Answer:(2x + 9i)(2x - 9i)
Step-by-step explanation:
a^2 - b^2 = (a+b)(a-b)
a^2 + b^2 = (a+bi)(a-bi) = a^2 + abi - abi - b^2 i^2
But -b^2 i^2 = +b^2
Answer:
[tex](4x+9i)(4x-9i)[/tex]
Step-by-step explanation:
Here, we have to apply this complex numbers property:
[tex]a^2 + b^2 = (a+bi)(a-bi)[/tex]
So, the given expression [tex]4x^2+81[/tex], can be rewrite as factor using the property:
[tex]4x^2+81=(4x+9i)(4x-9i)[/tex]
Because, if
[tex]a^2=x^2 \ and \ b^2=81\\\ then \ a=x \ and \ b=9[/tex]
Therefore, the factors are [tex](4x+9i)(4x-9i)[/tex]
Help me with these math questions.. WITH SCREENIES
Answer: 3
Step-by-step explanation:
log₇343 = x
343 = 7ˣ
7³ = 7ˣ
3 = x
******************************************
Answer: 1950
Step-by-step explanation:
s = r θ
325π = r * 30 * [tex]\frac{\pi}{180}[/tex]
325 = r * [tex]\frac{\pi}{6}[/tex]
6(325) = r
1950 = r
******************************************
domain: x is All Real Numbers --> (-∞, ∞)
range: y > 0 --> (0, ∞)
y-intercept: when x = 0, y = e² --> e²
horizontal asymptote: since y ≠ 0, then H.A. is --> y = 0
Use the graph of f(x) = |x(x2 − 1)| to find how many numbers in the interval [0.5, 0.75] satisfy the conclusion of the Mean Value Theorem.
Answer:
1 time
Step-by-step explanation:
f(x) = |x(x^2 − 1)|
The mean value theorem states
f'(c) = f(b) -f(a)
-------------
b-a
b = .75
a = .5
f(b) = abs(.75 * (.75^2 -1)) = abs (.75*(-.4375))=abs(-.328125)
= .328125
f(a) = abs(.5 * (.5^2 -1)) = abs(.5*(-.75))=abs(-.375) = .375
.328125- .375
f'(c) = -------------------------------------------------
.75-.5
f'(c) = -.1875
Real estate values in a town are increasing at a rate of 9% per year.
Mr. Townsend purchased a building for $375,000 in 2010.
How much can he expect to sell the building for in 2020, assuming this trend continues?
Enter your answer in the box.
Round to the nearest whole dollar.
$
Answer:
In 2020 building price is $ 887761
Step-by-step explanation:
Time = 2020 - 2010 = 10 years
In 2011 building price = 375000 × [tex]\frac{9}{100}[/tex] + 375000 =$408750
In 2012 building price = 408750 × [tex]\frac{9}{100}[/tex] + 408750 =$445537.5
In 2013 building price = 445537.5 × [tex]\frac{9}{100}[/tex] + 445537.5 =$485635.88
In 2014 building price = 485635.88 × [tex]\frac{9}{100}[/tex] + 485635.88 = $529343.11
In 2015 building price = 529343.11 × [tex]\frac{9}{100}[/tex] + 529343.11 = $576983.99
In 2016 building price = 576983.99 × [tex]\frac{9}{100}[/tex] + 576983.99 =$628912.55
In 2017 building price = 628912.55 × [tex]\frac{9}{100}[/tex] + 628912.55 =$685514.68
In 2018 building price = 685514.68 × [tex]\frac{9}{100}[/tex] + 685514.68 = $747211
In 2019 building price = 747211 × [tex]\frac{9}{100}[/tex] + 747211 =$814459.99
in 2020 building price = 814459.99 × [tex]\frac{9}{100}[/tex] + 814459.99 =$887761.38 ≈ $887761
Second method
Total time(t) = 10 years
Rate(r) = 9%
Principal value = $375000
Now,
selling price (in 2020) = principal value [tex](1+\frac{r}{100}) ^{t}[/tex]
= 375000 [tex](1+\frac{9}{100} )^{10}[/tex] = $887761.38 ≈$887761
A horseback riding trail is 1 mi 40.8 ft long. How long is the trail in yards, feet, and inches?
Answer: 1773.6 yards 5320.8 feet 64324.8 inches
Step-by-step explanation:
1 mile in yards = 1760 40.8 feet in yards = 13.6 1760 + 13.6 = 1773.6 yards
1 mile in feet = 5280 + 40.8 = 5320.8 feet
1 mile in inches = 63360
40.8 feet in inches = 964.8
63360 + 964.8 = 64324.8 inches
hope this helps :)
At a local fitness center, members pay an $8 membership fee and $4 for each aerobics class. Nonmembers pay $6 for each aerobics class. For what number of aerobics classes will the cost for members and nonmembers be the same?
Let X be the number of classes:
You need to multiply the cost per class by the number of classes.
For members you also need to add in the membership fee.
Members pay a total of 8 +4x
Non members pay a total of 6x
Set them to equal to solve for x, which is the number of classes taken:
8 + 4x = 6x
Subtract 4x from both sides:
8 = 2x
Divide both sides by 2:
x = 8/2 = 4
The answer is 4 classes.
6. The median-median line for a dataset is y=1.133x+0.489
The least-squares regression line for the same dataset is y=1.068x+0.731. Which regression equation better predicts the y-value for the point (50, 60)
A. The median-median line regression line is a better prediction.
B. The least squares regression line is a better prediction.
C. The models predict the same value
D. The models predict different values that are equally inaccurate
(1 point)
Answer: The answer is B...........
Answer:
The correct option is A. The median-median line regression line is a better prediction.
Step-by-step explanation:
The given median-median line for a dataset is
[tex]y=1.133x+0.489[/tex]
The least-squares regression line for the same dataset is
[tex]y=1.068x+0.731[/tex]
The given point is (50,60).
Substitute x=50 in each given equation.
[tex]y=1.133(50)+0.489=57.139[/tex]
[tex]y=1.068(50)+0.731=54.131[/tex]
Since the value of median-median line at x=50 is near to 60 than the value of least-squares regression at x=50.
The median-median line regression line is a better prediction. Therefore the correct option is A.
Please help Mrs.Johnson spend $611 buying lunch for 78 students. If all lunches cost the same, about how much did she spend on each lunch
Answer:
She spend 7.33 on each lunch.
Step-by-step explanation:
We have been given that Mrs. Johnson spend $611 buying for 78 students
If each lunch cots the same we have to find how much did she spend on each lunch:
We can calculate the price of each lunch by dividing the total cost she spend upon the lunch she bought.
let the cost of each lunch be x
Hence, [tex]x=\frac{611}{78}=7.33[/tex]
A 25-foot ladder is leaning against the side of a house. The top of the ladder is 20 feet above the ground. To the nearest degree, find the angle of elevation between the ground and the ladder.
To find the angle of elevation between the ground and the ladder, we can use the tangent function and the given measurements. The angle is approximately 39.8 degrees.
Explanation:To find the angle of elevation between the ground and the ladder, we can use trigonometry. Since the top of the ladder is 20 feet above the ground and the ladder is 25 feet long, we can use the opposite and adjacent sides of a right triangle. The trigonometric function that relates these sides is the tangent function:
tan(angle) = opposite/adjacent
Plugging in the known values, we get: tan(angle) = 20/25
Using a calculator to find the inverse tangent (arctan) of both sides, we get the angle to be approximately 39.8 degrees to the nearest degree.
In the pully system shown in this figure, MQ = 10 in, NP = 3in and QP=24in. Find MN
a. 25
b. 26
c. 27
d. 28
Answer:
The correct option is a. The length of MN is 25.
Step-by-step explanation:
Given information: MQ = 10 in, NP = 3 in and QP=24 in.
If the centers of two circles of radius r₁ and r₂ are d units apart, then the length of the direct common tangent between them is
[tex]l=\sqrt{d^2-(r_1-r_2)^2}[/tex]
[tex]24=\sqrt{d^2-(10-3)^2}[/tex]
Square both sides.
