Answer:
The intersection of the two intervals = 4, 5, 6,.......+∞ = (4, +∞)
The union of the two intervals = -3, -2, -1, 0, 1, 2, 3, 4, 5,.....,+∞ = (-3, +∞)
Step-by-step explanation:
The given intervals are;
First interval = (-3, +∞)
Second interval = (4, +∞)
Using the number line, we therefore, the first interval includes, -3, -2, -1, 0, 1, 2, 3, 4, 5,.....,+∞
The second interval includes, 4, 5,.....,+∞
Which gives the intersection as 4, 5, 6,.......+∞
The union is the interval that combines the two sets of intervals which is given as follows;
The union of the two intervals = -3, -2, -1, 0, 1, 2, 3, 4, 5,.....,+∞
(Please help!) Find the horizontal asymptote of f(x)=-2x^2+3x+6/x^2+1
Answer:
[tex]\large \boxed{\sf \ \ y=-2 \ \ }[/tex]
Step-by-step explanation:
Hello,
To guess the end behaviours when x tends to [tex]\infty[/tex] you only take into account the highest terms of polynomial expressions.
So the expression will be equivalent to
[tex]\dfrac{-2x^2}{x^2}=-2[/tex]
In other words we can say
[tex]\displaystyle \lim_{x\rightarrow+\infty} \dfrac{-2x^2+3x+6}{x^2+1}=\lim_{x\rightarrow+\infty} \dfrac{-2x^2}{x^2}=-2\\\\\displaystyle \lim_{x\rightarrow-\infty} \dfrac{-2x^2+3x+6}{x^2+1}=\lim_{x\rightarrow-\infty} \dfrac{-2x^2}{x^2}=-2\\\\[/tex]
So, the correct answer is y = -2
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Find the solution of y= 4x+ 2 for x = -5.
Answer:
[tex]y=-18[/tex]
Step-by-step explanation:
[tex]y=4x+2[/tex] for [tex]x=-5[/tex]
[tex]y=4(-5)+2\\y=-20+2\\y=-18[/tex]
Answer:
y = -18
Step-by-step explanation:
y = 4x+2
Let x = -5
y = 4(-5) +2
y = -20 +2
y = -18
Wally rides his bicycle at an average speed of 13 miles per hour. How many miles will he travel in 4 1/2 hours? Please answer this quickly!
Answer:
58.5
Step-by-step explanation:
Distance = rate * time
so if it's 4.5 hours:
Distance = 13 mph* 4.5 hours
= 58.5 miles
Describe methods you can use to show a proportional relationship between two variables ,x and y. Each method, explains how you can find the unit rate and the slope.
Answer: Find answer and explanation in the attached document.
Step-by-step explanation:
Answer:
Step-by-step explanation:
Tables of value: The ratio of Y to X gives the unit rate slope.
Equation: Make a table of VALUES. The ratio of Y to X gives the unit rate and slope.
Graph: The SLOPE of the graph is also the unit rate.
If 35%discount is given on a trouser which costs #3,000.00k,how much will a buyer pay for the trouser?
Answer:
1950
Step-by-step explanation:
3000×35/100
=1050
so 3000-1050
=1950
Which expressions are equivalent to -6n+(-12)+4n−6n+(−12)+4nminus, 6, n, plus, left parenthesis, minus, 12, right parenthesis, plus, 4, n ? Choose all answers that apply: Choose all answers that apply: (Choice A) A 4(n-3) -6n4(n−3)−6n4, left parenthesis, n, minus, 3, right parenthesis, minus, 6, n (Choice B) B 2(2n-6)2(2n−6)2, left parenthesis, 2, n, minus, 6, right parenthesis (Choice C) C None of the above
Answer:
The correct option is;
Choice A 4·(n - 3) - 6·n
Step-by-step explanation:
The given expression is
Which gives;-6·n+(-12)+4·n
- 12 + 4·n-6·n = -2·n - 12 = - (2·n + 12)
The options given are Choice A and/or Choice B;
(Choice A) 4·(n - 3) - 6·n
Which can be simplified as follows;
4·(n - 3) - 6·n = 4·n - 12 - 6·n
Which gives;
4·n - 12 - 6·n = 4·n - 6·n- 12 = -2·n - 12 = -(2·n + 12)
Therefore, 4·(n - 3) - 6·n is equivalent to -6·n+(-12)+4·n
For choice B, we have;
2·(2·n - 6) which gives;
2·(2·n - 6) = 4·n - 12
Therefore, 2·(2·n - 6) is not equivalent to -6·n+(-12)+4·n
Which gives the correct option as Choice A.
4(n-3)-6n
Khan academy I got this right
If approximately 10% of people are left-handed, how many lefties would you expect in a high school graduating class of 424
Answer:
42
Step-by-step explanation:
P(left) = 0.10
Expected number of lefties among high school grads of 424
= 424 * 0.10
= 42 (to the nearest person)
Answer:
you do 20% of 424
1 0% of 424 =42.4
you could round it to 42
A circle has a radius of sqrt 37 units and is centered at (1.3, -3.5) write the equation fo the circle
Answer:
(x-1.3)^2 + (y+3.5)^2 = 37
Step-by-step explanation:
The equation of a circle is given by
(x-h)^2 + (y-k)^2 = r^2 where (h,k) is the center and r is the radius
(x-1.3)^2 + (y--3.5)^2 = (sqrt(37))^2
(x-1.3)^2 + (y+3.5)^2 = 37
what fractons time another equal a whole number
here is an example of a fraction that equals a whole number
2/2 would equal a whole number. The bottom number is 2. This means the whole is cut into two equal pieces (halves).
The top number is 2, so we are counting two-halves.
After shading two-halves, you see that the whole circle is shaded. Two-halves is equivalent to 1.
You would plot 2/2 at the same location as the whole number 1.
Which expression is equivalent to 4 square root 6 divided by 3 root 2?
Answer:
[tex]\sqrt[12]{55296}[/tex]/2
Step-by-step explanation:
[tex]\sqrt[4]{6}[/tex]/[tex]\sqrt[3]{2}[/tex]=1.2422
[tex]\sqrt[12]{27}[/tex]/2=0.66 <-- not matching with the top expression.
[tex]\sqrt[4]{24}[/tex]/2=1.11<--not matching with the top expression.
[tex]\sqrt[12]{55296}[/tex]/2=1.2422<-- matches!!
[tex]\sqrt[12]{177147}[/tex]/3=0.91<-- not matching with the top expression.
Answer:
It is C) ^12 square root 55296/2
Step-by-step explanation: I checked with my calculator.
Help ASAP! Will name brainliest!
Answer:
2 by 3
Step-by-step explanation:
please mark brainliest if it helped
The surface area of a solid is 10 square feet. The dimensions of a similar solid are
three times as great as the first. The surface area of the new solid in square feet
is...
PLEASE urgent
Answer:
90 ft²
Step-by-step explanation:
Given the sides of similar figures in the ratio a : b, then
ratio of areas = a² : b²
Here ratio of sides = 1 : 3 , thus
ratio of areas = 1² : 3² = 1 : 9
That is the surface area of the new solid is 9 times the first
SA = 9 × 10 = 90 ft²
The total surface area of the new solid in square feet is 90 square feet
Let the solid be a cube.
The surface area of a cube = 6L²
L is the length o the cube;
If the surface area of a solid is 10 square feet, then;
10 = 6L²
L² = 10/6
L = √10/6
If the dimensions of a similar solid are three times as great as the first, then;
New length Ln = 3√10/6
Total surface area of the new solid = 6Ln²
Total surface area of the new solid = 6(3√10/6)²
Total surface area of the new solid = 6(9*10/6)
Total surface area of the new solid = 6(90/6)
Total surface area of the new solid = 90 square feet
This shows that the total surface area of the new solid in square feet is 90 square feet
Learn more here: https://brainly.com/question/23756628
AB and BC form a right angle at point B. If A = (-3, -1) and B = (4, 4), what is the equation of BC?
A. x + 3y = 16
B. 2x + y = 12
C. -7x − 5y = -48
D. 7x − 5y = 48
===============================================
First we need the equation of line AB. Compute the slope through (-3,-1) and (4,4)
m = (y2-y1)/(x2-x1)
m = (4-(-1))/(4-(-3))
m = (4+1)/(4+3)
m = 5/7
This is the slope through points A and B, ie the slope of line AB.
To get the slope of line BC, we flip the fraction and change the sign.
Doing so has us go from 5/7 to -7/5. Note how 5/7 and -7/5 multiply to -1.
The slope of line BC is -7/5. Let m = -7/5.
--------
Use (x,y) = (4,4) along with m =-7/5 to find the equation of line BC
y = mx+b
4 = (-7/5)(4) + b
4 = -28/5 + b
20 = -28 + 5b ... multiply every term by 5 to clear out the fraction
20+28 = 5b
48 = 5b
5b = 48
b = 48/5
With m = -7/5 and b = 48/5, we go from y = mx+b to y = (-7/5)x+48/5
The slope intercept form for line BC is y = (-7/5)x+48/5
--------
Let's get this into standard form Ax+By = C
y = (-7/5)x+48/5
5y = -7x + 48 .... multiply everything by 5
7x+5y = 48 .... is one way to represent the equation in standard form
-7x - 5y = -48 ... your teacher has decided (for some reason) to multiply both sides by -1
Answer:
-5y-7y=-48
Step-by-step explanation:
distance between BC (4,4) C(x,y)
BC is perpendicular on AB (perpendicular line has opposite reciprocal slope)
slope of AB=y2-y1/x2-x1=4-(-1)/4-(-3)=5/7
slope of BC=-7/5
now input the value of B (4.4) and C(x,y)
y=mx+b
4=-7/5(4)+b
b=4+28/5
b=48/5
y=-7/5x+48/5
5y=-7x+48
5y+7x=48 multipy by -1
-5y-7y=-48
Please help ive been trying and i just cant get it right
what does the variable k represent in the following equation : k/2 +1/2=3
PLEASE HELP!!!
What is the interquartile range of this data set?
1,5, 27, 29, 34, 46, 48, 61, 64, 84, 96
Answer:
37
Step-by-step explanation:
Answer:
D. 37
Step-by-step explanation:
Your choice is correct!
Question 4 of 8
Consider the recursive function of an arithmetic sequence below.
f(1) = 3
f(n) = f(n − 1) + 4, for n = 2, 3, 4,...
What is the 6th term of the sequence?
19
23
27
22
Submit
Answer:
[tex]\large \boxed{\sf \ \ 23 \ \ }[/tex]
Step-by-step explanation:
Hello, please consider the following.
[tex]a_1=f(1)=3\\\\a_2=f(1)+4=3+4=7\\\\a_3=f(3)=a_2+4=7+4=11\\\\a_4=a_3+4=11+4=15\\\\a_5=a_4+4=15+4=19\\\\a_6=a_5+4=19+4=23[/tex]
So the answer is 23.
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Jacob had a six-sided number cube. Each side was labeled with one number, from 1
through 6. What is the probability that Jacob rolls a prime number?
Round to the nearest tenth.
Answer:
1 out of 6 because you have only one chance to get 4.
Step-by-step explanation:
Answer:
50% chance
Step-by-step explanation:
A prime number is a number that a natural number greater than 1 that is not a product of two smaller natural numbers. And the only prime numbers between 1 and 6 are 2,3, and 5. This is 3 numbers. So he has a chance of 3/6 =.5=50%
Two circles are drawn below. The diameter of the smaller circle is a radius of the larger circle. What is the ratio of the smaller circle's circumference to the larger circle's circumference? Give your answer in fully simplified form. It should look like "x:y", where x and y are replaced by integers. [asy] size(4cm); pair o=(0,0); pair x=(0.9,-0.4); draw(Circle(o,sqrt(0.97))); draw(Circle((o+x)/2,sqrt(0.97)/2)); dot(o); dot(x); dot(-x); draw(-x--x); [/asy] Hint(s): Read the question carefully. Does it ask about a ratio of areas? Of radii? Of diameters? Of circumferences? Which question did you answer? Which was asked?
Answer:
1 : 2
Step-by-step explanation:
The ratio is ...
small dia : large dia = 1 : 2 = small circumference : large circumference
__
Further explanation
The diameter of the small circle is the radius of the large circle. Since the large circle's diameter is twice the length of its radius, the ratio of circle diameters is ...
small : large = 1 : 2
We multiply the diameter by π to get the circumference. Multiplying both these numbers by π will give the ratio of the circumferences. In order to reduce the ratio to lowest terms we must divide by π again:
dia ratio = circumference ratio = lowest terms ratio
1 : 2 = π : 2π = 1 : 2
Answer: 1:2
Step-by-step explanation:
let [tex]p=x^{2}+6[/tex]
Which equation is equivalent to [tex](x^{2}+6)^{2}-21=4x^{2}+24[/tex] in terms of [tex]p[/tex]?
Answer:
Hello There. ☆~---~--___●♡●__~--☆ Since p = x² - 7, you can substitute/plug in p for x² - 7
So:
(x² - 7)² - 4x² + 28 = 5
(p)² - 4x² + 28 = 5 You can factor out -4 from (-4x² + 28)
p² - 4(x² - 7) = 5 Plug in p
p² - 4p = 5 Subtract 5
p² - 4p - 5 = 0 And, your correct answer is C.
Hope It Helps!~
ItsNobody~ ☆
Find the ordered pair $(s,t)$ that satisfieFor a certain value of $k,$ the system \begin{align*} 3a + 4b &= 7,\\ 6a + 4b &= k- 4b \end{align*}has infinitely many solutions $(a,b).$ What is $k$?s the system \begin{align*} \dfrac{s}{2} + 5t &= 3,\\ 3t - 6s &= 9. \end{align*}
Answer:
Step-by-step explanation:
HELP PLEASE!! I don't get it!!!!!!
Answer:
294.5 m²
Step-by-step explanation:
portion of circle is 360 - 130 = 230
πr²*x/360 = π(11.1)²*230/360 = 247.3
then add the non-right triangle area, 1/2ab sinC
1/2(11.1)(11.1) sin 130 = 47.2
247.3 + 47.2 = 294.5 m²
 Shelby baked 48 cookies with 6 scoops of flower. how many scoops of flour does Shelby need in order to bake 64 cookies? Solve using unit rates.
Answer:
8 scoops of flour
Step-by-step explanation:
It asks for you to solve using unit rates so we need to find out the rate of how much flour you need to bake a single cookie since the question is about how many scoops of flour Shelby needs to bake 64 cookies.
So first, do 6/48, which is 1/8.
It takes 1/8 scoop of flour to bake one cookie.
Unit rate: 1/8 scoop of flour per cookies.
Now, we can multiply 1/8 by 64 since 64 is the number of cookies Shelby needs and 1/8 is the amount of flour for one single cookies. 1/8 * 64 = 8.
Shelby needs 8 scoops of flour to bake 64 cookies
Expand. Your answer should be a polynomial in standard form. 3x(x to the second power, -5x+6)
Answer:
3x³ - 15x² + 18x
Step-by-step explanation:
Given
3x(x² - 5x + 6) ← distribute the parenthesis by 3x
= 3x³ - 15x² + 18x ← in standard form
The angle measurements in the diagram are represented by the following expressions.
Answer:
143°Step-by-step explanation:
<A and <B are corresponding angles
< A = < B
plugging the values
[tex]7x + 24 = 3x + 92[/tex]
Move variable to L.H.S and change its sign
[tex]7x - 3x + 24 = 92[/tex]
Move constant to R.H.S and change its sign
[tex]7x - 3x = 92 - 24[/tex]
Calculate
[tex]4x = 68[/tex]
Divide both sides of the equation by 4
[tex] \frac{4x}{4} = \frac{68}{4} [/tex]
Calculate
[tex]x = 17[/tex]
Replacing value
<A = [tex]7x + 24[/tex]
[tex] = 7 \times 17 + 24[/tex]
[tex] = 119 + 24[/tex]
[tex] = 143[/tex]
hope this helps...
A certain server works four 6-hour shifts a week at a restaurant and has a base salary of $9.75/ℎ. An average server sells $1400 in a single shift. If the server makes an average of 14% tip of a bill, what is the annual gross income of the server?
Answer:
The annual gross income of the server is $52936
Step-by-step explanation:
The server works four 6-hour shift a week.
the server earns $9.75/h
An average seller sells $1400 in a single shift, and makes 14% tip of a bill.
For the 6-hour shift, the server earns
6 x $9.75 = $58.5 a shift
in a week, the total money made for the four shifts in a week will be
4 x $58.5 = $234
The server makes an average of 14% of a bill, and makes about $1400 in a single shift.
In a single shift he makes a tip of
14% of $1400 = 0.14 x $1400 = $196
in a week he makes 4 x $196 = $784
Total money the server makes in a week is
==> $234 + $784 = $1018
There are 52 weeks in a year.
The server's annual gross income will be
52 x $1018 = $52936
Find the midpoint of the segment between the points (−5,13) and (6,4)
Answer:
(0.5, 8.5)
Step-by-step explanation:
use this formula ((x1+x2/2), (y1+y2/2)) if you use desmos graphing calculator and you type this formula in, all you have to do it put in the correct numbers and you get your midpoint.
Hope this helped :)
The midpoint of the segment between the points (−5,13) and (6,4) are (0.5 and 8.5)
We have given that, the points (−5,13) and (6,4)
We have to determine the midpoints
What is the formula for the midpoint?((x1+x2/2), (y1+y2/2))
x1=-5,x2=6,y1=13 and y2=4
-5+6/2=1/2=0.5
and next is,
13+4/2=17/2=8.5
The midpoint of the segment between the points (−5,13) and (6,4) are (0.5 and 8.5)
To learn more about the midpoint visit:
https://brainly.com/question/5566419
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Identify the image of ∆XYZ for a composition of a 50° rotation and a 40° rotation, both about point Y. Plz give an explanation will give brainiest.
Answer:
Answer D
Step-by-step explanation:
Triangle XYZ is rotated by a composition of 50°+40°=90° counter-clockwise. When a geometrical figure is rotated by any degree, then its shape or size does not change. A 90 degree rotation is a rotation by one quadrant, if you think of it on a coordinate plane. This inference should show you that choice D is the correct answer.
how do i solve for this help please \sqrt(x+5) = \sqrt(x)+1
Answer:
x=4
Step-by-step explanation:
sqrt(x+5) = sqrt(x)+1
Square each side
(sqrt(x+5))^2 = (sqrt(x)+1)^2
x+5 = (sqrt(x)+1)^2
Foil
x+5 = (sqrt(x)) ^2 + sqrt(x) + sqrt(x) + 1
x+5 = x + 2 sqrt(x) + 1
Subtract x from each side
5 = 2 sqrt(x) + 1
Subtract 1 from each sdie
4 = 2 sqrt(x)
Square each side
4^2 = (2 sqrt(x))^2
16 = 4 x
Divide by 4
16/4 = 4x/4
4 =x
Check to see if it is extraneous
sqrt(4+5) = sqrt(4)+1
sqrt(9) = sqrt(4) +1
3 = 2+1
3=3
It is a valid solution
Answer:
[tex]\boxed{x=4}[/tex]
Step-by-step explanation:
[tex]\sqrt{x+5} = \sqrt{x}+1[/tex]
Take the square on both sides.
[tex]x+5=( \sqrt{x}+1)^2[/tex]
Expand brackets.
[tex]x+5=( \sqrt{x}+1) ( \sqrt{x}+1)[/tex]
[tex]x+5= \sqrt{x} ( \sqrt{x}+1) +1 ( \sqrt{x}+1)[/tex]
[tex]x+5= x+ \sqrt{x}+ \sqrt{x}+1[/tex]
[tex]x+5= x+ 2 \sqrt{x}+1[/tex]
Subtract 2√x, x, and 5 on both sides.
[tex]x- 2 \sqrt{x} -x= 1-5[/tex]
[tex]-2 \sqrt{x} = -4[/tex]
Cancel negative signs.
[tex]2\sqrt{x} = 4[/tex]
Divide both sides by 2.
[tex]\sqrt{x} =2[/tex]
Square both sides.
[tex]x=2^2[/tex]
[tex]x=4[/tex]
Check if the solution in the equation works.
[tex]\sqrt{x+5} = \sqrt{x}+1[/tex]
Let [tex]x=4[/tex]
[tex]\sqrt{4+5} = \sqrt{4}+1[/tex]
[tex]\sqrt{9} = 2+1[/tex]
[tex]3=3[/tex]
The value of x as 4 works in the equation.
A unicorn daycare center requires there to be 2 supervisors for every 18 baby unicorns. Write an equation that shows the relationship between n, the number of supervisors, and u, the number of baby unicorns.
Answer:
18x-2
Step-by-step explanation:
Answer:
u=9n
Step-by-step explanation: