State the domain of 1b, then determine the equation of any vertical asymptotes and/or coordinates of any holes in the graph of the function.
Answers
We have
\(f(x)=\frac{2x^2+x}{x^2-5x+6}\)First we will factorize the function
\(f(x)=\frac{x(2x+1)}{\mleft(x-2\mright)(x-3)}\)The domain is
\(\: \mleft(-\infty\: ,\: 2\mright)\cup\mleft(2,\: 3\mright)\cup\mleft(3,\: \infty\: \mright)\)In this case, we have two vertical asymptotes
x-2=0
x=2
x-3=0
x=3
ANSWER
The domain is
\(\: \mleft(-\infty\: ,\: 2\mright)\cup\mleft(2,\: 3\mright)\cup\mleft(3,\: \infty\: \mright)\)
The vertical asymtotes
x-2=0
x=2
x-3=0
x=3
Related Questions
In the diagram a || b. Use the diagram to answer the question. Name the alternate interior angle to <2
Answers
The angle 7 is the alternative interior angle to angle 2.
Given that,In the diagram a || bWe need to find the alternate interior angle to <2 .Alternate interior angles are the angles that are formed when a transversal crosses two parallel lines.
They are the angles that are on opposite sides of the transversal and inside the two parallel lines.
Thus, in the given diagram, the angle that is opposite to angle <2 and is inside the two parallel lines a and b is the alternate interior angle to angle <2.
We can see that the alternate interior angle to angle <2 is <7. Therefore, the alternate interior angle to angle <2 is <7.
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Devon wants to build a ramp with the dimensions shown. How much wood does he need?
Answers
The image of the ramp with dimensions is missing, so i have attached it.
Answer:
680 in² of wood is needed.
Step-by-step explanation:
The way to find how much wood would be needed by devon would be to find the total surface area of the ramp.
From the attached image,
Let's find the area of the 2 triangles first;
A1 = 2(½bh) = bh = 15 x 8 = 120 in²
Area of the slant rectangular portion;
A2 = 17 x 14 = 238 in²
Area of the base;
A3 = 15 × 14 = 210 in²
Area of vertical rectangle;
A4 = 8 × 14 = 112 in²
Total Surface Area = A1 + A2 + A3 + A4 = 120 + 238 + 210 + 112 = 680 in²
jeremiah works as a sales person at an electronics store
Answers
Answer:
Good luck with that Jeremiah
Miguel deposited a certain amount of money in the bank. The bank paid him interest after one year at which point he had $757.12. After the next year he had $787.40. How much money did Miguel originally put into the bank? (Answer to the nearest dollar.)
Answers
The interest accumulated in the account after the first and second year indicates;
The amount Miguel originally put into the bank is about $728
What is interest accumulated on an amount?An interest is a reward or cost of borrowing or lending money.
Let P represent the amount Miguel deposited in the bank, and let r represent the interest rate in percentage, therefore, we get;
The amount in the account after the first year is; P + r·p = P·(1 + r)
P·(1 + r) = $757.12...(1)
The amount in the account after the second year can be obtained using the following formula;
Principal at the start of the second year = P·(1 + r)
Therefore; Amount = P·(1 + r) + P·(1 + r) × r = P·(1 + r) × (1 + r) = P·(1 + r)²
P·(1 + r)² = $787.40...(2)
Equation (1) indicates that we get; (1 + r) = 757.12/P
Therefore; P·(1 + r)² = P·(757.12/P)² = 787.40
757.12²/P = 787.40
P = 757.12²/787.40 ≈ 728
The amount Miguel deposited in the bank is about $728
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()
8
What is 11 - 2³?
