Solution:
The modulus of a complex number;
[tex]z=a+bi[/tex]is denoted by;
[tex]|z|=|a+bi|=\sqrt[]{a^2+b^2}[/tex]Thus, given the complex number;
[tex]2-6i[/tex]The modulus is;
[tex]\begin{gathered} a=2,b=-6 \\ |2-6i|=\sqrt[]{2^2+(-6)^2} \\ |2-6i|=\sqrt[]{4+36} \\ |2-6i|=\sqrt[]{40} \\ |2-6i|=\sqrt[]{4\times10} \\ |2-6i|=\sqrt[]{4}\times\sqrt[]{10} \\ |2-6i|=2\times\sqrt[]{10} \\ |2-6i|=2\sqrt[]{10} \end{gathered}[/tex]ANSWER:
[tex]2\sqrt[]{10}[/tex]ten B В 15 cm А 20 cm С C
Tangent segment, of a circle
Apply formulas
20^2 - 15^ 2 = AB^2
Also
15^2 = 20•( 20 - AB)
225 = 400 - 20AB
Then
20AB = 400-225= 175
AB = √ 175= 13 + 6/25 =13.24
A random number generator is used to select an integer from 1 to 100 (inclusively). What is the probability of selecting the integer 730?
If a random number generator is used to select an integer from 1 to 100, then the probability of selecting the integer 730 is zero.
Here a random number generator is used to select an integer from 1 to 100.
Therefore the range of the outcome = 1 to 100
Here we have to find the probability of selecting the integer 730
The probability = Number of favorable outcomes / Total number of outcomes.
Here a random number generator is used to select an integer from 1 to 100, but the given number is 730 which is out of range. Therefore the probability is zero
Hence, if a random number generator is used to select an integer from 1 to 100, then the probability of selecting the integer 730 is zero.
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If the coordinates of a are (3,4) and the coordinates of b are (-3,3) then the length of an is
The length of the line segment from a to b is 6.08 units or [tex]\sqrt{37}[/tex] units.
What is the length of a line segment and what is the role of coordinates?The length is described as the distance between the two points in a line. The coordinate usually refers to the dimensions of the point with respect to the two dimension graph.
Relation between the coordinates and length: [tex]\sqrt{(x_{1} -x_{2}) ^{2} +(y_{1} -y_{2} )^{2} }[/tex]
Now let point a be ([tex]x_{1},y_{1}[/tex]) and point b be ([tex]x_{2},y_{2}[/tex])
Thus putting values,
length = [tex]\sqrt{(3-(-3))^{2}+(4-3)^{2} }[/tex]
length = [tex]\sqrt{36+1}[/tex]
length = [tex]\sqrt{37}[/tex]
Hence the length of ab is [tex]\sqrt{37}[/tex] or 6.08 units.
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Is the graph of the distance a person has driven over time an example of a continuous or discrete graph?
Let us first understand what are discrete and continuous variables.
Discrete variable:
A discrete variable is countable in a finite amount of time.
For example:
The number of coins in your pocket
The number of trees in the garden
It is not possible to have 2.5 coins or 7.3 trees
Continuous variable:
A continuous variable can take any numeric value.
For example:
The height of the tree
The room temperature
These values can be in decimal like 7.3, 0.23 etc
Now let us come to the question, the distance a person has driven can take any value
for example, it can be 50 miles or 23.4 miles or 120.5 miles
So, decimal values are possible
This means that it must be a continuous graph
The distance a person has driven over time an example of a continuous graph.
A box has 14 candies in it: 3 are taffy, 7 are butterscotch, and 4 are caramel. Juan wants to select two candies to eat for dessert. The first candy will be selectedat random, and then the second candy will be selected at random from the remaining candies. What is the probability that the two candies selected are taffy?Do not round your intermediate computations. Round your final answer to three decimal places.
Okay, here we have this:
Considering the provided information we are going to calculate what is the probability that the two candies selected are taffy. So, for this, first we are going to calculate the probability that the first is taffy, and then the probability that the second is taffy. Finally we will multiply these two probabilities to find the total probability.
