Answer:
Average rate of change of functions r, q, p, s are 5, 3, -2 and 6 respectively.
Step-by-step explanation:
The formula for average rate of change of f(x) over [a,b] is
[tex]m=\dfrac{f(b)-f(a)}{b-a}[/tex]
The given function is
[tex]r(x)=x^2+2x-5[/tex]
[tex]r(0)=(0)^2+2(0)-5=-5[/tex]
[tex]r(3)=(3)^2+2(3)-5=10[/tex]
Now,
[tex]m_1=\dfrac{r(3)-r(0)}{3-0}[/tex]
[tex]m_1=\dfrac{10-(-5)}{3}=5[/tex]
From the graph it is clear that q(0)=-4 and q(3)=5.
[tex]m_2=\dfrac{q(3)-q(0)}{3-0}[/tex]
[tex]m_2=\dfrac{5-(-4)}{3}=3[/tex]
It is given that function p has as x-intercept at (3,0) and a y-intercept at (0,6). It menas p(0)=6 and p(3)=0.
[tex]m_3=\dfrac{p(3)-p(0)}{3-0}[/tex]
[tex]m_3=\dfrac{0-6}{3}=-2[/tex]
From the given table it is clear that s(0)=-13 and s(3)=5.
[tex]m_4=\dfrac{s(3)-s(0)}{3-0}[/tex]
[tex]m_4=\dfrac{5-(-13)}{3}=6[/tex]
Therefore, the average rate of change of functions r, q, p, s are 5, 3, -2 and 6 respectively.
Find the measure of b.
Please help
Answer:
125 degrees
Step-by-step explanation:
Using a theorem, you know that angle a is half of 110. Also, in all quadrilaterals inscribed in a circle, the opposite angles are supplimentary. So then, knowing that angle a is 55 degrees, you can come to the conclusion that b is 125 degrees.
Hope this is helpful! :)
The slope of the function ƒ (x) = 8 - 2x is _____. 2 - 2 8 -8
Answer:
-2
Step-by-step explanation:
your equation is
f(x) = -2x+8
-2x
-2 is the slope
Answer:
The slope is -2
Step-by-step explanation:
Rewriting f(s) as y
y = -2x+8
This is in slope intercept form
y = mx+b where m is the slope and b is the y intercept
y = -2x+8
The slope is -2
if you apply the changes below to the quadratic parent function f(x)=x^2.which of these in the equation of the new function? shift 1 unit right ,vertically stretch by a factor of 3,reflects over x-axis
Answer:
Transformed [tex]\,\,f(x)= -3\,(x-1)^2[/tex]
Step-by-step explanation:
The process of shifting the graph of the function 1 unite to the right can be obtained by subtracting 1 to the x-coordinate in the expression of the function:
[tex]f(x)=x^2\\new\,f(x) =(x-1)^2[/tex]
The process of stretching vertically the function, would be accomplished by multiplying now the full function by "3":
[tex]new \,\,f(x)= 3\,(x-1)^2[/tex]
the reflection over the x-axis is obtained by multiplying the full function by the constant "-1":
[tex]new \,\,f(x)= -3\,(x-1)^2[/tex]
Which equation can be used to solve for m, the greater integer? m(m – 3) = 108 m(m + 3) = 108 (m + 3)(m – 3) = 108 (m – 12)(m – 9) = 108
Answer:
m(m-3)=108
Step-by-step explanation:
Complete question below:
Two positive integers are 3 units apart on a number line. Their product is 108.
Which equation can be used to solve for m, the greater integer?
m(m – 3) = 108
m(m + 3) = 108
(m + 3)(m – 3) = 108
(m – 12)(m – 9) = 108
Solution
On the number line,
Let
m= larger integer
The integers are 3 numbers apart on the number line, so
m-3=smaller integer
The product (×) of the larger and smaller integers=108
(m)*(m-3)=108
m(m-3)=108
Therefore, the equation that can be used to solve for m, the larger integer is:
m(m – 3) = 108
Answer:
its a
Step-by-step explanation:
XD
Urgent help I need it right now!!!!
Answer:
[tex]\boxed{\sf 30 \ bean \ cans}[/tex]
Step-by-step explanation:
The ratio of bean cans to corn cans is 6 : 7
Given that Corn cans = 35
Let the bean can be x
So,
The proportion for it will be:
6 : 7 = x : 35
Product of Means = Product of Extremes
7 * x = 6 * 35
7x = 210
Dividing both sides by 7
x = 30
So, 30 bean cans have to be put on the table to hold the needed ratio
Which is a diagonal through the interior of the cube? Side A H Side B E Side C H Side F G
Answer:
Option (A)
Step-by-step explanation:
Every cube has 8 vertices and 6 faces.
Cube shown in the picture attached,
Diagonal through interior of the given cube will be the segments joining the vertices A-H, G-B, C-F and D-E.
