Answer:
it would be great if you provided a question here..!
Step-by-step explanation:
Determine any asymptotes (Horizontal, vertical or oblique). Find holes, intercepts and state it's domain.
[tex]g(x) = \frac{(2x+1)(x-5)}{(x-5)(x+4)^{2} }[/tex]
Answer:
1.
Horizontal Asymptote is y = 0
2.
Vertical Asymptote is x = -4
3.
No Slant Asymptote
4.
Hole at (5, 0.14)
5.
x-intercepts:
x-intercept [tex](-\frac{1}{2},0)[/tex]
y-intercepts:
y-intercept [tex](0,\frac{1}{16})[/tex]
6.
Domain is [tex]{x|x\neq -4,5}[/tex]
Step-by-step explanation:
1. Horizontal Asymptotes
* If the degree of the numerator is less than the degree of the denominator (this is our case since multiplying will give the numerator a degree of 2 and denominator a degree of 3), then y = 0 is the only horizontal asymptote
Horizontal Asymptote is y = 0
2. Vertical Asymptotes
* To get VA (vertical asymptote), we set the denominator equal to zero.
Before doing this, we see that we can cancel out (x-5) from both numerator and denominator so the denominator becomes (x+4)^2. Now we find VA:
[tex](x+4)^2=0\\x+4=0\\x=-4[/tex]
Vertical Asymptote is x = -4
3. Oblique asymptotes
* If the degree of numerator is less than the degree of the denominator (this is our case as explained above), then there is no slant asymptote.
No Slant Asymptote
4. Holes
There is hole in a rational function if there is the same factor in both numerator and denominator (before simplifying, only after factoring). Set that equal to 0 and solve. Then, cross out the common factor and put the x-value into the function and get the y-value of the hole.
We can see that there is a factor of (x-5) in both the numerator and denominator. We set it equal to 0 and solve for x:
[tex]x-5=0\\x=5[/tex]
Putting x = 5, we get:
Y value of hole = [tex]g(x)=\frac{2x+1}{(x+4)^2}\\g(5)=\frac{2(5)+1}{(5+4)^2}\\g(5)=0.14[/tex]
Hole at (5, 0.14)
5. Intercepts
To get x-intercepts, we set y = 0 (g(x) = 0) and for y-intercepts we set x = 0.
x-intercepts:
[tex]0=\frac{2x+1}{(x+4)^2}\\2x+1=0\\2x=-1\\x=-\frac{1}{2}[/tex]
x-intercept [tex](-\frac{1}{2},0)[/tex]
y-intercepts:
[tex]y=\frac{2x+1}{(x+4)^2}\\y=\frac{2(0)+1}{(0+4)^2}\\y=\frac{1}{16}[/tex]
y-intercept [tex](0,\frac{1}{16})[/tex]
6. Domain
This is the set of allowed x-values of the function. We simply disregard any value that would make the denominator equal to 0.
So we have:
x - 5 = 0, x = 5
and
(x+4)^2 = 0, x = -4
Domain is the set of all real numbers x EXCEPT x = -4 and x = 5
Domain is [tex]{x|x\neq -4,5}[/tex]
tabitha defines a sphere as the set of all points equidistant from a single point. Is Tabitha's definition valid?
answer; it is valid because all spheres fit this definition, and figures that are not spheres do not fit this definition.
definition is valid since center is exactly 1radius away from any point on the outersurface.
other figures do not fit this defn
Answer:
Tabitha's defintion is valid.Step-by-step explanation:
Her definition is valid because the sphere is basically defined by its radius, which is the equidistant points towards a center. If points are not equidistant, then that's not a sphere.
Also, Tabitha is considering "a set of points" referring to infinite points on the surface of the sphere. The single point she mentioned is the center.
Therefore, Tabitha's definition is valid because she's considering all elements that define a sphere.
Ava put 10 spoons of sugar in 5 coffees. How many spoons of sugar does Ava put in one coffee
Answer:
2 spoonfuls of sugar in each coffee.
Step-by-step explanation:
If there are 10 spoonfuls of sugar in 5 coffees, simply divide 10 by 5. Then you find that for every 1 coffee, she puts 2 spoonfuls.
Answer:
Ava puts two spoons of sugar in each coffee.
Step-by-step explanation:
We can find this by dividing the total number of spoons of sugar by the total number of coffees.
10 spoons/5 coffees = 2 spoons per coffee
A line has a slope of -3 and y-intercept of 5. write the equation of the line in slope intercept. form and explain how you would use the slope and y-intercept to graph the equation.
Equation: y= mx + b
y = -3x +5
Graph the y intercept first.
Go down three times on the y axis.
Go across one because of -3/1 .
The equation of the line is y = -3x + 5. To graph the equation, plot the y-intercept and use the slope to find additional points on the line.
Explanation:
The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is -3 and the y-intercept is 5, so the equation of the line is y = -3x + 5. To graph the equation, start by plotting the y-intercept of (0, 5). Then use the slope to find additional points on the line. For every increase of 1 on the x-axis, the y-value decreases by 3. You can use this pattern to plot more points and draw a straight line connecting them.
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Takeru has 444 birdfeeders. It takes \dfrac43 3 4 ? start fraction, 4, divided by, 3, end fraction bags of birdseed to fill each feeder. What is the minimum number of bags of birdseed Takeru needs to fill all the feeders?
Answer:
6 bags
Step-by-step explanation:
HELP! Nine friends share 3 pumpkin pies equally. What fraction of a pumpkin pie does each friend get? Please explain or show your work! :)
Answer:
1/3 of a pie.
Step-by-step explanation:
Givens
There are 3 pies
There are 9 people
Answer
Each person gets 3/9 or 1/3 of a pie
So each pie is cut into thirds.
Multiplying Polynomials Investigation:Arnold has a 6ftx6ft piece of cardboard to make a open box by cutting equal size squares from each corner,folding up the resulting flaps,and taping at the corners.Your task is to label dimensions on a sketch with the same size variable cut from each corner.
- How does each variable expression relate to length,width,and height of the box when folded?
-Based upon the variables you used,write a product for the volume?
-expand the product to write a volume function?
- what domain makes sense for the volume?
guess and check values to find the size cut that produces a maximum volume
*lgth ( )width ( ) hght ( ) volume ( )
you have to have 5 guesses
i don't think so.....
sorry
This answer explains how to determine the volume of an open box created by cutting squares from each corner of a piece of cardboard, discussing the relations between variables, volume calculation, domain restrictions, and a guess-and-check method for maximizing volume.
Variables: In the open box scenario, let's assume the size of the square cut from each corner is 'x'.
Relation to Dimensions: After cutting and folding, the length of the box would be (6ft - 2x), the width would be (6ft - 2x), and the height would be 'x'.
Product for Volume: The volume formula is length x width x height. Substituting the expressions, we get V = x(6 - 2x)(6 - 2x).
Domain: The domain for the volume function would be 0 < x < 3 (as the size of the cut cannot exceed half of the side length).
Guess and Check: To find the maximum volume, you can test values within the domain like x = 1, 1.5, 2, 2.5, and 3 to determine the optimal cut size and corresponding dimensions and volume.
Calculate the Difference Quotient for f(x)=2x^2-3
Answer:
Calculate the Difference Quotient for f(x)=2x^2-3
Find f(x+h) and f(x), and plug these values into the difference quotient formula.
4x+2hPercy paid $24.10 for a basketball the price of the basketball was $22.99 what was the sales tax rate
To find the sales tax rate, you need to find what percentage of the base price the difference in cost is.
First, subtract 22.99 from 24.10:
24.1-22.99=1.11
Now, divide 1.11 by 22.99:
1.11/22.99=0.0483
Multiply 0.0483 by 100 to convert the decimal to a percentage:
0.0483*100=4.83
The sales tax rate was 4.83%.
Hope this helps!!
Find the are of a triangle (picture provided)
Answer:
B
Step-by-step explanation:
Use the Heron's formula for the area of the triangle:
[tex]A=\sqrt{p(p-a)(p-b)(p-c)},[/tex]
where a, b, c are lengths of triangle's sides and [tex]p=\dfrac{a+b+c}{2}.[/tex]
Since [tex]a=11.5,\ b=13.7,\ c=12.2,[/tex] then
[tex]p=\dfrac{11.5+13.7+12.2}{2}=18.7.[/tex]
Hence,
[tex]A=\sqrt{18.7(18.7-11.5)(18.7-13.7)(18.7-12.2)}=\sqrt{18.7\cdot 7.2\cdot 5\cdot 6.5}=\\ \\=\sqrt{11\cdot 1.7\cdot 9\cdot 4\cdot 0.2\cdot 5\cdot 5\cdot 1.3}=30\sqrt{11\cdot 1.7\cdot 0.2\cdot 1.3}=30\sqrt{4.862}\approx 66.1\ un^2.[/tex]
Answer:
Choice b is correct.
Step-by-step explanation:
We have given the sides of triangle.
a = 11.5, b = 13.7 and c = 12.2
We have to find the area of the triangle.
The formula to find the area of the triangle when three sides are given is:
A = √p(p-a)(p-b)(p-c)
where p = (a+b+c) / 2
p = (11.5+13.5+12.2)/2
p = 18.7
A = √18.7(18.7-11.5)(18.7-13,7)(18.5-12.2)
A = 30√4.862 units²
A≈ 66.1 units²
Please help a girl out (:
According to the rational root theorem, which answer is not a possible rational root of 4x^3+3x^2-2x+12=0?
A.) -4
B.) -1/3
C.) 1/2
D.) 3
Answer:
B.) -1/3
Step-by-step explanation:
According to the rational root theorem, rational roots will be of the form ...
±(divisor of the constant)/(divisor of the leading coefficient)
= ±(one of {1, 2, 3, 4, 6, 12})/(one of {1, 2, 4})
You will note that 3 is not among the possible denominators, hence -1/3 is not a possible rational root.
the answer is b cause its is correct
which is a true statement about 10 days of production?
A. Plant C is just beginning to produce actual widgets.
B. None of these plants is yet producing actual widgets.
C. Plant A is the closest to producing actual widgets.
Answer:
B. None of these plants is yet producing actual widgets.
Step-by-step explanation:
As we can see in the graph, the number of days is on the x axis, and the number of widgets at y axis.
At 10 days, no line is above the '0' means no one is producing widgets at 10 days point.
Since the y axis represents number of widgets produced, this means none of the plants have produced more than 0 widgets yet.
So, option B is the answer.
Given sin0=6/11 and sec 0<0 find cos0 and tan0 (picture provided)
Answer:
[tex]cos(0\°)=-\frac{\sqrt{85}}{11}[/tex]
[tex]tan(0\°) = -\frac{6}{\sqrt{85}}\\\\[/tex]
Step-by-step explanation:
We know by definition that:
[tex]cos ^ 2(x) = 1-sin ^2(x)[/tex]
We also know that:
[tex]tan(x) = \frac{sin(x)}{cos(x)}[/tex]
[tex]sec(x) = \frac{1}{cos(x)}[/tex]
Then we can use these identities to solve the problem
if [tex]sin(0\°) = \frac{6}{11}[/tex] then [tex]cos^2(0\°) = 1-(\frac{6}{11})^2[/tex]
[tex]cos(0\°) = \±\sqrt{\frac{85}{121}}\\\\cos(0\°)=\±\frac{\sqrt{85}}{11}[/tex]
As [tex]sec(x) <0[/tex] then [tex]cos(x) <0[/tex]. Therefore we take the negative root:
[tex]cos(0\°)=-\frac{\sqrt{85}}{11}[/tex]
Now that we know [tex]sin(0\°)[/tex] and [tex]cos(0\°)[/tex] we can find [tex]tan(0\°)[/tex]
[tex]tan(0\°) = \frac{sin(0\°)}{cos(0\°)}\\\\tan(0\°) = \frac{\frac{6}{11}}{\frac{-\sqrt{85}}{11} }\\\\tan(0\°) = -\frac{6}{\sqrt{85}}\\\\[/tex]
A game for $40 and the sales tax is two dollars what percent of the game price are you paying sales tax
Answer: 5%
Step-by-step explanation: In order to calculate the sales tax rate you divide the amount of the sales tax by the purchase price.
$2/40 = .05 = 5%
The interest rate is 5%.
An equation of a line through (0, 0) which is perpendicular to the line y=-4x + 3 has slope:
And y-intercept at:
perpendicular slopes are those that are flipped and opposite signs to the original slope
Has the marrying age of a man changed over the years? The United States Bureau of the Census takes a formal count of everyone in the U.S. every 10 years and has provided the following data that gives the median age of an American man at the time of his first marriage.
Year / Median Age
1910 / 25.1
1920 / 24.6
1930 / 24.3
1940 / 24.3
1950 / 22.8
1960 / 22.8
1970 / 23.2
1980 / 24.7
1990 / 26.1
2000 / 26.8
Determine the average rate of change in median age per year from 1950 to 1990.
a.) 0.0825 years of age per year
b.) 0.825 years of age per year
c.) 1.21 years of age per year
d.) -1.21 years of age per year
Answer:
a.) 0.0825 years of age per year
Step-by-step explanation:
By the given table,
The median age at the time of first marriage on 1950 = 22.8 years,
While, the median age on 1990 = 26.1 years,
Hence, the average rate of change in median age per year from 1950 to 1990
[tex]=\frac{22.8 - 26.1}{1950 - 1990}[/tex]
[tex]=\frac{-3.3}{-40}[/tex]
[tex]=0.0825\text{ years of age per year}[/tex]
That is, OPTION a) is correct.
Answer:
It is D
Step-by-step explanation:
got it right on edge
simplify the sum or difference -6√10+5√90
A. 9√10 (CORRECT ANSWER)
B. -9√10
C -39√10
D - 10
Answer:
A. [tex]9\sqrt{10}[/tex]
Step-by-step explanation:
The given expression is [tex]-6\sqrt{10}+5\sqrt{90}[/tex]
Remove the perfect square from the second radical.
[tex]=-6\sqrt{10}+5\sqrt{9\times10}[/tex]
[tex]=-6\sqrt{10}+5\sqrt{9} \times \sqrt{10}[/tex]
This implies
[tex]=-6\sqrt{10}+15\sqrt{10}[/tex]
[tex]=(-6+15)\sqrt{10}[/tex]
[tex]=9\sqrt{10}[/tex]
The correct choice is A
A triangle has a base of 8 cm and a height of 12 cm. What is the area of the triangle? Enter your answer in the box. Cm?
Answer:
The area is 48 cm^2
Step-by-step explanation:
The formula for area of a triangle is
A = 1/2 b*h
A = 1/2 * 8cm*12cm
A = 1/2 *96cm^2
A = 48 cm^2
The area is 48 cm^2
Answer:
A = 48 cm^2
Step-by-step explanation:
k12
If both coordinates of a point are negative,in which quadrantis the point located?
A certain drug is made from only two ingredients: compound A and compound B. There are 3 milliliters of compound A used for every 4 milliliters of compound B. If a chemist wants to make 533 milliliters of the drug, how many milliliters of compound B are needed?
Answer:
[tex]304\dfrac{4}{7}\ milliliters[/tex]
Step-by-step explanation:
If there are 3 milliliters of compound A used for every 4 milliliters of compound B, then we can denote that we use 3x milliliters of compound A and 4x milliliters of compound B to get 533 milliliters of the drug. Thus,
[tex]3x+4x=533,\\ \\7x=533,\\ \\x=\dfrac{533}{7}\ milliliters.[/tex]
Hence, a chemist must take
[tex]4\cdot \dfrac{533}{7}=\dfrac{2132}{7}=304\dfrac{4}{7}\ milliliters[/tex]
of compound B.
Answer:
228.43 ml
Step-by-step explanation:
The ratio of compound A to compound B will be; 4: 3
4:3 is the same as 4x:3x where 4x is compound A and 3x is compound B.
We can solve for "x":
If amount of compound A is 4x and compound B is 3x;
Then; 4x + 3x = 533
7 x = 533
x = 533/7
Then amount of compound B is 3x = 3(533/7)
= 228.43 ml
A figure is translated using the rule (x, y) → (x – 3, y + 6). Which describes how the figure is moved? left 3 units and down 6 units right 3 units and down 6 units left 6 units and down 3 units left 3 units and up 6 units
Answer:
left 3 units and up 6 units
Step-by-step explanation:
we know that
The rule of the translation is equal to
[tex](x,y)------> (x-3,y+6)[/tex]
That means
(x-3)-----> The figure is moved 3 units to the left, because the number is negative
(y+6)----> The figure is moved 6 units up because the number is positive
Answer:
left 3 units and up 6 units
Step-by-step explanation:
Water is leaking out of an inverted conical tank at a rate of 8300.0 cubic centimeters per min at the same time that water is being pumped into the tank at a constant rate. The tank has height 13.0 meters and the diameter at the top is 3.5 meters. If the water level is rising at a rate of 15.0 centimeters per minute when the height of the water is 3.0 meters, find the rate at which water is being pumped into the tank in cubic centimeters per minute. Note: Let "R" be the unknown rate at which water is being pumped in. Then you know that if V is volume of water, dV/dt=R−8300.0. Use geometry (similar triangles?) to find the relationship between the height of the water and the volume of the water at any given time. Recall that the volume of a cone with base radius r and height h is given by 1/3πr^2h.
this is super confusing
In a city school, 60% of students have blue eyes, 55% have dark hair, and 35% have blue eyes and dark hair. What is the probability (rounded to the nearest whole percent) that a randomly selected student will have dark hair, given that the student has blue eyes?
Hint:
P(A|B)=P(A∩B) / P(B)
64%
58%
80%
20%
Answer:
58%
Step-by-step explanation:
This is a problem of conditional probability.
Let A represent the event that student has dark hair.
So P(A) = 55% = 0.55
Let B represents the event that student has blue eyes.
So, P(B) = 60% = 0.60
Probability that student has blue eyes and dark hairs = P(A and B) = 35% = 0.35
We are to find the probability that a randomly selected student will have dark hair, given that the student has blue eyes. Using the given formula and values, we get:
[tex]P(A|B)=\frac{P(A \cap B)}{P(B)}\\\\ P(A|B)=\frac{0.35}{0.60}\\\\ P(A|B)=0.58[/tex]
Therefore, there is 0.58 or 58% probability that the student will have dark hairs, given that the student has blue eyes.
If I have 2 quarters 12 dimes and 23 pennies how many more pennies will I need in order to have a toldal of $2.00
Answer:
You will need 7 more pennies.
Step-by-step explanation:
Answer:
7 more pennies.
Step-by-step explanation:
Quarters are .25 each and you have 2 so that is .50.
Dimes are .10 each and you have 12 so that is 1.20
Pennies are .01 each and you have 23 so that is .23.
Added together and you get 1.93. So all you need is 7 pennies to get 2 dollars.
Two geometry questions! Double the points thanks in advance!
2x-4+50=100
2x-4=50
2x=54
x=27º
2x+4x=90
6x=90
x=15º
1. Simplify 100 = (2x - 4) + 50
x = 27
2. Complementary mean the angles equal 90 degrees when added, so
90 = 2x + 4x
x = 15
Identify the area of a regular nonagon with side length 18 cm. Round to the nearest tenth. HELP ASAP PLEASE!!
Answer:
[tex]A=2,002.9\ cm^{2}[/tex]
Step-by-step explanation:
we know that
The area of a regular polygon is equal to
[tex]A=\frac{1}{2}rP[/tex]
where
r is the apothem
P is the perimeter
step 1
Find the perimeter
The perimeter of a regular nonagon is
[tex]P=ns[/tex]
where
n is the number of sides (n=9)
s is the length side (s=18 cm)
substitute
[tex]P=9*18=162\ cm[/tex]
step 2
Find the apothem
The apothem in a regular polygon is equal to
[tex]r=\frac{1}{2}(s)cot(180\°/n)[/tex]
we have
[tex]s=18\ cm[/tex]
[tex]n=9[/tex]
substitute
[tex]r=\frac{1}{2}(18)cot(180\°/9)[/tex]
[tex]r=9cot(20\°)=24.73\ cm[/tex]
step 3
Find the area of the regular nonagon
[tex]A=\frac{1}{2}rP[/tex]
substitute
[tex]A=\frac{1}{2}(24.73)(162)=2,002.9\ cm^{2}[/tex]
Me banks left work at 5:15cpm it took him 1 1/4 hours to drive home at what time did me banks arrive home
Answer:
the answer would be 6:30 pm
Step-by-step explanation:
if you left work at 5:15 and it took 1 1/4 min to get home
you would
find 1/4 witch would be 15 min because 60/4= 15
then add 1:15 to 5:15
1:15 + 5:15 = 6:30 pm
you arrived home at 6:30 pm
Mr. Banks would get home at 6:30 PM after leaving work at 5:15 PM and driving for 1 hour and 15 minutes.
The student asked what time Mr. Banks would arrive home if he left work at 5:15 PM and took 1 and 1/4 hours to drive home. To solve this, we need to add the travel time to the departure time. Since 1 and 1/4 hours is the same as 1 hour and 15 minutes, we simply add this to 5:15 PM. Adding 1 hour to 5:15 PM, we get 6:15 PM. Then, adding the remaining 15 minutes, we get 6:30 PM. This means Mr. Banks would arrive home around 6:30 PM.
The figures below are similar. Compare the smaller figure to the larger. Which of the following is the ratio of the perimeters of the figures?
Answer: first option
Step-by-step explanation:
As you can see in the figures shown in the image attached, the lenght of a side of the smaller figure is 2 inches and the the lenght of a side of the larger figure is 4 inches.
Therefore, you can find the ratio as following:
[tex]ratio=\frac{2in}{4in}[/tex]
Now, you must reduce the fraction. Therefore, you obtained that the ratio of the perimeters of the figures is:
[tex]ratio=\frac{1}{2}[/tex]
Which can be written in the following form:
[tex]ratio=1:2[/tex]
Then, the answer is the first option.
50 POINTS PLEASE HELP ME!!!!!!!! HURRY!!!!
Evaluate
6!
8P5
12C4
what are we supposed to evaluate, here? i dunno what your asking us to do
Lori bought gifts for her 3 borthers and 6 cousins. She bought 4 toy cars for each
Answer: 36 toy cars
Step-by-step explanation: If Lori bought gifts for her 3 brothers and 6 cousins then she bought gifts for 9 people (3+6). Since she bought 4 toy cars for each of them she bought 36, which is calculated by multiplying 9 x 4.
9 x 4 = 36
Lori bought a total of 36 gifts for her three brothers and six cousins since she bought four gifts for each of them. This was calculated by multiplying the total number of recipients (3+6) by the number of grants each person got (4).
Explanation:The question is asking how many gifts Lori bought in total. Since Lori bought four toy cars for each of her three brothers and six cousins, we need to multiply the total number of recipients by the number of gifts per person. This gives us (3 brothers + 6 cousins) * 4 skills = 36. So, Lori bought a total of 36 grants.
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