[tex]\dfrac{15 + 10i}{1 + 2i}=\\\\\dfrac{(15 + 10i)(1-2i)}{(1 + 2i)(1-2i)}=\\\\\dfrac{15-30i+10i+20}{1+4}=\\\\\dfrac{35-20i}{5}=\\\\7-4i[/tex]
Answer:
7-4i
Step-by-step explanation:
Multiplying the numerator and denominator by $1-2i$ gives
\begin{align*}
\frac{15+10i}{1+2i} &= \frac{15+10i}{1+2i}\cdot\frac{1-2i}{1-2i}\\
&= \frac{(15+10i)(1-2i)}{1^2 + 2^2} \\
&= \frac{5(3 + 2i)(1 - 2i)}{5} \\
&= (3 + 2i)(1 - 2i) \\
&= 3 + 2i - 6i - 4i^2 \\
&= 3 + 2i - 6i + 4 \\
&= \boxed{7 - 4i}.
Which describes how to graph g (x) = RootIndex 3 StartRoot x minus 5 EndRoot + 7 by transforming the parent function?
Answer:
[tex]f(x) =\sqrt[3]{x}[/tex]
Step-by-step explanation:
Hello!
Considering the parent function, as the most simple function that preserves the definition. Let's take the function given:
[tex]g(x) = \sqrt[3]{x-5}+7[/tex]
To have the the parent function, we must find the parent one, let's call it by f(x).
[tex]f(x) =\sqrt[3]{x}[/tex]
This function satisfies the Domain of the given one, because the Domain is still [tex](-\infty, \infty)[/tex] and the range as well.
Check below a graphical approach of those. The upper one is g(x) and the lower f(x), its parent one.
Answer:
5 units to the right and 7 units up (B on edge)
Step-by-step explanation:
Use the quadratic formula to find the exact solutions of x2 − 5x − 2 = 0. x equals negative b plus or minus the square root of b squared minus 4 times a times c, all over 2 times a x equals 5 plus or minus the square root of 33, all over 2 x equals negative 5 plus or minus the square root of 33, all over 2 x equals 5 plus or minus the square root of 17, all over 2 x equals negative 5 plus or minus the square root of 17, all over 2
Answer:
x = [ -b +- sqr root (b^2 - 4ac)] / 2a
a = 1
b = -5
c = -2
x = [- - 5 +- sqr root (-5^2 -4 * 1 * -2)] / 2 * 1
x = [5 +- sqr root (25 + 8)] / 2
x1 = 5.3723
x2 =-0.37228
Step-by-step explanation:
Exact solution for the give quadratic equation are
[tex]x=\frac{5+\sqrt{33}}{2},\:x=\frac{5-\sqrt{33}}{2}[/tex]
Quadratic EquationQuadratic equation of the form [tex]ax^2+bx+c=0[/tex]
For any quadratic equation we get two values for x. we can find the values for x by applying quadratic formula .
Quadratic formula
[tex]x=\frac{-b+-\sqrt{b^2-4ac} }{2a}[/tex]
Given equation is [tex]x^2-5x-2=0[/tex]
The value of a=1, b= -5 and c=-2
Substitute all the values in the formula.
To find out exact solutions , we need to simplify the final answer.
Exact solutions are without any decimals.
[tex]x=\frac{-\left(-5\right)\pm \sqrt{\left(-5\right)^2-4\cdot \:1\cdot \left(-2\right)}}{2\cdot \:1}\\x=\frac{-\left(-5\right)\pm \sqrt{33}}{2\cdot \:1}\\x=\frac{-\left(-5\right)\p+ \sqrt{33}}{2\cdot \:1}\\\\x=\frac{5+\sqrt{33}}{2}\\\\x=\frac{-\left(-5\right)- \sqrt{33}}{2\cdot \:1}\\\\x=\frac{5-\sqrt{33}}{2}\\[/tex]
Exact solutions are
[tex]x=\frac{5+\sqrt{33}}{2},\:x=\frac{5-\sqrt{33}}{2}[/tex]
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can someone please help me
Answer:
B
Step-by-step explanation:
Because this equation is just a normal greater than symbol, it has to be a dotted line.
This graph starts at -2 and goes up 1 and right 3(this cancels out C as an option)
Than you shade the region with the larger number vaules, since it is greater than.
2) The senior classes at High School A and High School B planned separate trips to the local
amusement park. The senior class at High School A rented and filled 2 vans and 14 buses with
294 students. High School B rented and filled 3 vans and 7 buses with 161 students. Each van
and each bus carried the same number of students. Find the number of students in each van and
in each bus.
A) Van: 9, Bus: 28 B) Van: 11, Bus: 27
C) Van: 20, Bus: 7 D) Van: 7, Bus: 20
Answer:
D) Van: 7, Bus: 20
Step-by-step explanation:
Add the amount of students together (455 students in total)
Then I added the amount of buses and vans together (5 Vans and 21 Buses)
Then I plugged in each answer
5 x 7 = 35
455 - 35 = 420
420 / 21 = 20
the question is in the attachment...
Answer:
11 minutes. 1/4 of 44 is 11
I need help ASAP THANK YOU!!
Answer:
A. Volume: 819, Surface Area: 598
B. Surface area
C. Volume
Step-by-step explanation:
Sorry I'm late, but here I go.
The volume of a rectangular prism is [tex]lwh[/tex] or [tex]bh[/tex]. (l being length, w being width, and h being height.)
So if we multiply the 3 values of 13, 9, and 7, we get 819. This is the volume.
To find the surface area, we can take note that 4 sides are the exact same, and the remaining two are the same. Let's find the area of the top/bottom of the prism.
[tex]13\cdot9=117[/tex]
Since there are two, bottom and top:
[tex]117\cdot2 = 234[/tex].
Now, there are the remaining 4 sides. Let's find the area of one then multiply it by 4.
[tex]13\cdot7=91\\91\cdot4=364[/tex]
Adding 364 and 234 gets up 598, so this is the surface area.
If we are painting something, the surface area is being painted, as we can't paint inside the box. However if we fill up the box with something (concrete in this case), it will be the volume.
Hope this helped!
Answer:
a.
v= 819 cm3
sa= 542 cm2
b. surface area
c. volume
Step-by-step explanation:
Volume of a rectangular prism: Length x width x height
Replacing with the values given:
V = 13 x 9 x 7 = 819 cm3
Surface area = S = 2 × (W × L + L × H + H × W)
S = 2 ( [9x13]+ [13 x7] +[7x9]) = 2 ( 117+91+63)= 542 cm2
b . Surface area, because we only have to paint the exterior of the brick.
c. Volume, because is the amount of concrete that the brick has.
These tables of values represent continuous functions. For which function will the y-values be the greatest for very large values of x?
Answer:
The table D represents the function that will have the greatest y-values for very large values of x.
Step-by-step explanation:
The table A represents a linear function, for which each one unit increment in the "x" variable produces a three unit increment in the "y" variable. This means that the growth rate of this function is 3.
The table B also represents a linear function, for which each one unit increment in the x variable produces a 100 unit increment in the y variable. This means that the growth rate of this function is 100.
The table C also represents a linear function, for which each one unit increment in the x variable produces a 10 unit increment in the y variable. This means that the growth rate of this function is 10.
The table D on the other hand does not represent a linear function, since the growth rate is variable and increases for greater values of x. This means that as x grows larger, the growth rate of the function also grows larger, resulting in a much greater y value for very large x values if we compare it to a linear function, like the other options.
Answer:
D
Step-by-step explanation:
BIGBRAIN
HELLLLLLPPPPPP MEEEE PLEASEEEEE!!!!!! Find the times (to the nearest hundredth of a second) that the weight is halfway to its maximum negative position over the interval . Solve algebraically, and show your work and final answer in the response box. Hint: Use the amplitude to determine what y(t) must be when the weight is halfway to its maximum negative position. Graph the equation and explain how it confirms your solution(s).
Answer:
0.20, 0.36 seconds
Step-by-step explanation:
We have already seen that the equation for y(t) can be written as ...
y(t) = √29·sin(4πt +arctan(5/2))
The sine function will have a value of -1/2 for the angles 7π/6 and 11π/6. Then the weight will be halfway from its equilibrium position to the maximum negative position when ...
4πt +arctan(5/2) = 7π/6 or 11π/6
t = (7π/6 -arctan(5/2))/(4π) ≈ 0.196946 . . . seconds
and
t = (11π/6 -arctan(5/2))/(4π) ≈ 0.363613 . . . seconds
The weight will be halfway from equilibrium to the maximum negative position at approximately 0.20 seconds and 0.36 seconds and every half-second thereafter.
Find m∠ABC__________
Answer:
ill help!
Step-by-step explanation:
find angle CBD
once you find that angle subtract it from 90 because that is the measure of ABC which is a right angle. Because all right angles are 90 degrees you can prove that it is the difference from angle CBD and 90.
hope it helped have good one!
5x+4y=25 - (5x+2y=3)
Answer:
T1he values for x and y of the equations is y = 11, and x = -19/5.
Step-by-step explanation:
To solve this question, we need to rearrange the expression:
5x+4y=25 - (5x+2y=3)
Look, if we subtract one equation to the other, then:
5x+4y=25 [1]
-(5x+2y=3) [2]
Which is the same as:
5x+4y=25
-5x-2y=-3
Subtract them:
5x+4y=25
-5x-2y=-3
---------------
2y =22
y = 22/2 = 11
Then, y = 11.
To find x, we can substitute y in either equation [1] or [2].
Let us use [1]
5x+4y=25
5x+4(11)=25
5x+44=25
5x=25-44
5x=-19
x = -19/5
Then, the values for x and y of the equations is y = 11, and x = -19/5.
Is 3/4 = 9/12 greater or less than 1/2
Answer:
greater than
Step-by-step explanation:
To compare 3/4 to 1/2, let's convert 1/2 so that it has a denominator of 4. This would then be 2/4. Because 3 > 2, 3/4 > 2/4 which means 3/4 > 1/2.
Answer:
Greater
Step-by-step explanation:
It is greater than 1/2 because when you divide the fractions you get- 1/2 = 0.5, 3/4 = 0.75 And this makes it greater.
What is the area of this polygon?
Enter your answer in the box.
units2
Answer:
39 units²
Step-by-step explanation:
The figure is composed of a rectangle VEDR and Δ RMV
Area of rectangle = VE × ED = 5 × 6 = 30 units²
Area of Δ = 0.5 × RV × perpendicular from M to RV
= 0.5 × 6 × 3 = 9 units²
Thus
Area of polygon = 30 + 9 = 39 units²
Exercise topic: Permutations and Combinations. A company wants to hire 3 new employees, but there are 8 candidates, 6 of them which are men and 2 are women. If the selection is random: a) In how many different ways can choose new employees? b) In how many different ways can choose a single male candidate? c) In how many different ways can choose at least one male candidate? with procedures. Help me please..
Answer:
(a) 56 ways
(b) 6 ways
(c) 56 ways
Step-by-step explanation:
Given:
candidates: 6 mail, 1 female
number to hire : 3
a) In how many different ways can choose new employees?
use the combination formula to choose r to hire out of n candidates
C(n,r) = C(8,3) = 8! / (3! (8-3)! ) = 40320 / (120*6) = 56 ways
b) In how many different ways can choose a single male candidate?
6 ways to choose a male, one way to choose two female, so 6*1 = 6 ways
c) In how many different ways can choose at least one male candidate?
To choose at least 1 male candidate, we subtract the ways to choose no male candidates out of 56.
Since there are only two females, there is no way to choose 3 female candidates.
In other words, there are 56-0 = 56 ways (as in part (a) ) to hire 3 employees with at least one male candidate.
Zhi bought 18 tickets for games at a fair. Each game requires 3 tickets. Zhi wrote the expression 18 – 3g to find the number of tickets she has left after playing g games. Diego correctly wrote another expression, 3(6 – g), that will also find the number of tickets Zhi has left after playing g games. Use the drop-down menus to explain what each part of Zhi's and Diego's expressions mean.
Answer: In zhi's equation, the 18 is the initial amount of tickets, and the 3g means 3 times the amount of games.
Diegos equation is the same, but write in factorised form. The 3 multiplies with the 6 to create 18, and the 3 multiple with the g to create 3g
The table shows the height increases in inches, of some of the girls in Gina’s class from last month to this month. What girl had a height increase that was greater than 1/2 inch?
The correct answer is Maxine
Explanation:
One of the easiest ways for knowing if a fraction is greater than another is by converting fractions to decimal numbers. This implies dividing the numerator (top number) by the denominator (bottom number). In the case of fraction, [tex]\frac{1}{2}[/tex] the decimal number is 0.5 considering 1 divided into 2 is equal to 0.5. Now to know if other fractions are greater or smaller, this process needs to be repeated.
Gina: [tex]\frac{3}{8} = 0.375[/tex]
Maxine: [tex]\frac{2}{3} = 0.666[/tex]
Shari: [tex]\frac{2}{4} = 0.5[/tex]
Vanessa: [tex]\frac{3}{12} = 0.25[/tex]
According to this, the girl with a heigh increased greater than 1/2 inch is Maxine because 0.666 (Maxine heigh increase) is greater than 0.5 (1/2 inch).
Taylor had \$147$147dollar sign, 147. Then she spent \$42$42dollar sign, 42 on sneakers. Then, Taylor earned \$53$53dollar sign, 53 by winning a race in her new sneakers! Estimate how much money Taylor has left
Answer:
She has 158 dollars.
Step-by-step explanation:
This problem tells us that originally Taylor had 147 dollars, but she spent 42 dollars on sneakers, thus she now has [tex]147-42 = 105[/tex] dollars. However, she later won a race wearing those sneakers and earned 53 dollars, therefore she now has [tex]105 + 53 = 158[/tex] dollars.
Thus, Taylor has 158 dollars left now.
Help ASAP! Will award brianliest!
Answer:
1: yes AB2×4
2:not possible
3:(11,2)
(20,12)
Step-by-step explanation:
1:compare the orders given which is 2×3 and 3×4 so to get if it's possible to multiply you just cancel out the same numbers if present i.e 3
2:so I took the first column of m multiply the first row of n (add values you get i.e -2×1+1×-4+0×2=-6) but on the second value of the first row I got 8 not 3 so I said not possible
3 you multiply row by column
(1×1+0×7+2×5=11. 1×4+0×2+-2×1=2)
(3×1+1×7+2×5=20. 3×4+1×2+2×-1=12)
therefore
(11,2)
(20,12)
10500 people visited an art gallery in 2002.This was an increase of 25% on 2001.How many visitors were there in 2001?
Answer:
The amount in 2001 is 8400
Step-by-step explanation:
Let x be the amount in 2001
There is an increase of 25% to get to the amount in 2002
x+ .25x = 1.25 x
1.25x = 10500
Divide each side by 1.25
1.25x / 1.25 = 10500/1.25
x =8400
The amount in 2001 is 8400
The equation of line l is -3y+4x=9 Write the equation of a line that is parallel to line l and passes through the point (-12,6). a) -3y+4x-69=0 b)-3y+4x-69=0 c)-3y+4x-39=0 d) 3x-3y+66=0
Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
- 3y + 4x = 9
3y = 4x - 9
Divide both sides by 3
y = 4/3x - 3
Comparing with the above formula
Slope / m = 4/3
Since the lines are parallel their slope are also the same
So slope of the parallel line l is also 4/3
Equation of the line using point (-12 , 6) is
y - 6 = 4/3(x + 12)
Multiply through by 3
That's
3y - 18 = 4(x + 12)
3y - 18 = 4x + 48
We have the final answer as
4x - 3y + 66 = 0Hope this helps you
What is the vertex of the graph of the function f(x) = x2 + 3x - 2?
Answer:
see below
Step-by-step explanation:
We need to write it on vertex form (f(x) = a(x - c)² + d where (c, d) is the vertex) and to do that we will complete the square.
f(x) = x² + 3x - 2
= (x² + 3x + 9/4) - 9/4 - 2
= (x + 1.5)² - 4.25
The vertex is (-1.5, -4.25).
if a student is selected at random find the probability the student is a male given that it's a senior. Round to the nearest whole percent.
Answer: 40%.
Step-by-step explanation:
From the table : Total Seniors = 2+3= 5
Number of male seniors = 2
If a student is selected at random find the probability the student is a male given that it's a senior:
P(Male | senior)[tex]=\dfrac{\text{Number of male seniors}}{\text{Total seniors}}[/tex]
[tex]=\dfrac{2}{5}[/tex]
In percent, [tex]\dfrac{2}{5}\times100=40\%[/tex]
Hence, the probability the student is a male given that it's a senior. =40%.
The probability of the student is a male senior is 7%.
Given, here from the 2- way table the total no. students will be 30.
We have to find out the probability of the student select at random, student is a senior male .
We know that, the probability of an event E, will be
[tex]P(E)=\dfrac{No.\ of \ favaurable\ outcomes}{Total\ outcomes}[/tex]
Now,
[tex]P( Senior\ male)= \dfrac{2}{30} \\\\P( Senior\ male)=0.06\\[/tex]
Representing it in percentage as,
[tex]P( Senior\ male)=0.06666\times100\%\\P( Senior\ male=6.66\%[/tex]
Hence the nearest whole percent will be 7%.
Thus probability of the student is a male senior is 7%.
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Which is the best estimate for the percent equivalent of 7 Over 15
Approximate what the value of [tex]7/15[/tex] is by using calculator.
[tex]7/15\approx0.47[/tex].
And now just multiply by 100 to get percentage.
[tex]100\cdot0.47=\boxed{47\%}[/tex].
Hope this helps.
Answer:
24%
Step-by-step explanation:
7\15 x 100
simplify and get=140\3
dived140\3=48\2
simplify 48\2=24%
Jake is going to call one person from his contacts at random. He has 30 total contacts. 16 of those contacts are people he met at school.
What is P(Call a person from school)
Answer:16/30
Step-by-step explanation:
Question 30 The Royal Fruit Company produces two types of fruit drinks. The first type is pure fruit juice, and the second type is pure fruit juice. The company is attempting to produce a fruit drink that contains pure fruit juice. How many pints of each of the two existing types of drink must be used to make pints of a mixture that is pure fruit juice
Answer:
The answer is below
Step-by-step explanation:
The Royal Fruit Company produces two types of fruit drinks. The first type is 65% pure fruit juice, and the second type is 90% pure fruit juice. The company is attempting to produce a fruit drink that contains 85% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 80 pints of a mixture that is 85% pure fruit juice?
Answer: Let x be the number of pints of the first fruit juice (i.e 65%) and y be the number of pints of the second fruit juice (i.e 90%).
Since the total number of pints to make the 85% pure fruit juice is 80, it can be represented using the equation:
x + y = 80 . . . 1)
Also, x pints of the first juice = 0.65x, y pints of the second juice = 0.9y and 80 pints of the mixture to be produced = 80(0.85) = 68. Therefore:
0.65x + 0.9y = 68 . . . 2)
We have to solve equation 1 and 2 simultaneously, first multiply equation 1 by 0.65 to get equation 3:
0.65x + 0.65y = 52 . . . 3)
Subtract equation 3 from 2 and solve for y:
0.25y = 16
y = 16/0.25 = 64
y = 64 pints
Put y = 64 in equation 1:
x + 64 = 80
x = 80 - 64 = 16
x = 16 pints
Therefore 16 pints of the 65% pure fruit juice, and 64 pints of the 90% pure fruit juice is required to make 80 pints of 80% fruit juice.
△ABC and △JKL are two triangles such that ∠A≅∠J and ∠B≅∠K. Which of the following would be sufficient to prove that the triangles are congruent? A ACJL=BCKL B ∠C≅∠L C AB≅JK D BC≅Jk
We need to know the rules of congruence of triangles to solve the given problem. The required condition that is sufficient to prove that the triangles are congruent is option (C) AB≅JK.
There are three rules of congruence of triangles, if two triangles satisfy any one of these rules then we can say that the triangles are congruent. The three rules are, SSS which means three sides are equal, ASA which means two angles and their corresponding sides are equal and SAS which means that two sides and the angle between them is equal. When two angles are said to be congruent it means they have the same measure that is they are equal. In this question we know that ∠A≅∠J and ∠B≅∠K , we can see that two angles are equal, if we can have the corresponding side of these two angles to be equal then we can say that the two triangles are congruent. The corresponding side of these angles are AB and JK.
Therefore we can see that the required condition to prove that the triangles are congruent is option (C) AB≅JK.
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Which glide reflection describes the mapping ABC DEF. This is practice for me plz, give answer with explanation. Non-sense answer will get reported
Answer:
c. translation (x,y) -> (x-4, y-1) followed by reflection about y=0
Step-by-step explanation:
The strategy is to translate B to E then reflect about the x-axis (y=0)
From B to E, the process is
(x,y) -> (x-4, y-1)
Therefore it is a translation (x,y) -> (x-4, y-1) followed by reflection about y=0
Driving on the highway, you can safely drive 60 miles per hour. "How far can you drive in ‘h' hours?" What is the range of the function which defines this situation? A. 60 B.The number of hours you drive C.The amount of gas you use D.The distance you drive
Answer:
D.The distance you drive
Step-by-step explanation:
If you describe this situation as function, then it will look as:
f(h)= 60hFor h=1 you have f(1)= 60 milesFor h=2 you have f(2)= 120 miles etc.The range of the function is the set of output values
In this case the range is the distance you drive
Correct option is D.
Answer:
The distance you drive
Step-by-step explanation:
i just took the test
HELP ME PLEASSSSEE On a winter morning, the temperature before sunrise was -10℉. The temperature then rose by 1℉ each hour for 7 hours before dropping by 2℉ each hour for 3 hours. What was the temperature, in degrees Fahrenheit, after 10 hours?
Answer:
3 degrees F
Step-by-step explanation:
if the temperature rose 1* for 7 hours, times 1 by 7. which is 7 and add to -10. which is -3. then, since the temperature rose by 2* for 3 hours, times 2 by 3 which is 6 and add to -3, which is 3.
i hope this helped?
A carpenter makes wooden chairs. He has enough wood to make 30 chairs. He makes $60 profit on a dining chair and $90 profit on a rocking chair. It takes him 1 hour to make a dining chair and 2 hours to make a rocking chair. He only has 40 hours available to work on the chairs. The carpenter wants to maximize his profit given the constraints. He draws the graph below to represent this situation. Drag and drop the correct numbers to complete the statements below. Given the restraints, the carpenter can maximize profits by making Response area dining chairs and Response area rocking chairs. His total profit for all the chairs will be $Response area.
Answer:
The carpenter can maximize profits by making 20 dining chairs and 10 rocking chairs . His total profit for all the chairs will be $2100
Step-by-step explanation:
Let x be the no. of dining chairs and y be the no. of rocking chair
Time taken by carpenter to make 1 dining chair = 1 hour
Time taken by carpenter to make x dining chairs = x hours
Time taken by carpenter to make 1 rocking chair = 2 hour
Time taken by carpenter to make y rocking chairs = 2y hours
He only has 40 hours available to work on the chairs.
[tex]\Rightarrow x+2y \leq 40[/tex]
He has enough wood to make 30 chairs.
[tex]\Rightarrow x+y\leq30[/tex]
He makes $60 profit on a dining chair and $90 profit on a rocking chair.
So, profit =60x+90y
Plot the equations on graph
Refer the attached figure
Coordinates of feasible region
(0,20),(20,10) and (30,0)
Profit =60x+90y
At(0,20)
Profit = 1800
At(20,10)
Profit = 1200+900=2100
At(30,0)
Profit=900
So,the carpenter can maximize profits by making 20 dining chairs and 10 rocking chairs . His total profit for all the chairs will be $2100
What the answer now answer only if now answer corry
Answer:
Approximately 11.5 units.
Step-by-step explanation:
We need to find the side opposite to ∠W. We are given the two angles ∠W and ∠X. We are also given that Side X is equal to 7. Therefore, we can use the Law of Sines.
Now, like last time, use the Law of Sines:
[tex]\frac{\sin(V)}{v}=\frac{\sin(W)}{w}=\frac{\sin(X)}{x}[/tex]
We can ignore the first term. Plug in 144 for ∠W, 21 for ∠X, and 7 for x.
[tex]\frac{\sin(144)}{w}=\frac{\sin(21)}{7}[/tex]
Cross multiply:
[tex]7\sin(144)=w\sin(21)\\w=\frac{7\sin(144)}{\sin(21)} \\v\approx11.4812\approx11.5[/tex]