Find each of the following for f(x)=9x+4. (a) f(x+h) (b) f(x+h)−f(x) (c) h
f(x+h)−f(x)
(a) f(x+h)= (b) f(x+h)−f(x)= (c) h
f(x+h)−f(x)
=
(a) The expression \( f(x+h) \) is equal to \( 9x + 9h + 4 \).(b) The expression \( f(x+h) - f(x) \) simplifies to \( 9h \).(c) The expression \( h \cdot (f(x+h) - f(x)) \) can be simplified to \( 9h^2 \).
For each of the following expressions for the function \( f(x) = 9x + 4 \), we substitute the given values into the function.
(a) \( f(x+h) \):
Replacing \( x \) with \( (x+h) \) in the function \( f(x) = 9x + 4 \), we have:
\( f(x+h) = 9(x+h) + 4 = 9x + 9h + 4 \)
(b) \( f(x+h) - f(x) \):
Substituting \( f(x+h) \) and \( f(x) \) into the expression, we get:
\( f(x+h) - f(x) = (9x + 9h + 4) - (9x + 4) = 9h \)
(c) \( h \cdot (f(x+h) - f(x)) \):
Multiplying \( h \) with the expression \( f(x+h) - f(x) \), we obtain:
\( h \cdot (f(x+h) - f(x)) = h \cdot 9h = 9h^2 \)
Therefore:
(a) \( f(x+h) = 9x + 9h + 4 \)
(b) \( f(x+h) - f(x) = 9h \)
(c) \( h \cdot (f(x+h) - f(x)) = 9h^2 \)
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HELP ME PLZZ, ASAP!!!
If two angles are both vertical and supplementary, can we determine the angles? Is it possible to be both vertical and complementary? If so, can you determine the angles? Explain how you know.
Answer:
i. Two angles can be vertical and supplementary.
ii. Yes, we can determine the angles.
Step-by-step explanation:
When two angles are vertical, it implies that they are equal (with respect to vertical opposite property). While two angles are supplementary if and only if they add up to \(180^{o}\).
It is not mandatory for the two angles to be beside each other so as to be supplementary. So that in this special case, the only measure of angles that can be both vertical and supplementary is \(90^{o}\).
Yes, angles that are both vertical supplementary can be determined. They can be 90° each.
Determination of Vertical Supplementary AnglesVertical angles are opposite angles where two lines intersect. They are equal. So, angle 1 = angle 2,
A1 = A2 ...{i}
Supplementary angles are those which sum upto form 180. So, angle 1 + angle 2 = 180; i.e.
A1 + A2 = 180 ...{ii} By {i} and {ii} ,
putting i} in ii},
A1 + A1 = 180
Twice A1 = 180
A1 = \(\frac{180}{2}\)
= 90
As,
A1 = A2,
So,
A2 is also 90°
Thus, 90° is the correct answer.
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Drag the point on the coordinate plane to the solution of the system of equations shown below: y=-2x-1 y = x + 2
Answer:
(1,-1)
Step-by-step explanation:
-2x-1 = x+2
-3x = 3
x = -1
substitute
y = (-1) + 2
y = 1
point: (1,-1)
Solve for x
90°
\12x-22)
170°
Answer:
x = 6
Step-by-step explanation:
Using this theorem to get the other angles of the triangle.
Angle at the vertex is equal to half of the angle at the intercepted arc
For the arc with angle 170degrees
Angle at the vertex = 1/2 * 170
Angle at the vertex = 85 degrees
For the arc with angle 90degrees
Angle at the vertex = 1/2 * 90
Angle at the vertex = 45 degrees
Taking the sum of the 3 angles and equating to 180
85 + 45 + 12x - 22 = 180
130-22+12x = 180
12x = 180 - 108
12x = 72
x = 72/12
x = 6
Hence the value of x is 6
-24 = -3w +21 what is w?
Answer:
w=15
Step-by-step explanation:
(PICTURE PROVIDED)
HELPPPPPPP PLS
A: 5/4
B: 3/2
C: 6/5
D: 2/3
Answer:
I think its 6/5 or 2/3
Step-by-step explanation:
Answer:
1. A
2. C
3. D
4. C
5. D
Step-by-step explanation:
You're welcome
A new backpack costs $45.00 plus 7.4% for sales tax. Find the amount of tax you would have to pat for the backpack.
Answer:
$48.33
Step-by-step explanation:
1. Find the amount of the sales tax by multiplying the tax percentage by the sales price.
$45 × 7.4% = $3.33
2. Add the amount of the sales tax back to the sales price.
$45.00+$3.33 = $48.33
Perform the indicated operations. Write the answer in standard form, a+bi.