Answers
Answer:
\(11 - 2 {}^{3} \)
\(11 - 8\)
\(3\)
Can someone pls answer this
Answers
B) 8,20£/h
C) 13,20£/h
Step by step in a pic
Find two positive numbers satisfying the given requirements. The product is 216 and the sum is a minimum. (No Response) (smaller value) (No Response) (larger value)
Answers
Answer:
\(x1=\sqrt{216} \ and \ y1=\ \sqrt{216}\)
Step-by-step explanation:
Let the first number is x1 and other number is y1 then
\(x1 * y1 =216\)
Therefore
\(y1=\)\(\frac{216}{x1}\)
also there sum is
\(s1 =x1+y1\)....Eq(1)
Putting the value of y1 in the previous equation
\(s1\ =x1 + \frac{216}{x1}\)........Eq(2)
Differentiate the the Eq(2) with respect to x1 we get
\(\frac{ds1}{dx1} \ =\ 1+216*\frac{1}{-x1^{2} }\)
\(\frac{ds1}{dx1} \ =\ 1-\frac{216}{x1^{2} }\ =\ 0\)
\({x1^{2} }\ =\ 216\\ x1=\sqrt{216}\)
Putting the value of X1 in Eq(1) we get
\(y1=\frac{216}{\sqrt{216} } \\y1=\frac{216*\sqrt{216} }{216} \\y1=\ \sqrt{216}\)
So \(x1=\sqrt{216} \ and \ y1=\ \sqrt{216}\)
8. What is the value of x in the diagram?
A
E
429
B
49
D
32°C
Answers
Answer:
D. \(10^{\circ}\)
Step-by-step explanation:
Let the measure of minor arc \(AE\) be \(\alpha\) and the measure of minor arc \(BD\) be \(\beta\).
Using the secant-secant theorem, \(\frac{\alpha-\beta}{2}=32 \implies \alpha-\beta=64^{\circ}\).
By the inscribed angle theorem, \(\alpha=84^{\circ}\).
Thus, \(\beta=20^{\circ}\).
By the inscribed angle theorem, \(x=10^{\circ}\).
B: A rectangular block of material that acts as a paperweight is on your dad's desk. The measurements are 3cm. x 4cm. X 6cm, and ithas a mass of 184.32 grams. Determine what the paperweight is made of
Answers
Answer: Marble.
Explanation
• The, density, is a measure of the ,mass per unit volume ,of a substance, and it is specific of the material. The formula to calculate it is:
\(\rho=\frac{m}{V}\)where ρ represents the density, m the mass, and V the volume.
The first step to get ρ is to calculate V using the dimensions we are given:
\(V=3\times4\times6=72cm^3\)Then, as we are given the mass, we can replace these values in the formula of ρ:
\(\rho=\frac{184.32g}{72cm^3}=2.56\frac{g}{cm^3}\)Then, the density of the material is 2.56g/cm³, which is Marble.
EXPLORE ACTIVITY 2
TEKS 7.13.8
Analyzing a Family Budget
One way to present a budget is in a circle graph. You can see at a glance which
categories take the greatest part of the family's resources. You can also work
backward from a circle graph to figure out exactly how much money is in each
category.
Use the circle graph to complete
the table for the Baker family's
monthly budget. Their net
monthly income is $4,000.
STEP 1)
STEP 2
STEP 3
STEP 4
STEP 5
432 Unit 7
Enter the income in the table.
Enter the percent or amount of money for each
category from the circle graph in the table.
Calculate the amount of money or the percent
for each category in the table.
Determine which expenses are fixed and
which are variable. Place X's in the appropriate
columns.
Complete the Amount Available column.
Item
Net monthly income
means how much
income the family
has after taxes.
Net monthly
Income
Housing cost
Food
Savings
Entertainment
Clothing
Medical
Transportation
Emergency
fund
Amount
($)
Percent
(%)
Baker Family's Monthly Budget
Emergency fund
Transportation
(car expense,
bus passes)
$400
Medical
(insurance
and
additional
expenses)
$600
Clothing
8%
Entertainment
Savings
$320
Fixed
Variable
Amount
Expense Expense Available
($)
Housing
cost (house
payment and
Insurance!
$1,400
Food
15%
Answers
Note that the table of budget is attached accordingly, and steps 1-4 have been completed. See the table.
What happened during emergency repair of $305?4) Since the emergency fund for that month was $200, it means that they are in the short for $105. They can only affod it if they take from their savings.
5) they had a balance of $800 for the month. This is miscellaneous funds. They can make use of this for the trip to NASA. This way, they won't have to touch the savings or entertainment.
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Full Question:
See attached image.
Reflect
4. Analyze Relationships One month, the family must make an
emergency car repair for $305. Are they able to pay for it out of the
fixed emergency fund for that month? If not, how can they afford it?
5. The family wants to make a trip to Houston to visit the NASA Space
Center. What are some ways they can save without using all of the
allotted $160 for entertainment
PIEVIOUS
Select the correct answer from each drop-down menu.
B
De
B
CH
Quadrilateral A'B'C'D'is obtained by a reflection across the y-axis of quadrilateral ABCD, followed by a translation 3 units to the left and 3
units down. Create a function modeling the reflection and the translations.
Rx y = 1
Reset
Next
First drop down selection :
X+3
-x+3
X-3
-x-3
Second drop down selection:
Y+3
-y+3
Y-3
-y-3
Answers
9514 1404 393
Answer:
f(x, y) = (-x-3, y-3)
Step-by-step explanation:
Reflection across the y-axis is ...
r(x, y) = (-x, y)
Translation left and down 3 units each is ...
t(x, y) = (x -3, y -3)
Then the composition of reflection then translation is ...
f(x, y) = t(r(x,y)) = t(-x, y)
f(x, y) = (-x-3, y-3)
 ILL GIVE BRAINIEST to the correct answer Please I just need a answer
  Find the coordinates of the point 7/10 of the way from A to B.
Answers
Line AB length = (12- -4, 4 - -7) = (16,11)
The point 7/10 of the way is 7/10 of the x coordinates length and 7/10 of the y coordinate length, because that’s what makes up the line.
7/10 * 16 =1.6 * 7 = 11.2
7/10 * 11 = 1.1 * 7 = 7.7
We add these to our start points to get to our point 7/10 along the line
11.2 + -4 = 7.2
7.7 + -7 = 0.7
Answer = (7.2, 0.7)
Match each function on the left to all points on the right that would be located on the graph of the function. Help!! thanks
Answers
Each function on the left should be matched to all points on the right that would be located on the graph of the function as follows;
f(x) = 2x + 2 ⇒ (0, 2).
f(x) = 2x² - 2 ⇒ (-1, 0).
\(f(x) = 2\sqrt{x+1}\) ⇒ (0, 2).
What is a function?In Mathematics and Geometry, a function is a mathematical equation which defines and represents the relationship that exists between two or more variables such as an ordered pair in tables or relations.
Next, we would determine the point or ordered pair that represent a solution on the graph of each of the function as follows;
For the ordered pair (0, 2), we have:
f(x) = 2x + 2
2 = 2(0) + 2
2 = 2 (True).
For the ordered pair (-1, 0), we have:
f(x) = 2x² - 2
0 = 2(-1)² - 2
0 = 2 - 2
0 = 0 (True).
For the ordered pair (0, 2), we have:
\(f(x) = 2\sqrt{x+1}\\\\2= 2\sqrt{0+1}\\\\2 = 2\sqrt{1}\)
2 = 2 (True).
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University Trailer Sales Company sold 356 utility trailers during a recent year. If the gross annual sales for the company was $328128, what was the average selling price for each trailer?
The average selling price of each trailer was nearly $
(Round to the nearest whole number.)
Answers
Answer:
The Answer is 2000$..........
You rent an apartment that costs $1300 per month during the first year, but the rent is set to go up 7.5% per year. What would be the rent of the apartment during the 10th year of living in the apartment? Round to the nearest tenth (if necessary).
Answers
A square shaped pasture has an area of 144 square feet. What is the perimeter of the pasture?
Answers
Answer:
48 ft.
Step-by-step explanation:
sqr root 144= 12
12x4=48
we know that in a square, all the sides are the same length. the square root of 144 is 12, and we know the square root of a number (12) is what gives the square root (144) when multiplied by itself. the formula of area (in a square) is A = bh, where the b stands for base and the h stands for height. if the base and height multiplied equals 144, we know both the base and height are 12 square feet. so now that we know all of the sides are 12 square feet, we can finally solve perimeter. you find perimeter by adding up all the sides. 12 + 12 + 12 + 12 = 48. (you can also do 12 x 4). this is how we know the perimeter is 48 square feet.
^^ only included this in case you needed to give an explanation.
hey can someone plz help me with this??? *cute eyes*
Answers
Answer:
A. 5
B. -5, 5
C. 5, 5
Step-by-step explanation:
A. |-6+(-1)| = 5
B. -6-(-1)=-6+1=-5
-1-(-6)=-1+6=5
C. |-6-(-1)|=|-6+1|=5
|-1-(-6)|=|-1+6|=5
A jogger goes 0.8 mi east and then turns south. If the jogger finishes 1.7 mi fromthe starting point, how far south did the jogger go?
Answers
We can use Pythagoras theorem:
\(\begin{gathered} H^2=a^2+b^2 \\ \\ \end{gathered}\)Where H=hypotenuse and "a" and "b" are the other sides of the triangule.
In the current problem, we have:
H = 1.7, a = 0.8, b=?
Then:
At a local college, 61 of the male students are smokers and 549 are non-smokers. Of the female students, 156 are smokers and 444 are non-smokers. A male
student and a female student from the college are randomly selected for a survey. What is the probability that both are non-smokers?
Do not round your answer. (If necessary, consult a list of formulas.)
Answers
The probability of randomly selecting a male student and female student are non-smokers is 0.6771
What is probability?
Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.
Probability = (Number of possible outcomes)/(Total number of outcomes)
According to the given question:
Number of male students are smokers = 61
Number of male students are non smokers = 549
Total number of male students = 610
Number of female students are smokers = 156
Number of female students are non smokers = 444
Total number of female students = 600
Probability that both are non smokers is given by
P (non-smoker males) x P (non-smoker females)
= \(\frac{549}{610} . \frac{444}{600}\)
= 0.915 x 0.74
= 0.6771
Therefore the probability that both male and female are non-smokers is 0.6771.
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Three quarters of a number is 27. What is two ninths of the number?
Answers
Answer:
8
Step-by-step explanation:
let x be the number , then
\(\frac{3}{4}\) x = 27 ( multiply both sides by 4 to clear the fraction )
3x = 108 ( divide both sides by 3 )
x = 36
the number is 36, so
\(\frac{2}{9}\) × 36 = 2 × 4 = 8
The two ninths of the number is 8
We know that Three quarters of a number is \(\frac{3}{4}\) times of a number
Hence we will assume the number x ,
\(\frac{3}{4} of x = 27\)
\(x = 27 X \frac{4}{3}\)
\(x = 36\)
Now as we know the number is 36
Therefore , the two ninths of the number assumed as y
We will multiply the number 36 by 2 and then divide by 9
Hence,
\(y = 36 X \frac{2}{9}\)
\(y = 8\)
Thus, the two ninths of the number 36 is 8
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What could be shown about the diagonals of parallelogram PQRS to compare the proof that diagonals of a parallelogram bisect each other?
Answers
Answer:
C. PR and SQ have the same midpoing
Step-by-step explanation:
The theorems that could be shown hat the diagonals of parallelogram PQRS bisect each other are explained below.
Let the point where the diagonals intersect be called Point T.Now, looking at the parallelogram, we can say that;
∠QPT = ∠SRT (This is because the alternate angles between 2 parallel lines are always equal)
Secondly, ∠PQT= ∠RST.This is This is because the alternate angles between 2 parallel lines are always equal.
Thirdly; ∠PTQ=∠RTSThis is because they are vertically opposite angles.
Now, from AAA congruence theorem, we can say that;△PTQ is congruent to △RTS.
Thus, we can say that;
PT = RT and QT = ST
This proves that they bisect each other.
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select the correct answer from each drop down menu.  quadrilateral abcd is a parallelogram. complete the statements to prove that ab =cd and bc = ad
Answers
Due to the fact that the numbers 4 and 5 both refer to comparable triangles, the correct quadrilateral ABCD is a parallelogram.
What does a quadrilateral mean?The polygon consists of four vertices and four sides. Angles add up to 360. A form of quadrilateral with equal and parallel opposite sides is a parallelogram.
Given
A parallelogram is an ABCD quadrilateral.
Both AB and BC are parallel to CD and AD, respectively.
Consequently, it is a parallelogram's condition.
A form of quadrilateral with equal and parallel opposite sides is a parallelogram.
Here, CAB and ACD are congruent, and BCA and CAD are congruent.
Then ABC is comparable to ADC, CAB is to ACD, and BCA is to CAD.
Then ABC is comparable to ADC.
Yet AC is AC.
ADC and ABC are then congruent.
As a result, for the equivalent triangle, 4 and 5 have the same significance.
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Pls help will mark brainliest
Answers
Answer:
2462.4 square inches
Step-by-step explanation:
we know the shorted side of the wall is 36 inches so we divide 2.5 to 36 to see how much bigger the actual wall is to the scale
36/2.5= 14.4
The actual wall is 14.4 times bigger than the scale
14.4 x 4.75= 68.4
68.4 x 36= 2462.4 inches
which of the following is most likely the next step in the series
Answers
Answer:
A.
Step-by-step explanation:
Let's think of this as a clock. We can see that the 2 lines start in the same place, around 3 o'clock. Next, one of the line segments shifts down to around 6 o'clock. Next, it shifts to about 9 o'clock. Logically, the next step (in a clock) would be 12 o'clock, making A the correct choice.
We can also just use a regular circle, with one of the line segments moving 90 degrees each time.
Hope this helps! :)
find the perimeter of a triangle where one side is 2 inches, one side is 6 inches and another side is 10 inches.
(a) 2in.
(b) 9in.
(c) 36in.
(d) 18in.
Answers
Answer:
(d) 18 in.
Step-by-step explanation:
When we're given the three sides of a triangle, one formula we can use for perimeter of a triangle is:
P = s1 + s2 + s3, where
P is the perimeter,and s1, s2, and s3 are the three sides:P = 2 + 6 + 10
P = 8 + 10
P = 18
Thus, the perimeter of the triangle is 18 in.
Learning Task 3 Answer the questions that follow. Put a check mark (/) on the space provided. Copy and answer in your math notebook. 1. The units for Volume are always ______squared _____cubed 2. Volume is the amount of space an object takes up. ___True ___False Calculate for the volume of solid. 3. Chona is selling Pringle Chips to raise money for a field trip. The container has a diameter of 9 inches and a height of 32 inches. 4. A 3-tier cake with the same height of 10 in and radius of 12 in, 8 in, 5 in respectively is to be delivered to a birthday party. How much space does this cake take up? Use 3.14 for π. 5. A Styrofoam model of a volcano is in the shape of a cone. The model has a circular base with a diameter of 48 centimeters and a height of 12 centimeters. Find the volume of foam in the model to the nearest tenth. Use 3.14 for π.
Answers
3. The volume of the Pringle Chips container is approximately 2034.72 cubic inches.
4. The cake takes up approximately 7317 cubic inches of space.
5. The volume of foam in the model of the volcano is approximately 7234.08 cubic centimeters.
1. The units for Volume are always cubed.
2. Volume is the amount of space an object takes up. True.
3. To calculate the volume of the Pringle Chips container, we need to find the volume of a cylinder. The formula for the volume of a cylinder is V = πr^2h, where π is a constant (approximately 3.14), r is the radius, and h is the height. Given that the diameter is 9 inches, the radius would be half of that, which is 4.5 inches. Substituting the values into the formula, we have:
V = 3.14 * (4.5)^2 * 32
V = 3.14 * 20.25 * 32
V ≈ 2034.72 cubic inches
4. To find the volume of the 3-tier cake, we need to find the volume of each tier separately and then add them together. Since all the tiers are cylinders, we can use the formula V = πr^2h.
Tier 1:
V1 = 3.14 * (12)^2 * 10 = 4521.6 cubic inches
Tier 2:
V2 = 3.14 * (8)^2 * 10 = 2010.4 cubic inches
Tier 3:
V3 = 3.14 * (5)^2 * 10 = 785 cubic inches
Total volume:
Total V = V1 + V2 + V3
Total V = 4521.6 + 2010.4 + 785
Total V ≈ 7317 cubic inches
5. To find the volume of the Styrofoam model of the volcano, we can use the formula for the volume of a cone, V = (1/3)πr^2h. Given that the diameter is 48 centimeters, the radius would be half of that, which is 24 centimeters. Substituting the values into the formula, we have:
V = (1/3) * 3.14 * (24)^2 * 12
V = (1/3) * 3.14 * 576 * 12
V ≈ 7234.08 cubic centimeters
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(a) A survey of the adults in a town shows that 8% have liver problems. Of these, it is also found that 25% are heavy drinkers, 35% are social drinkers and 40% are non-drinkers. Of those that did not suffer from liver problems, 5% are heavy drinkers, 65% are social drinkers and 30% do not drink at all. An adult is chosen at random, what is the probability that this person i. Has a liver problems?
Answers
Answer:
The probability that the selected adult has liver problems is 0.08
Step-by-step explanation:
In this question, from the data given, we want to calculate the probability that an adult selected at random has liver problems.
Let E(L) be the event that an adult has liver problems.
The probability is directly obtainable from the question and it is given as 8%
Thus, the probability that the selected adult has liver problems; P(L) = 8% = 8/100 = 0.08
In a class of 25 students, 13 have a brother and 9 have a sister. There are 7 students who do not have any siblings. What is the probability that a student chosen randomly from the class has a brother and a sister?
Answers
Answer:
Step-by-step explanation:
Discussion
9 with a sister
13 with a brother
7 with neither.
The total is 29 so you are counting some siblings twice. There are 29 - 25 students that have both, so 4 students have both.
P(brother and sister) = 4/25
P(brother and sister) = 0.16
Answer
P = 0.16
standard deviation of 0.37, 0.13, 0.06,0.15,0.29
Answers
A standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1. Tables of the standard normal distribution are frequently used to show different regions of the normal distribution.
How do I calculate standard deviation?First, determine the mean. Step 2: Calculate the square of each data point's variance from the mean. Add the values from Step 2 in Step 3. Divide by the total number of data points in step 4.
Mean = 0.37+0.13+0.06+0.15+0.29\s=1.00
It gauges how far away from the mean each observed value is. Approximately 95% of values in any distribution will be within two standard deviations of the mean.
Standard deviation is the square root of variance, which is the average squared deviations from the mean. Both metrics capture distributional variability, although they use different measurement units:
The units used to indicate standard deviation are the same as the values' original ones (e.g., minutes or meters).
The units used to express variation are substantially greater.
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5(20 + _ )= 100 + 85
I need help fast
Answers
Answer:
_ = 5
Step-by-step explanation:
Answer:
17Step-by-step explanation:
5(20 + x) = 100 + 85100 + 5x = 100 + 855x = 85x = 17