2.
A line goes through the points (0, 10) and (-1, 1).
2a
What is the slope of the line?

Answer:Can somebody also help me with this. i'm confused please hurry!

Step-by-step explanation:

Answer:

Option 3 is the correct answer.

Answer: The number of tickets sold is the independent variable because it affects the amount of money earned.

Step-by-step explanation: I just took test got 100%

The number of tickets sold is the independent variable because it affects the amount of money earned.

The required answer to the given term is 2.

What is simplification?

Finding the answer from a complex calculation is what is meant by simplification. To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue.

By eliminating all common elements from the numerator and denominator and putting the fraction in its simplest/lowest form, fractions can be made simpler.

By combining and grouping like terms, mathematical expressions can be made simpler. This makes the phrase simple to comprehend and solve.

Given, 2/5 x 5

=  \(\frac{2}{5} *5\)

= 2

Hence, the required answer to the given term is 2.

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(i) Probability is a notion in Mathematics which describes the likelihood of an event or a set of events occurring. It is a measure of uncertainty when estimating the outcome of an experiment or an observation.

(ii) The axioms of probability are:

the non-negativity (that the probability of an event is greater than or equal to zero), and

the additivity (that the probability of the union of two or more mutually exclusive events is equal to the sum of their individual probabilities).

(iii) When two fair dice are thrown the probability of getting:

a) The sum of 9 = 1/9

b) Two odd numbers = 1/4

c) two prime numbers = 1/9

d)  two factors of 12 = 1/9

(iv) Statistics is a branch of mathematics that deals with data collection, analysis, interpretation, presentation, etc.

To find probability when two dice are thrown, we have:

(a) The sum of 9:

We will estimate the number of ways to get a sum of 9: (3,6), (4,5), (5,4), and (6,3) = 4 ways

A die has 6 possible outcomes, the total number of possible outcomes is 6x6=36 = 4/36 = 1/9.

(b) Two odd numbers:

We count the number of ways to get two odd numbers: (1,3), (1,5), (1,7), (3,1), (3,5), (3,7), (5,1), (5,3), and (5,7).

possible outcomes = 9,

So, the total possible outcomes = 6x6=36 = 9/36 = 1/4.

(c) Two prime numbers

We estimate the number of ways we can get two prime numbers: (2,3), (3,2), (5,2), and (2,5)

possible outcomes = 4,

So, the total possible outcomes = 6x6 =36 = 4/36, = 1/9.

(d) Two factors of 12:

We count the number of ways and divide by the total possible outcomes.

The factors of 12 are 1, 2, 3, 4, 6, and 12: (2,6), (3,4), and (4,3) = 3 ways

possible outcomes = 6

Therefore, the total number of possible outcomes = 6x6=36 = 3/36, = 1/12

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Answer:

1 out of 6

Step-by-step explanation:

Each roll of the die is an independent event. This means that the second roll does not rely on the first roll. The probability of rolling a six is one out of six. The probability of rolling a two is also one out of six. Since the two events are independent of each other, you would take the average of the two probabilities, which since they are both one out of six, the probability of rolling a six and then a two is one out of six.

The ladder will reach a Height of approximately 43.46 meters on the building.

To find out how high on the building the ladder will reach, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the ladder forms a right triangle with the ground and the building. The base of the ladder is 7 meters, the height of the building is what we need to find, and the length of the ladder is given as 44 meters.

Using the Pythagorean theorem, we can set up the equation:

(Height of the building)^2 + 7^2 = 44^2

Simplifying the equation, we have:

(Height of the building)^2 + 49 = 1936

Subtracting 49 from both sides, we get:

(Height of the building)^2 = 1887

To find the height of the building, we take the square root of both sides:

Height of the building = √1887

Calculating the square root of 1887, we find that the height of the building is approximately 43.46 meters.

Therefore, the ladder will reach a height of approximately 43.46 meters on the building.

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Answer:

\(Solution,\\Area(A)=441m^{2} \\Now,\\Length=\sqrt{Area} \\Length=\sqrt{441m^{2} } \\Length=21m\)

Step-by-step explanation:

Hope it will help you a lot.

The given box plot represented by the data sets in option A and B.

From the given box plot, we have

Minimum value = 3

Maximum value = 18

First quartile (Q1) = 7

Third quartile (Q3) = 13

Median = 10

Option A:

3, 4, 8, 9, 9, 12, 12, 13, 13, 16, 18

Median = 12

First quartile (Q1) = 8

Third quartile (Q3) = 13

Option B:

3, 4, 7, 9, 9, 10, 12, 13, 13, 16, 18

Median = 10

First quartile (Q1) = 7

Third quartile (Q3) = 13

Option C:

3, 4, 8, 9, 9, 10, 12, 13, 13, 16, 18

Median = 10

First quartile (Q1) = 8

Third quartile (Q3) = 13

Option D:

2, 4, 7, 9, 9, 10, 12, 13, 13, 16, 18

Median = 10

First quartile (Q1) = 7

Third quartile (Q3) = 13

Therefore, the correct options are B and D.

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9514 1404 393

Answer:

  336 cm^2

Step-by-step explanation:

The area of a trapezoid is given by the formula ...

  A = 1/2(b1 +b2)h

where b1 and b2 are the base lengths, and h is the height. Filling in the values shown gives ...

  A = (1/2)(28 +14)(16) = (1/2)(42)(16) = 336 . . . . cm^2

The second pair of coordinates on the line parallel to q that passes through (0,1) is (1,-4/5) and that of (3,5) is (1,7).

The general form of the equation of a line is y=mx+c

where

m=slope

c is a constant

The equation of the line is

m= \(\frac{y-y_{1} }{x-x_{1} }\)

M=\(\frac{5-4}{3+2}\)

m=1/5

From the slope formula

m = -1/5

X₎=0

y₎=1

substitute these in the formula for slope

\(\frac{-1}{5} =\frac{y-1}{x-0}\)

x=5y-5

x-5y=5

Now, with the above-derived equation, we need to find the other co-ordinate as these coordinates will satisfy this equation.

when x=1,

x-5y=5

1-5y=5

-5y=5-1

y=\(\frac{-4}{5}\)

The other coordinate is (1,-4/5)

11.   In the second line (3,5)

Using the slope formula

m=\(\frac{Y_{2}-Y_{1} }{X_{2}-X_{1} }\)

\(\frac{-1}{5} =\frac{y-5}{x-3}\)

x-3=-y+2

x+y=5+3

x+y=8

Also, with the above-derived equation, we need to find the other co-ordinate as these coordinates will satisfy this equation.

when x=1,

x+y=8

1+y=8

y=8-1

y=7

Therefore the second coordinate is (1,7)

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Answer:

1302

Step-by-step explanation:

Answer:

6 x 6 x 3 cm

Step-by-step explanation:

The base of the box needs to fit the base of the hemisphere.

The maximum width and length of the hemisphere is the diameter of the base of the hemisphere (which is circular)

Diameter of a circle = 2r

As the radius = 3 cm,  the diameter = 2 x 3 = 6 cm

Therefore, the width and length of the box should both be 6cm

The height of the box needs to accommodate the height of the hemisphere.  The height of the hemisphere is the radius, so the height of the box should be 3 cm.

Therefore, the dimensions of the box should be 6 x 6 x 3 cm

Answer: A: I know that X is 15.

B: -5

C: 10

D. -10

Step-by-step explanation: i honeslty don't know how man y solutions a and b has but ik what x is. And C and D is corrcet.

The table of integrals can be a useful tool for simplifying the integration process, but it's important to have a solid understanding of calculus concepts in order to use it effectively.

The table of integrals is a tool used in calculus to simplify the process of finding antiderivatives. It lists various functions and their corresponding antiderivatives, or integrals.

To use the table of integrals, you first need to identify the function you are trying to integrate. Then, find a similar function in the table and use the corresponding antiderivative to solve your integral.

It's important to note that not all functions have a corresponding antiderivative listed in the table, and in those cases, other integration techniques must be used.

Additionally, it's always a good idea to double check your work and make sure the answer makes sense in the context of the original problem.

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If we use the table of integrals, the solution would be In | tan(x+7) + sec(x+7)|+C. Option A

Using the table of integral, we say

∫ (1/cos(x +7)) dx ⇒ ∫sec (x+7) dx

u = x+7   ⇒ du = dx

= ∫sec (u) du

Expand the fraction by tan (u) + sec (u)

= ∫(sec(u) (tan(u) + sec (u))/ tan (u) + sec (u)

= ∫((sec(u) tan(u) + sec²(u))/ (tan (u) + sec (u))) du

Substitute v= tan(u) + sec (u) ⇒ dv = (sec(u) tan(u) + sec²(u))du

= ∫(i/v)dv

= In(v)

Undo substitution v = tan(u) + sec(u)

=In(tan(u) + sec(u))

= In(tan(x+7) + sec(x +7))

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Answer:

The cost of 1 scarf = 14.5

Step-by-step explanation:

29 / 2 = 14.5

\(let \: x \: be \: the \: length \\ let \: y \: be \: the \: width\)

\(perimeter = 2x + 2y \\ area = xy\)

\(2x + 2y = 80 \\ xy = 380 \\ \\ x + y = 40 \\ xy = 380 \\ \\ x = 40 - y \\ (40 - y)y = 380 \)

\(40y - y {}^{2} = 380 \\ y {}^{2} - 40y + 380 = 0 \\ y {}^{2} - 40y + 400 = 20 \\ (y - 20) {}^{2} = 20 \\ y - 20 =± \sqrt{20} \\ y_{1}=20-√20≈15.52786\\ y_{2}=20+√20≈24.4721\)

The solution of the given Question with help of BODMAS is\(-4\)

A mathematical expression is simplified by being replaced with a more straightforward equivalent.

I) Important Considerations for Handling Simplification Questions

II) Substitute "of" for "multiplication," and "/" for "division."

III) Always carry out operations in accordance with "BODMAS."

IV) Division and multiplication are equally important (start from the left)

V)  Both addition and subtraction are equally important.

\(16 - (6*2)/4(16-6) +5*2\)

Step 1: solve Brackets

\(16- (62)/4(16-6)+52\)

Step 2: solve Division

\(16- 3(10)+10\)

Step 3: solve Multiplication:

\(16-30+10\)

Step 4: solve Addition:

\(26-30\)

Solve :solve Subtraction

\(-4\)

Therefore the answer for the above simplification is\(-4\)

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Answer:

if you convert inches to cm...

Step-by-step explanation:

9inch=22.86cm

12inch=30.48cm

V=TTr²h

TT= 3.14

V= 3.14×22.86²×30.48

V= 50014.6cm³

if you don't convert inches to cm...

V=TTr²h

V=3.14 ×9×12

V=339.12cm³

To find the amount of wet food Luck mixed with the dry food, we can use the fact that he put 5/4 cups into each of the 4 bowls. Therefore, he used a total of 5/4 x 4 = 5 cups of wet food.

Thus, Luck mixed 3 cups of dry food and 5 cups of wet food to prepare the dog's meal.

The ordered pair solutions for the system of equations are:

(4, 5) and (-1, 0).

We have,

To find the ordered pair solutions for the system of equations, we need to solve the equations simultaneously.

The given equations are:

f(x) = x² - 2x - 3

f(x) = x + 1

Since both equations are equal to f(x), we can set them equal to each other:

x² - 2x - 3 = x + 1

Now, let's solve this quadratic equation:

x² - 2x - 3 - x - 1 = 0

x² - 3x - 4 = 0

To solve this quadratic equation, we can either factor it or use the quadratic formula.

Let's use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

For our equation,

a = 1, b = -3, and c = -4.

Substituting these values into the quadratic formula:

x = (-(-3) ± √((-3)² - 4(1)(-4))) / (2(1))

x = (3 ± √(9 + 16)) / 2

x = (3 ± √25) / 2

x = (3 ± 5) / 2

We have two possible solutions:

When x = (3 + 5) / 2 = 8 / 2 = 4

When x = (3 - 5) / 2 = -2 / 2 = -1

Therefore, the ordered pair solutions for the system of equations are:

(4, f(4)) and (-1, f(-1))

Now, let's substitute these values into either equation to find the corresponding y-values (f(x)):

For x = 4:

f(4) = 4 + 1 = 5

So, one solution is (4, 5).

For x = -1:

f(-1) = -1 + 1 = 0

So, another solution is (-1, 0).

Therefore,

The ordered pair solutions for the system of equations are:

(4, 5) and (-1, 0).

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Answer:

7.5

Step-by-step explanation:

it is feometeic progression

r=0.5

The volume of the solid generated about the x-axis by revolving region r is equal to V  = \(\int\limits^a_b \pi {[y]^{2} } \, dx\) .

As given in the question,

Volume of the solid which is generated by revolving a plane region 'r' about vertical line which does not pass through the given plane:

'r' be the radius of the circle.

Area of the cross section is the circle area = πr²

As it is given it is about the x-axis then radius 'r' is the function of x

f(x) = r

Let 'V' be the volume.

Volume of the solid generated by revolving the region 'r' about the x‐axis on the interval [ a, b] is given by :

V = \(\int\limits^a_b \pi {[f(x)]^{2} } \, dx\)

As f(x) = y

⇒V  = \(\int\limits^a_b \pi {[y]^{2} } \, dx\)

Therefore, the integral used to represent the volume of the given solid generated by revolving about the x-axis is equal to V  = \(\int\limits^a_b \pi {[y]^{2} } \, dx\)

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Answer:  \((r,\theta) = \left(\sqrt{6}, \frac{\pi}{4}\right)\)

In other words, \(r = \sqrt{6} \ \text{ and } \ \theta = \frac{\pi}{4}\) where theta is in radians.

=====================================================

Work Shown:

\((\text{x},\text{y}) = (\sqrt{3},\sqrt{3})\\\\r = \sqrt{\text{x}^2+\text{y}^2}\\\\r = \sqrt{(\sqrt{3})^2+(\sqrt{3})^2}\\\\r = \sqrt{3+3}\\\\r = \sqrt{6}\\\\\)

and,

\(\theta = \tan^{-1}\left(\frac{\text{y}}{\text{x}}\right)\\\\\theta = \tan^{-1}\left(\frac{\sqrt{3}}{\sqrt{3}}\right)\\\\\theta = \tan^{-1}\left(1\right)\\\\\theta = \frac{\pi}{4} \text{ radians}\\\\\)

Use a calculator or the unit circle to arrive at the last step. Keep in mind that (√3, √3) is in the first quadrant where \(0 < \theta < \frac{\pi}{2}\) since both x and y are positive.

The perimeter of triangle PQR is 17 ft

From the question, we are to determine the perimeter of triangle PQR

The

First, we will determine the value of y

Since, the two triangles are congruent

Then,

We can write that

3y - 2 = y + 4

3y - y = 4 + 2

2y = 6

y = 6/2

y = 3

Now,

The perimeter of triangle PQR = 4 ft + 6 ft + (3y - 2) ft

Substitute the value of y

Perimeter of ΔPQR = 4 ft + 6 ft + (3(3) - 2) ft

Perimeter of ΔPQR = 4 ft + 6 ft + (9 - 2) ft

Perimeter of ΔPQR = 4 ft + 6 ft + 7 ft

Perimeter of ΔPQR = 17 ft

Hence, the perimeter is 17 ft

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Answer:

log9

Step-by-step explanation:

Using the rules of logarithms

logx + logy = log(xy)

logx - logy = log(\(\frac{x}{y}\))

log\(x^{n}\) ⇔ nlogx

Given

2(log18- log3) + \(\frac{1}{2}\)log\(\frac{1}{16}\)

= 2(log(\(\frac{18}{3}\) ) ) + log\((\frac{1}{16}) ^{\frac{1}{2} }\)

= 2log6 + log\(\frac{1}{4}\)

= log6² + log\(\frac{1}{4}\)

= log36 + log\(\frac{1}{4}\)

= log( 36 × \(\frac{1}{4}\) )

= log9

Answer:

x = 5 + 5y/4

Step-by-step explanation:

I think its like this: 4x - 5y = 20

Add 5y to both sides: 4x = 20 + 5y

Divide both sides by 4: x = 20/4 + 5y/4

Simplify: x = 5 + 5y/4

I'm pretty sure it is like this

Hope this helps!

a) The algebraic fraction \(\frac{{x + 2}}{{(x - 1)^2}}\) is proper. b) The algebraic fraction \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}}\) can be expressed as \(-\frac{{31}}{{x - 4}} - \frac{{25}}{{(x - 4)^2}}\).

Let's solve each part step by step and determine whether the fraction is proper or improper, and then express it accordingly.

a) \(\frac{{x + 2}}{{(x - 1)^2}}\):

Step 1: Determine the degree of the numerator and the denominator:

  - Degree of the numerator = 1 (linear term)

  - Degree of the denominator = 2 (quadratic term)

Since the degree of the numerator is less than the degree of the denominator, the fraction is proper.

Step 2: Express the proper fraction in partial fractions:

\(\frac{{x + 2}}{{(x - 1)^2}} = \frac{A}{{x - 1}} + \frac{B}{{(x - 1)^2}}\).

Step 3: Find the values of A and B:

Multiply both sides of the equation by \(((x - 1)^2)\) to eliminate the denominators:

  (x + 2) = A(x - 1) + B.

Expand the equation and collect like terms:

  x + 2 = Ax - A + B.

Equate the coefficients of like terms:

  Coefficient of x: 1 = A.

  Constant term: 2 = -A + B.

Solve the system of equations to find the values of A and B:

From the coefficient of x, A = 1.

Substituting A = 1 into the constant term equation: 2 = -1 + B, we find B = 3.

Therefore, the partial fraction decomposition is:

  \(\frac{{x + 2}}{{(x - 1)^2}} = \frac{1}{{x - 1}} + \frac{3}{{(x - 1)^2}}\).

b) \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}}\):

Step 1: Determine the degree of the numerator and the denominator:

  - Degree of the numerator = 2 (quadratic term)

  - Degree of the denominator = 2 (quadratic term)

Since the degree of the numerator is equal to the degree of the denominator, the fraction is proper.

Step 2: Express the proper fraction in partial fractions:

  \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}} = \frac{A}{{x - 4}} + \frac{B}{{(x - 4)^2}}\).

Step 3: Find the values of A and B:

Multiply both sides of the equation by \(((x - 4)^2)\) to eliminate the denominators:

  (4x^2 - 31x + 59) = A(x - 4) + B.

Expand the equation and collect like terms:

  4x^2 - 31x + 59 = Ax - 4A + B.

Equate the coefficients of like terms:

Coefficient of \(x^2\): 4 = 0 (No \(x^2\) term on the right side).

Coefficient of x: -31 = A.

Constant term: 59 = -4A + B.

Solve the system of equations to find the values of A and B:

From the coefficient of x, A = -31.

Substituting A = -31 into the constant term equation: 59 = 4(31) + B, we find B = -25.

Therefore, the partial fraction decomposition is:

  \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}} = -\frac{{31}}{{x - 4}} - \frac{{25}}{{(x - 4)^2}}\).

The above steps provide the solution for each part, including determining if the fraction is proper or improper and expressing it in partial fractions.

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Answer:

No, the Normal/large sample condition is not met. A confidence interval assumes that the underlying population follows a normal distribution and that the sample size should be at least 30. Since the sample size in this case is only 10, the Normal/Large Sample condition is not met and the conditions for constructing a confidence interval are not met.

Answer:

x = -8, 8

Step-by-step explanation:

Set y = 0 to find the x intercepts

0 = x^2 -64

Add 64 to each side

64 = x^2

Take the square root of each side

±sqrt(64) = sqrt(x^2)

±8  =x