What is the slope of 0,0 and 1/3, 7/3

The solutions to the system of equations are x = 2 and 4

From the question, we have the following parameters that can be used in our computation:

f(x) = x - 3

g(x) = 1/(x - 3)

The solution to the system of equations implies that

f(x) = g(x)

So, we have

x - 3 = 1/(x - 3)

Cross multiply the equation

This gives

(x - 3)² = 1

So, we have

x - 3 = ±1

Add 3 to both sides

x = 3 ± 1

So, we have

x = 2 and 4

Hence, the solutions to the system of equations are x = 2 and 4

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The tuxedo was rented for 4 days.

Let's start by assigning variables to the unknowns. Let "x" be the number of additional days rented, and "d" be the total number of days rented (including the first day).

From the given information, we know that the flat fee for the rental is $150, so the cost of the additional days is the total cost minus the flat fee, which is $300 - $150 = $150. We also know that the cost for each additional day is $50. Therefore, we can set up the equation:

$150 + $50x = $300

Subtracting $150 from both sides, we get:

$50x = $150

Dividing both sides by $50, we get:

x = 3

So the tuxedo was rented for 3 additional days, making the total number of days rented:

d = 1 + 3 = 4

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Using the radius of the Ferris wheel and the angle between the two positions, the time spent on the ride when they're 28 meters above the ground is 12 minutes

The radius of the Ferris wheel is 30 / 2 = 15 meters.

The highest point on the Ferris wheel is 15 + 4 = 19 meters above the ground.

The time spent higher than 28 meters is the time spent between the 12 o'clock and 8 o'clock positions.

The angle between these two positions is 180 degrees.

The time spent at each position is 10 minutes / 360 degrees * 180 degrees = 6 minutes.

Therefore, the total time spent higher than 28 meters is 6 minutes * 2 = 12 minutes.

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Answer:

0.64 = 64% probability that two randomly sampled new employees will both be able to survive their first year

Step-by-step explanation:

For each employee, there are only two possible outcomes. Either they survive the first year, or they do not. The probability of an employee surviving the first year is independent of other employees. This means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

A San Francisco-based tech firm is able to keep 80% of its new employees after one year.

This means that \(p = 0.8\)

Q1. What is the chance that two randomly sampled new employees will both be able to survive their first year

This is P(X = 2) when n = 2. So

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 2) = C_{2,2}.(0.8)^{2}.(0.2)^{0} = 0.64\)

0.64 = 64% probability that two randomly sampled new employees will both be able to survive their first year

The par value per share before the stock dividend is $5; after the stock dividend, the par value remains $5.

The par value is the entity's stated nominal value.

It does not affect the market value of the shares.

With a stock dividend, the value of the common stock increases by the par value and the number of shares outstanding, making the par value remain the same.

The par value changes when there is a stock split.

Common stock, $5 par value $382,000

Common stock shares = 76,400 shares ($382,000/$5)

Paid-in capital in excess of par-common stock 20,000

Retained earnings 166,000

Total stockholders' equity $568,000

October 1: Retained Earnings $109,960 (7,640 x $14) Stock Dividend Distributable $38,200 Paid-in Capital Capital $71,760

Stock Dividend Distributable $38,200 Common Stock $38,200

Common stock shares = 84,040 shares (76,400 + 7,640)

Common stock value = $420,200

Par value after the stock dividend = $5 ($420,200/84,040)

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Answer:

1/7

Step-by-step explanation:

You have to multiply across the top then the bottom.

after 2 days(48 hours):

The number of outcomes would be:

24 different sandwiches

Answer:

Step-by-step explanation:

(2x+5)(x+3)

2x^2+6x+5x+15

2x^2+11x+15

Answer:

2x^2+11x+15

Step-by-step explanation:

(2x+5) (x+3)

Foil

first 2x*x = 2x^2

outer 2x *3 = 6x

inner 5*x = 5x

last 5*3 =15

Add them together

2x^2 +6x+5x+15

Combine like terms

2x^2 +11x+15

Answer:

b)3.5km per hour

Step-by-step explanation:

Answer:

a) 4km an hour

b) 3.5km an hour

Step-by-step explanation (only for b):

The answer is 3.5 kilometers because if he walked 28 kilometers in 8 hours, that means he walked an average of 28/8 km in 8/8 hours, or 3.5 kilometers in 1 hour.

The simplified value of (2x - 4)² is 4x² - 16x + 16.

First, let us understand the algebraic identities;

Algebraic identities are equations in which the left hand side of the equation is identically equal to the right hand side of the equation.

Some of the identities are:

We are given (2x - 4)².

Use the identity (a - b)² = a² - 2ab + b² to expand to the given expression.

So, a = 2x and b = 4.

Put it into the identity, we will get;

Therefore,

(2x - 4)² = (2x)² - 2 * 2x * 4 + (4)² = 4x² - 16x + 16

Thus, the simplified value of (2x - 4)² is 4x² - 16x + 16.

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Segments MS and QS are therefore congruent by the definition of bisector. Therefore, the correct answer option is: D. MS and QS.

In Mathematics and Geometry, a perpendicular bisector is a line, segment, or ray that bisects or divides a line segment exactly into two (2) equal halves and forms an angle that has a magnitude of 90 degrees at the point of intersection.

This ultimately implies that, a perpendicular bisector bisects a line segment exactly into two (2) equal halves, in order to form a right angle that has a magnitude of 90 degrees at the point of intersection.

Since line segment NS is a perpendicular bisector of isosceles triangle MNQ, we can logically deduce the following congruent relationships;

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Complete Question:

The proof that ΔMNS ≅ ΔQNS is shown. Given: ΔMNQ is isosceles with base MQ, and NR and MQ bisect each other at S. Prove: ΔMNS ≅ ΔQNS

We know that ΔMNQ is isosceles with base MQ. So, MN ≅ QN by the definition of isosceles triangle. The base angles of the isosceles triangle, ∠NMS and ∠NQS, are congruent by the isosceles triangle theorem. It is also given that NR and MQ bisect each other at S. Segments _____ are therefore congruent by the definition of bisector. Thus, ΔMNS ≅ ΔQNS by SAS.

NS and NS

NS and RS

MS and RS

MS and QS

Answer:

\(x=-10\)

Step-by-step explanation:

\(\frac{x}{2}=-5\\\mathrm{Multiply\:both\:sides\:by\:}2\\\frac{2x}{2}=2\left(-5\right)\\Simplify\\x=-10\)

Answer:

the correct answer is A. 25 sandwiches.

Step-by-step explanation:

Assuming you have plenty of bread and jelly, you can make 25 sandwiches from the jar of peanut butter.

Each sandwich typically requires 2 tablespoons of peanut butter, one slice of bread with peanut butter and one slice of bread with jelly.

So, if you have 50 tablespoons of peanut butter, you can make 25 sandwiches with it, because 50 / 2 = 25.

Therefore, the correct answer is A. 25 sandwiches.

Answer: 25

Step-by-step explanation:

We have 50 tablespoons of peanut butter and we know that it requires 2 tablespoons to make a single sandwich. In order to find how many sandwiches we can make with our 50 tablespoons, we would have to do 50 divided by 2.

2+2...=50

The value of x is 8

According to the Pythagorean theorem, the square of the hypotenuse of a right-angle triangle will equal the sum of the squares of the perpendicular and base.

given that the triangle's sides are,

a = 15, b = x, c = 17

Apply the Pythagorean theorem in right angle triange,

a² + b² = c²

15² + x² = 17²

x² = 64

x = 8

Therefore, the value of x is 8

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Apply the Pythagorean theorem in right angle triange and The value of x is 8

The Pythagorean Theorem asserts that the square on the hypotenuse, or side across from the right angle, is equal to the sum of the squares on the legs of a right triangle, or, in common algebraic notation, a² + b² = c².

The Pythagorean theorem states that the hypotenuse square of a right-angle triangle will equal the total of the base, perpendicular, and hypotenuse squares.

Given that the edges of the triangle are,

a = 15,

b = x,

c = 17

Applying right-angle triangles to the Pythagorean Theorem

a² + b² = c²

15² + x² = 17²

x² = 64

x = 8

Therefore, the value of x is 8

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The complete question is attached below,

The value of the missing segment n using the product of intersecting chord theorem is 14cm

The product of the segments of two intersecting chords are equal.

The segments of the chords ;

Chord 1 = 4 and n

Chord 2 = 7 and 8

The principle can be related Mathematically thus ;

4 × n = 7 × 8

4n = 56

Divide both sides by 4

4n/4 = 56/4

n = 14

Therefore, the value of n in the question is 14cm

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Answer:

\(Solid\ A= 180km^3\)

\(Solid\ C = 28.8km^3\)

Step-by-step explanation:

Given

\(k_1 = \frac{2}{5}\) from A to B

\(k_2 = \frac{2}{5}\) from B to C

\(Solid\ B = 72km^3\)

Required

Find the volumes of solids A and C

The expression that gives solid B from A is:

\(Solid\ A * k_1 = Solid\ B\)

This gives:

\(Solid\ A * \frac{2}{5}= 72km^3\)

Make A the subject

\(Solid\ A= 72km^3 * \frac{5}{2}\)

\(Solid\ A= 36km^3 * 5\)

\(Solid\ A= 180km^3\)

Similarly:

The expression that gives solid C from B is:

\(Solid\ B * k_2 = Solid\ C\)

This gives:

\(72km^3 * \frac{2}{5} = Solid\ C\)

\(\frac{144km^3 }{5} = Solid\ C\)

\(28.8km^3 = Solid\ C\)

\(Solid\ C = 28.8km^3\)

Answer:

if you meant (b+3)+(2^b-2), the answer is b+1+2^b

Step-by-step explanation:

but if you meant (b+3)+(2b-2), the aanswer is 3b+1

Answer:

3b+1

Step-by-step explanation:

(b+3)+(2b-2)

b+3+2b-2

3-2

b+1+2b

b+2b

3b+1

For you to input the information in a Matix you only have to consider the coefficients corresponding to each variable in each equation, in this case the matrix is:

1 -1 4 : 4

6 -8 1 : -1

4 1 0 : 0

This is the matrix for the given equations

Michio's answer not correct. He made a mistake when he was trying to convert the equation to logarithmic form. The right answer is  2.57

Looking at the equation 2(3)ˣ = 34, the best way to convert to logarithm is by isolating x.

we divide  2(3)ˣ = 34 by 2 on both side.

= (3)ˣ = 17

In logarithm form 3 becomes the base of the log

x = log₃(17)

x= 2.578

The answer above is based on the information seen in the picture.

Michio wanted to find the value of x in the equation 2(3)ˣ = 34. He first converted the equation to log₃2x = 17. Next, he wrote 2x = 3¹⁷ and used a calculator to find x = 64,570,081.5. Was his answer correct? If not, what was his mistake and what is the right answer? Justify your answer.

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Answer:

14

Step-by-step explanation:

Answer:

y=3x-3

Step-by-step explanation:

Answer:

Step-by-step explanation:

To solve this problem, we can use the following formula:

(quantity of tea 1 x price of tea 1) + (quantity of tea 2 x price of tea 2) = total quantity x price of mixture

Let x be the number of pounds of black tea that the store owner needs to mix with the oolong tea.

We know that:

The store owner has 35 pounds of oolong tea that sells for $2.40 per pound.

The store owner wants to sell the final mixture for $2.10 per pound.

The black tea is worth $1.80 per pound.

Using the formula above, we can write:

(35 x 2.40) + (x x 1.80) = (35 + x) x 2.10

Simplifying this equation, we get:

84 + 1.8x = 73.5 + 2.1x

0.3x = 10.5

x = 35

Therefore, the store owner needs to mix 35 pounds of black tea with the oolong tea.

I hope this helps! Let me know if you have any other questions.

Answer:

Step-by-step explanation:

Let's assume the store owner needs to mix x pounds of black tea with the 35 pounds of oolong tea.

The cost of the oolong tea is $2.40 per pound, so the total cost of the oolong tea is:

Cost of oolong tea = 35 pounds × $2.40/pound = $84

The cost of the black tea is $1.80 per pound, and the final mixture needs to be sold for $2.10 per pound. To achieve an average price of $2.10 per pound, the total cost of the mixture should be:

Total cost of mixture = (35 + x) pounds × $2.10/pound = $73.5 + $2.10x

Since the cost of the mixture should equal the sum of the costs of the oolong and black teas, we can set up the equation:

$73.5 + $2.10x = $84

Now, let's solve for x to find the amount of black tea needed:

$2.10x = $84 - $73.5

$2.10x = $10.5

x = $10.5 / $2.10

x ≈ 5

Therefore, the store owner needs to mix approximately 5 pounds of black tea with the 35 pounds of oolong tea in order to sell the final mixture for $2.10 per pound.

Answer:

B

Step-by-step explanation:

since -33>-3x-6

AND -3x-6>=-36

The answer is B

Hope this helps

Answer:

b

Step-by-step explanation: