6 which solves to x = 2 after dividing both sides by 3.

Now let's use this x value to find y

2x-y = 3

2(2)-y = 3

4-y = 3

-y = 3-4

-y = -1

y = 1

Or we could use the other equation

x+y = 3

2+y = 3

y = 3-2

y = 1

which gets us there in fewer steps.

So that's how we get to the final answer of (x,y) = (2,1)

The graph is shown below.

Answer:

25/99; Dependent event

Step-by-step explanation:

This is the probability that an even ticket will be chosen out of 100 tickets times the probability that an odd ticket will be chosen out of the remaining 99 tickets.

There 50 even out of 100 to start off with. After 1 even is chosen there are still 50 odd but only 99 more tickets.

(50/100)(50/99)=2500/9900= 25/99

This is a dependent event because an odd number should come after the even number only.

Answer:

25/99

Dependent event

Step-by-step explanation:

1. Multiply the possibilities

There are 50 even numbers out of 100 numbers. If one even number is drawn and not replaced, that would leave the odd ticket to be drawn out of 99 tickets. Because an even number was drawn first, all 50 odd numbers would remain.

[tex]\frac{50}{100}[/tex] · [tex]\frac{50}{99}[/tex] = [tex]\frac{2500}{9900}[/tex]

Simplify

[tex]\frac{2500}{9900}[/tex] = [tex]\frac{25}{99}[/tex]

2. This is a dependent event because the chances of an odd number being drawn was altered. If the even ticket was replaced, the probability of the odd number being drawn would not have been affected.

Answer:

An integer is any rational number without a decimal or fraction. This includes negative numbers, and 0. But decimals and fractions are not integers.

Step-by-step explanation:

Brainliest, please!

___________________A

The function that represents the inequality of the given graph is;

Option A

From the given graph, the curve with the shaded dot shows less than or equal to because the dot indicates that the maximum input value of x is at that point.

Secondly, the curve without a shaded dot shows that the input function of x is only greater than 3.

Looking at the options, option A is right and we will prove it thus;

for y = x³ - 3

At x = 2, we see that;

y = 2³ - 3

y = 5

This corresponds with the given equation

For the second curve, for y = x² + 6;

At x = 2, we have;

y = 2² + 6

y = 4 + 6

y = 10

This corresponds with what is given and is thus correct.

Thus, option A is the correct answer

Read more about graphed inequalities at; https://brainly.com/question/11234618

Answer:

Hey there!

This is false, because if the sides of one triangle are congruent to the sides of another, then the triangles are actually congruent. The Side-Side-Side similarity theorem states that if all three pairs of corresponding sides of two triangles are proportional, then the two triangles are similar.

Hope this helps :)

Answer:

C) C < 4

Step-bay-step explanation:

> means "greather than"

< means "less than"

The only statement that is true:

C) C< 4

Answer:

[tex]W= 4700+0.02S[/tex]

Step-by-step explanation:

Given that

W is the monthly wage

S is the monthly sales

According to the problem statement, salesperson receives a monthly salary of $4700 (sales or no sales made he/she gets that amount)

Also plus 2%  commission of sales made for the month added to the wage

we can model his/her wage as follows

[tex]W= 4700+ (2/100)S\\\\ W= 4700+0.02S[/tex]

Hence the model for the monthly wage is [tex]W= 4700+0.02S[/tex]