[tex]a(t+z)=45z+67\implies at+az=45z+67\implies az=45z+67-at \\\\\\ az-45z=67-at\implies \stackrel{common~factoring}{z(a-45)}=67-at\implies z=\cfrac{67-at}{a-45}[/tex]
What is the slope? (15,-4) & (-50,16)
If an arena charges $7. 50 to park in satellite parking and $12. 00 to park in an arena lot, how much will be made from parking 11,000 vehicles at the arena and 4,600 in satellites?.
Parking 11,000 automobiles at the venue and 4,600 in satellites will bring in total $166,500.
Define multiplication.One of the four fundamental mathematical operations, along with addition, subtraction, and division, is multiplication. Multiply in mathematics refers to the continual addition of sets of identical size. Let's use the ice creams as a multiplication example to help us comprehend. There are two such groupings, and each group has ice cream.
Given,
If an arena charges $7. 50 to park in satellite parking and $12. 00 to park in an arena lot,
Multiplying:
$7.5 x 4,600 = satellite parking
$34,500 = satellite parking
The next step is to determine how much it will cost to park in the arena lot.
$11,000 ×12 = arena lot
$32,000 = arena lot
Let's now calculate the entire revenue from parking.
Total earnings equal $132,000 + $34,500.
Amount made in total is $166,500.
In conclusion Parking 11,000 automobiles at the venue and 4,600 in total satellites will bring in $166,500.
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Write an algebraic expression for “Julie runs three miles less than twice the number of miles, n, that Hannah runs.”
A. 2n – 3
B. 3n – 2
C. 2n + 3
D. 3n + 2
The algebraic expression is 2n - 3 if Julie runs three miles less than twice the number n that Hannah runs. So option (a) is correct
An algebraic expression is a mathematical expression made up of variables, constants, and algebraic operations.
It is assumed:
"Julie runs three miles less than twice as far as Hannah runs," the expression goes.
It states three miles less than a number, so you get a -3 and twice the number n, which is the same as 2n, and then you rearrange it to get 2n-3
The expression is 2n - 3
Thus, the algebraic expression is 2n - 3, if Julie runs three miles less than twice the number n that Hannah runs.
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A polynomial function P(x) with rational coefficients has the given roots. Find two additional roots of P(x)=0. 17+7 and 2i
The two additional roots are:-0.17-7i and -2i
Given,
A polynomial function P(x) with rational coefficients has the given roots.
P(x) = 0.17+7i and 2i
we are asked to determine the two additional roots of the given P(x).
we know that a+bi is a root of P(x)=0, then a-bi is also a root of P(x)=0
we have:
0.17+7i and 2i are two roots pf P(x)
so, -0.17-7i and -2i are two additional roots of P(x).
Hence we get the required roots.
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a pollster wishes to estimate the proportion of united states voters who favor capital punishment. how large a sample is needed in order to be 95% confident that the sample proportion will not differ from the true proportion by more than 5%?
The sample size must be 543 so the sample proportion is will not differ by 5%
We are given the following in the question:
Margin of error = 5%
Confidence interval:
p ±z√(p'(1 - p')/n)
Margin of error =
p = ±z√(p'(1 - p')/n)
Since no particular proportion is given, we take
p' = 0.5
Z critical at α 0.02 is ± 2.33
Putting values, we get,
p = ±z√(p'(1 - p')/n)
2.33 x √(0.5(1 - 0.5)/n)
√n = 2.33x 0.5/0.05
n = 542.89 = 543
Thus, the sample size must be 543 so the sample proportion is will not differ by 5%
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rectangles beneath a semicircle a rectangle is constructed with its base on the diameter of a semicircle with radius 5 and its two other vertices on the semicircle. what are the dimensions of the rectangle with maximum area
Using the area of rectangle, the dimensions of the rectangle with maximum area are 5√2 and 5/√2.
In the given question we have to find the dimensions of the rectangle with maximum area.
Given Semicircle Radius is 5.
As we know that standard equation of circle is [tex]x^2+y^2=a^2[/tex]
a=5, so the equation is [tex]x^2+y^2=(5)^2[/tex]
[tex]x^2+y^2=25[/tex]
Therefore, Half circle y=[tex]\sqrt{25-x^2}[/tex]
Area of Rectangle(A) =xy
Because Half of the rectangle is lies in first quadrant and half lies in second quadrant
Therefore,
Area of Rectangle(A) = 2xy
Now putting the value of y
Area(A) = 2x[tex]\sqrt{25-x^2}[/tex]
Here we need to maximize the area of Rectangle, so find derivative and set equal to zero.