Therefore, from the given options diagonal of the interior of the cube will be Side AH.
Option A will be the answer.
Answer:
the awnser is A
Step-by-step explanation:
i took a quiz
If today is Sunday, then Theodore is either playing soccer or watching television. If Theodore is playing soccer (regardless of the day of the week), it means that he hasn't finished his homework or taken out the trash. If the trash is taken out, and Theodore is watching television, then he has finished his homework. Today is Sunday and the trash is taken out. Then it has to be true that:
A) His homework is finished
B) His homework isn't finished
C) This situation is impossible
D) There isn't one right answer
Answer:
His homework isn't finished.
Step-by-step explanation:
As in this sentence: "If the trash is taken out, and Theodore is watching television, then he has finished his homework.". It says that if trash is taken out, then Theodore has not finished his homework He has just taken out the trash.
Answer:b his homework isnt finished
Step-by-step explanation:
Solve for x. 60 10 20 120
Answer:
Hey there!
We have the angle is equal to half the measure of the arc of 120 degrees. (Just another rule for circles)
7x-10=0.5(120)
7x-10=60
7x=70
x=10
Hope this helps :)
Answer:
x = 10
Step-by-step explanation:
Tangent Chord Angle = 1/2 Intercepted Arc
7x-10 = 1/2 ( 120)
7x -10 = 60
Add 10 to each side
7x -10+10 = 60+10
7x = 70
Divide by 7
7x/7 = 70/7
x = 10
Please help me, im in desperate need of help for these questions
Answer:
For the first one, answer is dilation of 2
Step-by-step explanation:
you see the coordinates for triangle A'B'C' are all doubled the coordinates of triangle ABC
Banita has a piece of string that is One-tenth times 7 inches long. Which fraction is equal to the length of Banita’s string?
Answer: The length is 7/10 inches.
Step-by-step explanation:
So if is says that the string is 1/10 times 7 inches long, then it represents the length of the string.
So L = [tex]\frac{1}{10}*7[/tex]
L = 7/10
Answer:
l=7/10
Step-by-step explanation:
In rectangle ABCD the diagonals intersect each other at point O and m∠ABD=30°. Find BC if AC = 16 in....
Answer:
BC = 8
Step-by-step explanation:
16 ( sin 30 degrees ) = BC
16 (0.5)
16/2
BC = 8
Give the other person brainliest they deserve it.
Compute the value of each expression 7−17
Answer: -10
Step-by-step explanation:
7 - 17 = -10. An easy way to do this (with only two terms) is to just flip it, and do 17 - 7 = 10, then make 10 negative(-10)
Hope it helps <3
Shelley and David have a sweet tooth. Shelley spent \$2.65 for 15 sour keys and 2 chocolate bars. David bought 3 chocolate bars and 10 sour keys for \$3.35 at the same store. Find the cost of each chocolate bar and each sour key at this store. If you need 8 chocolate bars and 24 sour keys to give to friends coming to your birthday party, how much will they cost you at this store?
Answer:
Chocolate bars: $0.95 each
Sour keys: $0.05 each
Total cost for 8 chocolate bars and 24 sour keys: $8.80
Step-by-step explanation:
sour keys=x
chocolate bars=y
15x+2y=2.65
10x+3y=3.35
multiply the second equation by 1.5
15x+4.5y=5.025
2.5y=2.375
y=0.95
Chocolate bars are $0.95 each.
Now substitute the y value in one of the equations
15x+2(0.95)=2.65
15x+1.9=2.65
15x=0.75
x=0.05
Sour keys are $0.05 each.
For the second part of the question, just multiply the number of chocolate bars by the cost and same thing with the sour keys and add them.
Final answer: $8.80
2. Ravi purchased an old house for Rs. 76.5000 and
spent Rs. 115000 on its. Then he sold it at a
gain of 5%. How many
much did he get.
Answer:
Rs. 924000.
Step-by-step explanation:
Cost of house = 765000
Additional money spent on it = 115000
Total cost incurred by Ravi = 765000 + 115000 = 880000
Gain = 5% of total cost
gain in Rs = 5/100 * 880000 = Rs. 44000
Total selling price of house = total cost incurred + profit = 880000+ 44000
Total selling price of house = Rs. 924000
Thus, Ravi got Rs. 924000.
The roots of 100x2 – 20x + 1 = 0 is:
Answer:
x = 0.1Step-by-step explanation:
[tex]100x^2-20x+1=0\\\\(10x)^2-2\cdot10x\cdot1+1^2=0\\\\(10x-1)^2=0\\\\10x-1=0\\\\10x=1\\\\x=0.1[/tex]
i will give brainliest.The product of 5 and the sum of 12 and a certain number is 10. What is the number
Answer: x=-10
Step-by-step explanation:
5*(12+x)=10
Distribute
60+5x=10
Subtract(60)
5x=-50
x=-10
Hope it helps <3
Answer:
Heeyyy hope it helps
Step-by-step explanation:
Ok, so the product is the answer to a multiplication problem.
The product of 5 and the sum of a number(X) and 3 is
5(X + 3) = 12
5X + 15 = 12
5X = 12 - 15
5X = -3
X = -3/5
10. Read the following word problem, then choose which linear equation models the problem.
The length of a rectangle is six feet more than twice the width. The rectangle’s perimeter is 84 feet. Find the width and length of the rectangle.
A. 2w + 6 + w = 84
B. 2(2w + 6) + 2w = 84
C. 2(2w +6) • (2w) = 84
D. (2w + 6) • (w) = 84
Answer:
D. ( 2w+6). (w)
i tried my best
hope this is the answer
stay at home stay safe
A school wants to plant some trees in 53 rows. The Gardener bought 15019 saplings from nursery. How Many least number of saplings should he bring more so that each number of trees_?
Answer:
33
Step-by-step explanation:
15019 / 53 = 283 R20
53 − 20 = 33
He needs 33 more trees so that every row can have the same number of trees.
You have $1000 to invest in an account and need to have $2000 in one year. What interest rate would you need to have in order to have this if the amount is compounded weekly? Round your answer to the nearest percent.
Answer:
[tex]\large \boxed{\sf \ \ 70\% \ \ }[/tex]
Step-by-step explanation:
Hello,
We assume that the year is 52 weeks, and we note r the interest rate we are looking for. The rate is expressed in percent and is annually, meaning that the investment is, after the first week :
[tex]1000\cdot (1+\dfrac{r\%}{52})=1000\cdot (1+\dfrac{r}{5200})[/tex]
For the second week
[tex]1000\cdot (1+\dfrac{r}{5200})^2[/tex]
After 52 weeks
[tex]1000\cdot (1+\dfrac{r}{5200})^{52}[/tex]
and we want to be equal to 2000 so we need to solve:
[tex]1000\cdot (1+\dfrac{r}{5200})^{52}=2000\\\\\text{*** divide by 1000 both sides ***}\\\\(1+\dfrac{r}{5200})^{52}=\dfrac{2000}{1000}=2\\\\\text{*** take the ln **}\\\\52\cdot ln(1+\dfrac{r}{5200})=ln(2)\\\\\text{*** divide by 52 ***}\\\\ln(1+\dfrac{r}{5200})=\dfrac{ln(2)}{52}\\\\\text{*** take the exp ***}\\\\\displaystyle 1+\dfrac{r}{5200}=exp(\dfrac{ln(2)}{52})=2^{(\dfrac{1}{52})}=\sqrt[52]{2}\\\\r = 5200\cdot (\sqrt[52]{2}-1)=69.77875...[/tex]
Rounded to the nearest percent, the solution is 70%.
If you want to double your capital in one year with weekly compounding you need an interest rate of 70% !!
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Answer:
4%
Step-by-step explanation:
Please answer this question now in two minutes
Answer:
20
Step-by-step explanation:
use the cos or sin function to solve
Step-by-step explanation:
using 30°
we use cos
cos 30 =10√3/UU = 10√3/Cos30 =20cmusing 60
we use Sin
Sin 60=10√3/UU = 10√3/Sin60 = 20Help! Pls pls pls! Fast!
it is transformed [tex]|x|[/tex] function. moved down by and right by 1 unit,
so $y=|x-1|-1$
A bag contains two red marbles, two green ones, one lavender one, five yellows, and six orange marbles. HINT [See Example 7.] How many sets of four marbles include one of each color other than lavender?
Answer: 120
Step-by-step explanation:
Given: A bag contains two red marbles, two green ones, one lavender one, five yellows, and six orange marbles.
The total number of marbles in the bag : 2+2+1+5+6=16
Now, the number of ways of selecting sets of four marbles include one of each color other than lavender is
[tex]\( C(2,1) \times C(2,1) \times C(5,1) \times C(6,1)=2 \times 2 \times 5 \times 6\)=120[/tex] [[tex]\because\ C(n,1)=n[/tex]]
Hence, the number of sets of four marbles include one of each color other than lavender = 120
Follow the steps to solve for the variable in this two step equation 5x-10=0
Answer:
x = 2
Step-by-step explanation:
5x = 10
x = 2
Answer:
x = 2
Step-by-step explanation:
5x-10=0
Add 10 to each side
5x-10+10=0+10
5x = 10
Divide by 5
5x/5 = 10/5
x = 2
A company offering online speed reading courses claims that students who take their courses show a 5 times (500%) increase in the number of words they can read in a minute without losing comprehension. A random sample of 100 students yielded an average increase of 415% with a standard deviation of 220%. Calculate a 95% confidence interval for the average increase in number of words students can read in a minute without losing comprehension. Choose the closest answer.
Answer:
C.I = (371.88 , 458.12)
Step-by-step explanation:
Given that:
sample size n = 100
sample mean [tex]\overline x =[/tex] 415
standard deviation = 220
The objective is to calculate the 95% confidence interval for the average increase in number of words students who can read in a minute without losing comprehension.
At 95% confidence interval; level of significance ∝ = 1 - 0.95
level of significance ∝ = 0.05
[tex]z_{\alpha/2} = 0.05/2[/tex]
[tex]z_{\alpha/2} = 0.025[/tex]
The critical value at [tex]z_{\alpha/2} = 0.025[/tex] is 1.96
C.I = [tex]\overline x \pm M.O,E[/tex]
C.I = [tex]\overline x \pm z_{\alpha/2} \dfrac{\sigma }{\sqrt{n}}[/tex]
C.I = [tex]415\pm 1.96 \dfrac{220 }{\sqrt{100}}[/tex]
C.I = [tex]415\pm 1.96 *\dfrac{220 }{10}[/tex]
C.I = [tex]415\pm 1.96 *22[/tex]
C.I = [tex]415\pm 43.12[/tex]
C.I = (371.88 , 458.12)
discriminant of xsqaure - 1/2x +1/2=0
Answer:
[tex]\boxed{D = 15/8}[/tex]
Step-by-step explanation:
=> [tex]x^2-\frac{1}{2} x +\frac{1}{2} = 0[/tex]
Comparing it with the standard form of quadratic equation [tex]ax^2+bx+c = 0,[/tex] we get
a = 1, b = -1/2 and c = 1/2
Discriminant = [tex]b^2-4ac[/tex]
[tex]D = (-1/2)^3+4(1)(1/2)\\D = -1/8 + 2\\D = \frac{-1+16}{8} \\D = \frac{15}{8}[/tex]
Please help don't understand at all
(i) Note that it is given to you that 3a + 2b = 9
You are trying to find the value of 9a + 6b. Find what is multiplied to both the variable a & b. Divide:
(9a + 6b)/(3a + 2b) = 3
Next, multiply 3 to the 9 on the other side of the equation:
3 x 9 = 27
27 is the value of 9a + 6b.
(ii) Note that it is given to you that 8x + 6y = 60
You are trying to find the value of 4x + 3y. Find what is multiplied to both the variable x & y. Divide:
(8x + 6y)/(4x + 3y) = 2
Next, divide 2 from the 60 on the other side of the equation:
60/2 = 30
30 is the value of 4x + 3y.
~
Answer:
(i) 27, (ii) 30
Step-by-step explanation:
i. since 9a + 6b is 3 times 3a + 2b then the and is 3 times 9 = 27
ii. since 4x + 3y is half of 8x + 6y then 60 /2 = 30
write the sum of twice a number and eleven as an algebraic expression
Answer:
2x-11
Step-by-step explanation:
2 x X = 2x + 11
sinxcosy=1/2(sin(x+y)+cos(x-y))
True or False?
Thanks for the help!
Answer:
False
Step-by-step explanation:
To be able to answer this, we will need to make a reference to the sum and product formula.
What we have in the question is the product and we want to see if the sum correlates.
Using the sum formula, we have the value on the right hand side as;
(1/2)[sin(x+y)+sin(x-y)]
Seeing that the expression we have here is not equal to that which was given, we can conclude that the answer is false
plz help will give brainliest
Answer:
77
Step-by-step explanation:
slope equation
Determine whether the underlined number is a statistic or a parameter. Upper A sample of professors is selected and it is found that Modifying 35 % with underline own a television. Choose the correct statement below. Parameter because the value is a numerical measurement describing a characteristic of a population. Statistic because the value is a numerical measurement describing a characteristic of a population. Parameter because the value is a numerical measurement describing a characteristic of a sample. Statistic because the value is a numerical measurement describing a characteristic of a sample
Answer:
Option : Statistic because the value is a numerical measurement describing a characteristic of a sample.
Step-by-step explanation:
A sample of professors is selected and it is found that Modifying 35 % with underline own a television.
The 35% is the value that summarizes the characteristic of the sample taken from the population. Thus, the value 35% is a statistic.
While a parameter gives a value describing the characteristic of the population itself
Given: Sample proportion is (P)=[tex]35%[/tex]%.
Statistics are the constants that are computed from sample observations alone. This is a simple definition of statistics.
Answer: The correct statement is Statistic because the value is a numerical measurement describing a characteristic of a population.
Explanation: That is, statistic because the value is a numerical measurement describing the characteristic of a sample.
The remaining statements are incorrect.
As parameters are the constants of the population. They describe only the population not the sample.
Learn more: https://brainly.com/question/10211620