For our pyramid, this gives us the volume of the pyramid (1/3)x²y.
Let the length of base be x and height be y
Volume of pyramid = [tex]\frac{1}{3}[/tex]× l× b× h
The volume of a right rectangular prism is found by finding the area of the base and multiplying by the height. This is because there are "layers" of the base from the bottom to the top, making the height the number of "layers."
However, in a pyramid, the shape comes to a point. This makes the volume of a pyramid 1/3 of that of the corresponding prism.
For our pyramid, the area of the base would be x(x) = x².
There are y layers of this base, so this would be x²y.
Since it is a pyramid, this gives us the volume of the pyramid (1/3)x²y.
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the two non-parallel sides of an isosceles trapezoid are each 7 feet long. the longer of the 2 bases measures 22 feet. the sun of the base angles is 140 degrees.
Use the Law of Cosines to find the length of the diagonal.
Use the Law of Sines to find the length of the shorter base
Answer:
formula:
c^2 = a^2 + b^2 - 2abcos(C)
where c is the length of the diagonal, a and b are the lengths of the legs of the triangle (the non-parallel sides of the trapezoid), and C is the angle between them.
In this case, a = b = 7 feet and C = (180 - 140)/2 = 20 degrees. We can plug these values into the formula to find:
c^2 = 7^2 + 7^2 - 2(7)(7)cos(20)
c = sqrt(98 + 49cos(20))
To use the Law of Sines to find the length of the shorter base, we can use the following formula:
a/sin(A) = b/sin(B) = c/sin(C)
where a, b, and c are the sides of the triangle and A, B, and C are the angles opposite those sides.
Since we know a and b, we can use the formula to find:
x/sin(140) = 7/sin(20)
x = 7sin(140) / sin(20)
Note that the value of c will be in squared units, so you need to take the square root to get the actual length of the diagonal.
A group of children 6 to 10 years old were asked how many video games they owned. the scatter plot shows the results. what is the range of the number of video games owned for the cluster? responses 2 to 10 2 to 10 6 to 9 6 to 9 6 to 10 6 to 10 8 to 10
On solving the provide question, we can say that by plotting data they can own 8 to 10 video games.
what is plotting data?The most typical approach to display data using a chart is a graph that shows the relationship between two additional variables. Diagrams created by hand or on a computer are also acceptable. Move 2 units to the right after starting at the origin before going 3 units up. The coordinates for the points 2, 3, should be shown on the coordinate plane. Clearly state your points. The pink dot with the letter P thus stands for 2.3. Before creating a line chart, you need first generate a number line for each value in your data collection. Put an X (or dot) over each value of the data on the number line after that. For each instance when a value appears in a record, place an X over the corresponding number.
Here,
We can therefore deduce from the provided number that the cluster owns between 8 to 10 video games.
How do we know the range is 8 to 10 then? In the example figure, the dots are referred to as the cluster.
Based on this, we may deduce that our range is between 8 and 10, the amount of games that are owned as a minimum and maximum, respectively.
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The complete question is " A group of children, 6 to 10 years old, were asked how many video games they owned. The scatter plot shows the results.
What is the range of video games owned for the cluster?"
Please help me with this
find a cartesian equation for the curve and identify it. r2 cos(2θ) = 1
For the given polar equation the cartesian form of the equation is x² - y² = 1
The term polar equation in math is defined as another way to represent a complex number.
The general form the complex number is written as
=> z = a + bi
It is also known as the rectangular coordinate form of a complex number. And the horizontal axis is the real axis and the vertical axis is the imaginary axis.
Here we have given an equation r²2cos(2θ) = 1.
It can be rewritten as,
=> r²cos2θ − r²sin2θ = 1
Then here we substitute x as rcosθ and y as rsinθ, we get the cartesian equation as,
=> x² − y² = 1.
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7. When it is 9:00A.M. eastern standard time (EST)
in Pittsburgh, it is 6:00A.M. pacific standard time
(PST) in Los Angeles. A plane takes off from
Pittsburgh at 9:00 A.M. EST and arrives in Los
Angeles at 11:00 A.M. PST. If a second plane
were to leave Los Angeles at 10:00 A.M. PST and
take exactly the same amount of time for the trip,
what would be the plane's arrival time (EST) in
Pittsburgh?
A. 6:00 P.M. EST
B. 5:00 P.M. EST
C. 4:00 P.M. EST
D. 3:00 P.M. EST
Please guys I need this tomorrow help tysm I rlly appreciate it
Answer:
A, 6:00 P.M. EST
Step-by-step explanation:
The time difference between EST and PST is -3 hours
11 am - 9am = 2 hours
2 - (-3) = 2+3 = 5 hours
The flight time is 5 hours
Then:
The time difference between PST and EST is +3 hours
5 + 3 = 8
If the fly leaves Los Angeles at 10:00 AM PST
10 + 8 = 18
The plane will arrive at 6:00PM EST
Find the missing number so that the equation has no solutions.
4x + 10= __x + 8
The missing coefficient of the linear equation 4 · x + 10 = __ · x + 8 such that it has no solutions is equal to 4.
How to determine the value of coefficient such that a linear equation has no solution
In this problem we find a linear equation of the form a · x + b = c · x + d, where a, b, c, d are real coefficients. This kind of equation has no solution for the case when a = c. The complete procedure is shown below.
First, write the incomplete expression:
4 · x + 10 = __ · x + 8
Second, add the missing coefficient according to the definition for linear equations with no solutions:
4 · x + 10 = 4 · x + 8
Third, use algebra properties to simplify the expression:
10 = 8 (CRASH!)
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see screenshot for the question
The area of the triangle ΔKLM, obtained using Routh's theorem is 4/13
What is Routh's theorem?Routh Theorem outlines the ratio relationship between the triangle formed by three cevians of a triangle and the area of the original triangle.
Mathematically it states that the ratios (x, y, and z) of the segments formed the intersection of the cevians and the three sides of the triangle produces the area of the triangle when expressed in the form;
A = (x·y·z - 1)² ÷ ((x·y + y + 1)·(y·z + z + 1)·(z·x + x + 1)).
The specified dimensions are;
BD : DC = CE : EA = A_F: FB = 1 : 3
The point of intersection of AD, BE and CF = K, L, and M
Area of triangle ΔABC = 1
The area of triangle ΔKLM is found as follows;
Where the length of AB = 4 units, we get;
Length of A_F = 1 unit and the length of FB = 3 units
We get;
BD/DC = x, CE/EA = y, A_F/FB = z
x = y = z = 1/3
Routh's theorem states that the area of the triangle formed by AD, BE, and CF is obtained using the formula;
Area of ΔKLM = (x·y·z - 1)² ÷ ((x·y + y + 1)·(y·z + z + 1)·(z·x + x + 1))
Plugging in the values of x, y, z, we get;
x = y = z, therefore;
Area of ΔKLM, A = (x³ - 1)² ÷ ((x² + x + 1)·(x² + x + 1)·(x² + x + 1))
A = (x³ - 1)² ÷ ((x² + x + 1)³)
x = 1/3, therefore;
A = ((1/3)³ - 1)² ÷ (((1/3)² + (1/3) + 1)³) = 4/13
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Find the answer: (-7) - (-10) =
Answer: The answer is 3
Step-by-step explanation:
(-7)-(-10)
=(-7)+10
=10-7
=3
Answer: 3
Step-by-step explanation: First, to make this easy, let's rewrite the equation:
-7 + 10
I did this because whenever you change subtraction to an addition problem, with decimals, you need to change the sign of the number on the right side (always) So, (-7) - (-10) is the same as (-7) + 10.
So, to make this even easier, we can model this as 10 - 7, which is 3. As we know, it's the same as (-7) + 10 because we are adding 10 more to (-7) which is 3. Also, if you can, using a numberline really helps to! I hope this helped!
a box contains one 2-inch rod, one 3-inch rod, one 4-inch rod, and one 5-inch rod. what is the maximum number of different triangles that can be made using these rods as sides?
On solving the provided question, we can say that we excluded example 2 above, a maximum of 3 triangles can be created with those rods.
What is triangle?A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear.
[tex]2-inch, 3 inch, 4-inch[/tex]
triangle, because 2+3 > 4, 2+4 > 3, and 3+4 > 2
[tex]2-inch, 3 inch, 5-inch[/tex]
This is doesn't make a triangle as [tex]2+5 > 3, and 3+5 > 2,[/tex]
2+3 is not more than 5,, they cannot make triangle.
