Answer:
1234567890
Step-by-step explanation:
1234567890-zxhjk
write the quadratic question f(x)=3x^2-24x+49 in the form of f(x)= a(x-h)^2+k
Answer:
f(x) = 3(x -4)^2 +1
Step-by-step explanation:
Usually you start by factoring the leading coefficient from the first two terms:
f(x) = 3(x^2 -8x) +49
Now, you add the square of half the x-coefficient inside parentheses, and subtract the same quantity outside.
f(x) = 3(x^2 -8x +(-4)^2) -3(-4)^2 +49
= 3(x -4)^2 -48 +49
f(x) = 3(x -4)^2 +1 . . . . . . . . the vertex form you desire
Twelve friends share 4 bread loaves equally. What fraction of bread loaf does each friend get
Answer:
1/3.
Step-by-step explanation:
Since there are 12 friends and 4 bread loaves, you would divide 4/12 by 4 which is 1/3.
Analyze the data set below. Which of the following statements are true? Select all that apply.
In analyzing the data set and the corresponding box plot, we can determine the accuracy of several statements. It is true that 25 percent of the data are at most five. However, it is false to say that there is the same amount of data from 4-5 as there is from 5-7. Additionally, there are data values of three, but it is false to say that 50 percent of the data are four.
Explanation:A. True – the first quartile (Q1) is equal to the 25th percentile, which means that 25 percent of the data fall at or below Q1. If Q1 is at most five, then at least 25 percent of the data is at most five.
B. False – the second quartile (Q2) is equal to the median, which separates the data into two halves. If there is the same amount of data from 4-5 as there is from 5-7, then the median would not be in the middle of the data.
C. False – there are data values of three, as shown by the lower whisker in the box plot.
D. False – the second quartile (Q2) is equal to the median, which is the value that separates the data into two halves. If 50 percent of the data are four or less, then the median would be four or less.
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I have no clue how to do 2.3
Answer:
A D and E are the answers
Step-by-step explanation:
The general formula is n * CD so all you do is multiply n times the original length.
A is true. 3/2 * 12 = 36/2 = 18 True.
============
B is not true 4*12 = 48 not 3
B would be true if n = 1/4
1/4 * 12 = 3
============
C is not true 8*12 = 96 not 20
============
D is true 2 * 12 = 24
============
E is true 3/4 * 12 = 36/4 = 9
A D and E are the answers
table Given the graph of a linear function, identify the steps used to find the initial value. Check all that apply. Find the rate of change using rise over run. Find corresponding y values when x = 6, x = 7, and x = 8. Then plot the points to finish the line. Find corresponding y values when x = 2, x = 1, and x = 0. Then plot the points to finish the line. The initial value corresponds to the y value when x = 1. The initial value corresponds to the y value when x = 0.
To find the initial value of a linear function from its graph, examine the y-intercept where x=0, and use the slope to verify the linearity. The initial value is the y value at x=0.
Explanation:Identifying the initial value of a linear function from its graph involves examining the y-intercept, where x=0. The steps to find it include:
Finding the rate of change using rise over run. This step helps to confirm the linearity and slope of the function.Finding corresponding y values when x = 0. Since the initial value, also known as the y-intercept, corresponds to the value of y when x = 0, this is the most direct way to ascertain the initial value.The notion that the initial value corresponds to the y value when x = 1 is incorrect for linear functions. The initial value or y-intercept is always found where x = 0. Adjustments or predictions for other values of x, such as x = 1, 2, 6, 7, or 8, involve using the line's slope or rate of change but do not directly determine the initial value.
Answer:
its a, c, e
hope this helps!!
What is the measure of the inscribed angle ABC if the measure of the arc, which this angle intercepts is: 48, 57, 90, 124, 180.
➷ The rule is:
The inscribed angle would be half the measure of the intercepted arc
If the arc was 48, the inscribed angle = 48/2 = 24 degrees
If the arc was 57, the inscribed angle = 57/2 = 28.5 degrees
If the arc was 90, the inscribed angle = 90/2 = 45 degrees
If the arc was 124, the inscribed angle = 124/2 = 62 degrees
If the arc was 180, the inscribed angle = 180/2 = 90 degrees
✽➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
↬ ʜᴀɴɴᴀʜ ♡
I hope you understand it well :)
The measure of an inscribed angle is half the measure intercepted arc.
With that rule
If the arc is 48 the inscribed angle would be [tex]\frac{48}{2}=24[/tex]If the arc is 57 the inscribed angle would be [tex]\frac{57}{2}=28.5[/tex]If the arc is 90 the inscribed angle would be [tex]\frac{90}{2}=45[/tex] If the arc is 124 the inscribed angle would be [tex]\frac{124}{2}=62[/tex]If the arc is 180 the inscribed angle would be [tex]\frac{180}{2}=90[/tex]Hope this helps :)
If you have a doubt just reply over here, I would be happy to help you further :)
2.6 repeated simplified as a fraction Please help asap!!!
Answer:
8/3
Step-by-step explanation:
Let S represent the value of 2.666...(repeated). Then 10S will have the value 26.666...(repeated). Subtracting S from 10S, we have ...
10S -S = 26.666... - 2.666... = 24
9S = 24
S = 24/9 = 8/3
The improper fraction equivalent of 2.666...(repeated) is 8/3.
_____
In general, if the number of repeated digits is n, you do this procedure multiplying the number by 10^n before you do the subtraction. The result is a fraction with (10^n)-1 as a denominator. That is, for a 2-digit repeat, the denominator will be 99; for a 6-digit repeat, 999999.
Knowing this, you can immediately recognize that 0.6...(repeated) = 6/9 = 2/3. Then your number 2.666...(repeated) is 2 2/3 = 8/3.
The repeating decimal 2.6 (2.66...) can be simplified as a fraction by setting it equal to a variable, multiplying by a power of 10 to eliminate the decimal, subtracting the original equation, and solving for the variable. This process results in the simplified fraction 8/3.
Explanation:The number 2.6 repeated refers to the number where the digit 6 repeats indefinitely. To simplify it as a fraction, we can do the following steps:
Let's call the repeating decimal x. So, x = 2.66...Next, to eliminate the decimal, you multiply by a power of 10. Here, because there is one repeating digit, we multiply by 10. So, 10x = 26.66...Subtract the two equations: 10x - x = 26.66... - 2.66..., which simplifies to: 9x = 24.Finally, solve for x by dividing both sides by 9, you get x = 24/9. This fraction can be simplified to 8/3.Learn more about Repeating Decimals here:https://brainly.com/question/31325113
The volume of a square prism is 144x^3 +216x^2 +81x
What is an expression that could describe the perimeter of one of the prism's square faces? Please state the steps in word form. Will give 25 points
Answer:
Equation for the perimeter of prism's square face: 16x + 12
Step-by-step explanation:
Volume of Square prism = Length * Width * Height
= 144 x^3 + 216 x^2 +81 x
taking 9x common = 9x( 16 x^2 + 24 x + 9)
= 9x ( (4x)^2 + 2(4x)(3) + (3)^2 )
= 9x ( 4x+3)^2
so the length is 9x, width is 4x+3 and height is 4x+3
Now, Perimeter of prism's square face = 2* Width + 2 * Height
= 2* (4x+3) + 2* (4x+3)
= 8x +6 + 8x + 6
= 16x +12
Final answer:
Factoring the volume expression of the square prism reveals the square's base area. Once identified, the perimeter can be found by multiplying one side length by four.
Explanation:
The volume V of a square prism can be expressed as the product of the area A of its square base and its height h, so V = A × h. Given the polynomial expression for the volume, we can factor it to find the square base area. The given volume is 144x³ + 216x² + 81x. Factoring out the greatest common factor of 9x, we get 9x(16x² + 24x + 9). Recognizing this as a perfect square trinomial, we can further factor it to 9x(4x + 3)². Therefore, the area A of the base is (4x + 3)². To find the perimeter P of the square base, we take four times one side of the square, which is P = 4(4x + 3). Simplifying, we get P = 16x + 12.
Georgia will use the pattern shown to make a square pyramid out of cardboard. The square pyramid will not have a bottom. How much cardboard will she need if a = 14 in. and b = 9 in.? PLEASE HELP
Answer:
252 square inches
Step-by-step explanation:
Georgia needs 4 triangles, each of which has a base of 9 inches and a height of 14 inches. The area of a triangle is ...
A = (1/2)bh
so one face of Georgia's pyramid will have an area of ...
A = (1/2)(9 in)(14 in) = 63 in^2
Then all four faces will have a total area of ...
(63 in^2) · 4 = 252 in^2
_____
Comment on the pattern
The pattern shown includes the base of the pyramid. The problem text says the base is not included. We have assumed that the base is not included. (For Georgia's pyramid, a different pattern would be more to the point: see attachment.)
252 square inches of cardboard she needed if a = 14 in. and b = 9 in
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
The square pyramid will not have a bottom.
We have to find the lateral surface area as the base area is not included.
Georgia needs 4 triangles, each of which has a base of 9 inches and a height of 14 inches.
The area of lateral face is A = (1/2)bh
A = (1/2)(9 in)(14 in)
= 63 square inches
There are four faces so, 4×63 = 252 square inches
Lateral surface area is 252 square inches
Hence, 252 square inches of cardboard she needed if a = 14 in. and b = 9 in
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At the movie theater, child admission is $5.10 and adult admission is $9.10. On Monday, 151 tickets were sold for a total sales of $1030.10. How many adult tickets were sold that day?
Answer:
65
Step-by-step explanation:
Let "a" represent the number of adult tickets sold. Then the number of child tickets sold is 151-a and the total revenue for the day is ...
9.10·a + 5.10·(151-a) = 1030.10
4a = 260 . . . . . . subtract 770.10
a = 65 . . . . . . . . . divide by 4
The number of adult tickets sold on Monday was 65.
_____
Check
65 adult tickets and 86 child tickets will produce a revenue of ...
65·9.10 + 86·5.10 = 591.50 + 438.60 = 1030.10 . . . . answer checks OK
Answer: 65 adult tickets were sold that day
Step-by-step explanation:
Let's call:
c: number of child tickets sold on Monday.
a: number of adult tickets sold on Monday.
Set up the following system of equations:
[tex]\left \{ {{c+a=151} \atop {5.10c+9.10a=1030.10}} \right.[/tex]
You can solve it by Substitution method, as following:
- Multiply the first equation by -5.10
- Add both equations.
- Solve for a.
Then:
[tex]\left \{ {{-5.10c-5.10a=-770.1} \atop {5.10c+9.10a=1030.10}} \right.\\---------\\4a=260\\a=65[/tex]
Which of the following are examples of exponential decay?
A: The population of a Florida is increasing by 43% every year.
B: The pesticide DDT has a half-life of 15 years.
C: March Madness has 64 teams in the bracket. Each round, half the teams are eliminated.
D: After an antibiotic is added to a culture of bacteria, the number of bacteria is reduced by half every three hours.
E: A tree frog population doubles every three weeks.
Answer:
B: The pesticide DDT has a half-life of 15 years.C: March Madness has 64 teams in the bracket. Each round, half the teams are eliminated.D: After an antibiotic is added to a culture of bacteria, the number of bacteria is reduced by half every three hours.Step-by-step explanation:
Exponential decay describes a situation in which the dependent variable is reduced by the same factor when the independent variable is increased by the same amount.
A — the population is increasing, not being reduced
B — the amount is cut in half when time increases by 15 years (exp. decay)
C — the number of teams is cut in half when the number of rounds increases by 1 (exp. decay)
D — the amount is cut in half when time increases by 3 hours (exp. decay)
E — the population is increasing, not being reduced
10 is 20% of, please answer
Answer:
50
Step-by-step explanation:
20% is the same as 0.2 times something.
So you can create the equation 0.2x = 10. The solution of this equation is x=50.
A cubical tank with an edge length of 20 cm is filled with 3.75 liters of water. How much more water is needed to fill the tank completely? Give your answer in liters.
Answer:
4.25 Liters
Step-by-step explanation:
Edge of Cubical tank
= 20 cm
= 20 (0.01 m)……………..1 meter = 100 cm
= 0.2 m
Volume of Tank
= ( Edge ) ^ 3
= ( 0.2 m ) ^3
= 0.008 m^3
= 8 liters…………….. 1 m^3 = 1000 Liters
Volume required to fill the tank
= 8 - 3.75
= 4.25 Liters
A power line extends from a light pole 43 meters to the ground and makes an angle of 60 degrees with the ground. To the nearest tenth of a meter, how tall is the light pole?
Answer: 37.2 meters
Step-by-step explanation:
The triangle shown in the image attached is a right triangle.
Therefore, to calculate the height of the light pole (x), you can apply the proccedure shown below:
-Apply [tex]sin\alpha=\frac{opposite}{hypotenuse}[/tex]
-Substitute values.
-Solve for the height of the light pole (x).
Then you obtain the following result:
[tex]sin\alpha=\frac{opposite}{hypotenuse}\\\\sin(60\°)=\frac{x}{43}\\\\x=43*sin(60)\\x=37.2[/tex]
Answer:
37.2 meters
Step-by-step explanation:
Since this is the right triangle, the side that is 43 m is the hypotenuse.
Note: the side opposite of 90 degree angle is hypotenuse.
Also, we want the height of the pole, which is the side that is "opposite" to the angle 60 degree given.
Now, which trigonometric ratio relates "opposite" and "hypotenuse"??
It is SINE. Now we can write and solve (let the height of the pole be h):
[tex]Sin(\theta)=\frac{Opposite}{Hypotenuse}\\Sin(60)=\frac{h}{43}\\h=Sin(60)*43\\h = 37.24[/tex]
The light pole is 37.24 meters tall, to the nearest tenth, it is 37.2 meters
i need help with this problem please
Answer:
(a) reduction
(b) 1/2
Step-by-step explanation:
The image figure A'B'C'D' is smaller than the original figure ABCD, so the dilation is a reduction.
Each of the points A'B'C'D' is half as far from the origin as the original points ABCD, so the scale factor is 1/2.
_____
Draw lines C'C and D'D. You will see they meet at the origin, which is the center of dilation. Then look at how far the points are along those lines. C' is one grid square diagonal along the line; C is 2 grid square diagonals along that line, so is twice as far from the origin. That is, C' is 1/2 the distance of C, so represents a reduction by a scale factor of 1/2.
The same distance considerations are observed along the line D'D. The point D' is the diagonal of a 2x1 rectangle from the origin (A distance of √5.) The point D is the diagonal of a 4x2 rectangle from the origin, so is twice as far. Once again D' is 1/2 the distance of D, so represents a reduction by a factor of 1/2.
At a gas station the price of gas is $2.40 a gallon. Draw a graph to represent the relationship between the cost of gas and the volume purchase. Also write an equation using Y= MX + B form.
Answer:
Part A) The graph in the attached figure
Part B) [tex]y=2.40x[/tex]
Step-by-step explanation:
Let
y------> the price of gas
x-----> the volume of gas purchase
we know that
The relationship between the cost of gas and the volume purchase represent a direct variation and remember that a relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form
In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin
In this problem the constant of proportionality k is equal to
[tex]m=k=2.40\frac{\$}{gallon}[/tex]
and the y-intercept b is equal to zero because the line passes through the origin
[tex]b=0[/tex]
therefore
the linear equation is
[tex]y=2.40x+0\\y=2.40x[/tex]
using a graphing tool
see the attached figure
Please help it would be a greatly supported.
Answer:
D. N = w² + 8w + 12
Step-by-step explanation:
The current size is w by w+4, so the area is ...
A = w(w+4)
When each dimension is increased by 2, the new size is (w+2) by (w+4+2). The latter dimension can be simplified to (w+6). Now, the new area is ...
N = (w+2)(w+6) = w² +8w +12 . . . . . . . matches choice D
2 2/7 divided 2 1/2=
Answer: [tex]\frac{32}{35}[/tex]
Step-by-step explanation:
We need to convert the mixed numbers into fractions.
The new numerator will be the sum of the numerator of the fractional part and the product obtained by multiplying the denominator of the fractional part by the whole number part.
The new denominator will the the same denominator of the fractional part.
Then:
[tex]2\ \frac{2}{7}=\frac{2+(2*7)}{7}=\frac{16}{7}[/tex]
[tex]2\ \frac{1}{2}=\frac{1+(2*2)}{2}=\frac{5}{2}[/tex]
Dividing the fractions, we get:
[tex]\frac{\frac{16}{7}}{\frac{5}{2}}=\frac{16*2}{7*5}=\frac{32}{35}[/tex]
Please help me! I will give brainliest to the person who answers correctly.
In triangle XYZ provide the following ratios:
sin X ____ (express in fractional form, don't simplify)
XY ____ (to the nearest tenth)
cos X ____ X (express in fractional form, don't simplify)
tan X ____ (express in fractional form, don't simplify)
Thanks!
Answer:
sin(X) = 6/7.5XY = 4.5cos(X) = 4.5/7.5tan(X) = 6/4.5Step-by-step explanation:
It is convenient to use the Pythagorean theorem to find XY to start with. That theorem tells you ...
XZ² = YZ² + XY²
Solving for XY, you find ...
XY² = XZ² - YZ²
XY = √(XZ² - YZ²) = √(7.5² -6²) = √(56.25 -36) = √20.25
XY = 4.5
The mnemonic SOH CAH TOA is very helpful here. It reminds you that ...
Sin = Opposite/Hypotenuse
sin(X) = 6/7.5
Cos = Adjacent/Hypotenuse
cos(X) = 4.5/7.5
Tan = Opposite/Adjacent
tan(X) = 6/4.5
_____
Comment on the triangle and ratios
The side lengths of this triangle are in the ratios ...
XY : YZ : XZ = 3 : 4 : 5
If you recognize that the given sides are in the ratio 4 : 5, this tells you that you have a "3-4-5" right triangle with a scale factor of 1.5. At least, you can find XY = 1.5·3 = 4.5 with no further trouble.
The trig ratios could be reduced to sin(X) = 4/5; cos(X) = 3/5; tan(X) = 4/3, but the wording "don't simplify" suggests you want the numbers shown on the diagram, not their reduced ratios.
In the expression (x+y)^8, if x=0.3 and y=0.7 , what is the numerical value of the third term?
Answer:
0.01000188
Step-by-step explanation:
The third term is ...
8C2·x^6·y^2 = 28 x^6 y^2
Putting in the given values for x and y, we get ...
28·3^6·7^2·10^-8 = 1000188×10^-8 = 0.01000188
_____
8C2 = 8!/(2!·(8-2)!) = 8·7/(2·1) = 28
tried to solve but failed
Try suggested solution, note, the answers are marked with green colour.
The probability for drawing marbles without replacement varies with each draw as both the available and desired outcomes decrease. By applying this rule, the probabilities can be calculated for drawing 5 marbles with all, exactly two, or none being red.
To answer these questions, we first need to know the total number of marbles in the bag. The bag contains 5 red, 8 white, and 10 blue marbles, yielding a total of 23 marbles. When answering probability questions when drawing without replacement, the denominator (total possible outcomes) decreases with each draw, while the numerator (desired outcomes) remains constant if the kind of object drawn remains the same and decreases otherwise.
For the first question, we're drawing 5 marbles all of which are red. The probability is calculated as follows: (5/23) * (4/22) * (3/21) * (2/20) * (1/19). This is because with each draw, both the total number of marbles and the number of red marbles decrease by 1.
For the second question, we're drawing 5 marbles, 2 of which are red. This can happen in various ways (e.g., red, red, not red, not red, not red, etc.). Each of these sequences has a probability and we sum these probabilities. Assuming we draw 2 red then 3 not red, the probability is: (5/23) * (4/22) * (18/21) * (17/20) * (16/19). The 18 in the third fraction is derived from the total number of non-red marbles (8 white + 10 blue).
For the last question, we're drawing 5 marbles, none of which are red. The probability is: (18/23) * (17/22) * (16/21) * (15/20) * (14/19), similar to the previous example, we only consider non-red marbles.
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The probable question may be:
A bag contains 5 red marbles, 8 white marbles, and 10 blue marbles. You draw 5 marbles out at random, without
replacement. What is the probability that all the marbles are red?
The probability that all the marbles are red is _____
What is the probability that exactly two of the marbles are red?
The probability that exactly two of the marbles are red is _______
What is the probability that none of the marbles are red?
The probability of picking no red marbles is __________
Consider the points (3, 4) and (−3, 4). When the two points are compared, which statement is NOT TRUE? A) The y-coordinates have the same value. B) The x-coordinates have the same absolute value. C) The x-coordinates are opposite numbers. D) Both points are 4 units above the y-axis.
Answer:
A) The y-coordinates have the same value.
Step-by-step explanation:
Answer:
D) Both points are 4 units above the y-axis.
Step-by-step explanation:
Consider the points (3, 4) and (−3, 4). When the two points are compared, which statement is NOT TRUE?
A) The y-coordinates have the same value. TRUE. The y-coordinates have the value 4.
B) The x-coordinates have the same absolute value. TRUE. 3 and -3 have the same absolute value, |-3| = |3| = 3.
C) The x-coordinates are opposite numbers. TRUE. 3 and -3 are opposite numbers.
D) Both points are 4 units above the y-axis. NOT TRUE. Both points are 4 units above the x-axis.
Given: m
KL
=25°, m
MJ
=85°
Find: m∠MEJ
Answer:
30°
Step-by-step explanation:
If the measure of the arc KL is 25°, then the central angle KOL has measure 25° and the inscribed angle KML subtended on the arc KL has the measure 12.5°.
If the measure of the arc MJ is 85°, then the central angle MOJ has measure 85° and the inscribed angle MLJ subtended on the arc MJ has the measure 42.5°.
Thus, the measure of the angle ELM is 180°-42.5°=137.5°.
Consider triangle EML. In this triangle,
m∠MEL=180°-137.5°-12.5°=30°.
Thus, m∠MEJ=30°.
Answer:
30°
Step-by-step explanation:
x=(a-b)/2 because of secants exterior angles
x=(85-25)/2 Substitution
x=60/2 Algebra
x=30° Answer
Find the zeroes of the following equation:
1/x = x - 1
What is special about one of the zeroes?
Answer: [tex]\bold{x=\dfrac{1\pm \sqrt5}{2}}[/tex]
both zeros are irrational numbers
Step-by-step explanation:
Note: The question would have made more sense if if it was 2/x = x - 1 but I will answer it as written.
[tex]\dfrac{1}{x}=x-1\qquad \text{Restriction: }x\neq 0\\\\\\\text{Cross multiply, simplify, and set equal to zero:}\\1=x(x-1)\\\\1=x^2-x\\\\0=x^2-x-1\\\\\\\text{This is not factorable so you will need to use Quadratic Formula:}\\\\x=\dfrac{-(-1)\pm \sqrt{(-1)^2-4(1)(-1)}}{2(1)}\\\\\\x=\dfrac{1\pm \sqrt5}{2}[/tex]
Please help asap!!!!
Answer:
465.988 mph
Step-by-step explanation:
The two speed vectors form two sides of a triangle. Their included angle is 45°, so the law of cosines can be used to find the resultant magnitude x.
x^2 = 500^2 +50^2 -2·500·50·cos(45°) ≈ 217,144.66
x ≈ √217,144.66 ≈ 465.988 . . . . miles per hour
_____
You may find you need to round the answer to the nearest whole number.
How do i do this question
Answer:
A. The dilated line lies on the original line.
Step-by-step explanation:
Dilation changes sizes, but not slopes or angles. The dilated line is guaranteed to have the same slope as the original.
The center of dilation is "invariant" (doesn't move) as a result of the dilation. Here, the point (3, 0) is the center of dilation. It is the x-intercept of the original line, so will also be on the dilated line.
The dilated line has the same slope as the original and goes through a point that the original line goes through. Hence it lies on the original line.
_____
How do you do this question?
1. make use of the properties of dilation, as we have done above.
2. plot some points on the original line—(0, 3) and (3, 0) are the intercepts—apply the dilation, and see where the line goes. (You will find (0, 3) ⇒ (-6, 9), and (3, 0) ⇒ (3, 0). Both are on the original line.)
Two students use different methods to solve this multiplication problem: 2/5 x -15 5/8
Answer:
see attachment for answers and correction
Step-by-step explanation:
Your answer is correct for Wyatt.
The missing blanks for Abigail are filled with the integer part and the fractional part of the mixed number Abigail started with.
___
Beware signs. In this problem -6 + 1/4 is not the same as -6 1/4.
someone please help me !!
Answer: Y=-13/4 + 4
Hope this helps! :)
sketch the asymptotes and graph the function y=4/(x-1)+5
Answer:
Step-by-step explanation:
The function to be analyzed is:
[tex]y = \frac{4}{x-1}+5[/tex]
This function has a vertical and a horizontal asymptote. The vertical asymptote is located where discontinuity exist. That is:
[tex]x = 1[/tex]
Besides, the horizontal asymptote coincides with the limit of function, which is:
[tex]\lim_{x \to \pm \infty} \left(\frac{4}{x-1} + 5\right)[/tex]
[tex]\lim_{x \to \infty} \frac{4}{x-1} + \lim_{x \to \infty} 5[/tex]
[tex]L = 0 + 5[/tex]
[tex]L = 5[/tex]
The horizontal asymptote is:
[tex]y = 5[/tex]
The function and the asymptotes are presented in the image attached below.
Bradley made a house for his dog, Bowser, out of wood with a cube base and a triangular prism top. The dimensions of the dog house are a = 5 feet, b = 1 foot, and c = 2.7 feet.
Note: Figure is not drawn to scale.
If Bradley plans to paint the outside of the dog house blue, not including the bottom, how many square feet of paint will he use?
A.
182 square feet
B.
157 square feet
C.
129.5 square feet
D.
132 square feet
Answer: 132 Square Feet
Step-by-step explanation:
Answer:
132
Step-by-step explanation: