[tex]f(x)=x^2-2x;\ g(x)=6x+4\\\\(f+g)(x)=f(x)+g(x)\\\\(f+g)(x)=0\Rightarrow(x^2-2x)+(6x+4)=0\\\\x^2+(-2x+6x)+4=0\\\\x^2-4x+4=0\\\\x^2-2x-2x+4=0\\\\x(x-2)-2(x-2)+0\\\\(x-2)(x-2)=0\iff x-2=0\\\\\boxed{x=2}[/tex]
Write y=-4/5x-2 in standard form using integers?
Answer:
4/5x + y = -2
Step-by-step explanation:
Answer:
4x+5y=-10
Step-by-step explanation:
We have to arrange [tex]y=\frac{-4}{5}x-2[/tex] in the standard form using integers.
The standard form of the equation of a line is represented as Ax+By=C, where A,B,C are integers and A≥0.
Therefore, multiplying the given equation by 5 on the both sides, we have,
[tex]5y=-4x-10[/tex]
On rearranging,we get,
[tex]4x+5y=-10[/tex]
Which is the required standard form using integers.
If we want to be 95% confident of our estimate, does the sample proportion obtained, 20 out of 50, fall within the margin of error developed from the simulation? Why or why not?
20/50 = 2/5 = 0.40 which is found in the dot plot given. Since this value is in the dot plot, this means that it is possible to obtain this value with a random simulation.
Answer: Yes, the sample proportion 20/50 falls within the margin of error.
Answer
20/50 = 2/5 = 0.40
Ok.
Nancy is 5 years younger than her brother Stan. Last year she was twice as young as he was. How old is each of them now?
Answer:
Nancy is 6 years old and Stan is 11 years old now.
Step-by-step explanation:
Let the present age of Stan be x.
Then age of Nancy = y
x - y = 5
Last year she was twice as young as he was
Age of Nancy last year = y-1
Age of Stan last year = x-1
2 × (y-1)= x-1
2y -2 = 5 + y -1
y = 6
x = y + 5 = 6 + 5 = 11
Nancy is 6 years old and Stan is 11 years old now.
Please help! Thank you
M and O are congruent
N, M and O are similar
Your answer is: M and N are similar but not congruentM and N are similar because the sides of M are proportional to sides of N:
[tex]\dfrac{2}{4}=\dfrac{1}{2}[/tex]
Two figures are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.
I am planting 50 apple trees and 30 peach trees. I want the same number and type of trees per row. What is the maximum number of trees I can plant per row?
The maximum number of trees the student can plant per row is 10. This is found by identifying the greatest common divisor of the total number of apple trees and peach trees he has which is 10.
Explanation:To solve this problem, you need to find the greatest common divisor of 50 (the number of apple trees) and 30 (the number of peach trees). The greatest common divisor is the highest number that can divide both numbers without a remainder.
Both 50 and 30 can be divided by 10 without any remainder, but they can't be divided evenly by any number higher than 10. Therefore, 10 is the greatest common divisor of 50 and 30.
In this context, being able to divide the number of trees evenly means that you can plant the same number of each type of tree in each row. So, given the total numbers of apple and peach trees, the maximum number of trees you can plant per row is 10.
Learn more about Greatest Common Divisor here:https://brainly.com/question/23270841
#SPJ3
To determine the maximum number of trees that can be planted per row when planting 50 apple trees and 30 peach trees with uniformity, calculate the greatest common divisor (GCD) of the two quantities, which is 10. This means the maximum number of trees per row that can evenly divide both 50 and 30 is 10 trees per row.
The question involves finding the maximum number of trees that can be planted per row when planting 50 apple trees and 30 peach trees with the same number and type of trees per row. To find this number, we need to determine the greatest common divisor (GCD) of the two quantities, which will tell us the largest number of trees that can uniformly fit into each row for both types of trees.
First, list the factors of 50 (1, 2, 5, 10, 25, 50) and the factors of 30 (1, 2, 3, 5, 6, 10, 15, 30).
Find the largest factor that appears in both lists. In this case, it is 10.
The maximum number of trees per row that can evenly divide both 50 and 30 is 10 trees per row.
Therefore, you can plant up to 10 trees per row for a neat and organized orchard layout.
does the equation 7x-4y=0 represent a direct variation? what is the constant of variation?
Yes, the equation 7x-4y=0 represents a direct variation with the constant of variation being 7/4.
The equation 7x-4y=0 does represent a direct variation. To see this, we can rearrange the equation into the form y = kx, which is the general form for direct variation. Solving for y, we divide both sides by -4 to get:
y = (7/4)x
Here, the coefficient of x, which is 7/4, is the constant of variation. Thus, in the given equation, the constant of variation is 7/4, meaning for every unit increase in x, y increases by 7/4 units. This proportional relationship where y varies directly as x, with a constant ratio of 7/4, confirms it's a direct variation.
3rs - 5cr - 15cs + 25c2
[tex]3rs-5cr-15cs+25c^2=r(3s-5c)-5c(3s-5c)\\\\=(3s-5c)(r-5c)\\\\Answer:\ \boxed{3rs-5cr-15cs+25c^2=(3s-5c)(r-5c)}[/tex]
please help me with this question!!
Answer:
40
Step-by-step explanation:
5+1 3/8n=60
Subtract 5
1 3/8n=55
11/8n=55
8/11(55/1)
n=40
How to divide the polynomial using long division
[tex]\mathbb{ANSWER:}[/tex]
Refer to the attachment to view the answer.
3/4( 1/6 x+16)= 3/7 (4 3/8 x−21)
Answer:
x=12
Step-by-step explanation:
Solve for x:
(3 (x/6 + 16))/4 = (3 ((4 + 3/8) x - 21))/7
Put 4 + 3/8 over the common denominator 8. 4 + 3/8 = (8×4)/8 + 3/8:
(3 (x/6 + 16))/4 = (3 ((8×4)/8 + 3/8 x - 21))/7
8×4 = 32:
(3 (x/6 + 16))/4 = (3 ((32/8 + 3/8) x - 21))/7
32/8 + 3/8 = (32 + 3)/8:
(3 (x/6 + 16))/4 = (3 ((32 + 3)/8 x - 21))/7
32 + 3 = 35:
(3 (x/6 + 16))/4 = (3 ((35 x)/8 - 21))/7
Put each term in x/6 + 16 over the common denominator 6: x/6 + 16 = x/6 + 96/6:
3/4 x/6 + 96/6 = (3 ((35 x)/8 - 21))/7
x/6 + 96/6 = (x + 96)/6:
3/4 (x + 96)/6 = (3 ((35 x)/8 - 21))/7
3/6 = 3/(3×2) = 1/2:
(x + 96)/(2×4) = (3 ((35 x)/8 - 21))/7
Put each term in (35 x)/8 - 21 over the common denominator 8: (35 x)/8 - 21 = (35 x)/8 - 168/8:
(x + 96)/(2×4) = 3/7 (35 x)/8 - 168/8
(35 x)/8 - 168/8 = (35 x - 168)/8:
(x + 96)/(2×4) = 3/7 (35 x - 168)/8
2×4 = 8:
(x + 96)/8 = (3 (35 x - 168))/(8×7)
8×7 = 56:
(x + 96)/8 = (3 (35 x - 168))/56
Multiply both sides by 56:
(56 (x + 96))/8 = (56×3 (35 x - 168))/56
56/8 = (8×7)/8 = 7:
7 (x + 96) = (56×3 (35 x - 168))/56
(56×3 (35 x - 168))/56 = 56/56×3 (35 x - 168) = 3 (35 x - 168):
7 (x + 96) = 3 (35 x - 168)
Expand out terms of the left hand side:
7 x + 672 = 3 (35 x - 168)
Expand out terms of the right hand side:
7 x + 672 = 105 x - 504
Subtract 105 x from both sides:
(7 x - 105 x) + 672 = (105 x - 105 x) - 504
7 x - 105 x = -98 x:
-98 x + 672 = (105 x - 105 x) - 504
105 x - 105 x = 0:
672 - 98 x = -504
Subtract 672 from both sides:
(672 - 672) - 98 x = -672 - 504
672 - 672 = 0:
-98 x = -672 - 504
-672 - 504 = -1176:
-98 x = -1176
Divide both sides of -98 x = -1176 by -98:
(-98 x)/(-98) = (-1176)/(-98)
(-98)/(-98) = 1:
x = (-1176)/(-98)
The gcd of -1176 and -98 is -98, so (-1176)/(-98) = (-98×12)/(-98×1) = (-98)/(-98)×12 = 12:
Answer: x = 12
at the amusement park each student is given $16 for food this covers the cost of two meals plus $4 for snacks how much money does the school expect the students to spend per meal. which equation could be used to represent this dituation
solve for x
(3x-6)(-x+3)-0
smaller x=?
larger x=?
Answer:
x=2 and x=3
Step-by-step explanation:
(3x-6)(-x+3)=0
We can use the zero product property to solve for x
3x-6 = 0 and -x+3 =0
3x-6 = 0
Add 6 to each side
3x-6+6 = 6
3x=6
Divide by 3
3x/3 =6/3
x =2
-x+3 =0
Add x to each side
-x+x+3 = +x
3 =x
In a group of 25 students, 12 students play basketball, 11 students play football. Five students play both sports. A student is chosen randomly from this group.
What is the probability that the student plays both basketball or football?
Answer:
2/25 chance for both.
Step-by-step explanation:
There is a total of 25 students = 25 as my denominator.
11 + 12 = 23.
25 -23 = 2
Therefore my numerator is 2.
----> 2/25
Which equation's graph has a steeper slope y=8x+4 or y=6x-4
Answer:
y=8x+4 has a steeper slope. itś slope is 8 while y=6x-4 has a slope of 6.
Step-by-step explanation:
The graph of the equation y=8x+4 is steeper because it has a higher slope.
What is the equation of a line?The equation of a line is given as
y = mx + c
Where m is the slope and c is the y-intercept.
The given equations are y=8x+4 and y=6x-4. Compare the equations with the standard form to find the slope.
y = mx + c
y=8x+4
y=6x-4.
The slope of the first equation is 8 and the other equation is 6.
Therefore, the graph of the equation y=8x+4 is steeper because it has a higher slope.
More about the equation of line link is given below.
https://brainly.com/question/21511618
#SPJ2
4. What is the LCM of 4, 3, 10, and 8? *
80
240
120
30
5. Which statement is true? *
29/35 < 20/30
14/21 > 17/24
18/32 > 16/32
20/15 < 28/23
A scatter plot was constructed and a line of best fit was drawn, 25x 80. What is the equation of this best line of fit?
Y=5x+5
y=x+5
Y=5x+25
Y=x+125
Answer:
y = 5x + 25
Explaination:
To get the equation of a line, first get the slope of the line.
Slope = (change in y)/(change in x)
= (60-30)/(7-1)
= 30/6
= 5
Now use one point in the line (4,45) and a general point (x,y).
Slope = (change in y)/(change in x)
5 = (y - 45)/(x - 4)
5(x - 4) = (y - 45)
5x - 20 = y - 45
y = 5x -20 + 45
Need an educated answer fast
Answer:
y-2 = 2/3(x-8)
Step-by-step explanation:
We have the line 6x-9y = -7
Let's rewrite it in the form y=mx+b
6x-9y = -7
Subtract 6x from each side
6x-6x-9y = -7 -6x
-9y = -6x-7
Divide by -9
-9y/-9 = -6x/-9 -7/-9
y = 2/3 x + 7/9
The slope is 2/3
If the line is parallel, the slope will be the same so the slope will be 2/3
We have the slope and a point (8,2) on the new line, so we can use the point slope form of a line
y-y1 = m(x-x1)
y-2 = 2/3(x-8)
How would you do this problem?
(7+√6)(7+√6)
BEST ANSWER GETS BRANLIEST AND 99 POINTS
Answer:
55 + 14 sqrt(6)
Step-by-step explanation:
(7+√6)(7+√6)
We can figure out this problem by FOILing
First : 7*7 = 49
Outer: 7* sqrt(6) = 7 sqrt(6)
Inner: 7* sqrt(6) = 7 sqrt(6)
Last: sqrt(6) * sqrt(6) = 6
Add these together
49+ 7 sqrt(6)+ 7 sqrt(6)+6
55 + 14 sqrt(6)
find the value of x in 2x+20=3x-8
Answer:
X=28
Step-by-step explanation:
3x-8=2x+20. So x=28
Please help please help
Answer:
D
Step-by-step explanation: 1/3 x 3 = 1/9 same with 2/3
Answer:
B is the one here as well
Solve the following equation for b, a=b over 15
Answer:
15a=b
Step-by-step explanation:
so you have a=b/15.. we want b to be on its own.. you have to use inverse operations to get by by itself. so, we need to get rid of the 15.. it is being divided, so therefore multiply both sides by 15..
15a=b
PLEASE HURRY
Use the frequency table. Find the probability that a person goes to the movies at least 2 times a month. Round to the nearest thousandth.
A 0.137 B 0.138 C 0.394 D 0.707
Answer:
0.707 to nearest thousandth
Step-by-step explanation:
People who go at least 2 times a month = 219 + 180 + 96
= 495
So the required probability = 495 / 700
= 0.707 14
can someone help with this
Answer:
(1,3)
Step-by-step explanation:
From the graph, determine the coordinates of the point of intersection of the two. They are x=1 and y=3: (1,3)
This is the last of the four given possible answers.
Answer:
(1,3)
Step-by-step explanation:
The solution to a system of equations that is graphed is where the two graphs intersect. The two lines intersection at 1, 3. We can check this by putting them into the equation
y = 3x
3 = 3*1
True
y =x+2
3 = 1+2
3=3
True
This is the solution to the system of equations
given: m = 1/2 and b=4
Answer:
y = [tex]\frac{1}{2}[/tex] x + 4
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + b ( m is the slope and b the y-intercept )
here m = [tex]\frac{1}{2}[/tex] and b = 4, hence
y = [tex]\frac{1}{2}[/tex] x + 4 ← equation of line
Answer:
where is the question?
To make a sandwich, Steve uses 1/8 1b of ham and 1/5 1b of cheese how much more cheese than ham does he use?
A 1/3
B 3/40
C 1/20
D 1/10. PLEASE ANSWER THIS
Answer: B - 3/40
Step-by-step explanation: in order to find their difference, set up their common denominators equally, resulting in them having 5/40 and 8/40. subtract and you will get 3/40 as your final answer.
6. Maya is driving 120 miles to her grandmother’s house. She drives 35% of the distance before stopping for lunch. How far does she drive before lunch? (1 point)
Answer:
42 miles
Step-by-step explanation:
She drove 35% of 120 miles.
To find a percent of a number, multiply the percent by the number.
35% of 120 miles =
= 35% * 120 miles
= 0.35 * 120
= 42
n first gear, or low gear, an automobile's engine runs about three times as fast as the drive shaft. In second gear, the engine does not have to run as fast; usually it runs about 1.6 times faster than the drive shaft. Finally, in third, or high gear, the engine runs at the same speed as the drive shaft. Engine speed = 1,850 r.p.m. Transmission in second gear Drive-shaft speed =
Answer:
Consider the following cases
Case 1: In n first gear, an automobile's engine runs about three times as fast as the drive shaft.
So, if Speed of Engine = 1,850 r.p.m
Then Speed of Drive Shaft [tex]=\frac{1850}{3}=616.67[/tex] r.p.m
Case 2 : In second gear, the engine does not have to run as fast; usually it runs about 1.6 times faster than the drive shaft.
So, if Speed of Engine = 1,850 r.p.m
Then Speed of Drive Shaft [tex]=\frac{1850}{1.6}=1156.25[/tex] r.p.m
Case 3: Finally, in third, or high gear, the engine runs at the same speed as the drive shaft.
So, if Speed of Engine = 1,850 r.p.m
Then Speed of Drive Shaft is also equal to 1,850 r.p.m
How to solve for b in p=2(a+b)
[tex]2(a+b)=p\qquad\text{divide both sides by 2}\\\\a+b=\dfrac{p}{2}\qquad\text{subtract a from both sides}\\\\\boxed{b=\dfrac{p}{2}-a}\\\\or\\\\2(a+b)=p\qquad\text{use distributive property}\\\\2a+2b=p\qquad\text{subtract 2a from both sides}\\\\2b=p-2a\qquad\text{divide both sides by 2}\\\\\boxed{b=\dfrac{p-2a}{2}}[/tex]
9/10+7/100 WHAT DOES THE EQUAL
Answer:
97/100
Step-by-step explanation:
9/10 = 90/100
90/100 + 7/100 = 97/100
What is the probability of someone being born on Feb.28 given that they were born in February?
Answer:
4/113
Step-by-step explanation:
1/28 for non leap years and 1/29 for leap years
However if u put those together it would be 4/113 overall
This is because every 4 years there are 113 days in February and 4 of those days will be the 28th.
Final answer:
The probability of someone being born on February 28th given that they were born in February is 1/28, assuming a non-leap year scenario.
Explanation:
The student is asking about the probability of being born on February 28th, given that they were born in February. Given that February usually has 28 days, except for leap years when it has 29 days, to find this probability, we consider a non-leap year scenario.
The total number of possible birth dates in February, in a non-leap year, is 28. Since being born on any given day in February is equally likely, the probability of being born on February 28th is simply 1 divided by the number of days in February.
Therefore, the probability is:
P(born on Feb. 28) = 1/28