Given:
The limit problem is:
[tex]lim_{x\to -5}\dfrac{\dfrac{1}{5}+\dfrac{1}{x}}{10+2x}[/tex]
To find:
The value of the given limit problem.
Solution:
We have,
[tex]lim_{x\to -5}\dfrac{\dfrac{1}{5}+\dfrac{1}{x}}{10+2x}[/tex]
It can be written as:
[tex]=lim_{x\to -5}\dfrac{\dfrac{x+5}{5x}}{2(5+x)}[/tex]
[tex]=lim_{x\to -5}\dfrac{x+5}{5x}\times \dfrac{1}{2(5+x)}[/tex]
[tex]=lim_{x\to -5}\dfrac{1}{5x\times 2}[/tex]
[tex]=lim_{x\to -5}\dfrac{1}{10x}[/tex]
Applying limit, we get
[tex]lim_{x\to -5}\dfrac{1}{10x}=\dfrac{1}{10(-5)}[/tex]
[tex]lim_{x\to -5}\dfrac{1}{10x}=\dfrac{1}{-50}[/tex]
Therefore, the value of given limit problem is [tex]-\dfrac{1}{50}[/tex].
According to the Centers for Disease Control and Prevention, the proportion of U.S. adults age 25 or older who smoke is .22. A researcher suspects that the rate is lower among U.S. adults 25 or older who have a bachelor's degree or higher education level.What is the null hypothesis in this case
Answer:
The null hypothesis is [tex]H_0: p = 0.22[/tex]
Step-by-step explanation:
According to the Centers for Disease Control and Prevention, the proportion of U.S. adults age 25 or older who smoke is .22
This means that at the null hypothesis, it is tested if the proportion is in fact 0.22, that is:
[tex]H_0: p = 0.22[/tex]
A researcher suspects that the rate is lower among U.S. adults 25 or older who have a bachelor's degree or higher education level.
At the alternative hypothesis, it is tested if the proportion is lower than 0.22, that is:
[tex]H_1: p < 0.22[/tex]
You are standing 186 feet away from the base of a building and your clinometer
measures 23° when it's looking at the top of the building. (This angle is the one between
the ground and the top of the building). Please calculate the height of the building.
9514 1404 393
Answer:
about 79 ft
Step-by-step explanation:
The relevant trig relation is ...
Tan = Opposite/Adjacent
In this scenario, the angle is 23°, the adjacent side is the distance to the building, and the opposite side is the building height. Then we have ...
height = tan(23°)·(186 ft) ≈ 78.95 ft ≈ 79 ft
cho tam giác ABC cân tại A trung tuyến AM.Biết BC=6cm,AM=4cm .Tính độ dài các cạnh AB và AC
Vì tam giác ABC cân tại A (gt) mà AM là đg trung tuyến nên AM đồng thời là đg cao của t/giác đó:
AM là trung tuyến của t/giác ABC nên M là trung điểm BC:
=> BM =BC/2 =6:2=3(cm)
Xét tam giác AMB vuông tại M
AB^2 =AM^2+BM^2 ( theo định lý Py-ta -go)
Please help explanation if possible
The 5. one please 100 points
Answer:
Ok so 5 and tens least common denominator is 10. So 6/10- 2/10 (1/5×2=2/10)= 4/10. so now take 4/10 and 1/4 and find the lcm Which is 20 so 4/10×2 is 8/20+10/20=
18/20
[tex]\\ \sf\longmapsto \dfrac{6}{10}-\dfrac{1}{5}+\dfrac{1}{4}[/tex]
[tex]\\ \sf\longmapsto \dfrac{2-4+5}{20}[/tex]
[tex]\\ \sf\longmapsto \dfrac{-2+5}{20}[/tex]
[tex]\\ \sf\longmapsto \dfrac{3}{20}[/tex]
Given that the two triangles are similar, solve for x if AU = 20x + 108, UB = 273, BC = 703, UV = 444, AV = 372 and AC = 589. You must show all of your work to receive credit.
PLSSS SHOW WORK <3
Answer:
x = 18
Step-by-step explanation:
First, let's find the ratios between the two triangles
We'll use AV and AC
372 ÷ 589 = 12/19
All of the sides of the smaller triangle are 12/19 of the bigger triangle
Now let's find x
We know that AU + UB = AB
So it's 20x + 108 + 273 = AB
12/19 of a bigger triangle side equals a small triangle side
(12/19)AB = AU
For this equation multiply both sides by 19/12 to isolate AB
(12/19)AB x 19/12 = AU x 19/12
AB = (19/12)AU
Now we have this
20x + 108 + 273 = (19/12)(20x + 108)
20x + 381 = (19/12)(20x + 108)
Distribute the 19/12
20x + 381 = 95/3x + 171
Move all like terms to one side
20x + 381 = 95/3x + 171
- 171 - 171
20x + 210 = 95/3x
- 20x - 20x
Don't forget about common denominators
210 = 95/3x - 60/3x
210 = 35/3x
Multiply both sides by 3
210 x 3 = 35/3x x 3
630 = 35x
Divide both sides by 35
630/35 = 35x/35
x = 18
Answer:
Step-by-step explanation:
[tex]\frac{20x+108}{20x+381}[/tex] = [tex]\frac{372}{589}[/tex]
589( 20x + 108 ) = 372( 20x + 381 )
11780x + 63612 = 7440x + 141732
4340x = 78120
x = 18
Prove:1/sin²A-1/tan²A=1
Step-by-step explanation:
1/sin^2A -cos^2A/sin^2 A. ~tan = sin/cos
(1-cos^2)/sin^2A. ~ take lcm
sin^2A/sin^ A. ~ 1-cos^2A = sin^2A
1
for more free ans check bio
Answer:
[tex]\displaystyle \frac{1}{\sin^2x}-\frac{1}{\tan^2x}=1[/tex]
Step-by-step explanation:
Prove that:
[tex]\displaystyle \frac{1}{\sin^2x}-\frac{1}{\tan^2x}=1[/tex]
Recall that by definition:
[tex]\displaystyle \tan x=\frac{\sin x}{\cos x}[/tex]
Therefore,
[tex]\displaystyle \tan^2x=\left (\frac{\sin^2x}{\cos^2x}\right)^2=\frac{\sin^2x}{\cos^2x}[/tex]
Substitute [tex]\displaystyle \tan^2x=\frac{\sin^2x}{\cos^2x}[/tex] into [tex]\displaystyle \frac{1}{\sin^2x}-\frac{1}{\tan^2x}=1[/tex]:
[tex]\displaystyle \frac{1}{\sin^2x}-\frac{1}{\frac{\sin^2x}{\cos^2x}}=1[/tex]
Simplify:
[tex]\displaystyle \frac{1}{\sin^2x}-\frac{\cos^2x}{\sin^2x}=1[/tex]
Combine like terms:
[tex]\displaystyle \frac{1-\cos^2x}{\sin^2x}=1[/tex]
Recall the following Pythagorean Identity:
[tex]\sin^2x+\cos^2x=1[/tex] (derived from the Pythagorean Theorem)
Subtract [tex]\cos^2x[/tex] from both sides:
[tex]\sin^2=1-\cos^2x[/tex]
Finish by substituting [tex]\sin^2=1-\cos^2x[/tex] into [tex]\displaystyle \frac{1-\cos^2x}{\sin^2x}=1[/tex]:
[tex]\displaystyle \frac{\sin^2x}{\sin^2x}=1,\\\\1=1\:\boxed{\checkmark\text{ True}}[/tex]
so i need help with this pls i suck at algebra
Answer:
The 5x^2 vs -5x^2 will reflect over "X" axis
the +1 vs -2 will shift the graph down three units
the first answer is the correct answer
Step-by-step explanation:
I need help on this A box contains 3 red, 4 green, and 3 yellow balls. If a ball is drawn at random, find the probability that the ball is red.
Answer:
3/10
Step-by-step explanation:
3 red, 4 green, and 3 yellow balls = 10 balls
P(red) = number of red balls / total balls
= 3/10
ײ × ×⁴=ײ+⁴ find the ×
An investor has an account with stock from two different companies. Last year, his
stock in Company A was worth $6600 and his stock in Company B was worth $3500.
The stock in Company A has increased 7% since last year and the stock in Company B
has increased 1%. What was the total percentage increase in the investor's stock
account? Round your answer to the nearest tenth (if necessary).
PLEASE HELP!!! very confused
Answer:
Step-by-step explanation:
The vertices lie on the x-axis, as is determined by their coordinates. This makes the center of this hyperbola (0, 0) because the center is directly between the vertices. The fact that the foci also lie on the x-axis tells us that this is the main axis. What this also tells us is which way the hyperbola "opens". This one opens to the left and the right as opposed to up and down. The standard form for this hyperbola is:
[tex]\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1[/tex] and so far we have that h = 0 and k = 0.
By definition, a is the distance between the center and the vertices. So a = 5, and a-squared is 25. So we're getting there. Now here's the tricky part.
The expressions for the foci are (h-c, k) and (h+c, k). Since we know the foci lie at +/-13, we can use that to solve for c:
If h+c = 13 and h = 0, then
0 + c = 13 and c = 13.
We need that c value to help us find b:
[tex]c^2=a^2+b^2[/tex] and
[tex]13^2=5^2+b^2[/tex] and
[tex]169=25+b^2[/tex] and
[tex]144=b^2[/tex] so
b = 12. Now we're ready to fill in the equation:
[tex]\frac{x^2}{25}-\frac{y^2}{144}=1[/tex] and there you go!
Find the least length of a rope which can be cut into whole number of pieces of lengths 45cm, 75cm and 81 cm
Which property of equality would be used to isolate the variable b in this equation?
3/4 x b = 12
A. addition property of equality
В. subtraction property of equality
C. multiplication property of equality
D. symmetric property of equality
Answer:
C. multiplication property of equality
Step-by-step explanation:
3/4b = 12
Multiply each side by 4/3 using the multiplication property of equality
4/3* 3/4b = 12*4/3
b = 16
Rewrite as a simplified fraction.
3.2 = ?
(Repeating)
Answer:
Step-by-step explanation:
29/9 or 3 2/9
Javier works at a print shop. He starts printing at 8:00 a.m. The number of printed brochures is a linear function of the number of minutes since Javier started printing. By 8:50 a.m. he had printed 240 brochures, and by 9:00 a.m. he had printed 288. Write an equation in the form y = mx + b that represents the number of brochures, y, that were printed after x minutes.
Answer:
y = 4.8(x) + 0
Step-by-step explanation:
In this question, Javier managed to print 240 brochures in 50minutes from 8:00 to 8:50. If we divide these values we see that he printed 4.8 brochures per minute. The same result is given for the 10 minutes from 8:50 to 9:00 where he printed 48 brochures. Therefore, we can get the following linear formula from these values.
y = 4.8(x) + 0
In this case, b would equal 0 because Javier is starting from 0 brochures made when he gets to work at 8:00 a.m
en el coliseo de una ciudad, se jugo la final de un campeonato de voley . En total , 1200 personas asistieron al coliseo . esta cantidad de personas representa a los 3/4 de su capacidad. ¿Cual es la capacidad que tiene este coliseo?
a)900
b)1200
c)1600
d)4800
c. 1600
1200 : 3 * 4
= 400 * 4
= 1600
The capacity of this coliseum is 1600
The correct option is (C)
What is fraction?A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator.
Given:
Total people attended the Coliseum= 1200
let he capacity be x
3/4*x= 1200
x= 1200*4/3
x= 1600
Learn more about fraction here:
https://brainly.com/question/10354322
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Your question is incomplete/other language, probably the traslated question/missing part is:
In a city coliseum, the final of a volleyball championship was played. In total, 1,200 people attended the Coliseum. this number of people represents 3/4 of its capacity. What is the capacity of this coliseum?
What is the slope of the line that
passes through these two points?
(0, 2)
(3, 8)
Remember, given two points,
(x1, yı)
Slope
rise (y2-yı)
(X2,92) run (x2-x1)
Simplify your answer completely.
Enter
Answer:
2
Step-by-step explanation:
We can use the slope formula
m = ( y2-y1)/(x2-x1)
m = ( 8-2)/(3-0)
= 6/3
= 2
Answer:
2
Brainliest, please!
Step-by-step explanation:
(0, 2)(3, 8)
y = +6
x = +3
y/x = 6/3 = 2
Hello:) how to do question 6? :) I’m not sure which property to use :/
Answer:
which grade are you in so that i can tell you according to that
i, vì AD//BC nên góc A +góc B =180°
ii, góc A=góc B nên góc C=góc D -> ABCD là hình bình hành
And AB=BC=> ABCD là hình thoi
y' = (x+1/[tex]\sqrt{x^{2} +1[/tex]
Answer:
Solving for x (rearranging) you get:
(x^3+x+(x^2+1)^1/2)/x^2+1=y
Step-by-step explanation:
Solve for x by simplifying both sides of the equation and solving for y by isolating y
1. The position of a particle moving along a coordinate axis is given by: s(t) = t^2 - 5t + 1. a) Find the speed of the particle b) Find the acceleration of the particle c) Find the velocity of the particle
Answer: [tex]\left | 2t-5\right |,\ 2,\ 2t-5[/tex]
Step-by-step explanation:
Given
Position of the particle moving along the coordinate axis is given by
[tex]s(t)=t^2-5t+1[/tex]
Speed of the particle is given by
[tex]\Rightarrow v=\dfrac{ds}{dt}\\\\\Rightarrow v=\dfrac{d(t^2-5t+1)}{dt}\\\\\Rightarrow v=\left | 2t-5\right |[/tex]
Acceleration of the particle is
[tex]\Rightarrow a=\dfrac{dv}{dt}\\\\\Rightarrow a=2[/tex]
velocity can be negative, but speed cannot
[tex]\Rightarrow v=\dfrac{ds}{dt}\\\\\Rightarrow v=\dfrac{d(t^2-5t+1)}{dt}\\\\\Rightarrow v=2t-5[/tex]
A pile of sand has been stored in the shape of a cone. Mr. Terwilliker knows that the pile is 20 feet tall and 102 feet in circumference at the base. What is the area of the conical tarpaulin needed to cover the pile?
