Answers
we know that
If (x-a) is a factor of P(x)
then
For x=a
the value of P(a)=0
therefore
the answer is option DRelated Questions
For the following function, briefly describe how the graph can be obtained from the graph of a basic logarithmic function. Then, graph the function and state the domain and the vertical asymptote. f(x) = 7 - In x Describe how the graph of f(x) can be obtained from the graph of a basic logarithmic function. The graph of f(x) = 7 - In x is a transformation of the graph of f(x) = In x by a reflection across the and then a translation units. Use the graphing tool to graph the equation.
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Answer
1) Graph is shown below in the 'Explanation'.
2) Domain: x > 0
In interval notation,
Domain: (0, ∞)
3) Vertical asymptote: x = 0
Horizontal asymptote: y = 7
4) The transformations required to turn f(x) = In x into f(x) = 7 - In x include
A reflection of f(x) = In x about the x-axis.
Then, this reflected image is then translated 7 units upwards.
Explanation
The graph of function is attached below
For the domain and asymptote,
Domain
The domain of a function refers to the values of the independent variable (x), where the dependent variable [y or f(x)] or the function has a corresponding real value. The domain is simply the values of x for which the output also exists. It is the region around the x-axis that the graph of the function spans.
We know that the logarithm of a number only exists if the number is positive.
So,
Domain: x > 0
In interval notation,
Domain: (0, ∞)
Asymptote
Asymptotes are the points on either the x-axis or the y-axis where the graph of the function doesn't touch.
They are usually denoted by broken lines.
For this question, we know that the value of f(x) cannot go beyond f(x) = 7 and x = 0
Vertical asymptote: x = 0
Horizontal asymptote: y = 7
For the transformation
When a function f(x) is translated horizontally along the x-axis by a units, the new function is represented as
f(x + a) when the translation is by a units to the left.
f(x - a) when the translation is by a units to the right.
When a function f(x) is translated vertically along the y-axis by b units, the new function is represented as
f(x) + b when the translation is by b units upwards.
f(x) - b when the translation is by b units downwards.
So, if the original function is
f(x) = In x
f(x) = -In x
This reflects the original function about the x-axis.
Then,
f(x) = 7 - In x
This translates the reflected function by 7 units upwards.
Find 164.4% of 289 round to the nearest tenths
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Answer:
475.1
Step-by-step explanation:
Percent means per hundred so 164.4 % means [tex]\frac{164.4}{100}[/tex] When you divide by 100 you move the decimal 2 places to the left
1.644 x 289 = 475.116 This rounded to the nearest tenths is
475.1
hi, can you please explain mistake made on one side the other side the correct work with the answer thanks
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Notice that:
[tex]3x-3x\ne x,[/tex]therefore the mistake is the last step.
Now, all the work of the student is correct up to:
[tex]undefined[/tex]Nancy is the proud owner of a new car. She paid $1,500 upfront and took out a loan for the rest of the amount. The interest rate on the loan is 5%. If the total cost of buying the car (including the interest Nancy owes) is more than $16,213.02, how much money did Nancy borrow?.1st Question: Assume that x represents the amount of money Nancy borrowed. Write an expression that represents the amount borrowed (the principal) plus the interest owed on that amount.
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1st Question:
Assume that x represents the amount of money Nancy borrowed. The interest rate on the loan is 5%. This means that the amount of interest that on the loan would be
5/100 * x = 0.05x
An expression that represents the amount borrowed (the principal) plus the interest owed on that amount is
x + 0.05x
= 1.05x
Secondly
She paid $1,500 upfront and took out a loan of $x for the rest of the amount. If the total cost of buying the car (including the interest Nancy owes) is more than $16,213.02, it means that
1500 + 1.05x > 16,213.02
Subtracting 1500 from both sides of the equation, we have
1500 - 1500 + 1.05x > 16213.02 - 1500
1.05x > 14713.02
Dividing both sides of the inequality by 1.05, we have
1.05x/1.05 = 14713.02/1.05
x > 14012.4
The amount borrowed is greater than $14012.4
the following table shows student test scores on the first two tests in into three chemistry class. If a student scored a 74 on his first test, make a prediction for his score on the second test . Assume the regression equation is appropriate for prediction. Round your answer to two decimal places if necessary
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68.29
ExplanationIf we locate each point (x, y) on the plane we will obtain the following graph:
We can approximate the resulting figure to a straight line:
In order to discover the equation of this line we use a linear regression calculator and enter the values as follows:
The calculator gives as the following equation as an approximation:
ŷ = 0.82X + 7.61
Using this equation we can predict the score of the second test of the exam using the score of the first test.
On this case, we want to make a prediction for a score on the second test if a student scored a 74 on his first test.
This means, we want to find ŷ when X=74. Let's replace it on the equation:
[tex]\begin{gathered} ŷ=0.82X+7.61 \\ \downarrow \\ ŷ=0.82\cdot74+7.61 \\ ŷ=68.29 \end{gathered}[/tex]That is why we can say that the student will have 68.29 as his score on the second test.
Please someone can help me please #1
Answers
Complete the following Division
Quotient of 96, 55, 84 and 63 is 12, 11, 14 and 21 respectively
What is Division?
One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division. The other operations are multiplication, addition, and subtraction.
1) 96
Divisor = 8
96 / 8
= 12
Quotient = 12
2) 55
Divisor = 5
55 / 5
= 11
Quotient = 11
3) 84
Divisor = 6
84 / 6
= 14
Quotient = 14
4) 63
Divisor = 3
63 / 3
= 21
Quotient = 21
Hence , Quotient of 96, 55, 84 and 63 is 12, 11, 14 and 21 respectively
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use the angle shown to determine if the line are parallel
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If the lines were parallel then
angle H would be corresponding to angle L and then
[tex]\measuredangle H\cong\measuredangle Z.[/tex]Since angles H and Z are a linear pair then if the lines were parallel angle H, Z and L would have to be right angles. Since the problem never states that those angles are right angles, then the lines are not necessarily parallel.
Answer: No.
reduce to lowest term.5p+5q/4p+4q
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Explanation
[tex]\frac{5p+5q}{4p+4q}[/tex]Step 1
factorize
[tex]\begin{gathered} 5p+5q\rightarrow5\text{ is a common factor, so}\rightarrow5(p+q) \\ 4p+4q\rightarrow4\text{ is a common factor, so}\rightarrow4(p+q) \end{gathered}[/tex]hence, the expression would be
[tex]\begin{gathered} \frac{5p+5q}{4p+4q}=\frac{5(p+q)}{4(p+q)} \\ \frac{5(p+q)}{4(p+q)} \end{gathered}[/tex]Step 2
now, we can see there is the same factor in numerator and denominator (p+q), so it can be eliminated.
[tex]\begin{gathered} \frac{5(p+q)}{4(p+q)}=\frac{5}{4} \\ \frac{5}{4} \end{gathered}[/tex]therefore, the answer is
[tex]\frac{5}{4}[/tex]I hope this helps you
An analyst notices that a CEO has consistently achieved 25% growth in profits from one year to the next. The CEO's company currently has annual profits of $870,000. If the trend continues, what will the annual profits be in 6 years?
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The currennt annual profit of the company is $ 870,000.
The growth percentage is 25%.
The annual profit of the company in the 6 years can be determined,
[tex]\begin{gathered} \text{Annual Profit=870000(1+}\frac{25}{100})^6 \\ =870000(\frac{5}{4})^6 \\ =3318786.62 \end{gathered}[/tex]Thus, the aanyal profits after 6 years will be $ 3318786.62
P(A) = 1/4 P(A n B) = 1/12 P(AUB) = 13/24 Find P(B) c 21/24 5/24 O O O 3/8 11/24
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Okay, here we have this:
Considering that P(AUB)=P(A)+P(B)-P(AintersectionB), we obtain that:
P(B)=P(AUB)-P(A)+P(AnB)
P(B)=(13/24)-(1/4)+(1/12)
P(B)=3/8
Finally we obtain that P(B) is equal to 3/8.
Use the graph below to write the formula (in factored form) for a polynomial of least degree.negative even degree function. Y intercept at -3. x intercepts at -3,-2,3 and 4If you have a non-integer coefficient then write it as a fraction. Organize factors (left to right) from smallest zero to largest. Answer:
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A polynomial function is in standard form when the terms in its formula are ordered from highest to lowest degree.
The factored form of a polynomial function as a function of "x" is expressed as:
[tex]f(x)=(x-a)(x-b)(x-c)(x-d)[/tex]where a, b, c, and d are the x-intercepts or zeros of the polynomial function.
From the given graph, the zeros of the polynomial graph are the point where the curve cuts the x-axis. The zeros of the polynomial are at x = -3, -2, 3 and 4
The factors of the polynomial function will be (x+3)(x+2)(x-3)(x-4)
The formula (in factored form) for a polynomial of least degree will be:
[tex]\begin{gathered} f(x)=(x-(-3))(x-(-2))(x-3)(x-4) \\ f(x)=(x+3)(x+2)(x-3)(x-4) \end{gathered}[/tex]The length of time (T) in seconds it takes the pendulum of a clock to swing through one compete cycle is givenby the formulaT= 2T✔️L/32 Where L is the length, in feet, of the pendulum, and is pie approximately 22/7. How long must the pendulum be of one complete cycle takes 2 seconds? Answer as a fraction or round to at least 2 decimal places.The pendulum must be__ feet.
