The value of the function f(x + a) - f(x) is √(x + a - 9) - √(x - 9)
How to evaluate the function value?The function definition is given as
f(x) = √(x - 9) + 6
We start by calculating the function f(x + a)
So, we have
f(x + a) = √(x + a - 9) + 6
The function definition f(x + a) - f(x) is calculated as
f(x + a) - f(x) = √(x + a - 9) + 6 - (√(x - 9) + 6)
Open the bracket
So, we have
f(x + a) - f(x) = √(x + a - 9) + 6 - √(x - 9) - 6
Evaluate the difference
So, we have
f(x + a) - f(x) = √(x + a - 9) - √(x - 9)
Hence, the value of the function f(x + a) - f(x) is √(x + a - 9) - √(x - 9)
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what are 2 common sources of income?
passive income
dividends, real estate, interest income
active income
salary, business income,
4. Write the numbers between the following numbers.
(a) 2,390, 340 and 2,390,345
(b) 18,851 and 19,857
(c) 4,004 and 4,010
(d) 761,681 and 761,686
(e) 624,180 and 624,185 to
Answer:
2,390
18,851
4,004
761,681
624,180
A(n) ____ of a polyhedron is the intersection of the _____ of the polyhedron
An Edge of a polyhedron is the intersection of the Vertex of the polyhedron.
What is a polyhedron?A polyhedron can be described as the 3-dimensional solid that is been formed through the combination of more than one polygons and they usually have different faces which is been used in knowing them as well as their classification.
It should be noted that this polyhedrons can be categorized based on the number of faces that can be found on them, however in this case we can conclude that the Vertex serves as the point of intersection that the edges of polyhedron has.
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Answer:
edge, vertex
Step-by-step explanation:
What are the solutions to the inequality (x-3)(x+5) ≤0
O (x13≤x≤5}
Oxl-5≤x≤-3}
Ox-5≤x≤3}
O x-3≤x≤5}
The solutions to the given inequality is: C. {x| -5 ≤ x ≤ 3}.
What is an inequality?An inequality can be defined as a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following arguments:
Less than (<).Greater than (>).Less than or equal to (≤).Greater than or equal to (≥).The given inequality can be rewritten as follows:
(x - 3) ≤ 0.
(x + 5) ≤ 0.
Evaluating the inequalities, we have:
(x - 3) ≤ 0
x - 3 ≤ 0
x ≤ 0 + 3
x ≤ 3
(x + 5) ≤ 0
x + 5 ≤ 0
x ≤ 0 - 5
x ≤ -5
Combining the inequalities together, we have:
-5 ≤ x ≤ 3
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The diameter of the sun is approximately 1.4x10^9 Km and the diameter of Earth is approximately 1.28x10^4 Km. About how many times Earth's diameter is the sun's diameter?
The sun's diameter as described in the task content is; ; 1.09 × 10⁵ times the earth's diameter.
This follows from the given premise that; the diameter of the sun is approximately 1.4x10⁹ Km and the diameter of Earth is approximately 1.28x10⁴ Km
By how much is the sun's diameter greater than the earth's diameter?According to the task content; The diameter of the sun is approximately 1.4x10^9 Km and the diameter of Earth is approximately 1.28x10^4 Km.
The number of times by which the sun's diameter is greater than the earth's diameter can be evaluated as follows;
= 1.4 × 10⁹/1.28 × 10⁴
= 1.09 × 10⁵
Ultimately, The sun's diameter as described in the task content is; 1.09 × 10⁵ times the earth's diameter.
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One spring day, Camila noted the time of day and the temperature, in degrees Fahrenheit. Her findings are as follows: At 6 a.m., the temperature was 60° F. For the next 4 hours, the temperature rose 2° per hour. For the next 2 hours, it rose 3° per hour. The temperature then stayed steady until 6 p.m. For the next 3 hours, the temperature dropped 2° per hour. The temperature then dropped steadily until the temperature was 66° at midnight. On the set of axes below, graph Camila's data.
The graph of Camila's data representing temperature on the y-axis and time on the x-axis is as attached
How to Graph a Table of Values?
The question is a word problem that involves constructing a table of values and then graph the table values data as below;
Time Temperature
6:00 56
7:00 59
8:00 62
9:00 65
10:00 66
11:00 67
12:00 68
13:00 69
14:00 70
15:00 70
16:00 70
17:00 70
18:00 70
19:00 67
20:00 64
21:00 61
00:00 60
The graph of Camila's data representing temperature on the y-axis and time on the x-axis is as attached
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2x - (x + 1) = - 4 + 3(x-3)
Answer:
-1
Step-by-step explanation:
6. What value of x cannot be
evaluated in the function
F(x)?
The value of x that cannot be evaluated in the function F(x) is 3
What is the domain of a function?The domain of the function is the set of input values of the graph
What is the range of a function?The range of a function is the set of output values of the graph.
This in other words mean the range of a function is the set of y values of the graph.
How to determine the value of x that cannot be evaluated in the function F(x)?The function is given as
f(x) = (x + 13)/(x - 3)
Set the denominator of the function to 0
So, we have
x - 3 = 0
Evaluate the equation
x =3
This means that x =3 is not in the domain of the function
Hence, the value of x that cannot be evaluated in the function F(x) is 3
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what is an equation of the line that passes through the points (-4,-7) and (2,8)
Answer:
y=5/2x+3 or [tex]y=\frac{5}{2}x+3[/tex]
Step-by-step explanation:
Step 1:
Compute the slope (-4, -7), (2,8):
m=5/2
Step 2:
Compute the y intercept:
b=3
Step 3:
Add the results together:
y=5/2x+3 or [tex]y=\frac{5}{2}x+3[/tex]
Hence, the final answer is y=5/2x+3 or [tex]y=\frac{5}{2}x+3[/tex]
Greetings from Brasil...
One way to solve this question is through determinant
| X Y 1 |
| X₁ Y₁ 1 | = 0
| X₂ Y₂ 1 |
We have:
(X₁; Y₁) = (-4; -7)
(X₂; Y₂) = (2; 8)
then
| X Y 1 |
| -4 -7 1 | = 0
| 2 8 1 |
- 15X + 6Y - 18 = 0________________________________
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I STILL NEED HELP URGENTLY
The coordinates of the endpoints of
FG are F(–8,3) and G(–2,–9). Point H is on FG and divides it such that FH:GH is 1:2.
What are the coordinates of H?
The coordinates of H are (-9,-1) when H is on FG and divides it such that FH:GH is 1:2.
Section formula is employed to search out the magnitude relation within which a line section is split by some extent internally or outwardly. it's accustomed resolve the centre of mass, incenter and excenters of a triangle.Section formula is employed to see the coordinate of some extent that divides a line section change of integrity 2 points into 2 elements specified the magnitude relation of their length is m:n.Let P and alphabetic character be the given 2 points (x₁,y₁) and (x₂,y₂) severally, and M be the purpose dividing the line-segment PQ internally within the magnitude relation m:n, then kind the sectional formula for determinative the coordinate of some extent M is given by: (x , y ) = mx₂+ nx₁/m + n , my₂ + ny₁ / m + n .It is given that F(–8,3) and G(–2,–9) and ratio of FH:GH is 1:2.
The diagram of this question is given below.
Let coordinates of H be ( x , y) .
By using sections formula , we get
(x , y) = ( 1(-2) + 2(-8) / 1+2 , 1(-9) +2(3) / 1+2 )
(x , y) = ( -2 -16 / 1 +2 , -9 +6 / 1 +2 )
(x , y) = ( -18 / 3 , -3/3)
(x , y) = ( -9 , -1)
On comparing , we get x = -9 and y = -1.
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Write the ratio 4/5 with the numerator of 16
Answer:
16/20
Step-by-step explanation:
4 × 4 =16
therefore
16/(4×5)=ratio
16/20
Bottoms Up Diaper Service is considering the purchase of a new industrial washer. It can purchase the washer for $7,200 and sell its old washer for $2,500. The new washer will last for 6 years and save $1,700 a year in expenses. The opportunity cost of capital is 15%, and the firm’s tax rate is 21%.
Answer:
ysfsfdf
Step-by-step explanation:
frfrfrfrb
rewrite 17/18 and 11/12 so that they have a common denominator.
Answer: 17/18=34/36
11/12=33/36
Step-by-step explanation:
17/18 and 11/12
First find the LCM, least common multiple, of the denominators 18 and 12.
In order to do that, list the factors of 18 and 12 and find the least common factors of them excluding 1.
18: 1, 2, 3, 6, 9, 18
12: 1, 2, 3, 4, 6, 12
Notice any common small factors? Yes they are 2 and 3. Now, multiply them with 18 and 12.
18*2=36
12*3=36
Hence, LCM is 36.
17/18=(17*2)/(18*2)=34/36
11/12=(11*3)/(12*3)=33/36
solve system of equations by using elimination method. (solve for (x,y,z) please explain the steps im so confused.
4x-y-2z=-8
-2x+4z=-4
x+2y=6
The solutions of the system of equations are:
x = -2, y = 4, z = -2
How to solve a system of equations by the elimination method?
Here we have the system of equations:
4x - y - 2z = -8
-2x + 4z = -4
x + 2y = 6
To eliminate one variable, we can add the second equation and two times the third equation, we will get:
(-2x + 4z) + 2*(x + 2y) = -4 + 2*6
Now we can simplify that so we get:
4z + 4y = -4 + 12
4*(z + y) = 8
z + y = 8/4 =2
z + y = 2
With that we can write z in terms of y.
z = 2 - y
And with the third equation we can write x in terms of y.
x = 6 - 2y
Replacing that in the first equation we get:
4*(6 - 2y) - y - 2*(2 - y) = -8
Now we can solve this for y.
24 - 8y - y +2y - 4 = -8
20 - 11y = -8
-7y = -28
y = 28/7 = 4
Now that we know the value of y we can find the values of x and z.
x = 6 - 2y = 6 - 2*4 = -2
z = 2 - y = 2 - 4 = -2
The solutions of the system of equations are:
x = -2, y = 4, z = -2
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What is the answer to 9+10= ?
Answer:
19 (if we're being real)
If you're talking abt the meme, 21
Step-by-step explanation:
The Thai Pepper has a hotness rating of 7.5 x 10^4 on the Scoville scale.
The Red Savina Habanero has a hotness rating of 4.6 x 10^5 on the Scoville scale.
How many times hotter is the Red Savina Habanero than the Thai Pepper?
a
Divide (4.6 x 10^5) / (7.5 x 10^4) = (4.6 / 7.5) x (10^(5-4)) = .613 x 10^1 = 6.13 times hotter
b
Multiply (7.5 x 10^4) x (4.6 x 10^5) = (7.5 x 4.6) x (10^(4+5)) = 34.5 x 10^ 9 = 3.45 x 10^10
c
Divide (7.5 x 10^4) / (4.6 x 10^5) = (7.5 / 4.6) x (10^(4-5)) = 1.63 x 10^ 1 = 16.3 times hotter
d
Multiply (7.5 x 10^4) x (4.6 x 10^5) = (7.5 x 4.6) x (10^(4+5)) = 34.5 x 10^ 9 = 3.45 x 10^10 times hotter
The Red Savina Habanero is 6. 13 times hotter than the Thai Pepper. Option A
What is ratio?A ratio can be defined as the comparison of two or more numbers on the basis of their sizes in relation to each other;
Given that;
Thai Pepper has a hotness rating of 7.5 x 10^4 Red Savina Habanero has a hotness rating of 4.6 x 10^5To determine the ratio, we have to divide Red Savina Habanero hotness rating by Thai Pepper hotness rating
This is represented as;
= 4.6 x 10^5 / 7.5 x 10^4
= 6. 13 times
The Red Savina Habanero is 6. 13 times hotter
Thus, the Red Savina Habanero is 6. 13 times hotter than the Thai Pepper. Option A
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By taking the quotient between the ratings, we can see that Red Savina Habanero is 6.13 times hotter than the Thai Pepper.
How many times hotter is the Red Savina Habanero than the Thai Pepper?We know that the Thai Pepper has a hotness rating of 7.5*10⁴, while the Red Savina Habanero has a hotness rating of 4.6*10⁵.
We want to see how many times hotter is the Red Savina Habanero than the Thai Pepper, to find that we need to take the quotient between the rating for the Habanero and the rating for the Pepper.
It gives:
Q = (4.6*10⁵)/(7.5*10⁴)
This can be rewritten as:
Q = (4.6/7.5)*(10⁵/10⁴)
=0.613*(10 ⁵⁻⁴) = 0.613*10
Now, we want to write this in scientific notation, so we need to have a single digit different than zero in the left side of the decimal point.
Then we can rewrite:
0.613*10 = 6.13*10⁰ = 6.13
We conclude that the Red Savina Habanero is 6.13 times hotter than the Thai Pepper.
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(x+5)(x-2) please solve this equation fast
[tex] \large \bf \implies{ {x}^{2} + 3x - 10}[/tex]
Step-by-step explanation:[tex](x + 5)(x - 2)[/tex]
Step 1) : Using the identity
[tex] \bf \longrightarrow{(x+a)(x+b) = x² + (a+b)x + ab}[/tex]
Step 2) : Simplify it with using the identity told earlier in step 1) .
[tex] \bf \longrightarrow(x + 5)(x - 2) \\ \\ \bf \longrightarrow{x}^{2} + (5 + ( - 2))x + (5)( - 2) \\ \\\bf \longrightarrow {x}^{2} + (5 - 2)x + ( - 10) \\ \\\bf \longrightarrow {x}^{2} +3x - 10[/tex]
Step 3) : We have got the answer in step 2) .
[tex] \large\bf \longrightarrow { {x}^{2} + 3x - 10}[/tex]
If you have two quarters, five dimes, and three pennies how much money do you have?
Answer:
2 quartes is equal to 50 cent, 5 dimes is equal to 50 cent, and 3 pennies is equal to 3 cents.
50 + 50 + 3 = 103
$1.03
Step-by-step explanation:
Hope it helps! =D
Answer:
1 dollar and 3 cents.
2 cents=0.5 dollars
5 dimes=0.5 dollars
3 pennies=0.03 dollars
$1.03
Suppose that two balls are selected with replacement from a bag that contains 10 white and 5 black balls. What is the probability that both balls are black?
The probability that both the balls are black is [tex]\frac{1}{9} \\[/tex] .
Probability is the section of mathematics which deals with the likelihood of an event happening.
The value of probability is a fraction which always lies between 0 and 1. it is defined as the ratio of the favorable outcomes of an event to the total outcome of an event.
Given the bag has 10 white balls and 5 black balls. Therefore the total number of balls in the bag is 15 .
Hence the sample space is 15 .
The balls are drawn with replacement. Therefore for the first ball pick:
Number of favorable outcomes = 5
Total number of outcomes = 15
Probability = favorable outcome ÷ total outcome
Therefore [tex]P_1=\frac{5}{15}=\frac{1}{3}[/tex]
Now the ball is placed back and the second ball is picked.
Number of favorable outcomes = 5
Total number of outcomes = 15
Probability = favorable outcome ÷ total outcome
Therefore [tex]P_2=\frac{5}{15}=\frac{1}{3}[/tex]
Now the total probability that both the balls are black is :
P = P₁×P₂
[tex]P=\frac{1}{3}\times \frac{1}{3}\\\\P=\frac{1}{9}[/tex]
Hence the probability of picking two black balls is [tex]\frac{1}{9} \\[/tex] .
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Bisecting something achieves which of the following? Select all that apply.
*
Adds circles to a line segment.
Cuts in half.
Makes two equal pieces.
Moves an object along a path.
The answer choices which represent the meaning of bisecting something from the answer choices are;
Cuts in half.Makes two equal pieces.What is the meaning of bisecting something?It follows from the task content that the choices achieved by bisecting something are to be identified.
As the word implies, the term bisecting simply means cutting into equal pieces.
This follows from the prefix bi- in the word as it means two while sectioning simply involves the division.
Ultimately, the answer choices achieved by bisecting something are;
Makes two equal pieces.Cuts in half.Read more on bisection;
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Erin wants to put in a fence around her rectangular garden. If the fence will be 20 ft. wide by 25 ft. long, what is the area of the garden?
Answer:
500
Step-by-step explanation:
20*25
I don't know if this is right this is just how my teacher taught my class
Find the mean, median, and mode of the data, if possible. If any of these measures cannot be found or a measure does not represent the center of the data, explain why.
A sample of seven admission test scores for a professional school are listed below.
11.3, 9.9, 9.6, 11.5, 9.6, 11.2, 10.6
The mean is 12.28
The mode is 9.6.
The median is 10.25.
What is the median, median and mode?Mean, median, and mode are measures of central tendency. Mean is the average of a set of numbers. Median is the number that is at the center of a dataset when the dataset is arranged in ascending or descending order. Mode is the number that occurs most frequently in a dataset.
Mean = sum of numbers / total number
(11.3 + 9.9 + 9.6 + 11.5 +9.6 + 11.2 + 10.6) / 6
= 73.7 / 6
= 12.28
The number that occurs most frequently is 9.6. It occurs twice in the dataset. 9.6 is the mode.
The median = (total number + 1) / 2
(6 + 1) / 2
= 7/2 = 3.5 digit
9.6, 9.6, 9.9, 10.6, 11.2, 11.3
(9.9 + 10.6) / 2
= 20.5 / 2 = 10.25
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please help me i’ll give you brain list as long as it’s right
Answer:
Rational & Integer
Step-by-step explanation:
Rational numbers are real numbers. Unlike Irrational numbers, they have a clear value.
Integers are just counting numbers but including 0 and negative numbers.
Hope this helps :)
the point (3, 5) is on the graph of the function f, then the point (x, y) =
is on the graph of F-1.
let me give you a mouthful of something
the domain of f(x) is the range of its inverse, or namely the domain of f(x) is the same set as the range of f⁻¹(x), so for any (a , b) pair on the domain of f(x), there's a (b , a) on the range of f⁻¹(x).
now, that's a bit of of a mumble, but in short it means, if f(x) has a point of (3 , 5), then the graph of f⁻¹(x) has a point which is the same pair but flipped sideways, namely (5 , 3).
that's pretty much true for any function that has an inverse.
there are two rates that relate meters and kilometers. in the second Model it, why is 1/1000 the unit rate that is used to convert 3,200 meters to kilometers
3200 meters by using the units of conversion will be equal to 3.2 km.
We are given:
3200 meters.
We know that the unit of conversion for the meters and kilometers is given by:
1 km = 1000 m
1 m = 1 / 1000 km
For 3200 m, we will use the operation of multiplication.
So, we get that:
3200 m = 1 / 1000 × 3200 km
3200 m = 3.2 km.
Therefore, we get that, 3200 meters by using the units of conversion will be equal to 3.2 km.
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Show that the binomial is a factor of the polynomial. Then factor the polynomial completely.
s(x) = x¹ +4x³ - 64x - 256; x+4
Answer:
Hello,
Step-by-step explanation:
[tex]x^4+4x^3-64x-256\\=x^3(x+4)-64(x+4)\\=(x+4)(x^3-64)\\-----------\\s(x)=x^4+4x^3-64x-256\\=(x+4)(x^3-4^4)\\=(x+4)(x-4)(x^2+4x+16)\\[/tex]
help help help help !!!!!!! please
The evaluations of the quadratic equation at the values of 0, 7 and - 5 are 5, 1356 and - 460, respectively.
How to evaluate a polynomial function
In this question we have the definition of a quadratic equation, which has to be evaluated at three distinct values of x. Evaluating a function consists in substituting the independent variable by a value and simplify the expression. Now we proceed to evaluate the function:
f(0) = 4 · 0³ - 7 · 0 + 5
f(0) = 5
f(7) = 4 · 7³ - 7 · 3 + 5
f(7) = 1372 - 21 + 5
f(7) = 1356
f(- 5) = 4 · (- 5)³ - 7 · (- 5) + 5
f(- 5) = - 460
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Enter a fraction that is equivalent to 4/5 with a numerator of 28.
Answer:
28/35
Step-by-step explanation:
4/5 *7/7=28/35
Answer:
pre-test
Step-by-step explanation:
(1) identifity my own strengths
interest and challenges.
Which number line represents the solution set for the given inequality?
x+1 ≤-3 or-4x<-8
Answer:
x ≤-4 or x> 2
Step-by-step explanation:
x+1 ≤-3 or-4x<-8
First solve the inequality on the left
x+1 ≤-3
Subtract 1 from each side
x+1-1 ≤-3-1
x ≤-4
Then solve the inequality on the right
-4x<-8
Divide each side by -4, remembering to flip the inequality
-4x/4 > -8/-4
x > 2
Put them back together
x ≤-4 or x> 2
Closed circle at -4 and line going to the left and open circle at 2 and line going to the right
[tex]1/2(4x-2)\leq 9+7x[/tex]
[tex]\cfrac{1}{2}(4x-2)\leqslant 9+7x\implies 2x-1\leqslant 9+7x\implies -1\leqslant 9+5x \\\\\\ -10\leqslant 5x\implies \cfrac{-10}{5}\leqslant x\implies {\LARGE \begin{array}{llll} -2\leqslant x \end{array}}[/tex]
le's notice that, we divided by a positive number, thus the inequality sign didn't flip.