A Mater Exam
Q2 SA 1
4 Points
What is the slope of a line that is perpendicular to the line f(x) = 2x + 6? Justify your answer
by typing out your calculations or explaining your reasoning.
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The equation modeling the displacement 'd' as a function of time  is d (t) = 7 sin ( 3π t)

Simple harmonic motion can be defined as a periodic motion of a point in a straight line, such that its acceleration is towards a fixed point and is proportional to its distance from that point to the line.

It is derived from the projection to the axis of a circle of a point in constant speed on the circumference

Displacement is represented thus;

d ( t ) = A sin⁡ ( 2 π f t )

T = 1/f

Where,

Note that there is no phase shift

d (t) = 7 sin ( 2π × 1/ 6 t)

d (t) = 7 sin ( 2π/6 t)

d (t) = 7 sin ( 3π t)

Thus, the equation modeling the displacement 'd' as a function of time  is d (t) = 7 sin ( 3π t)

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Answer:

B.) 19

Step-by-step explanation:

According to F(5), the question wants you to plug x = 5 into the equation. Then, you need to simplify to find the output.

F(x) = x² - 2x + 4                             <----- Original equation

F(5) = (5)² - 2(5) + 4                        <----- Plug 5 into "x"

F(5) = 25 - 10 + 4                            <----- Solve 5² and -2 x 5

F(5) = 19                                         <----- Combine like terms

Answer:

[tex]y=\frac{2}{3}x+\frac{4}{3}[/tex]

Step-by-step explanation:

Let's write the equation of the line in the slope-intercept form. That is, y= mx +c, where m is the slope and c is the y-intercept.

Identify 2 coordinates on the line to calculate the slope.

The 2 points are (1, 2) and (4, 4).

Slope

[tex]=\frac{y_1-y_2}{x_1-x_2}[/tex]

= [tex]\frac{4-2}{4-1}[/tex]

= [tex]\frac{2}{3}[/tex]

Substitute the value of the slope into m:

[tex]y=\frac{2}{3}x+c[/tex]

Substitute any point into the equation to find c:

When x= 1, y= 2,

[tex]2= \frac{2}{3}(1)+c[/tex]

Solve for c:

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

c= [tex]\frac{4}{3}[/tex]

Thus, the equation that represents the line is [tex]y=\frac{2}{3}x+\frac{4}{3}[/tex].

Additional:

Should you wish to learn more about slope-intercept form, do check out the following!

Answer: 6 %

Step-by-step explanation: 6 % of 12.5 = 0.75. 12.5 plus 0.75 = 13.25

So the correct statement is:

" The GCF of the numbers in each term in the expression is 2"

Here we have the expression:

12d - 26c

To rewrite ti as a product, we need to find the greatest common factor between 12 and 26.

The decomposition of these two numbers is:

12 = 2*2*3

26 = 2*13

The greatest common factor between the two numbers is 2, then we can rewrite:

12d - 26c = 2*(6d - 13c)

So the correct statement is:

" The GCF of the numbers in each term in the expression is 2"

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The graphed function is: y = (x + 2)(x − 1)(x − 3).

Option (a) is correct.

From the graph given in the question, it can be seen that the graph has 3 critical points, namely, x= -2, x = 1 and x = 3.

From all the five options given, the first option, that is, y = (x + 2)(x − 1)(x − 3), has the critical points x= -2, x = 1 and x = 3.

The critical points for a function are obtained by substituting the function to be equal to zero.

So, (x + 2)(x − 1)(x − 3) = 0

That is, x= -2, x = 1 and x = 3.

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The simplest form of the expression given in the task content is; 5.5x +7.42.

The expression given in the task content is;

5.5(x+6 1/2)-(x+9 1/3) - (19-x)

Hence, the expression can be written in its simplest form as follows;

5.5x + 35.75 -x -9.33 -19 +x

= 5.5x +7.42.

Remarks: The complete task requires that the expression be written in its simplest form.

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The quadratic equation has the following results: (p, q) = (8, 15), minimum point: (h, k) = (1, 4), range of values: - 4 < x < - 3

In this question we have a quadratic equation of the form y = x² + p · x + q , whose missing coefficients can be found by solving on the following system of linear equations:

- 5 · p + q = - 25

- 3 · p + q = - 9

(p, q) = (8, 15)

The vertex represents the minimum point, which is found by changing the form of the equation from standard form into vertex form:

y = x² + 8 · x + 15

y + 1 = x² + 8 · x + 16

y + 1 = (x + 4)²

(h, k) = (1, 4)

And lastly we must solve for x in the following inequality:

x² + 8 · x + 15 < x + 3

x² + 7 · x + 12 < 0

(x + 3) · (x + 4) < 0

- 4 < x < - 3

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Considering the definition of permutation, in 5040 ways can the letters in the word ''PAYMENT'' be arranged if the letters are taken 6 at a time.

Permutation is placing elements in different positions. So, permutations of m elements in n positions are called the different ways in which the m elements can be arranged occupying only the n positions.

That is, permutations refer to the action of arranging all the members of a set in some sort of order or sequence.

In other words, permutations (or Permutations without repetition) are ways of grouping elements of a set in which:

To obtain the total of ways in which m elements can be placed in n positions, the following expression is used:

[tex]mPn=\frac{m!}{(m-n)!}[/tex]

where "!" indicates the factorial of a positive integer, which is defined as the product of all natural numbers before or equal to it.

In this case, you have:

Then, you know that:

Replacing in the definition of permutation:

[tex]7P6=\frac{7!}{(7-6)!}[/tex]

Solving:

[tex]7P6=\frac{7!}{1!}[/tex]

7P6= 5040

Finally, in 5040 ways can the letters in the word ''PAYMENT'' be arranged if the letters are taken 6 at a time.

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Answer:

IM  and  YM

Step-by-step explanation:

not sure about the symbol part, but it's a ray !!

Answer: IM and YM

Step-by-step explanation:

It can be broken down into to different rays

The simplified expression for h(x) = f(x)/g(x) is [tex]h(x) = \frac{1}{3}\cdot \frac{x-4}{x-\frac{2}{3} }[/tex] and the domain of the function is all real numbers except x = 2/3.

In this problem we have a rational function, the domain of rational functions is the set of all real numbers except the values such that the denominator becomes zero. First, we need to simplify the division of two rational functions:

[tex]h(x) = \frac{\frac{3\cdot x^{2} + 17\cdot x + 20}{3\cdot x^{2} + 10\cdot x - 8} }{\frac{3 \cdot x^{2} + 8\cdot x + 5}{x^{2}-3\cdot x - 4} }[/tex]

[tex]h(x) = \frac{(3\cdot x^{2}+17\cdot x + 20)\cdot (x^{2}-3\cdot x - 4)}{(3\cdot x^{2}+10\cdot x - 8)\cdot (3\cdot x^{2}+8\cdot x + 5)}[/tex]

[tex]h(x) = \frac{1}{3}\cdot \frac{\left(x^{2}+\frac{17}{3}\cdot x + \frac{20}{3} \right)\cdot (x^{2}-3\cdot x - 4)}{\left(x^{2}+\frac{10}{3}\cdot x -\frac{8}{3}\right)\cdot \left(x^{2}+\frac{8}{3}\cdot x +\frac{5}{3} \right)}[/tex]

[tex]h(x) = \frac{1}{3}\cdot \frac{\left(x + \frac{5}{3} \right)\cdot (x+4)\cdot (x - 4)\cdot (x+ 1)}{\left(x-\frac{2}{3} \right)\cdot (x + 4)\cdot (x + 1)\cdot \left(x + \frac{5}{3} \right)}[/tex]

[tex]h(x) = \frac{1}{3}\cdot \frac{x-4}{x-\frac{2}{3} }[/tex]

The simplified expression for h(x) = f(x)/g(x) is [tex]h(x) = \frac{1}{3}\cdot \frac{x-4}{x-\frac{2}{3} }[/tex] and the domain of the function is all real numbers except x = 2/3.

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The given statement about the Florida VPK assessment administered at two assessments periods across the school year is; B: False

Progress monitoring or CBM is a term used in the education field to describe the process whereby the progress of students in areas like mathematics, reading, and writing are monitored on a daily and weekly basis.

Now, in Florida in the United States, This progress monitoring is called Florida Voluntary Prekindergarten (VPK) Assessment. There is usually a different version of each assessment measure that will be administered at three different times during the school-year VPK Program.

Thus, the given statement is false.

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Answer:

Step-by-step explanation:

false

The distance are

a. 42.42

b. 15. 52

80 = 65 + <ABC

<ABC = 80 - 65

= 15

Through the use of sine rule we would have

By using sine rule,

Sine 15/a = sine 135/b =

sin 30/30.

Next we have to solve b by cross multiplying

b = (30× sin135) / sin 30

= 21.21/0.5

b = 42.42 km

Also, the value of a will be:

= (42.42 × sin 15) / sin 135

= 10.98/0.7071

= 15.52

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Answer:

- Please see the attached picture for full solution!:)

------------ HappY LearninG <3 ----------

-3x is a term in the expression -3x - 7(x+4)

The expression is given as:

-3x - 7(x+4)

Considering the following expression

Ax + B(x  - b)

The terms in the expressions are Ax and B(x  - b)

This means that -3x is a term in the expression -3x - 7(x+4)

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See below for the response to each question

The study is experimental.

This is so because, the administer surveyed random college students

This is the total number of students in the college

Hence, the population of interest is the students in the college

This is the value that gives the required information.

Hence, the parameter of interest is the proportion of college students that work part-time

This is the students that were randomly surveyed

Hence, the sample in the study is the  2,512  students that were randomly surveyed

The statistic is the sample mean

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Answer:

p(x)=x3-3x2+4x+50 and g(x)=x-3

The next two terms of the sequence based on the information given is 37 and 50.

It should be noted that from the information given, the numbers illustrated are 5, 10, 17, and 26.

In this case, there is an addition of 2 to the previous difference.

Therefore, 26 - 17 = 9.

The next number will be:

= 26 + 9 + 2 =37

The following number will be:

= 37 + 11 + 2

= 50

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based on the given area for the six habitats, Dullinger and his colleagues can find the p-value to be 0.0018.

a chi-squared test is the best test for to find the p-value and when the data given is put through a chi-square model, the observed values are:

= 7, 9, 2, 11, 2, 0

the expected values should be:

= 1/6, 1/6, 1/6, 1/6, 1/6, 1/6

the p-value will be 0.001819

df = 5

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Answer:

-129

Step-by-step explanation:

good luck

By definition of the zeros of ta quadratic function,  for 5.5 seconds the ball is in the air before it hits the ground.

The points where a polynomial function crosses the axis of the independent term (x) represent the so-called zeros of the function.

That is, the zeros represent the roots of the polynomial equation that is obtained by making f(x)=0.

In summary, the roots or zeros of the quadratic function are those values ​​of x for which the expression is equal to 0. Graphically, the roots correspond to the abscissa of the points where the parabola intersects the x-axis.

In this case, the height "h" of a ball thrown straight up with a velocity of 88 ft/s is given by h = -16t² + 88t, where "t" is the time it is in the air.

When the ball hits he ground, he height h has a value of zero. This is h=0. Replacing in the previous expression for the height you get:

0= -16t² + 88t

It can be solved by extracting the term "t" as a common factor:

0= t×(-16t + 88)

The Zero Product Principle says that if the product of two numbers is 0, then at least one of the factors is 0. Then:

t= 0

or

0= -16t + 88

Solving: -88= -16t

(-88)÷ (-16)=t

5.5= t

Finally, this means that for 5.5 seconds the ball is in the air before it hits the ground.

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Step-by-step explanation:

. Find the factors of 330.

(a)2 x 4 x 5 x 11

(b)2 x 3 x 7 x 13

(c)2 x 3 x 5 x 13

(d)2 x 3 x 5 x 11

Show Answer

2. Find the factors of 1122.

(a)3 x 9 x 17 x 2

(b)3 x 11 x 17 x 2

(c)9 x 9 x 17 x 2

(d)3 x 11 x 17 x 3

Show Answer

3. 252 can be expressed as a product of primes as

(a)2 x 2 x 3 x 3 x 7

(b)2 x 2 x 2 x 3 x 7

(c)3 x 3 x 3 x 3 x 7

(d)2 x 3 x 3 x 3 x 7

Show Answer

4. Which of the following has most number of divisors?

(a)99

(b)101

(c)176

(d)182

Show Answer

5. A number n is said to be perfect if the sum of all its divisors (excluding n itself) is equal to n. An example of perfect number is

(a)6

(b)9

(c)15

(d)21

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6. 1095/1168 when expressed in simplest form is

(a)13 / 16

(b)15 / 16

(c)17 / 26

(d)25 / 26

Show Answer

7. Reduce 128352 / 238368 to its lowest terms

(a)3/4

(b)5/13

(c)7/13

(d)9/13

Show Answer

8. The simplest reduction to the lowest terms of 116,690,151 / 427,863,887 is

(a)3/11

(b)7/11

(c)11/3

(d)None of these

Show Answer

9. The highest common factor of 0 and 6 is

(a)0

(b)3

(c)6

(d)Undefined

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10. The H.C.F. of 2² x 3³ x 5⁵, 2³ x 3² x 5² x 7 and 2⁴ x 3⁴ x 5 x 7² x 11 is

(a)2² x 3² x 5

(b)2² x 3² x 5 x 7 x 11

(c)2⁴ x 3⁴ x 5⁵

(d)2⁴ x 3⁴ x 5⁵ x 7 x 11

Show Answer

11. The H.C.F. of 2⁴ x 3² x 5³ x 7, 2³ x 3³ x 5² x 7² and 3 x 5 x 7 x 11 is

(a)105

(b)1155

(c)2310

(d)27720

Show Answer

12. H.C.F. of 4 x 27 x 3125, 8 x 9 x 25 x 7 & 16 x 81 x 5 x 11 x 49 is

(a)180

(b)360

(c)540

(d)1260

Show Answer

13. Find the highest common factor of 36 and 84.

(a)4

(b)6

(c)12

(d)18

Show Answer

14. Even numbers are formed by taking at least two at a time from the numbers 0, 4, 8, 9. Their H.C.F. is

(a)2

(b)4

(c)10

(d)None of these

Show Answer

Answer: 175 ft squared

Step-by-step explanation: A= a + b / 2h= 20 + 152 · 10 = 175

Answer:

2

Step-by-step explanation:

You have the correct answer selected: 2.

The reason for this is that when there are exponents inside and outside of the parenthesis like this, they are multiplied.

2 times 2 is 4. That's why (8^2)^2 = 8^4

Answer:

p = 2

Step-by-step explanation:

[tex](8^{2}) ^{p}[/tex] = [tex]8^{4}[/tex]

  [tex]8^{2p}[/tex] =    [tex]8^{4}[/tex]

   [tex]8^{p}[/tex] = [tex]8^{\frac{4}{2}[/tex]

    p = 2

The probability is illustrated below.

1) Raffles game is a gambling competition in which people get numbered tickets and each number has an equal chance of winning.

2) When two dice are rolled then there will be totally 36 outcomes. Of those the outcomes with sum 8 are (2,6),(3,5),(4,4),(5,3),(6,2).

These are 5 in number.

So,P( sum =8)= 5/36.

3)This is a true statement.

4) Here win, lose, or tie is just the outcomes where their probabilities are different from each other and those values depend upon different situations.

5) Tossing a coin is a random experiment which means that the result of the experiment (ie head or tail) cannot be predicted.

6) If 60% said yes to " study during the week" then 40% will say yes to "either won't study or study at weekend".

7) When two coins are tossed, the outcomes are as follows

H,H

H,T

T,H

T,T.

So, P( head, tail ) =2/4 =1/2

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The reasons for each incorrect statement are as follows;

The term probability put simply is the ratio of the desired outcome to the possible outcomes. It therefore follows that probability as the name implies is used to predict the chance of an occurrence.

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Answer:

203681

203,681

Two hundred and three thousand, six hundred eighty-one

Step-by-step explanation:

The number 203681 in words can be written as two hundred and three thousands, six hundred and eighty-one.

In the question, we are asked to write the number 203681 in words.

In the given number, we have:

Keeping the thousands as different section, we have 203 in thousands section, and 681 in the remaining.

203 can be named as two hundred and three.

681 can be named as six hundred and eighty-one.

Since, 203 is in the thousands section, we add thousand in its name.

Thus, the name we get is two hundred and three thousands, six hundred and eighty-one.

Thus, the number 203681 in words can be written as two hundred and three thousands, six hundred and eighty-one.

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Answer:

x=1

Step-by-step explanation:

[tex] \sqrt{( - 3 - x) ^{2} + {( - 2 - 3)}^{2} } = \\ \sqrt{ {(4 - x)}^{2} + {(5 - 3)}^{2} } \\ \\ 9 + 6x + {x}^{2} + 25 = \\ 16 - 8x + {x}^{2} + 4 = = = > \\ 34 + 6x = 20 - 8x = > \\ 14 = 14x = = = > x = 1[/tex]

Done

The value of x that makes up the coordinate of B is -1

To find the value of x, we need to determine the coordinates of point B.

Since A to (B) = B to (C), the distance from point A to point B is equal to the distance from point B to point C. The distance between two points in a coordinate plane can be calculated using the distance formula:

Distance = √((x₂ - x₁)² + (y₂ - y₁)²)

Let's calculate the distances:

Distance A to (B):

x₁ = -3 (x-coordinate of point A)

y₁ = -2 (y-coordinate of point A)

x₂ = x (x-coordinate of point B)

y₂ = 3 (y-coordinate of point B)

Distance A to (B) = √((x - (-3))² + (3 - (-2))²)

Distance A to (B) =√((x + 3)² + 5²)

Distance A to (B) = √(x² + 6x + 9 + 25)

Distance A to (B) = √(x² + 6x + 34)

Distance B to (C):

x₁ = x (x-coordinate of point B)

y₁ = 3 (y-coordinate of point B)

x₂ = 4 (x-coordinate of point C)

y₂ = 5 (y-coordinate of point C)

Distance B to (C) = √((4 - x)² + (5 - 3)²)

Distance B to (C) = √((4 - x)² + 2²)

Distance B to (C) = √((4 - x)² + 4)

Distance B to (C) = √(x² - 8x + 20)

Since A to (B) = B to (C):

√(x² + 6x + 34) = √(x² - 8x + 20)

Now, we can square both sides to get rid of the square root:

x² + 6x + 34 = x² - 8x + 20

Next, move all the x terms to one side of the equation:

x² - x² + 6x + 8x = 20 - 34

Combine like terms:

14x = -14

Finally, solve for x:

x = -14 / 14

x = -1

So the value of x is -1. Point B is located at (-1, 3).

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The domain f the function is (-∞, 1/3) U (1/3, ∞)

The composite functions are also known as function of a function

Given the following functions

f(x) = √2-6x

g(x) = -1/x

In order to determine the composite function g(f(x))

g(f(x)) = g(√2-6x)

Replace x with √2-6x in g(x)

g(f(x))  = -1/√2-6x

The expression does not exist when √2-6x = 0

2-6x = 0

x = 1/3

The values shows that the domain of the function exists on all real numbers except 1/3.

Hence the domain f the function is (-∞, 1/3) U (1/3, ∞)

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Answer: 2.01

Step-by-step explanation:

[tex]5\ln x=3.5\\\\x=\frac{3.5}{5}\\\\x=e^{3.5/5}\\\\x \approx 2.01[/tex]