The solution to the first algebraic equation is x = 7, and the solution to the second equation is x = -3. Both problems involve setting up and solving algebraic equations to find the value of the unknown number.
To solve the problems stated, we need to set up algebraic equations and solve for the unknown number x.
For the first one:
Fourteen less than five times a number is three times the number: 5x - 14 = 3x.
After simplifying, we get 2x = 14.
Divide both sides by 2 to find x = 7.
For the second one:
Twelve more than seven times a number equals the number less six: 7x + 12 = x - 6.
Rearrange to find 6x = -18.
Divide both sides by 6 to find x = -3.
We have found that the unknown number in the first equation is 7 and in the second equation, it is -3.
Fatima is shading this model to show 0.08x3 . shade the correct amount of boxes that will show the product
Shade 0.08 3 times
In total that's 24 hundreths to shade
all im doing is trying to get points Lol
A cone has a radius of five feet and a height of 18 feet. If the radius of the cone is tripled but the volume but the volume remains unchanged, what will be the new height of the cone
If 8 times a number is decreased by 20,the result is the same as 3 times the number increased by 80
Final answer:
The algebraic expression for the problem is '8n - 20 = 3n + 80', which simplifies to 'n = 20'. Therefore, the number in question is 20.
Explanation:
The question presents a classic algebra problem where we have to find the value of a variable that satisfies a given condition. Specifically, this problem states:
"If 8 times a number is decreased by 20, the result is the same as 3 times the number increased by 80."
To solve this, we'll convert the words into an algebraic equation and solve for the number. Let's use 'n' to represent the number:
8n - 20 = 3n + 80This equation tells us that when you multiply the number by 8 and subtract 20, it's equal to the result of multiplying the number by 3 and adding 80. To find 'n', we combine like terms and solve:
8n - 3n = 80 + 205n = 100n = 100 / 5n = 20Thus, the number we're looking for is 20.
A wedge is cut out of a circular cylinder of radius 10 by two planes. one plane is perpendicular to the axis of the cylinder. the other intersects the first at an angle of 30° along a diameter of the cylinder. find the volume v of the wedge, taking rectangular cross-sections to be parallel to the line of intersection of the two planes, which is the x-axis. (let r = 10.)
The volume of the wedge is 50π/3 - 25√3.
Explanation:To find the volume of the wedge, we need to calculate the volume of the cylindrical segment between the two intersecting planes. The formula for the volume of a cylindrical segment is V = h((R^2θ)/2 - (R^2sinθ)/2), where h is the height of the segment, R is the radius of the cylinder, and θ is the angle of the intersection between the planes. In this case, h is 10 and θ is 30°, so the formula becomes V = 10((10^2 * π/6)/2 - (10^2 * sin(π/6))/2). Simplifying the equation gives V = 50π/3 - 25√3.
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Solve each system. Then drag each one to the column headed by a point which could be its solution. (5,y) or (x,2)
2x-2y=12
-2x-3y=-22
2x-6y=10
x+8y=5
3x-y=-5
x+4y=7
x+y=2
2x+y=13
Answer: system 2 (5,0) and system 3 (-1 2)
2x-6y=10 3x-y=-5
x+8y=5 x+4y=7
Step-by-step explanation:
Solve each system. Then drag each one to the column headed by a point which could be its solution. (5,y) or (x,2)
system 1
2x - 2y =12
-2x-3y = -22
solve simultaneous equation
2x - 2y =12
-2x-3y = -22
add the equations gives
2x +(-2x) =0
-2y+(-3y) =-5y
12+ (-22) = -10
-5y =-10
y =2
2x -2(2) =12
2x-4 =12
2x = 12+4
x= 16/2 =8 x=8 and y =2 = (8,2)
system 2
2x-6y=10 *(-1) = -2x + 6y =-10
x+8y=5 *(2) = 2x + 16y =10 add the equations
22y =0 y =0
x : 2x - 6(0) =10
x = 10/2 = 5
(5, 0)
system 3
3x-y=-5 *(-1) = -3x + y =5
x+4y=7 * (3) = 3x + 12y = 21
add the equations = 13y = 26 y = 2
3x -2 =-5 = 3x = -3 =x =-1
(-1 2) answer
system 4
x+y=2 *(-2) = -2x -2y = -4
2x+y=13 *(1) = 2x +y = 13
add the two equations = -y =9
y = -9
substitute 2x-9= 13= 2x =22 x =11
(11 -9)
The only solution of the equation x^2 +bc+16=0 is x=4 why is the value of b
Al drives from Boston to Washington D.C. and then returns. On his trip to Washington, he travels 60 miles per hour. On his return trip, he travels 50 miles per hour. His trip to Boston takes an hour and a half longer than his trip to Washington. How far apart are Washington and Boston? Make a equation
The distance apart from Washington and Boston is 450 miles.
What is speed?Speed is the ratio of distance and time.
It shows how fast an object is moving at a given time.
We have,
Trip from Boston to Washington:
Speed (2) = 60 miles per hour
Trip from Washington to Boston:
Speed (1) = 50 miles per hour
Speed = Distance / Time
Time = Distance / Speed
Distance is the same for both trips.
Time taken for the trip from Washington to Boston = t(1)
Time taken for the trip from Boston to Washington = t(2)
His trip to Boston takes an hour and a half longer than his trip to Washington.
This can be written as,
t(1) - t(2) = 1.5 hours
Distance ( 1/50 - 1/60) = 1.5
Distance ( (6 - 5)/300 ) = 1.5
Distance (1 / 300) = 1.5
Distance = 1.5 x 300
Distance = 450 miles
Thus,
The distance apart from Washington and Boston is 450 miles.
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Two people start from the same point and move in opposite directions. The
first person jogs west traveling 5 mph, and the second person walks east
traveling 3 mph. In how many hours will the two people be 48 miles apart?
Which graph represents the solution set for the system 6x + y > -3 and 2x + y ≤ 4?
A. graph A
B. graph B
C. graph C
D. graph D
Answer:
Option B. Graph B
Step-by-step explanation:
The given system of the inequalities are 6x + y > -3 and 2x + y ≤ 4
If we take the first inequality which represents the area below the line 6x + y = -3 or y = -6x - 3 (Slope of the line -6 and y-intercept is -3)
Second graph is represented by 2x + y ≤ 4 which represents the area below the line y = 4 - 2x ( slope = -2 and y intercept = 4)
Option B shows the shaded area which the common area representing the solution set of these systems.
A cooking group made 240 oz of spaghetti sauce to sell at a county fair. The group can pour the sauce into small jars that hold 8 oz and large jars that hold 16 oz. The group leader made a sketch to show the line representing the different combinations of jar sizes the group can use. The x-axis represented the number of small jars and the y-axis represented the number of large jars. The group leader labeled only the intercepts.
Which points did the group leader label?
(0, 8) and (16, 0)
(0, 30) and (15, 0)
(0, 15) and (30, 0)
(0, 16) and (8, 0)
the correlation coefficient (r) between the number of hours worked x and the amount of money earned y is 0.456 what percent of the variation in the amount of money earned can be explained by differences in the number of hours worked
A :79.2%
B:54.4%
C:45.6%
D:20.8%
If f(x) = x 2 + 1 and g(x) = 3x + 1, find 2f(1) + 3g(4).
1. 45
2. 43
3. 42
A drama club wants to raise at least $500 in tickets sales for its annual show. The members of the club sold 50 tickets at a special $5 rate. The usual ticket price the day of the show is $7.50. At least how many tickets do they have to sell the day of the show to meet the goal. Let t=tickets
To meet their fundraising goal, the drama club needs to sell 34 tickets at $7.50 each.
Answer:
The drama club wants to raise at least $500 in ticket sales. They already sold 50 tickets at $5 each. Let the number of tickets they need to sell at $7.50 be represented by 't'.
Revenue from $5 tickets: $5 × 50 = $250To find the number of $7.50 tickets needed: $500 - $250 = $250Number of $7.50 tickets needed: $250 / $7.50 = 33.33Therefore, the drama club needs to sell at least 34 tickets at $7.50 each to meet their goal.
How to find the length and width of a rectangle when given the area and perimeter?
Sammy has a 10-foot ladder, which he needs to climb to reach the roof of his house. the roof is 12 feet above the ground.
Arithmetic sequence find the next next term in the sequence 44, 51, 58, 65
Hii!
_________________________________________________________
[tex]\rightsquigarrow\circ\boldsymbol{Answer}\circ\leftharpoonup[/tex]
72
[tex]\rightsquigarrow\circ\boldsymbol{Explanation.}\circ\leftharpoonup[/tex]
To find the next term in the arithmetic sequence, we should first find the common difference.
The common difference is the amount we add or subtract to obtain the next term. In the given sequence we add 7.
So, let's find the next term.
[tex]\twoheadrightarrow\sf65+7[/tex]
[tex]\bullet[/tex] Add 7
[tex]\twoheadrightarrow\sf72[/tex]
[tex]\bullet[/tex] Great job! We found the next term
--
Hope that this helped! Best wishes.
[tex]\textsl{Reach far. Aim high. Dream big.}\\\boldsymbol{-Greetings!-}[/tex]
--
What is the standard form of the equation of a parabola that opens left or right
Answer:
The equation of the parabola which opens left or right is [tex]x=ay^2+by+c[/tex].
Step-by-step explanation:
We know that,
If in the equation of the parabola,
1. If x is squared, then the parabola opens upwards or downwards.
2. If y is squared, then the parabola opens towards left or right.
Since, we want the equation of the parabola which opens left or right.
So, we get that,
The variable 'y' is being squared in the equation of the given parabola (from 1).
Thus, the equation of the parabola which opens left or right is [tex]x=ay^2+by+c[/tex].Answer:
x = ay^2 + by + c
Step-by-step explanation:
it was correct for me
What are the solutions of the inequality? -2(3x + 2) greater than or equal to -6x - 4
By definition a simple random sample of size n is any sample
A small publishing company is planning to publish a new book. The production costs will include one-time fixed costs (such as editing) and variable costs (such as printing). There are two production methods it could use. With one method, the one-time fixed costs will total $18,853 , and the variable costs will be $19.75 per book. With the other method, the one-time fixed costs will total $64,853 , and the variable costs will be $8.25 per book. For how many books produced will the costs from the two methods be the same?
A train leaves a train station at 1 p.m. it travels at an average rate of 60 mi/hr. a high-speed train leaves the same station an hour later. it travels at an average rate of 96 mi/hr. the second train follows the same route as the first train on a track parallel to the first. in how many hours will the second train catch up with the first train?
The second train will catch up with the first train after 5/3 hours.
What is Equation Modelling?
Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
Given is a train that leaves a train station at 1 p.m. it travels at an average rate of 60 mi/hr. A high-speed train leaves the same station an hour later. it travels at an average rate of 96 mi/hr. The second train follows the same route as the first train on a track parallel to the first.
We have -
Assume that the second train catches the first in x hours. Then, we can write -
60(x + 1) = 96x
60x + 60 = 96x
96x - 60x = 60
36x = 60
x = 60/36
x = 5/3 hours
Therefore, the second train will catch up with the first train after 5/3 hours.
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Help me please thanks
What's the probability of getting an even number and a head when rolling a die and then tossing a coin?
Answer: 1/4
Step-by-step explanation:
What is the slope below
Simplify 6 - 4[x + 1 - (y + 3)] + 5y.
Which is the line shown in the figure?
line XY
line XZ
line WX
line WZ
Option B is the correct answer.
We need to check which is the line shown in the figure.
What is a line?In geometry, a line is an infinitely long object with no width, depth, or curvature. Thus, lines are one-dimensional objects, though they may exist in two, three, or higher-dimension spaces. The word line may also refer to a line segment in everyday life, which have two points to denote its ends.
Now, from the given figure we can see XZ is a line.
Therefore, option B is the correct answer.
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The number of years that Brad has been on the soccer team is 2 less than five times a number of years Scott has in total the boys have been on the soccer team for about 10 years how long has Brad been on the soccer team
What value of n would make point A the circumcenter?
1. 2
2. 3
3. 4
4. 5
Answer:
The correct option is 2. The value of n is 3.
Step-by-step explanation:
Circumcenter is the point, where the perpendicular bisectors of a triangle intersect each other.
Circumcenter is also known as the center of the triangle. The distance from circumcenter to each vertex are same.
In triangle DEF, if A is the circumcenter.
[tex]AE=AD[/tex]
[tex]10=2n+4[/tex]
Subtract 4 from both sides.
[tex]10-4=2n[/tex]
[tex]6=2n[/tex]
Divide both sides by 2.
[tex]3=n[/tex]
Therefore the value of n is 3 and option 2 is correct.
Answer:
Option 2 is true
Step-by-step explanation:
We have to find the value of n for which point A becomes circumcenter.
Circumcenter: It is that point where perpendicular bisectors of triangle intersects.
The circumcenter is also knows as center of triangle.
Circumcenter is at equal distance from each vertex of triangle.
If point A is circumcenter then
AE=AD
We have AE=10 units
AD=2n+4
Substitute the value
10=2n+4
[tex]2n=10-4[/tex]
By subtraction property of equality
[tex]2n=6[/tex]
[tex]n=\frac{6}{2}=3[/tex]
Hence, the value of n is 3 would make point A the circumcenter.
The length of the hypotenuse of a right triangle is 13 cm. the length of one leg is 5 cm. find the length of the other leg. (1 point) 14 cm 144 cm 8 cm 12 cm
Answer: 12
Step-by-step explanation:
You and your friend are selling raffle tickets for a new laptop. you sell 14 more then your friend sells. Together you and your friend sell 58 tickets. Write a system of linear equations that represent this situation. How many did each of you sell?
You sold 36 tickets and your friend sold 22 tickets.
Explanation:Let's represent the number of tickets you sell as x and the number of tickets your friend sells as y.
We know that you sell 14 more tickets than your friend, so we have the equation:
x = y + 14
We also know that together you and your friend sell 58 tickets, so the equation becomes:
x + y = 58
Now we can solve these two equations simultaneously to find the values of x and y.
Substitute the value of x from the first equation into the second equation:(y + 14) + y = 58
Combine like terms:2y + 14 = 58
Subtract 14 from both sides to isolate the variable:2y = 44
Divide both sides by 2 to solve for y:y = 22
Now substitute the value of y back into one of the original equations to solve for x:x = 22 + 14
Simplify:x = 36
Therefore, you sold 36 tickets and your friend sold 22 tickets.
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The system of equations representing the problem is y = x + 14 and x + y = 58. Solving this system we get x = 22 (friend's sold tickets) and y = 36 (your sold tickets).
Explanation:We'll use a system of linear equations to model this situation. Let's define x as the number of tickets your friend sells, and y as the number of tickets you sell. From the problem, we know two things:
1. You sell 14 more tickets than your friend: y = x + 14.
2. Together, you and your friend sell 58 tickets: x + y = 58.
To solve this system, we can substitute y in the second equation with x + 14 from the first equation. This gives us:
x + (x + 14) = 58.
Solving this we get x = 22 and substituting x into the first equation gives: y = 22 + 14 = 36.
So, your friend sold 22 tickets, and you sold 36 tickets.
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