[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-4}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-4}-\stackrel{y1}{5}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{(-2)}}} \implies \cfrac{-9}{3 +2}\implies {\Large \begin{array}{llll} -\cfrac{9}{5} \end{array}}[/tex]
Find the equation of the line that passes through (-1,5) and (0,1)
We have to find the equation of the line that passes through the points (-1,5) and (0,1). We will write the equation in the slope-intercept form, which is given by:
[tex]y=mx+b[/tex]Where m represents the slope of the function, and b the y-intercept. We will find the slope, and then the y-intercept.
1. Finding the slope
For finding the slope we will use the formula:
[tex]m=\frac{y_2-y_1_{}}{x_2-x_1}[/tex]where (x₁,y₁) and (x₂,y₂) are two points that passes through the line. In this case, the points (-1,5) and (0,1).
Replacing, we obtain:
[tex]m=\frac{1-5}{0-(-1)}=\frac{-4}{1}=-4[/tex]Thus, the slope is -4.
2. Finding the y-intercept
For doing this step, we want to know the value of the function when x equals zero. But, as we have that the line passes through (0,1), this means that this value will be 1. This is, the y-intercept is 1.
3. Putting all together
Now, we just have to put the values obtained in the slope-intercept form:
[tex]\begin{gathered} y=mx+b \\ y=-4x+1 \end{gathered}[/tex]And this means that the equation of the line that passes through (-1,5) and (0,1) is y=-4x+1.
How do i solve this problem?
The function exists a Power function. The power of function is 3 and the constant variation is - 1/3
What is meant by Power function?Any function where y = x n, where n is any real constant integer, is referred to be a power function. In reality, many of our parent functions, including linear and quadratic functions, are power functions. A few other power functions are y = x³, y = 1/x, and y = x squared.
A parameter function used in statistical testing that represents the likelihood of rejecting the null hypothesis for a given value of the parameter, assuming that value is true.
Therefore, the power of function is 3 and the constant variation is - 1/3.
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Apples are 99 cents a pound and pears are $1.25 a pound. Write an expression thatrepresents the total cost, in dollars, of a pounds of apples and p pounds of pears.
Answer
$(0.99 + 1.25p)
Explanation
Note: 100 cents = $1
Apples cost $(99/100) = $0.99 a pound
Pears cost $1.25 a pound
Since 1 pound of pears cost $1.25,
∴ p pounds of pears will cost $1.25p
Now total cost in $ of a pound of apples and p pound of pears = $(0.99 + 1.25p)
Hence, the expression that represents the total cost is $(0.99 + 1.25p)
Write the equation of the line that is parallel
to y = x-7 and passes through the point
(-3, 1)
Equation parallel to y = x+4,
How do you write an equation for a parallel line?Equations that are parallel have the same slope.The standard equation of an equation is written through slope intercept form, which is
y = mx + b
where m is your slope and b is the y intercept
So, in the equation provided, 1 is the slope.
To write an equation when given a slope and points, you use point slope form, which is
y −y1 =m(x−x1)
y1 is the y in the set of points you are given, same with x1
So,
y1 =1 and x1= -3
As stated before, m is the slope, and the slope is given as 1
Plug in the numbers into the equation
y −1 =1 (x+3)
y= x +4 ;
And there you have a equation parallel to
y=x +4
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Harry just deposited $1500 into a savings account giving 6% interest compounded monthly. How much will be in the account after 10 years and 20 years ?
Compound Interest
It occurs when the interest is reinvested rather than paying it out.
When it happens interest in the next period is then earned on the principal sum plus previously accumulated interest.
The formula is:
[tex]{\displaystyle A=P\mleft(1+{\frac{r}{n}}\mright)^{nt}}[/tex]Where:
A=final amount
P=initial principal balance
r=interest rate
n=number of times interest applied per time period
t=number of time periods elapsed
Harry deposited an initial amount of P = $1500.
The savings account gives r = 6% = 0.06 interest
Since the interest is compounded monthly, n = 12 (there are 12 months in a year)
The time is t = 10 years.
Now we apply the formula:
[tex]\begin{gathered} {\displaystyle A=1500(1+{\frac{0.06}{12}})^{12\cdot10}} \\ \text{Calculating:} \\ {\displaystyle A=1500(1+0.005)^{120}} \end{gathered}[/tex]Using a calculator:
A = $2729.095
Rounding to two decimals,
A = $2729.10
Harry will have $2729.10 in his account after 10 years
Now for t = 20 years:
[tex]{\displaystyle A=1500(1+{\frac{0.06}{12}})^{12\cdot20}}[/tex]Calculating again:
A = $4965.31
Harry will have $4965.31 in his account after 20 years
Resting body temperatures are normally distributed with an average of 98.25 degreesFahrenheit and a standard deviation of 0.73 degrees Fahrenheit. A nurse examines 40 patients in one hour. What is the probability the average temperature of the 40 patients is between 98.0 degrees Fahrenheit and 98.50 degrees Fahrenheit? (Round to the hundredths)A)0.97B)0.11542313C)0.99D)Sample size is not larger than 40 so we cannot compute probability
Resting body temperatures are normally distributed with an average of 98.25 degrees
Fahrenheit and a standard deviation of 0.73 degrees Fahrenheit. A nurse examines 40 patients in one hour. What is the probability the average temperature of the 40 patients is between 98.0 degrees Fahrenheit and 98.50 degrees Fahrenheit? (Round to the hundredths)
A)0.97
B)0.11542313
C)0.99
D)Sample size is not larger than 40 so we cannot compute probability
step 1
Find the z-scores
For x=98.0 degrees
z=(98-98.25)/0.73 --------> z=-0.3425
For x=98.50
z=(98.50-98.25)/0.73 ------> z=0.3425
using a Z-score Calculator
we have that
P=0.26803
step 2
we have that
Question 8 of 15
Triangle ABC with vertices A(-1, 2), B(-1, -2), and C(-4,-2) is dilated by a scale factor of 2 to form triangle A'B'C'.
у
A
C
4321
-4-3-2-10 이 1234
1
OHN 3 +
B
+2+
-3+
Submit Test
-4-
What is the length, in units, of side A'B'?
units
2223 Math Grade 8 IA1
X
The formula that most accurately captures the dilatation that Triangle ABC underwent to produce A'B'C will be:
(x, y) → (1/2x, 1/2y)
Detailed explanation?
A triangle's vertices are given.
A(-2, -4) (-2, -4)
B(2, -4) (2, -4)
C(-8, -4) (-8, -4)
The vertices of an image triangle should be after the dilatation
A' (-1, -2) (-1, -2)
B '(1, -2) (1, -2)
C' (-4, -2) (-4, -2)
If we look attentively, we can see that the vertices of the image triangle, A'B'C', make up half of the original triangle ABC.
For example, (x, y) (1/2x, 1/2y)
verification
A(-2, -4) → A'(-2/2, -4/2) = A'(-1, -2) (-1, -2)
B(2, -4) → B'(2/2, -4/2) = B'(1, -2) (1, -2)
C(-8, -4) → C'(-8/2, -4/2) = C'(-4, -2) (-4, -2)
As a result, it is confirmed, and we come to the conclusion that the rule that best captures the dilatation that Triangle ABC underwent to form A'B'C' will be:
(x, y) → (1/2x, 1/2y)
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Sarah is working towards paying off the rest of her student loan. The graph models the amount owed, in dollars, for x months. What does the slope represent?
The slope of the graph that models the amount Sarah owed after a given number of x months, represents the monthly payment Sarah makes to repay the loan
What is a monthly payment on a loan?Monthly payment on a loan is the payment made each month within the period specified in the loan, to repay the loan and the interest on the loan.
The given parameters of the graph are;
Information on the graph = The amount owed for a number of x months
Taking the y–axis (Vertical axis) of the graph as specifying the amount owed given in Dollars, and the x–axis as the number of months of payment, we have;
[tex] \displaystyle{Slope = \frac{\Delta y}{\Delta x}} [/tex]
Where;
∆y = Change in the amount Sarah owes
∆x = Change in the time
Which gives;
[tex] \displaystyle{Slope = \frac{Change\: in\: the\: amount \:owed}{Change\: in\: time }}[/tex]
Whereby the graph is a straight line graph, we have;
The slope = Constant
Therefore, the change in the amount owed over a given time frame such a month, is constant
Which gives;
The slope represents the amount by which the Sarah's student loan changes each month, which is equivalent to and therefore;
The amount Sarah repays each month (monthly payments on the loan) towards paying off the student loan.Learn more about calculating the monthly payment on a loan here:
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Elizabeth drew a right triangle and labeled the sides as follows: leg lengths = 5 inches and 8 inches, hypotenuse = 14 inches. Can the side lengths form a right triangle? Explain your reasoning. I need a good explaination
X_X
The side length of the triangle Elizabeth drew cannot form a right triangle.
How to find the sides of a right triangle?A right triangle is a triangle that has one of its angle as 90 degrees.
The sides of a right triangles are hypotenuse side, adjacent side and the opposite side. This is base on the angle position.
Right triangle obeys Pythagoras's theorem.
a² + b² = c²
where
a and b are the legs of the right trianglec is the hypotenuse side of the right triangle.Therefore, let's test if the labelled side of the triangle Elizabeth drew is a right triangle. We will use Pythagoras theorem to confirm it
5² + 8² = 14²
25 + 64 = 196
Therefore,
89 ≠ 196
Therefore, the side length cannot form a right triangle
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Divide and solve: r^2/r^12
Given:
[tex]\frac{r^2}{r^{12}}[/tex]Let's solve using law of indices below:
[tex]\frac{a^m}{a^n}=a^m\ast a^{-n}=a^{m-n}[/tex]Using the same method, we have:
[tex]\frac{r^2}{r^{12}}=r^2\ast r^{-12\text{ }}=r^{2-12}=r^{-10}[/tex]ANSWER:
[tex]r^{-10}[/tex]A flower bed is in the shape of a triangle with one side twice the length of the shortest side and the third side is 21 feet
more than the length of the shortest side. Find the dimensions if the perimeter is 121 feet.
What is the length of the shortest side?
The length of the shortest side is
Answer: 25 ft
Step-by-step explanation:
Let the shortest side be s. Then, the other two sides are 2s and s+21.
[tex]s+2s+s+21=121\\\\4s+21=121\\\\4s=100\\\\s=25[/tex]
What is a formula for the nth term of the given sequence 15,24,33
Answer:
87
Step-by-step explanation:
the whole sequence would be 15, 24, 33, 42, 51, 60, 69, 78, 87
Complete the table for the arithmetic sequence.
Airthemetic Sequence : arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.
It express as :
[tex]a_n=a_1+(n-1)d[/tex]In the given question the 88 term is ( 25)
Substitute the value in the expression of n terms
[tex]\begin{gathered} a_n=a_1+(n-1)d \\ \text{for : n =25, a}_n=88,a_1=(-8) \\ a_n=a_1+(n-1)d \\ 88=(-8)+(25-1)d \\ 88=-8+24d \\ 88+8\text{ =24d} \\ 24d=96 \\ d=\frac{96}{24} \\ d=4 \end{gathered}[/tex]In the given Airthmetic sequence the constant difference, d = 4
Now for the position of term 8
[tex]\begin{gathered} a_n=a_1+(n-1)d \\ \text{for a}_n=8,a_1=(-8),\text{ d =4} \\ 8=-8+(n-1)4 \\ 16=4(n-1) \\ 4=n-1 \\ n=5 \end{gathered}[/tex]for n= 5 terms is 8
Now for the term of position 8:
[tex]\begin{gathered} a_n=a_1+(n-1)d \\ \text{for n=8, a}_1=(-8),d=4 \\ a_n=-8+(8-1)4 \\ a_n=-8+7\times4 \\ a_n=20 \end{gathered}[/tex]So, the term with position 8 is 20
Now for the position of term 36 :
[tex]\begin{gathered} a_n=a_1+(n-1)d \\ \text{for :a}_n=36,a_1=(-8),\text{ d = 4} \\ 36=-8+(n-1)4 \\ 36+8=4(n-1) \\ 44=4(n-1) \\ n-1=\frac{44}{4} \\ n-1=11 \\ n=10 \end{gathered}[/tex]Thus, for n = 10, an = 36
Now, for the term of position 19
[tex]\begin{gathered} a_n=a_1+(n-1)d \\ \text{for n=19, d=4, a}_1=(-8) \\ a_n=-8+(19-1)4 \\ a_n=-8+(18)4 \\ _{}a_n=-8+72 \\ a_n=64 \end{gathered}[/tex]Thus at n = 19 the term i 64
A coffee shop currently sells 440 lattes a day at $2.50 each. They recently tried raising the by price by $0.25 a latte, and found that they sold 60 less lattes a day.
a). Assume that the number of lattes they sell in a day, N, is linearly related to the sale price, p (in dollars). Find an equation for N as a function of p.
N(p)= (blank)
b). Revenue (the amount of money the store brings in before costs) can be found by multiplying the cost per cup times the number of cups sold. Again using p as the sales price, use your equation from above to write an equation for the revenue, R as a function of p.
R(p)= (blank)
c). The store wants to maximize their revenue (make as much money as possible). Find the value of p that will maximize the revenue (round to the nearest cent).
p= (blank) which will give a maximum revenue of $ (blank)
Show your work!
Explain your answer!
No incorrect answer!
No nonsense answers!
No spam answers!
Thanks!
Using linear function concepts, it is found that:
a) The amount of lattes sold function is: N(p) = -240p + 1040.
b) The revenue function is: R(p) = -240p² + 1040p.
c) The revenue is maximized when p = $2.17.
What is a linear function?A linear function, in slope-intercept format, is modeled according to the following rule:
y = mx + b
In which:
The coefficient m is the slope of the function, which is the rate of change of the function, that is, the change in y divided by the change in x.The coefficient b is the y-intercept of the function, which is the the value of y when the function crosses the x-axis(x = 0).For this problem, we have a linear function with the points having the following format:
(price, lattes sold).
Hence two points are given as follows:
(2.50, 440), (2.75, 380).
The slope is given by change in y divided by change in x, hence:
m = -60/0.25 = -240.
Then:
N(p) = -240p + b.
When p = 2.50, N(p) = 440, hence we solve for b as follows:
440 = -240(2.5) + b
b = 1040.
Thus the function is:
N(p) = -240p + 1040.
The revenue function is:
R(p) = pN(p)
Hence:
R(p) = p(-240p + 1040)
R(p) = -240p² + 1040p.
Which is a concave down quadratic function, with a = -240 and b = 1040. A concave down quadratic function is maximized when:
p = -b/2a
Hence:
p = -1040/2(-240) = $2.17.
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Jumbo shrimp are defined as those that require 10 to 15 shrimp to make a pound. Suppose that the number of jumbo shrimp in a 1-pound bag
averages u 12.5 with a standard deviation of a 1.5 and forms a normal distribution. Using the Distributions tool, find the probability of random
picking a sample of n = 25 1-pound bags that average more than M = 13 shrimp per bag.
Standard Deviation - 1.0
The probability of randomly picking a sample of n 25 1-pound bags that average more than M - 13 shrimp per bag is p =
Answer:
0.0475
Step-by-step explanation:
What do all rectangles have that some parallelograms do not have?
A. Opposite angles that are congruent
B. Diagonals that are congruent
C. Opposite sides that are congruent
D. Diagonals that bisect each other
Answer:
B. Diagonals that are congruent
Para resolver una operación matemática ¿por qué es importante
primero conocer los signos y los números?
