the fact that both functions are polynomial of degree 1 we get that the domain and range of both functions are the real numbers. In intervalo notation this is:
[tex]\begin{gathered} \text{domain:}(-\infty,\infty) \\ \text{range:}(-\infty,\infty) \end{gathered}[/tex]In the figure, m < 1= (x-6)º and m2 2= (5x).
We have the measure of angles 1 and angle 2, as we can see from the diagram in the image, angles 1 and 2 added form the right angle (90°) in the figure.
Thus, the sum of x-6 and 5x, must be equal to 90°.
(a) Write an equation:
[tex]x-6+5x=90[/tex](b) To find the degree measure of each angle, first we need to solve for the value of x in the equation.
Combining like terms:
[tex]6x-6=90[/tex]Adding 6 from both sides:
[tex]\begin{gathered} 6x-6+6=90+6 \\ 6x=96 \\ \end{gathered}[/tex]Divide both sides by 6:
[tex]\begin{gathered} \frac{6x}{6}=\frac{96}{6} \\ x=16 \end{gathered}[/tex]Now that we have x, we find angle 1:
[tex]m\angle1=x-6=16-6=10[/tex]And the measure of angle 2:
[tex]m\angle2=5x=5(16)=80[/tex]Determine the real number x and y if (x-yj)(3+5j) is the conjugate of -6-24j
The values of the variables x and y such that the conjugate of - 6 - j 24 is found are 3 and 3, respectively.
How to find the value of two variables associated with the conjugate of a complex number
Let α + i β be a complex number, whose conjugate is the complex number α - i β. In this problem we find the values of the variables x and y such that:
(x + i y) · (3 + i 5) = - 6 + i 24
3 · x + i 3 · y + i 5 · x + i² 5 · y = - 6 + i 24
(3 · x - 5 · y) + i (5 · x + 3 · y) = - 6 + i 24
Then, we need to solve the following system of linear equations:
3 · x - 5 · y = - 6
5 · x + 3 · y = 24
Now we proceed to solve the system algebraically. Clear x in the first equation:
x = (- 6 + 5 · y) / 3
x = - 2 + (5 / 3) · y
Substitute x on the second equation and clear y:
5 · [- 2 + (5 / 3) · y] + 3 · y = 24
- 10 + (25 / 3) · y + 3 · y = 24
34 / 3 · y = 34
(1 / 3) · y = 1
y = 3
Finally, we substitute on y in the first equation:
x = - 2 + (5 / 3) · 3
x = - 2 + 5
x = 3
The values of the variables x and y are 3 and 3, respectively.
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Score: U OQuestion Help3.3.29CeringritdA train travels 140 km in the same time that a plane covers 630 km. If the speed of the plane is 30 km per hr less than 5 times the speed ofTrain140the train, find both speeds.Planey 630The train's speed is km per hr
Notice that the time for both trips is the SAME but not known (let's use the letter T to address this unknown).
We also assign St to the speed of the train, and Sp to the speed of the plane.
Then, the relationship between the speeds according to the information they provide, is given by the equation:
Sp = 5 * St - 30
we also know that the train covers 140 km in the time T, Then according to the formula for speed (distance divided by time) we can say:
St = 140 km / T, therefore T = 140 km / St
We do something similar with the information on the distance covered by the plane:
Sp = 630 km / T which solving for T gives:
T = 630 km / Sp
Now we equal the expressions for T (since that time is the SAME as we noticed before, and get:
630 km / Sp = 140 / St
we corss-multiply to get the speeds in the numerator:
630 St = 140 Sp
ANd we use the very first equation we wrote (Sp = 5 * St - 30)
to replace Sp in terms of St:
630 St = 140 (5 St - 30)
Now use distributive property on the right to eliminate the parenthesis:
630 St = 700 St - 4200
add 4200 to both sides, and subtract 630 St from both sides :
4200 = 700 St - 630 St
4200 = 70 St
divide both sides by 70 to isolate St completely:
St = 4200 / 70
St = 60 km/h (this is the speed of the train)
Now we can find the value of the speed of the plane, using the first equation again:
Sp = 5 * St - 30 = 5 (60) - 30 = 300 - 30 = 270 km/h
Then the speed of the plane is: 270 km/h
Read the following scenario and develop a method for answering the question posed. Be sure to define all variables used, justify your thinking mathematically, and fully answer the questions posed in complete sentences. Orbital Toys sells two types of sets of magnetic spheres, silver, and brass. The store owner, Lucy Ball, pays $8 and $16 for each one set of silver magnetic spheres and brass magnetic spheres respectively. One set of silver magnetic spheres yields a profit of $5 while a set of brass magnetic spheres yields a profit of $7. Ms. Ball estimates that no more than 2000 sets of magnetic spheres will be sold every month and she does not plan to invest more than $20,000 in the inventory of these sets. How many sets of each type of magnetic spheres should be stocked in order to maximize her total monthly profit? What is her maximum monthly profit?
8 dlls for silver
16 dlls for brass
5 dlls profit silver
7 dlls profit spheres
Then the price is
8+5= 13 dlls for silver
16+7=23 dlls for brass
Let S and B be the amount of magnetic silver and brass sphers that are sold, respectively.
Then, Ms. Ball estimation is that
[tex]S+B\leq2000[/tex]Also, she doesn't want to invest more than 20000, so
[tex]\begin{gathered} 8S+16B\leq20000 \\ S+2B\leq2500 \end{gathered}[/tex]The objective function is
[tex]V=5S+7B[/tex]Subjected to:
[tex]\begin{gathered} S+B\leq2000 \\ S+2B\leq2500 \\ S\ge0,\text{ B}\ge0 \end{gathered}[/tex]GRAPH
The interection is at
[tex]\begin{gathered} S=2000-B \\ S=2500-2B \\ 2000-B=2500-2B \\ B=500 \\ S=2000-500 \\ S=1500 \end{gathered}[/tex]So, the extremes must be at (0,1250), (1500,500), (2000,0) , (0,0).
So, if we replace the points
[tex]\begin{gathered} V(0,1250)=5(0)+7(1250)=8750 \\ V(1500,500)\text{ = 5(1500)+7(500)=}11000 \\ V(2000,0)=5(2000)+7(0)=10000 \end{gathered}[/tex]So, the amount she will need to stock to maximize her profit is 1500 of silver and 500 of brass, and the maximum profit is going to be 11000 dlls.
Please help me, i struggle with these types of problems
Solution
[tex]\begin{gathered} 11x-3=9x+15 \\ \\ 2x=18 \\ \\ x=9 \end{gathered}[/tex]Therefore, we find m < 7
[tex]\begin{gathered} 11x-3 \\ \\ 11(9)-3 \\ \\ 99-3 \\ \\ 96\degree \end{gathered}[/tex]f(-9)=7x+6
what would the value of F(-9) be?
I need to know the initial size of the culture Find the doubling period Find the population after 65 min When will the population reach 10000
Given:
The population was 100 after 10 mins.
The population was 1500 after 30 mins.
To fill the blanks:
Explanation:
According to the problem, we write,
[tex]\begin{gathered} P=P_0e^{kt} \\ 100=P_0e^{10k}.........(1) \\ 1500=P_0e^{30k}............(2) \end{gathered}[/tex]Dividing equation (2) by equation (1), we get
[tex]\begin{gathered} \frac{1500}{100}=\frac{P_0e^{30k}}{P_0e^{10k}} \\ 15=e^{20k} \\ ln15=20k \\ 2.708=20k \\ k=\frac{2.708}{20} \\ k=0.1354 \end{gathered}[/tex]So, the equation becomes,
[tex]P=P_0e^{0.1354t}....................(3)[/tex]a) To find: The initial population
When P = 100 and t = 10, then the initial population would be,
[tex]\begin{gathered} 100=P_0e^{0.1354(10)} \\ 100=P_0e^{1.354} \\ 100=P_0(3.873) \\ P_0=\frac{100}{3.873} \\ P_0\approx25.82 \end{gathered}[/tex]Therefore, the initial population is 25.82.
b) To find: The doubling time
Using the formula,
[tex]\begin{gathered} t=\frac{\ln2}{k} \\ t=\frac{\ln2}{0.1354} \\ t=5.1192 \\ t\approx5.12mins \end{gathered}[/tex]The doubling time is 5.12 mins.
c) To find: The population after 65 mins
Substituting t = 65 and the initial population is 25.82 in equation (3) we get,
[tex]\begin{gathered} P=25.82e^{0.1354(65)} \\ P\approx171467.56 \end{gathered}[/tex]Therefore, the population after 65 mins is 171467.56.
d) To find: The time taken for the population to reach 10000
Substituting P = 10000 and the initial population is25.82 in equation (3) we get,
[tex]\begin{gathered} 10000=25.82e^{0.1354t} \\ e^{0.1354t}=\frac{10000}{25.82} \\ e^{0.1354t}=387.297 \\ 0.1354t=\ln(387.297) \\ 0.1354t=5.959 \\ t=\frac{5.959}{0.1354} \\ t\approx44.01 \end{gathered}[/tex]Therefore, the time taken for the population to reach 10000 is 44.01 mins.
Final answer:
• The initial population is 25.82.
,• The doubling time is 5.12 mins.
,• The population after 65 mins is 171467.56.
,• The time taken for the population to reach 10000 is 44.01 mins.
The first quartile of a data set is 32, and the third quartile is 52. Which of
these values in the data set is an outlier?
Answer: As we know that the formula of outlier is
IQR = Q3 - Q1
= 52 - 32
= 20
52 + 1.5(20) = 82...
so anything above 82 is an outlier
now
32 - 1.5(20) = 2.
..anything below 2 is an outlier
so...the 83 is outlier
so correct option is D
hope it helps
Step-by-step explanation:
he center of the circle below is at P. If arc AB measures 86 °, then what is the measure of the angle < APB ?
Answer:
D. 86°
Explanation:
Given:
• The center of the circle = P
,• The measure of arc AB = 86°
We want to find the measure of the angle APB.
By Circle's theorem: The measure of an arc is equal to the measure of the central angle subtended by the same arc.
Applying this theorem, we have that:
[tex]\begin{gathered} m\angle APB=m\widehat{AB} \\ \implies m\angle APB=86\degree \end{gathered}[/tex]The measure of the angle APB is 86 degrees.
Option D is correct.
how is the metric system important to a pharmacy Technician?
The metric system is a system of decimals in which all the measurements are taken as multiples or divisions based on a factor of 10. We have to convert between different units of measurements while working in a pharmacy. Metric system helps to make fast and easy conversions of units of measurements. Therefore, metric system is important to a pharmacy technician.
28 * 81.5 can you help me
so the answer is 2282
hi, i need help finding the mean and standard deviation. the reeses pieces are just a filler for the sample subject.
Solution
For this case we can calculate the mean in the following way:
[tex]E(X)=np=30\cdot0.52=15.6[/tex]And the standard deviation would be:
[tex]Sd(x)=\sqrt[=]{30\cdot0.52\cdot(1-0.52)}=2.736[/tex]Solve the following simultaneous equation with elimination or substitution method
So, to solve the system:
To solve it, we could substitute the first equation in the second one and then solve for x:
We could solve the previous quadratic by factoring:
To find the values of y, just replace each vaue of x:
Therefore, the solutions of the system are
(x,y) = (-3,-1)
(x,y)=(1,3)
Use dimensional analysis to determine which rate is greater. The pitcher for the Robins throws a baseball at 90.0 miles per hour. The pitcher on the Bluebirds throws a baseball 125.4 feet per second. Which pitcher throws a baseball faster? Complete the explanation:When I convert the Bluebirds pitcher's speed to the same units as the Robins pitcher's speed the speed is __ mi/h. Since the Bluebirds pitcher's speed is ____ the Robins pitcher's speed, the pitcher on the ____ throws a faster ball.
ANSWER and EXPLANATION
We want to solve the problem by using dimensional analysis.
To do this, let us convert the speed of the Bluebirds baseball to miles per hour.
We have that:
1 feet per second = 0.6818 miles per hour
125.4 feet per second = 85.50 miles per hour
As we can see the baseball of the Bluebirds is slower than the Robins (90 miles per hour)
Now, to complete the explanation:
When I convert the Bluebirds pitcher's speed to the same units as the Robins pitcher's speed, the speed is _85.50_ mi/h.
Since the Bluebirds pitcher's speed is _less than_ the Robins pitcher's speed, the pitcher on the __Robins_ throws a faster ball.
If possible, give the input and output variables of the equation f(r) = 兀r2.
The input variable of the function is r, while the output variable is f(r)
How to determine the variables?The definition of the function is given as
f(r) = πr²
In the above function definition, we have the function to be
f(r)
The definition f(r) implies that
r represents the input variablef(r) represents the output variableThe above is true because, the variable π has its constant value of 22/7
i.e. π= 22/7
While the variable r can change its value
Take for instance:
If r = 7, then we have
f(7) = π x 7²
Evaluate
f(7) = 154
If r = 14, then we have
f(14) = π x 14²
Evaluate
f(14) = 616
See that the value of f(r) changes as r changes
This means that, the stated parameters above are true i.e.
r represents the input variablef(r) represents the output variableRead more about functions at
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Pls help me!!!!!!!!!
2. 4+ (-10)
3. 3+(-15)
4.2+5
5. (-10)+(-5)
I need help what is the sum of five squared and five
You have the following expression:
"the sum of five squared and five"
the previous statement, in a mathematical form is:
5² + 5
It is important to point out that you have "the sum" of two numbers, which numbers? five squared and five.
The simplified form is:
5² + 5 = 25 + 5 = 30
The figure below shows a rectangular court. 74 ft (a) Use the calculator to find the area and perimeter of the court. Make sure to include the correct units. Area: 93 ft Perimeter: (b) The court will have a wood floor. Which measure would be used in finding the amount of wood needed? Perimeter O Area (c) A strip of tape will be placed around the court. Which measure would be used in finding the amount of tape needed? Perimeter O Area ft X ft² Ś ft³ ?
Given a rectangle with sides "a" and "b":
The area of the rectangle is:
[tex]A=ab[/tex]The perimeter of the rectangle is:
[tex]P=2a+2b[/tex]Given the sides of the rectangle:
a = 74 ft
b = 93 ft
(a)
The area of the rectangle is:
[tex]\begin{gathered} A=74ft*93ft \\ A=6882ft^2 \end{gathered}[/tex]The perimeter of the rectangle is:
[tex]\begin{gathered} P=2*74ft+2*93ft \\ P=148ft+186 \\ P=334ft \end{gathered}[/tex](b) The wood will cover all the area of the court, then the area must the used.
(c) The tape will be placed around the court, then the perimeter must be used.
Answer:
(a)
(b)
(c) Perimeter
Use the formula for the probability of the complement of an event.A single card is drawn from a deck. What is the probability of not drawing a 7?
occur
the answer is 12/13 or 0.932
Explanation
when you have an event A, the complement of A, denoted by.
[tex]A^{-1}[/tex]consists of all the outcomes in wich the event A does NOT ocurr
it is given by:
[tex]P(A^{-1})=1-P(A)[/tex]Step 1
find the probability of event A :(P(A)
The probability of an event is the number of favorable outcomes divided by the total number of outcomes possible
[tex]P=\frac{favorable\text{ outcomes}}{\text{total outcomes}}[/tex]so
let
favorable outcome = 4 (there are four 7 in the deck)
total outcomes=52
hence,replacing
[tex]\begin{gathered} P=\frac{4}{52}=\frac{1}{13} \\ P(A)=\frac{1}{13} \end{gathered}[/tex]Step 2
now, to find the probability that the event does NOT ocurrs ( not drawing a 7)
let's apply the formula
[tex]P(A^{-1})=1-P(A)[/tex]replace
[tex]\begin{gathered} P(A^{-1})=1-\frac{1}{13} \\ P(A^{-1})=\frac{13-1}{13}=\frac{12}{13} \\ P(A^{-1})=0.923 \end{gathered}[/tex]therefore, the answer is 12/13 or 0.932
I hope this helps you
Solve the following system of linear equations using elimination.
x – y - 3z = 4
2x + 3y – 3z = -2
x + 3y – 2z = -4
By applying the elimination method, the solutions to this system of three linear equations include the following:
x = 2.y = -2.z = 0.How to solve these system of linear equations?In order to determine the solutions to a system of three linear equations, we would have to evaluate and eliminate each of the variables one after the other, especially by selecting a pair of linear equations at each step and then applying the elimination method.
Given the following system of linear equations:
x – y - 3z = 4 .........equation 1.
2x + 3y – 3z = -2 .........equation 2.
x + 3y – 2z = -4 .........equation 3.
From equation 1 and equation 3, we would eliminate x as follows:
x – y - 3z = 4
x + 3y – 2z = -4
-4y - z = 8 .........equation 4.
Next, we would pick a different pair of linear equations to eliminate x:
(x – y - 3z = 4) × 2 ⇒ 2x - 2y - 6z = 8
2x - 2y - 6z = 8
2x + 3y - 3z = -2
-5y - 3z = 10 ........equation 5.
From equation 4 and equation 5, we would eliminate z to get the value of y:
(-4y - z = 8) × 3 ⇒ -12y - 3z = 24
-12y - 3z = 24
-5y - 3z = 10
-7y = 14
y = 14/7
y = -2.
For the value of z, we have:
-4y - z = 8
z = -4y - 8
z = -4(-2) - 8
z = 8 - 8
z = 0
For the value of x, we have:
x – y - 3z = 4
x = 4 + y + 3z
x = 4 - 2 + 3(0)
x = 2
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what operation helps calculate unit rates and unit prices
Division operation is operation helps calculate unit rates and unit prices.
Division operation -
A rate with 1 as the denominator is referred to as a unit rate. If you have a rate, such as a price per a certain number of items, and the quantity in the denominator is not 1, you can determine the unit rate or price per unit by performing the division operation: numerator divided by denominator.What method do you employ to determine the unit rate?
Simple division of the numerator and denominator yields the unit rate. The outcome tells us how many of the units in the numerator to anticipate for each unit in the denominator.
What in mathematics are rate and unit rate?
A ratio called a rate compares two amounts of DIFFERENT types of UNITS. When expressed as a fraction, a unit rate has a denominator of 1. Divide the rate's numerator and denominator by the denominator to represent the rate as a unit rate.Learn more about Division operation
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Graph the solution of the linear inequality and answer the questions on the bottom
The inequality is given
[tex]-2y\leq6x+18[/tex]To draw the graph of the inequality which is less than equal to
after a 30% discount, Kay's sneakers cost $36, if she would have waited another week to buy them, they would have been on sale for 40% off the original price, how much more money could she have saved
Let the original price of sneakers be x.
Determine the original price of the sneakers.
Write the following number in standard decimal form.five and seventy-nine hundredths
five and seventy-nine hundredths = 5.79
Which equation is true when the value of x is - 12 ?F: 1/2x+ 22 = 20G: 15 - 1/2x = 21H: 11 - 2x = 17 J: 3x - 19 = -17
Substitute x = - 12 in each of the given equation, if the equation satisfy then tha x = -1 2
F) 1/2x + 22 = 20
1/2 ( -12) + 22 = 20
(-6) + 22 = 20
16 is not equal to 22
G) 15 -1/2x = 21
Substitute x = -12 in the expression :
15 - 1/2( -12) = 21
15 + 1/2(12) =21
15 + ( 6) = 21
21 = 21
Thus, The equation 15 - 1/2x = 21 is true for x = -12
H) 11 - 2x = 17
Susbstitute x = ( -12) in the equation :
11 - 2x = 17
11 - 2( -12) = 17
11 + 24 = 17
35 = 17
Since, 35 is not equal to 17
D) 3x - 19 = -17
SUsbtitute x = ( -12)
3( -12) - 19 = -17
-36 - 19 = -17
-36 = -17 + 19
-36 = 2
Since - 36 is not equal 2
Answer : G) 15 - 1/2x = 21
There is a 50% chance of rain here and a 10% chance of rain on Mars. Therefore, there is a 45% chance that it will rain in neither place.
The statement that " There is a 45% chance that it will rain in neither place" is true.
In the question ;
it is given that
Probability of raining here = 50% = 0.5
Probability of raining on mars = 10% = 0.1
So, the probability of not raining here = 1-0.5 = 0.5
and probability of not raining on mars = 1-0.1 = 0.9
Hence the probability of rain in neither place = (probability of not raining here)×(probability of not raining on mars) .
Substituting the values , we get
probability of rain in neither place = 0.5×0.9
= 0.45
= 45%
Therefore , the statement " There is 45% chance that it will rain in neither place" is true.
The given question is incomplete , the complete question is
There is a 50% chance of rain here and a 10% chance of rain on Mars. Therefore, there is a 45% chance that it will rain in neither place.
Is the statement True or False ?
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rst builds ons 3 Veronda has a bag of mixed shapes. She chooses 3 shapes and fits them together to form a figure as shown. 17 cm What is the area of the figure Veronda creates? Use 1 = 3.14 5 Holly A 136 cm? B 107.14 cm C 96.56 cm D 76.57 cm?
We have three different figures
Semicircle
r = 4cm
[tex]\begin{gathered} A_r=\frac{\pi\cdot r^2}{4} \\ A_r=\frac{3.14\cdot4^2}{4} \\ A_r=\frac{3.14\cdot16}{4} \\ A_r=12.56 \end{gathered}[/tex]Square
l = 8cm+
Exercises Complete the following: 11. Find the intercepts and (a) 9x² - 164 = 144 (c) 25x - 4y = 100 (e) x² + y² = 1 29x² + 16y² = 144
The intercepts for a function can be on either of the two axis, y or x.
when finding the intercepts of x, means that y = 0
when finding the intercepts of y, means that x = 0
finding the x intercepts
[tex]\begin{gathered} -x^2+(0)^2=1 \\ -x^2=1 \\ x^2=-1 \\ x=\sqrt[]{-1} \end{gathered}[/tex]since the solution for the square root of -1 has not any solution on the real numbers, we can say that there is no intercept over the x axis.
finding the y intercepts
[tex]\begin{gathered} -(0)^2+y^2=1 \\ y^2=1 \\ y=\pm\sqrt[]{1} \\ y=1;y=-1 \end{gathered}[/tex]there are 2 intercepts on the y axis, these are at y=1 and y=-1
information can be proven by graphing the function
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
The probability distribution for arandom variable x is given in the table.-105101520Probability.2015051.25115Find the probability that -5 < x < 5
Answer:
P = 0.30
Explanation:
From the table, we see that:
When: x = -5, Probability = 0.15
When: x = 0, Probability = 0.05
When: x = 5, Probability = 0.1
Therefore, the probability of -5 ≤ x ≤ 5 is obtained by the sum of the probabilities from -5 to 5, we have:
[tex]\begin{gathered} P=0.15+0.05+0.10 \\ P=0.30 \end{gathered}[/tex]Therefore, the probability is 0.30