A'= [tex]\frac{d}{dx}(2x\sqrt{25-x^2})[/tex]
A'= 2[tex][x\frac{d}{dx}\sqrt{25-x^2}+\sqrt{25-x^2}\frac{d}{dx}x][/tex]
A'= 2[tex][x\cdot\frac{-x}{\sqrt{25-x^2}}+\sqrt{25-x^2}\cdot1][/tex]
A'= 2[tex][\frac{-x^2}{\sqrt{25-x^2}}+\sqrt{25-x^2}][/tex]
A'= 2[tex](\frac{-x^2+25-x^2}{\sqrt{25-x^2}})[/tex]
A'= 2[tex](\frac{25-2x^2}{\sqrt{25-x^2}})[/tex]
For critical Number A' = 0
2[tex](\frac{25-2x^2}{\sqrt{25-x^2}})[/tex] = 0
25-2x^2 = 0
2x^2=25
x^2=25/2
x=±√25/2
x=±5/√2
Therefore,
Base of the Rectangle = 2x
Base of the Rectangle = 2×5/√2
Base of the Rectangle = 5√2
and
height of rectangle = [tex]\sqrt{25-x^2}[/tex]
height of rectangle = [tex]\sqrt{25-(5/\sqrt{2})^2}[/tex]
height of rectangle = [tex]\sqrt{25-(25/2)}[/tex]
height of rectangle = √(50-25)/2
height of rectangle = √25/2
height of rectangle = 5/√2
Hence, the dimensions of the rectangle with maximum area are 5√2 and 5/√2.
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After one day, you read 40 pages of a book. On each
following day, you read 10 more pages.
Write an equation in point-slope form to model the number
of pages you have read, y, after a days.
Then use your equation to determine the number of pages
of the book will you have read after 9 days.
pages
The equation of the number of pages is y = 40 + 10x and for 9 days, you read 130 pages
How to determine the equation of the number of pages?From the question, we have
Initial number of pages = 40
Rate per day = 10 pages per day
The equation of the number of pages is then represented as
y = Initial number of pages + Rate per day x Number of days
Substitute the known values in the above equation, so, we have the following representation
y = 40 +10 * x
Evaluate
y = 40 + 10x
For 9 days, we have
x = 10
This gives
y = 40 +10 * 9
Evaluate
y = 130
Hence, the number of pages is 130
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can someone help me, please?
Answer:
I would say answer D is correct since it is closest to 1,760 yards.
Step-by-step explanation:
;)
Write an inequality that represents the graph below
please help!!!!
Answer:
x < 0
Step-by-step explanation:
You want an inequality that represents the number line graph with an open circle at 0 and shading to the left.
End pointThe end point of an interval on a number line graph is indicated by either an open circle or a filled circle (dot). The circle is open if that end point is not included in the set being graphed. If the end point is included, then the circle is filled to become a solid dot.
The circle at x=0 on this graph is an open circle, so x=0 is not part of the solution set.
ShadingThe shading on the number line indicates the values that are included in the solution set. Here, shading is to the left of x=0, so includes all values less than 0. This is written as the inequality ...
x < 0
__
Additional comment
If you write number-line intervals using the left-pointing symbols < or ≤, then the location of x relative to the symbol is the same as the location of the shading relative to the end point.
Here, shading is to the left of 0, so we can write the inequality ...
x < 0
where x is to the left of 0 in the inequality expression. (As we said above, we use < for the open circle. ≤ is used for a filled dot.)
Solve (x – 3)2 = 49. Select the values of x.
Answer:
27.5
Step-by-step explanation:
2x-6=49
2x=55
x=27.5
Cooper's Cafe has regular coffee and decaffeinated coffee. This morning, the cafe served 96
coffees in all, 72 of which were regular. What percentage of the coffees were regular?
Answer:
75%
Step-by-step explanation:
To solve this equation, we need to turn the fraction 72/96 into a percentage.
72 ÷ 96 = 0.75
0.75 as a percentage is 75%
Therefore, 75% of the coffees were regular.
1000,500,250,125 arithmetric, geometric, or neither
Answer:
[tex] G [/tex]eometric.
Step-by-step explanation:
To get the common ratio in a Geometric Progression (GP), T2/a(T1). a(T1) = 1000, T2 = 500.
So, 500/1000 = 1/2. Therefore, common ratio = 1/2
Now, multiply by the the given term to find the next term i.e
1/2 × 1000 = 500, 1/2 × 500 = 250, 1/2 × 250 = 125, 1/2 × 125 = 62.5, etc.
I hope this helpsFind the quotient and write the answer in simplest form 2 4/3 ÷1 8/7 =
first off let's convert the mixed fractions to improper fractions and then divide.
[tex]\stackrel{mixed}{2\frac{4}{3}}\implies \cfrac{2\cdot 3+4}{3}\implies \stackrel{improper}{\cfrac{10}{3}} ~\hfill \stackrel{mixed}{1\frac{8}{7}}\implies \cfrac{1\cdot 7+8}{7}\implies \stackrel{improper}{\cfrac{15}{7}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{10}{3}\div \cfrac{15}{7}\implies \cfrac{10}{3}\cdot \cfrac{7}{15}\implies \cfrac{10}{15}\cdot \cfrac{7}{3}\implies \cfrac{2}{3}\cdot \cfrac{7}{3}\implies \cfrac{14}{9}\implies 1\frac{5}{9}[/tex]
The table shows the closing stock prices of a new energy company for the past 5 days. One of the closing prices is
missing from the table.
Day
Monday
Tuesday
Wednesday
Thursday
Friday
OB. $53.88
If the 5-day simple moving average was $54.27, what was the closing price on Thursday?
OA $53.78
O C. $54.27
►
OD $56.24
Closing Price
$52.45
$53.18
$52.37
?
$57.11
If the 5-day simple moving average was $54.27, then the stock's closing price on Thursday was $56.24.
The table shows the closing stock prices of a new energy company for the past 5 days. One of the closing prices is missing from the table. The 5-day simple moving average is $54.27. The closing price of the stock on Monday, Tuesday, Wednesday, and Friday was $52.45, $53.18, $52.37, and $57.11. We need to find the closing price on Thursday. Let the missing value of the stock price be denoted by the variable "x". The average is the sum of all the values divided by the total number of values. We can solve the given equation.
A = (52.45 + 53.18 + 52.37 + x + 57.11)/5
54.27 = (52.45 + 53.18 + 52.37 + x + 57.11)/5
54.27*5 = (52.45 + 53.18 + 52.37 + x + 57.11)
271.35 = 215.11 + x
x = 271.35 - 215.11
x = 56.24
Hence, the closing price of the stock on Thursday is $56.24.
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Find the coordinates of point P that lies on the line segment MQ. M(-5, 3), Q(4. 9), and partition the segment at a ratio of to 3. Graph line segment MG and Pin the coordinate plane.
The coordinates of point P that lies on the line segment MQ is P(-11/4 , 9/2).
Given:
M(-5, 3), Q(4, 9), and partition the segment at a ratio of 1 : 3.
(x1,y1) and (x2,y2) in the ratio m:n then,
(x,y) = (mx2+nx1 / m+n , my2+ny1 / m+n)
= (1*4+3*-5 / 1+3 , 1*9+3*3 / 1+3
= (4 - 15 / 4 , 9 + 9 / 4)
= (-11/4 , 18/4)
= (-11/4 , 9/2)
Therefore the coordinates of point P that lies on the line segment MQ is P(-11/4 , 9/2).
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A local farmer had a mouse problem in his barn. He estimated there were about 800
mice to start with. He adopted some cats and noticed that the number of mice was
decreasing by 8%/wk. The graph models the number of mice x weeks after the
farmer adopted the cats.
Identify and interpret the key features of the exponential function modeled in terms
of this situation!
Answer: try a c and e
Step-by-step explanation:
a farmer is enclosing a rectangular area for his sheep to graze, where one side will be a wall that already exists. he wants the area to be 20,000 20,000 square feet. what is the least amount of fencing he can use to create the area for his sheep?
Using the concepts of area of rectangle, we got that 72 feet is the the least amount of fencing he can use to create the area for his sheep.
Lets, suppose that the length of rectangle as x feet,
and width of rectangle as y feet.
So perimeter of rectangle as 2×( length + breadth)
We are given perimeter of rectangle as 72 feet
So, length of two sides of rectangle + width of rectangle=72feet.
=>2x+y=72 feet----------(eq1)
Now, we know that area of rectangle is given by =(length × breadth),or
=>(x × y)=20000
Putting values of y from eq1,we get
=>x × (72-2x)=20000
=>72x-2x²=20000
We need to find the least amount of fencing, so we find the local minima by using the differentiation
=>d(72x)/dx-d(2x²)/dx=d(20000)/dx
=>72-4x=0
=>x=18feet
Therefore, y=72-2×18=72-36=36feet
Hence, length of rectangle is 18 feet, and width is 36 feet
Therefore, length of fencing is =2x+y=2×18+36=72 feet.
Hence, if a farmer is enclosing a rectangular area for his sheep to graze, where one side will be a wall that already exists. he wants the area to be 20,000 square feet, then the least amount of fencing he can use to create the area for his sheep is 72 feet.
