The best method to apply in solving the given equation x² = 9 is the factorization method.
Factorisation is defined as the breaking or deterioration of an entity (for example a number, a matrix, or a polynomial) into a product of another entity, or factors, which when multiplied together give the original number or a matrix, etc.
In x² = 9, we need to remove the power of 2 in order to separate just x.
This implies finding the square root √x² which is equal to x.
However, there are 2 possible answers to any square root, a positive or a negative answer.
x = √9
x = ± 3
0r we can solve this equation by the splitting method.
Rearrange the equation
x² = 9
(x - 3)(x + 3) = 0
On solving, we get
x = +3 and x = -3
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Maisie knows that she needs 3 kg of grass seed to make a rectangular lawn 5 m by 9m.
Grass seed is sold in 2 kg boxes
Maisie wants to make a rectangular lawn 10 m by 14m.
She has 5 boxes of grass seed.
(a) Has Maisie got enough grass seed to make a lawn 10 m by 14m!
You must show all
your working
(4)
Total Seeds required 9.33 kg and she has 10 kg.so, she has enough grass seed to make a lawn 10m by 14 m.
If you're fortunate enough to have a rectangular lawn, determining the size is straightforward. Multiply the length and breadth measurements together to get the total. You now have your region/area.
So, Maisie knows that she needs 3 kg of grass seed to make a rectangular lawn 5 m by 9m.
Grass seed is sold in 2 kg boxes,
Maisie wants to make a rectangular lawn 10 m by 14 m,
She has 5 boxes of grass seed
To Find, Has Maisie got enough grass seed to make a lawn 10m by 14 m
Solution:
3 kg of grass seed to make a rectangular lawn 5 m by 9m.
=> 3 kg of grass seed needed for 5 x 9 = 45 m²
=> 1 m² required = 3/45 kg seed
a rectangular lawn 10 m by 14 m,
area = 10 x 14 = 140 m²
Hence 140 m² required = 140 x 3/45 = 9.33 kg
Grass seed is sold in 2 kg boxes,
She has 5 boxes of grass seed
Hence total seeds = 5 x 2 = 10 kg
Therefore, total seeds required 9.33 kg and she has 10 kg.so, she has enough grass seed to make a lawn 10m by 14 m.
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A newsletter publisher believes that more than 31% of their readers own a personal computer. Is there sufficient evidence at the 0.02 level to substantiate the publisher's claim?
State the null and alternative hypotheses for the above scenario
The null hypothesis is: H0: p ≤ 0.31
The alternative hypothesis is : H1: p > 0.31
What is a null hypothesis?A common statistical theory called the null hypothesis asserts that there is no statistical link or significance between two sets of observed data and measurable events for a given single observed variable.
The null states that the probability of the readers have the personal computers have to be lower than or equal to 31 percent.
What is the alternative hypothesis?
An alternate hypothesis is a claim that the two variables have some kind of statistical relationship.
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What does range () function returns Mcq?
The range is found by finding the vertex and noting that it is the minimum or maximum (depending on direction) of the function. You can find the vertex by using -b/2a for the x value and then plugging in to get y value.
What is a function?
A mathematical phrase, rule, or rule that establishes the link between explanatory variables or a dependent variable In mathematics, curves exist everywhere, and they are crucial for constructing physical links in the sciences.
A Method can be defined by a module, an object, or another function. An internal feature of a class is called a method. Methods are listed inside a base class to make the connections between it class and thus the method clear. A method can be called or invoked using different syntax. We can convert a type into an object before being able to access its methods.
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Are these answers correct?? If not, please help
Answer:
Step-by-step explanation:
Question 4 I got something different x= 5, y= -4 (double check my work to make sure i used correct equation and all)
Also for slopes does your teacher want you to include the "x". Cuz when I think of slope its only the "m" part which means it should only be -1, -4 but its your call.
All three members of the Harrison family want to take a cruise with Luxury Starline. Estimate how much the family would spend if a cruise costs $1,825 per person by rounding the cost per person to the nearest thousand. $
In the word problem ,the total cost for cruise for total family is $5475.
What is word problem?
Word problems are often described verbally as instances where a problem exists and one or more questions are posed, the solutions to which can be found by applying mathematical operations to the numerical information provided in the problem statement. Determining whether two provided statements are equal with respect to a collection of rewritings is known as a word problem in computational mathematics.
Here the Total members of the Harrison family = 3
Cost of cruise per person = $1825
Now, Total cost for cruise of Harrison family is,
=> Total members × Cost per person
=> 3 × 1825
=> $5475
Hence the total cost for cruise for total family is $5475.
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Suppose a ball was dropped from a TV tower 2120 feet high. The time it takes an object to free-fall from the top of this tower to the ground can be represented by the equation s = -16t^2 + 2120, where s is the distance from the ground in feet and t is the time in seconds. Approximately how long will it take the object to reach the ground?
If a ball is dropped from 2120 feet, it will take approximately_________ seconds to reach the ground.
The time taken by the ball to reach the ground is 11.5 seconds.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Suppose a ball was dropped from a TV tower 2120 feet high. The time it takes an object to free-fall from the top of this tower to the ground can be represented by the equation s = -16t² + 2120.
The time will be calculated as,
s = -16t² + 2120
Equate with zero as the ball reaches the ground the height s becomes zero.
-16t² + 2120 = 0
-16t² = -2120
t² = 2120 / 16
t² = 132.5
t = √132.5
t = 11.5 seconds
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John wants to measure the height of a tree. He walks exactly 100 feet from the base of the tree and looks up. The angle from the ground to the top of the tree is 33 degrees. How tall is the tree?
The height of the tree, given the angle from the ground and the distance from the base of the tree, is 64. 94 feet.
How to find the height of the tree ?Assuming that this situation was modelled as a right angled triangle, then the angle from the ground to the top of the tree would be such that the distance from the base of the tree would be the adjacent measure and the height of the tree would be the opposite measure.
This means that the relevant operation to use would be Tan.
Using the Tan operation, and assuming the height of the tree was x, the formula would be:
Tan (33 degrees ) = x / Distance from base
Tan (33 degrees ) x / 100
x = 64. 94 ft
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What is the solution for [tex]x^{2} + 4x\ \textgreater \ 77[/tex]?
x < –7 or x > 11
x < –11 or x > 7
–7 < x < 11
–11 < x < 7
The solutions of x² + 4x > 77 is x < –11 or x > 7
Solutions of an equation:An equation is a mathematical expression that states that two algebraic expressions must be equal in nature. Finding the value of a variable in an equation indicates the process of solving an equation. The solution of the equation is the value that was determined while solving the equation.
Here we have
x² + 4x > 77
Subtract -77 from both sides
=> x² + 4x - 77 > 77 - 77
=> x² + 4x - 77 > 0
The above expression can be factorized as follows
=> x² + 11x - 7x - 77 > 0 [ Split middle term ]
=> x(x + 11) - 7(x + 11) > 0
=> (x + 11) (x - 7) > 0
=> (x + 11) > 0 (x - 7) > 0
=> x < -11 x > 0
Therefore,
The solutions of x² + 4x > 77 is x < –11 or x > 7
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Jose swam 8 kilometers against the current in the same amount of time it took him to swim 16 kilometers with the current. The rate of the current was 1 kilometer per hour. How fast would Jose swim if there were no current?
The rate at which Jose will swim if there was no current would be = 2 km / hour
What is speed ?Speed is defined as the scalar quantity that is used the express the relationship of the distance of a moving object with respect to its time.
Jose swims with the current of the water and against the current of the water within the same time.
When swimming with the current he covers = 8 km
The rate he used with the current = 1 km / hour
When he is swimming against the current he covers = 16 km
Therefore the rate at which he swims against the current = 16/8 = 2km/hour.
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the perimeter of a rectangle is 70 cm. if its length is decreased by 5 cm and its width is increased by 5 cm,its area will increase by 50 cm^2.find the length and the width of the original rectangle
The length of the rectangle is 25 cm and the width is 10 cm.
How to evaluate for the length and width of the original rectangleWe shall represent the length and width of the original rectangle with x and y respectively so that the perimeter is;
2(x + y) = 70 {divide through by 2}
x + y = 35...(1)
length of new rectangle = x - 5
width of new rectangle = y + 5
area of new rectangle:
(x - 5)(y + 5) = xy + 50
xy + 5x - 5y - 25 = xy + 50
xy - xy + 5x - 5y = 50 + 25
5x - 5y = 75 {divide through by 5}
x - y = 15...(2)
add equations (1) and (2) we have;
x + y + x - y = 35 + 15
2x = 50 {divide through by 2}
x = 25
substitute 25 for x in equation (1), we have;
25 + y = 35
y = 35 - 25 {subtract 25 from both sides}
y = 10
Therefore, have the length and width of the original rectangle to be x = 25 cm and y = 10 cm respectively.
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What is the value of x in X² 9?
The value of x in the given equation x² = 9 is x = ± 3.
In x² = 9, we need to remove the power of 2 in order to separate just x.
This implies finding the square root √x² which is equal to x.
However, there are 2 possible answers to any square root, a positive or a negative answer.
x = √9
x = ± 3
0r we can solve this equation by the splitting method.
Rearrange the equation
x² = 9
(x - 3)(x + 3) = 0
On solving, we get
x = +3 and x = -3
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graph 2y-4x<8 please
We have drawn the graph of the given linear inequality.
What is linear inequality?
A linear inequality is a mathematical statement involving a linear function and one of the symbols <, >, ≤, or ≥. The general form of a linear inequality in one variable is:
ax + b <, >, ≤, or ≥ c
where a, b, and c are constants, and x is the variable.
To graph the inequality 2y - 4x < 8, we first need to put it in slope-intercept form, y = mx + b, so we can see the slope and y-intercept of the line. We can do this by adding 4x to both sides:
2y - 4x < 8
2y < 4x + 8
Then we divide both sides by 2 to get y by itself:
y < 2x + 4
Now we have y = 2x + 4 in slope-intercept form, where the slope is 2 and the y-intercept is 4. To graph the line, we can use the y-intercept as a starting point and use the slope to find additional points on the line.
To graph the line, we can follow these steps:
Plot the y-intercept, which is (0,4) on the graph.
Using the slope of 2, find a second point by going up 2 units and over 1 unit. This point is (1,6)
Draw a line through these two points.
Hence, we have drawn the graph of the given linear inequality.
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What is the total area of the three triangle?
Answer: triangle 1's 1/2 length* triangle 1's width+triangle 2's 1/2 length* triangle 2's width+triangle 3's 1/2 length* triangle 3's width
Step-by-step explanation: triangle 1/2 length* triangle width=triangle area.
help asap please math hw
Answer:
First question:
y intercept = 3
slope = -1/3
y = -1/3x+3
Second Question:
y intercept = -3
slope = -3/2
y = -3/2x=3
Third Question:
y intercept = -1
slope = 3
y = 3x-1
youre welcome buddy :)
What causes eye dilation?
Light and emotional variables are affected by eye dilation. Under typical conditions, pupils are meant to dilate as a result of changes in lighting and psychological factors.
Why do your pupils continue to dilate?A physical or psychological condition, certain substances or prescriptions, or an injury could be the cause of this. The term "blown pupil" is occasionally used by doctors to describe more severe mydriasis when the pupils are fixed and dilated. This disorder may be a sign of brain damage brought on by a stroke or other physical trauma.Light and emotional variables are affected by eye dilation. Under typical conditions, pupils are meant to dilate as a result of changes in lighting and psychological factors.Under typical conditions, pupils are meant to dilate as a result of changes in lighting and psychological factors. A dilated pupil will typically return to its normal size on its own.To learn more about eye dilation refer to:
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What vertical translation is applied to y = x2 if the transformed graph passes through the point (5, 18)?
Step-by-step explanation:
well,
y = x²
would give us
y = 5² = 25
(5, 25)
but we have
(5, 18) so, what is the difference ?
we see that y is reduced by 7 units.
so,
y = x² - 7
the whole curve is moved down by 7 units.
A line pae through the point (–6,5) and (8,–2). What i it equation in point-lope form?
The equation of the line passing through the point (-6, 5) and (8, -2) in point-slope form is y - 5 = -0.5(x + 6).
The point-slope form of a line is
y - y1 = m(x - x1)
where (x1, y1) is a point on the line, and m is the slope of the line.
To find the equation of a line given two points, we can use either point and find the slope of the line using the formula:
m = (y2 - y1) / (x2 - x1)
So, we can use the point (-6, 5) and (8, -2)
m = (y2 - y1) / (x2 - x1) = (-2 - 5) / (8 - (-6))
m = -7/14
m = -1/2
Now we can use this slope and the point (–6,5) to find the equation of the line in point-slope form:
y - 5 = -1/2(x - (-6))
y - 5 = -0.5(x + 6)
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What is ¾ divided by 4?
The solution to this ¾ divided by 4 is 0.1875.
To visualize the question we are trying to solve, let's put 3/4 and 4 side-by-side so it's easier to see:
3/4÷4
The numbers in 3/4 divided by 4 are labeled below:
3 = numerator
4 = denominator
4 = whole number
All we need to do here is keep the numerator exactly the same (3) and multiply the denominator by the whole number:
3/4 x4= 3/16.
Once you have your final fraction, just divide the numerator by the denominator to get your answer in decimal form:
3/16=0.1875
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Use the distributive
property to write an
expression
that is
equivalent
to 32 + 4r.
Answer:
4 (8+r)
Step-by-step explanation:
Pablo shares his birthday cake with a friend. Pablo eats 3/8 and his friend eats 1/4. How much of the cake was left over? (Represent your answer as a fraction)
Answer:3/8 was left over
Step-by-step explanation: 3/8 plus 1/4 x 2 equals 5/8... remainder 3/8
Answer:
3/8 (this is the answer)
Four glasses of milk and 2 snack bars have a total of 86 carbohydrates (carbs), and 2 glasses of milk and 3 snack bars have a total of 69 carbs. Determine how many carbs are in one glass of milk and in one snack bar.
Answer:
One glass of milk: 15 carbs
One snack bar: 13 carbs
Step-by-step explanation:
This problem is an example of systems of linear equations. We can set this problem up by defining variable. I used [tex]m[/tex] for the glass of milk and [tex]b[/tex] for the snack bar.
First, we have: 4 glasses of milk and 2 snacks bar have a total of 86 carbs. We can write this as
[tex]4m+2b=86[/tex]
Next: 2 glasses of milk and 3 snack bars have a total of 69 carbs.
We can write this as
[tex]2m+3b=69[/tex]
Now we set it up.
[tex]4m+2b=86[/tex]
[tex]2m+3b=69[/tex]
By dividing both sides of the first equation by 2, we can use the subtraction method to get rid of the variable [tex]m[/tex]. Now we have
[tex]2m+b=43[/tex]
[tex]2m+3b=69[/tex]
Subtract like terms and solve for [tex]b[/tex]
[tex]-2b=-26[/tex]
[tex]b=13[/tex]
Now we substitute [tex]b[/tex] back into the original equation to find [tex]m[/tex].
[tex]2m+(13)=43[/tex]
[tex]2m=30[/tex]
[tex]m=15[/tex]
There you have it. I hope this helps!
Non -examples of the property 0
When we multiply any number by zero, the outcome is always a zero, according to the definition of the zero property of multiplication, examples as 8 x 0 = 0.
What is zero property?When we multiply any number by zero, the end result is always a zero, according to the definition of the zero property of multiplication. Zero need not always be the first or second number. When multiplied by another number, it could be anywhere. This indicates that the outcome of the multiplication is unaffected by the placement of the digit zero.
All different kinds of numbers fall under the umbrella of this property. They could be fractional, decimal, or integer numbers. Thus, the results of some such numbers will be as follows:
10 x 0 = 0 6.4 x 0 = 0
½ x 0 = 0 1 x 2 x 3 = 0
A non-example of property 0 is: 5 × 1 = 5, the number is not multiplied by 0, therefore, it does not denote the zero property of multiplication.
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Compete question is: Give non-example of the property 0.
The volume of a sphere is given by the equation $V=\frac{1}{6\sqrt{\pi}}S^{3/2}$V=
1
6√πS3/2 , where cap s$S$S is the surface area of the sphere. Find the volume of a sphere, to the nearest cubic meter, that has a surface area of 60 square meters. Use 3.14 for pi$\pi$π .
The volume of a sphere, to the nearest cubic meter is; 44 cubic meter
How to find the Volume of a sphere?
We are given that the formula for the volume of a sphere is;
V = [1/(6√π)]S^(3/2)
where;
V is volume
S is the surface area of the sphere
π = 3.14
We are given that surface area is 60 square meters. Thus, we will now have;
V = [1/(6√3.14)]60^(3/2)
V = 43.713 m³
Approximating to the nearest cubic meter gives;
V = 44 cubic meter
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How many types of images are there in class 8?
There are 2 types of images namely virtual and real image
The point where light rays from an object meet or appear to contact after reflection or refraction is sometimes referred to as the image. In this concept, a "object" might be anything that light rays are emanating from.
Real images and virtual images are the two types of images. The method by which they are created distinguishes a genuine image from a virtual image. Light beams must converge to create an actual image, whereas they must diverge to create a virtual image.
Real images are those that are created when light rays collide at a specific location after being reflected or refracted by a mirror or lens.
Virtual pictures are those that only seem to form when viewed from behind a mirror. Behind the mirror, the picture is not actually there. When light beams are refracted or reflected, a virtual picture is created.
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What are the 4 quadrants in order?
The 4 (four) quadrants in order are: Quadrant I, Quadrant II, Quadrant III, and Quadrant IV.
A coordinate plane is divided into four sections called quadrants. These quadrants are numbered I, II, III, and IV in a counterclockwise direction, starting with the top right.
Quadrant I is the top right section of the coordinate plane, and it contains all the points where the x-coordinate and y-coordinate are positive.
Quadrant II is the top left section of the coordinate plane, and it contains all the points where the x-coordinate is negative and the y-coordinate is positive.
Quadrant III is the bottom left section of the coordinate plane, and it contains all the points where the x-coordinate and y-coordinate are negative.
Quadrant IV is the bottom right section of the coordinate plane, and it contains all the points where the x-coordinate is positive and the y-coordinate is negative.
Understanding this concept is important for solving mathematical problems, especially in algebra and geometry.
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Sue ha 20 bicuit in a tin. There are: 12 plain bicuit
5 chocolate bicuit
3 currant bicuit
Sue take two random bicuit from the tin. Work out the probability that the two bicuit are not the ame type
So, the probability that the two biscuits are not the same type is 0.15 or 15%.
To find the probability that the two biscuits are not the same type, we need to calculate the probability that Sue takes one biscuit of each type.
First, we will calculate the probability that Sue takes one plain biscuit, one chocolate biscuit, and one currant biscuit.
The probability of Sue taking one plain biscuit is 12/20, since there are 12 plain biscuits out of a total of 20.
The probability of Sue taking one chocolate biscuit after taking a plain biscuit is 5/19, since there are now 5 chocolate biscuits out of 19 remaining.
The probability of Sue taking one currant biscuit after taking a plain and chocolate biscuit is 3/18, since there are now 3 currant biscuits out of 18 remaining.
To find the overall probability that Sue takes one biscuit of each type, we multiply the individual probabilities together:
P = (12/20) * (5/19) * (3/18) = 0.15
So, the probability that the two biscuits are not the same type is 0.15 or 15%.
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A manufacturer records the number of errors each work station makes during the week. The data are as follows 6 3 2 3 5 20 254201 Which of these choices display the correct dotplot?
O A. Number of Errors for the Week for Workstations
O B. Number of Errors for the Week for Workstations 0 10 10
O C. Number of Errors for the Week
O D. Number of Errors for the Week for Workstations for Workstations 10 10
The correct dot plot for the given data would be option A. Number of Errors for the Week for Workstations.
A dot plot is a graph that displays the frequency of a data set by plotting a dot above the number for each occurrence of that number. The x-axis represents the data values and the y-axis represents the frequency of each data value.
In this case, the data represents the number of errors each workstation makes during the week, so the correct way to display the data in a dot plot would be to have the x-axis represent the number of errors and the y-axis represents the frequency of each error. Each dot on the dot plot would be above the number of errors for each workstation.
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What is the additive inverse of 8 /- 13?
The additive inverse of 8 /- 13 is -8 /+ 13. This means that when you add 8 /- 13 to its additive inverse, the result is 0.
The additive inverse of 8 /- 13 is its opposite number. This means that the sign of the number must be flipped. The inverse of 8 /- 13 is -8 /+ 13. To find the inverse of a number, you must switch the sign of the number from positive to negative or from negative to positive.
When two numbers are added together, the result will be zero if the numbers are opposites. This means that 8 /- 13 and its inverse, -8 /+ 13, when added together, will equal 0. This is because the two numbers have the same value but opposite signs. The positive 8 is cancelled out by the negative 8, and the negative 13 is cancelled out by the positive 13, leaving 0.
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Give the first five terms of the sequence:
2/5,A₂ =4/5; ªn‚ = ª,-2 (for n ≥ 3)
Answer: 2/5, 4/5, -4/5, 8/5, -16/5
I dunno that's what I got I could be wrong
A company manufactures two types of cabinets, type 1 and type 2. It produces 110 total cabinets each week. Last week, the number of type 2 cabinets produced exceeded twice the number of type 1 cabinets produced by 20. If x is the number of type 1 cabinets produced and y is the number of type 2 cabinets produced, the system of equations that represents this situation is x + y = 110 and y = 2x + 20.
X for type 1 cabinets = 30
Y for type 2 cabinets = 80
And that proven that type 2 cabinets (Y) produced exceeded more than twice the number of type 1 cabinets (X)
As per the equations stated
X + Y = 110 ……….. (1)
Y = 2x + 20 …...... (2)
We substitute Y at equation (1) with equation (2), to find X
X + Y = 110
X + (2X + 20) = 110
3X + 20 = 110
3X = 110 – 20
3X = 90
X = 90 / 3
X = 30
Then, We substitute value X at equation (1 ) with the value that we have discovered before
X + Y = 110
30 + Y = 110
Y = 110 – 30
Y = 80
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