Answer:
-14-2i
Step-by-step explanation:
-9-i+(-5-i)
collect like terms(real-real, imaginary-imaginary)
=(-9-5)+(-i-i)
=-14-2i
Solve the equation. - 2(2x-4)= 4x
Answer:
-2(2x-4) = -4x+8 or 2(2x-4) ≠ 4x ; -4x+8 ≠ 4x
Step-by-step explanation:
Did you accidentally write =4x after your expression? If so, then let me explain why my answer is correct. I used distributive property of multiplication, so I multiplied -2 with 2x to get -4x, and -2 multiplied with -4 to get 8. So my final answer was -4x+8. If you did not accidentally put -4x, then my answer would be, 2(2x-4) ≠ 4x or -4x+8 ≠ 4x. Hope this helped.
If a person invested half of her money at 9% and half at 7% and received $160 interest, find the total amount of money invested.
Answer:
$2000
Step-by-step explanation:
let x be the money she invested
lets assume this was for 1 year
0.09(x/2) + 0.07(x/2) = 160
multiply each side by 2 to cancel the denominators:
0.09x + 0.07x = 320
0.16x = 320
x = 2000
Answer: $2000
Let the amount of money she invested be x
Lets assume the time of investment as 1 year
ATQ
0.09(x/2) + 0.07(x/2) = 160
0.09x + 0.07x = 320
0.16x = 320
x = 2000
Must click thanks and mark brainliest
What are the zeros of the polynomial function f(x)=x3-7x2+8x+16
Answer: x=4, -1
Step-by-step explanation:
Assuming you meant [tex]x^3-7x^2+8x+16[/tex], the zeros of the question are x = 4 and -1.
Step 1. Replace f(x) with y.
[tex]y = x^3-7x^2+8x+16[/tex]
Step 2. To find the roots of the equation, replace y with 0 and solve.
[tex]0 = x^3-7x^2+8x+16[/tex]
Step 3. Factor the left side of the equation.
[tex](x-4)^2 (x+1)=0[/tex]
Step 4. Set x-4 equal to 0 and solve for x.
[tex]x-4=0[/tex]
Step 5. Set [tex]x+1[/tex] equal to 0 and solve for x.
[tex]x=-1[/tex]
The solution is the result of [tex]x-4=0[/tex] and [tex]x+1=0[/tex].
[tex]x=4,-1[/tex]
What is the measure
Pls help i will give brainliest
Picture included
I need help ASAP thank you guys
Answer:
The fraction is undefined when x=-2
Step-by-step explanation:
The fraction will be undefined when the denominator is zero
x+2 = 0
x+2-2 = 0-2
x = -2
The fraction is undefined when x=-2
Answer:
as to me 5
Step-by-step explanation:
ask someone else to say that I am not sure if you have any questions or need any further information please contact me at the end of the world
find the solution to the system of equations.
y= -7x + 3
y= -x - 3
Answer:
x = 1 y = -4
Step-by-step explanation:
-7x + 3 = -x - 3
-7x = -x - 6
-6x = -6
x = 1
y = - (1) - 3
y = -1 - 3
y = -4
I need help guys thanks so much
Answer:
2
Step-by-step explanation:
8 ^ (5/3) ^ 1/5
We know a^b^c = a^(b*c)
8^ (5/3*1/5)
8^ 1/3
Rewriting 8 as 2^3
2^3 ^1/3
2 ^(3*1/3)
2^1
2
Answer:
2
Step-by-step explanation:
((2^3)^5/3)^1/5
= (2^5)^1/5
= 2
Answered by Gauthmath
The carpet in the school library needs to be replaced. The dimensions of the library floor or shell each square foot of cart bit cost $1.25. What is the total cost of the new carpet for the library
To find the cost, we must:
First, find the area of the carper. It can be found dividing the carper into a rectangle and a right triangle.Then, with the area, in square foot, we have the cost per square foot, which makes it possible to find the total cost.Doing this, we get that the cost is: $3,815, and the correct option is B.
