I need some help x-7>10

QUESTION POSTED AT 19/08/2019 - 05:56 PM

Related questions

Please help ASAP! The point (5, -1) is a solution of the equation: y = 2x − 11 Question 1 options: True False Question 2 (1 point) Which point is on the graph of y = -2x + 1? Question 2 options: (2, 7) (3, -8) (6, 8) (4, -7) Question 3 (1 point) Determine if the ordered pair is a solution of the equation. Is the point (2,1) is a solution of the equation: y = 3x - 3? Question 3 options: True False Question 4 (1 point) Determine if the ordered pair is a solution of the equation. Is (2,4) a solution of y = 10 -3x? Question 4 options: True False Question 5 (1 point) Determine if the ordered pair is a solution of the equation. Is (-1,4) a solution of y = -2x+2? Question 5 options: True False Question 6 (1 point) Determine if the ordered pair is a solution of the equation. Is (-1,-30) a solution of y =10x? Question 6 options: True False Question 7 (1 point) Which ordered pairs are a solution to y = -4x? Select all that apply. Question 7 options: (0,0) (1,-3) (2,-8) (-1,4) Question 8 (1 point) Which ordered pairs are a solution to the equation? y = 8x Select all that apply. Question 8 options: (-1,-7) (2,16) (1,8) (-2,-6) Question 9 (1 point) Which ordered pairs are a solution to the equation? y = 2x - 3 Select all that apply. Question 9 options: (4,2) (1, -1) (-1, -7) (2, 1) Question 10 (1 point) Which ordered pairs are a solution to the equation? y = 6 - 2x Select all that apply. Question 10 options: (-1,2) (-1,8) (-2,6) (1,4)

So all you have to do to solve these problems is substitute the y coordinate and the x coordinate into the equation.

So question 1 would be true because when you substitute the numbers in it equals the y value.

Question 2 is (4, -7)

Question 3 is False

Question 4 is true

Question 5 is true

See if you can do the rest!

ANSWERED AT 22/09/2019 - 06:29 AM


QUESTION POSTED AT 22/09/2019 - 06:29 AM

Solve 6(x-7)=10(x+4) for x

6x - 42 = 10x + 40
6x - 82 = 10x
-82 = 4x
-82 / 4 = -20.5
x = -20.5

6(-20.5 - 7) = -165
10(-20.5 + 4) = -165


ANSWERED AT 21/09/2019 - 11:01 PM


QUESTION POSTED AT 21/09/2019 - 11:01 PM

If x= -3, then x2 -7x 10 equals

(-3)^2 - 7(-3) × 10 = 219

ANSWERED AT 21/09/2019 - 01:26 PM


QUESTION POSTED AT 21/09/2019 - 01:26 PM

Which of the following correctly expresses .0000045 in scientific notation 1).4.5 x 10-6 2).4.5 x 106 3). 45 x 10-7

The answer is 1).4.5 x 10-6

ANSWERED AT 21/09/2019 - 09:05 AM


QUESTION POSTED AT 21/09/2019 - 09:05 AM

Let f(x) = x + 8 and g(x) = x2 - 6x - 7. Find f(g(2)). Select one: a. -7 b. -3 c. 10 d. 33

\boxed{A. \ f(g(2)) = -7 \ }

Further explanation

In this problem we will find out the value of the function composition. There are two ways to do it.

\boxed{ \ f(x) = x + 8 \ }

\boxed{ \ g(x) = x^2 - 6x - 7 \ }

\boxed{ \ f(g(2)) = ? \ }

First way

Step-1: compose (f o g)(x) = f(g(x))

Here g(x) as input into f(x). In other words, first we apply g(x), then apply f(x) to that result:

g(x) = x^2 - 6x - 7 \rightarrow f(x) = x+8

f(g(x)) = (x^2 - 6x - 7) + 8

f(g(x)) = x^2 - 6x - 7 + 8

And we get,

\boxed{ \ f(g(x)) = x^2 - 6x + 1 \ }

Step-2: calculate the value of f(g(2))

After getting f(g(x)) we proceed by calculating the value f (g(2)).

x = 2 \rightarrow f(g(2)) = (2)^2 - 6(2) + 1

 f(g(2)) = 4 - 12 + 1

And we obtain the final result:

\boxed{ \ f(g(2)) = -7 \ }

Second way

Step-1: count g(2) initially

x = 2 \rightarrow g(2) = (2)^2 - 6(2) - 7

 g(2) = 4 - 12 - 7

And we get,

\boxed{ \ g(2) = -15 \ }

Step-2: calculate the value of f(g(2))

Here the value of g(2), i.e. -15, as input into f(x).

g(2) = -15 \rightarrow f(-15) = -15 + 8

And we obtain the final result:

\boxed{ \ f(g(2)) = -7 \ }

Learn more

  1. Let f(x) = x-3 and g(x ) = x^2 find f(g(4)) brainly.com/question/1052893
  2. Which expression is equal to f(x) · g(x)? brainly.com/question/9622736
  3. Find (f - g)(x) and its domain brainly.com/question/12000925

Keywords: Let f(x) = x + 8 and g(x) = x² - 6x - 7, find f(g(2)), composition function, input, f(g(x)), value, initially,

ANSWERED AT 21/09/2019 - 09:05 AM


QUESTION POSTED AT 21/09/2019 - 09:04 AM

The function f(x) is represented by the table below. What are the corresponding values of g(x) for the transformation g(x) = 6f(x)? X | f(x) -7 | 8 -3 | 3 0 | -1 2 | 7 10|5

Answer:

Given: The transformation g(x) =6f(x)                  ......[1]

To find the corresponding values of g(x) for the given transformation.

At x = -7, f(x) = 8

then,

By substituting the value of f(x) = 8 in [1] we have

g(x) = 6 \cdot 8 =48

Similarly,

For x= -3 , f(x) = 3, then

By substituting the value of f(x) = 3 in [1] we have

g(x) = 6 \cdot 3 =18

For x= 0, f(x) = -1 , then

By substituting the value of f(x) = -1 in [1] we have

g(x) = 6 \cdot -1 =-6

For x= 2, f(x) = 7, then

By substituting the value of f(x) = 7 in [1] we have

g(x) = 6 \cdot 7=42

For x= 10, f(x) = 5, then

By substituting the value of f(x) = 5 in [1] we have

g(x) = 6 \cdot 5=30

Therefore ; we have the corresponding values of g(x) as shown below;

x                f(x)           g(x)

-7                8                48

-3                3                 18

0                -1               -6

2                 7                42

10                5                30

ANSWERED AT 21/09/2019 - 08:05 AM


QUESTION POSTED AT 21/09/2019 - 08:05 AM

PRETTY PLEASE HELP??????1. John can spend up to $40 for gasoline and a carwash at a service station. The carwash will cost $6.00 and gasoline costs $4.50 per gallon. The inequality below can be solved for g, the number of gallons of gasoline John can buy. 4.5g + 6 ≤ 40 Which of the following is a true statement? (1 point) A. John can buy over 10 gallons of gasoline. B. John can buy at most 7 gallons of gasoline. C. John can buy 6 gallons but not 7 gallons. D. John can buy 7 gallons but not 8 gallons. 2. A baseball team had $800 to spend on supplies. The team spent $250 on a new bat. New baseballs cost $3 each. The inequality 250 + 3b ≤ 800 can be used to determine the number of new baseballs (b) that the team can purchase. Which statement about the number of new baseballs that can be purchased is true? (1 point) A. The team can purchase 184 new baseballs. B. The minimum number of new baseballs that can be purchased is 183. C. The maximum number of new baseballs that can be purchased is 183. D. The team can purchase 183 new baseballs but this number is neither the maximum nor the minimum. 3. Solve the following inequality. (1 point) 3x + 6 > 15 A. x < 3 B. x > 3 C. x < 7 D. x > 7 4. Solve the following inequality. (1 point) 4x – 6 < 2x + 8 A. x > 1 B. x < 1 C. x > 7 D. x < 7 5. What is the greatest integer that makes the inequality 3 – 2x > 9 a true statement? (1 point) A. -2 B. 2 C. 5 D. -4 7. Solve the following compound inequality. (1 point) 3x – 3 < -12 OR -4x ≤ -32 A. x ≤ 8 B. -3 < x ≤ 8 C. x < -3 D. x < -3 OR x ≥ 8 8. Solve the following compound inequality. (1 point) -7x + 9 < 72 AND 5x – 3 ≤ 7 A. x ≤ 2 B. x < -9 AND x ≥ 2 C. -9 < x ≤ 2 D. -10 < x ≤ 2

