O GRAPHS AND FUNCTIONSFinding a difference quotient for a linear or quadratic function
Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given difference quotient formula
[tex]\frac{f(x+h)-f(x)}{h}[/tex]STEP 2: Write the given function f(x)
[tex]f(x)=-2x^2-4x+7[/tex]STEP 3: Get f(x+h)
[tex]\begin{gathered} f(x)=-2x^2-4x+7,\text{ we n}eed\text{ to get }f(x+h) \\ f(x+h)=-2(x+h)^2-4(x+h)+7 \\ -2(x+h)^2-4(x+h)+7=-2(x^2+2xh+h^2)-4x-4h+7 \\ \Rightarrow-2x^2-4xh-2h^2-4x-4h+7 \\ \Rightarrow-2x^2-2h^2-4xh-4x-4h+7 \end{gathered}[/tex]STEP 4: Rewrite the expression by substitution
[tex]\begin{gathered} \frac{f(x+h)-f(x)}{h}\Rightarrow\frac{-2x^2-2h^2-4xh-4x-4h+7-(-2x^2-4x+7)}{h} \\ \Rightarrow\frac{-2x^2-2h^2-4xh-4x-4h+7+2x^2+4x-7_{}}{h} \\ Re-\text{arrange the expression} \\ \frac{-2x^2+2x^2-2h^2-4xh-4x+4x-4h+7-7}{h} \\ \Rightarrow\frac{-2h^2-4xh-4h}{h} \\ \Rightarrow\frac{-h(2h)}{h}-\frac{(4x)h}{h}-\frac{h(4)}{h} \\ \Rightarrow-2h-4x-4 \end{gathered}[/tex]Hence, the result of the simplification is:
[tex]-2h-4x-4[/tex]Related Questions
this is precents
60% of 90
please leave a sloution
Answers
To calculate the 60% of 90, we need to understand what means 60% in terms of fractions. Converting a percentage into a fraction has a simple method: Dividing the percentage by 100. So 60% in fraction form is just
[tex]\frac{60}{100}=\frac{3}{5}[/tex]Now, to solve the problem, we only need to multiply our number 90 by this fraction; it gives us
[tex]90\cdot\frac{3}{5}=\frac{270}{5}=54[/tex]Thus the 60% of 90 is 54.
help me please k=12 (4k+2) ÷ 10
Answers
Answer:
The answer is 5
Step-by-step explanation:
( 4k+2 ) / 10 = x
( 4(12) + 2 ) / 10 = x
( 48 + 2 ) / 10 = x
50 / 10 = x
x = 5
( 4(12) + 2)/ 10
(48 + 2) / 10
50 / 10
5
which of the following are not an example of a rigid transformation
Answers
When we talk of rigid transformation, we refer to transformation that occurs, and the size of the shape is not affected. Of the three options, dilation is the only sort of transformation that affects the size of the object.
DILATION
What is m<1?
Please someone help me! Thank you
Answers
Answer:
108°
Step-by-step explanation:
[tex]m\angle 3=72^{\circ}[/tex] (corresponding angles)
[tex]m\angle 1=108^{\circ}[/tex] (linear pair)
Polygon BCDE ≅ polygon RSTU. Find the value of X and the value of Y
Answers
By comparing both polygons, we can tell that they are not the same polygon, since one of the sides has length 11 in one trapezoid and 12 in the other. So, this polygons are similar. We notice that the variables X and Y are part of the angles. In polygons that are similar, the measure of the homologous angles are equal. By homologous we mean angles that are located at the same place in both figures. To determine the homologous angles, we should have both figures drawn in the same orientation. To do so, we will flip the trapezoid on the left, so its orientation matches the one fromt the right. I picture of this flipping would be
From this picture, by comparing it to the other polygon, we determine that the angle EDC is homologous to the angle UTS. So, their measure should be the same. So, we get the following equation
[tex]2y\text{ - 37 = }y+2[/tex]By adding 37 on both sides and subtracting y on both sides, we get
[tex]2y\text{-y = +2 +37 = 39}[/tex]This implies that y = 39°.
By doing the same procedure, we find that the angles URS and CBE are homologous. So their measures are equal and we get the equation
[tex]51\text{ = }2x+13[/tex]Then, by subtracting 13 on both sides
[tex]2x\text{ = 51-13 = 38}[/tex]If we divide both sides by 2 we get
[tex]x=\frac{38}{2}=19[/tex]So x = 19°.
