Solution
We are given
Distance = 5/2 miles
Time = 1/4 hours
Answer:
The speed would [tex]10~\text{mph}[/tex].
Step-by-step explanation:
Step 1: State the formulas required
The formula for speed is:
[tex]\text{Speed}=\frac{\text{Distance}}{\text{Time}}[/tex]
Step 2: Substitute the values into the formula
The distance is [tex]\frac{5}{2}~\text{miles}[/tex] and the time is [tex]\frac{1}{4}~\text{hours}[/tex].
Substitute these values into the formula:
[tex]\text{Speed}=\frac{\text{Distance}}{\text{Time}}\\\text{Speed}=\frac{\frac{5}{2}}{\frac{1}{4}}\\[/tex]
Step 3: Calculate
[tex]\text{Speed}=\frac{\frac{5}{2}}{\frac{1}{4}}\\\\\text{Speed}={\frac{5}{2}}\div {\frac{1}{4}}\\\\\text{Speed}={\frac{5}{2}}\times 4\\\\\text{Speed}={\frac{20}{2}}\\\\\text{Speed}=10[/tex]
So, the speed is [tex]10~\text{miles per hour}[/tex] or [tex]10~\text{mph}[/tex].
The longest side of a right angle triangle
is √46cm
One of the shorter sides has a length of
√7cm
What is the perimeter of the triangle?
Answer:
The exact answer would be:
[tex]\sqrt{39}[/tex] + [tex]\sqrt{7}[/tex] + [tex]\sqrt{46}[/tex] an approximate answer to the nearest whole number would be 7
Step-by-step explanation:
To find the missing side we would use the Pythagorean Theorem.
[tex]a^{2}[/tex] + [tex]b^{2}[/tex] =[tex]c^{2}[/tex]
[tex]\sqrt{7} ^{2}[/tex] + [tex]b^{2}[/tex] = [tex]\sqrt{46} ^{2}[/tex]
7 + [tex]b^{2}[/tex] = 46 Subtract 7 from both sides
[tex]b^{2}[/tex] = 39
[tex]\sqrt{b^{2} }[/tex] = [tex]\sqrt{39}[/tex]
b = [tex]\sqrt{39}[/tex]
The perimeter, the distance around the triangle, is [tex]\sqrt{39}[/tex] + [tex]\sqrt{7}[/tex] + [tex]\sqrt{46}[/tex]
1. 2 ² x 5b³
2. (3a²) ² x 2 (b ²) ³
3. 15d ³ divided by 3d ²
1. 2 ² x 5b³ = 20b³
2. (3a²) ² x 2 (b ²) ³ = 3[tex]a^{4}[/tex] x 2[tex]b^{6}[/tex] 5d
3. 15d ³ divided by 3d ² = 5d
What is Operations?
An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value. The operation's acuity is determined by the number of operands.
The given problems are:
1. 2 ² x 5b³
2. (3a²) ² x 2 (b ²) ³
3. 15d ³ divided by 3d ²
1. 2 ² x 5b³
= 4 x 5b³
= 20b³
2. (3a²) ² x 2 (b ²) ³
By the exponent rule:
[tex](x^{n} )^m[/tex] = [tex]x^{n * m}[/tex]
= [tex]x^{nm}[/tex]
∴ 3[tex]a^{2*2}[/tex] x 2[tex]b^{2*3}[/tex]
= 3[tex]a^{4}[/tex] x 2[tex]b^{6}[/tex]
3. 15d ³ divided by 3d ²
15d ³ ÷ 3d ²
By the exponent rule:
[tex]a^{m}[/tex]÷[tex]a^{n}[/tex] = [tex]a^{m-n}[/tex]
∴ 5[tex]d^{3-2}[/tex] = 5[tex]d^{1}[/tex]
= 5d
Hence, The solutions are 20b³, 3[tex]a^{4}[/tex] x 2[tex]b^{6}[/tex] and 5d
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When creating a graph, it is important to _____ the x and y axis?
"When creating a graph, it is important to assign the x and y axis."
Assigning the x and y axes is crucial when making a graph because the x-axis is referred to as the line on a Cartesian coordinate system that runs horizontally. A point or line's separation from the y-axis can be determined using the x-axis. The y-axis displays a point's location on a Cartesian plane in the y (vertical) direction. Additionally, it serves as the origin (zero) point for calculating how far a point is from the x-axis.
What is Graph?A graph is a structure that resembles a set of objects in mathematics, more specifically in graph theory, in which some pairs of the objects are conceptually "related." The objects are represented by mathematical abstractions known as vertices, and each pair of connected vertices is referred to as an edge.
What is x and y axis?Two parallel lines, known as axes (pronounced AX-eez), that are perpendicular to each other make up a coordinate grid. Typically, the term "x-axis" refers to the horizontal axis. The y-axis is the common name for the vertical axis. The origin is the location where the x- and y-axes intersect.
"When creating a graph, it is important to assign the x and y axis."
Because the x-axis is referred to as the line on a Cartesian coordinate system that runs horizontally, determining the x and y axes is essential when creating a graph. The x-axis can be used to calculate a point or line's distance from the y-axis. A point's position on a Cartesian plane is shown on the y-axis in the y (vertical) direction. It also acts as the origin (zero) point for determining a point's distance from the x-axis.
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Zahra and some friends are going to the movies. At the theater, they sell a bag of
popcorn for $3.50 and a drink for $5. How much would it cost if they bought 8 bags
of popcorn and 5 drinks? How much would it cost if they bought p bags of popcorn
and d drinks?
Total cost, 8 bags of popcorn and 5 drinks:
Total cost, p bags of popcorn and d drinks:
After performing some mathematical operations, we know that the total cost of 8 popcorn bags and 5 drinks is $53.
What are mathematical operations?An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value. The operation's arity is determined by the number of operands. The rules that specify the order in which we should solve an expression involving multiple operations are known as the order of operations. PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction (from left to right).So, the total cost:
1 bag of popcorn costs $3.50.1 drink costs $5.Cost of a total of 8 bags of popcorn and 5 drinks:
(8 × 3.50) + (5 × 5)28 + 25$53Therefore, after performing some mathematical operations, we know that the total cost of 8 popcorn bags and 5 drinks is $53.
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The correct question is given below:
Zahra and some friends are going to the movies. At the theater, they sell a bag of popcorn for $3.50 and a drink for $5. How much would it cost if they bought 8 bags of popcorn and 5 drinks?
A solution needs to contain between 46% glucose and 50% glucose. Find the least and greatest amount of a 60% glucose solution that should be mixed with a 40% glucose solution in order to
end up with 30 kilograms of a solution containing the allowable percentage of glucose.
Answer:
least: 9 kggreatest: 15 kgStep-by-step explanation:
You want the range of amounts of 60% solution that can be added to a 40% solution to achieve 30 kg of a solution that lies in the range of 46% to 50%.
SetupLet x represent the mass in kg of 60% solution added. The fraction of the total solution that is glucose will be ...
0.46 ≤ (0.60x +0.40(30 -x))/30 ≤ 0.50
SolutionMultiplying by 30 and simplifying the inequality, we have ...
13.8 ≤ 0.20x +12 ≤ 15
1.8 ≤ 0.2x ≤ 3 . . . . . . . . subtract 12
9 ≤ x ≤ 15 . . . . . . . . . . divide by 0.2
The least amount of 60% solution that should be added is 9 kg. The greatest amount is 15 kg.
__
Check
9 kg of 60% +21 kg of 40% has 5.4 +8.4 = 13.8 kg of glucose, the minimum.
15 kg of 60% +15 kg of 40% has 9 +6 = 15 kg of glucose, the maximum.
(The minimum and maximum values are seen in the solutions steps after the initial multiplication by 30.)
find the area of the polygon from the efigure give below
8. On a school basketball team, 13 out of 16 students are in Grade 8.
a) Write a proportion that you could use to calculate the percent of the students who are in Grade 8.
write each percent as a fraction in simplest form. 20%
Answer:
1/5
Step-by-step explanation:
"percent" means "per hundred"
(because cent means hundred like years in a century or cents in a dollar)
anyway
20% means
20 per 100
write it as 20/100
Now simplify it.
20/100
= 2/10
= 1/5
What would the transformation be for this figure and what does the transformation result in a figure that is congruent to the original?
Solution
Transform figure using the rule (x , y) = (-x , y - 8)
A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure. The original shape of the object is called the Pre-Image and the final shape and position of the object is the Image under the transformation.
[tex](x_1,y_1)-->(-x_1,y_1-8)[/tex]in how many ways can three pairs of siblings from different families be seated in two rows of three chairs, if siblings may not sit next to each other in the same row, and no child may sit directly in front of their sibling?
Three pairs of siblings from different families can be seated in two rows of three chairs so that siblings may not sit next to each other in the same row, and no child may sit directly in front of their sibling in 96 ways.
There are 3 pairs of siblings. We can name them as a₁, a₂, b₁, b₂, c₁ and c₂, a total of 6 children.
There are 2 rows of 3 seats each.
We will try to find the number of ways each seat can be filled.
So considering the first seat in first row, it can be filled in 6 different ways. Because any one from 6 children, say a₁, can be seated.
Now for the second seat in first row can only be filled by one of b₁, b₂, c₁ or c₂ because the first seated child a₁ along with the sibling a₂ of the same cannot be seated in the second seat. So in 4 different ways.
For the third seat remaining in the first row, one out of the remaining pair of siblings c₁ or c₂ can be seated. This can be done in 2 ways.
Now after filling the first row in this manner, the second row can be filled in only 2 ways.
So total number of ways the children can be seated = 6 x 4 x 2 x 2 = 96 ways
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The graph shows the printing rate of Printer A. Printer B can print at a rate of 25 pages per minute.
How does the rate for Printer B compare to the rate for Printer A? Use the drop-down menus to explain your answer.
The unit rate of Printer B = 25 pages per minute, which is greater than the unit rate of Printer A that is 15 pages per minute.
How to Find the Unit Rate of a Linear Graph?The unit rate of a graph can b determined by using any point, (x, y), on the graph and solve by finding, m, which is the ratio of y to x, if x and y represents the variables of the relationship that is graphed.
Thus, unit rate (m) = y/x.
The printing rate for Printer A is represented by the graph. To find the unit rate for Printer A, use a point on the graph, (2, 30) to find the unit rate, m.
Printer A's Unit rate (m) = y/x = 30/2
Printer A's unit rate (m) = 15 pages per minute.
The printing rate for Printer B is given as 25 pages per minute. 25 pages per minute is a greater unit rate compared to 15 pages per minute.
Therefore, we can conclude that Printer B has a greater printing rate than Printer A, because the unit rate of 25 pages per minute is greater than 15 pages per minute.
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A hotel housekeeper earns an hourly wage of $15 per hour. What is this wage in dollars per year? (Assume a 40-hour work week.)
Answer: $31,200 per year
Step-by-step explanation:
The question tells us that they are working 40 hours a week and making 15 dollars an hour. We can find out how much they make a week and then multiply by 52 (number of weeks in a year) to find the amount they make in a year.
Per week:
15 * 40 = $600
Per Year:
600 * 52 = $31,200
Answer:
$31,285.74 per year
Step-by-step explanation:
What we know:
- $15 per hour
- 40 hour weeks
- 52.1429 weeks per year
What we need to find out:
- How much money per year
Step 1: Multiply for how much made per week
We know that we need $15 dollars for 40 hours so we start with multiplying them together to see how much we make a year.
40 x 15 = $600 per week
Step 2: Now multiply the amount of weeks a year by the amount made per week
So now we know that we make $600 per week now we have to multiply the amount of weeks in a year by the money made per week so.
52.1429 x 600 = $31,285.74 per year. So the house keeper makes $31,285.74 per year.
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Which expression is equivalent to 2x ^ 2 - 2x + 7 ?
Answer:
(x² -5x +13) + (x² +3x -6)
Step-by-step explanation:
(x² -5x +13) + (x² +3x -6)
x² -5x +13 + x² +3x -6
|x² + x²| |-5x + 3x| |+13 -6|
2x² -2x +7
I need help with this math question all parts please
we have the function
[tex]P(t)=\frac{60(1+0.4t)}{0.01t+3}[/tex]Part A
For t=0
substitute
[tex]\begin{gathered} P(t)=\frac{60(1+0.4(0))}{0.01(0)+3} \\ \\ P(t)=\frac{60(1)}{3} \\ \\ P(t)=20 \end{gathered}[/tex]The initial population was 20 insectsPart B
For t=5 years -------> Convert to months
t=60 months
substitute
[tex]\begin{gathered} P(t)=\frac{60(1+0.4(60))}{0.01(60)+3} \\ \\ P(t)=\frac{60(1+24)}{0.6+3} \\ \\ P(t)=\frac{1500}{3.6} \\ \\ P(t)=416.67 \end{gathered}[/tex]The answer is 417 insectsPart C
Determine horizontal asymptote
[tex]\begin{gathered} P(t)=\frac{60\left(1+0.4t\right)}{0.01t+3} \\ \\ rewrite \\ P(t)=\frac{60+24t}{0.01t+3} \end{gathered}[/tex]The horizontal asymptote is given by the ratio of
[tex]\frac{24}{0.01}=2,400[/tex]P(t)=2,400 ---------> horizontal asymptote
that means
as the value of time t increases ------> the value of the population tends to 2,400 insects
the population cannot be greater than 2400 insects
The range for the function P(t) is the interval [20, 2400)
All real numbers greater than or equal to 20 insects and less than 2400 insects
Part D
Using a graphing tool
Estimate 70⎯⎯⎯⎯√3 to the nearest integer.
Answer:
Step-by-step explanation:
round up
√3 = √4
70-√4= 70-2
=68
F G Name a pair of overlapping congruent triangles in the diagram. State whether the triangles are congruent by SSS, SAS, ASA, AAS, or HL. I H AFHS AGHI by SAS. AFIH S AHGI by SAS. AFIH = AGHI by SSS AFIH AGHI by HL.
In the two triangles FIH and GHI
IH is a common side
FI = GH
[tex]m\angle I=m\angle H=90[/tex]The angles are between the equal sides
Then the two triangles are congruent by SAS postulate
The answer is A
A political gathering in south america was attended by 8475 people. each south americas 12 3 territories was equally repesented.how many representatives atteded from each country
We will use simple division to solve the problem. The number of representatives attended from each country is 706.
In the given question we know that a political gathering in South America was attended by 8475 people and each 12 territories of South America were equally represented. We need to find out how many representatives attended from each country. Inorder to find the number of representatives we can divide 8475 by 12.
number of representatives= 8475/12 =706
Therefore number of representatives from each country is 706.
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You deposit $400 in an account that earns 3. 5% interest compounded annually. What is the account balance after 2 years?
Account balance after 2 years $441.
Based on the given condition, here the details:
P = $400
r = 5 % = 0.05
n = 1
t = 2
Formulate and substitute all above:
F = P · (1 + [tex]\frac{r}{n}[/tex][tex])^{nt}[/tex]
F = 400. 1 + [tex]\frac{0.05}{1}[/tex])²
F = $441
From this as general, account balance is:
A checkbook, a savings account, or an investment account, for example, has a balance that shows how much money is available in the account. This is also called the current account value. The current value of account balances is shown by financial institutions on both paper statements and online tools.
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19. You have 15 pencils in your pencil case.1/5 of the pencils are green.
How many are not green?
Answer:
12
Step-by-step explanation:
You have 15 pencils in your pencil case.1/5 of the pencils are green. How many are not green?
= 1 - 1/5
= 5/5 - 1/5
= 4/5
This means that 4/5 of the 15 pencils are not green. So:
4/5 * 15 = 12 pencils are not green.
The amount of charge on a capacitor in an electric circuit decreases by 30% every second. Assume the original charge on the capacitor is
1
millicoulombs. A) What is the charge
0.06
seconds after that. B) Set up and solve the equation to find when the charge is
0.1
millicoulombs.
The amount of charge on the capacitor after 0.06 seconds = 0.042 millicoulombs
What is an electric circuit?An electric circuit is defined as the device that aids in transmission of electricity generated by a battery or a generator.
A capacitor is defined as the device that has the ability to store energy in an electric circuit.
The amount of charge in a capacitor decreases in one second by = 30%
The original charge on the capacitor = 1 millicoulombs
30 % of 1millicoulombs = 30/100 * 1 = 0.3
1millicoulombs - 0.3 millicoulombs = 0.7 millicoulombs .
If 0.7 millicoulombs = 1 second
X millicoulombs = 0.06 second
Make X millicoulombs the subject of formula;
X millicoulombs = 0.06 × 0.7 = 0.042 millicoulombs.
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Explain each step in the space provided below.
Answer:
1) multiply and divide by 2 on right hand side
2) multiply by 24 on both sides ( LHS and RHS)
3) divide by -1 on both sides so that negative sign on RHS will be cancelled
6/15=3/x.
I'm going insane
Answer:
x = 7.5
Step-by-step explanation:
[tex] \frac{6}{15} = \frac{3}{x} [/tex]
cross multiply expressions
6x = 45 divide both sides by 6
x = 7.5
In each of the following, describe the rate of change between the first pair and the second, assuming that the first coordinate is measured in minutes and the second coordinate is measured in feet. What are the units of your answer? (a) (2, 8) and (5, 17) (b) (3.4, 6.8) and (7.2, 8.7) (c) (3/2, - 3/4) and (1/4, 2)
The rate of change are:
a. 3 ft/min
b. 0.5 ft/min
c. -2.2 ft/min
How to Find the Rate of Change?The formula for finding the rate of change of a relationship is given as:
Rate of change = Change in y/change in x = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex].
a. (2, 8) = [tex](x_1, y_1)[/tex]
(5, 17) = [tex](x_2, y_2)[/tex]
Rate of change = (17 - 8)/(5 - 2)
Rate of change = 9/3
Rate of change = 3 ft/min
b. (3.4, 6.8) = [tex](x_1, y_1)[/tex]
(7.2, 8.7) = [tex](x_2, y_2)[/tex]
Rate of change = (8.7 - 6.8)/(7.2 - 3.4)
Rate of change = 1.9/3.8
Rate of change = 0.5 ft/min
c. (3/2, - 3/4) = [tex](x_2, y_2)[/tex]
(1/4, 2) = [tex](x_2, y_2)[/tex]
Rate of change = (2 - (-3/4))/(1/4 - 3/2)
Rate of change = 11/4 / -5/4
Rate of change = 11/4 × -4/5
Rate of change = -11/5 = -2.2 ft/min
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L
6
A savings account balance can be modeled by the graph of the linear function shown on the grid.
Balance (dollars)
450
400
350
300
250
200
150
100
50
y
Savings Account
0 1 2 3 4 5 6 7 8 9
Number of Deposits
X
What is the rate of change of the balance with respect to the number of deposits?
An algebraic expression known as a linear expression has terms that are either constants or variables raised to the first power. Alternatively put, none of the exponents can be greater than 1. As an illustration, while x is a variable raised to the first power, x2 is a variable raised to the second power. An illustration of a constant is 5.
Linear expression: what is it?The number of deposits will change at a 100 percent rate.
Given that, consider the image of the linear function's graph.
Currently, the graph's two points are (3, 350) and (2, 250).
Rate of change is therefore equal to (250 - 350) / (2 - 3)
= -100/-1
= 100.
The rate of change will therefore be 100 in relation to the number of deposits.
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Find the measures of the interior angles of the triangle.
The value of interior angle is 60.
What is triangle?
A triangle is a simple polygon with 3 sides and 3 interior angles. It is one of the basic shapes in geometry in which the 3 vertices are joined with each other and it is denoted by the symbol.
What is interior angle?
In a triangle, there are three interior angles at each vertex. The sum of those interior angles is always 180°. The bisectors of these angles meet at an point known as incenter. As the sum of interior angles of a triangle is 180°, there is only one possible right angle or obtuse angle possible in each triangle.
The sum of interior angle is 180
Given angles is 30, 90, x.
Therefore, sum is given by
90 + 30 + x = 180
120 + x = 180
x = 180-120
x = 60
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SOS PLEASE HELP QUICKLY WILL MARK BRAINLYIST
Submit a picture of your work to the assignment page:
its a two column proof
Prove: If two parallel lines are cut by a transversal then the alternate exterior angles are congruent. Do not use the alternate exterior angles theorem. Use a diagram and the corresponding angles theorem.
Proved that if two parallel lines are cut by a transversal then the alternate exterior angles are congruent.
What is the Exterior Angle of a Triangle Property?An exterior angle of a triangle is equal to the sum of the opposite interior angles.
By the property of alternate interior angles;
From the figure attached;
∠XWY ≅ ∠ZYW
The Property of the alternate angles states that if two parallel lines are cut by a transversal, then the alternate angles are congruent.
Here, ∠XWY and ∠ZYW shows the interior angles between the parallel lines and the transversal.
The interior alternate angles ∠XWY and ∠ZYW will be congruent.
Hence, Proved that if two parallel lines are cut by a transversal then the alternate exterior angles are congruent.
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Please explain how you get the answer
The measure of the angle is calculated using the attached figure.
What is an angle?
An angle is a figure in Euclidean geometry created by two rays, called the sides of the angle, that share a common termination, called the vertex of the angle. Angles created by two rays are located in the plane containing the rays. Angles are also generated when two planes intersect. These are known as dihedral angles. An angle defined by two intersecting curves is the angle of the rays lying tangent to the respective curves at their point of junction. Angle can also refer to the measurement of an angle or of a rotation. This measurement is the length of a circular arc divided by its radius. The arc is centered at the vertex in the case of a geometric angle.
From figure,
angle x = 180° - 110° = 70° (linear pair)
angle y = 37° (alternate interior angles)
Measure of angle 1 = 70° + 37° (exterior angle in a triangle is equal to the sum of opposite interior angles)
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This data can best be modeled withwhich type of function?ху018,250118,730a. Linearb. QuadraticC. Exponential219,210319,690420,170
A linear function is a function in which we add multiple of a constant.
Given data:
We have
[tex]\begin{gathered} y=18,250+480(1)\text{ at x=0} \\ y=18,730=18,250+480(1)\text{ at x=1} \\ y=19,210=18,250+480(2)\text{ at x=2} \\ y=19,690=18,250+480(3)\text{ at x=3} \\ y=20,170=18,250+480(4)\text{ at x=4} \end{gathered}[/tex]Clearly, we have add multiples of 480 to 18,250.
So, the given function represents a linear function.
So, the correct option is (a).
Which expression is equivalent to 3 x − 2 − 5 2 − 4 x − 2 ? 2x-8/13-5x -5x-8/2x-8 -5x-4/x-2 13-5x/2x-8
The equivalent expression of the expression given as [tex]\frac{\frac{3}{x - 2} - 5}{2 - \frac{4}{x - 2}}[/tex] is (13 - 5x)/(2x - 8)
How to determine the equivalent expression?From the question, the expression is given as
[tex]\frac{\frac{3}{x - 2} - 5}{2 - \frac{4}{x - 2}}[/tex]
Take the LCM of the fractions in the above expression
So, we have
[tex]\frac{\frac{3 - 5x + 10}{x - 2}}{\frac{2x - 4 - 4}{x - 2}}[/tex]
Evaluate the like terms of the expressions
So, we have
[tex]\frac{\frac{13 - 5x}{x - 2}}{\frac{2x - 8}{x - 2}}[/tex]
Divide the common factor x -2 in the expression
So, we have
[tex]\frac{13 - 5x}{2x - 8}[/tex]
Rewrite as
(13 - 5x)/(2x - 8)
The expression cannot be further simplified
Hence, the solution is (13 - 5x)/(2x - 8)
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-3x – 10 = 32Help me I need the answer
Answer:
x = - 14
Step-by-step explanation:
-3x – 10 = 32 Help me I need the answer
-3x – 10 = 32
-3x = 32 + 10
-3x = 42
x = 42 :(-3)
x = - 14
-----------------
check
-3 × (-14) - 10 = 32 (remember pemdas)
42 - 10 = 32
32 = 32
the answer is good