-5-7i / 13+4i
Answer:
\(thank \: you\)
2x + 10 = x + 40
(W/ solution pls)
Answer:
The answer for x is 30
Step-by-step explanation:
2x+10=x+40
C.L.T.
2x-x=40-10
x=30
Answer:
Step-by-step explanation:
2x + 10 = x + 40
2x + 10 - 10 = x + 40 - 10
2x = x + 30
2x - 30 = x + 30 - 30
2x - 30 = x
x = 30
Isa is building a picture frame. The perimeter of the frame is 114 cm. If the frame is 30 cm tall, how wide is it? And how much cloth Isa will need to cover the frame?
Answer:
810 cm squared
Step-by-step explanation:
30 = height
multiply 30 by 2 = 60
subtract 60 from 114 = 54
divide 54 by 2 = 27 = width
multiply 27 x 30 to get 810 cm squared
2/7×4 2/3 what is the answer plzzzz?
Answer:
\(\frac{4}{3}\)
Step-by-step explanation:
Change 4 \(\frac{2}{3}\) into an improper fraction, that is
4 \(\frac{2}{3}\) = \(\frac{14}{3}\) , thus
\(\frac{2}{7}\) × 4 \(\frac{2}{3}\)
= \(\frac{2}{7}\) × \(\frac{14}{3}\) ( cancel 7 and 14 by 7 )
= 2 × \(\frac{2}{3}\)
= \(\frac{4}{3}\)
Hurry timed test !
What is the lateral surface area of a cylinder with a base diameter of 6 inches and a height of 6 inches?
F. 52.56 in ²
G. 113.04 in ²
H. 141.3 in ²
J. 169.56 in ²
r+b=7
3.75r+2.75b=22.25
Answer:
Step-by-step explanation:
hello :
r+b=7... (*)
3.75r+2.75b=22.25.... (**)
use (*) : r = 7 - b
put this value in (**) :
3.75(7 - b)+2.75b = 22.25
26.25 -375b +2.75b = 22.5
-375b +2.75b = 22.5 - 26.25
- b = -3.75
so : b = 3.75
but : r = 7 - b
r = 7 - 3.75
r = 3.25
find the length of the curve. r(t) = 6t, t2, 1 9 t3 , 0 ≤ t ≤ 1
The length of the given curve between t=0 and t=1 is approximately 13.573 units.
Now, let's move on to the given parametric curve: r ( t ) = ⟨ 6t , t² , 1/9t³ ⟩ , 0 ≤ t ≤ 1. To find the length of this curve, we need to use a formula that involves integrating the length of small line segments along the curve.
The formula we'll use is the arc length formula:
\(L = \int _a^b \sqrt{(dx/dt)^2 + (dy/dt)^2 + (dz/dt)^2 dt}\)
This formula calculates the length of a curve between two points a and b, by integrating the square root of the sum of the squares of the first derivatives of the x, y, and z coordinates with respect to the parameter t.
Using this formula, we can find the length of the given curve as follows:
\(L = \int _0^1 \sqrt{(6)^2 + (2t)^2 + (2/27t^4)^2 dt}\)
\(L = \int _0^1 \sqrt{(36 + 4t^2 + 4/729t^8) dt}\)
\(L = \int_0^1 \sqrt{(2916t^8 + 11664t^6 + 15552t^4 + 6912t^2 + 1296) / 729 dt}\)
This integral is not easy to evaluate directly, but we can simplify it by making a substitution. Let u = 6t² + 6/27t⁶. Then du/dt = 12t + 4/9t⁵, and we can write the integrand as:
\(= > \sqrt{(2916t^8 + 11664t^6 + 15552t^4 + 6912t^2 + 1296) / 729} \\ \\= \sqrt{(u^4 + 3u^2 + 1) / 18t^3}\)
Now we can express the integral in terms of u:
\(L = (1/9) \int _0^6 \sqrt{(u^4 + 3u^2 + 1) / u du}\)
This integral cannot be solved exactly, but we can approximate it numerically using a computer or a calculator. The result is approximately 13.573 units of length.
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Complete Question:
Find the length of the curve. r ( t ) = ⟨ 6t , t², 1/9t³ ⟩ , 0 ≤ t ≤ 1
Linetotal is always present and is not stored as a currency. Data in column is representative of how many decimal places are stored. Highest allowed value is ten thousand i. E. 10000
The most suitable data type for storing annual employee salaries ranging from $25,000 to $700,000 would be option (c) decimal(10,4).
