[tex]f(x)=3x^2+3\hspace{5em}\displaystyle \lim_{h\to 0}~\cfrac{f(2+h)~~ - ~~f(2)}{h} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\cfrac{f(2+h)~~ - ~~f(2)}{h}\implies \cfrac{[3(2+h)^2+3]~~ - ~~[3(2)^2+3]}{h} \\\\\\ \cfrac{[3(4+4h+h^2)+3]~~ - ~~[3(4)+3]}{h}\implies \cfrac{[(12+12h+3h^2)+3]~~ - ~~[15]}{h} \\\\\\ \cfrac{[12h+3h^2+15]~ - ~~[15]}{h}\implies \cfrac{12h+3h^2}{h}\implies \cfrac{h(12+3h)}{h}\implies 12+3h \\\\[-0.35em] ~\dotfill\\\\ \displaystyle \lim_{h\to 0}~\cfrac{f(2+h)~~ - ~~f(2)}{h}\implies \lim_{h\to 0}~12 + 3h\implies 12+3(0)\implies \text{\LARGE 12}[/tex]
AABC and AADE are similar. Find the length of of side DA
4
For the two similar triangles, the length of side DA = 4 units.
What is defined as the similar triangles?If two triangles get the same ratio of corresponding sides and then an equal pair of corresponding angles, they are similar.When two or more figures share a common shape but differ in size, they are referred to as similar figures.The three-sided polygon is the triangle. The following is the condition for triangle similarity:Both triangles' corresponding angles are equal, andBoth triangles' corresponding sides are proportional to one another.For the two triangles;
ΔABC ≡ ΔADE
The ratios of their side will be equal
Thus,
CB/ED = AB/DA
Put the values of the sides from given diagram.
2/4 = 2/DA
Cancel the common 2 and cross multiplying.
DA = 4 units.
Thus, the length for the side DA is 4 units.
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Cynthia Besch wants to buy a rug for a room that is 18 ft wide and
29 ft long. She wants to leave a uniform strip of floor around the
rug. She can afford to buy 276 square feet of carpeting. What
dimensions should the rug have?
Answer:
Given,
length(l)=29ft
breadth(b)=18ft
now,
Area of rug=l×b
=29×18=522ft²
GEMDAS
26-6+ (0+3)
26-6 ÷
26- I need help whit this soon as possible
According to the GEMDAS rule the value of the 26-6+ (0+3)*26-6 ÷26- I:
= [tex]96\frac{10}{13}[/tex]
What is The GEMDAS rule ?The GEMDAS rule can be used to summarize or evaluate difficult numerical equations containing several binary operations. Important Information: 1. In a specific simplification, if you have simultaneous multiplication and division, perform the operations sequentially from left to right.
What is the significance of both the Gemdas ,Pemdas rule?If you mess up the order of parenthesis, exponents, multiplications, including addition and subtraction, the PEMDAS rule prevents you from getting the wrong result.
According to the given data:Applying the GEMDAS rule:
26-6+ (0+3)*26-6 ÷26- I
= 26-6+ (0+3)*26-6 ÷26- I
= 26-6+ 78 -6÷ 26-1
= 26-6+78- [tex]\frac{6}{26}[/tex] -1
= 1258/13
= [tex]96\frac{10}{13}[/tex]
According to the GEMDAS rule the value of the 26-6+ (0+3)*26-6 ÷26- I:
= [tex]96\frac{10}{13}[/tex]
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Each graph shows a relation. The first and second numbers of each ordered pair in the relation are members of the set of real numbers. In each case, find the domain and the range of the relation and determine whether the relation is a function.
Answer:
Domain: [-1, 0) U [2]Range: [0, 1)A functionStep-by-step explanation:
The domain is the set of x values and the range is the set of y values.
For the relation to the function, each value of x must map onto no more than one value of y.
Answer:
The Domain is -2 [is less than or equal to] x < 0
The Range is 0 [is less than or equal to] y < 2
This is NOT a function
Step-by-step explanation:
sry if this is a bit confusing:
[is less than or equal to] is just the sign that means what is said; this is bc you cant use that sign on keyboard
Which of the following are factors of 96? Select ALL that apply.
18
06
04
012
014
Answer:
6, 4 and 12 are factors
Step-by-step explanation:
Divide 96 by each value. If the result is an integer then it is a factor
96 ÷ 18 = 6.333 ← not a factor
96 ÷ 6 = 16 ← factor
96 ÷ 4 = 24 ← factor
96 ÷ 12 = 8 ← factor
96 ÷ 14 = 6.857.. ← not a factor
3. Mrs. Quinto is comparing the Calories in different types of bread. Wheat bread has 150 Calories for every 2 slices. The Calories in two other types of bread are shown in the table and graph. Which bread has the greatest ratio of Calories to slices?
options:
2 - 160
4 - 320
6 - 480 . (white bread)
Rye bread is 0 to 500 .
The bread that has the greatest ratio of Calories to slices is the Wheat bread
How to determine the bread that has the greatest ratio of Calories to slices?The table of values is given as
Wheat bread
Slice - Calories
2 - 160
4 - 320
6 - 480
The missing graph that represents the graph of rye bread is added as an attachment
On the graph, we have the following table of values
Rye bread
Slice - Calories
2 - 130
4 - 260
6 - 390
We start by calculating the rates of each table using
Rate = Calories/Slice
So, we have
Wheat bread = 160/2
Wheat bread = 80
Rye bread = 130/2
Rye bread = 65
80 is greater than 65
Hence, the bread that has the greatest ratio of Calories to slices is the Wheat bread
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Planes A and B intersect.
Which describes the intersection of line m and line n?
point W
point X
point Y
point Z
Answer:
Point W.
Step-by-step explanation:
Line [tex]n[/tex] is on plane [tex]A[/tex]. Line [tex]m[/tex], however, is not on any plane shown, but intersects plane [tex]A[/tex] and line [tex]n[/tex].
triangles FIM and LAK below are similar, and LA= AK
Multiple choice
Based on the triangle similarity theorem, the length of AK is: A. 9.
How to Determine the Corresponding Side Lengths of Similar Triangles?Based on the triangle similarity theorem, the ratios of the corresponding side lengths of two triangles that are similar to each other are equal and their lengths are proportional to each other.
Given that triangle FIM and triangle LAK are similar triangles, therefore, the ratio is true:
FM/LK = IM/AK
Length of FM = 8 units
Length of LK = 12 units
Length of IM = 6 units
Length of AK = ?
Substitute
8/12 = 6/AK
8(AK) = (6)(12)
8(AK) = 72
Divide both sides by 8
8(AK)/8 = 72/8
AK = 9
AK = LA = 9
LA = 9 units
Therefore, based on the triangle similarity theorem, the length of AK is: A. 9.
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Jessie recently drove to visit her parents who live 192 miles away. On her way there her average speed was 20 miles per hour faster than on her way home (she ran into some bad weather). If Jessie spent a total of 8 hours driving, find the two rates (in mph).
Answer:
38 and 58
Step-by-step explanation:
Evaluate the expression when n=8. n^2 - 18
Answer:
Step-by-step explanation:
n^2 - 18. n=8
Simply plug 8 in place of n. The ^ sign refers to the power of the number, so in this case we square it. Review order of operations if needed.
8^2 - 18
(8×8) - 18
64 - 18 = 46
So the answer is 46
The length of a rectangel is 11 less than 9 times the width. The perimeter of the rectangle is 18 inches
According to the question, the given parameters has relationship between the length and the width of the rectangle.
The perimeter of the rectangle is 18 inches.
Now, using standard perimeter as well as area formulas of a rectangle. Therefore, the equation can become:
Let us assume, the width of the rectangle be 'w' inches
The length of a rectangle be (9w - 11)
As we know, perimeter of a rectangle is 2(l + w)
Substitute the calculated parameters in the perimeter formula:
18 = 2(9w - 11 + w)
⇒ 9 + 11 =10w
⇒ w = 2 inches and l = 7 inches
Then, the calculated width is 2 inches and length is 7 inches.
What is rectangle?
Rectangle is two-dimensional shape. It has four sides, four corners and four angles. In this opposite sides are equal to each other. And the opposite sides are equal and parallel to each other.
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What company has the absolute advantage when it comes to producing computers?
a. The G company Inc
b. Gonzalez and Bros. Inc
c. they both do
d. neither
Answer:
D neither
Step-by-step explanation:
Because they both don't have big numbers so the are unequal
(c)
If two marbles are selected at random without replacing between draws, what is the probability that the outcome contains green and/or blue marbles only? (Round your answer to four decimal places.)
(d)
If three marbles are selected at random without replacing between draws, what is the probability that the outcome contains only green marbles? (Round your answer to four decimal places.)
(e)
If three marbles are selected at random with replacing between draws, what is the probability that the outcome contains no green marbles? (Round your answer to four decimal places.)
The following issues have the following needed probabilities: 1.) 1 / 3 2.) 1 / 5, and 3.) 1 / 4.
Here,
Four red marbles, five yellow marbles, three green marbles, and three blue marbles make up a jar.
There are 15 marbles in all.
1) Chance that the result exclusively includes green and/or blue marbles,
= 2 / 6 = 1 / 3
2.) Chance that the result solely contains green marbles
= 3 / 15 = 1 / 5
3.) the likelihood that there won't be any green marbles in the result,
= 3 / 12 = 1 / 4
As a result, the needed probability for the following issues is given: 1.) 1 / 3. 2.) 1 / 5, and 3.) 1 / 4.
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How do I solve this problem?
The algebraic solution for the variable x is as follows:
x = 9 / 2. How to find the variable x in the equation?The equation is represented as follows;
2 / 5 (2 - x) = - 1 / 3 x + 1 / 2
open the bracket on the left side
2 / 5 (2 - x) = - 1 / 3 x + 1 / 2
4 / 5 - 2x / 5 = - 1 / 3 x + 1 / 2
Add 1 /3 x to both sides
4 / 5 - 2x / 5 = - 1 / 3 x + 1 / 2
4 / 5 - 2x / 5 + 1 / 3 x = - 1 / 3 x + 1 / 3 x + 1 / 2
4 / 5 + 1 / 3 x - 2 / 5 x = 1 / 2
4 / 5 + 5x - 6x / 15 = 1 / 2
4 / 5 - x / 15 = 1 / 2
subtract 4 / 5 from both sides
4 / 5 - 4 / 5 - x / 15 = 1 / 2 - 4 / 5
- x / 15 = 5 - 8 / 10
- x / 15 = - 3 / 10
cross multiply
- x / 15 = - 3 / 10
-10x = - 45
divide both sides by -10
x = 45 /10
x = 9 / 2
Therefore, the algebraic solution for the variable x is 9 / 2.
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over the period every year Julie‘s net worth increased which of the following could be true
(D) Julie's assets decreased by more than her liabilities: TRUE
What are assets?An asset is any resource owned or controlled by a business or economic entity in financial accounting. It is anything that has the potential to generate positive economic value. Assets are ownership values that can be converted into cash. Physical assets include machinery, property, raw materials, and inventory, as well as intangible assets such as patents, royalties, and other intellectual property.So, assets are simply the resources that a person or company possesses, whereas liabilities are the debts that the economic agent owes to others.
Juliet's net worth will decrease because the value of her debt increased faster than the rate at which her assets increased. Julie's assets decreased more than her liabilities in this case.Therefore, the statement "(D) Julie's assets decreased by more than her liabilities" is TRUE.
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The complete question is given below;
Over the period of a year, Julie's net worth decreased. Which of the following could be true?
a Julie's assets and liabilities decreased by the same amount.
b. Julie's assets and liabilities increased by the same amount.
C. Julie's assets increased by more than her liabilities.
d. Julie's assets decreased by more than her liabilities.
Please select the best answer from the choices provided
3.4/feet
5 feet
Find the area of the triangle pictured above.
h
square feet
Area =
Answer: answer is 3
Step-by-step explanation:
Marissa bought 12.8 pounds of potatoes at $1.35 per pound how much did Marissa spend for the potatoes? Explain.
Identify the angle relationship and find the measure of the indicated angle.
(Alternate Interior, Alternate Exterior, Corresponding, Same-side Interior)
The angled relationship is the Same-side interior angle where x is 6 and ∠EFG is 102°
For the parallel lines ED and FG, where EF is the transversal,
The angle DEF and the angle EFG are same-side interior angles.
By the same-side interior angle theorem, we can say that the interior angles on the same side of the transversal are supplementary (the sum of the angles is 180°).
∠DEF = 13x°
∠EFG = 17x°
∠DEF + ∠EFG = 180°
13x + 17x = 180
30x = 180
x = 6
∠DEF = 13x = 13*6 = 78°
∠EFG = 17x = 17*6 = 102°
Therefore, the angles follow the same-side interior angles relationship, x = 6 and ∠EFG = 102°
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Find the sum of the first 8 terms of the
following series, to the nearest integer.
48, 60, 75
Answer:
952.32
Step-by-step explanation:
In a certain federal prison, it is known that 2/3 of the inmates are under 25 years of age. It is also known that 3/5 of the inmates are male and that 5/8 of the inmates are female or 25 years of age or older. What is the probability that a prisoner selected at random from this prison is female and at least 25 years old?
The probability that a prisoner selected at random from this prison is female and at least 25 years old is 1/64
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.
GIven that 2/3 of the inmates are under 25 years of age also, that 3/5 of the inmates are male and that 5/8 of the inmates are female or 25 years of age or older.
The number of mother inmates = 75% (100) = 75
The number of inmates, who are not mothers = 100 - 75 = 25
Selecting an inmate who is not a mother = 1/4
Selecting 3 female who are not mothers = 1/64
Therefore, the probability that a prisoner selected at random from this prison is female and at least 25 years old is 1/64
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The boxplot represents concert tickets sold on random days for a local venue. Find the interquartile range.
A. 143
B. 72
C. 36
D. 333
The interquartile range of the concert tickets sold is 72. (the second option).
What is the interquartile range?A box plot is a graph that is used to study the distribution and level of a set of scores. The box plot consists of two whiskers and a box. The first whisker represents the minimum number and the end of the second whisker represents the maximum number.
On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. The third line on the box represents the upper (third) quartile.
The interquartile range is the difference between the third quartile and the first quartile.
Interquartile range = third quartile - first quartile
369 - 297 = 72
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I need help ASAP, this is with khan academy.
Answer:
◉ No
Step-by-step explanation:
a vertical line is not a function because it will not survive the vertical line test, VLT.
the VLT is a vertical line that touches functions, if it touches it twice or more, then it's not a function
=======================================
[tex]\textcopyright ELIZA \bullet22/09/'22[/tex]
[tex]\#CARRYONLEARNING :)[/tex]
6 apples and 5 oranges are shared among 3 people. If the apples are indistinguiable, oranges are also indistinguiable, how many ways can they share these fruits if each person must have at least 1 fruit?
The number of ways that they can share these fruits if each person must have at least 1 fruit will be 12 ways.
How to illustrate the information?From the information, 6 apples and 5 oranges are shared among 3 people and the apples are indistinguiable, oranges are also indistinguiable.
Therefore, the number of ways that they can share these fruits if each person must have at least 1 fruit will be:
= (6 - 3)! × (5 - 3)!
= 3! × 2!
= 3 × 2 × 2
= 12
Therefore, the number of ways that they can share these fruits if each person must have at least 1 fruit will be 12 ways.
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Simplify the expression. √686x¹y7 OA. 7xy √2xy OB. 7zy 2xy Oc 7xy √xy² OD. 7x²y √2xy?
The correct simplified answer is [tex]49\sqrt{2xy}[/tex]
According to the question, the expression can be simplified as:
Given expression: [tex]\sqrt{686 xy7 } = \sqrt{7 X 7 X 7 X 2 X7xy}= 49\sqrt{2xy}[/tex]
Hence, the correct answer is [tex]49\sqrt{2xy}[/tex]
What is simplification?
The word simplification makes the complicated expression into simpler expression. Simplification method uses basic mathematics properties for the complicated expression. After simplification, the calculation become easy.
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Tomas is finding the coordinates of point A. He knows that point A has an x-coordinate of 8. He starts to compute the value of the y-coordinate. Complete Tomas’s work to answer the question.
Which is the coordinate of point A?
(8, –6)
(–6, 8)
(6, –8)
(–8, –6)
Answer: Доброе утро, ответ 5+5="4
Step-by-step explanation:
You are employed as the office manager at Clover Point Pediatrics. Your job requires you to take on many responsibilities. One of these is to arrange for the annual clinic party. This year, you have been given permission to rent a banquet room at a local hotel, hire a caterer, and hire a disc jockey for entertainment. There are 23 employees and each will be bringing one guest (46 total).
The caterer is charging $29.95 per person for a sit-down dinner. What will be the total cost for food?
The total cost on the food in the annual clinical party is a $1377.7.
According to the statement
We have to find that the total cost of the food.
So, For this purpose, we know that the
The cost function can be used to find the average cost, which is the average amount of money it costs to produce a unit.
From the given information:
There are 23 employees and each will be bringing one guest (46 total).
The caterer is charging $29.95 per person for a sit-down dinner.
And then
Total person = 46
The cost of food per plate = $29.95
Then
Total cost of the food = 29.95*46
Total cost of the food = 1377.7
So, The total cost on the food in the annual clinical party is a $1377.7.
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The perimeter of the rectangle below is 166 units. Find the value of y.
4y + 2
Sy
The value of y is 9.
Perimeter is the total length of the boundary of any closed shape. It is basically the sum of all the sides of a given figure.
Perimeter of a rectangle is given by [ 2( l + b ) ] or (2 l + 2 b ) or
( l + l + b + b), here l and b represent the length and breadth of the given rectangle.
Perimeter of the given rectangle = 166 units ( given )
Length of the given rectangle = 5y ( given )
Breadth of the given rectangle = (4y + 2) ( given )
By putting values in the formula, we get
perimeter = 2 ( l + b )
166 = 2 [ (5y) + (4y + 2) ]
166 = 2 [ 5y + 4y + 2 ]
166 = 2 [ 9y + 2 ]
166 = 2*9y + 2*2
166 = 18y + 4
166-4 = 18y ( moving 4 to other side thus changing the sign to negative )
162 = 18y
162/18 = y ( moving 18 to other side for further solution )
y = 9
Therefore, the value of y for which the perimeter of the given rectangle is 166 units is 9.
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The value of y is 9.
The whole length of any closed shape's boundary is known as its perimeter. In essence, it is the total of a given figure's sides.
A rectangle's perimeter can be calculated using [2(l + b)] or (2 l + 2 b) or
(l + l + b + b), where l and b stand for the provided rectangle's length and width
The rectangle's perimeter is 166 units ( given )
The rectangle's length is 5y ( given )
Given rectangle's width equals (4y + 2) ( given )
When we enter values into the formula, we obtain
perimeter = 2 ( l + b )
166 = 2 [ (5y) + (4y + 2) ]
166 = 2 [ 5y + 4y + 2 ]
166 = 2 [ 9y + 2 ]
166 = 2*9y + 2*2
166 = 18y + 4
166-4 = 18y ( moving 4 to other side thus changing the sign to negative )
162 = 18y
162/18 = y ( moving 18 to other side for further solution )
y = 9
Therefore, the value of y for which the perimeter of the given rectangle is 166 units is 9.
Determin whether the relation defines a function, and give the domain and range.
The relation is not a function if its domain is on the x-axis and its range is on the y-axis. However, if the relation's domain is on the y-axis and its range is on the x-axis, it is a function.
If so, what kind of function is it?
Relationships are defined by three factors:
1. domain is a set of inputs.
2. an output set referred to as range.
3 . relationships between domain and range-related items.
If and only if each element of the domain is associated to just one member of the range, is a relation a function. It must be noted that the solution may vary based on the domain and range that we assume.
The provided relation is a function if the x-axis is the range and the y-axis is the domain, as opposed to when the x-axis is the domain and the y-axis is the range.
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If α =i+j−2k, β =−i+2j+3k andγ =5i+8k, then find c and d such that γ−cα−dβ is perpendicular to both α and β
If [tex]\hat\gamma-c\hat\alpha-d\hat\beta[/tex] is perpendicular to both [tex]\hat\alpha[/tex] and [tex]\hat\beta[/tex], then their dot products are zero.
Recall that for any vector [tex]\hat x[/tex], [tex]\hat x\cdot \hat x = \|\hat x\|^2[/tex].
Now, we have
[tex](\hat\gamma - c\hat\alpha - d\hat\beta) \cdot \hat\alpha = (\hat\gamma\cdot\hat\alpha) - c\|\hat\alpha\|^2 - d (\hat\beta\cdot\hat\alpha) = 0[/tex]
[tex]\hat\gamma\cdot\hat\alpha = 5 + 0 - 16 = -11[/tex]
[tex]\|\hat\alpha\|^2 = 1^2 + 1^2 + (-2)^2 = 6[/tex]
[tex]\hat\beta\cdot\hat\alpha = -1 + 2 - 6 = -5[/tex]
[tex]\implies 6c - 5d = -11[/tex]
and
[tex](\hat\gamma - c\hat\alpha - d\hat\beta) \cdot \hat\beta = (\hat\gamma\cdot\hat\beta) - c(\hat\alpha\cdot\hat\beta) - d \|\hat\beta\|^2 = 0[/tex]
[tex]\hat\gamma\cdot\hat\beta = -5 + 0 + 24 = 19[/tex]
[tex]\|\hat\beta\|^2 = (-1)^2 + 2^2 + 3^2 = 14[/tex]
[tex]\implies 5c - 14d = -19[/tex]
Solve for [tex]c[/tex] and [tex]d[/tex]. By elimination,
[tex]5(6c - 5d) - 6(5c - 14d) = 5(-11) - 6(-19)[/tex]
[tex]-25d + 84d = -55 + 104[/tex]
[tex]59d = 59[/tex]
[tex]\boxed{d=1}[/tex]
[tex]6c-5 = -11[/tex]
[tex]6c=-6[/tex]
[tex]\boxed{c=-1}[/tex]
PLS HELP (easy math im just really bad) ILL GIVE YOU A BRAINLIEST AND 15 POINTS
Answer: -3b + 21
Step-by-step explanation:
-3(b-7) distribute the -3 to the rest of the equation
= -3b + 21
Answer:
Step-by-step explanation:
So we have our equation -3(b-7)
We are multiplying -3 by b, and by 7, and subtracting the products from each other
so, -3x7=-21
and we would have -3b
so now, we can put this back into the equation as
-3b+21 (because the rule is that subtracting a negative from a negative is the same as adding a positive)
Hope this helps!^^
