Answer:
v= -4i-j
Step-by-step explanation:
we subtract the coordinates and we achieve the coordinates and we replace them in the equation of the straight line in the form y=ai+bj.
It's for my calculus class, I'm terrible in his class, please help.
The value of the integral [tex]\int\limits^2_0 {f(x)} \, dx[/tex] is 5. The value of the integral [tex]\int\limits^5_2 {f(x)} \, dx[/tex] is 0. The value of the integral [tex]\int\limits^8_0 {f(x)} \, dx[/tex] is 25.
What is definite integral mean?The definite integral of a function over a limit represents the area under the curve bounded by the limit as given in integration.
The integral represents the area under the curve.
(a) [tex]\int\limits^2_0 {f(x)} \, dx[/tex] = area of the triangle with base 2 and height 5.
Area = (1/2)2 x 5 = 5 units square
(b) [tex]\int\limits^5_2 {f(x)} \, dx[/tex] = area under the triangle with base 1 and height 5 - area above the triangle with base 1 and height 5 = 0
(c) [tex]\int\limits^8_0 {f(x)} \, dx=\int\limits^2_0 {f(x)} \, dx+\int\limits^4_2 {f(x)} \, dx+\int\limits^8_4 {f(x)} \, dx[/tex]
⇒ 5 + 0 + 4 x 5 = 25 units sqaure.
Hence "integral [tex]\int\limits^2_0 {f(x)} \, dx[/tex] is 5. Integral [tex]\int\limits^5_2 {f(x)} \, dx[/tex] is 0. The value of the integral [tex]\int\limits^8_0 {f(x)} \, dx[/tex] is 25".
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The following graph shows a proportional relationship.
What is the constant of proportionality between y and x in the graph?
Constant of proportionality =
KHAN ACADEMY QUIZ 1
The equation of the line that represents the straight line in the graph will be y = (3/2)x.
What is a linear equation?An association between various factors brings about a straight model when a diagram is shown. The variable will have a level of one.
The straight condition is given as,
y = mx + c
Where m is the incline of the line and c is the y-block of the line.
From the figure, the line is passing through the origin. Then we have
y = mx + c
0 = m (0) + c
c = 0
Then the equation of the line is written as,
y = mx
From the figure, the line also passes through points (4, 6). Then we have
6 = 4m
m = 3/2
Then the equation of the line is given as,
y = (3/2)x
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let be a scalar field and let be a vector field. describe each expression. 1. curl is [ select ] 2. grad(div ) is [ select ] 3. div(curl(grad ))) is
1) curl = del x
2) grad(div ) = del(div )
3) div(curl(grad )) = div(curl(grad))
What is Scalar field and Vector field?
1) The curl of a vector field is a vector field that describes the local rotational motion of the field. It is defined as the cross product of the del operator (a vector operator that operates on scalar and vector fields) and the vector field:
curl = del x
2) The gradient of the divergence of a vector field is a scalar field that describes the local rate of change of the divergence of the field. It is defined as the del operator applied to the divergence of the field:
grad(div ) = del(div ).
3) The divergence of the curl of the gradient of a scalar field is a scalar field that describes the local rate of change of the curl of the gradient of the field. It is defined as the divergence of the curl of the gradient of the field:
div(curl(grad )) = div(curl(grad)).
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Inside a cooling tower, the temperature fell 5each hour for a total change of -35Find the number of hours it took for the change in temperature
Answer:
7 hours
Step-by-step explanation-35/-5=7
Use the scale to help you solve the equation and find the value of x. Enter the
value of x below.
x+9=13
X=
Yesterday the temperature at noon was 26.4°F. By midnight, it had decreased by
32.4°F. What was the temperature at midnight?
Answer:
-6°
Step-by-step explanation:
26.4 - 32.4 = -6
Subtract the absolute values of the both number and give the sign of the larger absolute value.
32.4 - 26.4 = 6
The sign will be negative because -32.4 has a larger absolute value (farther from zero) than 26.4
Answer:
- 6°F.
Step-by-step explanation:
26.4
- 32.4
= -6.0
The temperature at midnight:
-6°F.
the center of a semisimple lie algebra {\displaystyle {\mathfrak {g}}}{\mathfrak {g}} is trivial proof. t/f
Answer:
False. The center of a semisimple Lie algebra is usually not trivial.
Step-by-step explanation:
The center of a semisimple Lie algebra is the set of elements of the Lie algebra that commute with all other elements in the algebra. In most cases, the center of a semisimple Lie algebra is not trivial, meaning it contains at least one non-zero element. For example, the center of the simple Lie algebra sl(2,C) contains the two-dimensional Lie algebra spanned by the scalar matrices I and -I. The center of the Lie algebra so(5,C) is spanned by the five-dimensional Lie algebra spanned by the matrices diag(1,1,1,-1,-1). These examples demonstrate that the center of a semisimple Lie algebra is usually not trivial.
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What’s the difference between solving a whole number and a fraction?
There’s these two methods I saw but not sure when I should use them when I do stumble on a problem.
1 method: start by multiply the numerator towards the whole number and once u do then divide the numerator and denominator separately.
2 method: start by giving the whole number a 1 of the denominator and find the lCD of the fraction and start finishing the problem from either adding or subtracting.
Both the methods can be used to solve a mixed fraction including a whole number and a fraction or solving the difference of a whole number and a fraction.
What is Mixed Fraction?Mixed fractions are type of fractions which involve a whole number and a fraction. This is of the form a [tex]\frac{b}{c}[/tex]. This is actually a + [tex]\frac{b}{c}[/tex].
You can use either methods when solving a whole number and a fraction.
Let us take a whole number 3 and a fraction [tex]\frac{2}{10}[/tex] for instance.
First Method :
Solve it by cross multiplication.
Let the denominator of the whole number 3 be 1.
[tex]\frac{3}{1}[/tex] ± [tex]\frac{2}{10}[/tex] = [(3 × 10) ± (2 × 1)] / (1 × 10) = [30 ± 2] / 10
If the question is for adding, we get, [tex]\frac{3}{1}[/tex] + [tex]\frac{2}{10}[/tex] = (30 + 2) / 10 = 32/10
If the question is finding difference, we get, [tex]\frac{3}{1}[/tex] - [tex]\frac{2}{10}[/tex] = (30 - 2) / 10 = 28/10
Second Method :
Again let the denominator of the whole number be 1.
Find the LCD (Least Common Denominator) of 1 and 10.
This is 10.
So we have to make the denominator of [tex]\frac{3}{1}[/tex] to 10.
Multiply both numerator and denominator with 10, we get 30/10.
A normal multiplication of fractions, if the denominator is same add or subtract the numerators let the denominator be as such.
Now add or subtract [tex]\frac{30}{10}[/tex] ± [tex]\frac{2}{10}[/tex] = (30 ± 2) / 10.
Hence both the methods can be used.
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The value of a certain car, in dollars, x years from its model year can be predicted by the function f(x)=12,000(0.89)x. The value of a certain SUV, in dollars, x years from its model year can be predicted by the exponential function shown in the table. How much more will the SUV be worth than the car 5 years after their model years? Enter your answer, rounded to the nearest cent, in the box.
The SUV will be $5,299.13 worth than the car 5 years after their model years.
What is the meaning of rounded to the nearest cent?
Look at the number to the right of the whole cents when rounding money to the closest cent. In this instance, it is 9. Increase the cents by one if the figure is five or above. The cents should remain the same if the number is four or less. Given that 9 is more than 5, $3.299 equals $3.30.
Given that,
The value of a car can be predicted by using the function
f(x)=12,000(0.89)^x
Where x years from its model year.
To find the current value of the car, put x = 0 in the model equation:
f(0)=12,000(0.89)^0
f(0) = 12,000.
To find the value of the car after 5 years, put x = 5 in the model equation:
f(5)=12,000(0.89)^5
f(5) = 6700.871
The difference of the value of car is 12,000 - 6700.871 = $5299.129 = $5299.13 (rounded to the nearest cent)
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Find the slope of each of the following functions at the given points. f(x)=x²; (-3,9)
Answer:
the eqn given by the function is y=9---(1)
given point is(-3,9)=(X,y)
we know,
y=mx
mx=9 [from 1]
or,m(-3)=9 [from point]
or,m=9/-3
:.m=-3
hence, slope=-3
Write an equation to solve. Be sure to identify your variable.
Mrs. Kenney's class is
holding a canned food drive for Thanksgiving. Tara collected 10 more cans than Phil.
Laurie collected twice as many cans as Tara, If they collected 130 cans altogether, how
many cans did Tara collect?
The number of cans Tara collected is 35.
How to represent and solve equation?Mrs. Kenney's class is holding a canned food drive for Thanksgiving. Tara collected 10 more cans than Phil. Laurie collected twice as many cans as Tara. They collected 130 cans altogether.
Therefore, let's find the number of cans Tara collected.
Hence, using equation,
let
x = number of cans Phil collected
Number of cans Tara collected = x + 10
Number of cans Laurie collected = 2(x + 10) = 2x + 20
Therefore,
x + x + 10 + 2x + 20 = 130
4x + 30 = 130
4x = 130 - 30
4x = 100
x = 100 / 4
x = 25
Hence, Tara collected 25 + 10 = 35 cans.
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suppose the correlation coefficient is .4. what percentage of the total variation in salar can be explained by gender
If the correlation coefficient is 0.4, the total variation in salary can be explained by gender is 16%.
What is correlation coefficient?A statistical concept known as the correlation coefficient aids in establishing a relationship between expected and actual values gained through statistical experimentation. The estimated correlation coefficient's value explains how well the expected and actual values match.
Correlation Value of the coefficient is always between -1 and +1. If the correlation coefficient value is positive, the two variables have a similar and same relationship. Otherwise, it shows how the two variables are different.
If the correlation coefficient (R) = 0.4
Coefficient of determination (R²) = (0.4)²
Coefficient of determination (R²) = 0.16
So that, the total variation in salary can be explained by gender is 16%.
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Write the fraction 18/48 in simplest form.
Answer:
3/8
Step-by-step explanation:
Simplify the following:
18/48
The gcd of 18 and 48 is 6, so 18/48 = (6×3)/(6×8) = 6/6×3/8 = 3/8:
Answer: 3/8
A circular kiddie pool has an area of about 28 square feet. An inflatable full-size circular pool has an area of about 113 square feet. How much greater
The radius of the full-sized pool is 2 times larger than the radius of the kiddie pool.
By using the expression to approximate the radius of a circle, we want to compare the radius of the two pools.
The expression for the radius of a circle is:
R = √(A/3)
Where A is the area of said circle.
The circular kiddie swimming pool has an area of 28ft^2, we just replace that in the above expression to get:
R = √(28 ft^2/3) = 3 ft
The full-sized pool has an area of 113 ft^2, then its radius is:
R' = √(113 ft^2/3) = 6 ft
To see how much greater is the radius of the full-sized pool than the radius of the kiddie pool, we just take the quotient:
R'/R = 6ft/3ft
= 2
Hence, the radius of the full-sized pool is 2 times larger than the radius of the kiddie pool.
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x² - 16√x = 12 ise ; x-2√x kaçtır ?
Answer: The value of x-[tex]\sqrt{x}[/tex]= 2
Step-by-step explanation: [tex]x^{2}[/tex] - 16[tex]\sqrt{x}[/tex]
Let [tex]u= \sqrt{x}[/tex], then
[tex]u^{2} = x\\^u{4} =x^{2}[/tex]
substituting these into the original equation
[tex]u^{4} -16u -12 =0[/tex]
This factor is easy as -
[tex](u^{2} -2u -2) (u^{2} +2u +6) =0[/tex]
[tex]u^{2} -2u -2=0\\[/tex]
I will give BRAINLIEST if correct the question is in the photo attached please answer Part A
Answer:
0-2 sec
Step-by-step explanation:
From the graph you can see the height is going UP from 0-2 sec...from then on it is going downward....
A nonprofit maintains a list of how many laptops they provide to each school in the county. in the table, there is a column called number of laptops. a data analyst wants to determine which schools were given the fewest laptops. how should they sort the data to return these schools first?
O Sort alphabetically in descending order
O Sort numerically in ascending order
O Sort numerically in descending order
O Sort alphabetically in ascending order
In order to determine the school that was given the fewest laptops, sort numerically in ascending order (second option)
How to sort a numerical data in ascending order?A numeric data is a dataset that is made up of numbers. An example of a numeric data is the age of students in a class. The best colours of students in a class is not an example of numeric data.
The data that contains information on the number of laptops that was given to a school would be numeric. For example, a school can recieve 100 laptops while another school would receive 10 laptops.
In order to sort a numeric data in ascending order, it means that the smallest numbers would be arranged first.
For example consider this data set 2, 5 100, 1000, 4, 90. In order to arrange in ascending order, this would be the order of the numbers: 2, 4, 5, 90, 100, 1000.
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. A sheet of card is 20 centimetres by 30 centimetres. What is
the maximum number of circular name badges, of diameter
60 millimetres, that can be cut from this piece of card?
The number of badges that can be cut from a piece of card, which is 20 centimeters by 30 centimeters, is 21.
What is the area?
A region's size on a plane or curved surface is expressed by a measurement known as an area. Unlike the area of a plane region or plane area, which refers to the area of a shape or planar lamina, surface area describes the area of an open surface or the boundary of a three-dimensional object.
Given:
A sheet of the card is 20 centimeters by 30 centimeters,
The diameter of a badge, d = 60 mm or 6 cm,
Calculate the area of the sheet as shown below,
[tex]Area = length \times width[/tex]
Area = 20 × 30 = 600 cm²
Calculate the area of the badge as shown below,
[tex]Area = \pi d^2 / 4[/tex]
Area = 3.14 × 6² / 4
Area = 28.26 cm²
To calculate the number of badges[tex]No\ of\ badges = Area\ of \ sheet / Area \ of badge[/tex], use the formula given below,
Number of badges = 600 cm² / 28.26 cm²
Number of badges = 21.23 or 21
Therefore, the number of badges that can be cut from a piece of card, which is 20 centimeters by 30 centimeters, is 21.
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At Fromazing, Frozen yogurt costs $0.50 per ounce. The cost of frozen yogurt per ounce at Frotastic is shown below:
Amount(oz) Cost
5 $2.40
8 $3.84
11 $5.28
14 $6.72 Silas says Frotastic is a better deal.
Sterling says Fromazing is a better deal.
Silas or Sterling. Justify your answer.
As Silas says Frotastic is a better deal. Because at Frotastic we get 1 ounce at $0.48
Define OunceThe ounce is derived from the Ancient Roman uncia, which was equal to one-twelfth (1/12) of a Roman pound and weighed around 27.35 grams, or 0.967 of an Avoirdupois ounce (libra). This originally meant "unit" because it originates from the Latin uno ('one'). The word "uncia" was borrowed twice: once into Old English as "ynsan" or "yndsan" from an unrecorded Vulgar Latin version that palatalized the "c" before the I to become the present English word "inch."
Here at Fromazing, 1 ounce of Frozen Yougurt costs $0.50 per ounce
whereas at Frotastic 5oz = $2.40
1oz = 2.40/5
= 0.48$
8oz = $3.84
1oz = 3.84/8
= $0.48
11 oz = $5.28
10z = 5.28/11
=$0.48
similar case for 14 oz = $6.72
1oz = 6.72/11
=$0.48
Therefore Frotastic is a better deal as Silas said
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what is the solution for the system of linear equations shown in the graph?
Photo with question
The solution to the system of linear equations is where they intersect which is at (- 0.5, 1.5).
What is the graphical solution of a system of equations?Graphical solutions of a system of equations are a way of finding the intersection points of all the equations given.
A system with two or more than two equations has a solution only when they have a common intersection point.
From the graph of two lines in the coordinate system, every square box has a side length of 1 unit.
Now, The solution of the system is the point at which these two lines intersect.
By, Observing the graph we conclude that at (- 0.5, 1.5) they intersect and it is the solution of these two linear equations.
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10. (04.02 LC)
For the following system, if you isolated x in the second equation to use the substitution method, what expression would you substitute into the first equation? (1 point)
2x + y = 8
-x - 3y = -12
3y + 12
-3y + 12
3y - 12
-3y - 12
If you isolated x in the second equation to use the substitution method. -3y + 12 expression we substitute into the first equation.
What is Substitution Method ?The algebraic approach to solving simultaneous linear equations is known as substitution method. The value of one variable from one equation is substituted in the second equation in this procedure, as the name implies.
The substitution method has three straightforward steps, which are listed below:
In any equation, determine the value of any one variable in terms of the other variable.Replace that in the other equation, then solve it.In any of the equations, replace the value of the second variable once more.2x + y = 8
-x - 3y = -12
__________
-3y + 12
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Question 2 of 10
Which statement regarding salaried employees is true?
A. Salaried employees get paid more for additional hours worked.
B. Salaried employees have taxes with held from each paycheck.
c. Salaried employees do not receive an agreed-upon annual pay.
D. Salaried employees never receive medical benefits.
Salaried employees get paid more for additional hours worked but they must keep up with their responsibilities and complete necessary tasks even if that means working extra hours. The correct option is A
What is salaried employees?Salaried employees can be defined as someone who receives a fixed amount of pay salary regardless of how many hours they work each weeks. Salaried employees enjoy the security of steady paychecks and they tend to pull in higher overall income than hourly worker.
Therefore the correct option is A Salaried employees get paid more for additional hours worked.
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A fair die is rolled three times. A 4 is considered "success," while all other outcomes are "failures." Find the probability of 3 successes.
The probability of getting 3 successes is 0.00463 Or 0.46%.
What is a binomial distribution in probability?In an experiment with two possible outcomes, the likelihood of exactly x successes on n repeated trials is known as the binomial probability (commonly called a binomial experiment). The binomial probability is [tex]P(x) = ^nC_xp^xq^{n-x}[/tex] if the likelihood of success on a given trial is p.
Given, A fair die is rolled three times. Getting a 4 is considered 'success', while all other outcomes are 'failures'.
So, The probability(p) of getting a 4 on a die is (1/6), and hence the probability of failure(q) = 1 - 1/6 = 5/6.
Also given, n = 3.
Therefore, The probability of getting 3 successes is,
[tex]P(x = 3) = ^3C_0(1/6)^3\times(5/6)^0[/tex].
[tex]P(x = 3) = 1\times\frac{1}{216}\times1[/tex]
[tex]P(x = 3) = \frac{1}{216}[/tex].
So, the probability of 3 successes is 1/216.
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A survey of 25 randomly sampled judges employed by the state of Florida found that they earned an average wage (including benefits) of $65.00 per hour. The sample standard deviation was $6.25 per hour.
The 99% confidence interval for the mean wage of all judges is given as follows:
($61.5, $68.5).
How to obtain the confidence interval?We have the standard deviation only for the sample, hence the t-distribution is used to obtain the confidence interval.
The equation that defines the bounds of the confidence interval is given as follows:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which the variables of the equation are presented as follows:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical value, using a t-distribution calculator, for a two-tailed 99% confidence interval, with 25 - 1 = 24 df, is t = 2.797
The remaining parameters are given as follows:
[tex]\overline{x} = 65, s = 6.25, n = 25[/tex]
Hence the lower bound of the interval is calculated as follows:
65 - 2.797 x 6.25/5 = $61.5.
The upper bound of the interval is of:
65 - 2.797 x 6.25/5 = $68.5.
Missing InformationThe problem asks for the 99% confidence interval for the mean wage of all judges.
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11 4/10 the the nearest whole number
The solution of the mixed number as a whole number is 11.4.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
A mixed number is the combination of a whole number and a proper fraction. It usually denotes a number between two whole numbers.
The given fraction is 11(⁴/₁₀). The mixed number can be simplified as below,
E = 11(⁴/₁₀)
E = 114 / 10
E = 11.4
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How many integral solution(s) is/are there for x if -69 ≤ 7x + 9 ≤ 49?
Answer:
To find the number of integral solutions for x in the given inequality, we can first solve the inequality to find the range of values that x can take on. To do this, we need to isolate the x term on one side of the inequality, so let's start by subtracting 9 from both sides of the inequality:
-69 ≤ 7x + 9 ≤ 49
-9 ≤ 7x ≤ 40
Next, we can divide both sides of the inequality by 7 to isolate the x term:
-9/7 ≤ x ≤ 40/7
The result of this calculation is a range of values for x, but we are looking for the number of integral solutions, which means we need to find the number of whole numbers that x can take on within this range. In this case, we can see that the range of possible values for x is from -1 to 5, and there are 5 whole numbers within this range (-1, 0, 1, 2, 3, 4, 5), so there are 5 integral solutions for x in this inequality.
In general, to find the number of integral solutions for x in an inequality of the form a ≤ bx + c ≤ d, where a, b, c, and d are constants, you can follow these steps:
1.Solve the inequality to isolate the x term on one side, by subtracting c from both sides and then dividing both sides by b. This will give you the range of possible values for x.
2.Count the number of whole numbers within this range to find the number of integral solutions for x.
Step-by-step explanation:
there appears to be a strong positive correaltion between the number of firefighters at a fire and the amount of damage the fire does choose the statemnt that is most likely true a, b, or c? a. We should assign fewer firefighters to a fire to decrease the amount of fire damage. b. The more firefighters present, the less damage a fire is likely to cause. C. Bigger fires cause more fire damage and more firefighters are likely to be present at bigger fires.
The relationship between the quantity of firemen and the amount of damage brought on by a fire is, in fact, created by a third party. Thus, choice A is the best one.
Firefighter
A fireman is a first responder and rescuer who has received significant training in firefighting. They are primarily responsible for putting out dangerous flames that endanger life, property, and the environment as well as for rescuing humans and, in some circumstances, animals from perilous situations.
The third aspect
The numbers that divide 3 in three equal parts with no remainders are known as its factors. As is well known, the earliest odd prime number is three. The three components and their pair can be expressed in both good and negative ways. For illustration, the pair factor of 3 is shown.
It is true to say that a third party is to blame for the correlation between the number of firefighters and the amount of damage a fire causes. So, option A is the best choice.
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The factors of 3 are the numbers that split it into three equal pieces with no remainders. The oldest odd prime number is three, as is common knowledge. The three elements and their paired expressions have both positive and negative connotations. The pair factor of three is displayed as an illustration.
It is accurate to say that there is a third party at fault for the association between the quantity of firefighters and the scope of a fire. As a result, option A is the best one.
If f(x)\ =\ x^{2}+3f(x) = x 2 +3 , find f(-2)f(−2) .
The solution for f(-2) in the function f(x) = x² + 3 is 7
How to determine the solution for f(x) in the function?From the question, we have the following equation that can be used in our computation:
f(x) = x 2 +3
To make the equation legible, we need to rewrite it
So, we have the following representation
f(x) = x² + 3
Also from the question, we have
f(-2)
This means that the value of x is -2, and we calculate f(x) when x = -2
Substitute the known values in the above equation, so, we have the following representation
f(-2) = x² + 3
So, we have the following equation
f(-2) = (-2)² + 3
Evaluate
f(-2) = 7
Hence, the solution is 7
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prove that a triangle with the sides x cm, 2x cm and √5 x cm form a right-angled triangle
Answer:
use the Pythagoras theorem
Step-by-step explanation:
x²+(2x)²=x²+4x²=5x²
square root of 5x²= (square root of 5)x
Margo solves several equations and then states that all of them have a solution of x = 7. However, Kenneth disagrees. Determine which of the following equations have a solution of x = 7 and then justify your response.
A. 6x + 11 = 55
B. -3x -18 = 39
C. 2x - 14 = - 28
D. 7x + 9 = 58
SHOW YOUR WORK!!!
a. [tex]6x+11=55[/tex]
Subtract 11 from both sides:
[tex]6x+11-11=55-11[/tex]
[tex]6x=44[/tex]
Divide both sides by 6:
[tex]\dfrac{6x}{6} =\dfrac{44}{6}[/tex]
[tex]x=7.333333[/tex]
___________________________
b. [tex]-3x-18=39[/tex]
Add 18 to both sides:
[tex]-3x-18+18=39+18[/tex]
[tex]-3x=57[/tex]
Divide both sides by -3:
[tex]\dfrac{-3x}{-3} =\dfrac{57}{-3}[/tex]
[tex]x=-19[/tex]
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c. [tex]2x-14=-28[/tex]
Add 14 to both sides:
[tex]2x-14+14=-28+14[/tex]
[tex]2x=-14[/tex]
Divide both sides by 2:
[tex]\dfrac{2x}{2} =\dfrac{-14}{2}[/tex]
[tex]x=-7[/tex]
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d. [tex]7x+9=58[/tex]
Subtract 9 from both sides:
[tex]7x+9-9=58-9[/tex]
[tex]7x=49[/tex]
Divide both sides by 7:
[tex]\dfrac{7x}{7} =\dfrac{49}{7}[/tex]
[tex]x=7[/tex]
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Only option d had a solution of x = 7.