Answer:
-3
Step-by-step explanation:
The length of a segment is
sqrt( ( y2-y1)^2 + (x2-x1) ^2) = 2 sqrt(10)
sqrt( ( a-4 - -1)^2 + (2a -4) ^2) = 2 sqrt(10)
sqrt( ( a-4 +1)^2 + (2a -4) ^2) = 2 sqrt(10)
Combine like terms
sqrt( ( a-3)^2 + (2a -4) ^2) = 2 sqrt(10)
Square each side
( a-3)^2 + (2a -4) ^2) = 4 *(10)
FOIL the left side
a^2 -6a +9 + 4a^2 -16a +16 = 40
Combine like terms
5a^2 -22a +25 = 40
Subtract 40 from each side
5a^2 -22a -15 =0
Factor
(a - 5) (5 a + 3) = 0
Using the zero product property
a-5 =0 5a +3 = 0
a = 5 5a = -3
a=5 a = -3/5
The product of the terms is
5 * -3/5 = -3
look the image below
Answer:
Does the answer help you?
Does the answer help you?Please choose my answer as a brainliest answer and please rate.
Does the answer help you?Please choose my answer as a brainliest answer and please rate.It take a few mins to solve your question.
Answer:
V≈696.91
Step-by-step explanation:
V=4
3πr3=4
3·π·5.53≈696.90997
A chemical company makes two brands
of antifreeze. The first brand is 30% pure
antifreeze, and the second brand i$ 80% pure
antifreeze. In order to obtain 80 gallons of a
mixture that contains 70o£ pure antifreeze, hov
mabry gallons of each band ot antifneze must
bo used?
Answer:
16 bags for the first(30% pure) and 64 bags of the second(80% pure)
Step-by-step explanation:
If they are mixed in a ratio of x bags to y bags
(0.3x+0.8y)/(x+y) = 0.7
0.3x + 0.8y = 0.7(x+y)
Multiply both sides with 10
3x + 8y = 7(x+y)
4x = y ——(1)
x + y = 80 ——(2)
Solve simultaneously
x + 4x = 80
5x = 80
x = 16 bags
y = 4x = 64 bags
To prove a statement by mathematical induction, all we have to do is show that it is true for n+1. (True or False)
Answer:
False
Step-by-step explanation:
We also need to show that it is true for n=1
and for n=k+1
For a certain instant lottery game, the odds in favor of a win are given as 81 to 19. Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive.
Answer: 0.81
Step-by-step explanation:
[tex]81:19\ \text{can be written as the fraction}\ \dfrac{81}{81+19}=\dfrac{81}{100}=\large\boxed{0.81}[/tex]
If f(x)=ax+b and f(2)=1 and f(-3)=11, what is the value of A?
Answer:
a = -2
Step-by-step explanation:
f(x)=ax+b
f(2)=1
f(-3)=11
f(2) = 1 means 2a+b =1
f(-3)=11 means -3a + b = 11
Subtracting the two equations
-(-3a +b =11) becomes 3a -b = -11 so we can add
2a+b =1
3a - b = -11
----------------------
5a = -10
Divide by 5
5a/5 = -10/5
a=-2
Select the best answer for the question . 7. At a public swimming pool , the probability that an employee is a lifeguard is P(L) = 0.85 , and the probability that an employee is a teenager is P(T) = 0.58 . What's the probability that an employee is a lifeguard , given that the employee is a teenager ? O A. There isn't enough information given. O B. 1.47 OC. 0.68 O D.0.49
Answer:
D) 0.49
Step-by-step explanation:
0.85 * 0.58 = 0.49
The probability is:
D 0.49
Please answer this correctly without making mistakes
Answer:
Put 1/10 in the box.
Step-by-step explanation:
Since, Bluepoint and Milford are at same distance from Weston, the distance further than this to Oakdale is 1/10 miles.
Best Regards!
Answer:
To Oakdale to Milford:
2/5 mi
Step-by-step explanation:
1/10 + 3/20 + 3/20
1/10 = 2/20
then;
2/20 + 3/20 + 3/20 = (2+3+3)/20 = 8/20
8/20 = 2/5
Let x1 represent a quantitative independent variable and x2 represent a dummy variable for a 2-level qualitative independent variable. Which of the following models is the equation that produces two parallel curves, one for each level of your QL variable?
A. E(y) = ?0 + ?1x1 + ?2x12 + ?3x2
B. E(y) = ?0 + ?1x1 + ?3x2
C. E(y) = ?0 + ?x11 + ?3x2 + ?4x1x2
D. E(y) = ?0 + ?1x1 + ?2x12 + ?3x2 + ?4x1x2 + ?5x12x2
Answer:
D. E(y) = ?0 + ?1x1 + ?2x12 + ?3x2 + ?4x1x2 + ?5x12x2
Step-by-step explanation:
Quantitative variables are measured in terms of numbers, and figures. Independent variables are those which are reason for change in other variables. Dummy variables are numerical that represents categorical data. The range of these variables is small and they can take on only two quantitative values.
Find the maximum and minimum values of the function f(x,y)=2x2+3y2−4x−5 on the domain x2+y2≤100. The maximum value of f(x,y) is:
First find the critical points of f :
[tex]f(x,y)=2x^2+3y^2-4x-5=2(x-1)^2+3y^2-7[/tex]
[tex]\dfrac{\partial f}{\partial x}=2(x-1)=0\implies x=1[/tex]
[tex]\dfrac{\partial f}{\partial y}=6y=0\implies y=0[/tex]
so the point (1, 0) is the only critical point, at which we have
[tex]f(1,0)=-7[/tex]
Next check for critical points along the boundary, which can be found by converting to polar coordinates:
[tex]f(x,y)=f(10\cos t,10\sin t)=g(t)=295-40\cos t-100\cos^2t[/tex]
Find the critical points of g :
[tex]\dfrac{\mathrm dg}{\mathrm dt}=40\sin t+200\sin t\cos t=40\sin t(1+5\cos t)=0[/tex]
[tex]\implies\sin t=0\text{ OR }1+5\cos t=0[/tex]
[tex]\implies t=n\pi\text{ OR }t=\cos^{-1}\left(-\dfrac15\right)+2n\pi\text{ OR }t=-\cos^{-1}\left(-\dfrac15\right)+2n\pi[/tex]
where n is any integer. We get 4 critical points in the interval [0, 2π) at
[tex]t=0\implies f(10,0)=155[/tex]
[tex]t=\cos^{-1}\left(-\dfrac15\right)\implies f(-2,4\sqrt6)=299[/tex]
[tex]t=\pi\implies f(-10,0)=235[/tex]
[tex]t=2\pi-\cos^{-1}\left(-\dfrac15\right)\implies f(-2,-4\sqrt6)=299[/tex]
So f has a minimum of -7 and a maximum of 299.
What is the difference in their elevations?
An airplane flies at an altitude of 26,000 feet. A submarine dives to a depth of 700 feet below sea level
Answer:
their difference in elevations are: they both don't fly one fly and one dive if you take the airplane it works quicker but if you take the submarine you won't reach faster
PLEASE ANSWER ASAP THANK YOU!!! How much money will be in a bank account after 3 years if $9 is deposited at an interest rate of 5% compounded annually? Round to the nearest dollar.....
Answer:
10 bucks
Step-by-step explanation:
Money=9*(1+0.05)^3
Money=9*(1.05)^3=10.41≈10
Express the quotient of z1 and z2 in standard form given that [tex]z_{1} = -3[cos(\frac{-\pi }{4} )+isin(\frac{-\pi }{4} )][/tex] and [tex]z_{2} = 2\sqrt{2} [cos(\frac{-\pi }{2} )+isin(\frac{-\pi }{2} )][/tex]
Answer:
Solution : [tex]-\frac{3}{4}-\frac{3}{4}i[/tex]
Step-by-step explanation:
[tex]-3\left[\cos \left(\frac{-\pi }{4}\right)+i\sin \left(\frac{-\pi \:}{4}\right)\right]\:\div \:2\sqrt{2}\left[\cos \left(\frac{-\pi \:\:}{2}\right)+i\sin \left(\frac{-\pi \:\:\:}{2}\right)\right][/tex]
Let's apply trivial identities here. We know that cos(-π / 4) = √2 / 2, sin(-π / 4) = - √2 / 2, cos(-π / 2) = 0, sin(-π / 2) = - 1. Let's substitute those values,
[tex]\frac{-3\left(\frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2}i\right)}{2\sqrt{2}\left(0-1\right)i}[/tex]
=[tex]-3\left(\frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2}i\right)[/tex] ÷ [tex]2\sqrt{2}\left(0-1\right)i[/tex]
= [tex]3\left(-\frac{\sqrt{2}i}{2}+\frac{\sqrt{2}}{2}\right)[/tex] ÷ [tex]-2\sqrt{2}i[/tex]
= [tex]\frac{3\left(1-i\right)}{\sqrt{2}}[/tex]÷ [tex]2\sqrt{2}i[/tex] = [tex]-3-3i[/tex] ÷ [tex]4[/tex] = [tex]-\frac{3}{4}-\frac{3}{4}i[/tex]
As you can see your solution is the last option.
Find x. A. 3√3 B. 3 C. 2√3/3 D. √63
Answer:
[tex]\huge\boxed{\sf x = 3\sqrt{3}}[/tex]
Step-by-step explanation:
Cos 30 = Adjacent / Hypotenuse
Where Adjacent = x , Hypotenuse = 6
[tex]\frac{\sqrt{3} }{2}[/tex] = x / 6
x = [tex]\frac{\sqrt{3} }{2}[/tex] * 6
[tex]\sf x = 3\sqrt{3}[/tex]
Solve the equation. - 2(2x-4)= 4x
Answer:
-2(2x-4) = -4x+8 or 2(2x-4) ≠ 4x ; -4x+8 ≠ 4x
Step-by-step explanation:
Did you accidentally write =4x after your expression? If so, then let me explain why my answer is correct. I used distributive property of multiplication, so I multiplied -2 with 2x to get -4x, and -2 multiplied with -4 to get 8. So my final answer was -4x+8. If you did not accidentally put -4x, then my answer would be, 2(2x-4) ≠ 4x or -4x+8 ≠ 4x. Hope this helped.
Evaluate the expression for q = -2. 8q=
Answer:
-16
Step-by-step explanation:
8q
Let q = -2
8*-2
-16
Find the measure of a.
A. 60
B. 57
C. 40
D. 80
Answer:
Option (C)
Step-by-step explanation:
Since angle 'a' is the inscribed angle of the given triangle
Therefore, angle measure of the intercepted arc will be equal to the double of the inscribed angle.
x = 2a ⇒ a = [tex]\frac{x}{2}[/tex]
By the tangent-chord theorem,
"Angle between a chord and tangent measure the half of the angle measure of intercepted minor arc"
[tex]\frac{x}{2}[/tex] = 40°
Therefore, a = [tex]\frac{x}{2}[/tex] = 40°
Option (C) will be the answer.
A population culture begins with 20 strands of bacteria and then doubles every 4 hours. This can be modeled by , where t is time in hours. How many strands of bacteria are present at 20 hours?
Question 13 options:
A)
425 strands of bacteria
B)
567 strands of bacteria
C)
640 strands of bacteria
D)
375 strands of bacteria
Answer:
C) 640 strands of bacteria
Step-by-step explanation:
We are told in the question that the population doubles every 4 hours
Hence, formula to solve this question =
P(t) = Po × 2^t/k
From the question, we have the following information:
Beginning amount (Po) = 20 strands of bacteria
Rate(k) = 4 hours
Time(t) = 20 hours
Ending time (P(t)) = unknown
Ending amount = 20 × 2^20/4
= 20 × 2^5
= 20 × 320
= 640 strands of bacteria.
Therefore, the number of strands left after 20 hours is 640 strands of bacteria.
Find all values of x on the graph of f(x) = 2x3 + 6x2 + 7 at which there is a horizontal tangent line.
Answer:
the equation is not correct, u have to write like
ax'3+bx'2+cx+d
Answer:
x=-2 and x=0
Step-by-step explanation:
So I know it isn't x=-3 and x=0. So my guess is that it is x=0 and x=-2 and heres why.
First, I find the derivative of f(x)=2x^3+6x^2+7 which is 6x^2+12x
Then, I plugged in all the values of x's I had and I found out that you get 0 for -2 and 0 when you plug them in
So, in conclusion I believe the answer to be x=-2 and x=0
While walking in the country, you count 39 heads and 116 feet in a field of cows and chickens. How many of each animal are there?
Answer: 58
Step-by-step explanation:
its 58 because chickens have two feet each so divide 2 % 166 and its 58
because each chicken has 2 legs count the 2 legs up to 116 then u get ur answer
Giving a test to a group of students, the grades and gender are summarized below
A B C Total
Male 19 4 12 35
Female 3 13 5 21
Total 22 17 17 56
Let pp represent the percentage of all male students who would receive a grade of A on this test. Use a 99.5% confidence interval to estimate p to three decimal places.
Enter your answer as a tri-linear inequality using decimals (not percents).
< p
Answer:
Using Anova for a tri linear probability at ∝= 0.005
Step-by-step explanation:
Here simple probability cannot be used because we want to enter your answer as a tri-linear inequality using decimals (not percents).
So we can use ANOVA
Null hypothesis
H0: µA = µB=µC
all the means are equal
Alternative hypothesis
H1: Not all means are equal.
The significance level is set at α-0.005
The test statistic to use is
F = sb²/ sw²
Which if H0 is true has an F distribution with v₁=k-1 and v₂= n-k degrees of freedom .
The computations are as follows
XA (XA)² XB (XB)² XC (XC)² Total ∑X²
Male 19(361) 4(16) 12(144) 35 521
Female 3(9) 13 (169) 5 (25) 21 203
TotalTj 22 17 17 56 724
T²j (22)(22)
484 289 289 1062
∑X² 370 285 169
Correction Factor = CF = Tj²/n = (56)²/6= 522.67
Total SS ∑∑X²- C. F = 724- 522.67= 201.33
Between SS ∑T²j/r - C.F = 1062/ 2 - 522.877 =8.33
Within SS = Total SS - Between SS
=201.33- 8.33= 193
The Analysis of Variance Table is
Source Of Sum of Mean Computed
Variation d.f Squares Squares F
Between
Samples 1 8.33 8.33 8.33/ 48.25= 0.1726
Within
Samples 4 193 48.25
The critical region is F >F ₀.₀₀₅ (1,4) = 31.3328
Calculated value of F = 0.1726
Since it is smaller than 5 % reject H0.
However the decimal probability will be
Male 19 4 12 35
Female 3 13 5 21
Total 22 17 17 56
There are total 22 people who get an A but only 19 males who get an A
So the probability that a male gets an A is = 19/22= 0.8636
On a coordinate plane, line P Q goes through (negative 6, 4) and (4, negative 4). Point R On a coordinate plane, a line goes through (negative 4, 0) and (4, negative 4). A point is at (2, 3). What is the equation of the line that is parallel to the given line and passes through the point (2, 3)? x + 2y = 4 x + 2y = 8 2x + y = 4 2x + y = 8
Answer:
x + 2y = 8.
Step-by-step explanation:
Line goes through (-4, 0) and (4, -4).
The slope is (-4 - 0) / (4 - -4) = -4 / (4 + 4) = -4 / 8 = -1/2.
Since we are looking for the equation of the line parallel to that line, the slope will be the same.
We have an equation of y = -1/2x + b. We have a point at (2, 3). We can then say that y = 3 when x = 2.
3 = (-1/2) * 2 + b
b - 1 = 3
b = 4.
So, we have y = -1/2x + 4.
1/2x + y = 4
x + 2y = 8.
Hope this helps!
ANSWEAr
x + 2y = 8
because it is
Find the value of m.
L
R
A
3m +21 U
6m
O A. 14
ОВ. 7
Answer:
B
Step-by-step explanation:
Since LR=LA, RU=RA. 3m+21=6m, 3m=21, m=7
In 2018, the population of a district was 25,000. With a continuous annual growth rate of approximately 4%, what will the
population be in 2033 according to the exponential growth function?
Round the answer to the nearest whole number.
Answer:
40,000 populationsStep-by-step explanation:
Initial population in 2018 = 25,000
Annual growth rate (in %) = 4%
Yearly Increment in population = 4% of 25000
= 4/100 * 25000
= 250*4
= 1000
This means that the population increases by 1000 on yearly basis.
To determine what the population will be in 2033, we need to first know the amount of years we have between 2018 and 2033.
Amount of years we have between 2018 and 2033 = 2033-2018
= 15 years
After 15 years, the population will have increased by 15*1000 i.e 15,000 more than the initial population.
Hence the population in 2033 will be Initial population + Increment after 15years = 25,000+15000 = 40,000 population.
A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 407 gram setting. It is believed that the machine is underfilling the bags. A 20 bag sample had a mean of 397 grams with a standard deviation of 13. A level of significance of 0.05 will be used. Assume the population distribution is approximately normal. State the null and alternative hypotheses.
Answer:
Null hypothesis: μ = 407
Alternative hypothesis: μ < 407.
Step-by-step explanation:
In this case, the machine is SUPPOSED to fill the bag so that the bag weighs 407 grams. So, the null hypothesis will be that the machine is doing what it is supposed to be doing. And so, μ = 407 grams would be the null.
The worker thinks the machine is filling the bags to LESS THAN what it is supposed to. So, the alternative hypothesis is that the machine is NOT doing what it is supposed to and μ < 407 grams.
Hope this helps!
What is the value of b.
C=25
s=9
B=4c-s2
Answer:
82
Step-by-step explanation:
Plug in the variables into the equation and solve for B but remember your order of operations when solving multiplication/division before addition/subtraction.
B = 4*25-9*2
B = 100-18
B = 82
Solve x/10 = -7 A. x = 3 B. x = -0.7 C. x = -17 D. x = -70
Answer:
x = -70
Step-by-step explanation:
x/10 = -7
Multiply each side by 10
x/10*10 = -7*10
x = -70
What is the volume of the sphere shown below with a radius of 6?
A. 483 Cu, units
B. 2887 cu units
C. 1627 cu units
D. 14431 Cu, units
Answer:
B
Step-by-step explanation:
Volume of the sphere = (4/3)*pi*6^3=288*pi
Answer:
288 pi units^3
Step-by-step explanation:
The volume of a sphere is given by
V = 4/3 pi r^3
V = 4/3 pi (6)^3
V = 4/3 pi (216)
V = 288 pi units^3
If a dog has 2,000,000 toys and he gives 900,000 away. Then gets 2,000 more, also looses 2,000,000. He's sad but then also got 5,000,000,000 more and gives 1,672,293 out. How much does he have now? And how much he gave away. And how much he got.
Answer:
See below.
Step-by-step explanation:
He does not have enough to loose 2,000,000 at that point, so this whole problem is nonsense.
What is the slope of the line showed?
Answer:
2
Step-by-step explanation:
The formula for the slope of a line is rise over run. We know that the slope of the line will be positive because the line is going up from left to right.
Rise is the change on the y-axis, going up and down. Run is the change on the x-axis, going from left to right.
Let's start from the origin (0,0). To reach the next point on the line, we have to go up two points (rise) and over one point (run).
Slope = rise/run
Slope = 2/1
Slope = 2
Hope that helps.
Answer:
slope=2
Step-by-step explanation:
take two points from graph (0,0) and (1,2)
m=y2-y1/x2-x1
m=2-0/1-0
m=2
Which graph best represents the equation –x + 2y = 4?
Answer:
C
Step-by-step explanation:
Convert the equation into slope intercept form : y=mx+b
2y=x+4
y=1/2x + 2
The m is the slope and the b is the y intercept
In this equation, the slope is 1/2 and the y intercept is 2
The only graph with y intercept 2 is C