They have to use 17.03 pounds of cashews and 17.03 pounds of nuts to make a 32 pounds mixture that sells for $5.75 per pounds
The cost of cashews per pounds = $7.20
The cost of nuts per pounds = $4.10
Consider the number of pounds of cashews as x and number of pounds of nuts as y
Total pounds of mixture = 32 pounds
The equation will be
x+y = 32
x = 32-y
Cost of the mixture for one pound = $5.75
Cost of the mixture for 32 pounds = 32×5.75
= $184
Then the equation will be
7.20x+4.10y = 184
Here we have to use the substitution method
Substitute the value of x in the equation
7.20(32-y)+4.10y = 184
230.4-7.20y+4.10y = 184
230.4-3.1y = 184
-3.1y = 184-230.4
-3.1y = -46.4
y = 14.97 pounds
x+y = 32
x+14.97 = 32
x = 17.03 pounds
Hence, they have to use 17.03 pounds of cashews and 17.03 pounds of nuts to make a 32 pounds mixture that sells for $5.75 per pounds
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Use the table of values for
y = f(x)
to complete a table for
y = f −1(x).
(Order your answers from smallest to largest x-value.)
The table containing the values of the inverse function is given at the end of the answer.
How to find the set of points (x,y) of a inverse function?A function will have a set of points (x,y). In the inverse function, the values of x and y are exchanged with each other, hence the rule is:
(x,y) -> (y,x).
Hence, the points are found as follows:
On the original function, when x = -4, f(x) = 10. Then, on the inverse function, when x = 10, f^-1(x) = -4.On the original function, when x = -3, f(x) = 0. Then, on the inverse function, when x = 0, f^-1(x) = -3.On the original function, when x = -2, f(x) = -10. Then, on the inverse function, when x = -10, f^-1(x) = -2.On the original function, when x = -1, f(x) = -20. Then, on the inverse function, when x = -20, f^-1(x) = -1.On the original function, when x = 0, f(x) = -30. Then, on the inverse function, when x = -30, f^-1(x) = 0.On the original function, when x = 1, f(x) = -40. Then, on the inverse function, when x = -40, f^-1(x) = 1.The table containing these values is given at the end of the answer.
What is the missing information?The tables are missing, and are given at the end of the answer.
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What is the income distribution of super shoppers? A supermarket super shopper is defined as a shopper for whom at least 70% of the items purchased were on sale or purchased with a coupon. In the following table, income units are in thousands of dollars, and each interval goes up to but does not include the given high value. The midpoints are given to the nearest thousand dollars.
Income range 5-15 15-25 25-35 35-45 45-55 55 or more
Midpoint x 10 20 30 40 50 60
Percent of super shoppers 22% 13% 21% 17% 20% 7%
A button hyperlink to the SALT program that reads: Use SALT.
(a) Using the income midpoints x and the percent of super shoppers, do we have a valid probability distribution? Explain.
No. The events are indistinct and the probabilities sum to more than 1.
Yes. The events are distinct and the probabilities do not sum to 1.
Yes. The events are distinct and the probabilities sum to 1.
Yes. The events are indistinct and the probabilities sum to less than 1.
No. The events are indistinct and the probabilities sum to 1.
Correct: Your answer is correct.
(b) Use a histogram to graph the probability distribution of part (a). (Because the data table has summarized the data into categories, use SALT to create a bar chart.)
Maple Generated Plot Maple Generated Plot
Maple Generated Plot Maple Generated Plot
Correct: Your answer is correct.
(c) Compute the expected income of a super shopper. (Round your answer to two decimal places.)
=
Incorrect: Your answer is incorrect.
thousands of dollars
(d) Compute the standard deviation for the income of super shoppers. (Round your answer to two decimal places.)
=
Incorrect: Your answer is incorrect.
thousands of dollars
From the given probability distribution, it is found that:
a) Yes. The events are distinct and the probabilities sum to 1.
b) The histogram is given at the end of the answer.
c) The mean is of 32.1.
d) The standard deviation is of 16.02.
What is the probability distribution?
Using the midpoint rule, the distribution is given as follows:
P(X = 10) = 0.22.P(X = 20) = 0.13.P(X = 30) = 0.21.P(X = 40) = 0.17.P(X = 50) = 0.20.P(X = 60) = 0.07.The outcomes are distinct, and their sum is of:
0.22 + 0.13 + 0.21 + 0.17 + 0.20 + 0.07 = 1.
Hence it represents a probability distribution.
The mean is given by the sum of each outcome multiplied by it's respective probability, hence:
E(X) = 10 x 0.22 + 20 x 0.13 + 30 x 0.21 + 40 x 0.17 + 50 x 0.20 + 60 x 0.07 = 32.1
The standard deviation is the square root of the sum of the difference squared between each observation and the mean, multiplied by it's respective probability, hence:
S(X) = sqrt((10-32.1)² x 0.22 + (20-32.1)² x 0.13 + (30-32.1)² x 0.21 + (40-32.1)² x 0.17 + (50-32.1)² x 0.20 + (60-32.1)² x 0.07) = 16.02.
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Find the equation (in terms of xx ) of the line through the points (-4,1) and (5,-3)
EXPLANATION
Given two points of a line, we can find the the equation of that line using the steps below:
• Step 1
Determine the slope of the line, using the formula below:
[tex]\text{slope(m)}=\frac{y_2-y_1}{x_2-x_1}[/tex]The points given are (-4, 1) and (5, -3). This implies that the coordinates are
x₁= -4 y₁=1 x₂=5 y₂=-3
Substitute the values into the formula and simplify.
[tex]m=\frac{-3-1}{5+4}=-\frac{4}{9}[/tex]• Step 2
Determine the y-intercept(b) of the line.
Substitute x₁= -4 y₁=1 and m=-4/9 into y=mx + b and solve for intercept(b).
1 = (-4/9)(-4) + b
[tex]1=\frac{16}{9}+b[/tex]Subtract 16/9 from both-side of the equation.
[tex]b=1-\frac{16}{9}[/tex][tex]b=\frac{9-16}{9}=-\frac{7}{9}[/tex]The intercept (b) = -7/9
• Step 3
Form the equation by substituting the value of the slope and intercept into y=mx + b.
Hence, the equation of the line is:
[tex]y=-\frac{4}{9}x-\frac{7}{9}[/tex]what is the image point (6,-9) after the rotation of 270 degrees counterclockwise about the origin
Image of the point (6,-9) after rotation in the cartesian plane of 270 degrees counterclockwise about the origin will be (-9, -6)
As per the question statement, we are supposed to find the image of the point (6,-9) after rotation in the cartesian plane of 270 degrees counterclockwise about the origin.
We should know that a 270° anticlockwise rotation is exactly the same thing as a 90° clockwise rotation.
So the point (x, y) becomes (y, -x)
So the image of the point (6,-9) after rotation in the cartesian plane of 270 degrees counterclockwise about the origin will be (-9, -6)
Cartesian Plane: A Cartesian coordinate system in a plane is a system of coordinates that uniquely identifies each point by a pair of numerical coordinates. These numerical coordinates are the signed distances from two fixed perpendicular oriented lines to the point, measured in the same unit of length.To learn more about Cartesian Plane, click on the link given below:
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I have been stuck in this problem for 2 hours please help
We need to find the values of "x" and "y" from two triangles that are congruent. If the triangles are congruent it means that the corresponding angles are equal. This means that angle R and angle N are the same, and from the angle sum theorem w know that the interior angles of triangle QPR sum 180, that is mathematically:
[tex](9x-18)+84+\angle R=180[/tex]Since angle N is 3x+y, we replace that in the equation:
[tex](9x-18)+84+(3x+y)=180[/tex]Simplifying we get:
[tex]\begin{gathered} 12x+y+66=180 \\ 12x+y=180-66 \\ 12x+y=114,\text{ (1)} \end{gathered}[/tex]That gives us equation (1), but we need another equation since we have two variables. The other equation we get it from angles L and P, since this two angles must be equal. So we get the following equation:
[tex]4x+17=9x-18[/tex]Solving for "x", we get:
[tex]\begin{gathered} 4x-9x=-18-17 \\ -5x=-35 \\ x=-\frac{35}{-5}=7 \end{gathered}[/tex]The value of "x" is 7. Now we input this value in equation (1), like this:
[tex]\begin{gathered} 12x+y=114 \\ 12(7)+y=114 \\ 84+y=114 \end{gathered}[/tex]Solving for "y", we get:
[tex]\begin{gathered} y=114-84 \\ y=30 \end{gathered}[/tex]therefore, the value of "y" is 30.
Use the number line to answer the question.
A number line is shown with end points 0 and 2. Hash marks are at every 0.2. Heavy marks are at 0, 1, and 2.
Zach bought 8 pieces of bubble gum that were $0.20 each. He used a number line to find the total cost. Choose the numbers to complete the sentences.
Zach started on the number line at 0.2 for the cost of one piece of gum. He moved
Choose...
hash marks. The total cost is
Choose...
.
Zach began at 0.2 for the price of one piece of gum on the number line. Has moved eight times. The whole price is $1.60.
Since each hash mark is worth.2, moving eight times will result in 1.6, or eight times $0.20.
This is further explained below.
What is a Number line?Generally, A number line is a depiction of a graded straight line that is used to represent real numbers visually.
It is assumed that every point on a number line corresponds to a real number and that every real number corresponds to a point.
A horizontal line with evenly spaced numerical increments is referred to as a number line.
How the number on the line may be answered depends on the numbers present. How a number is utilized depends on the issue it is associated with, such as when graphing a point
In conclusion, On the number line, Zach started at 0.2, which was equal to the cost of one piece of gum. Has relocated a total of eight times. The whole cost is a dollar and sixty cents.
Moving eight times will result in 1.6, which is equal to eight times $0.20, given that each hash mark is worth.2.
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2) Jennifer makes a hexagon by arranging 6 equilateral triangles, each of which has a vertex at
the center of the hexagon. If the length of one side of a triangle is 4, what is the area in
square units of the hexagon? Leave in simplest radical form if necessary. Show work and
circle final answer
The area in square units of the hexagon will be 12√3.
What is Hexagon?
A polygon with six sides are called a hexagon.
Given that;
Jennifer makes a hexagon by arranging 6 equilateral triangles.
The length of one side of a triangle is 4.
Now, To find the area of hexagon, we find the height of the equilateral triangle and then multiply by the 6.
So, In ΔABC;
AB = BC = CA = 4
Then, Measure of DC = BD = 2
Now, using Pythagoras theorem to find height of triangle (AD) as;
AD² = AC² - DC²
AD² = 4² - 2²
AD² = 16 - 4
AD² = 12
Take square root both side;
AD = √12
AD = 2√3
So, The area of hexagon = 6 × Height of triangle
= 6 × 2√3
= 12√3
Thus, The area in square units of the hexagon will be 12√3.
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If x + 1/x = 83, find the value of x^2 + 1/x^2
Answer:
6887
Step-by-step explanation:
given
x + [tex]\frac{1}{x}[/tex] = 83 ( square both sides )
(x + [tex]\frac{1}{x}[/tex] )² = 83² = 6889 ← expand factor on left using FOIL
x² + 2( x × [tex]\frac{1}{x}[/tex] ) + [tex]\frac{1}{x^2}[/tex] = 6889
x² + 2(1) + [tex]\frac{1}{x^2}[/tex] = 6889 ( subtract 2 from both sides )
x² + [tex]\frac{1}{x^2}[/tex] = 6887
PLS HELP MEEEEEEEEEEEEEEEEEEEEE PLS I BEG U
how could you use a graph of a proportional relationship to find any ratio in the the proportional relationship why does this work?
The fact that a connection is proportional if its graph is a line that runs through its origin should be stressed. This can be used to find the ratio in the proportional relationship.
How to explain the information?When the graph of a connection is a line passing through the origin, the connection is proportionate. If it is not a line or ray that fails to do this, the ratio is not proportional. The equation for the proportionality constant is K = y/x. This is the same equation used to get the slope of a straight line with respect to the origin.
If the graph of a relationship is a line or ray that goes through the origin, the relationship is proportional. If the line or ray does not pass through the origin, it is not proportional.
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Use the drawing tool(s) to form the correct answer on the provided graph.
The rectangle shown is dilated by a scale factor of 1.5 with the origin as the center of dilation.
Draw the resulting rectangle.
If the rectangle shown is dilated by a scale factor of 1.5 with the origin as the center of dilation , then the resulting rectangle is shown below .
In the question ,
From the figure given below , we can see that the coordinates of the rectangle are (4,2) , (4,4) , (-2,2) , (-2,4) .
let us name the coordinates of the rectangle as A(4,2) , B(4,4) , C(-2,4) , D(-2,2) .
and to dilate the rectangle by a scale factor of 1.5 with center of dilation at the origin , we multiply coordinates of the original shape with the dilation factor
so the rule to describe the dilation will be
(x,y)→(1.5x,1.5y)
Using this rule to find the new coordinates of the rectangle A'B'C'D' .
