Function 1 has a greater y-intercept than function 2
Step-by-step explanation:
Solve each of these equations. Explain or show your reasoning.
2(x+5)=3x+1
3y-4=6-2y
3(n+2)=9(6-n)
1.
[tex]
2(x+5)=3x+1 \\
2x+10=3x+1 \\
-x=-9 \\
x=9
[/tex]
2.
[tex]
3y-4=6-2y \\
5y=10 \\
y=2
[/tex]
3.
[tex]
3(n+2)=9(6-n) \\
3n+6=54-9n \\
12n=48 \\
n=\frac{48}{12}=4
[/tex]
Hope this helps.
By applying basic algebraic techniques, the solutions to the given equations: 2(x+5)=3x+1, 3y-4=6-2y, and 3(n+2)=9(6-n) are x = 9, y = 2, and n = 4 respectively.
Explanation:We will solve these equations one-by-one using basic algebraic techniques:
Equation 1:
2(x+5) = 3x+1. First, distribute the 2 on the left side of the equation to get 2x + 10 = 3x + 1. Now, we'll move 2x to the right side to get 10 = x + 1. Subtracting 1 from both sides gives us the solution: x = 9.
Equation 2:
3y - 4 = 6 - 2y. Let's move all the y terms to one side and constants to the other: 3y + 2y = 6 + 4. Sum the sides to get 5y = 10. Solving for y gives y = 2.
Equation 3:
3(n + 2) = 9(6 - n). This requires distribution on both sides which results in 3n + 6 = 54 - 9n. Adding 9n to both sides gives 12n + 6 = 54. Subtracting 6 from both sides gives 12n = 48, and finally, dividing by 12, gives "n = 4".
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Marco drew 20 pictures .He drew 3/4 of them in art class.How many pictures did Marco draw in art class
Answer: 15
5,10,15,20
3/4 is 15
The bar chart shows the percent of times each color marble was drawn from a bag after 1000 draws with replacement after each draw. If there are 20 marbles in the bag, predict how many are red, how many are blue, and how many are white. Explain your reasoning.
Answer:
Total number of red marbles = 10 red marbles.Total number of blue marbles = 5 blue marbles.Total Number of white marbles = 5 white marbles.Step-by-step explanation:
The bar shows the following information that can we fetch to solve the problem.
Red marbles drawn nearly 50% of the timeBlue marbles drawn nearly 25% of the time White marbles drawn nearly 25% of the timePredicting how many are red marbles:
If there are 20 marbles in the bag, it logically means that each marble, averagely, should likely be drawn 5% of the time.
As the bar shows that Red marbles drawn nearly 50% of the time, it means that we will have to divide 'Red marbles drawn nearly 50% of the time" by the " each marble from 20 marbles be drawn 5% of the time".
So,
Total number of red marbles = 50% / 5% = 10 red marbles.
Predicting how many are blue marbles:
If there are 20 marbles in the bag, it logically means that each marble, averagely, should likely be drawn 5% of the time.
As the bar shows that blue marbles drawn nearly 25% of the time, it means that we will have to divide 'blue marbles drawn nearly 25% of the time" by the " each marble from 20 marbles be drawn 5% of the time".
So,
Total number of blue marbles = 25% / 5% = 5 blue marbles.
Predicting how many are white marbles:
If there are 20 marbles in the bag, it logically means that each marble, averagely, should likely be drawn 5% of the time.
As the bar shows that white marbles drawn nearly 25% of the time, it means that we will have to divide 'white marbles drawn nearly 25% of the time" by the " each marble from 20 marbles be drawn 5% of the time".
So,
Total number of white marbles = 25% / 5% = 5 white marbles.
Keywords: bar chart, prediction
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Find 35% of 400 help me please
Answer:140
Step-by-step explanation:
35% of 400=0.35x 400 because of means multiply.
So 0.35x400=140
Answer: 140
Step-by-step explanation:
First you find 10% of 400.0 so you move the decimal point once to the left to get 40. Then you do 40 x 3 which is 120 this is 30%. To work out 5% you half 10% was 40. Half of 40 is 20. So 30%+5% is 35%. 30% is 120 and 5% is 20. 120+20 is 140
a container shaped like a right circular cylindar having diameter 6cm and height 7.5cm is full of ice cream.The ice cream is to be filled into cones of height 6cm and diameter 3cm,having a hemispherical shape on the top.Find the number of cones which can be filled with ice cream
Answer:
Step-by-step explanation:
Cylinder:
d= 6cm; r =6/2 = 3cm
h =7.5cm
Volume of ice cream in cylinder = πr²h
= π * 3 * 3 * 7.5 = 67.5 π cubic cm
Cone:
h = 6 cm;
d = 3cm ; r = 3/2 = 1.5cm
Volume =(1/3)πr²h
= (1/3) * π * 1.5 * 1.5 * 6
= π * 1.5*1.5 * 2 = 4.5π cu. cm
Hemisphere on top:
r = 1.5cm
Volume = (2/3)πr³
=(2/3)* π * 1.5 *1.5 * 1.5
= 2 *π * 0.5*1.5*1.5
= 2.25π cu.cm
Volume of ice cream in each cone = 4.5 π + 2.25π = 6.75π cubic cm
No of cones = volume of cylinder/ Volume of ice cream in each cone
=π *67.5 / 6.75 * π
= 67.5 * 100 / 6.75 * 100
= 6750 / 675
= 10
number of cones which can be filled with ice cream = 10 cones
volume of a regular quadrilatral pyramid is 400 cm^3.and it's height is 12 then it's lateral surface area=?
Answ For Lateral Area : When all the side faces are the same: Multiply the perimeter by the "slant length" and divide by 2. This is because the side faces are always triangles and the triangle formula is "base times height divided by 2"er:
Step-by-step explanation:
Ms. Clark spends $89.85 on science kits that cost of each plus $4.85 tax on the total bill, how many kits did she buy?
Mrs. clark spends $89.85 on science kits that cost $5 each plus $4.85 tax on the total bill. How many kits did she buy?
Answer:Mrs. Clark bought 17 science kits
Solution:Given that Mrs. clark spends $89.85 on science kits that cost $5 each plus $4.85 tax on the total bill
To find: number of kits she bought
Cost of one kit = $ 5
Tax amount = $ 4.85
Total amount spend including tax = $ 89.85
Lets first get rid of the tax in the total amount
Amount without tax = Total amount spend including tax - Tax amount
Thus amount without tax = $ 89.85 - $ 4.85 = $ 85
Since we know that each kit costs $5, we would divide 85 by 5 to see find how many kits she bought
[tex]\begin{array}{l}{\text { number of kits bought }=\frac{\text { amount spent }}{\text { cost of one kit }}} \\\\ {\text { number of kits bought }=\frac{85}{5}=17}\end{array}[/tex]
Thus Mrs. clark has bought 17 science kits
Answer:
Ms. Clark bought 17 science kits
Step-by-step explanation:
NEED ANSWER FAST PLEASEE
Answer: [tex]y=2x+7[/tex]
Step-by-step explanation:
The equation of the line in Slope-Intercept form is:
[tex]y=mx+b[/tex]
Where "m" is the slope and "b" the y-intercept.
Given the equation:
[tex]y=-\frac{1}{2}x-4[/tex]
You can identify that:
[tex]m=-\frac{1}{2}[/tex]
Since the slopes of perpendicular lines are negative reciprocals, the slope of the line perpendicular to [tex]y=-\frac{1}{2}x-4[/tex] must be:
[tex]m=2[/tex]
Substitute the slope and the coordinates of the given point into [tex]y=mx+b[/tex] and solve for "b":
[tex]3=(2)(-2)+b\\\\3+4=b\\\\b=7[/tex]
Therefore, the equation of that line is:
[tex]y=2x+7[/tex]
a pulley 18 inches in diameter is driven by a belt at the rate of 90 revolutions per minute. what is the angular velocity of the pulley in radians per minute? what is the speed of the belt in feet per second?
Answer:90*2π，90/60*18/2
Step-by-step explanation:
(PLEASE ANSWER...I FORGOT TO DO THIS OVER BREAK)
What is the value of x in the equation −x = 4 − 3x + 6? (5 points) Group of answer choices 5 10 −5 −10
Answer:
so the solution is in the picture please mark me brainliest.
the Answer is 5
Answer:
-x+3x=4+6 because when we collected liketerms
2x=10 now divided both side by 2
2x/2=10/2
x=5 so the value of x is 5
The constraints of a problem are graphed below. What are the vertices of the feasible region?
(0, 0), (0, 15), (20, 25), (40, 0)
(0, 0), (0, 40), (25, 20), (15, 0)
(0, 15), (20, 25), (40, 0)
(0, 40), (25, 20), (15, 0)
Answer:
(0, 0), (0, 15), (20, 25), (40, 0)
Step-by-step explanation:
The diagram shows shaded region in the form of quadrilateral bounded with two given lines and x- axis and y-axis. Four vertices of this quadrilateral are point of intersection of those lines or lines with coordinate axes.
The first vertex of this quadrilateral lies at the origin (point of intersection of two axes), then its coordinates are (0,0).
The second vertex lies on the x-axis and its coordinates are (40,0) (placed at 40 on the x-axis)
The third vertex lies on the y-axis and its coordinates are (0,15) (placed half way between 10 and 20 on the y-axis).
The fourth vertex is the intersection of two lines. Its coordinates are (20,25) (draw vwrtical line from this vertex t x-axis, it will intersect x-axis at 20, draw horizontal line to y-axis, it will intersect the y-axis at 25).
So, correct option is A: (0, 0), (0, 15), (20, 25), (40, 0)
Answer:
(0, 0), (0, 15), (20, 25), (40, 0)
Step-by-step explanation:
The feasible region is the shaded area in the graph. This region has four vertices which are:
(0, 0) at the bottom left
(0, 15) at the top left
(20, 25) at the top center
(40, 0) at the bottom right
Note: the points have the notation (x, y)
In the warehouse there is a stack of 7 crates. Each crate is 102/3 inches high. How many inches high is the stack
Answer:
The stack is [tex]\frac{224}{3}[/tex]inches high.
Step-by-step explanation:
Given date:-
A stack of 7 crates means
1 stack=7 crates
Total number of crate=7
Height of 1 crate = [tex]10\frac{2}{3}\ inches[/tex]
Height of 1 crate =[tex]\frac{30+2}{3}[/tex] inches
Height of 1 crate =[tex]\frac{32}{3}[/tex] inches
To find height of stack=?
Now,
Height of a stack = Height of 1 crate [tex]\times[/tex] Total number of crates
Height of a stack =[tex]\frac{32}{3}\times7[/tex]
Height of a stack =[tex]\frac{32\times7}{3}[/tex]
Height of stack = [tex]\frac{224}{3}[/tex] inches
Therefore the stack is [tex]\frac{224}{3}[/tex] inches high.
Jamie says that the expression s6x-2x+4 and 4(x+1)are not equivalent because one expression has a term that is subtracted and the other does not. Do you agree? Explain
Answer:
I do not agree. When the expressions have like terms collected and are factored, they are the same.
Step-by-step explanation:
Make 6x-2x+4 the same as 4(x+1):
6x - 2x + 4 Collect the like terms 6x and -2x
= 4x + 4 Factor. Divide each term by 4 and take it out of a bracket
= 4(x + 1)
4(x+1) = 4(x+1)
They are equivalent expressions, just written differently.
Answer:
No Jamie is incorrect
Step-by-step explanation:
No, because in the expression 4(x+1) you will first need to multiply 4 by x, your result is 4x, and then you multiply 4 by 1, you get 4, so the answer will be 4x+4.
Also in the expression 6x-2x+4 ,you will first need to subtract 2x from 6x, your result is 4x ,and then you add 4 , so the answer will be 4x + 4
Our final answer is:
6x-2x+4 = 4x + 4 and 4(x+1) = 4x + 4
Comparing and ordering integers
Answer:
what about it?
Step-by-step explanation:
Catera has found that as she increases her price, p, the quantity she sells q, decreses.
The following equation relates q, the quantity she sells, to p, the price she charges.
p = 284 - 4q Catera's price is $232.
what is the quantity that she sells? Show your work.
Answer
The quantity "q" sold by Catera is 13
Solution:
Given that Catera has found that as she increases her price, p, the quantity she sells q, decreases
The following equation relates q, the quantity she sells, to p, the price she charges:
p = 284 - 4qWhere, "p" is the price and "q" is the quantity she sells
Given that Catera price is $ 232
To find: quantity she sells
Substitute p = 232 in given equation
232 = 284 - 4q
4q = 284 - 232
4q = 52
[tex]q = \frac{52}{4} = 13[/tex]
q = 13
Therefore the quantity she sells is 13
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A lottery ticket has a grand prize of $44.8 million. The probability of winning the grand prize is 000000020.
Determine the expected value of the lottery ticket. (Round your answer to 3 declmal places.)
Expected value
Answer:
Expected value would be $ 0.896
Step-by-step explanation:
Given,
The price of the lottery ticket = $44800000,
Also, the probability of winning the grand prize = .000000020,
Thus, the expected value of the lottery ticket = value of the lottery ticket × probability of getting the lottery ticket
= 44800000 × .000000020
= $0.896
Note : value of lottery ticket = prize amount - cost of each ticket,
Here the cost price of a ticket is not given,
That's why we did not consider it.
Final answer:
The expected value of a lottery ticket with a grand prize of $44.8 million and a winning probability of 0.00000002 is $0.896, assuming the ticket has no cost.
Explanation:
To calculate the expected value of a lottery ticket, we need to consider both the payout and the probability of each outcome. Given that the grand prize is $44.8 million with a probability of winning of 0.00000002, we can compute the expected value.
To find the expected value (EV) of the lottery ticket, we use the following formula:
EV = (Payout × Probability of winning) - (Cost of ticket × Probability of losing)
Plugging in the values, we get:
EV = ($44,800,000 × 0.00000002) - ($0 × (1 - 0.00000002))
EV = $0.896.
Since the cost of the ticket is not given, we assume it's $0 for the purpose of this illustration. The expected value of the lottery ticket when rounded to three decimal places is $0.896.
how to solve 3a - ( -1 ) = -5
4 adult and 10 student tickets cost 58$ overall on the first day on the second 5 adult and 1 student cost 38$ overall how much is each ticket sold for
Cost of 1 adult ticket is $ 7 and cost of 1 student ticket is $ 3
Solution:
Let "a" be the cost of 1 adult ticket
Let "s" be the cost of 1 student ticket
Given that,
4 adult and 10 student tickets cost 58$ overall on the first day
So we can frame a equation as:
4 adult ticket x cost of 1 adult ticket + 10 student ticket x cost of 1 student ticket = $ 58
[tex]4 \times a + 10 \times s = 58[/tex]
4a + 10s = 58 ------ eqn 1
On the second 5 adult and 1 student cost 38$ overall
So we can frame a equation as:
5 adult ticket x cost of 1 adult ticket + 1 student ticket x cost of 1 student ticket = $ 38
[tex]5 \times a + 1 \times s = 38[/tex]
5a + 1s = 38 ------- eqn 2
Let us solve eqn 1 and eqn 2 to find values of "a" and "s"
Multiply eqn 2 by 10
50a + 10s = 380 ---- eqn 3
Subtract eqn 1 from eqn 3
50a + 10s = 380
4a + 10s = 58
( - ) --------------------
46a = 322
a = 7Substitute a = 7 in eqn 1
4a + 10s = 58
4(7) + 10s = 58
28 + 10s = 58
10s = 58 - 28
10s = 30
s = 3Thus cost of 1 adult ticket is $ 7 and cost of 1 student ticket is $ 3
5(x+3) greater than or equal to 3x - 13
Answer:
x greater than or equal to -14
Step-by-step explanation
1/2 of 180 is what number
Answer:
90
Step-by-step explanation:
Answer:
90
Step-by-step explanation:
Bill has 10 apples. He uses 8 of them
to make muffins. Josh has 6 apples.
How many should he use so he has
the same number as Bill?
10-8= 6-_
_apples
Answer:
4
Step-by-step explanation:
10-8=2
6-4=2
Final answer:
Josh should use 4 apples to have the same number remaining as Bill. After Bill uses 8 out of his 10 apples, he has 2 left. Josh, starting with 6 apples, needs to use 4 to also have 2 left.
Explanation:
The question at hand involves simple subtraction to find the number of apples Josh should use to have the same number as Bill after Bill uses some for making muffins.
Bill starts with 10 apples and uses 8 of them, which leaves him with 2 apples.
To determine how many apples Josh should use, we need to perform the following calculation for Josh, who starts with 6 apples: 6 - x = 2, where 'x' represents the number of apples Josh uses.
Solving this, we get x = 6 - 2, hence, x = 4 apples.
Therefore, Josh should use 4 apples to have the same number remaining as Bill.
How many solutions does the equation -3+3a+6=7 have
Answer: The equation has No Solution.
Step-by-step explanation:
Given the following equation:
[tex]-3a+3a+6=7[/tex]
You can simplify it by adding the like terms.
It is important to remember the, by definition, the like terms have the same variable and the same exponent.
In this case, you can identify that the term [tex]-3a[/tex] and the term [tex]3a[/tex] are "like terms", because their variables and their exponents are the same.
So, if you add them, you get:
[tex]-3a+3a=0[/tex]
Then:
[tex]0+6=7\\\\6=7\ (FALSE)[/tex]
Therefore, since there is no value that satisfies the equation, you can conclude that the equation has No Solution.
Find the y - intercept of y=3x+15 and then interpret it
Answer:
The y-intercept to the given line equation y=3x+15 is (0,15).
Step-by-step explanation:
Given line equation is y=3x+15
To find the y-intercept from the given line equation y=3x+15:
y-intercept when x=0
That is substitute x=0 in the given line equation
y=3x+15
y=3(0)+15
y=0+15
y=15
Therefore y=5
The point (0,15) on the graph where the line y is intersected is y-intercept.
In other words y-intercept is the point (0,15) where the given line equation y=3x+15 crosses the y-axis.
Therefore the y-intercept to the given line equation y=3x+15 is (0,15).
Final answer:
The y-intercept of y=3x+15 is 15 and it represents the value of y when x is zero.
Explanation:
The y-intercept, b, of the equation y=3x+15 is 15. It represents the value of y when x is equal to zero. In other words, when x is zero, y is equal to 15.
Interpretation: In the context of the equation y=3x+15, the y-intercept of 15 means that when there is no input or x-value, the output or y-value is 15. This suggests that when the x-value is zero, the value of y is 15. This can be visualized on a graph as the point where the line intersects the y-axis at the coordinate (0, 15).
Selects the correct answer
What is the domain of the function shown on the graph?
The domain of the given function shown on the graph is -∞<x<∞.
We have given the function,
We have to determine the domain of the given graph.
What is the domain?
The domain of a function is the complete set of possible values of the independent variable.
From the graph, the domain of the graph is option B.
We can see that the graph is From -infinity to +infinity.
and it does not touch the point (0,0).
Therefore the graph shows the point at the domain.
Therefore the domain of the given function is -∞<x<∞.
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Find the length of the missing side of a rectangle if the diagonal is 13 cm and the shortest side is 5cm
And please show the steps and explain
Answer:
12 cm
Step-by-step explanation:
I drew a picture of a rectangle with a diagonal measurement of 13 units and what appear to be the shortest side to be 5 units. (This picture was not drawn to scale.) We were has to find the longest side which I said was b. Notice the diagonal cuts the rectangle into right triangles.
We will need to use Pythagorean Theorem to find the length of the longer side of the rectangle.
[tex]5^2+b^2=13^2[/tex]
[tex]25+b^2=169[/tex]
Subtract 25 on both sides:
[tex]b^2=144[/tex]
Take square root of both sides:
[tex]b=\sqrt{144}[/tex] (I did not worry about the negative answer to this because we are dealing with lengths.)
[tex]b=12[/tex]
Kay's mother taught her how to make handmade ornaments to sell at a craft fair. Kay rented a table at the fair for $30 and set up her work station. Each ornament that she makes costs approximately $2.50 for materials. She sells each ornament for $6.00. If x represents the number of ornaments sold at the craft fair, which of the following expression would represent Kays profit?
Answer:
profit= 6. 00x - (30+2. 50x)
Tom is thinking of two numbers,a and b,where a is a positive and b is negative. write to inequalities that Tim can use to compare a and b
Explain
Final answer:
Two inequalities that Tim can use to compare a positive number, a, and a negative number, b, are |a| > |b| and a > 0 and b < 0.
Explanation:
To compare two numbers, a and b, where a is positive and b is negative, we can use two inequalities:
The magnitude of a must be greater than the magnitude of b. This can be represented as |a| > |b|.
The value of a must be greater than 0 and the value of b must be less than 0. This can be represented as a > 0 and b < 0.
These inequalities help Tim compare the positive and negative numbers a and b based on their magnitudes and values.
what is 4.14x10*9 in standard form
Answer:
372.6
Step-by-step explanation:
While at the gym levon spent 25 minutes on the treadmill and 35 minutes lifting weight what is the ratio of the levon spent on the treadmill to the time he spent lifting?
The ratio of the time levon spent on the treadmill to the time he spent lifting is 5/7 or 5:7
Step-by-step explanation:
Given
Time spent on treadmill = [tex]T_t = 25\ min[/tex]
Time spent on weight lifting = [tex]T_w = 35\ min[/tex]
We have to find the ratio of the time Levon spent on the treadmill to the time he spent lifting
The ratio will be denoted by r
[tex]r = \frac{T_t}{T_w}\\=\frac{25}{35}\\[/tex]
Simplifying the fractions
[tex]=\frac{5*5}{7*5}\\=\frac{5}{7}[/tex]
The ratio of the time levon spent on the treadmill to the time he spent lifting is 5/7 or 5:7
Keywords: Ratio, fraction
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What is the answer to this math problem
Answer:
Domain: c)
Range: d)
Step-by-step explanation:
The domain means all of the possible x-values. To find the domain, find the leftmost and rightmost value of x. They are 0 and 8.5.
The range means all of the possible y-values. To find the range, find the lowest and higher values for y. They are 0 and 12.5.
"All numbers" means x or y can be any number, decimal decimal numbers. "Whole numbers" mean x or y can only be numbers that don't have decimals.
Both x and y can be decimal numbers because the graph is not broken up. If it could only be whole numbers, the graph would be dots.