[tex]2-inch, 4 inch, 5-inch[/tex]
triangle, because 2+4 > 5, 2+5 > 4, and 4+5 > 2
[tex]3-inch, 4 inch, 5-inch[/tex]
a triangle, because 3+4 > 5, 3+5 > 4, and 4+5 > 3
Therefore, since we excluded example 2 above, a maximum of 3 triangles can be created with those rods.
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what is a visual representation of data where numbers on the left side of a chart show one part of each value, while numbers on the right side of the chart show the other?
A visual representation of data where numbers on the left side of a chart show one part of each value and numbers on the right side of the chart show the other is called a bar chart. A bar chart is a chart that uses rectangular bars to represent different values or categories. Each bar has a length that represents a value or a category. The left side of the chart is called the y-axis, or the vertical axis, and the right side of the chart is called the x-axis, or the horizontal axis. The x-axis typically shows the categories, and the y-axis shows the values of those categories. The height of each bar represents the value of the data point, with the height on the y-axis and the categories on the x-axis. This type of graph is useful for comparing the relative sizes of different groups or categories, as well as spotting trends and patterns.
Solve the following compound inequality: 3 less-than negative 2 x minus 1 less-than-or-equal-to 7. a. Negative 2 less-than x less-than-or-equal-to negative 4 c. Negative 1 less-than x less-than-or-equal-to negative 3 b. Negative 2 greater-than x greater-than-or-equal-to negative 4 d. Negative 1 greater-than x greater-than-or-equal-to negative 3 Please select the best answer from the choices provided A B C D
The solution for the compound inequality is -2>x≥-4. Therefore, option C is the correct answer.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
The given inequality is 3<-2x-1≤7.
Here, 3<-2x-1
Add 1 on both the sides of an inequality, we get
4<-2x
Divide -2 on both the sides of an inequality, we get
-2>x
Here, -2x-1≤7
Add 1 on both the sides of an inequality, we get
-2x≤8
Divide -2 on both the sides of an inequality, we get
x≥-4
The solution is -2>x≥-4
Therefore, option C is the correct answer.
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Look at the picture
1 and 7/12
Divide the 2 fractions (multiply by reciprocal.)
1/4 + 1/2 × 8/3
1/4 + 8/6
Find common denominators.
6/24 + 32/24
38/24
Turn that into a mixed number.
1 14/24
Simplify.
1 7/12
let f be the function given by . what are all values of c that satisfy the conclusion of the mean value theorem of differential calculus on the closed interval [0,3]?
The only value of c that satisfies the conclusion of the Mean Value Theorem on the closed interval [0,3] is c = 2.
The Mean Value Theorem states that if a function f is continuous on a closed interval [a, b], then there exists some c in the interval such that
f'(c) = (f(b) - f(a)) / (b - a).
In the case of f(x) = x(x-3) , on the closed interval [0,3], we can solve for c using the equation above.
We begin by calculating f'(c), which is equal to 2c - 3. Then, we set the equation equal to (f(3) - f(0)) / (3 - 0), which is equal to -3 / 3.
Substituting this into our equation for f'(c), we get 2c - 3 = -1, which simplifies to c = 2.
Therefore, the only value of c that satisfies the conclusion of the Mean Value Theorem on the closed interval [0,3] is c = 2.
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Mg mg borrowed a sum of ks 2000 from his friend on may 1 at rate of 5%. An emergency arose and he again borrowed Ks 1000 on september 24 at the same rate of interest. IF he returned his loan, along with interest ,how much was the total amount returned?
Step-by-step explanation and Answer
Since the interest rate is 5%, and the first loan was borrowed on May 1, we can calculate the interest on the first loan by using the formula:
Interest = Principal x Rate x Time
In this case, the principal is 2000, the rate is 5% (expressed as a decimal), and the time is (September 24 - May 1) = 4.5 months
So, Interest = 2000 x 0.05 x 4.5/12 = 50
The same applies to the second loan of 1000, so the interest on this loan is:
Interest = 1000 x 0.05 x (4.5/12) = 25
To find the total amount returned, we add the interest on both loans to the total principal borrowed:
total = 2000 + 1000 + 50 + 25 = 3075
Therefore, the total amount returned is Ks 3075
Taylor has xx nickels and yy dimes, having no less than 15 coins worth a maximum of $1 combined. At least 14 of the coins are nickels. Solve this system of inequalities graphically and determine one possible solution.
Answer:
Step-by-step explanation:
The system of inequalities can be written as follows:
x ≥ 14
x + y ≥ 15
0.5x + 0.1y ≤ 1
We can graph the system by plotting the three lines representing the three inequalities.
The first inequality, x ≥ 14, is a vertical line with x-intercept at (14, 0).
The second inequality, x + y ≥ 15, is a line with a slope of 1, passing through the point (0, 15) and with y-intercept at (0, 15).
The third inequality, 0.5x + 0.1y ≤ 1, is a line with a slope of -5, passing through the point (2, 0.2) and with y-intercept at (0, 0.2).
The solution to the system of inequalities is the region below the line representing the first inequality, above the line representing the second inequality, and to the right of the line representing the third inequality.
One possible solution is x = 16 and y = 1. This means that Taylor has 16 nickels and 1 dime, which is exactly 15 coins worth a maximum of $1 combined.
Answer: the person is right above just made sure that .5 is .05 since it’s cents. A nickel is worth .05 cents not .5 cents.
Step-by-step explanation:
https://hegartymath of 15 O Find the size of the final unknown interior angle in a polygon whose other interior angles are: 162, 115, 125°, 138, 105° and 98°.
The size of the final unknown interior angle is 157°
Given the interior angles of a polygon are 162°,115°,125°,138°,105°, and 98°.
Considering the given polygon to be 7-sided,
The sum of the interior angles of a polygon is:
(n-2) x 180
where n= number of sides of the polygon
Substituting the values:
(7 - 2) x 180
= 5 x 180
= 900
Let the unknown angle be x°
So,
162+115+125+138+105+98+x = 900
x = 900 - 743
x = 157°
Thus the final interior angle is 157°
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Lola takes the train from paris to nice. the distance between the two cities is about 920,000 meters. if the train travels at a speed of 230 kilometers per hour, how long will it take lola to travel from paris to nice?
Answer:
We know that the distance between Paris and Nice is about 920,000 meters. To convert this distance to kilometers we divide by 1000: 920,000/1000= 920 kilometers
We also know that the train travels at a speed of 230 kilometers per hour. To find out how long it will take Lola to travel from Paris to Nice, we divide the distance by the speed:
920/230 = 4 hours
So it will take Lola 4 hours to travel from Paris to Nice by train.
Answer: 4 hours actually kinda ez not gonna lie
Step-by-step explanation: 230 kilometers = 230000 meters. 230 * 1000 = 230000. Distance / speed = time. 920000/230000 = T(as in time). T = 4
114 the length of a rectangle multiplied by 3 is equal to 4 times its width. the perimeter is 8 2 5 feet. find the length and the width.
The length of the rectangle is 2.4 and breadth is 1.8
Now, According to the question:
The given information is :
The length of a rectangle multiplied by 3 is equal to 4 times its width.
The perimeter is 8[tex]\frac{2}{5}[/tex].
To find the length and the width.
We take,
Length=L
Width=W
3L=4W
Divide by 3 on both sides
L = [tex]\frac{4}{3}[/tex]W
We know that, The perimeter of rectangle:
Perimeter of rectangle is = 2(L + W)
2W + 2L=8.4
2W + 2([tex]\frac{4}{3}[/tex]W) = 8.4
2W + [tex]\frac{8}{3}[/tex]W=8.4
[tex]\frac{6}{3}[/tex]W + [tex]\frac{8}{3}[/tex]W = 8.4
[tex]\frac{14}{3}[/tex]W = 8.4
14W = 25.2
Divide by 14 on both sides.
W = [tex]\frac{25.2}{14}[/tex]
W =1.8
L = 4/3W
L= [tex]\frac{4}{3}1.8[/tex]
L=2.4
L=2.4; W=1.8
Hence, The length of the rectangle is 2.4 and breadth is 1.8
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Find 3 ratios that are equivalent to the given ratio.18:21
Three ratios that are equivalent to 18:21 are 6 : 7, 36 : 42 and 72 : 84
How to find 3 ratios that are equivalent to 18:21?
An equivalent ratio is a ratio that represents the same relationship between numbers as another ratio, but with different values.
You can create equivalent ratios by multiplying or dividing both parts of the ratio by the same non-zero number. For example, if a ratio is 4:8, an equivalent ratio would be 2:4.
Thus, 3 ratios that are equivalent to 18:21 can be:
18 : 21 = 6 : 7 (divide both sides by 3)
18 : 21 = 36 : 42 (multiply both sides by 2)
18 : 21 = 72 : 84 (multiply both sides by 4)
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Question 1 of 5
pete drives from his house to the store and then to the fair. how many miles
does he drive in all?
y
8
7
store
(48)
pete's house
(8,8)
6
5
4
3
2
fair
(4,3)
1
1
23
4 5
5
7 8
1 unit = 1 mile
As per the given distance, he surrounded around 20 miles
Here we have given that Pete drives from his house to the store and then to the fair.
While we have given the distance covered by the Pete driver as,
=> 6, 5, 4, 3, 2
Then the total travelling distance is calculated by sum up all the details,
Then we get,
=> 6 + 5 + 4 + 3 + 2
=> 20 units.
Here we have also given that 1 unit is equal to 1 miles.
Therefore, the resulting distance is 20 miles.
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The following inequalities form a system. y is less than or equal to two-thirds times x plus 1 y is greater than negative one-fourth times x plus 2 Which ordered pair is included in the solution to this system? (6, −2) (6, 0.5) (6, 5) (6, 8)
Answer:
(6, −2), (6, 0.5)--------------------------------
Given system of inequalities:
y ≤ 2/3x + 1y > - 1/4x + 2Plot the inequality and the given points to determine which of them fall into solution area.
See attached.
As we see only two points fall in the solution area, brown zone on the bottom: (6, −2), (6, 0.5).
(Answer:
(6, 5)
Step-by-step explanation:
For this question, there are not two correct choices.
Given systems:
y ≤ 2/3x + 1
y > -1/4x + 2
For the first equation, the y-intercept is 1, and the rate of change is 2/3 (rise over run). The inequality symbol is less than or equal to (≤), meaning this will be a solid line and the area shaded will be below the line.
For the second equation, the y-intercept is 2, and the rate of change is -1/4 (this means it is decreasing in number, therefore the line is going down). The inequality symbol is greater than (>), meaning this will be a dashed line and the area shaded will be above the line.
the area overlapped is where the solution will be. The answer is (6, 5) because it lies on the solid line of the first inequality, indicating it does satisfy the first inequality. Any point on the solid line satisfies the inequality. The point also lies above the second inequality, meaning it is a solution to the system.
Also, if you plug it into the system of inequalities, all the outcomes will make sense.
The function f(x)f(x) is a quadratic function and the zeros of f(x)f(x) are 11 and 22. Assume the leading coefficient of f(x)f(x) is 11. Write the equation of the quadratic polynomial in standard form.
The equation for the given quadratic polynomial is f(x) = x^2-33x+242.
When the highest degree term in a second-degree polynomial equals 2, the polynomial is said to be quadratic. A quadratic equation has the generic form ax^2 + bx + c = 0. Here, x is the unknown variable, a and b are coefficients, and c is the constant term.
A polynomial with an exponent degree of 2 or higher is said to be quadratic. A quadratic polynomial has the general form f (x) = ax^2 + bx + c, where a 0 and b a n d c are real numbers. A parabola is the name of the quadratic polynomial's curve.
f(x) = (x-11)(x-22)
f(x) = x^2-33x+242
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a large company states in their promotional literature that 80% of their employees have college degrees. if 5 employees are selected at random from this company, what is the probability that all 5 will have college degrees? 0.0003 0.3277 0.6723 0.9997
There is a 0.32768 or 32.77% probability that all 5 employees selected at random from the company have college degrees.
The probability of all 5 employees selected at random from the company having college degrees is calculated by using the following formula: P = (0.8)^5. Substituting 0.8 for the probability of having a college degree, this equation simplifies to P = 0.32768.
Therefore, P = (0.8)^5 = 0.32768.
This implies that there is a 0.32768 or 32.77% probability that all 5 employees selected at random from the company have college degrees.
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find the x for 4+3x=x+6 linear equation
here is your Answer.
hope it is helpful,
Please mark me brainiest
Answer:
x =1
Step-by-step explanation:
4 + 3x = x + 6
minus 4 from both side
6-4 = 2
3x = x + 2
then minus x from both side
3x-x=2
(pretend there's a 1 beside the x)
2x = 2
then divide 2 from both side and 2/2 =1
s0 x=1
that doesn't make sense but ye
What is the nature of roots of the quadratic equation 4x 2 )- 12x 9 0?
Nature of roots of the quadratic equation 4x^2 - 12x - 9 = 0 are real and unequal by Discriminant method.
Given quadratic equation is 4x^2 - 12x - 9 = 0
Comparing the given equation with the standard form i.e ax^2 - bx - c = 0.
Here we have, a = 4
b = -12 and
c = -9
Now discriminant, D = b^2 - 4ac
= (-12)^2 - 4(4)(-9)
= 144 - (-144)
D = 288
Now check for discriminant D, D=288 and 288 >0
Therefore, (D>0)
Hence the roots of given equation are real and unequal.
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3 semicircles are connected to 3 sides of a square. Each side of the square measures 4 centimeters. What is the area of the composite figure?
The area of the composite figure which consist 3 semicircles and a square with 4 centimeters is (6π+16) cm².
What is the area of the semicircle?The area of the semicircle is the space occupied by it. It can be given as,
[tex]A_{s} = \frac{d^{2} }{8} \pi[/tex]
Here, (d) is the diameter of the semicircle.
Each side of the square measures 4 centimeters. The area of the square is square of its side. Thus,
Area of the square, [tex]A_{s}[/tex] = 4² = 16cm²
3 semicircles are connected to 3 sides of a square. Thus, the diameter of the semicircle is equal to 4 cm. The area of 3 semicircles is,
[tex]A_{sc} = 3 *\frac{4^{2} }{8} \pi\\A_{sc} = 6\pi[/tex]
The area of the composite figure is,
[tex]A = A_{s} + A_{sc} \\A = (6\pi + 16) cm^{2}[/tex]
Thus, the area of the composite figure which consist 3 semicircles and a square with 4 centimeters is (6π+16) cm².
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which algebraic expression is a trinomial? O X3 + X2 - √x
O 2X3 + X2
O 4X3 + X2 – 1/x
O X6 - X - √6
The following algebraic expression are trinomial.
The term expression in math is also known as algebraic expression consists of unknown variables, numbers and arithmetic operators.
Here we must know what is meant by trinomial,
The term trinomial is referred as
Here we have given algebraic expression that is written as x³ + x² - √x is a trinomial with one variable ‘x’ and it having three non-zero terms.
Then the next given algebraic expression which is 2x³ - x², is NOT a trinomial. Because this expression is a binomial with one variable ‘x’, having two non-zero terms.
Then the another given algebraic expression that is 4x³ + x² - 1/x, is a trinomial with one variable ‘x’, having three non-zero terms.
Finally the given algebraic expression which can be written as x⁶ - x +√6, is a trinomial with one variable ‘x’, having three non-zero terms.
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a researcher is interested in the effect of an electrolytic sports drink on the endurance of adolescent boys. a group of 30 boys is selected and half are given a treadmill endurance test while consuming the sports drink and the other half take the test while drinking water. for this study, what is the population?
The population in this study would be adolescent boys.
The researcher is interested in the effect of the electrolytic sports drink on the endurance of adolescent boys. The sample of 30 boys that are selected for the study is representative of the larger population of adolescent boys, and the results of the study will be generalized to this population. The study is designed to draw inferences about the population of adolescent boys based on the sample that is selected.
The population in this study would be adolescent boys.
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you ordered a 12 in pizza for a party of five for the pizza to be distributed evenly how should i be cut in triangular pieces
Answer: 2.4 inches per guest
Step-by-step explanation:
2.4 inches per guest
2.4 x 5 = 12
What value of c makes this equation true x/6 - 7 = -4
Answer:[tex]x = 18[/tex]
* also think you meant x instead of c*
Step-by-step explanation:
[tex]\frac{x}{6} - 7 = -4[/tex] --> +7 on both sides
[tex]\frac{x}{6} - 7 + 7 = -4 + 7[/tex]
[tex]\frac{x}{6} = 3[/tex] --> multiple by 6 by both sides
[tex]6 * \frac{x}{6} = 3 * 6[/tex] --> the 6 and the [tex]\frac{x}{6}[/tex] cancel out
[tex]x = 18[/tex]