When A = (4,2)
A' = (1.5*4,1.5*2)
A' = (6,3)
When B = (4,4)
B' = (15*4,1.5*4)
B' = (6,6)
When C = (-2,4)
C' = (1.5*(-2),1.5*4)
C' = (-3,6)
When D = (-2,2)
D' = (1.5*(-2),1.5*2)
D' = (-3,3)
So the coordinates of the rectangle A'B'C'D' is A' = (6,3) , B' = (6,6) , C' = (-3,6) , D' = (-3,3) .
the new resulting rectangle is drawn below
Therefore , if the rectangle shown is dilated by a scale factor of 1.5 with the origin as the center of dilation , then the resulting rectangle is shown below .
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In 2008, 1.7m iPhones were sold. In 2012, 35.2m iPhones were sold. Assuming the sales of iPhones increases exponentially, how many iPhones should be expected to be sold in 2017?
The number of iPhones that should be sold in 2017 (since growth is exponential) is $ 6,476,635 x 10⁶. See the explanation below.
What is exponential Growth?Exponential growth is a data pattern that exhibits greater increases with time. Compounding produces exponential profits in finance. Compounding interest savings accounts may provide exponential growth.
The calculation for the above solution is as follows:
Recall that the formula for exponential growth is:
f(x) = a (1+r)ˣ
Where:
f(x) = exponential growth function
a = initial amount
r = growth rate
{x} = number of time intervals
Hence f(x) = 1.7 (1+ r)⁵
Note that x = 2017-2012 =5
r = (present value - past value)/ past value
Present value = 35.2
Past Value = 1.7
Hence r = (35.2-1.7)/1.7
r = 19.7058823529
Approximately 19.71
Hence,
f(x) = 1.7 (1+ 19.71)⁵
= 1.7 (20.71)⁵
= 1.7 x 3809785.2361
= 6476634.90137
Which is approximately = 6,476,635
Recall that our computation was done in millions hence the answer if left in standard notation is:
Increase in 2017 = $ 6,476,635 x 10⁶
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Ms.Vega read 20% of the Star Wars book. She read 8 pages of the book
The total number of the pages in the star war book which Ms. Vega is reading is 40.
percentage- a relative value indicating hundredth parts of any quantity. One percent (symbolized 1%) is a hundredth part.
Let the number of pages = X
percentage of read pages = 20%
Number of read pages by her = 8
to find the total number in star war book
20% of X = 8
20/100 x X = 8
X = (8 x 100)/ 20
X = 4 X 10
X = 40
Total number of pages in star war book is 40.
The question is incomplete the complete question is
Ms. Vega read 20% 8of the Star Wars book. She read 8 pages of the book. Write pages in the Star Wars book.
The total number of the pages in the star war book which Ms. Vega is reading is 40.
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Find the surface area and volume of the hemisphere FormulaSA = 3 * 3.14 * r^2V = 2/3 * 3.14 * r^3
ANSWER
[tex]\begin{gathered} SA=98\pi ft^2 \\ V=228.7\pi ft^3 \end{gathered}[/tex]EXPLANATION
To find the surface area of the hemisphere, we apply the formula for the surface area of a hemisphere (without a base):
[tex]SA=2\cdot\pi\cdot r^2[/tex]where r = radius = 7 ft
Therefore, the surface area of the hemisphere is:
[tex]\begin{gathered} SA=2\cdot\pi\cdot7^2 \\ SA=98\pi ft^2 \end{gathered}[/tex]To find the volume of the hemisphere, we apply the formula for the volume of a hemisphere:
[tex]V=\frac{2}{3}\cdot\pi\cdot r^3[/tex]Therefore, the volume of the hemisphere is:
[tex]\begin{gathered} V=\frac{2}{3}\cdot\pi\cdot7^3 \\ V=228.7\pi ft^3 \end{gathered}[/tex]find the slope of the line that goes through the given points (-2,-4) (1/4,5)
Solution
find the slope of the line that goes through the given points (-2,-4) (1/4,5)
[tex]\begin{gathered} slope\text{ =m} \\ m=\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex][tex]\begin{gathered} x_1=-2 \\ x_2=\frac{1}{4} \\ y_1=-4 \\ y_2=5 \end{gathered}[/tex][tex]m=\frac{5--4}{\frac{1}{4}--2}=\frac{9}{2.25}=4[/tex]Therefore the slope of the line = 4
Two accounts each begin with a deposit of $9000. Both accounts have rates of 3.1%, but one account compounds interest once a year while
the other account compounds interest continuously. Make a table that shows the amount in each account and the interest earned after one
year, five years, ten years, and 20 years.
Given : Initial deposit or the principal amount = $ 9000
Rate of interest = 3.1 %
Compound interest annually
= principal (1 + r/ 100)^t
here put value principal rate and time period 1, 5 10 and 20 years
and we get the amount for each time period
than for interest = amount - principal we get interest
as that we calculate all value:
given in the attachment
When do we use compound interest ?When interest on a balance in a savings or investment account is reinvested, you receive compound interest, which results in higher interest payments. Money makes money, a wise man once said. And money makes money by making more money. Compound interest speeds up the long-term growth of your savings and investments.
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What happens to the x and y-values when you translate an object up?
When we translate an object up, the values of x remain the same, but the values of y change by a positive value.
Joanne deposits $4,300 into a l-year CD at a rate of 2.3%, compounded daily.a. What is her ending balance after the year, to the nearest cent?b. How much interest does she earn, to the nearest cent?c. What is her annual percentage yield to the nearest hundredth of a
Joanne deposits $4,300 into a l-year CD at a rate of 2.3%, compounded daily.
a. What is her ending balance after the year, to the nearest cent?
b. How much interest does she earn, to the nearest cent?
c. What is her annual percentage yield to the nearest hundredth
Remember that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
P=$4,300
t=1 year
r=2.3%=2.3/100=0.023
n=365
Part a
Find out the value of A
substitute the given values in the formula
[tex]A=4,300(1+\frac{0.023}{365})^{365\cdot1}[/tex]A=$4,400.04
Part b
I=A-P
I=4,400.04-4,300
I=$100.04
Part c
we have
4,300 -----> represent 100%
so
Applying proportion
Find out how much percentage is 4,400.04
100/4,300=x/4,400.04
x=(100/4,300)*4,400.04
x=102.33%
therefore
102.33-100=2.33%
A = P(1+r) solve for r
Answer:
50
Step-by-step explanation:
csehufe;whweih/a=r+9+9
_(&*%^&*&^%^&*765678987654567890(*&*()_)(*()_(*()_+=9
Nautical flags are used to communicate on
ships. Kimani uses the
scale drawing at the
right to sew a nautical Z flag. The scale from
her flag to the drawing is 20
Each color is
4
of the flag. How many square inches of
each color of fabric does Kimani need?
Answer:
5
Step-by-step explanation:
according to my own understanding since her flag to the drawing is 20. each colour is 4,then u divide 20 by 4. The answer is 5
Perform the indicated operation. Don't forget to simplify if possible.
Subtract 6x + 2 from 4x-6.
Answer: 2x + 8
Step-by-step explanation:
( 6x + 2 ) - ( 4x - 6 ) =
6x - 4x = 2x
2 - -6 = 8
Help.
A. RS
B. ST
C. Ut
Answer: THE ANSWER TO THAT IS B
Step-by-step explanation:
Determine the solution of the given system of equations.
-x+y=-5
-4x - 5y=7
Answer:
x =2 y = -3
Step-by-step explanation:
hope it helps!!!!!
1)
Solve the equation for y. Then, complete the
5x + 4y = 20
y=
Preview
20
Answer:
-5/4
Step-by-step explanation:
debemos de usar la ecuacion dy/dx
Which statements about the line that passes through (-2, 0) and (2, -4) are true? Select all that apply.
OA. The slope of the line is 1.
B. The line intersects the y-axis at (0, -2).
Considering the expression of a line, the statements:
"The line intersects the y-axis at (0, −2).""The equation of the line is y = −x − 2.""The line intersects the x-axis at (−2, 0)."about the line that passes through (-2, 0) and (2, -4) are true.
Linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope m of said line can be calculated using the following expression:
m= (y₂ - y₁)÷(x₂ - x₁)
Substituting the value of the slope m and the value of one of the points in the expression of a linear equation, y = mx + b, the value of the ordinate to the origin b can be obtained.
This caseBeing (x₁, y₁)= (-2, 0) and (x₂, y₂)= (2, -4), the slope m can be calculated as:
m= (-4 - 0)÷(2 - (-2))
m= (-4)÷ 4
m= -1
Considering point 1 and the slope m, you obtain:
0= -1×(-2) + b
0= 2 +b
-2= b
Finally, the equation of the line that passes through the pair of points (-2,0) and (2,-4) is y= -x -2, wich has a slope of -1. The line intersects the x-axis at (−2, 0).
If x=0, you get:
0= -x -2
2= -x
2÷ (-1)=x
-2= x
Finally, the line line intersects the y-axis at (0, −2).
Your question was incomplete. Please check below the full content.
Which statements about the line that passes through (−2, 0) and (2, −4) are true? Select all that apply.
A. The slope of the line is 1.
B. The line intersects the y-axis at (0, −2).
C. The equation of the line is y = −x − 2.
D. The line intersects the x-axis at (−2, 0).
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There are 6 triangles and 15 squares. What is the simplest ratio of triangles to squares?
Answer:
2:5
Step-by-step explanation:
6:15= 2:5
The function f(x) = 2x − 1 is transformed to function g through a horizontal shift of 7 units left. What is the equation of function g?
Replace the values of h and k in the equation.
g(x) = 2x+h + k
When the function f is transformed to g, the equation is g(x) = 2x + 14 - 1
How to determine the equation of function g?The equation of function f is given as
f(x) = 2x - 1
The transformation is given as
Horizontal shift of 7 units left.
The above transformation rule can be represented as
Horizontal shift of 7 units left.: (x, y) = (x + 7, y)
When the above rule is applied, we have the following equation
g(x) = f(x + 7)
So, we have
g(x) = 2(x + 7) - 1
Open the brackets
g(x) = 2x + 14 - 1
Hence, the equation of function g is g(x) = 2x + 14 - 1
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At the city museum, child admission is $6.00 and adult admission is $9.60. On Sunday, twice as many adult tickets as child tickets were sold, for a total sales of $630.00. How many child tickets were sold that day?
Answer:
25 child tickets and 50 adult tickets
Step-by-step explanation:
Let c be the number of child tickets and a be the number of adult tickets. We have this system of equations:
6.00c + 9.60a = 630.00
a = 2c
Substitute 2c for a in the top equation:
6.00c + 9.60(2c) = 630.00
6.00c + 19.20c = 630.00
25.20c = 630.00
c = 25, a = 50
Solve for Lowercase w
Which has a terminal point of (square root 2/2 and square root 2/2). What is the terminal point of 5pi/4?
To find 5π/4 as terminal point, we will take the angle as 5π/4
The first coordinate is the x coordinate = cos θ
The second coordinate is the y coordinate = sin θ
[tex]\begin{gathered} We\text{ n}eed\text{ to convert the angle to degre}e\colon \\ 1\pi\text{ rad = 180}\degree \\ \frac{5\pi}{4}\text{ rad = 225}\degree \\ \\ sin\text{ is negative in third quadrant} \\ 225\text{ - 180 = 45} \\ \sin \text{ 45 = }\frac{\sqrt[]{2}}{2} \\ \\ \sin \text{ 225}\degree\text{ =- }\frac{\sqrt[]{2}}{2} \end{gathered}[/tex][tex]\begin{gathered} \theta\text{ = 225}\degree\text{ }is\text{ in third quadrant} \\ \\ 180\text{ -225 = 45}\degree \\ \cos \text{ 45}\degree\text{ = }\frac{\sqrt[]{2}}{2} \\ \text{ 225 is negative in third quadrant} \\ \\ \cos \text{ 225}\degree\text{ =- }\frac{\sqrt[]{2}}{2} \end{gathered}[/tex]Hence, the terminal of 5π/4:
[tex]\text{(-}\frac{\sqrt[]{2}}{2},\text{ -}\frac{\sqrt[]{2}}{2})\text{ (option C)}[/tex]How many units are (-2,-3) & (5,7) from each other on the coordinate plane
Let's begin by listing out the information given to us:
(x, y) = (-2, -3), (5, 7)
The distance between the two points is given by:
[tex]\begin{gathered} d=\sqrt[]{\mleft(\mleft(x_2-x_1\mright)^2+\mleft(y_2-y_1\mright)^2\mright)} \\ d=\sqrt[]{(5--2)^2+(7--3)^2} \\ d=\sqrt[]{7^2+10^2} \\ d=\sqrt[]{49+100} \\ d=12.207\approx12.21 \\ d=12.21 \end{gathered}[/tex]