BUILD PERSEVERANCE Point
C
(
6
,
9
)
is located on the segment between point
A
(
4
,
8
)
and point B. The ratio of AC to CB is 1:3. What are the coordinates of point B?
Answers
The co ordinates of the point B is (12, 12)
Given,
The co ordinates:
Point C = (6, 9)
Point A = (4, 8)
Point B = (x, y)
AC : CB(m : n) = 1 : 3
We have to find the co ordinates of point B.
Lets use the formula to find the coordinates of point C.
C = 1 / (m + n) × (mx₂ + nx₁, my₂ + ny₁)
Where,
C = (6, 9)
m = 1
n = 3
x₁ = 4
x₂ = x
y₁ = 8
y₂ = y
So,
(6, 9) = 1 / (1 + 3) × ((1 × x) + (3 × 4), (1 × y) + (3 × 8))
(6, 9) = 1/4 × (x + 12, y + 24)
(6 × 4, 9 × 4) = (x + 12, y + 24)
(24, 36) = (x + 12, y + 24)
Lets evaluate:
x + 12 = 24 and y + 24 = 36
Solve for x,
x + 12 = 24
Add -12 to both sides
x + 12 - 12 = 24 - 12
We get,
x = 12
Now solve for y,
y + 24 = 36
Add -24 to both sides
y + 24 - 24 = 36 - 24
We get,
y = 12
That is, the co ordinates of the point B is (12, 12)
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how do you do order of operations with negitive signs
Answers
Let's use some examples where we have order of operations and also there are negative numbers and signs involved:
Let's evaluate the following:
(-4) x 5 + (-6)
So order of operations tells us to first take care of the multiplications and after that, deal with the additions or subtractions.
So the multiplication goes first here:
(-4) times 5 = - 20
Recall that a positive number times a negative number gives alwasy a negative number. So negative times positive gives the negative sign to the multiplication, and then, once the sign is taken care of, you multiply the numbers (4 x 5 = 20)
Next, we do the indicated addition
-20 + (-6) = -20 - 6 = -26
weher again we use the property that the + times the - inside the parenthesis gives a minus. ad we finalize by doing -20 - 6 = -26 (combining of two negative numbers).
Another example:
(8 + (-5)) x (-8)
So we first work on solving what is inside the first parenthesis :
8 + (-5) this is 8 - 5 (as we did before, the plus outside the parenthesis where -5 is, results in a minus sign as it multiplies the "-" that is shown ahead of 5.
So, inside this parenthesis we get: 8 - 5 = 3
Now we are left to multiply 3 times (-8)
This is a product of a positive number (3) times a negative number (-8). Again, do the rule for product of the signs (positive times negative equals negative) , ad then the product of the numbers: 3 x 8 = 24
so the answer is - 24
Another example:
(-9) x ((-10)+ 10)
We need to start by solving the operation indicated inside the parenthesis:
(-10) + 10 This is the same as: - 10 + 10 = 0
Now, whenwe use this result in the full expression, we get:
(-9) x 0 = 0 SInce any number multiplied times zero is zero.
a jewelry company loses $450 as a result of a delivery delay.The 9 owners of the company must share the loss equally. Which integer was represents the change in profit for each owner A. $-50 B. $-35 C. $5 D. $50
Answers
We know that they lots of $450.
If they want to share the loss equally, we just have to divide the amount by 9 owners.
[tex]\frac{450}{9}=50[/tex]Therefore, the loss per owner is A. $-50.Remember that losses are represented by negative numbers.
the sum of 3 and w is greater than or equal to -22.
Answers
1) Let's write the inequality and solve it
w+3≥-22 Subtracting 3 from both sides
w ≥ -22 -3
w ≥ -25
2) Now let's write the solution as an interval. Considering that the solution is a set for all values greater than or equal to -25 for w. Including the -25 (closed) up to infinite (open).
[tex]S=\lbrack-25,\infty)[/tex]7. Write the equation of the line in slope-intercept form given the following:Point (-5, -3), slope =3/5
Answers
start by writing in the form
[tex]y=mx+b[/tex]where you already have the slope and you must find b, which is the y-intercept
[tex]y=\frac{3}{5}x+b[/tex]use the point given (-5,-3) to find b
[tex]\begin{gathered} -3=\frac{3}{5}(-5)+b \\ -3=-3+b \\ -3+3=b \\ b=0 \end{gathered}[/tex]What is the answer to this question?
Answers
Answer:
C. (5, 5)
Step-by-step explanation:
To do this, you take each coordinate and perform the function that is shown in the translation.
So for (x-2, y+3),
you are going to take the x value of the coordinate you are given:
(7,2) and subtract 2, and then take the y value of (7,2) and add 3.
(7 - 2, 2 + 3)
Then solve this:
(5, 5)
Rashida was given 48 problems for homework. she has worked out 7/12 of them. how many more left unsolved
Answers
Answer:
she has left 28 unsolved problem or whatever it is
Step-by-step explanation:
48:12=4
4x7=27
Written Assignment #5
3.) Your stats test has five multiple choice questions, each having four possible answers with one correct
answer per question. If you completely guess (which you would never do), what is the probability (in
decimal form) that each of the following will happen? Show your work.
a.) get all of the questions correct
b.) get none of the questions correct
c.) get at least one of the questions incorrect
d.) get the first three questions correct and the last two incorrect
Answers
The probability of doing all questions correct is 1/3.
What is probability?Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution. The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a proposition is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.So, the probability to get all questions correct:
Probability formula: P(E) = Favourable outcomes/Total outcomes
The number of questions is 5.The options for each question are 4. Possible answers are 1.Then,
Favourable events = 1 × 5 = 5Total events = 3 × 5 = 15Now, find the probability by putting the values as follows:
P(E) = Favourable outcomes/Total outcomesP(E) = 5/15P(E) = 1/3Therefore, the probability of doing all questions correct is 1/3.
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The correct question is given below:
Your stats test has five multiple-choice questions, each having four possible answers with one correct answer per question. If you completely guess (which you would never do), what is the probability (in decimal form) that each of the following will happen? Show your work.
A) Get all of the questions correct
What ordered lair is closest to a local minimum of the function, f(x)?A. (-1, -3)B. (0, -2)C. (1, 4)D. (2, 1)
Answers
We have the following function given:
x f(y)
-2 -8
-1 -3
0 -2
1 4
2 1
3 3
And we can see that the minimum of the function is for the lowest f(y) value on this case -8
And the closest pair to this local minimum is:
A. (-1,3)
What is the perimeter of the figure shown below which is not drawn to scale
Answers
The perimeter of a figure is found adding the length of all its sides.
In this case, the perimeter is:
P = (x + 6) + (3x - 2) + (x- 3) + (x+ 2) + (x) + (x + 5)
P = (x +3x + x +x + x + x) + (6 - 2 -3 +2 + 5)
P = 8x + 8
Select all the equations for which 7 is a solution. A.) x-5=12B.) 5+x=12C.) x+12=19D.) x-5=-12
Answers
a) 7 - 5 = 12
2 = 12 This is not a solution
b) 5 + 7 = 12
12 = 12 This is a solution
c) 7 + 12 = 19
19 = 19 This is a solution
d) x - 5 = -12
7 - 5 = -12
2 = -12 This is not a solution
Solving a word problem using a system of linear equations
Answers
In order to determine the weighs of the boxes, name x as the larger box and y as the smaller one.
Then, based on the given situation, you can write the following equations:
3x + 2y = 86
8x + 4y = 209
Solve the previous system of equations as follow:
Multiply the first equation by -2 and add the result to the second equation:
(3x + 2y = 86)(-2)
-6x - 4y = -172
8x + 4y = 209
-6x - 4y = -172
2x = 37
Solve the previous equation for x by dividing by 2 both sides:
x = 37/2
x = 18.5
Next, replace the previous value of x into any of the equations of the system, for instance, into the first equation, and solve for y:
3x + 2y = 86
3(18.5) + 2y = 86
55.5 + 2y = 86
2y = 86 - 55.5
2y = 30.5
y = 30.5/2
y = 15.25
Hence, the weighs of the boxes are:
larger box = 18.5 kg
smaller box = 15.25 kg
Subjects in a marketing study were shown a movie and at the end of the movie were given a test to measure their recall. The scores are listed below. 10, 22, 97, 49, 61, 85, 35, 57, 31, 26, 27, 40, 86, 88, 28, 61, 87, 62, 92, 58, 101, 210 Construct a box-plot for the test scores. Are there any outliers?
Answers
One observation (210) given a test at the end of the movie to measure their recall is an outlier because it is above the fence above, as can be seen.
Data should first be arranged as follows in ascending order:
10, 22, 26, 27, 28, 31, 35, 40, 49, 57, 58, 61, 61, 62, 86, 86, 87, 88, 92, 97, 101, 210
There are n = 22 observations. Here n is even. Hence median is the mean of the middle two observations.
Median = (11 + 12) th observation /2 = (58 + 61)/2 = 59.5
We now divide the ordered data equally into two halves. Therefore, there are 11 observations in the lower section and 11 observations in the upper part.
The first quartile now corresponds to the median of the lower half.
Q1 = [(11 + 1)/2] the observation = 6th observation = 31
The third quartile represents the upper half part's median.
Q3 = [(11 + 1)/2] the observation = 6th observation = 87
IQR = Q3 - Q1 = 87 - 31 = 56
Lower fence = Q1 - 1.5 × IQR = 31 - 1.5 × 56 = -53
Upper fence = Q3 + 1.5 × IQR = 87 + 1.5 × 56 = 171
One observation (210) is an outlier since it is above the upper fence, as can be seen.
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Make sure to show your work when answering the question. The insurance company pays the full cost of 3,900 prescriptions claims out of 4,500 prescriptions claims submitted. What is the rate of the claims paid expressed as a percent? Round to two decimal places.
Answers
The rate of the claims paid expressed as a percent is 86.67%.
Out of the 4,500 prescription claim submissions, it has been stated that the insurance company covers 3,900 prescription claims in full.
We must determine what percentage of 4,500 is 3,900 in order to solve the presented problem.
Percent of the claims paid = 3,900 / 4,500 x 100
Percent of the claims paid = 0.8666666 × 100
Percent of the claims paid 86.66666%
Percent of the claims paid = 86.67%
As a result, 86.67% would be the rate of claims paid represented as a percentage.
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Which statement does NOT represent an expression? A (8 + x) - 7 B 4 + x = 12 C x2 = 24 D 5
Answers
Answer
The statement that does not represent an expression are 4 + x = 12 and x^2 = 24 which are option B and C respectively
Explanation:
An expression is a set of term combined using the operators +, - /
From the option given
8+ x - 7 this can be further expressed as
8 + x - 7
x + 8 - 7
x - 1
The only expression in the option are x - 1, and 5
4 + X = 12 is an equation. This is because it is a combination of two expressions that are equal to each other
x^2 = 24 is also an equation
Therefore, the statement that does not represent an expression are 4 + x = 12 and x^2 = 24 which are option B and C respectively
Solve for x 3(2^x-3)=384
Answers
Answer:
Solve for x: 3[2^(x-3) ]=384:solution:
Here,3[ 2^(x-3) ] = 384
or, 2^(x-3) = ( 384 /3 )
or, 2^(x-3) = 128
or, 2^(x-3) = 2^(7)
or, x-3 = 7 [ ∵ laws of indices ]or, x = 7+3
∴ x = 10 ans
Select the correct answer. Jessica is 5 years older than her sister Jenna. Jenna tells her sister that in 5 years, she will be as old as Jessica was 5 years ago. If Jenna’s age is x, which equation represents the situation? How many solutions does the equation have? A. x + 5 = (5 − x) − 5, which has one solution B. x + 5 = (x + 5) − 5, which has infinitely many solutions C. x + 5 = (x + 5) − 5, which has no solution D. x + 5 = (5 − x) − 5, which has infinitely many solutions E. (x + 5) + 5 = (x + 5) + 5, which has infinitely many solutions
Answers
2. Suppose you traveled from Saturn to Jupiter, and then from Jupiter to Mars. What would be the total distance in scientific notation
Answers
We have that approximately, the distance from Saturn to Jupiter is:
[tex]4.56x_{}10^8\text{ miles}[/tex]and the distance from Jupiter to Mars approximately is:
[tex]3.42x10^8\text{miles}[/tex]then, the total distance traveled would be the sum of these two quantities:
[tex](4.56x10^8)+(3.42x10^8)=7.98x10^8[/tex]therefore the total distance is 7.98x10^8 miles
how do I solve this problem?
Answers
The complete table describing the probability distribution of X is:
x | P(x)
0 0.027
1 0.189
2 0.441
3 0.343
The values of the random variable X are given and the corresponding probabilities are to be found.
The probability distribution is binomial.
That is, P(X = x) = ⁿCₓ pˣ (1-p)ⁿ⁻ˣ, where p is the probability of success of X in n trials.
So here values of x are given.
From the table, it is clear that p = 0.7
and 1-p = 0.3
Number of trials, n = maximum number of x = 3
Now consider each x.
When x = 2,
P(X = 2) = P( getting 2 tails out of 3 flips)
= P(TTH or THT or HTT)
= P(TTH) +P(THT) +P(HTT) [since each of them are independent events]
= ³C₂ p²(1-p)³⁻²
= 3 (0.7)²(0.3)
= 0.441
When x = 3,
P(X = 3) = P( getting 3 tails out of 3 flips)
= P(TTT)
= ³C₃ p³(1-p)³⁻³
= 1 (0.7)³(0.3)⁰
= 0.343
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Craig uses 5 cups of flour to make 10 cookies. How many cups of flour would Craig need to make 35 cookies?
NEED HELP!
Answers
Answer:
15
Step-by-step explanation:
5/2=2.5
35/2.5=15
Step-by-step explanation:
To make 5 batches of cookies, 10 cups of flour are required.
To make 1 batch of cookies:
10 cups ÷ 5 cups = 2 cups of flour
Ravi built a large wooden storage box. The box was in the shape of a rectangular prism, as shown below. He covered all the sides of the box with special wallpaper that cost a total of $856. How much did the wallpaper cost per square foot?
Answers
The area, A, of a rectangle with dimensions l and b is given by:
A = l times b
Therefore the total area of the two opposite and congruent rectangular sides with
the dimension 6 by 5 is:
[tex]2\times6\times5=60ft^2[/tex]The total area of the two opposite and congruent rectangular sides with
the dimension 6 by 7 is:
[tex]\begin{gathered} 2\times6\times7=84ft^2 \\ The\text{ total area of the two opposite and congruent rectangular sides with the dimension} \\ 5\text{ by 7 is:} \\ 2\times5\times7=70ft^2 \\ \\ \text{Hence the total surface area = 60+84+70=214 square ft} \\ \\ \text{Therefore the cost per square foot = }\frac{856}{214}=4dollars\text{ per square foot} \end{gathered}[/tex]The following data set represents the ACT scores for students in Mrs. Smith's collegescience class.18 32 16 2319 21 28 2922 30 19 21What is the range for the ACT scores for the class?
Answers
The range is the difference between the greatest and the smallest number, so it is 32 - 16 = 16.
water stations will be placed every 400 metets of a 5 kilometer racehow many water staions are neeedded
Answers
13 water stations will be placed every 400 meters of a 5 kilometer.
Given: Water stations will be placed ; every 400 meters
Also the total distance = 5 km = 5000 meters
Thus if a water station is supposed to be kept at every 400 meter distance then that means we can find out this distance by using unitary method
this means by using unitary method we get;
Number of water stations needed is = 5000 divided by 400
12.5 = 13 water stations would be required.
Thus 13 water stations will be placed every 400 meters of a 5 kilometer.
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Write a function rule for the table. X f(x) 3 5 9 101
Answers
Based on the data of the table, you can notice that the following function f(x):
f(x) = x + 4
represents the relation in between the values of the columns of the table.
For instance, you have:
f(3) = 3 + 4 = 7
f(4) = 4 + 4 = 8
f(5) = 5 + 4 = 9
f(6) = 6 + 4 = 10
Expressions: Tutorial
Simplify this expression:
4(126) + 76 - 10.
Type the correct answer in the box.
IM
(0) 101
0
Vo 4
X
=
A
VI
IV
T
a B
A
E 9
لا
P РФ
sin
cos tan
CSC sec cot
Answers
The simplified form of expression 4(126) + 76 - 10 is 6 (100 - 5).
What is a expressions?A mathematical expression is a sentence that contains a minimum of two numbers or variables and at least one mathematical operation. Let's learn how to write expressions.
A number is 6 more than half of another number, and that other number is called x. In a mathematical expression, this statement is represented as x/2 + 6. Complex puzzles can be solved using mathematical expressions.
We have been asked to simply the expression
4(126) + 76 - 10
= 4(60 + 66) + 66
= 4(60) + 4(66) + 66
= 4(60) + 5(66)
= 4(60) + 5( 60 + 6)
= 4(60) + 5(60) +5(6)
= 60(4+5) + 6(5)
= 60(9) + 6(5)
= 6(90 + 5)
= 6(95)
= 6 (100 - 5) simplified form
= 600 - 30
= 570
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