Answers
Answers:
A = 3
B = -7
C = 3
D = -7
======================================================
Explanation:
You could use the AC method to factor, but I think the method described below is a more efficient way of factoring.
Set the given expression equal to zero and solve for x using the quadratic formula. So the goal is to find the roots for [tex]9x^2-42x+49=0[/tex]
We'll plug in a = 9, b = -42, and c = 49.
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(-42)\pm\sqrt{(-42)^2-4(9)(49)}}{2(9)}\\\\x = \frac{42\pm\sqrt{0}}{18}\\\\x = \frac{42+0}{18}\\\\x = \frac{42}{18}\\\\x = \frac{7}{3}\\\\[/tex]
Because the root is x = 7/3, it leads to the factor 3x-7 = 0
Note that we go from x = 7/3 to 3x = 7 after multiplying both sides by 3. Then we subtract 7 from both sides.
It turns out that we have two copies of the identical factor (3x-7) because x = 7/3 is a double root.
So in reality we have the factorization (3x-7)(3x-7) which we can shorten into (3x-7)^2 if we wanted.
Use the box method or FOIL method to expand (3x-7)(3x-7) and you should get 9x^2-21x-21x+49 which simplifies to 9x^2-42x+49. This confirms we have the correct factorization.
Therefore, A and C are both 3, while B and D are both -7.
Related Questions
A volunteer group picked up 3 times as many plastic bottles as cans in their community. The number of papers they picked up was 15 more than of the number
of cans. If the volunteers picked up 288 cans, how many more plastic bottles than papers did they pick up?
Answers
try 4,320 for your answer
The table shows the ratio between the number of books ordered and their cost: Number of Books Cost (dollars) 7 14 8 16 9 18 Find equivalent ratios when the number of books ordered is 1, 2, and 3. Write them as ordered pairs in the form (x-coordinate, y-coordinate). Starting from the origin, explain how to plot the three equivalent ratios on a coordinate grid. (10 points)
Answers
14/7 = 2
16/8 = 2
18/9 = 2
This shows the cost of one book is $2
Multiply the number of books bought by 2 to get the cost:
1 x 2 = 2
2 x 2 = 4
3 x 2 = 6
Answer: (1,2) (2,4) (3,6)
Starting from the origin (0,0) for every 1 book bought ( x axis) move 2 more up than the previous total (y axis)
Using the 3 ordered pairs in the answer at x value 1 place a dot at y 2, then a dot at x2,y4 and again at x3,y6
Answer:
I'm doing the same test right now the ratios are 1 to 2 but the answers would be 1 to 2, 2 to 4, and 3 to 6 . you have to double the numbers that are shown
Step-by-step explanation:
I didn't copy the guy above it's litterallty simple multiplication hope my answer helped
I need Unit 3 parallel and perpendicular lines Homework 5 slope of lines it’s due today!
Answers
14. Slope (m) of PQ = -4
Slope (m) of RS = 1/4
The lines are perpendicular.
15. mPQ = -3
mRS = 3
They are neither perpendicular nor parallel lines.
16. mPQ = 0
mRS = 0
The lines are parallel.
17. x = -6
18. x = -2
What are the Slopes of Parallel and Perpendicular Lines?If two lines have the same slope (m), then both lines are parallel to one another. On the other hand, if the slopes of two lines are negative reciprocals to each other, then both lines are regarded as perpendicular lines because the product of their slopes is equal to -1.
Slope (m) = change in y / change in x
14. Slope (m) of PQ = (-3 - 17) / (1 -(-4))
Slope (m) of PQ = -20/5 = -4
Slope (m) of RS = (4 - 3) / (-5 -(-9))
Slope (m) of RS = 1/4
(1/4)(-4) = -1, therefore, the lines are perpendicular.
15. Slope (m) of PQ = (-1 - 14) / (2 -(-3))
Slope (m) of PQ = -15/5 = -3
Slope (m) of RS = (-10 - 8) / (-2 - 4)
Slope (m) of RS = -18/-6 = 3
They are neither perpendicular nor parallel lines.
16. Slope (m) of PQ = (-1 - (-1)) / (-3 - 2)
Slope (m) of PQ = -0/-5 = 0
Slope (m) of RS = (9 - 9) / (-7 -(-11))
Slope (m) of RS = 0/4 = 0
The lines are parallel.
17. If CD║EF, their slope will be equal. Therefore:
Slope of CD = slope of EF
(-4 - 16)/(2 - x) = (4 - 14)/(-2 -(-6))
-20/(2 - x) = -10/4
-20/(2 - x) = -5/2
Cross multiply
-20(2) = -5(2 - x)
-40 = -10 + 5x
-40 + 10 = 5x
-30 = 5x
-30/5 = x
-6 = x
x = -6
18. Slope of JK = slope of l
(-5 -(-8))/(-1 - x) = 6/2
3/(-1 - x) = 3
3(-1 - x) = 3
-3 - 3x = 3
-3x = 3 + 3
-3x = 6
-3x/-3 = 6/-3
x = -2
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Algebra 1
Q.13 Complete a function table from an equation 273
Complete the table.
f(x) = 2x - 10
х f(x)
6
7
8
9
Submit
Answers
Answer with step-by-step explanation:
To solve this, all we have to do is replace x in 2x - 10 with the number from the table.
6: 2(6) - 10 = 2
7: 2(7) - 10 = 4
8: 2(8) - 10 = 6
9: 2(9) - 10 = 8
There you have it! Have a good day :)
answer FAST please and i will give brainliest
Answers
This is simply a rearranged version of Pythagoras’ theorem
What is 2/3, 7/6, 3 1/9, and 5 5/18 written as a decimal?
Please give an explanation and a correct answer!
I will give brainliest to whoever answers first!
Answers
Step-by-step explanation:
[tex] \frac{2}{3} = 2 \times \frac{1}{3} = 2 \times 0.333 = 0.666 \\ \\ \frac{7}{6} = 7 \times \frac{1}{6} = 7 \times \frac{1}{2} \times \frac{1}{3} = 7 \times 0.5 \times 0.333 = 1.1655 \\ \\ 3 \frac{1}{9} = 3 + \frac{1}{9} = 3 + ( \frac{1}{3} \times \frac{1}{ 3} ) = 3 + (0.333 \times 0.333) = 3 \times 0.11088 = 3.11088 \\ \\ 5 \frac{5}{18} = 5 + (5 \times \frac{1}{18} ) = 5 + (5 \times \frac{1}{3} \times \frac{1}{3} \times \frac{1}{2} ) = 5 +(5 \times 0.333 \times 0.333 \times 0.5) = 5 + 0.27722 = 5.27722[/tex]
y = 6x - 4 when x = -7
Answers
Answer:
It's - 28
Step-by-step explanation:
6*-7=-42-4=-28
Answer:
y is -46
Step-by-step explanation:
y= 6x -4 ....means
y =6 *x -4......so replace x with -7
y = 6*-7 -4
y=-42 -4
y= -46
how to find the nth term
Answers
Answer:
Write full question
I cannot understand
Step-by-step explanation:
The nth term of an arithmetic sequence is given by an = a + (n – 1)d. So, to find the nth term, substitute the given values a = 2 and d = 3 into the formula.
Triangle ABC has two known angles. Angle A measures 55 degrees. Angle B measures 30 degrees. What is the measure of angle C?
Answers
Answer:
According to the properties of a triangle, all internal angles of a triangle must add up to 180 degrees.
Since we know A and B are 55 degrees and 30 degrees respectively, C = 180-55-30 = 95 degrees.
Thus, the measure of angle C is 95 degrees.
what is the equation of the line that passes through the point (-6,6) and has a slope of -5/3?
Answers
Answer: The equation of the line that passes through the point (-6,6) and has a slope of -5/3 is y = -5/3x + -3.96.
Explanation:
y = 6, x = -6
By putting above values in equation (i)
6 = approximately -1.66 (-6) + b
6 = approximately 9.96 + b
approximately -3.96 = b
b = approximately -3.96
y = -5/3x + -3.96
Circumference if circle is_________
Answers
Answer: The distance around the edge of a circle
Step-by-step explanation:
Which expression is equivalent to StartFraction RootIndex 7 StartRoot x squared EndRoot Over RootIndex 5 StartRoot y cubed EndRoot? Assume y not-equals 0. (x Superscript two-sevenths Baseline) (y Superscript negative three-fifths Baseline) (x Superscript two-sevenths Baseline) (y Superscript five-thirds Baseline) (x Superscript two-sevenths Baseline) (y Superscript three-fifths Baseline) (x Superscript seven-halves Baseline) (y Superscript negative five-thirds Baseline).
Answers
Answer:
[tex]\frac{5}{X^{2} } y^{2}[/tex]
Step-by-step explanation:
sorry the Y isn't under the 5 anyway hope this helped
Answer:
A is the answer.
Step-by-step explanation:
(X^7/2)(y^-3/5)
Select the quadrant or axis where each ordered pair is located on a coordinate plane.
Quadrant I Quadrant II Quadrant III Quadrant IV x-axis y-axis
(-2 1/2, -7)
(0,6)
(-5,0)
Answers
Answer:
IV
y-axis
x-axis.
Step-by-step explanation:
(-2 1/2, -72) - 2 negative values so: Quadrant IV.
(0, 6): When x = 0 we are on the y-axis,
(-5, 0): if y = 0 its the x-axis.
Y+1=1/5(x-10)
Solve for y
Answers
Answer:
y = (x-10 / 5) - 1
Step-by-step explanation:
Hope this helps :)
Answer:
y=1/5x-3
Step-by-step explanation:
y+1=1/5(x-10)
y=-1 +1/5(x-10)
y= -1 +1/5x-2
y=1/5x-3
I'm bad at math helpppppp
Answers
Answer:
2x + y = 18
y = 4x - 12
x = 5, y = 8
Step-by-step explanation:
x = 1st number
y = 2nd number
We can use the substitution method as we know what 'y' equals; that value will get plugged in for 'y' in the first equation as follows:
2x + 4x - 12 = 18
6x - 12 = 18
6x = 30
x = 5
y = 4(5) - 12 which is 20-12 or 8
y = 8
Which of the following is an equation of a line perpendicular to the equation
y - 3x +1?
O A = - 3x + 5
B. y --3x+5
O C. y -3x5
O D. y = x+5
Answers
Answer:
There is something wrong in the answer options. Please check the equations and formatting.
Step-by-step explanation:
Assuming the referenced equation is y = 3x + 1 (and not y - 3x + 1), we can say the following.
This is written in the form of y=mx+b, where m is the slope and b the y-intercept (the value of y when x=0).
The slope, as I've written it, is 3. Parallel lines will have the same slope (but a different b). Perpendicular lines will have a slope that is the negative inverse of the slope of the reference line. In this case, it would have a slope of -(1/3).
None of the answer options come close to this. So something is wrong in the question, unless "NONE" is an option.
What is the cash payment of a article costing RS.2020 allowing a discount of Rs.20 and levying 13% VAT?
Answers
The cash payment for the article is RS. 2,260.
A discount reduces the price of an item. The article becomes cheaper after the discount.
Cost of the article after the RS. 20 discount = RS. 2020 - 20 = RS 2000
VAT means value added tax. VAT increases the price of an item. The cost of the article increases by 13% after the VAT is levied,
Cost of the article = (100 + 13%) x 2000
1.13 x 2000 = RS 2,260.
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Please help I don’t understand this
Answers
Answer:
d. √(1/(x+1))
Step-by-step explanation:
Just as operations can be performed on numbers and variables, so can operations be performed on functions. Here, you're asked to simplify the ratio of two functions.
[tex]\displaystyle\left(\frac{g}{f}\right)(x)=\frac{g(x)}{f(x)}=\frac{\sqrt{x-1}}{\sqrt{x^2-1}}=\sqrt{\frac{x-1}{x^2-1}}[/tex]
At this point, you're supposed to know the factoring of the difference of squares:
[tex]\displaystyle=\sqrt{\frac{x-1}{(x-1)(x+1)}}=\boxed{\sqrt{\frac{1}{x+1}}}[/tex]
Rich borrowed $5000 at a 7% interest rate for 6 years. What was the total interest? Enter your answer in the box. Hint: Use the formula I= P*R*T where I= Interest Earned/Owed P= Principal R= Rate T= Time
Answers
Answer:
$700.000 is the interest
Step-by-step explanation:
hope the answer helps
Simple interest is the interest calculated on the principal at a given rate for a time period.
The simple interest is given as,
SI = (Px R x T) / 100
The total interest is $2100.
What is simple interest?It is the interest calculated on the principal at a given rate for a time period.
The simple interest is given as,
SI = (Px R x T) / 100
We have,
P = $5000
R = 7%
T = 6 years
SI = P x R x T / 100
SI = 5000 x 7 x 6 / 100
SI = 50 x 7 x 6
SI = 50 x 42
SI = $2100
Thus,
The total interest is $2100.
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You are going to a private apple orchard to pick apples. There is a one-time entry fee that everyone pays, and you also pay a certain amount per pound of apples you pick. It costs $46 to buy 5 pounds of apples, and it costs $58 to buy 7 pounds of apples.
Answers
The one-time entry fee is $6 and the price per pound is $4.
In order to determine the one time entry fee and the cost to pick an apple per pound, two equations would be formed from the question:
x + 5y = 46 equation 1
x + 7y = 58 equation 2
Where:
x = one-time entry fee
y = price per pound
In order to determine the value of y, subtract equation 1 from 2
2y = 12
y = 12 / 2 = 6
In order to determine the value of x, substitute for y in equation 1:
x + 5(6) = 46
x + 30 = 46
x = 40 - 36
x = 4
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Estimate the product. Then find the actual product
483 x 9.3
please label the actual product and the estimate
Answers
Actual Product:
4491.9
Estimated Product:
4492
How is it 4492?
4491.9
The 9 is greater than 5 making it go up,
aka, making the 1 turn into a 2.
Suppose TD=SG and what additional information is needed to prove the two triangles congruent SAS
a)
PLEASE HELP
Answers
Answer:c
Step-by-step explanation:
Answer:
If TD = SG and MD = SL, then angle D would have to equal angle S in order to prove the triangles congruent by SAS.
Step-by-step explanation: C
4200 in the scientific notation.
Answers
Answer:
4.2*10^3
Hope This Helps!!!
Answer:
The answer is 4.2×10^3
Step-by-step explanation:
To convert 4200 into scientific notation, follow these steps:
- Move the decimal 3 times to left in the number so that the resulting number, m = 4.2, is greater than or equal to 1 but less than 10
- Since we moved the decimal to the left the exponent n is positive
n = 3
- Write in the scientific notation form, m × 10^n
= 4.2 × 10^3
Therefore, the decimal number 4200 written in scientific notation is 4.2 × 10^3 and it has 2 significant figures.
worth 10 points thankyou
Answers
Answer:
DCBA
Step-by-step explanation:
3-6
5. United States senators serve
year
teims. A senator serving 4 terms
would serve for how many total
years?
Answers
Answer:
16
Step-by-step explanation:
1 term is 4 years; and 4 terms times 4 years is 16 years
A camp charges $75 per day to use the camp plus $15 per day for food and supplies for each student. The cost for one day can be modelled using the equation C= 15s + 75.
a) What do the variables C and s represent?
b) A school raised $375 for a one-day trip. How many students can go?
((see pic for textbook question))
Answers
b:375:75=5 or 370:100=3.75 but it doesn't make sence B=5
Which of the following statements is the only
sentence that is error-free?
Answers
Select all the ordered pairs that are solutions to the equation 2x+y=−12
(−10, 8)
(−9, −6)
(−8, −2)
(0, −12)
(4, −20)
Answers
Answer:
(-10,8)(0,12)(4,-20)
Step-by-step explanation:
You just have to insert the points into the equation and then solve.
Ex: 2(4)-20=-12- True
What are coordinate of (2,-3) when it is reflected over X axis.
Answers
Answer:
the asnwer is (2,3)
Step-by-step explanation:
Please please help!!
Answers
Step-by-step explanation:
get add and add on ok