A.P.E.X Algebra 1 Sem 2

The pair of limits that would verify the existence of a vertical asymptote at x = –1 is:

[tex]\lim_{x \rightarrow -1^-} = \infty, \lim_{x \rightarrow -1^+} = \infty[/tex]

The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.

For a vertical asymptote at x = -1, the denominator is zero at -1, hence both lateral limits at x = -1 go to infinity, that is:

[tex]\lim_{x \rightarrow -1^-} = \infty, \lim_{x \rightarrow -1^+} = \infty[/tex]

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Answer:

[tex]\cfrac{-4}{3} [/tex] and [tex]\cfrac{1}{2} [/tex].

Step-by-step explanation:

Equation:

[tex] \rm \: \: (2x - 1)(3x + 4) = 0[/tex]

Solution:

Set factors equal to zero,that is:

[tex](2x - 1) = 0 \: \: \: \: \: \: \: \: \: \: \: ...(1)[/tex]

[tex](3x + 4) = 0 \: \: \: \: \: \: \: \: \: \: \: \: ...(2)[/tex]

Solving for equation 1:

Solving for equation 2:

Hence,the solutions to the quadratic equation in factored form is [tex]\cfrac{-4}{3} [/tex] and [tex]\cfrac{1}{2} [/tex].

[tex]\rule{225pt}{2pt}[/tex]

Good luck on your assignment!

x=1/2 and x=-4/3 are the solutions of the equation (2x - 1)(3x + 4) = 0

A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .

The given equation is (2x - 1)(3x + 4) = 0

We have to find the solutions of the equation

As the equation is in factored form

We take each factor and solve for solution

2x-1=0

2x=1

Divide both sides by 2

x=1/2

Now 3x+4=0

3x=-4

Divide both sides by 3

x=-4/3

Hence, x=1/2 and x=-4/3 are the solutions of the equation (2x - 1)(3x + 4) = 0

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Answer: f(-2) = 8

Step-by-step explanation: On the graph there’s a point (-2,8), so f(-2), which just means -2’s y value on the graph, is 8.

A graph is a way to represent a lot of data in such a visual format that it is easy for the user to understand the complete information in one go. The correct option is D.

A graph is a way to represent a lot of data in such a visual format that it is easy for the user to understand the complete information in one go. Usually, the line of the graph is a function that follows the graph.

For the given graph of the function f(x) = –x² – 4x + 5, the domain of the function is all the real numbers, while the range of the function is all real numbers less than or equal to 9.

Hence, the correct option is D.

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Part (a)

[tex]247 \approx 200\\\\201 \approx 200\\\\\implies 247 \times 201 \approx 200 \times 200=\boxed{40000}[/tex]

Part (b)

[tex]756 \approx 800\\\\8674 \approx 9000\\\\\implies 756 \times 8674 \approx 800 \times 9000 =\boxed{7200000}[/tex]

Part (c)

[tex]3025 \approx 3000\\\\2007 \approx 2000\\\\\implies 3025 \times 2007 \approx 3000 \times 2000=\boxed{6000000}[/tex]

Answer:

D

Step-by-step explanation:

the zero is the value of x where the line crosses the x- axis, that is

zero is x = - 2

Answer:

C

Step-by-step explanation:

using the rule of exponents

[tex](\frac{a}{b}) ^{m}[/tex] = [tex]\frac{a^{m} }{b^{m} }[/tex] , then

[tex](\frac{-2}{3}) ^{3}[/tex]

= [tex]\frac{(-2)^{3} }{3^3}[/tex]

= [tex]\frac{-8}{27}[/tex]

= - [tex]\frac{8}{27}[/tex]

Definition:

[tex]a^2=a\cdot a\\\\a^3=a\cdot a\cdot a\\\\a^4=a\cdot a\cdot a\cdot a\\\vdots\\a^n=\underbrace{a\cdot a\cdot a\cdot...\cdot a}_{n}[/tex]

also

[tex]a^1=a\\\\a^0=1[/tex]

We have

[tex]\left(-\dfrac{2}{3}\right)^3=\left(-\dfrac{2}{3}\right)\cdot\left(-\dfrac{2}{3}\right)\cdot\left(-\dfrac{2}{3}\right)=-\dfrac{2\cdot2\cdot2}{3\cdot3\cdot3}=-\dfrac{8}{27}[/tex]

[tex]\huge\boxed{C:\ -\dfrac{8}{27}}[/tex]

Answer:

(5,18)  & (-5 , 38)

Step-by-step explanation:

  A linear equation represented by a line in a graph intersect the quadratic equation represented by a parabola zero, one or two times.

f(x) = x² - 2x + 3   -------------------(I)  

f(x) = -2x + 28   ---------------------(II)

x² - 2x + 3 = -2x + 28

x² - 2x + 2x + 3 - 28 = 0

x² - 25 = 0

x²         = 25

         x = √25 = √5*5

        x = ± 5

Plugin x = 5 in equation (II),

                    f(5) = -2*5 + 28

                          = -10 + 28

                          = 18

(5 , 18)

Plugin x = -5 in equation (II),

 f(-5) = -2*(-5) + 28

         = 10 + 28

         = 38

(-5, 38)

Answer:

(5, 18) and (-5, 38)

Step-by-step explanation:

Given system of equations:

1) f(x) = x² - 2x + 3 ⇒ y = x² - 2x + 3

2) f(x) = -2x + 28 ⇒ y = -2x + 28

Solve using the Substitution Method:

Step 1: Substitute the the first equation into the second equation.

⇒ x² - 2x + 3 = -2x + 28

Step 2: Solve for x.

x² - 2x + 3 = -2x + 28 [ Add 2x to both sides. ]

x² - 2x + 2x + 3 = -2x + 2x + 28

⇒ x² + 3 = 28 [ Subtract 28 from both sides. ]

x² + 3 - 28 = 28 - 28

⇒ x² - 25 = 0 [ Factor using the following rule: a² - b² = (a - b)(a + b). ]  

(x - 5)(x + 5) = 0

⇒ x - 5 = 0, x + 5 = 0 [ Solve for the values of x. ]

x - 5 + 5 = 0 + 5, x + 5 - 5 = 0 - 5

⇒ x = 5, x = -5

Step 3: Solve for y.

Substitute the found x-values into one of the given equations.

y = x² - 2x + 3 ⇒ y = (5)² - 2(5) + 3 ⇒ y = 25 - 10 + 3 ⇒ y = 18

y = x² - 2x + 3 ⇒ y = (-5)² - 2(-5) + 3 ⇒ y = 25 + 10 + 3 ⇒ y = 38

The solutions to the system of equations are:

⟹ x₁ = 5, y₁ = 18 ⇒ (5, 18)

⟹ x₂ = -5, y₂ = 38 ⇒ (-5, 38)

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The first difference and second difference of the equation will be given below.

The quadratic equation is given as ax² + bx + c = 0. Then the degree of the equation will be 2. Then we have

The quadratic function is given below.

y = x² + 7x + 6

Let the value of the y for x = 0, 1, 2, 3, 4 will be

y(0) = 6

y(1) = 14

y(2) = 24

y(3) = 36

y(4) = 50

The first difference and second difference will be

x       y      first difference        second difference

0       6               ...                                   ...

1       14              8                                   ...

2       24            10                                   2

3       36            12                                   2

4       50            14                                   2

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Answer:

The answer is the second choice: 2, 3, 6, 13, 16.

Step-by-step explanation:

Which set of numbers that has an average of 8. To find the mean, which is the same as average, we have to add the number and divide by how many numbers there are. Let's check the first set of numbers:

3+5+7+8+12=35. 35/5=7. So, we can cross out the first choice.

Let's check the second one:

2+3+6+13+16=40. 40/5=8.

The answer is the second choice: 2, 3, 6, 13, 16.

Hope this helps!

If not, I am sorry.

Answer:

Its B

Step-by-step explanation:

If you add up all the numbers and divide by the number of numbers their is your answer

Answer:

People surveyed: 79

a) p(s) = 46/79

b) p(snv) = 13/79

c) p(suv) = 96/79

hope this helps, and tell me if you get it right! It's prob wrong though, im bad at venn diagrams (×_×)⌒☆

Answer:

60 minutes

Step-by-step explanation:

we can see that the number of minutes increases by 8 each day

(12 + 8 = 20, 20 + 8 = 28, 28 + 8 = 36...)

So, because we have the value for the previous day (day 6) we know that we can simply add 8

52 + 8 = 60

So, the predicted number of minutes for day 7 is 60

hope this helps!!

The correlation coefficient of the data given in the table, using a calculator, is of 0.35

To find the coefficient, we need to insert the points (x,y) in the calculator.

In this problem, we have that:

Using a calculator, the coefficient is of 0.35.

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Answer:

Therefore, an integer that's divisible by both 6 and 9 has at least one 2 and two 3s in its prime factorization. That means it is divisible by 2 and 3: 2 x 3 6, 3 x 3 9, and 2 x 3 x 3 = 18. It's not necessarily divisible by 12 or 36, each of which includes two 2s in its prime factorization

The option third "P(Male or Type B) < P(Male | Type B)" is correct because 0.575 < 0.76

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

P(Male or Type B) = (number of male + number of type B - number that are both)/total population

[tex]\rm = \dfrac{103 + 50- 38}{200 }[/tex]

= 0.575

P(Male | Type B) = (number of male people inside the type B)/(number of Type B people)

= 38/(38 + 12)

= 0.76

0.575 < 0.76

P(Male or Type B) < P(Male | Type B)

Thus, the option third "P(Male or Type B) < P(Male | Type B)" is correct because 0.575 < 0.76

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Answer:
183/8 or 22.875

Step-by-step explanation:

Take 22.5 and put it over 1 so 22.5/1

And then multiply by 8 to get a common denominator (180/8) then add the 3/8 and you get 183/8 or 22.875

Answer:

  a) positive real zeros: 2 or 0; negative real zeros: 2 or 0; complex zeros: 0, 2, or 4. (rule of signs)

  b) ∪-shaped, as for an even-degree polynomial with positive leading coefficient. See attached.

  c, d) See attached

Step-by-step explanation:

Descarte's rule of signs gives bounds on the number of positive and negative real roots. The numbers it gives may be reduced by multiples of 2, as complex roots will come in conjugate pairs. The total number of roots of all kinds will match the degree of the polynomial.

Synthetic division is essentially polynomial long division with some modifications:

__

The signs of the terms of the given polynomial are + - - - +. There are two sign changes, so 2 possible positive real roots.

When the signs of the odd-degree terms are changed, the signs become + + - + +. There are still two sign changes, so 2 possible negative real roots.

Either or both of these numbers can be reduced by 2 if the roots include a conjugate pair. That is, there may also be 0 possible positive real roots, and 0 possible negative real roots.

The number of non-real (complex) zeros may be any multiple of 2 up to the degree of the polynomial. The may be 0, 2, or 4 possible non-real zeros.

__

The graph is the first attachment. It shows 4 real zeros: x = -4, -2, 1, 6.

Since the polynomial is of even degree (4) and has a positive leading coefficient (+1), we expect the general shape to be ∪-shaped. It is.

__

The second attachment shows synthetic division using x = -4. (The binomial divisor is (x+4).) The remainder (lower right value in the tableau) is the value of y when x=-4. The third attachment shows synthetic division using the value x=3. (y is -210 when x=3.)

Maybe this is the table you want:

  [tex]\begin{array}{|c|c|c|}\cline{1-3}x&-4&3\\\cline{1-3}y&0&-210\\\cline{1-3}\end{array}[/tex]

__

The second attachment shows synthetic division by the factor (x+4).

_____

Additional comment

The synthetic division attachments show instructions for carrying out the synthetic division and interpreting the results. As we said above, "the entry on the left" is the opposite of the constant in the binomial divisor. It is the actual value of x you want to use to evaluate the function.

The equations shown are merely for the purpose of indicating the operations that are used. An actual synthetic division tableau is simply a 3-row table of numbers, with the bottom row being the quotient coefficients and remainder.

Based on the information given the length of one side of the hot tub is 4. 8 ft. So the correct option is B.

The complete question is given as:-

Ricardo has a square hot tub. He wants to build a square pool next to it that is a dilation of the hot tub using a scale factor of 5. Point Q is the centre of dilation. Square A B C D is dilated to create square A prime B prime C prime D prime. The length of B prime C prime is 24 feet. If the pool is to be 24 ft on each side, what is the length of one side of the hot tub? 4 ft 4.8 ft 6 ft 7.2 ft

The scale factor is defined as the proportion of the new image's size to that of the previous image. decision-making.

Length: Using this formula

Length=B prime C prime length/Scale factor

Where:

B prime C prime length=24 feet

Scale Factor=5

Let plug in the formula

Length=24ft/5

Length=4.8ft

In conclusion, the length of one side of the hot tub is 4. 8 ft.

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Answer:

Part A: The appropriate design for the study includes;

Treatment used; Chamomile oil treatment

Method of treatment; Application of the chamomile oil to the cervical region of patients experiencing pain due to pinched nerves

Treatment assignment; Treatment should be assigned to patients with pinched nerves

Variables that should be measured; Reduction or relief of pain as reported by the patients

Part B; The study should be administered equally to both male and female as the symptoms can be experienced by both male and female

Part C; The design could be double blind by replacing the chamomile administered by placebo, thereby preventing bias from both researcher and participants in the results of the research.

Step-by-step explanation:

The graph second represents the line that is perpendicular to the line y = 4x - 2 option  (B) is correct.

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

The question is incomplete:

The complete question is:

Consider the equation y = 4x - 2 Which graph shows a line that is perpendicular to the line defined by the given equation?

Please refer to the attached picture.

The given line:

y = 4x - 2

The slope of the line m = 4

The slope of the line which is perpendicular to the above line:

M = -1/4 = -0.25

The graph second has a slope of -0.25

[tex]\rm y\ -2\ =\ \dfrac{\left(2-0.5\right)}{-4-2}\left(x+4\right)[/tex]

y - 2 = -0.25x - 1

y = -0.25x + 1

Thus, the graph second represents the line that is perpendicular to the line y = 4x - 2 option  (B) is correct.

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[tex]\textsf {Finding y :}[/tex]

[tex]\implies \mathsf {1^{2} + y^{2} = 3^{2}}[/tex]

[tex]\implies \mathsf {y^{2} = 8}[/tex]

[tex]\implies \mathsf {y = 2\sqrt{2}}[/tex]

[tex]\textsf {Finding z :}[/tex]

[tex]\implies \mathsf {(2\sqrt{2})^{2}+8^{2}=z^{2}}[/tex]

[tex]\implies \mathsf {z^{2} = 72}[/tex]

[tex]\implies \mathsf {z = 6\sqrt{2}}[/tex]

Answer:

z =8.49 or 6[tex]\sqrt{2}[/tex]

Step-by-step explanation:

Do the Pythagorean theorem = [tex]a^{2} +b^{2} =c^{2}[/tex]

Length of hypotenuse = 8+1=9

length of one side = 3

so, a²+3²=9²

     a²+3²=9²

     a²=81-9

     a²=72

     a=√72=8.49 or 6[tex]\sqrt{2}[/tex]

The relationship between the variables in the data will be as the number of months increases, the average monthly precipitation, in inches, decreases. Then the correct option is D.

A statement, principle, or policy that creates the link between two variables is known as a function.

The table gives the average monthly precipitation, in inches, in Seattle, Washington, from January through July, where January is month 1 and July is month 7.

Month                                                     1       2       3       4       5       6       7

Average monthly precipitation          5.2    3.9    3.3    2.0    1.6     1.4    0.6

Then the relationship between the variables in the data will be as the number of months increases, the average monthly precipitation, in inches, decreases.

Then the correct option is D.

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5.12 minutes ≈ 5 minutes 7.2 seconds

Distance. The length along a line or line segment between two points on the line or line segment.

Here, The flight path of the airplane is along the line ...

y = -125/135x = -25/27x

The perpendicular line through Mt. Rainier's location is ...

 y = 27/25(x -56) -40

In standard form, these two equations are ...

25x +27y = 0

27x -25y = 2512

The point of closest approach has the coordinates that are the solution to these two equations:

(x, y) = (33912/677, 31400/677)

The distance d from the origin to this point is given by the Pythagorean theorem (distance formula) as ...

d = 1256√(2/677) . . . . . km

This distance can be converted to time using the speed of the airplane:

1256√(2/677) X 60/800 =  94.2√(2/677) ≈ 5.120019 mins

Thus, 5.12 minutes after departing JBLM you will be closest to Mt. Rainier.

The attached graph shows the geometry of the problem.

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Subtraction is a mathematical operation that reflects the removal of things from a collection. The ribbon that Millie already had is 7.1 feet.

Subtraction is a mathematical operation that reflects the removal of things from a collection. The negative symbol represents subtraction.

Given Millie needs a total of 7.8 feet of ribbon for a school project. Also, She needs 0.7 more feet of ribbon. Therefore, the ribbon that Millie needs is,

Ribbon Millie had = Total Ribbon - ribbon that is needed

                              = 7.8 feet - 0.7feet

                              = 7.1 feet

Hence, the ribbon that Millie already had is 7.1 feet.

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The total cost of the dinner is $176.20.

The total cost of the dinner is the sum of the bill for the dinner, the tax and the tip.

Total cost = tip + bill of the dinner + tip

Tax = 0.08 x 140 = $11.20

Total cost = $140 + $25 + $11.20 = $176.20

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Answer:

The probability that a student earns a grade of A is 1/7.

Let E be an event and S be the sample space. The probability of E, denoted by P(E) could be computed as:

P(E) = n(E) / n(S)

As the total number of students = n(S) = 35

Students getting the grade A = n(E) = 5

So, the probability that a student earns a grade of A:

                     P(E) = n(E) / n(S)

                             = 5/35

                             = 1/7

Hence, the probability that a student earns a grade of A is 1/7.

Keywords: probability, sample space, event

Answer:

1/2

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(3-1)/(4-0)

m=2/4

m=1/2

The slope of the given points (0,1) and (4,3) will be ( 1 / 2 ).

The increase divided by the run, or the ratio of the rise to the run is known as the line's slope. In the coordinate plane, it describes how steep a line is.

The slope of the line is calculated by the formula given below:-

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

[tex]m=\dfrac{3-1}{4-0}=\dfrac{2}{4}=\dfrac{1}{2}[/tex]

Therefore the slope of the given points (0,1) and (4,3) will be ( 1 / 2 ).

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Answer:

4800

Step-by-step explanation:

If a question is asking for the "sum" of numbers, this just means we have to add them altogether.

975+983+923+913+985 = 4779

To find the hundredth place, we use our place value. 4 is in the thousands column, and 7 is in the hundreds. Once we find the hundreds, we need the number to the right of it (7).

7 > 5 so we round up. 7 becomes 8.

4800.

Answer:

C is the answers for the question

Step-by-step explanation:

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The sinusoidal function for the height as a function of time will be h= -15 cos (πt/15)+19 meter

As the Ferris wheel starts with the rider from the bottom position (which is the minimum point in the cycle), we can represent the position of the rider with a negative cosine function.

The general form of the cosine function representing the displacement of the rider is:

f(t) = a cos(bt+c) + d, where:

amplitude = |a| which is the distance that travels above and below the midpoint

period = 2 π/|b| which is the time period i.e. time required to complete one cycle

-c/b is the phase shift.

d = vertical displacement of the function

Given the diameter of the wheel is 30 m, then r = 30/2 = 15 m.

So the distance that travels above and below the midpoint is the radius for which a=15. As we have the negative cosine function, a = -15.

The time period is 0.5min. As it is given the frequency is 2 revolutions per min for which b= 2(2π) rad/min.= 4π/60 rad/sec.= π/15 rad/sec.

The rider starts from the bottom position, so there will be no phase shift, so c=0

Given that the center of the wheel is 19 m above the ground, so d=19m

Therefore the equation will be

height of rider as function of time(t) = h = -15 cos (πt/15)+19 meter

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