Why is it important to learn, in algebra, the proper order in which to read algebraic expressions and solve algebraic equations?
Learning the proper order in which to read algebraic expressions and solve algebraic equations is important in algebra for understanding the order of operations, developing logical reasoning, and ensuring consistency in mathematical communication.
Explanation:It is important to learn the proper order in which to read algebraic expressions and solve algebraic equations in algebra for several reasons:
Order of operations: Understanding the order of operations (PEMDAS) is crucial to correctly evaluating algebraic expressions. This ensures that the operations are performed in the correct order and leads to the correct result. For example, without following the order of operations, the expression 8 + 2 x 3 could be evaluated as 10 x 3 = 30 instead of 8 + 6 = 14.Logical reasoning: Solving algebraic equations requires logical reasoning and following a step-by-step process. Learning the proper order helps develop this logical reasoning and helps students approach problems systematically. It allows them to break down complex problems into simpler steps and solve them more efficiently.Consistency and communication: Following the proper order in algebra ensures consistency in mathematical communication. It allows students and mathematicians to communicate their solutions and reasoning effectively. When everyone understands and follows the same order, they can accurately communicate and discuss algebraic expressions and equations.what is 0.83 repeating as a fraction?
A total of 376 tickets were sold for the school play. they were either adult tickets or student tickets. the number of student tickets sold was three times the number of adult tickets sold. how many adult tickets were sold?
Final answer:
Using algebra, we set up equations based on the information given: the number of student tickets is three times the number of adult tickets, and the total number of tickets is 376. Solving for the number of adult tickets, we find that 94 adult tickets were sold.
Explanation:
The question asks us to figure out how many adult tickets were sold for the school play when a total of 376 tickets were sold, and student tickets sold were three times the number of adult tickets.
Let's denote the number of adult tickets sold as A and the number of student tickets sold as S. According to the problem, S = 3A. We are also told that the total number of tickets sold is 376, so A + S = 376.
Substituting the first equation into the second one, we get A + 3A = 376. Simplifying this equation, 4A = 376. Dividing both sides by 4, A = 94. Therefore, 94 adult tickets were sold.
Final answer:
As per the values, 94 adult tickets were sold.
Explanation:
The question asks us to determine how many adult tickets were sold for a school play, given a total number of tickets and a ratio of student tickets to adult tickets.
To solve this problem, let's define adult tickets as x and student tickets as 3x, since there are three times as many student tickets as adult tickets.
The total tickets sold is 376, therefore the equation we need to solve is:
x + 3x = 376
Combining like terms, we get:
4x = 376
Dividing both sides by 4, we find that:
x = 94
Therefore, 94 adult tickets were sold.
A classmate claims that having no slope and having a slope of 0 are the same. Is your classmate correct? Explain. ...?
Vicki works 19 hours per week. Her take home pay is $17.30 per hour. If Vicki is able to save all of her earnings, how long will it take her to save at least $4,000?
a.
12 weeks
b.
13 weeks
c.
14 weeks
d.
15 weeks
Answer: B
Step-by-step explanation:
on edg
The axis of symmetry for a quadratic equation can be found using the formula x = -b/2a , where a and b are coefficients in the quadratic equation and x represents the values along a vertical line on the coordinate plane.
When the equation is solved for a, such that b is the numerator of the resulting fraction, what is the denominator of the fraction?
2x
–2x
1/2x
–1/2x
The denominator of the fraction is -2x.
The correct answer is option (b)
What is equation?"It is a mathematical statement which consists of equal symbol between two algebraic expressions."
What is numerator?"In a fraction, the value placed above the horizontal line."
What is denominator?"In a fraction, the value placed below the horizontal line."
For given question,
The axis of symmetry for a quadratic equation can be found using the formula [tex]x=-\frac{b}{2a}[/tex]
where a and b are coefficients in the quadratic equation and x represents the values along a vertical line on the coordinate plane.
[tex]\Rightarrow x=\frac{-b}{2a}\\\\ \Rightarrow \frac{a}{x} \times x=\frac{-b}{2a}\times \frac{a}{x}\\\\\Rightarrow a=\frac{b}{-2x}[/tex]
For the fraction [tex]\frac{b}{-2x}[/tex] the numerator is b and denominator is -2x.
Therefore, the denominator of the fraction is -2x.
The correct answer is option (b)
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A stemplot is one way to display these batting averages, as shown below. In this type of display, the entry 0.32|9 denotes one occurrence of the batting average _____.
0.32 | 9
0.33 | 0 1 1 3 3 3 4 4 4 6 7 8 8 8
0.34 | 0 0 1 1 2 2 2 4 4 5 6 9
0.35 | 6 8
0.36 | 6 ...?
Answer:
0.356
Step-by-step explanation:
Based on the batting averages denoted in the stemplot, the entry of 0.32|9 shows an occurrence of 0.329.
What average is shown by 0.32|9?In a stemplot, the numbers that are stems are on the left side and will be the first numbers that should be denoted.
The numbers on the right are leaf numbers and come after the stem. This means that a stemplot showing 0.32|9 is a way of writing 0.329.
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a golf ball travels a distance of 600 feet as measured along the ground and reaches an altitude of 200 feet. If the origin represents the tee and the ball travels along a parabolic path that opens downward, find an equation for the path of the golf ball.
...?
Answer:
y=1.32x-0.0022[tex]x^{2}[/tex]
Step-by-step explanation:
Let the standard equation of parabola be y=a[tex]x^{2}[/tex]+bx+c ....... (1)
Let y be the altitude of the ball and x be the distance traveled by the ball.
Now by putting the points one by one, we get the required equation.
first point = (0,0)
golf ball travels a distance of 600 feet along the ground. Therefore point = (600,0)
At altitude of 200, it travels the distance of 300 feet(mid point) = (300,200)
By putting y=0 and x=0 in (1),
we get c=0,
By putting y=0 and x=600 we get
0 = 360000a+600b ..............(2)
By putting y=200 and x=300, we get
200=90000a+300b ................(3)
Solving (2) and(3) we get, a=-0.0022 and b = 1.32
So the required equation is :
y= =0.0022[tex]x^{2}[/tex]+1.32x
Brandon is on one side of a river that is 50 m wide and wants to reach a point 300 m downstream on the opposite side as quickly as possible by swimming diagonally across the river and then running the rest of the way. find the minimum amount of time if brandon can swim at 2 m/s and run at 5 m/s
Brandon can reach a point 300m downstream on the opposite side of the river in a minimum of 60 seconds by swimming diagonally across the river and then running the rest of the way.
Explanation:In order to determine the minimum amount of time for Brandon to reach a point 300m downstream on the opposite side of a river, we can use the concept of relative velocities.
First, we need to find the velocity of the current. We can use the formula v = d/t, where v is the velocity, d is the distance, and t is the time.
The distance Brandon needs to cross the river is 50m, and he wants to reach a point 300m downstream, so the total distance he needs to travel horizontally is 50m + 300m = 350m.
Since the current is perpendicular to Brandon's swimming direction, it doesn't affect the time it takes for him to swim across the river. Therefore, we only need to consider his running speed.
The time it takes for Brandon to run the remaining distance of 300m is equal to the distance divided by his running speed, which is 300m / 5m/s = 60s.
So, the minimum amount of time for Brandon to reach the point 300m downstream is 60 seconds.
To find the minimum amount of time for Brandon to reach the point across the river, divide the problem into two components: swimming and running. Use the Pythagorean theorem to find the resultant velocity of Brandon's swimming motion. To find the total minimum time, add the swimming time and the running time.
Explanation:To find the minimum amount of time for Brandon to reach the point across the river, we can use the concept of vector addition. Since the river is flowing downstream, Brandon needs to swim at an angle with respect to the direction of the river current. Let's break down the problem into two components: swimming and running.
Swimming:
Using the Pythagorean theorem, we can find the resultant velocity of Brandon's swimming motion. The width of the river is the base, the downstream distance is the height, and the resultant velocity is the hypotenuse. By substituting the given values, we can find the resultant velocity of Brandon's swimming motion as 5.12 m/s. This is the velocity he will need to swim at an angle to counteract the river current.
Running:
After crossing the river, Brandon needs to run the remaining distance of 300 m at a speed of 5 m/s. The time it takes to run this distance is 300 m / 5 m/s = 60 seconds.
To find the time it takes for Brandon to swim across the river, we can use the formula:
time = distance / velocity
. The distance is 50 m, and the velocity is 5.12 m/s. Therefore, the time it takes for Brandon to swim across the river is 50 m / 5.12 m/s = 9.77 seconds.
Finally, we can add the swimming time and the running time to find the total minimum time it takes for Brandon to reach the point across the river: 9.77 seconds + 60 seconds = 69.77 seconds.
where is the opposite of 8 located on a number line?
A company has started selling a new type of smartphone at the price of $120 - 0.1x where x is the number of smartphones manufactured per day. The parts for each smartphone cost $60 and the labor and overhead for running the plant cost $4000 per day. How many smartphones should the company manufacture and sell per day to maximize profit?
To maximize profit, derive the profit equation ((120 - 0.1x) * x - (60x + 4000)) and set it to zero to find the critical points. These points will dictate the number of smartphones the company needs to manufacture and sell each day.
Explanation:The subject of this question is the maximization of profit, which is a concept in economic mathematics. To maximize the profit, you'll need to determine the number of smartphones that the company should produce and sell each day.
The profit is the revenue (the money earned from selling goods) minus the costs. Revenue is given by the equation R = (120 - 0.1x) * x, and the total cost is given by the equation C = 60x + 4000, where x is the number of smartphones produced.
So, the profit P becomes P = R - C = (120 - 0.1x) * x - (60x + 4000). To maximize this profit, we'd take the derivative of P in terms of x and set it equal to zero to find the critical points. After finding the critical points, we then test these values back in the profit equation to find which gives the highest value and hence maximizes the profit.
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Solve for x: –4(3x – 2) = 6x + 2
A.
2003-05-01-00-00_files/i0050000.jpg
B.
2003-05-01-00-00_files/i0050001.jpg
C.
2003-05-01-00-00_files/i0050002.jpg
D.
2003-05-01-00-00_files/i0050003.jpg
Hence, the value of x is:
[tex]x=\dfrac{1}{3}[/tex]
Step-by-step explanation:We have to solve for x i..e we have to find the value of 'x' by solving this equation.
The equation is given as:
[tex]-4(3x-2)=6x+2[/tex]
firstly we will solve the bracket term as:
[tex]-4\times 3x-4\times (-2)=6x+2\\\\-12x+8=6x+2[/tex]
Now we take like terms together i..e the variable term is taken to the right hand side of the equation and the constant term is kept on the left side of the equation as:
[tex]8-2=6x+12x\\\\\\6=18x[/tex]
on dividing both side of the equation by 18, we obtain:
[tex]x=\dfrac{6}{18}\\\\x=\dfrac{1}{3}[/tex]
Hence, the value of x is:
[tex]x=\dfrac{1}{3}[/tex]
Answer:
B
Step-by-step explanation:
How to write a real-world situation that could be modeled by the equation 3 2/3x=5/6x-7/8?
A real-world situation that can be modeled by the equation 3 2/3x = 5/6x - 7/8 is when you have a certain amount of money, and you are earning money at a certain rate while also incurring expenses.
Explanation:To write a real-world situation that could be modeled by the equation 3 2/3x=5/6x-7/8, let's consider a scenario where you have $3.67, and you are earning additional money at a rate of $0.833 per hour. On the other hand, you have expenses of $0.875 per hour. We can represent the money you have earned and the money you have spent using the equation 3 2/3x=5/6x-7/8.
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To write a real-world situation that could be modeled by the equation 3 2/3x=5/6x-7/8, we can consider a scenario where a store is selling two different types of products and the equation represents the difference in the number of sales for the two products.
Explanation:To write a real-world situation that could be modeled by the equation 3 2/3x=5/6x-7/8, we need to think about a scenario where two quantities are being compared or related. For example, let's consider a situation where a store is selling two different types of products. The equation could represent the difference in the number of sales for the two products over a certain period of time. The left side of the equation represents the number of sales for one product, and the right side represents the number of sales for the other product, with a difference of 7/8 units.
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A small business purchases a
piece of equipment for $875. After 5 years the equipment will be outdated, having no value.
(a) Write a linear equation giving the value of the equipment y in terms of the time
(b) Find the value of the equipment when X=2
(c) Estimate (to two-decimal-place accuracy) the time when the value of the equipment is $200. ...?
Using the straight-line depreciation method, the linear equation for the equipment's value over time is y = -175t + 875. After 2 years, the equipment's value is $525. To find when the equipment's value is $200, solve for t and get approximately 3.86 years.
To calculate the depreciation of the equipment using a linear equation, we'll use the straight-line depreciation method. The business purchases the equipment for $875 and it will be worthless after 5 years, so it depreciates $875 over 5 years.
Part A
To write the linear equation representing the value of the equipment y over time t, we need to find the slope (m) of the line which in this case is the annual depreciation. The slope is the change in value divided by the time, thus m = -$175/year. The initial value (intercept) is $875. The equation is:
y = -175t + 875
Part B
Substitute t = 2 into the equation to find the value of the equipment at year 2:
y = -175(2) + 875
y = -350 + 875
y = $525
Part C
We want to find the time t when the value y is $200. Substitute y = $200 into the equation:
200 = -175t + 875
-175t = 200 - 875
-175t = -675
t = [tex]\frac{-675}{-175}[/tex]
James made a deposit in a savings account 5 years ago. The account pays 4% simple annual interest. Since then, he has earned $120 in interest. What is the current balance in his account?
A. $200
B. $600
C. $720
D. $780
Answer:
720 is correct
solve the exponential equation using the method of relating the bases by first rewriting the equation in the form of e^u=e^v
1/e ^6x =√e ÷e ^6−x ...?
y<=x-5, and y<=-x-4 would be points (1,10)? or
(-1,10)
(10,1)
1,-10)
at how many points does the graph of the function y=16x^2-8x+1 intersect the x axis
Answer:aAPEX1
Step-by-step explanation:
General admission tickets to the fair cost 3.50 per person. Ride passes cost an additional 5.50 per person. Parking costs 6 dollars for the family. the total costs for ride passes and parking was 51 dollars. How many people in the family attend the fair
A water cooler can hold 50 pt of water. About how many liters of water can it hold? (1 L ≈ 1.06 qt)
23.6 L 26.5 L 94.3 L 106.0 L
Find y when x equals 10 if y equals eight what x equals 20
Which of the following has a graph that is a straight line?
Equation 1: y = 4x^3 + 6
Equation 2: y = 5x − 4.5
Equation 3: y^2 = x − 1
Equation 4: y = 2x^2 + 6
Answer:
y=5x - 4.5
Step-by-step explanation:
I took the test
what is the value of the expression 10 C 6? A.210 B.720 C.5040 D.151,200
Answer: A. 210
Step-by-step explanation:
We know that the number of combinations of n things taking r at time is given by expression :-
[tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex] (1)
The given expression : [tex]^{10}C_{6}[/tex] which basically gives the number of combinations of 10 things taking 6 at a time.
Using (1) , we have
[tex]^{10}C_{6}=\dfrac{10!}{6!(10-6)!}\\\\=\dfrac{10\times9\times8\times7\times6!}{6!4!}\\\\=\dfrac{10\times9\times8\times7}{4!}\ \ [\text{Cancel }6!\text{ from numerator and denominator}]\\\\=\dfrac{10\times9\times8\times7}{4\times3\times2\times1}\\\\=210[/tex]
Hence, the correct answer is A. 210 .
a table that originally cost $196 is on sale for $160.00. What is the percent of decrease, rounded to the nearest tenth?
A cable 20 feet long connects the top of a flagpole to a point on the ground that is 16 feet from the base of the pole. How tall is the flagpole?
The height of the flagpole is 12 feet.
To determine the height of the flagpole, we can use the Pythagorean theorem.
Given: The length of the cable (hypotenuse) is 20 feet.The distance from the point on the ground to the base of the flagpole (one leg) is 16 feet.Let the height of the flagpole be h (the other leg).Using the Pythagorean theorem:
c² = a² + b²
Here, c = 20 feet (length of cable), a = 16 feet (distance from flagpole base to ground point), and h = b (height of the flagpole).
Therefore, we have:
202 = 162 + h²
400 = 256 + h²
To find h, subtract 256 from 400:
400 - 256 = h²
144 = h²
h = √144 = 12.
The graph of f(x) = 6(0.25)x and its reflection across the y-axis, g(x), are shown.
What is the domain of g(x)?
all real numbers
all real numbers less than 0
all real numbers greater than 0
all real numbers greater than or equal to 0
The correct answer is the first option: All real numbers.
I just did the quiz and got it right.
For all the non BrainlyPlus members
The shop charges $60 per hour and 7% sales tax on parts (no tax on labor). The total cost of the repair is $180.80. A. True B. False The statement is False.
If a right circular cone intersects a plane that passes through one of its nappes but the plane is not parallel to an edge of the cone the resulting curve will be:
parabola
circle
ellipse
hyperbola
Answer:
D) Hyperbola.
Step-by-step explanation:
If a right circular cone intersects a plane that passes through one of its nappes, but the plane is not parallel to an edge of the cone, the resulting curve will be one arc of a hyperbola.
Therefore, the answer is Hyperpola.
Hope this will helpful.
Thank you.
Round 7.832 to the nearest tenth
How do you find the reciprocal of 3.6?? ...?
To find the reciprocal of 3.6, divide 1 by 3.6.
Explanation:To find the reciprocal of 3.6, you divide 1 by 3.6. The reciprocal of a number is obtained by flipping the number. So, the reciprocal of 3.6 is
1/3.6
or approximately 0.2778.