Answer:
para hacer la repuesta xd
4 over 15 divided by 10 over 13
4/15 = 3.75
10/13 = 1.3
you have to divide it from its higher number or you'll get something like this: 0.7692307692307692 but if it helps it = 0.00205128205
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Molly is making peanut butter cookies to make a batch of cookies. She needs 3/4 cups of peanut butter 1.5 cups of sugar and 1 egg if Molly is 3 cups of peanut butter, 9 cups of sugar and 5 eggs how many batches can she make
Can u please help me solve this problem
Given that the initial point of vector "u" is:
[tex](4,8)[/tex]And the terminal point:
[tex](-12,14)[/tex]You need to find the Component Form of the vector with this formula:
[tex]u=\langle x_2-x_2,y_2-y_1\rangle[/tex]In this case:
[tex]\begin{gathered} x_2=-12 \\ x_1=4 \\ y_2=14 \\ y_1=8 \end{gathered}[/tex]Then, you get:
[tex]u=\langle-12-4,14-8\rangle=\langle-16,6\rangle[/tex]Find the Magnitude using this formula:
[tex]||u||=\sqrt{x^2+y^2}[/tex]In this case:
[tex]\begin{gathered} x=-16 \\ y=6 \end{gathered}[/tex]Therefore, by substituting values and evaluating, you get:
[tex]||u||=\sqrt{(-16)^2+(6)^2}\approx17.088[/tex]In order to find the direction of the vector "u", you need to use this formula:
[tex]\theta=tan^{-1}(\frac{y}{x})[/tex]Then, when you substitute the values of "x" and "y" into the formula and evaluate, you get:
[tex]\theta=tan^{-1}(\frac{6}{16})\approx20.556°[/tex]Hence, the answer is:
The ratio of boys to girls in Fiona's class is
1 to 3. There are 24 students in the class.
How many of the students are girls?
Answer:
Step-by-step explanation:
Given,
The ratio of boys to girls in Fiona's class is 1:3
The total student in the class is 24
To find,
how many students are girls
Solution,
It is clear that the total number of boys and girls is 24
i.e., boys + girls=24 ------ (equation 1)
Let the ratio be in the terms of x
Consider boys ratio as x
And the girl's ratio as 3x
Now as per the equation 1,
x + 3x= 24
4x= 24
x= 6
Hence, Boys (x)= 6
And Girls (3x)= 3× (6)= 18
You can verify it by adding 6+18= 24
Assume that 600 births are randomly selected and 309 of the births are girls. Use subjective judgment to describe the
number of girls as significantly high, significantly low, or neither significantly low nor significantly high.
Choose the correct answer below.
A. The number of girls is significantly low.
B. The number of girls is neither significantly low nor significantly high.
C. The number of girls is significantly high.
D. It is impossible to make a judgment with the given information.
Option b. The number of girls is neither significantly low nor significantly high.
How is the subjective judgement given?
Total number of births selected= 600
Half of the total number = 300
Number of girls = 309
As we can see, the number of girls is slightly higher than the half and not significantly higher . Therefore I can subjectively describe and conclude that the number 309 is neither significantly low nor significantly high. The total population of boys and girls are almost similar.What is subjective judgement ?
Subjective judgement is something that is based more on the individual's thoughts and feelings than on actual facts. The dominating eigenvector of a matrix of paired comparisons is a widely used technique for quantifying subjective judgement .To learn more about population, refer:
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How to find the range of data. 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26
Answer:
22
Step-by-step explanation:
To find the rage, you subtract the smallest number from the largest number in the set of numbers.
So...
26 - 4 = 22
What is the unit rate for the situation represented in the table?
Hours 3 5 7 9
Wages $35.25 $58.75 $82.25 $105.75
a $7.05/hour
b $2/hour
c $11.75/hour
d $16.45/hour
Answer:
c $11.75/hour
Step-by-step explanation:
You want the unit rate represented by the table of (hours, wages) = (3, $35.25), (5, $58.75), ....
Unit rateThe unit rate of dollars per hour is found by dividing dollars by hours:
$35.25/(3 hour) = $11.75/hour
You can check the other table values to see if they represent the same unit rate. (They do.)
What is answer????????
Answer is 6
9 - 6 = 3
The difference of a number and 9 means to subtract said number from 9.
What can be concluded about the line represented in the table? Select 3 options.
x
y
–6
–7
2
–3
8
0
The slope is 2.
The slope is One-half.
The y-intercept is –4.
The y-intercept is 8.
The points (–2, –5) and (8, 0) are also on the line.
The points (–5, –2) and (1, 10) are also on the line.
Conclusions that can be made about the line in the table include:
The slope is One-half.The y-intercept is –4.The points (–2, –5) and (8, 0) are also on the line.How to find the slope of a line?The slope of a line is found by the formula:
= Change in y / Change in x
Two points from the table:
(-6, -7) (2, -3)
Slope is:
= (-3 - (-7)) / 2 - (-6))
= 4 / 8
= 1/2
The y-intercept is:
y = Slope (x) + y-intercept
-3 = 2(1/2) + y-intercept
y-intercept = -3 - 1
y-intercept = -4
Points on the line as shown on the table:
(-2, -5) and (8,0)
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Four friends have $525 that they want to share equally. To start, they divide the money so that each friend gets a $100 bill. What is the most useful next step?
If four friends have $525 that they want to share equally and they divide the money so that each friend gets a $100 bill, then next step will be divide the remaining money so that each friend gets a $31.25
Total money the have = $525
they divide the money so that each friend gets a $100 bill
The amount of money they split equally = 4×100
= $400
Remaining money = 525-400
= $125
Split the remaining money into 4 = 125/4
= $31.25
Hence, If four friends have $525 that they want to share equally and they divide the money so that each friend gets a $100 bill, then next step will be divide the remaining money equally so that each friend gets a $31.25
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1.)Based on the average.how many people will usethe ramp each week? Setup ratio.2.) What will the surface areaof the ramp be? Writeequation & solve. Roundto the nearest hundredth.3.) What percentage of thepeople do not need theramp?4.) How high will the ramp be9 feet from the front walk?Draw a diagram & solve.5.) How high will the ramp be6 feet fromthe front walk?Draw a diagram & solve.Please help with these questions.thank you.
1)
Let:
N = Total people every week = 207
r = People which needs a ramp = 1:9 = 1/9
So:
[tex]N\cdot r=207\cdot\frac{1}{9}=23[/tex]Answer: 23 people
2)
[tex]\begin{gathered} SA=b\cdot h+pw \\ _{\text{ }}where\colon \\ b=18ft \\ h=4ft \\ p=b+h+l \\ l=\sqrt[]{h^2+b^2} \\ l=\sqrt[]{340} \\ w=4.75ft \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} SA=72+192.09 \\ SA=264.09ft^2 \end{gathered}[/tex]3)
The percentage of the people that don't need the ramp will be given by:
[tex]1-r=1-\frac{1}{9}=\frac{8}{9}\approx0.89[/tex]Answer: Approximately 89%
4)
[tex]\begin{gathered} h=\sqrt[]{(\sqrt[]{340})^2-9^2} \\ h=\sqrt[]{259} \\ h\approx16.09ft \end{gathered}[/tex]5)
[tex]\begin{gathered} h=\sqrt[]{(\sqrt[]{340})^2-6^2} \\ h=\sqrt[]{340} \\ h\approx17.44ft \end{gathered}[/tex]f(x)=-3x^2+3x, find f(f)x))
The value of the composite function f(f(x)) is -3(-3x^2 + 3x)^2 + 3(-3x^2 + 3x)
How to determine the composite function?The functions are given as
f(x) = -3x^2 + 3x
The definition of the composite function is given as
f(f(x))
This composite function is calculated using the following composite function formula
f(f(x))= (f o f)(x)
Substitute the known values in the above equation
So, we have the following equation
f(f(x)) = -3f(x)^2 + 3f(x)
So, we have
f(f(x)) = -3(-3x^2 + 3x)^2 + 3(-3x^2 + 3x)
Hence, the composite function is f(f(x)) = -3(-3x^2 + 3x)^2 + 3(-3x^2 + 3x)
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Solve the system of equations
-2x - 6y + 8z = 14
3x + 2y - z = 4
2x - y + 2z = 10