Answer:
3[tex]a^{4}[/tex] - 48
Step-by-step explanation:
Given
(a + 2)(3a² + 12)(a - 2)
= (a + 2)(a - 2)(3a² + 12) ← expand the first pair of parenthesis using FOIL
=(a² - 4)(3a² + 12) ← expand using FOIL
= 3[tex]a^{4}[/tex] + 12a² - 12a² - 48 ← collect like terms
= 3[tex]a^{4}[/tex] - 48
He Perimeter of a
regular decagon is 328cm
stake the length of one of its
sides
Answer:
32.8 cm
Step-by-step explanation:
decagons have 10 sides, so 328/10=32.8
Answer:
32.8 cm
Step-by-step explanation:
A regular decagon has 10 equal sides.
The perimeter of the decagon is 328 centimeters. The perimeter is the measure of all 10 sides added together. Since this is a regular decagon, all 10 sides are equal. Therefore, we can divide 328 by 10.
328 / 10
32.8
Add units, in this case, centimeters or cm.
32.8 cm
Each side of the decagon is 32.8 centimeters.
PLZZZZZZ HELP I NEED IT I AM GOING TO FAIL PLZZZZ I AM COUNTING ON YOU For which situations is it appropriate to use a sample? Select three options. A. What percentage of pick-up truck drivers want their next vehicle purchase to be another pick-up truck? B. What is the average number of rainbows each year in Honolulu? C. How many pedestrians would use a walkway built over a busy road? D. How many police cars are equipped with computers? E. What is the most popular car color in the teachers’ parking lot?
Answer:
b-What is the average number of rainbows each year in Honolulu?
c-How many pedestrians would use a walkway built over a busy road?
d-How many police cars are equipped with computers?
this is the answer
Step-by-step explanation:
E D G E N U I T Y
The situations it is appropriate to use a sample:
B. What is the average number of rainbows each year in Honolulu?
C. How many pedestrians would use a walkway built over a busy road?
D. How many police cars are equipped with computers?
What is a simple sample technique?Simple random sampling is a sampling technique in which each member of a population has an equal chance of being chosen, through the use of an unbiased selection method. The sample is chosen by a random method as every subject in the sample is assigned a number.
Why do we use sampling techniques?Sampling saves money by granting researchers to gather the same answers from a sample that they would receive from the population. Non-random sampling is significantly cheaper than random sampling because it lowers the cost associated with searchinh people and collecting data from them.
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Determine whether the study is an observational study or an experiment.
Research is conducted to determine if there is a relation between hearing loss and exposure to mumps. Does the description correspond to an observational study or an experiment?
Researchers are observing those with mumps to see how it affects hearing loss at all. There may be strong correlation, weak correlation, or no correlation at all.
With an experiment, researchers would break the participants into two groups: control group and treatment group. Those in the control group get the placebo (fake treatment) while the treatment group gets the treatment applied to them. If we were dealing with an experiment for this context, then the treatment group would get exposed to mumps on purpose. Of course, this is unethical and dangerous so an experiment for this type of project is not a good idea. It's better to go with an observational study.
Use the ratio of a 30-60-90 triangle to solve for the variables. Leave your answers as radicals in simplest form. x= y=
Answer:
x = 10 units, y = 5 units
Step-by-step explanation:
Given triangle ABC is a 30-60-90 triangle,
m∠C = 60°
By applying Sine rule in the given triangle,
Sin(60)°= [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
Sin(60)° [tex]=\frac{\text{AB}}{\text{AC}}[/tex]
[tex]\frac{\sqrt{3}}{2}=\frac{\text{AB}}{\text{AC}}[/tex]
[tex]\frac{\sqrt{3}}{2}=\frac{5\sqrt{3}}{x}[/tex]
x = 10 units
Similarly, by applying Cosine rule in the given triangle,
Cos(60)° = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]
Cos(60)° = [tex]=\frac{\text{BC}}{\text{AC}}[/tex]
[tex]\frac{1}{2}=\frac{y}{x}[/tex]
y = [tex]\frac{x}{2}[/tex]
y = 5 units
Therefore, x = 10 units and y = 5 units will be the answer.
Devi’s mother is three times as old as Devi. Five years ago, Devi’s mother was four times as old as Devi was then. Find their present ages
Answer:
Devi's present age = 15 years
Devi's Mother's present age = 45 years
Step-by-step explanation:
Let the present age of Devi be x years.
Therefore, mother's present age = 3x
Five years ago:
Devi's age = (x - 5) years
Mother's age =( 3x - 5) years
According to the given condition:
Five years ago:
Devi's mother's age = 4 times Devi's age
3x - 5 = 4( x - 5)
3x - 5 = 4x - 20
20 - 5 = 4x - 3x
15 = x
x = 15 years
3x = 3* 15 = 45 years
Hence,
Devi's present age = 15 years
Devi's Mother's present age = 45 years
Which describes how square S could be transformed to square S prime in two steps? Assume that the center of dilation is the origin. On a coordinate plane, square S has points (0, 0), (5, 0), (5, negative 5), (0, negative 5). Square S prime has points (0, 1), (0, 3), (2, 3), (2, 1). a dilation by a scale factor of Two-fifths and then a translation of 3 units up a dilation by a scale factor of Two-fifths and then a reflection across the x-axis a dilation by a scale factor of Five-halves and then a translation of 3 units up a dilation by a scale factor of Five-halves and then a reflection across the x-axis
Answer:
The correct option is;
A dilation by a scale factor of Two-fifths and then a translation of 3 units up
Step-by-step explanation:
Given that the coordinates of the vertices of square S are
(0, 0), (5, 0), (5, -5), (0, -5)
Given that the coordinates of the vertices of square S' are
(0, 1), (0, 3), (2, 3), (2, 1)
We have;
Length of side, s, for square S is s = √((y₂ - y₁)² + (x₂ - x₁)²)
Where;
(x₁, y₁) and (x₂, y₂) are the coordinates of two consecutive vertices
When (x₁, y₁) = (0, 0) and (x₂, y₂) = (5, 0), we have;
s = √((y₂ - y₁)² + (x₂ - x₁)²) = s₁ = √((0 - 0)² + (5 - 0)²) = √(5)² = 5
For square S', where (x₁, y₁) = (0, 1) and (x₂, y₂) = (0, 3)
Length of side, s₂, for square S' is s₂ = √((3 - 1)² + (0 - 0)²) = √(2)² = 2
Therefore;
The transformation of square S to S' involves a dilation of s₂/s₁ = 2/5
The after the dilation (about the origin), the coordinates of S becomes;
(0, 0) transformed to (remains at) (0, 0) ....center of dilation
(5, 0) transformed to (5×2/5, 0) = (2, 0)
(5, -5) transformed to (2, -2)
(0, -5) transformed to (0, -2)
Comparison of (0, 0), (2, 0), (2, -2), (0, -2) and (0, 1), (0, 3), (2, 3), (2, 1) shows that the orientation is the same;
For (0, 0), (2, 0), (2, -2), (0, -2) we have;
(0, 0), (2, 0) the same y-values, (∴parallel to the x-axis)
(2, -2), (0, -2) the same y-values, (∴parallel to the x-axis)
For (0, 1), (0, 3), (2, 3), (2, 1) we have;
(0, 3), (2, 3) the same y-values, (∴parallel to the x-axis)
(0, 1), (2, 1) the same y-values, (∴parallel to the x-axis)
Therefore, the lowermost point closest to the y-axis in (0, 0), (2, 0), (2, -2), (0, -2) which is (0, -2) is translated to the lowermost point closest to the y-axis in (0, 1), (0, 3), (2, 3), (2, 1) which is (0, 1)
That is (0, -2) is translated to (0, 1) which shows that the translation is T((0 - 0), (1 - (-2)) = T(0, 3) or 3 units up
The correct option is therefore a dilation by a scale factor of Two-fifths and then a translation of 3 units up.
Answer:
a
Step-by-step explanation:
Which set of ordered pairs represents a function?
{(-3,4), (-7,2), (-7,-4),(-9, -5)}
{(-2,4), (0,5),(-9,9),(-9,7)}
{(-4,-6), (-7, -5),(-4,-7), (1,1)}
{(5,-2), (-8,-6),(4, -2), (-6,3)}
Answer:
The correct answer is D.
Step-by-step explanation:
A function is when an input value has only one output value.
It cannot be A, because -7 produces both 2 and -4.
It cannot be B, because -9 produces both 9 and 7.
It cannot be C, because -4 produces both -6 and -7.
Therefore, it has to be D.
Select the correct answer.
What is the justification for step 2 in the solution process?
10x − 25 − 3x = 4x − 1
Step 1: 7x − 25 = 4x − 1
Step 2: 7x = 4x + 24
A.
the multiplication property of equality
B.
the division property of equality
C.
the addition property of equality
D.
the subtraction property of equality
Answer:
The answer is C addition property of equality.
Step-by-step explanation:
In step 1, 7x − 25 = 4x − 1 there are the numbers -25 and -1
In step 2, 7x = 4x + 24 The -25 is removed and -1 is replaced with 24
Meaning that in step 2 25 was added to those numbers meaning the answer C addition property of equality.
Answer:
C
Step-by-step explanation:
Which statement(s) is(are) true about cones? Statement 1: A cone has a triangular base. Statement 2: A cone is 3 times larger than a cylinder with the same height and radius. Statement 3: A cone is one-third the size of a cylinder with the same height and radius. Statement 4: A cone has a circular base.
Answer:
Statement 3: A cone is one-third the size of a cylinder with the same height and radius.
Statement 4: A cone has a circular base.
Step-by-step explanation:
Statement 3: A cone is one-third the size of a cylinder with the same height and radius.
Statement 4: A cone has a circular base.
The true statement is:
Statement 3: A cone is one-third the size of a cylinder with the same height and radius.
Statement 4: A cone has a circular base.
What is Cone?A cone is a three-dimensional solid geometric shape having a circular base and a pointed edge at the top . A cone has one face . There are no edges for a cone.
Properties of Cone
A cone is a shape that has a curved surface and a circular base. The following properties of a cone help us identify it easily. They are as follows.A base of a cone is circular.There is one face, one vertices, and no edges for a cone.The slant height of a cone is the length of the line segment joining the of the cone to any point on the circumference of the base of the cone.A cone have circular base at a perpendicular distance is called a right circular cone.A cone have circular base is an oblique cone.As, from the properties of cone we can say that.
A cone is one-third the size of a cylinder with the same height and radius. and, : A cone has a circular base..
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precalc! how do you solve by completing the square? i have 2 examples! (17 & 18 please) tysm <3
Answer:
17) x = 11, -8
18) exact form: x = + 2 sqaure root 6/ 3 + 2
I hope this helps :)
evaluate sine squared theta for theta equals 45 degrees
Find the area in square centimeters of the composite shape shown
below. Enter only a number as your answer.
A
E
13 cm
D
11 cm
7 cm
B
18 cm
C
Answer:
73cm²
Step-by-step explanation:
Area of rectangle=½ length×width
=½×18×7
=63cm²
Area of triangle=½b×h
base=18-13= 5cm
height=11-7 =4cm
½×b×h
½×5×4
=10cm²
Area of total=63+10
73cm²
Answer: 73c2
Step-by-step explanation:
PLEASE HELP! Manufacturers often alter different packages to save money and to grab customers attention. Explain using an example, how changes in the dimensions of common geometric shapes will affect the volume of the following shapes: prisms, cylinders, cones and spheres.
Answer:
An example of a prism could be a an amazon box to represent a rectangular prism. As the height, length, or width of the box increases, the volume increases allowing more items to fit within the box.
An example of a cone would be an ice cream cone. As the height or the radius of the cone increases, the more volume the cone can hold, meaning more ice cream for you.
An example of a cylinder could be a cup. As the height or the radius of the cup increases, the larger the volume. More drink for you.
An example of a sphere would be a soccer ball. As the radius increases, the volume of the ball increases. Hence, larger soccer balls have a bigger radius than smaller soccer balls. This allows for different varients of the ball to be created (i.e., youth, highschool, college, pro).
Note, the volume can also be decreased by simply shrinking the measurements instead of increasing them.
Step-by-step explanation:
Let's simply look at the equations of each shape.
Volume of a prism = base * height
Volume of a cone = Pi * r^2 * (height/3)
Volume of a cylinder = Pi * r^2 * height
Volume of a sphere = (4/3) Pi r^3
Notice that the volumes of prisms, cones, and cylinders directly correlate to height. As height increases, the volume increases. The sphere is unique in that the height is 2 * radius; however, the volume is related to the cube of the radius. Consider if you expanded the radius of the sphere, the volume will increase.
Answer:
Increase or decrease the dimensions of objects. See below for an explanation!
Step-by-step explanation:
An amazon box, which is a rectangular prism, is an example of a prism. If you increase the height, length, or width of the box, you can fit more stuff inside.
A cup is an example of a cylinder; by increasing the height or radius of the cup, you can fit more of a drink inside.
An icecream cone is an example of a cone; if the height or radius were increased, you might fit more ice cream inside.
A soccer ball is an example of a sphere; increasing the radius makes it larger, and various sizes are available for different levels.
You may also shrink the dimensions for each of these objects to make them smaller.
Hope this helps!
Tonia and trinny are twins. Their friends give them identical cakes for their birthday. Tonia eats 1/8 of her cake and trinny eats 1/6 of her cake. How much cake is left? please show working thank youu
Answer:
[tex]\frac{7}{12}[/tex] of the cake
Step-by-step explanation:
add [tex]\frac{1}{8}[/tex] and [tex]\frac{1}{6}[/tex] to see the total amount of cake eaten.
a. find the common denominator: 8 x 3 = 24 and 6 x 4 = 24
b. multiply accordingly to get the correct numerator: [tex]\frac{3}{24}[/tex] + [tex]\frac{4}{24}[/tex]
c. add: [tex]\frac{3}{24}[/tex] + [tex]\frac{4}{24}[/tex] = [tex]\frac{7}{24}[/tex]
subtract found value from total to find left over cake.
a. 24 - 7 = 14
simplify.
a. [tex]\frac{14}{24}[/tex] = [tex]\frac{7}{12}[/tex]
You are left with [tex]\frac{7}{12}[/tex] of the cake.
The formula for working out the cost of hiring a canoe is : cost=£15+6* number of hours. Megan paid £27 to hire a canoe. How long did she hire the canoe for
Answer:
Megan hired the canoe for 2 hours
Step-by-step explanation:
Given:
Cost(h) = 6h+15 = 27
Solution
6h+15 = 27
6h = 27-15 = 12
h = 2
the product of two rational number is -10/9. If one of the number is -5/27 ,find the other.
Answer:
Step-by-step explanation:
Let the unknown number = x
[tex]x *\frac{-5}{27}=\frac{-10}{9}[/tex]
x = [tex]\frac{-10}{9}[/tex] ÷ [tex]\frac{-5}{27}[/tex]
[tex]x=\frac{-10}{9}*\frac{-27}{5}\\\\\\x=-2* - 3\\x = 6[/tex]
Pleas answer this question now
Answer:
[tex]x = 17[/tex]
Step-by-step explanation:
According to the two tangent theory, tangent MN and tangent NP, which are both from point N, are congruent.
That is, [tex]x + 4 = 21[/tex]
Solve for x
[tex]x + 4 = 21[/tex]
Subtract 4 from both sides
[tex]x + 4 - 4 = 21 - 4[/tex]
[tex]x = 17[/tex]
Provide an appropriate response. At a college there are 120 freshmen, 90 sophomores, 110 juniors, and 80 seniors. A school administrator selects a random sample of 12 of the freshmen, a random sample of 9 of the sophomores, a random sample of 11 of the juniors, and a random sample of 8 of the seniors. She then interviews all the students selected. Identify the type of sampling used in this example.
Answer: Stratified Sampling
Step-by-step explanation: Stratified Sampling involves creating subdivisions of the population such that each subdivisions is seen as a subgroup or smaller chunk of the population which is split based on certain criteria or attribute. The stratified random sampling may be employed in delineating certain characteristics or to investigate further how a feature or characteristics vary between one subdivision to the other.
In the scenario above, the researcher made use of the stratified sampling by performing a random sampling selection of its subjects based on the different subdivisions of students available in the college
True or False? All equiangular triangles are similar.
Answer:
True
Step-by-step explanation:
All equiangular triangles are similar.
Find the value.
X3-4 when x=3
PLEASE HELP!!! ASAP!!!
Answer:
23
Step-by-step explanation:
Raise 3 to the power of 3
27 - 4
Subtract 4 from 27
23
Hope this was correct
Answer:
23
Explanation:
step 1 - rewrite the expression with the value of x
[tex]x^3 - 4[/tex]
[tex](3)^3 - 4[/tex]
step 2 - solve the exponent
[tex](3)^3 - 4[/tex]
[tex]27 - 4[/tex]
step 3 - subtract
[tex]27 - 4[/tex]
[tex]23[/tex]
therefore, the value of the expression is 23.
Zero product property
x(2x+4)(x+5)=0
A) x=0, x=-2, X=-5
B) x=0, x=2, x=5
C) x greater than or equal to 0
D) x=-2, x=5
Answer:
A
Step-by-step explanation:
Using ZPP we get x = 0, 2x + 4 = 0, x + 5 = 0. Solving these, we get x = 0, x = -2, x = -5.
Let f(x) = 1/x . Find the number b such that the average rate of change of f on the interval [2, b] is − 1/8
Answer:
b=4
Step-by-step explanation:
So, we have the function [tex]f(x)=1/x[/tex]. We need to find b such that the average rate of change or the slope is -1/8 between the intervel [2, b]. First, let's find f(2).
f(2) = 1/(2) = 1/2
So, we have the point (2, 1/2)
At point b, f(b) = 1/b.
Let's plug this into the slope formula:
[tex]\frac{y_2-y_1}{x_2-x_1}=\frac{.5-\frac{1}{b} }{2-b} =-1/8[/tex]
Now, we just need to solve for b. First, let's multiply both the numerator and denominator by b (to get rid of the annoying fraction in the numerator).
[tex]\frac{.5b-1}{2b-b^2} =\frac{-1}{8}[/tex]
Now, cross multiply.
[tex]4b-8=b^2-2b[/tex]
[tex]b^2-6b+8=0[/tex]
Solve for b. Factor using the numbers -4 and -2.
[tex]=(b-4)(b-2)=0[/tex]
Thus, b=4 or b=2.
However, b=2 is not a possible solution since the interval [2,2] means nothing. Thus, b=4.
We want to find an interval such that the given equation, f(x) = 1/x, has an average rate of change of -1/8 in that interval.
We will see that the interval is [2, 4]
-------------------------------
For a function f(x), the average rate of change in the interval [a, b] is given by:
[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]
Here we have:
[tex]f(x) = 1/x[/tex]
And the interval is [2, b] such that r in that interval is -1/8, so we need to solve:
[tex]r = -1/8 = \frac{f(b) - f(2)}{b - 2} = \frac{1/b - 1/2}{b - 2}[/tex]
We can rewrite it to:
[tex]-1/8 *(b - 2)= 1/b - 1/2\\\\-1/8 *(b - 2)= 2/2b - b/2b = (2 - b)/2b = -(b - 2)/2b[/tex]
Now we can remove the term (b - 2) because it appears on both sides, so we get:
[tex]-1/8 = -1/2b\\1/8 = 1/2b\\2/8 = 1/b\\1/4 = 1/b\\b = 4[/tex]
Then we found that b must be equal to 4, so the interval is [2, 4]
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The tennis club is selling water bottles and hats to raise money for tennis tournament a water bottle cost four dollars and a hat cost six dollars the club wants to raise $1200 Graph the linear equation Write three ordered pairs(x,y) that exist on the line
Given: A water bottle cost 4 dollars and a hat cost 6 dollars.
Let x = Number of water bottles
y = Number of hats
The club wants to raise $1200.
i.e. Required equation : 4x+6y=1200
At x=0,
[tex]0+6y=1200\Rightarrow\ y=\dfrac{1200}{6}\Rightarrow\ y=200[/tex]
At x= 300
[tex]4(300)+6y=1200\\\Rightarrow\ 1200+6y=1200\Rightarrow\ 6y=0\Rightarrow y=0[/tex]
At x= 240
[tex]4(240)+6y=1200\\\Rightarrow\ 960+6y=1200\Rightarrow\ 6y=240\Rightarrow y=40[/tex]
So,three ordered pairs(x,y) that exist on the line : (0,200), (300,0) and (240,40)
Plot these point on graph and join them.
Answer: the other guy is correct. Got it right on my test. Have a nice day. :|
Step-by-step explanation:
to solve the equation 3 x + 1 = 4 x + (negative 4)
Answer:
x=5
Step-by-step explanation:
3x+1 = 4x -4
Subtract 3x from each side
3x+1-3x = 4x-3x-4
1 = x-4
add 4 to each side
1+4 = x-4+4
5 =x
Answer: x=5
Step-by-step explanation:
3x+1=4x+(-4)
3x+1=4x-4
3x+5=4x
5=x
A submarine is only allowed to change its depth be Racing toward the surface in 60 meter stages. If the submarine starts off at 340 meters below sea level, what is its depth after 4 stages of rising to surface
Answer:
[tex]Depth = 100m[/tex]
Step-by-step explanation:
Given
Initial Level = 340 m
Number of stages = 4
Difference in each stage = 60 m
Required
Determine the depth of the submarine after 4 stages
First, we have to calculate the total distance moved towards the surface of the sea;
This is calculated as
[tex]Total\ Distance = Number\ of\ Stages * Difference\ in\ each\ stage[/tex]
[tex]Total\ Distance = 4 * 60m[/tex]
[tex]Total\ Distance = 240m[/tex]
This implies that the submarine moved a total distance of 240 metres;
It;'s new depth is calculated as follows;
[tex]Depth = Initial\ Depth - Total\ Distance[/tex]
[tex]Depth = 340m - 240m[/tex]
[tex]Depth = 100m[/tex]
Hence, its new depth after 4 stages of rising is 100m
Callie has a new kitten. The kitten weighs 3 pounds less than half the weight of Callie’s cat. Together, the cat and the kitten weigh 18 pounds. Which system of equations could be used to find the weight of each animal?
Answer:
y = [tex]\frac{1}{2} x - 3[/tex]
x + y = 18
Step-by-step explanation:
Let the kitten's weight be y and the cat's weight be x
Condition # 1:
y = [tex]\frac{1}{2} x - 3[/tex]
Condition # 2:
x + y = 18
pleaz!!! some body help with number #4 at the bottom
Answer:
See my explanation
Step-by-step explanation:
-2x + (x - 4) = 18
-x - 4 = 18
-x = 22 <- this is wrong in question writing as x = 22
so, x = -22
Ginnie plans to paint a wall. She measures its height and width. She finds that she needs enough paint to cover 8 square meters. Which measurement does 8 square meters represent?
Answer:
The 8 square meters represent the product of the height by the width of the wall and therefore, its area.
Step-by-step explanation:
Ginnie is going to paint a wall and measures the height and the width, the walls are usually in the form of a rectangle or square. To find the area of both we need to multiply the height by the width (in the case of the square both are the same) and this will give us the total amount of paint that we need to paint the wall.
In this example, Ginnie finds that she needs enough paint to cover 8 square meters, therefore, these 8 square meters represent the product of the height by the width (that we don't know but it doesn't matter) of the wall and therefore, its area.
ASAP!!! Please help me with this question!!!!!
r = radius
h = r+12 = height, 12 more than the radius
[tex]V = \text{Volume of cone (oblique or not)}\\\\V = \frac{1}{3}\pi*r^2*h\\\\V = \frac{1}{3}\pi*r^2*(r+12)\\\\V = \frac{1}{3}\pi*r^2*r+\frac{1}{3}\pi*r^2*12\\\\V = \frac{1}{3}\pi*r^3+\frac{1}{3}*12\pi*r^2\\\\V = \frac{1}{3}\pi r^3+4\pi r^2\\\\[/tex]
Answer: Choice BANSWER: SECOND OPTION
Solve the equation by completing the square.
3x^2-12x=96
Answer:
x = 8
or
x = -4
Step-by-step explanation:
3x² - 12x = 96
Divide both sides by 3
x² - 4x = 32
Add 4 to both sides
x² - 4x + 4 = 32 + 4
(x - 2)² = 6²
Find the square root of both sides
√(x - 2)² = √6²
x - 2 = +/- 6
x - 2 = +6 or -6
x - 2=+6
x=6+2
x=8
x - 2=-6
x=-6+2
x=-4
x = 8
or
x = -4