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(Complete question) is:
a farmer is enclosing a rectangular area for his sheep to graze, where one side will be a wall that already exists. Perimeter of rectangle is given as 72 feet. He wants the area to be 20,000 square feet. what is the least amount of fencing he can use to create the area for his sheep?
PLEASE HELP
If Janice is building a garden and the perimeter is 20 (P = 20) and the length is 4 (L = 4), find w (the width)
Answer:
w = 6 units
Step-by-step explanation:
The perimeter is found by adding all the sides of a rectangle. The perimeter can be found using this equation:
[tex]P=2w+2l[/tex]
Where w represents width and l represents length.
To find the width, rearrange the equation so it is in terms of w:
[tex]P=2w+2l\\2w=P-2l\\w=\frac{P-2l}{2}[/tex]
Now, plug in the known values!
[tex]w=\frac{20-2(4)}{2}[/tex]
Simplify!
[tex]w=\frac{12}{2} \\w=6[/tex]
Put the following equation of a line into slope-intercept form, simplifying all fractions. 3x−6y= −30
Answer: y = 1/2x + 5
Step-by-step explanation:
3x-6y= -30
Step 1: Subtract 3x to cancel it out and put it on the other side.
3x-6y= -30 -3x
- 3x
After doing that, the equation should look like this: -6y = -3x - 30
Step 2: Divide by -6 to get y alone
-6y/-6= (-3x - 30)/-6
Step 3: Solve
After dividing everything by -6, we get our answer!!
y = 1/2x + 5
*Slope-Intercept form will always end up being in the same format as y=mx+b
I hope this helps :))
unit 3 function notation and evaluating function homework gina wilson (all things algebra), 2013
Answer:
b
Step-by-step explanation:
it is the answer
Please fill in the missing blanks! I will give brainly to the best!
Answer:
1. 0
2. 7
3. -2
4. 10
5. -7
6. -8
7. -2
8. -6
9. -4
10. -5
11. 2
12. -9
13. -9
14. -9
Step-by-step explanation:
Find the absolute value of the complex number.
3i - 2
Absolute value of Complex Number -2 + 3i is [tex]\sqrt{13}[/tex]
Absolute value of complex number:
z = x + iy is the general form of the complex number where x is real part and y is the imaginary part.
If we talk about absolute value of complex number z = x + iy then it is represented by |z| = |x + iy|.It is also rad as modulus of z.Absolute value is always going to be a positive value.
and,
|z| = |x + iy|
= [tex]\sqrt{x^{2} + y^{2} }[/tex]
Now,
We have to find the absolute value of complex number, 3i - 2
z = 3i - 2
= -2 + 3i
Absolute value of z is,
|z| = | -2 + 3i |
= [tex]\sqrt{(-2)^{2} + 3^{2} }[/tex]
= [tex]\sqrt{4 + 9}[/tex]
= [tex]\sqrt{13}[/tex]
Thus,
Absolute value of Complex number -2 + 3i is [tex]\sqrt{13}[/tex]
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There are 20 people in a room. 4 of them are people you know. When 2 people are selected at random at the same time, what is the probability that at least one of them is someone you know?
(this is a basic question but its 4am, my brain isnt working properly)
Answer:
4/20=1/5 or 20% or 0.2
Step-by-step explanation:
if u write 4/20 simplify it which becomes 1/5
u can write in percentage or in decimal depending on what the question wants
In 2010, there were 3,669 people living in Bridgeview, IL. Chicago, IL has 681 times as
many people. How many more people live in Chicago?
Answer:
There are roughly 2,488,600 more people living in Chicago.
Calculate the next two terms in each of these Fibonacci-type sequences.
a) 1, 4, 5,
5, 9,
o task
b) 2,
9, 14, ...
4, 6, 10, 16,
Watch video
Ans
The next two tems of the Fabonacci sequence are (a) 14, 23 (b) 23, 37 (c) 26, 42.
What is Fabonacci type sequence ?
The first two terms are already defined in the this sequence. The nth term of a Fabonacci type sequence is given by the following expression:
[tex]F_n=F_{n-1}+F_{n-2}[/tex]
(a)
In this case 5 terms are given hence, calculate the 6th term.
[tex]F_6=F_5+F_4\\F_6=9+5\\F_6=14[/tex]
Now, calculate the 7th term.
[tex]F_7=F_6+F_5\\F_7=14+9\\F_7=23[/tex]
(b)
Calculate the 4th term.
[tex]F_4=F_3+F_2\\F_4=14+9\\F_4=23\\[/tex]
Calculate the 5th term.
[tex]F_5=F_4+F_3\\F_5=23+14\\F_5=37[/tex]
(c)
The series is 4, 6, 10, 16, ...
[tex]F_5=F_4+F_3\\F_5=16+10\\F_5=26[/tex]
[tex]F_6=F_5+F_4\\F_6=26+16\\F_6=42[/tex]
Hence, the next two tems of the Fabonacci sequence are (a) 14, 23 (b) 23, 37 (c) 26, 42.
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K
The voltage V of an audio speaker can be represented by V=2√P, where P is the power of the speaker. An engineer wants to design a speaker with 576 watts of power. What will
the voltage be?
volts
According to the given voltage function, the value of the voltage for the power of 576 watts is 48 watts.
Function:
The relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.
Given,
The voltage V of an audio speaker can be represented by V=2√P, where P is the power of the speaker. An engineer wants to design a speaker with 576 watts of power.
Here we need to find the voltage of the given power.
In the given question we have the voltage function
v = 2√P
Where P refer the power of the speaker.
Here we have to find the voltage if engineer wants to design a speaker with 576 watts of power.
Which means the value of P is 576.
Then the value of V is calculated as,
v = 2 √576
We know that the value of √576 = 24,
So,
v = 2 x 24
v = 48.
Therefore, the voltage is 48 watts.
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Which of the following explains why (x + 3) = (x − 6))
has no solution?
Answer:
The is no number that I can substitue in for x to make the statement true.
Step-by-step explanation:
s + 3 = x -6 Subtract x from both sides
3 = -6 We get a false statement.
A rectangle has length 72 cm and width 56 cm. A second rectangle has the same area as this one, but its width is 21 cm. Do these quantities (length and width) vary directly or inversely?
The length and the width vary inversely.
What is variation?A variation is a relation between a set of values of one variable and a set of values of other variables.
In the equation y = mx + b, if m is a nonzero constant and b = 0, then you have the function y = mx (often written y = kx), which is called a direct variation.
If first rectangle length = 72cm and width = 56cm
Then, area = length x width = 72 x 56 = 4032[tex]cm^{2}[/tex]
If length of second rectangle = x
and width = 21
Area of second rectangle = 21x
so both areas are equal, which means
21x = 4032
x = 4032/21
x = 192cm
Since the first rectangle had a width of 56cm and length, 72 and second rectangle has a reduced width 21 cm and an increased length 192cm. it means that the length and the width vary inversely since the reduction in width led to an increase in length.
In conclusion, the two quantities length and width vary inversely.
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in the diagram below of triangle KLM, N is the midpoint of KM and O is the midpoint of LM if NO equals 3+ 7X and KL equals 4X +16 what is the measure of no
If O is the midpoint of LM and N is the midpoint of KM then the measure of NO is 10.
What are Linear equations?Linear equations are a combination of constants and variables where the value of the variable is calculated using mathematical operations.
We have given that Triangle KLM, N is the midpoint of KM and O is the midpoint of LM if NO equals 3+ 7X and KL equals 4X +16, we are supposed to find the measure of NO.
Using the Midpoint theorem, we can say that in Triangle KLM;
NO = KL / 2
Substituting values,
3+ 7X = 4X +16/ 2
3+ 7X = 2X + 8
7x - 2x = 8 - 3
5x = 5
x = 1
NO = 3+ 7X
NO = 3+ 7(1) = 10
NO equals 10
Hence the measure of NO is 10.
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f(x) = x^2. What is g(x)?
Answer:
[tex]\textsf{B.} \quad g(x)=-x^2-2[/tex]
Step-by-step explanation:
Transformations
[tex]f(x)+a \implies f(x) \: \textsf{translated $a$ units up}.[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated $a$ units down}.[/tex]
[tex]-f(x) \implies f(x) \: \textsf{reflected in the $x$-axis}.[/tex]
[tex]f(-x) \implies f(x) \: \textsf{reflected in the $y$-axis}.[/tex]
From inspection of the given graph, we can see that g(x) is function f(x) reflected in the x-axis and translated 2 units down.
Given function f(x):
[tex]f(x)=x^2[/tex]
Reflected in the x-axis:
[tex]-f(x) \implies g(x)= -x^2[/tex]
Translated 2 units down:
[tex]-f(x)-2 \implies g(x)=-x^2-2[/tex]
Therefore:
[tex]g(x)=-x^2-2[/tex]
Note:
If the leading coefficient of a quadratic function is positive, the parabola opens upwards.
If the leading coefficient of a quadratic function is negative, the parabola opens downwards.
Therefore, as g(x) opens downwards, the term in x² will be negative.