The two solutions of the system of equations are (4, -1) and (-1, 4).
How to solve the system of equations?Here we want to solve the system of equations below:
x + y = 3
x^2 + y^2 = 17
We can isolate x on the first equation to get:
x = 3 - y
And replace that in the other equation to get:
(3 - y)^2 + y^2 = 17
9 - 6y + y^2 + y^2 = 17
2y^2 - 6y + 9 - 17 = 0
2y^2 - 6y - 8 = 0
y^2 - 3y -4 = 0
Using the quadratic formula we will get the solutions:
[tex]y = \frac{3 \pm \sqrt{(-3)^2 - 4*1*(-4)} }{2} \\\\y = \frac{3 \pm5 }{2}[/tex]
So the two solutions are:
y = (3 + 5)/2 = 4
y = (3 - 5)/2 = -1
The correspondent values of x are given by evaluating the line.
x + 4 = 3
x = 3 - 4 = -1
So we have the point (-1, 4)
x - 1 = 3
x = 3 + 1
x = 4
So we have the point (4, -1)
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How many times as long as a THimble jellyfish is a Lion's Mane jellyfish? Thimble jellyfish = 1 inch, Lion's mane jellyfish = 7 feet
84 inches times as long as a Thimble jellyfish is a Lion's Mane jellyfish.
Now, According to the question:
"Information available from the question"
A Thimble jellyfish is a Lion's Mane jellyfish.
Thimble jellyfish = 1 inch,
Lion's mane jellyfish = 7 feet
Convert feet into inches.
To calculate a value in feet to the corresponding value in inches, just multiply the quantity in feet by 12 (the conversion factor).
Here is the formula:
Value in inches = value in feet × 12
Formula: multiply the value in feet by the conversion factor '12'.
So, 7 feet = 7 × 12 = 84 inches.
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what is the name for an equilateral triangle
Answer:
equiangular triangle
Step-by-step explanation:
PLEASE HELP ASAP??!!
What is the end behavior of the function f(x) = −x³ + 2x² +1
As a approaches infinity, f(x) approaches infinity. As approaches negative
infinity, f(x) approaches negative infinity.
As a approaches infinity, f(x) approaches negative infinity. As a approaches
negative infinity, f(x) approaches negative infinity.
As a approaches infinity. f(x) approaches negative infinity. As a approaches
negative infinity, f(x) approaches infinity.
As approaches infinity, f(x) approaches infinity. As a approaches negative
The end behavior of the function f(x) = −x³ + 2x² +1 is:
as x → ∞, f(x) → -∞
as x → -∞, f(x) → ∞
What is the end behavior of the function?Here we want to find the end behavior of the function below:
f(x) = −x³ + 2x² +1
Notice that the degree is odd, this means that the end behaviors are opposite in opposite values of x.
Because we have a negative sign on the term with the highest exponent, then as x tends to infinity, the function will tend to negative infinity.
And thus, because the degree is odd, the value of f(x) as x tends to negative infinity tends to positive infinity.
Thus we can write:
as x → ∞, f(x) → -∞
as x → -∞, f(x) → ∞
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If you guys can solve the sheet, I will crown your braincrown thing
Goodluck
The values of x from the given figures are 3 √29 and 24 respectively.
What is triangle ?
Triangle can be defined in which it has three sides , three angles and sum of three angles is always 180 degrees.
Given
In the figure,
The two given triangles are similar ,
So, in the first figure it is given that they are similar ,
√29 / 5 = x / 15
x = √29 * 15 / 5
x =√29 * 3
x = 3 √29
And in the second figure , here also they gave they are similar
so we get,
12 / 13 = x / 26
x = 12 * 26 / 13
x = 12 * 2
x = 24
Hence, The values of x from the given figures are 3 √29 and 24 respectively.
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height is an example of a variable that uses the _____ scale.
Height is an example of a variable that uses the ratio scale.
Hence, option (a) is the correct choice.
Weight, height, and distance are all ratio variables. The ratio scale allows you to add, subtract, divide, and multiply data. Ratio scales are further distinguished from interval scales by the presence of a 'true zero'.
Height is an excellent example of a measuring scale based on a ratio. It is not nominal or ordinal since each change in the height unit (inches, metres, feet, etc.) has a standard distance between them, and it is not interval because height has a genuine zero.
Height, for example, is ratio data. There is no such thing as negative height. If the height of an item is 0, there is no object. This is not the same as talking about temperature.
The complete question should be:
Height is an example of a variable that uses the scale.
a. ratio b. interval c. nominal d. ordinal
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what is the image of (9,8) after a dilation by a scale factor of 5 centered at the origin?
Answer: (-45 , -25)
Step-by-step explanation:
Please mark brainliest!!
Emma wants to paint her house light pink. She adds 6 cans of white paint to every 4 cans of pink
paint to make the desired color. How many cans of white paint will she need to mixed with 12 cans of
pink?
To find out how many cans of white paint Emma will need to mix with 12 cans of pink paint, we can use the proportion of white paint to pink paint that she is currently using: 6 cans of white paint to every 4 cans of pink paint.
We can set up an equation using the proportion:
white paint/pink paint = 6/4 =3/2
We know that Emma wants to use 12 cans of pink paint, so we can use this information to solve for the number of cans of white paint she needs:
white paint/pink paint = 3/2
white paint = (3/2) * pink paint
white paint = (3/2) * 12 cans
white paint = 18 cans
So Emma will need 18 cans of white paint to mix with 12 cans of pink paint to get the desired color.
Mr.Todd want to paint the outide of the birdhoue. How much paint doe he need to buy to cover the outide of the entire birdhoue( rounded to the nearet hundredth). Explain how much and how you know in at leat two entence.
The amount of paint needed is 176/36000 = 0.0049 gallons, which is equivalent to 4.9 milliliters, rounded to the nearest hundredth.
To calculate how much paint Mr.Todd needs to buy to cover the outside of the entire birdhouse, we must first know the dimensions of the birdhouse. Let's assume the birdhouse has the dimensions of 10 inches long, 8 inches wide and 6 inches tall, and each side requires 1 coat of paint. The total surface area of the birdhouse is then 10 x 8 + 10 x 6 + 8 x 6 = 176 inches squared. Next, we need to know the coverage of the paint, which we will assume is 250 square feet per gallon. Since 1 square foot is equal to 144 square inches, the coverage of the paint is 36000 square inches per gallon. To find out how many gallons of paint are needed to cover the birdhouse, we need to divide the total surface area of the birdhouse (176 square inches) by the coverage of the paint (36000 square inches per gallon). Therefore, the amount of paint needed is 176/36000 = 0.0049 gallons, which is equivalent to 4.9 milliliters, rounded to the nearest hundredth.
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Write an equation that represents the line use exact numbers
The equation of the line is 6x-5y = 25.
What is equation of line?
When the slope of the line being studied is known, and the provided point is also the y intercept, the slope intercept formula, y = mx + b, is utilised (0, b). It provides both a slope and an intercept, which is why the form is known as the slope-intercept equation.
Here in the given graph the points are [tex](x_1,y_1)=(0,-5)[/tex] and [tex](x_2,y_2)=(5,1)[/tex]
Now using slope formula m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
=> slope m = [tex]\frac{1-(-5)}{5-0}[/tex]
=> m = [tex]\frac{1+5}{5} = \frac{6}{5}[/tex]
Now using equation formula [tex]y-y_1 = m(x-x_1)[/tex] then
=> [tex]y - (-5) = \frac{6}{5}(x-0)[/tex]
=> y+5 = [tex]\frac{6}{5}[/tex]x
=> 5y+25 = 6x
=> 6x-5y = 25.
Hence the equation of line is 6x-5y = 25.
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John sells cupcakes. He has been offered a salary position at two different companies to make and sell his cupcakes. The first company offered him a weekly salary of $ 800.00 $800.00 plus a commission of $ 0.30 $0.30 for each cupcake he sells. The second company offered him a weekly salary of $ 350.00 $350.00 plus a commission of $ 1.30 $1.30 for each cupcake he sells. How many cupcakes must John sell each week for the total pay from each company to be the same?
PLEASE ANSWER FAST WORTH 92 POINTS
Answer:
450 cupcakes
Step-by-step explanation:
Let x be the number of cupcakes sold for John's total pay to be the same for both companies
For the first company
Salary = $800/week
Commission is $0.30 per cupcake
For sales of x cupcakes, total commission = 0.30x
Total pay = Weekly salary + Total commission from sales
Total Pay = 800+ 0.3x
For the second company
Salary = 350 /week
Commission: $1.30 per cupcake
For sales of x cupcakes, total commission = 1.30x
Total Pay = Weekly salary + Total commission from sales
Total Pay = 350 + 1.3x
If both pay must be he same,
800 + 0.3x = 350 + 1.3x
800-350 = 1.3x - 0.3x
450 = 1x
x = 450 cupcakes ANSWER
Answer: 450
Step-by-step explanation:
If we let x and y represent the number of cupcakes John sells and his total weekly income, respectively, we get the following system of equations.
=0.35x+845
=1.4x+372.5
Since both equations are solved for y, any substitution for y will result in the following
211.4 x+372.5&=0.35
x+845
1.4x+372.5
=0.35x+845
Solving for x will give us the number of cupcakes John needs to sell weekly for each paycheck to be the same. Doing so, we get
1.4 x+372.5&=0.35 x+845
1.05 x&=472.5x=450
1.4x+372.5
1.05x
x
=0.35x+845
=472.5
=450
Therefore, John needs to sell 450450 cupcakes each week for both salaries to be the same.
21•15 equals
(20+1)•15
For what value of x is JKLM a parallelogram?
4x + 13
4x-1
3x + 20
5X-8
To represents JKLM is a parallelogram the required value of x is equal to 7.
In the parallelogram JKLM,
Let us consider the measure of each side in form of 'x' is represented by :
JK = 4x + 13
KL = 4x - 1
LM = 3x + 20
MJ = 5x - 8
Opposite side of the parallelogram JKLM are congruent to each other.
JK = LM
⇒ 4x + 13 = 3x + 20
⇒ 4x - 3x = 20 - 13
⇒ x = 7
When
KL = MJ
⇒ 4x - 1 = 5x - 8
⇒ 5x - 4x = 8 - 1
⇒ x = 7
JK = 4(7) + 13
= 41
LM = 3(7) + 20
= 41
KL = 4(7) -1
= 27
MJ = 5(7) - 8
= 27
Therefore, the value of x which represents that JKLM is a parallelogram is equal to 7.
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at time , a tank contains oz of salt dissolved in gallons of water. then brine containing oz of salt per gallon of brine is allowed to enter the tank at a rate of gal/min and the mixed solution is drained from the tank at the same rate. (a) how much salt is in the tank at an arbitrary time? 200-140e^(-t/25) oz. (b) how much salt is in the tank at time min?
The amount of salt in the tank is decreasing exponentially with time.
At time t, the amount of salt in a tank containing oz of salt dissolved in gallons of water can be calculated using the following formula:
Salt in tank (oz) = 200 - 140e^(-t/25)
For example, at time t = 10 min, the amount of salt in the tank is 200 - 140e^(-10/25) = 200 - 140(0.7787) = 124.42 oz.
This calculation assumes that brine containing oz of salt per gallon of brine is allowed to enter the tank at a rate of gal/min and the mixed solution is drained from the tank at the same rate. Thus, the amount of salt in the tank is decreasing exponentially with time.
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Carol is cross-country skiing. The table shows the distance she traveled after various numbers of minutes. What is the rate of change?
The rate of change for the Carol with respect to time is 3/16 miles per minute.