[tex]576=d^2-49[/tex]
[tex]625=d^2[/tex]
Take square root both sides.
[tex]25=d[/tex]
Therefore length of MN is 25 and option a is correct.
To find MN in the given pulley system, we can use the concept of similar triangles.
Explanation:In the pulley system shown in the figure, we can use the concept of similar triangles to find MN. The triangle MQP is similar to the triangle MNP. This means that the ratios of their corresponding sides are equal.
So we have:
MQ/MP = NP/MN
Substituting the given values:
10/24 = 3/MN
Cross multiplying:
10 * MN = 24 * 3
MN = (24 * 3) / 10
MN = 72/10
MN = 7.2 inches
Therefore, the length MN is approximately 7.2 inches.
Shiloh opens a savings account in which interest is compounded annually. The balance in the account is given by the following exponential expression, where t represents the time in years. Which statement correctly interprets the given expression? 125(1.025)t
A. Shiloh initially invested $125, which grows annually at a rate of 2.5%.
B. Shiloh initially invested $125, which grows annually at a rate of 1.025%.
C. Shiloh initially invested $1,025, which grows annually at a rate of 12.5%.
D. Shiloh initially invested $1,025, which grows annually at a rate of 1.25%.
Help asp
Answer:
Shiloh initially invested $125, which grows annually at a rate of 2.5%.
Step-by-step explanation:
The balance in the account is given by the following exponential expression,
[tex]125(1.025)^t[/tex]
Exponential growth formula is
[tex]A= P(1+r)^t[/tex]
Where P is the initial amount invested
r is the rate of interest
When we compare the formula with given expression , we can see that we have 125 in the place of P
So initial amount invested is $125
Now we find out 'r'
1+ r = 1.025
Subtract 1 on both sides
r= 0.025
To get percentage we multiply by 100
0.025 * 100 = 2.5%
Shiloh initially invested $125, which grows annually at a rate of 2.5%.
A student multiplied –8 × 334 as shown. One step is missing. Which is the missing step? –8 × 334 = ? = –8 × 3 + (–8) × 34 = –24 + −8 × 324 = –24 + −244 = –24 + (–6) = –30
Answer:
–24 + −8 × 324
Step-by-step explanation:
Well, if you go through the answer choices, there is only one that gives you the correct answer. The product is -2672, and the only answer choice that this satisfies is the second one.
Answer:
It's C
Step-by-step explanation:
The sum of two numbers is 37
and the difference is 13
. What are the numbers?
Answer:
25, 12
Step-by-step explanation:
let x represent one number and y represent the other number
x+y=37 (sum is addition)
x-y=13 (difference is subtraction)
Im solving using the substitution method
x-y=13 add y to both sides to get x by itself
x=13+y
13+y+y=37 substitute x for the solution above in the other equation and simplify
2y=24
y=12
plug in y into one of the equations
x+12=37 subtract 12 from both sides
x=25
Find the square root of these numbers to the nearest tenth.
72 =
32 =
481 =
Write an expression to represent: Nine minus the quotient of two and a number x.
Answer:
9 - 2/x
Step-by-step explanation:
Carmen sells electronics. She made a 10% commission on every dollar sale that she makes. One month Carmen got a commission check for $2500. What were her sales in dollars that month.
Answer: 25000
Step-by-step explanation:
.1=10%
So, 2500/.1=25000
25000*.1=2500
The length of a rectangular storage room is 3 feet longer than its width. if the area of the room is 40 square feet, find the width.
Answer:
Width of rectangular storage room= 5 feet.
Step-by-step explanation:
Let x be the width of storage room.
We have been given that the length of a rectangular storage room is 3 feet longer than its width. So the length of storage room will be x+3.
We are also given that the area of the room is 40 square feet.
Since the area of a rectangle is length times width.
[tex]\text{Area of rectangle}=\text{Length* Width}[/tex]
Let us substitute our given values in area formula.
[tex]40=x*(x+3)[/tex]
Upon distributing x we will get,
[tex]40=x^2+3x[/tex]
[tex]x^2+3x-40=0[/tex]
Now let us factor out our quadratic equation using splitting the middle term.
[tex]x^2+8x-5x-40=0[/tex]
[tex]x(x+8)-5(x+8)=0[/tex]
[tex](x+8)(x-5)=0[/tex]
[tex]x+8=0[/tex] or [tex]x-5=0[/tex]
[tex]x=-8[/tex] or [tex]x=5[/tex]
Since width can not be negative, therefore, the width of rectangle will be 5 feet.
Let us verify our answer.
Length of rectangular storage room is 3 feet longer than its width. So length will be 5+3=8.
Given: Area=40 square feet.
5*8=40.
Hence, width of rectangular storage room is 5 feet.
2. Use a graph to find the solution.
You want to set up an aquarium and need to determine what size tank to buy...
Answer:
The correct option is 3. Capacity of smallest tank is 15-gallons.
Step-by-step explanation:
The graph shows the relationship between capacity of tank and combined length of fish it can hold.
The line passing through (0,1) and (1,2).
Slope of the line is
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{2-1}{1-0}=1[/tex]
Slope intercept form of a line is
[tex]y=mx+b[/tex]
Where, m is slope and b is y-intercept.
The slope of the line is 1 and the y-intercept is 1, therefore the equation of line is
[tex]y=x+1[/tex] ..... (1)
If we want four 2-inch platys, three 1-inch guppies and a 3-inch loach, then the combined length of fish is
[tex]4\times 2+3\times 1+1\times 3=8+3+3=14[/tex]
Therefore the combined length of fish is 14.
Put x=14 in equation 1.
[tex]y=14+1=15[/tex]
Therefore, the capacity of smallest tank is 15-gallons and option 3 is correct.
Answer: got answer from someone, 12 and 14 were wrong.
Step-by-step explanation:
connexus unit 8 lesson 1 PRACTICE!
1) B
2) C
3) A
4) C
5) B
6) A
7) D
8) A
9) D
10) A
11) A
12) not C
13) D
14) not C
15) B
25 PTS
The graph of the piecewise function is shown.
What is the range of f(x)?
{ f(x)| –∞ < f(x) < ∞}
{ f(x)| –∞ < f(x) ≤ 4}
{ f(x)| 4 < f(x) < ∞}
{ f(x)| 0 ≤ f(x) < ∞}
The range of the function f(x) is:
{ f(x) | –∞ < f(x) ≤ 4}
Step-by-step explanation:By looking at the graph of the function f(x) we see that in the interval :
(-∞,0]
The function f(x) takes a constant value as: f(x)=4
and after that i.e. for x≥0 , the function f(x) is decreasing continuously.
Hence, we could say that the function f(x) takes all the real values which are less than and equal to 4.
Hence, the range of the function is:
{ f(x)| –∞ < f(x) ≤ 4}
Which angles are corresponding angles
Answer:
Step-by-step explanation:
corresponding angles are congruent to eachother for example 1&3, 5&7, 2&4, 8&6
Answer:
Option B, C, D are the correct options
Step-by-step explanation:
When two parallel lines are intersected by a transverse then two angle which are relatively at the the same position are called as corresponding angles.
As given in the picture attached, ∠1 and ∠2 are corresponding angles.
Similarly, ∠3 and ∠4 re corresponding angles.
Now we come to our question. In this question corresponding angles are
1) 2 and 4
2) 6 and 8
3) 1 and 3
4) 5 and 7
Therefore, Options. B, C and D are the correct options.
HELP ASAP 98 points and brainliest
Look at the parallelogram ABCD shown below: The table below shows the steps to prove that if the quadrilateral ABCD is a parallelogram, then its opposite sides are congruent:
Statement Reasons 1 AB is parallel to DC and AD is parallel to BC Definition of parallelogram 2
angle 1 = angle 2, angle 3 = angle 4 If two parallel lines are cut by a transversal then the _______________ are congruent 3
BD = BD Reflexive Property 4
triangles ADB and CBD are congruent If two angles and the included side of a triangle are congruent to the corresponding angles and side of another triangle then the triangles are congruent by ASA postulate 5
AB = DC, AD = BC Corresponding parts of congruent triangles are congruent
Which choice completes the missing information for reason 2 in the chart?
alternate interior angles
corresponding angles
same-side interior angles
vertical angles
Answer:
The correct option is 1.
Step-by-step explanation:
Statement 1: AB is parallel to DC and AD is parallel to BC.
Reason: Definition of parallelogram
Statement 2: ∠1 = ∠2, ∠3 = ∠ 4.
Reason: If two parallel lines are cut by a transversal then the alternate interior angles are congruent.
Statement 3: BD = BD.
Reason: Reflexive Property.
Statement 4: ΔADB≅ΔCBD.
Reason: If two angles and the included side of a triangle are congruent to the corresponding angles and side of another triangle then the triangles are congruent by ASA postulate.
Statement 5: AB = DC, AD = BC.
Reason: Corresponding parts of congruent triangles are congruent.
The missing information for reason 2 in the chart is alternate interior angles .
Therefore the correct option is 1.
A school replaced 20% of its computers with new ones what is the total number of computers in the school if 55 computers were replaced
Answer:
There were 275 computers
Step-by-step explanation:
Computers replaced = total computers * percent replaced
What do we know?
The percent replaced is 20 = .2
55 computers were replaced.
Substitute this in
55 = total computers * .2
Divide each side by .2
55/.2 = total computers *.2 /.2
275 = total computers
There were 275 computers
To find the total number of computers in the school, you set up the equation 0.20 * x = 55, where x is the total number of computers. Solving for x gives us x = 275, meaning there are 275 computers in the school.
The question is asking us to find the total number of computers in the school knowing that 20% of them were replaced and knowing that 55 computers were replaced. To find the total number of computers, we need to understand that the 55 computers represent the 20% that were replaced. So, we set up a proportion where 20% (0.20) of the total number of computers (which we will call x) equals to 55. The equation will look like this: 0.20 * x = 55.
We divide both sides of the equation by 0.20 to solve for x:
x = 55 / 0.20
x = 275
Thus, the total number of computers in the school is 275.
A flagpole casts a 16-foot shadow at the same time a 4-foot pole casts a 5-foot shadow. How tall is the flagpole?
Set up a proportion:
The 4 foot pole casts a 5 foot shadow is written as 4/5
Let the height of the flagpole = x.
The flag pole casts a 16 foot shadow so it is written as X/16
Now set the two proportions equal to each other:
4/5 = X/16
Solve for X by cross multiplying:
5X = 64
Divide both sides by 5:
X = 64/5
X = 12.8
The flag pole is 12.8 feet tall.
Based on the information the tall of the flagpole is 12.8 feet tall .
Tall of the flagpoleSet up a proportion and let x = Height of the flagpole
4/5 =16/x
Solve x by cross multiplying
5x = 64
Divide both sides by 5x
x= 64/5
x=12.8 feet tall
Inconclusion the tall of the flagpole is 12.8 feet tall .
Learn more about tall of the flagpole here:https://brainly.com/question/317739
Simplify the expression
Answer:
729
Step-by-step explanation:
[(-1)^3]^2 /[(-3)^-3]^2
= 1 * [(-3)^3]^2
= 1 * 729
= 729
Answer:
729
To solve this, we need to start on the inside and work out; solving one part at a time.
[{(-1)^3 / (-3)^-3}]^2
1. (-1)^3 = -1
2. (-3)^-3 = - 1/27
3. (-1) / (- 1/27) = 27
4. 27^2 = 729
if f(x)=x^2-1 what is the equation for f^-1(x)
Answer:
see below
Step-by-step explanation:
Swap y and x, then solve for y.
