Answer:
Yes
Step-by-step explanation:
Factoring is the process of breaking a polynomial into its factors.
Standard Form
It is easiest to factor when in standard form. Standard form is when the terms are listed from highest power to lowest.
Standard form is [tex]x^2-6x+8[/tex]Factoring
To find if two expressions are equal we can either factor the quadratic or multiply out the binomials. I find factoring to be faster and easier, so I will show that.
There are multiple techniques to factor; I will be explaining one of them. One way to factor quadratics is to find 2 numbers that multiply to c (the constant) and sum to b (the second term). In this case, the numbers -4 and -2 fit these requirements.
-4 * -2 = 8-4 + -2 = -6This means that [tex]x^2-6x+8[/tex] factored is [tex](x-4)(x-2)[/tex]. Thus, they are equivalent.
caffeine takes a certain amount of time to leave your system. if you drink 3 cups of coffee in the morning, the function that represents the amount of caffeine remaining in your body after drinking the coffee is given by g(t)=130(.8246)t where t is time in hours
A. How much caffeine remains in your system after day 1
B. How much caffeine remains in your system after 2 days?
Given:
The function g(t) represents the amount of caffeine remaining in your body after drinking the coffee.
[tex]g(t)=130(.8246)^t[/tex]
where t is time in hours.
To find:
The caffeine remains in your system after day 1.
The caffeine remains in your system after day 2.
Solution:
We know that,
1 day = 24 hours.
2 day = 48 hours.
The given function is
[tex]g(t)=130(.8246)^t[/tex]
Substitute t=24 in the given function to find the remaining caffeine in the system after day 1.
[tex]g(24)=130(.8246)^{24}[/tex]
[tex]g(24)=130(0.00977)[/tex]
[tex]g(24)=1.2701[/tex]
Therefore, the remains caffeine in your system after day 1 is about 1.2701.
Substitute t=48 in the given function to find the remaining caffeine in the system after day 1.
[tex]g(48)=130(.8246)^{48}[/tex]
[tex]g(48)=130(0.000095)[/tex]
[tex]g(48)=0.01235[/tex]
[tex]g(48)\approx 0.0124[/tex]
Therefore, the remains caffeine in your system after day 1 is about 0.0124.
Answer: for one day, it’s 0.0124
Step-by-step explanation:1d=24h
g(24)
How do I find the dimension of this cylinder
Answer:
10 in
Step-by-step explanation:
Volume of a Cylinder :
V = pi r² h
h = V / pi r²
h = 10,000pi / pi 32²
simplify pi
h = 10,000/1024 = 9.76
h = approx 10 in
(7, -1) 2. What is the slope of a line that is perpendicular to the line joining point A (9, 9)? and point B
Answer:
-1/5Step-by-step explanation:
Given the point A (9, 9) and B(7, -1)
The slope of the line AB is expressed as:
slope = Δy/Δx
slope = y2-y1/x2-x1
slope = -1-9/7-9
slope = -10/-2
slope = 5
For two lines to be perpendicular, the product of their slope must be -1
mM = -1
M is the slope of the line perpendicular to AB
Substitute m = 5 into the equation
5M = -1
M = -1/5
Hence the slope of a line that is perpendicular to the line joining point A and B is -1/5
find the LCM of 3 and 12
Answer:
12
Step-by-step explanation:
want money. answer this.
¼(5x + 16/3) - ⅔(¾x + ½) = -5
solve for x. this be some seriously big brain stuff. i'm just a child :(
Answer:
x = −8
Step-by-step explanation:
Solve the system of equations. 4y + 11x – 67 = 0 2y + 5x - 19 = 0 x= y=
Answer:
x = 29, y = -63
Step-by-step explanation:
Solve the following system:
{4 y + 11 x - 67 = 0 | (equation 1)
{2 y + 5 x - 19 = 0 | (equation 2)
Express the system in standard form:
{11 x + 4 y = 67 | (equation 1)
v5 x + 2 y = 19 | (equation 2)
Subtract 5/11 × (equation 1) from equation 2:
{11 x + 4 y = 67 | (equation 1)
{0 x+(2 y)/11 = -126/11 | (equation 2)
Multiply equation 2 by 11/2:
{11 x + 4 y = 67 | (equation 1)
{0 x+y = -63 | (equation 2)
Subtract 4 × (equation 2) from equation 1:
{11 x+0 y = 319 | (equation 1)
{0 x+y = -63 | (equation 2)
Divide equation 1 by 11:
{x+0 y = 29 | (equation 1)
{0 x+y = -63 | (equation 2)
Collect results:
Answer: {x = 29, y = -63
Answer:
[tex]y=\frac{136}{9},\:x=\frac{7}{9}[/tex]
Step-by-step explanation:
[tex]\begin{bmatrix}4y+11x-67=2\\ y+5x-19=0\end{bmatrix}[/tex]
Isolate y for 4y+11x-67=2:
[tex]y=\frac{-11x+69}{4}[/tex]
[tex]\mathrm{Substitute\:}y=\frac{-11x+69}{4}[/tex]
[tex]\begin{bmatrix}\frac{-11x+69}{4}+5x-19=0\end{bmatrix}[/tex]
[tex]Simplify[/tex]
[tex]\begin{bmatrix}\frac{9x+69}{4}-19=0\end{bmatrix}[/tex]
Isolate x for [tex]\frac{9x+69}{4}-19=0:[/tex]
[tex]x=\frac{7}{9}[/tex]
[tex]\mathrm{For\:}y=\frac{-11x+69}{4}[/tex]
[tex]\mathrm{Substitute\:}x=\frac{7}{9}[/tex]
[tex]y=\frac{-11\cdot \frac{7}{9}+69}{4}[/tex]
[tex]\frac{-11\cdot \frac{7}{9}+69}{4}=\frac{139}{9}[/tex]
[tex]y=\frac{136}{9}[/tex]
[tex]\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}[/tex]
[tex]y=\frac{136}{9},\:x=\frac{7}{9}[/tex]
Write an equation to represent each problem. Do not solve.
1. The sum of fifteen and six times a number t is eighty-one. What is the number?
Answer:
(15 + 6) · t = 81
MEKS is a rectangle. Find mEKM if mEMK =30
Help! I would like a walkthrough of how to do this problem, as i cant figure out how to. Thanks!
Answer:
a = 4.5b = 7.5Step-by-step explanation:
You want the lengths of sides marked 'a' and 'b' in the given right triangle figure.
Similar trianglesAll of the triangles in the figure are similar to each other. This gives rise to some proportional relations that are useful for solving this problem.
short side/long side = 6/8 = a/6
8a = 36 . . . . . . cross multiply
a = 36/8 = 4.5
long side/hypotenuse = 8/10 = 6/b
8b = 60 . . . . . . . cross multiply
b = 60/8 = 7.5
The lengths 'a' and 'b' are 4.5 and 7.5, respectively.
__
Additional comment
These are sometimes given as "geometric mean" relationships:
6 = √(8·a)
b = √(a·(a+8))
10 = √(8·(8+a))
where √(pq) is the geometric mean of p and q.
Another way to solve this is to recognize the given triangle is a 3-4-5 right triangle. The other similar triangles will have these same ratios:
3 : 4 : 5 = a : 6 : b ⇒ a = 3(6/4) = 4.5, b = 5(6/4) = 7.5
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the height of a cone shaped building is 50 ft, and the radius of its base is 20 ft. find the buildings slant height
Answer:
1,000
Step-by-step explanation:
How many solutions does 23y+50+27y=50y+50 have
23y + 50 + 27y = 50y + 50 original equation
50y + 50 = 50y + 50 combine like terms
Because both sides of the equation are the same, meaning they are equal, the equation has INFINITELY MANY SOLUTIONS (y can be any number) .
Make d the subject of the formula h = d/3 + 2
9(h + 3) + 18 = 108
Can I please have the answer with the work?
Thanks a bunch!
- Jimmy is 440 miles from home, but he is driving back at a speed of 60 mph. Which equation
represents this scenario where d represents the distance from home and t represents the time in
hours?
440d=60t it would take jimmy 7.33 hours to get home if he drove at a constant rate of 60 Miles Per Hour
Find the midpoint M of the line segment joining the points P = (-5, 7) and Q = (1, -3)
Brooke plays volleyball and also plays the trumpet in the middle school band. Brooke spends two (2) hours after school participating in volleyball activities. At home, Brooke practices playing her trumpet for 1/8 of the time that spends on volleyball activities at school. How long does she practice the trumpet?
Answer:
15 minutes
Step-by-step explanation:
2 hours equals 120 minutes.
so if you divide 120 by 1/8 you get 15
which would be the amount of time she spent playing the trumpet.
Hope this helps!! :)
5 40/60 simpified no decimals
Answer:
5 2/3
Hope this helps! Please mark Brainliest!
Answer:
17/3
Hope this helps!!! :)
T Stands For Tether
If Cos T = 0.6 And Sin T = 0.8, Find Tan T
Answer:
tan T = [tex]\frac{4}{3}[/tex]
Step-by-step explanation:
using the identity
tan T = [tex]\frac{sinT}{cosT}[/tex] = [tex]\frac{0.8}{0.6}[/tex] = [tex]\frac{8}{6}[/tex] = [tex]\frac{4}{3}[/tex]
Which expression is equivalent to -4.6 + (-0.4) + (-7.2)?
A. – 4.6 - (0.4 + 7.2)
B. (4.6 + 0.4 + 7.2)
C. – (4.6 – 0.4) + ( -7.2)
D. (4.6 + 0.4) + (-7.2)
Please help!!!
6 - x - x = 16 what’s the answer please
Answer:
Answer is -5!
Step-by-step explanation:
Answer: x = -5
Explanation:
6-x-x=16
6-2x=16
6-6-2x=16-6
-2x=10
-2x/-2=10/-2
x = -5
Please help me
Jjsjs
Answer:
1-70mm
2-77m
Step-by-step explanation:
so to do this, take the first one as an exmple, to find the unknown line on the ground I added 15+8 to find the total on the bottom
still on the first question, to find the unknown number on the side, I subtracted 12-7
I hope this makes any sense, but I dont know
whats important is that you have the answers.
The equation of a circle in general form is x2+y2+20x+12y+15=0 .
What is the equation of the circle in standard form?
(x+10)2+(y+6)2=121
(x+10)2+(y+6)2=225
(x+20)2+(y+12)2=121
(x+20)2+(y+12)2=225
Answer:
[tex](x+10)^2+(y+6)^2=121[/tex]
Step-by-step explanation:
The standard form of a circle's equation is
[tex](x-h)^2 + (y-k)^2 = r^2[/tex]
Where (h,k) is the center and r is the radius of the circle.
The equation is given in general form, we need to convert it to the standard form. This can be done by completing squares.
The equation is:
[tex]x^2+y^2+20x+12y+15=0[/tex]
Rearrange x's and y's separate:
[tex]x^2+20x+y^2+12y=-15[/tex]
We have also subtracted 15. Now to complete squares, recall the formula:
[tex](a+b)^2=a^2+2ab+b^2[/tex]
The first two terms are equivalent to the first two terms of the above formula. It's clear that the second term is 2ab=20x. Solving for b:
b=10. Thus, to complete the square, we add 100 to the equation.
The third and fourth terms can also be used to complete the squares for y, knowing that 2ab=12y. In this case:
b=6. To complete this square, we add 36. The equation is now:
[tex](x^2+20x+100)+(y^2+12y+36)=-15+100+36=121[/tex]
Operating and simplifying, knowing that 121=11^2:
[tex]\boxed{\mathbf{(x+10)^2+(y+6)^2=121}}[/tex]
This corresponds to the first choice
Please help me 50 points and brainliest for all questions
A cylinder has a height of 10 feet and a diameter of 14 feet. What is its volume? Use ≈ 3.14 and round your answer to the nearest hundredth.
cylinder volume = base area x height
= pi x r² x h
≈ 3,14 x 7² x 10 ≈ 1500
The GCF of two whole numbers is 9 and the LCM of the
same two numbers is 135. What could the two numbers be? Prove it.
Answer:
9 and 135
Step-by-step explanation:
The GCF is 9, and 135 is divisble by 9. The GCF of a standalone number is itself, and the aforementioned divisibility of 135 by 9 rules 9 as one of the numbers. Since 9 is a multiple of 135, and 9 can multiply to be 135, this makes the second number 135.
7 of 10
Sara was thinking of a number. Sara doubles it, then adds 7 to get an answer of 92.9. What
was the original number?
Answer:
42.95
Step-by-step explanation:
We just reverse the steps. So we take 92.9 and subtract by 7 to get 85.9. Then we divide that number by 2. So we get 42.95. To check our work, we can use this number and follow the steps Sara did. So 42.95*2=85.9+7=92.9
The original number that Sara was thinking of is 42.95.
What is the number system?A number system is defined as a way to represent numbers on the number line using a set of symbols and approaches. These symbols, which are known as digits, are numbered 0 through 9.
Let's represent the original number "x".
According to the question, we know that:
x × 2 + 7 = 92.9
To determine the original number, we'll want to undo the operations that were done to it.
First, we'll subtract 7 from both sides to undo the addition:
x × 2 = 92.9 - 7
x × 2 = 85.9
Then, we'll divide both sides by 2 to undo the doubling:
x = 85.9 / 2
x = 42.95
Therefore, the original number that she was thinking of is 42.95.
Learn more about the number system here:
https://brainly.com/question/21751836
#SPJ2
Can someone help me with this question
Answer:
∠ CDE = 134°
Step-by-step explanation:
the sum of the interior angles of a polygon is
sum = 180° (n - 2) ← n is the number of sides
here n = 6 , then
sum = 180° × 4 = 720°
let ∠ BCD = x then ∠ CDE = 2x
sum the angles and equate to 720
121 + 144 + 129 + 125 + x + 2x = 720 , that is
519 + 3x = 720 ( subtract 519 from both sides )
3x = 201 ( divide both sides by 3 )
x = 67
Then
∠ CDE = 2x = 2 × 67 = 134°
Rectangle LMNO was translated 4 units down and 5 units left. After the translation, N’ was at (-6, 5). What was the original
x-coordinate of N?
Answer:
(-2, 10)
Step-by-step explanation:
All you have to do is add 4 to -6 and add 5 to 5. Since it was moved 4 units down and 5 units left, that means that those numbers were subtracted from the original coordinates. Although you are trying to find the original points, so instead you add 4 and 5 to the coordinates you have right now.
I hope that makes sense!
HELP PLEASE HELP HELP PLESAE HELP!
Answer:
15
Step-by-step explanation: