Given:
[tex]f(x)=(x+2)^2[/tex]Required:
To find the first principles
Explanation:
First principle,
[tex]\lim_{h\to0}\frac{f(x+h)-f(x)}{h}[/tex][tex]=\lim_{h\to0}\frac{(x+h+2)^2-(x+2)^2}{h}[/tex][tex]=\lim_{h\to0}\frac{x^2+(h+2)^2+2x(h+2)-x^2-4-4x}{h}[/tex][tex]=\lim_{h\to0}\frac{h^2+4+4h+2xh+4x-4-4x}{h}[/tex][tex]\begin{gathered} =\lim_{h\to0}\frac{h^2+4h+2xh}{h} \\ \\ =\lim_{h\to0}\frac{h(h+4+2x)}{h} \\ \\ =\lim_{h\to0}(h+4+2x) \\ =2x+4 \end{gathered}[/tex]Final Answer:
[tex]2x+4[/tex]Select all the pairs that represent alternate interior angles.See image for instruction
Alternate means on the opposite side of the transversal, or line n
interior means inside of the parallel lines l and m
The alternate interior angles are 4 and 5
and 3 and 8
Check the boxes for both pairs
Any math tutors available to help me ? I need help
Hello!
First of all, let's write the initial temperature:
• 6am: 58ºF
In next 5 hours, the temperature rose 1ºF per hour, so:
• 7am: 59ºF
,• 8am: 60ºF
,• 9am: 61ºF
,• 10am: 62ºF
,• 11am: 63ºF
In the next 3 hours, it rose 3ºF per hour:
• 12pm: 66ºF
,• 1pm: 69ºF
,• 2pm: 72ºF
The temperature stayed steady until 6pm:
• In this part, we'll have a constant line until 6pm (it will be 72ºF in all).
In the next 4 hours, the temperature dropped 2ºF per hour:
• 7pm: 70ºF
,• 8pm: 68ºF
,• 9pm: 66ºF
,• 10pm: 64ºF
Dropped steadily until 63ºF at midnight
• 12am: 63ºF
Now, let's make the graph!
Take away 5 from p????????????????
Answer:
p - 5
Step-by-step explanation:
5 - p = p - 5
Estimate 15 5/7- 8 2/7
3. Square SQRE has coordinates S(2, 2) Q (5,2)R (5. – 1). Find the coordinates of E. I gotta turn it in tomorrow
Given:
Square SQRE has coordinates S(2, 2) Q (5,2), and R (5. – 1).
To find:
The coordinates of E.
Explanation:
Let (x, y) be the coordinates of E.
Using the midpoint formula,
[tex]p=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]As we know,
The diagonals of the square are intersected by its midpoint.
So, the Midpoint of SR and QE is the same in a given square SQRE.
[tex]\begin{gathered} Midpoint\text{ of SR = Midpoint of QE} \\ (\frac{2+5}{2},\frac{2-1}{2})=(\frac{5+x}{2},\frac{2+y}{2}) \\ (\frac{7}{2},\frac{1}{2})=(\frac{5+x}{2},\frac{2+y}{2}) \end{gathered}[/tex]Equating the coordinates we get,
[tex]\begin{gathered} \frac{7}{2}=\frac{5+x}{2} \\ 7=5+x \\ x=2 \\ \frac{1}{2}=\frac{2+y}{2} \\ 1=2+y \\ y=-1 \end{gathered}[/tex]Therefore, the coordinate of E is (2, -1).
Final answer:
The coordinate of E is (2, -1).
The measure of the supplement of an angle exceeds twice the measure of the complement of the angle by 20. Find the measure of half of the complement
The supplement is when two angles add up to 180° and complement is when two angles add up to 90°
let:
x = the angle.
180 - x = its supplement.
90 - x = its complement
then x = 2(90-x) + 20 means the measure of the supplement of an angle exceeds twice the measure of the complement of the angle by 20
Graph the equation after rewriting it in slope-intercept form. Y-3x=4
We have this equation
[tex]y-3x=4[/tex]The following is the slope intercept form
[tex]y=mx+b[/tex]add 3x on both sides of the equation
[tex]y-3x+3x=4+3x[/tex]simplify
[tex]y=4+3x[/tex]rearrange
[tex]y=3x+4[/tex]So, the above is the equation in slope-intercept form
Now, let's graph the equation
since this is a linear equation, we need to find 2 points and plot them in the chart
let's find point 1. Let's say x = 0 and replace: y = 3x+4 = 3*0 + 4 = 0 + 4 = 4
so, when x=0, then y = 4 , so our 1st point is (0,4)
now, let's suppose, y=0 , in that case, y = 3x + 4 = 0 , then 3x = -4 , so the value of x is -4/3 = -1.3333
in that case, our seconds point is (-4/3 , 0)
just to make sure, we can also plot a 3rd point, let's say we make x = 2, then y = 3*2 + 4 = 6 + 4 = 10
so, our 3rd point is (2, 10)
using the points above, we can plot something like this...
Jacob is taking part in a month long Reading challenge at his school. He can earn point for each book he reads, up to two dozen books. As shown in the graph P (b) gives the number of points Jacob earns as a function of the number of books he reads.
Observe the given graph carefully.
It is evident that 'b' is the independent variable (representing the number of books read) for the function f(b) (representing the number of points earned).
The domain of a function is the set of all values of the independent variable that lie within the function.
The graph is plotted from x=0 to x=24.
And the number of books cannot be fractional.
So it can be concluded that the domain of the function is the set of whole numbers from 0 to 24. Also, the function is also defined at the end-points. So the set will be inclusive of the end-points 0 and 24.
Therefore, the 2nd option is correct for the first blank.
The domain is a subset of all possible values of variable 'b'. So it will represent the number of books that Jacob reads.
Thus, the 1st option is the correct choice for the second blank.
Christina's purchasing a new TV. She was approved to finance the TV with zero interest. If Christina gives a one-time payment of $300 and pays $65 per month, how much has she paid in 5 months? (show work)
Given:
One time payment, p = $300
Payment per month, q = $65
Number of months paid, n = 5
The objectiv is to find the amount she paid in 5 months.
Let x be the amount she paid in 5 months. Then the the formula is,
[tex]x=p+nq[/tex]Let's substitute the values.
[tex]\begin{gathered} x=300+5(65) \\ x=300+325 \\ x=625 \end{gathered}[/tex]Hence, total amount paid in 5 months is $625.
Hello for this particular problem can I change the final results to a whole number? or it is not possible?
We are asked which of the given combinations will produce a number that is less or equal to 25.
For A we have:
[tex]A=3(8\frac{3}{4})[/tex]Let's remember that for a mixed fraction we have:
[tex]a\frac{b}{c}=a+\frac{b}{c}[/tex]Therefore, we can change the mixed fraction and we get:
[tex]A=3(8\frac{3}{4})=3(8+\frac{3}{4})[/tex]Solving the operations:
[tex]A=26.25[/tex]Since we get a number greater than 25 this is not a trail he can ride.
For B we have:
[tex]B=2(10\frac{1}{4})[/tex]Changing the mixed fraction:
[tex]B=2(10\frac{1}{4})=2(10+\frac{1}{4})[/tex]To solve the operation we will apply the distributive property:
[tex]B=20+2\times\frac{1}{4}[/tex]Now, we simplify the fraction:
[tex]B=20+2\times\frac{1}{4}=20+\frac{1}{2}[/tex]Now, we use the fact that 1/2 = 0.5:
[tex]B=20+\frac{1}{2}=20+0.5=20.5[/tex]Since we get a number that is less than 25 this is a train he can ride.
For C we have:
[tex]C=2(7\frac{1}{2})+10\frac{1}{4}[/tex]Changing the mixed fraction:
[tex]C=2(7+\frac{1}{2})+10+\frac{1}{4}[/tex]Now, we apply the distributive property:
[tex]C=14+1+10+\frac{1}{4}[/tex]Solving the operations. We use the fact that 1/4 = 0.25:
[tex]C=25+0.25=25.25[/tex]Since we get a number greater than 25 this is not a trail he can ride.
