Find the average rate of change of f ( x ) = 9 x 2 − 7 on the interval [ 2 , a ] . Your answer will be an expression involving a
Answer:
9a + 18
Step-by-step explanation:
so the first step is to evaluate the value of f(2).
[tex]f(2) = 9(2)^2-7\\f(2)=9(4)-7\\f(2)=36-7\\f(2)=29[/tex]
Now that we have this value we can use the slope formula (y2 - y1) / (x2 - x1) where y2 is f(a), y1 is 29, x2 is a, and x1 is 2
[tex]\frac{f(a)-29}{a-2}\\\\\frac{(9a^2-7)-29}{a-2}\\\frac{9a^2-36}{a-2}[/tex]
Now from here we can use long division to simplify it further
[tex]9a^2/a = 9a\\9a(a-2)=9a^2-18a\\(9a^2-36)-(9a^2-18a)\\18a-36\\\\18a/a=18\\18(a-2)=18a-36\\(18a-36)-(18a-36)\\0\\\\9a+18[/tex]
Which of the following displays is a relative frequency bar graph?
A bar graph titled eye color has color on the x-axis. Blue, 8; brown, 10; green, 6; hazel, 5; gray, 1.
A bar graph titled social media preferences has platform on the x-axis. Upstart, 0.10; Aster, 0.25; Babble, 0.30; Techy, 0.35.
A bar graph titled Caffeinated Drinks has drink on the x-axis. Coffee, 9; tea, 8; soda, 8; energy, 3.
A bar graph titled social media preferences has platform on the x-axis . Upstart, 4; Aster, 18; Babble, 15; Techy, 12.
Mark this and return
The answer choice which represents a relative frequency bar graph is; A bar graph titled social media preferences has platform on the x-axis. Upstart, 0.10; Aster, 0.25; Babble, 0.30; Techy, 0.35.
What is Relative frequency?The statistical definition of relative frequency is simply the ratio of the frequency of an event in a statistical experiment with respect to the total frequency. Hence, since the frequencies in the social media bar chart as decimals (fractions of a whole), it follows that it is a relative frequency representation.
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Answer Its B
Step-by-step explanation:Edge 2022 I guess
Give the domain and range. A relation. An arrow goes from negative 2 to 4, from 0 to 6, from 2 to 8. a. domain: {–2, 0, 2}, range: {4, 6, 8} b. domain: {0, 2}, range: {6, 8} c. domain: {4, 6, 8}, range: {–2, 0, 2} d. domain: { 6, 8}, range: {0, 2} Please select the best answer from the choices provided A B C D
Answer:
domain= (-2,0,2)
range= (0,4)
Parallel lines m and n are cut by a transversal t. Which pair of angles is a pair of alternate interior angles?
A. 2 and 5
B. 1 and 5
C. 4 and 6
D. 2 and 6
Step-by-step explanation:
2and5 is 7
1and 5 is 6
4and 6 is 10
2and 6is 8
On a number line, 6.87 would be located
6.87
A. To the right of 6.81
B. Between 6 and 6.5
C. Between 6.5 and 7
D. To the left of 6.81
Check all that apply.
Karl, Serene and Pauline have 1281 stickers altogether. 08
Pauline had 3 times as many stickers as Serene.
Karl had 175 stickers fewer than Pauline.
How many stickers did Pauline have?
Pauline has 371 stickers. Karl, Serene, and Pauline have 1281 stickers altogether.
What is the equation?A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.
Let Karl, Serene and Pauline have x, y, and z stickers.
Given condition;
Karl, Serene, and Pauline have 1281 stickers altogether;
x+y+z = 1281
Pauline had 3 times as many stickers as Serene.
z = 3 y
y=z/3
Karl had 175 stickers fewer than Pauline.
x=z -175
Substitute all the values in the terms of z;
x+y+z = 1281
z -175 + z/3 + z = 1281
8z/3 = 1281 +175
z=546
Pauline have;
x = z -175
x =546 -175
x = 371
Hence Pauline has 371 stickers.
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Sketch the graph that has an area of under the standard normal curve and to the left of the z-score. Then find the associated z-score.
The normal distribution is also known as the Gaussian distribution. The correct option is B, while the approx z-score is 0.31.
What is Normal Distribution?The normal distribution, also known as the Gaussian distribution, is a symmetric probability distribution about the mean, indicating that data near the mean occur more frequently than data distant from the mean. The normal distribution will show as a bell curve on a graph.
Since the normal distribution is symmetrical about the mean. Therefore, the correct option is B, while the approx z-score is 0.31.
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Which algebraic expression is equivalent to the expression below
5(4x + 5) - 17
A.
20x + 9
B.
5x + 9
C.
20x + 42
D.
20x + 8
Answer:
20x + 8
Step-by-step explanation:
5*4x + 5*5 -17
20x +25 -17
20x + 8
The volume of a tree stump can be modeled by considering it as a right cylinder. Jin measures its radius as 11 in and its volume as 13685 cubic inches. Find the height of the stump in inches. Round your answer to the nearest tenth if necessary.
If the radius of tree stump is 11 inches and volume is 13685 cubic inches then the height will be equal to 36 inches.
Given Radius of tree stump is 11 inches and volume is 13685 cubic inches.
We know that the volume of cylinder will be equal to π[tex]r^{2} h[/tex].
Volume which is given as 13685 cubic inches.
13685=π[tex]r^{2}h[/tex]
π=22/7
13685=π[tex](11)^{2}[/tex]h
h=13685*7/22*121
h=95795/2662
h=35.98
if we round it to nearest tenth then the value of h be 36 inches.
Hence if radius is 11 inches, volume is 13685 cubic inches then the height of tree stump will be 36 inches.
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Answer:36
Step-by-step explanation:
The value of the expression 2x2/x+(100-15x) when x=5 is
Answer:
27
Step-by-step explanation:
find the first 4 terms and the 10th term from 3n+4
Answer:
16 and 34
Step-by-step explanation:
The general form = 3n+4
The 4th term = 3(4)+4 = 12+4 = 16
The 10th term = 3(10)+4= 30+4= 34
Find the x-intercept of 2x+2y=2
Answer:
x-intercept: (1,0)
y-intercept: (0,1)
Step-by-step explanation:
Given: Find the x and y intercepts of 2x + 2y = 2
X-interceptTo solve for a x - intercept we have to substitue 0 in for y and solve for [tex]x[/tex]
Lets do it:
2x + 2(0) = 2
2x + 0 = 2
2x = 2
x = 1
Therefore, this means that when y = 0, x = 1 or (1,0)
Y-intercept
To solve for a y - intercept we have to substitue 0 in for x and solve for [tex]y[/tex]
Lets do it:
2(0) + 2y = 2
0 + 2y = 2
2y = 2
y = 1
Therefore, this means that when x = 0, y = 1 or (0,1)
Each serving of a cereal is 80 calories.which expression can be used to find the number of calories In 3 servings
Answer:
[tex]80\times3[/tex]
Step-by-step explanation:
Based on the given conditions, formulate: [tex]80\times3[/tex]
Calculate the product or quotient: 240
get the result: 240
Answer: 240
To find this answer, we had to use the expression 80 * 3, therefore making it the answer.
Answer:
240
Step-by-step explanation:
80*3=240
so u multiply the equation
Which information could he have used to determine this?
O GLH = ILM
O m KLM = 5m ILMO
O m GLI = 2m GLH
O m GLI = 1/2m GLH + 1/2m HLI
Answer:
m∠GLI = 2m∠GLH
Step-by-step explanation:
Angle GLI (red) is made of angles GLH (purple) and HLI (green).
m∠GLI = m∠GLH + m∠HLI
First option: ∠GLH ≅ ∠ILM (Angle GLH is congruent to angle ILM.)
This doesn't tell us anything about the relationship between angles GLI, GLH and HLI. So it can't be used.
Second option: m∠KLM = 5m∠ILM (Measure of angle KLM is 5 times the measure of angle ILM.)
This also cannot be used, because it doesn't include angles GLI, GLH or HLI.
Third option: m∠GLI = 2m∠GLH (Measure of angle GLI is two times the measure of angle GLH.)
Now this option is more interesting. It includes two angles of three that we are interested in.
If angle GLI is two times angle GLH, then that means that angle GLH is congruent to angle HLI!
Let's prove this with equations.
1) m∠GLI = m∠GLH + m∠HLI (from picture)
2) m∠GLI = 2m∠GLH (from third option)
Substitute m∠GLI in first equation with m∠GLI in second.
m∠GLI = m∠GLH + m∠HLI
2m∠GLH = m∠GLH + m∠HLI
m∠GLH = m∠HLI
So this proves that the angles GLH and HLI have the same measure, therefore ray LH is bisector of GLI.
Fourth option: m∠GLI = 1/2m∠GLH + 1/2m∠HLI
There are all angles we are interested in, but there is a mistake. We can see in the picture that angle GLI is made of angle GLH and HLI and not of half of them. This just is not true. The correct equation would be m∠GLI = m∠GLH + m∠HLI.
How do l do this please help
The attached graph represents the graph of the parallel lines
How to plot the lines?The equation of the lines are linear equation
A linear equation is represented as:
y = mx + b
Where b represents the y-intercept.
Using the above form of linear equation as a guide, the equations of the lines are
y = -x + 5
y = -x + 2
y = -x - 3
y = -x - 2
Where -5, 2, -3 and -2 are the given y-intercepts and y = -x is the base equation.
Next, we plot the equations on a coordinate grid
See attachment
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find the midpoint A and B where A has a coordinates (2, 7) and B has coordinates (6,3)
Answer:
(2+6)/2= 4 (x-coordinate of midpoint)
(7+3)/2= 5(y=coordinate of midpoint)
Answer:
Hope it will help you:)
Step-by-step explanation:
Solution:
here,
A(2,7)-([tex]x_{1,}y_{1[/tex])
B(6,3)-([tex]x_{2},y_{2[/tex])
Now using midpoint formula,
midpoint of ab=(x1 + x2)/2, (y1 + y2)/2
=(2+6)/2,(7+3)/2
=(8/2,10/2)
=(4,5)
The midpoint of AB is(4,5).
DO NOT PUT A WRONG ANSWER OR ELSE I WILL START TO REPORT YOU!!!
A person who is 6 feet tall is walking away from a lamp post at the rate of 40 feet per minute. When the person is 10 feet from the lamp post, his shadow is 20 feet long. Find the rate at which the length of the shadow is increasing when he is 30 feet from the lamp post.
Identifying an Error
Identify the error in the student solution shown
below. Find the correct answer.
2ln(x)= In(3x) - [In(9) - 2ln(3)]
In(x²) In(3x)-[In(9) - In(9)]
In(~2) 1/25)
The incorrect step is ln(x²) = ln(3x/0) because ln(x/y) = lnx - lny and the solutions are x = 0, 3
What is a logarithm?It is another way to represent the power of numbers, and we say that 'b' is the logarithm of 'c' with base 'a' if and only if 'a' to the power 'b' equals 'c'.
[tex]\rm a^b = c\\log_ac =b[/tex]
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have:
2ln(x) = In(3x) - [In(9) - 2ln(3)]
In(x²) = In(3x) - [In(9) - In(9)]
ln(x²) = ln(3x) - 0
ln(x²) = ln(3x/0) (incorrect step)
ln(x²) = ln(3x)
x² = 3x (correct step)
x² - 3x =0
x(x - 3) = 0
x = 0, 3
Thus, the incorrect step is ln(x²) = ln(3x/0) because ln(x/y) = lnx - lny and the solutions are x = 0, 3
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Suppose there is a big drop in interest rates in Mexico and a small drop in U.S. interest rates. Everything else equal, what is likely to happen to value of the MXN?
If we suppose that there is a big drop in the interest rates in Mexico and a small drop in the interest rates in the U.S.A, with everything else equal, the value of MXN will decrease.
The foreign exchange market works according to the principles of firms, households, and investors:
These three constituent factors of the foreign exchange market determine the demand and supply patterns in the market. Demand for a foreign currency might increase in the foreign exchange market is linked to the expectation of an increase in the value of a foreign currency. Supply of a foreign currency in the foreign exchange market is linked to an inverse principle, where the expectation of a decrease in the value of foreign currency pushes supply upwards. If we are to suppose that there is a big drop in the interest rates in Mexico and a small drop in the interest rates in the U.S.A., then the value of the MXN will decrease, with everything being equal. A higher interest rate leads to the appreciation of a foreign currency relative to other currencies in the foreign exchange market. A lower interest rate leads to the depreciation of a foreign currency relative to other currencies in the foreign exchange market.Therefore, if we suppose that there is a big drop in the interest rates in Mexico and a small drop in the interest rates in the U.S.A, with everything else equal, the value of MXN will decrease.
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Find the value of y when x equals 4.
-3x + 9y = -57
Answer:
y = -5
Step-by-step explanation:
Isolate y:
-3x + 9y = -57
9y = -57 + 3x
y = (-57/9) + (3/9)x
Substitute for x:
y = (-57/9) + (3/9)(4)
y = (-57/9) + (12/9)
y = (-45/9)
y = -5
Answer:
[tex]\mathsf {y = -5}[/tex]
Step-by-step explanation:
[tex]\textsf {Given :}\\\textsf {-3x + 9y = -57}[/tex]
[tex]\textsf {Divide throughout by 3 :}[/tex]
[tex]\mathsf {\frac{1}{3} \times (-3x + 9y) = \frac{1}{3} \times -57}[/tex]
[tex]\mathsf {-x + 3y = -19}[/tex]
[tex]\textsf {Substitute x = 4 :}[/tex]
[tex]\mathsf {-(4) + 3y = -19}[/tex]
[tex]\mathsf {3y = -15}[/tex]
[tex]\textsf {Divide by 3 on both sides :}[/tex]
[tex]\mathsf {\frac{3y}{3} = \frac{-15}{3} }[/tex]
[tex]\mathsf {y = -5}[/tex]
40 points please Please help me
Answer:
19.51 units = x
Step-by-step explanation:
Here is one way :
Height = 18 cos 47 = 12.276
then cos 51 = 12.276 / x
x = 12.276 / cos 51 = 19.51
The high temperature on Friday was 8 degrees above zero. The low temperature was 3 degrees below zero. Which expression gives the average of the low and high temperatures?
Negative (3 + 8) divided by 2
(negative 3 + 8) divided by 2
(negative 3 + 8) divided by (negative 2)
Left-bracket negative 3 + (negative 8) right-bracket divided by (2) Right-bracket
Using the mean concept, the expression that gives the average of the low and high temperatures is:
(-3 + 8)/2.
What is the mean?The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.
In this problem, the two observations are -3 and 8, hence their average is given by:
(-3 + 8)/2.
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You can make a tent by throwing a piece of cloth over a clothesline, then securing the edge to the ground with stakes so that an isosceles triangle is formed. How long would the cloth have to be so that the opening of the tent was 8 feet wide and 3 feet high?
Based on the required width and height of the tent, the length of the cloth would have to be 14.4 ft.
How long should the length of the cloth be?The opening of the tent would be an isosceles triangle but if it is divided in two from the top, a right-angled triangle will be formed and the hypotenuse will be the length of the cloth on one side.
That length - according to the Pythagoras theorem - would be:
= √(6² + (8 /2)²)
= √(36 + 16)
= 7.2 ft
As this is the length of one side of the cloth, the length of the entire cloth is:
= 7.2 x 2
= 14.4 ft
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Determine the value(s) for which the rational expression −5u+12−2u+2 is undefined. If there's more than one value, list them separated by a comma, e.g. u=2,3.
The value(s) for which the rational expression −5u+12−2u+2 is undefined is u = 1.
What is radial expression?The expression or an equation which can be undefined at some point is a celled the radial expression.
f(u) = -5u +12 / -2u +2
For the function to be undefined, denominator must be equal to zero.
-2u +2 =0
-2u =-2
u = 1
Thus, the value for which the given expression is undefined is 1.
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What value represents the vertical translation from the graph of the parent function f(x)=x² to the graph of the function
g(x)=(x+5)2+3?
-5
-3
O
3
O5
The value is 3 which represents the vertical translation from the graph of the parent function f(x)=x² option third 3 is correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a function:
f(x) = x²
The above function is a parent function.
The translation: vertical translation from the graph of the parent function.
F(x) → f(x) + 3
F(x) = x² + 3
The above function will shift vertical up by 3 units.
Thus, the value is 3 which represents the vertical translation from the graph of the parent function f(x)=x² option third 3 is correct.
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Consider the equation below. "-2(5x+8)=14+6x" The equation was solved using the following steps.
The equation -2(5x+8) = 14+6x solved using step by step representation is x = -15/8.
Solving steps for the EquationThe equation to be considered as given in the task content is; -2(5x+8)=14+6x.
It follows from the task content that the steps for solving the equation are as follows;
-2(5x+8) = 14+6x
Step 1: opening parenthesis-10x - 16 = 14 + 6x
Step 2: collect like terms-10x - 6x = 14 + 16
Step 3: evaluate-16x = 30
Step 4: Divisionx = 30/-16
x = -15/8
Hence, the value of x upon solving the equation is; -15/8.
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17 = a + b
b is one more than a
work out the values of a and b
(simultaneous equation)
Answer:
Step-by-step explanation:
Solution
17 = a + b
b = a + 1 Substitute b into the top equation
17 = a + a+1 Combine
17 = 2a + 1 Subtract 1 from both sides
17-1 = 2a+1-1 Combine
16 = 2a Divide both sides by 2
16/2 = 2a/2
a = 8
b = 8 + 1 = 9
Answer
a = 8
b = 9
X-y=5 and x^2y=5x+6
By applying algebraic handling on the two equations, we find the following three solution pairs: x₁ ≈ 5.693 ,y₁ ≈ 10.693; x₂ ≈ 1.430, y₂ ≈ 6.430; x₃ ≈ - 0.737, y₃ ≈ 4.263.
How to solve a system of equations
In this question we have a system formed by a linear equation and a non-linear equation, both with no trascendent elements and whose solution can be found easily by algebraic handling:
x - y = 5 (1)
x² · y = 5 · x + 6 (2)
By (1):
y = x + 5
By substituting on (2):
x² · (x + 5) = 5 · x + 6
x³ + 5 · x² - 5 · x - 6 = 0
(x + 5.693) · (x - 1.430) · (x + 0.737) = 0
There are three solutions: x₁ ≈ 5.693, x₂ ≈ 1.430, x₃ ≈ - 0.737
And the y-values are found by evaluating on (1):
y = x + 5
x₁ ≈ 5.693
y₁ ≈ 10.693
x₂ ≈ 1.430
y₂ ≈ 6.430
x₃ ≈ - 0.737
y₃ ≈ 4.263
By applying algebraic handling on the two equations, we find the following three solution pairs: x₁ ≈ 5.693 ,y₁ ≈ 10.693; x₂ ≈ 1.430, y₂ ≈ 6.430; x₃ ≈ - 0.737, y₃ ≈ 4.263.
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Elian is placing a rectangle in the coordinate plane. He knows that the shorter side of the rectangle is half the length of the longer side. He places the longer side on the x-axis. What coordinates should he assign to the top-left vertex of the rectangle? Enter your answer in the boxes. ( , )
A rectangle is in the coordinate plane so that the bottom left vertex is at 0 comma 0, the top left vertex is on the positive side of the y-axis and is labeled question mark comma question mark, the top right vertex is in the first quadrant, and the bottom right vertex is on the positive side of the x-axis and is labeled 2 a comma 0.
Answer:
(0, a)
Step-by-step explanation:
We can start by imagining this rectangle as a square.
(This is written as if it is a square:)
The distance that a square reaches on the x-axis (assuming it has its lower left point at the origin, like this one does) is the same distance that it reaches on the y-axis.
meaning that we will have (length, 0) along the x-axis and (0, length) along the y-axis
so, if we are to treat this as a square, the point (2a, 0) means that our opposite vertex is (0, 2a)
However, because this length is only half of the length that it would be (if it were a square), we must divide our length by 2
2a ÷ 2 = a
So, the coordinates of the top-left vertex of this rectangle:
(0, a)
Answer:
coordinates of top left vertex: (0, a)
help me with this please i will gave u bralinet answer who ever answer first
Answer:
[tex]\fbox {5 times}[/tex]
Step-by-step explanation:
Days where both will be done :
⇒ 2nd day × 3rd day
⇒ 6th day
Number of times in September :
⇒ The month has 30 days
⇒ Number of times = 30/6
⇒ Number of times = 5
Answer:
5 times
Step-by-step explanation:
• Calculate the lowest common multiple (LCM) of 2 and 3 to find the first day of the month in which she will do both:
LCM (2 and 3) = 2 x 3
= 6
This means, she will do both every 6th day.
• There are 30 days in September. To find how many days she will do both in September, we have to calculate how many 6-day blocks there are in 30 days:
⇒ 30 ÷ 6
= 5 times