What is the rate of change?The rate of change (ROC) measures how quickly a variable alters over a predetermined amount of time. When discussing momentum, the term "rate of change" (ROC) is frequently used. It is typically defined as the ratio of a change in one variable to a matching change in another; visually, the rate of change is represented by the slope of a line.
Given The table shows the distance Carol traveled after various numbers of minutes,
Input Output
2 1/6
3 17/48
4 13/24
5 35/48
6 11/12
Here, the output values from 1/6 to 11/12 indicate the distance in miles whereas the input values from 2 to 6 describe the time in minutes.
by utilizing the first two sets of input-output numbers, calculating the rate of change
Relative change = change in distance/change in time
(17/48 - 1/6)/(3-2) = (17/48 - 8/48) /1 = 9/48 = 3/16 miles per minute
Hence the rate of change is 3/16 miles per minute.
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John is making apple pies and apple cobblers to sell at his stand at the Farmer's Market.
A pie uses 4 cups of apples and 3 cups of flour.
A cobbler uses 2 cups of apples and 3 cups of flour.
John has 16 cups of apples and 15 cups of flour.
When John sells the pies and cobblers at the Farmer's Market, he will make $3.00 profit per pie and $2.00 profit per cobbler.
Let x = the number of pies John makes.
Let y = the number of cobblers John makes.
Which inequality shows the constraint on the amount of apples John has to make pies and cobblers?
Let x = the number of pies John makes.
Let y = the number of cobblers John makes.
An inequality which shows the constraint on the amount of apple John has to make pies and cobblers is: D. 4x + 2y ≤ 16.
How to write an equation to model this situation?In order to write an equation that model this situation, we would assign a variable to the number of pies John makes and the total number of cobblers John makes respectively, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the number of pies John makes.Let the variable y represent the total number of cobblers John makes.Since a pie uses 4 cups of apples and 3 cups of flour while a cobbler uses 2 cups of apples and 3 cups of flour, the constraint on the amount of flour is given by:
4x + 2y ≤ 16
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Identify the linear function I’ll give brainliest
Answer:
A
Step-by-step explanation:
Any equation with a single independant variable (often an 'X') that is not ( x2,x3 ) is linear.
Find the area of the polygon with the given vertices. $K(-3,3),L(3,3),M(3,-1),N(-3,-1)$
The area of the polygon is 24 unit².
What is Polygons?Polygons are closed figures which has at least three set of line segments joined together.
The polygon with least number of sides is triangle.
We have four coordinates of vertices given, K(-3,3), L(3,3), M(3,-1), N(-3,-1).
So the polygon must be a quadrilateral.
Length of KL = [tex]\sqrt{(3--3)^{2} + (3-3)^2 }[/tex] = [tex]\sqrt{6^2}[/tex] = 6
Length of LM = [tex]\sqrt{(3-3)^2+(-1-3)^2}[/tex] = [tex]\sqrt{(-4)^2}[/tex] = 4
Length of MN =[tex]\sqrt{(-3-3)^2+(-1--1)^2}[/tex] = [tex]\sqrt{(-6)^2}[/tex] = 6
Length of NK = [tex]\sqrt{(-3--3)^2+(3--1)^2}[/tex] = [tex]\sqrt{4^2}[/tex] = 4
So we get that, opposite sides are having equal length.
So the polygon must be a rectangle.
Area of the rectangle = Length × Width
= 6 × 4
= 24 units²
Hence the area of the polygon with the given vertices is 24 unit².
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Construct ∠Y so that ∠Y ≅ ∠Z.
The angle ∠Y so that ∠Y ≅ ∠Z is added as an attachment
How to construct the angleFrom the question, we have the following parameters that can be used in our computation:
Construct ∠Y so that ∠Y ≅ ∠Z.
