Find the range and standard deviation of the set of data.
12,9,5,13,21
Answer: range = 16 standard deviation = 5
Step-by-step explanation:
A 28% income tax on a 80,000 income
Answer:
22,400
Step-by-step explanation:
80,000 x .28
Find the equation to the line below.
y=4/5x +?
Answer:
y =x - 1
Step-by-step explanation:
Slope intercept of a line: y =mx + bHere, m is the slope and b is the y-intercept.
Plot any two points on the line. (5,4) & (0,-1)
[tex]\sf \boxed{Slope =\dfrac{y_2-y_2}{x_2-x_1}}[/tex]
[tex]\sf =\dfrac{-1-4}{0-5}\\\\=\dfrac{-5}{-5}\\\\=1[/tex]
m = 1
At y-intercept x = 0. So, the -1 is the y-intercept.
m = 1 & b = -1
y = 1x + (-1)
The expense function is E= 15q+750.
A) What is the price per item?
B) What is the variable cost of 100 units?
C) What is the fixed expense?
D) What is the expense if you needed 100 units?
The price per item is 765.
The variable cost of 100 units is 1500.
The fixed expense is 750.
The expense for 100 units is 2250
What is the fixed cost and variable cost?Fixed costs are costs that do not vary with output. e,g, rent, mortgage payments. Variable cost change with the unit of output.
The variable cost of 100 units = variable cost per unit x number of units
15 x 100 = 1500
The expense for 100 units = fixed cost + total variable cost
750 + 1500 = 2250
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Given:
p: x – 5 =10
q: 4x + 1 = 61
Which is the inverse of p → q?
If x – 5 ≠ 10, then 4x + 1 ≠ 61.
If 4x + 1 ≠ 61, then x – 5 ≠ 10.
If x – 5 = 10, then 4x + 1 = 61.
If 4x + 1 = 61, then x – 5 = 10.
The inverse of the statement p → q is "If x – 5 ≠ 10 then
4x + 1 ≠ 61"
How to determine the inverse of the statement?The statement is given as
p: x – 5 =10
q: 4x + 1 = 61
The inverse of a statement is such that:
The hypothesis and conclusion are negated.
This means that a conditional statement referred to as p → q would have the inverse of -p → -q.
When the above rule is applied on the statement
p: x – 5 ≠ 10
q: 4x + 1 ≠ 61
This means that the inverse of the statement p → q is "If x – 5 ≠ 10 then
4x + 1 ≠ 61"
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Answer:
A
MF up there wont tell u but its A
The perimeter of a rectangular field is surrounded by 96 meters of fencing. If the field is partitioned into two parts as shown, a total of 110 meters of fencing is required. Find the dimensions of the field.
The dimensions of the field is Length = 34 meters, width = 14 meters.
Let rectangle: x for width, y for length.
2 ( x + y ) = 96
x + y = 48
2 ( x + y ) + x = 110
x = 110 - 96
x = 14
x + y = 48
y = 48 - 14 = 34
Length = 34 meters, width = 14 meters.
A quadrilateral with equal angles and parallel opposing sides is referred to as a rectangle. Around us, there are a lot of rectangle items. The length and breadth of any rectangle form serve as its two distinguishing attributes. The width and length of a rectangle, respectively, are its longer and shorter sides.
A closed shape with four sides that forms a 90° angle is known as a rectangle. A rectangle can have many different characteristics. The following list includes some of a rectangle's key characteristics.
A quadrilateral is a rectangle.
A rectangle's opposing sides are equal and parallel to one another.
Each vertex of a rectangle has a 90° internal angle.
360° is the total of all interior angles.
The diagonals cut each other in half.
The diagonals are all the same length.
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COMPLETE
You can verify that your answer is a solution to the original equation by checking -1/2(-14)-3=4 is a
true statement. Which property of equality allows you to do this?
Oreflexive
Otransitive
substitution
Explanation:
Think of a substitute teacher. They temporarily replace your original teacher. The same idea applies with replacing the variable with a number.
For example, the equation x+2 = 7 has the solution x = 5. We can check this by substituting or replacing x with 5 to say 5+2 = 7, which is indeed a true mathematical statement. This confirms the solution.
Find the value of unknown
The value of x is 52° and the value of y is 104 ° as calculated using the chord properties of a circle.
A circle is defined as the locus of a moving point such that the distance of the point from a fixed point is always same.
A chord is a straight line joining any two points on a circle.The diameter is the largest chord.The angle subtended by the diameter at the center is always 90° .In the given figure AC is the diameter of the circle.
We know that the angle subtended by the chord is always 90°.
∴∠CBA = 90°
Now in ΔABC
∠ABC+∠BCA+ ∠CAB =180° (sum of all angles of a triangle is always 180°)
or, 90° + 38° + x° = 180°
or, 128° + x° =180°
or, x = 52°
Again in ΔDBC ,
DB=DC (radius of the circle)
∴∠DCB = ∠DBC (base angles of an isosceles triangles are equal)
∴∠DBC = 38°
Again in ΔDBC
∠DBC+∠BCD+ ∠CDB = 180° (sum of all angles of a triangle is always 180°)
or, y = 180° - 76°
or, y = 104°
Therefore the value of x is 52° and the value of y is 104 ° .
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Sally is running laps around a track. She runs 12 laps to warm up. Then she runs 13² laps.
How many laps does Sally run in all? Move numbers to the boxes to show the answer.
Answer:
181
Step-by-step explanation:
Sally is running laps around a track. She runs 12 laps to warm up. Then she runs 13² laps.
First write the equation. we know she alr ran 12 laps so its going to be +12
to 13^2. so the equation will be 12+13^2 then using PEMDAS we know that we have to do the exponents first so 13^2 is just 13 * 13 which is 169. so now the equation is 169+12 now just add. the answer is 181
A map is drawn to a scale of 1/2 inch = 20 miles How many miles apart are two cities that are 3 1/4 inches apart on the map?
Work Shown:
1/2 = 0.5
1/4 = 0.25
0.5 inch = 20 miles, which is the given scale
1 inch = 40 miles, after multiplying both sides by 2
3.25 inches = 130 miles after multiplying both sides by 3.25
A) The derivative of f(x) = 6x ^ 2 is given by f^ prime (x)=lim h——>0 ________=____.
B) The derivative of f(x) = 2x ^ 2 - 7x + 8 is given by f () lim h—->______=____.
Here we go ~
A.) Derivative of 6x² :
[tex]\qquad \sf \dashrightarrow \:f {}^{ \prime}(x) = \: \sf\displaystyle { \lim_{h\to0}} \sf\: \: \frac{f(x + h) - f(x)}{h} [/tex]
[tex]\qquad \sf \dashrightarrow \: \sf\displaystyle { \lim_{h\to0}} \sf\: \: \frac{6(x + h) {}^{2} - 6(x) {}^{2} }{h} [/tex]
[tex]\qquad \sf \dashrightarrow \: \sf\displaystyle { \lim_{h\to0}} \sf\: \: \frac{6(x {}^{2} + 2xh + h {}^{2} ) {}^{} - 6(x) {}^{2} }{h} [/tex]
[tex]\qquad \sf \dashrightarrow \: \sf\displaystyle { \lim_{h\to0}} \sf\: \: \frac{ \cancel{6x {}^{2}} + 12xh +6 h {}^{2} {}^{} - \cancel{6x{}^{2}} }{h} [/tex]
[tex]\qquad \sf \dashrightarrow \: \sf\displaystyle { \lim_{h\to0}} \sf\: \: \frac{ 12xh +6 h {}^{2} {}^{} }{h} [/tex]
[tex]\qquad \sf \dashrightarrow \: \sf\displaystyle { \lim_{h\to0}} \sf\: \: \frac{ \cancel{ h}( 12x +6h ) {}^{} {}^{} }{ \cancel{h}} [/tex]
[tex]\qquad \sf \dashrightarrow \: \sf\displaystyle { \lim_{h\to0}} \sf\: \: 12x + 6h[/tex]
[tex]\qquad \sf \dashrightarrow \: 12x + 0[/tex]
[tex]\qquad \sf \dashrightarrow \: f {}^{ \prime} (x) = 12x[/tex]
B.) The derivative of f(x) = 2x² -7x + 8 :
[tex]\qquad \sf \dashrightarrow \:f {}^{ \prime}(x) = \: \sf\displaystyle { \lim_{h\to0}} \sf\: \: \frac{f(x + h) - f(x)}{h} [/tex]
[tex]\qquad \sf \dashrightarrow \: \sf\displaystyle { \lim_{h\to0}} \sf\: \: \frac{ 2(x + h) {}^{2} - 7(x + h) + 8 - (2 {x}^{2} - 7x + 8)}{h} [/tex]
[tex]\qquad \sf \dashrightarrow \: \sf\displaystyle { \lim_{h\to0}} \sf\: \: \frac{ 2(x {}^{2} + 2xh + {h}^{2} ) {}^{} - \cancel{7x} + 7h+ \cancel8 - 2 {x}^{2} + \cancel{7x } - \cancel 8)}{h} [/tex]
[tex]\qquad \sf \dashrightarrow \: \sf\displaystyle { \lim_{h\to0}} \sf\: \: \frac{ \cancel{ 2x {}^{2}} + 4xh + 2{h}^{2} {}^{} - 7h - \cancel{2 {x}^{2}} }{h} [/tex]
[tex]\qquad \sf \dashrightarrow \: \sf\displaystyle { \lim_{h\to0}} \sf\: \: \frac{ \cancel {h}( 4x + 2{h}^{} {}^{} - 7) }{ \cancel{h} }[/tex]
[tex]\qquad \sf \dashrightarrow \: \sf\displaystyle { \lim_{h\to0}} \sf\: \: 4x + 2{h}^{} {}^{} - 7[/tex]
[tex]\qquad \sf \dashrightarrow \: 4x - 0 - 7[/tex]
[tex]\qquad \sf \dashrightarrow \: f {}^{ \prime} (x) = 4x - 7[/tex]
Write the slope, intercept form of the equation of the line describe
Through (3,-2) and parallel to y=-x+5
Answer:
y = - x + 1
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - x + 5 ← is in slope- intercept form
with slope m = - 1
• Parallel lines have equal slopes , then
y = - x + c ← is the partial equation of the parallel line
to find c substitute (3, - 2 ) into the partial equation
- 2 = - 3 + c ⇒ c = - 2 + 3 = 1
y = - x + 1 ← equation of parallel line
Find the missing number: 11, 29, 11, when average (mean) Is 17
The missing number (x) from the sequence → 11, 29, 11, x is 17.
We have the mean of given set of numbers.
We have to identify the missing number.
What is mean of a given set of data ?The mean in math and statistics summarizes an entire dataset with a single number representing the data's center point or typical value. It is calculated using the formula -
Mean (M) = ∑a[i] / n
where -
∑a[i] = sum of the elements in a data set
n = total number of elements
According to the question - assume that the missing number is x. Then, we have -
11, 29, 11, x
Now, using the formula of mean -
M = ∑a[i] / n
17 = (11 + 29 + 11 + x)/4
68 = 51 + x
x = 68 - 51
x = 17
Therefore, the missing number is 17.
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Country A produces about six times the amount of diamonds in carats produced in country B.If the total produced in both countries is 28,000,000 carats
The diamonds produced by country A and B are 24,000,000 and 4,000,000 carats respectively.
Here, we are given that Country A produces about six times the amount of diamonds in carats produced in country B.
Let the diamonds produced by country B be x
Then, the diamonds produced by country A will be 6x
The total diamonds produced by the two countries = 28,000,000
Thus, we can get the following equation-
x + 6x = 28,000,000
7x = 28,000,000
x = 28,000,000/ 7
x = 4,000,000
⇒ 6x = 24,000,000
Thus, the diamonds produced by country A and B are 24,000,000 and 4,000,000 carats respectively.
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Drag the purple points to show the location of G, H, and I after a 90° clockwise rotation around (0, 0) Then enter the coordinates of G', H, and I' in the table.
Answer:The value of coordinates G', H', and F' are (1,6) , ( 7,3) and (4 , 0) respectively.What are coordinates?A pair of numbers that employ the horizontal and vertical distinctions from the two reference axes to represent a point's placement on a coordinate plane. typically expressed by the x-value and y-value pairs (x,y).Coordinates are always written in the form of small brackets the first term will be x and the second term will be y.For example (5,3) here 5 will be for the x and 3 will be for the y.Another example is (9,0) here 9 is for x and 0 is for y.
Step-by-step explanation:
For a total accumulated amount of $3688.86, a principal of $2000, and a time period of 5 years, use the compound interest formula to find r, if interest is compounded
monthly.
r=
The interest rate required to get a total amount of $3,688.86 from compound interest on a principal of $2,000.00 compounded 12 times per year over 5 years is 12.306% per year.
Given,
The total amount (A)= $3688.86
Principal (P) = $2000
time period (t) = 5 years.
compounded monthly (n) = 12
rate of interest per year = ?
we know that r=n[(A/P)¹/ⁿt -1]
substitute the above values.
r = 12 × [(3688.86/2000)¹/⁽¹²⁾⁽⁵⁾ - 1]
r = 12 × [(1.84443)¹/⁶⁰ - 1]
r = 12 × 0.0102
r = 0.12306
Now convert r to R as a percentage.
R = r × 100
R = 0.12306 × 100
R = 12.306%
Hence the rate of interest compounded monthly is 12.306%
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Find B if A=70° and a + b = 80°
Answer:
B=30°
Step-by-step explanation:
Recall that the sum of interior angles of a triangle equals to 180°. So basically
[tex]A+B+\alpha+\beta=180^{\circ}[/tex]
[tex] \implies B + {70}^{ \circ} + {80}^{ \circ} = {180}^{ \circ} \\ \implies B = {180}^{ \circ} - {150}^{ \circ} \\ \implies B = \boxed{{30}^{ \circ} }[/tex]
(-2/3)(6/7)
Please show work if possible!
I’m not sure what to do
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
First of all, it's a graph of mod function, which is transformed.
So, let's proceed with taking graph of modulus initially ~
[tex]\qquad \sf \dashrightarrow \: y = |x| [/tex]
The required can be tranformed by moving it three units left and four units down.
so, we need to add 3 to x within the function to move it left by units.
i.e
[tex]\qquad \sf \dashrightarrow \: y = |x + 3| [/tex]
Now, to move it down by 4 units we need to subtract 4 from the whole function.
[tex]\qquad \sf \dashrightarrow \: y = |x + 3| - 4[/tex]
So, the correct choice is : C
the required can be transformed by moving at 3 units left and 4 units down do you understand ? after that are 3 and x
y = x + 3
now to move it down by 4 units we need to subtract for from the whole function which is y is equal to x + 3 - 4
y = |x+3| - 4
the answer is c
Let f(x) = x^2 + 2 and g(x) = -3. Find f(x) • g(x).
A. X^3-6x^2+12x-6
B. X^3-5x^2+8x-6
C. X^3-3x^2+6x-6
D. X^3-2x^2+5x-6
1. Solve the following polynomial equations by factoring
b. x4+4x3-8x-32=0
[tex]x^4+4x^3-8x-32=0[/tex]
Can be factoried into:
[tex](x^3-8)(x+4)=0\\[/tex]
Now you're looking for which values of x will make the equations in the brackets equal to 0, since as long as one is equal to 0, they will be multiplied into 0.
First we'll do:
[tex]x^3-8=0[/tex]
We're looking for what number cubed is equal to 8, which is 2.
Note: -2 is also a possibility, but if you plug it in, you'll see that it doesn't work.
Second we'll do:
[tex]x+4=0[/tex]
This one's pretty easy, x will be -4.
So your solutions are:
x = 2, -4
The solutions of the polynomial [tex]x^{4}[/tex] + 4x³ - 8x - 32 = 0 are 2 and -4.
What is a polynomial?Polynomials are sums of terms of the form k⋅xⁿ.
where k is any number
n is a positive integer.
Example:
2x + 4x - 7 is a polynomial
We have,
[tex]x^{4}[/tex] + 4x³ - 8x - 32 = 0 _______(1)
Divide into two parts.
[tex]x^{4}[/tex] + 4x³
-8x - 32
Take out the common from each part.
x³ ( x + 4 )
- 8 ( x + 4 )
Now,
We have,
x³ ( x + 4 ) - 8 ( x + 4 ) = 0
We can write this as:
(x³ - 8) (x + 4) = 0
Now,
We need to find the x values.
x³ - 8 = 0
x³ = 8
x = ±2
Put x = 2 in (1)
[tex]x^{4}[/tex] + 4x³ - 8x - 32 = 0
x = 2
16 + 32 - 16 - 32
0 = 0
x = 2 is satisfied
Put x = -2 in (1)
16 - 32 + 16 - 32 = 0
-64 ≠ 0
x = -2 is not satisfied
x + 4 = 0
x = -4 putting in (1)
256 - 256 + 32 - 32 = 0
0 = 0
x = -4 is satisfied
Thus the solutions of the polynomial [tex]x^{4}[/tex] + 4x³ - 8x - 32 = 0 are 2 and -4.
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Find the equation the line with a slope of 2 and that passes
through the point (1, 6).
Enter your answer in slope-intercept form, y = mx + b
Answer:
y = 2x +4
Step-by-step explanation:
Equation of a line in slope-intercept form is
y = mx + b
where m is the slope and b is the y-intercept, the point at which the line crosses the y axis (at x = 0)
Given slope is 2 we get the equation as
y = 2x + b
We have to solve for b by plugging in the x and y values for point(1,6)
Thus we get y = 6 = 2(1) + b
Or 6 = 2 + b
b= 6-2 = 4
Equation in slope-intercept form is
y = 2x +4
Hi!
Apply the Point-Slope formula:
[tex]\textsl{y-y1=m(x-x1)}[/tex]◈Where:
y₁ -> the y-coordinate of the pointm -> slopex₁ -> x-coordinate◈We know that:
y₁ -> 6m -> 2x₁ -> 1◈Plug in the values:
[tex]\boldsymbol{y-6=2(x-1)}[/tex](simplify) [tex]\boldsymbol{y-6=2x-2}[/tex](add 6 to both sides) [tex]\boldsymbol{y=2x+4}[/tex][tex]\bigstar\textsf{\textbf{Solution: \boxed{\textsf{\textbf{2x+4}}}}}[/tex]
Have a great day!
I hope this helped!
-stargazing
Find the distance of the line segment below.
___ units
Answer:
let (5,4)=(x1,y1)
(-3,-2)=(x2,y2)
now, by using distance formula
we get distance between line segment =10 unit
therefore distance =10 units ans
Solution,
As the formula...
[tex] = \sqrt{( - 3 - 5 {)}^{2} + ( - 2 - 4 {)}^{2} } [/tex]
[tex] = \sqrt{( - 8 {)}^{2} + ( - 6 {)}^{2} } [/tex]
[tex] = \sqrt{64 + 36} [/tex]
[tex] = \sqrt{100} [/tex]
= 10 units...
☘☘☘....
Solve the inequality and express your answer in interval notation.
x^2+ 12x+7<0
The solution in interval form is given as (-∞, -6-√29
] or [-6+√29, ∞)
Inequality expressionGiven the quadratic inequality below;
x^2+ 12x+7<0
Using the general formula
x = -12±√12²-4(1)(7)/2(1)
x = -12±√144-28/2
x = -6±√116/2
x = -6±√29
Hence the solution in interval form is given as (-∞, -6-√29
] or [-6+√29, ∞)
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To swimmers Angie aTwo swimmers Angie and Beth from different states wanted to find out who had the fastest time for the 50 m freestyle when compared to her team which swimmer had the fastest time when compared to her team
Using z-scores, it is found that due to the lower z-score, Beth had the fastest time when compared to her team.
What is the missing information?This problem is incomplete, but researching on the internet, we have that:
Angie had a time of 26.2 seconds, while her team had a mean time of 27.2 seconds with a standard deviation of 0.8 seconds.Beth had a time of 27.3 seconds, while her team had a mean time of 30.1 seconds with a standard deviation of 1.4 seconds.What are z-scores?The z-score of a measure X in a distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.For this problem, lower times means that the swimmer is faster, hence the swimmer that had the fastest time when compared to her team is the swimmer with the lowest z-score.
Angie's z-score is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (26.2 - 27.2)/0.8
Z = -1.25.
Beth's z-score is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (27.3 - 30.1)/1.4
Z = -2.
Due to the lower z-score, Beth had the fastest time when compared to her team.
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After 30 baseball games Aaron Smith had 24 hits. If after 100 games he had 80 hits, what is his average hits per baseball game?
Aaron Smith would has average hits per baseball game as 0.79 hits per game.
What is the interpretation of average?Average provides ill information in case of skewed data.
Arithmetic mean is the best central measure available for representing the values of a data set. It is also called average of the values of the considered data set. It serves as predicted value(in case no other information of the data is available) of that data set.
WE have been given that After 30 baseball games Aaron Smith had 24 hits. If after 100 games he had 80 hits, then he would has average hits per baseball game;
Average = Hits in game / number of games
Average = 24- 80 / 30-100
Average = 56 / 70
Average = 0.79 hits per game
Hence, Aaron Smith would has average hits per baseball game as 0.79 hits per game.
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=?
२०
21090 (x -1 ) + 109.07 = 1
)
The value of "x" which will satisfy the equation [{21090(x -1 ) + 109.07 } = 1] is 1.01.
As per the question statement, we are provided with an equation [tex][{21090(x -1 ) + 109.07 } = 1][/tex].
We are required to solve the above mentioned equation for "x", such that the value of x when substituted in the equation, satisfies the same.
To solve this question, we will simply use the methods of rearranging and opening up of brackets, as shown below.
[tex][{21090(x -1 ) + 109.07 } = 1] \\or, 21090x - 21090+109.07=1\\or, 21090x - (21090-109.07)=1\\or, 21090x - 20980.93=1\\or, 21090x=(1+20980.93)\\or, 21090x=20981.93\\or,x=\frac{21090}{20981.93}\\or,x=1.00515\\or,x=1.01[/tex]
Therefore, the value of "x" which will satisfy the equation
[{21090(x -1 ) + 109.07 } = 1] is 1.01.
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Find the sum. 2 3/8 + 4 4/8
please help asap no one has been able to solve it :(
I need help
Answer:
givenMultiplication property of equalityMultiplicative inverse propertyMultiplicative identity propertyAddition property of equalityAdditive inverse propertyAdditive identity propertyStep-by-step explanation:
You are given the solution to a 2-step linear equation and asked to identify the properties of equality and operations that support the steps of the solution.
Steps5(x -3) = 20 . . . . This is the Given equation we're solving.
(1/5)(5(x -3)) = (1/5)(20) . . . . Both sides are multiplied by 1/5. The Multiplication property of equality says you can do this without changing the value of the variable.
1(x -3) = 4 . . . . (1/5)(5) is replaced by 1. The Multiplicative inverse property tells you the product of a number and its multiplicative inverse is 1.
x -3 = 4 . . . . 1(x -3) is replaced by (x -3). The Multiplicative identity property tells you multiplication by 1 changes nothing. These properties of multiplication are what allow you to remove the factor of 5 from the equation.
Now, we're about to do the same thing with addition: use its properties to remove the unwanted -3.
x -3 +3 = 4 +3 . . . . 3 is added to both sides. The Addition property of equality says you can do this without changing the value of the variable.
x +0 = 7 . . . . -3+3 is replaced by 0. The Additive inverse property tells you the sum of a number and its additive inverse is zero.
x = 7 . . . . x+0 is replaced by x. The Additive identity property tells you addition of 0 changes nothing. These properties of addition are what allow you to remove the added -3 from the equation.
__
Additional comment
Clearly, for exercises like this, it is essential to know the names of these properties and what they mean. Once you understand cancelling multiplication using multiplicative inverses, and cancelling addition using additive inverses, you are on your way to solving most algebra problems.
You must always keep in mind the properties of equality that tell you the same operation must be performed on both sides of the equal sign.
Understanding these properties can also help you understand the relation between multiplication and division, addition and subtraction. Division is multiplication by the multiplicative inverse; subtraction is addition of the additive inverse.
∠J and ∠E are congruent. If ∠J = (6x + 4)° and ∠E = (2x + 32)°, then what is the value of ∠E?
Answer: 46
Step-by-step explanation:
Since we know that angles J and E are congruent, we can do the equation 6x + 4 = 2x +32. We then solve for x which gives us 7. After that, we plug in the 7 into the equation for E which would be = 2(7) + 32. Once we solve that, we end up with 46.