Answer:
The domain of the function is all real values of x, except [tex]x = 4[/tex] and [tex]x = 2[/tex]
Step-by-step explanation:
We are given the following function:
[tex]f(x) = \frac{x+1}{x^2-6x+8}[/tex]
It's a fraction, so the domain is all the real values except those in which the denominator is 0.
Denominator:
Quadratic equation with [tex]a = 1, b = -6, c = 8[/tex]
Using bhaskara, the denominator is 0 for these following values of x:
[tex]\Delta = (-6)^2 - 4(1)(8) = 36-32 = 4[/tex]
[tex]x_{1} = \frac{-(-6) + \sqrt{4}}{2} = 4[/tex]
[tex]x_{2} = \frac{-(-6) - \sqrt{4}}{2} = 2[/tex]
The domain of the function is all real values of x, except [tex]x = 4[/tex] and [tex]x = 2[/tex]
In the diagram below, POR is a diameter, <QPR is a°,<PRS is (4a+12)°. find the value of a
Answer:
22=4
Step-by-step explanation:
0977-=ytb
Need answer urgently
Answer:
x = -2; y = 1
Step-by-step explanation:
See picture below.
We are told matrices B is the inverse of matrix A.
The product of a matrix and its inverse is the identity matrix.
4) Write the equation of the line passing
through (-5, 6 ) and has slope equal to 4.
Answer:
y = 4x + 26
Step-by-step explanation:
y = mx + b
The slope (m) is equal to 4.
y = 4x + b
To find the y-intercept (b), plug in the point given.
6 = 4(-5) + b
6 = -20 + b
26 = b
The answer is y = 4x + 26.
Answer:
The equation of the line passing through (-5, 6) with a slope of 4 is
y = 4x + 26
Step-by-step explanation:
An equation of a line would always have the following structure...
y = mx + b
In this equation, "y" is the y coordinate of the point, "x" is the x coordinate of the point, "m" is the slope, and "b" is the y coordinate of the y-intercept. We know all the values except "b", but we can find the value of "b" by substituting all the other values into the equation...
y = mx + b
6 = 4(-5) + b
6 = b - 20
b = 6 + 20
b = 26
Therefore, the equation of the line passing through (-5, 6) with a slope of 4 is y = 4x + 26
Last week at the business where you work, you sold 120 items. The business paid $1 per item and sold them for $3 each. What profit did the business make from selling the 120 items?
Answer:
240
Step-by-step explanation:
minus how much u sold them and how much it cost to make
3-1=2
times 2 and 120
2(120)
240
If a person high jumps 6 feet 2 inches, how many inches is the jump?
Answer:
74 inches
Step-by-step explanation:
1 foot is 12 inches, so 6 x 12 = 72, and just add the other 2 inches to get 74 inches.
Answer:
74 inches.
Step-by-step explanation:
Each foot has 12 inches, so multiply 6 by 12 to get 72 inches. Then add the remaining two inches to get a total of 74 inches.
A car and a motorcycle whose average rates are in the ratio of 4:5 travel a distance of 160 miles. If the motorcycle
travels 1/2 hour less than the car, find the average rate of each.
Answer:
Step-by-step explanation:
I always advise my students to make a table of information for these story problems because trying to keep track of the information otherwise is a nightmare. The table will look like this:
d = r * t
m
c
m is motorcycle and c is car.
First thing we are told is that the ratio of m's speed to c's speed is 5:4; that means that we can divide 5/4 to find out how many times faster m is going than c.
5/4 = 1.25 so we have a couple of values to put into the table right away, along with the fact that they are both traveling the same distance of 160 miles.
d = r * t
m 160 = 1.25r
c 160 = r
The last thing we have to fill in is the time. If m travels a half hour less than c, c is driving a half hour more than m, right? Filling that in:
d = r * t
m 160 = 1.25r * t
c 160 = r * t + .5
Now we have our 2 equations. Looking at the top row of the table gives us the formula we need to solve this problem. It tells us, in other words, what we are going to be doing with these columns of numbers. Distance equals the rate times the time. For the motorcycle, the equation is:
160 = (1.25r)t and that seems pretty useless since we still have 2 unknowns in there and you can only have 1 unknown in 1 equation. Let's see what the equation for the car is.
160 = (t + .5)r Same problem.
Let's go back to the equation for the motorcycle and since we are looking for the rates of each, let's solve that equation for time in terms of rate (solve it for t):
[tex]t=\frac{160}{1.25r}[/tex] and sub that into the car's equation in place of t:
[tex]160=r(\frac{160}{1.25r})+.5r[/tex] and simplify. The r's to the left of the plus sign cancel out leaving us with:
[tex]160=(\frac{160}{1.25})+.5r[/tex] and divide those numbers inside the parenthesis to get:
160 = 128 + .5r and subtract 128 from both sides to get:
32 = .5r and finally divide by .5 to get
r = 64 miles/hour
The car goes 64 mph and the motorcycle goes 1.25 times that so,
m = 1.25(64) and
m = 80 mph
Solve the equation −96=3(8x)^(5/3).
Answer:
x= - 1
Step-by-step explanation:
870,640 rounded to the nearest ten thousand
Answer: 870,000
Step-by-step explanation: First find the digit in the rounding place
which in this case is the 7 in the ten thousands place.
Next, we look at the digit to the right of the 7, which is 0.
According to the rules of rounding, if the digit to the right
of the rounding place is less than 5, we round down.
So the 7 in the rounding place stays the same
and all digits to the right of the become 0.
So 870,640 rounded to the nearest ten thousand is 870,000.
Juan and Lizette rented a car for one week to drive from Phoenix to Boise. The car rental rate was $250 per week and $0.20 per mile. By the most direct route, the drive is 926 miles. How much did they spend on the rental car?
( solution at pic)
Describe how the graph of y = |x - 2| - 5 is a transformation of the graph of y = |x|. Use terms such as "shifted", "reflected", "stretched", or "compressed".
Answer:
The original graph was shifted 2 units to the left and 5 units down.
Step-by-step explanation:
y = |x|
From this, we go to: y = |x - 2|.
When we want to shift a function f(x) a units to the left, we find f(x - a). So first, the graph was shifted 2 units to the left.
y = |x - 2|.
From this, we go to: y = |x - 2| - 5.
Shifting a function f(x) down b units is the same as finding f(x) - b, so the second transformation was shifting the graph 5 units down.
why no one helping me please help please please please please please
Answer:
a) A
b) C and E
c) C, D and F
d) two
e) Equal
Escreva a matriz A = (aij) do tipo 3x4 sabendo que aij = 3i – 2j.
Answer:
[tex]A = \left[\begin{array}{cccc}1&-1&-3&-5\\4&2&0&-2\\7&5&3&1\end{array}\right][/tex]
Step-by-step explanation:
A = (aij)
i representa a linha e j a coluna.
Tipo 3x4
Isto implica que a matriz tem 3 linhas e 4 colunas.
aij = 3i – 2j.
Primeira linha:
[tex]a_{1,1} = 3(1) - 2(1) = 1[/tex]
[tex]a_{1,2} = 3(1) - 2(2) = -1[/tex]
[tex]a_{1,3} = 3(1) - 2(3) = -3[/tex]
[tex]a_{1,4} = 3(1) - 2(4) = -5[/tex]
Segunda linha:
[tex]a_{2,1} = 3(2) - 2(1) = 4[/tex]
[tex]a_{2,2} = 3(2) - 2(2) = 2[/tex]
[tex]a_{2,3} = 3(2) - 2(3) = 0[/tex]
[tex]a_{2,4} = 3(2) - 2(4) = -2[/tex]
Terceira linha:
[tex]a_{3,1} = 3(3) - 2(1) = 7[/tex]
[tex]a_{3,2} = 3(3) - 2(2) = 5[/tex]
[tex]a_{3,3} = 3(3) - 2(3) = 3[/tex]
[tex]a_{3,4} = 3(3) - 2(4) = 1[/tex]
Matriz:
A matriz é dada por:
[tex]A = \left[\begin{array}{cccc}1&-1&-3&-5\\4&2&0&-2\\7&5&3&1\end{array}\right][/tex]
Jason planted and staked a tree. The stakes are 21 ft from the base of the tree. They are connected to wires that attach to the trunk at a height of 20 ft. Find the length of a wire.
14 ft
15 ft
20 ft
29 ft
Based on the height that the wires attach, and the base length of the stakes, the length of the wire is 29 ft.
How long are the wires?This can be solved with the Pythagorean theorem because the height can be treated as the height of a right-angled triangle. The base as the base of the triangle.
The length of the wire is the hypothenuse.
Length:
c² = a² + b²
c² = 21² + 20²
c² = 841
c = √841
= 29 ft
Find out more on the Pythagorean theorem at https://brainly.com/question/343682.
#SPJ1
What is this expression in simplified form?
Answer:
16 √(3)
and then the decimal form if needed is: 27.7128129211
Step-by-step explanation:
I need help with this math problem not sure what to do?
Answer:
B. 14
Step-by-step explanation:
It's asking for function f + function g. Then it wants you to use 2 as the x value. So you have:
(f+g)(x) = 2x^2 + 3x + x - 2
(f+g)(x) = 2x^2 + 4x -2
Then using 2 as x:
(f+g)(2) = 2(2^2) + 4* 2 -2
(f+g)(2) = 8 + 8 - 2
(f+g)(2) = 14
Hope that helps, and let me know if I did any of that wrong.
One hundred sixty people were surveyed and asked if believed in ufos, ghosts, and bigfoot. 42 believed in ufos 45 believed in ghosts 21 believed in bigfoot 11 believed in ufos and ghosts 6 believed in ghosts and bigfoot 4 believed in ufos and bigfoot 2 believed in all three how many people surveyed believed in at least one of these ?
Answer:
[tex]P(A\cup B \cup C)=89[/tex]
Step-by-step explanation:
From the question we are told that:
Believed in UFO's [tex]A=42[/tex]
Believed in Ghosts [tex]B=45[/tex]
Believed in Bigfoot [tex]C=21[/tex]
Believed in UFO's & Ghosts [tex]A&B=11[/tex]
Believed in Ghosts & Bigfoot [tex]B&C=6[/tex]
Believed in UFO's & Bigfoot [tex]A&B=4[/tex]
Believed in ALL [tex]A&B&C=2[/tex]
Generally with a well detailed Set diagram of the Number of People that that believed in at least one of them is mathematically given by
[tex]P(A\cup B \cup C)=n(A\cap C)-n(B\cap C) +n(A\cap B \cap C)[/tex]
[tex]P(A\cup B \cup C)=42+45+21-11-6-4+2[/tex]
[tex]P(A\cup B \cup C)=89[/tex]
Consignment Sale. Just Between Friends is the leading pop-up consignment sales event franchise in North America. The Des Moines event for Just Between Friends takes place each year at the Iowa State Fairgrounds for one week in the spring and one week in the fall. Families can earn money on gently used baby clothes, baby gear, maternity items, kids' clothes, shoes, toys, and books. Families sign-up as consignors and then price and tag their own items. At the end of the sale, consignors are given a check based on their item sales. Using historical records, the Des Moines event organizers advertise that their consignor check amounts follow a bell-shaped distribution (symmetric and unimodal) with a mean of $480 and a standard deviation of $110. Use the Empirical Rule: What percentage of consignors receive a check for more than $370
Answer:
Just Between Friends
The percentage of consignors who receive a check for more than $370 is:
= 16%.
Step-by-step explanation:
Mean of consignor check, μ = $480
Standard deviation, σ = $110
Value of check received, x > $370
Solution: find the z-score to determine the percentage of consignors who receive a check for more than $370:
z = (x-μ)/σ
z= ($370 - $480)/$110
z = -$110/$110
z = -1.00
Percentage of consignors who receive a check for more than $370
= 0.15866
= 0.16
= 16%
Assigned Media
Use integers to represent the values in the following statement.
Jon Applebee deposited $619 in his savings account. He later withdrew $230.
The integer that represents the amount Jon Applebee deposited is
Answer:
Jon Applebe withdrew 37.15% of the amount he initially deposited.
Step-by-step explanation:
Given that Jon Applebee deposited $ 619 in his savings account, and I have later withdrew $ 230, to determine the integer that represents the amount Jon Applebee deposited the following calculation must be performed:
619 = 100
230 = X
230 x 100/619 = X
23,000 / 619 = X
37.15 = X
Therefore, Jon Applebe withdrew 37.15% of the amount he initially deposited.
Question 1 of 10
The triangles shown below may not be congruent.
66V
100
100
00
2017
A. True
B. False
SUBMIT
Answer:
A. TRUE
Step-by-step explanation:
To determine if two triangles are congruent, we need to establish the facts that the three angles and three side lengths of one is congruent to corresponding angles and side lengths of the other triangle.
The diagram given only tells us the angle measure of the two triangles which are congruent to each other. The side length wasn't given. Therefore, the triangles may not be congruent.
What is 70% less than 55?
Answer:
100-70=30 so
55*0.3=16.5
Hope This Helps!!!
Answer:
Answer :
70% less than 55 is
16.5
find the slope of the line passing through the points (6,-7) and (3,-3) .
Answer:
y2-y1 / x2-x1
-4/3
Step-by-step explanation:
Answer:
-4/3
Step-by-step explanation:
When given two points, the slope is found by
m = (y2-y1)/(x2-x1)
= (-3- -7)/(3 -6)
= (-3+7)/(3-6)
= 4/-3
= -4/3
5. What is the value of x if the quadrilateral is a kite? B X+2 C С 13 A Xth12 D
Answer: just had this problem! X = 11
8. When someone buys a ticket for an airline flight, there is a 0.0995 probability that the person will not show up for the flight. An agent for Air America wants to book 24 people on an airplane that can seat only 22. If 24 people are booked, find the probability that not enough seats will be available. You must show your work using a calculator function to receive credit.
Answer:
0.2952
Step-by-step explanation:
Not enough seats will be available if 23 or 24 people show up.
Required probability = 24C24(0.9005)24 + 24C23(0.9005)23*0.0995 = 0.2952
NO LINKS OR ANSWERING WHAT YOU DON'T KNOW!!!
9. Suppose y varies inversely with x, and y = 49 when x = 1/7. What is the value of x when y = 7?
a. 14
b. 2
c. 1
d. 7
10. Suppose y varies inversely with x, and y = 5 when x = 3. What is the inverse variation equation that relates x and y?
a. y = 3/x
b. y = 5/x
c. y = 15/x
d. y = 15x
9514 1404 393
Answer:
9. c. 1
10. c. y = 15/x
Step-by-step explanation:
The equation for inverse variation can be written as ...
y = k/x
The value of k can be determined from given values of x and y. Multiply by x to get ...
k = xy
Solving for x, you get ...
x = k/y
___
9. k = (1/7)(49) = 7
x = k/y = 7/7
x = 1
__
10. k = (3)(5) = 15
y = 15/x
Question 1 of 10
Estimate the difference of the decimals below by rounding to the nearest
whole number. Enter your answer in the space provided.
46.327
-4.801
Answer:
Step-by-step explanation:
46.327=46 ( neaarest whole number)
-4.801=-5 (nearest whole number)
46-(-5)=46+5=51
The expansion of (x-2)(x+2) is …..
Answer:
x2-4
Step-by-step explanation:
Answer:
(x+2)(x-2)(x²-2²)(x²-4)hope it helps
stay safe healthy and happy...The foot of a ladder is placed 9 feet away from a wall. If the top of the ladder rests 13 feet up on the wall, find the length of the ladder.
4 feet
15.81 feet
8.81 feet
13 feet
Answer:
15.81 ft .
Step-by-step explanation:
This question is based on " Pythagoras Theorem " . If we imagine the given situation as a right angled triangle , then the base will be " 9ft " , and the perpendicular will be " 13 ft" . And the length of the ladder will be equal to hypontenuse of the triangle.
Using Pythagoras Theorem :-
[tex]\implies\rm h^2= p^2+b^2 \\\\\implies\rm h^2 = (9ft)^2+(13ft)^2 \\\\\implies\rm h^2 = 81 ft^2 + 169 ft^2 \\\\\implies\rm h^2 = 250ft^2 \\\\\implies \boxed{ \rm Ladder's \ Length = 15.81 \ ft }[/tex]
Hence the length of the ladder is 15.81 ft.
Omar has a gift card for $40.00 at a gift shop. Omar wants to buy a hat for himself for $13.50. For his friends, he would like to buy souvenir
bracelets, which are $3.25 each. All prices include taxes.
Which inequality can be used to solve for how many bracelets Omar can buy?
ОА.
3.25x + 13.50 S 40
OB.
3.25x + 13.50 240
Oc.
13.50x +3.25 S 40
OD.
13.50x +3.25 2 40
Answer:
A. 3.25x + 13.50 ≤ 40
The number of bracelets is x. It's a variable.
The 13.50 is a constant.
The total needs to be less than or equal to 40 because that's all the money he has.
Answer:
3.25x + 13.50 ≤ 40
Step-by-step explanation:
For this problem, you have to directly make the equation. Using the givens, it shows that he has only 40 dollars, and wants to buy only one hat for 13. 50. He wants to buy his friends braclets 3.25, but since you dont know how many friends its for, you will leave it as x.
There is only 40 dollars so you will use: ≤
The answer will be:
3.25x + 13.50 ≤ 40
Hope this helps.
The park is 18 miles east of my home. The library is 12 miles north of the park. How far is my home from the library?
35 miles
21.6 miles
8.2 miles
18.6 miles
Answer:
21.6 miles
Step-by-step explanation:
If you draw, it'll be a right triangle with legs 12 miles and 18 miles, we need to find the hypotenuse.
So,
[tex] \sqrt{ {12}^{2} + 18^{2} } [/tex]
[tex] = \sqrt{144 + 324} [/tex]
[tex] = \sqrt{468} [/tex]
[tex] = 6\sqrt{13} [/tex]
6√13 ≈ 21.6
Answered by GAUTHMATH
What is the area of a parallelogram if the length is 4+ x and it's height is x+3
Answer:
[tex]x^{2}[/tex] + 7x + 12
Step-by-step explanation:
The area of a parallelogram is A = bh, where the base is the length.
To solve this, you have to multiply 4 + x and x + 3.
(4 + x)(x + 3)
If you factor this more, it should be equal to:
[tex]x^{2}[/tex] + 3x + 4x + 12.
This simplified is equal to:
[tex]x^{2}[/tex] + 7x + 12.
