To find the distance from the bear to the base of the waterfall, we can use the tangent function, which relates the angle of depression to the distance. Using the given angle of depression of 27° and height of 365 feet, we can calculate that the bear is approximately 632 feet from the base of the waterfall.
Explanation:To find the distance from the bear to the base of the waterfall, we can use the tangent function, which relates the angle of depression to the distance.
In this case, we have an angle of depression of 27° and a height of 365 feet.
Let's denote the distance we're trying to find as x.
The tangent of the angle of depression is equal to the opposite side (365 feet) divided by the adjacent side (x).
So we can set up the equation tan(27°) = 365/x and solve for x.
Rearranging the equation, we have x = 365/tan(27°). Plugging in the values and using a calculator, we find that x is approximately 632 feet.
The bear is approximately 717 feet away from the base of the waterfall.
To find out how far the bear is from the base of the waterfall, use trigonometry, specifically the tangent of the angle of depression. Tangent relates the opposite side and the adjacent side in a right triangle.
1. Given Information:
- Height of the waterfall (opposite side), h = 365 feet.
- Angle of depression, [tex]\( \theta = 27\textdegree[/tex].
2. Formulate the Tangent Function:
The tangent of an angle in a right triangle is given by [tex]\( \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \)[/tex].
So in our case, [tex]\( \tan(27\textdegree) = \frac{365}{d} \)[/tex].
3. Solving for d (the distance from the base of the waterfall to the bear):
Rearranging for d:
[tex]\[ d = \frac{365}{\tan(27\textdegree)} \][/tex]
4. Calculate the Value:
Using a calculator to find [tex]tan(27\textdegree)[/tex] which is approximately 0.5095.
[tex]\[ d = \frac{365}{0.5095} \approx 716.5 \text{ feet} \][/tex]
5. Round to the Nearest Foot:
[tex]\[ d \approx 717 \text{ feet} \][/tex]
So, the distance between the bear and base of the waterfall is approximately 717 feet.
In the event of delinquency, the Buyer may divide any payment not received into not more than three equal installments to be included on the next consecutive monthly payments. Notification of the Buyer’s intent to do so must be made by written letter or phone call to the phone number and address listed below within one business week of delinquency.”
According to the contract, which of the following is not a responsibility of the buyer?
a.
Pay the monthly payment on time.
b.
Notify the bank if a payment is going to be late.
c.
Pay an additional $75.00 with a payment made after the 15th day of the month it was due.
d.
Notify the bank of his or her intent to split a late payment into three partial payments.
Answer:
Option B
Step-by-step explanation:
Given:
As per the contract "Notification of the Buyer’s intent to do so must be made by written letter or phone call to the phone number and address listed below within one business week of delinquency.”
So,buyer needs to only notify the bank about the monthly payments in case of delinquency and not about if payment is going to be late or not.
Option B is correct
Notify the bank if a payment is going to be late !
The buyer is not responsible for paying an additional $75.00 for payments made after the 15th of the month it was due; this is not specified in the contract's provided clauses.
According to the contract, the responsibility that is not a part of the buyer's obligations is option (c): Pay an additional $75.00 with a payment made after the 15th day of the month it was due. The contract stipulates that the buyer should pay the monthly payment on time (a), notify the bank if a payment is going to be late (b), and notify the bank of his or her intent to split a late payment into three partial payments (d) in the event of delinquency. However, there is no mention within the provided excerpt of the contract that indicates an additional fee of $75.00 is imposed for late payments. It is important for individuals facing financial difficulties, such as inability to make timely payments, to communicate effectively with their lenders to find potential solutions and avoid the repercussions of default.
Do you guys know the answer for number 2
What is the value of p?
Answer:
A
Step-by-step explanation:
The angle adjacent to 133 and 133 form a straight angle and are supplementary, hence
adjacent angle = 180° - 133° = 47°
The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles. The angle 90 is an exterior angle, thus
p + 47 = 90 ( subtract 47 from both sides )
p = 43° → A
The rectangle below has an area of x^2-25 square meters and a length of x+5.
What expression represents the width of the rectangle?
Answer:
(x-5)
Step-by-step explanation:
factor the equation and the sign is x-5 because the equation has to be negative at the 25.
The width of the rectangle is found by dividing the area by the length, which simplifies to x - 5.
Explanation:The area of a rectangle is given by the product of its length and width. Given the area is x² - 25 and the length is x + 5, you can find the width by dividing the area by the length.
So, the width = area / length = (x² - 25) / (x + 5).
Factoring the numerator gives us (x + 5) (x - 5), therefore, the width = [(x + 5) (x - 5)] / (x + 5). As you can see, (x + 5) is a common factor in the numerator and denominator so we can cancel them out.
The resulting expression for the width is x - 5.
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Figure ABCD has vertices A(-2,3), B(4,3), C(4,-2), and D(-2,0). What is the area of figure ABCD
Answer:
24 units
Step-by-step explanation:
As we can see in the attached picture. The area will be given by the sum of the area of the rectangle and the area of the triangle in the bottom.
The rectangle has a base of 6 units and a height of 3 units. Therefore:
A1 = bh = 6*3 = 18 units.
The triangle has a base of 6 units and a height of 2 units. Therefore:
A2 = (1/2)bh = (6*2)/ 2 = 6 units
Then, the total area is:
A = A1 + A2 = 6 + 18 = 24 units
Which is not a characteristic of an exponential parent function?
Answer:
It goes through the origin, is not a characteristic of an exponential parent function.Explanation:
The exponential parent function is the most basic form of the exponential form, which is:
[tex]f(x)=a^x[/tex]That is so because other expnential functions, named daughter functions, can be obtained as a stretching, compression, or translation of such parent function.
Let's see every option:
The range is positive real number (y > 0)That is true: the end behavior of the function is y approaches zero from above, when x goes to negative infinite, never getting the zero value, and y increases indefintely as x goes to positive infinite, then y is always positive.
It goes trhoug the origin.This is false: the origin is the point (0,0). When you make x = 0, you get y = a⁰ , which is 1. So instead of the origin it goes through (0, 1).
The domain is all real numbers.This is true: the function is defined for all the values of x, from negative infinity to positive infinity. which is all real numbers.
It passes through (0,1)This is true as shown above.
Although exponential parent functions have characteristics such as a horizontal asymptote at y=0, positivity, and either exponential growth or decay, they do not have a constant slope or rate of change. This is unlike linear functions which maintain a consistent slope.
Explanation:The characteristics of an exponential parent function, depicted in mathematical terms as f(x) = a*b^x, generally include several properties. Such properties include a horizontal asymptote at y=0, the function being always positive since it's above the x-axis, and it showing exponential growth if b is greater than 1, or exponential decay if b is between 0 and 1.
However, one feature that is not characteristic of an exponential parent function is having a constant slope or rate of change. The rate of change in exponential functions varies across the graph, which is contrary to linear functions that maintain a constant slope.
As an example: the function y = 2^x is an exponential one. The slope between any two points is not consistent. For instance, between x=0 and x=1, the slope would be 2, while between x=1 and x=2, the slope is 2, indicating that the rate is not constant.
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Let f(x) = 2x − 5 and g(x) = 7x − 3. What is (f(g(x))
Answer:
14x-11
Step-by-step explanation:
f(x) = 2x − 5
g(x) = 7x − 3
(f(g(x))=
Substitute g(x) into f(x) for every x
f(g(x) = 2 (g(x) -5
=2 (7x-3) -5
Distribute
=14x-6 -5
=14x-11
in 9 hours 2 in of rain fell at this rate how many inches will fall in 12 hours
Answer:
2 2/3 or
2.666667 inches rainfall or
8/3 inches of rainfall.
Step-by-step explanation:
Set up a proportion. Since you are going to be looking for inches of rainfall, it should go in the numerator.
2 in rainfall/9 hours = x / 12 inches. Multiply both sides by 12
2*12 /9 = x
8/3 inches = x
2 2/3 inches should fall in 12 hours.
Answer:
2.67 in
Step-by-step explanation:
∵ In 9 hours amount of rainfall = 2 in
∴ In 1 hours amount of rainfall = 2/9 in
∴ in 12 hours amount of rainfall = (2/9) × 12
= [tex]\frac{24}{9}[/tex] = [tex]\frac{8}{3}[/tex]
≈ [tex]2\frac{2}{3}[/tex] in or 2.67 in.
In 12 hours 2.67 in. rain fell.
A delivery truck company just bought a new delivery truck...
Answer:
A) 760 ft³
Step-by-step explanation:
The surface area of the figure has to be calculated.
Step 1: Divide the figure
The figure is divided into the following parts to calculate the volume.
Part 1: Box without ledge
Formula for volume of rectangle = length x width x height
Volume = 14.3 x 7.8 x 6.6
Volume = 736.164 ft³
Part 2: Box with ledge-we will only calculate height and width since the length has already been included in part 1 therefore including it again would result in double counting and give the wrong answer.
Volume = height x width
Volume = 2.7 x 7.8
Volume = 21.06 ft³
Step 2: Add both volumes to find the total volume
Volume part 1 + Volume part 2 = 736.164 ft³ + 21.06 ft³
= 757.224 ft³ rounded off to nearest tenth = 760 ft³
Therefore, answer A is correct.
!!
how many positive integers are between 3/2 and 21/4 ?
A : 2
B : 3
C : 4
D : 5
Answer:
4 integers
Step-by-step explanation:
We are given with two fractions
3/2 = 1.5 and 21/4 = 5.25
Let us draw a number line first and then we plot these two numbers on them.
Please refer to the picture attached. Here we see the number line in black line , where the integers are starting with 0. We have plotted the numbers 1.5 and 5.25 in red.
We are asked to determine the number of integers that lies between 1.5 and 5.25.
The definition of integer says , the whole numbers which be negative also including 0.
Hence we can see that there are 4 whole numbers between 1.5 and 5.25 ,
2,3,4,5
Hence our answer is 4 integer
Complete the table for the given rule y=x/4
The table of values consists of a grouped data representing the function. The corresponding vaues of x if y is 4,2, and 9 are 16, 8 and 36
Table of values and functionThe table of values consists of a grouped data representing the function.
Given the equation y = x/4
If y = 4
4 = x/4
x = 16
If y = 2
2 = x/4
x = 8
If y = 9
9 = x/4
x = 36
Hence the corresponding vaues of x if y is 4,2, and 9 are 16, 8 and 36
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True or False? Def is a right triangle.
Answer:
Step-by-step explanation:
We can determine if the triangle is a right triangle by using the Pythagorean theorem
a^2 +b^2 = c^2 where a and b are the legs and c is the hypotenuse
25^2 + 27^2 = 48^2
625+729=2304
1354 ≠2304
This is not true, so this is not a right triangle
Answer:
FALSE - this is not a right triangle.Step-by-step explanation:
If a ≤ b < c are a length of sides of a right triangle, then
a² + b² = c²
We have a = 25, b = 27 and c = 48.
Substitute:
25² + 27² = 48²
625 + 729 = 2304
1354 = 2304 FALSE
Points A and B have opposite x-coordinates but the same y-coordinates. How many units away are each of the points from the y-axis?
Answer:
2
Step-by-step explanation:
i got it right on the quiz
Points with opposite x-coordinates and the same y-coordinate are symmetrically placed with respect to the y-axis. Their distance from the y-axis is the absolute value of their x-coordinate.
If points A and B have opposite x-coordinates but the same y-coordinates, we can deduce that they are positioned symmetrically with respect to the y-axis. The distance of each point from the y-axis is equal to the absolute value of their x-coordinate. This is because the y-axis serves as a reference line where the x-coordinate is zero.
For example, if point A has coordinates (-5, 3) and point B has coordinates (5, 3), then both points are 5 units away from the y-axis. The only difference between their positions is the direction relative to the y-axis; point A is on the left side and B is on the right side.
So, the general rule is that no matter the y-coordinate, the distance of a point from the y-axis is simply the absolute value of its x-coordinate.
what is the answer for : f(x)=x^3 - 4x^2 +2x -6 divided by x-3
Answer:
[tex]x^2-x-1+\frac{-9}{x-3}[/tex]
Step-by-step explanation:
I prefer to use synthetic division when possible. Here it is possible since we are dividing by a linear factor.
Since we are dividing by x-3, 3 goes on the outside.
If we were dividing by x+3, -3 goes on the outside.
3| 1 -4 2 -6
| 3 -3 -3
_______________
1 -1 -1 -9
So the quotient is 1x^2-1x-1 + (-9)/(x-3).
Let's simplify this and also put in the pretty math code:
[tex]x^2-x-1+\frac{-9}{x-3}[/tex]
There are 15 red, 10 green and 9 white balls in the dark room. Jack wants to take a minimal number of balls such that at least 8 of them have the same color. How many balls does he take?
Please add an explanation and show work!!
=================================================
Explanation:
If Jack were to get really lucky and draw either
* 8 red balls in a row
* 8 green balls in a row, or,
* 8 white balls in a row
then the answer would be 8. However, this event of drawing the same color ball 8 times in a row is fairly unlikely. What is more likely is that there will be multiple colors involved (because we have roughly the same number for each color mors or less). So consider the scenario in the next section below.
----------
If Jack were to draw a red ball first, then a green ball second, and then a white ball third, then so far has selected 3 balls from the drawer. None of the colors match up. This is leading to the worst case scenario in terms of the number of balls to select. In other words, Jack is really unlucky to not get any colors match up so far. When aiming for a guarantee like this, it is wise to think of the worst case scenario.
If we repeat the pattern (red, green, white) then so far we have 2 balls of each color. In total we have selected 6 overall. Note how 3*2 = 6.
Repeat this a third time, then we'll select 9 balls total (3*3 = 9)
The fourth iteration of this pattern has 3*4 = 12 balls overall picked out, and so on.
If we continue the pattern, then we'll see that we will need to select 3*8 = 24 balls to guarantee that we have at least 8 of the same color (eg: 8 red balls). Chances are that we'll have 8 of the same color before we hit the 24 ball mark, but we wont have a 100% guarantee of such. Reaching 24 balls is the only way to guarantee the claim is true.
So to summarize: I pictured the worst case scenario (red,green,white) and extended out the pattern so that it led to 24 as the final answer.
He would have 8 balls of one color and 7 of each of the other two colors, making a total of 23 balls, which is less than the total number of balls available.
In this problem, we have a dark room with a total of 15 red balls, 10 green balls, and 9 white balls. Jack wants to take the minimum number of balls such that he has at least 8 balls of the same color. We'll find out how many balls he needs to achieve this goal.
Let's assume Jack takes "x" balls. To find the minimum number of balls he needs to have at least 8 of the same color, we can apply the Pigeonhole Principle. This principle states that if there are "n" pigeonholes and "m" items to be placed in them, and if "m" is greater than "n," then there must be at least one pigeonhole with more than one item.
In our problem, the colors of the balls represent the pigeonholes, and the balls that Jack takes represent the items to be placed in those pigeonholes. To guarantee that at least 8 balls have the same color, we need to find the minimum value of "x" such that at least one color has 8 balls.
The worst-case scenario for the minimum number of balls needed is when Jack takes 7 balls of each color. In this case, he would have 7 red balls, 7 green balls, and 7 white balls, making a total of 21 balls. However, this is more than the total number of balls available (15 + 10 + 9 = 34).
Thus, Jack can take 8 balls to ensure that he has at least 8 balls of the same color. In the worst-case scenario, he would have 8 balls of one color and 7 of each of the other two colors, making a total of 23 balls, which is less than the total number of balls available.
So, the minimum number of balls Jack needs to take is 8.
Let "R," "G," and "W" represent the sets of red, green, and white balls, respectively.
Given:
|R| = 15, |G| = 10, |W| = 9
Let "x" be the number of balls Jack takes.
We need to find the minimum "x" such that:
max(|R∩x|, |G∩x|, |W∩x|) ≥ 8
The worst-case scenario is when Jack takes 7 balls of each color, so:
|R∩x| ≤ 7, |G∩x| ≤ 7, |W∩x| ≤ 7
Total balls available in the worst-case scenario:
Total = |R∩x| + |G∩x| + |W∩x| ≤ 7 + 7 + 7 = 21
However, Total < |R| + |G| + |W|, so Jack can take 8 balls (x = 8) to guarantee that he has at least 8 balls of the same color, and the worst-case scenario would result in a total of 23 balls, which is less than the total number of balls available.
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Please please answer this correctly
Answer:
189ish
Step-by-step explanation:
use a calculator
and I think that this is right...
The probability of winning a race is 5/12. What are the odds in favor of winning the race?
Answer:
7/12
Step-by-step explanation:
If the probability of winning a race is 5/12, the odds in favor of winning the race is 7/12.
Probability of winning a race: 5/12 or a 5 out of 12 chance.
12 - 5 = 7
Numerator = 7
The denominator would stay 12.
Denominator = 12
Therefore, the odds of winning the race is 7/12.
What is the Gfc of 3p^4 and 4p
For this case we have by definition, the GFC of two numbers is given by the largest factor that divides both numbers without leaving residue.
We have the following expression:
[tex]3p ^ 4[/tex] and [tex]4p[/tex]
So, we look for the factors of 3 and 4:
3: 1.3
4: 1, 2, 4
Thus, the GFC of both numbers is "1".
The GFC of both expressions is: [tex]1p = p[/tex]
Answer:
p
In the diagram of circle O, what is the measure of ∠ABC if m(arc)AC= 234 and the measure of little arc AC=126
Answer:
54
Step-by-step explanation:
234-126 = 108
108/2 = 54
what is the y-intercept of the line with a slope of -7 that passes through the point (-1,-5
Answer:
-12
Step-by-step explanation:
Slope-intercept form of a line is y=mx+b where m is the slope and b is the y-intercept.
We are given m=-7 and a point (x,y)=(-1,-5) in on the line.
Entering this information into y=mx+b, we will be allowed enough information to find the y-intercept, b.
y =mx+b with m=-7 and (x,y)=(-1,-5):
-5=-7(-1)+b
-5=7+b
Subtract 7 on both sides:
-5-7=b
-12=b
So the y-intercept is -12.
Solve 8x+ c = k for X.
Answer:
[tex]x=\frac{k}{8} -\frac{c}{8} \\[/tex]
The Solution of x in the given equation [tex]8x+ c = k[/tex] is [tex]x =\frac{k-c}{8}[/tex]
How can the value of x be known?An equation with two polynomial sides or a set of polynomial equations is known as an algebraic equation or a polynomial equation. They are further divided into levels: linear formula for level one. degrees 2 quadratic equation.
Given that [tex]8x+ c = k[/tex]
[tex]8x = k-c[/tex]
[tex]x =\frac{k-c}{8}[/tex]
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URGENTLY NEED HELP ON THIS WORD PROBLEM!!! PLEASE HELP ME OUT :)
Answer:
B there were 4 ducks living in Anoops pond when he first built it
Step-by-step explanation:
The equation is in the form
y = a b^x
The a is the initial value at time x =0
The b is the growth rate
x is the time
So
4 * 3^t
4 is the initial amount of ducks
3 is the growth rate, or the duck population increase by a factor of 3 each time period
t is the time period in years
Simplify: 8−4x+10−6x
Answer:
-10x+18
Step-by-step explanation:
combine like terms.
The expression 8−4x+10−6x can be simplified by adding and subtracting similar terms. Add 8+10 which gets 18. Subtract -4x - 6x which gets -10x. So, the simplified expression is 18 - 10x.
Explanation:The expression given is 8−4x+10−6x. In this expression, similar terms are grouped together to simplify it. By similar terms, we mean terms that involve the same variable raised to the same power. In this case, the similar terms are -4x and -6x (the 'x' terms) and 8 and 10 (the constant terms). So let's add and subtract these similar terms.
First, add 8 and 10 to get 18.
Secondly, subtract -4x - 6x. This gives you -10x.
So, the simplified form of your expression (8−4x+10−6x) is 18 - 10x.
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What is the product x^2-16/2x+8*x^3-2x^2+x/x^2+3x-4
Answer: First Option
[tex]\frac{x(x-4)(x-1)}{2(x+4)}[/tex]
Step-by-step explanation:
We have the following expression
[tex]\frac{x^2-16}{2x+8}*\frac{x^3-2x^2+x}{x^2+3x-4}[/tex]
First factorize the denominators:
[tex]\frac{x^2-16}{2(x+4)}*\frac{x^3-2x^2+x}{(x+4)(x-1)}[/tex]
Now we factor the numerators
[tex]\frac{(x-4)(x+4)}{2(x+4)}*\frac{x(x^2-2x+1)}{(x+4)(x-1)}[/tex]
[tex]\frac{(x-4)(x+4)}{2(x+4)}*\frac{x(x-1)^2}{(x+4)(x-1)}[/tex]
now we simplify the expression
[tex]\frac{(x-4)}{2}*\frac{x(x-1)}{(x+4)}[/tex]
[tex]\frac{x(x-4)(x-1)}{2(x+4)}[/tex]
The answer is the first option
Answer:
A on Edge
Step-by-step explanation:
Good Luck!
Luis, Diego, and Cecil are going fishing.
Luis brings 4 cans of worms. Diego brings
3 cans of worms plus 2 extra worms. Cecil
brings 2 cans of worms. If they have a
total of 65 worms and each can contains
the same number of worms, how many
worms are in each can?
Answer:
7 worms
Step-by-step explanation:
Let each can have x worms, so we can say
Luis has 4x worms
Diego has 3x + 2 worms
Cecil has 2x worms
Since, in total they have 65 worms, we can write and equation and solve:
4x + 3x + 2 + 2x = 65
9x + 2 = 65
9x = 63
x = 63/9
x = 7
There are 7 worms in each can.
Answer:
7
Step-by-step explanation:
which is the area of a rectangle with a length of 21 feet and a width of 15 feet
Answer:
315 ft^2
Step-by-step explanation:
Answer: [tex]315\ ft^2[/tex]
Step-by-step explanation:
In order to calculate the area of a rectangle, you can use the following formula:
[tex]A=lw[/tex]
Where "l" is the lenght of the rectangle and "w" is the width.
In this case you know that this rectangle has a length of 21 feet and a width of 15 feet. Then:
[tex]l=21\ ft\\w=15\ ft[/tex]
Therefore, you can substitute these values into the formula, getting that the area of this rectangle is:
[tex]A=(21\ ft)(15\ ft)\\\\A=315\ ft^2[/tex]
LeAnn wants to gift wrap a present she got for her little brother. How many square inches of gift wrap will be needed to cover a box that is 5in x 7in x 3in?
A box has six sides.
Using the dimensions of the box:
2 sides are 5 x 7
2 sides are 7 x 3
2 sides are 5 x 3
Now calculate the total area:
2 x 5 x 7 = 70
2 x 7 x 3 = 42
2 x 5 x 3 = 30
Total area = 70 + 42 + 30 = 142 square inches.
Answer:
The answer is 142 square inches.
Step-by-step explanation:
Let length be = 5
Let the width be = 7
Let the height be = 3
The gift box is a 3 D box with 6 faces.
So, we get three possible combinations, and each combination is multiplied by 2 for a parallel face.
Hence, we get;
[tex](5)(7)(2)=70[/tex] square inches
[tex](5)(3)(2)=30[/tex] square inches
[tex](7)(3)(2)=42 [tex] square inches
Therefore, the amount of gift wrap needed will be:
[tex]70+30+42=142[/tex] square inches.
solve the right triangle given that A=30 degrees, C=90 degrees and a =15
Answer:
B = 60°; c = 30; b = 25.98
Step-by-step explanation:
1. Calculate ∠B
∠A + ∠B + ∠C =180°
30° + ∠B + 90° = 180°
∠B + 120° = 180°
∠B = 60°
2. Calculate c
sinA = a/c
sin30° = 15/c
½ = 15/c
c = 2 × 15 = 30
3 .Calculate b
sinB = b/c
sin60° = b/30
√3/2 = b/30
b = (30√3)/2 = 15√3 = 25.98
Your class started at 12:17 PM and ended at 12:49 PM. What angle did the minute hand of a watch sweep through during the class?
A. 186
B. 192
C. 180
D. 168
Answer:
192
Step-by-step explanation:
12:49 - 12:17 = 32min
if 60min = 360°
32min = ?
32×360
60
=192°
Answer:
B. 192 degrees
Step-by-step explanation:
First, calculate how many degrees a minute equals.
The minute hand rotates 360 degrees every 60 minutes.
Thus, one minute is equivalent to dividing 360 degrees by 60 minutes, that is 360/60 = 6 degrees per minute.
Now, we subtract the minutes from the two hours given,
12:49 PM - 12.17 PM = 32 minutes
Finally, we calculate the angle traveled by the minute hand by multiplying 6 degrees by 32 minutes, that is
Angle = 6 * 32 = 192 degrees.
I hope this helps!
8. What is the solution to the equation 2x + 8 - 6 = 4. Show your worn.
Answer:x=1
Step-by-step explanation: 2x+8-6=4
2x+2=4
2x=2
x=1
Answer:
[tex]x = 1[/tex].
Step-by-step explanation:
Apply the associative property of addition to rewrite the left-hand side of the equation.
The two addition operators on the left-hand side are typically evaluated from left to right.
[tex](2x + 8) - 6 = 4[/tex].
However, by the associative property of addition, the second addition can be evaluated before the first:
[tex]2x + (8 - 6) = 4[/tex].
[tex]2x + 2 = 4[/tex].
Move all terms with the unknown ([tex]x[/tex] in this case) to one side of the equation and move all numbers to the other side. For example, add [tex]-2[/tex] to both side of this equation will move the number [tex]2[/tex] to the right-hand side.
[tex]2x +2 -2 = 4 - 2[/tex].
[tex]2x = 2[/tex].
Multiply both sides of the equation by [tex]1/2[/tex] to find the value of [tex]x[/tex].
[tex]x = 1[/tex].