For D.
[tex]D=7\frac{1}{2}+2(8\frac{3}{4})[/tex]Now, we change the mixed fractions:
[tex]D=7+\frac{1}{2}+2(8+\frac{3}{4})[/tex]Now, we use the distributive property:
[tex]D=7+\frac{1}{2}+16+2\times\frac{3}{4}[/tex]Simplifying the fraction:
[tex]D=7+\frac{1}{2}+16+\frac{3}{2}[/tex]Now, we add the fractions, we have into account that when fractions have the same denominator we can add the numerators and use the common denominator, like this:
[tex]D=7+\frac{4}{2}+16[/tex]Simplifying the fraction we get:
[tex]D=7+2+16[/tex]Solving the operations:
[tex]D=25[/tex]Since we get 25 this is a trail that he can ride.
Draw the reflection of the figure in the x-axis. Polygon + Move - Redo 5 4 3 2 1 4 -3 -2 -29 1 5
Answer
Explanation
To draw the image of this figure, we need to first obtain the coordinates of the edge of the image of this figure.
And to do that, we need to first write the coordinates of the edges of the original figure.
When a given coordinate A (x, y) is reflected across the x-axis, the coordinates become A' (x, -y).
The coordinates of the original image include (-2, -4), (1, -3) and (3, -4)
After the reflection, we will now have
(2
8. MOVIE TICKETS Tickets to a movie cost $25 for adults and 5.50 formodents A group of friends purchased 8 tickets for $52.75 a Write a system of equations to represent the station
Tickets for adults --> $25
Tickets for formodents --> $5.50
The equations that would represent the number of adults and formodents in th group of friends:
Let x be adults
Let y be formodents
$25x+$5.50y=$52.72
x+y=8
The options are A,B,C,D can we make this quick please I am in a rush to turn this in!! thank you so much.
The function we have is:
[tex]y=-x+4[/tex]First, we need to find the rate of change of this function and then we can compare it with the rate of change of each option.
To find the rate of change, we compare the given equation with the general slope-intercept equation:
[tex]y=mx+b[/tex]Where m is the slope, also called the rate of change and b is the y-intercept.
By comparing the two equations, we find that the rate of change is:
[tex]m=-1[/tex]So now we will analyze the given options to see in which of them we find a rate of change of -1.
Option A:
In this option (and in option B) we have a table of values for x and y.
We calculate the rate of change by taking two (x,y) points from the table,
Here, we will take the first two (x,y) values and label them as follows:
[tex]\begin{gathered} x_1=-4 \\ y_1=1 \\ x_2=-2 \\ y_2=2 \end{gathered}[/tex]And we calculate the rate of change "m" using the slope formula:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \end{gathered}[/tex]Substituting the values we get:
[tex]m=\frac{2-1}{-2-(-4)}[/tex]Solving the operations:
[tex]\begin{gathered} m=\frac{1}{-2+4} \\ m=-\frac{1}{2} \end{gathered}[/tex]The rate of change if NOT -1, this option is not correct.
Option B. We do the same as in the first option.
Label the first two (x,y) values as follows:
[tex]\begin{gathered} x_1=4 \\ y_1=5 \\ x_2=8 \\ y_2=8 \end{gathered}[/tex]And use the slope formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Substituting the values:
[tex]\begin{gathered} m=\frac{8-5}{8-4} \\ m=\frac{3}{4} \end{gathered}[/tex]Again, the slope or rate of change is NOT -1, this is also not the option we are looking for,
Option C. In options, C and D we have a graph. To find the rate of change from the graph of a line, we take two points where the line passes, and find the rate of change as follows:
[tex]m=\frac{\text{change in y}}{change\text{ in x}}[/tex]For the graph in C, we will take the following red points
Drawing a triangle between the points we can find the change in y and the change in x:
[tex]\begin{gathered} \text{change in y=-1} \\ \text{change in x=1} \end{gathered}[/tex]Thus, the rate of change is:
[tex]\begin{gathered} m=-\frac{1}{1} \\ m=-1 \end{gathered}[/tex]C is the correct option.