There are several ways to do this, some of them are:
Construct an isosceles triangle and name the base angles Y and ZConstruct a rectangle or a square and name any of the vertices Y and ZThe above statements are true because the base angles of an isosceles triangle are congruent and all angles in a rectangle/square are congruent
See attachment
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sorry for the side view if any one could do this step by step you would be a life saver
Answer:
pls see attached
Step-by-step explanation:
Eddie is getting balloons for his mothers birthday party. He wants each ballon string to be 6 feet long. At the party store, string is sold by the yard. If Eddie wants to get 77 balloons, how many yards of string will he need
Answer:
462
Step-by-step explanation:
do 6x77 which is 462. alternative forms: 4.62 x 10^2
4. A 15-kg child is tossed up into the air by her parent. The child is 2.5 meters off the ground traveling 3 m/s.
Circle one: KE / GPE / both
Show your work for finding the values of each type of energy the object has:
The object has both kinetic energy and potential energy.
The values of each type of energy the object has are KE = 67.5 J
GPE = 367.5 J
How to find the energy of the object?Energy is the ability to do work. It can take many forms, such as kinetic energy (energy of motion), potential energy (stored energy) etc.
If a 15-kg child is tossed up into the air by her parent and the child is 2.5 meters off the ground traveling 3 m/s.
Then boy has kinetic energy due to his motion and also has potential energy due to his height.
Thus, M = 15-kg, h = 2.5 meters and V = 3 m/s
KE = 1/2(M)(V)² = 1/2 × 15 × 3² = 67.5 J
GPE = mgh = 15 × 9.8 × 2.5 = 367.5 J
KE + PE = 67.5 + 367.5 = 435 J
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SEND HELP PLS IM BEGGING YIU
Answer:
B
Step-by-step explanation:
Because all four packages of baseball cards added up together makes 76 cards, and since 6 is over 5 that makes it closer to 80.
Answer: 1st Package: 17 = 20
2nd Package: 21 = 20
3rd Package: 22 = 20
4th Package: 16 = 20
Total Amount of Cards: 20 + 20 + 20 + 20 = 80
I hope this helps! :)
Step-by-step explanation:
1. a certain college wants to estimate the amount of time students, who live off campus, spend commuting to classes each week. a random sample of 45 off-campus students is surveyed. a) identify the population and sample for this study. b) what data is being collected? what type of data is this? c) what type of study is this?
The objective of this research is to collect data on a specific component of the off-campus student population.The amount of time they spend travelling to courses each week.
a) The population for this study is all off-campus students at this college, and the sample is a random sample of 45 off-campus students who are polled. The sample is chosen at random to be representative of the entire population.
b) The data being gathered is the amount of time the surveyed students spend each week travelling to school. Because it reflects a numerical measurement, this is quantitative data. This information will be used to calculate the average commuting time for off-campus students and to identify any possible concerns or areas for improvement in commuting.
c) This is a descriptive research, since it seeks to characterise and summarise the features of the off-campus student population in terms of commuting time. The study's purpose is to better understand off-campus students' commuting patterns and gather ideas into how to enhance their commuting experience.
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Multiply.
(2x² - 4x)(6x² - 5x)
O A. 124-34x² + 20x
OB. 124-10x³ + 20x²
O C. 12x - 34x³ + 20x²
OD. 12-10x² + 20x
A
Which of the following is equivalent to
3^sqrt32x³y^6/ 3^ sqrt 2x^9 y^2
If the expression be [tex]$\frac{\sqrt[3]{32 x^3 y^6}}{\sqrt[3]{2 x^9 y^2}}$[/tex] then the equivalent expression exists [tex]$\frac{\sqrt[3]{16 y^4}}{\sqrt[3]{x^6}}$$[/tex].
What is meant by expression?A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. It is possible to multiply, divide, add, or subtract in math.
Expression is a term used in mathematics to describe a grouping of numbers, variables, and operators that illustrates the value of something. A mathematical statement that has two expressions that are equal is known as an equation. A phrase fragment can be used as an expression to represent a single numerical value.
An expression in mathematics is a sentence made up of terms and operations. Terms may be variables with coefficients or constant (numeric) values. Addition, subtraction, multiplication, and division are all possible operations.
