The point which will lie in the solution set to the following system of inequalities is:
(2,5)
Step-by-step explanation:The system of inequality is given by:
y>-3x+3--------(1)
and y>x+2----------(2)
Now, the point that will lie in the solution set to the following system of inequality are the point that satisfies both the inequality.
a)
(2,-5)
when x=2 and y= -5
then by first inequality we have:
-5>-3×2+3
i.e.
-5>-6+3
i.e.
-5>-3
which is a false identity.
This means that the point will not lie in the solution set.
b)
(-2,5)
when x= -2 and y=5
then by first inequality we have:
5>-3×(-2)+3
i.e.
5>6+3
i.e.
5>9
which is a false identity.
Hence, option: b is incorrect.
c)
(2,5)
when x=2 and y=5
then by first inequality:
5>-3×2+3
i.e. 5>-6+3
i.e. 5>-3
which is true
and by second identity:
5>2+2
i.e. 5>4
which is again true.
Hence, (2,5) lie in the solution set.
d)
(-2,-5)
when x= -2 and y= -5
then by first inequality we have:
-5>-3×(-2)+3
i.e.
-5>6+3
i.e.
-5>9
which is a false identity.
Hence, the point (-2,-5) do not lie in the solution set.
Which geometric term is best described as a straight path between two points?
A. Angle
B. Point
C. vertex
D. Line Segment
Answer:
the answer is d
Step-by-step explanation:
A line segment is best described as a path between two points.
What is a line segment?A line segment is a line that is definite from one point to another. The length of a line segment can be measured and it is not infinite.
We can choose the correct answer below:Four options are given.
We have to find the geometric term that is best described as a straight path between two points.
From the given options, the only term that satisfies these conditions is a line segment.
A line segment is a line that is definite from one point to another. The length of a line segment can be measured and it is not infinite.
Therefore, we have found that a line segment is best described as a path between two points. The correct answer is option D.
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2. Tell which measure of central tendency best describes the data
3. Tell which measure of central tendency best describes the data
Answer:
Step-by-step explanation:
Mean, it is the average of all numbers and most accurately represents the data set.
The best measure of central tendency depends on the data set characteristics: the mean is suitable for outlier-free data, the median is better for skewed data or when outliers are present, and the mode indicates the most common value.
Explanation:Choosing the Best Measure of Central Tendency
When analyzing a data set, selecting the appropriate measure of central tendency is crucial. The three main measures are the mean, median, and mode. The mean is the arithmetic average and is best used when the data set does not contain outliers that can skew the results. The median is the middle value when the data is ordered and offers a better representation when outliers are present. The mode is the most frequently occurring value and provides insight into the most common data point.
In a symmetrical data set where the data are evenly distributed, all three measures of central tendency—the mean, median, and mode—will be equal or close to each other. In a skewed distribution or when the data contains outliers, the median is generally the most reliable measure of the center, as it is unaffected by extreme values.
The number of frogs in a certain lake is inversely related to the number of snakes in the lake. If x represents the number of snakes in the lake, then y = 100/x represents the number of frogs in the lake. Describe the reasonable domain and range values. Graph the function.
1. Domain: The set of natural numbers / Range: The set of natural numbers
2. Shown below
Step-by-step explanation:1. Domain and Range.In this problem, we have that the number of frogs in a certain lake is inversely related to the number of snakes in the lake. Hence we are facing an Inverse Variation, so this means that if the number of snakes in the lake increases then the number of frogs in the lake decreases, because snakes eat frogs! The function that describes this is a rational function defined as:
[tex]y=\frac{100}{x}[/tex]
Where:
[tex]x: \ represents \ the \ number \ of \ snakes \ in \ the \ lake \\ \\ y: \ represents \ the \ number \ of \ frogs \ in \ the \ lake[/tex]
As you can see, [tex]x[/tex] is in the denominator, therefore [tex]x\neq 0[/tex]. Since we need to provide a reasonable domain, we say that the domain is the set of natural numbers and this doesn't include the number 0. Why aren't negative values included in the domain as well? Well, although negative values are included in the function, they aren't reasonable because [tex]x[/tex] represents the number of snakes and you always get positive numbers when counting things.
To get the range, let's take the inverse of this function, so:
[tex]y=f(x)=\frac{100}{x} \\ \\ \\ Interchange \ x \ and \ y: \\ \\ x=\frac{100}{y} \\ \\ \\ Isolate \ y: \\ \\ y=\frac{100}{x} \\ \\ f^{-1}(x)=\frac{100}{x}[/tex]
So the domain of [tex]f^{-1}(x)[/tex] is the range of our given function [tex]y=f(x)[/tex]. As you can see the inverse function is the same as our given function, then the range is the set of natural numbers as well.
2. Graph.First of all, we can define the pattern of the rational function as:
[tex]y=g(x)=\frac{1}{x}[/tex]
So our function will be:
[tex]f(x)=100g(x)=100\frac{1}{x}=\frac{100}{x}[/tex]
So the graph of [tex]f(x)[/tex] will be the same graph of [tex]g(x)[/tex] but it's been stretched vertically by a constant of 100, that is, each y-value is multiplied by 100. Also, since [tex]x \neq 0[/tex] and [tex]y \neq 0[/tex] then at [tex]x=0[/tex] there is a vertical asymptote and at [tex]y=0[/tex] there is an horizontal asymptote. Finally, the graph is shown below for [tex]x>0 \ and \ y>0[/tex], but remember: Whenever [tex]x \ and \ y[/tex] are natural numbers.
Answer:
Both the number of snakes and the number of frogs will be positive, so positive values are reasonable for the domain and range.
Step-by-step explanation:
find the mean of these values 100, 200, 300, 400
250
100 + 200 + 300 + 400 = 1000
1000/4 = 250
Answer:
250
Step-by-step explanation:
Simplify 12a2b3 / 3ab
[tex] \frac{12 {a}^{2} {b}^{3} }{3ab } \\ = \frac{3 \times a \times b \times 4 \times a \times {b}^{2} }{3ab} \\ \\ cancelling \: common \: factors \\ \\ = 4a {b}^{2} [/tex]
Hence answer is 4ab²
Hope it helps...
Hope it helps...Regards;
Hope it helps...Regards;Leukonov/Olegion.
Which of the following is a list of equivalent numbers?
A. 1.25,114,12.5%
B. 0.125,14,12.5%
C. 12.5,1212,125%
D. 1.25,114,125%
ANSWER
D. 1.25,1¼,125%
EXPLANATION
The number 1.25 can be rewritten as a fraction to obtain:
[tex]1 \frac{1}{4} [/tex]
We can covert 1.25 into percentage by multiplying by 100%
This implies that,
[tex]1.25 = 1.25 \times 100\% = 125\%[/tex]
Therefore the equivalent numbers are:
1.25,1¼,125%
The correct answer is D
ASAP ANSWER
Bobby has 4 ½ gallons of soda to share. Each serving is 1 pint. How many servings does he have to share?
each gallon has 8 pints
4 [tex]\frac{1}{2}[/tex] * 8 = 36
so there would be 36 servings
Compare the monthly payment amount of Annabelle's dream car at two different car dealerships.
Dealership A: The car costs $30,000, and the loan has an annual interest rate of 4.8%.
Dealership B: The car costs $29,800, and the loan has an annual interest rate of 5.4%.
Determine the monthly payment for each dealership, and decide which is cheaper. Both interest rates are compounded
monthly. Both loans are for 5 years, or 60 months. Assume that there is no down payment.
Answer:
Dealership A is cheaper. Hope it helps.
Answer:
By comparing both the payments we can say that Dealer A is cheaper by $4.50.
Step-by-step explanation:
Dealership A: The car costs $30,000, and the loan has an annual interest rate of 4.8% for 5 years.
The EMI formula is :
[tex]\frac{p\times r\times(1+r)^{n} }{(1+r)^{n}-1 }[/tex]
Now, p = 30000
r = [tex]4.8/12/100=0.004[/tex]
n = [tex]5\times12=60[/tex]
Putting values in formula we get;
[tex]\frac{30000\times0.004\times(1+0.004)^{60} }{(1+0.004)^{60}-1 }[/tex]
=> [tex]\frac{30000\times0.004\times(1.004)^{60} }{(1.004)^{60}-1 }[/tex]
EMI is = $563.34
Dealership B: The car costs $29,800, and the loan has an annual interest rate of 5.4% for 5 years.
p = 29800
r = [tex]5.4/12/100=0.0045[/tex]
n = [tex]5\times12=60[/tex]
Putting values in formula we get;
[tex]\frac{29800\times0.0045\times(1+0.0045)^{60} }{(1+0.0045)^{60}-1 }[/tex]
=> [tex]\frac{29800\times0.0045\times(1.0045)^{60} }{(1.0045)^{60}-1 }[/tex]
EMI = $567.84
By comparing both the payments we can say that Dealer A is cheaper by $4.50.
Can someone answer this for me ASAP please ?
Answer:
The expression which is equivalent to (k ° h)(x) is [tex]\frac{1}{(5 + x)}[/tex] ⇒ 2nd answer
Step-by-step explanation:
* Lets explain the meaning of the composition of functions
- Composition of functions is when one function is inside of an another
function
# If g(x) and h(x) are two functions, then (g ° h)(x) means h(x) is inside
g(x) and (h ° g)(x) means g(x) is inside h(x)
* Now lets solve the problem
∵ h(x) = 5 + x
∵ k(x) = 1/x
- We need to find (k ° h)(x), that means put h(x) inside k(x)
* Lets replace the x of k by the h(x)
∵ k(x) = [tex]\frac{1}{x}[/tex]
∵ h(x) = 5 + x
- Replace the x of k by 5 + x
∴ k(5 + x) = [tex]\frac{1}{5 + x}[/tex]
∴ The expression which is equivalent to (k ° h)(x) is [tex]\frac{1}{5+x}[/tex]
Find the image of (–7, –3) reflected across the x-axis. A. (–7, 3) B. (7, –3) C. (7, 3) D. (–7, –3)
Answer:
(-7, -3) (Answer A)
Step-by-step explanation:
We start with the point (-7, -3). The x-coordinate does not change at all if we reflect this point across the x-axis. Whereas the y-value of (-7, -3) is -3, we end up with +3 after this reflection. The desired image is (-7, +3) (Answer A)
The coordinates of the point (-7, - 3) reflected along the x-axis is
(- 7, 3).
What are transformations?Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.
Dilation: The preimage is scaled up or down to create the image.
Reflection: The picture is a preimage that has been reversed.
Rotation: Around a given point, the preimage is rotated to create the final image.
Translation: The image is translated and moved a fixed amount from the preimage.
We know reflection along the x-axis of a point (x, y) converts it into a
point (x, - y).
Given, A points (-7, - 3) is reflected along the x-axis.
Therefore, The new coordinates of the points (-7, - 3) reflected along the x-axis is (- 7, 3).
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im taking the flvs test and need the answer asapppppp
During a certain time of the year, the angle of the sun's rays at location C is smaller than the angle of the sun's rays at location D. Which location experiences cooler temperatures at that time?
Location C, because the smaller angle means the sunlight is spread out over more area
Location D, because the larger angle means the sunlight is spread out over more area
Location C, because Earth is tilted away from the sun at this time
Location D, because Earth is tilted towards the sun at this time
Answer:
d
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
I just finished the quiz, and this was my only incorrect one. The correct answer is A. Also, think logically. If the sun is spread out over more area, then it must be at a smaller angle. This leads to cooler temperatures, of course.
Someone help me with this question
Hello There!
The answer would be 0.6
This is because you have to multiply the probability of each of these. First, I know that 0.5 is 1/2 in fraction form and that 0.3 is 3/10
Which of the following is an even function?
Answer:
I believe it is the third one (C)
Step-by-step explanation:
Hello There!
Your answer would be the first one.
f(x) = \x/
F of x has to equal f of -x
What is the slope of this line?
Answer: [tex]-\frac{8}{5}[/tex]
Remember: RISE/RUN (y/x). Lines that are increasing have a positive slope, and lines that are decreasing have a negative slope.
You can find the slope in two ways:
1. Useful if the line is graphed: count the units between 2 points on the line.
Let's use the points (-1, 4) and (4, -4).(-1, 4) is 8 units higher than (4, -4) and 5 units to the left of (4, -4).Because the line is decreasing, the slope is negative.Therefore, the slope is [tex]-\frac{8}{5}[/tex].2. Useful if the line is not graphed: find the difference between the y-coordinate values divided by the difference of the x-coordinate values.
Let's use the points (-1, 4) and (4, -4).[tex]\frac{-4 - 4}{4 - (-1)} = \frac{-8}{5}[/tex]Therefore, the slope is [tex]-\frac{8}{5}[/tex].Answer:
[tex]m=-\frac{8}{5}[/tex]
Step-by-step explanation:
Let
[tex]A(-1,4),B(4,-4)[/tex]
we know that
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute the values
[tex]m=\frac{-4-4}{4+1}[/tex]
[tex]m=\frac{-8}{5}[/tex]
[tex]m=-\frac{8}{5}[/tex]
Mike spent $7920 on his vacation, which was 11% of his monthly salary. What was his monthly salary?
Answer : 72,000
Ex: Let x be his monthly salary.
The equation to set up would be
7920=0.11x
This equation represents 11% of monthly salary = 7920
To solve you divide 0.11x by 0.11 to get x by itself. then you do what you do to one side to the other. therefore you divide 7920 by 0.11 and you get 72,000
Plz help me with this
Answer: C) the variance
Step-by-step explanation:
Variance is the "average" of the squared differences from the Mean.
Write an equation for the perpendicular line in slope intercept form for (-3,5);y=1/3x-2
Hey there! :)
We're given the equation : y = 1/3x - 2 & coordinates : (-3, 5)
If we're looking for an equation for a perpendicular line, then we know that the slope of our new equation MUST be the negative reciprocal of the original slope. This means that you flip the slope and add or remove a negative. Example : slope = -2 ⇒ negative reciprocal slope = 1/2
Before using this information, we must first find the slope of our original equation.
Using slope-intercept form, which is : y=mx+b ; where m=slope, b=y-intercept
Ask yourself : which value is in the "m" spot and which value is in the "b" spot?
Using this, we now know that 1/3 is our slope, and -2 is our y-intervept.
So, our negative reciprocal is -3.
Use point-slope form to find the y-intercept, and coordinates (-3, 5)
Point-slope = y - y1 = m(x - x1)
y - 5 = -3(x - (-3))
Simplify.
y - 5 = -3(x + 3)
Simplify.
y - 5 = -3x - 9
Add 5 to both sides.
y = -3x + 4 ⇒ slope-intercept form
~Hope I helped! :)
9. The points (4, –6) and (9, -6) represent the location of two towns on a
coordinate grid, where one unit is equal to one mile. What is the distance, in miles, between the two towns?
Answer:
5 miles apart
Step-by-step explanation:
(4,-6) is 5 units away from (9,-6)
find the value of n such that b^2 + 16b + n is a perfect square trinomial
Answer:
64
Step-by-step explanation:
To complete the square
add ( half the coefficient of the b- term )² to b² + 16b
b² + 2(8)b + 8²
= b² + 16b + 64 = (b + 8)²
Determine which diagram could be used to prove ABC - EDC using similarity transformations.
Answer: A The first Answer to the left
Step-by-step explanation:
The diagram could be used to prove that ABC-EDC using similarity transformations is option A.
The first Answer to the left
We have given that,
The diagram could be used to prove ABC - EDC using similarity transformations.
What is the transformation?
A similarity transformation is one or more rigid transformations (reflection, rotation, translation) followed by a dilation.
We have to determine which diagram could be used to prove ABC-EDC.
Therefore the answer is the first diagram.
The diagram could be used to prove that ABC-EDC using similarity transformations is option A.
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#5! And #4 revisions!
Answer:
4. Your working and answers are correct: x = 44, y = 43.
5. GH = 60°
Step-by-step explanation:
5. Arc GH is double the inscribed angle GFH, so we have ...
2(4x+2) = 9x-3
8x +4 = 9x -3 . . . . . simplify
7 = x . . . . . . . . . . . . add 3-8x
Then the arc's measure is ...
(9·7 -3)° = (63 -3)° = 60°
Answer:
Step-by-step explanation:
Your working and answers are correct: x = 44, y = 43.
5. GH = 60°
PLEASEE HEELPPP I NEED THIS QUESTION ANYONE HELP!!!
Answer:
4u= - 4i - 24j
u +w = -9i - 3j
Step-by-step explanation:
The question is on operation of vectors
Given u= -i -6j and w= -8i+3j
Then 4u = 4{ -i-6j}
4u= - 4i - 24j
u+w= -i -6j + -8i+3j......................collect like terms
= -i -8i + -6j +3j
= -9i + -3j
= -9i - 3j
Point C(3.6, -0.4) divides in the ratio 3 : 2. If the coordinates of A are (-6, 5), the coordinates of point B are .
If point D divides in the ratio 4 : 5, the coordinates of point D are .
Reset Next
Answer:
Point B is (10 , -4)
Point D is (10/9 , 1)
Step-by-step explanation:
* Lets revise the rule of the point which divides of a line segment in
a ratio
- If point (x , y) divides the line segment AB, where A is (x1 , y1) and
B is (x2 , y2) in the ratio m1 : m2
∴ x = [m2(x1) + m1(x2)]/(m1 + m2)
∴ y = [m2(y1) + m1(y2)]/(m1 + m2)
* Now lets solve the problem
- Point C (3.6 , -0.4) divides AB in the ratio 3 : 2, where A is (-6 , 5)
# x = 3.6 , y = -0.4
# A is (x1 , y1) , B is (x2 , y2)
∴ x1 = -6 , y1 = 5
∵ m1 : m2 = 3 : 2
- Substitute these values in the rule
∵ x = [m2(x1) + m1(x2)]/(m1 + m2)
∴ 3.6 = [2(-6) + 3(x2)]/(3 + 2)
∴ 3.6 = [-12 + 3x2]/5 ⇒ multiply both sides by 5
∴ 18 = -12 + 3x2 ⇒ add 12 to both sides
∴ 30 = 3x2 ⇒ divide both sides by 3
∴ 10 = x2
* The x-coordinate of B is 10
∵ y = [m2(y1) + m1(y2)]/(m1 + m2)
∴ -0.4 = [2(5) + 3(y2)]/(3 + 2)
∴ -0.4 = [10 + 3y]/5 ⇒ multiply both sides by 5
∴ -2 = 10 + 3y2 ⇒ subtract 10 from both sides
∴ -12 = 3x2 ⇒ divide both sides by 3
∴ -4 = y2
* The y-coordinate of B is -4
∴ Point B is (10 , -4)
- Point D divides AB in the ratio 4 : 5 where A (-6 , 5) and B (10 , -4)
- To find the coordinates of point D use the same rule above
# D is (x , y)
# A is (x1 , y1) and B is (x2 , y2)
# m1 : m2 is 4 : 5
∵ x1 = -6 and y1 = 5
∵ x2 = 10 and y2 = -4
∵ m1 = 4 and m2 = 5
- Substitute these values in the rule
∵ x = [m2(x1) + m1(x2)]/(m1 + m2)
∴ x = [5(-6) + 4(10)]/(4 + 5) ⇒ multiply the numbers
∴ x = [-30 + 40]/9 ⇒ add
∴ x = [10]/9 ⇒ Divide
∴ x = 10/9
* The x-coordinate of D is 10/9
∵ y = [m2(y1) + m1(y2)]/(m1 + m2)
∴ y = [5(5) + 4(-4)]/(5 + 4) ⇒ multiply the numbers
∴ y = [25 + -16]/9 ⇒ add
∴ y = [9]/9 ⇒ Divide
∴ y = 1
* The y-coordinate of point D is 1
∴ Point D is (10/9 , 1)
The work of a student to find the dimensions of a rectangle of area 8 + 12x and width 4 is shown below:
Step 1: 8 + 12x
Step 2: 4(2) 4x2)
Step 3: 4(4 + 8x)
Step 4: Dimensions of the rectangle are 4 and 4 + 8x
In which step did the student first make an error and what is the correct step?
