Step-by-step explanation:
multiply both equations with factors so that the terms of the targeted variable (in our case x) have the same constant factor. and then we can subtract one equation from the other, abd the variable is eliminated in the result.
in our case the least common multiple of 4 and 9 is 36.
so, we multiply equation 1 by 9, and equation 2 by 4, abd then we subtract
36x - 54y = 90
- 36x + 8y = 28
-------------------------
0 -62y = 62
so, x is "eliminated", and we can solve for y : y = -1.
and then we can use one of the original equations to solve for x.
e.g.
9x + 2×-1 = 7
9x - 2 = 7
9x = 9
x = 1
Answer:
First, we'll need to find the LCM (least common multiple) which, in this case, is 36. Now that we know this, we can get 4x and 9x to be 36x and -36x so that they can cancel out. To do this, we have to multiply Equation 1 by 9 and Equation 2 by -4.
9(4x - 6y = 10) is equivilant to 36x - 54y = 90
-4(9x + 2y = 7) is equivilant to -36x - 8y = -28
Now that we have our new system of equations, we can proceed with the process of elimination! The first step is to add the two equations together. This will result in:
-62y = 62 we have successfully eliminated x!
The last step will be to divide both sides by -62
-62y/-62 = 62/-62
y = -1
Foundations of Algebra B
ous Activity
Week
Juan's Fundraising Progress
Total Sold in
Fruit Baskets
($)
Total Sold
in Pencils
($)
O
Juan is selling fruit baskets and pencils for his
fundraisers. He started his fundraising early and has 12
weeks to reach his goal of selling $300.00 worth of
goods to pay for his trip's cost.
If Juan uses the table shown to represent all of his
data, what interval for the weeks would you use in
column 1 so that all 12 weeks are represented?
Week labels:
English
1, 2, 3, 4
2, 4, 6, 8
3, 6, 9, 12
1, 3, 6, 10
Juan have to sell 4 fruit baskets to make enough money.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given that, Juan's Fundraising Progress Juan sold fruit baskets for $16.50 each and pencils for $1.50 each. His goal is to sell $300 worth of goods to pay for his trip's cost.
His goal is to sell $300, the pencil sold a total of $81, so the fruit basket will sell a total of 300-81=219
Las three week: 219-165 =$54
Fruit baskets for $16.50 per each
54/16.50 =3.27
So, he have to sell 4 fruit baskets to make enough money
Hence, Juan have to sell 4 fruit baskets to make enough money.
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"Your question is incomplete, probably the complete question/missing part is:"
Juan's Fundraising Progress Juan sold fruit baskets for $16.50 each and pencils for $1.50 each. His goal is to sell $300 worth of goods to pay for his trip's cost. How many fruit baskets will Juan need to sell the last three weeks to achieve his goal?
How do you determine if three points are in a straight line in 3D?
To determine if three points are in a straight line in 3D, you can calculate the vector between the first two points and then check if the third point is in the same direction as the vector.
What is straight line?Straight line is a line that extends infinitely in two opposite directions and has no curves or bends. It is the shortest distance between two points and is the basic form of geometry. A straight line is composed of two end points and all the points in between that make up the line. Straight lines are used to create shapes and constructions in mathematics, science and engineering.
If the dot product of the vector and the point is 0, then the three points are in a straight line. Alternatively, you can calculate the area of the triangle formed by the three points and if it is 0, then the points are in a straight line. Another option is to calculate the determinant of the matrix formed by the three points and if it is 0, then the points are in a straight line. Finally, you can calculate the angle between the two vectors formed by the three points and if it is 0, then the points are in a straight line.
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estimate 5.26 × 4.9
I NEED IT ASAP
Answer:
25.774
Step-by-step explanation:
5 x 4.9 = 24.5
0.26 x 4.9 = 1.274
24.5 + 1.274 = 25.774
X
Incorrect
1 try left. Try once more
A certain state legislature has senators and representatives. The combined nu
the numbers is 150. There are more representatives than senators.
How many senators and how many representatives are in this state's legislatu
Number of senators: 130
Number of representatives: 150
G
Need help with this question?
X
Ś ?
(150 + x) + 130 >= 150 is the inequality equation for the state legislature, which consists of senators and members.
what is inequality ?Mathematics uses the term inequality to describe a link between two expressions or values that is not equal. Thus, imbalance is the cause of inequality. The relationship between two non-equal values in mathematics is established by an inequality. Egality and inequality are not synonymous. Whenever two values are not equal, use the not equal sign (). Various inequalities are used to compare values, whether they are small or large. You can eliminate a lot of simple inequalities by modifying both sides until only the variables are left. Inequality is brought on by a number of things, though: On both sides, subtract or multiply negative values. Alternate between left and right.
given
Number of senators: 130
Number of representatives: 150
more representatives than senators
(150 + x) + 130 >= 150 is the inequality equation for the state legislature, which consists of senators and members.
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Please help! Trig!!!!!!!l. Look at the image! And answer the question! Thank u!
On solving the provided question, we can say that - there are 67 numbers less than 100 are divisible by 3, by divisibility test.
what is divisibility test?The divisibility rule is a concise and practical approach to check, often by looking at the integer's digits, whether a given integer is divisible by a given set divisor without actually executing division. Without actually doing the division procedure, you may quickly discover if a given number can be divided by a defined divisor using the divisibility test. When dividing two numbers exactly, the quotient must be an integer and the remainder must be zero.
= n(A ∪ B)
= n(A) + n(B) - n(A ∩ B)
= 33 + 50 - 16
= 67
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On solving the provided question, we can say that by trigonometry, t = [tex]4\pi /3[/tex]; x = cos([tex]4\pi /3)[/tex] = [tex]-\sqrt{2}/4[/tex] and y = sin([tex]4\pi /3)[/tex] = [tex]-3\sqrt{2}/11[/tex]
what is trigonometry?The area of mathematics known as trigonometry examines the correlation between triangle side lengths and angles. The area first appeared in the Hellenistic era, around the third century BC. from the use of geometry in astronomical study. The area of mathematics known as exact methods deals with specific trigonometric functions and how they might be used in calculations. There are six popular trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their respective names and acronyms (csc). Studying the characteristics of triangles, particularly right triangles, is called trigonometry. The study of geometry, however, is the characteristics of all geometric figures.
here,
by trigonometry,
t = [tex]4\pi /3[/tex]
x = cos([tex]4\pi /3)[/tex] = [tex]-\sqrt{2}/4[/tex]
y = sin([tex]4\pi /3)[/tex] = [tex]-3\sqrt{2}/11[/tex]
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What is the image point of ( 6 , 5 ) after the transformation D 5 ∘ 0 ∘T 0,0 ?
The image point of P(x,y) = ( 6 , 5 ) after applying a horizontal reflection is P'(x,y) = (1, 5).
How to determine the image after transformation?In geometry, a rigid transformation is a transformation applied onto a geometric object such that Euclidean distance in every point of it is conserved. Translations are examples of rigid transformations and are defined by this formula:
P'(x,y) = P(x,y) + T(x,y) (1)
Where:
P(x,y) - Original point
T(x,y) - Translation vector
P'(x,y) - Image point
If we know that P(x,y) = (6, 5) and T(x,y) = (5, 0), then the image point is:
P'(x,y) = (6, 5) + (5, 0)
P'(x,y) = (1, -6)
The image point of P(x,y) = (6, 5) after applying a horizontal reflection is P'(x,y) = (1, 5).
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Correct form of the question
What is the image point of (x, y) = (6, 5) after the transformation of translating horizontally the point 5 units to the y-axis?
Tell whether the lengths 3, 14, and 10 form the sides of an acute, right, obtuse, or not a triangle.
A. acute
B. right
C. not a triangle
D. obtuse
The lengths 3, 14, and 10 form a obtuse triangle
How to Determine if Three Side Lengths Are a Triangle?It's simpler than it seems to determine whether a triangle has three side lengths. The Triangle Inequality Theorem, which asserts that the sum of a triangle's two side lengths is always greater than the third side, will suffice. You will have a triangle if this holds true for each of the three possibilities of increased side lengths.
Theorem of Triangle Inequality. This theorem merely states that the third side of a triangle cannot be smaller than the total of the first two sides. You will have a valid triangle if this holds true for each of the three possible combinations. To confirm that the triangle is feasible, you will need to go through each of these combinations one at a time. Theorem a+b > c, a+c > b, and b+c > a can alternatively be thought of as an inequality. The triangle has sides of lengths a, b, and c.
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The following bar graph summarizes the weather conditions in Crayonton for each day this month so far.
The reasonable estimate of the probability that it is sunny tomorrow is 25%.
What is Probability?Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.
The value of probability will be always in the range from 0 to 1.
Probability of an event is calculated by dividing the number of desirable outcomes by the total number of events possible.
From the graph, we have,
Number of days weather is sunny = 3
Total number of days = Days weather is sunny + Days weather is cloudy + Days weather is rainy + Days weather is snowy
Total number of days = 3 + 5 + 2 + 2 = 12
Probability that weather is sunny = 3 / 12 = 1/4 = 0.25 = 25%
Hence there is a 25% probability that weather is sunny.
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The complete question is as follows :
The following bar graph summarizes the weather conditions in Crayonton for each day this month so far. Based on this data, what is a reasonable estimate of the probability that it is sunny tomorrow? Choose the best answer.
A particle rotates in a clockwise
motion according to the equation
x = 3 cos (0.2t - 0.813)
where t is in seconds
What is its frequency?
The frequency of the motion is given as follows:
0.0318 Hz.
How to obtain the frequency of the motion?A standard cosine function is defined as follows:
g(x) = acos(b(x+c))+d.
The coefficients have these following roles:
a: amplitude.b: The period is of 2π/B.c: phase shift.d: vertical shift.Hence we must look first at coefficient b to obtain the period of the function.
The coefficient b is given as follows:
b = 0.2.
Hence the period of the function is of:
p = 2π/0.2
p = 10π.
The frequency is one divided by the period, hence:
f = 1/10π
f = 0.0318 Hz.
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A jacket costs $75, and it is on sale for 60% off. What is the discounted price of the jacket?
Explain what you did.
Answer:$30
Step-by-step explanation:
$75 jacket is 60% off
Step 1: Plug in numbers
Use is/of=%/100 method
is/75=60/100=45
Step 2: Find the Price of Discounted Jacket
75-45=$30
Answer:
The discounted price of the jacket is $30-----------------------------------
Initial cost is $75 and the discount is 60%.
Subtract 60% to find the discounted amount:
75 - 60% = 75 - 75*60/100 = 75 - 45 = 30What is the full table of 4?
After responding to the question, we can therefore say that the numbers in the four-way tables are 4,8,12,16,20,24,28,32,36, and 40.
Describe a table.A mathematical table is a collection of numbers that shows the outcome of a calculation using multiple inputs. data with numbers and descriptions that is arranged in rows and columns. The table and 10 pattern are easy to remember. The following is the order of the numbers:2,4,6,8,10,12,14,16,18,20. Value maps are used to show how different data pieces are related to one another. You can incorporate the values table into your science lecture. Scientists and researchers use tables of values to store data and seek for patterns in that data. Then, this pattern is used in forecasting.
Here,
Thus,
table of four are as follows:
4,8,12,16,20,24,28,32,36 and 40.
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Translate the sentence into an equation.
Six more than the quotient of a number 2 and 4 equals .
Use the variable y for the unknown number.
Answer:
y / 4 + 6 = 2
Step-by-step explanation:
The most Lastri can afford to pay per year in mortgage payments is $13,900, and her credit score is 498. According to the following table for a $150,000 mortgage, by how many points would she need to improve this credit score in order to take a mortgage for $150,000?
According to the table for a $150,000 mortgage, Lastri's credit score needs to improve by 62 points for her to take a mortgage for $150,000.
What is the credit score?The credit score refers to an individual's or entity's creditworthiness rating.
The credit score predicts a person's credit behavior and ability to repay credit.
Financial institutions and lenders use the credit score to determine the amount of credit to offer a borrower, the attached credit risks, and the accompanying interest rate, including monthly payments.
Annual mortgage payments Lastri can afford = $13,900
Monthly payment = $1,158 ($13,900 ÷ 12)
Current credit score = 498
Minimum credit score for a monthly payment of $1,158 = 560
Additional credit score improvement = 62 (560 -498)
Thus, for Lastri to qualify for a $150,000 mortgage, her FICO credit score must improve by 62 points.
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Question Completion:Table
FICO Interest Monthly
Score Rate Payment
720 - 850 5.59% $860
700 - 719 5.71% $872
675 - 699 6.25% $924
620 - 674 7.40% $1,039
560 - 619 8.53% $1,157
500 - 559 9.29% $1,238
Lucas has 36 pages of a book left to read. If he reads 6 pages a day, how many days will it take Lucas to finish the book?
Answer:
6
Step-by-step explanation:
36/6
equals 6
Answer:
6 days.
Step-by-step explanation:
36 total pages
6 page a day
Then:
36/6 = 6
Diego says the expression 14−0.6t14−0.6t14−0.6t helps him understand this situation. In this situation, what does this expression represent, and what does the variable ttt stand for?
The expression 14 - 0.6t represents the number of gallons left for t number of days.
The variable t means the number of days.
What does the expression mean?In Mathematics, it is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information.
In this case, each day the car uses 0.6 gallons of fuel. A warning light comes on when the remaining fuel is 1.5 gallons or less. The expression is 14 - 0.6t.
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Complete question
Diego’s family car holds 14 gallons of fuel. Each day the car uses 0.6 gallons of fuel. A warning light comes on when the remaining fuel is 1.5 gallons or less.
Diego says the expression 14 - 0.6t helps him to understand this situation. What does this expression represent, and what does the variable t stand for
Plot a point on the coordinate plane to represent each of the ratio values in the table.
The points on the coordinate plane which represent the ratio values given in the table are given attached, where Distance is on the Y-Axis and Time is on the X-Axis.
Ratio data is a type of numerical (quantitative) data. It computes the distance between neighboring numbers on a continuous scale.
While it shares these characteristics with interval data (another form of quantitative data), ratio data is distinguished by the presence of a 'real zero.' In other words, a ratio scale measure of zero is absolute: ratio data can never be negative.
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Write the rational number as a decimal: 4 1/6
Answer: 4.17
Step-by-step explanation:
.
Line e has a slope of -4/9. Line f is parallel to line e. What is the slope of line f? Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Answer:
-4/9
Step-by-step explanation:
Line f has the same slope as line e. Parallel lines have the same slope.
Line e has the slope -4/9.
Line f has the slope -4/9.
25. Higher Order Thinking How are the ratios 24 laps 1 hour different? 192 laps 8 hours alike? How are they different?
These ratios are different because they express the number of laps for two different numbers of hours.
How do these ratios compare?To better understand how these ratios compare, let's simplify the second ratio:
192 laps/ 8 hours = 24, which means the ratio would be 24 laps per hour
This means that the ratios express the same number of laps per hour.
What makes the ratios different?Basically, the two ratios tell us the number of laps but using different hours. In this way, the first ratio expresses the number of laps in only one hour, while the second ratio amplifies this ratio to eight hours.
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-3x-3y=3 solve by substitution
Answer: x = 2, y = -3
Step-by-step explanation: From the question,
-3x -3y = 3 ---------- this becomes the first equation
Make y the subject
-3y = 3 + 3x
y = (3 + 3x)/ -3 ----------this becomes our second equation
Substitute the value of y into the first equation
-3x -3(3 + 3x) = 3
-3x -9 + 9x = 3
Collect like terms
-3x + 9x = 3 + 9
6x = 12
Divide both sides by 6
6x/ 6 = 12/ 6
x = 2
Substitute x = 2 into the second equation to find y
y = (3 + 3(2) )/ -3
y = ( 3 + 6) / -3
y = 9/ -3
y = -3
write the slope intercept form of the equation of a line with a slope of -5/8 that passes through the point (-14, 6)
Answer:
Step-by-step explanation:
Slope intercept for y=mx+b
point it passes (-14, 6) wherein b (0, b) is b=6
slope m = -5/8
substitute: y = mx+b
y= (-5/8)x+6
each paper clip is 3/4 of an inch long and cost $0.02. exactly enough paper clips are laid end to end to have a total length of 36 inches what is the total length of 36 inches what is the total cost of these paper clips
dani had $200 in her savings account. When she turned 18, the bank began charging her a $5.00/month fee. Write a function in terms of a for the balance of her savings account if she doesn't notice the monthly fee.
Complete the following. Use standard slope-intercept form.
We can write a function in terms of 'a' for the balance of Dani's savings account if she doesn't notice the monthly fee as:
f(a) = 200 - 5a
where 'a' represents the number of months that have passed since Dani turned 18 and the bank began charging her the monthly fee.
So, f(0) = 200 represents the initial balance in Dani's savings account when she turned 18.
f(1) = 200 - 5(1) = 195 represents the balance in Dani's savings account after 1 month.
f(2) = 200 - 5(2) = 190 represents the balance in Dani's savings account after 2 months and so on.
Therefore, the function f(a) = 200 - 5a represents the balance of Dani's savings account after 'a' number of months if she doesn't notice the monthly fee.
Let me know if this helps! :)
Please help fast guys
Simone practices her violin for hour each day. How much time does she spend practicing her violin each week? (A week has 7 days.)
Answer:
simone spends 7 hours a week
Step-by-step explanation:
Simone practices 1 hour every day
a week has 7 days, so
we multiply 7 x 1 = 7 hours per week
7= days of the week
1= hours simone practices every day
What is a constant of dilation?
A constant of dilation is a number used to change the size of a figure while preserving its shape. It is also known as a scale factor.
The constant of dilation is used in a dilation transformation, a type of transformation that changes the size of a figure without changing its shape or orientation.
The constant of dilation is typically represented by the letter "k" and is a number greater than 0. If the constant of dilation is greater than 1, the dilation will increase the size of the figure. If the constant of dilation is less than 1, the dilation will reduce the size of the figure. And if the constant of dilation is equal to 1, the dilation will not change the size of the figure.
It's important to note that the constant of dilation is a factor that applies to all the points of the figure, and it's the same for all the points of a figure during a dilation transformation.
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What is the area of 8cm and 5cm triangle?
The area of an 8 cm by 5 cm triangle is 20 cm^2.
The area of a triangle is calculated using the formula A = 1/2 * b * h, where b is the length of the base and h is the height. In this case, the base is 8 cm and the height is 5 cm, so the area of the triangle can be calculated as follows:
A = 1/2 * 8 * 5
A = 20 cm^2
Therefore, the area of an 8 cm by 5 cm triangle is 20 cm^2.
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write an expression for “the quoitient of 9 and c
The expression that the quotient of the number 9 and the letter 'c' will be 9 / c.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The quotient of the number 9 and the letter 'c' is written as,
⇒ 9 / c
The expression that the quotient of the number 9 and the letter 'c' will be 9 / c.
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The vertical distance of a falling ball is directly proportional min to the square of the time of the fall. The ball falls 80 m 4 seconds.
(a) Find the vertical distance fallen in 6 seconds.
(b) If the ball is dropped from a height of 240 m, find the time it takes to hit the ground.
Answer:
180 m , ≈ 6.9 seconds
Step-by-step explanation:
let vertical distance be represented by d and time t
given d is directly proportional to t² , then the equation relating them is
d = kt² ← k is the constant of proportion
to find k use the condition , the ball falls 80 m in 4 seconds , then
80 = k × 4² = 16k ( divide both sides by 16 )
5 = k
d = 5t² ← equation of proportion
(a)
when t = 6
d = 5 × 6² = 5 × 36 = 180 m
(b)
when d = 240
240 = 5t² ( divide both sides by 5 )
48 = t² ( take square root of both sides )
[tex]\sqrt{48}[/tex] = t , that is
t ≈ 6.9 seconds ( to the nearest tenth )
A gymast practices 6 days each week. She practices he same number of hours each day. If she practices a total of 120 in a 4- week period , how many hours each day does she practice.
The gymnast trains 5 hours per day making a total of 120 hours in a 4 week period
What is an equation?An equation is a expression that shows the relationship between numbers and variables.
Let x represent the number of hours practiced per day. A gymnast practices 6 days each week, hence:
Number of hours practiced per week = 6x
If she practices a total of 120 hours in a 4- week period. Therefore:
6x hours per week * 4 weeks = 120 hour
24x = 120
x = 5
The gymnast trains 5 hours per day.
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