The average rate of change for a function over an interval is the slope
How to explain the steps?Take for instance, we have the function to be
Function f(x)
And the interval is (a,b)
The average rate of change for the function over the interval is
Rate = (f(b) - f(a))/(b - a)
The above represents the slope
Take for instance, we have:
f(x) = x^2 [2, 4]
We have:
f(2) = 2^2 = 4
f(4) = 4^2 = 16
So, we have:
Rate = (16 - 4)/(4 - 2)
Rate = 6
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Given that y varies directly as x², find the percentage increase in y when x doubles.
Answer:400%
Step-by-step explanation: by the commutativity of multiplication we find (2x)^2=4(x^2)=4(y)
annalise makes rectangular patchworks quilts out of leftover fabric scraps. the first scrap she is using to make a quilt has a width of 2x feet and a length of 5x feet. when finished, the entire quilt will be 5 feet wider and 3 feet longer than the first scrap used. which of the following functions will give the area, f(x), of the quilt in square feet ?
The area is given by f(x) = 10x² + 31x + 15.
The function is a rectangle's area function. We know that a rectangle is a flat, four-sided shape with straight sides and right-angled interior angles. Additionally, the opposing sides are parallel and of the same length.
Rectangle Area = Length * Width
The length of fabric scrap is 5x. So, the rectangular patchwork's length will be 5x + 3.
Since the width of the fabric scrap will be 2x, the rectangular patchwork's width will be 2x + 5.
Then area = f(x) = (5x + 3)(2x + 5) = 10x² + 25x + 6x + 15 = 10x² + 31x + 15
Therefore the area is given by f(x) = 10x² + 31x + 15.
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Question 2
In Question 1, what do you notice about the y-coordinates before and after a horizontal stretch? What do you notice about the x-coordinates
before and after a vertical stretch?
Answer:
The y-coordinates do not change under a horizontal stretch. The x-coordinates do not change under a vertical stretch.
Step-by-step explanation:
Which of the following are solutions to the equation below?
Check all that apply.
(3x - 5)² = 19
☐A. X=
14
B. X= -√19+5
□ C. x= -√19 +5
3
□ D. X = √19 +5
3
DEX=√14
OF X= √19+
Answer:
[tex]\sf x = \dfrac{\sqrt{19}+5}{3} \ ; \ x = \dfrac{-\sqrt{19}+5}{3}[/tex]
Step-by-step explanation:
(3x - 5)² = 19
To find the solution for the equation, take square root on both sides.
[tex]\sf 3x - 5 = \± \sqrt{19}\\\\ Add \ 5 \ to \ both \ sides \\\\ 3x = \±\sqrt{19} + 5\\\\ Divide \ both \sides \ by 3\\\\ x = \dfrac{\±\sqrt{19}+5}{3}\\\\x = \dfrac{\sqrt{19}+5}{3} \ ; \ x = \dfrac{-\sqrt{19}+5}{3}[/tex]
B. 21cm 32° L 122° D 0 The perimeter of kite LODI is 74 cm. Find:
1. m/LOD=
2. mLODI =
3. Measure of LO = Why?
4.Measure of ID= Why?
1) Angles IDO and ILO are congruent, and both measure 122 degrees. So, as angles in a quadrilateral add to 360°, angle LOD measures 360-122-122-32=84°
2) As referred to in the first question, angle ODI measures 122°
3) In a kite, there are two pairs of disjoint congruent sides. This means that in this case, ID=IL=21 and LO=OD. As the perimeter is 74, this means LO=(74-21(2))/2=16
4) LI=ID, so ID=21
Aro diagram his rafting trip
The speed of Aro's paddling and speed of the river will be 1.56 miles per hour and 0.52 miles respectively.
How to calculate the speed?Aro diagrams his river rafting trip, estimating the time it will take him to paddle upstream against the current, and then back downstream with the current. His campsite destination is 5.2 miles upstream. Determine how fast Aro can paddle and how fast the river water is moving. Round to the nearest hundredth as needed. Upstream: Downstream: Let x be the speed of Aro’s paddling and let y be the speed of the river. Upstream: 1.04 = x – y Downstream: 2.08 = x + y Aro can paddle at a speed of miles per hour. The river’s speed is miles per hour.
Based on the information given, the equations will be:
x + y = 1.04
x + y = 2.08
Add both equations together. This will be:
x = 1.56
Now substitute the value of x into equation ii. This will be:
1.56 + y = 2.08
y = 2.08 - 1.56
y = 0.52
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Which number is in the solution set of the inequality -5x - 7 > 28?
Hello!