Answer:
The area of tarpaulin is 1315.63 ft^2.
Step-by-step explanation:
height, h = 20 feet
circumference, C = 102 feet
Let the radius is r.
Circumference, C = 2 x 3.14 x r = 102
r = 16.24 feet
Let the slant height is L.
[tex]L = \sqrt{h^2 + r^2}\\\\L = \sqrt{20^2 + 16.24^2}\\\\L = 25.8 ft[/tex]
The curved surface area is
S = 3.14 x r x L
S = 3.14 x 16.24 x 25.8 = 1315.63 ft^2
Answer:
400pi square feet
Step-by-step explanation:
Find the radius
Find the slant height
Put it in the formula for a cone but take the circumference part out
Divide your answer by pi
The question asks for the closest answer
400pi square feet is the closest option to 418.17pi square feet.
can you help me i got two wrong if I get one wrong I will have a falling grade
Answer:
the bottom left is wrong
Step-by-step explanation:
if u add 40+5+7/10+1/100 it'll only equal to 45.71
Answer:
40 + 5 + [tex]\frac{7}{10}[/tex] + [tex]\frac{1}{100}[/tex] = 45.71
Step-by-step explanation:
The one needs to be in the thousandths place.
Draw graphs of the following inequalities.
a.) X>3
Answer:
Step-by-step explanation:
which choice is equivalent to the expression √20 + √80
Answer:
13.41
Step-by-step explanation:
Hope it helps!
Answer:
6[tex]\sqrt{5}[/tex]
Step-by-step explanation:
Using the rule of radicals
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]
Simplifying the radicals
[tex]\sqrt{20}[/tex]
= [tex]\sqrt{4(5)}[/tex]
= [tex]\sqrt{4}[/tex] × [tex]\sqrt{5}[/tex] = 2[tex]\sqrt{5}[/tex]
[tex]\sqrt{80}[/tex]
= [tex]\sqrt{16(5)}[/tex]
= [tex]\sqrt{16}[/tex] × [tex]\sqrt{5}[/tex] = 4[tex]\sqrt{5}[/tex]
Then
[tex]\sqrt{20}[/tex] + [tex]\sqrt{80}[/tex]
= 2[tex]\sqrt{5}[/tex] + 4[tex]\sqrt{5}[/tex]
= 6[tex]\sqrt{5}[/tex]
What is the value of a in the equation 3 a plus b equals 54, when b equals 9?
15
18
21
27
Answer:
a=15
Step-by-step explanation:
3a+b = 54
Let b=9
3a+9 = 54
Subtract 9 from each side
3a+9-9= 54-9
3a = 45
Divide each side by 3
3a/3 = 45/3
a = 15
Answer:
[tex]3a+b=54[/tex]
[tex]3a+9=54\:[b=9][/tex]
[tex]3a=54-9[/tex]
Subtract 9 from both sides
[tex]3a=45[/tex]
Divide both sides by 3
[tex]\frac{3a}{3}=\frac{45}{3}[/tex]
[tex]a=15[/tex]
OAmalOHopeO
Proportion problems
8 chickens would lay 20 eggs in 3 days.
If chickens always lay eggs at the same rate,
a) how many days would it take to chickens to lay 100 eggs?
= 10 days
b) how many chickens would be required if a farmer needed 30 eggs each day?
i need help how to do question b. i know answer bu,.t i need explaining.
:]
Solve d−85=p for d .
Answer:
d = p + 85
Step-by-step explanation:
We don't have a lot to go on for this problem. We have two undefined variables.
In order to solve for d, we need to isolate it:
d - 85 = p
Add 85 to both sides
d = p + 85
Someone please help
HELP PLEASE ITS URGENT PLEASE
Answer: 17
Step-by-step explanation:
Using Pemdas, simplify the exponents, and then solve the multiplication and division inside the parentheses before subtracting. 10-9 = 1 so 1*7 =7
10 +7 is 17.
also i hope this helps and i hope this is not a test...