Carpet:
The carpet can be divided into:
A rectangle of dimensions 56 ft and 38 ft.A right triangle of legs 71 - 38 = 33 ft and 56 ft.----------------------------------------------
Area of the rectangle:
The area of a rectangle of dimensions l and w is given by:
[tex]A_r = lw[/tex]
In this question, the dimensions are l = 56 ft, w = 38 ft, so the area, in square feet, is:
[tex]A_r = 56*38 = 2128[/tex]
-------------------------------------------
Area of a right triangle:
The area of a right triangle of legs a and b is given by:
[tex]A_t = \frac{ab}{2}[/tex]
In this question, the legs are a = 56, b = 38, so the area, in square feet, is:
[tex]A_t = \frac{56(33)}{2} = 924[/tex]
----------------------------
Total area:
The total area is the sum of the area of the rectangle with the area of the right triangle, thus:
[tex]A = A_r + A_t = 2128 + 924 = 3052[/tex]
-------------------------
Cost:
Each square foot costs $1.25.
There are 3,052 square feet. So, the cost is:
[tex]C = 1.25*3052 = 3815[/tex]
Thus, the cost is $3,815, and the correct option is B.
A similar question is found at https://brainly.com/question/13209573
find the mid-point of the line segment joining the points (10, 13) and (-7, 7)?
Answer:
(3/2,10)
Step-by-step explanation:
Mid point is ((10-7)/2,(13+7)/2)=(1.5,10)
A certain model of automobile has its gas mileage (in miles per gallon, or mpg) normally distributed, with a mean of 28 mpg and a standard deviation of 4 mpg. Find the probability that a car selected at random has the following gas mileages. (Round your answers to four decimal places.) (a) less than 26 mpg (b) greater than 34 mpg (c) between 22 and 34 mpg
Answer:
Step-by-step explanation:
We are finding the probability, which is a percentage, of each of these intervals on our standard bell curve. In order to find this percentage, we need to find the z-score that provides this percentage. To find the z-score:
[tex]z=\frac{x_i-\bar{x}}{\sigma}[/tex] which is the number in question minus the mean, all divided by the standard deviation. We're first looking for the probability that the gas mileage on a certain model of car is less than 26 mpg.
To find this z-score:
[tex]z=\frac{26-28}{4}=-.5[/tex] Depending upon which table you look at for the z-score determines how you will find it. The z-score that measure from the value and to the left of it is what we need. This decimal is .3085375, or 30.8538%.
Onto b., which is for the percentage of cars that have gas mileage over 34 mpg. Find the z-score, and this time, we look to the right of the value for the percentage:
[tex]z=\frac{34-28}{4}=1.5[/tex] and to the right of 1.5 standard deviations we will find .0668072, or 6.68072%
Then finally c., which wants the probability that the gas mileage on one of these cars is greater than 22 but less than 34 mpg. To do this we have to find the z-scores of each and then do some subtracting. First the z-scores:
[tex]z=\frac{22-28}{4}=-1.5[/tex] The percentage of data that lies to the right of that z-score is .9331927
The z-score for the other value, 34, was already found as 1.5, having .0668072 of the data to the right of that z-score. We subtract the smaller from the larger to determine what's left in-between:
.9331972 - .0668072 = .86639, or as a percentage, 86.639% of the cars fall into this interval for gas mileage.
Square root 1.000441
Answer: 1.00022048
Step-by-step explanation:
Is the relationship shown by the data linear? If so, model the data with an equation.
Answer:
4th option
Step-by-step explanation:
The relationship is linear,
putting the value of x in the right side of the equation of option 4, you'll get the value of the left side
putting, x=1
y+4=-1/2(x-1)
y=-1/2(1-1)-4
y=-4
putting, x=7
y+4=-1/2(7-1)
y=-1/2(6)-4
y=-6/2-4
y=-3-4
y=-7
If $ 10000 is deposited at an "interest rate" of 4% per year, annually compounded, what amount will depositors get after 5 years?
Answer:
PTR upon hundreds .by putting these formulas you can solve ti and is 2000
tính công thức Taylo đến x^13
Answer:
أنت مجنون ، هل تعرف ذلك؟
Step-by-step explanation:
بنسلفانيا
Divide p(x)=x^3-4x^2+x+6 by (x-3). Find the remainder and the quotient.
Answer:
Quotient is x² - x - 2
Remainder is 0
The manufacturer of cans of salmon that are supposed to have a net weight of 6 ounces tells you that the net weight is actually a normal random variable with a mean of 6.05 ounces and a standard deviation of .18 ounces. Suppose that you draw a random sample of 36 cans.
a. Find the probability that the mean weight of the sample is less than 5.97 ounces.
b. Suppose your random sample of 36 cans of salmon produced a mean weight that is less than 5.97 ounces. Comment on the statement made by the manufacturer.
Answer:
a) 0.0038 = 0.38% probability that the mean weight of the sample is less than 5.97 ounces.
b) Given a mean of 6.05 ounces, it is very unlikely that a sample mean of less than 5.97 ounces, which means that the true mean must be recalculated.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean of 6.05 ounces and a standard deviation of .18 ounces.
This means that [tex]\mu = 6.05, \sigma = 0.18[/tex]
Sample of 36:
This means that [tex]n = 36, s = \frac{0.18}{\sqrt{36}} = 0.03[/tex]
a. Find the probability that the mean weight of the sample is less than 5.97 ounces.
This is the p-value of z when X = 5.97. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{5.97 - 6.05}{0.03}[/tex]
[tex]Z = -2.67[/tex]
[tex]Z = -2.67[/tex] has a p-value of 0.0038.
0.0038 = 0.38% probability that the mean weight of the sample is less than 5.97 ounces.
b. Suppose your random sample of 36 cans of salmon produced a mean weight that is less than 5.97 ounces. Comment on the statement made by the manufacturer.
Given a mean of 6.05 ounces, it is very unlikely that a sample mean of less than 5.97 ounces, which means that the true mean must be recalculated.
Find the missing side round your answer to the nearest tenth
Answer:
x=13.2
Step-by-step explanation:
cos(43)=x/18
x=18×cos(43)
x=13.2
Answered by GAUTHMATH
The sum of four
consecutive odd number is 8o. Find the number
Answer:
The sum of 4 consecutive odd number is 80
Let X be the first of these numbers
Then the next odd number is X+2
The third is X+4The fourth is X+6
All of these add up to 80
(X) + (X+2) + (X+4) + (X+6) = 80
Using the commutative and associative laws, let's transform this equation into
(X + X + X + X) + (2 + 4 + 6) = 804X + 12 = 80
Subtract 12 from both sides of the equation gives4X = 68
Divide both sides by 4 gives
X = 17
Going back to the original question:What are the 4 consecutive odd numbers: 17, 19, 21, 23Checking our answer:17 + 19 + 21 + 23 = 80 Correct!
A line is perpendicular to the line y = 4x - 3 and has x-intercept (2,0). Which of the following is an equation of the line?
Answer:
y = -1/4x+1/2
Step-by-step explanation:
y = 4x - 3
This is in slope intercept form, y = mx+b where the slope is m
The slope is 4
Perpendicular lines have slopes that are negative reciprocals
-1/4 is the slope of the perpendicular line
y = -1/4x+b
Using the point (2,0)
0 = -1/4(2)+b
0 = -1/2+b
b = 1/2
y = -1/4x+1/2
Ram and his sister Kalpana win a prize of Rs 2000. They decide to share the prize in the ratio of their ages. Ram is 15 years old and Kalpana is 10 years old. How much do each of them receive
9514 1404 393
Answer:
Ram -- ₹1200Kalpana -- ₹800Step-by-step explanation:
Their age total is 15+10=25, so Ram will get 15/25 = 0.6 of the total. Kalpana will get the remaining 0.4 of the total.
Ram receives 0.6 × ₹2000 = ₹1200
Kalpana receives 0.4 × ₹2000 = ₹800
A regular polygon is drawn in a circle so that each vertex is on the circle and is connected to the center by a radius.
Each of the central angles has a measure of 40°. How many sides does the polygon have?
THE
9
Answer: 90 sides
Step-by-step explanation:
Let's say the circle has a center at A and B and C are at the vertices of a polygon. Since this figure is inscribed in a circle, we can draw two radii through the vertices. Because all radii are congruent, we know segment BA is congruent to Segment CA. If a triangle has at least 2 congruent sides, we can identify the triangle as an isosceles triangle. With this we can conclude <ACB is congruent to <ABC. By the definition of congruent angles, m<ACB = M<ABC. Let's say m<ACB = x. By the Triangle Sum Theorem, 40 + x + m<ABC = 180. By substitution, 40 + x + x = 180. When we solve we get x =70. Since radii bisect interior angles we know that each interior angle of this polygon is 140 degrees. If we plug in 140 to our equation, [tex]\frac{(n-2)180}{n}[/tex] where n is the number of sides, we get n = 90. So we can conclude this polygon has 90 sides
Ray’s weight increased by 11% in the last two years. If he gained 16.5 pounds, what was his weight two years ago?
Answer:
Ray weighed 150 pounds two years ago.
Step-by-step explanation:
11/100 = 16.5/x
11x = 16.5(100)
11x = 1,650
(11x)/11 = (1,650)/11
x = 150
About time that he should start going to the gym!
The distance from the plane to the building __ meters
Answer:
1200 ×90÷8 is not correct ans
Which of the following pairs of functions are inverses of each other?
A. f(x) = 5 + x and g(x) = 5 - x
B. f(x) = 2x -9 and g(x)=x+9/2
C. f(x) = 3-6 and g(x)=x+6/2
D. f(x)= x/3+4 and g(x) = 3x - 4
The pair of functions that are inverses of each other is B. f(x) = 2x - 9 and g(x) = x + 9/2.
To determine if two functions are inverses of each other, we need to check if the composition of the functions results in the identity function, which is f(g(x)) = x and g(f(x)) = x.
Let's analyze the given options:
A. f(x) = 5 + x and g(x) = 5 - x
To check if they are inverses, we compute f(g(x)) = f(5 - x) = 5 + (5 - x) = 10 - x, which is not equal to x. Similarly, g(f(x)) = g(5 + x) = 5 - (5 + x) = -x, which is also not equal to x. Therefore, these functions are not inverses.
B. f(x) = 2x - 9 and g(x) = x + 9/2
By calculating f(g(x)) and g(f(x)), we find that f(g(x)) = x and g(f(x)) = x, which means these functions are inverses of each other.
C. f(x) = 3 - 6 and g(x) = x + 6/2
Similar to option A, we compute f(g(x)) and g(f(x)), and find that they are not equal to x. Hence, these functions are not inverses.
D. f(x) = x/3 + 4 and g(x) = 3x - 4
After evaluating f(g(x)) and g(f(x)), we see that f(g(x)) = x and g(f(x)) = x. Therefore, these functions are inverses of each other.
In summary, the pair of functions that are inverses of each other is B. f(x) = 2x - 9 and g(x) = x + 9/2.
Learn more about function here:
https://brainly.com/question/782311
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Which equation can she use as statement 5? 60:x = 48:(48 + 36) 60 + x = 48 + 36 60 − x = 48 − 36 60:(60 + x) = 48:(48 + 36)
write your answer in simplest radical form
Answer:
[tex]9\sqrt{3}[/tex]
Step-by-step explanation:
This is a 30-60-90 triangle.
It's good to remember this. The side length opposite to the 60 degree angle is always the base multiplied by [tex]\sqrt{3}[/tex]
Answer:
9√3.
Step-by-step explanation:
tan 60 = √3
So w/9 =√3
w = 9√3
how do I do this?????????????????????????????
Find the domain and range of the function, f(x)=sin|x|
Answer:
[tex]Domain = (-\infty,\infty)[/tex]
[tex]Range = (0,1)\\[/tex]
Step-by-step explanation:
Given
[tex]f(x) = \sin|x|[/tex]
Solving (a): The domain
There is no restriction on the given function because it is not a root function and doesn't have a x denominated fraction
Hence, the domain is:
[tex](-\infty,\infty)[/tex]
Solving (b): The range
The minimum of a sine function is 0
The maximum of a sine function is 1
So, the range is:
[tex](0,1)[/tex]
Please help! Thank you.
Answer:
B at -1 minus we go to - ∞
at -1 plus we to + ∞
Step-by-step explanation:
x^2 -x
g(x) = ---------
x+1
Factor out x
x(x-1)
g(x) = ---------
x+1
As x is to the left of -1
x is negative (x-1) is negative
x+1 will be slightly negative
g(-1 minus) = -*-/ - = - and we know that the denominator is very close to zero we are close to infinity so we go to - ∞
As x is to the right of -1
x is negative (x-1) is negative
x+1 will be slightly positive
g(-1 plus) = -*-/ + = + and we know that the denominator is very close to zero we are close to infinity so we go to ∞
josue bought 7 pounds of pretzels at a local wholesaler for $16.80. his friend ricardo bought 5 pounds of pretzels at the supermarket for $12.75. Ricardo thinks he got the better deal because $12.75 is less than $16.80. Is Ricardo's reasoning correct? Explain why or why not.
Answer:
Ricardo's reasoning is not correct
Step-by-step explanation:
Find who got the better deal by dividing the price by the number of pounds of pretzels:
16.80/7 = $2.40 a pound
12.75/5 = $2.55 a pound
So, Josue got the better deal because he only spent $2.40 a pound on the pretzels, while Ricardo spent $2.55 a pound.
Ricardo did not get the better deal, because he spent more per pound on the pretzels.
Ricardo's reasoning is not correct.