can someone please help me solve and graph this the past few have been incorrect and this is my homework and i really need help
step 1
Solve the inequality
[tex]\begin{gathered} 3x+8\leq11 \\ 3x\leq11-8 \\ 3x\leq3 \\ x\leq1 \end{gathered}[/tex]the solution for the first inequality is the interval
(-infinite, 1]
step 2
Solve the inequality
[tex]\begin{gathered} 3x+8\text{ > 20} \\ 3x\text{ > 20-8} \\ 3x\text{ > 12} \\ x\text{ > 4} \end{gathered}[/tex]the solution for the second inequality is the interval
(4, infinite)
step 3
the general solution for the first inequality or the second inequality is
(-infinite, 1] U (4, infinite)see the attached figure to better understand the problemWally's grandmother started a college savings account for him with $3,000. What is the total amount of money in the account after 5 years if the annual simple interest rate is 3%?
ANSWER
$3,450
EXPLANATION
She started the savings account with $3,000.
The simple interest rate is 3% and the number of years is 5 years.
To find the amount of money in the account after 5 years, we have to first find the interest and then add it to the initial amount saved.
Simple Interest on an amount of money (Principal) at a rate R for a number of years T is given as:
[tex]I\text{ = }\frac{\text{P }\cdot\text{ R }\cdot\text{ T}}{100}[/tex]Therefore, the interest is:
[tex]\begin{gathered} I\text{ = }\frac{3000\cdot\text{ 5 }\cdot\text{ 3}}{100} \\ I\text{ = \$450} \end{gathered}[/tex]Therefore, the amount in the account after 5 years is:
Amount = Principal + Interest
Amount = 3000 + 450
Amoun = $3,450
That is the amount in the account.
A model of a triangular prism is shown below. Whats is the surface area of the prism?
We are asked to find the surface area of a triangular prism. To do that we must add the areas of each of the faces of the prism, that is, three rectangles and two triangles. The area of each rectangle is:
[tex]A_{\text{rectangles }}=5\operatorname{cm}\times12\operatorname{cm}+5\operatorname{cm}\times12\operatorname{cm}+5\operatorname{cm}\times12\operatorname{cm}[/tex]Solving the operations we get:
[tex]A_{\text{rectangles}}=180cm^2[/tex]Now we find the area of the triangles, knowing that the area of a triangle is the product of its base by its height over two, like this:
[tex]A_{\text{triangle}}=\frac{(base)(height)}{2}[/tex]The base is 5 cm and the height is 6cm, replacing we get:
[tex]A_{\text{triangle}}=\frac{(5\operatorname{cm})(6\operatorname{cm})}{2}=15cm^2[/tex]Now we add both areas having into account that there are two triangles, like this:
[tex]A=A_{\text{rectangle}}+2A_{\text{triangle}}[/tex]Replacing we get:
[tex]\begin{gathered} A=180+2(15) \\ A=210 \end{gathered}[/tex]therefore, the surface area is 210 square centimeters
What is the solution to 2x + 2(x – 5)=6,explainhow you solved the equation.explain with words
Answer
The solution to the equation is x = 4.
Explanation
We are told to find the solution to the equation
2x + 2(x - 5) = 6
The first step is to open the bracket by multiplying through by the number outside the bracket, that is, 2.
2x + 2x - 10 = 6
4x - 10 = 6
Add 10 to both sides to leave only 4x on the Left Hand Side.
4x - 10 + 10 = 6 + 10
4x = 16
Divide both sides by 4 to obtain the value of x.
(4x/4) = (16/4)
x = 4
Hope this Helps!!!
Larry answered 8 out of every 10 questions correctly. The test had 70 questions. How many correct answers did Larry give?---What represents the "x" or unknown in this problem?
Representation of fractional numbers
Larry's rate of succesful questions is 8/10.
Then must find how many times is divided 70 in 10 questions
70/10 = 7
if there were a 100% succesful then 70 rresulted
but the rate is 8/10 , then multiply 8x 7 = 56 succesful questions for Larry.
7(-a-3)=3(2a-6) I have the answer but I need help checking it.
SOLUTION:
Step 1:
In this question, we are meant to solve the following:
[tex]7\text{ ( - a - 3 ) = 3 ( 2a - 6 )}[/tex]Step 2:
Simplifying, we have that:
[tex]\begin{gathered} -7a\text{ - 21 = 6a - 18} \\ \end{gathered}[/tex]collecting like terms, we have that:
[tex]\begin{gathered} -21\text{ + 18 = 6 a + 7a} \\ 13\text{ a = -3} \\ \text{Divide both sides by 13, we have that:} \\ a\text{ = }\frac{-3}{13} \end{gathered}[/tex]Step 3:
To verify that:
[tex]a\text{ =}\frac{-3}{13}[/tex]is a solution, we have that:
[tex]7\text{ ( - a - 3 ) = 7 \lbrack -(}\frac{-3}{13}\text{ ) - 3 \rbrack}[/tex][tex]7\lbrack\text{ }\frac{3}{13}\text{ - 3\rbrack = 7 \lbrack }\frac{3}{13}\text{ - }\frac{39}{13}\text{ \rbrack = 7 x }\frac{-36}{13}\text{ = }\frac{-252}{13}\text{ ( Left Hand Side)}[/tex]Next,
[tex]3\text{ ( 2 a - 6 ) = 3 \lbrack{}2(}\frac{-3}{13})\text{ - 6 }\rbrack\text{ = 3 \lbrack}\frac{-6}{13}\text{ - 6\rbrack= 3\lbrack}\frac{-6}{13}\text{ - }\frac{78}{13}\rbrack[/tex][tex]=\text{ 3 \lbrack }\frac{-84}{13}\text{ \rbrack = }\frac{-252}{13}\text{ ( Right Hand Side)}[/tex]CONCLUSION:
From the solution and from the verification of the answers, we can see that the correct answer is:
[tex]a\text{ = }\frac{-\text{ 3}}{13}[/tex]I need help on this equation. It’s algebra. SAT PREP.
Answer:
r = 1.14
Explanation:
The value of a product (A) over time with an increasing rate "i" can be calculated as follows:
A = C(1+i)^t
where:
C is the value of the product at time 0;
A is the value of the product at time t;
i is the increasing rate.
If we compare the expression V=300r^t with A = C(1+i)^t. We can observe that:
r = 1+i
r = 1+0.14
r = 1.14
For the problem below, find the reference angle, to the nearest 10th (if necessary), and also the two possible quadrants in which θ could lie.tan(θ)=−3
The two possible quadrants are the second and the fourth
I need help. I think I left out a step. I need to find the volume of the rectangle prism.
Given a rectangular prism with the following dimensions:
H = Height = 26
L = Length = 20
W = Width = 12
To be able to determine its volume, we will be using the following formula:
[tex]\text{ Volume = L x W x H}[/tex]We get,
[tex]\text{ Volume = L x W x H}[/tex][tex]\text{ = 20 x 12 x 26}[/tex][tex]\text{ Volume = }6240[/tex]Therefore, the volume of the rectangular prism is 6,240.
There are 27 students in Mr. Mello's class. Find the total number of pages the students
read by the end of November.
WILL GET 100 POINTS AND BRAINLIST.
Answer:
No solution.
Step-by-step explanation:
Why I say this problem has no solution is due to the fact that the amount of pages is unclassified. This leads you to guessing how many pages there might be for each chapter of the students' individual books, and guessing would not be an effective method as it could lead you to thinking of any random number between 1 - 60 at the most. Therefore, this problem has no solution. If you have further concerns about this problem, I recommend addressing them to your teacher. Otherwise, have a great day. :)
Really need help solving this practice from my ACT prep guide It’s a trig practice
Given:
- The amplitude of the Sine Function:
[tex]A=10[/tex]- The midline:
[tex]y=4[/tex]- And the period:
[tex]Period=2[/tex]- You know that the function does not have a Phase shift.
