Jerome solved the equation below by graphing.
log2(x) + log2(x-2) = 3
Which of the following shows the correct system of equations and solution?

Answer:

The answer is 1D , 2A , 3C , 4B ⇒ answer (c)

Step-by-step explanation:

* Lets talk about the transformation

- If the function f(x) reflected across the x-axis, then the new

 function g(x) = - f(x)

- If the function f(x) translated horizontally to the right  

 by h units, then the new function g(x) = f(x - h)

- If the function f(x) translated horizontally to the left  

 by h units, then the new function g(x) = f(x + h)

* Lets explain each function

∵ y = tan(x)

∵ y = -tan(x - π/2)

# (x - π/2) means the graph translated horizontally to

  the right π/2 units

# -tan(x - π/2) means the graph reflected across the x-axis

∴ The graph is (D)

* 1) y = -tan(x - π/2) ⇒ (D)

∵ y = tan(x + π/2)

# (x + π/2) means the graph translated horizontally to

  the left π/2 units

∴ The graph is (A)

* 2) y = -tan(x - π/2) ⇒ (A)

∵ y = -cot(x - π/2)

# (x - π/2) means the graph translated horizontally to

  the right π/2 units

# -cot(x - π/2) means the graph reflected across the x-axis

∴ The graph is (C)

* 3) y = -cot(x - π/2) ⇒ (C)

∵ y = cot(x + π/2)

# (x + π/2) means the graph translated horizontally to

  the left π/2 units

∴ The graph is (B)

* 4) y = -tan(x - π/2) ⇒ (B)

∴ The answer is 1D , 2A , 3C , 4B answer (c)

4. You total the songs to find out how many possibilities all together = 20

Then how many of those are rap songs = 5

So the probability of getting rap songs is 5/20 or (simplified) 1/4

Explanation of sandwich combinations using a tree diagram and computation of the probability for Joel's first song being rap.

Tree Diagram for David's Sandwich Combinations:

Probability for Joel's Jumble:

Answer:

5.545

Step-by-step explanation:

This problem can be easily solved by using the law of cosines, which relates the lengths of the sides of a triangle to the cosine of one of its angles.

in this case, the formula can be applied in the following way

a^2 = b^2  + c^2  - 2*b*c*cos(α)

Where

a,b,c are each of the sides of the triangle,

α is the angle between sides b and c

(See attached picture)

If we use the formula we get

a^2 = (9)^2 + (6)^2 - 2*(9)(6)*cos(37°)

a^2 = 81 + 36 - 86.2526

a^2 = 30.747

a = sqrt(30.747)

a = 5.545

That expression is the expected value of your winnings, or "the average amount you will win (or lose) per game in the long run".

Answer:

Step-by-step explanation:

Given that a game has 3 possible outcomes, with probabilities p1, p2, and p3

The amount win or lose for each outcome is v1, v2, and v3, respectively.

If X is the amount of win or lose then x has the following prob distribution

[tex]X      v_1       v_2      v_3\\Pr.    p_1       p_2     p_3\\[/tex]

Hence Expected value of x = average of x

=[tex]p1v1 + p2v2 + p3v3[/tex]

Thus answer is

Option b) The average amount you will win (or lose) per game in the long run.

Answer:

Step-by-step explanation:

5 out of 8 because there are four one spaces and one pink space so that equals 5 and there are a total of 8 spaces to hit

Answer:

5/8.

Step-by-step explanation:

There are a total of 8 sectors of which 4 are 1 and 1 is pink.

So Prob (hitting a 1) = 4/8 = 1/2.

Prob (hitting a pink) = 1 /8.

So the probability of hitting a pink or a 1 = 1/2 + 1/8

= 5/8.

The amount of fluid used in 4 days will be 18 ounces

Since each of them use 1 1/2 cups and they are 3

so the collective amount in 1 day will be

3 * 1 1/2 = 9/2

Now

The amount in 4 days will be

4 * 9/2 = 18

Therefore they will collectively use 18 ounces in 4 days

Answer:

9 miles.

Step-by-step explanation:

We have been given that Yi is told that the item that she wants to buy is still available at a store that is 3/4 inch on a map from her current location. The scale of the map is 1 inch= 12 miles.

To find the actual distance between Yi and store we will multiply 3/4 by 12 as:

[tex]\text{The distance between Yi and store}=\frac{3}{4}\text{ inch}\times \frac{\text{12 miles}}{\text{inch}}[/tex]

[tex]\text{The distance between Yi and store}=\frac{3}{4}\times \text{12 miles}[/tex]

[tex]\text{The distance between Yi and store}=3\times \text{3 miles}[/tex]

[tex]\text{The distance between Yi and store}=9\text{ miles}[/tex]

Therefore, Yi is 9 miles away from the store.

➷ If a line is parallel to the line, then the slope will remain the same

Now, you just need to substitute the values of that coordinate into the equation

1/2 = -1/2(3) + c

Simplify:

1/2 = -1.5 + c

Add 1.5 to both sides

c = 2

Therefore, the equation of the line would be:

y = -1/2x + 2

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - [tex]\frac{1}{2}[/tex] x + 3 is in this form

with m = - [tex]\frac{1}{2}[/tex]

• Parallel lines have equal slopes, hence

slope of parallel line = - [tex]\frac{1}{2}[/tex], thus

y = - [tex]\frac{1}{2}[/tex] x + c ← is the partial equation

To find c substitute (3, [tex]\frac{1}{2}[/tex]) into the partial equation

[tex]\frac{1}{2}[/tex] = - [tex]\frac{3}{2}[/tex] + c ⇒ c = 2

y = - [tex]\frac{1}{2}[/tex] x + 2 ← equation of parallel line

Answer:

(x + 12)² + (y + 32)² = 1031  

Step-by-step explanation:

137 + 64y = -y² - x² - 24x

Arrange the terms in descending powers of x and y.

x² + 24x  + y² + 64y = -137

Complete the squares  for x and y

(x² + 24x  + 144) + (y² + 64y + 1024) = -137 + 144 + 1024

Write the equation as the  squares of binomials of x and y

(x + 12)² + (y + 32)² = 1031

This is the equation of a circle with centre at (-12, -32) and radius r = √1031.

Answer:

Answer x  = 8

Step-by-step explanation:

(5x + 4) + (8x - 18)= 90      The two angles must be complementary for this to work. Remove the brackets

5x + 4 + 8x - 18 = 90          Collect like terms

13x - 14 = 90                        Add 14 to both sides

13x = 104                              Divide by 13  

x = 8 Answer

Check

Sin(8*8 - 18) = sin(64 - 18) = sin(46) = 0.7193

Cos(5*8 + 4) = cos(44) = 0.7193

This problem is very interesting. Thanks for posting.

Answer:

Jeremy has 45 nickels.

Step-by-step explanation:

I'm guessing the question is how many nickels does Jeremy have.

n + 55 = 100

n = 45

Answer:

45 nickels.

Step-by-step explanation:

We have been given that Jeremy and Robin like to collect nickels. Jeremy has n nickels, and Robin has 55 nickels. Together they have a total of 100 nickels.

We can represent our given information in an equation as:

[tex]n+55=100[/tex]

[tex]n+55-55=100-55[/tex]

[tex]n=45[/tex]

Therefore, Jeremy has 45 nickels.

Answer:

  [tex]\dfrac{z_1}{z_2}=\dfrac{1}{2}\,\text{cis}\,\dfrac{7\pi}{12}[/tex]

Step-by-step explanation:

The quotient of complex numbers is the quotient of their magnitudes at the difference of their angles.

  [tex]\dfrac{z_1}{z_2}=\dfrac{\text{cis}\,\dfrac{2\pi}{3}}{2\,\text{cis}\,\dfrac{\pi}{12}}=\dfrac{1}{2}\,\text{cis}\left(\dfrac{2\pi}{3}-\dfrac{\pi}{12}\right)\\\\\bf{\dfrac{z_1}{z_2}=\dfrac{1}{2}\,\text{cis}\,\dfrac{7\pi}{12}}[/tex]

Answer:

d. does not exist

Step-by-step explanation:

The given limits are;

[tex]\lim_{x \to 4} f(x) =5[/tex], [tex]\lim_{x \to 4} g(x) =0[/tex] and [tex]\lim_{x \to 4} h(x) =-2[/tex]

We want to find

[tex]\lim_{x \to 4} \frac{f}{g}(x)= \lim_{x \to 4} \frac{f(x)}{g(x)}[/tex]

By the properties of limits, we have;

[tex]\lim_{x \to 4} \frac{f}{g}(x)= \frac{\lim_{x \to 4} f(x)}{\lim_{x \to 4} g(x)}[/tex]

This gives us;

[tex]\lim_{x \to 4} \frac{f}{g}(x)= \frac{5}{0}[/tex]

Division by zero is not possible. Therefore the limit does not exist.

Answer: Option D.

Step-by-step explanation:

To solve this exercise you must keep on mind the Angle at the Center Theorem.

According to the  Angle at the Center Theorem, an inscribed angle is half of the central angle.

Therefore, given in the inscribed angle m∠BAC=35°, you can calculate the central angle m∠EFD as following:

[tex]BAC=\frac{EFD}{2}[/tex]

- Solve for EFD.

[tex]EFD=2*BAC[/tex]

- When you substitute values. you obtain:

[tex]EFD=2(35\°)\\EFD=70\°[/tex]

Answer:

Option B. ∠EFD = 35°

Step-by-step explanation:

In a circle F, it has been given mED = mDB = mBC

We have to find the measure of ∠EFD

We should always remember the inscribed angle theorem which states that the measure of an inscribed angle is always half the measure of intercepted arc.

m(arc BC) = 2×∠CAB = 2×35 = 70°

Now it has been given in the question

mED = mBC

Therefore m(arc ED) = 70°

Again applying the same theorem

m(arc ED) = 2×∠EFD

70° = 2×∠EFD

m∠EFD = [tex]\frac{70}{2}=35[/tex]

Option B. 35° is the answer.

The parabola's line of symmetry is the x-axis.

y = 1/4p x²

Replace  x  with  −  x  and  y  with  − y  to check if there is x-axis, y-axis , or origin symmetry.  

Symmetric with respect to the y-axis

First we must subtract 25 in 18 because we are doing percentages.

So we do [tex]25 - 18  = 7[/tex]

So we get 7.

Now we need to do [tex]7/25 * 100% = 28%[/tex]

We would get a total of 18% of on the discount.

Answer:

C

Step-by-step explanation:

C is the most logical answer

Answer:

We know that [tex]\triangle ACE[/tex] is isosceles, that means [tex]\angle A \cong \angle E[/tex], by definition.

Also, [tex]\angle BDC \cong \angle DBC[/tex], because [tex]BD \parallel AE[/tex].

Then, we have [tex]115\° + \angle BDC = 180\°[/tex], by sumpplementary angles.

[tex]\angle BDC = 180 -115 = 65\° = \angle DBC[/tex]

Which means,

[tex]\angle C= 180 - 65 - 65[/tex], by definition.

[tex]\angle C= 50[/tex]

Then,

[tex]\angle A + \angle E + 50 = 180\\2\angle A = 180 - 50\\\angle A= \frac{130}{2}=65 = \angle E[/tex]

Therefore, the measures of vertex angles are 65 for the base angles of triangle and 50 for the different angle.

Answer:

78.09

Step-by-step explanation:

Answer:

1.78.09

2. 2755.59

Step-by-step explanation:

you go to the whome insurance company for auto insurance the charge $525.00 as a base rate for six months of insurance for your vehicle they offer a 15% discount for safe driver habits and a 10% discount for an excellent credit rating of 5% for a good rating the increase the rate by 5% and 10% respectively for a fair or poor credit rating you have a fair credit rating and qualify for the safe driver discount how much do the insurance cost you per month?

Insurance is more like a protection against any risk associated with vehicles, assets, buildings and lives.

the charge form the insurer is $525 with a 15% discount means

525 * 0.85 = 446.25    

or525-(525*15%)

aand increment in rate after 6 months

446.25 * 1.05 = 468.56  or  

446.25+446.25+5%

468.56 / 6 =

78.09

2. if the cost of the vehicle is 17000

a discount of 10%b for an excellent credit rating equals

17000*.90

$15300+1.05

16065

therefore per month he is going to pay 16065/6

$2677.5

add answer +78.09=2755.59

To find the coordinate of K', we first rotate point a (-7,-2) 270 degrees clockwise. Then, we shift the resulting coordinates 3 units down. The coordinate of K' is (-7, -5).

To find the coordinate of K', we first need to rotate point a (-7,-2) 270 degrees clockwise. To do this, we can use the rotation matrix:

[cos(theta)  -sin(theta)] [x]
[sin(theta)  cos(theta)]  [y]

Plugging in the values, we get:

[cos(270)  -sin(270)] [-7]
[sin(270)  cos(270)]  [-2]

Simplifying, we have:

[-0 -1] [-7]
[1  0]]  [-2]

Multiplying, we get:

[0 -7]
[1  0]]

Now, we shift the resulting coordinates 3 units down. Adding -3 to the y-coordinate, the coordinate of K' is (-7, -5).

Answer:

The probability would be 97.8%

Step-by-step explanation:

In order to find that, lets look at the amount of standard deviations away the amount given is. Since the number is 30 away from the mean, and the standard deviation is 15, we can find the total number of deviations it is away.

30/15 = 2

Now that we have that, we can look at the probability curve for standard deviations. Outside of 2 standard deviations above is only a 2.2% likelihood. Since that is the case, we can find the amount that would be under that as 100% minus the amount we just found.

100% - 2.2% = 97.8%

Answer: True, the measure of the angle formed by two intersecting perpendicular lines should be 90 degrees.

Answer:

True.

Step-by-step explanation:

You can see it with the cartesian plane. The cartesian plane are two intersecting perpendicular lines. The intersection point is the (0,0) and each cuadrant is 90°. 90°(4 cuadrants) = 360° .

Answer:

NO SOLUTION.

Step-by-step explanation:

4x - y    =  -5

12x - 3y  = 15

Multiply the first equation by 3:

12x - 3y = -15

Note that the left side of this equation is the same as the left side of the second one, but the right sides are different.  The left side cannot be equal to 2 different values. Therefore there  is NO SOLUTION.

Note if we subtract the last 2 equations we get:

0 = 30  which is, of course, absurd.

Answer:

There are 46 seats in row 10

Step-by-step explanation:

In order to find that we need to write this as an equation. We know that 6 is the constant and 4 is the coefficient for the variable. This would give us the equation:

y = 4x + 6

And this satisfies the equation for row 1, since when we put in the row number for x, it gives us the correct number of seats.

y = 4x + 6

y = 4(1) + 6

y = 4 + 6

y = 10

Now we can use that equation for any row. Let's use it for row 10

y = 4x + 6

y = 4(10) + 6

y = 40 + 6

y = 46

Let the time taken by 2nd computer be = x

Time taken by first computer = 60 seconds

Total time taken by both = 40 seconds

So, equation becomes:

[tex]\frac{1}{60}+\frac{1}{x}=\frac{1}{40}[/tex]

[tex]\frac{-1}{x}=\frac{1}{60}-\frac{1}{40}[/tex]

Solving this we get,

x=120 seconds

Hence, the 2nd computer will take 120 seconds to finish a search alone.

It would take the second computer 120 seconds to finish the same search

An equation is an expression used to show the relationship between two or more variables and numbers.

Let x represent the rate of the first computer and y represent the rate of the second computer.

Two computers working together can finish a search in 40 seconds. Hence:

It takes one of the computer 60 seconds, hence:

40/x + 2/3 = 1

x = 120 seconds

Therefore it would take the second computer 120 seconds to finish the same search

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Answer:

Step-by-step explanation:

Check the picture below.

Answer:

[tex]10.8 units[/tex]

Step-by-step explanation:

To find the answer, we need to use the distance formula.

[tex]d=\sqrt{(x-x)^2 +(y-y)^2}[/tex]

Let us look at our points. We have:

[tex](-2, 5)[/tex] and [tex](-6, -5)[/tex]

Now, let's identify our x's and y's:

x₁ = -2

y₁ = 5

x₂ = -6

y₂ = -5

Plug it in to the distance formula and simplify:

[tex]d=\sqrt{(-6+2)^2+(-5-5)^2}[/tex]

[tex]d=\sqrt{(-4)^2+(-10)^2}\\d=\sqrt{16 +100} \\d=\sqrt{116}\\[/tex]

[tex]d=2\sqrt{29}[/tex] OR [tex]10.77032961...[/tex]

Answer:

12

Step-by-step explanation:

Let's calculate how many possible outfits does Tobias has.

Hats: 2, Shirts: 3, Pants: 2

If he's picking everything at random blindly from his closet, he could pick any of the hats, any of the shirts and any of the pants.  That makes a total of:

2 x 3 x 2 = 12 possible combinations.  

That doesn't mean the arrangement will look pretty :-)

Tobias has 12 possible outfit combinations from his closet. This is calculated by multiplying the choices he has for each item of clothing: 2 hats, 3 shirts, and 2 pairs of pants.

In this mathematics problem, Tobias has 2 hats, 3 shirts, and 2 pairs of pants. In such problems, an easy rule to remember is that for independent choices you multiply your options. So, for his hats, he has 2 options. For shirts, he has 3 options and for pants, he has 2 options. To find the total number of outfit combinations, just multiply these options: 2 (hats) * 3 (shirts) * 2 (pants) = 12 possible outfit combinations. Therefore, Tobias can mix and match his clothing items to make 12 different outfits.

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Answer:

L = 18 and w = 16

Step-by-step explanation:

The area of a rectangle is found by A = l*w. Since the length here is 2 more than the width or 2 + w and the width is w, substitute these values and A = 288 to solve for w.

[tex]A = l*w\\288 = w(2+w)\\288 = w^2 + 2w[/tex]

To solve for w, move 288 to the other side by subtraction. Then factor and solve.

[tex]w^2 + 2w  - 288 = 0 \\(w +18)(w-16) = 0\\[/tex]

Set each factor equal to 0 and solve.

w - 16 = 0 so w = 16

w + 18 = 0 so w = -18

Since w is a side length and length/distance cannot be negative, then w = 16 is the width of the rectangle.

This means the length is 16 + 2 = 18.