Answer:
$500
Step-by-step explanation:
We are given;
Amount saved for the trip is $2500Amount spent on the gas and hotel room is 3/5 of the saved moneyAmount on food is 1/2 of the remainderWe are supposed to determine the amount spent on food;
Therefore;
Amount on gas and hotel room = 3/5 × $2500
= $ 1500
Thus;
Remaining amount = $2500 - $1500
= $1000
But;
1/2 of the remainder was spent for the food
Thus;
Amount on food = 1/2 × $1000
= $500
Hence, the family spent $500 on food
6m-2(7+3m)>5(2m-3)-m
Answer:
Therefore the value is
[tex]m<\dfrac{1}{9}[/tex]
Step-by-step explanation:
Given:
[tex]6m-2(7+3m)>5(2m-3)-m[/tex] ....Given
Step 1. Applying Distributive Property A(B+C)=AB+AC we get
[tex]6m-2\times7-2\times 3m>5\times 2m-5\times 3-m[/tex]
[tex]6m-14-6m>10m-15-m\\-14>9m-15[/tex]
Step 2. Add 15 both the side
[tex]-14+15>9m-15+15\\1>9m[/tex]
Step 3. Dividing both the side by 9
[tex]\dfrac{1}{9}>\dfrac{9m}{9}\\\\\dfrac{1}{9}>m[/tex]
Therefore the value is
[tex]m<\dfrac{1}{9}[/tex]
Bradley and 23 of his classmates went on a trip to the aquarium. There are 8 more boys than girls on the trip. Write a system of equations to model the problem. Then solve the system algebraically. How many boys and girls were on the trip?
Answer:
Step-by-step explanation:
Total number on the trip is 24
Let the number of girls be x
Then the boys are x + 8
So... x + x + 8 = 24
2x + 8 = 24.......... This is the equation
2x = 24 - 8
2x = 16
x = 16/2
x = 8
Number of girls = 8
And number of boys = x + 8
Which is = 8+8 = 16
There were 8 girls and 16 boys on the trip.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, Bradley and 23 of his classmates went on a trip to the aquarium.
∴ There are a total of 24 students.
There are 8 more boys than girls on the trip.
Assuming the no.of girls to be x, hence no. of boys is (x + 8).
So, x + (x + 8) = 24.
2x + 8 = 24.
2x = 16.
x = 8.
So, no. of girls on the trip is 8, and no. of boys on the trip is (8 + 8) = 16.
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Y= -3x +5
5x -4y = -3
Answer:
The solution of the system of equations is the point (1,2)
Step-by-step explanation:
It is required to solve the system of equations:
y= -3x + 5
5x - 4y = -3
So, substitute with y from the first equation at the second equation:
∴ 5x - 4(-3x + 5) = -3
Solve for x
∴ 5x + 12x - 20 = -3
∴ 17x = -3 +20 = 17
∴ x = 17/17 = 1
∴ y = -3 * 1 + 5 = -3 + 5 =2
So, the solution of the system of equations (1,2)
Another solution:
The give system of equations can be solved by graph both of them.
So, the solution will be the intersection between the lines.
See the attached figure.
why 2+2=4 and not 2+2=22 ?
2 + 2 = 4 because 4 is a sum of 1-digit numbers
2 + 2 ≠ 22 because 22 is the sum of 1-digit and 2-digit numbers
Step-by-step explanation:
Lets explain some important notes:
The 1-digit number consists of one digit, 4 is a one-digit numberThe 2-digit number consists of two digits, ones digit and tens digit, 23 is a 2-digit number, the ones digit is 3 and the tens digit is 2, so its value is 20 + 3The 3-digit number consists of ones digit, tens digit and the hundreds digit, 123 is a 3-digit number, the ones digit is 3, the tens digit is 2 and the hundreds digit is 1, so its value is 100 + 20 + 3∵ 2 + 2 is the addition problem of two 1-digit numbers
∴ There sum will be 4 which is also 1-digit number
∴ 2 + 2 must be 4
∵ 22 is a two digit number
∴ Its value is 20 + 2 ⇒ not 2 + 2
∴ 2 + 2 can not be 22
2 + 2 = 4 because 4 is a sum of 1-digit numbers
2 + 2 ≠ 22 because 22 is the sum of 1-digit and 2-digit numbers
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You want to find the equation for a line that passes through the point (3,-4) and has a slope of -1/2.
Answer:
[tex]y = -\frac{1}{2}x -\frac{5}{2}[/tex]
Step-by-step explanation:
We are given;
A point where the line is passing through as (3, -4)The slope of the line -1/2We are required to determine the equation of the line;
Note that, one way we can get the equation of a straight line is when we are given a point where the line is passing through and its slope.Thus, in this case, we can determine the equation;Taking another point (x, y)
Then; (x, y) , ( 3, -4) and slope -1/2 can give us the equation;
That is;
[tex]\frac{y+4}{x-3}=-\frac{1}{2}[/tex]
Cross multiplication;
[tex]2(y+4) = -1 (x-3)[/tex]
[tex]2y + 8 = -x +3[/tex]
Combining the like terms;
[tex]2y=-x-5\\y = -\frac{1}{2}x-\frac{5}{2}[/tex]
Thus, the equation of the line is; [tex]y = -\frac{1}{2}x -\frac{5}{2}[/tex]
this is worth 25(50)points please answer this is asap! there are three questions!
Answer:number 1 is x<6750number 2 is $22.05 number 3 is $105
Step-by-step explanation:
8(5s-13)-16(2s+6)=0
Answer:
s=25
Step-by-step explanation:
8(5s-13)-16(2s+6)=0
40s-104-32s-96=0
40s-32s-104-96=0
8s-104-96=0
8s-200=0
8s=0+200
8s=200
s=200/8
s=25
Answer: s=25
Step-by-step explanation:
What will the graph of a system of equations look like if two lines have the same slope but different y-intercepts? How many solutions will the system will have?
What are the three ways that systems can be classified and what does that mean for the number of solutions each system will have?
40 Point Offer for a REAL ANSWER. Any other answers will be reported. Don't be rude about it.
Answer:
I have attached a graph of such a system. The two lines have the same slopes but different y-intercepts, this means the lines are parallel, and therefore the system of equations that they represent has no solutions because the lines never intersect.
Going into your next question, there are three ways the system of equations can be classified: the ones that have a solution, with infinitely many solutions, with no solutions.
The graphs of the system of equations that have a solution intersect exactly at one point.
The graphs of the system of equations that have infinitely many solutions are mapped onto each other (are on top of each-other), and therefore have infinite points of intersection.
The graphs of the system of equations that have no solutions never intersect; these are represented by lines that are parallel.
Hope this helps!
Match the system of equations with their solution
11, 16, 12, 7, 23, 9, 5, 5 What is the median of the data?
Answer:
Step-by-step explanation:
add all numbers together
all of them should equal 88
then divide it by how many numbers there are. so 8.
this equals 11
The median of the given data set, 11, 16, 12, 7, 23, 9, 5, 5, is 10. This is found by arranging the data in numerical order, identifying the two middle numbers, and finding their average.
Explanation:The subject of this question is the calculation of the median of a given data set in mathematics. The data given is: 11, 16, 12, 7, 23, 9, 5, 5. To find the median, the data must first be arranged in numerical order from smallest to largest. Once arranged: 5, 5, 7, 9, 11, 12, 16, 23, it can be seen that this data set contains an even number of data points.
In these instances, the median is found by taking the average of the two middle numbers. Here, the middle numbers are 9 and 11. The median is found by adding these numbers together and dividing by 2. Thus, the median for this data set is 10.
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I’d your percent discount is 25% and your sales price is $40, how do you find the original price
Answer:
40
Step-by-step explanation:
How to solve 8(3p-1)+9=3(p+2)-1 ?
Answer:
4/21
Step-by-step explanation:
1. distribute
24p-8+9=3p+6-1
2. combine like terms on each side
24p+1=3p+5
3. solve for p
21p=4
p=4/21
How do I do this
X+y=-4
3x-6y=15
Answer:
x=-1, y=-3. (-1, -3).
Step-by-step explanation:
x+y=-4
3x-6y=15
---------------
x=-4-y
3(-4-y)-6y=15
-12-3y-6y=15
-12-9y=15
9y=-12-15
9y=-27
y=-27/9
y=-3
x+(-3)=-4
x-3=-4
x=-4+3
x=-1
A sequence is defined by the formula f(n+1)=f(n)-3. If f(4)=22, what is f(1)?
The value of f(1) is 31
Solution:
Given that the sequence is defined by formula:
[tex]f(n+1) = f(n) - 3[/tex]
To find: f( 1 )
Also given that,
[tex]f(4) = 22[/tex]
So, we can say,
[tex]f(4) = f(3+1) = 22[/tex]
Substitute n = 3 in given formula
[tex]f(3+1) = f(3) - 3\\\\f(4) = f(3) - 3\\\\Substitute\ f(4) = 22\\\\22 = f(3) -3\\\\f(3) = 25[/tex]
Now we got, f(3) = 25
Use the similar steps to find for f(2)
Substitute n = 2 in given function
[tex]f(2+1) = f(2) - 3 \\\\f(3) = f(2) -3\\\\25 = f(2) - 3\\\\f(2) = 28[/tex]
Use the similar steps to find for f(1)
Substitute n = 1 in given function
[tex]f(1+1) = f(1) - 3\\\\f(2) = f(1) - 3\\\\28 = f(1) - 3\\\\f(1) = 28+3\\\\f(1) = 31[/tex]
Thus value of f(1) is 31
Which of the following describes the transformation of g (x) = 3 (2) Superscript negative x Baseline + 2 from the parent function f (x) = 2 Superscript x?
reflect across the x-axis, stretch the graph vertically by a factor of 3, shift 2 units up
reflect across the y-axis, stretch the graph vertically by a factor of 2, shift 3 units up
reflect across the x-axis, stretch the graph vertically by a factor of 2, shift 3 units up
reflect across the y-axis, stretch the graph vertically by a factor of 3, shift 2 units up
Option d: reflect across the y-axis, stretch the graph vertically by a factor of 3, shift 2 units up.
Step-by-step explanation:
The parent function is [tex]f(x)=2^{x}[/tex]
The transformation function is [tex]g(x)=3(2)^{-x} +2[/tex]
In the transformed function, the function is added +2, which shifts the graph by 2 units up.
Also, the function is multiplied by 3, which stretches the function [tex]f(x)=2^{x}[/tex] vertically by a factor of 3 units.
The variable x is multiplied by -1, such that the function reflects across y-axis.
Thus, the correct answer is option d.
The graph is attached below which shows the parent function and the transformed function.
The transformation function is reflect across the y-axis, stretch the graph vertically by a factor of 3, shift 2 units up.
Answer:
d
Step-by-step explanation:
Please help!!! Need ASAP
Answer:
1=R, 2=O, 3=A, 4=D
Step-by-step explanation:
Help i dont understand
The given equation in standard form is:
[tex]3x+5y=7[/tex]
Step-by-step explanation:
Given equation is:
[tex]x = -\frac{5}{3}y+\frac{7}{3}[/tex]
The standard form of linear equation is:
[tex]Ax+By = C[/tex]
In order to convert the given equation in standard form
Multiplying both sides by 3
[tex]3x = -5y+7[/tex]
Adding 5y on both sides
[tex]3x+5y = -5y+5y+7\\3x+5y = 7[/tex]
Hence,
The given equation in standard form is:
[tex]3x+5y=7[/tex]
Keywords: Linear equation, variables
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What is 7x-4y-8-3x-8y+12
Answer: total comes to 4X - 12Y + 4
Step-by-step explanation:
Answer:
7x - 4y - 8 -3x - 8y + 12
Step-by-step explanation:
7x - 3x = 4x
-4y - 8y = 12y
-8 + 12 = 4
4x - 12y + 4
plz mark brainliest i just need 3 more until expert plz plz plz
this is an easy question: amani saw a sale of $3.60 for 6 bottles of soda. how much would she pay if she only wanted to buy 1 bottle?
Answer:0.6 cents
Step-by-step explanation:
For a school play the teacher asked the class to set up chairs in 20 rows with 25 chairs they were 5 chairs short how many chairs did the class set up
Answer:
Step-by-step explanation:
The original amount there should be:
20 x 25 = 500
Take the extra 5 chairs and subtract it from the original amount, 500.
500 - 5 = 495
Therefore, the amount of chairs that got set up would be 495.
I hope this helped! :)
Which number can each term of the equation be multiplied by to eliminate the fractions before solving? -3/4m-1/2=2+1/4m
Answer:
Please read the answer below.
Step-by-step explanation:
To eliminate the fractions before solving, each term can be multiplied by:
-3/4m by 4 or any multiple of 41/2 by 2 or any multiple of 22 it's a whole number and it's not necessary to eliminate the fraction1/4m by 4 or any multiple of 4glen bakes 16 cookies. Alice bake 32 cookies.they put cookies into each bag. how nqny bags of cookies do they make?
Answer:
The number of bags of cookies do they make together is 11 .
Step-by-step explanation:
Given as :
The number of cookies baked by Glen alone = x = 16 cookies
The number of cookies baked by Alice alone = y = 32 cookies
Let the number of cookies baked by both together = z cookies
Now, According to question
Number of cookies baked by both together = number of cookies baked by Glen alone + number of cookies baked by Alice alone
Or, [tex]\dfrac{1}{z}[/tex] = [tex]\dfrac{1}{x}[/tex] + [tex]\dfrac{1}{y}[/tex]
Or, [tex]\dfrac{1}{z}[/tex] = [tex]\dfrac{1}{16}[/tex] + [tex]\dfrac{1}{32}[/tex]
Taking LCM
[tex]\dfrac{1}{z}[/tex] = [tex]\dfrac{2 + 1}{32}[/tex]
Or, [tex]\dfrac{1}{z}[/tex] = [tex]\frac{3}{32}[/tex]
Or, z = [tex]\dfrac{32}{3}[/tex]
i.e z = 10.67 ≈ 11
So, The number of bags of cookies do they make together = z = 11
Hence, The number of bags of cookies do they make together is 11 . Answer
At a sale, Salazar bought 4 T-shirts and 3 pairs of jeans for $181. At the same store, Jenna bought 1 T-shirt and 2 pairs of jeans for $94. The T-shirts were all the same price, and the jeans were all the same price. Write a system of equations that can be used to represent this situation
A system of equations can be used to represent the situation. The system can be set up with x representing the price of a T-shirt and y representing the price of a pair of jeans.
Explanation:To represent this situation, we can set up a system of equations. Let x represent the price of a T-shirt and y represent the price of a pair of jeans.
The first equation will be: 4x + 3y = 181, since Salazar bought 4 T-shirts and 3 pairs of jeans for $181.
The second equation will be: x + 2y = 94, since Jenna bought 1 T-shirt and 2 pairs of jeans for $94.
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Round the number 283.57 to the ones place
Answer:
284
Step-by-step explanation:
when the number to the left is 5 and up then the number is rounded up
The round off is 284.
what is rounding off?
Rounding off means a number is made simpler by keeping its value intact but closer to the next number. It is done for whole numbers, and for decimals at various places of hundreds, tens, tenths, etc.
given number:
283.57
To round off nearest ones place we have to focus on the place value of tenth place.
If the number at tenth place value is greater than 5 then round off will be 284 otherwise if it less than 4 then the round off will be 283
hence, the rounding off is 284.
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The perimeter of a sand volleyball court is 50 meters. It is 9 meters wide. How long is it?
Answer:
16
Step-by-step explanation:
You have to find y in the answer
Final answer:
The volleyball court is 16 meters long, which was calculated by using the formula for the perimeter of a rectangle and the given width of 9 meters.
Explanation:
To find the length of the volleyball court, we need to use the formula for the perimeter of a rectangle which is P = 2l + 2w, where P is the perimeter, l is the length, and w is the width. Since we know the perimeter is 50 meters and the width is 9 meters, we can substitute these values into the formula to solve for the length l.
First, we calculate the total contribution of the width to the perimeter, which is 2w, so 2 times 9 meters = 18 meters. We then subtract this from the total perimeter to find the combined contribution of both lengths: 50 meters - 18 meters = 32 meters. Finally, we divide by 2 to find the length of one side: 32 meters / 2 = 16 meters.
Therefore, the volleyball court is 16 meters long.
A guy-wire extends from the top of a cell phone tower to a point on the ground that is 25 ft from the base of the tower. What is the approximate length of the guy-wire if the height of the cell phone tower is 75 ft?
Answer:
79.1 ft. I just took the test and got it correct. (:
To find the length of the guy wire attached to a cell phone tower, use the Pythagorean theorem to calculate the total length of the wire. In this case, the approximate length of the guy wire is about 79.06 ft.
The length of the guy-wire can be calculated using the Pythagorean theorem.
First, find the height of the guy-wire, which is the same as the height of the tower: 75 ft.
Next, use the Pythagorean theorem to find the length of the guy-wire: Guy-wire length = [tex]\sqrt{(752 + 252)}[/tex] = [tex]\sqrt{(5625 + 625) }[/tex]= [tex]\sqrt{6250}[/tex] = 79.06 ft (approximate).
How to find the surface area of 3D shapes
Answer:
First, find the area of each side, and the just add them together. It sounds like a lot of work, but getting the question right is totally worth it.
Step-by-step explanation:
The steps to find the Surface Area of different 3D shapes is discussed below:
What is Surface Area?Surface area refers to the total area of the outer surface of a three-dimensional object.
To find the surface area of 3D shapes, you need to calculate the sum of the areas of all the individual faces of the shape.
The specific formulas for each shape vary, so let's go through some common 3D shapes and their surface area formulas:
1. Cube:
The surface area of a cube is given by the formula: SA = 6s², where s² is the area of square faces.
2. Rectangular Prism:
The surface area of a rectangular prism is given by the formula: SA = 2lw + 2lh + 2wh, where l, w, and h represent the length, width, and height of the prism.
3. Cylinder:
The surface area of a cylinder is given by the formula: SA = 2πrh + 2πr², where 2πrh is area of side circular and 2πr² is Area of base.
4. Sphere:
The surface area of a sphere is given by the formula: SA = 4πr², where r is the radius of the sphere.
5. Cone:
The surface area of a cone is given by the formula: SA = πr(r + √(r² + h²)), where r is the radius of the base and h is the height of the cone.
6. Pyramid:
The surface area of a pyramid depends on the shape of its base. For example, the surface area of a square pyramid is given by the formula: SA = l² + 2lw, where l is the slant height and w is the base width.
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Describe two real-world quantities that have a proportional linear relationship. Explain how you could change the situation to make the relationship nonproportional.
Answer:
Proportional: Mike, a plumber charges $5 per hour for his service.
Non-proportional: Mike charges a initial cost of $10 plus $3 for each hours of service.
Step-by-step explanation:
Let us assume that Mike, a plumber charges $5 per hour for his service.
So, the number of hours (h) of service and the total charge (C) are proportional, which is
C(h) = 5h ....... (1)
If the condition changes like, Mike charges an initial cost of $10 plus $3 for each hour of service.
Here, the equation that models the situation is
C(h) = 10 + 3h .......... (2)
Now, relation (1) is non-proportional. (Answer)
Final answer:
Real-world examples of directly proportional relationships include the relationship between distance and time at a constant speed, and cost and weight of fruit. These relationships become nonproportional when a base charge or flat fee is introduced, respectively.
Explanation:
Two real-world quantities that have a proportional linear relationship are speed and distance traveled in a given amount of time, assuming constant speed. For example, the farther you travel at a steady speed, the longer it takes. This relationship can be represented by y = kx, where y is the distance, x is the time, and k is the constant speed.
To make this relationship nonproportional, we could introduce a starting fee or base charge, making the total cost not just dependent on the distance but also an additional amount. Another example of a directly proportional relationship is the cost of fruit, where cost and weight are proportional (y = kx). By adding a flat packaging charge regardless of weight, the relationship between cost and weight becomes nonproportional.
| 4x +2|=10 confirm your solution using a graph or table
Answer:
x = -3 or +2
Step-by-step explanation:
Such an equation resolves into two equations. The argument of the absolute value function can be either positive or negative, so there is one equation for each case.
4x +2 = 10
4x = 8 . . . . subtract 2
x = 2 . . . . . divide by 4
4x +2 = -10
4x = -12 . . . subtract 2
x = -3 . . . . . divide by 4
The two solutions are x=-3 and x=2.
help me solve for 1,2,3,and 4 PLEASE
1.[tex](-7,-3)[/tex]
2.[tex][5,\alpha )[/tex]
3.[tex](-4,-\alpha )[/tex]
4.[tex](-1,0)[/tex]
Explanation
a shaded circle in number line indicates that the number in the shaded point is also included in the interval. In the interval notation this limit is expressed using a square bracket.
A circle that is not shaded in a number line indicates that the number is not included in the interval. In interval notation a bracket is used to represent that point on the number line.
An arrow shows the extension to negative or positive infinity. The symbol [tex]\alpha[/tex] is used to represent infinity and is always included in bracket.