Quadrilateral ABCD is inscribed in a circle with m<A = (x2)°, m<B = (7x - 10)°,
and
m<C = (3x)°.
What is m<D?
Answers
Answer:
106°
Step-by-step explanation:
A quadrilateral inside a circle is a cyclic quadrilateral.
It means that the angles opposite are supplementary (add up to 180).
If we draw the quadrilateral ABCD, the angles A and C are supplementary and the angles B and D are supplementary.
Since we know A and C, we can write:
A + C = 180
x^2 + 3x = 180
x^2 +3x - 180 = 0
(x+15)(x-12) = 0
x= -15, or x = 12
Now, if we put x = -15, some angles become negative, so we disregard it and take x = 12.
Now finding B:
B = 7x - 10
B = 7(12) - 10
B = 74
We also know that B + D = 180, so:
B + D = 180
74 + D = 180
D = 180 - 74 = 106
Related Questions
Leila has $360 in twenty-dollar bills. How many twenty-dollar bills does she have?
Answers
18 $20 Dollar Bills
5 Bills In 100
10 Bills In 200
15 Bills In 300
18 Bills In 360
select the equation of the line that passes through the point (3,-1) and is parallel to the line on the graph
Answers
ANSWER
y=-1
EXPLANATION
The given line in the graph has equation
[tex]y = 2.5[/tex]
This line is a horizontal line.
All horizontal line has a slope of 0.
Let the equation of the line that is parallel to this line be
[tex]y = mx + b[/tex]
The slope of this line must also be zero.
We substitute the slope, m=0 and the point (3,-1) into this equation to get:
[tex] - 1 = 0(3) + b[/tex]
[tex] \therefore \: b = 0[/tex]
Hence the required equation is
[tex]y = - 1[/tex]
ANSWER
y= -1
Step-by-step explanation:
The given line in the graph has equation
This line is a horizontal line.
All horizontal line has a slope of 0.
Let the equation of the line that is parallel to this line be
The slope of this line must also be zero.
We substitute the slope, m=0 and the point (3,-1) into this equation to get:
Hence the required equation is
Which statistic gives the most meaningful information about the central tendency of the data {23, 25, 26, 26, 27, 29, 29, 30, 450, 450, 450}?
Answers
Answer:
The median. Since there are some values in the data set that are arger than most, if you used the mean, the mean would not be a very accurate representation of the data set. When using median, the large numbers do not greatly effect the data set.
Step-by-step explanation:
An Easter basket contains eggs of three different colors. Find the total number of eggs in the basket if 2 7 of all eggs are green, 1 4 of all are blue and the rest 26 eggs are red.
Answers
Answer:
Total number of eggs in basket = 56
Step-by-step explanation:
Let z be the total number of eggs
Green eggs = [tex]\frac{2}{7}[/tex] × z ........1
Blue eggs = [tex]\frac{1}{4}[/tex] × z .......2
Rest of eggs = 26 ........3
The addition of 1, 2 and 3 is equal to z
[tex]\frac{2}{7}[/tex] × z + [tex]\frac{1}{4}[/tex] + 26 = z
[tex]\frac{8z + 7 z}{28}[/tex] + 26 = z ∵GCF for 4 and 7 is 28
[tex]\frac{15z}{28}[/tex] + 26 = z
15z + (26 × 28) = 28z ∵ multiply both sides by 28
15z + 728 = 28z
28z - 15z = 728 .......... rearranging above equation
13z = 728 ⇒ z = [tex]\frac{728}{13}[/tex] ⇒ z = 56
Total number of eggs = z = 56
Answer: There are total 56 eggs in the basket.
Step-by-step explanation: Given that an Easter basket contains eggs of three different colors, out of which [tex]\dfrac{2}{7}[/tex] are green, [tex]\dfrac{1}{4}[/tex] are blue and rest 26 eggs are red.
We are to find the total number of eggs in the basket.
Let x be the total number of eggs in the Easter basket.
Then, according to the given information, we have
[tex]\dfrac{2}{7}\times x+\dfrac{1}{4}\times x+26=x\\\\\\\Rightarrow \dfrac{8x+7x}{28}+26=x\\\\\\\Rightarrow \dfrac{15x}{28}+26=x\\\\\\\Rightarrow x-\dfrac{15x}{28}=26\\\\\\\Rightarrow \dfrac{28x-15x}{28}=26\\\\\\\Rightarrow \dfrac{13x}{28}=26\\\\\Rightarrow x=\dfrac{26\times 28}{13}\\\\\Rightarrow x=56.[/tex]
Thus, there are total 56 eggs in the basket.
find the volume of the sphere. express your answer in term of Pie
Answers
Answer:
[tex]\large\boxed{36\pi}[/tex]
Step-by-step explanation:
The formula of a volume of a sphere:
[tex]V=\dfrac{4}{3}\pi R^3[/tex]
R - radius
We have R = 3 ?. Substitute
[tex]V=\dfrac{4}{3}\pi(3^3)=\dfrac{4}{3}\pi(27)=(4)\pi(9)=36\pi[/tex]
If the radius is 30, then the volume is:
[tex]V=\dfrac{4}{3}\pi(30^3)=\dfrac{4}{3}\pi(27,000)=(4)\pi(9,000)=36,000\pi[/tex]
If 30 is the length of diameter, then the radius R = 30 : 2 = 15.
Therefore the volume:
[tex]V=\dfrac{4}{3}\pi(15^3)=\dfrac{4}{3}\pi(3,375)=(4)\pi(1,125)=4,500\pi[/tex]
4. Samantha went out to eat with her
friends on Monday, Tuesday, Wednesday,
and Friday. She spent $5.65 on Monday,
$7.50 on Tuesday, $9.75 on Wednesday,
and $5.95 on Friday. How much
more money did Samantha spend on
Wednesday and Friday than on Monday
and Tuesday?
Answers
$28.85 (just add it if u dont get it)
On Wednesday and Friday she spent, $9.75+$5.95=$15.70
On Monday and Tuesday she spent, $5.65+$7.50= $13.15
Its a subtraction problem so $15.70-$13.15=$2.55
The answer is $2.55
I apologize if this is not what you meant.
A product costs $29.75 for 5 pounds. How much does it cost per ounce? (1 pound = 16 ounces)
Answers
Answer:
The product costs $0.37 per ounce.
Step-by-step explanation:
$29.75 for 5 pounds = x for 1 pound (Cross-Multiply)
5x/5 = $29.75/5
x = $5.95 per pound
$5.95 per pound/16 ounces = $0.37
$0.37 per ounce!
Answer:
$0.371875 does it cost per ounce.
Step-by-step explanation:
Use conversion:
1 pound = 16 ounces.
As per the statement:
A product costs $29.75 for 5 pounds.
In 5 pounds = product cost $ 29.75
then;
In 1 pound = [tex]\$\frac{29.75}{5}[/tex]
Using conversion we have;
In 16 ounces = [tex]\$\frac{29.75}{5}[/tex]
then;
in 1 ounces = [tex]\$\frac{29.75}{80} = \$0.371875[/tex]
Therefore, $0.371875 does it cost per ounce.
Andrew is paid $4 per hour for the first 30 hours he works each week. He makes $5 per hour for each hour he works over 30 hours per week. In other words, total wages = fixed wages for 30 hours + additional wages at $5 per hour. Apply function notation to answer the following questions about Andrew’s wages. Part A Write a function that gives Andrew’s total wages when he works more than 30 hours. Use the variables w for wages and h for hours.
Answers
Answer:
w = 120 + 5*(h-30)
Step-by-step explanation:
Part A;
We are informed that Andrew is paid $4 per hour for the first 30 hours he works each week and makes $5 per hour for each hour he works over 30 hours per week. This implies that the $4 per hour for the first 30 hours is fixed while the $5 per hour overtime depends on the number of extra hours worked.
If we let w denote the wage and h denote the hours worked per week, then;
$4 per hour for the first 30 hours; 4*30 = 120
The number of extra hours worked would be; h-30
w = 120 + 5*(h-30)
This is the function that gives Andrew’s total wages when he works more than 30 hours each week.
Help me please please
Answers
It is in the hundredths place
Hundredths
Two places after the decimal is always the hundredths place.
-x^1 -10x -24 = 0 I’ll melt your popsicle
Answers
I don't have popsicle but I'm sure you will melt by this answer.
[tex]
-x^1-10x-24=0 \\
x+10x+24=0 \\
11x=-24 \\
\boxed{x=\frac{-24}{11}}
[/tex]
Hope this helps. (please don't melt)
r3t40
Pepper Jackie has 5.8 kg of rainbow sprinkles. If she divides them equally into 8 star containers, how much will be in each star?
Answers
Answer:
725 grams
Step-by-step explanation:
You divide 5.8 kg by 8 (the star containers)
and the final answer is 0.725 kg or 725 grams
How does the variable of Data Set A compare to the variability of Data Set B?
Data Set A: 18, 24, 29, 30, 39
Data Set B: 26, 29, 39, 40, 52
Select from the drop-down menus to correctly complete the statements.
Data Set A has Data Set B because the range of Data Set A is the range of Data Set B
Answers
Answer:
Data Set A has less variability Data Set B because the range of Data Set A has less range of Data Set B
Step-by-step explanation:
Data Set A: 18, 24, 29, 30, 39
Data Set B: 26, 29, 39, 40, 52
Variability means you have more range so....
Sandy mixed together 9 gallons of one brand of juice and 8 gallons of a second brand of juice which contains 48% real fruit juice. Find the percent of real fruit juice in the first brand if the mixture contained 30% real fruit juice.
A) 18%
B) 140%
C) 180%
D) 14%
Answers
Answer:
D) 14%
Step-by-step explanation:
Let the percent of the real fruit in the first brand = x
Given that number of gallons of real fruit in the first brand = 9 gallons
Given that percent of the real fruit in the second brand = 48%
Given that number of gallons of real fruit in the second brand = 8 gallons
Given that percent of the real fruit in the mixture = 30%
then number of gallons of real fruit in the mixture = (9+8) = 17 gallons
Then we get equation:
[x% of 9 gallons] + [48% of 8 gallons] = [30% of 17 gallons]
9x+48(8)=30(17)
9x+384=510
9x=510-384
9x=126
x=126/9
x=14
Hence final answer is D) 14%
Answer:D
Step-by-step explanation:jus took test
20 points
Which expression is a polynomial?
A. 7/x^2
B. x - √ 7
C. 7/ √ x
D. √ 7x
Answers
Answer:
B.Step-by-step explanation:
A polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.
[tex]A.\ \dfrac{7}{x^2}=7x^{-2}\qquad\bold{NOT}\\\\B.\ x-\sqrt7\qquad\bold{YES}\\\\C.\ \dfrac{7}{\sqrt{x}}=7x^{-\frac{1}{2}}\qquad\bold{NOT}\\\\D.\ \sqrt{7x}=\sqrt7\cdot\sqrt{x}=\sqrt7 x^\frac{1}{2}\qquad\bold{NOT}[/tex]
jane lives 1 3/8 miles from the airport. She drove from her house to the airport and back 2 times. How far did Jane drive? Move a number or numbers into the blank to show the answer
Answers
Answer:
[tex]5\frac{1}{2}\ mi[/tex]
Step-by-step explanation:
we know that
[tex]1\frac{3}{8}\ mi=\frac{1*8+3}{8}=\frac{11}{8}\ mi[/tex]
She drove from her house to the airport and back 2 times
so
Multiply the distance from her house to the airport by 4
[tex](4)*\frac{11}{8}=\frac{11}{2}=5\frac{1}{2}\ mi[/tex]
doroteo determined that the correlation coefficient for a set data was -0.9. what percent of the total variation in the y-values is not explained by the regression line?
Answers
Answer:
19% of the total variation in the y-values is not explained by the regression line
Step-by-step explanation:
The correlation coefficient, r, is a measure of the degree of association between two variables. It gives information on the direction and strength of the relationship.
On the other hand, [tex]R^{2}[/tex] is the coefficient of determination and is a measure of the percent of the total variation in the y-values explained by the regression line.
[tex]R^{2}[/tex] is simply the square of r;
[tex]R^{2}=r^{2}=(-0.9)^{2}=0.81[/tex]
This implies that 81% of the total variation in the y-values is explained by the regression line. Therefore, only 19% is not explained.
ASAP HELP PLEASE A cylinder and its dimensions are shown. Which equation can be used to find V, the volume of the cylinder in cubic centimeters?
A)
V = π(4.5h)2
B)
V = π(9h)2
C)
V = π(4.5)2h
D)
V = π(9)2h
Answers
Answer:
Option A, π(4.5)²
Step-by-step explanation:
Volume of a cylinder is-
V = πr²h
Substitute the value of the radius. (9 is the diameter of the base, so it needs to be half of it)
V = π(4.5)²h
Bring the "h" inside with 4.5
V = π(4.5h)²
Hope this helps
The volume of the cylinder is [tex]\pi (4.5)^{2} h[/tex] and thus option c) [tex]\pi (4.5)^{2} h[/tex] is the correct option
Given: a cylinder of diameter 9 cm and height h cm
To find: equation to find the volume of the cylinder
We know that the volume of a cylinder can be calculate by using the formula:
[tex]\text{volume} = \pi r^{2} h[/tex]
where r is the radius of the cylinder and h is the height
It is given that the diameter of cylinder is 9 cm so radius of the cylinder will be half of the diameter:
[tex]\text{radius} = \frac{9}{2} = 4.5[/tex] cm
Now putting the values in the formula of volume:
[tex]\text{volume} = \pi (4.5)^{2} h[/tex]
Therefore, the volume of the cylinder is [tex]\pi (4.5)^{2} h[/tex] and the option that is same as our answer is option C. So, option C) [tex]\pi (4.5)^{2} h[/tex] is the correct answer
A set of quiz scores is shown in the histogram below. The mean of the data set is 20.2, and the (population) standard deviation is 2.4.
PLEASE PLEASE PLEASE How many numbers in the data set are within 1 standard deviation of the mean?
13
14
15
16
Answers
Answer:
[tex]13[/tex]
Step-by-step explanation:
As the mean is 20.2 and the standard deviation is 2.4
The range within the first standard deviation is
(17.8,22.6)
This means that we can safely use the range of (18,22) as we cannot confirm whether the other values fall within the range.
Within this range there are
[tex]2+3+4+3+1=13[/tex]
The standard deviation of the mean is 13.
Standard deviation of the meanAs the mean is 20.2 and the standard deviation is 2.4
The range within the first standard deviation is (17.8,22.6)
This means that we can safely use the range of (18,22) as we cannot confirm whether the other values fall within the range.
Within this range there are
2 + 3 + 4 + 3 + 1 = 13
Therefore, the correct answer is option (a) 13.
To learn more about the standard deviation of the mean
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The mean of a data is 52.4 and the standard deviation is 11.8.What percent of the data is between 40.6 and 64.2?
A.50%
B.68%
C.95%
D.99.7%
Answers
Answer:
B. 68%
Step-by-step explanation:
Any number within 1 positive or negative deviation of the mean represents 68% of normally distributed data.
Math explanation:
52.4+11.8=64.2
52.4-11.8=40.6
Your answer is b, 68%
What is the order of the mcu?
Answers
If your talking about just movies then...
Captain America the first avenger
Captain marvel
Black widow
Iron man
Iron man 2
Thor
The Incredible Hulk
Avengers
Iron man 3
Thor the dark world
Captain America the winter soldier
Guardians of the galaxy
Guardians of the galaxy vol 2
Avengers age of ultron
Ant-man
Captain America civil war
Black panther
Spider-man homecoming
Doctor Strange
Thor the dark world
Ant-man and the wasp
Avengers infinity war
Avengers endgame
Spider-man far from home
But if you mean all the movies, tv shows, and one-shots then...
Captain America the first avenger
Agent carter season one
Agent carter season two
Agent carter (one-shot)
Captain marvel
Black widow
Iron man
Iron man 2
A funny thing happened on the way to Thor’s hammer (one-shot)
Thor
The Incredible Hulk
The consultant (one-shot)
Avengers
Item 47 (one-shot)
Iron man 3
All hail the king (one-shot)
Agents of S.H.I.E.L.D. Season one (episodes 1-7)
Thor the dark world
Agents of S.H.I.E.L.D. Season one (episodes 8-16)
Captain America the winter soldier
Agents of S.H.I.E.L.D. Season one (episodes 17-22)
Guardians of the galaxy
Guardians of the galaxy vol 2
Daredevil season one
Agents of S.H.I.E.L.D. Season two (episodes 1-10)
Jessica jones season one
Agents of S.H.I.E.L.D. Season two (episodes 11-19)
Avengers age of ultron
Agents of S.H.I.E.L.D. Season two (episodes 20-22)
Daredevil season two
Luke cage season one
Ant-man
WHIH newsfront season one
Agents of S.H.I.E.L.D. Season three (episodes 1-19)
Iron fist season one
Captain America civil war
WHIH newsfront season two
agents of S.H.I.E.L.D. Season three (episodes 20-22)
The defenders season one
Agents of S.H.I.E.L.D. Season four (episodes 1-6)
Black panther
Spider-man homecoming
Agents of S.H.I.E.L.D. Season four (episodes 7-8)
Agents of S.H.I.E.L.D. Slingshot season one
Agents of S.H.I.E.L.D. Season four (episodes (9-22)
Doctor strange
Thor ragnarok
Inhumans season one
The punisher season one
Runaways season one
Agents of S.H.I.E.L.D. Season five (episodes 1-10)
Jessica jones season two
agents of S.H.I.E.L.D. season five (episodes 11-18)
cloak and dagger season one
Luke cage season two
Iron fist season two
Daredevil season three
Ant-man and the wasp
Avengers infinity war
The punisher season two
Avengers endgame
Spider-man far from home
Jessica jones season three
The order as of now is:
Captain America: The First Avenger (2011)
Iron Man (2008)
The Avengers (2012)
Captain America: The Winter Soldier (2014)
Guardians of the Galaxy (2014)
Avengers: Age of Ultron (2014)
Captain America: Civil War (2016)
Spider-Man: Homecoming (2017)
Thor: Ragnarok (2017)
Ant-Man and The Wasp (2018)
Avengers: Infinity War (2018)
7 example of independent event
8 pieces of fruit are drawn twice with replacement what is P
Answers
Answer:
7.
rolling two number cubes
8.
2/25
Step-by-step explanation:
7.
Events A and B are said to be statistically independent if the probability of A happening, P(A), in no way affects the probability of event B occurring, P(B);
P(A∩B) = P(A) P(B)
If A and B are independent the above equation is always true.
From the list given, rolling two number cubes is an example of independent events since the outcome from the first cube does not affect the outcome of the second cube.
8.
We are informed the bag contains 4 apples, 1 plum, 2 apricots, and 3 oranges. We are required to determine the following probability;
P(Apple then Apricot) given that the fruits are drawn with replacement.
The probability of drawing an apple from the bag is;
(number of apples)/(total number of fruits)
= 4/10 = 2/5
The probability of drawing an apricot from the bag given that the apple drawn is replaced is;
(number of apricots)/(total number of fruits)
= 2/10 = 1/5
Now, P(Apple then Apricot) = 2/5 * 1/5 = 2/25
Find an equation for the nth term of the arithmetic sequence.
a10 = 32, a12 = 106 (2 points)
an = -301 + 37(n - 1)
an = -301 + 37(n - 2)
an = -301 + 37(n + 1)
an = -301 - 37(n + 1)
Answers
I hope this helps witb you.
Final answer:
To find the nth term of the arithmetic sequence, we calculated the common difference to be 37, and deduced the first term as -301. The equation for the nth term is an = -301 + 37(n - 1). Therefore, option a is correct answer.
Explanation:
To find an equation for the nth term of the arithmetic sequence given two terms, a10 = 32 and a12 = 106, we first need to determine the common difference. The common difference d in an arithmetic sequence is the consistent interval between consecutive terms, calculated by subtracting one term from the next. In this case:
d = a12 - a10
d = 106 - 32
d = 74
Since the terms are two positions apart, this common difference corresponds to two steps, meaning the common difference per step is 74 / 2 = 37.
Now, we know that the general formula for the nth term of an arithmetic sequence is:
an = a1 + (n - 1)d
Where a1 is the first term. To find a1, we can plug in the values for a10:
32 = a1 + (10 - 1)×37
32 = a1 + 9×37
32 = a1 + 333
a1 = 32 - 333
a1 = -301
Now, the equation for the nth term of the sequence is:
an = -301 + 37(n - 1)
Therefore, option a is correct answer.
The odometer of a new automobile functions improperly and registers only 2 miles for every 3 miles driven. If the odometer indicates 48 miles, how many miles has the automobile actually been driven?
Answers
Final answer:
The odometer reads 2 miles for every 3 actual miles driven. To find the actual distance when the odometer shows 48 miles, a proportion is used, leading to the calculation that the automobile has driven 72 actual miles.
Explanation:
The student is dealing with a proportion problem in mathematics where the automobile's odometer is inaccurate. Given that the odometer registers 2 miles for every 3 miles driven, we can set up a proportion to find the actual distance driven. If the odometer indicates 48 miles, we can write the proportion as follows:
2 miles (odometer) / 3 miles (actual) = 48 miles (odometer) / x miles (actual)
Cross-multiply to solve for x: 2x = 48 × 3
Calculate x: 2x = 144
Divide both sides by 2 to isolate x: x = 144 / 2
Find the value of x: x = 72 miles
Therefore, the automobile has actually been driven 72 miles.
Trig: Which complex number's graph is shown?
Answers
ANSWER
[tex]2 \sqrt{2} ( \cos( \frac{7\pi}{4} + i \sin( \frac{7\pi}{4} ) ) [/tex]
EXPLANATION
The complex number shown has coordinates (2,-2)
or
[tex]z = 2 - 2i[/tex]
The modulus is
[tex] |z| = \sqrt{ {2}^{2} + {( - 2)}^{2} } [/tex]
[tex]|z| = \sqrt{ 8} = 2 \sqrt{2} [/tex]
The argument is
[tex] \theta= \tan^{ - 1} ( \frac{ - 2}{2} )[/tex]
[tex] \theta= \tan^{ - 1} ( -1) = \frac{7\pi}{4} [/tex]
The polar form is
[tex]2 \sqrt{2} ( \cos( \frac{7\pi}{4} + i \sin( \frac{7\pi}{4} ) ) [/tex]
The first option is correct.
Answer:
The first option (the one all the way at the top)
Step-by-step explanation:
a.pex
An irregular polygon has its external angles as 28°,40°,120°,142° and x. Find the value of x
Answers
Answer:
X=30
Step-by-step explanation:
The whole polygon is 360 degrees so:
360-28-40-120-142=X, which is 30
The value of x = 30°.
What is an exterior angles of an Irregular Polygon?
As in the case with a regular polygon, an irregular polygon even contains exterior angles that count up to 360°. Each exterior angle in an irregular polygon even exists (180° - its linear pair). Therefore the exterior angles add up to 360°.
The entire external angle is equal to 360.
28° + 40° + 120° + 142° + x = 360°
Simplifying the above equation, we get
330° + x = 360°
x = 360°- 330°
x = 30°
Therefore, the value of x = 30°.