1. 4.5g + 6 < = 40
    4.5g < = 40 - 6
    4.5g < = 34
    g < = 34/4.5
    g < = 7.56
True statement : John can buy 7 gallons but not 8

2. 250 + 3b < = 800
    3b < = 800 - 250
    3b < = 550
    b < = 550/3
    b < = 183.33
True statement : The maximum number of new baseballs that can be purchased is 183

3. 3x + 6 > 15
    3x > 15 - 6
    3x > 9
     x > 9/3
     x > 3

4. 4x - 6 < 2x + 8
    4x - 2x < 8 + 6
     2x < 14
      x < 14/2
      x < 7

5. 3 - 2x > 9
    -2x > 9 - 3
    -2x > 6 ...when dividing by a negative, u flip the inequality sign
      x < -6/2
      x < -3
     True statement : - 2

7. 3x - 3 < -12         OR     -4x < = -32
    3x < -12 + 3                    x > = -32/-4
    3x < - 9                           x > = 8
      x < -9/3
      x < -3
answer : x < - 3 OR x > = 8

8. -7x + 9 < 72    AND   5x - 3 < = 7
    -7x < 72 - 9                5x < = 7 + 3
    -7x < 63                     5x < = 10
     x > -63/7                     x < = 10/5
     x > - 9                         x < = 2
answer : -9 < x < = 2

ANSWERED AT 20/09/2019 - 06:47 AM


QUESTION POSTED AT 20/09/2019 - 06:47 AM

Which number is not in scientific notation? 9 x 10^19 7.8 x 10^6 1.45 x 10^-7 0.33 x 10^-15

1.45 x 10^-7 isn't in scientific notation because if it's negative, the decimal starts before the first real number, right?

ANSWERED AT 20/09/2019 - 01:18 AM


QUESTION POSTED AT 20/09/2019 - 01:18 AM

Find the distance between (3, 8) and (7, -11). Round to the nearest hundredth. Find the coordinates of the midpoint of JK if J (-9, 5) and K(21, -7). Find the coordinates of the midpoint of AB if A(-8, 7) and B(-9, 11). If the midpoint between (8, y) and (-11, 6) is (-1.5, 5), find the value of y. Find the slope of the line that passes through the points (3, -6) and (6, 12). Find the value of x so that the line passing through (x, 10) and (-4, 8) has a slope of 2/3 Find the value of y so that the line passing through (9, 0) and (3, y) has a slope of 1/2 Find the slope of the line that passes through the points (8, 7) and (11, 7).

Distance formula : d = sqrt (x2 - x1)^2 + (y2 - y1)^2
(3,8)(-7,11)
d = sqrt (-7 - 3)^2 + (11 - 8)^2
d = sqrt (-10^2) + (3^2)
d = sqrt (100 + 9)
d = sqrt 109
d = 10.44
===============
mid-point formula : ((x1 + x2) / 2 , (y1 + y2) / 2)
(-9,5)(21,-7)

midpoint = ((-9 + 21)/2 , (5 + (-7)/2)
               = ((12/2) , (-2,2))
               = (6, -1) <==
=======================
(-8,7)(-9,11)
midpoint = ((-8 + (-9) / 2, (7 + 11)/2 )
               = (-17/2, 18/2)
               = (-8.5, 9) <==
======================
(8,y)(-11,6).....midpoint = (-1.5/5)
midpoint = ((8 + (-11)/2, (y + 6)/2)
               = (-3/2), (4 + 6)/2
               = (-1.5,5)
               y = 4 <==
======================
slope = (y2 - y1) / (x2 - x1)
(3,-6)(6,12)
slope = (12 - (-6) / (6 - 3) = (12 + 6) / 3 = 18/3 = 6 <==
======================
(x,10)(-4,8)...slope = 2/3

y = mx + b
slope(m) = 2/3
(-4,8)...x = -4 and y = 8
sub and find b
8 = 2/3(-4) + b
8 = -8/3 + b
8 + 8/3 = b
24/3 + 8/3 = b
32/3 = b
equation is : y = 2/3x + 32/3 or 3y = 2x + 32
when y = 10
3(10) = 2x + 32
30 - 32 = 2x
-2 = 2x
-2/2 = x
-1 = x <===
=================
(9,0)(3,y)...slope = 1/2

y = mx + b
slope(m) = 1/2
(9,0)...x = 9 and y = 0
sub and find b
0 = 1/2(9) + b
0 = 9/2 + b
-9/2 = b
equation is : y = 1/2x - 9/2 or 2y = x - 9
sub in 3 for x and solve for y
2y = 3 - 9
2y = -6
y = -6/2
y = -3 <==
=================
(8,7)(11,7)...notice how the y values are the same. This means it is a horizontal line. A horizontal line has a slope of 0.
====================
sorry...not too good with the picture graphs







ANSWERED AT 19/09/2019 - 03:15 AM


QUESTION POSTED AT 19/09/2019 - 03:15 AM

6 x 10^-7 in scientific notation

This is already in scientific notation

ANSWERED AT 19/08/2019 - 05:25 PM


QUESTION POSTED AT 19/08/2019 - 05:25 PM

Please answer all 10 questions with all steps thank you 1) 5n+3=14-6n 2) 3(2x+11)=6x+33 3) 4(x-5)-5=6x+7.4-4x 4) 1/2(2n+6)=5n-12-n 5)3y-1=13-4y 6) 4n+8=9n-7 7)5n+20n=5(n+20) 8)3(4x-2)=12x 9) 100(x-3)=450-50x 10) 2P-12=12-2P

Simplifying 2p + -12 = 12 + -2p Reorder the terms: -12 + 2p = 12 + -2p Solving -12 + 2p = 12 + -2p Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '2p' to each side of the equation. -12 + 2p + 2p = 12 + -2p + 2p Combine like terms: 2p + 2p = 4p -12 + 4p = 12 + -2p + 2p Combine like terms: -2p + 2p = 0 -12 + 4p = 12 + 0 -12 + 4p = 12 Add '12' to each side of the equation. -12 + 12 + 4p = 12 + 12 Combine like terms: -12 + 12 = 0 0 + 4p = 12 + 12 4p = 12 + 12 Combine like terms: 12 + 12 = 24 4p = 24 Divide each side by '4'. p = 6 Simplifying p = 6

ANSWERED AT 19/08/2019 - 11:46 AM


QUESTION POSTED AT 19/08/2019 - 11:46 AM

10) 17x-2=7x+811) solve the simultaneous equations 4x+3y=16 5x-y=112) solve -3x-7= -1

10.x=1
11.3/4y+4 , x=1/5y+1/5
12.x=2

ANSWERED AT 19/08/2019 - 01:00 AM


QUESTION POSTED AT 19/08/2019 - 01:00 AM

1. The midpoint of the segment joining points (a, b) and ( j, k) is: a. (j-a,k-b) b. ((j-a)/2,(k-b)/2) c. (j+a,k+b) d. ((j+a)/2,(k+b)/2) 2. Point T is the midpoint of JH . The coordinate of T is (0, 4) and the coordinate of J is (0, 2). The coordinate of H is: a.(0, 6) b.(0, 3) c.(0, 7) d.(0, 11) 3. What about this one Point (-4, 3) lies in Quadrant a.I b.II c.III d.IV 4. Point (6, 0) lies on the. a.x-axis b.y-axis c.line y = x 5. Any line with no slope is parallel to the a.x-axis b.y-axis c.line y = x 7. If the point (a,3) lies on the graph of the equation 5x + y = 8, then a= a.1 b.-1 c.-7 8. If the equation of a circle is (x + 5)^2 + (y - 7)^2 = 36, its center point is a.(5, 7) b.(-5, 7) c.(5, -7) 9. If the equation of a circle is (x + 5)^2 + (y - 7)^2 = 36, its radius is a.6 b.16 c.36 10. If the equation of a circle is (x - 2)^2 + (y - 6)^2 = 4, the center is point (2, 6). True or False.

Answer:  The answers are given below.

Step-by-step explanation:  The calculations are as follows:

(1). The mid-point of a line segment divides it in the ratio m : n = 1 : 1.

So, the co-ordinates of the mid-point of the segment joining the points (a, b) and (j, k) are

\left(\dfrac{mj+na}{m+n},\dfrac{mk+nb}{m+n}\right)\\\\\\=\left(\dfrac{\times j+1\times a}{1+1},\dfrac{1\times k+1\times b}{1+1}\right)\\\\\\=\left(\dfrac{j+a}{2},\dfrac{k+b}{2}\right).

So, the co-ordinates of the mid-point are \left(\dfrac{j+a}{2},\dfrac{k+b}{2}\right).

Thus, (d) is the correct option.

(2). The co-ordinates of the points 'T' and 'J' are (0, 4) and (0, 2) respectively.

Let, (a, b) be the co-ordinates of the point 'H'.

Since 'T' is the mid-point of the line segment JH, so we have

(0,4)=\left(\dfrac{0+a}{2},\dfrac{2+b}{2}\right)\\\\\\\Rightarrow (0,4)=\left(\dfrac{a}{2},\dfrac{2+b}{2}\right)\\\\\\\Rightarrow \dfrac{a}{2}=0,~~~\dfrac{2+b}{2}=4\\\\\\\Rightarrow a=0,~~\Rightarrow 2+b=8~~~\Rightarrow b=6.

So, the co-ordinates of 'H' are (0, 6).

Thus, (a) is the correct option.

(3). The given point is (-4, 3).

Since 'x' co-ordinate is negative and 'y' co-ordinate is positive, so the given point lies in Quadrant II.

Thus, (b) is the correct option.

(4). The given point is (6, 0).

Here, 'y' co-ordinate is zero, so the point lies on the X-axis.

Thus, (a) is the correct option.

(5). The slope-intercept form of a line is

y = mx + c, where, 'm' is the slope and 'c' is the y-intercept.

If slope, m = 0, then the equation becomes

y = 0 × m + c

⇒ y = c, which is the equation of a line parallel to X-axis.

Thus, option (a) is correct.

(7). The point (a, 3) lies on the graph of the equation 5x + y = 8, so we have

5x+y=8\\\\\Rightarrow 5\times a+3=8\\\\\Rightarrow 5a=5\\\\\Rightarrow a=1.

Thus, (a) is the correct option.

(8). Given that the equation of a circle is

(x+5)^2+(y-7)^2=36~~~~~~~~~~~~~~~~~~~~~~~~~(i)

We know that the equation of a circle with centre (g, h) and radius 'r' units is given by

(x-g)^2+(y-h)^2=r^2.

Comparing equation (i) with the above general equation, we get

(g, h) = (-5, 7).

So, the centre point is (-5, 7).

Thus, option (b) is correct.

(9).  Given that the equation of a circle is

(x+5)^2+(y-7)^2=36~~~~~~~~~~~~~~~~~~~~~~~~~(ii)

We know that the equation of a circle with centre (g, h) and radius 'r' units is given by

(x-g)^2+(y-h)^2=r^2.

Comparing equation (ii) with the general equation, we get

r² = 36   ⇒ r = 6 units.

So, the radius is 6 units.

Thus, option (a) is correct.

(10). Given that the equation of a circle is

(x-2)^2+(y-6)^2=4~~~~~~~~~~~~~~~~~~~~~~~~~(iii)

We know that the equation of a circle with centre (g, h) and radius 'r' units is given by

(x-g)^2+(y-h)^2=r^2.

Comparing equation (iii) with the above general equation, we get

(g, h) = (2, 6).

So, the centre point is (-5, 7). Hence, the given statement is TRUE.

All the questions are ANSWERED.

ANSWERED AT 18/08/2019 - 10:56 PM


QUESTION POSTED AT 18/08/2019 - 10:56 PM

25 + 10(12 - x) = 5(2x-7) What is x? Use the PROPERTIES of EQUALITY and other properties to justify your solution.

I hope this helps you 25+10 (12-x)=5 (2x-7) 25+10.12-10x=5.2x-5.7 25+120-10x=10x-35 145-10x=10x-35 145+35=10x+10x 180=20x x=9

ANSWERED AT 18/08/2019 - 12:44 PM


QUESTION POSTED AT 18/08/2019 - 12:44 PM

Simplify 5(x - 2) 3x 8x - 2 8x - 10 -7x

5(x - 2) + 3x = 5x - 10 + 3x = 8x - 10

ANSWERED AT 17/08/2019 - 11:50 PM


QUESTION POSTED AT 17/08/2019 - 11:50 PM

Write 7,004,000 in scientific notation. A. 7.004 x 10^6 B. 7.004 x 10^-6 C. 0.7004 x 10^7 D. 0.7004 x 10^-7

7,004,000 in scientific notation.
=
7.004 x 10^6
as 7 is the first non zero digit 
so decimal jumbed 6 numbers from right to left and exponent will be positive
option A is correct
hopr this helps

ANSWERED AT 17/08/2019 - 02:38 PM


QUESTION POSTED AT 17/08/2019 - 02:38 PM

Choose the equivalent system of linear equations that will produce the same solution as the one given below. 4x - 2y = 6 2x + y = 5 A) -4x - 2y = 10 -4y = 4 B) -4x - 5y = -1 -7y = 5 C) 3x + 2y = 6 7x = 12 D) 4x + 2y = 10 8x = 16

4 x - 2 y = 6
2 x + y = 5       /  * 2  ( we will multiply both sides by 2 )
-------------------
4 x  - 2 y = 6
+
4 x  + 2 y = 10
---------------------
8 x = 16;    x = 2
4 + y = 5
y = 5 - 4;   y = 1
In the system of equations D :
8 x = 16;  x = 2 ,
8 + 2 y = 10
2 y = 2,  y = 1
Answer: D ) is the equivalent system

ANSWERED AT 17/08/2019 - 02:26 PM


QUESTION POSTED AT 17/08/2019 - 02:26 PM

F(x)= sqrt of 5x+7 and g(x)= the sqrt of 5x-7 find (f+g)(x) OPTIONS: A) sqrt 10x B) x sqrt 10 C) sqrt of 5x+7+ sqrt of 5x-7 D) 5x

F(x) = √(5x + 7)

g(x) = √(5x - 7)

(f + g)(x) = f(x) + g(x)

(f + g)(x) = √(5x + 7) + √(5x - 7)

Answer: C)

ANSWERED AT 02/08/2019 - 05:05 PM


QUESTION POSTED AT 02/08/2019 - 05:05 PM

Copy each statement. Insert +,-,x, or ÷ symbols to make this statement true. 14-2-7-3-9=10 please help

(14×2)÷7-3+9=10 because 14x2=28, 28÷7=4, 4-3=1+9= 10

ANSWERED AT 02/08/2019 - 01:55 AM


QUESTION POSTED AT 02/08/2019 - 01:55 AM

1. Which of the following is the factored form of the expression: 3x2 – 4x? A. x(3x - 4) B. x(3 – 4x) C. (3x -1) (x -1) D. (3x +1)(x -1) 2. Which is a completely factored form of the expression: x2 + 21x +20 ? A. (x + 5)(x + 4) B. (x + 10)(x + 2) C. (x + 20)(x + 1) D. (x + 21)(x - 1) 3. Which expression is factored form of 4x2 -9? A. 2(x - 3)2 B. (x - 3)2 C. 2(x + 3)(x - 3) D. (2x + 3)(2x - 3) 4. Below are factored forms of the expression: 12x3 – 36x2 . Which expression has the greatest common factor as the first term? A. 3x (4x2 – 12x) B. 4x2(3x -9 C. 12x2(x – 3) D. 12x(x2 - 3x) 5. Adele’s lawn has an area of (x2 -5x -6) square feet and a length of (x + 1) feet. What is the width of the lawn in feet? A. (x -6) B. (x +6) C. (x2 -4x -5) D. (x2 -6x -7) 6. The expression below represents the area, in square meters, of a rectangle: X2 + 5x -24 Which of the following pairs of expressions could represent the length and width, in meters, of the rectangle? A. (x – 3) and (x + 8) B. (x – 4) and (x + 6) C. (x – 6) and (x + 4) D. (x – 8) and (x + 3) 7. What is the complete factorization of 32 – 8z2? A. -8(2 + z)(2 –z) B. 8(2 + z)(2 – z) C. -8(2 + z)2 D. 8(2 – z)2 8. What is the greatest common factor of: 12x2 , 24x2y2 , and 46xy? A. 4x B. 3x C. 6x D. 2x 9. Which expression is equivalent to: 2x2 -3x -35? A. (2x + 7)(x - 5) B. (2x - 7) (x + 5) C. (2x - 5)(x + 7) D. (2x + 5)(x - 7) 10. What are the factors of 81x2 + 36x + 4? A. (9x + 2)(x +2) B. (9x +2)(9x +2) C. (9x -2)(9x -2) D. (9x +2)(9x -2) 11. The top of a rectangular table has an area of: 18x2+ 69x +60. The width of the table is 3x + 4. What is the length of the table? (Show proof by multiplying – show your work) 12. Simplify: (x2 +2x)(5x -3) A. 11x2 -3 B. 6x3 -6x C. 5x3 + 7x2 – 6x D. 5x3 – 13x2 -6x 13. Factor by grouping: 30g5 +24g3h – 35g2h2 - 28h3 Show your work! 14. Which is the correct way to factor the polynomial : x2 -16? A. (x -4)(x -4) B. (x -4)(x +4) C. (x +4)(x -2)(x +2) D. Not factorable 15. The area of a square painting is: 81p2 + 90p +25. What is the length of one side? Prove by multiplication – show your work.

1.  3x^2-4x=x(3x-4) - A.

2.  x^2 + 21x +20=(x-x_1)(x-x_2)

Find the roots:

 D=21^2-4\cdot 20=441-80=361, \ \sqrt{D}=19,\\ \\x_1=\dfrac{-21-19}{2}=-20, \ x_2=\dfrac{-21+19}{2}=-1    ,

then

 x^2 + 21x +20=(x+20)(x+1) - C.

3.  4x^2 -9=(2x)^2-3^2=(2x-3)(2x+3) - D.

4.  12x^3-36x^2=12x^2(x-3) - C.

5.  x^2 -5x -6=(x-x_1)(x-x_2)

Find the roots:

 D=(-5)^2-4\cdot (-6)=25+24=49, \ \sqrt{D}=7,\\ \\x_1=\dfrac{5-7}{2}=-1, \ x_2=\dfrac{5+7}{2}=6    ,

then

 x^2 -5x -6=(x-6)(x+1) and the width of the lawn is x-6 - A.

6. Since  x^2 + 5x -24=(x+8)(x-3) the length and width are x+8 and x-3 - A.

7.  32 -8z^2=8(4-z^2)=8(2^2-z^2)=8(2-z)(2+z) - B.

8.  12x^2=2\cdot 2\cdot 3\cdot x\cdot x, \\24x^2y^2=2\cdot 2\cdot 2\cdot3\cdot x\cdot x\cdot y\cdot y , \\ 46xy=2\cdot 23\cdot x\cdot y .

So the greatest common divisor is  2\cdot x=2x - D.

9.  2x^2 -3x -35=2(x-x_1)(x-x_2)

Find the roots:

 D=(-3)^2-4\cdot (-35)\cdot 2=9+280=289, \ \sqrt{D}=17,\\ \\x_1=\dfrac{3-17}{2\cdot 2}=-\dfrac{7}{2}, \ x_2=\dfrac{3+17}{2\cdot 2}=5    ,

then

 2x^2 -3x -35=2(x+\dfrac{7}{2})(x-5)=(2x+7)(x-5) - A.

10.  81x^2 + 36x + 4=(9x)^2+2\cdot 9x\cdot 2+2^2=(9x+2)^2 - B.

11.  18x^2+ 69x +60=3(6x^2+23x+20)=3\cdot 6(x+\dfrac{5}{2})(x+\dfrac{4}{3})=(6x+15)(3x+4) , the length is 6x+15.

12.  (x^2 +2x)(5x -3) =x^2\cdot 5x-x^2\cdot 3+2x\cdot 5x-2x\cdot 3=5x^3-3x^2+10x^2-6x=5x^3+7x^2-6x - C.

13.  30g^5 +24g^3h- 35g^2h^2 - 28h^3=(30g^5 +24g^3h)-(35g^2h^2+ 28h^3)=6g^3(5g^2+4h)-7h^2(5g^2+4h)=(5g^2+4h)(6g^3-7h^2) .

14.  x^2 -16=(x-4)(x+4) - B.

15.  81p^2 + 90p +25=(9p)^2+2\cdot 9p\cdot 5+5^2=(9p+5)^2 , the length of one side is 9p+5.

ANSWERED AT 01/08/2019 - 10:00 PM


QUESTION POSTED AT 01/08/2019 - 10:00 PM

×>10 is a solution to which inequality a}×-7>3 b}×-7>3 c}x-7<3 d}x-7<3

A) x - 7 > 3    |add 7 to both sides
     x > 10

b) x - 7 > 3    |add 7 to both sides
     x > 10

ANSWERED AT 01/08/2019 - 07:26 PM


QUESTION POSTED AT 01/08/2019 - 07:26 PM

Find the quotient of 2.632 x 10^4 and 2 x 10^-7

(2.632\cdot10^4):(2\cdot10^{-7})=(2.632:2)\cdot(10^4:10^{-7})\\\\=1.316\cdot10^{4-(-7)}=1.316\cdot10^{4+7}=\boxed{1.316\cdot10^{11}}

ANSWERED AT 01/08/2019 - 06:50 PM


QUESTION POSTED AT 01/08/2019 - 06:50 PM

Which of the following systems of equations has no solution? a. 9x + 5y = 1; 15y = 18x − 4 b. -7x − 7 = 3y; -14y − 8 = -6x c. 4x − 3y = 9; 6y = 8x − 18 d. 7y = 5x − 10; 10x − 14y = 8

The system of equations that has no solution are the equations that has the same slope which means they are parallel and do not intersect with each other at any point. From the choices, the correct answer is option D.

 7y = 5x − 10
y = (5/7) - 10/7
slope = 5/7

10x − 14y = 8

-14y = -10x + 8
y = (5/7) - 4/7
slope = 5/7

ANSWERED AT 01/08/2019 - 06:20 PM


QUESTION POSTED AT 01/08/2019 - 06:20 PM

Solve the equation for y. 5x – 7y = 10. A. y=-7/5x-7/10 B. y=5/7x+10/5 C. 5/7x-10/7 D. y=-5x-7

We are asked to express the equation 5x – 7y = 10 in terms of y. In this case, the first step is to add 7y to both sides, then subtract 5x , add 10 and divide the whole equation by 7. The resulting equation after the operation is C. y = 5/7x-10/7

ANSWERED AT 01/08/2019 - 02:07 PM


QUESTION POSTED AT 01/08/2019 - 02:07 PM

Write 5,000,039 in scientific notation. a) 0.5000039 x 10^-7 b) 5.000039 x 10^-6 c) 5.000039 x 10^6 d) 0.5000039 x 10^7

5,000,039 = 5.000039 x 10^6

ANSWERED AT 28/07/2019 - 09:34 AM


QUESTION POSTED AT 28/07/2019 - 09:34 AM