Answer:
The possible values of [tex]b[/tex] are -2.944 and -9.055, respectively.
Step-by-step explanation:
From statement we know that [tex]AB = 2\cdot BC[/tex]. By Analytical Geometry, we use the equation of a line segment, which is an application of the Pythagorean Theorem:
[tex]AB = 2\cdot BC[/tex]
[tex]\sqrt{(x_{B}-x_{A})^{2}+(y_{B}-y_{A})^{2}} = 2\cdot \sqrt{(x_{C}-x_{B})^{2}+(y_{C}-y_{B})^{2}}[/tex] (1)
Where:
[tex]x_{A}[/tex], [tex]x_{B}[/tex], [tex]x_{C}[/tex] - x-Coordinates of points A, B and C.
[tex]y_{A}, y_{B}, y_{C}[/tex] - y-Coordinates of points A, B and C.
[tex](x_{B}-x_{A})^{2}+(y_{B}-y_{A})^{2} = 4\cdot (x_{C}-x_{B})^{2}+4\cdot (y_{C}-y_{B})^{2}[/tex]
Then, we expand and simplify the expression above:
[tex]x_{B}^{2}-2\cdot x_{A}\cdot x_{B} +x_{A}^{2} +y_{B}^{2}-2\cdot y_{A}\cdot y_{B} + y_{A}^{2} = 4\cdot (x_{C}^{2}-2\cdot x_{C}\cdot x_{B}+x_{B}^{2})+4\cdot (y_{C}^{2}-2\cdot y_{C}\cdot y_{B}+y_{B}^{2})[/tex]
[tex]x_{B}^{2}-2\cdot x_{A}\cdot x_{B} + x_{A}^{2} +y_{B}^{2}-2\cdot y_{A}\cdot y_{B} + y_{A}^{2} = 4\cdot x_{A}^{2}-8\cdot x_{C}\cdot x_{B}+4\cdot x_{B}^{2}+4\cdot y_{C}^{2}-8\cdot y_{C}\cdot y_{B}+4\cdot y_{B}^{2}[/tex]
If we know that [tex]x_{A} = 5[/tex], [tex]y_{A} = 6[/tex], [tex]x_{B} = 1[/tex], [tex]y_{B} = b[/tex], [tex]x_{C} = 1[/tex] and [tex]y_{C} = -3[/tex], then we have the following expression:
[tex]1 -10 +25 +b^{2} -12\cdot b+36 = 100 -8 +4 +36+24\cdot b +4\cdot b^{2}[/tex]
[tex]b^{2}-12\cdot b +52 = 4\cdot b^{2}+24\cdot b +132[/tex]
[tex]3\cdot b^{2}+36\cdot b +80 = 0[/tex]
This is a second order polynomial, which means the existence of two possible real solutions. By Quadratic Formula, we have the following y-coordinates for point B:
[tex]b_{1} \approx -2.944[/tex], [tex]b_{2} \approx -9.055[/tex]
In consequence, the possible values of [tex]b[/tex] are -2.944 and -9.055, respectively.
hey guys i got one more- 8 mi.=_yd. Thanks!!!(PLEASE ANWER FAST!!)
Answer:
if mi stands for miles then 8 miles = 14080 yards
Step-by-step explanation:
8 x 1760
Answer:
14080
Step-by-step explanation:
8 * 1760 = 14080
Calculate the balance for a $4,465 deposit in an account with an APR of 3.0% that compounds interest daily that is invested for 5 years?
Express your answer rounded correctly to the nearest cent. Do not include units on your answer.
help hurry
Compound interest formula:
Total = start value x ( 1 + rate/compound rate) ^( compound rate x time)
Total = 4,465(1 + .03/365)^(365x5)
Total = $5,187.56
The balance after 5 years will be $5177 and 10 cents.
How to calculate compound interest?
Compound interest is calculated by following formula:
[tex]A(1+\frac{r}{n})^{nt}[/tex]
Here:
A=principle amount=$4465
r=rate of interest/100=3/100=0.03
n=no. of days interest is applied=365 days
t=time period of interest=5 years
Putting all the values in the formula we get:
[tex]4465(1+0.03/365)^{365*5}=$5177.1[/tex]
Therefore, The amount at the end will be $5177 and 10 cents.
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Can someone tell me how to do this and give me the answer please
Answer:
C. 94 Supplementary angles
Step-by-step explanation:
What causes a sequence to be arithmetic? Geometric?
Answer:
An arithmetic sequence has a constant difference between each term. ... A geometric sequence has a constant ratio (multiplier) between each term. An example is: 2,4,8,16,32,… So to find the next term in the sequence we would multiply the previous term by 2.
Step-by-step explanation:
Two lines, A and B, are represented by the following equations:
Line A: 2x + y = 6
Line B: x + y = 4
Which statement is true about the solution to the set of equations? (4 points)
a It is (2, 2).
b There are infinitely many solutions.
c It is (4, 0).
d There is no solution.
Answer:
The answer is B! if you want to do more of these problems may I recommend using Desmos?
Answer:
It is (2, 2).
Step-by-step explanation:
The radius of a circle is 16 cm. Find its area in terms of \piπ
Answer256pi
Step-by-step explanation:
Area=pi*r^2
=pi*16^2
256pi
Jackson has 180 pieces of gum. He wants to share the pieces equally with his friends. Which table shows the relationship between n, the number of people who received gum, and p the number of pieces of gum each person receives?
Answer:
Step-by-step explanation:
Below is the graph of a trigonometric function. It has a maximum point at (-5, 2.5) and a minimum point at
(-1.7, -4.5).
Answer:-1
Step-by-step explanation:
2.5+(-4.5) then / 2
Joe bought four books at a bookstore. Here are their prices (in dollars). 7.34, 11, 13.2, 5.3 What is the total amount Joe paid at the bookstore?
Answer:
36.84
Step-by-step explanation:
just add them it is all really just basic addition nothing more to it
What is the mode of the data set?
A. 90
B. No mode
C. 85.5
D. 49
Hurry and give a SERIOUS answer! Will give brainliest.
Answer:
mode is the number listed most often and data can have more then 1 mode
the numbers most listed in the image are: 5 and zero
Step-by-step explanation:
I hope this helped!
Answer:
90
Step-by-step explanation:
mode = A number that appears most often is the mode.
Seth needs to buy mulch to cover a circular garden. The garden has a radius of 5ft. Mulch costs $0.25 per square foot. How much will it cost Seth to cover his garden in mulch?
Answer:
?????
Step-by-step explanation:
12x 0.25=? ?x 5= $?
Round the nearest hundredth. 53.789
Answer: 53.79
Step-by-step explanation:
The average value of a function f(x, y, z) over a solid region E is defined to be fave = 1 V(E) E f(x, y, z) dV where V(E) is the volume of E. For instance, if ???? is a density function, then ????ave is the average density of E. Find the average value of the function f(x, y, z) = 3x2z + 3y2z over the region enclosed by the paraboloid z = 4 − x2 − y2 and the plane z = 0.
Answer:
The average function [tex]f_{avg}[/tex] value = 4
Step-by-step explanation:
Given that:
[tex]f(x,y,z) = 3x^2z+3y^2z[/tex]
The enclosed region [tex]z = 4 -x^2 -y^2[/tex] and the plane z = 0.
Over an area E, the average value of a function f(x,y,z) is:
[tex]f_{avg} = \dfrac{1}{V_{E}} \iiint_E f(x,y,z) dV ------ (1)[/tex]
where;
[tex]V_E[/tex] = volume of region E
To find the volume use cylindrical coordinates;
[tex]x=rcos \theta; \ \ \ y = rsin \theta; \ \ \ z = z[/tex]
Then;
E = 0 ≤ r ≤2, 0 ≤ θ ≤ 2π, 0 ≤ z ≤ 4 - r²
[tex]V_E = \int^{2 \pi}_{0} \int^{2}_{0} \int^{4-r^2}_{0} \ rdzdrd \theta[/tex]
[tex]V_E = \int^{2 \pi}_{0} \int^{2}_{0} r(4-r^2) \ drd \theta[/tex]
[tex]V_E = \int^{2 \pi}_{0} \int^{2}_{0} (4r-r^3) \ drd \theta[/tex]
[tex]V_E = \int^{2 \pi}_{0} \Big(2r^2- \dfrac{r^4}{4} \Big)^2_0 \ d \theta[/tex]
[tex]V_E = 4(2 \pi)\\\\ V_E = 8 \pi[/tex]
However, from equation (1):
[tex]f_{avg} = \dfrac{1}{V_E} \iiint_E f(x,y,z) \ dV \\ \\ = \dfrac{1}{8 \pi} \iiint_E (3x^2z + 3y^2 z) dV \\ \\ = \dfrac{1}{8 \pi } \int^{2 \pi}_{0} \int^{2 }_{0} \int^{4 - r^2}_{0} \ \ 3zr^2 \ rdzdrd\theta \\ \\ = \dfrac{3}{8 \pi} \int^{2 \pi}_{0} \int^{2 }_{0} \Big(\dfrac{z^2}{2}\Big)^{4-r^2}_{0} \ r^3 drd\theta \\ \\ = \dfrac{3}{16 \pi} \int^{2 \pi}_{0} \int^{2 }_{0} (4-r^2)^2 \ r^3 \ dr d\theta[/tex]
[tex]= \dfrac{3}{16 \pi} \int^{2 \pi}_{0} \int^{2 }_{0} (16-8r^2 + r^4)r^3 \ dr d\theta \\ \\ = \dfrac{3}{16 \pi} \int^{2 \pi}_{0} \int^{2 }_{0} (16r^3 -8r^5 + r^7) \ dr d \theta \\ \\ = = \dfrac{3}{16 \pi} \int^{2 \pi}_{0} \Big (4r^4 - \dfrac{8}{6}r^6 + \dfrac{r^8}{8} \Big)^2_0 \ d \theta \\ \\ = \dfrac{3}{16 \pi } (2 \pi) \Big (64 - \dfrac{8}{6} \times 64 \times \dfrac{256}{8} \Big) \\ \\ = \dfrac{3}{16 \pi} (2 \pi) (\dfrac{32}{3}) \\ \\ = 4[/tex]
your most exciting day of school
Answer:
first day. yehahhhhhhhh
Answer:
School isn't exciting for me, lol.
Step-by-step explanation:
Yolanda painted 2/5 of a wall in 40 minutes. If she keeps painting at the same rate, how much longer will it take her to finish painting the wall
Answer:
60 minutes
Step-by-step explanation:
She painted 2/5 of the wall.
She still needs to paint 3/5 of the wall.
3 is 50% more than 2, so 3/5 is 1.5 times 2/5, so it will take her 1.5 times the time it took so far.
1.5 * 40 minutes = 60 minutes.
Answer: 60 minutes
A football stadium holds 5000 people.
On a match day 5 of the stadium is full.
40% of the children are girls.
The ratio of adults to children is 2 : 3
How many of the children attending are boys?
Answer:
720 boysss
Step-by-step explanation:
Yep thts the answerrr...
32 ÷ 24 plese help me
Answer: 1.333
Step-by-step explanation:
Answer:
1.33
Step-by-step explanation:
nothing much to explain
Graph the line.
Y= 4/3 x
Answer:
hope this helps :)
Step-by-step explanation:
HELP ASAP!!!!!. A spinner has three sections colored green, purple, and pink. If the spinner is spun twice, how many branches would the tree diagram that represents this situation have? 6 5 9 12
Answer:
9
Step-by-step explanation:
you would do 3+3+3 because there are 3 colors
And i just got it right on my quiz.
There will be 9 branches in the tree diagram of the situation.
What is tree diagram?In probability theory, tree diagrams can be used to represent probability spaces. A tree diagram can represent a set of independent events or conditional probabilities. Each node in the graph represents an event and is associated with the probability of that event.
Given,
A spinner of three sections colored green, purple and pink.
Number of outcomes = 3
spinner is spun twice,
then number of outcomes = 3 × 3 = 9
Number of branches in tree = 9
Hence, 9 branches will be there in probability tree diagram.
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Assume that the weight of cereal in a "12.6 ounce box" is N(µ,0.42). The Food and Drug Association (FDA) allows only a small percentage of boxes to contain less than 12.6 ounces. You collect a random sample of n = 35 boxes and find that the sample mean is 12.8. Test the null hypothesis H0: µ = 13 against the alternative hypothesis HA: µ < 13 at level of significance α = 0.01
Answer:
We reject the null hypothesis and accept the alternate hypothesis, that is, that the mean is less than 13 ounces.
Step-by-step explanation:
The null hypothesis is:
[tex]H_{0}: \mu = 13[/tex]
The alternate hypotesis is:
[tex]H_{a}: \mu < 13[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
13 is tested at the null hypothesis:
This means that [tex]\mu = 13[/tex]
N(µ,0.42)
This means that the standard deviation is 0.42, that is, [tex]\sigma = 0.42[/tex]
You collect a random sample of n = 35 boxes and find that the sample mean is 12.8.
This means that [tex]n = 35, X = 12.8[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{12.8 - 13}{\frac{0.42}{\sqrt{35}}}[/tex]
[tex]z = -2.82[/tex]
Pvalue of the test:
The pvalue of the test is the pvalue of z = -2.82.
Looking at the z table, z = -2.82 has a pvalue of 0.0024
0.0024 < 0.01, which means that we reject the null hypothesis and accept the alternate hypothesis, that is, that the mean is less than 13 ounces.
Can someone answer this.
Answer:
The first choice
Step-by-step explanation:
3(6x-5)-7(3x+10)=0. solve for x
Answer:
x = -85/3
Step-by-step explanation:
The solution is, the value of x is - 33.33 in 3(6x-5)-7(3x+10)=0.
What is simplification?Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.
here, we have,
given expression is:
3(6x-5)-7(3x+10)=0
now, we have to simplify the expression to solve for x
we get,
3(6x-5)-7(3x+10)=0
or, 18x - 30 - 21x - 70 = 0
or, 18x - 21x -30 - 70 = 0
or, - 3x - 100 = 0
or, 3x = -100
or, x = -100/3
or, x = - 33.33
Hence, The solution is, the value of x is - 33.33 in 3(6x-5)-7(3x+10)=0.
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I need the answer to
Answer:
I think its B
Hope this helps
Susie says that it she has a quick way to determine the least common multiple of two numbers; you just multiply the numbers. Susie checked it with 3 and 5 and with 4 and 7 and method worked both times. Is Susie’s method a valid way to determine the least common multiple of two counting numbers? Explain.
Answer:
No, it is not a valid way
Step-by-step explanation:
Required
Is Susie's method valid?
Susie's method worked because 4 & 7 and 3 & 5 do not have a common factor.
In other words, Susie's method will not work when the two numbers have a common factor.
Take for instance, the LCM of 2 and 4.
Using Susie's method, the LCM will be 8 (i.e. 2 * 4) whereas the LCM is 4.
HELP ME PLEASE
15 points and brainliest if right
Step-by-step explanation:
area of a rectangle bh
4x7=28
7x9=63
9x4=36
the only rectangle that has an area equal to 28 is the 4x7 which is the front face and back face.
Hope that helps :)
Pls help with this problem. This is due today!
Answer:
2.8 > 2.8< i think
Step-by-step explanation:
Please help
here the question
Rosalina just started a new job. She has $500 in her bank account. Every week, she deposits $40 into her bank account.
A)
Write an expression to represent how much Rosalina has in her account at any given time using x to represent the number of weeks.
I ALREADY SOLVED A BUT I NEED HELP WITH B!!
B) Rosalina wants to save $700 for the new smart tv write and equation to determine how many weeks (x) it will take for rosalina to have enough money to purchase her new tv
HELP ME PLEASE WITH B I ALREADY SOLVED A
THANK YOU!!
Answer:x=18
Step-by-step explanation:
if she deposites 40 every week 40 times 18 is 720 so in 18 weeks she can have a t.V
Solve the equation 6 = p -8
Answer:
p = 14
Step-by-step explanation:
6 = p - 8
We want to isolate p, so add 8 to both sides.
6 + 8 = p
Add.
14 = p
Hope this helps!
Answer is: P = 14
Switch up the numbers.
6 = p - 8 → 6 + 8 = P
Solve for P.
6 + 8 = 14
Hence, 14 is the answer.
A marble is drawn at random from the bag shown below. The bag contains 3 green, 4 yellow, 5 blue, and 8 pink
marbles.
What is P(not yellow)?
A 1/5 B 2/5 C 4/5
Answer: c 4/5
Step-by-step explanation: out of 5 only four are chosen leaving us with an answer of 4/5 :D hope it helped
Owen and Ethan have $175 together. How much money does each of them have if Ethan has $33 more than Owen.
Owen has $
Ethan has $
Answer:
Owen has $71 and Ethan has $104
Step-by-step explanation:
Create a system of equations where o is how much money Owen has, and e is how much Ethan has
x + e = 175
e = x + 33
Solve by substitution by plugging in o + 33 in as e, in the first equation
o + e = 175
o + (o + 33) = 175
2o + 33 = 175
2o = 142
o = 71
So, Owen has $71 dollars
To find how much Ethan has, add 33 to this, since he has $33 more than Owen
71 + 33
= 104
So, Owen has $71 and Ethan has $104