The formula for y in terms of x is a cubic equation:
y = 0.25*x³
How to find the relation between x and y?We know that y is directly proportional to x³, then we can write the equation:
y = k*x³
Where k is the constant of proportionality.
In this case, we know that when x = 10, the value of y is 250, then we can replace these values in the above equation to find the value of x:
250 = k*10³
250 = k*1,000
Dividing both sides by 1,000 we get:
250/1,000 = k
0.25 = k
Then the equation is:
y = 0.25*10³
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A standard die is rolled. Find the probability that the number rolled is less than 3. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
Answer:
When a die is rolled, here it's Total possible outcome is= 6
and sample space is = 2 ( i.e. 1 & 2)
So. Probability of getting less than 3 = 26
=13
That's it.
Step-by-step explanation:
Five hours and 20 minutes after a raft left a dock, a patrol boat left the dock and traveled in the same direction as the raft. The boat caught up to the raft 20 km away from their starting point. What was the speed of the raft if the speed of the patrol boat was 12km/hr ?
The speed of the raft was 2.86 km/hr.
What is speed?Speed is defined as the rate of change of position of an object in any direction.
Given that, a patrol boat with speed of 12 km/hr caught a raft after travelling for 20 km and patrol boat left the dock after 5 hours and 20 minutes the raft left,
The time taken by the patrol boat to catch the raft is;
t = 20/15 = 5/3 hours
5/3 hours = 1 hour 40 minutes
Thus, it took 1 hour 40 minutes for the patrol boat to catch the raft
Thus, the raft was travelling for 5 hours 20 minutes plus 1 hour 40 minutes which 7 hours,
The speed of raft = 20/7 = 2.86 km/hr
Hence, The speed of the raft was 2.86 km/hr.
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A jewelry store buys a necklace for $75. They decide to mark the necklace up 55% and put it in their store. The store is running a promotion that everything purchased during the month of February will be 15% off. A customer comes in with a coupon that gives them an additional 10% off the sale price (after all other discounts were applied). After all discounts customers will be changed an 8% sales tax. Determine the final cost of the necklace if the customer bought the necklace February 28th and March 1st.
The final cost of the necklace if the customer bought it on February 28th or March 1st is $96.05 or $113, respectively.
How is the final cost determined?The final cost of the necklace purchased on February 28th includes the markup and excludes the promotional and coupon discounts, before adding the sales tax.
Similarly, the final cost of the necklace purchased on March 1st includes the markup and excludes the coupon discount, before adding the sales tax.
February 28 Purchase:Cost price to the store = $75
Markup =55%
Marked-up selling price = $116.25 ($75 x 1.55)
February sales discount = 15%
Promotional price during February = $98.81 ($116.25 x 1 - 15%)
Discount coupon rate = 10%
Discounted price = $88.93 ($98.81 x 1 - 10%)
Sales tax = 8%
Final selling price = $96.05 ($88.93 x 1.08)
March 1 Purchase:Cost price to the store = $75
Markup =55%
Marked-up selling price = $116.25 ($75 x 1.55)
Discount coupon rate = 10%
Discounted price = $104.63 ($116.25 x 1 - 10%)
Sales tax = 8%
Final selling price = $113 ($104.63 x 1.08)
Thus, the customer pays an additional $16.95 if they purchase the necklace on March 1st without the promotional discount, instead of February 28th.
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a track coach creates an obstacle course for his team. the coach plots the locations of the three obstacles on the coordinate plane shown to the right. each unit on the coordinate plane represents three yards. a student starts at Obstacle A. Then runs south to obstacle b, and then runs west to obstacle c. what is the total distance, in yards, the student runs to get from obstacle a to obstacle c?
The Total Distance is 51 yards.
What are Coordinates?Coordinates are a pair of integers (Cartesian coordinates), or sporadically a letter and a number, that identify a certain place on a grid, also referred to as a coordinate plane. The x axis (horizontal) and y axis are the two axes that make up a coordinate plane (vertical).
Given:
As, A and B have same x- coordinate
AB = | (y- coordinate of A) - (y- coordinate of B)|
= |5 - (-2)|
= 7
and, B and C have same y- coordinate
AB = | (x- coordinate of B) - (x- coordinate of A)|
= |3 - (-7)|
= 10
Then, Total distance= 7+ 10= 17
and, Total distance in yards = 17 x 3= 51 yards
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Square of 10^4 is ?
(a) Write an equation representing the fact that the product of two consecutive odd Integers is 143. Use x to represent the smaller
integer.
(b) Solve the equation from part (a) to find the two integers.
(a) The equation is
The equation representing the fact that the product of two consecutive odd Integers is 143 is x(x+2) = 143 where x represents the smaller number and the value of x is 11 or -13.
According to the question,
We have the following information:
The product of two consecutive odd Integers is 143.
Now, let's take the smaller integer to be x.
Now, next consecutive odd integer:
(x+2)
So, we have the following expression:
x(x+2) = 143
[tex]x^{2} +2x = 143\\[/tex]
[tex]x^{2} +2x -143 = 0[/tex]
[tex]x^{2}[/tex]+13x-11x-143 = 0
Taking x as the common factor from first two terms and -11 from the last two terms:
x(x+13)-11(x+13) = 0
(x-11)(x+13) = 0
x-11 = 0 and x+13 = 0
x = 11 or x = -13
Next odd integer = 13 or -11
Hence, the equation representing the fact that the product of two consecutive odd Integers is 143 is x(x+2) = 143 where x represents the smaller number and the value of x is 11 or -13.
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You have 100 feet of fencing to enclose a rectangular plot that borders on a river. If you do not fence the side along the river, find the length and width of the plot that will maximize the area.
Note: The length of the sum of three sides is 100. Let w be the width, find the length in terms of w, setup an equation for the area, then find the vertex (maximum) of your equation. Area of rectangle is length * width.
The length and width of the rectangular plot that will maximize the area are 50 feet and 25 feet respectively.
The vertex (maximum) of this equation is equal to 1,250 square feet.
How to calculate the area of a rectangle?Mathematically, the area of a rectangle can be calculated by using this formula:
A = lw
Where:
A represents the area of a rectangle.w represents the width of a rectangle.l represents the length of a rectangle.Since one side of this rectangular plot along the river does not require fencing, the perimeter equation is given by:
P = 2(l + w)
100 = 2w + l
Making length the subject of formula, we have:
l = 100 - 2w
Therefore, the area of this rectangular plot would now be:
A = (100 - 2w)w
A = 100w - 2w²
Next, we would take the first derivative and equate to zero in order to obtain the maximum area:
dA/dw = 100 - 4w
0 = 100 - 4w
4w = 100
Width, w = 25 feet.
For the length of this rectangular plot, we have:
Length, l = 100 - 2w
Length, l = 100 - 2(50)
Length, l = 50 feet.
Now, we can find the vertex (maximum) of this equation is given by:
Maximum area = 50 × 25
Maximum area = 1,250 square feet.
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Solve one sixth times quantity x plus 24 end quantity equals negative 6
The value of one-sixth times quantity x plus 24 end quantity equals negative 6 is -180.
What is an expression?The expression simply refers to the mathematical statements which have at least two terms that are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.
In this case, the expression given will be illustrated as:
1/6x + 24 = -6
Collect like terms
x / 6 = -6 - 24
x/6 = -30
Cross multiply
x = -30 × 6
x = -180
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Kakashi is filling his new bookshelf. The shelf holds 40 books. If he fills the bookshelf 4/5 of the way, how many books will Kakashi need?
Answer: 8 books
Step-by-step explanation:
First, she has 40 books.
1) Then she fills 4/5 of it. 4/5 of 40 is 32.
2) (4/5) x (40) = 32.
3) 40 - 32 = 8
4) So she needs to add 8 books.
Hope this helps :)
Ms. High brought each class a shout-out box. The
length of the box was 2.6 inches and the width was
0.8 inches. What is the area of the shout-out box?
can someone simplify 2\sqrt(6 and 3\sqrt(54))ft
Will mark brainliest
Answer:
2/sqrt6 = sqrt6/3
3/sqrt54 = sqrt6/6
2/sqrt6 + 3/sqrt54
= sqrt6/2
Step-by-step explanation:
Simplifying when there are radicals involved usually means "rationalizing".