• You need to remember that, by definition, the General Equation for a Sine Function has this form:
[tex]y=Asin\mleft(B\mleft(x+C\mright)\mright)+D[/tex]Where "A" is the amplitude, "C" is the phase shift, "D" is the vertical shift and this is the period:
[tex]Period=\frac{2\pi}{B}[/tex]Since the midline is given by the vertical shift, you can identify that, in this case:
[tex]D=4[/tex]And, knowing the period, you can set up that:
[tex]2=\frac{2\pi}{B}[/tex]Solving for "B", you get:
[tex]\begin{gathered} 2B=2\pi \\ \\ B=\frac{2\pi}{2} \\ \\ B=\pi \end{gathered}[/tex]• It is important to remember the following Transformation Rule for Functions:
When:
[tex]-f(x)[/tex]The function is reflected over the x-axis.
Therefore, knowing all the data, you can set up this equation:
[tex]f(x)=-10\sin (\pi x)+4[/tex]Hence, the answer is: First option.
May I please get help with this math problem please I have tried so many times but still could not get the right answers
We know that the sum of interior angles of a triangle equals 180, then, in this case we have the following:
[tex]90+2x+17+3x+28=180[/tex]solving for x, we get:
[tex]\begin{gathered} 90+2x+17+3x+28=180 \\ \Rightarrow135+5x=180 \\ \Rightarrow5x=180-135=45 \\ \Rightarrow x=\frac{45}{5}=9 \\ x=9 \end{gathered}[/tex]therefore, x = 9
the parent function name for y=|x|
This function is an absolute type of function
cole is studying ceramics and he was asked to submit 5 vessels from his collection to exhibit at the fair. he has 15. vessels that he thinks are show worthy. in how many ways can the vessels be chosen
Since he has 15 vessels and needs to choose 5, we can use a combination of 15 choose 5 to calculate the number of possible ways, since the order of the vessels inside the group of 5 is not important.
The formula to calculate a combination of n choose p is:
[tex]C(n,p)=\frac{n!}{p!(n-p)!}[/tex]Then, for n = 15 and p = 5, we have:
[tex]\begin{gathered} C(15,5)=\frac{15!}{5!(15-5)!}=\frac{15!}{5!10!}=\frac{15\cdot14\cdot13\cdot12\cdot11\cdot10!}{5\cdot4\cdot3\cdot2\cdot10!} \\ =\frac{15\cdot14\cdot13\cdot12\cdot11}{5\cdot4\cdot3\cdot2}=3003 \end{gathered}[/tex]So there are 3003 ways to choose the 5 vessels.
I know this is easy and i should know but im actually stumped on this one
For the given triangles:
There are 3 pairs of congruent angles
the triangles can not be proved using the congruent angles
the congruent angles used to prove the similarity of the triangles
So, the answer will be:
For the given triangle, we can not prove they are congruent.
What is the surface area of the solid that this net can form?8 mm25 mm8 mm5 mm5 mm8 mm8 mm5 mm5 mm8 mm8 mm25 mmO 730 square millimetersO 875 square millimeters0 1,000 square millimetersO 1,444 square millimeters
The solid is formed by 6 rectangles.
Calculate the area of each one and then add them to obtain the surface area (SA),
Area of a rectangle: Length x width
A1 = 8 x 5 = 40 mm2
A2= 25x5 = 125 mm2
A3 = 8 x 5= 40 mm2
A4 = 25 x 8 = 200 mm2
A5 = 25x5 = 125 mm2
A6 = 25 x 8 = 200mm2
SA = A1+A2+A3+A4+A5+A6 = 40 + 125 +40 +200 +125+ 200 = 730 mm2
If 2 dogs cross over a road and 1 dog disappear in the road how did the other dog made it
Answer:
he was quick???
Step-by-step explanation:
Mark me brainliest!