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we have the formula
[tex]T=2\pi\sqrt{\frac{L}{32}}[/tex]For T=2 seconds
substitute in the given formula
[tex]\begin{gathered} 2=2\pi\sqrt{\frac{L}{32}} \\ \\ 1=\frac{22}{7}\sqrt{\frac{L}{32}} \\ \\ squared\text{ both sides} \\ \\ (\frac{7}{22})^2=\frac{L}{32} \\ \\ L=\frac{7^2*32}{22^2} \\ \\ L=3.24\text{ ft} \end{gathered}[/tex]Factor the expression using the GCF. 11. 24 - 9 12. 14x + 63
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Recall that the GCF of two ( or more numbers) is the highest number that divides exactly the two numbers.
11.- Notice that:
[tex]\begin{gathered} 24=3\cdot8, \\ 9=3\cdot3. \end{gathered}[/tex]Therefore:
[tex]9-24=3(8-3)\text{.}[/tex]12.- Notice that.
[tex]\begin{gathered} 14x=7\cdot2x, \\ 63=7\cdot9. \end{gathered}[/tex]Therefore:
[tex]14x+63=7(2x+9)\text{.}[/tex]Answer:
11.-
[tex]3(8-3)\text{.}[/tex]
12.-
[tex]7(2x+9)\text{.}[/tex]
Find the slope of line segment AB where the coordinates of A are
(3,-3) and B are (1,2).
A: -2/5
B: -5/2
C: 2/5
D: 5/2
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The slope formula is y2-y1 over x2-x1 from there you should get your answer. Hope this helps.
Using the GCF you found in Part B, rewrite 72 + 81 as two factors. One factor is the GCF and the other is the sum of two numbers that do not have a common factor. Show your work.
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The factors of 72 and 81 are
[tex]\begin{gathered} 72=2^3\cdot3^2 \\ 81=3^4 \end{gathered}[/tex]Therefore, their GCF is equal to 3^2=9
Then,
[tex]72+81=9\cdot8+9\cdot9=9(8+9)[/tex]The answer is 9(8+9).
The factors of 8 and 9 are
[tex]\begin{gathered} 8\to2,4,8 \\ 9\to3,9 \end{gathered}[/tex]If the ratio of KL to JK is 2.7. and JL = 162, find JK
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KL / JK = 2:7
JL = 162
JK = ?
JL = KL + JK = 162 KL = 2 JK = 7
KL / JK = 2.7
KL = 162 - JK
Substitution
(162 - JK) / JK = 2.7
Solve for JK
162 - JK = 2.7 JK
162 = 2.7 JK + JK
162 = 3.7 JK
JK = 162 / 3.7
JK = 43.8
Find the next two terms in this sequence. 1 3 7 15 [?] 2'4'8' 16' T'I
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We will solve as follows:
*First: We identify the pattern, that is:
[tex]\frac{3}{4}-\frac{1}{2}=\frac{1}{4}[/tex][tex]\frac{7}{8}-\frac{3}{4}=\frac{1}{8}[/tex][tex]\frac{15}{16}-\frac{7}{8}=\frac{1}{16}[/tex]From this, we can see tat the pattern follows the rule:
[tex](\frac{1}{2})^{n+1}[/tex]So, the next terms of the sequence will be:
[tex]\frac{15}{16}+(\frac{1}{2})^{4+1}=\frac{31}{32}[/tex]And the next one is:
[tex]\frac{31}{32}+(\frac{1}{2})^{5+1}=\frac{63}{64}[/tex]And those are the next two terms of the sequence.
Find the area when length = 5.2
(Equilateral Triangle)
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Answer: 3√3 / 4
Step-by-step explanation:
A = 8^2√3 where s √3
A = ( √3)^2 * √3 / 4
A = 3√3/4
X Y2 146 4211 77Find the constant of proportionality (r) in the equation y=rx.
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From the question
We are given the equation
[tex]y=rx[/tex]We are to find r given that
When x = 2, y = 14
When x = 6, y = 42
When x = 11, y = 77
Substituting the first value, x = 2, y = 14 into the equation we get
[tex]14=r\times2[/tex]Solving for r we get
[tex]\begin{gathered} r=\frac{14}{2} \\ r=7 \end{gathered}[/tex]This is true for all values of x and y
Hence, r
which ordered pair is a solution of 6X + 7 < 21
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Substitute 2 for x and 1 for in the inequality to verify that ordered pair satisfy the inequality or not.
[tex]\begin{gathered} 6\cdot2+7\cdot1<21 \\ 12+7<21 \\ 19<21 \end{gathered}[/tex]The inequality is trus so point (2,1) satisfy the inequality.
Substitute 4 for x and 1 for y in the inequality to verify that ordered pair satisfy the inequality or not.
[tex]undefined[/tex]Which of the following statements follows from (x - 3)2 = 7? ox2 +9=7 Ox-3=1 / OX-3 = +49 NEXT QUESTION O ASK FOR HELP
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So, given the equation:
We could take the square root to both sides of the equation to obtain that:
So the correct option is B.
Amanda y Pedro realizaron queques iguales, Lurdes se comió 2/4 partes, Amanda 2/3 y Pedro 3/4, quien comió menos?
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Express 80 as the product of its prime factors Write the prime factors in ascending order.
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Answer:
2×2×2×2×5
Step-by-step explanation:
Express 80 as the product of its prime factors Write the prime factors in ascending order.
2 × 2 × 2 × 2 × 5
2×2×2×2×5 = 80
Margie uses 36 inches of lace to make one pillow. She makes 24 pillows for the school fair. How many total inches of lace does Margie use on the pillows?
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Margie used a total of 264 inches of lace for the 24 pillows
How to calculate the total inches of lace used ?
Margie used 36 inches of lace for one pillow
She needs to make 24 pillows
The total inches of lace that was used for the 24 pillows can be calculated as follows
= 36 × 24
= 864
Hence Margie used 864 inches of lace for 24 pillows
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The unit rate for peaches is $2.00 per pound. The unit rate for grapes is $2.50 perpound. If you had $10 to spend, would you be able to buy a greater weight ofpeaches or of grapes? Explain your answer.
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According to the problem, the total amount of money we have is $10.
Additionally, we know that the cost of peaches is $2 per pound, and the cost for grapes is $2.50 per pound.
Notice that the cost for grapes is greater than the cost for peaches, that means we'll by fewer pounds of grapes with $10 than for peaches.
For example, if we buy peaches, it would be
[tex]\frac{10}{2}=5[/tex]This means we would be able to buy 5 pounds of peaches.
But, for grapes
[tex]\frac{10}{2.50}=4[/tex]Which means we can by only 4 pounds of grapes.
Therefore, we would be able to buy a greater amount of peaches than grapes.Is y = 8 a solution to the inequality below?
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Answer:
Yes
Step-by-step explanation:
136/8 = 17
17 +3 = 20
20 is less than or equal to 123 so 8 does work as a solution
Find the equation of the line perpendicular to the line y=-1, going through the points (-5,4) using the formula y-y1=m(x-x1)
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We are asked to determine the equation of a line that is perpendicular to the line:
[tex]y=-1[/tex]This is the equation of a horizontal line therefore a perpendicular line is a vertical line. Therefore, it must have the form:
[tex]x=k[/tex]The value of "k" is determined by a point "x" where the line passes. Since the line passes through the point (-5, 4), this means that the equation of the line is:
[tex]x=-5[/tex]And thus we have determined the equation of the perpendicular line.
Given ABC below, with m B=25°, a = 9, and c = 16, find the area of the triangle.
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It is given that the sides of the triangle are a =9 and c=16 . The angle is given mB=25 degree.
The area of triangle is determined as
[tex]A=\frac{1}{2}a\times c\times\sin B[/tex][tex]A=\frac{1}{2}\times9\times16\times\sin 25=72\sin 25^{\circ}[/tex][tex]A=30.428sq\mathrm{}\text{unit}[/tex]Thus the area of triangle is 30.428 sq.unit.
A person buys a 900-milliliter bottle of soda from a vending machine. How many liters of soda did the person buy?
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Answer: 0.9 Liters.
Step-by-step explanation:
Divide the volume value by 1000.
900 ÷ 1000
Because 1000 mililiters are the same that one liter.
64XOA. VZ is the smallest side.OB. vz is the longest side.OC. XV is the smallest side.OD. XV is the longest side.5759Z
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SOLUTION
The triangle XYZ shown below :
The angle with the longest side is said to be the angle with the largest angle:
The largest angle faces the longest side
Hence the Option B is t
[tex]YZ=x=longest\text{ side}[/tex]