Answer:
Given that angle abc = 70° and angle bcd = 110°. Is it possible (consider all cases): That line AB intersects line CD?
yes.Step-by-step explanation:
#CarryOnLearning
help with 27 please. thanks
Answer:
See Below.
Step-by-step explanation:
We are given the function:
[tex]\displaystyle y=\sqrt{\sin x}[/tex]
And we want to show that:
[tex]\displaystyle 4y^3\frac{d^2y}{dx^2}+y^4+1=0[/tex]
Find the first derivative of y using the chain rule:
[tex]\displaystyle \frac{dy}{dx} = \frac{1}{2\sqrt{\sin x}}\cdot \cos x = \frac{\cos x}{2\sqrt{\sin x}}[/tex]
And find the second derivative using the quotient and chain rules:
[tex]\displaystyle \begin{aligned} \frac{d^2y}{dx^2} &= \frac{1}{2}\left(\frac{(\cos x)'(\sqrt{\sin x})-(\cos x)(\sqrt{\sin x})'}{(\sqrt{\sin x})^2}\right) \\ \\ &=\frac{1}{2}\left(\frac{-\sin x\sqrt{\sin x} - \left(\cos x\right) \left (\dfrac{\cos x}{2\sqrt{\sin x}}\right)}{\sin x}\right) \\ \\ & = \frac{1}{2}\left(\frac{ -\sin x(2\sin x) -\cos x(\cos x) }{\sin x \left(2\sqrt{\sin x}\right) }\right) \\ \\ &= -\frac{1}{2} \left(\frac{2\sin^2 x + \cos^2 x}{2\sin^{{}^{3}\!/\! {}_{2}}x}\right)\end{aligned}[/tex]
Find y³:
[tex]\displaystyle y^3 = \left((\sin x)^{{}^{1}\!/\!{}_{2}}\right) ^3= \sin^{{}^{3}\! / \! {}_{2} }x[/tex]
And find y⁴:
[tex]\displaystyle y^4 = \left((\sin x)^{{}^{1}\!/\!{}_{2}}\right)^4 = \sin^2 x[/tex]
Substitute:
[tex]\displaystyle 4\left( \sin^{{}^{3}\! / \! {}_{2} }x\right)\left(-\frac{1}{2}\left(\frac{2\sin ^2x + \cos ^2 x}{2\sin^{{}^{3}\!/ \! {}_{2}}x}\right)\right)+\left(\sin ^2 x\right) + 1= 0[/tex]
Simplify:
[tex]-\left(2\sin^2 x + \cos^2 x\right) + \sin ^2 x + 1=0[/tex]
Distribute:
[tex]-2\sin ^2 x - \cos^2 x + \sin ^2 x + 1=0[/tex]
Simplify:
[tex]-\sin ^2 x - \cos^2 x + 1= 0[/tex]
Factor:
[tex]-(\sin ^2 x + \cos^2 x ) + 1=0[/tex]
Pythagorean Identity:
[tex]-(1)+1=0\stackrel{\checkmark}{=}0[/tex]
Q.E.D.
Find the missing side of the triangle
Answer:
x = 7[tex]\sqrt{2}[/tex]
Step-by-step explanation:
Pytago:
[tex]7^2 + 7^2 = x^2\\x = \sqrt{7^2 + 7^2} \\x = 7\sqrt{2}[/tex]
Step-by-step explanation:
In a right triangle, you can find the leg of the triangle by using the Pythagorean theorem.
[tex]a^2+b^2=c^2[/tex]
In this case, we have [tex]7^2+7^2=c^2[/tex], or
[tex]c^2=98[/tex]
[tex]\sqrt{98}[/tex]≅[tex]9.9[/tex]
what’s the formula to find the shaded area?
shaded area = area of outer figure - area of inner figure........
The sum of the interior angles of a regular nonagon (9-gon) is equal to
The sum of the interior angles is 1260°
Which expression is equivalent to (b^n)m?
Step-by-step explanation:
By the law of exponent :
(a^n)^m=a^n×m
Option C
b^n×m is the correct answer...
hope it helps
Find the first five terms of the following sequence, starting with n=1. tn=(−1)n+1(n2−9) Give your answer as a list, separated by commas. For example, if tn=n, you would give your answer as 1,2,3,4,5.
Answer:
-8, 5 , 0 , -7 , 16
Step-by-step explanation:
Given
[tex]t_n = (-1)^{n+1}(n^2 - 9)[/tex]
Required
The first five terms
When [tex]n = 1[/tex]
[tex]t_1 = (-1)^{1+1}(1^2 - 9)[/tex]
[tex]t_1 = (-1)^{2}(1 - 9)[/tex]
[tex]t_1 = -8[/tex]
When [tex]n =2[/tex]
[tex]t_2 = (-1)^{2+1}(2^2 - 9)[/tex]
[tex]t_2 = (-1)^3 * (4 - 9)[/tex]
[tex]t_2 = 5[/tex]
[tex]t_3 = (-1)^{3+1}(3^2 - 9)[/tex]
[tex]t_3 = (-1)^{4}(9 - 9)[/tex]
[tex]t_3 = 0[/tex]
[tex]t_4 = (-1)^{4+1}(4^2 - 9)[/tex]
[tex]t_4 = (-1)^5(16 - 9)[/tex]
[tex]t_4 = -7[/tex]
[tex]t_5 = (-1)^{5+1}(5^2 - 9)[/tex]
[tex]t_5 = (-1)^{6}(25 - 9)[/tex]
[tex]t_5 = 16[/tex]
So, the first five terms are: -8, 5 , 0 , -7 , 16
Use the equation d=z–9 to find the value of d when z=10.
d=
Step-by-step explanation:
d = z - 9
d = 10 - 9 ----> substitute
d = 1
PLS SSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS
Answer:
10 is -5
Step-by-step explanation:
Which of the following show the factored equivalent of
f(x) = (2x^2 +7x + 3)(x - 3) and its zeros?
Answer:
the answer is "D"
(2x+1)(x+3)(x-3) //// -3,-.5,3
Step-by-step explanation:
Factored Form: y= (2x+1)(x+3)(x-3)
Answer:
D
Step-by-step explanation:
[tex]f(x) = (2x^2 +7x + 3)(x - 3)[/tex] is factored into: [tex]f(x)= (2x+1)(x+3)(x-3)[/tex]
That takes out the choices B and C.
The roots are -0.5, 3, and -3.
Therefore, the answer is D.
I hope this helps!
pls ❤ and mark brainliest pls!
In Waterville, the average daily rainfall in July is 10 mm with a standard deviation of 1.5 mm. Assume that this data is normally distributed. How many days in July would you expect the daily rainfall to be more than 11.5 mm
Answer:
You should expect 5 days in July with daily rainfall of more than 11.5 mm.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
In Waterville, the average daily rainfall in July is 10 mm with a standard deviation of 1.5 mm.
This means that [tex]\mu = 10, \sigma = 1.5[/tex]
Proportion of days with the daily rainfall above 11.5 mm.
1 subtracted by the p-value of Z when X = 11.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{11.5 - 10}{1.5}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a p-value of 0.84.
1 - 0.84 = 0.16.
How many days in July would you expect the daily rainfall to be more than 11.5 mm?
July has 31 days, so this is 0.16 of 31.
0.16*31 = 4.96, rounding to the nearest whole number, 5.
You should expect 5 days in July with daily rainfall of more than 11.5 mm.
There are nickles and quarters worth $2.20 in total. If there are 28 coins, how many nickels are there?
I need some help please!!!
9514 1404 393
Answer:
13 < √181 < 14
Step-by-step explanation:
Apparently, you're supposed to know that ...
13² = 169
14² = 196
so √181 will lie between 13 and 14.
13 < √181 < 14
A poll of 400 people from Dobbs Ferry showed 250 preferred chocolate raspberry coffee while 170 out of 350 in Irvington preferred the same flavor. To test the hypothesis that there is no difference in preferences in the two villages, what is the alternate hypothesis
Answer: The alternate hypothesis would disprove the null hypothesis and state that there are a significant difference in preferences/proportions between the two villages.
For instance, let's say:
p₁ = proportion of preference from Dobbs Ferryp₂ = proportion of preference from IrvingtonThe null hypothesis would be that p₁ = p₂, while the alternative hypothesis would be that p₁ ≠ p₂.
In the picture below, which lines are lines of symmetry for the figure?
A. none
B. 1, 2, and 3
C. 1 and 3
D. 2 and 4
Answer:
i gues none... bcuz its irregular symmetry shape
Answer:
1 because it takes a full rotation to get back to a symmetrical shape. or 2 because it is the same halfway around.
Find the area of the region bounded by y=1/x^2,y=4, and x=5. Use dy to differentiate and/or integrate.
Step-by-step explanation:
Let [tex]f(x) = 4[/tex] and [tex]g(x) = \frac{1}{x^2}[/tex]. The area A of the region bounded by the given lines is
[tex]\displaystyle A = \int [f(x) - g(x)]dx[/tex]
Note that [tex]g(x) = \frac{1}{x^2}[/tex] intersects y = 4 at x = 1/2 so the limits of integration go from x = 1/2 to x = 5. The area integral can then be written as
[tex]\displaystyle A = \int_{\frac{1}{2}}^{5}\left(4 - \dfrac{1}{x^2}\right)dx[/tex]
[tex]\:\:\:\:= \left(4x + \dfrac{1}{x}\right)_{\frac{1}{2}}^5[/tex]
[tex]\:\:\:\:= (20 + \frac{1}{5}) - (2 + 2) = \dfrac{81}{5} = 16\frac{1}{5}[/tex]
given the series 1+2+3+4+5+6+...+5000. Write the series in sigma notation if all the powers of 4 are removed from the series.
We have 4⁶ = 4096 and 4⁷ = 16,384, which is to say that the given sum only contains the first six powers of 4.
Now,
[tex]\displaystyle 1+2+3+\cdots+5000 = \sum_{k=1}^{5000}k[/tex]
and you subtract the sum of the first six powers of 4 to get the sum S that you want,
[tex]\displaystyle S = \boxed{\sum_{k=1}^{5000}k - \sum_{k=1}^64^k}[/tex]
(A) The weight of cans of vegetables is normally distributed with a mean of 1380 grams and a standard deviation of 80 grams. What is the probability that the sample mean of weight for 15 randomly selected cans is more than 1410
Answer:
7.35%
Step-by-step explanation:
μ = 1380
σ = 80
n = 15
P(x>1410)
= (1410-1380)/((80)/(sqrt(15)))
= 1.4524
P(z>1.4524) = 0.4265 (from the graph)
P(z>1.4524) = 0.5 - 0.4265 = 0.0735
The profit earned by a hot dog stand is a linear function of the number of hot dogs sold. It costs the owner $48 dollars each morning for the day’s supply of hot dogs, buns and mustard, but he earns $2 profit for each hot dog sold. Which equation represents y, the profit earned by the hot dog stand for x hot dogs sold? y=48x−2 y=48x+2 y=2x−48 y=2x+48
Answer:
c. y=2x−48
Explanation:
It is telling us that it costs $48 each morning to buy the day's supply of hot dogs, so we must subtract that from our pay, and it will be our y intercept
It also says he earns $2 per hot dog, so that will be our slope (rate of change)
Hope it helps! :]
y = 2x - 48 equation represents the profit earned by the x hot dog sold.
What is linear equation?A linear equation is an algebraic expression in which highest power of the given variable is equals to one.
Given that, the profit earned by a hot dog stand is a linear function of the number of hot dogs sold.
It costs the owner $48 dollars each morning for the day’s supply of hot dogs, buns and mustard, but he earns $2 profit for each hot dog sold.
We need to establish an equation that represents the total profit,
According to the question,
x represents the number of hot dogs sold
y represents the total profit earned
Cost required for supply = $48
Profit on each hot dog sold = $2
As per the condition given, the required linear equation is =
y = 2x - 48
Hence, y = 2x - 48 equation represents the profit earned by the x hot dog sold.
Learn more about linear equation here :
brainly.com/question/11897796
#SPJ7
Find the length of the arc. Round your answer to the nearest tenth
Answer:
12.6 mi
Step-by-step explanation:
Arc length = 2πr (Θ/360)
2π(12) (60/360)
= 12.6 mi
Answered by g a u t h m a t h
The sum of 3x2 +x+8 and x- 9 can be expressed as
Answer:
2x + 5
Step-by-step explanation:
((3x2)+x+8) + (x-9)
= ((6) + x +8) + (x -9)
= (14 +x) + (x-9)
= 14 + x + x -9
= 2x + 5
answered by g a u t h m a t h
Which equation is represented by the graph below?
find the length of the arc . round your answers to the nearest tenth
Answer:
10.2
Step-by-step explanation:
Length of arc=(2*pi*r)*(theta/360)
Length of arc=(2*pi*3)*(195/360)=10.2
The lines shown below are parallel. If the green line has a slope of 5, what is a
the slope of the red line?
Answer:
A. 5
Step-by-step explanation:
Parallel lines have the same slope.
Answer:
5
Step-by-step explanation:
IF YOU DONT ANSWER THIS AND GET IT RIGHT YOUR MOM IS PREGO WITH YOUR KID a store sells pencils pens and markers that sells two times as many markers as pencils and three times as many pens as pencils is the store sells a total of 1950 pencils and pens and markers in a week how many of each were sold
Answer:
Pencils = 325 ; Pens = 975 ; Markers = 650
Step-by-step explanation:
Let :
Number of Pencils = x
Number of pens = y
Number of markers = z
2 times as many markers as pencils
z = 2x
3 times as many pens as pencils
y = 3x
x + y + z = 1950
Write z and y in terms of x in the equation :
x + 3x + 2x = 1950
6x = 1950
Divide both sides by 6
6x / 6 = 1950 / 6
x = 325
Number of pencils = 325
Pens = 3 * 325 = 975
Markers = 2 * 325 = 650
Pencils = 325 ; Pens = 975 ; Markers = 650
Tom bought 750 shares of a company’s stock for $11.06/share. He pays a broker a commission of $12 to buy and sell stock. After one year, Tom sold all his shares, when they were worth $10.24/share. How much did it cost Tom to buy the stock? Show your work. What was Tom’s net gain or loss? Show your work. What was Tom’s annual rate of return? Show your work.
Answer:
Answer:
-7.692%
Step-by-step explanation:
a.)Buying: total cost
Total cost= commission + (price per share* # of shares ) ;
Total cost= 12 + (11.06*750)= 12+8295 = $8,307
b.)Net gain or loss;
First, find cash received from sale of stock and deduct commission;
Cash from sale =10.24 * 750= 7,680
deduct commission= 7680-12= $7,668
Gain or loss= sale-cost = 7668-8307 = -$639, meaning there is a loss.
c.) Annual rate of return= (net gain or loss/amount paid)*100%
return= -639/(8307)*100 = -7.692%
Step-by-step explanation:
find the measure of a
Answer:
C
Step-by-step explanation:
e = 20 ° angles subtended by the same arc are equal
d = 20° opp base angles of an isosceles are equal
a+d =90° angles subtended by a diameter = 90°
a+20=90°
a=70°
Move the numbers to the lines to order them from least to greatest.
least
greatest
67.98
68.6
68.11
Please answer ASAP
Answer:
67.98,68.11, 68.6
Kevin baked 44 cookies. His family ate d of them. Using d, write an expression for the number of cookies that remained
Answer:
44-d
Step-by-step explanation:
Take the total number of cookies and subtract the number eaten. That is the number remaining
44-d
When Asia was young, her father marked her height on the door frame every month. He noticed that between the ages of one and three, he could predict her height (in inches) by taking her age in months, adding 75 inches, and multiplying the result by one-third.
Create an equation linking her predicted height, h, with her age in months, m, and solve to find when her height will be 30 inches.
Answer:
15 months old.
Step-by-step explanation:
Let m = months and h = height:
h = 1/3(m + 75) ⇔ h = 1/3m + 25
Let h = 30:
[tex]30=\frac{1}{3}m+25\\5=\frac{1}{3}m\\15=m[/tex]
Therefore, when Asia is 30 inches tall, she will be 15 months old.
Question 3 plz show ALL STEPS
Answer:
7,0, -1 and -2
Step-by-step explanation:
Just substitute the values,
a. f(g(7))=f(-1) [g(7)=-1 given]
=7 [f(-1)=7 given]
b.f(g(-1))=f(3)=0 [g(-1)=3 Given]
c.g(f(-1))=g(7)=-1 [f(-1)=7 given]
d.g(f(7))=g(5)=-2 [f(7)=g(5) given]
