Cedric multiplied (6x+11) by a second factor to get a product of 36x^2-121. Find the second factor. ​

Answer:

Sora's work:m + 16 dollars and 31 cents = 40 dollars. M = 23 dollars and 69 cents. is correct

Answer:

Sora’s work, B on edge 2022! i took the test :)

Answer: To find A and B such that g(x) = f(x) is bijective, we need to ensure that g(x) satisfies the conditions for a bijective function, namely, that it is both injective and surjective.

To show that g(x) is injective, we need to show that for any distinct x1, x2 in A, g(x1) ≠ g(x2). We can do this by assuming that g(x1) = g(x2) and then showing that it leads to a contradiction.

So, let's assume that g(x1) = g(x2). Then, we have:

f(x1) = f(x2)

x1(x1-1) = x2(x2-1)

x1^2 - x1 = x2^2 - x2

x1^2 - x2^2 - x1 + x2 = 0

(x1 - x2)(x1 + x2 - 1) = 0

Since x1 and x2 are distinct, we must have x1 + x2 = 1.

But this is impossible, since x1 and x2 are both real numbers, and the sum of two real numbers cannot equal 1 unless one of them is complex. Therefore, our assumption that g(x1) = g(x2) must be false, and g(x) is injective.

To show that g(x) is surjective, we need to show that for any y in B, there exists at least one x in A such that g(x) = y. In other words, we need to find an expression for x in terms of y.

So, let's solve the equation f(x) = y for x:

x(x-1) = y

x^2 - x - y = 0

Using the quadratic formula, we get:

x = (1 ± √(1 + 4y))/2

Since we want to define g(x) on R, we need to ensure that the expression under the square root is non-negative. This means that 1 + 4y ≥ 0, or y ≥ -1/4.

Therefore, we can define A = [-1/4, ∞) and B = [0, ∞), and g(x) = f(x) is a bijective function from A to B.

When Seema used compatible numbers to estimate the product of (–25.31)(9.61), her estimate is A. -250.

From the information, it should be noted that Seema used compatible numbers to estimate the product of (–25.31)(9.61).

It should be noted that -25.31 when rounded will be -25.

It should be noted that 9.61 when rounded will be 10.

Therefore, the multiplication will be:

= -25 × 10

= -250.

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Seema used compatible numbers to estimate the product of (–25.31)(9.61). What was her estimate?

-250

-240

240

250

Answer:

$720 divided by 2 = $360

$360-106=$254

$360+106=$466

$254+$466=$720

Person 1 has $254

Person 2 has $466

9514 1404 393

Answer:

  a. reflection over the x-axis

  b. vertical expansion by a factor of 2

  c. right shift 3 units

  d. shift upward 4 units

Step-by-step explanation:

It is a good idea to become familiar with what these various factors do. You will see them repeatedly.

__

a. Multiplying a function by a negative value reflects its graph over the x-axis.

__

b. A multiplier of 2 will expand the graph vertically by a factor of 2.

__

c. Subtracting 3 from each x-value will shift the graph right 3 units.

__

d. Adding 4 to each function value will shift the graph up 4 units.

The solution of the equation using the substitution method is given as x = -1 and x = 2.

The algebraic approach to solving simultaneous linear equations is known as substitution method. The value of one variable from one equation is substituted in the second equation in this procedure, as the name implies. By doing this, a pair of linear equations are combined into one linear equation with just one variable, making it much simpler to solve.

The two equations are y+3x=0 and y-6=-3x².

The first expression can be written as:

y + 3x = 0

y = -3x

Substitute the value of y in the second equation:

y-6=-3x²

-3x - 6 = - 3x²

Rearrange the equation:

3x² - 3x - 6 = 0

Take 3 as the common term from the equation:

x² - x - 2 = 0

x² - 2x + x - 2 = 0

x(x - 2) + 1(x - 2) = 0

(x + 1) (x - 2) = 0

x = -1 and

x = 2

Hence, the solution of the equation using the substitution method is given as x = -1 and x = 2.

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162

Step-by-step explanation:

(12 square - 15 + 17) + 16

=(144 - 15 + 17) + 16

=146 + 16

=162

The probability for the given case is 1/3.

Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.

The probability of any event always lie in the close interval of 0 and 1 [0,1].

A spinner has numbers indicated on it from one to six.

Suppose A be the event spinner lands on 1.

And, B be the event the spinner land on 4.

Now, the probability of any event is the ratio of number of favorable outcome to the total number of outcomes which is given as,

P(A) = 1/6

And, P(B) = 1/6

Thus, the probability of event A or B is given as,

P(A or B) = P(A) + P(B)

              = 1/6 + 1/6

              = 1/3

Hence, the probability that the spinner lands on 1 or 4 is 1/3.

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Answer:

i pretty sure it is waxing

Step-by-step explanation:

9514 1404 393

Answer:

  (C)  9600, 19600

Step-by-step explanation:

The interest is given by ...

  I = Prt

  I = 10,000×0.16×6 = 9,600 . . . interest earned

The amount of the investment is the total of the principal and the interest earned:

  10,000 +9,600 = 19,600 . . . amount of investment after 6 years

The required side length DK is 15 units for the given triangle JKL.

When a line parallel to one side of a triangle intersects the other two sides in distinct spots, the other two sides are separated in the same ratio.

Given that,

JK = 9x - 5 and EF = 6x - 13,

As we can see that ΔJKL and ΔDEF are similar triangles,

According to Thales's Theorem,

EF/JK = DE/KL

(6x - 13) / (9x - 5) = 1/2

2(6x - 13) = 9x - 5

12x - 26 = 9x - 5

3x = 21

x = 7

Substitute the value of x = 7 in JK = 9x - 5,

JK = 9 × 7 - 5 = 30 units

So DK = JK/2 = 30/2 = 15 units.

Thus, the required side length DK is 15 units.

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The pattern for the sequence 1.3, 8.3, 27.3, 64.3,… is f(n) = (n)³.3

The pattern in the question is given as

1.3, 8.3, 27.3, 64.3,…

In the above expressions and pattern, we can see that

From the above, we have the following

Current term = (n)³.3

Note that the decimal does not represent product

And also the pattern is a geometric sequence

Hence, the pattern for the sequence is f(n) = (n)³.3

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Answer:

You divide each fraction by the highest multiple.

4/16 can be divided by 4 to get 1/4

12/18 can be divided by 6 to get 2/3

4/10 can be divided by 2 to get 2/5

16/20 can be divided by 4 to get 4/5

Step-by-step explanation:

hope this helps

Answer:

72.1 degrees... 72 point 1 degress in case you cant see the ( . )

Step-by-step explanation:

62.4 minus -9.7= is 72.1

Answer:

y-3= 4(x-4)

y-3= 4x-4

y=4x-4+3

y=4x-1

Given statement solution is :- None of the given options (a, b, c, or d) match the meaning of the slope. The correct interpretation is that the car travels approximately 0.8 miles every minute.

To determine the meaning of the slope of the linear model for the given data, let's analyze the information provided. The table represents the distance traveled by a car at different time intervals.

Minutes | Distance Traveled (in miles)

50 | 20

20 | f

40 | 60

100 | a

125 | 80

100 | 100

To find the slope of the linear model, we need to calculate the change in distance divided by the change in time. Let's consider the intervals where the time changes by a fixed amount:

Between 50 minutes and 20 minutes: The distance changes from 20 miles to 'f' miles. We don't have the exact value of 'f', so we can't calculate the slope for this interval.

Between 20 minutes and 40 minutes: The distance changes from 'f' miles to 60 miles. Again, without knowing the value of 'f', we can't calculate the slope for this interval.

Between 40 minutes and 100 minutes: The distance changes from 60 miles to 'a' miles. We don't have the exact value of 'a', so we can't calculate the slope for this interval.

Between 100 minutes and 125 minutes: The distance changes from 'a' miles to 80 miles. Since we still don't have the exact value of 'a', we can't calculate the slope for this interval.

Between 125 minutes and 100 minutes: The distance changes from 80 miles to 100 miles. The time interval is 25 minutes, and the distance change is 100 - 80 = 20 miles.

Therefore, based on the given data, we can conclude that the car travels 20 miles in 25 minutes. To determine the meaning of the slope, we divide the distance change by the time change:

Slope = Distance Change / Time Change

= 20 miles / 25 minutes

= 0.8 miles per minute

So, none of the given options (a, b, c, or d) match the meaning of the slope. The correct interpretation is that the car travels approximately 0.8 miles every minute.

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What Yoshi uses is the multiplication property of equality, so the correct option is B.

The step that Yoshi did is:

(1/2)*s = 112

s = 112*(2/1) = 224.

What Yoshi does there is multiplicating both sides by the inverse of (1/2), so it is cancelled in the left side and the variable is isolated.

What he is using there is "Multiplication property of the equality".

Then that is what he should have written, the correct option is B.

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Answer: 1. P = 1/64

             2. P = 1/32

             3. P = 1/8

Step-by-step explanation:

In genetics, an ofspring inherits one copy of an allele of each parent, which can be described in the tables below called Punnett Square:

For crossing Aa x Aa:

       A      a

A    AA   Aa

a    Aa    aa

For crossing Bb x Bb:

        B      b

B     BB    Bb

b     Bb    bb

For crossing Cc x Cc:

       C      c

C    CC    Cc

c     Cc     cc

We can separate them because they are assorted independently.

For offspring with genotype AABBcc, probability will be:

P(AA) = 1/4

P(BB) = 1/4

P(cc) = 1/4

As all three probabilities has to happen at the same time, it is a "E" rule:

P(AABBcc) = \((\frac{1}{4}) (\frac{1}{4}) (\frac{1}{4})\)

P(AABBcc) = 1/64

Probability for the individual to be AABBcc is 1/64 or 1.56%.

Genotype AaBBcc:

P(Aa) = 2/4 = 1/2

P(BB) = 1/4

P(cc) = 1/4

P(AaBBcc) = \((\frac{1}{2}) (\frac{1}{4}) (\frac{1}{4})\)

P(AaBBcc) = 1/32

Probability for the individual to be AaBBcc is 1/32 or 3.12%

Genotype AaBbCc:

P(Aa) = 1/2

P(Bb) = 1/2

P(Cc) = 1/2

P(AaBbCc) = \((\frac{1}{2}) (\frac{1}{2}) (\frac{1}{2})\)

P(AaBbCc) = 1/8

Probability for the individual to be AaBbCc is 1/8 or 12.5%.

Answer:

Step-by-step explanation:

The graph of the linear equation cuts the x-axis at (5,0)

Answer: 1.82 m

Step-by-step explanation:

Ratios

0.14     n              0.14 x 13 = 1.82

 1.         13                    1.82/1 = 1.82

Answer:

(-2,-3)

Step-by-step explanation:

Well in the system,

x−5y=13

4x−3y=1

We need to find x or y in either equation.

Let's do x - 5y = 13 for x.

+5y to both sides

x = 5y + 13

Now we substitute 5y + 13 for y in 4x - 3y = 1.

4(5y + 13) - 3y = 1

20y + 52 - 3y = 1

17y + 52 = 1

-52 to both sides

17y = -51

Divide all by 17

y = -3

Now we can substitute -3 for y in 4x - 3y = 1.

4x - 3(-3) = 1

4x + 9 = 1

-9 to both sides

4x = -8

Divide 4 to both sides

x = -2

Thus,

the solution is (-2,-3).

Hope this helps :)

Answer:

Step-by-step explanation:

x - 5y = 13

4x - 3y = 1

Solve the equation for x

\(x - 5y = 13\)

Move '5y' to R.H.S and change it's sign

\(x = 13 + 5y\)

Substitute the given value of X into the equation

4x - 3y = 1

\(4(13 + 5y) - 3y = 1\)

Solve the equation for y

distribute 4 through the parentheses

\(52 + 20y - 3y = 1\)

Collect like terms

\(52 + 17y = 1\)

Move constant to R.H.S and change it's sign

\(17y = 1 - 52\)

Calculate

\(17y = - 51\)

Divide both sides of the equation by 17

\( \frac{17y}{17} = \frac{ - 51}{17} \)

Calculate

\(y = - 3\)

Now, substitute the given value of y into the equation

x = 13 + 5y

\(x = 13 + 5 \times ( - 3)\)

Solve the equation for x

Multiply the numbers

\( = 13 - 15\)

Calculate the difference

\( = - 2\)

The possible solution of the system is the ordered pair

( x , y )

( x , y ) = ( - 2 , - 3 )

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

Check if the given ordered pair is the solution of the system of equation

\( - 2 - 5 \times ( - 3) = 15\)

\(4 \times ( - 2) - 3 \times ( - 3) = 1\)

Simplify the equalities

\(13 = 13\)

\(1 = 1\)

Since all of the equalities are true, the ordered pair is the solution of the system

Hope this helps..

Best regards!!

Answer:

D.) X=23

Step-by-step explanation:

cause you add 8 to each side then simplify and you get 23

Answer:

50 Miles

Step-by-step explanation:

Let the miles traveled be x when cost for both taxi A and Taxi B is same

Lets calculate for Taxi A

charge to get in cab = $8

cost of traveling 1 mile = $ 0.75

cost of traveling for x miles = x * cost of traveling 1 mile= $ 0.75x

Total cost for traveling x miles = charge to get in cab +cost of traveling for x mile

Total cost for traveling x miles in Taxi A = $8 + $ 0.75x

______________________________________________

Lets calculate for Taxi B

charge to get in cab = $3

cost of traveling 1 mile = $ 1.25

cost of traveling for x miles = x * cost of traveling 1 mile= $ 1.25x

Total cost for traveling x miles = charge to get in cab +cost of traveling for x mile

Total cost for traveling x miles in Taxi B= $3 + $ 1.25x

As we have to find distance when cost for both is same

Thus

Total cost for traveling x miles in Taxi A=Total cost for traveling x miles in Taxi B

8 +  0.75x = 3 +  1.25x

8 - 3 = 1.25x -  0.75x

5 = 0.5x

x = 5/0.5 = 50

Thus, you must travel 50 miles so that cost in both the taxi A and Taxi B is the same

Answer:

B. y=-x – 7

Step-by-step explanation:

Hope this helps!

The width RQ of the river is approximately 61.98 ft.

To find the width RQ of the river, we can use the properties of perpendicular lines and collinearity.

Given that Karl starts at point R and walks perpendicular along the edge of the river 42 ft to point S, we can draw a line segment RS of length 42 ft.

From point S, Karl walks 28 ft further to point T. We can draw another line segment ST of length 28 ft.

Now, Karl turns 90° from point T and walks until his location (point U), point S, and point Q are collinear. Let's denote the length of this line segment as UQ.

From the given information, we know that TU = 68 ft.

Since U, S, and Q are collinear, we can form a right triangle by connecting UQ and US.

The length of UQ can be found using the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, we have:

UQ² = TU² - US²

UQ² = 68² - 28²

UQ² = 4624 - 784

UQ² = 3840

Taking the square root of both sides, we have:

UQ = √3840

UQ ≈ 61.98 ft

Therefore, the width RQ of the river is approximately 61.98 ft.

Note: It's important to keep in mind that this solution assumes the river is a straight line and that Karl's path is perpendicular to the river's edge. In reality, the river's edge may not be perfectly straight, and the path Karl walks may not be exactly perpendicular.

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Answer:

80 pgs per hour

Step-by-step explanation:

480 divided by 6 = 80

Step-by-step explanation:

4x +13 +79+79+ 11x-6 = 360

15x +165 = 360

15x = 195

x =13

QRS = 11(13)-6 = 137