Split the second term in 4m^2 + 16m + 15 into two terms
4m^2 + 10m + 6m + 15
Factor out the common terms in the first two terms, then in the last two terms
2m(2m + 5) + 3(2m + 5)
Factor out the common term 2m + 5
(2m + 5)(2m + 3)
4m^2 + 16m + 15
With the way the trinomial is, we cannot factor it in it's current state.
We must check to see if splitting the middle term is possible.
List factors of 60
1 * 60
-1 * -60
2 * 30
-2 * -30
3 * 20
-3 * -20
4 * 15
-4 * -15
5 * 12
-5 * -12
6 * 10 (this digits satisfy the criteria for splitting the middle term.)
Split the middle term.
4m^2 + 6m + 10m + 15
Group the polynomials in terms of 2.
(4m^2 + 6m) + (10m + 15)
Factor each binomial.
2m(2m + 3) + 5(2m + 3)
Rearrange the binomials.
(2m + 5)(2m + 3)
0.7 7/9 7/8 greatest to least
First, turn the two fractions into decimals : 7/9 = .77777 7/8 = .875
Now, all of the numbers are in common form so you can identify which is largest, etc. : .875, .77777, .7
Now put the values back to fractions : 7/8, 7/9, .7
what is 2.1 times 10^4 in standard form
Standard form of non-polynomials is purely to solve them.
10^4 = 10,000
2.1 * 10,000 = 21,000
Anyone ??
I’m confused
compare the ratios 2 to 7 and 5:7 using the circles to model
To compare the ratios 2 to 7 and 5:7 using the circles to model we need to make two circles first.
Then we need to make 7 parts of each circle.
For 2:7 ratio, we need to shade 2 parts of the total 7 parts of the circle.
For 5:7 ratio, we need to shade 5 parts of the total 7 parts of the circle.
So, the first circle represents 2:7 ratio and second circle represents 5:7 ratio.
Answer:
To compare the ratios 2 to 7 and 5:7 using the circles to model we need to make two circles first.
Then we need to make 7 parts of each circle.
For 2:7 ratio, we need to shade 2 parts of the total 7 parts of the circle.
For 5:7 ratio, we need to shade 5 parts of the total 7 parts of the circle.
So, the first circle represents 2:7 ratio and second circle represents 5:7 ratio.
Step-by-step explanation:
Jane is X years old today. her brother Kenny is four years older l. after seven years of their total combined age will be 24 years. Write a linear equation for their total combination age after seven years
Answer:
The linear equation for the total combination age is [tex]X+7+(X+4)+7=24[/tex]
Step-by-step explanation:
If Jane is X years old today. And her brother is 4 years older then her brothers age is,
X+4.
Jane's age after 7 years = X+7
Jane's Brothers age after 7 years = (X+4)+7
So after seven years their combined age will be 24, Lets write this in an equation form,
[tex]X+7+(X+4)+7=24[/tex]
So the linear equation for the total combination age is,
[tex]X+7+(X+4)+7=24[/tex]
at 1:30 in the afternoon an old freight train and a new dart express train pull out of the new garland station going in opposite directions the dart express train goes three times faster than the hold freight train. fifteen minutes later the two trains are already 30 miles apart find the speed of each train?
Answer:
[tex]V_{E} = -22.5 / 15 = 1.5 miles/minute\\V_{F} = 7.5 / 15 = 0.5 miles/minute[/tex]
Step-by-step explanation:
To answer this problem, we must bear in mind that the express train travels 3 times faster than the freight train.
If we call F the distance that the freight train travels and we call E at the distance that the express train travels, we must have the distance between them after 15 minutes it must be 30 miles.
So
[tex]F + E = 30\\[/tex]
We also know that:
[tex]E = 3F[/tex]
Since the express train travels 3 times faster than the freight train.
So, like both equations, we have to:
[tex]F + 3F = 30\\F = 30/4\\F = 7.5 miles\\[/tex]
Then [tex]E = 7.5*3 = 22.5[/tex] miles in the opposite direction.
This is the distance you traveled in 15 minutes.
Therefore, the speed of the express train ([tex]V_{E}[/tex]) is the distance traveled between the time it did
[tex]V_{E} = -22.5 / 15 = 1.5 miles/minute\\V_{F} = 7.5 / 15 = 0.5 miles/minute[/tex]
Please help me !!!!!
Whenever you want to write the equation of a parallel line through some point (h, k), you can ...
remove any added constant in the original given equationreplace x with (x-h)replace y with (y-k)rearrange the resulting equation to the form required by the problem.Using this formula here, we get
... 2(y +5) = 3(x -2)
Your answer form requires you solve this for y.
... 2y + 10 = 3x -6 . . . . . eliminate parentheses
... 2y = 3x -16 . . . . . . . . subtract the constant on the left (10)
... y = (3/2)x -8 . . . . . . divide by 2
why are diagrams that show how matter moves through organisms and the environment called cycles
"The correct answer is that diagrams showing how matter moves through organisms and the environment are called cycles because they depict continuous, circular pathways.
In ecosystems, matter is not created or destroyed but is continuously recycled. This recycling process occurs in a loop or cycle, where matter moves from the environment to organisms and then back to the environment. For example, in the carbon cycle, carbon dioxide is taken in by plants during photosynthesis, then passed on to animals that consume the plants, and eventually returned to the environment through processes like respiration and decomposition.
These cycles are essential for the sustainability of ecosystems because they ensure that nutrients and other materials are reused and not depleted. The term ""cycle"" reflects the repeating and ongoing nature of these processes, highlighting the interconnectedness and interdependence of organisms and their environment. By using diagrams to represent these cycles, we can visualize and better understand the complex interactions and pathways that matter follows in ecosystems."
Which graph shows a slope of m = −1 / 2 and a y intercept of b = -4?
Letter D, because the y intercept is on -4 and if you look at the slope and use the method "Rise over Run" you can see that the rise is one and negative a half.
If a regular polygon has an exterior angles that measure 60 degrees each, how many sides does a polygon have
Answer:
6
Step-by-step explanation:
a pex
y=2x+5
Complete the missing value in the solution to the equation.
(2, ?)
To find the y value in this line, we can simply plug 2 into the variable x and solve.
2(2) + 5
4 + 5 = 9
The y value for x 2, is 9.
This can be displayed as (2, 9).
Using the slope intercept relation, the missing y value in the points given is 9.
Given the slope intercept equation :
y = 2x + 5 Points ;(x, y) = (2,?)Substituting the value of x into the equation and solving for y :
y = 2(2) + 5
y = 4 + 5
y = 9
Therefore, the value of y which is missing is 9 ; the point is( 2, 9)
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Ally made a net to find the surface area of a box she was designing. The box measure 12 centimeters long by 9 centimeters high by 9 centimeters deep. What is the surface area, in square centimeters, of the box?
Final answer:
Ally's box has a total surface area of 594 square centimeters, calculated using the surface area formula for a rectangular prism: Surface Area = 2lw + 2lh + 2wh.
Explanation:
The surface area of a box can be calculated by finding the area of all six faces and adding them together. Since the box Ally is designing has dimensions of 12 cm long, 9 cm high, and 9 cm deep, we will have two faces for each dimension. To calculate the surface area of Ally's box, we use the formula:
Surface Area = 2lw + 2lh + 2wh
Where l is the length, w is the width, and h is the height of the box. Now, plugging in Ally's box dimensions:
Surface Area = 2(12 cm)(9 cm) + 2(12 cm)(9 cm) + 2(9 cm)(9 cm)
Surface Area = 2(108 cm2) + 2(108 cm2) + 2(81 cm2)
Surface Area = 216 cm2 + 216 cm2 + 162 cm2
Surface Area = 594 cm2
Therefore, the total surface area of Ally's box is 594 square centimeters.
A road crew is widening a street that is 24 m wide. Their scale drawing says the new street has to be 125% of the width of the old street. How wide should the new street be? A. 19.2 m B. 28 m C. 30 m D. 300 m
If the street is already 24 m wide, and it is being expanded by 125%, then the correct answer is C. 30 m!
125% simply means 1 1/4. 1/4 of 24 is 6. So, you have 24 + 6 = 30!
Answer:
The correct answer is C: the new street should be 30m wide.
Step-by-step explanation:
This is a simple problem of per-cents. Perhaps the easiest way to do it is to use a basic ‘‘rule of three’’. In this particular case the 100% is the width of the old street, i.e. 24 m; and we want to know the new width, that is 125% of the old street. So,
24 ---- 100%
x ----- 125%
To find x we use the formula
[tex]x = \frac{24*125}{100} = 3000/100=30[/tex]
So, the width of the new street is 30m.
A boy jogs 250 meters in 110 seconds. What is his average speed in m/s?
Answer:
2.72 m/s
Step-by-step explanation:
We are given that
Boy jogs=250 meters
Time taken by boy=110 seconds
We have to find the average speed in m/s
In order to find the average speed then we will divide distance by time
[tex]Average\;Speed=\frac{distance}{time}[/tex]
Using the formula then we get
Average speed=[tex]\frac{250}{110}=2.72 m/s[/tex]
Hence, the average speed=2.72 m/s
Final answer:
To calculate the average speed, the boy's distance jogged (250 meters) is divided by the time taken (110 seconds), yielding an average speed of 2.27 m/s.
Explanation:
The student's question asks how to calculate the average speed of a boy who jogs a certain distance in a given amount of time. To find the average speed, you divide the total distance traveled by the total time taken. In this case, the boy jogs 250 meters in 110 seconds.
The calculation for the average speed (v) would be:
Distance (d) = 250 meters
Time (t) = 110 seconds
Average Speed (v) = d / t
Plugging the values into the equation yields:
Average Speed (v) = 250 m / 110 s = 2.27 m/s
Hence, the boy's average speed is 2.27 meters per second.
simplify (2x^2+6x+5) - (6x^2+3x+5)
Your answer will turn out to be −4x^2+3x.
Simplify. Distribute -1 to all terms within the second parenthesis
-(6x² + 3x + 5) = -6x² - 3x - 5
Combine like terms
2x² - 6x² = -4x²
6x - 3x = 3x
5 - 5 = 0
-4x² + 3x is your answer
~Rise Above the Ordinary
Please help!! Worth 20 points!
Henry deposited $420 into a savings account. There is a $5.00 per month service fee on the account. Also, Henry decides he wants to withdraw $25 a week for spending money. In how many months will Henry run out of money? A) 3 months Eliminate B) 4 months C) 5 months D) 6 months
Answer:
Step-by-step explanation:
Given that Henry deposited $420 into a savings account. There is a $5.00 per month service fee on the account. Also, Henry decides he wants to withdraw $25 a week for spending money.
Let us convert everything into days.
30 days a month and 7 days in a week
Service charges for 30 days = 5
withdrawn amount for 7 days = 25
Let x be the total no of days
Then [tex]\frac{25x}{7} +\frac{5x}{30}= 420\\\\750x+35x=420(7)(30)\\785x=420(7)(30)\\x=112.3567[/tex]
i.e. between 3 and 4 months
We can say in 3 months this will be exhausted.
Option A
Which of the following numbers can be expressed as decimals that terminate? 5/2 4/5 2/7 4/3
help me out please!
Solve for z.
[tex]\dfrac{8(4-z)}{7}=-z\\\\8(4-z)=-7z\\\\32-8z=-7z\\\\-7z+8z=32\\\\z=32[/tex]
8(4 - z)/ 7 = -z
8(4 - z) = -7z
32 - 8z = -7z
-8z + 7z = -32
-z = -32
z = 32
Solve the following proportion (solve p) p/6=7/8
Answer is: p = [tex]\frac{21}{4}[/tex]
The second of three numbers is 6 more than the first. The third number is twice the first. The sum of the three number is 26. Find the three numbers
Let's have the first number be x, the second number y, and the third number z.
Because the second number is six more than the first, y = x + 6.
Because the third number is twice the first, z = 2x.
The three numbers added together equals 26, so 26 = x + y + z.
Let's substitute y = x + 6 and z = 2x into 26 = x + y + z. This gives us:
26 = x + x + 6 + 2x
26 = 4x + 6
We subtract 6 from both sides of the equation and divide by 4 to get:
5 = x
Now, we'll put x = 5 into our previous to equations to find y and z:
y = 5 + 6
y = 11
z = 2*5
z = 10
Let's check out answer. 10 + 11 + 5 = 26. 10 is twice of 5 and 11 is 6 more than 5. Thus our three numbers are 10, 11, and 5.
The three numbers are 5, 11 (5 + 6), and 10 (2 * 5)
Explanation:Let's call the first number x
The second number is 6 more than the first, so it is x + 6
The third number is twice the first, so it is 2x
The sum of the three numbers is 26, so we have the equation x + (x + 6) + 2x = 26
Combining like terms, we get 4x + 6 = 26
Subtracting 6 from both sides, we get 4x = 20
Dividing both sides by 4, we get x = 5
So the three numbers are 5, 11 (5 + 6), and 10 (2 * 5)
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someone please help me i need help w all 4
The solution of the system of equations and inequalities, indicates that the solution are;
x = 4, y = -3x = 1, y = -2.5Please find attached the graph showing the feasible region, which is the solution of the system of inequalities, created with MS ExcelPlease find attached the graph showing the solution of the system of inequalitiesHow can the solution of a system of equations be found graphically?In order to find the solution of the system of equations by graphing, the lines are graphed on the same coordinate plane and the point at which the two graphs intersect is the solution of the system of equations.
1) y = (1/4)·x - 4, y = (-1/2)·x - 1,
The x-coordinates at the point of intersection, can be found by noting that the y-values of both equations are the same
Please find attached the graph of the system of equations with the point of intersection, (4, -3), which corresponds to x = 4, and y = -3, created with MS Excel
The solution of the system of equations therefore is; x = 4, y = -3
2. 3·x - 2·y = 8
x - 2·y = 4
Making y the subject of both equations, we get;
y = (3/2)·x - 4
y = (1/2)·x - 2
The graph of the above two equations can be plotted on the same coordinate plane using MS Excel, is attached
The point of intersection of the two graphs is (1, -2.5)
The solution of the system of equations is therefore; x = 1, and y = -2.5
3) The solution of the system of inequalities is the feasible region, corresponding to the region that satisfies both inequalities;
Please find attached the graph of the inequalities, showing the positive region that satisfies both inequalities, which is the triangle with vertices, (0.51, 0), (1, 1), and (1.5, 0)
4) The inequalities can be graphed by making y the subject of both inequalities and graphing the equations on the same coordinate plane.
x + y > -2, therefore; y > -2 - x
6·x - y ≥ 3, therefore; y ≤ 6·x - 3
6·x - 3 = -2 - x
The points in the feasible region of the graph are; points below and on the line, y = 6·x - 3, above the line y = -2 - x, and to the right of the point (1/7, -2 1/7)
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0.00216140848x^2-.43046552x+315.0091012= 315.00910 solve this equation
The answer is 199.198.
Answer: x = {199.28959, 0.00000278768}
Step by step explanation:
0.00216140848x² - 0.43046552x + 0.0000012=0
[tex]x = \frac{-b +/- \sqrt{b^{2}- 4ac} }{2a}[/tex]
[tex]x = \frac{-(-0.43046552) +/- \sqrt{-0.43046552^{2}- 4(0.00216140848)(0.0000012)} }{2(0.00216140848)}[/tex]
You can do each step manually or use a quadratic calculator to do the calculations.
x = 199.28959, x = 0.00000278768
What is the simplified value of the expression below?
Answer:
B
Step-by-step explanation:
The plates at the local restaurant have a diameter of 6.3 inches. What is the circumference of the plates?
Use 3.14 for π.
A.
12.6 inches
B.
18.9 inches
C.
19.732 inches
D.
19.782 inches
Answer:
B: 18.9
Step-by-step explanation:
Why is it good to have holes in your t-shirts
Answer:
They make it easier to get your arms through
Please help me with this
Each of 25 students in Group A read for 45 minutes. Each of 21 students in Group B read for 48 minutes. Which group read for more minutes? Explain.
David can jog 4 miles in 75 minutes What is David’s jogging rate per hour
4/75 = x/60
75x = 240
divide each side by 75
x = 3.2
Davids jogging rph/rate per hour would most likely be 3.5 /3.7
What is 47,482 rounded to the nearest thousand?
Rounded to the nearest thousand is 47,000 because the number to the right of it is not 5 or up, so this is the answer.
hope that helps :)