To learn more about Irregular Polygon
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can anybody help me solve this please?
Answers
Calculate the volume of each shape then add them together.
4 x 32 x 10 = 1280
12 x 16 x 10 = 1920
Total volume = 1280 + 1920 = 3,200 cubic in.
How do you simplify the expression “3x (2/x + 5) +4”?
Answers
Answer:
15x + 10
Step-by-step explanation:
distribute the 3x to the 2/x and 5 inside the parentheses:
3x(2/x) + 3x(5) + 4
multiply:
6x/x + 15x +4
There is x in the numerator and the denominator of 6x/x, so the xs cancel:
6 + 15x + 4
15x + 10
Answer:
15x+10
Step-by-step explanation:
3x (2/x + 5) +4
Distribute the 3x
3x*2/x + 3x*5 +4
6x/x + 15x +4
6+15x+4
Combine like terms
15x+10
andre drinks 15 ounces of water, which is 3/5 of a bottle. How much does the bottle hold? Use x for the number of ounces of water the bottle holds.
Answers
Answer:
25 ounces of water
Step-by-step explanation:
3/5 = 15
Cross multiplying this:
1 = x
3/5 = 15
3/5x=15
x=25
Answer:
The bottle hold 25 ounces of water
Step-by-step explanation:
To find the amount of water the bottle hold, we will follow the steps below;
let x be the number of ounces of water the bottle holds
3/5 of x = 15 ounces
3/5 × x = 15
[tex]\frac{3X}{5}[/tex] = 15
Multiply both-side of the equation by 5
[tex]\frac{3X}{5}[/tex] × 5 = 15×5
At the left-hand side of the equation 5 will cancel-out 5 leaving us with 3x
3x = 75
Divide both-side of the equation by 3
[tex]\frac{3X}{3}[/tex] = [tex]\frac{75}{3}[/tex]
(On the left-hand side of the equation 3 at the numerator will cancel-out 3 at the denominator leaving us with x while on the right-hand side of the equation 75 will be divided by 3)
x = 25 ounce
For what values of a and m does f(x) have a horizontal asymptote at y = 2 and a vertical asymptote at x = 1?
Answers
for a rational expression the vertical asymptotes occur when the denominator equals 0, in this case that will be when x + a = 0.
now, if there were to be a vertical asymptote of x = 1, that simply means that
x = 1 ==> x - 1 = 0.
meaning that a = -1.
horizontal asymptotes occur when the denominator has a higher degree than the numerator OR when both have the same degree.
when the degree of the denominator is higher, then the only horizontal asymptote occurring is y = 0.
when the degrees are the same, then the horizontal asymptote occurs at the leading terms' coefficient fraction.
now, if this expression were to have a horizontal asymptote of y = 2, that simply means
[tex]\bf \cfrac{2x^m}{x+a}\implies \cfrac{2x^1}{1x^1+a}\implies \stackrel{\textit{horizontal asymptote}}{\cfrac{2}{1}\implies y=2}\qquad \textit{meaning m = 1}[/tex]
ANSWER
a=-1,m=1
EXPLANATION
The given function is
[tex]f(x) = \frac{2 {x}^{m} }{x + a} [/tex]
For this rational function to have a horizontal asymptote at y=2, the degree of the numerator must equal the degree of the denominator.
This implies that, we must have m=1.
For the function to have a vertical asymptote at x=1, then,
[tex]1 + a = 0[/tex]
This implies that,
[tex]a = 0 - 1[/tex]
[tex]a = - 1[/tex]
The correct choice is the third option.
help plz i dont know what to do
Answers
Answer:
The area of the irregular figure is 140 sq. ft.
Step-by-step explanation:
Triangle:
16-12=4
6 x 4 = 24
24 x 0.5 = 12
Triangle = 12
Rectangle:
16 x 8
= 128
Rectangle = 128
Total figure:
128+12
= 140
Plzz give me brainlist!!!