Rationalizing means getting rid of the square root on the bottom of a fraction.
See image.
For a segment of a radio show, a disc jockey can play 5 records. If there are 7 records to select from, in how many ways can the program for this segment be arranged?
There are 2520 possible ways to arrange the programs
How to determine the ways the program can be arranged?From the question, we have
Total number of jockey records, n = 7
Total number of disc jockey records to select, r = 5
To determine the ways the program can be arranged, we make use of permutation
The number of ways of selection could be drawn is calculated using the following permutation formula
Total = ⁿPᵣ
Where
n = 7 and r = 5
Substitute the known values in the above equation
So, we have the following representation
Total = ⁷P₅
Apply the permutation formula
ⁿPᵣ = n!/(n - r)!
So, we have
Total = 7!/2!
Evaluate
Total = 2520
Hence, the number of ways is 2520
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There are three consecutive odd integers.Three times the largest is seven times the smallest. What are the integers?
The three consecutive odd intergers are 3,5 and 7
What do you mean by algebraic expression ?
An algebraic expression is the idea of using letters or alphabets to represent numbers without specifying the actual values. Algebra Basics taught us how to use letters like x, y, and z to represent unknown values. These characters are called variables here.
An algebraic expression can be a combination of variables and constants. Any multiplied value that is prefixed to a variable is a factor.
Let the three consecutive odd integers are x, x+2 and x+ 4
Here x is the smallest odd integer and x+4 is the largest odd integer
According to the question:
3(x +4) = 7x
3x + 12 = 7x
7x - 3x = 12
4x = 12
x = 12/4
x = 3
Three consecutive odd integers become:
x = 3
x + 2 = 3 +2 = 5
x + 4 = 3 + 4 = 7
Hence, the three consecutive odd intergers are 3,5 and 7
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Part of the pride of being an American comes from the fact that most people that want jobs have jobs. However, this is not always the case. Sometimes, as happened in 2008, the economy slows down, and jobs become harder to find or keep. Businesses make less money and so can keep fewer people employed. Those people who lost their jobs then have less money to spend. Because they have less money to spend, other businesses make less money, and then they, too, have to cut workers. In the United States, these cycles always end and the economy recovers, but it can take a while. People have to get creative about making money if they lose their jobs. Sometimes, they can use the skills they used at their old jobs to make money independently. For example, people don’t buy many car stereos when the economy is bad. So, car stereo stores have to layoff some of their stereo installers. If an installer has a place to work, that person can install stereos without a store. Often, this person will charge less than the store where he or she used to work. Also, the installer will get to keep all of the money he or she charged. At the store where the installer used to work, the store would have made most of the money. During hard times, it is important to be open-minded. There are always ways to make money outside of a formal job, if a person is willing to do things he or she wouldn’t normally do. A computer programmer, for example, might not be able to find work as a computer programmer. However, if the programmer is good with his or her hands, he or she may be able to find work in construction. Lawns never stop growing, and many aspects of life do not stop just because the economy has slowed down. A person who lost a job at a supermarket may be able to mow lawns for money, or do many other things. Most importantly, a person who loses a job must not give up. One’s attitude is very important in determining if he or she will be successful. A hopeful person is more likely to find a new job. Also, a hopeful person will
The sentence which supports the idea that people can use the skills they used at their old jobs to make money independently is "If an installer has a place to work, that person can install stereos without a store."
The correct answer option is option C
A summary about employees and American economy down timeThe essay is about American employees where people who actually needs a job gets a job. Although, this is not always the case especially when the economy slows down.
This slow down in the economy causes businesses to make less profit, thereby, making most people to lose their jobs. The purchasing power of the unemployed (people who lost their job) will reduce causing a decrease in the amount of money made by businesses. This is like a vicious cycle.
However, people who are skilled can still earn a living by doing other available jobs or those who are creative can create new jobs for themselves. For instance, an accountant can become a sales person in a supermarket if he or she lost their job.
In conclusion, a person who lost their job must be determined, hopeful and hard-working and must never give up, most importantly, they should never be idle because an idle mind is the devil's workshop.
Complete question:
Which sentence supports the idea that people can use the skills they used at their old jobs to make money independently?
Answer choices
A"So, car stereo stores have to layoff some of their stereo installers."
B"Often, this person will charge less than the store where he or she used to work."
C. "If an installer has a place to work, that person can install stereos without a store."
D. "At the store where the installer used to work, the store would have made most of the money."
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The arithmetic mean of the ages of 30 pupils is 15.3 years. One boy leaves the class and one girl is enrolled and the new average age of 30 pupils in the class becomes 15.2 years. How much older is the boy than the girl
The answer will be 3 years.
1st 30 pupils at average age of 15.3 yrs. give total age of 15.3 x 30 = 459yrs
2nd group of 30 pupils at average age of 15.2 yrs
give total age of 15.2 x 30 = 456yrs
Difference in age = 459 - 456
= 3 years.
need help with geometry
According to the concept of polynomial division, the equivalent expression is option (a). x+7 + 26/(x-3)
Polynomial division
Polynomial division refers the process of dividing one polynomial with another.
Given,
Here we have the expression (x² + 4x + 5) / x - 3.
Now, we have to find the equivalent polynomial expression when x - 3 is not equal to 3.
In order to find the equivalent expression, we have to do the following steps:
1. Divide the first term of the dividend by the first term of the divisor
2. Write down the calculated result x in the upper part of the table.
3. Multiply it by the divisor
4. Subtract this result from the dividend
Repeat this 4 steps until no further division.
This process is illustrated below.
According to this process, the equivalent fraction for the given fraction is
x + 7 + 26/(x - 3)
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How many 2/5 can go into 1/2?
help plsssss
Function f is an exponential function.
x 2 3 4 5 6
f(x) 9 27 81 243 729
What is the ratio of outputs for any two inputs that are 2 units apart? Divide the output for the larger x-value by the output for the smaller x-value.
Answer: 9
Step-by-step explanation:
The ratio of two outputs for any two input values that are 2 units apart is
27
What is a ratio?Ratio refers to fractions of two numbers say a and b written in the form
a / b
How to find the required expressionThe problem involves dividing the output for the larger x-value by the output or the smaller x-value
choosing output for x = 3 and x = 6, the two values are 2 units apart
the outputs are y = 27 and y = 729 respectively
taking the ratios
= 729 / 27
dividing gives the lowest term of the fraction
= 27 / 1
= 27
Hence dividing the output values for x = 3 and x = 6 is 27
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Guidance Missile System A missile guidance system has eight fail-safe components. The probability of each failing is 0.35
Assume the variable is binomial. Find the following probabilities. Round your answers to at least four decimal places.
Part: 0/4
Part 1 of 4
com Rem
(a) Exactly six will fail.
P(exactly six will fail) =
The probability of exactly six will fail = 0.0808
What is Probability?
Calculating the likelihood of experiments happening is one of the branches of mathematics known as probability. We can determine everything from the likelihood of receiving heads or tails when tossing a coin to the likelihood of making a research blunder, for instance, using a probability. It is crucial to grasp this branch's most fundamental concepts in order to fully comprehend it, including the formula for computing probabilities in equiprobable sample spaces, the likelihood of two events joining together, the probability of the complementary event, etc.
In the given question, we have:
We know that Probability in binomial distribution with total components ' n ', probability of success ' p ', and the number "of successes " = [tex]{ }^n c_k p^k(1-p)^{n-k}[/tex]
we know that:
[tex]{ }^n c_k=\frac{n !}{(n-k) ! k !}[/tex]
[tex]\begin{aligned}P(\text { success }) &=P(\text { a part fails })=0.35 \text {. So, } \\P(x=5) &={ }^8 C_5 \times(0.35)^5(0.65)^3 \\&=56 \times(0.005252) \times(0.274625) \\&=0.0808 \\& \text { (Round to } 4 \text {-decimals) }\end{aligned}[/tex]
Hence,
The probability of exactly six will fail = 0.0808
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What is the slope of the line 8x + 3y = 8 – 2x?
The slope of the line, 8x + 3y = 8 – 2x, is -10/3
Determining the slope of the equation of a lineFrom the question, we are to determine the slope of the given equation.
The given equation is
8x + 3y = 8 – 2x
To determine the slope of the line, we will express the equation in the general form of the slope-intercept form of the equation a line.
The general form of the slope-intercept form of a line is
y = mx + b
Where m is the slope
and b is the y-intercept
Expressing the equation in the slope-intercept form of a line
8x + 3y = 8 - 2x
Subtract 8x from both sides of the equation
8x - 8x + 3y = 8 - 2x - 8x
3y = 8 - 10x
3y = -10x + 8
Divide through by 3
3y/3 = -10x/3 + 8/3
Y = -10/3 x + 8/3
By comparison,
m = -10/3
Hence, the slope is -10/3
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Graph the equation 4x−5y=1 by plotting points.
y=4/5x-2/5 is the equation used to plot the graph.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
The given equation is 4x−5y=1
Four times of x minus five times of y equal to one
4x−5y=1
Let us write this equation in slope intercept form
-5y=1-4x
5y=-2+4x
y=-2/5+4/5x
y=4/5x-2/5
x 0 1 2 3
y -2/5 2/5 6/5 10/5
y -0.4 0.4 1.2 2
by using these points we plot the graph.
Hence y=4/5x-2/5 is the equation used to plot the graph.
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Use the digits -9 to 9 to complete the puzzle below. Try all the combinations. But as you begin doing that, you will realize that in some cases you are looking for factor combinations with a particular sum or difference. You will see that some numbers have to be greater than a particular value in order to produce the product you are looking for. Show your work to confirm your solution.
According to the concept of complex numbers, the solution function is (5 - 6i) (2 + 4i) = (34 + 8i)
Complex numbers:
Complex numbers means a combination of a real number and an imaginary number.
The standard form of complex number is,
a + ib
Where a complex number, where a,b are real numbers and i = √-1.
Given,
Here we have the following complex number expression
(_ + _i) (_ + _i) = 34 + 8i
Here we need find the value of the dashes and the number must lies between -9 to +9.
Let us consider a, b, c and d as the number presented in the dashes then it can be written as,
=> (a + bi) (c + di)
Now, we have to expand this expression then we get,
=> ac + adi + bci + bdi²
Combine the like terms,
=> (ac − bd) + (ad + bc)i
Now, we have to match the coefficients as,
30 < ac − bd < 80
We also know that,
=> ad + bc = 0
Now, we need to pick four integers between -9 and 9 such that these two equations are satisfied.
We also know that
=> ac − bd = 34
=> ad + bc = 8
Therefore, it makes sense to assume b is negative.
After some trial and error, one possible answer is a = 5, b = -6, c = 2, d = 4
Therefore, the expression is written as,
=> (5 - 6i) (2 + 4i) = (34 + 8i)
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A Tyrannosaurus rex weighed about 1.4 tons more than one tenth the weight of a Patagotitan mayorum. About how much did the Tyrannosaurus rex weigh?
Tyrannosaurus rex weighs about 0.14 times the weight of Patagotitan mayorum
How to determine by how much Tyrannosaurus rex weigh
In solving the proportion of the weights we use multiplication of fractions
Multiplication is a mathematical operator to handle such operation
A Tyrannosaurus rex weighed about 1.4 tons more than one tenth the weight of a Patagotitan mayorum
This is is written mathematically as
Tyrannosaurus rex weight, x = 1.4 * 1/10 * Patagotitan mayorum weight, y
x = 1.4 * 1/10 * y
x = 0.14 *y
x = 0.14y
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15.75 + .5x = 16.53 - .13x
The compression ratio in a certain engine is 7.5 to 1. If the expanded volume of a cylinder is 45 cu in., what is the
compressed volume?
If the expanded volume of a cylinder is 45 in³ , then the compressed volume is 6 in³ .
In the question ,
it is given that ,
the compression ratio in a certain engine is 7.5 : 1 .
the expanded volume of a cylinder is = 45 in³ .
we have to find the compressed volume of the cylinder ,
let the compressed volume of the cylinder be = v .
the above situation can be represented as
7.5 : 1 = expanded volume : compressed volume
7.5/1 = 45/v
7.5 = 45/v
v = 45/7.5
v = 6 cubic inches .
Therefore , If the expanded volume of a cylinder is 45 in³ , then the compressed volume is 6 in³ .
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find slope intercept form and graph (-3,0) and (-3,-7)
Answer:
x = -3
Step-by-step explanation:
Slope = Rise/Run
Slope = Difference in y/Difference in x
Slope = -7/0
Slope = undefined (can not divide by 0)
This means that this is a vertical line
Sophie put $3330 in a savings account at a simple interest rate of 7.4% per year. Adam put $2795 in a savings account at a simple interest rate of 8.1% per year.
Who will have earned more interest after 5 years? How much more?
Adam earned $100.12 more interest than the Sophie
Consider Sophie
The principal amount = $3330
The interest rate = 7.4%
The time period = 5 years
Simple interest = PRT
Where P is the principal amount
R is the interest rate
T is the time period
Substitute the values in the equation
Simple interest = 3330× (7.4/100) × 5
= $1232.1
Consider Adam
The principal amount = $2795
The interest rate = 8.1%
The time period = 5 years
Simple interest = 2795 × (8.1/100) × 5
= $1131.98
The difference = 1232.1 - 1131.98
= $100.12
Hence, the Adam earned $100.12 more interest than the Sophie
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What is the answer to c?
Answer:
The answer is 6.5
Step-by-step explanation:
The equation is y=3x-1. Plug in 2.5 as the value for x and solve.
3×2.5=7.5
7.5-1=6.5
Match the equations with the value of x that makes them true. 2(2x − 3) = 6 5x − 2x − 4 = 5 x + 2x + 3 = 9 5(x + 3) = 25 4x − (2x + 1) = 3 5x − (3x − 1) = 7
Each of the equations should be matched with the value of x that makes them true as follows:
x = 2; x + 2x + 3 = 9, 5(x + 3) = 25, and 4x − (2x + 1) = 3.
x = 3; 2(2x − 3) = 6, 5x - 2x - 4 = 5, and 5x − (3x − 1) = 7.
How to determine the true equations?In order to determine which x-values are true solutions based on the given equations, we would have to test each of the values of x by substituting them into the equations as follows;
When x = 2, we have:
2(2x − 3) = 6
4x − 6 = 6
4(2) - 6 = 6
8 - 6 = 6
2 = 6 (False).
When x = 3, we have:
2(2x − 3) = 6
4x − 6 = 6
4(3) - 6 = 6
12 - 6 = 6
6 = 6 (True).
When x = 2, we have:
5x - 2x - 4 = 5
3x - 4 = 5
3(2) - 4 = 5
6 - 4 = 5
1 = 5 (False).
When x = 3, we have:
5x - 2x - 4 = 5
3x - 4 = 5
3(3) - 4 = 5
9 - 4 = 5
5 = 5 (True).
When x = 2, we have:
x + 2x + 3 = 9
3x + 3 = 9
3(2) + 3 = 12
9 = 12 (False).
When x = 3, we have:
x + 2x + 3 = 9
3x + 3 = 9
3(3) + 3 = 12
12 = 12 (True).
5(x + 3) = 25
5x + 15 = 25
5x = 25 - 15
5x = 10
x = 2 (True).
4x − (2x + 1) = 3
4x - 2x - 1 = 3
2x = 3 + 1
2x = 4
x = 2 (True).
5x − (3x − 1) = 7
5x - 3x + 1 = 7
2x = 7 - 1
2x = 6
x = 3 (True).
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Find a so that the point (-1,5) is on the graph of f(x)=ax^2+2
Answer:
a=3
Step-by-step explanation:
To find a, you plug the known numbers into the given equation (coordinates). f(x) is the same as the y-coordinate.
With that, you get:
5=a(-1)^2+2
Then you solve for a
3=a(-1)^2
3=a(1)
3=a