Cliek an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the
correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag
the item to the trashcan click the trashcan to clear all your answers
Factor completely, then place the answer in the proper location on the grid
2107.57a+ 30
123456789
Answers
===============================================================
Explanation:
I'll use the variable x in place of 'a'
The expression we need to factor is [tex]21x^2-57x+30[/tex] which is in the form [tex]ax^2+bx+c[/tex]
So,
a = 21b = -57c = 30We'll plug those three values into the quadratic formula
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(-57)\pm\sqrt{(-57)^2-4(21)(30)}}{2(21)}\\\\x = \frac{57\pm\sqrt{729}}{42}\\\\x = \frac{57\pm27}{42}\\\\x = \frac{57+27}{42} \ \text{ or } \ x = \frac{57-27}{42}\\\\x = \frac{84}{42} \ \text{ or } \ x = \frac{30}{42}\\\\x = 2 \ \text{ or } \ x = \frac{5}{7}\\\\[/tex]
The two roots of [tex]21x^2-57x+30 =0[/tex] are [tex]x = 2 \text{ and } x = \frac{5}{7}[/tex]
The root x = 2 leads to the factor (x-2) after subtracting 2 from both sides.
The root [tex]x = \frac{5}{7}[/tex] leads to the factor (7x-5) after first multiplying both sides by 7, and then subtract 5 from both sides.
So we have this set of steps:
[tex]x = \frac{5}{7}\\\\7x = 5\\\\7x-5=0\\\\[/tex]
The two factors are (x-2) and (7x-5).
This leads to (x-2)(7x-5)
The last step is to replace x with 'a' so that the variables match up.
We arrive at (a-2)(7a-5)
However, as the next section shows, we have a bit of a problem. Don't worry, it can be easily fixed.
---------------------
Let's expand out that factored expression we found earlier.
[tex](a-2)(7a-5)\\\\b(7a-5)\ \text{ ..... let b = a-2}\\\\7ab - 5b\\\\7a(b) - 5(b)\\\\7a(a-2) - 5(a-2)\ \text{ ..... plug in b = a-2}\\\\7a^2-14a - 5a+10\\\\7a^2-19a+10\\\\[/tex]
That's not good. We should have arrived at the original expression [tex]21a^2-57a+30[/tex]. To fix this discrepancy, we can stick a 3 out front and then notice that:
[tex]3(a-2)(7a-5) = 3(7a^2-19a+10) = 21a^2-57a+30[/tex]
The error has been fixed.
We have the full factorization of 3(a-2)(7a-5)
The order of the factors doesn't matter, so we could have written the answer as 3(7a-5)(a-2). Usually the factor without any variables will be listed first.
Based on the screenshot you posted, if that '7' is locked in place, then the only possible answer is 3(7a-5)(a-2) since you'll have 3 in the first slot, then a ( in the next slot. The other slots are filled out in a similar manner. There are no spaces between any symbol or letter.
Related Questions
If you walked for 5 minutes, what would the ratio of feet to minutes be? Use your steps to minutes ratio from Task 1 to determine a ratio of feet to minutes. Show your calculation.
Answers
Answer:
2:1 RATIO
Step-by-step explanation:
If you walked for 5 minutes, the ratio of feet to minutes would be approximately 2.1665 feet per minute.
How did we get the value?To determine the ratio of feet to minutes, we can use the steps to minutes ratio from Task 1. Let's find the steps-to-feet ratio first:
Steps:Feet
4:10
6:15
12:30
30:40
Now, let's calculate the steps-to-feet ratio by finding the average of the steps-to-feet ratio from all the given data points:
Average Steps-to-Feet Ratio = [(10/4) + (15/6) + (30/12) + (40/30)] / 4
Average Steps-to-Feet Ratio = (2.5 + 2.5 + 2.5 + 1.333) / 4
Average Steps-to-Feet Ratio = 2.1665
Now, for the question at hand, if you walked for 5 minutes, the ratio of feet to minutes would be approximately 2.1665 feet per minute.
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You have a total of 21 pens and pencils on your desk. You have 3 more pens than pencils. Write a system linear equations that represent this situation. How many of each do you have?
Answers
Answer:
x + y = 21x - y = 3
Step-by-step explanation:
solve the following x2-2x-24=0
Answers
Answer:
[tex]x=6[/tex] and [tex]x=-4[/tex]
Step-by-step explanation:
[tex]x^2-2x-24=0[/tex]
[tex](x-6)(x+4)=0[/tex]
[tex]x=6[/tex] and [tex]x=-4[/tex]
The perimeter of the figure below is 140 ft.
Find the length of the missing side.
Answers
Answer:
9.2 ft
Step-by-step explanation:
140 - 9.6 - 10.2*8 - 19.8*2 = 9.2
mark me as brainliest PLEASE
Part A: Find the LCM of 7 and 8. Show your work. (3 points)
Part B: Find the GCF of 54 and 81. Show your work. (3 points)
Part C: Using the GCF you found in Part B, rewrite 54 + 81 as an expression of two factors. One factor is the GCF and the other is the sum of two numbers that do not have a common factor. Show and explain your work.
Answers
Answer:
Part A:
LCM of 7 and 8 is 56.
7*8 = 56
-------------------------------------
Part B:
GCF of 54 and 81 is 27.
54: 1, 2, 3, 6, 9, 18, 27, 54.
81: 1, 3, 9, 27, 81.
-------------------------------------
Part C:
GCF of 54 and 81 is 27.
54 / 27 = 2
81 / 27 = 3
Final expression: 27(2 + 3)
Answer:
Part A: 56
Work:
7: 7, 14, 21, 28, 35, 42, 49, 56
8: 8, 16, 24, 32, 40, 48, 56, 64
Part B: 27
Work:
54: 54, 27, 9, 3, 1
81: 81, 27, 9, 3, 1
Part C: 27(2+3)
Work:
27×2 = 54
27×3 = 81
(27×2)+(27×3) = 54+81
(27×2)+(27×3)=27(2+3)
Explaining work:
First you find the numbers that multiply the GCF by to get the product (for 54 it is 2 and for 81 it is 3). Then you replace the the products with the equations (27×2) for 54 and (27×3) for 81 to get (27×2)+(27×3). Then simplify to get 27(2+3).
show that
[tex] \frac{2}{3 + \sqrt{7} } = 3 - \sqrt{7} [/tex]
I don't know what to do
please help with the steps.
for brainliest
Answers
Answer:
multiply by (3-√7)/(3 -√7) and simplify
Step-by-step explanation:
When there are radicals or complex numbers in the denominator, you can rewrite the expression so it has a real, rational denominator. You do this by multiplying numerator and denominator by the conjugate of the denominator. That value is the denominator with its sign changed.
This takes advantage of the factoring of the difference of squares.
(a -b)(a +b) = a² -b²
__
[tex]\dfrac{2}{3+\sqrt{7}}=\dfrac{2}{3+\sqrt{7}}\times\dfrac{3-\sqrt{7}}{3-\sqrt{7}}=\dfrac{2(3-\sqrt{7})}{3^2-(\sqrt{7})^2}=\dfrac{2}{9-7}\times(3-\sqrt{7})\\\\=\boxed{3-\sqrt{7}}[/tex]
Examine Kaitlyn’s steps for solving the system of equations. â€"3x 2y = 8 3x 2y = â€"6 Step 1: 4y = 2 Step 2: y = 2 Step 3: â€"3x 2(2) = 8 Step 4: â€"3x = 4 Step 5: x = â€"1. 333 Kaitlyn found the solution to be (1. 3, 2). Is her solution correct? Explain. Yes, she correctly solved the system of equations. No, she made an error in step 1. The y variable should have been eliminated when adding the system of equations. No, she made an error in step 2. She should have found y = 0. 5. No, she substituted y into the wrong equation to solve for x in step 3.
Answers
The error made by Kaitlyn when solving the system of equations is in step 2. Her solution will be incorrect.
The right option will be: No, she made an error in step 2. She should have found y = 0. 5.
Given the system of linear equations:
-3x + 2y = 8 ---> eqn. 1
3x + 2y = -6 ---> eqn. 1
First add both equations together:
Step 1: 4y = 2
Next, divide both sides by 4:
Step 2: y = 2/4
y = 0.5
Kaitlyn got y = 2 instead of 0.5 in this second step. The solution she would get will be incorrect since an error has occurred here.Therefore, the error made by Kaitlyn when solving the system of equations is in step 2. Her solution will be incorrect.
The right option will be: No, she made an error in step 2. She should have found y = 0. 5.
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12 divided by -3 is what?
Answers
-4
explanation:
when dividing with positives you would get “ 4 “ but since it’s a negative just add the minus at the start
how to evaluate in math?
HELP PLEASE
Answers
Concrete tiles are made using buckets of cement, sand and gravel mixed in the ratio 1:4:6. If 20 buckets of sand are used, how many buckets of EACH of the following will be
needed?
a)
Cement:
T
b) Gravel:
Answers
Evaluate the expression. 5 x (-6 / -1 + -10)
Answers
Answer:
-20
Step-by-step explanation:
[tex]5 * (-6 / -1+ -10)[/tex]
According to PEMDAS, we need to do the math in the parentheses first.
[tex]-6 / -1 + -10[/tex]
Applying PEMDAS to the inside of the parentheses, then we have to divide -6 by -1, where we would get 6.
[tex]6 + -10[/tex]
Adding a negative is the same as subtracting, so adding negative 10 is the same as subtracting 10.
[tex]6 - 10[/tex]
Subtracting, we get 6 - 10 = -4 and we're left with:
[tex]5 * (-4)[/tex]
Multiplying, our final answer is -20.
Hope this helps!
34x+24x^2=35+57y
Solve for x
Answers
1) Move all terms to one side.
[tex]34x+24x^{2} -35-57y=0[/tex]
2) Use Quadratic Formula.
[tex]x=\frac{-34+2\sqrt{1368y+1129} }{48} ,\frac{-34-2\sqrt{1368y+1129} }{48}[/tex]
3) Simplify solutions.
[tex]x=-\frac{17-\sqrt{1368y+1129} }{24} ,-\frac{17+\sqrt{1368y+1129} }{24}[/tex]
simplify the expression.
Answers
Answer:
-6m^2 *n^2
Step-by-step explanation:
formula: (m^x)/(m^y)= m^(x-y)
apply formula for (4m^2)/(2m^-3)
=(4m^(2--3)/(2)
=4m^5/2
divide 4/2
=2m^5
next part 3n^5/(-mn)^3
3n^5/(-mn)^3
expand
=3n^5/ (-m^3*n^3)
=3n^(5-3)/ -m^3
=3n^2/ -m^3
both parts:
(2m^5* 3n^2)/ -m^3
= -(2m^5* 3n^2)/ m^3
= -(2m^(5-3)* 3n^2)/ 1
= -(2m^2* 3n^2)
= -(6m^2*n^2)
= -6m^2 *n^2
The recipe for 4 people says I need 300g of sugar. I am making for 10 people. How much sugar do I need in g?
Answers
Answer:
750g
Step-by-step explanation:
300 divided by 4, for amount of sugar per person
you'll get 75
then multiply 75 by 10 for 10 people
you get 750g
a) A triangular plot is being constructed having its base twice to its altitude. What will be the base and altitude of the plot if the cost of levelling it at the rate of ₹25 per square meter is ₹11,025.
b)If the same plot from above question is being reconstructed into a square field, having the same area, then find the perimeter of square
THE BEST ANSWER WILL BE MARKED BRAINLIEST PLEASE GIVE PROPER ANSWER
THANK U
Answers
The base and altitude of the triangular plot are [tex]42m[/tex] and [tex]21m[/tex] respectively.
The perimeter of the square plot having the same area as the triangular plot is [tex]84m[/tex]
a) Calculate the base and altitude of the triangular plot
The relationship between the Total cost of leveling the triangular plot, the cost per unit area, and the area of the triangular plot is
[tex]\text{unit cost}=\frac{\text{total cost}}{\text{area}}\\\\\text{area}=\frac{\text{total cost}}{\text{unit cost}}\\\\=\frac{\text{11025Rs.}\rupee}{25Rs./m^2}=441m^2[/tex]
The formula for calculating the area of a triangle, given the base and altitude is
[tex]\text{area of triangle}=\frac{1}{2}\text{base}\times\text{altitude}[/tex]
From the question
[tex]\text{base}=2\times\text{altitude}[/tex]
so
[tex]\text{area of triangle}=\frac{1}{2}\times 2\times\text{altitude}\times\text{altitude}\\\\\text{area of triangle}=\text{altitude}^2\\441=\text{altitude}^2\\\text{altitude}=\sqrt{441}=21m[/tex]
from this we can get the base
[tex]\text{base}=2\times\text{altitude}\\=2\times21m=42m[/tex]
b) Calculate the perimeter of a square plot having the same area
Since we found the area of the triangular plot to be [tex]441m^2[/tex], we will use this value for the area of the square plot, so that we can obtain the side
[tex]\text{area of square plot}=side^2\\441=side^2\\\sqrt{441}=side=21m[/tex]
Hence, the perimeter is equal to
[tex]perimeter=4\times side\\=4\times21=84m[/tex]
Learn more about area here: https://brainly.com/question/1447350
Please help, I don’t understand this and I did this from a while ago but I’m still confused on how to do it now.
Answers
Answer:
A.) -3p +8
b.) (10/p) -3
3.)
a.) -3(5)+8= -7
b.) (10/5)-3= -1
Step-by-step explanation:
For A and B you just have to read it over and over until you understand what is happening. A tip is when it says "fewer than" then that number usually goes after the second part of the statement.
For 3 it is asking you to plug 5 in for the value of p and solve.
Hope this helps:) Have a good day!
9. In the figure below, Angle 1 is congruent to Angle 2.
What reason can be used to prove that mis parallel to n?
A. if a pair of verticals angles is congruent, then the lines forming them are parallel
B. If a pair of angles formed by a transversal is corresponding and supplementary, then two lines are parallel
C. If a pair of angles is congruent and the sum of their measures 180 degrees, then the line forming the angles are parallel
D. If two line are intersected by a transversal, and a pair of corresponding angles is congruent, then the two lines are parallel
Answers
Answer:
D
Step-by-step explanation:
When 2 angles are congruent and corresponding, the lines are parallel
Adam is planning a pool party to celebrate the last day of school. He wants to give out beach towels to his guests as party favors. Adam ordered 14 beach towels from Sunshine Party Supply. Since this was a bulk order, Sunshine Party Supply reduced the price of each towel by $3.25. Adam paid $105 in all. How much does Sunshine Party Supply normally charge for a beach towel?
Answers
Answer:
10.75
Step-by-step explanation:
first step is to find how much adam paid for each towel
so, the equation used will be x/y=c
where x is total cost, y is number of products bought, and c equals individual cost (with discount)
we end up with 105/14= 7.5$ per towel.
and to close out, we add the given discount of 3.25 to the discounted price of 7.5
which brings the usual price per towel to 10.25
Answer:
Step-by-step explanation:
The length of a metal rod is 9 3/4 feet. What is the length of 1/4 of the rod?
Answers
Answer:
2 [tex]\frac{5}{16}[/tex]
Step-by-step explanation:
2 [tex]\frac{5}{16}[/tex] × 4 = 9 3/4
9 3/4 × 1/4 = 2 5/16
I hope this helps!
Answer:
3 1/4 feet
Step-by-step explanation:
1/4 of 9 3/4
change 9 3/4 into an improper fraction → 39/3
1/4 x 39/3 = 39/12
convert back to a mixed number by dividing 12 into 39
which goes in three times with a remainder of 3 → 3 3/12
however, 3/12 can be simplified to equal 1/4
Here is a free 100 points annnnd brainliest
This question is about strategy
Skill
Precision
Alr here it is:
Problem one: Molly bought and infinite amount of bottles of dish soap. She had an infinite amount of money. When she bought the dish soap, she lost all of it.
How is this possible?
Problem one (part two): Molly then called her friend Blitzo over. Blitzo then gave Molly and infinite amount of money without losing all of his money.
How is this possible
If you have questions or want hints, ask in comments below this question
Answers
1. She bought the infinite dish soap with her money
2. you can't lose anything infinite
3. remeber our deal? brainliest pls.
he first step that Sarah performed to simplify the expression StartFraction 4(6.8 minus 4.2) plus 8.2 over 2 EndFraction before entering it into the calculator is shown.
2(3.4 – 2.1) + 4.1
Which statement is true?
Sarah performed the first step correctly.
The first step should have been 2(6.8 – 4.2) + 8.2.
The first step should have been StartFraction 27.2 minus 4.2 plus 8.2 over 2 EndFraction.
The first step should have been StartFraction 4(2.6) plus 8.2 over 2 EndFraction.
Answers
Sarah performed the first step correctly.
Given the function that Sarah performed as:
[tex]\dfrac{4(6.8-4.2)+8.2}{2}[/tex]
To simplify the function, the first step Sarah carries out is to divide the numerator by 2:
[tex]\dfrac{4(6.8-4.2)+8.2}{2} \\= \frac{2(2)(2(3.4)-2(2.1)+2(4.1))}{2}\\=2(3.4 - 2.1) + 4.1[/tex]
This shows that Sarah performed the first step correctly.
Learn more on decimal here: https://brainly.com/question/20123476
will mark brainleist pls hep
Answers
Answer: 242
Brainliest plsssssss
Jason was given a triangle that had a side length of 10m and a hypotenuse of
15m. When he substituted these values into the Pythagorean Theorem, he got 102 + 152 = c2
.
Part A. Find Jason’s mistake and explain it.
Part B. Solve for the missing length, show your mathematical thinking, and justify your answer.
Answers
Answer:
The pythagorean theorem is:
H = [tex]\sqrt{s_1^2 + s_2^2}[/tex]
With H being the hypotenuse, s1 one side, s2 the other one. He already has a side and the hypotenuse so he has to calculate the inverse formula:
s2 = [tex]\sqrt{H^2 - s_1^2}[/tex]
So the real side will be:
square root of (15^2 - 10^2) = square root of (225 - 100) = 125 m
Jason made a mistake calculating the squares of the hypotenuse and the side, he didn't subtract and didn't take the root of the result.
10) $48,000 at 16% for 6 years
Answers
Answer:
No solution
Step-by-step explanation:
idek
if f(x)=-x+2 find f(6)
Answers
Answer:
Answer: -4
Step-by-step explanation:
[tex]{ \rm{f(x) = - x + 2}} \\ \\ { \rm{f(6) = - (6) + 2}} \\ \\ { \rm{f(6) = - 4}}[/tex]
The value for f(6) = -4
What is the function of f(x)?The function of f(x) is set to a term such that for every value of x, there is a unique value for it on the graph.
From the given information, we are given a function
f(x) = -x + 2To find f(6), we replace x with 6.
f(6) = -6 + 2f(6) = -4Learn more about function of f(x) here:
https://brainly.com/question/544653
What are the domain and range of the function below? Domain[0, ∞). range (-∞, ∞). Domain[0, ∞). Range (-∞,4). Domain(0,4). Range (-∞, ∞). Domain(-∞,4]. Range[0, ∞).
HELP IMMEDIATELY PLEASE
Answers
Answer:
Domain[0, ∞). Range (-∞,4).
Step-by-step explanation:
domain is your lowest x (zero) to your highest x (infinity)
range is the lowest y (negative infinity) to your highest y (four)
Answer:
its b
Step-by-step explanation:
2616.95 rounded to the nearest tenth
Answers
Make y the subject of the formula
12m + 24y = 20
Answers
Answer: m=5/3-2y or if your solving for y y=-m/2+5/6
Step-by-step explanation:
Answer:
y = 5/6 - m/2
Step-by-step explanation:
4(3m + 6y) = 20
3m + 6y = 5
6y = 5 - 3m
y = 5/6 - 3m/6
y = 5/6 - m/2
what is 65% more of 140
Answers
65% more than 140 is 231
The formula for determining the frequency, f, of a note on a piano is mc016-1. Jpg, where h is the number of half-steps from the A above middle C on the keyboard. A note is six half-steps away from the A above middle C. The frequency of the A above middle C is 440 Hz. How much greater is the frequency of the new note compared with the frequency of the A above middle C? 29. 3% 41. 4% 70. 7% 182. 3%.
Answers
Answ
its a just did this
Step-by-step explanation:
Answer:
7
Step-by-step explanation: