As both the terms have different signs, the terms will be subtracted and the sign in the answer will be of the larger terms (the term with greater coefficient)
So the answer of -3x+9x is 6x
2. Finding the sum of -7x and 4x + 2
For sum,
-7x + (4x+2)
= -7x + 4x + 2
= -3x + 2
3. Finding the difference when 6x is subtracted from 2x - 4
= 2x - 4 - (6x)
= 2x - 4 - 6x
= 2x - 6x - 4
= -4x - 4
4. Finding the difference when -3x - 7 is subtracted from x + 4
= (x+4) - (-3x-7)
= x + 4 + 3x + 7
= x + 3x + 4 + 7
= 4x + 11
5. Finding the result when 13x + 2 is subtracted from 11 + 5x
= (11 + 5x) - (13x + 2)
= 11 + 5x - 13x - 2
= 5x - 13x + 11 - 2
= -8x + 9
6. Finding the result when -18x - 4 is added to 4x - 14
Here we ave to find the HCF of the polynomial . In order to the same we will simplify each term of the polynomial into its reduced form and then extract the common among them.
Hence we see that [tex]2v^5[/tex] is common in them , hence this is our HCF
Question 5 :
We have to find the product of the binomial. In order to do that we will multiply the polynomial to itself using distributive law and then rearrange the terms with same power and then simplify them. The detailed solution is provided below.
The maximum speed of the wildebeest is v=66 ft/s. Speed is defined as the ratio between the distance covered (d) and the time taken (t):
[tex]v=\frac{d}{t}[/tex]
Re-arranging the formula, we get
[tex]d=vt[/tex]
And substituting v=66 ft/s, we find
[tex]d=66t[/tex]
2. c. y = 5 - n
In fact, we can check that this rule satisfies all the numbers of the sequence:
n=3 --> y = 5 - 3 = 2
n=4 --> y = 5 - 4 = 1
n=5 --> y = 5 - 5 = 0
n=6 --> y = 5 - 6 = -1
3. d. $5.50, $11.00, $16.50; E = 5.50h
In fact, if we use the rule E=5.50 h, we see that the table is completed as follows:
h=1 --> E=(5.50)(1 h)=5.50$
h=2 --> E=(5.50)(2 h)=11.00 $
h=3 --> E=(5.50)(3 h)=16.50$
h=4 --> E=(5.50)(4 h)=22.00$
h=5 --> E=(5.50)(5 h)=27.50$
4. c. if d ≥ 5 then C = 4.70d, if d < 5 then C = 4.70d - 1; $17.80, $32.90
If the number of days is more than 5, the cost is 4.70$ per day, therefore c=4.70d (where d is the number of days); if the number of days is less than 5, one dollar is returned, so the cost will be C=4.70d-1. By applying this rule, we can calculate the rental cost after d=4 days and d=7 days:
- d=4 --> c=4.70*4-1=17.80$
- d=7 --> c=4.70*7=32.90$
5. b. y = 3x + 3
In fact, we can check this is the correct rule by substituting the numbers:
x=0 --> y=3*0+3=3
x=1 --> y=3*1+3=6
x=2 --> y=3*2+3=9
x=3 --> y=3*3+3=12
x=4 --> y=3*4+3=15
7. x -2 -1 0 1 2
y (-16 ) (-6 ) (4 ) (14 ) (24 )
The rule we have to apply is:
-10x + y = 4
Re-arranging it, we can solve for y:
y = 10x + 4
So, let's substitute the different values of x:
x=-2 --> 10*(-2)+4=-20+4= -16
x=-1 --> 10*(-1)+4=-10+4= -6
x=0 --> 10*0+4= 4
x=1 --> 10*1+4=10+4= 14
x=2 --> 10*2 +4 =20+4 = 24
8. y = -5x - 1
In fact, if substitute the different values of x given by the problem, we find:
Now that we know x, we use its value (1) in the substitution equation in order to find "y" and complete the ordered pair:
[tex]y=x+3\\y=1+3\\y=4[/tex]
Then the solution pair (x, y) is: (1, 4)
Therefore, according to the numbers provided in the list of possible steps, the order is:
5, 6, 1, 4, 7, 3, 2
Second problem:
The solution to the system is where the two lines two lines intersect: "the point -1.5 on the x axis. Notice that -1.5 can be written in fraction form as -3/2, this is the x-coordinate of the intersection point. The y-coordinate is y-0 since the point is on the x-axis. Therefore the point is (-3/2, 0) which is given by answer B).
Third problem: The boundary line seems to go through the points: (-4, -10) and (0, -2), so we can calculate the slope via the equation:
since the line's y-intercept is (0, -2), then the equation of the boundary line in slope-intercept is:
[tex]y=2x-2[/tex]
Since the shaded region includes the boundary line and the zone above it (with y-values larger than or equal to those point in the line), we can say that the inequality that represents this graph is:
1)45 2)5 3)20 4)x-9=17 5) 2x+3=35 6)0 7)-2/9(THIS IS NOT IN THE CHOICES BUT IT IS THE RIGHT ANSWER). 8)x-(-2) 9)Subtract 7 and then divide by -2 10)-16 11)5x=11 12)Division property 13)-27 14)20 15)2x-5=15 16)-16 17)168 18)-5
can you rewrite it I don't understand so rewrite so I can help you
Step-by-step explanation:
1. 6x
2. -3x + 2
3. -4x - 4
4. 4x + 11
5. -8x + 9
6. -14x - 18
Step-by-step explanation:
1. Finding sum of -3x+9x
As both the terms have different signs, the terms will be subtracted and the sign in the answer will be of the larger terms (the term with greater coefficient)
So the answer of -3x+9x is 6x
2. Finding the sum of -7x and 4x + 2
For sum,
-7x + (4x+2)
= -7x + 4x + 2
= -3x + 2
3. Finding the difference when 6x is subtracted from 2x - 4
= 2x - 4 - (6x)
= 2x - 4 - 6x
= 2x - 6x - 4
= -4x - 4
4. Finding the difference when -3x - 7 is subtracted from x + 4
= (x+4) - (-3x-7)
= x + 4 + 3x + 7
= x + 3x + 4 + 7
= 4x + 11
5. Finding the result when 13x + 2 is subtracted from 11 + 5x
= (11 + 5x) - (13x + 2)
= 11 + 5x - 13x - 2
= 5x - 13x + 11 - 2
= -8x + 9
6. Finding the result when -18x - 4 is added to 4x - 14
= (4x - 14) + (-18x - 4)
= 4x - 14 - 18x -4
= 4x - 18x - 14 - 4
= -14x - 18
..
Step-by-step explanation:
1 t=16/21
2.m=2
3.n=13/7
4.a=2
5.x=6/17
6.x=15
7.s=21/4
8. t=7/3
9. s=1
10. s=6/61
11. x=1/3
12. r=27/16
13. c=−1
14.m=9/5n
15. j=−117/58
1. x/-3=-15
x=45
2. -7+3(-12)÷-3
-7+12
5
3. f(-4)=(-4)²-(-4)
f(-4)=16-(-4)
f(-4)=20
4. x-9=17
5. 2x+3=35
6. -8-12-(-20)
-20-(-20)
0
7. -2(-3)²(-1)
-2(9)(-1)
-18(-1)
18
8. x-(-2)
9. subtract 7 then divide by -2
10. 6+(-18)+(-13)+9
-12-4
-16
11. 5x=11
12. division property
13. -3³ = -27
14. x/2-3=7
x/2=10
x=20
15. 2x-5=15
16. x/-4-(-8)=12
x/-4=4
x=-16
17. 168
18. 16-20-(-8)-9
-4-(-8)-9
4-9
-5
Answers :
Answers.
Step-by-step explanation:
Question 1.
1. First we will open the brackets and bring together the terms with same degrees in decreasing order of their power.
[tex]5x^3+3x^2-7x+10+3x^3-x^2+4x-1\\[/tex]
[tex]5x^3+3x^3+3x^2-x^2-7x+4x+10-1\\[/tex]
2. Then we will simplify the terms with same degrees.
[tex]8x^3+2x^2-3x+9[/tex]
3. Now we see that the highest power in the polynomial. which is 3 in our case. Hence , Degree of the polynomial is 3.
4. The total number of terms in the polynomial is 3 as we can see in the simplified form below
[tex]8x^3+2x^2-3x+9[/tex]
Question 2.
In this question also we will follow the same process as we have done in the previous problem.
Open the brackets and rearrange them as per their degrees . The highest power in the polynomial will be our Degree of the polynomial. Let us see how :
[tex]9w-4w^2+10+8w^2+7+5w\\-4w^2+8w^2+9w+5w+10+7\\4w^2+14w+17\\[/tex]
Hence the Degree of the polynomial is 2 and the number of terms in polynomial is 3.
Question 3 :
In this we have to find the product. In order to find the product we will use the distributive law and multiply -3x with each term inside the bracket.
[tex](-3x * x^2)+ (-3x*3x) + (-3x*-1)\\-3x^3-9x^2+3x\\\\[/tex]
by using the law
[tex]x^m*x^n = x^(m+n)[/tex]
Question 4 :
Here we ave to find the HCF of the polynomial . In order to the same we will simplify each term of the polynomial into its reduced form and then extract the common among them.
[tex]8v^6+2v^5-10v^9\\2*4*v^5*v + 2*v^5 -2*5*v^5*v^4\\2v^5*4v + 2v^5*1-2v^5*5v^4\\[/tex]
Hence we see that [tex]2v^5[/tex] is common in them , hence this is our HCF
Question 5 :
We have to find the product of the binomial. In order to do that we will multiply the polynomial to itself using distributive law and then rearrange the terms with same power and then simplify them. The detailed solution is provided below.
[tex][5t+4]^2\\[5t+4]*[5t+4]\\5t*5t+5t*4+4*5t+4*4\\25t^2+20t+20t+16\\25t^2+40t+16\\[/tex]
1) D
2) C
3) D
4) C
5) B
6) B
Step-by-step explanation:
1. d. d = 66t
The maximum speed of the wildebeest is v=66 ft/s. Speed is defined as the ratio between the distance covered (d) and the time taken (t):
[tex]v=\frac{d}{t}[/tex]
Re-arranging the formula, we get
[tex]d=vt[/tex]
And substituting v=66 ft/s, we find
[tex]d=66t[/tex]
2. c. y = 5 - n
In fact, we can check that this rule satisfies all the numbers of the sequence:
n=3 --> y = 5 - 3 = 2
n=4 --> y = 5 - 4 = 1
n=5 --> y = 5 - 5 = 0
n=6 --> y = 5 - 6 = -1
3. d. $5.50, $11.00, $16.50; E = 5.50h
In fact, if we use the rule E=5.50 h, we see that the table is completed as follows:
h=1 --> E=(5.50)(1 h)=5.50$
h=2 --> E=(5.50)(2 h)=11.00 $
h=3 --> E=(5.50)(3 h)=16.50$
h=4 --> E=(5.50)(4 h)=22.00$
h=5 --> E=(5.50)(5 h)=27.50$
4. c. if d ≥ 5 then C = 4.70d, if d < 5 then C = 4.70d - 1; $17.80, $32.90
If the number of days is more than 5, the cost is 4.70$ per day, therefore c=4.70d (where d is the number of days); if the number of days is less than 5, one dollar is returned, so the cost will be C=4.70d-1. By applying this rule, we can calculate the rental cost after d=4 days and d=7 days:
- d=4 --> c=4.70*4-1=17.80$
- d=7 --> c=4.70*7=32.90$
5. b. y = 3x + 3
In fact, we can check this is the correct rule by substituting the numbers:
x=0 --> y=3*0+3=3
x=1 --> y=3*1+3=6
x=2 --> y=3*2+3=9
x=3 --> y=3*3+3=12
x=4 --> y=3*4+3=15
7. x -2 -1 0 1 2
y (-16 ) (-6 ) (4 ) (14 ) (24 )
The rule we have to apply is:
-10x + y = 4
Re-arranging it, we can solve for y:
y = 10x + 4
So, let's substitute the different values of x:
x=-2 --> 10*(-2)+4=-20+4= -16
x=-1 --> 10*(-1)+4=-10+4= -6
x=0 --> 10*0+4= 4
x=1 --> 10*1+4=10+4= 14
x=2 --> 10*2 +4 =20+4 = 24
8. y = -5x - 1
In fact, if substitute the different values of x given by the problem, we find:
x = -2 --> y = -5*(-2) -1= 10 -1 = 9
x = -1 --> y = -5*(-1) -1 = 5 -1 = 4
x = 0 --> y = -5*0 -1 = -1
x = 1 --> y = -5*1 - 1 = -6
x = 2 --> y = -5*2 -1 = -11
A
Step-by-step explanation: use the formula
According to the numbers provided, the sequence is:
5, 6, 1, 4, 7, 3, 2
Solution of the two lines intersecting in the graph is answer B
The inequality that represents the graph is that of answer A
Step-by-step explanation:
First problem:
This is the sequence to solve for "x" once the substitution was made;
[tex]3x +2\,(x+3)=11\\3x+2x+6=11\\5x+6=11\\5x=11-6\\5x=5\\x=1\\[/tex]
Now that we know x, we use its value (1) in the substitution equation in order to find "y" and complete the ordered pair:
[tex]y=x+3\\y=1+3\\y=4[/tex]
Then the solution pair (x, y) is: (1, 4)
Therefore, according to the numbers provided in the list of possible steps, the order is:
5, 6, 1, 4, 7, 3, 2
Second problem:
The solution to the system is where the two lines two lines intersect: "the point -1.5 on the x axis. Notice that -1.5 can be written in fraction form as -3/2, this is the x-coordinate of the intersection point. The y-coordinate is y-0 since the point is on the x-axis. Therefore the point is (-3/2, 0) which is given by answer B).
Third problem: The boundary line seems to go through the points: (-4, -10) and (0, -2), so we can calculate the slope via the equation:
[tex]slope=\frac{y_2-y_1}{x_2-x_1} \\slope=\frac{-2-(-10)}{0-(-4)}\\slope=\frac{8}{4}\\slope=2[/tex]
since the line's y-intercept is (0, -2), then the equation of the boundary line in slope-intercept is:
[tex]y=2x-2[/tex]
Since the shaded region includes the boundary line and the zone above it (with y-values larger than or equal to those point in the line), we can say that the inequality that represents this graph is:
[tex]y\geq 2x-2[/tex]
which corresponds to answer A
1)45
2)5
3)20
4)x-9=17
5) 2x+3=35
6)0
7)-2/9(THIS IS NOT IN THE CHOICES BUT IT IS THE RIGHT ANSWER).
8)x-(-2)
9)Subtract 7 and then divide by -2
10)-16
11)5x=11
12)Division property
13)-27
14)20
15)2x-5=15
16)-16
17)168
18)-5