Given difference quotient is f(x) = -x²+2x+5.
Simplified version is (f(x + h) - f(x))/h = 1.
What is difference quotient?If f(x) = x - 5, then
f(h) = h - 5
f(x + h) = (x + h) - 5
(f(x + h) - f(x))/h = (((x + h) - 5) - (x - 5))/h
(f(x + h) - f(x))/h = (x + h - 5 - x + 5)/h
(f(x + h) - f(x))/h = h/h
(f(x + h) - f(x))/h = 1
since h ≠ 0.
The average rate of change of the function over an interval is measured by the difference quotient (in this case, an interval of length h). The instantaneous rate of change is hence the limit of the difference quotient (i.e., the derivative).
The slope of secant lines can be calculated using the difference quotient. Almost identical to a tangent line, a secant line traverses at least two points on a function.
That equation is known as a difference quotient because both the numerator and denominator are differences.
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what is the domain of h
h: The domain
-5 ≤ x ≤ 5
Find A u B. (Use the roster method to write the set.)
A = {1, 0, 1}, B = {0, 1, 7}
Answer:
{ 0, 1 , 7}
Step-by-step explanation:
A U B= {1,0,1}. {0,1,7}
={0,1,7}
es
Angela Simpson is considering the purchase of a home entertainment center. The product attributes she plans to consider and the
weights assigned to each attribute are listed in the table below.
Product Attributes
Portability
Sound projection
Warranty
Angela rated the brands as follows.
Brand A
Brand B
Brand C
0.2
0.5
0.3
Brand A
Brand B
Brand C
Sound
Portability Projection Warranty
7
8
10
5
Product
Evaluation Rating
87100
Using the consumer buying matrix, conduct a quantitative product evaluation rating for each brand. What other factors is Tammy likely
to consider when making her purchase? (Do not round intermediate calculations. Round your answers to 1 decimal place.)
9
7
Product Evaluation Rating for Brand A = 7.5
Product Evaluation Rating for Brand B = 7.4
Product Evaluation Rating for Brand C = 8.3
A product's acceptability for customers or a specific group is determined through the methodical process of product evaluation.
A visual representation of consumer behavior in terms of purchasing choices is a consumer buyer matrix. It also serves as a marketing tool for strengthening and expanding brands.
Given that :
Product Attributes -
Probability = 0.2
Sound projection = 0.5
Warranty = 0.3
Probability of Brand A = 7
Probability of Brand B = 10
Probability of Brand C = 6
Sound projection of Brand A = 8
Sound projection of Brand B = 6
Sound projection of Brand C = 10
Warranty of Brand A = 7
Warranty of Brand B = 8
Warranty of Brand C = 7
Calculation of Product Evaluation Rating :
Brand A = (7 x 0.2) + (8 x 0.5) + (7 x 0.3) = 1.4 + 4 + 2.1 = 7.5
Brand B = (10 x 0.2) + (6 x 0.5) + (8 x 0.3) = 2 + 3 + 2.4 = 7.4
Brand C = (6 x 0.2) + (10 x 0.5) + (7 x 0.3) = 1.2 + 5 + 2.1 = 8.3
Therefore,
Product Evaluation Rating for Brand A = 7.5
Product Evaluation Rating for Brand B = 7.4
Product Evaluation Rating for Brand C = 8.3
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Julian saved between $30 and $52
over the summer. His friend Daniela
saved twice as much. Let n represent
the amount of money Daniela saved.
What is the compound inequality?
The compound inequality is 60 < n < 104.
Let 'x' denote the amount of money saved by Julian.
Then x is between $30 and $52.
I.e., x>30 and x<52.
This can be written as a single inequality by combining the both.
i.e., 30 < x < 52
His friend Daniela saved twice as much as Julian.
Let 'n' denotes the amount of money Daniela saved.
Then n = 2x
We need to write the compound inequality for the money saved by Daniela.
As Daniela saved twice as much as Julian, it will be between 2 x 30 = $60 and 2 x 52 = $104
So the compound inequality is 60 < n < 104.
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4. A rocking horse has a weight limit of 60 pounds.
a. What percentage of the weight limit is 33 pounds?
b. What percentage of the weight limit is 114 pounds?
c. What weight is 95% of the limit?
Show your work
a. 55% of the maximum weight is 33 pounds.
b. 114 pounds is 190% of the weight limit.
c. 57 pounds is 95% of the maximum.
Answer to Part a:
Let c be the weight limit percentage for 33 pounds.
Then we have (60 x c)/100 = 33 pounds
This implies 3c/5 = 33
This means that 3c = 33 x 5 = 165.
This means that c = 165 / 3 = 55.
Therefore 55% of the weight limit is 33 pounds.
Answer to Part b:
Let d be the weight limit percentage for 114 pounds.
Then we have (60 x d)/100 = 114 pounds
This implies 3d/5 = 114
This means that 3d = 114 x 5 = 570.
This means that d = 570 / 3 = 190.
Therefore 190% of the weight limit is 114 pounds.
Answer to Part c:
95% of the weight limit is
= 95 x 60 /100
= 95 x 3/5
= 19 x 3
= 57
Therefore, 95% of the weight limit is 57 pounds.
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For this 10-point assignment, please describe the context of the mathematics by doing the following:
• Explain how circles are related to the Pythagorean Theorem. You may include triangles in your discussion, too.
• One city is located at (45, -123) and the other is located at (53.65, -6.7). describe how you would compute the distance between the
cities, momentarily ignoring the curvature of the Earth (what would you do if you didn't ignore the curvature?).
Circles are related to Pythagorean theorem in the sense that the equations are alike and the sides conforms to:
radius ≅ hypotenuse(x2 - x1)^2 ≅ opposite(y2 - y1)^2 ≅ adjacentThe distance between the two cities is 116.62 units (ignoring curvature)
If the curvature is not ignored then we sort for the angle subtended
How to compare circle to Pythagorean theoremThe Pythagorean theorem relates the square of hypotenuse, square of the opposite, and the square of the adjacent as follows
hypotenuse^2 = opposite^2 + adjacent^2 equation 1
Representing a circle in a coordinate axis will give it values in coordinate form. Assuming the coordinate of the center is (x1, y1) and a point in the circumference is (x2, y2). The radius of the circle, r is given as
r^2 = (x2 - x1)^2 + (y2 - y1)^2 equation 2
comparing equation 1 and 2 shows that
radius ≅ hypotenuse, (x2 - x1)^2 ≅ opposite, and (y2 - y1)^2 ≅ adjacent
How to find the between two citiessay A = (45, -123)
say B = (53.65, -6.7)
Let the distance between the two cities be d
d^2 = (53.65 - 45)^2 + (-6.7 - (-123) )^2
d^2 = 8.65^2 + 116.3^2
d = √13600.5125
d = 116.62 units (ignoring the earth curvature)
if the curvature is not ignored then we look for the angle subtends
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Write an equation of the line with the given slope and the given y-intercept. Express the answer in standard form.
[tex]slope \frac{5}{8} , y-intercept (0,\frac{1}{4} )[/tex]
Answer:
5x - 8y = -2
Step-by-step explanation:
m = 5/8, x = 0, y = 1/4
so y = mx + b
1/4 = 5/8(0) + b
b = 1/4
so y = 5/8x + 1/4
8y = 5x + 2
5x - 8y = -2
5(2y-3)=40y what is the answer to this question
Answer:
y=-2
Step-by-step explanation:
5(2y-3)=40y
10y-15=40y
-15=30y
-2 = y
y = -2
1. The height of a right triangular prism is 1 inches. Each side of the triangular base measures 10 inches, and the height of the base is 82 inches. The triangular prism is placed atop a cube whose side measures 10 inches so that one of the triangular prism's bases lies completely on one side of the cube.
What is the surface area of the solid formed?
If a right triangular prism's height is 1 inch. The produced solid has the following surface area: = 2,930.05 in².
Right triangular prism describing:A polyhedron with six vertices, nine edges, and five faces is a right triangular prism. Regular prisms have all of their triangles faces equilateral. The prism's rectangular faces will be congruent in this situation.
What is the method for determining a triangular prism's total surface area?A triangular prism's total surface area is the sum of the areas of its three lateral faces (rectangles) as well as two bases (triangles). For something like the surface area of any prism, the most generic formula is:
According to the given data:Given:
Hight = 1 inches
Base of the prism = 10 inches.
The Hight if the base = 82 inches.
Surface area = (Perimeter of the base × Length of the prism) + (2 × Base Area)
Surface area = 5(10× 10) + (0.5÷ 10 × 1) + 3(10× 82)
Surface area = 5(100) +0.05+ 3(810)
Surface area = 500 +0.05 + 2430
Surface area = 2,930.05 in²
The produced solid has a surface area of approximately = 2,930.05 in².
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7 x 7 - 2 ( 11/8 - 3/8 ) pls help me
It's 47. I used a calculator.
Keilantra has $660 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax.
She buys a new bicycle for $488.20.
She buys 2 bicycle reflectors for $11.17 each and a pair of bike gloves for $19.05.
She plans to spend some or all of the money she has left to buy new biking outfits for $37.26 each.
Write and solve an inequality which can be used to determine xx, the number of outfits Keilantra can purchase while staying within her budget.
The number of outfits she can buy is 3.
How many outfits can she buy?The The first step is to determine the total cost of all the items already bought.
Total cost = cost of new bicycle + (cost of one reflector x number of reflectors) + cost of the gloves
$488.20 + (2 x $11.17) + 19.05
$488.20 + 19.05 + $22.34 = $529.59
Now, determine the amount that is left to buy the outfits :
$660 - $529.59 = $130.41
Here are inequality signs and what they mean:
> means greater than
< means less than
≥ means greater than or equal to
≤ less than or equal to
The inequality sign that would be used is ≤
(cost of one outfit x number of outfits) ≤ amount left
$37.26x ≤ $130.41
x ≤ 130.41 / 37.26
x ≤ 3.5
x = 3
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Which expression are equivalent to 13^6 divide by (13^8)(13^-4)/13^-2
Describe the transformation from the graph off to the graph of g. PLEASE HELP!
Answer:
translation 3 units up: g(x) = f(x)+3
Step-by-step explanation:
You are given graphs of f(x) and g(x) and want to know the transformation that gives g(x) from f(x).
Transformations of graphsThe sorts of transformations of graphs that we study are translation, scaling (horizontally or vertically), and reflection about an axis.
Here, both graphs have the same shape, but one is in a different place than the other. The applicable transformation is one of translation.
TranslationThe vertex of f(x) is at (0, -1). The vertex of g(x) is at (0, 2). We note the x-value has not changed, but the y-value has had 3 added to it. (-1 +3 = 2)
g(x) = f(x) +3 . . . . . . the function f is translated 3 units upward.
Jemuel and Lemuel are asked to paint a house.Jemuel can paint the house by himself 16hrs and Lemuel can paint by himself in 12hrs .How long would it take to paint the house if they work together?
Answer:
9 and 3/5 hours or 9 hours and 36 minutes
Step-by-step explanation:
Rate x times = number of jobs
Jemuel's rate is 1 job/ 16 hours.
Lemuels's rate is 1 job/12 hours.
1/16T + 1/14T = 1 Get a common denominator of 48
3/48T + 2/48 t = 1
5/48T = 1 Multiply both sides by 48/5
(45/5)(5/48)T = 1(48/5)
t = 48/5 = 9 3/5 hours.
PLEASE HELP. STEP BY STEP NEEDED
So solutions of the linear quadratic systems are (-5,-3) and (1,3)
Given,
y = x²+5x -3 . . . . . . . . . .. ..1
y-x= 2 . . . . . .. . . . . . . . . . . 2\
From 1 and 2
y=x+2
substitute y=x+2 in 1
x+2= x²+5x -3
x²+5x -x-3-2 = 0
x²+4x -5=0
x²+5x-x -5=0
x(x+5) -1(x+5) = 0
(x+5)(x-1)=0
x= -5 and x=1
at x=-5
y=x+2=-5+2=-3
at x=1
y=x+2=1+2=3
So solutions of the linear quadratic systems are (-5,-3) and (1,3)
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A square acre of land is 5,280 square yards.
Between which two integers is the length of one side?
Between 17 and 18 yards
Between 72 and 73 yards
Between 24 and 243 yards
Between 1,320 and 1,321 yards
The two integers which the length of one side is in between are 72 yards and 73 yards
How to determine between which two integers is the length of one side?The given parameters are
Area = 5280 square yards
Shape = Square
The area of a shape is calculated using
Area = Length^2
So, we have
Length^2 = 5280 square yards
Take the square root of both sides
Length = 72.66 yards
72.66 yards is between 72 yards and 73 yards
Hence, the two integers which the length of one side is in between are 72 yards and 73 yards
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The area of the walkway and garden is represented by the expression
2x2 + 12x + 16. Write an expression in factored form that represents
the area of the walkway. Then find the area of the walkway if x is
3 meters. (Hint: Subtract the expression that represents the area of the
garden from the expression that represents the area of both before
factoring.)
The factorized form of the quadratic is 2*(x + 2)*(x + 4), and when x = 3m, the walkway area is 52 square meters.
How to factorize the area equation?
Here we know that the area is given by the expression:
2x^2 + 12x + 16
To factorize this, we need to find the roots of the quadratic equation, these are the solutions of:
2*x^2 + 12x + 16 = 0
The solutions are given by:
x = (-12 ± √(12^2 - 4*2*16))/(2*2)
x = (-12 ± 4)/4
The two solutions are:
x = (-12 + 4)/4 = -2
x = (-12 - 4)/4 = -4
Then the factored form is:
y = 2x^2 + 12x + 16 = 2*(x^2 + 6x + 8) = 2*(x + 2)*(x + 4)
Now we want to get the area if the walkway if x = 3, the total area of the walkway and the garden will be:
y = 2*(3 + 2)*(3 + 4) = 70
And the garden measures x by 2x, then if x = 3, the area of the garden is:
a = x*2x = 3*(2*3) = 18
Then the area of the walkway alone is:
70 - 18 = 52
The area of the walkway is 52 square meters.
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Two factory plants are making TV panels. Yesterday, Plant A produced 10,000 panels. Three percent of the panels from Plant A and 10% of the panels from Plant B were defective. How many panels did Plant B produce, if the overall percentage of defective panels from the two plants was 5%
If the overall percentage of the defective panels from the two plants is 5% then plant B produced 4000 panels in total.
This question can be solved by formulating the problem into the form of a linear equation having two variables. Linear equation in two variables can be represented in the form of ax+by+c=0 where a, b and c are real numbers and x, y are variables or the coefficients, and a, b ≠ 0.
Let the production from plant A be x, and according to the question x=10000.
Also, let the production from plant B be y.
Now, as 3% of products are found defective from plant A and 10% of products are found defective from plant B and overall defective products is 5%.
Thus, 0.03x+0.1y=0.05(x+y)
As x=10000 then
0.03×10000+0.1y=0.05(10000+y)
300+0.1y=500+0.05y
0.05y=200
=>y=4000
Thus, the total number of panels produced by plant B is equal to 4000.
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(b) After his first month he had more than he expected to have due to interest the bank provided. This let
Rob come up with a better expression, w^2/25 +45w+155, where w is the number of weeks. How much will he have in 1 year?
The amount he is expected to have due to interest in the bank after a year is; $2603.16
How to solve algebraic equations?We are given the equation;
w²/25 + 45w + 155
where;
w is number of weeks
Now, this equation above represents the function of the amount he is expected to have due to interest in the bank. Thus;
After 1 year, the number of weeks is 52 weeks. Thus, we now have;
A(52) = 52²/25 + 45(52) + 155
A(52) = $2603.16
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Identify the terms, coefficients, and the constants in the expression. 11q + 2
The term, coefficient and constant in the expression are 11q, 11 and 2 respectively.
What are the parts of an algebraic expression?The parts of an algebraic expression are;
TermsCoefficientsConstantsTerms: A term can be defined as a number, a variable, or the product of two or more variables or that of a product of a number and a variable.
The term is 11q
Coefficients: A coefficient is defined as an integer multiplied by the variable.
The coefficient is 11
Constants: A constant is a number that do not change.
The constant is 2
Thus, the term, coefficient and constant in the expression are 11q, 11 and 2 respectively.
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x
12
20
48
y
9
15
24
The table gives values from a linear relationship.
• Complete the table
• Write an equation that represents the relationship shown in the
table.
Select the correct answer. Julie ran a race 2 minutes faster than Teri did. If Julie ran the race in 28 minutes, which equation can be used to find the number of minutes, m, it took Teri to run the race? A.m+2=28 B.m-2=28 C.2m=28 D.1/2m=28
Answer:
Step-by-step explanation:
its A. If julie ran 2 minutes more, then your simply adding 2 minutes to whatever teri got to get 28 (what julie got).
Find the exact value of the trigonometric function of 0 from the given information.
sin 0=
4
5'
tan 00, find sec 0
The value of the trigonometric function secθ is 3/4.
Given the value of the trigonometric function sinθ is 4/5
we know that sinθ = Perpendicular (P)/Hypotenuse(h)
Therefore, sinθ = 4/5;
perpendicular (p) = 4 and
hypotenuse (h) = 5
In trigonometry, the secant function is a periodic function. The ratio of the hypotenuse's length to the base's length in a right-angled triangle is known as the secant function, or sec function. It is also written as sec x = 1 / cos x since it is the reciprocal of the cosine function.
secθ = base(b) / perpendicular(p)
Therefore, Base (b) = √(h² ₋ p²)
= √(5² ₋ 4²)
= √(25 ₋ 16)
= √9
= 3
Now, therefore secθ = base(b) / perpendicular(p)
= 3/4
Hence we get the value of secθ as 3/4.
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Ben bought a house for $78,850 and received a rebate of 15% off. He paid 6% in sales tax. How much did he save?
$525
Step-by-step explanation:
Ben bought the house for $78,850 so 78,850 divided by 0.15 equals 525. So the answer is $525.
The figure below shows parallel lines cut by a transversal:
A pair of parallel lines is shown, cut by a transversal.
Which statement is true about ∠7 and ∠8?
For the given parallel ines cut by a transversal line the correct statement is (4). ∠7 and ∠8 are supplementary because they are a pair of adjacent angles that form a straight line.
What types of angles are formed when a transversal cuts paralle lines?The intersections of two parallel lines formed by a transversal form several angles. These are referred to as transversal angles. Here are some examples of transversal angles:
Corresponding anglesAlternate Interior AnglesAlternate Exterior AnglesCo-interior AnglesAngles are said to be supplementary to each other when two adjacent angles are formed at a point on a line so that the sum of their measures is 180°.
∠7 and ∠8 are supplementary in the attached figure since they represent a pair of adjacent angles which constitute a straight line.
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The correct question:
Please Help! The figure below shows parallel lines cut by a transversal:
Which statement is true about ∠7 and ∠8?
1. ∠7 and ∠8 are supplementary because they are a pair of corresponding angles.
2. ∠7 and ∠8 are complementary because they are a pair of adjacent angles on a straight line.
3. ∠7 and ∠8 are congruent because they are a pair of adjacent angles on a straight line.
4. ∠7 and ∠8 are supplementary because they are a pair of adjacent angles that form a straight line.
36. THOUGHT PROVOKING
Draw a different figure that
has the same perimeter as
the triangle shown. Explain
why your figure has the
same perimeter.
x+3
3x
2x + 1
A figure with the same perimeter as the one shown is a rectangle of base 3x and height 2, as given in the end of the question.
What is the perimeter of a figure?The perimeter of a figure is given by the sum of all the outer sides of the figure.
Hence, for this problem, the perimeter is given by:
P = x + 3 + 2x + 1 + 3
P = 6x + 4.
A figure with the same perimeter as the one shown is a rectangle of base 3x and height 2, as given in the end of the question, as:
3x + 3x + 2 + 2 = 6x + 4.
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What is 48 = 3x - 15
Answer: x=21
Step-by-step explanation:
Find the measure of indicated angle or solve variable if necessary
Value for the 3 straight lines are 180,28 , 152.
What is a straight line, exactly?
Simply put, a straight line is a line devoid of bends. A straight line is one that does not curve and reaches to infinity on both sides.
CBE = 28 + 90 = so the angle is 118 degrees
ABF = you already got the answer written down, 28
CBA = this is not 180 like you wrote, CBA = ABD - CBD
Straight lines = 180, so ABD = 180
You already found out that CBD = 28
so CBA = 180 - 28 so the answer CBA = 152
So, answers for the 3 lines are 180,28 , 152
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Pls solve a question on my hw (1/5)p=15
Write the expression |x − 9| + |x − 6| without the absolute value symbols if x is in the given interval.
(−∞, 1)
Recall the definition of absolute value.
[tex]|x| = \begin{cases} x & \text{if } x \ge 0 \\ -x & \text{if } x < 0 \end{cases}[/tex]
Now,
[tex]x<1 \implies x-9 \le -8 < 0 \implies |x-9| = -(x-9) = 9 - x[/tex]
and
[tex]x<1 \implies x-6 \le -6 < 0 \implies |x-6| = -(x-6) = 6 - x[/tex]
so that
[tex]|x-9| + |x-6| = (9-x) + (6 - x) = \boxed{15 - 2x}[/tex]