Step 2: 4(2) + 4x(2)
Step 2: 4(2) + 4(3x)
Step 3: 4 + (4+8x)
Step 3: 4 + (4• 8x)
Answer:
Step 2: 4(2) + 4(3x)
Step-by-step explanation:
By definition, the area of a rectangle is given by:
Area = Length × Width
In this case, we know that:
Area = 8 + 12x
Width = 4
Therefore:
Step 1: 8 + 12x
Step 2: 4(2) + (4)(3x)
Step 3: 4(2 + 3x)
Therefore, the dimensions of the rectangle are 4 and 2 + 3x.
The mistake was made in STEP 2. Instead of 4(2) + 4(x2) it should be 4(2) + 4(3x). Which is the second option.
Need help fast do not understand this one. Solve: (x+5) / (x+8)=1+(6) / (x+1) showing all work.
Answer: [tex]x=-\frac{17}{3}[/tex]
Step-by-step explanation:
Given the equation [tex]\frac{(x+5)}{(x+8)}=1+\frac{6}{(x+1)}[/tex], you need to make the addtition indicated on the right side of the equation:
[tex]\frac{(x+5)}{(x+8)}=\frac{(x+1)+6}{(x+1)}\\\\\frac{(x+5)}{(x+8)}=\frac{(x+7)}{(x+1)}[/tex]
Now, multiply both sides of the equation by (x+8) and (x+1):
[tex](x+1)(x+8)\frac{(x+5)}{(x+8)}=\frac{(x+7)}{(x+1)}(x+1)(x+8)\\\\(x+1)(x+5)=(x+7)(x+8)[/tex]
Now, apply Distributive property:
[tex]x^2+5x+x+5=x^2+8x+7x+56[/tex]
Simplifying, you get:
[tex]6x+5=15x+56[/tex]
Subtract 5 and 15x from both sides:
[tex]6x+5-15x-5=15x+56-15x-5\\\\-9x=51[/tex]
Finally, divide both sidesby -9:
[tex]\frac{-9x}{-9}=\frac{51}{-9}\\\\x=-\frac{17}{3}[/tex]
kayla is sending invitations to 20 of her freinds for a pizza party. if there are 12 invitatons left to end out, how many invitations has she already mailed?
Kayla has mailed out 8 invitations
Use the pattern to answer the question. 27, 18, 12, 8. Which expression can be used to find the nth term of the pattern?
A. 27-6n
B. 27-6(n-1)
C. 27(2/3)^n
D. 27(2/3)^n-1
If you cross check with the answer , you’ll find option C to be the most appropriate option.
The difference between the first two terms is 9 and 9 is not a multiple of six, therefore first two are wrong.
Similarly, if you check option D for the first two terms , you get the second term as 27 which is false.
Therefore option C is the answer, also , it satisfies the series.
Final answer:
The correct expression to find the nth term of the given pattern is Option D: [tex]27(2/3)^{(n-1)}[/tex], as it accurately represents the geometric sequence of the provided numbers.
Explanation:
To find the nth term of the given pattern 27, 18, 12, 8, we will consider each option and see which one fits the sequence of numbers.
The first term (n=1) is 27.
The second term (n=2) is 18, which is 27 multiplied by ⅔ or 2/3.
The third term (n=3) is 12, which is the second term (18) multiplied by ⅔ or 2/3.
Similarly, the fourth term (n=4) is 8, which is the third term (12) multiplied by ⅔ or 2/3.
We can see that with each step, the term is being multiplied by a factor of ⅔ or 2/3. Therefore, an expression that uses multiplication by ⅔ repeatedly would likely represent the pattern.
Let's test the options:
Option A: 27-6n does not fit as it suggests a linear pattern with a constant subtraction, which does not match our sequence.
Option B: 27-6(n-1) also suggests a linear pattern and will not result in the given sequence when evaluated for n=1,2,3,4.
Option C: [tex]27(2/3)^n[/tex] represents a geometric sequence with a common ratio of ⅔, but for n=1, this expression gives us 27*⅔ which is not equal to 27.
Option D: [tex]27(2/3)^{(n-1)}[/tex] when evaluated for n=1 gives us 27*[tex](2/3)^{(1-1)}[/tex] = 27*1 = 27, which is the correct first term of our sequence. Applying this for subsequent terms also gives the correct sequence. Therefore, this is the correct expression for the nth term of the pattern.
Thus, the expression to find the nth term of the pattern is Option D: [tex]27(2/3)^{(n-1)}[/tex].
Leila is considering buying her first home. The house she is interested in buying is priced at $125,000. Leila can put down a $20,000 payment, and she qualifies for a 30-year mortgage at 6%. What will her monthly mortgage payment be?
Answer:
* The monthly mortgage payment is $629.53 ⇒ answer C
Step-by-step explanation:
* Lets explain how to solve the problem
- Leila is considering buying her first home
- The house she is interested in buying is priced at $125,000
∴ She can put $20000 down payment
* Lets find the balance to be paid off on mortgage
∴ The balance = 125000 - 20000 = 105000
- She qualifies for a 30-year mortgage at 6%
* Lets find the rule of the monthly payment
∵ [tex]pmt=\frac{\frac{r}{n}[P(1+\frac{r}{n})^{tn}]}{(1+\frac{r}{n})^{tn}-1}[/tex] , where
- pmt is the monthly mortgage payment
- P = the initial amount
- r = the annual interest rate (decimal)
- n = the number of times that interest is compounded per unit t
- t = the time the money is invested or borrowed for
∵ P = 105000
∵ r = 6/100 = 0.06
∵ n = 12
∵ t = 30
∴ [tex]pmt=\frac{\frac{0.06}{12}[105000(1+\frac{0.06}{12})^{30(12)}}{(1+\frac{0.06}{12})^{30(12)}-1}[/tex]
∴ [tex]pmt=\frac{0.005[105000(1.005)^{360}]}{(1.005)^{360}-1} =629.528[/tex]
* The monthly mortgage payment is $629.53
(08.01)
Line R is represented by the following equation: x + y = 2
Which equation completes the system that is satisfied by the solution (1, 1)?
2x + y = 2
4x − 2y = 2
2x − 2y = 2
x + y = 4
Answer:
B: 4x − 2y = 2
B: 4x − 2y = 2 equation completes the system that is satisfied by the solution (1, 1).
What is a linear equation?A linear equation has one or two variables.
No variable in a linear equation is raised to a power greater than 1.No variable is used as the denominator of a fraction. A linear equation is defined as an equation that is written in the form of ax+by=c. When solving the system of linear equations, we will get the values of the variable, which is called the solution of a linear equation.solving this we will get the valve of Y if x is given.
explanation:
line R = x + y = 2
putting the value of X=1 & y=1 as given (1,1)
x+y =2
1+1= 2
therefore, 4x - 2y = 2
4(1) - 2(1)= 2 answer
Learn more about linear equations here:-https://brainly.com/question/14323743
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the factored form of a quadratic equation is x (x-4). the ordered pair (0,0) represents one of the zeros of the associated quadratic function. which ordered pair represents the other zero?
Answer:
the other zero is represented by the ordered pair (4, 0)
Step-by-step explanation:
We have the factored expression
[tex]x (x-4)[/tex]
We must find out for what values of x this function is equal to zero.
Then we equal the function to zero and solve for the variable x
[tex]x (x-4)=0[/tex]
The function is equal to zero when one of the two terms of the product is equal to zero.
So
[tex]x =0[/tex] We already know that this is a solution
or
[tex]x-4=0\\x =4[/tex]
Then the other zero is represented by the ordered pair (4, 0)