Remember that the simple probability of an event is equal to favorable events, over possible events.
First is taffy:
At the beginning there are 14 sweets, and 3 are taffy, so there are 3 favorable events and 14 possible, then:
First is taffy=3/14
Second is taffy:
Now, in the bag there are 13 sweets left, and of those 2 are taffy, so now there are 2 favorable events out of 13 possible:
Second is taffy=2/13
The first and second are taffy:
First is taffy*Second is taffy=3/14*2/13
First is taffy*Second is taffy=3/91
First is taffy*Second is taffy=0.033
First is taffy*Second is taffy=3.3%
Finally we obtain that the probability that the two candies selected are taffy is aproximately 0.033 or 3.3%.
2. In the xy-plane above, ABCD is a square and point E is the center of the square. The coordinates of points C and E are (7,2) and (1,0), respectively. Write an equation of the line that passes through points A, E, and C. B 1 2 -С E X -6 2 4. 16 A -2
Ready
Points A = (-5, -2) C = (7, 2) E = (1, 0)
1.- Find the slope
m = (y2 - y1) / (x2 - x1)
m = (2 + 2) / (7 + 5)
m = 4/ 12
m = 1/3
2.- Find the equation of the line
y - y1 = m(x - x1)
y + 2 = 1/3(x + 5)
y + 2 = 1/3x + 5/3
y = 1/3x + 5/3 - 2
y = 1/3 x + 5/3 - 6/3
This is the equation:
y = 1/3 x - 1/3
my pleausre
You have the option of loaning money to one friend who promises to pay simple interest or to another friend who promises to pay the same APR but compound the interest. Which would you choose, and why?
I would loan my money to the one who pays the compound interest.
This is because more money would be generated from the compound interest as it is based on the principal (Amount loaned) and also the interest generated from the loan. Unlike simple interest that is only based on the principal.
The days high temperature in Detroit , Michigan was recorded as 41 degrees F . Use the formula C = 5/9 ( F- 32) to write 41 degrees F as degrees celsius
Step 1
Given;
Step 2
[tex]\begin{gathered} C=\frac{5}{9}(F-32) \\ F=41 \\ C=\frac{5}{9}(41-32) \\ C=\frac{5}{9}(9) \\ C=5^{\circ}C \end{gathered}[/tex]Answer;
[tex]5^{\circ}C[/tex]Solve this system of linear equations. Separatethe x- and y-values with a comma.7x - by = -414x + 5y = 43
Answer
x = 2, and y = 3
Explanation:
given the following linear equation
7x - 6y = -4------------- equation 1
14x + 5y = 43 ---------- equation 2
This equation can be solve simultaneously by using elimination method
Step 1 : eliminate x
To eliminate x, multiply equation 1 by 2 qnd equation 2 by 1
7x * 2 - 6y * 2 = -4 * 2
14x * 1 + 5y * 1 = 43 * 1
14x - 12y = -8 ----------------- equation 3
14x + 5y = 43------------------ equation 4
Substract equation 4 from3
(14x - 14x) - 12 - 5y = -8 - 43
0 - 17y = -51
-17y = -51
Divide both sides by -17
-17y/-17 = -51/-17
y = 51/17
y = 3
To find x, put the value of y into equation 1
7x - 6y = -4
7x - 6(3) = -4
7x - 18 = -4
Collect the like terms
7x = -4 + 18
7x = 14
Divide both sides by 7
7x/7 = 14/7
x = 2
Therefore, x = 2 and y = 3
How do you solve the y-intercept of y = 9x + 9 and what is it simplified?
to know y -intercept we only need to replace x by 0. And we get
[tex]y=9\cdot0+9=9[/tex]so the y-intercept is 9
Given the function f(x)={4x+7 if x<0 6x+4 if x>0 _
Given:
[tex]f(x)=\begin{cases}4x+7ifx<0{} \\ 6x+4ifx\ge0{}\end{cases}[/tex]Required:
To find the value of f(-8), f(0), f(4), and f(-100)+f(100).
Explanation:
f(-8) :
Clearly -8<0,
So
[tex]\begin{gathered} f(x)=4x+7 \\ f(-8)=4(-8)+7 \\ =-32+7 \\ =-25 \end{gathered}[/tex]f(0) :
Clearly 0=0,
[tex]\begin{gathered} f(x)=6x+4 \\ =6(0)+4 \\ =4 \end{gathered}[/tex]f(4) :
Clearly 4>0,
[tex]\begin{gathered} f(x)=6x+4 \\ f(4)=6(4)+4 \\ =24+4 \\ =28 \end{gathered}[/tex]f(-100)+f(100) :
-100<0
[tex]\begin{gathered} f(x)=4x+7 \\ f(-100)=4(-100)+7 \\ =-400+7 \\ =-393 \end{gathered}[/tex]100>0
[tex]\begin{gathered} f(x)=6x+4 \\ f(100)=6(100)+4 \\ =600+4 \\ =604 \end{gathered}[/tex][tex]\begin{gathered} f(-100)+f(100)=-393+604 \\ \\ =211 \end{gathered}[/tex]Final Answer:
[tex]\begin{gathered} f(-8)=-25 \\ \\ f(0)=4 \\ \\ f(4)=28 \\ \\ f(-100)+f(100)=211 \end{gathered}[/tex]Help please and thank you
If f(x) is a linear function and gives f(3) = 3 and f(9) = -2
Part a
The slope of the line = -5/6
Part b
The y-intercept = 11/2
Part c
f(x) = (-5/6)x + 11/2
The values of
f(3) = 3
f(9) = -2
The points are (3,3) and (9,-2)
Part a
The slope of the line is the change in y coordinate with respect to the change in x coordinate.
Slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
= [tex]\frac{-2-3}{9-3}[/tex]
=-5/6
Part b
The slope intercept form of the line
y = mx+b
b is the y intercept
Substitute the values in the equation
3 = (-5/6)×3 + b
3= -5/2 + b
b = 11/2
Part c
Then the linear function f(x) = (-5/6)x + 11/2
Hence, if f(x) is a linear function and gives f(3) = 3 and f(9) = -2
Part a
The slope of the line = -5/6
Part b
The y-intercept = 11/2
Part c
f(x) = (-5/6)x + 11/2
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Which of the following tools did the Greeks limit themselves to in their
The Greeks limited themselves to using only compass and ruler in their formal geometric constructions.
Answer: Options B and D.
y = (x+3)^3 find the zeros of each function
Given,
[tex]y=(x+3)^3[/tex]We have,
[tex]y=0[/tex]when,
[tex]\begin{gathered} x+3=0 \\ \Rightarrow x=-3 \end{gathered}[/tex]The zeros of the function are x=-3,-3,-3
Write the slope intercept equation through the point (1,2) and it’s parallel to the line y=1+4x
Given:
Line equation, y=1+4x
The point, (1,2)
To find the slope intercept form:
The general slope intercept form is, y=mx+b.
First to find m:
From the line equation,
y=4x+1
We have, m=4
Next to find b:
Substitute m=4, and (1,2) in the general intercept form is,
[tex]\begin{gathered} (2)=4(1)+b \\ 2=4+b \\ b=-2 \end{gathered}[/tex]Now, substitute m=4 and b=-2 in the slope intercept form
Thus, the slope intercept form is,
[tex]y=4x-2[/tex]4. The relationship between temperature expressed in degrees Fahrenheit(F) and degrees Celsius (C) is given by the formula F= (9/5)C + 32. If the temperature is 5 degrees Fahrenheit, what is it in degrees Celsius ?
To calculate which value in Celsius the temperature of 5 Fº equates to, we first need to rewrite the expression isolating the "C" variable on the left side.
[tex]\begin{gathered} F=\frac{9}{5}\cdot C+32 \\ \frac{9}{5}\cdot C=F-32 \\ 9\cdot C=5\cdot F-160 \\ C=\frac{5}{9}\cdot F-\frac{160}{9} \\ \end{gathered}[/tex]We now need to replace F by 5.
[tex]\begin{gathered} C=\frac{5}{9}\cdot5-\frac{160}{9} \\ C=\frac{25}{9}-\frac{160}{9} \\ C=\frac{-135}{9} \\ C=-15 \end{gathered}[/tex]The temperature is -15 degrees in Celsius.
Hi. I can send a picture. can you help? thank u
we have the equation
y=x^2-6x+2
this equation represents a vertical parabola open upward (because the leading coefficient is positive)
that means
the vertex is a minimum
Convert to vertex form
y=a(x-h)^2+k
where
(h,k) is the vertex
Complete the square
y=(x^2-6x+9)+2-9
y=(x-3)^2-7
therefore
the vertex is (3,-7)
the answer is the option AFind the value of b if it is known that the graph of y=-3x+b goes through the point_
M(-2, 4)
Answer:
b = -2
Step-by-step explanation:
y = mx + b; (-2, 4)
y = -3x + b (x₁, y₁)
m = -3
y - y₁ = m(x - x₁)
y - 4 = -3(x -( -2))
y - 4 = -3(x + 2)
y - 4 = -3x - 6
+4 +4
------------------------
y = -3x - 2
I hope this helps!
Forproblems 5-10, determine what type of symmetry each figure has. If the figure has line symmetry, determine how many lines of symmetry the figure has. If the figure has rotational symmetry, determine the angle of rotational symmetry and if the figure also has point symmetry. (A figure can have both line and rotational symmetries or neither of these symmetries)
7. The figure has line and rotational symmetries. There are 2 lines of symmetry. The angle of symmetry is 180°
8. The figure has no symmetry
The figure is not drawn to scale. Find the unknown angle.
ThereforeGiven the image, we can find the missing angle using the sum of angles at a point rule.
The sum of angles at a point is known to be 360 degrees.
Therfore,
[tex]\begin{gathered} a^0+315^0=360^0 \\ a^0=360^0-315^0 \\ a^0=45 \end{gathered}[/tex]Therefore, the measure of "a" is
Answer:
[tex]45^0^{}[/tex]To produce g, function f was reflected over the x-axis andFunction g can be defined as
The graph of the functions f and g are given.
It is required to complete the statement concerning how to produce g.
The graph of the parent function f is shown:
Reflect the graph of f across the x-axis:
Translate the function 5 units vertically upwards:
The given parent function is y=f(x).
Reflect the graph across in the x-axis to get the equation y=-f(x).
Translate the graph 5 units up to get y=-f(x)+5
Answers:
To produce g, the function f was reflected over the x-axis and shifted up 5 units.
Function g is defined as g(x)=-f(x)+5.
Is the number -3.7 a natural number, a whole number, an integer, a rational number, an irrational number or a real number?
ANSWER
Rational number and Real number
EXPLANATION
We want to identify what type of number -3.7 is.
A natural number is a number that is a positive integer, used in counting things. Examples are 4, 7 and 55.
A whole number is a number that is used in counting, including 0 i.e. natural numbers including 0.
An integer is a whole number but the difference is that an integer can be positive, negative or zero.
A rational number is a number that can be expressed as a fraction of two integers i.e. a/b while an irrational number is one that cannot be expressed as a fraction of two integers.
A real number is any number that can be found as a distance between two points on the number line.
From the definitions above, we see that we can classify -3.7 as a rational number and a real number.
It is not a natural number, whole number, irrational number or an integer.
Refer to your equation for the line that models the association between latitude and temperature of the cities: Yours y = -12 + 120 Computer calculated y = -1.07 + 119 What does the slope mean in the context of this situation?
The slope in the equations represent the change in temperature by the change in lattitude. This means that for each unit change in the latitude the temperature will decrease by an amount given by the slope.
help meeeee pleaseeeee!!!
thank you
The values of f(0), f(2) and f(-2) for the polynomial f(x) = [tex]-x^{3} +7x^{2} -2x+12[/tex] are 12, 28 and 52 respectively.
According to the question,
We have the following information:
f(x) = [tex]-x^{3} +7x^{2} -2x+12[/tex]
Now, to find the value of f(0), we will put 0 in place of x.
f(0) = [tex]-0^{3} +7(0)^{2} -2(0)+12[/tex]
f(0) = 0+7*0-0+12
(When a number has some power then it means that in order to solve this we have expand the expression and multiply the number as many times as the power is given. For example, in the case of 3 as power, we will multiply any number 3 times and in case of 2 as power, we will multiply the given number 2 times.)
f(0) = 0+0-0+12
f(0) = 12
Now, to find the value of f(2), we will put 1 in place of x:
f(2) = [tex]-2^{3} +7(2)^{2} -2(2)+12[/tex]
f(2) = -8+7*4-4+12
f(2) = -8+28-4+12
f(2) = 40 -12
f(2) = 28
Now, to find the value of f(2), we will put -2 in place of x:
f(-2) = [tex]-(-2)^{3} +7(-2)^{2} -2(-2)+12[/tex]
f(-2) = -(-8) + 7*4+4+12
f(-2) = 8+28+4+12
f(-2) = 52
Hence, the value of f(0) is 12, f(2) is 28 and f(-2) is 52.
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4. Adam had $200. He spent $75 on clothes and $55 on a video game. Then his Momgave him $20 more dollars. How much money does Adam have now?
Adam had $200
He spent $75 on clothes and $55 on video game
The total money spent by Adam is
[tex]=75+55=\text{ \$130}[/tex]The amount left with Adam is
[tex]=200-130=\text{ \$70}[/tex]Then his mom gave him $20
The total amount of money Adam have now is
[tex]=70+20=\text{ \$90}[/tex]Hence, the answer is $90
Кр2.345 67 8Identify each angle as acute, obtuse, or right123345678.
we have the following:
Therefore:
Please get help with us for I am confused as to have should draw the rotation after a 90° clockwise rotation
In the given figure we can observe a triangle with vertices located at:
(-3,-2)
(-5,-4)
(1,-5).
We need to draw it after a 90° clockwise rotation.
We can apply the rule for 90° clockwise rotation, which is:
Each point of the given figure has to be changed from (x, y) to (y, -x) and then we need to graph the new coordinates.
By applying the rule to the given coordinates we obtain:
[tex]\begin{gathered} (x,y)\to(y,-x) \\ (-3,-2)\to(-2,3) \\ (-5,-4)\to(-4,5) \\ (1,-5)\to(-5,-1) \end{gathered}[/tex]Now we have to draw the new coordinates:
please determine 8/12 - 3/8 =
8/12 -3/8=16/24-9/24=7/24
You should make like numbers then subtract
If you need to simplify at the end
What is the slope and y-intercept?
y=7x+2
Options:
Blank # 1
Blank # 2
Answer:
Step-by-step explanation:
18098
Macky Pangan invested ₱2,500 at the end of every 3-month period for 5 years, at 8% interest compounded quarterly. How much is Macky’s investment worth after 5 years?
Compound interest with addition formula:
[tex]A=P(1+\frac{r}{n})^{nt}+\frac{PMT(1+\frac{r}{n})^{nt}-1}{\frac{r}{n}}[/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
PMT = Regular contributions (additional money added to investment)
in this example
P = 2500
r = 8% = 0.08
n = 4
t = 5 years
PMT = 2500
[tex]A=2500(1+\frac{0.08}{4})^{4\cdot5}+\frac{2500\cdot(1+\frac{0.08}{4})^{4\cdot5}-1}{\frac{0.08}{4}}[/tex]solving for A:
[tex]A=189408.29[/tex]Therefore, his investment after 5 years will be
$189,408.29