The first coefficient is 2 and the last term is 6. They multiply to 2*6 = 12.
Now we must find two factors of 12 that add to 7 (the middle coefficient).
Through trial and error, you should find that:
3*4 = 12
3+4 = 7
So 3 and 4 are the numbers we're after. We'll split the 7m into 3m+4m and use the factor by grouping method as shown in the steps below.
2m^2 + 7m + 6
2m^2 + 3m + 4m + 6
(2m^2 + 3m) + (4m + 6)
m(2m + 3) + 2(2m + 3)
(m + 2)(2m + 3)
(2m + 3)(m + 2)
The order of the factors doesn't matter since something like 2*3 is the same as 3*2.
------------------------------------------------
Verifying the answer:
You can use technology like you did to check the answer, but here's one way to do it without a calculator.
(2m + 3)(m + 2)
n(m + 2) ...... let n = 2m+3
mn + 2n .... distribute
m( n ) + 2( n )
m(2m+3) + 2(2m+3) .... plug in n = 2m+3
m*2m + m*3 + 2*2m + 2*3 .... distribute
2m^2 + 3m + 4m + 6
2m^2 + 7m + 6
We arrive back at the original trinomial, so we have confirmed the answer.
what is the diameter of a circular field whose area is 616cm^2
Answer:
28cmStep-by-step explanation:
[tex]d=2\sqrt{\frac{A}{\pi}} =2\sqrt{\frac{616}{\pi} }[/tex]≈[tex]28.00563cm[/tex]
rounding 28.00563 to 28.
So hence, your answer is 28cm
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Answer:
28
Step-by-step explanation:
area of a circle
[tex]\pi{r}^{2} [/tex]
616=3•142×r×r
616/3•142=r^2
196=r^2
r=√196
r=14
d=2r
d=2×14
d=28
16
21
Jade works as a decorator.
She is paid £22.80 per hour for the first 35 hours she works each week.
She is paid 15% more per hour for each extra hour she works.
One week, Jade was paid £981.54
In total, how many hours did she work that week?
You must show your working.
Let's assume that all hours she worked were the first 35 hours of the week.
She would've made £22.80 x 35 = £798
So, she would've made 981.54 - 798 = 183.54 less than the actual amount
She is paid 15% more per hour after the first 35 hours -> She will get £26.22 per hour.
So, she work for 183.54 : 26.22 = 7(hours) after the first 35 hours
So in total, she worked for 35 + 7 = 42(hours).
Answer:
42 hours
We know she works at least 35 hours, so 35x22.80=798. This is her base pay without any extra hours.
981.54-798 =183.54. This is the amount she earnt for working extra hours. if we divide this by the rate she earns for extra hours (22.80x1.15=26.22), 184.54/26.22=7, we know she worked an additional 7 hours.
and 35 plus 7 = 42 :)
Please help ASAP!
The domain of this function is {-12, -6, 3, 15}.
y= 2/3x + 7
Complete the table based on the given domain.
This should be easy for me but I just can't get it right.
Please Help Me! ASAP! :) Thank you hope your day was alright.
Will try to mark Brainliest!
Answer:
1. 32
2. 47
3. See explanation for number 3 below
Step-by-step explanation:
All you have to do is simply add 17 to however old Titus is. So if he's 15 years old, you just simply have to do 15+17, which is 32. For number 3, I'm assuming that they just want an explanation for how you do this process, in which case, this explanation is the answer to number 3. If that's not what they're looking for in number 3, then I'm sorry. But I'm pretty sure that's what they want there.
what is 6.7 x 192 ÷ 0.051 ?
Answer: Reduce the expression, if possible, by cancelling the common factors
25223.52941176
Hoped this helped :)
Given that the measure of 2x is 45°, and the measure of zy is 499, find the
measure of z
Answer:
86 degrees
Step-by-step explanation:
The angles of a triangle all add up to 180.
x is 45 degrees
y is 49 degrees
49 + 45 = 94
180 - 94 = 86
The last angle of the triangle is 86 degrees. Since z is on the opposite side of it, it is equal to 86
It cost marci 33 cents to mail a postcard and 49 cents to mail a letter. she sent either a postcard or a letter to each of 28 people and spent $13.08. let x represent the number of postcards she wrote and write an algebraic expression for each item in parts a through c.
Answer:
24 Letters and 4 Postcards
Step-by-step explanation:
We have to set up a system of equations, since we have two unknown variables. Lets say postcards is the variable "x" and letters is the variable "y".
Our first equation will be the money spent: 0.33x + 0.49y = 13.08, this comes from knowing that it costs 0.33 dollars to mail a postcard and 0.49 dollars to send a letter.
The second equation is the total sent: x + y =28.
Now we need to solve for a single variable, let's do y (or letters). If we subtract y from both sides we get: x = 28 - y.
We can plug that into our first equatino to get: 0.33(28 - y) + 0.49y = 13.08.
If we multiply things out we get: 9.24 - 0.33y + 0.49y = 13.08, and now we have like terms. 9.24 + 0.16y = 13.08.
Subtract 9.24 from both sides to get: 0.16y = 3.84
Divide both sides by 0.16 to get: y = 24.
Now we can plug this into x + y = 28 to see that x= 4.
You could make sure this is correct by solving for x instead of y and do the same process.
Hope this helps.
Write1 3/4 as a decimal and as a percent
Answer:
the decimal is 1.75 and The percentage is 175%
Step-by-step explanation:
Find the measure of the missing angle
Answer:
g=118 degrees h=62 degrees
Step-by-step explanation:
So we can use some angle rules that I forget the name of to solve this.
Let's look at angle g first. We know that the opposite angle is 118 degrees. So that also means that g is going to be 118 degrees.
Since g is 118 degrees we can find h. The angle of a line is 180 degrees. This means that we can do 180-118 to find h. h=62 degrees.
We can do the same thing for k and m. Try doing what I did for g and h for those two. Comment if you need help.
A grocery store recently sold 20 cartons of yogurt, of which 5 were cherry. Based on past data, how many of the next 16 cartons of yogurt sold should you expect to be cherry?
Answer: 4
Step-by-step explanation:
The radius of a circle is 15 m. Find its circumference in terms of π
C = 2 x pi x r
C = 2 x pi x 15 = 30 π
Can someone please help me out with this question?
Use the slope formula and pick any two points to find the slope.
m= Y2- Y1/x2-x1
I picked the points (1,8) (3,14).
14-8/3-1= 6/2= 3
Hope this helps .
Max made a journey of 700km partly by train and partly by bus.He started his journey at 8.00am. by train which travelled at 50km/hr. After alighting from the train, he took a lunch break of 30 minutes. He then continued his journey by bus which travelled at 75km/hr.The whole journey took 11.75hours. Determine the distance travelled by bus.
I really don't know I'm not big on school subjects
complementary
supplementary
neither
Answer:
Two angles are called complementary if their measures add to 90 degrees, and called supplementary if their measures add to 180 degrees. Note that in these definitions, it does not matter whether or not the angles are adjacent; only their measures matter.
Step-by-step explanation:
hope its help po
correct me if im wrong
Two angles say x and y, are said to be complementary iff the sum of both angles x and y is 90° , while on the another hand, if their sum is 180°, they're called supplementary angles. So, here 75° + 105° = 180°, so both the angles are supplementary.
Hence, the required answer is supplementary
Here is an expression 3/5 divided by 1/4 Which situation matches this expression?
Which situation matches this expression?
A: An athlete runs 3/5 kilometers in 4 minutes. At that rate, how many kilometers does the athlete run in 1 minute?
B: A teacher fills an empty white pitcher with 3/5 gallons of water and an empty blue pitcher with 1/4 gallon of water. How many more gallons of water are now in the white pitcher than in the blue pitcher?
C: Mr. Smith has 3/5 pounds of beans. He uses 1/4 pound of beans each week. At the rate, for how many weeks will beans last?
D: A worker cuts pieces of string that are each 3/5 yards in length. How many pieces of string can the worker cut from a piece of string that is 1/4 yard in length?
Answer:
C
Step-by-step explanation:
To find A you have to divide 3/5 by 4 so that would not work.
To find B you have to subtract 1/4 from 3/5 and that doesn't match the problem.
To find C you do divide 3/5 by 1/4 which matches the problem.
And lastly for D you would divide 1/4 by 3/5 which is the opposite of what the question is asking for.
The following stem-and-leaf plot represents the scores earned by Mr. Wood's class on their most recent science test.
How many of the students scored less than an 85?
10
12
11
9
Answer:
11
Step-by-step explanation:
If you count the total values
it equals 11
A lifeguard fills a pool with water at a constant rate. After 1/2 hour, 1/3 of the pool is filled.
At this rate, what fraction of the pool is filled per hour?
A. 1/6 of the pool
B. 1/3 of the pool
C. 1/2 of the pool
D. 2/3 of the pool
Answer:
D
Step-by-step explanation:
1/2 hour -> 1/3 pool
multiply this by 2
1 hour -> 2/3 pool
so D 2/3 pool
The fraction of the pool that would be filled per hour at the given rate is: D. 2/3 of the pool.
What is a Constant Rate?A constant rate can be described as a quantity that changes steadlity over time.
The rate that the pool gets filled is given as:
1/2 hr = 1/3 of the water that would be filled in the pool
1 hr would be: 1/3 × 2 = 2/3
Therefore, the fraction of the pool that would be filled per hour at the given rate is: D. 2/3 of the pool.
Learn more about rate on:
https://brainly.com/question/25184007
A soccer stadium had a capacity of 25000 seats, but with the new area built this increased by 20%.
Calculate the number of people in the stadium if on a match only 65% of the seats are occupied.
Answer:
19,500 people
Step-by-step explanation:
20% of 25,000 is 5,000.
Add 5,000 to 25,000 - this will give you 30,000. That is a 20% increase.
65% of 30,000 is 19,500, thus there are 19,500 people in the stadium.
anyone know the answer to this
Answer: The bottom three: [tex]\frac{48}{-17}[/tex], [tex]\frac{-48}{17}[/tex], and -2 [tex]\frac{14}{17}[/tex]
Step-by-step explanation:
The first option is not because the numerator and denominator are flipped.
The second option is not because this one is positive while the one given is negative.
The third option is equivalent.
The fourth option is equivalent.
The fifth option is equivalent because - 48 / 17 = -2 [tex]\frac{14}{17}[/tex] when turned into a mixed number.
Answer:
[tex]\frac{48}{-17}, \frac{-48}{17}, -2\frac{14}{17}[/tex] (the last 3 options)
Step-by-step explanation:
As long as the negative is in either the numerator or the denominator (if it is in both then it is positive because the negatives cancel out), the entire fraction will be negative, so both [tex]\frac{48}{-17}[/tex] and [tex]\frac{-48}{17}[/tex] work as answers. The last option is just a simplified version of the fraction.
HELP!!!! I can’t figure this out
Answer:
A
Step-by-step explanation:
A rocket is shot off from a launcher. The accompanying table represents the height of
the rocket at given times, where x is time, in seconds, and y is height, in feet. Write a
quadratic regression equation for this set of data, rounding all coefficients to the
nearest hundredth. Using this equation, find the height, to the nearest foot, at a time
of 14.7 seconds.
Time in Seconds (x) Height in Feet (v)
1.1
301
2
518
3.1
756
3.6
833
4.3
956
Copy Valoes for Calculator
Open Statistics Calculator
Regression Equation:
Final Answer:
Submit Answer
Answer:The quadratic model obtained using a quadratic regression solver with Coefficient rounded to the nearest hundredth is :y = - 15.57x² + 179.32x + 0.20height = yx = time Using the model obtained;The height, to the nearest foot, at a time, x = 6.4 seconds.y = - 15.57x² + 179.32x + 0.20y = - 15.57(6.4^2) + 179.32(6.4) + 0.20y = 510.1008y = 510
Step-by-step explanation:
Find the value of x.
(3x+9)
(4x + 3)
Answer:
For two different equations:
(3x+9)
x = -3
(4x+3)
x = -3/4
Finding x using both equations:
plug x = -3 into the other equation
4(-3) + 3 = -9
x = -9
plug x = -3/4 into the other equation
3(-4/3) + 9 = 27/4
x = 27/4
Set the equations equal to each other:
3x+9=4x+3
3x-4x = 3-9
-x = -3
x=3
PLEASE RATE!! I hope this helps!!
If you have any questions comment below
Find the critical t-value that corresponds to % confidence. Assume degrees of freedom
Using a t-distribution, with 20 degrees of freedom, the critical t-value that corresponds to 95% confidence is t = 2.0860.
How to find the critical value for a t-distribution confidence interval?It is found with the help of a calculator, having two inputs:
The confidence level.The number of degrees of freedom, which is one less than the sample size.Hence, using a calculator, with 20 degrees of freedom, the critical t-value that corresponds to 95% confidence is t = 2.0860.
More can be learned about the t-distribution at https://brainly.com/question/16162795
find x , y , sin alpha, tg beta and area of triangle
Answer:
Step-by-step explanation:
Compare using < , > , or =-1.75 and -1 3/4
Answer:
1.75 = 1 3/4
Step-by-step explanation:
1 3/4 = 1.75
Answer:
=
Step-by-step explanation:
-1.75 is the same as -1 3/4
The part of the clock that is shaded is_______________________.
A) one-half hour
B) one-quarter hour
C) three-quarters hour
D) one-third hour
Answer:
b) one quarter hour
Step-by-step explanation:
every section is worth 5 minutes, there are three sections, which equals 15 minutes, 15 minutes is a one-quarter hour. hope this helps :)
Answer:
B
Step-by-step explanation:
it Is one quarter of an hour because they are exactly 15 minutes
I know the measure of angle m is 100 degrees. I did this multiple times and J and L are not 80 degrees so what are the measures of angles L and J?
Answer:
[tex]m\angle L = 100^{\circ}[/tex].
[tex]m\angle J = 80^{\circ}[/tex].
[tex]m\angle M = 100^{\circ}[/tex].
Step-by-step explanation:
Since segment [tex]JM[/tex] is parallel to segment [tex]KL[/tex], quadrilateral [tex]JKLM[/tex] is a trapezoid.
Segment [tex]JK[/tex] and segment [tex]LM[/tex] (the two legs of this trapezoid) are equal in length. Hence, trapezoid [tex]JKLM[/tex] would be an isoscele trapezoid. By symmetry, [tex]m\angle L = m \angle K = 100^{\circ}[/tex].
Line [tex]JK[/tex] traverses line [tex]JM[/tex] and line [tex]KL[/tex]. [tex]\angle J[/tex] and [tex]\angle K[/tex] are a pair of consecutive interior angles as they are both between [tex]JM\![/tex] and [tex]KL\![/tex] and are on the same side of the traversal, [tex]JK\![/tex].
Since line [tex]JM[/tex] is parallel to line [tex]KL[/tex], any pair of consecutive interior angles between these two lines would add up to [tex]180^{\circ}[/tex] (supplementary angles.) Thus, [tex]\angle J[/tex] and [tex]\angle K[/tex] are supplementary angles; [tex]m\angle J + m\angle K = 180^{\circ}[/tex].
Since [tex]m\angle K = 100^{\circ}[/tex], [tex]m\angle J = 180^{\circ} - m\angle K = 180^{\circ} - 100^{\circ} = 80^{\circ}[/tex].
(Pls Help ASAP) (If you don't know don't Answer)
Answer:
Step-by-step explanation:
4x + y = 8
x + 3y = 8
[tex]Here, \dfrac{a_{1}}{a_{2}}=\dfrac{4}{1}\\\\\\\dfrac{b_{1}}{b_{2}}=\dfrac{1}{3}\\\\\\\dfrac{a_{1}}{a_{2}} \neq \dfrac{b_{1}}{b_{2}}[/tex]
So, this system of equations is consistent and independent.
-4x + 6y = -2
2x - 3y = 1
[tex]\dfrac{a_{1}}{a_2}}=\dfrac{-4}{2}=\dfrac{-2}{1}\\\\\\\dfrac{b_{1}}{b_{2}}=\dfrac{6}{-3}=\dfrac{-2}{1}\\\\\\\dfrac{c_{1}}{c_{2}}=\dfrac{-2}{1}\\\\\\\dfrac{a_{1}}{a_{2}}=\dfrac{b_{1}}{b_{2}}=\dfrac{c_{1}}{c_{2}}[/tex]
So, the system of linear equations are consistent and dependent.
5x -2y = 4
5x - 2y = 6
[tex]\dfrac{a_{1}}{a_{2}}=\dfrac{5}{5}=1\\\\\\\dfrac{b_{1}}{b_{2}}=\dfrac{-2}{-2}=1\\\\\\\dfrac{c_{1}}{c_{2}}=\dfrac{4}{6}=\dfrac{2}{3}\\\\\\ \dfrac{a_{1}}{a_{2}}=\dfrac{b_{1}}{b_{2}} \neq \dfrac{c_{1}}{c_{2}}[/tex]
This system of equations is inconsistent.
A 50 ml IVPB bag of ampicillin 500 mg in normal saline is to be run in over 20 minutes. What is the infusion rate in ml/hr?
Using proportions, it is found that the infusion rate is of 150 ml/hr.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In this problem, 50 ml are administered over 20 minutes. How much is administered over one hour = 60 minutes? The rule of three is:
50 ml - 20 min
x ml - 60 min
Applying cross multiplication:
x = 50(60)/20
x = 50(3)
x = 150.
The infusion rate is of 150 ml/hr.
More can be learned about proportions at https://brainly.com/question/24372153
Is (1, 0) a solution to the equation y= –9x + 1?
Answer:
No
Step-by-step explanation:
→ Substitute the x value into the equation
-9 × 1 + 1
→ Simplify
-8
→ Compare to given y value
0 ≠ -8
Answer:
no
when you substite the values you don't get the same values