Question 2 Multiple Choice Worth 2 points)
Find an equation in standard form for the hyperbola with vertices at (0, +9) and foci at (0, +11).
Oy?
x2
= 1
40 81
y² x²
= 1
81 121
y?
x2
= 1
81
40
O
y?x
121 81
= 1

Answer:

STo solve for m in the equation -319.45 = m, we can isolate the variable m by adding 319.45 to both sides of the equation:

-319.45 + 319.45 = m + 319.45

This simplifies to:

0 = m + 319.45

Finally, we can subtract 319.45 from both sides to solve for m:

0 - 319.45 = m + 319.45 - 319.45

-319.45 = m

Therefore, the value of m is -319.45.tep-by-step explanation:

Answer:  226 T-shirts and 21 shorts

Step-by-step explanation:

Let the number of T-shirts be x and the number of shorts be y

Hence,

2(x)+4(y)=536

Divide both parts of the equation by 2:

x+2y=268

x+y+y=268

(x+y)+y=268

(x+y)+y-(x+y)=268-(x+y)    

y=268-(x+y)    (1)

x+y=247      (2)

Substitute equation (2) into equation (1):

y=268-247

y=21

Hence,

x+21=247

x+21-21=247-21

x=226

\(\text{Find the values of x:}\\\\x(x+3)(x+3)=0\\\\\text{We know for the x outside of the parenthesis, it has to equal 0}\\\\\text{For the x inside the parenthesis, we would need to equal it to 0 and }\\\text{solve for x}\\\\x+3=0\\\\x=-3\\\\\text{There are two of them, so we would have two of the same answer}\\\\\boxed{\text{x= 0 or x = -3 or x = -3}}\)

Answer:

\( \frac{40}{32} = 1.25 \: meters \: per \: minute\)

and

\( \frac{30}{25} = 1.2 \: meters \: per \: second\)

40 meters in 32 minutes is greater

Answer:

To solve the quadratic equation 9×^2-15×-6=0, we can use the quadratic formula, which is given by:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a, b, and c are the coefficients of the quadratic equation ax^2 + bx + c = 0.

In this case, a = 9, b = -15, and c = -6, so we can substitute these values into the quadratic formula:

x = (-(-15) ± sqrt((-15)^2 - 4(9)(-6))) / 2(9)

Simplifying this expression gives:

x = (15 ± sqrt(225 + 216)) / 18

x = (15 ± sqrt(441)) / 18

x = (15 ± 21) / 18

So the two solutions to the quadratic equation are:

x = (15 + 21) / 18 = 2

x = (15 - 21) / 18 = -1/3

Therefore, the solutions to the quadratic equation 9×^2-15×-6=0 are x = 2 and x = -1/3.

The first three non zero terms in the Taylor polynomial approximation to the given DE is y(t) = t + t²/2 -(3/2)t³ .

In the question ,

it is given that ,

the differential equation is

y'' + 9y + 5y³ = Cos(10t)   ...equation(1)

y(0) = 0, y'(0) = 1

for y = 0 , the differential equation is

y''(0) + 9y(0) + 5{y(0)}³ = Cos90)

y''(0) + 9 + 5 = 1 ;

y''(0) = 1.

differentiating equation(1) with respect to "t" , we have

y''' + 9y' + 15y²y' = -10Sin(10t)

y'''(0) + 9y'(0) + 15{y(0)}².y'(0) = -10Sin(0)

y'''(0) + 9 + 0 = 0

y'''(0) = -9

The Taylor series is given by

y(t) = y(0) + y'(0)t + 1/2.y''(0)t² + 1/3!.y'''(0)t³ + ....

Now substituting the values of y(0) , y'(0) , y''(0) , y'''(0) , we have

y(t) = 0 + 1.t + 1/2.t² + 1/6.(-9)t³ + ....

= t + t²/2 - 3/2.t³ + ...

Therefore , the first three terms are t , t²/2 , -3/2.t³   .

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Answer:

98.91

Step-by-step explanation:

rounded to 2 decimal places

Part A :

Yes, the statement is true that  P( A and B ) = 0 .

Given,

Event A and Event B are mutually exclusive.

Thus P ( A and B ) = 0

Part B:

A and B are mutually exclusive events if they do not occur at the same time.

This means that A and B do not share any common outcomes and

P(A and B) = 0.

Part C:

Let,

The sample space W = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.

Let A = {1, 2, 3, 4, 5}, Y = {4, 5, 6, 7, 8}, and B = {7, 9}.

A and B do not have any numbers in common so P(A and B) = 0.

Hence, A and B are mutually exclusive.

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Answer:

Please Mark as Brainliest!!!!!!

Step-by-step explanation

In an auditorium, there are 21 seats in the first row and 29 seats in the second row. The number of seats in a row continues to increase by 8 with each additional row. How would you find the 100th row?

We can take this as an arithmetic sequence, as the seats in next row is calculated by adding 8 to previous row

So here common difference will be 8

the first term is 21

the arithmetic sequence is given by:

Putting the values of a1 and d

for 100th row,

Putting n=100

3. The sequence 6, 18, 54, 162, … shows the number of pushups Kendall did each week, starting with her first week of exercising.

Give the rule you would use to find the 20th week.

Given sequence is:

6, 18, 54, 162, …

we can see that the common difference is not same so we will find the common ratio

The given sequence is a geometric sequence as are the same for consecutive terms

The geometric sequence is given by:

Hence,

2. Seats in 100th Row = 813

3. Rule is:

Keywords: Sequence, ratio

Answer:

see explanation

Step-by-step explanation:

The sequence is

22, 28, 34, ....

Since there is a common difference of 6 the sequence is arithmetic with n th term

\(a_{n}\) = a₁ + (n - 1)d

a₁ is the first term and d the common difference

Here a₁ = 22 and d = 6, then

\(a_{n}\) = 22 + 6(n - 1) = 22 + 6n - 6 = 6n + 16

Equate to 100 and solve for n

6n + 16 = 100 ( subtract 16 from both sides )

6n = 84 ( divide both sides by 6 )

n = 14

Thus the 14 th row has 100 seats

The multiplication of the fraction 2/3 by 3 3/5 is 12/5 or 2 2/5

Given:

2/3 x 3 3/5

change 3 3/5

= {3(5) + 3} / 5

= (15+3) / 5

= 18/5

So,

2/3 x 3 3/5

= 2/3 × 18/5

= (2 × 18) / (3 × 5)

= 36 / 15

= 12/5

= 2 2/5

Therefore, 2/3 x 3 3/5 as a fraction equals 12/5 or 2 2/5

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A person would need to buy 60 square yards of carpet for a rectangular room with dimensions of 10 yards by 18 feet.

How to determine the amount of carpet needed for a rectangular room?

To determine the amount of carpet needed for a rectangular room, you need to convert the measurements to the same unit of measurement. Since the carpet is sold in square yards, we need to convert the dimensions of the room to yards.

The length of the room is given in yards, so we don't need to make any conversions for that dimension. However, the width of the room is given in feet, so we need to convert it to yards by dividing by 3 (since there are 3 feet in a yard),

18 feet ÷ 3 feet/yard = 6 yards

So the dimensions of the room in yards are 10 yards by 6 yards.

To find the total area of the room, we need to multiply the length and width,

10 yards × 6 yards = 60 square yards

Therefore, a person would need to buy 60 square yards of carpet for a rectangular room with dimensions of 10 yards by 18 feet.

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The data set (B) could be represented by the shown box plot.

A box and whisker plot (also known as a box plot) expresses a five-number summary of a set of data: lowest, lower quartile, median, upper quartile, and maximum.

The box plot is given in the question as shown, as per the data :

Minimum = 41

First quartile Q1 = 43

Median = 44

Third quartile Q3 = 48

Maximum = 50

According to set (B), we have:

41, 42, 43, 43, 43, 45, 47, 48, 50, 50

Here, Minimum = 41

First quartile Q1 = 43

Median = (43+45/2) = 44

Third quartile Q3 = 48

Maximum = 50

Therefore, the data set (B) could be represented by the shown box plot.

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Introducing numeracy to young children can be done through various types of equipment and resources that engage their senses and make learning math concepts more interactive and enjoyable.

Here are some different types of equipment commonly used to introduce numeracy to young children:

Thus, by incorporating a variety of equipment and resources, educators and parents can create a rich learning environment that supports children's numeracy development and fosters a positive attitude towards math.

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Answer:

x=19 degrees

Step-by-step explanation:

(3x+3)+(2x-8)=90 degrees

5x-5=90 degrees

   +5 +5

5x=95 degrees

/5   /5

x=19 degrees

Answer:

x = 37

2x-8+3x+3=180

5x-5=180

5x=185

x=37

Answer:

4:3

Step-by-step explanation:

They list first first but then ask for turtles to fish.

\(\frac{24}{18}\)  Divide the top and the bottom by 6 to get \(\frac{4}{3}\) or 4:3

To find the measure of the geometry-big circle, we need to sum up the measures of all the arcs around the circle.

We are given the following measures:

\(\sf\:m\angle AB = 56 \\\)

\(\sf\:m\angle BC = 59 \\\)

\(\sf\:m\angle CD = 63 \\\)

\(\sf\:m\angle DE = 63 \\\)

\(\sf\:m\angle EF = 31 \\\)

To find the measure of the geometry-big circle, we add up these measures:

\(\sf\:m\angle AB + m\angle BC + m\angle CD + m\angle DE + m\angle EF \\\)

Substituting the given values:

\(\sf\:56 + 59 + 63 + 63 + 31 \\\)

Simplifying the expression:

\(\sf\:272 \\\)

Therefore, the measure of the geometry-big circle is 272.

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\textcolor{red}{\underline{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer:

54

Step-by-step explanation:

54

The distance between points R and S is  \(\sqrt{ (185)\). The correct answer is D. She made no errors.

Heather's work to find the distance between two points, R(-3,-4) and S(5,7), is shown:

RS = √(-4) (-3))² + (7 − 5)²

= √(-1)² + (2)²= √1 + 4

= √5

The error is with the order of subtraction in the formula for the distance between two points.

Heather did not make any errors in calculating the distance between two points. Therefore, the correct answer to the question above is (OD) She made no errors.

The formula for the distance between two points, A (x1, y1) and B (x2, y2), in the coordinate plane is given as;

dAB = \(\sqrt{  ((x^2 - x1)^2 + (y2 - y1)^2)\)

Comparing the given question with the formula above, we have;

A = R (-3, -4) and B = S (5, 7)The distance, AB = RS.

Therefore, we have;

RS = \(\sqrt{ ((5 - (-3))^2 + (7 - (-4))^2)\)

On solving the above equation;RS = \(\sqrt{ ((5 + 3)^2 + (7 + 4)^2)\)RS

= \(\sqrt{ (8^2 + 11^2)RS\)

= \(\sqrt{ (64 + 121)RS\)

= \(\sqrt{ (185)\)

Therefore, the distance between points R and S is  \(\sqrt{ (185)\).

From the calculation, it is clear that Heather did not make any errors while calculating the distance between two points. The answer obtained by Heather is correct.

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Answer:

Slope = -1 .     Parallel lines have the same slope.  The slope is a coefficient of the x-term.

Step-by-step explanation:

y - x = 5

y = x + 5    slope = 1

The slope of the line parallel to the given line is 1.

Slope is a value that describes the steepness and direction of a line. In variable format, it is commonly represented by the letter m.

The slope of a line is also called its gradient or rate of change. The slope formula is the vertical change in y divided by the horizontal change in x, sometimes called rise over run.

Given that the equation of a line y - x = 5, we need to find the slope of the parallel to the same,

Converting the equation in slope-intercept form,

y - x = 5

y = x + 5

Comparing with standard form of the equation of the line y = mx + c, where m is the slope,

Hence, the slope of the given line is 1,

We know that the slopes of the parallel lines are equal.

So, the slope of the asked line is 1.

Hence, the slope of the line parallel to the given line is 1.

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Answer:

$14.20

Step-by-step explanation:

$42.60 ÷ 3

$14.20

The triangle is obtuse because 11^2 + 21^2 does not equal 29^2.

The Pythagorean Theorem states that the sum of the squares of the two shorter sides of a triangle must equal the square of the longest side in order for the triangle to be a right triangle.

We can use this theorem to determine the type of triangle by calculating the square of the longest side (29^2), and then comparing it to the sum of the squares of the other two sides (11^2 + 21^2). Since 11^2 + 21^2 does not equal 29^2, the triangle is obtuse.

The Pythagorean Theorem states that the sum of the squares of the two shorter sides of a triangle must equal the square of the longest side in order for the triangle to be a right triangle.

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Answer:

y = 2x-3

Step-by-step explanation:

y – 1 = 2(x – 2)

Distribute

y-1 =2x-4

Add 1 to each side

y-1+1 = 2x-4+1

y = 2x-3

Answer:

66/8

Explanation

8x8+2=66/8  

66/8 simplafied is 33/8

The equation for the graph sketched below is given as y = -3(3)^x

The standard form of an exponential equation is given as y = ab^x

Using the coordinate points on the graph (-1, 1) and (0, -3)

The equivalent equations are;

1 = ab^-1

-3 = ab^0

From equation2;

a= -3

Substitute into equation 1;

1 = ab^-1

1 = 3b^-1

1 =3/b

b =3

Determine the equation

y = ab^x

y = -3(3)^x

This gives the required exponential equation

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Answer:

D

Step-by-step explanation:

Z doesn't have to be positive... it can be negative as well. It can also equal 0 and 1, so that leaves D... there are no restrictions.

Answer:

B. Combination; number of ways = 15

Step-by-step explanation:

Since order doesn't matter, this is a combination:

6 choose 2 = 6 nCr 2 = 6!/(6-2)!2! = 720/(24)(2) = 720/48 = 15

Therefore, there are 15 possible ways to choose 2 co-captains out of 6.

Combination; the number of ways = 15.

Option B is the correct answer.

It is an arrangement of a set of numbers from a total set where the order of the set is not relevant.

We have,

The problem involves selecting two seniors out of a group of six seniors, which is a combination problem.

The number of ways to choose two seniors out of six seniors is given by the formula:

C(6,2) = 6! / (2! * 4!) = 15

Therefore,

Combination; the number of ways = 15.

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