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
...................................
Answers
Answer:
tha.nks for the p.oints buddy!
Walter can make 7 holiday cards with the cardstock he already has on hand. He is also buying more paper, and he can make 12 additional cards with each package of cardstock he buys. If Walter buys 6 packages of cardstock, how many cards can he make in all?
Answers
Answer:
dsde
Step-by-step explanation:
which one is not congruent SSS,SAS,AAS,ASA,HL?
Answers
Answer:
none of the above
Step-by-step explanation:
All of these abbreviations represent postulates that can be used to prove congruence. The HL postulate only applies to right triangles, but all of the others apply to any shape triangle.
All can be used to show congruence.
Jenny asked 48 classmates whether they prefer granola bars over muffins. she used a calculator to compare the number of classmates who said yes to the total number she surveyed. The calculator showed the result as 0.66666667.
PART A: Write this number as a fraction.
PART B: How many students prefer granola bars over muffins.
Answers
A) The number 0.66666667 as fraction is = [tex]\frac{66666667}{100000000}[/tex]
B) 32 students prefer granola bars over muffins.
The total number of classmates = 48
The probability that a student says yes = 0.66666667
Note that 0.66666667 can also be written as [tex]\frac{0.66666667}{1}[/tex]
To convert 0.66666667 to fraction, multiply both the numerator and the denominator by 100000000
The probability that a student says yes = [tex]\frac{66666667}{100000000}[/tex]
Therefore, the number 0.66666667 as fraction is = [tex]\frac{66666667}{100000000}[/tex]
Number of students that prefer granola bars over muffins = 0.66666667 x 48
Number of students that prefer granola bars over muffins = 32
Therefore, 32 students prefer granola bars over muffins.
Learn more on decimal to fraction conversion here: https://brainly.com/question/23038
Answer 1 question. Thanms
Answers
Let's solve your inequality step-by-step.
[tex]11+\frac{a}{2}\le 16[/tex]
Step 1: Simplify both sides of the inequality.
[tex]\frac{1}{2}a+11 \le 16[/tex]
Step 2: Subtract 11 from both sides.
[tex]\frac{1}{2}a+11-11\le 16-11[/tex]
[tex]\frac{1}{2}a\le 5[/tex]
Step 3: Multiply both sides by 2.
[tex]2\cdot \left(\frac{1}{2}a\right)\le (2)*(5)[/tex]
[tex]a\le 10[/tex]
Answer:a≤10(-x + 3) + (4x - 10)
Answers
PLEASE HELP!!
This is worth 20 points please help me!
Answers
Under his cell phone plan, Joseph pays a flat cost of $48 per month and $3 per gigabyte, or part of a gigabyte. (For example, if he used 2.3 gigabytes, he would have to pay for 3 whole gigabytes.) He wants to keep his bill under $55 per month. What is the maximum whole number of gigabytes of data he can use while staying within his budget?
Answer:
gigabytes
gigabytes
Answers
Answer: 2 is the maximum number of gigabytes
Step-by-step explanation:
Name the solution
A.
(2, -3)
B.
(3, 2)
C.
(3, -1)
D.
(0, -2)
Answers
Answer:
C. (3, -1) is a solution
Step-by-step explanation:
It is inside in the double shaded area.
please help!!!!!
Solve.
−4/9x+2.4=6
Enter your answer as a decimal or as a mixed number in simplest form in the box.
x =
Answers
-8.1
Step-by-step explanation:
[tex] \frac{ - 4}{9} x + 2.4 = 6[/tex]
Times all by 9 to get rid of fraction
[tex] - 4x + 21.6 = 54[/tex]
Take 21.6 away from both sides
[tex] - 4x = 32.4[/tex]
Divide by -4
[tex]x = - 8.1[/tex]
Answer: -8 1/10
Step-by-step explanation:
On a certain hot summer's day, 477 people used the public swimming pool. The daily prices are 1.50 for children and 2.25 for adults. The receipts for admission totaled 914.25 How many children and how many adults swam at the public pool that day?
Answers
Answer:
212 children, and 265 adults
Step-by-step explanation:
To find the number of children and adults, we can set up a systems of equations.
x= number of children
y= number of adults
Equation 1: Price
1.50x+2.25y=914.25
Equation 2: Total number of people
x+y=477
Now, let's solve the equation using substitution.
Rearrange the second equation to solve for one variable.
x+y=477
x=477-y
Now plug x equals into the first equation, and solve for y.
1.50x+2.25y=914.25
1.50(477-y)+2.25y=914.25
715.5-1.50y+2.25y=914.25
715.5+0.75y=914.25
0.75y=198.75
y=265
We just solved for the number of adults. Now let's plug y equals into the second equation to find the number of children.
x+y=477
x+265=477
x=212
A line passes through the points (8, -1) and (-4, 2).
10
8
6
4
-10 -3 -6 6 -2
2
4
6
8
10
X
4
-6
do
8
-10
What is the y-intercept of this line?
Answers
Answer:
The y-intercept of this line is 1 (or (0, 1) )
Step-by-step explanation:
Going from (8, -1) to (-4, 2), the x-coordinate decreases by 12 and the y-coordinate increases by 3. Thus, the slope of this line is m = rise/run = 3/(-12), or m = -1/4.
Let's use this information (x = 8, y = -1, m = -1/4) and the slope-intercept formula y = mx + b to find the y-intercept (b):
-1 = (-1/4)(8) + b, which simplifies to -4 = -8 + 4b. Solving for b, we get
4 = 4b, so that b must be 1.
The y-intercept of this line is 1 (or (0, 1) )
Find x. Round your answer to the nearest tenth of a degree.
Answers
Answer:
42°
Step-by-step explanation:
8 is the opposite
12 is the hypotenuse
We know from SOHCAHTOA to use sine
Since we are looking for the angle, we use sin^-1
sin^-1(opposite/hypotenuse)=x
sin^-1(8/12)=x
Input into calculator
x=42°
Step-by-step explanation:
we use the law of sine :
a/sin(A) = b/sin(B) = c/sin(C)
where the the side and related angle are always opposite to each other.
so,
12/sin(90) = 8/sin(x)
12/1 = 8/sin(x)
12 = 8/sin(x)
3 = 2/sin(x)
sin(x) = 2/3
x = 41.8103149...° ≈ 41.8°
C.
Find the 4th term in the expansion of (y + 2)
Answers
Need help NOW on HS geometry
Answers
plz help its taxes!!! just questions not real lol
Answers
Answer:
pay: 32,000*12 ( since its per month) =384,000
income tax: 384,000*0.45 = 172,800
EI: 384,000*0.0173=6,643.20
CPP: 384,000*0.0495=19,008
Yearly Pay will be 384,000-172,800-6,643.20-19,008= $185,584.80
Weekly pay (paycheck) = 42320.91/52 = $ 3,568.25
Step-by-step explanation:
Lillian multiplies two numbers as follows: A Times. B = C. Given that A has five significant figures and two decimal places and B has six significant figures and four decimal places, which equals the number of significant figures in C? two four five six.
Answers
The total number of significant figures in C is 5 because when the two numbers are multiplied then the result obtained has the least significant figure.
Given :
Lillian multiplies two numbers.A has five significant figures and two decimal places and B has six significant figures and four decimal places.The following steps can be used in order to determine the total number of significant figures of C:
Step 1 - According to the given data, 'A' has five significant figures and two decimal places and 'B' has six significant figures and four decimal places.
Step 2 - It is also given that C is equal to A times B.
Step 3 - So, the total number of significant figures in C is 5 because when the two numbers are multiplied then the result obtained has the least significant figure.
Therefore, the correct option is C).
For more information, refer to the link given below:
https://brainly.com/question/11904364
Answer: c
Step-by-step explanation:
I want a picture of magnitic force and electric force
Answers
Answer:
Step-by-step explanation:
123
Which option is an example of a survey?
A. Asking students in a school how much time they spend exercising
B. Flipping a coin 50 times and counting the number of heads
C. Measuring the heights of the players on the basketball team
D. Testing the effectiveness of a new reading program by allowing a
classroom to use it and comparing the results with another
classroom that doesn't use it
Answers
Answer:
I think the answer is A
Step-by-step explanation:
The example of a survey are; A. Testing the effectiveness of a new reading program by allowing a classroom to use it and comparing the results with another classroom that doesn't use it
What is an survey?An survey is a technique used to confirm or deny a hypothesis, as well as assess the likelihood or effectiveness of something that has never been tried before.
Since Experiments show what happens when a specific factor is modified, which sheds light on cause-and-effect relationships.
The survey asks participants to quantify their trust in politicians while a numerical scale, with 1 being the least amount of trust.
Example of a survey;
Testing the effectiveness of a new reading program by allowing a classroom to use it and comparing the results with another classroom that doesn't use it
To learn more about experiments refer to:
brainly.com/question/25303029
#SPJ2
i don't understand how to do this someone help me math!!
Answers
Answer:
-8
Step-by-step explanation:
ky^2 = -5y + 7y^2 +9y - 15y^2 -4y
ky^2 = -8 y^2
k = -8
Answer:
8
Step-by-step explanation:
We believe the problem here requires that all of the coefficients in the expression on the left be zero. That is, the equation will be true for any value of y.
We can work this a couple of ways. One of them is to simplify the given expression. Let 'a' represent our unknown coefficient.
[tex]-ay^2-[-5y-y(-7y-9)]-[-y(15y+4)]=0\\\\-ay^2-[-5y+7y^2+9y]+[15y^2+4y]=0\\\\-ay^2-[7y^2+4y]+15y^2+4y=0\\\\(-a-7+15)y^2+(-4+4)y=0\\\\(-a+8)y^2=0[/tex]
In order for this to be zero for all values of y, we must have (-a+8) = 0.
a = 8
The missing coefficient is 8.
_____
Since this expression must be true for every value of y, another way to work this is to choose a value of y. This will tell us what the coefficient must be for the expression to be zero. Let y = 1.
-a·1² -[-5·1 -1(-7·1 -9)] -[-1(15·1 +4)] = 0
-a -[-5-(-16)] -[-19] = 0
-a -11 +19 = 0
-a +8 = 0
a = 8 . . . . . . same as above
_____
Additional comment
The many minus signs are intended to make sure you're comfortable with arithmetic with negative coefficients and negative numbers. The key, of course, is that -(-a) = +a. The opposite of the opposite is the original.
We have assumed that the dash at the beginning of the line (before the answer box) is intended to be a minus sign. If that is not the case, then your answer will be -8, instead of 8.
What is the slope-intercept equation of the line below?
O A. y=-2x+1
B. y = 2x + 1
Oo
C. y = -2x-1
O D. y = 2x-1
Answers
Answer:
C
Step-by-step explanation:
It has a negative slope and it crosses the y axis at -1
5x-6>1+2(4x+1)
I need answers now please and an explanation
NO BOTS I HAVE NO TIME FOR THEM
Answers
Answer:
-3
Step-by-step explanation:
I just need 20 characters to help out so yeah
A function f(x) is graphed on the coordinate plane.
What is the function rule in slope-intercept form?
Enter your answer in the box below.
f(x) = ____
Answers
Answer:
mx+b
Step-by-step explanation:
One way to express linear function rules is called slope-intercept form. Sometimes, f(x)=mx+b is used. In either case, m and b describe the general characteristics of the line. m indicates the slope, and b indicates the y-intercept.
The required function of the line would be y = 2x + 1 which is shown in the given graph.
What is the function rule in slope-intercept form?The slope-intercept form is one rule to represent linear function rules. f(x)=mx+b is sometimes used. In any scenario, m and b describe the line's overall features. The slope is denoted by m, while the y-intercept is denoted by b.
According to the given figure,
We clearly see that the coordinates of the y-intercept would be (0, 1).
The value of the x-coordinate is 1 when y-coordinate is 3.
Here the line passes through points (0, 1) and (1, 3).
