What is the difference quotient of the function, g (x) = startroot x endroot, x greater-than-or-equal-to 0?
The difference quotient of the function g(x) = √x is [√(x+h) -√x]/h
Difference quotient of the function:
Difference quotient of the function means a measure of the average rate of change of the function over an interval.
The difference quotient formula of a function y = f(x) is,
[ f(x + h) - f(x) ] / h
where
f (x + h) is obtained by replacing x by x + h in f(x)
f(x) is the actual function
Given,
Function g(x) = √x where x≥0.
Here we need to find the difference of the quotient of the function.
For that,
First we have to calculate the value of g(x + h),
By simply replacing the value of x as x + h,
So,
g(x + h) = √(x+h)
Now apply the values on the formula in order to solve it,
=> [√(x+h) -√x]/h
We can't simplify it further.
So, the difference quotient of function is,
=> [√(x+h) -√x]/h
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Answer: D
Step-by-step explanation:
took one for the team
PLS HELPPP
identify the graph of the ellipse.
[tex]\frac{(x-3)^{2} }{16} +\frac{y-4^{2} }{9} =1[/tex]
The correct graph of the ellipse is identified and attached below.
Given the equation is (x₋3)²/16 ₊ (y₋4)²/9 = 1
step 1: identify the center (h,k) of the ellipse in standard form:
(x₋h)²/a² ₊ (y₋k)²/b² = 1
In the standard form of an ellipse, notice that there is a minus sign in front of the h and k.
In our equation (x₋3)²/16 ₊ (y₋4)²/9 = 1 , we have:
h = 3 and k = 4
Therefore, center (h,k) = (3,4)
Step 2: Identify the orientation by determining the major axis and minor axis in (x₋h)²/a² ₊ (y₋k)²/b² = 1
if a>b, the major axis is horizontal and the minor axis is vertical, making the ellipse a horizontal ellipse.
if a<b, the minor axis is horizontal and the major axis is vertical, making the ellipse a vertical ellipse.
For (x₋3)²/16 ₊ (y₋4)²/9 = 1
a² = 16, a = 4 and b² = 9 , b = 3
so, 4>3, the major axis is horizontal and the minor axis is vertical, making the ellipse a horizontal ellipse.
Step 3:
Plot the co-vertices along the minor axis and the vertices along the main axis (endpoints). No matter which way around, draw points a horizontal distance of a to the left and right from the center and points b above and below the center.
Therefore the vertices are marked along the major axis.
vertices are (3,7) and (3,1)
and co vertices are marked along the minor axis
co vertices are (₋1,4 ) and (7,4)
step 4: connect the vertices and co vertices making a smooth horizontal ellipse.
Hence a horizontal ellipse is made.
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Q.5 - Solve the equation 3(2x - 4) = 8 + 2x + 6. Show your work.
Answer: x=6.5
Step-by-step explanation:
3(2x - 4) = 8 + 2x + 6
6x-12=14+2x
4x-12=14
4x=26
x=26/4
x=6.5
Of the students at Milton Middle School, 192 are girls. If 60% of the students are girls, how many total students are there at Milton Middle school?
Answer:
320 Students
Step-by-step explanation:
Hope this helps :)
Quadrilateral WXYZ with vertices W(0,-4), X(13,0), Y(9,-12), and Z(5,-12); scale factor: k = 3/4, center of dilation: (1,0)
Dilation involves changing the size of a quadrilateral or any shape
The coordinates of the image of the dilation are: [tex]W^{\prime}=(1 / 4,-3), X^{\prime}=(10,0)$, $Y^{\prime}=(7,-9)$[/tex] and [tex]$Z^{\prime}=(4,-9)$[/tex]
This is further explained below
How to determine the vertices of the image?The vertices of the pre-image are given as:
W=(0,-4)
X=(13,0)
Y=(9,-12)
Z=(5,-12)
The scale factor is given as:
k=3 / 4
The center of dilation is given as:
(a, b)=(1,0)
To calculate the vertices of the image, we make use of the following formula [tex]$\left(x^{\prime} y^{\prime}\right)=(k(x-a)+a, k(y-b)+b)$[/tex]
So, we have:
W'=(3 / 4(0-1)+1,3 / 4(-4-0)+0)
W'=(1 / 4,-3)
X'=(3 / 4(13-1)+1,3 / 4(0-0)+0)
X'=(10,0)
Y'=(3 / 4(9-1)+1,3 / 4(-12-0)+0)
Y'=(7,-9)
Z'=(3 / 4(5-1)+1,3 / 4(-12-0)+0)
Z'=(4,-9)
Hence, the coordinates of the image of the dilation are:
W'=(1 / 4,-3),
X'=(10,0),
Y'=(7,-9)
Z'=(4,-9)
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5/6 - 1/9 = ?/? - ?/? = ?/?
please help 20 points
i need to know what each ( ?/? ) is
5/6 - 1/9=?/? - ?/? = ?/? , value of each (?/?) is
5/6 -1/9 =15 /18 -2/18 =13 /18.
As given,
5/ 6 - 1/9 =?/? -?/? =?/?
Convert the given terms into like terms
Least common multiple of (6,9)=18
Value of each ( ?/?)
(5/6 ) × ( 3/3) -(1/9) × (2/2)
= 15 /18 - 2/18
= 13 /18
Therefore,5/6 - 1/9 = ?/? - ?/? = ?/? , value of each (?/?) is equal to
5/6 -1/9 = 15 /18 -2/18 = 13/18.
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The sum of eight and half
of a number
We get the expression for the statement "The sum of eight and half of a number" as (16 + x) / 2.
We are given a statement:
The sum of eight and half of a number.
We have to form an expression for the same.
An expression means a combination of numbers and variables.
Let the number be a variable say x.
Now we need the half of a number.
1 / 2 of x = x / 2
Now we need the sum of 8 and x / 2.
So, it will be:
8 + x / 2
= (16 + x) / 2
Therefore, we get the expression for the statement "The sum of eight and half of a number" as (16 + x) / 2.
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The branch of statistical studies called descriptive statistics summarizes important aspects of a data set. True or false?.
The branch of statistical studies called descriptive statistics summarizes important aspects of a data set is true.
It is required to find the statement.
What is a statement?A statement is a declarative sentence that is either true or false but not both. A statement is sometimes called a proposition. The key is that there must be no ambiguity. To be a statement, a sentence must be true or false, and it cannot be both.
Given:
The branch of statistical studies called descriptive statistics summarizes important aspects of a data set.
Descriptive statistics refers to the summary of important aspects of a data set.
Therefore, the branch of statistical studies called descriptive statistics summarizes important aspects of a data set is true.
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A cylindrical vase has a diameter of 6 inches and a height of 8 inches. The vase already contains 20 cubic inches of water. A faucet can fill the vase at
a rate of 8 cubic inches per second.
To the nearest second, how long will it take the faucet to fill the vase? Enter the answer in the box.
Use the info
seconds
In 25.76 seconds we will fill the total volume of the cylinder.
how long will it take the faucet to fill the vase?The total volume of the cylinder is given by the equation:
V = pi*R^2*H
Where pi = 3.14, R is the radius and H is the height.
Here we know that the diameter is 6 inches, then the radius is:
R= 6in/2 = 3in
And the height is 8 inches, then the volume is:
V = 3.14*(3in)^2*8in = 226.08 in^3
We already have 20 cubic inches of water there, so what we need to fill is:
226.08 in^3 - 20in^3 = 206.08in^3
If we fill it at a rate of 8in^3/s, the time in which we will completely fill the cylinder is:
T = 206.08in^3/8in^3/s = 25.76s
In 25.76 seconds we will fill the total volume of the cylinder.
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Find the equation of the line shown.
Answer:
y = -2x + 9
Step-by-step explanation:
The standard form of a linear function is y = mx + b, where m is the slope and b is the y-intercept.
The line intersects the y-axis at 9, thus b = 9.
The slope formula is rise/run. The line falls 2 and runs 1, thus m = -2/1, or -2.
y = -2x + 9
-10+|6+-17| - - 14 show how you got the answer
Answer:
15
Step-by-step explanation:
[tex]-10+\left|6+\left(-17\right)\right|-\left(-14\right)[/tex]
[tex]=-10+\left|6-17\right|+14[/tex]
Subtract.
[tex]=-10+\left|-11\right|+14[/tex]
Now, add.
[tex]=4+\left|-11\right|[/tex]
Apply absolute rule.
[tex]=4+11[/tex]
= 15
To complete bookshelves a customer at your store needs to purchase vertical brackets to attach to the wall the customer wants the shelving to be 9 ft high and 10 ft long the wall brackets come in 48 in and 60-in sections the 48-in sections cost $12.95 each the 60-in sections cost $16.95 each the brackets should be 1 ft from each end and no more than 24 inches apart what will be the total cost of the brackets before tax
The total cost of the brackets before tax = $89.70
Height = 9 feet
length = 10 feet
Wall brackets come in 48-in cost $12.95 and 60-in costing $16.95
Distance of brackets from ends = 1 foot
Maximum distance between brackets = 24 inches
The brackets are:
48/12= 4feet, and 60/12 = 5feet
One of each must be used to cover the height of the shelf.
The length of the shelf is 60 inches
On subtracting 1 foot from each side of the allowance we get, 60-2 = 58-in
Then dividing by 24 we get
58/24 ≈3
The Total cost = (12.95 + 16.95)×3
= $89.70
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With steps please, if it’s correct I’ll give full rate please
A gull can fly at a speed of 22 miles per hour i.e. equal to 116,160feett/hour and An AMTRAK train travels at 125 miles per hour i.e. equal to 2.1 miles/minute
Given that 1)A gull can fly at a speed of 22 miles per hour and asked to convert its units to foot/hour
2)An AMTRAK train travels at 125 miles per hour and is asked to convert its units to miles/minute
1 mile=5280 feet
22 miles/hour=22 × 5280 foot/hour
22 miles/hour=116,160 foot/hour
1 hour=60 minute
125 miles/hour= 125/60 miles/minutes
125 miles/hour= 2.083 miles/minutes≈ 2.1miles/minutes
Therefore, A gull can fly at a speed of 22 miles per hour i.e. equal to 116,160 feet/hour and An AMTRAK train travels at 125 miles per hour i.e. equal to 2.1 miles/minute
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Use the equation y-6= to fill in the missing values in the table below
Using the given equation, the missing values in the table are:
x y
32 14
12 9
0 6
-8 4
-36 -3
How to Apply an Equation?Given the equation, y - 6 = x/4, we can rewrite the equation as:
y = x/4 + 6
For x = 12, we have:
y = 12/4 + 6 = 3 + 6
y = 9
For x = 0, we have:
y = 0/4 + 6 = 0 + 6
y = 6
For y = 4, we have:
4 = x/4 + 6
4 - 6 = x/4
-2 = x/4
-8 = x
x = -8
For y = -3, we have:
-3 = x/4 + 6
-3 - 6 = x/4
-9 = x/4
-36 = x
x = -36
Thus, using the given equation, the missing values in the table are:
x y
32 14
12 9
0 6
-8 4
-36 -3
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how do you write 4.93 as a percentage
Answer:
493%
Step-by-step explanation:
To convert a decimal to percentage, muiltiply the decimal by 100.
If two cellphones are randomly selected from the box what is the probability there will be one green cellphnone and one yellow cellphone?
The probability that one green and one yellow is selected (without replacement) is 3/7.
What are examples and probability?
It is predicated on the likelihood that something will occur. The justification for probability serves as the basic foundation for theoretical probability. For instance, the theoretical chance of receiving a head while tossing a coin is 12.Probability that one green and one yellow is selected (without replacement).
Since the cellphone is not replaced, the probability is calculated as follows
Pr = [tex]\frac{G}{n} * \frac{Y}{n - 1 } + \frac{Y}{n} * \frac{G}{n- 1}[/tex] The subtraction means the cellphones are not replaced
This gives
[tex]Pr = \frac{6}{8} * \frac{2}{8 - 1} + \frac{2}{8} * \frac{6}{8 - 1}[/tex]
[tex]Pr = \frac{3}{4} * \frac{2}{7} + \frac{1}{4} * \frac{6}{7}[/tex]
[tex]Pr = \frac{3}{14} + \frac{3}{14}[/tex]
take lcm
[tex]Pr = \frac{3}{7}[/tex]
Hence, the probability that one green and one yellow is selected (without replacement) is 3/7.
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If the length of the shorter arc AB is 22cm and C is the center of the circle then the circumference of the circle
The circumference of the circle with arc AB as 22 cm and C as the center will be 176 cm.
We are given that:
Length of the shorter arc forming an angle of 45° with the center = 22 cm
AB = 22 cm
C is the center of the circle.
We know that the length of the arc is calculated as:
Length of an Arc = θ × (π / 180) × r
22 = 45 × (3.14 / 180) × r
22 = 0.785 r
r = 22 / 0.785
r = 28.0255
Circumference = 2 π r
Circumference = 2(3.14) (28.0255)
C = 176 cm
Therefore, we get that, the circumference of the circle with arc AB as 22 cm and C as the center will be 176 cm.
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what's the area of the triangle
Answer:
32 is it
Step-by-step explanation:
A new car is priced at £7500.
In a sale it is reduced by 20%.
Calculate the reduction in price.
Answer:£1500
7500 divided by 10=750. £750 is 10% so 750x2 which is 1500, is 20%. Therefore, it is reduced by £1500
Answer:
£1500
Step-by-step explanation:
20% = 20/100 = 0.2
7500 - (7500*0.2)
= 7500 - 1500
= 6000
The reduction in price is:
£ 1500
Find the area of the shaded figure.
OF
80 mm 120 mm
PLS HELP
Answer: 2000π mm^2
Step-by-step explanation:
A=area of entire circle. B=Area of Inside circle. C=Area of shaded region
A-B=C
π(120/2)^2 -π(80/2)^2=
π(60)^2 -π(40)^2=
3600π-1600π=2000π mm^2
through: (1, −5), parallel to` y = −8x +4
Answer: y=-8x+3
Step-by-step explanation:
Parallel lines have the same slope.
y=-8x+b
-5=-8(1)+b
-5=-8+b
b=3
y=-8x+3
Triangle BCD is rotated 80° clockwise about the origin to form ΔKLM. If m∠KLM = 30°, what is m∠BCD?
A.
80°
B.
110°
C.
50°
D.
30°
Can ya'll help me? This problem has stumped me for a few days.
Andy is scuba diving. He starts at sea level and then goes down 14.5 feet in 2 minutes. How many feet did Andy go in one minute?
Answer:
7.25 feet
Step-by-step explanation:
Which is equivalent to 6
41/4
Answer:
16 1/4
Step-by-step explanation:
4*10=40, add one more 1/4 and you get 41. So simplified, 41/4 = 10 1/4
Add the 6 and you get 16 1/4
After making several plates of empanadas, you are down to your last bag of shredded cheese. You realize that it’s not full; there is about / three-fourths of a bag left. If you want to make 4 plates with the remaining cheese, what fraction of a bag can you put on each plate?
The fraction of a bag that you can put on each plate is 3 /16.
What is the fraction you can put on each plate?A fraction is a non-integer that is made up of a numerator and a denominator. The numerator and the denominator are divided by a line. An example of a fraction is 1 / 2.
The fraction of the cheese that you can put on each plate can be determined by dividing the amount of cheese left by the number of plates. Division is the process of grouping a number into equal parts using another number.
Amount that can be put on each plate = fraction left / number of plates
3 /4 ÷ 4
3/4 × 1/4 = 3 /16.
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A Laboratory technician needs to make a 81-liter batch of a 20% acid solution. How can the laboratory technician combine a batch of an acid solution that is pure acid with another that is 10% to get the desired concentration
Answer:
You would need 9 liters of pure acid and 72 liters of 10% acid to make a mixture of of 81 liters of 20% acid.
Step-by-step explanation:
See attached picture.
Osvoldo has a goal of getting at least 30%, percent of his grams of carbohydrates each day from whole grains. today, he ate 220grams of carbohydrates, and 55 grams were from whole grains.
Osvoldo did not meet his goal of getting at least 30% carbohydrates
Although a part of your question is missing, you might refer to this full question: Osvoldo has a goal of getting at least 30% of his grams of carbohydrates each day from whole grains. Today, he ate 220 grams of carbohydrates, and 55 grams were from whole grains. Did Osvoldo meet his goal?
Total carbohydrates he ate = 220 grams
Carbohydrates intake from whole grains = 55 grams
Percentage of carbohydrates in whole grains = (Carbohydrates from whole grain/Total carbohydrate intake)*100
=(55/220)*100
=0.25*100
=25%
Osvoldo got 25% carbohydrates as against his goal of at least 30% carbohydrates
Hence, he did not meet his goal of getting at least 30% carbohydrates
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16 2/3% to simplified question w explination pls
Bonjour,
Answer:
16 2/3 = 50/3
Step-by-step explanation:
16 2/3 = 16.6666666…
Change the percent to a decimal number by moving the decimal two places to the left.
Call this x = 0.16666666…
10x = 1.66666666…
100x 16.66666666…
Subtract 100x - 10x = 15
90x = 15
x = 15/90 = 1/6
16 2/3 % = 1/6
Suppose that the ratio of males to females in the sales field of a large company is 4:5. if there
are 81 sales representatives in the company, how many are male and how many are female?
There are 36 males and 45 females in the sales field.
Ratio of the number:
Ratios compare two numbers, usually by dividing them.
For example,
If you are comparing one data point (A) to another data point (B), your formula would be
=> A/B.
This means you are dividing information A by information B.
Given.
Suppose that the ratio of males to females in the sales field of a large company is 4:5.
Total number of representatives = 81.
Now, we need to find the number of males and number of females.
Let x be the number of representatives.
So, based on the ratio we have written this as,
=> 4x : 5x = 81
So, the total number of representatives is,
=> 4x + 5x = 81
=> 9x = 81
=> x = 81/9
=> x = 9
So, the number of males is
=> 4x => 4(9) = 36
And the number of females is,
=> 5x => 5(9) = 45
Therefore, there are 36 males and 45 females in the sales field.
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