Next, we can consider float and double data types, which can store decimal values with a higher range and precision than integers. However, they can be imprecise and cause rounding errors when used to store currency values, which can be a significant issue in financial calculations.
The most appropriate data type for storing currency values is the decimal data type, which is designed to handle decimal values with high precision and accuracy. The decimal data type can store exact numeric values up to 38 digits, with a user-defined scale (the number of digits to the right of the decimal point).
Therefore, option (c) decimal(10,4) would be the best data type for storing annual employee salaries ranging from $25,000 to $700,000.
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Complete Question:
Annual salary of each employee has to be stored in dollars and cents. The salaries vary from minimum of $25,000 to maximum of $700,000. Which of the following would be the most suitable data type?
a) decimal(8.2)
b) decimal
c) decimal(10.4)
d) Small money
e) money
the composite scores of individual students on the act college entrance examination in 2009 followed a normal distribution with mean 21.1 and standard deviation 5.1. (a) what is the probability that a single student randomly chosen from all those taking the test scores 23 or higher? show your work. (b) now take an srs of 50 students who took the test. what is the probability that the mean score x of these students is 23 or higher? show your work.
a) The probability that a single student randomly chosen from all those taking the test scores 23 or higher is 0.3557
b) The probability that the mean score x of these students is 23 or higher is 0.0043
What is Probability?
Probability is synonymous with possibility. It is a mathematical branch that deals with the occurrence of a random event.
Given that ,
mean = \mu = 21.1
standard deviation = \sigma = 5.1
a) P(x ≥ 23 ) = 1 - P(x ≤ 23)
= 1 - P[(x - \mu) / \sigma ≤ (23-21.1) /5.1 ]
= 1 - P(z ≤ 0.37)
= 1 - 0.6443 = 0.3557
Probability= 0.3557
b) n = 50
mu\bar x = \mu = 21.1
σbar x = σ / \\(\sqrt{n}\) = 5.1/ \\(\sqrt{50}\) = 0.7212
P(\bar x ≥ 23) = 1 - P(\bar x ≤ 23 )
= 1 - P[(\bar x - \mu\bar x ) / \sigma\bar x ≤ (23 - 21.1) / 0.7212 ]
= 1 - P(z ≤ 2.63)
= 1 - 0.9957 = 0.0043
Probability = 0.0043
a) The chance of a single student picked at random from all those taking the test scoring 23 or higher is 0.3557.
b) The chance that the mean x of these students is 23 or greater is 0.0043.
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Help me I’ll mark brainliest!!!!!!!
Answer:
1 first you would find the volume of the pryimid which is-
27in²
2 then you'd find the volume of the rectangular prism which is-
108in²
3 then you add the two together-
27in² + 108in² = 135in²
brainliest ;)
HELP ASAP NEEDS TO BE TURNED IN TONIGHT
Answer:
y= 2x + 9
Step-by-step explanation:
Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options. 2.3p – 10.1 = 6.4p – 4 2.3p – 10.1 = 6.49p – 4 230p – 1010 = 650p – 400 – p 23p – 101 = 65p – 40 – p 2.3p – 14.1 = 6.4p – 4
The measures of the angles of a triangle are shown in the figure below. Solve for x.
(6x+20)
(7X-10)
105
Answer:
x = 5
Step-by-step explanation:
Angles in a triangle = 180°
(6x + 20) + (7x - 10) + 105 = 180°
13x + 10 +105 = 180
13x + 115 = 180
-115 = -115
13x = 65
x = 65/13
x = 5
some airlines have restrictions on the size of items of luggage that passengers are allowed to take with them. suppose that one has a rule that the sum of the length, width and height of any piece of luggage must be less than or equal to 150 cm. a passenger wants to take a box of the maximum allowable volume. if the length and width are to be equal, what should the dimensions be?
Any piece of luggage must have a length, width, and height combined that is less than or equal to 150 cm. A traveler requests to take a package with the maximum permitted volume. if the length and width are to be equal, then the dimensions would be 48*96*72
Any piece of luggage must have a length, breadth, and height combined that is 216 cm or less.
L+W+H=216 (because we want the max volume, we may ignore the "less than part" and set them equal) (since we want the max volume, we can ignore the "less than part" and set them equal)
L = W if the length and width are equal.
Let's construct this new equation by swapping L for W.
Arrange H to the left so that H=216-2W when 2W+H = 216
Consequently, what is volume V=L*W*H=W=W2*(216-2W) =216W2-2W3 div./dW=432W-6W?
2\s432W-6W^2=0
72w-w2=0 divided by 6 on both sides.
W = 72 L H = 72 cm
L=2W is the only item that has altered.
Given that L+W+H=216 and that V=L*W*H=2W*W*(216-3W) =432W2-6W, 3W+H=216
864W-18W2 x 3 V prime
Set V prime to 0, solve it by dividing both sides by 18, and you'll get W = 48. dimensions will be
48, 96, and 72 cm in width ,lenght and height
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Work out the surface area of this solid prism.
Answer:
\(2( \frac{1}{2} \times 15 \times 28 ) + ( 25 \times 30 ) + ( 17 \times 30) + ( 28 \times 30 ) \\ = 2520 {cm}^{2}\)
Two cards are drawn from a standard deck. What is the probability that both are aces or both are face cards?
Answer: 25%
Step-by-step explanation:
You could get both aces or both faces or you could get a face and ace
Answer: 12/221
Step-by-step explanation: 4P2/52P2 + 12P2/52P2= 12/221
A corner store sells two kinds of baked goods: cakes and pies. A cake costs $15 and a pie costs $13. In one
day, the store sold 9 baked goods for a total of $121. How many cakes did they sell?
a. 8 cakes
c. 7 cakes
b. 2 cakes
d. 4 cakes
Answer:
a. 8
Step-by-step explanation: Out of 12 baked goods sold , let the number of cakes sold, be x in number and pies sold were 12 − x in number. Total sell was $ 144 , 1 cake costs $ 14 and 1 pie costs, $ 8 ∴ 14 ⋅ x + ( 12 − x ) ⋅ 8 = 144 or 14 x − 8 x = 144 − 96 or 6 x = 48 ∴ x = 8
Earn 100 points for this question and a brainiest
Answer:
the answer is C
Step-by-step explanation:
\( \frac{7}{7} - \frac{4}{7} + \frac{2}{7} \)
Step-by-step explanation:
Step 1 :-
> 7/7 - 4/7
> 7-4/7
> 3/7
Step 2 :-
> 3/7 + 2/7
> 3 + 2/7
> 5/7
Option C is correct
Alan's and Mary's incomes are modeled in the graph. Which part of the graph indicates that Mary's income is greater than Alan's?
Answer:
In the 18th year
Step-by-step explanation:
pls help, this is too hard for me
The value that will be included in section D is C option 0.
The number that could not be included in the section B is D option \(\sqrt{32}\).
An example of a value that could be represented by C is -10.
As we can observe from the figure, we can write the following:-
E is the set of natural numbers.
D is the set of whole numbers.
C is the set of integers.
D is the set of rational numbers.
A is the set of irrational numbers.
The biggest rectangle is the set of real numbers comprising of rational and irrational numbers.
Hence,
The value that will be included in section D is C option 0 as it is whole number.
The number that could not be included in the section B is D option \(\sqrt{32}\) as it is an irrational number and will be included at A.
An example of a value that could be represented by C is -10 as C represents the set of integers.
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Bob has a collection of 450 pens. If he gave 90 pens to his friend
Jenny, find the percent of pens left with Bob?
Answer: The answer is: 360
Step-by-step explanation:
Subtract 450 by 90
450 - 90 = 360.
Hope this helped <//3
Determine whether the origin is included in the shaded region and whether the shaded region is above or below the line for the graph of the following inequality: y >3/5 x − 2
The graph of the inequality y > 3/5x - 2 includes the origin also and the shaded region is above the line for the graph that is attached below.
Inequality:
Inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.
While we plot the inequality on the graph instead of make a line it will make the shaded region on it.
Given,
Here we have the inequality. y > 3/5x - 2
Now, we need to determine whether the origin is included in the shaded region and whether the shaded region is above or below the line for the graph of the inequality.
In order to solve this, first we have to plot the graph for this inequality.
To plot the graph for the inequality here, we have to use the graphing calculator.
Then we get the graph like the following.
While we looking in the graph we have identified that the origin (0,0) is included in the shaded region.
And the shaded region will be placed above the line for the inequality.
Which means the resulting values of he inequality are placed upwards.
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PLEASE HELLP!!!!! Multiply. Type the answer into the box. For mixed numbers, use a hyphen; for fractions, use a slash. Do not use any spaces. (ex., 4\frac{2}{3}\:=\: 4-2/3) please show how you got this answer
2.8x.31=
Answer:
0.868
Step-by-step explanation:
you js have to times it not hard hope u have a good day,night