Answer:
The number that gives the same result if it is multiplied by 999/998 or if any number is added to it is zero (0).
The property of a number being unchanged after being multiplied by a fraction and a constant is called an "Identity element". The identity element for multiplication is 1 and for addition is 0.
When any number is multiplied by 1, it stays the same. So, if we multiply any number by 999/998, which is equivalent to multiplying by 1, it stays the same.
Similarly, when any number is added to zero, it stays the same. So, if we add any number to 0, it stays the same.
Therefore, the only number that gives the same result if it is multiplied by 999/998 or if any number is added to it is zero (0).
Given the function y=|x+1|. State the domain over which the function is increasing.
A bank loaned out $19,000, part of it at the rate of 7% per year and the rest at 17% per year. If the interest received in one year totaled $2000, how much was loaned at 7%
Answer:
$12300
Step-by-step explanation:
You want to know the amount loaned at 7% if $19000 loaned at 7% and 17% earns $2000 in one year.
InterestThe interest on an investment P at rate r for t years is ...
I = Prt
The sum of the amounts of interest on a 7% investment of x and a 17% investment of (19000 -x) is given as 2000:
0.07x +0.17(19000 -x) = 2000
-0.10x +3230 = 2000 . . . simplify
1230 = 0.10x . . . . . . . . . . add 0.10x -2000
12300 = x . . . . . . . . . . . . divide by 0.10
The amount loaned at 7% was $12,300.
paula is making hot apple cider using apple juice and cinnamon candy. her recipe calls for 0.5 cups of cinnamon candy for every 2 pints of apple juice. how many pints of apple juice does she need for 2 cups of cinnamon candy?
On solving the provided question, we can say that by unitary method 8 pints of apple juice does she need for 2 cups of cinnamon candy
What is unitary method ?The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.
Paula is brewing hot apple cider with cinnamon caramel and apple juice.
her recipe calls for = 0.5 cups of cinnamon
candy for every = 2 pints of apple juice
she need for 2 cups of cinnamon candy are -
for 1 = she need 2/0.5
for 2 = she needs 2/0.5 * 2 = 8
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Segment $s_1$ has endpoints at $(4,1)$ and $(-8,5)$. Segment $s_2$ is obtained by translating $s_1$ by $2$ units to the right and $3$ units up. Find the midpoint of segment $s_2$. Express your answer as $(a,b)$ with $a$ and $b$ integers.
The midpoint [tex]s_{2}[/tex] is = (0,4).
Midpoint refers to a point that is in the middle of the line connecting two points. The two mentioned points are the endpoints of a line and the midpoint is lying in between the two points. The midpoint divides the line connecting these two points into two equal halves
According to the question,
The endpoints [tex]s_{2}[/tex] are 2 units to the right and 3 units up from the endpoints [tex]s_{1}[/tex].
[tex]s_{1}[/tex] has endpoints at (4, 1) and (-8, 15).
[tex]s_{2}[/tex] has endpoints at (4+2, 1+3) and (-8+2, 1 +3)
[tex]s_{2}[/tex] has endpoints at (6, 4) and (-6, 4).
The midpoint of [tex]s_{2}[/tex] = [tex](\frac{6-6}{2} , \frac{4 + 4}{2} )[/tex] = ( 0, 4)
So, the midpoint [tex]s_{2}[/tex] is = (0,4).
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Without using paper and pencil how would you find the sum of 9.8 and 2.6
Answer:
12.4
Step-by-step explanation:
Here are two spinners.
6
spinner a
spinner b
3
spinner a
2
2
4
6
the two arrows are spun and the score is obtained
ows are
ng the t by multiplying the two numbers.
a) complete the possibility space.
1
3
spinner b
3
12
e the pe
un
10
5
b) what is the probability of scoring a total of 6?
10
c) what is the probability of scoring a total greater than 10?
me probability of scoring a total of 7
The probability of scoring a total of 6 is 1/36 and the probability of scoring a total greater than 10 is 25/36.
a) The possibility space for two spinners is all the possible combinations of numbers that the two spinners can produce. The possibilities for spinner A are 1, 2, 3, 4, 5, and 6, and for spinner B are also 1, 2, 3, 4, 5, and 6. Therefore, the possibility space is 1x1, 1x2, 1x3, 1x4, 1x5, 1x6, 2x1, 2x2, 2x3, 2x4, 2x5, 2x6, 3x1, 3x2, 3x3, 3x4, 3x5, 3x6, 4x1, 4x2, 4x3, 4x4, 4x5, 4x6, 5x1, 5x2, 5x3, 5x4, 5x5, 5x6, and 6x1, 6x2, 6x3, 6x4, 6x5, 6x6.
b) The probability of scoring a total of 6 is 1/36, since there is only one possibility (3x2) that produces a score of 6.
c) The probability of scoring a total greater than 10 is 25/36, since there are 25 combinations of numbers (4x3, 4x4, 4x5, 4x6, 5x2, 5x3, 5x4, 5x5, 5x6, 6x1, 6x2, 6x3, 6x4, 6x5, 6x6) that produce a score greater than 10.
The possibility space for two spinners is all the possible combinations of numbers that the two spinners can produce, which is 1x1, 1x2, 1x3, 1x4, 1x5, 1x6, 2x1, 2x2, 2x3, 2x4, 2x5, 2x6, 3x1, 3x2, 3x3, 3x4, 3x5, 3x6, 4x1, 4x2, 4x3, 4x4, 4x5, 4x6, 5x1, 5x2, 5x3, 5x4, 5x5, 5x6, and 6x1, 6x2, 6x3, 6x4, 6x5, 6x6. The probability of scoring a total of 6 is 1/36 and the probability of scoring a total greater than 10 is 25/36.
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In the first table of values, how does n differ from f(n)? in other words, what do n and f(n) mean?
N and f(n) is totally different by their own circumstances.
how does n differ from f(n)?N is independent variables
And f(n) is dependent variable
These are the main difference about n and f(n),You can typically depend on f(n) to represent the value of the function f at n. fn might mean f(n), especially when the domain is natural numbers, but it usually denotes the nth function in a sequence of functions.
F(a,b) would mean that the function takes two values, a and b. Your function takes one argument, n.
For example, f(n) might be the number of eggs in n packages, where each package has a dozen eggs. That would be f(n) = 12n, so f(3) = 12 * 3 = 36.
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Find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio.
A(−7, — 5), B(-2, 0); 1 to 4
The coordinates of P are
Therefore , the solution of the given problem of ratio comes out to be the coordinate P = (7, 0.4).
A ratio is defined.A ratio as well as fraction in mathematics shows how frequently one value is present in another. For instance, if there are eight grapefruit and six lemons in a fruit plate, the ratio from oranges to citrus is eight to six, or 8:6, which is comparable to the ratios 4:3 or the decimal 1.333.
Here,
Ratios are a useful tool for segmenting lines into smaller units.
P's coordinate is P = (7, -0.4)
The criteria are as follows:
A = (8,0)\sB = (3,-2) (3,-2)
m: n=1:4
Using P = mx2+nx1 my2+ny
m+n
m+n, line ratio is computed.
The result is:
P 1x3+4x8 /1x-2+4x0 = 1+4 / 7
=> P = 35, 2
=>P = (7, -0.4) (7, -0.4)
1+4
P therefore has the coordinate P = (7, 0.4).
Therefore , the solution of the given problem of ratio comes out to be the coordinate P = (7, 0.4).
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mariela took out a mortgage and purchased a house located in the v zone of an nfip participating community. what does that mean for mariela?
Mariela's purchase of a house located in the V Zone of an NFIP participating community means that the house is located in a high amount of risk flood zone and that she is required to purchase flood insurance if she has a mortgage. This insurance will help to protect her investment in the event of a flood.
Mariela must purchase flood insurance if she has a mortgage on her house, which is located in a high amount of risk flood zone in an NFIP participating community. This insurance will help to protect her investment in the event of a flood.
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Melissa purchased a new car. the car had a list price of $20,540. melissa made a down payment of $3,900 and financed the rest, paying 8.6% interest compounded monthly over a payment period of 5 years. if melissa also had to pay 8.25% sales tax, a $995 vehicle registration fee, and a $57 documentation fee, what is her monthly payment?
Melissa's monthly payment is $450 if the down payment is $3,900.
To calculate the monthly payment, we first need to calculate the total amount financed. This is done by adding the list price of the car ($20,540), the sales tax (8.25% of $20,540 = $1,690.35), the registration fee ($995), and the documentation fee ($57) for a total of $23,282.35.
We then need to calculate the total amount of interest that Melissa will pay over the 5-year loan period. This is done by multiplying the interest rate (8.6%) by the total amount financed ($23,282.35) and multiplying that by the number of years (5).
This gives us a total interest payment of $7,634.84. We then add the total amount financed ($23,282.35) and the total interest payment ($7,634.84) and subtract the down payment ($3,900), which gives us the total amount that Melissa will pay over the 5-year loan period: $27,016.99.
We then divide this total amount by the number of months in the loan period (60) to get the monthly payment: of $450
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Mr. Weinstein has a savings account with a balance of $19,211.34. It pays 4% interest compounded daily.
a. What is his ending balance after three years, if no other deposits or withdrawals are made?
b. How much interest does he earn over the three years?
assuming a year is 365 days
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$19211.34\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{daily, thus 365} \end{array}\dotfill &365\\ t=years\dotfill &3 \end{cases}[/tex]
[tex]A = 19211.34\left(1+\frac{0.04}{365}\right)^{365\cdot 3} \implies \stackrel{balance}{\boxed{A \approx 21660.58}}~\hfill \underset{interest}{\stackrel{21660.58~~ - ~~19211.34}{\boxed{\approx 2449.24}}}[/tex]
Is Dawn or Denise correct?
Answer:
Dawn is correct maybe because -3 is less than 4
correct if I'm wrong
A watering can dispenses water at the rate of 0.3 gallon per minute. The original volume of water in the can was 7 gallons. Which set of ordered pairs shows the volume of water in the can in gallons (y), as a function of time in minutes (x), from the first minute after the can starts dispensing water
The set of ordered pairs depicts the volume of water in the can in gallons (y) as a function of time in minutes (x), beginning with the first minute after the can begins distributing water and ending with {(1, 6.7) , (2, 6.4) , (3, 6.1)}.
What is ordered pairs?An ordered pair is a pair of objects in mathematics. The order of the objects in the pair is important: the ordered pair differs from the ordered pair unless a = b. Ordered pairs are also known as 2-tuples or 2-length sequences. An ordered pair is a composite of the x coordinate (abscissa) and the y coordinate (ordinate), with two values expressed between parenthesis in a predetermined order. It aids visual comprehension by locating a point on the Cartesian plane. An ordered pair's numeric values can be integers or fractions.
Here,
A watering can dispenses water at the rate of 0.3 gallon per minute.
The original volume of water in the can was 7 gallons.
If you plot a graph of volume of water in the can (gallons) against time (minutes),
The set of points on the graph will be:
After 1 minute: (1, 7 - 0.3) = (1, 6,7)
After 2 minutes: (2, 7 - 0.6) = (2, 6.4)
After 3 minutes: (3, 7 - 0.9) = (3, 6.1)
i.e the set {(1, 6.7) , (2, 6.4) , (3, 6.1)}
The set of ordered pairs shows the volume of water in the can in gallons (y), as a function of time in minutes (x), from the first minute after the can starts dispensing water is {(1, 6.7) , (2, 6.4) , (3, 6.1)}.
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Which statement are true about xyz
any one good at math that can help here
So on n solving the provided question, we can say that the value of the slope intercept is 2x - 3y -12 =0
what is slope intercept?In mathematics, the intersection point is the place on the y-axis where the slope of the line crosses. a place where the y-axis crosses on a line or curve. Y = mx+c, where m stands for the slope and c for the y-intercept, is used as the equation for the straight line to show this. The slope (m) of the line and its y-intercept (b) are emphasised in the equation's intercept form. When an equation has the intercept form (y=mx+b), the slope is m and the y-intercept is b. Some equations can also be rewritten such that they seem to be slope intercepts. If y=x is rewritten as y=1x+0, for instance, the slope and y-intercept are both changed to 1.
Given, x - intercept of a line is 6
so,
The line will pass through the point (6, 0)
Also given. the y - intercept ofthe line is —4 c = —4
So, the line will pass through the point (0, —4)
Now,
Slope, m = y2 - y1/x2 - x1
m = -4-0/0-6 = 2/3
y = mx + c
y = 2x/3 - 4
3y = 2x - 12
2x - 3y -12 =0
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The Math Club is selling shirts as a fund-raiser. The company charges a set-up fee plus a certain cost for each shirt. The function rule C = 9n + 45 represents the Math Club's cost, with C representing the total cost of the order, and n representing the number of shirts. What could the numbers in the function represent? Select all that apply.
Responses
45 is the minimum number of shirts
45 is the minimum number of shirts
9 is the price per shirt.
9 is the price per shirt.
9 is the initial set-up fee charged to design the shirts.
9 is the initial set-up fee charged to design the shirts.
45 is the price per shirt.
45 is the price per shirt.
45 is the initial set-up fee charged to design the shirts.
45 is the initial set-up fee charged to design the shirts.
Answer: The function rule C = 9n + 45 represents the cost of the shirts that the Math Club is selling. The variable C represents the total cost of the order and the variable n represents the number of shirts.
The number 9 in the function represents the price per shirt, this is because as the number of shirts increases by 1, the total cost increases by 9. This tells us that the cost of each shirt is $9.
The number 45 in the function represents the initial set-up fee charged to design the shirts. This is because even if no shirts are ordered, there is still a cost of $45. This represents a fixed cost that the Math Club must pay to have the shirts designed.
Step-by-step explanation:
hello! please help me find the x & y intercepts, domain & range, relative minimum & maximum, increasing & decreasing intervals, and positive & negative intervals.. thank you :)
Solve the equation y = f(x) to determine the values of the independent variable x and obtain the domain.
How do you find the domain and range of X and Y?We can easily identify the values of the independent variable x and the domain by solving the equation y = f(x). The range may then be found by solving for x.
For a relation, the domain and range are defined as sets of all the x-coordinates and all the y-coordinates of ordered pairs, respectively. For instance, if the relationship is R = (1, 2), (2, 2), (3, 3), and (4, 3), then
The collection of all x-coordinates with values 1, 2, 3, and 4 is known as the domain.Range is the set of all y-coordinates with values of 2, 3.
The elements that make up a function are its domain and range. A function's domain is the set of all potential input values, while its range is the range of possible output values. Range, Function, and Domain.
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Isosceles triangle ABC contains angle bisectors segment BF, segment AD, and segment CE that intersect at X.
The measure of angle ∠CXA is 134°
What is the Isosceles triangle?
In geometry, an isosceles triangle is a triangle that has two sides of equal length. Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal length, the latter version thus including the equilateral triangle as a special case.
Triangle ABC is an isosceles triangle where AB = BC
∵ AB = BC
- The base angles in the isosceles triangle are congruent
∴ m∠BAC = m∠BCA
∵ m∠ BCA = 46° ⇒ given
∴ m∠ BAC = 46°
- The sum of the measures of the interior angles in any triangle is 180°
∵ m∠BAC + m∠BCA + m∠ABC = 180°
- Substitute the values of angle BAC and BCA in the equation above
∴ 46 + 46 + m∠ABC = 180
∴ 92 + m∠ABC = 180
- Subtract 92 from both sides
∴ m∠ABC = 88°
- BF, AD, and CE are bisectors segments of angles B, A, and C and they are intersected at point X
∵ CE bisects ∠BCA
∵ X ∈ CE
∴ m∠XCA = 1/2 m∠BCA
∴ m∠XCA = 1/2 (46) = 23°
∵ AD bisects ∠BAC
∵ X ∈ AD
∴ m∠XAC = 1/2 m∠BAC
∴ m∠XAC = 1/2 (46) = 23°
- In Δ AXC
∵ m∠XAC = 23° ⇒ proved
∵ m∠XCA = 23° ⇒ proved
∵ m∠CXA + m∠XAC + m∠XCA = 180° ⇒ interior angles of Δ
Substitute the values of angles XAC and XCA
∴ m∠AXC + 23 + 23 = 180
∴ m∠CXA + 46 = 180
- Subtract 46 from both sides
∴ m∠CXA = 134°
Hence, The measure of angle ∠CXA is 134°.
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The complete question is:
Isosceles triangle ABC contains angle bisectors segment BF, segment AD, and segment CE that intersect at X. triangle ABC with diagonals BF, AD, and EC that intersect at point X If segment BA is congruent to segment BC and m∠BCA = 46°, what is m∠CXA?
one of many librarians at a large city library is interested in how many books an average visitor checks out. she keeps a tally of how many books are checked out by each visitor who uses her check-out station in the children's section of the library. what type of sample is this?
This is a convenience sample as it is based on accessibility and availability of visitors.
What is average ?
The average, also known as the mean, is a measure of central tendency that is commonly used to summarize a set of numerical data. It is calculated by adding all of the values in a dataset and then dividing by the number of values in the dataset.
This is an example of a convenience sample ,
A convenience sample is a type of sample where the researcher selects participants based on accessibility and availability, rather than using a random selection method. In this case, the librarian is only collecting data on visitors who are checking out books at her specific check-out station in the children's section of the library, which is a subset of the total population of visitors to the library. The data may not be representative of the entire population of visitors to the library, as it only includes data from visitors who are checking out books in the children's section of the library.
This is a convenience sample as it is based on accessibility and availability of visitors.
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Find the slope of the graphed line please help asap I'll give brainliest answer pleasee
plsssssshelppppppppppp
Answer:
1
Step-by-step explanation:
A mattre tore i having a ale all mattree are 30 % off nate want to know the ale price of a mattre that i regulary 1000
Sale price of the mattress is $700.
What is a sales price in math?
The price after the original price has been reduced by a discount.
The discount equals the difference between the price paid for and it's par value. Discount is a kind of reduction or deduction in the cost price of a product.
Mattress that is of $1000 is sold at discount 30%.
Original price of mattress = $1000
Percentage of discount on mattresses = 30%
So,
Amount of discount on mattresses
= [ 30 / 100 ] × 1000
= $300
sale price of the mattresses = $1000 - $300 = $700
Therefore, the sale price of the mattresses is $700.
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Calculate the mean using the outlier and without the outlier Data Set 14, 16, 15, 48, 17 -5, -2, 38, -4, -6, -1 0.5, 0.8, -24.7, -0.4, 0.3 -16.7. 15.7, 13.9, 14.2, 16.4 -5.3, 13.4, -6.8. -6.1, -25.9 Mean With Outlier(s) Mean Without Outlier(s)
Therefore , the solution of scatter plot is construct this fence, we multiply the IQR by 1.5, subtract Q1 from this result, and add Q3 to the result.
What is the mean calculation formula?Taxes calculated in the manner above can be considered regular tax liabilities. tax calculated at 15% of book profit (plus any applicable surcharges and cess) (manner of computation of book profit is discussed in later part). The tax that is calculated by applying 15% (plus any applicable surcharge and cess) to book profit is known as MAT.
Here,
In bivariate data, a scatter plot is helpful for identifying outliers (data with two variables).
Because they will be separated from the majority of points on the scatter plot, the outliers are simple to identify.
We can compare each observation to the minimum and maximum fence posts as a result. Outliers are any observations that fall more than 1.5 IQR outside Q1 or rise more than 1.5 IQR outside Q3.
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please answer my mock revision hw xx
Answer:
Step-by-step explanation:
AB = √36 = 6 cm
Area of semicircle πr²/2 or 9π/2
Area of 4 semicircles = 18 π
Total area = 36 + 18 π ≈ 92.5 cm²
Which is true about the legs of a 45 − 45 − 90 triangle?
A. The legs of a 45-45-90 triangle are congruent.
B. Now, a 45-45-90 triangle will be a right triangle because one of the angles is 90°.
C. Further, it will also be an isosceles triangle since the two angles are equal and the sides opposite to equal angles in a triangle are always equal.
D. Since it becomes an isosceles triangle, the two of its legs will definitely be equal, or congruent to each other.
A 45-45-90 triangle is a right and isosceles triangle, whose legs are congruent or equal, and have one right angle of 90°. Thus all the statements are correct.
A 45-45-90 triangle is a special kind of triangle, which has the following characteristics:
It’s isosceles with two congruent or equal sides and two congruent anglesIt has one right angle of 90° and two acute angles of 45°The length of the hypotenuse is √2 times the length of a leg. Thus the ratio of the length of sides is 1 : 1 : √2The attached picture gives a better understanding of these characteristics.
If we take a look at the given problem, we can conclude that all the given statements are correct.
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Help me I really need to answer to this thanks
Answer:
Please provide a question to be answered, as you have only given us the piecewise function that would be used to solve a problem.
What are two possible transformations that together could have been used to create the image of (mc022-1 ) ---> A' from A?
(<-- the graph (see picture))
A. a reflection across the x axis followed by a reflection across the y axis
B. a translation of 6 units down followed by a rotation of 90 degrees clockwise about the origin
C. a reflection across the y axis followed by a reflection across the x axis
D. a translation of 6 units down followed by a reflection across the y axis
The only option that represents the two possible transformations that together could have been used to create the image is; D. a translation of 6 units down followed by a reflection across the y axis
What transformation rule was used?In geometry, a transformation is defined as an operation that moves, flips, or changes a shape that is called the preimage in order to create a new shape that is called the image. Some of the types of transformations includes; Translation, Reflection, Dilation e.t.c
Let us analyze each of the options;
A. This is not correct because the transformation rule for a reflection over the x -axis is (x, y) → (x, −y) while the transformation rule for the reflection of point (x, y) across the y-axis is (-x, y). This will not correspond with the final transformation given.
B) This is not correct because it will not produce the complete match as the rotation given will not allow for proper mapping.
C) This is NOT correct just like is seen in option A above.
D) This is correct because after translation by 6 units downwards, when we reflect across the y-axis, it produces the final transformed image.
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One coin in a collection of 16 coins has two heads, the rest being fair coins with a head and a tail each. A coin is chosen at random from the collection and tossed four times, coming up with a head on each of the four tosses. What is the probability that the chosen coin is the two-headed one?
my work:
bayes' theorem. Bayes' theorem states that:
P(A|B) = P(B|A) * P(A) / P(B)
where A is the event that the chosen coin is the two-headed one, B is the event that the coin comes up heads on all four tosses, P(A|B) is the probability of A given B, P(B|A) is the probability of B given A, P(A) is the prior probability of A, and P(B) is the total probability of B.
in this case, P(A) is the probability that the chosen coin is the two-headed one out of the collection of 16 coins, which is 1/16. P(B|A) is the probability that the two-headed coin comes up heads on all four tosses, which is 1. P(B) is the total probability that the coin comes up heads on all four tosses, which can be found by considering all possible coins:
P(B) = (1/16) * 1 + (15/16) * (1/2)^4
P(A|B) = P(B|A) * P(A) / P(B) = 1 * (1/16) / P(B)
so the probability that the chosen coin is the two-headed one given that it comes up heads on all four tosses is (1/16) / P(B)
is it 1/16
The probability that the chosen coin is the two-headed one will be 1/16.
How to calculate the probabilityIt should be noted that probability simply means the chance that a particular thing or event will happen. It is the occurence of likely events.
In this situation, one coin in a collection of 16 coins has two heads, the rest being fair coins with a head and a tail each.
When a coin is chosen at random from the collection and tossed four times, coming up with a head on each of the four tosses, the probability that the chosen coin is the two-headed one will be:
= Number of two headed coins / Total coins
= 1/16
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IF ANYONE KNOWS, IT WOULD BE A GREAT HELP, help
Determine the points on the x-axis whose distance from the point (5, 0) is 13 and Determine the points on the y-axis whose distance from the point (5, 0) is 13.
The points on the x-axis whose distance from the point (5, 0) is 13 units is given as follows:
(-8, 0) and (18,0).
The points on the y-axis whole distance from the point (5, 0) is 13 are given as follows:
(0, -12) and (0, 12).
How to obtain the distance between two points?The general coordinates of the two points are given as follows:
[tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex]
Hence the distance between them is of:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
A point on the x-axis has the coordinates given as follows:
(x,0).
For the distance of 13 units from point (5,0), the possible points are given as follows:
5 - 13 = -8, hence point (-8,0).5 + 13 = 18, hence point (18, 0).On the y-axis, the coordinates are given as follows:
(0,y).
Hence the possible values of y are obtained as follows:
[tex]13 = \sqrt{5^2 + y^2}[/tex]
Applying the square root to both sides, we have that:
25 + y² = 13²
y² = 144
y = -12 or y = 12.
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Solve the system by using elementary row operations on the equations. Follow the systematic elimination procedure
x1+4x2 =11
2x1+7x2=18
The equations ( x1+4x2 ) = 11 and ( 2x1+7x2 ) = 18 give the solution as x1 = -5 and x2 = 4.
In order to solve the equation using elementary row operation it is required to multiply the first equation with -2, so that the term with x1 is eliminated from both equations and the value of x2 can be found.
Now
-2. ( x1+4x2 ) = -2 . 11
(-2x1 - 8x2 ) = -22
Now, this equation is added to the second equation (the left-hand sides of both equations are added together and the right-hand side of the equations are added together).
(-2x1 - 8x2 ) + ( 2x1+7x2 ) = ( -22 + 18 )
-2x1 + 2x1 - 8x2 + 7x2 = -4
-x2 = -4
(x2 = 4)
The value of x2 = 4 is now put in equation 1 to get the value of x1,
( x1 + 4x2 ) = 11
x1+ 4 (4) = 11
x1 + 16 = 11
x1 = (11 - 16)
(x1 = - 5)
So solution is x1 = -5 and x2 = 4.
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