Answer:
B ((2.-1), (5,3), (8, 7). (11.11 )}
Step-by-step explanation:
Linear function:
The rate of change is always the same.
Item a:
x = 2 to x = 5 -> y = 1 to y = 3. Rate of change of 2/3.
x = 5 to x = 6 -> y = 3 to y = 7. Rate of change of 4.
Different rates of change, so not linear.
Item b:
We can look that for each point, when x changes by 3, y changes by 4, so the rate of change is the same and this set of points represents a linear function, and the answer is option b.
In a triangle ABC, angle BAC = 53° and angle ACB = 28°. If AB is produced to D, find angle CBD.
Angle CBD= 81°
I hope it helps you...
Answer:
81
Step-by-step explanation:
∠CBD is the exterior angle of the ΔABC.
Exterior angle property:
Exterior angle equals the sum of opposite interior angles.
∠CBD = ∠ABC + ∠ACB
= 53 + 28
= 81°
What is the length of BC? Round to the nearest tenth.
Answer:
BC ≈ 14.5 cm
Step-by-step explanation:
Using the sine ratio in the right triangle
sin65° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{BC}{AB}[/tex] = [tex]\frac{BC}{16}[/tex] ( multiply both sides by 16 )
16 × sin65° = BC , then
BC ≈ 14.5 cm ( to the nearest tenth )
Can someone explain and give an example of spurious correlation?
Answer:
A spurious correlation wrongly implies a cause and effect between two variables. For example, the number of astronauts dying in spacecraft is directly correlated to seatbelt use in cars: Use your seatbelt and save an astronaut life!
Interesting correlations are easy to find, but many will turn out to be spurious. Three examples are the skirt length theory, the Super Bowl indicator, and a suggested correlation between race and college completion rates.
Step-by-step explanation:
A basketball team received a care package and split it evenly among
5 players. If each player received 9 candy bars, how many candy bars
were in the care package?
Help please
Answer:
45
Step-by-step explanation:
9x5
In an A.P the term is -10 and the 15th term is 11 and the last term is 41. Find the sum of all terms in this progression.
This is equivalent to the fraction 1085/2
===============================================================
Explanation:
AP stands for "arithmetic progression", which is another name for "arithmetic sequence"
a1 = -10 is the first term
the 15th term happens when n = 15, so
an = a1 + d*(n-1)
a15 = -10 + d(15-1)
a15 = 14d-10
Set this equal to 11 (the stated 15th term) and solve for d
a15 = 11
14d-10 = 11
14d = 11+10
14d = 21
d = 21/14
d = 3/2
d = 1.5 is the common difference
Let's find the nth term
an = a1 + d(n-1)
an = -10 + 1.5(n-1)
an = -10 + 1.5n - 1.5
an = 1.5n - 11.5
-------------------------------
The last term is 41, so we'll replace the 'an' with that and solve for n
an = 1.5n - 11.5
41 = 1.5n - 11.5
41+11.5 = 1.5n
52.5 = 1.5n
1.5n = 52.5
n = (52.5)/(1.5)
n = 35
So the 35th term is 41.
-------------------------------
We're summing n = 35 terms from a1 = -10 to an = 41
S = sum of the first n terms of arithmetic progression
S = (n/2)*(a1 + an)
S = (35/2)*(-10+41)
S = 542.5
The 35 terms add up to 542.5 which is the final answer
As an improper fraction, this converts to 1085/2
Let f(x) = 3x − 2 and g(x) = x + 1. Find (g ∘ f)(2).
Help plsssssssssssssssss
Answer:
(g ∘ f)(2) =5
Step-by-step explanation:
f(x) = 3x − 2
g(x) = x + 1
(g ∘ f)(2).
Find f(2) = 3(2) -2 = 6-2 = 4
Then find g(4) = 4+1 = 5
△ABCis reflected to form △A′B′C′. The vertices of △ABC are A(3, 1), B(1, 5), and C(6, 9). The vertices of △A′B′C′ are A′(−1, −3), B′(−5, −1), and C′(−9, −6). Which reflection results in the transformation of △ABC to △A′B′C′? Reflection across the x-axis reflection across the y-axis reflection across y = x reflection across y=−x I NEED HELP PLS The answer choies are: A. Reflection across the x-axis B. Reflection across the y-axis C. Reflection across y = x D. Reflection across y=−x
Answer: D) reflection across y = -x
Explanation:
When we reflect over y = x, we basically swap x and y. So for instance, the point (3,1) becomes (1,3).
When reflecting over y = -x, we will do the same thing but we'll make each coordinate swap in sign from positive to negative (or vice versa). The rule for reflecting over y = -x is [tex](x,y) \to (-y,-x)[/tex]
So if we apply that rule to point A(3,1) then it becomes A ' (-1, -3).
Similarly, B(1,5) moves to B ' (-5, -1)
Finally, C(6,9) becomes C ' (-9, -6)
Divisibility rules with algebra
Answer:
D=8
Step-by-step explanation:
normal division rules
33 goes into 47 1 time
then it leaves 17D
if we divide 170 by 33, we get 5 and if we divide 179 by 33, we still get 5. So we have 17D-165. That leaves us with something that you multiply 33 with to have a 2 in the ones place so that you get a remainder of 2. (In order to get 2 in the remainder, we need a 2 in the ones place because 4-2=2. In order to get that we need to see which number multiplied with 33 would get us a number smaller than 179 but also has a 2 in the ones place. Theres only one number and thats 4. 33*4=132. So in order to get only 2 in the remainder, we need the rest to be subtracted. This means that 17D-165=134. This way we can see that D=8
How do I simplify this? With steps please :)
Answer:
[tex]{ \tt{ = \frac{ {p}^{2} + 8p + 16 }{ {p}^{2} - 16 } }} \\ \\ = { \tt{ \frac{ {(x + 4)}^{2} }{(x - 4)(x + 4)} }} \\ \\ = { \tt{ \frac{(x + 4)}{(x - 4)} }}[/tex]
2. What are the last 2 digits of 1 + 2 + 3 + + 2005 2006
Let S be the sum. So you have
S = 1 + 2 + 3 + … + 2004 + 2005 + 2006
as well as
S = 2006 + 2005 + 2004 + … + 3 + 2 + 1
Then
2S = (1 + 2006) + (2 + 2005) + … + (2005 + 2) + (2006 + 1)
2S = 2007 + 2007 + … + 2007 + 2007
2S = 2006 × 2007
S = (2006 × 2007)/2
S = 2,013,021
which makes the last two digits 21.
Can someone help me with this task please? !!
Answer:
we need to get your brain thinking in this way. that you begin to understand how to do these things.
airways to say that your brain is not working that way, is not a valid excuse. we need to change that. your brain needs to get used to this way of thinking.
so, please, please, PLEASE go through the explanations below and tell me, where exactly in these explanations you stopped understanding what I was saying. so that I can better explain to you what is happening.
1. (0, -2)
2. 4
3. a geometric sequence. the common ratio is -2.0
4. the third option
5. the fourth option
Step-by-step explanation:
1. as x increases, y decreases. until, suddenly after x=0, this tendency reverses, and with increasing x also y increases. so, this is a turning point.
2. look at the line. it only starts with x>0 (it looks like x is around 1).
"input" is all the values of x the function has a defined result for (y = result values).
so, as there is no line for negative x, we can eliminate the first 2 answers.
x=0 is no valid answer either (as mentioned above, the line only starts well after x=0).
in the answer options the only x value having an y value above or below this x value is x=4.
3. look at the difference between 2 numbers next to each other in the sequence.
2.4 to -4.8
-4.8 to 9.6
and so on.
what do we need to do to get from the left to the right ?
we need to multiply by -2.
so, the relationship between "sequence item n" (an) to "sequence item n-1" (an-1) is a ratio, a multiplication factor :
an/an-1 = -2
4. it is completely simple. a function can be many things. on an x/y coordinate grid it can have gaps, it can have sharp direction changes,...
but there us one thing a function can never have : multiple different y values for one x value.
in the first graph x=2 has two different y values (-1 and -3). so, it is not clear what the result for x=2 would be. and that means, it is not a function.
in the second graph x=4 has two different y values.
in the third graph all is OK.
in the fourth graph x=-2 has two different y values.
so, only the third option is a function.
5. this function calculates the height of the thrown rock after t seconds of flight.
therefore, only the fourth answer makes sense.
If today is Tuesday, May 6, this year July 4 will fall on a _____
(A) Sunday
(B) Monday
(C) Thursday
(D) Friday
Answer:
July 4th will fall on Sunday
The date, July 4 will be Friday, the correct option is D.
What are Calendars?Calendars represent an year of 12 months, each month has 30 or 31 days, exceptionally February has 28 days.
If today is Tuesday, May 6,
Every 7th day is going to be a Tuesday .
From May 6 to July 4, the number of days is 59
Hence we divide 59 by 7. Quotient = 8 Remainder = 3
7 x 8 = 56
56 th day is Tuesday
57 th day is Wednesday
58th day vis Thursday
59th day is Friday
To know more about Calendars
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Oliver invested $970 in an account paying an interest rate of 7 1/2 % compounded continuously. Carson invested $970 in an account paying an interest rate of 7 3/8% compounded annually. To the nearest of a hundredth of a year, how much longer would it take for Carson's money to double than for Oliver's money to double?
Answer:
0.50 or about half a year longer.
Step-by-step explanation:
We can write an equation to model bot investments.
Oliver invested $970 in an account paying an interest rate of 7.5% compounded continuously.
Recall that continuous compound is given by the equation:
[tex]A = Pe^{rt}[/tex]
Where A is the amount afterwards, P is the principal amount, r is the rate, and t is the time in years.
Since the initial investment is $970 at a rate of 7.5%:
[tex]A = 970e^{0.075t}[/tex]
Carson invested $970 in an account paying an interest rate of 7.375% compounded annually.
Recall that compound interest is given by the equation:
[tex]\displaystyle A = P\left(1+\frac{r}{n}\right)^{nt}[/tex]
Where A is the amount afterwards, P is the principal amount, r is the rate, n is the number of times compounded per year, and t is the time in years.
Since the initial investment is $970 at a rate of 7.375% compounded annually:
[tex]\displaystyle A = 970\left(1+\frac{0.07375}{1}\right)^{(1)t}=970(1.07375)^t[/tex]
When Oliver's money doubles, he will have $1,940 afterwards. Hence:
[tex]1940= 970e^{0.075t}[/tex]
Solve for t:
[tex]\displaystyle 2 = e^{0.075t}[/tex]
Take the natural log of both sides:
[tex]\ln\left (2\right) = \ln\left(e^{0.075t}\right)[/tex]
Simplify:
[tex]\ln(2) = 0.075t\Rightarrow \displaystyle t = \frac{\ln(2)}{0.075}\text{ years}[/tex]
When Carson's money doubles, he will have $1,940 afterwards. Hence:
[tex]\displaystyle 1940=970(1.07375)^t[/tex]
Solve for t:
[tex]2=(1.07375)^t[/tex]
Take the natural log of both sides:
[tex]\ln(2)=\ln\left((1.07375)^t\right)[/tex]
Simplify:
[tex]\ln(2)=t\ln\left((1.07375)\right)[/tex]
Hence:
[tex]\displaystyle t = \frac{\ln(2)}{\ln(1.07375)}[/tex]
Then it will take Carson's money:
[tex]\displaystyle \Delta t = \frac{\ln(2)}{\ln(1.07375)}-\frac{\ln(2)}{0.075}=0.4991\approx 0.50[/tex]
About 0.50 or half a year longer to double than Oliver's money.
limx²-9x+20
x->4 x-4?
Answer:
-1
Step-by-step explanation:
lim x tends to 4 (x^2-9x+20)/(x-4). (x^2-9x+20)(x-4)=x-5.
So the limit is 4-5=-1
A rectangle has an area of 72 swaure units. The width of the rectangle is 9 units. The length of the rectangle is 2x + 4. What is the rectangle's length?
Answer:
8 units
Step-by-step explanation:
Area of a rectangle = Width multiplied by Length
Substitute in all the known numbers into this formula to get
72 = (9) × [tex](2x+4)[/tex]
Solve the equation for x, to find out the length
[tex]9(2x+4)=72[/tex]
[tex]2x+4=72/9[/tex]
[tex]2x+4=8[/tex]
[tex]2x=8-4[/tex]
[tex]2x=4[/tex]
[tex]x=4/2[/tex]
[tex]x=2[/tex]
Length of the rectangle = [tex](2x+4)[/tex]
[tex]2(2)+4[/tex]
[tex]4+4=8[/tex]
Solve the inequality 12(1/2 x - 1/3) > 8 - 2x
O A. x>-1
O B. x > 3
O C. X>1/2
O D. x>3/2
Answer:
[tex]D. \\x>\frac{3}{2}[/tex]
Step-by-step explanation:
12(1/2x - 1/3) > 8 - 2x
6x - 4 > 8 - 2x
6x + 2x - 4 > 8 - 2x + 2x
8x - 4 > 8
8x - 4 + 4 > 8 + 4
8x > 12
8x ÷ 8 > 12 ÷ 8
x > 1.5
I need help on this question 5=7+x/5
Answer:
-10 = x
Step-by-step explanation:
5=7+x/5
Subtract 7 from each side
5-7=7-7+x/5
-2 = x/5
Multiply each side by 5
-2 *5 = x/5 *5
-10 = x
Find the missing side lengths
Answer:
x = 11√3
y = 11
Step-by-step explanation:
Let 60 be the reference angle
sin 60 = p/h
√3/2 = x/22
or, 22√3 = 2x
or, x = (22√3)/2
so, x = 11√3
now
[tex]h^2 = p^2 + b^2\\or, 22^2 = (11\sqrt{3} )^2+y^2\\or, 484 = 363 + y^2\\or, 484-363 = y^2\\or, 121 = y^2\\or, \sqrt{121} = y\\so, y = 11[/tex]
Help Please!!!
Find volume of the sphere
Answer:
Step-by-step explanation:
Hey GurpTheDestoyer! Find the volume of the sphere. Round to the nearest whole number. Radius= 8 what is the volume? The Volume = 2,144.660585 cm3. Hope this helped! <3
If the discriminant of an equation is zero, which of the following is true of the equation?
[tex]\sf Your \: question \: is \: incomplete. \: [/tex]
______________________
[tex]\sf \: I \: believe \: this \: is \: the \: answer \: you \: wanted[/tex] ⟹
[tex]\sf If \: the \: discriminant \: of \: an \: equation \: is \: zero, \: then \\ \sf \: the \: equation \: will \: have \:\underline{ 1 \: real \: solution \: with \: real \: and \: equal \: roots}.[/tex]
[tex]\boxed{ \sf{Explanation}} [/tex]
[tex]\sf If \: discriminant \: of \: quadratic \: equation \: ax^{2} + bx + c \: \\ \sf is \: b^{2} - 4ac = 0 \: then \: it \: will \: have \\ \sf↦\underline{1 \: real \: solution \: with \: real \: and \: equal \: roots.} [/tex]
Answer:
see explanation
Step-by-step explanation:
If b² - 4ac = 0
Then the roots are real and equal
4x-2y=10
y=-2x-5
A.(-1,-3)
B.(-1,-6)
C.(3,1)
D.(-3,-1)
Answer:
D.-3,-1 for 4x-2y=10 y=2x-5
I NEED JUSTIFICATION AND WORK ON PART A AND B
Part A: The sun produces 3.9 ⋅ 1033 ergs of radiant energy per second. How many ergs of radiant energy does the sun produce in 1.55 ⋅ 107 seconds? (5 points)
Part B: Which is the more reasonable measurement of the diameter of a human hair:
1.8 ⋅ 10−2 mm or 1.8 ⋅ 102 mm? Justify your answer. (5 points)
Answer:
6.045 * 10 ^40 ergs
1.8 * 10^-2 mm
Step-by-step explanation:
3.9 ⋅ 10^33 erg per second * 1.55 * 10 ^7 seconds
3.9 * 1.55 * 10^(33+7)
6.045 * 10 ^40 ergs
Human hair is around .1 mm thick
.1 = 1 * 10 ^ -1
This is closer to 1.8 * 10^-2
1.8 *10^2 = 180 mm which is too thick This is approximately 18 cm
Answer:
6.045 * 10 ^40 ergs
1.8 * 10^-2 mm
Step-by-step explanation:
3.9 ⋅ 10^33 erg per second * 1.55 * 10 ^7 seconds
3.9 * 1.55 * 10^(33+7)
6.045 * 10 ^40 ergs
Human hair is around .1 mm thick
.1 = 1 * 10 ^ -1
This is closer to 1.8 * 10^-2
1.8 *10^2 = 180 mm which is too thick This is approximately 18 cm
Step-by-step explanation:
Can someone please just help me fill in those three boxes I’ve been struggling
If m ≠ 1 and mn - 3 = 3 - n , then what is the value of n?
A) 6/ m+1
B) 6/ m-1
C) 6/ m+n
D) 6/ m-n
[tex]n = \frac{6}{m + 1} [/tex]
Hope it helps you...
The value of n is n= 6/( m+1).
What is expression?An expression is a set of terms combined using the operations +, – , x or , /.
Given:
mn - 3 = 3 - n
mn + n = 6
n(m+ 1) =6
n= 6/( m+1)
Learn more about expression here:
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the graph of a linear function is given below
Answer:
The "zero" is where it crosses the x axis which is -2 in this graph
Step-by-step explanation:
PLEASE HELP ME! I REALLY NEED HELP
Answer:
a)
(i) 5.8 hours
(ii) 6.5 hours
(iii) 6 hours
(iv) 6 hours
b) 180 hours
Express 0.00506 in standard form
Answer:
[tex]5.06 x 10^{-3}[/tex]
Step-by-step explanation:
Move decimal 3 place to right.
Because the decimal was moved to right, the exponent is negative.
If there were 36 candies and only 12 children, how many candies would each child get?
Answer:
3 each
Step-by-step explanation:
36 / 12 = 3
.................................................
Do you remember how to solve a multistep linear equation with variables on both sides? Review with a Quick Check.
Solve:
5(a−1)−15=3(a+2)+4
Answer:
Step-by-step explanation:
5(a-1) -15 = 3(a+2) +4, distribute multiplication over subtraction and addition
5a -5 -15 = 3a +6 + 4, isolate the variable on one side
5a -3a = 6 +4 +5 +15, combine like terms
2a = 30, divide both sides by 2
a= 15
Solve the following system of equations by graphing. Label the solution and all intercepts.
4x-2y=8
y=1/2x+2
Please show me also how to graph it. Thanks a ton!
Answer:
(4,4)
y = 4
x = 4
Step-by-step explanation:
First we need to input y = 1/2x + 2 into 4x - 2y = 8.
4x - 2 (1/2x + 2) = 8 <-- Then solve
4x - 1x + -4 = 8
3x - 4 = 8
+4 +4
---------------------
3x = 12
3 3
x = 4
Now we need to use x and apply it to find y.
y = 1/2x + 2
y = 1/2(4) + 2
y = 2 + 2
y = 4
Now to graph go on the x axis (horizontal axis) and go to 4, then up 4 on the y axis.
You need to graph the point (4,4).
I hope this helps!
Answer:
see graph (4,4)
to manually graph just pick any two values for X in the first equation and calculate the corresponding Y value ... put a "dot" (a point on the graph)
do for both points , and draw al LINE between them...
repeat fore the second equation... the "solution" is where the two lines cross
Step-by-step explanation:
