Write and solve a system of equations for each situation. Check your answers.A shop has one-pound bags of peanuts for 2 and three-pound bags of peanuts for 5.50 . If you buy 5 bags and spend 17 , how many of each size bag did you buy?
I bought 3 one-pound bags of peanuts and 2 three-pound bags of peanuts.
Firstly forming the equation according to the given information in question. Let us represent one-pound bags of peanuts with x and three-pound bags of peanuts with y.
Equation based on number of bags bought -
x + y = 5 - Equation 1
Rearranging equation 1 according to x
x = 5 - y - Equation 2
Equation based on cost of bags -
2x + 5.5y = 17 - Equation 3
Keep the value of x from Equation 2 in Equation 3
2 (5 - y) + 5.5y = 17
Performing multiplication of brackets
10 - 2y + 5.5y = 17
Rearranging the equation and performing subtraction
3.5y = 7
Shifting 3.5 to denominator on Right Hand Side of the equation
y = 7 ÷ 3.5
Performing division
y = 2
Calculating value of x by keeping value fo y in Equation 2
x = 5 - 2
x = 3
Thus, I bought 3 one-pound bags of peanuts and 2 three-pound bags of peanuts.
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Which of the following are arithmetic sequences? Select all that apply.
115, 105, 95, 85, ...
-12, -8, -4, 0, ..., 152
5, 10, 20, 40, ...
18, 25, 32, 39, ..., 214
1, -7, 49, -343, ..., 5764801
18, -22, 26, -30, ...
The arithmetic sequences are given as follows:
115, 105, 95, 85, ...-12, -8, -4, 0, ..., 15218, 25, 32, 39, ..., 214What is an arithmetic sequence?In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.
The nth term of an arithmetic sequence is given by:
[tex]a_n = a_1 + (n - 1)d[/tex]
Hence, the arithmetic sequences are given as follows:
115, 105, 95, 85, ... d = -10.-12, -8, -4, 0, ..., 152. d = 4.18, 25, 32, 39, ..., 214. d = 7.For the other sequences, there are different differences between consecutive terms, hence the sequence is not arithmetic, for example:
10 - 5 = 5, 20 - 10 = 10.
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Every year, the Rock and Roll Hall of Fame and Museum inducts legendary musicians and musical acts to the Hall. The table shows the number of inductees for each year.
What are the domain and range of this relation?
Range - { 6, 7, 8,9 ,10, 11 } is the domain and range of this relation.
What is domain and range in math?
The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.How are the domain and range determined?
In order to identify the values of the independent variable x and acquire the domain, we simply solve the equation y = f(x). Simply put, x=g(y) will calculate the function's range after we identify g's domain (y).the domain and range of this relation -
Domain - { 1 , 2, 3, 4, 5, 6 }
Range - { 6, 7, 8,9 ,10, 11 }
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7 x 10-8 in standard form
Answer:
7×10= 70
70-8= 62
Answer62
What is the vertical change?
What is the horizontal change?
Write the slope as a fraction or decimal.
A line is seen on the graph. The horizontal displacement is 2 units, and the graph's rate of change is 0.5.
Point A's coordinates are: (2,1).
Point B's coordinates are: (4,2).
The coordinates of the point change from (2.1) to (2.1) as you go from point A to point B. (4,2).
Consequently, the change in x-coordinate is what determines the point's horizontal displacement and will be,
4 2 2
Therefore, the horizontal displacement is two units.
The vertical displacement is also one unit.
Now, the graph's rate of change may be calculated by looking at the graph's line's slope.
The rate of change will thus be,
m = y2- y1 / x2 - x1
m =2-1 / 4-2
m = 1/2
Consequently, the rate of change = 0.5
horizontal displacement = 2 units.
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Complete question -What is the vertical change from Point A to Point B?
1
What is the horizontal change from Point A to Point B?
What is the rate of change shown on the graph? Give the answer as a decimal rounded to the nearest tenth, if necessary
- How does writing the weight for potatoes in expanded form show why
the same digit can have different values?
What is the relationship between the values of the two 4s in the weight
of the potatoes?
Suppose the given number is 3.441
The first 4 is in the tenth place that is written like or 0.4
The second 4 is in the hundredth place that is written like or 0.04
We can see that the second 4 is one tenth times the first 4.
This is shown like,
1/10 x 1/10 = 1/100
Or we can say the opposite that the first 4 is ten times the second 4.
Place value is the value of each digit in a number. For example, the 5 in 350 represents 5 tens, or 50; however, the 5 in 5,006 represents 5 thousands, or 5,000. It is important that children understand that while a digit can be the same, its value depends on where it is in the number.Place Value is important because it provides the foundation for regrouping, multiple-digit multiplication, and more in the decimal system, as well as a starting point for the understanding of other base systems.Place value helps us make decisions that are used in our daily lives ex) costs, weight, distances, time etc. Our number system is based on a Base Ten system. Base ten means our number system has a base of ten.A place value chart is a table that is used to find the value of each digit in a number based on its position, as per the numeral systemto know more about place value;
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Apply it! A regular 92-sided figure has ___ lines of symmetry.
Answer:
I think the answer is 92 lines because of the regularity of the figure
A rectangular prism has a base with side lengths x and x+3 and height 2 x . Find the surface area and volume of the prism.
The surface area is 10x²+18x sq. units and volume of the rectangular prism is 2x³ + 6x² cubic units.
As given,
In rectangular prism
Base side lengths x and x+3
Height = 2 x
Volume of a rectangular prism V = l w h
V = volume , l =length, w= width h =height.
For rectangular prism,
V = (x). (x +3). (2x)
= (x² +3x)2x
=2x³ +6x²cubic units
Surface Area of Rectangular Prism:
=2(x*2x)+2(x(x+3))+2(2x(x+3))
=4x²+2x²+6x+4x²+12x
=10x²+18x sq. units
Hence, the surface area is 10x²+18x sq. units and volume of the rectangular prism is 2x³ + 6x² units
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Solve each equation. Check each solution. 1/4 - x = x/8
The value of x for the equation 1/4 - x = x/8 is x = 2/9.
According to the given question.
We have an equation 1/4 - x = x/8.
As we know that, an equation is a condition on a variable such that two expressions in the variable should have equal value.
Here, we have to find the solution of the equation 1/4 - x = x/8 for x.
So, the solution of the given equation 1/4 - x = x/8 for x is given by
1/4 - x = x/8
⇒ 1/4 = x/8 + x (adding x both the sides)
⇒ 1/4 = x + 8x/8
⇒ 1/4 = 9x/8
⇒ (1/4)(8) = 9x
⇒ 2 = 9x
⇒ x = 2/9 (dividing both the sides by 9)
Hence, the value of x for the equation 1/4 - x = x/8 is x = 2/9.
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24% of the students in a class are left-handed. What's the minimum number of students that could be in the class?
Answer:
Another way to ask this question would be “what is the fraction 24 out of 100 in simplest form?”
The simplest ratio that is equivalent is six out of 25. The denominator represents the total number of students and six of them are left-handed. So the smallest possible class size is 25. Any number smaller than that would result in a numerator that is not a whole number.
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Compare the two numbers. Use > or < .
-√3,-√5
As the value of Square root -√5 is equal to -2.23, and the value of Square root -√3 is -1.73, which is larger.
A square root is what?The square root of a number x is the number y whose square (the result of multiplying the number by itself, or y y), equals x in mathematics.The term "radicand" refers to the word (or number) whose square root is being considered.The term or number under the radical sign in this instance is known as the radicand, and it is 9.One can discuss square roots of negative values while discussing complex numbers.Any time the idea of an object's "square" is mentioned, square roots can be more extensively considered.These include square matrices and function spaces, among other mathematical structures.The value of Square root -√5 = -2.23, and the value of Square root
-√3 = -1.73, which is larger.
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Express each fraction as a decimal to the nearest hundredth. 17/54
The fraction 17/54 as a decimal to the nearest hundredth is 0.32
Given fraction is 17/54
In decimal form it is 0.3148.
To round it to the nearest hundredth, we have to make round it to two decimal places.
So 17/54 = 0.3148 = 0.32
0.32 is the decimal form of 17/54 to the nearest hundredth.
We can verify this by multiplying and dividing 100 to 0.32,
That is 0.32 = 32/100.
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F(x)=|x|+5 horizontal shrink of factor 3 Please help
The function f(x) = |x| + 5 undergoes horizontal shrinking by a factor of 3 to get; f(x) = |¹/₂x| + 5
How to interpret Shrinking Transformation?There are different ways of transforming a function such as dilation, translation, reflection, stretching, shrinking e.t.c
Now, To stretch or shrink the graph in the y direction, what needs to be done is to multiply or divide the output by a constant. Now, f(2x) simply means that the function f(x) is stretched in the x direction by a factor of 2,. Meanwhile, f(¹/₂x) means that the function f(x) is shrunk in the x direction by a factor of 2 (or stretched by a factor of ¹/₂).
Now, we are told that the function f(x) = |x| + 5 undergoes horizontal shrinking by a factor of 3. Applying the above rule for shrinking gives us;
f(x) = |¹/₂x| + 5
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ASAP pls..............
Answer: t = 6/11
Step-by-step explanation:
3t - 2 + t = 4 - 7t
4t - 2 = 4 - 7t
4t + 7t = 4 + 2
11t = 4 + 2
11t = 6
Divide both by 11
Answer : t = 6/11
Answer:
t = 6/11
Step-by-step explanation:
Hello!
Solve the equation for t by isolating the variable.
Solve for t3t - 2 + t = 4 - 7t Add like Terms4t - 2 = 4 - 7t Collect Like terms 11t - 2 = 4 Isolate the Variable11t = 6 Isolate the Variablet = 6/11The value for t is 6/11.
Silver gym costs $75 to join their gym plus $25 per training session, world fitness costs $100 to join and only $20 per training session. How many sessions will it take for the cost to be the same?
Answer:
5 Sessions
Step-by-step explanation:
$75+$25. $100+20 | Prices
125. 140. | + Cost of Session
150. 160
175. 180
200. 200
225. 220
y = -3x - 10
I have to graph points. The first point is at (0, -10) because of the y-intercept. How should I graph the next point using the slope? The graph they gave me cuts off at 0, -10 so I can't go any lower for y. Help.
The next point to be graphed after graphing the y-intercept since the slope is negative and the graph cuts of at; (0, -10) is; (-5, 5).
What is the next point to be graphed apart from the y-intercept since the graph cuts off at (0, -10)?According to the task content; it follows that the next point to be graphed apart from the given y-intercept is to be determined.
It follows from comparison with the slope-intercept form of a linear equation;
y = mx+c that the slope of the given equation is; -3.
Hence, considering the point, x = -5, the value of y is;
y = -3(-5) -10
y = 15 - 10
y = 5.
Therefore, the required coordinate to be graphed is; (-5, 5).
Ultimately, the next point to be graphed after graphing the y-intercept since the slope is negative and the graph cuts of at; (0, -10) is;
(-5, 5).
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You invested money in a fund and each month you receive a payment for your investment. Over the first four months, you received $ 50, $ 52, $ 55 , and $ 59 . If this pattern continues, how much will you receive in the tenth month?b. Identify your formula as explicit or recursive.
Money received in tenth month: $104, as found by the formula of arithmetic progression.
The formula used here is recursive.
What is arithmetic progression?A series of numbers called an arithmetic progression or arithmetic sequence (AP) has a constant difference between the terms.
Given: Money received in first four months: $50, $52, $55, %59.
To find: Money received in tenth month.
Finding:
As we can see, the pattern followed here is: increment in each amount received each month by $1. Thus it is an arithmetic progression.
That is: 50, 52 (0+2), 55 (2+3), 59 (2 + 3 + 4) and so on.
Thus, for the tenth month, we can use the formula of recursion, given by: [tex]a_n=a_{n-1}+d[/tex], n ≥ 1.
For a₁ = 50, a₂ = a₁ + 2
=> a₂ = 50 + 2
This way, a₅ = a₄ + 5
=> a₅ = 59 + 5 = 64
a₆ = a₅ + 6
=> a₆ = 64 + 6 = 70
a₇ = a₆ + 7
=> a₇ = 70 + 7 = 77
a₈ = a₇ + 8
=> a₈ = 77 + 8 = 85
a₉ = a₈ + 9
=> a₉ = 85 + 9 = 94
a₁₀ = a₉ + 10
=> a₁₀ = 94 + 10 = 104
Thus, the payment received in tenth month will be $104.
The formula so used is recursive, as the consequent values of the given arithmetic sequence are obtained from the preceding values.
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what is the probability of drawing a club from a deck of cards
The probability of drawing a club from a deck of cards is 1/4
How to determine the probability of drawing a club from a deck of cards?In a standard deck of cards, we have the following parameters
Club = 13
Cards = 52
The probability of drawing a club from a deck of cards is calculated as
P = Club/Cards
This gives
P = 13/52
Simplify the fraction
P = 1/4
Hence, the probability of drawing a club from a deck of cards is 1/4
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Four birds are sitting on a telephone wire. What is the probability that a fifth bird landing at a randomly selected point between birds 1 and 4 will sit at some point between birds 3 and 4?
Probability that a fifth bird landing at a randomly selected point between birds 1 and 4 will sit at some point between birds 3 and 4 is 1/3.
As given,
Total number of birds sitting on a telephone wire=4
Possible sitting arrangement is
Bird1__Bird2 __Bird3___Bird4
Total possible number of space between birds 1 to 4=3
Possible favourable outcomes (between 3 and 4)=1
Probability fifth bird sitting between point 3 and 4
= (Number of favourable outcomes)/ Total number of outcomes
= 1/3
Therefore, probability of a fifth bird sitting at some point between birds 3 and 4 is 1/3.
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i need help again yall..............................
Answer:
the answer is c !!!!!!!!!!!!!!!!!!
help me.............................................,.
Answer:
Step-by-step explanation:
a. 0.5+0.3 = 0.8
b. 2.7+28.2 = 30.9
c. 3.1+2.4+9.9 = 15.4
d. 15.2+1.4+0.8 = 17.4
e. 39.2+2.5+0.9 = 42.6
Reflect ABC over the x axis translate by <-3,-1>, and rotate 180 degrees around the origin
Following a 180-degree rotation, the new points are (3,1)
The size of the image will either rise or decrease depending on the answer to the question. And there are two ways to rotate: clockwise and counterclockwise. The coordinate values will vary depending on the quadrant.
Consequently, the new points upon rotation are (3,1).
What do translation, rotation, and reflection mean?The word "reflection" flips or creates a mirror image of the object. An picture is rotated by rotating it either clockwise or anticlockwise. Finally, translation moves certain parts of the picture.
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help pls id help u too
Answer:
x = 1
y = -4
but I am not sure about z
Step-by-step explanation:
please check with your calculator first
Write the equation of the line through each point. Use slope-intercept form.
(-2,1) ; perpendicular to 3 x+y=1
The equation of the line in slope-intercept form passing through the point (-2 , 1) and perpendicular to 3x + y = 1 is y = (1/3)x + 5/3.
The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.
The slope-intercept form of the equation of a line is given by the formula:
y = mx + b
where m is the slope of the line
b is the y- intercept
If the line is perpendicular to 3x + y = 1, then their slopes are negative reciprocal of one another. To get the slope, m, of the equation, express it in slope-intercept form.
3x + y = 1
y = -3x + 1
m = -3
m = 1/3
Substitute the values of the slope and the point to solve for the y-intercept, b.
y = mx + b
1 = 1/3(-2) + b
b = 5/3
Write the equation of the line by plugging in the value of the slope and y-intercept.
y = mx + b
y = (1/3)x + 5/3
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a. Evaluate the expression 2(2x² - x) - 3(x² - x) + x² - x for x=3 . Do not simplify the expression before evaluating it.
The value of the expression 2(2x²-x)-3(x²-x)+x²-x at x=3 is 18.
An algebraic expression is an expression having constant and variable joined with algebraic operation(+,-,×,÷).
According to the question
2(2x²-x) - 3(x²-x) + x²-x
Since we do not have to simplify the expression before evaluating it we will substitute the value of x=3 in the above expression .
=2(2*3² -3)-3(3² -3)+3²-3
=2(2*9-3)-3(9-3)+9-3
=2(18-3)-3(6)+6
Simplifying further we get
=2(15)-18+6
=30-18+6
=36-18
=18
Therefore , the value of the expression 2(2x²-x)-3(x²-x)+x²-x for x=3 is 18.
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Write –0.67 as a fraction.
I need help please
Answer:
[tex]-\frac{67}{100}[/tex]
Step-by-step explanation:
Answer:
67/100
Step-by-step explanation:
0.67/1×100/100=67/100
if wrong i tried T^T
An online furniture store sells chairs for $200 each and tables for $800 each. Every day, the store can ship at most 19 pieces of furniture and must sell a minimum of $8000 worth of chairs and tables. If 7 chairs were sold, determine the minimum number of tables that the store must sell in order to meet the requirements. If there are no possible solutions, submit an empty answer.
Answer must be in this form (,)
Tables cost $800 each, while chairs go for $200 each in an online furniture retailer. The store must sell at least $8000 worth of chairs and tables each day and can only ship a maximum of 19 pieces of furniture per day. Find the bare minimum of tables that the shop must sell to satisfy the requirements if 7 chairs were sold.
If chairs were sold, the minimum number of tables that the store must sell in order to meet the requirements is 4 tables.
Let x be number of chairs
y be number of tables
Given every day, the store can ship at most 19 pieces of furniture
Then we can write x+y=19--------->equation(1)
Given an online furniture store sells chairs for $200 each and tables for $800 each.
200x is the revenue of number of chairs.
800y is the revenue of number of tables.
And given must sell a minimum of $8000 worth of chairs and tables.
Then we can write 200x+800y=8000---------->equation(2)
We have to find out If 7 chairs were sold, determine the minimum number of tables that the store must sell in order to meet the requirements.
When x=7 what is y=?
By substituting x=7 in equation (1)
7+y=19
y=19-7
y=12
Now, substitute the x=7 in equation(2)
200(7)+800y=8000
1400+800y=8000
800y=8000-1400
800y=6600
y=[tex]\frac{6600}{800}[/tex]
y=8.25
y=9
We got 2 required values when x=7.
They are y=9 and y=12.
Therefore, the possible values we get are y=9,10,11,12.
If chairs were sold, the minimum number of tables that the store must sell in order to meet the requirements is 4 tables.
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Find the slope of the line through (3,5) , parallel to y=5 x-1
Find the slope of the line through (3,5) , parallel to y=5 x-1
Slope=5
How to find slope?
Given:
y=5x-1 ( where, slope=5)
Any line parallel to y=5x-1 also has slope 5
What is the line?
y=5x+b
We can find b ,using the given points (3,5)
5=15+b
b=-10
The line is, y=5x-10
What is a slope?
In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.The letter m is frequently used to represent slope; the reason for this usage is unclear, but it can be found in O'Brien's and Todhunter's versions of the equation for a straight line, respectively, where they are written as y = mx + b and y = mx + c.To learn more about slope, refer:
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Malik bought 0.8 pounds of turkey and 1.45 pounds of ham from deli. if turkey costs $6.45 per pound and ham costs $4.80 per pound, find the total cost.
On solving the equations, the total cost is 25.86.
The cost of ham is $4.80 a pound.
The cost of cheese is $6.3 for a pound.
Cheese weighing pounds was provided for $14.76.
Let "a" represent the cost of a pound of ham, and "b" represent the cost of a pound of cheese.
Given the available information,
1.3a + 0.8b = 11.28 —— (1)
1.50 +1.2b = 14.76 —— (2)
From the equation now (1).
11.28 -0.8b 1.3 (3)
Now, using equations (2) and (3), we obtain the following: 11.28 0.8 b. 1.3)+1.2 b. 14.76. 12.97 0.92 b+1.2 b. 14.76 0.28 b. 1.79 b. 6.3
The result of adding the value of b to equation (3) is 11.28 0.8. (6.3)
1.3 a = 4.8
The cost of ham is $4.80 a pound.
The cost of cheese is $6.3 for a pound.
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find the values of x and y
Answer:
x=46 and y=42
Step-by-step explanation:
make 2y+6 equal to 8y-102 to solve for y as they are vertically oppisate angles which make them equal.
then substitute the new value for y into either expression and solve x using the rule a straight line is equal to 180.