Let the given expression be [tex]$\frac{\sqrt[3]{32 x^3 y^6}}{\sqrt[3]{2 x^9 y^2}}$$[/tex]
Apply radical rule: [tex]$\frac{\sqrt[n]{a}}{\sqrt[n]{b}}=\sqrt[n]{\frac{a}{b}}, \quad$[/tex] assuming [tex]$a \geq 0, b \geq 0$[/tex]
[tex]$$\begin{aligned}& \frac{\sqrt[3]{32 x^3 y^6}}{\sqrt[3]{2 x^9 y^2}}=\sqrt[3]{\frac{32 x^3 y^6}{2 x^9 y^2}} \\& =\sqrt[3]{\frac{32 x^3 y^6}{2 x^9 y^2}}\end{aligned}$$[/tex]
simplifying the above equation, we get
[tex]$\frac{32 x^3 y^6}{2 x^9 y^2}: \frac{16 y^4}{x^6}$[/tex]
[tex]$=\sqrt[3]{\frac{16 y^4}{x^6}}$$[/tex]
Apply radical rule: [tex]$\sqrt[n]{\frac{a}{b}}=\frac{\sqrt[n]{a}}{\sqrt[n]{b}}, \quad$[/tex] assuming [tex]$a \geq 0, b \geq 0$[/tex]
[tex]$=\frac{\sqrt[3]{16 y^4}}{\sqrt[3]{x^6}}$$[/tex]
Therefore, the correct answer is option c.
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Answer:
option c
Step-by-step explanation:
edge 2023
Question 19
Luke invests 34000 into an account that pays 3. 4% compound interest per annum for the first two years, and 2. 3%
thereafter.
Given that the interest is paid into his account monthly (and calculated monthly), work out how much money Luke
will have in his account after 6 years and 3 months.
As per the formula of compound interest the amount in his account after 6 year 3 months is $40,085.307
In math the term called compound interest is defined as when you earn interest on both the money you've saved and the interest you earn.
Here we know that Luke invests 34000 into an account that pays 3. 4% compound interest per annum for the first two years and 2. 3% thereafter.
Here we need to find the amount in his account after 6 years and 3 months.
Then it can be calculated as,
FV = PV(1 + i)ⁿ
Here we know that PV = 34000 and i = 3.4% for two years,
Then the FV is value is calculated as,
=> FV = 34000(1 + 3.4/100)²
=> FV = 34000 ( 1 + 0.034)²
=> FV = 36351.304
Similarly, the FV value of 4 years 3 months is calculated as,
=> FV = 36351.304(1 + 2.3/100)⁴°³
=> FV = 36351.304(1 + 0.023)⁴°³
=> FV = 40085.307
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The path of a volleyball thrown over a net is modeled with the function
A(x) = -0.02x2 + 0.6x + 5, where x is the horizontal distance, in feet, from the
starting point, and A is the altitude of the ball in feet. Write an equation that can be solved to find out how far the ball travels horizontally before it hits the ground. Then find the distance to the nearest foot.
equation:
distance:
The ball travel horizontally 37 feet before it hits the ground.
What is Distance ?
Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.
we have;
A(x) = -0.02x2 + 0.6x + 5
where
The horizontal distance, x, is given in feet.
The ball's height is indicated by the symbol A ---> in feet.
The fact that
The ball's altitude was zero when it landed on the earth.
so,
For A(x)=0
-0.02x^2 + 6x +5 = 0
'
the quadratic equation to be solved
The equation solving formula for a quadratic equation of the type;
ax^2 + bx + c = 0
this equation is equal to ;
[tex]x = \frac{-b\pm \sqrt{b^{2}- 4ac } }{2a}[/tex]
we have ;
-0.02x^2 + 0.6x +5 = 0
So,
a = -0.02
b = 0.6
c = 5
Subsititue this values in the formula;
[tex]x = \frac{-0.6\pm \sqrt{0.6^{2} -4 *(-0.02)(5) } }{2*(-0.02)}[/tex]
[tex]x = \frac{-0.6\pm \sqrt{0.76 } }{-0.04}[/tex]
[tex]x = \frac{-0.6\pm \ 0.87 }{-0.04}[/tex]
[tex]x = \frac{-0.6\ + \ 0.87 }{-0.04}= -6.75[/tex]
[tex]x = \frac{-0.6\ - \ 0.87 }{-0.04}= 36.75[/tex]
therefore
The ball travel horizontally 37 feet before it hits the ground.
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2. Consider the set A = {-2, -1, 0, 1, 2} and the equation Y = -x³ + 2 where x is an element
of A. State the domain, range and determine whether or not the relation, Y = -x³ + 2 is a
function. If it is a function, write the relation in "function notation". Show all your work for
full credit. Hint: you might need to draw a diagram.
SOL FO
3. If f(x) = x² - 2x + 7, evaluate the following:
f(-5)
f (0)
ƒ (1)
The minimum value of Y is -6 and the maximum value is 10. The range is {-6, 1, 2, 3, 10}.
What is the domain and how is the range calculated range ?Domain of Y = -x³ + 2: A = {-2, -1, 0, 1, 2}. The equation is defined for all x in the set A.
Range of Y = -x³ + 2: To find the range, we need to find the minimum and maximum values of Y for x in the set A. Using the formula Y = -x³ + 2, we can substitute the values of x from the set A and find the corresponding values of Y:
x = -2, Y = -(-8) + 2 = 10
x = -1, Y = -(-1) + 2 = 3
x = 0, Y = -(0) + 2 = 2
x = 1, Y = -(1) + 2 = 1
x = 2, Y = -(8) + 2 = -6
Thus, the minimum value of Y is -6 and the maximum value is 10. The range is {-6, 1, 2, 3, 10}.
Relation Y = -x³ + 2 is a function: A relation is a function if every input x in the domain corresponds to only one output Y in the range. To check if the relation is a function, we need to ensure that no two different inputs in the domain result in the same output.
For this relation, every input x in the domain results in only one unique output Y, so the relation is a function.
Function Notation: If the relation is a function, we can write it in function notation as: f(x) = -x³ + 2, where f is the function name and x is the input.
Evaluating f(-5), f(0) and f(1):
f(-5) = -(-125) + 2 = 127
f(0) = -(0) + 2 = 2
f(1) = -(1) + 2 = 1
Thus, f(-5) = 127, f(0) = 2 and f(1) = 1.
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There is 3/4 of a large cake left over from a party. Pedro eats 1/2 of the cake that was left. How much cake did he eat?
Pedro ate 3/2 of the cake that was left.
We know that the fraction is used to represent the portion or part of the whole thing.
The fraction has two parts: numerator and denominator.
The top part of fraction is numerator and the bottom part is denominator.
Consider a fraction 1/5.
Here, numerator is 1, denominator is 5
When certain thing is divided into 5 equal parts then each part of is represented by fraction 1/5
In this situation, there is 3/4 of a large cake left over from a party.
Pedro eats 1/2 of the cake that was left.
This means, Pedro eats half of the remaning cake.
We need to find the half of fraction 3/4
We divide fraction 3/4 by 2 in order to find the amount of cake he ate.
[tex]\frac{\frac{3}{4} }{2} \\\\=2\times \frac{3}{4} \\\\=\frac{3}{2}[/tex]
Thus he ate 3/2 of cake.
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Use technology to find points and then graph the function
y
=
−
x
+
1
+
5
y=−
x+1
+5 following the instructions below.
done plotting points
Plot at least four points from the table of values with integer coordinates on the axes below. Click a point to delete it.
The graph and the points are added as an attachment
How to determine the graph?From the question, we have the following parameters that can be used in our computation:
y = -x + 1 + 5
Evaluate the like terms
y = -x + 6
Set x = values from 0 to 3
So, we have
y = -0 + 6 = 6
y = -1 + 6 = 5
y = -2 + 6 = 4
y = -3 + 6 = 3
So, the points are (0, 6), (1, 5), (2, 4) and (3, 3)
Next, we plot the graph and the points
See attachment
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