Answer:
[tex]\Large \boxed{\sf A. -7}[/tex]
Step-by-step explanation:
We have this inequality:
[tex]\sf -5x - 7 \geq 28[/tex]
Let's solve this inequality:
◼ Add 7 to both sides:
[tex]\sf -5x - 7+7 \geq 28+7[/tex]
◼ Simplify both sides:
[tex]\sf -5x \geq 35[/tex]
◼ Divide both sides by -5, so also change the sign of the inequality
[tex]\sf \dfrac{-5x}{-5} \leq \dfrac{35}{-5}[/tex]
◼ Simplify both sides:
[tex]\boxed{\sf x \leq -7}[/tex]
So the correct answer is A. -7
(a) By what least number must 27 be divided to make it perfect square
Answer:
3
Step-by-step explanation:
When you divide 27 by 3 it will give you 9 and the square root of 9 gives you a perfect answer indicating that 3 is the least number that must be divided into 27
Answer:
[tex]\fbox {3}[/tex]
Step-by-step explanation:
First, prime factorize 27 :
⇒ 27 = 3 × 3 × 3
If 27 was divided by 3, it would give 3 × 3, which would give 9, a perfect square.
The scale on a map is 1 : 25000
How many kilometres on the ground is represented by 7 cm on the map?
Answer:
175000 km
Step-by-step explanation:
the 1:25000 essentially means that every centimeter represents 25000 kilometers. so the answer is 175000 by multiplying 7 and 25000
The table to the right lists probabilities for the corresponding numbers of girls in three births. What is the random variable, what are its possible values, and are its values numerical?
The true statement is (b) the random variable is x, the possible values are 0 to 3 and the values are numerical
How to determine the true statement?The table is added as an attachment
From the attached image, we have:
Number of girls (x) P(x)
0 0.125
1 0.375
2 0.375
3 0.125
In the above, the random variable is x, while P(x) represents its probabilities.
Also, the possible values are 0 to 3 as shown in the table.
0 to 3 are numerical digits, and the values are numerical
Hence, the true statement is (b)
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Given the function f(x) = −5x2 − x + 20, find f(3).
Answer:
-28
Step-by-step explanation:
put 3 where is x
f(x) = −5(3)^2 − (3) + 20
exponents flrst
(−5*9) − (3) + 20
-45 -3 +20
-48 + 20
-28
Timothy is 13 5/6 years old. Camden is 1 1/3 years younger than Timothy and Jane is 1 1/4 years younger than Camden. How old is Jane?
Answer:
Jane is 11 1/4 years old.
Step-by-step explanation:
Subtract all of the numbers given.
[tex]13\frac{5}{6} -1\frac{1}{3} -1\frac{1}{4}[/tex].
To subtract this, we need to find a common denominator.
A common denominator in this situation is 12. To do this multiply the 5 and the 6 of 5/6 by 2. Multiply the 1 and the 3 of 1/3 by 4. And multiply the 1 and the 4 1/4 by 3.
The new expression will look like this:
[tex]13\frac{10}{12} -1\frac{4}{12} -1\frac{3}{12}[/tex].
Now we can subtract.
[tex]13\frac{10}{12} -1\frac{4}{12} -1\frac{3}{12}=11\frac{3}{12}[/tex]
Reduce the answer.
[tex]11\frac{3}{12}=11\frac{1}{4}[/tex]
In decimal form 11.25
Hope this helps!
If not, I am sorry.
9^2 times 9^-6 exponential form
The result of the expression in exponential form is 9^-4
Product of exponentsGiven the expression below
[tex]9^2 \times 9^{-6}[/tex]
According the product law, since the base are equal, we will add the exponent to have:
[tex]9^2 \times 9^{-6}=9^{-6+2}\\9^2 \times 9^{-6} = 9^{-4}[/tex]
Hence the result of the expression in exponential form is 9^-4
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System of equations
y = x² + 2x + 7
6x=y=3
state whether or not the relation is considered a function?
Answer:
A function is when each input has exactly one output
Step-by-step explanation:
Each input can only have one output, but an output can have multiple inputs.
Luis and Raul are playing Odds or Evens. Both friends flip a coin. If both coins land on heads or if both coins land on tails, then Luis wins both coins. If one coin lands on hea
No, the game is not fair because Raul has a higher probability of winning than Luis.
Yes, the game is fair because both friends have an equal probability of winning.
No, the game is not fair because Luis has a higher probability of winning than Raul.
Yes, the game is fair because the friends do not have an equal probability of winning.
Answer:
B
they both have equal probability of winning as both of them have a 50/50 chance of winning
Step-by-step explanation:
Yes, the game is fair because both friends have an equal probability of winning.
What is probability?Probability is a number that expresses the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
The game of Odds or Evens is not fair because Raul has a higher probability of winning than Luis.
In this game, the probability of both coins landing on heads or both coins landing on tails is 1/2 * 1/2 = 1/4.
Therefore, there is a 1/4 probability that Luis will win both coins.
However, there is a 1/2 probability that one coin will land on heads and the other will land on tails. In this case, Raul will win both coins because he chose "evens" and the sum of the numbers is even.
The sum of two random coin flips has an equal probability of being even or odd, so the probability of Raul winning both coins is 1/2.
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12. For which of the following quadratic equations are the roots 2 and 57
O A. x²-3x - 10=0
B. x² - 11x 10 = 0
c. x² - 7x + 10 = 0
D. x² + 7x-10=0
O
O
O
Answer: x²-59x+114=0
explanation:
If the roots are 2 and 57, then:-
sum of roots = 2+57 = 59
and, product of roots = 2×57 = 114
the quadratic equation is given by,
x²-(sum of roots)x+(product of roots)=0
so, x²-59x+114=0 will be the desired quadratic equation.
so, none of the options are correct.
the correct answer is x²-59x+114=0.
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PLS HELP
Select the correct answer.
Consider function f.
f(x) = 2x²
What is the value of (f of)(x)?
A.
B.
OC.
D.
8x4
16x4
4x4
4x²
Step-by-step explanation:
[tex]f(x) = 2 {x}^{2} [/tex]
[tex] \: [/tex]
[tex] = (f \circ f)(x)[/tex]
[tex] = f(f(x))[/tex]
[tex] = 2 {x}^{2} [/tex]
[tex] = 2 {(2 {x}^{2} )}^{2} [/tex]
[tex] = 2( {2}^{2} {x}^{2 + 2} )[/tex]
[tex] = 2(4 {x}^{4} )[/tex]
[tex] = 8 {x}^{4} [/tex]
The answer is A.
One possible integer of x for which 1/4 < k/10 < 1/3 is true?
Answer:
[tex]\fbox {x = 3}[/tex]
Step-by-step explanation:
Decimal form of the lower and higher limits :
1/4 = 0.251/3 = 0.33...Hence, the best one which lies in the middle of the limits would be 0.3.
Now, equate the middle part :
x/10 = 0.3x = 3Solve: −4b+4b≥6(−5b+7)−3(b+3)
Answer:
Inequality Form:
b ≥ 1
Interval Notation:
[1,∞)
Step-by-step explanation:
An airplane can seat up to 175 passengers. The airline has already sold 87 tickets for a flight on the airplane. Which graph represents the solution to the inequality that finds the number of tickets the airline can still sell?
The inequality x ≤ 88 represents the situation, and the line graph first represents the solution to the inequality option first is correct.
What is inequality?
It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
The missing options are in the picture, please refer to the picture.
We have:
An airplane can seat up to 175 passengers. The airline has already sold 87 tickets for a flight on the airplane.
Let's suppose the number of tickets is represented by x
Total number of passengers = 175
The inequality can be framed:
x + 87 ≤ 175
x ≤ 88
Thus, the inequality x ≤ 88 represents the situation, and the line graph first represents the solution to the inequality option first is correct.
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The summer solstice can occur on any day of the week, with each day being
equally likely. What is the probability the summer solstice will occur on a
weekday?
О А.
O B.
7
115
517
O C.
O D. 1/1/20
The probability that the summer solstice will occur on a weekday is equal to 5/7.
How to calculate the probability?Generally, there are seven days in a week and two among these days are weekends while five are weekdays. Thus, this can be represented as follows:
Total number of days = 7.Number of weekends = 2.Number of weekdays = 5.Therefore, the probability that the summer solstice will occur on a weekday is given by:
P = 5/7.
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the length of a rectangle is five times its width. If the perimeter of the rectangle is 84 in, find its length and width
Answer:
width=14 &Length = 70( can add unit behind the answer e.g.cm or mm etc..)
Step-by-step explanation:
we know that in a rectangle not all side are same compare to a square..
therefore:
1) write the formula for perimeter down
perimeter = the sum of all side
perimeter = 2x(width) + 2x(length)
P=2(w)+2(L)
2) substitute into the equation
P =2(w)+2(L)
84=2(w)+2(5*w)
3) perform opposite operation to make w become the subject of the formula inorder to find width
48=2(w)+2(5*w)
48=2w+10w
48=12w
48/12=12w/12( the twelves cancels out)
7=w or the width is 7
4) rewrite the formula and solve
P=2(w)+2(L)
P =2(7) + 2(5*7)
P = 14 + 70
P = 48
what is the answer I need this to pass
The correct answer is option A which is segment D which is closer to home.
What is a graph?A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.
From the given graph we can see that in segment D the distance between the home and the person is lesser than all the segments given in the graph.
Therefore the correct answer is option A which is segment D which is closer to home.
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Im kinda stuck i no like this type of math help please
Answer:
EAD
Step-by-step explanation:
Celo used the simple interest formula uppercase a = uppercase p (1 r t) to calculate the interest he earned on his savings last month. which equation is equivalent to the simple interest formula? uppercase p = startfraction uppercase a over 1 r t endfraction uppercase p = startfraction 1 r t over uppercase a endfraction uppercase p = uppercase a minus (1 r t) uppercase p = uppercase a (1 r t)
The equation equivalent to the simple interest formula A = P(1 + rt), that Celo used is P = A/(1 + rt). Hence, the first option is the right choice.
Equivalent equations are the equations that are transformed from one equation to another equation, but the final values they give are equal. It's just the change of the variable on which the equation is derived.
The simple interest equation that Celo used is A = P(1 + rt).
This is currently used to find the final amount A.
On isolating P to one side of the equation in the following ways:
A = P(1 + rt),
or, A/(1 + rt) = {P(1 + rt)}/(1 + rt) {Dividing both sides by (1 + rt)}.
or, A/(1 + rt) = P {Simplifying}.
or, P = A/(1 + rt) {Changing sides}.
Thus, the equation equivalent to the simple interest formula A = P(1 + rt), that Celo used is P = A/(1 + rt). Hence, the first option is the right choice.
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Write the relation as a set of ordered pairs. a. ordered pairs: {(–3, 3), (0, 0), (2, –2)} b. ordered pairs: {(3, –3), (0, 0), (–2, 2)} c. ordered pairs: {(3, –3), (0, 0), (2, d. ordered pairs: {(–2, 2), (0, 0), (3, –3)}
The relation written as a set of ordered pair is given as: : {(–2, 2), (0, 0), (3, –3)}. (Option D)
What is an ordered pair?An ordered pair is a in math is one that comprises coordinates of one point in the coordinate system where the first is the x coordinate and the other is representative of the y coordinate.
Thus the correct ordered pair is option D. See the graph attached.
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Eva has put down three rows of tiles across the width of the kitchen. Each square tile is 17.5 cm wide. Between the tiles she puts a layer of glue 4mm thick. work out the total length of the floor that Eva's three rows of tiles cover so far.
In the year 1999, the surface elevation of Lake Powell was 3893 feet above sea level. In the year 2005, the surface elevation of Lake Powell was 3425.6 feet above sea level. Interpret the rate of change in this situation.
Answer:
Rate of Change = -77.9 feet/year
My interpretation: "Is Bad."
Step-by-step explanation:
The rate of change is the number of feet that Lake Powell dropped, divided by the number of years the drop took place. We want a value with a unit of feet/year.
Year Feet
1999 3893
2005 3425.6
Change
Year = (2005 - 1999) or 6 years
Feet = (3425.6 - 3893) or -467.4 feet
Rate of Change = (-467.4 feet)/(6 years)
Rate of Change = -77.9 feet/year
=======================
FYI: Lake Powell is 22.39 feet lower today (June 23, 2022) than it was 1 year ago.
A rectangular parallelepiped has dimensions a, b and c. The volume is 100cm3. A second parallelepiped has dimensions α, β, γ, where α is 50% of a, β is 20% of b and γ is 10% of c. What is the volume of the second parallelepiped in cubic meters?
The volume of the second parallelepiped will be 1 cm³. According to the given conditions, α is 50% of a, β is 20% of b and γ is 10% of c.
What is volume?The term “volume” refers to the amount of three-dimensional space taken up by an item or a closed surface. It is denoted by V and its SI unit is in cubic cm.
Given condition;
α is 50% of a, β is 20% of b and γ is 10% of c
α = a/2
β = b/5
γ = c/10
The volume of the first parallelepiped:
V = abc
100cm³=abc
The volume of the second parallelepiped:
[tex]\rm V'= \alpha \times \beta \times \gamma \\\\ \rm V'= \frac{a}{2} \times \frac{b}{5} \times \frac{c}{10} \\\\ V' = \frac{abc}{100} \\\\ V'=\frac{100}{100} \\\\ V' = 1 cm^3[/tex]
Hence, the volume of the second parallelepiped willl be 1 cubic meter.
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