Let the required linear function would be y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x₂ -x]
x₁ = 0, y₁ = 1
x₂ = 1, y₂ = 3
⇒ y - y₂ = (y₂ - y₁)/(x₂ -x₁ )[x -x₂]
⇒ y - 3 = (3 - 1)/(1 - 0 )[x -1]
⇒ y - 3 = (2)[x -1]
⇒ y - 3 = 2x - 2
⇒ y = 2x - 2 + 3
⇒ y = 2x + 1
Therefore, the required function of the line would be y = 2x + 1 which is shown in the given graph.
Learn more about the Linear function here:
brainly.com/question/14511992
#SPJ5
Calculate the distance between the points M=(-1,-2) and C=(-9, 2) in the coordinate plane.
Round your answer to the nearest hundredth.
Answers
Answer:
8.9443
Step-by-step explanation:
d = √((x2-x1)2 + (y2-y1)2)
Step by step procedure:
Find the difference between coordinates:
(x2-x1) = (-9 - -1) = -8
(y2-y1) = (2 - -2) = 4
Square the results and sum them up:
(-8)2 + (4)2 = 64 + 16 = 80
Now Find the square root and that's your result:
Exact solution: √80 = 4√5
Approximate solution: 8.9443
I need help on this question
3n + 2 = 17
Answers
Answer:
The value of n is 5.
Step-by-step explanation:
Concept :
Here, we will use the below following steps to find a solution using the transposition method:
Step 1 :- we will Identify the variables and constants in the given simple equation.Step 2 :- then we Simplify the equation in LHS and RHS.Step 3 :- Transpose or shift the term on the other side to solve the equation further simplest.Step 4 :- Simplify the equation using arithmetic operation as required that is mentioned in rule 1 or rule 2 of linear equations.Step 5 :- Then the result will be the solution for the given linear equation.Solution :
By using the transposition method. we get,
[tex]{\dashrightarrow{\tt{3n + 2 = 17}}}[/tex]
[tex]{\dashrightarrow{\tt{3n= 17 - 2}}}[/tex]
[tex]{\dashrightarrow{\tt{3n= 15}}}[/tex]
[tex]{\dashrightarrow{\tt{n= 15 \div 3}}}[/tex]
[tex]{\dashrightarrow{\tt{n= \dfrac{15}{3}}}}[/tex]
[tex]{\dashrightarrow{\tt{n= \cancel{\dfrac{15}{3}}}}}[/tex]
[tex]{\dashrightarrow{\underline{\boxed{\tt{\red{n= 5}}}}}}[/tex]
Hence, the value of n is 5.
[tex]\rule{300}{1.5}[/tex]
Solve : 3n + 2 = 17
Answer:-n = 5
Explanation:-=> 3n + 2 = 17
=> 3n = 17-2
=> 3n = 15
=> n = 15/3
=> n = 5
(5a^3-2)(5a^3+2) expand and combine like terms
Answers
Step-by-step explanation:
(5a³-2)(5a³+2)
5a³×5a³+ 5a³×2 - 2× 5a³+ 5a³×2 5a³+10a³- 10a³ + 10a³5a³+10a³ + 10a³-10a³15a³ AnswerA bookstore sells 2 books for $22.50 which table represents the relationship between number of books and the total price
Answers
Answer:
Can you show what are the tables?-
What percent of the model is shaded green?
(answer quick please)
Answers
Answer:
30%
Step-by-step explanation:
3 rows out of 10 are shaded green. 3/10 is 30%
Explanation:
Ignore the horizontal lines. Think of this figure as 10 skinny rectangles line up side by side. Three of them are shaded, so we have 3/10 = 0.30 = 30% of it shaded.
If you wanted to include the horizontal lines, then we have 10*3 = 30 green little squares out of 10*10 = 100 total squares. This leads to the same answer 30/100 = 0.30 = 30%
What is the difference (2 x - 3) - (x - 1)?
x minus 4
x minus 2
x + 2
x + 4
Answers
Answer:
Step-by-step explanation:
It may help you to rewrite this problem in columns:
2x - 3
-( x - 1)
------------
x - 2 (answer) ("x minus 2")
Using a calculator or otherwise, calculate the exact value of 498.79×14.38. Round your answer to one (1) decimal place.
Answers
Answer:
7172.6
Step-by-step explanation: