Answer:
Simplify:
[tex]\frac{( {x}^{2} + 6x + 9) }{x - 3} [/tex]
Factoring:
[tex] {x}^{2} + 6x + 9[/tex]
The first term is, x2 its coefficient is 1 .
The middle term is, +6x its coefficient is 6 .
The last term, "the constant", is +9
Step-1 : Multiply the coefficient of the first term by the constant 1 • 9 = 9
Step-2 : Find two factors of 9 whose sum equals the coefficient of the middle term, which is 6 .
-9 + -1 = -10
-3 + -3 = -6
-1 + -9 = -10
1 + 9 = 10
3 + 3 = 6 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 3 and 3
[tex] {x}^{2} + 3x + 3x + 9[/tex]
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x+3)
Add up the last 2 terms, pulling out common factors :
3 • (x+3)
Step-5 : Add up the four terms of step 4 :
(x+3) • (x+3)
Which is the desired factorization.
Multiply (x+3) by (x+3)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (x+3) and the exponents are :
1 , as (x+3) is the same number as [tex](x+3) {}^{1}[/tex]
and 1 , as (x+3) is the same number as[tex](x + 3) {}^{1} [/tex]
The product is therefore, [tex](x + 3) {}^{(1 + 1)} = (x + 3) {}^{2} [/tex]
Cookies cost $5.40 per dozen. What is the unit rate Price per cookie
Answer:
$0.45 per cookie
Step-by-step explanation:
1 dozen = 12, so you divide both sides by 12. 5.40/12 would equal $0.45 per cookie
Answer:$0.45
Step-by-step explanation:
If it costs $5.40 for 12 cookies then you will need to find how much it costs for 1 cookie. To do this you will need to divide 5.4 by 12 so 5.4/12=0.45
To earn an a in mr.whites math class students must score a total of at at least 135 points on three test. On the first two test , kaylees scores were 47 and 48 . What is the minimum score she must get on the third test to earn an a
Answer:
Set an equation x+47+48= 136
solve for x
x+95=136
x= 40
so they need to score a 40
Find 3 ratios that are equivalent to the given ratio 3 over 6
solve for x, find the measure of all angles hurryyyyyyy!
Answer:
x=6 as 180 in triangle take away 150 30 by 5 is 6
Suitcases originally priced at $50 are now on sale for $41. What percentage is the discount?
Find all values of j for which the quadratic equation has one real solution.
3x² + 5x-j=0
Write your answer as an equality or inequality in terms of j.
Answer:
x = (-5+/- √(25 + 12j))/6
Step-by-step explanation:
The solution to this question requires the application of quadratic formula
Daniel spent 3 hours babysitting for his brother. He and the children played games for 1 3/4 hours and watched television for 1/2 hour. For the remainder of the time, Daniel read stories. How much time did Daniel spend reading stories?
Answer:
He spent 3/4 of an hour reading stories
Step-by-step explanation:
Sorry I dont have time :(
A line passes through the points (-4,5) and (1,-5). Write the equation of the line in slope-
intercept form.
A. y = - 2x - 3
B.y = - 2x +3
C. y=2x-3
D. y = 2x + 3
Answer:
y = -2x - 3
Step-by-step explanation:
Slope: (5 - - 5)/(-4 -1) = 10/-5 = -2
y-intercept: 5 - (-2)(-4) = -3
Which inequality represents this graph?
A) y ≤ 1/3x - 1
B) y > 1/3x - 1
C) y ≥ 1/3x - 1
D) y < 1/3x - 1
Answer:
D) y < 1/3x - 1
Step-by-step explanation:
the equation of the line is y= 1/3x-1, then the dark part represents all the values that less than the values of y. The broken line means 'strongly', then the sign should be '<'.
A survey was given to people who own a certain type of car. What percent of the people surveyed were completely satisfied with the car?
Answer:
60% if this is an edge question
What is the area (what is the height)
Answer:
5 i think
Step-by-step explanation:
The trapezoid's height (h) is 4 mm(millimeters).
Formula to calculate a trapezoid's height;
2 x Area ÷ by A(short base) + B(large base)
(3 x^-2 y^3)^3 Please help ASAP
Answer:
I don't understand what do you mean by (3 x^-2 y^3)^3
by itself?
f(x)={x+4….
for f(x)
Answer:
3f=5
Step-by-step explanation:
f(x) = x+4
3f=4x
x<5
5<_x<7
7<_x<_10
Which statements are true? Check all that apply.
3
1
-2.5=-2
2.
2.
-1.5 > -0.5
0.5 <0
-2.5 <-2
1
0
UD
1>15
-1
-2
-3
Answer:
3is the answer because t
s apply
Step-by-step explanation:
how do u simplify 4625/1000
Answer:
37/8
Step-by-step explanation:
Find the GCD (or HCF) of numerator and denominator. GCD of 4625 and 1000 is 125.
4625 ÷ 1251000 ÷ 125.
Reduced fraction: 378. Therefore, 4625/1000 simplified to lowest terms is 37/8.
Write an explicit rule and recursive rule for a geometric sequence with a 2nd term of 6 and a 3rd term of 12.
this is my attachment answer hope it's helpful to you
Grant plans to evaporate enough water from 22 gallons of a 16% ammonia solution to make a 24% ammonia solution. Which equation can he use to find n, the number of gallons of water he should remove? 3. 52 (22 minus n) = 0. 24 StartFraction 22 minus n Over 3. 52 EndFraction = StartFraction 24 Over 100 EndFraction StartFraction 3. 52 Over 22 minus n EndFraction = StartFraction 24 Over 100 EndFraction 3. 52 (22 minus n) = 0. 24.
Answer:
The correct answer is 33.4516
Approximately it is 33.452
9,000,000 times 30 divided by 2 plus three minus 36 time 1 divided 93
135000002.613! At least I think!
if y varies directly as x, and y is 20 when x is 4, what is the value of y when x is 80
Answer:The equation of that is y=kx
Substitute it in and you get
20=6k
Divide 6 on both sides
k=3 1/3
Then since it asks what is the value of y when x is 24 use k in the equation
y=3 1/3*24
so y=80 is the answer
Step-by-step explanation:
Pls help with the second one. Thank you to the person who helped me with the first one.
A radar station is 2000 ft from the launch site of a rocket. If the rocket is launched vertically at the
rate of 500 ft/sec, how fast is the distance between the radar station and the rocket changing 10 seconds
later?
Answer: f 500 Ft./sec
Step-by-step explanation:
By evaluating the derivate of the distance in t = 10s, we will see that at t = 10s the distance is changing at a rate of 464.2 ft/s
We can think of the situation as in a right triangle, one cathetus is equal to 2000ft, and the other cathetus increases at a rate of 500ft/sec.
The hypotenuse would be the distance between the radar and the rocket.
Then the distance function is:
[tex]D(t) = \sqrt{(2000ft)^2 + (500ft/s*t)^2}[/tex]
Now we need to get the rate of change, this is given by:
[tex]\frac{dD(t)}{dt} = (1/2)*\frac{2*(500ft)^2*t}{\sqrt{(2000ft)^2 + (500ft/s*t)^2} }[/tex]
Now we evaluate this in t = 10s to get:
[tex]\frac{dD(10s)}{dt} = (1/2)*\frac{2*(500ft/s)^2*10s}{\sqrt{(2000ft)^2 + (500ft/s*10s)^2} } = 464.2 ft/s[/tex]
If you want to learn more, you can read:
https://brainly.com/question/18904995
The value of y is directly proportional to the value of x.
If y = 12 when x = 15, what is the value of x when y = 40?
A.
12
B. 32
C.43
D.
50
Answer:
D
Step-by-step explanation:
Given y is directly proportional to x then the equation relating them is
y = kx ← k is the constant of proportion
To find k use the condition y = 12 when x = 15
12 = 15k ( divide both sides by 15 )
0.8 = k
y = 0.8x ← equation of proportion
When y = 40 , then
40 = 0.8x ( divide both sides by 0.8 )
50 = x → D
State the independent variable and the dependent variable in the linear relationship. Then find the rate of change for the situation.
Answer:
independent variable: the number of children
dependent variable: the cost of admission
rate of change: 11
Step-by-step explanation:
independent variable is what changes which in this case is the amount of children
dependent variable is the factor that changes because of the independent variable which in this case is the cost of admission
the rate of change is 11 because the cost of one kid would be $11
Solve the non-standard equation for x.
-18 + x = -4
Answer:
x = 14
Step-by-step explanation:
the slope of (5,3) AND (10,8)
Answer:
(5,5) is your slope: y=5 and x=5 too
Step-by-step explanation:
Step-by-step explanation:
what the guy above said is right
Write the equation that describes each line in slope intercept form
Hello there! :)
Let's use the slope formula:
m=[tex]\frac{y2-y1}{x2-x1} \\\frac{0-3}{3-0} \\\frac{-3}{3} \\=-1[/tex]
So the slope (m) is -1.
Now, let's find the y-intercept. It's where the graph touches the y-axis.
The y-intercept is 3.
So our equation looks like so:
y=-x+3
Hope this helps!
~Just a cheerful gal
#CarryOnLearning
[tex]SilentNature :)[/tex]
Can somebody help me with this question, im stuck on it.
Answer:
180 degrees
Step-by-step explanation:
Transformations don't change the size or angles of a triangle.
We know the angle of T & S. We need to find R.
To do this we will do...
180 - (60+40) =
= 180-100
=80
R is 80 degrees.
Now to find Triangle ABC we will add up 60+40+80 to get 180 degrees.
Also, remember that triangles will ALWAYS add up to 180 degrees.
Hope this helps! Please give this a rating and press the heart button! Thanks!
Is this right?
Pic below! :D
Answer:
I Don't Think So
But ask your parents or your older brother or sisters
That looks right about those questions you were asking me the last part where you got 1.50 is a little confusing could you explain maybe how you got that but the right answer is there
2x-y=4
-2x+y=7
is there a solution
[tex] \text{Given : 2x - y = 4 and x + 2y = 7}[/tex]
[tex] \text{Solution : according to the question here we are provided with} \\ \text{two equations separately. So, let's name them as eq(1) and eq(2).} \\ \text{ The rest is followed as we continue to get to our goal} \\ \\ \sf {1}^{st} \: equation : \\ \quad\dashrightarrow \frak{2x - y = 4} \\ \\ \quad \dashrightarrow \frak{ \red{x = \frac{y + 4}{2} }} \qquad \sf ...eq(1) \\ \rm{ now \: \: as \:per \: our \: plan \: we \: need \: to \: get \: eq(2) } \\ \\ \sf{ {2}^{nd} \:equation} : \\ \quad\dashrightarrow \frak{ x + 2y = 7} \\ \\ \quad\dashrightarrow \frak{ \red{y = \frac{7 - x}{2}}} \qquad \sf ...eq(2) \\ \\ \text{Now, finding x and y} \\ \\ \underline{ \frak{Finding \: x}}\\ \\ \quad \hookrightarrow \frak{x = \frac{y + 4}{2}} \\ \\ \quad \hookrightarrow \frak{2x = \frac{7 - x}{2} + 4} \\ \\ \quad \hookrightarrow \frak{2x = \frac{7 - x + 8}{2}} \\ \\ \quad \hookrightarrow \frak{2x = \frac{1 - x}{2}} \\ \\\quad \hookrightarrow \frak{4x = 1 - x} \\ \\ \quad \hookrightarrow \frak{5x = 1} \\ \\\quad \star \qquad \underline{ \boxed{ \green{ \frak{x = \frac{1}{5}}}}} \\ \\ \underline{ \frak{Finding \: y}} \\ \\ \quad \hookrightarrow \frak{y = \frac{7 - x}{2}} \\ \\ \hookrightarrow \frak{2y = 7 - \frac{1}{5} } \\ \\ \hookrightarrow \frak{2y = \frac{35 - 1}{5} } \\ \\ \hookrightarrow \frak{2y = \frac{34}{5}} \\ \\ \hookrightarrow \frak{y = \frac{34}{5} \times \frac{1}{2}} \\ \\ \hookrightarrow \frak{y = \frac{17}{5} } \\ \\ \star \qquad \underline{ \boxed{ \frak{ \green{y = 3 \frac{2}{5} }}}}[/tex]
cellus If investments double every 7 years and you start with a $600 investment, how much money would you have after 21 years?
Answer:
4800$
Step-by-step explanation:
1 day = 600
7 years = 600 x 2 = 1200$
14 years = 1200 x 2 = 2400$
21 years = 2400 x 2 = 4800$