Peter and his four brothers combined all of their money to buy a video game. If 20% of the total money is Peter's, and $4.00 of the total money is Peter's, how much do all five brothers have combined?

Answer:

C 3

Step-by-step explanation:

5x^2 + 6x + 7 = 2(x + 2)

Distribute the 2

5x^2 + 6x + 7 = 2x + 4

Subtract 2x from each side

5x^2+6x-2x +7 = 2x-2x+4

5x^2 + 4x + 7 = 4

Subtract 4 from each side

5x^2 +4x+7-4 = 4-4

5x^2 +4x+3 = 0

This is in the form ax^2 + bx +c  where c is 3

Answer:

Step-by-step explanation:

[tex]ax^2+bx+c=0\\\\5x^2+6x+7=2(x+2)\qquad\text{use the distributive property}\\\\5x^2+6x+7=2x+4\qquad\text{subtract}\ 2x\ \text{and 4 from both sides}\\\\5x^2+4x+\boxed{3}=0[/tex]

Answer:0.76

0.58

Conclusion you are More likely to win by playing regular defense

Step-by-step explanation:

Probability of winning when playing regular defense is greater than probability of winning when playing prevent defense.

Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.

The value of probability will be always in the range from 0 to 1.

Given that,

Taking the strategy of "regular" defense,

P(winning) = 42

P(losing) = 8

Total regular defense games = 50

Taking the strategy of "prevent" defense,

P(winning) = 35

P(losing) = 15

Total regular prevent games = 50

Total games = 100

Probability of winning when playing regular defense = 42 / 50 = 0.84

Probability of winning when playing prevent defense = 35 / 50 = 0.7

Hence, Probability of winning when playing regular defense is greater than probability of winning when playing prevent defense.

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Check the picture below.

so the top and bottom segments are simply 7 units, we can read that off the grid.  Let's find the length of the other two segments, "c".

[tex]\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2} \qquad \begin{cases} c=hypotenuse\\ a=\stackrel{adjacent}{2}\\ b=\stackrel{opposite}{3}\\ \end{cases} \\\\\\ c=\sqrt{2^2+3^2}\implies c=\sqrt{13} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{perimeter of the parallelogram}}{7+7+\sqrt{13}+\sqrt{13}}\qquad \approx \qquad 21.21[/tex]

Answer:

C: 30 units

Step-by-step explanation:

on edge 2021! hope this helps!!~ d=(´▽｀)=b

Answer:

The exact value of [tex]\sin(60\degree)[/tex] is [tex]\frac{\sqrt{3} }{2}[/tex].

Step-by-step explanation:

Recall that   [tex]\sin(60\degree)[/tex]  is a special angle that can be obtained using an equilateral triangle.

The right triangle obtained using one of the lines symmetry was used to find the exact value of  [tex]\sin(60\degree)[/tex]  using SOH-CAH-TOA

The exact value of [tex]\sin(60\degree)[/tex] is [tex]\frac{\sqrt{3} }{2}[/tex].

Answer:

She's being paid six hours per hour

Step-by-step explanation:

She's being paid six hours per hour

72/6 = 6

Answer:

The distance across the river from Omkar to the big rock is 131343149 meters

Step-by-step explanation:

* Lets study the information in the problem

- Let Omkar position is point A

- Let Melissa position is point B

- Let big rock position is C on the other side of the river

* Now we have triangle ABC

- The distance between Omkar and Melissa is 100100100 meters

  along the river

- The angle between Omkar and the big rock is angle BAC

∴ m∠BAC = 33°

- The angle between Melissa and the big rock is angle ABC

∴ m∠ABC = 98°

- The big rock is at angle C

* Now we can find the distance between Omkar and the big rock

 by finding the length of side AC in the triangle

- By using the sine rule

∵ sin A/BC = sin B/AC = sin C/AB

∵ AB = 100100100 meters

∵ m∠ABC = 98°

- Lets find m∠C

∵ In any triangle the sum of the measures of the interior angles is 180°

∴ m∠A + m∠B + m∠C = 180°

∵ m∠A = 33° , m∠B = 98°

∴ 33° + 98° + m∠C = 180° ⇒ add

∴ 131° + m∠C = 180° ⇒ subtract 131 from both sides

∴ m∠C = 49°

- Now lets use the sine rule

∵ sin ABC/AC = sin C/AB

∴ sin 98/AC = sin 49/100100100 ⇒ by using cross multiplication

∴ AC = (sin 98 × 100100100) ÷ sin 49 = 131343148.8

∴ AC ≅ 131343149 meters

* The distance across the river from Omkar to the big rock is

 131343149 meters

Answer:

The distance across the river from Omkar to the big rock is 72 meters.

Step-by-step explanation:

Using the given information draw as triangle as shown below.

According to angle sum property, the sum of interior angles of a triangle is 180°.

In triangle ABC,

[tex]\angle A+\angle B+\angle C=180^{\circ}[/tex]

[tex]98^{\circ}+33^{\circ}+\angle C=180^{\circ}[/tex]

[tex]131^{\circ}+\angle C=180^{\circ}[/tex]

[tex]\angle C=180^{\circ}-131^{\circ}=49^{\circ}[/tex]

The measure of angle C is 49°.

Sine formula:

[tex]\frac{a}{\sin a}=\frac{b}{\sin b}=\frac{c}{\sin c}[/tex]

Using sine formula in triangle ABC, we get

[tex]\frac{AC}{\sin B}=\frac{AB}{\sin C}[/tex]

[tex]\frac{AC}{\sin 33^{\circ}}=\frac{100}{\sin 49^{\circ}}[/tex]

[tex]AC=\frac{100}{\sin 49^{\circ}}\times \sin 33^{\circ}[/tex]

[tex]AC=\frac{100}{0.7547}\cdot0.544639[/tex]

[tex]AC=72.166[/tex]

[tex]AC\approx 72[/tex]

Therefore the distance across the river from Omkar to the big rock is 72 meters.

2sin^2xcos^2x

Using trig functions we know:

sin^2(x) = 1- cos(2x)/2

cos^2(x) = 1 + cos(2x) /2

Now we have:

2sin^2xcos^2x  =  2 * 1- cos(2x)/2 * 1 + cos(2x) /2

Simplify to: (1- cos(2x) * 1+cos(2x))/2

Difference of squares is (a-b) (a+b) = a^2 -b^2

(1- cos(2x) * 1+cos(2x))/2 = 1^2 -cos^2(x)/2 *1^2 +cos^2(x) /2

Multiply to get 1-cos(4x) /4

The answer is D.

Answer: D. 4167 Hertz

Step-by-step explanation:

We know that the formula to calculate frequency by using time period is given by :-

[tex]\nu= \dfrac{1}{T}[/tex], where T is the time period.

We are given that the time period of a musical note :

[tex]T=0.00024\text{ seconds}[/tex]

Then , the frequency of the musical note is given by :-

[tex]\nu= \dfrac{1}{0.00024}=4166.66666667\approx4167\text{ Hertz}[/tex]

Hence, the frequency of the musical note = 4167 Hertz

Answer:

1.  0.75

2. -0.8

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First when looking at dialations, ignore the negative signs. They do not affect the expansion or contraction.

An expansion is any number greater than 1 and a contraction is any number less than 1.

Expansion: b) -2 and d) 2

Contraction: b) - 0.8 and d) 0.8

we know that f(1)=2 so f^-1(2)=1

so B is correct!

Answer:  The correct option is

(B) [tex]f^{-1}(x)=\dfrac{1}{x-1}.[/tex]

Step-by-step explanation:  We are given to select the correct expression that is the inverse of the following function :

[tex]f(x)=\dfrac{x+1}{x}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

Let y denotes f(x). Then,

[tex]y=f(x)~~~~~~\Rightarrow x=f^{-1}(y).[/tex]

Substituting this value in equation (i), we get

[tex]f(x)=\dfrac{x+1}{x}\\\\\\\Rightarrow y=\dfrac{f^{-1}(y)+1}{f^{-1}(y)}\\\\\\\Rightarrow yf^{-1}(y)=f^{-1}(y)+1\\\\\Rightarrow yf^{-1}(y)-f^{-1}(y)=1\\\\\Rightarrow (y-1)f^{-1}(y)=1\\\\\Rightarrow f^{-1}(y)=\dfrac{1}{y-1}\\\\\Rightarrow f^{-1}(x)=\dfrac{1}{x-1}.[/tex]

Thus, the required inverse of the given function is

[tex]f^{-1}(x)=\dfrac{1}{x-1}.[/tex]

Option (B) is CORRECT.

Hopefully I read the question right, if not I'm sorry

Koen ran for 4 and a half hours, which is also 4.5 hours

Since he averaged a speed of 6 mph, I multiply the number of hours by speed each hour, which is 4.5*6

4.5*6=27

Koen ran 27 miles.

Answer:

38 miles

Step-by-step explanation:

study island

ANSWER

(-2,4)

EXPLANATION

The given equations are:

4x + 5y = 12

7x + 5y = 6

Subtract the first equation from the second equation.

7x-4x+5y-5y=6-12

3x=-6

Divide both sides by 3 to obtain:

x=-2

Put x=-2 into the first equation to get:

4(-2)+5y=12

-8+5y=12

5y=12+8

5y=20

y=20/5

y=4

Checking

4(-2)+5(4)=12

-8+20=12

12=12

Also

7(-2)+5(4)=6

-14+20=6

6=6

Answer:

The solution is (-2,4)

Step-by-step explanation:

* Lets revise how to solve the system of equations algebraically

- If the system of equation is ax+by=c and dx+ey=f, then we can use

 the elimination method to solve

- The steps of the elimination method

# Change the coefficient of one variable in one of the two equation

  to have the same coefficient with opposite sign of this variable in the

  second equation (a = -d)

# Add the two equations to eliminate this variable (by+ey=c+f)

# Solve to find the second variable (y=(c+f)/(b+e))

# Substitute the the value of the second variable in any equation to

  find the first variable

* Now lets solve the problem

∵ 4x+5y=12 ⇒ (1)

∵ 7x+5y=6 ⇒ (2)

- The variable y has the same coefficient in the two equations, then

 eliminate it by multiply one of the equation by -1 to make

 opposite sign

- Multiply equation (2) by -1

∴-7x-5y=-6 ⇒ (3)

- Add (1) and (3)

∴ -3x=6 ⇒ divide both sides by -3

∴ x=-2

- Substitute the value of x in (1) or (2)

∴ 4(-2)+5y=12

∴ -8+5y=12 ⇒ add 8 to both sides

∴ 5y=20 ⇒ divide each side by 5

∴ y = 4

- The solution of the system is the point which has the values of x and y

∴ The solution is (-2,4)

Answer:

c. (2, 1) and (−1, −2)

Step-by-step explanation:

Assuming you intended y=x²-3 and x-y=1, you can graph the parabola and the straight line (rewrite x-y=1 as y = x-1).

You can then see the intersections at x=-1, y=-2 and x=2, y=1.

Answer:

Do Addition

Step-by-step explanation:

x=76+78

x= 154

Answer:

x = 77°

Step-by-step explanation:

The measure of x is half the sum of the measures of the arcs intercepted by the angle and it's vertical angle, that is

x = 0.5 × (78 + 76)° = 0.5 ×154° = 77°

Answer:

A)

62/3 = 20.67 hours

B)

60.00 hours

C)

2074.29 miles

Step-by-step explanation:

If we assume the earth is a perfect circle, then in a complete rotation the earth covers 360 degrees or 2π radians.

A)

In 24 hours the earth rotates through an angle of 360 degrees. We are required to determine the duration it takes to rotate through 310 degrees. Let x be the duration it takes the earth to rotate through 310 degrees, then the following proportions hold;

(24/360) = (x/310)

solving for x;

x = (24/360) * 310 = 62/3 = 20.67 hours

B)

In 24 hours the earth rotates through an angle of 2π radians. We are required to determine the duration it takes to rotate through 5π radians. Let x be the duration it takes the earth to rotate through 5π radians, then the following proportions hold;

(24/2π radians) = (x/5π radians)

Solving for x;

x = (24/2π radians)*5π radians = 60 hours

C)

If the diameter of the earth is 7920 miles, then in 24 hours a point on the equator will rotate through a distance equal to the circumference of the Earth. Using the formula for the circumference of a circle we have;

circumference = 2*π*R = π*D

                         = 7920π miles

Therefore, the speed of the earth is approximately;

(7920π miles)/(24 hours) = 330π miles/hr

The distance covered by a point in 2 hours will thus be;

330π * 2 = 660π miles = 2074.29 miles

Answer:

Step-by-step explanation:

The goal to solving any equation is to have x = {something}.  That means we need to get the x out from underneath that radical.  It's a square root, so we can "undo" it by squaring.  Square both sides because this is an equation.  Squaring both sides gives you

[tex]x^2=-3x+40[/tex]

Get everything on one side of the equals sign and set the quadratic equal to 0:

[tex]x^2+3x-40=0[/tex]

Throw this into the quadratic formula to get that the solutions are x = 5 and -8.  We need to see if only one works, both work, or neither work in the original equation.

Does [tex]5=\sqrt{-3(5)+40}[/tex]?

[tex]5=\sqrt{-15+40}[/tex] and

[tex]5=\sqrt{25}[/tex]

and 5 = 5.  So 5 works.  Let's try -8 now:

[tex]-8=\sqrt{-3(-8)+40}[/tex] and

[tex]-8=\sqrt{24+40}[/tex] so

[tex]-8=\sqrt{64}[/tex]

-8 = 8?  No it doesn't.  So only 5 works. Your choice is the third one down.

Answer:

Step-by-step explanation:

alright,  lets get started.

Side 5 is opposite.

Side 12 is adjacent.

Side 13 is hypotenuse.

Using SOH CAH TOA,

sin Θ = [tex]\frac{opposite}{hypotenuse}[/tex]

sin Θ = [tex]\frac{5}{13}[/tex]

cos Θ=[tex]\frac{adjacent}{hypotenuse}[/tex]

cos Θ=[tex]\frac{12}{13}[/tex]

tan Θ=[tex]\frac{opposite}{adjacent}[/tex]

tan Θ=[tex]\frac{5}{12}[/tex]   :   Answer

Hope it will help :)

Answer:

x = 29.91

Step-by-step explanation:

Cos (53) = 18/x

x = 18 / Cos(53)

x = 18/ 0.6018

x = 29.91

For this case we have that by definition of trigonometric relations of a rectangular triangle, that the cosine of an angle is given by the leg adjacent to the angle on the hypotenuse of the triangle. Then, according to the figure we have:

[tex]cos (53) = \frac {18} {x}[/tex]

Clearing x:

[tex]x = \frac {18} {cos (53)}\\x = \frac {18} {0.60181502}\\x = 29,9095226969[/tex]

Rounding:

[tex]x = 29.91[/tex]

Answer:

29.91

Answer:

6.5 Gallons

Step-by-step explanation:

288 miles / 12 gallons = 24 mpg

156 miles / 24 mpg = 6.5 gallons

[tex]\bf x^{-1}-1\div x-1\implies \implies \cfrac{1}{x}-1\div x-1\implies \cfrac{\frac{1}{x}-1}{~~x-1~~}\implies \cfrac{~~\frac{1-x}{x}~~}{\frac{x-1}{1}} \\\\\\ \cfrac{1-x}{x}\cdot \cfrac{1}{x-1}\implies \cfrac{-(\begin{matrix} x-1 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix})}{x}\cdot \cfrac{1}{\begin{matrix} x-1 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}\implies -\cfrac{1}{x}\implies -x^{-1}[/tex]

Answer:

Step-by-step explanation:

the answer is $22.95

In order to break even store need to charge $22.25 per pair of shorts.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

In other words, an equation is a set of variables that are constrained through a situation or case.

Given,

Fixed cost = $450

Cost of each pair = $11

Number of pairs = 40

So,

The total cost of manufacturing

450 + 11(40) = $890

Now,

Let's say the store charges x per short

Total income = 40x

Now,

At break-even point

The total cost of manufacturing = Total income

890 = 40x

x = $22.25

Hence, In order to break even store need to charge $22.25 per pair of shorts.

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Answer:

Where's the list?

Answer:

1)49

2)231

Step-by-step explanation:

1)

4+9=13

4*2=8

8+1=9

2)

2+3+1=6

2+1=3

1*2=2

Answer:

#1. 49 #2. 231

Step-by-step explanation:

#1. 4 x 2 + 1 =

8 + 1 =

9

add 40 + 9 = 49

#2. x + 2x + (x + 2x) = 6

6x = 6  

x = 1  

2x = 2

x + 2x = 3  

(2 x 100) + (3 x 10) + 1 or 231.

Can I get Brainliest☺☺☺☺

Answer:

117

Step-by-step explanation:

182/14=13

13x9=117

Question 9:

cos x = 10/36

Take the inverse on both sides.

arccos(cos x) = arccos(10/36)

x = 73.8723797868

x = 73.87

Question 10:

tan 89 = x

57.2899616308 = x

57.29

Answer:

5 units

Step-by-step explanation:

Let's take point X and X' (it will be the same regardless of the point).

The distance is 3 units to the right then 4 units up.

A direct line will be diagonal and can be found using the pythagorean theorem (refer to visual).

(D: a > 0) 3² + 4² = a² --> 9 + 16 = a² --> a² = 25 --> a = 5

So the distance is 5 units.

When a figure is translated, or moved without rotation or change in size, the distances between corresponding points on the original and new figure remain the same. Therefore, the distance between any two corresponding points on Triangle XYZ and Triangle X'Y'Z' is the same as it was prior to the translation.

In this case, the triangle XYZ is being translated, which means that it is being shifted in the plane. The student has moved the triangle 4 units up and 3 units left. This operation does not alter the size, shape or orientation of the triangle, just its position. Therefore, the distance between any two points on the triangle remains the same before and after the translation. To clarify, if the distance between point X and Y initially is 'd', after the triangle has been translated to yield triangle X'Y'Z', the distance between X' and Y' remains 'd'. This is an important characteristics of translation, a core concept in geometry.

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Answer:

B) 15/91

Step-by-step explanation:

Probability of a girl as first choice is ...

number of girls / total number of students = 6/14 = 3/7

Probability of a girl as second choice (given a girl as first choice) is ...

number of girls / remaining number of students = 5/13

Then the probability of the two events is the product of their individual probabilities:

(3/7)·(5/13) = 15/91 . . . . . matches choice B

Answer:

Step-by-step explanation:

Their point of intersection, assuming there is one, will be somewhere on the line y = x.  This line, y = x, is the line of symmetry between a function and its inverse.  So if the two do in fact intersect, it will be at some point on that line

Answer:

C. (5, 3)

Step-by-step explanation:

this point is within the answer area... look below at the graph of both linear inequalities

For this case we have the following system of inequations:

[tex]y\leq2x-5\\y> -3x[/tex]

We must replace each of the points and verify that the inequalities are met:

Point A: (1,1)

[tex]1 \leq2 (1) -5\\1 \leq2-5\\1 \leq-3[/tex]

It is not fulfilled!

Point B: (-2,2)

[tex]2 \leq2 (-2) -5\\2 \leq-4-5\\2 \leq-9[/tex]

It is not fulfilled!

Point C: (5,3)

[tex]3 \leq2 (5) -5\\3 \leq10-5\\3 \leq5[/tex]

Is fulfilled!

[tex]3> -3 (5)\\3> -15[/tex]

Is fulfilled!

Point D: (-4,4)

[tex]4 \leq2 (-4) -5\\4 \leq -8-5\\4 \leq -13[/tex]

It is not fulfilled!

Thus, the point that is the solution of inequalities is:

(5,3)

ANswer:

(5,3)

Both x² and mx + b are differentiable functions of x (they are both polynomials), so if f(x) is also differentiable, we need to pay special attention at x = 2 where the two pieces of f meet.

Continuity means that the limit

[tex]\displaystyle \lim_{x\to2} f(x)[/tex]

must exist.

From the left side, we have x < 2 and f(x) = x², so

[tex]\displaystyle \lim_{x\to2^-} f(x) = \lim_{x\to2} x^2 = 4[/tex]

From the right, we have x > 2 and f(x) = mx + b, so

[tex]\displaystyle \lim_{x\to2^+} f(x) = \lim_{x\to2} (mx+b) = 4m+b[/tex]

It follows that 4m + b = 4.

Differentiability means that the limit

[tex]\displaystyle \lim_{x\to2} \frac{f(x) - f(2)}{x - 2}[/tex]

must exist.

From the left side, we again have x < 2 and f(x) = x². Then

[tex]\displaystyle \lim_{x\to2^-}\frac{f(x)-f(2)}{x-2} = \lim_{x\to2} \frac{x^2-4}{x-2} = \lim_{x\to2} (x+2) = 4[/tex]

From the right side side, we have x > 2 so f(x) = mx + b. Then

[tex]\displaystyle \lim_{x\to2^+}\frac{f(x)-f(2)}{x-2} = \lim_{x\to2} \frac{(mx+b)-(2m+b)}{x-2} = \lim_{x\to2} \frac{mx-2m}{x-2} = \lim_{x\to2}m = m[/tex]

The one-sided limits must be equal, so m = 4, and from the other constraint it follows that 16 + b = 4, or b = -12.