Original:
... y = f(x) = x² -1
Swap y and x:
... x = y² -1
Add 1:
... x + 1 = y²
Take the square root:
... ±√(x+1) = y . . . . . matches the 3rd selection
Rewrite as the inverse relation: (not a function)
... f^-1(x) = ±√(x+1)
_____
Comment on the graph
The attached graph shows the function f(x) in red, and the inverse relation g(x) in blue. You will note that g(x) is double-valued for most values of x, so is not a function. The function and its inverse relation are mirror images of each other in the line y=x. (That is, swapping y and x changes the function to its inverse, and vice versa.)
The inverse function of f(x)=x^2-1, denoted as f^-1(x), is calculated as f^-1(x) = sqrt(x+1), if x>=0 and f^-1(x) = - sqrt(x+1), if x<0.
Explanation:To find the inverse of the function f(x)=x^2-1, denoted as f^-1(x), first replace f(x) with y, so the equation becomes y = x^2 - 1. The next step is to swap x and y, giving you x = y^2 - 1. Now, you should solve this new equation for y, resulting in y = sqrt(x+1). However, considering the domain, we have to separate into positive and negative square roots. Therefore, the complete inverse function is f^-1(x) = sqrt(x+1), if x>=0 and f^-1(x) = - sqrt(x+1), if x<0.
Learn more about Inverse Function here:https://brainly.com/question/35509335
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Camp Oakes gets 32 juice boxes of orange juice and 56 boxes of apple juice each shelf in the cup board can hold eight boxes of juice what is the least number of cells needed for all the juice box
The cost of 5 cans of dog food is $4.35.At the price,how much do 11 cans of dog foo cost.
Answer:
11 cans cost $9.57
Step-by-step explanation:
There are two ways of doing this, one being the longer and the other being the shorter.
The shorter one is simply multiplying the number by the new number over 5:
[tex]4.35 * \frac{11}{5}[/tex]
This works because this finds the amount the 5 has increased from 5 to 11 and muliplies the number by this.
[tex]4.35 * \frac{11}{5}[/tex] = 9.57
So 11 cans cost $9.57
Item 9 A group of tourists spends $156 to rent snorkels and fins. A total of 15 snorkels and 18 pairs of fins are rented. Renting a snorkel costs four times as much as renting a pair of fins. How much does it cost to rent a snorkel?
Answer:
$8
Step-by-step explanation:
A group of tourists spends $156 to rent snorkels and fins.
They rented 15 snorkels and 18 pairs of fins.
Renting a snorkel costs four times as much as renting a pair of fins.
Let us assume that the rental cost of a pair of fins is x, so the rental cost of snorkel will be 4x.
Then total cost of 15 snorkels and 18 pairs of fins will be,
[tex]=15(4x)+18x[/tex]
[tex]=60x+18x[/tex]
[tex]=78x[/tex]
But it is given as $156, so
[tex]\Rightarrow 78x=156[/tex]
[tex]\Rightarrow x=2[/tex]
Therefore, the rental cost of a pair of fins is $2 and cost of snorkel is [tex]2\times 4=\$8[/tex]
Find the domain of the following graph:
−7 < x ≤9
−7 < y ≤ 9
−7 < x ≤5
−7 < y ≤ 5
Answer:
[tex]-7<x\leq 9[/tex]
Step-by-step explanation:
The domain is the set of all x-values. We can find the domain by finding the left boundary of the graph (the furthest left x-value) and then the right boundary (the furthest right x value).
The furthest left x-value is -7. Notice it has a large open circle here that is not filled in. This means the function does not include -7 but includes numbers very close to it like-6.999999..... We sue use an inequality sign without an equal to to write -7. x >-7.
The furthest right x value is 9. It has a closed circle or "filled in" circle so we write with an equal to sign. [tex]x\leq 9[/tex].
We combine the two into [tex]-7<x\leq 9[/tex].
Brandon buys a radio for 43.99 in a state where sales tax is 7%.What is the total brandon pays for the radio
Adriana made 30 pet collars to bring to the pet fair. She wants to display 3 pet collars on each hook. How many hooks will Adriana need to display all 30 pet collars
Answer:
10 hooks!
Step-by-step explanation:
if Adriana has 30 and wants to display 3 on each hook you would have to divide 30 by 3.