Step-by-step explanation:
I’m assuming that you’re asking about quadratic equations, but suffice it to say that the method may even work for polynomials of higher degrees.
Let’s take an example. You have x^2+6x+8.
First, multiply the term in x^2 with the constant; in this case we get 8x^2.Next, break the value in x into two numbers, such that when you add them, the value becomes that of the middle term and when you multiply them, the value becomes that which you have just calculated.
Step 1:
x^2 * 8= 8x^2
Step 2:
(break the middle term)
x^2+4x+2x+8 (notice how 4x when added to 2x gives 6x but when multiplied, gives 8x^2)
Step 3:
(separate the common terms)
x(x+4)+2(x+4)
(x+2)(x+4)
Given the functions:
f (x) = -6x - 19
g(x) = -11x + 9
h (x) = 17x +4
Find f (3)
Answer:
f(3) = -37
Step-by-step explanation:
f (x) = -6x - 19
Let x = 3
f (3) = -6*3 - 19
= -18-19
= -37
Which algebraic expression is equivalent to the expression below?
(3n+13) + (6+7n)
A. 9n + 20
B. 16n + 13
C. 10n + 19
D. 22n + 7
Answer: C) 10n +19
Step-by-step explanation:
Let's simplify the provided expression (3n+13) + (6+7n)
Since this is just addition we can just remove the parenthesis and use the commutative property to make adding easier
3n+13+6+7n
3n+7n+13+6
10n+19
What is the circumference of a circle with a radius of 8?
Use 3.14 for pi.
Also, can someone tell me what the pattern is, here? I need to know, I can never understand.
Answer:
Step-by-step explanation:
C≈50.27
r Radius
Solution
C=2πr=2·π·8≈50.26548
A pair of equations is shown below: y = 3x - 5 y = 6x - 8
Part A: Explain how you will solve the pair of equations by substitution or elimination. Show all the steps and write the solution. (5 points)
Part B: If the two equations are graphed, at what point will the lines representing the two equations intersect? Explain your answer. (5 points)
Answer:
See below
Step-by-step explanation:
y = 3x -5 <===== multiply this equation by -2 to get
-2y = -6x+10 now add it to the other equation(this will ELIMINATE x)
y = 6x-8
-y = +2
y = -2 then sub this in to oneof the quations to find x = 1
the two points will intersect at x,y = 1,-2 (because this satisfies both of the equations)
PART A
We start with: y = 3x - 5 y = 6x - 8
Elimination:
If we have two equations that = y, then we can make them equal each other:y = y3x - 5 = 6x - 8We then collect the x term together:3x - 6x = -8 + 5-3x = -3We can divide both sides by -3:x = 1Substitution
We can make one equation turn from a y= to an x=I decided to go with y = 3x - 5 (but it doesn't matter)We basically want to get it into x=y = 3x - 5y + 5 = 3x3x = y + 5 (I'm just flipping the equation to get x on the left for easiness)We then divide both sides by 3:x = [tex]\frac{y + 5}{3}[/tex]Don't forget we've also got y = 6x - 8So we just put x in!y = 6 × [tex]\frac{y + 5}{3}[/tex] - 8y = [tex]\frac{6}{3}[/tex] × (y + 5) - 8y = 2 × (y + 5) - 8y = 2y + 10 - 8y = 2y + 2Rearrange to get y on one side:-y = 2Times both sides by -1:y = -2We can now go back to...x = [tex]\frac{y + 5}{3}[/tex]By putting y = -2 in:x = [tex]\frac{-2 + 5}{3}[/tex]x = [tex]\frac{3}{3}[/tex] = 1PART B
We can find where they intersect/overlap by using elimination/substiutionWe've already covered both, and we get x = 1This means we've already go the x-coordinate of our point where the lines meet(x, y) = (1, ?)We just put our value of x into either equation (since x = 1 is where they meet)I'll go with y = 6x - 8y = 6 × 1 - 8y = 6 - 8 = -2We end up with (1, -2)!!!P.S.:
I've attached a screenshot of the graphs, notice how they meet at (1, -2)
Sally rents a life jacket for a one-time fee of 5$. She rents a canoe for $15 per hour. Which expression represents the total cost, in dollars, to rent the life jacket and the canoe for h hours?
A. 5+15h
B. 10h
C. 15+5h
D. 20h
Answer:
A. 5+15h
Step-by-step explanation:
A point is chosen randomly on KN. Identify the probability that the point is on KL or MN. The figure shows segment K N with two points L and M on it in order from left to right. The length of segment K L is 3 units. The length of segment L M is 7 units. The length of segment M N is 8 units.
A point is chosen randomly on KN. The probability that the point is on KL or MN would be 11/18.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events. The probability of all the events occurring need to be 1.
P(E) = Number of favorable outcomes / total number of outcomes
The length of segment K L is 3 units.
The length of segment L M is 7 units.
The length of segment M N is 8 units.
The length of the segment KL + MN
KL + MN = 11
The total length of the segment KN
KL +LM + MN
3 + 7 + 8 = 18
SO, The probability that the point is on KL or MN = 11/18
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x(x+1)(x+2)=0
solve for x
Answer:
-2; -1; 0.
Step-by-step explanation:
x(x+1)(x+2)=0;
[tex]\left[\begin{array}{ccc}x=0\\x+1=0\\x+2=0\end{array} \ = > \ \left[\begin{array}{ccc}x=0\\x=-1\\x=-2\end{array}.[/tex]
Evaluate tan (x + pi/2) for x = pi/2
Answer:
0
Step-by-step explanation:
tan(x + [tex]\frac{\pi }{2}[/tex] ) ← substitute x = [tex]\frac{\pi }{2}[/tex]
tan([tex]\frac{\pi }{2}[/tex] + [tex]\frac{\pi }{2}[/tex] )
= tanπ
= 0
i need some urgent help
the thing is to factor the expressions trinomial way
if you want extra points you could help me with my past 2 questions they are 50 each someone gave me a wrong answer so i would really appreciate some help with that too but that's optional
#1
15x²+4x-415x²+10x-6x-45x(3x+2)-2(3x+2)(5x-2)(3x+2)#2
16a²-50a+362(8a²-25a+18)2(8a-9)(a-2)#3
63n²+126n+483(21n²+42n+16)Not more factorable
A straight waterslide is 175 feet above ground and is 200 feet long. What is the angle of depression to the bottom of the slide?
Step-by-step explanation:
see this this will help you
how many solutions does the equation 5 + -5 + -12 equals 14 - 2 have?
0, 1, 2, many
Hey there!
5 + -5 + -12 = 14 - 2
ASSUMING….
5 - 5 - 12 = 14 - 2
0 - 12 = 14 - 2
-12 = 12
-12 ≠ 12
Thus, your answer should be:
FALSE or simply 0 solutions
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
The measure of one acute angle in this right triangle is 28°.
What is the measure of the other acute angle?
A. 22°
B. 28°
C. 32°
D. 62°
Answer:
[D] 62°
Step-by-step explanation:
A right triangle = 90 degree angle
A triangle = 180 degrees
Therefore,
90 + 28 = 118
180 - 118 = 62
Hence, the measure of the other acute angle is 62
Thus, the answer is [D] 62 degree
Kavinsky
Answer:
D. 62
Step-by-step explanation:
Multiply This Equation & Simplify:
Question Is In The Photo...
Answer:
= 12 x^8
Step-by-step explanation:
Least to greatest questions 7 and 8
Answer:
7.
4.7 * 10^14 , 9.99 * 10^14 , 2.9 * 10^15 , 4.5 * 10^15
8.
9.99 * 10^-8 , 4.8 * 10^-8 , 9.99 * 10^-4 , 6.5 * 10^-4
Please help me ASAP!! Calling all experts, will give brainliest too!
The height of a candle decreases from 10 centimeters to 6 3/4 centimeters after burning for 1/2 hour
The true statement is as follows:
The product 13 / 4 × 2 can be used to find the unit rate in cm per hour.
After one hour, the height of the candle will have decreased by 6 1 / 2 cm.
What is rate?Rate is the ratio between two related quantities in different units.
The height of the candle decreases from 10 cm to 6 3 / 4 cm after burning for 1 / 2 hours.
6 3 / 4 cm = 27 / 4 cm
10 - 27 / 4 = 40 - 27 / 4 = 13 / 4 cm
Therefore, 13 / 4 cm of candles were lost in 1 / 2 hours.
Rate = 13 / 4 × 2 = 26 / 4 = 13 / 2 cm per hour
Therefore, the product 13 / 4 × 2 can be used to find the unit rate in cm per hour.
13 / 4 + 13 / 4 = 13 + 13/ 4 = 26 / 4 = 13 / 2 = 6 1 / 2 cm.
Therefore, after one hour, the height of the candle will have decreased by 6 1 / 2 cm.
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i dont understand it can you help me with the rest?
Answer:
top: 0.7, 0.9
bottom:7/10
0.7 = 7/10 because 7 is under tens. If it was 0.34 = 34/100 because 34 is in the hundereds. If it was 0.100 = 100/1000 because 100 is under the thousands. pls brainly trying to level up
Find the sticker price and the dealer's cost for the Bobcat SX with a base price of $13,568.00. Options include air conditioning for $765.00, turbo for $643.00, towing package for $236.00, and custom wheels for $422.00. Destination charges total $365.00. The dealer pays 90% of the base price and 65% of the options.
The base of a prism has an area of 6.6 cm2. The height is 2.4 cm. What is the volume
So the volume is 15.84 cm The formula for the volume of a prism is given by the product of the area of the base and height of the prism. Thus, the volume of a prism can be given as V = B × H where V is the volume, B base area, and H height of the prism.
8. Select the expression that is equivalent to 12/48.
A. 6(8+6)
B. 12(4+1)
C. 4(44+3)
D. 8(6+4)
A:
6(8+6)
= 48+36
=84
B: 12(4+1)
=48+12
=60
C:
4(44+3)
=176+12
=188
D:
8(6+4)
=48+32
=80
What is the measure of angle y in this figure?
It is always helpful to rewrite a quadratic equation in standard form as a first step in solving it.
A. FALSE
B. TRUE
Answer:
A
Step-by-step explanation:
Now when I think of solving it, I think of finding the zeros. Now if you start with the form, for example:
[tex](x+3)(x-3)[/tex]
Then you can easily see the zeros are -3 and 3.
But if you start with the standard form:
[tex]ax^2+bx+c=0\\or\\x^2-9[/tex]
It will be harder to find the zeros and you would do the eqation or factor it.
So if your in the factored form don't go to standard to find the zeros.
The given statement is False.
What is a quadratic equation?An equation with highest degree two, is considered as a quadratic equation.
In standard form, the right side of an equation should be 0 and every component on the left side should be 1.
For example, x² = 4; to express this in standard form, move the number 4 to the left side of the equation, resulting in x² - 4 = 0.
If you are asked to find x in this circumstance, there is no need to write the equation in standard form; simply take this same real number of both of the equation's sides to find x.
Hence, it is not always necessary to write the quadratic equation in standard form then solve.
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please answer the question pls
In 2018, RAND Corporation researchers found that 71% of all individuals ages 66 to 69 are adequately prepared financially for retirement. Many financial planners have expressed concern that a smaller percentage of those in this age group who did not complete high school are adequately prepared financially for retirement.
In a random sample of 300 people from the 66-69 age group who did not complete high school, 165 were not prepared financially for retirement. What is the p-value for your hypothesis test (to 4 decimals)? If your answer is zero, enter "0".
Using the z-distribution, as we are working with a proportion, it is found that the p-value of the test is of 0.
What are the hypothesis tested?At the null hypothesis, it is tested if the proportion is of 71%, that is:
[tex]H_0: p = 0.71[/tex]
At the alternative hypothesis, it is tested if the proportion has decreased, that is:
[tex]H_1: p < 0.71[/tex].
What is the test statistic?The test statistic is given by:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
In which:
[tex]\overline{p}[/tex] is the sample proportion.p is the proportion tested at the null hypothesis.n is the sample size.In this problem, we have that the parameters are:
[tex]n = 300, \overline{p} = \frac{165}{300} = 0.55[/tex]
Hence, the value of the test statistic is found as follows:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0.55 - 0.71}{\sqrt{\frac{0.71(0.29)}{300}}}[/tex]
z = -6.11
What is the p-value of the test?Using a z-distribution calculator, with a left-tailed test, as we are testing if the proportion is less than a value, and z = -6.11, it is found that the p-value is of 0.
More can be learned about the z-distribution at https://brainly.com/question/26454209
Round the number. Write the result as the product of a single digit and a power of 10. 0.0000001801
Answer:
2x10 to the -7 power
Step-by-step explanation:
hope this helps!
SAT scores are used by colleges and universities to evaluate undergraduate applicants. The test
scores are normally distributed. A random sample of 65 student scores has a mean of 1489 and
standard deviation of 306.
Find the 95% confidence interval for the population mean based on this sample and round to
two decimal places.
Using the t-distribution, it is found that the 95% confidence interval for the population mean is (1413.18, 1564.82).
What is a t-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 65 - 1 = 64 df, is t = 1.9977.
The parameters of the interval are given as follows:
[tex]\overline{x} = 1489, s = 306, n = 65[/tex].
Hence, the bounds of the interval are given by:
[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 1489 - 1.9977\frac{306}{\sqrt{65}} = 1413.18[/tex]
[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 1489 + 1.9977\frac{306}{\sqrt{65}} = 1564.82[/tex]
The 95% confidence interval for the population mean is (1413.18, 1564.82).
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I Need Help ASAP or i will go to DETENTION!!!!!!!!
Answer:
m<FLS=108 degrees
m<SLT=72 degrees
m<ALG=18 degrees
Step-by-step explanation:
(3x) + (4x +12) = 180
x = 24
4x + 12 = 108 = m<FLS
180 - 108 = 72 = m<SLT
SLG = 72 + 90 + x
x = 18 = m<ALG
suppose you have a box with 3 blue marbles, 2 red marbles, and 4 yellow parmbles. you are going to pull out one marble, record its color, remove it from the box and draw another marble. what is the probability of pulling out a red marble followed by a blue marble? the multiplication rule says to use P(red) P(blue).
1. Describe the probability of finding a red marble.
2. describe the probability of finding a blue marble.
3. describe the process of finding the probability of finding a red marble followed by a blue marble if the first marble was permanently removed?
4. what effect did removing the first marble from the box have on the problem
5. describe the probability of finding a red marble followed by the blue marble if the first marble is removed?
Answer:
Step-by-step explanation:
Part A
The probability of finding a red marble. P(red) = red / total
Total = red + yellow + blue
Total = 2 + 4 + 3
Total = 9
P(red) = 2/9 = 0.22222
Part B
P(blue) = blue / total
P(blue) = 3/8 = 0.375
This means that the red marble is permanently gone. The total is different. It is eight not nine.
Part C
The probability of red followed by blue is just the answers to A and B multiplied.
P(red) followed by blue = 2/9 * 3/8
P(red) followed by blue = 0.22222 * 3.75
P(red) followed by blue = 0.0833333
If you are confident of your concellation abilities you could do this as
P(red followed by blue) = 2/9 * 3/8 = 1/3 *1/4 = 1/12 = 0.083333....
Part D
Removing the first marble had the affect of reducing the total number of marbles to 8 and the number of reds from 2 downto 1
Part E
The answer here is 1/12.
Please help. I cant figure it out
Choose the solution to this inequality.
72≥b+95
A. b≥25
B. b≤1710
C. b≤−23
D. b<227
Answer:
C
Step-by-step explanation:
72≥b+95
Group like them
72-95 ≤ b
the sign changes due to the negative
-23 ≥ b
y-3x=0
2y+5x=11
solve
with elimination and substitution method
Answer:
x=1, y=3
Step-by-step explanation:
using sublimation method
y-3x=0 ....eqn(1)
2y+5x=11....eqn(2)
from eqn 1
y-3x=0
y=3x
substitute y=3x into eqn 2
2y+5x=11
2(3x)+5x=11
6x+5x=11
11x=11 (divide both sides by the coefficient of x)
x=1
since x=1 , substitute x=1 into eqn 1 to get y
y-3x=0
y-3(1)=0
y-3=0
y=3
Using elimination method
y-3x=0....eqn (1)
2y+5x=11....eqn (2)
multiply eqn 1 through by 2 and eqn 2 through by 1 to eliminate y
2y-6x=0.... eqn 3
2y+5x=11.... eqn 4
subtract eqn 4 from from eqn 3
-11x=-11 (divide both sides by the coefficient of x)
x=1
substitute x=1 into eqn 2 to get y
2y+5x=11
2y+ 5(1) =11
2y+5=11
2y=11-5
2y= 6 (divide both sides by the coefficient of y)
y=3