Answer:
x = sqrt(13) - 4 or x = -4 - sqrt(13)
Step-by-step explanation:
Solve for x:
x^2 + 8 x + 3 = 0
Hint: | Solve the quadratic equation by completing the square.
Subtract 3 from both sides:
x^2 + 8 x = -3
Hint: | Take one half of the coefficient of x and square it, then add it to both sides.
Add 16 to both sides:
x^2 + 8 x + 16 = 13
Hint: | Factor the left hand side.
Write the left hand side as a square:
(x + 4)^2 = 13
Hint: | Eliminate the exponent on the left hand side.
Take the square root of both sides:
x + 4 = sqrt(13) or x + 4 = -sqrt(13)
Hint: | Look at the first equation: Solve for x.
Subtract 4 from both sides:
x = sqrt(13) - 4 or x + 4 = -sqrt(13)
Hint: | Look at the second equation: Solve for x.
Subtract 4 from both sides:
Answer: x = sqrt(13) - 4 or x = -4 - sqrt(13)
What is a Regression equation
Answer:
Regression equations can help you figure out if your data can be fit to an equation.This is extremely useful if you want to make predictions from your data- either future predictions or indications of past behavior.For example,you might want to know what your savings are going to be worth in the future.There are several types of regression equations,some of the more common include exponential and simoke linear regression.In elementary statistics,the regression equation you are most likely to come across is the linear form.
Write the perimeter of the floor plan shown as an algebraic expression in x.
Answer: 8+2x
Step-by-step explanation:
Hi, Perimeter is the distance around a two-dimensional shape.
To calculate it, we have to add all the side lengths of the figure. The missing side is the ? side (right side). To obtain it we have to subtract the top right side length (2) to the left side length (12)
So, the expression is equal to:
P = 12+ (x-4) + (x-12) +2 +(12-2)
P = 12+ x - 4 +x -12+2 +10
P = 12-4-12+2+10+x+x
P =8+2x
What’s the correct answer for this?
Answer:
6 units
Step-by-step explanation:
We find the distance by subtracting the "ends"
=-4-2= -6 (ignoring the negative)
We get
=6
help please quick 100 points quick tell me what to write please if you now how to do this
Answer:
8 footballs
18 basketballs
36 baseballs
24 softballs
Step-by-step explanation:
Let f = footballs
f = 8
Let b = basketballs
b = 2+2f = 2 +2(8) = 2 +16 = 18
Let B = baseballs
B = 5f -4 = 5(8) -4 = 40-4 = 36
Let s = softballs
s = 6+1/2B = 6+1/2(36) = 6+18 = 24
The total is 86
f+b+B +s = 86
8+18+36+24 = 86
86=86
There are 8 footballs.
Two more than twice the number of footballs are basketballs:
2f + 2 = b
f = number of footballs
b = number of basketballs
In the first statement, there are 8 footballs. So, f = 8
2(8) + 2 = b
16 + 2 = b
18 = b
Therefore, there are 18 basketballs.
Four less than 5 times the number of footballs are baseballs:
5f - 4 = a
f = number of footballs
a = number of baseballs
In the first statement, there are 8 footballs. So, f = 8
5(8) - 4 = a
40 - 4 = a
36 = a
Therefore, there are 36 baseballs.
Six more than half of the baseballs are softballs:
a/2 + 6 = s
a = number of baseballs
s = number of softballs
In the third statement, there are 36 baseballs. So, a = 36
(36)/2 + 6 = s
18 + 6 = s
24 = s
Therefore, there are 24 softballs.
Best of Luck!
Find the arc length of the partial circle. with a radius of 1
Answer:
1/2π
Step-by-step explanation:
For khan, you HAVE to put the pi symbol. just type pi and itll work
Answer:
1/2 pi (Sorry i don't have the pi symbol)
Step-by-step explanation:
Plane P cuts sphere o in a circle that has diameter
20. If the diameter of the sphere is 30, how far is the
plane from O?
Answer:
5√5 ≈ 11.18 units
Step-by-step explanation:
The Pythagorean theorem can be used to find the unknown leg of a triangle with hypotenuse 15 and one leg 10:
d = √(15^2 -10^2) = 5√(3^2 -2^2) = 5√5
The plane is 5√5 units from the center of the sphere.
A medical researcher is studying the spread of a virus in a population of 1000 laboratory mice. During any week, there is an 80% probability that an infected mouse will overcome the virus, and during the same week there is a 10% probability that a noninfected mouse will become infected. Three hundred mice are currently infected with the virus. How many will be infected next week and in 3 weeks
Answer:
The number of mice that will be infected next week are 130 while
The number of mice that will be infected in 3 weeks are 111
Step-by-step explanation:
From the information given , the researcher is studying the spread of a virus in a population of 1000 laboratory mice. i.e, n = 1000
Number of infected = 300
Non infected = 1000 - 300 = 700
Probability an infected mouse will overcome = 80% = 0.8
Probability a noninfected mouse becomes infected = 10% = 0.10
The number of infected that will overcome = 0.8 * 300 = 240
The number of non infected that will become infected = 0.1 * 700 = 70
The number that will be infected on the first week =
300 - 240 + 70
= 130
Number that will be healthy on the first week =
700 + 240 - 70
= 870
Calculating for week 2:
The number of infected that will overcome = 0.8 * 130 = 104
The number of non infected that will become infected = 0.10 * 870 = 87
The number that will be infected on the second week =
130 - 104 + 87
= 113
Number that will be healthy on the second week =
870 + 107 - 87
= 887
Calculating for week 3:
The number of infected that will overcome = 0.8 * 113 = 90.4
The number of non infected that will become infected = 0.10 * 887 = 88.7
The number that will be infected on the third week =
113 - 90.4 + 88.7
= 111.3 ≈ 111
Number that will be healthy on the third week =
887 + 90.4 - 88.7
= 888.7 ≈ 889
From our calculations, the number of mice that will be infected next week are 130
The number of mice that will be infected in 3 weeks are 111
Given the equation of the parabola - 36y = ?
The focus of the parabola is:
(0,9)
(-9,0)
(0,-9)
Correct question is ;
Given the equation of the parabola x² = -36y
The focus of the parabola is:
Answer:
Option C - Focus = (0,-9)
Step-by-step explanation:
The equation of the parabola is:
x² = -36y
Thus, y = - x²/36
Using the vertex form,
y = a(x − h)² + k, to determine the values of a, h, and k.
We will have;
y = (-1/36)(x − 0)² + 0
Thus,
a = - 1/36
h = 0
k = 0
The distance (p) from the vertex to a focus of the parabola is gotten by using the following formula.
p = 1/4a
So, p = 1/(4*(-1/36))
p = - 1/(1/9)
p = -9
Now, The focus of a parabola can be found by adding p to the y-coordinate k if the parabola opens up or down.
Focus is (h, k+p)
Plugging in the relevant values, we have;
Focus = (0, (0 + (-9))
Focus = (0,-9)
1567÷135
plz help 50 points
Answer:
11.60740741
Step-by-step explanation:
Answer:
11.6074074074
Step-by-step explanation:
There are 14 math teachers and 26 science teachers at
school today. What is the ratio of math teachers to math
and science teachers at school?
Answer: 2.86
Step-by-step explanation:
14+26=40
40/14
Answer:
2.86
Step-by-step explanation:
You invest $2,000 into a savings account that gets 5% interest compounded yearly. How much money will you have after 7 years? A. $2,814.20 B. $54,112.88 C. $14,713.23 D. $3,286.33
Answer:
You will have $2,814.20 after 7 years
Step-by-step explanation:
We are given that You invest $2,000 into a savings account that gets 5% interest compounded yearly.
Principal = $2000
Rate of interest = 5% =0.05
We are supposed to find How much money will you have after 7 years?
Formula : [tex]A = P(1+r)^t[/tex]
A= Amount
P = Principal
t =time
r = rate of interest in decimals
Substitute the values in the formula :
[tex]A = 2000(1+0.05)^7[/tex]
A=2814.20
So, Option A is true
Hence You will have $2,814.20 after 7 years
PLEASE HEL0LP ME MY TEACHER IS NOT GOING TO BE HAPPY - MATHS !!!!
Answer:
No
Step-by-step explanation:
Since shape a has 32 squares
And shape b has 42
So b is bigger
The perimeter of a rectangle is 62 meters. The length is 4 more than 2 times the width. What is the length?
Answer:
4x+ 1 = 24 + 1 = 25 m.
Step-by-step explanation:
Given, perimeter = 62 m. Perimeter : 2 (L+W) = 62 m. hence, L+W = 31 m. x = 30/5
Answer:
Step-by-step explanation:
let width be x
length = 2x + 4
2(x + 2x + 4) = 62
6x + 8 = 62
6x = 54
x = 9
length = 2(9) + 4 = 22cm
Twenty words were randomly selected from two textbooks. Each set gives the number of letters in each of the twenty words for that textbook.
Briefly describe how the word lengths compare between textbook 2 and textbook 1.
Briefly describe the variability in the length of words in textbook 2 compared to textbook 1. PLEASE HURRY :(
Answer:
k = 13The smallest zero or root is x = -10
Step-by-step explanation:
you can write "x^2" to mean "x squared"
f(x) = x^2+3x-10
f(x+5) = (x+5)^2+3(x+5)-10 ... replace every x with x+5
f(x+5) = (x^2+10x+25)+3(x+5)-10
f(x+5) = x^2+10x+25+3x+15-10
f(x+5) = x^2+13x+30
Compare this with x^2+kx+30 and we see that k = 13
Factor and solve the equation below
x^2+13x+30 = 0
(x+10)(x+3) = 0
x+10 = 0 or x+3 = 0
x = -10 or x = -3
The smallest zero is x = -10 as its the left-most value on a number line.
30 points!
The soccer team knows that if they score at least 8 goals, they will win the game. Which of the following inequalities shows the number of goals the team needs to win.
g ≥ 8 goals
g < 8 goals
g > 8 goals
g ≤ 8 goals
Answer:
g≥8
Step-by-step explanation:
They need at least 8 goals
g≥8
Answer:
g ≥ 8 goals
Step-by-step explanation:
Atleast 8 means greater than or equal to 8
Parallel lines s and t are cut by a transversal, r.
Parallel lines s and t are cut by transversal r. Clockwise from top left, the angles formed with r and s are 1, 2, 3, 4; the angles formed with r and t are 5, 6, 7, 8.
If the measure of angle 1 is 68°, what is the measure of angle 5?
22°
68°
112°
158°
Answer:
68°
Step-by-step explanation:
Angles 1 and 5 are corresponding angles on parallel lines, hence they are equal
Answer:
B.
Step-by-step explanation:
what’s the gcf of x^2 and 5x
Answer:
the GCF of x^2 and 5x is x
Find the prime factors of each term in order to find the greatest common factor (GCF).
I really need help!! HELP ASAP PLEASE!!!
Which figure has an area of 12 square units?
Answer:
Should be the bottom one
Step-by-step explanation:
You can find this by counting. It is the only one with 12 units.
Answer:
Step-by-step explanation:is number 4 i pick it and its correct
Sara Bought a computer that was originally priced at $896.The computer was on sale for 12% off. When she bought the computer, a 7% tax was added to the sale price. How much did Sara spend on the computer. Round to the nearest cent!
Answer:
$733.29. Simply because you take $896•0.12 to find the 12% off and then you take that subtracted by the starting total. After you get the 12% off then you multiply that number by .07 to get the sales tax. After you find that then you add the number you got after multiplying to the number you got after taking off the 12%.
Step-by-step explanation:
Can you work out this math puzzle?
The value of the puzzle is 17
The value of the triangle :
30/3 = 10Value of Circle :
10/2 = 5Value of whole yellow square :
8/2 = 4Value of half-yellow square :
4/2 = 2Using the above information:
Triangle + Circle + half-square
10 + 5 + 2 = 17
Therefore, the solution to the puzzle is 17
Learn more on puzzles : https://brainly.com/question/31416634
#SPJ6
if each of the 4 shelves holds 14 movies, how many movies does betty have on her shelving unit? show your work
copy paste this
4x + 6
4(14) + 6 (substituting x = 14)
56 + 6
62
2 x 6.9 - 4.6 + 1.3 =
Answer:
10.5
Step-by-step explanation:
Answer:
Here is the answer:
Step-by-step explanation:
10.5
What function has zeros at x=10 and x=2
Answer:
f(x) = x^2 -12x +20
Step-by-step explanation:
There are an infinite number of functions with zeros at those values of x. One simple polynomial function with those zeros is ...
f(x) = (x -10)(x -2) . . . . . each zero contributes a factor
f(x) = x^2 -12x +20
what type of function has a common rate of change
Answer:
linear
Step-by-step explanation:
A linear function has a constant rate of change.
_____
The word "common" is usually used to refer to a shared characteristic of two or more entities. It would not ordinarily be used to describe a characteristic of one function. We're not quite sure what you mean by "has a common rate of change."
Please help ASAP! I will mark Brainliest! Please answer CORRECTLY! No guessing! Show your work!
Answer:
P represents the population in year 0
Step-by-step explanation:
The exponential growth function is f(x) = a (1 + r)^t, where a is the initial
amount (at t = 0), (1 + r) is the factor of growth , r is the rate of growth
in decimal ant is the time of growth
the function C(t) = P(1 + r)^t represents the population of
centerville at year t, where P is the initial population and r is the
rate of increase
If your investment is increased 10% annually, then that means
each year, your total has multiplied itself by 110% (the growth factor
is 1 + 10/100 = 1.1)
(1 + r) is the factor grows each year
C(t) = P(1 + r)^t
C depends on P(starting population) , r(the increasing rate and
t(the time in year)
r is the rate of increase means the percentage of increasing , then
0 < r < 1
r is not less than 0
P is the initial amount when t = 0
P represents the population in year 0
Answer:
P represents the population in year 0
Step-by-step explanation:
0.6666666……… as a percentage
Answer:
2/3
Step-by-step explanation:
Answer: 66.66%
Step-by-step explanation: You multiply 0.66666... by 100 and that gives you 66.66
Simplifying products and quotients of powers
7^2•7^8/7^4=7^a/7^4=7^b
A=
b=
Answer:
a=10
b=6
Step-by-step explanation:
add 2 to 8, to get a, then subtract 4 from 10 to get b
Answer:
10 and 6
Step-by-step explanation:
Thirty percent of students in a calculus class and twenty percent of students in a statistics course receive A’s. Furthermore, 60 percent of students with an A in calculus receive an A in the statistics course. What is the probability that a student who receives an A in statistics will also receive an A in calculus?
Answer:
90% probability that a student who receives an A in statistics will also receive an A in calculus
Step-by-step explanation:
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: A in statistics.
Event B: A is calculus
Twenty percent of students in a statistics course receive A’s.
This means that [tex]P(A) = 0.2[/tex]
Furthermore, 60 percent of students with an A in calculus receive an A in the statistics course.
Thirty percent of students in a calculus class receive an A.
This means that [tex]P(A \cap B) = 0.6*0.3 = 0.18[/tex]
What is the probability that a student who receives an A in statistics will also receive an A in calculus?
[tex]P(B|A) = \frac{0.18}{0.2} = 0.9[/tex]
90% probability that a student who receives an A in statistics will also receive an A in calculus
Write an inequality that best matches this description
Mary has at least 3 times the amount of cash that ashley and oscar have combined
Answer:
[tex]x \geq 3(y + z)[/tex]
Step-by-step explanation:
I am going to say that:
Mary's amount is x.
Ashley's amount is y.
Oscar's amount is z.
Mary has at least 3 times the amount of cash that ashley and oscar have combined
Ashley's and Oscar's combined amount is y + z.
3 times this amount is 3(y + z).
At least 3 times means that z is equal or greater than 3(y + z).
So
[tex]x \geq 3(y + z)[/tex]
9/4 - 4/3 plz help me
Answer:
11/12
Step-by-step explanation:
Find the common denominator.
4 and 3 both go into 12.
4 goes into twelve three times so multiply the denom and the num.
9/4 = 27/12
3 goes into twelve four times.
4/3 = 16/12
Subtract.
27/12-16/12
= 11/12
Answer: 11/12
Step-by-step explanation:
multiply 3 and 4 to get a common denominator.
multiply 3 by 9 and 4 by 4
this gets u 27/12 and 16/12
subtract.
11/12
