Answer:
[tex]f(x)=-2^x[/tex]
Step-by-step explanation:
So generally an exponential equation is expressed in the form: [tex]f(x)=a(b)^x[/tex] and: [tex]b=1+r\text{ or }b=1-r \text{ depending on whether it's decaying or growing}[/tex]. In this case we see that as x increased by 1, the y-decreases, BUT the absolute value is increasing, so it's really just reflected.
Plug in known values:
[tex]-2=a(b)^1[/tex]
[tex]-4=a(b)^2[/tex]
So if you think about it. you really have
-2 = a * b
-4 = a * b * b
since ab = -2, then we can substitute this into the second equation
-4 = -2 * b
-4 = -2b
Divide both sides by -2
b = 2
You can also deduce that b=2, by realizing to go from -2 to -4, you have to subtract 100% of -2 from -2. This means r=1, so b=1+1, b=2
Anyways, now it's time to solve for a, by plugging in a point as well as b.
-4 = a(2)^2
-4 = 4a
-1 = a
You can verify this by using the other point
-2 = -(2)^1
-2 = -(2)
-2 = -2
So the equation is: [tex]f(x)=-2^x[/tex]
Given the following information, determine which lines, if any, are parallel. State the
postulate or theorem that justifies your answer.
1. Lines a and b are parallel by the converse of alternate interior angles theorem
2. l║m by the converse of consecutive interior angles theorem.
What is the Converse of Alternate Interior Angles Theorem?Given that the interior angles, ∠3 ≅ ∠7, according to the converse of alternate interior angles theorem, the lines they are found on, lines a and b would be parallel.
1. Lines a and b are parallel.
What is the Converse of Consecutive Interior Angles Theorem?Given that the interior angles, m∠5 + m∠12 = 180, according to the converse of consecutive interior angles theorem, the lines they are found on, lines l and m would be parallel.
2. Lines l and m are parallel.
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Which phrase best describes the translation from the graph y = (x – 5)2 + 7 to the graph of y = (x + 1)2 – 2?
The parent. function shifted up by 6 units to produce x + 1 and to the left by 9 units
What is translation?This is a way of changing the position of an object on an xy-plane.
Given the parent function expressed as y = (x – 5)^2 + 7
From the resulting image after translation, we can see that the parent. function shifted up by 6 units to produce x + 1 and to the left by 9 units
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The graph of F(x), shown below, has the same shape as the graph of G(x) =
x², but it is shifted to the left 2 units. What is its equation?
F(x)=_
5
A. F(x)=x²+2
B. F(x)=x²-2
C. F(x) = (x-2)²
OD. F(x) = (x + 2)²
Answer: D
Step-by-step explanation:
See attached image.
The cost of advertising for a radio station is £50+£5 x broadcasting time in minutes use the graph to show the cost of advertising for broadcasting up to 10 minutes of the advert
A function assigns the values. The cost of advertising for 10 minutes will be equal to £100.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
Let the number of minutes of advertising be represented by x, and the cost of advertising be represented by y.
Given the function through which the cost of advertising can be determined. Therefore, the cost of advertising for the 10 min program will be when the value of x is 10. Therefore, the cost of advertising for 10 mins will be £100.
Hence, the cost of advertising for 10 minutes will be equal to £100.
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Can someone help with these geometry fill in blank questions? Just 9, 10, 11, 12.. it’s urgent
Which of the following equations results in infinitely many solutions?
9x80 = 8(x + 10)
9x + 10- 1x = 8(x + 10)
9x + 80 1x = 8(x + 10)
9x + 80 1x = 9(x + 10)
The equation with infinitely many solutions is:
9x + 80 - 1x = 8*(x + 10)
Which equation has infinitely many solutions?
An equation has infinitely many solutions when the dependence on x vanishes.
If you look at the third equation, we get:
9x + 80 - 1x = 8*(x + 10)
If we simplify the left side and expand the right side, we get:
8x + 80 = 8x + 80
So we have the exact same thing in both sides, this means that the equation is true for any value of x, so the equation has infinite solutions.
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x^-4 for x=4
simplify this
Answer:
1/256
Step-by-step explanation:
4^-4 is the same thing as 1/4*1/4*1/4*1/4 which is 1/256
Answer:
1/256
Step-by-step explanation:
4⁻⁴ = 1/(4⁴) = 1/256
Use the table to find the products of the two polynomials. Write your answer in
descending order. B) (x2 + x – 2)(4x2 – 8x)
The products of the two polynomials (x² + x – 2) and (4x² – 8x) is 4x⁴ - 4x³ - 16x² + 16x
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The products of the two polynomials (x² + x – 2) and (4x² – 8x) is:
= 4x⁴ - 8x³ + 4x³ - 8x² - 8x² + 16x
= 4x⁴ - 4x³ - 16x² + 16x
The products of the two polynomials (x² + x – 2) and (4x² – 8x) is 4x⁴ - 4x³ - 16x² + 16x
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To solve -3 = -19 + d/5, what steps would you use?
19 add divide multiply subtract
5 add divide multiply subtract
To solve the expression, the steps are add 19 and multiply by 5
How to solve the expressionGiven the equation;
-3 = -19 + d/5
First,
Collect like terms
-3+ 19 = d/5
Add the values on the left side
We have
16 = d/5
Cross multiply
16 × 5 = d
We then have
d = 80
Thus, to solve the expression, the steps are add 19 and multiply by 5
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Alice is playing a game in which she will roll 4 6-sided dice at the same time. She gets 5 points for each die that shows an even result. Let x represent the total number of points awarded on any given toss of the dice. What is the expected value of x
The expected value of x is 10.
It is given that the number of dice that are showing an even number is a binomial random variable with n = 4, and p = 1/2 (because half the faces on the die are even and half are odd).
The expected value of this random variable is n*p = 4*1/2 = 2.
The number of points is simply 5 times this random variable, and by the rules of expected value, E(C*Y) = C*E(Y), where C is a constant and Y is a random variable.
Thus E(X) = 5*2 = 10.
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Which statistic is used to determine if there is a significant difference between three or more sets of related scores
The t-test is a type of inference statistic used to determine if there is a significant difference between the means of two groups that may be related to a particular characteristic. The t-test is one of many tests used to test statistical hypotheses.
Inference statistics have two main purposes. Estimates for population groups (for example, the average SAT score for all 11th graders in the United States). Hypothesis testing to draw inferences about the population
One-way ANOVA is a common method for comparing three or more group means. The usual goal is to determine if the mean (or median) of at least one group is different from the other. Subsequent multiple comparison tests are often used to determine where differences occur.
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The expression (x+5)(x+8)+(x+5)(2x-3) can be written as the product of (x+5) and
help aaahhhh
x =x=x, equals
^\circ
∘
degrees
Using supplementary angles, it is found that the measure of angle x is of 65º.
What are supplementary angles?Angles are called supplementary if the sum of their measures is of 180º.
In this problem, angles x, 25, and 90º are supplementary, hence:
x + 25 + 90 = 180
x = 180 - (25 + 90)
x = 65º.
The measure of angle x is of 65º.
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4/15 divided by 1 1/3 + 0.4
Answer: 2/13
Step-by-step explanation:
To solve this word problem expression, we can first convert the mixed number to an improper fraction so it's easier to work with.
1 1/3 = 4/3
Adding 4/3 to 0.4, we get 5.2/3.
4/15 divided by 5.2/3 is 4/26, or 2/13
Question 2 of 25
f(x) = 6x + 4. Find the inverse of f(x).
O A. f¹(x) = 4 − 6x
Ỏ B. f-1(2) = *
O c. f¹(x) = -6
OD. f¹(x) = 6x − 4
I NEED YA HELP BRO.!
The inverse function of f(x) = 6x + 4 is f^-1(x) = (x - 4)/6
How to determine the inverse function?The function is given as:
f(x) = 6x + 4
Rewrite as:
y = 6x + 4
Swap x and y
x = 6y + 4
Subtract 4 from both sides
6y = x - 4
Divide through by 6
y = (x - 4)/6
Rewrite as:
f^-1(x) = (x - 4)/6
Hence, the inverse function of f(x) = 6x + 4 is f^-1(x) = (x - 4)/6
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anybody can help me?
The graph that corresponds to the proportional relationship M = 3n is graph vs.
What is a proportional relationship?A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:
y = kx
In which k is the constant of proportionality.
In this problem, the relationship is:
M = 3n.
Considering that the montant is the vertical axis, the graph is composed by points (n, 3n), that is, the vertical axis is triple the horizontal axis, having points (100, 300), (200, 600) and so on, the graph is graph vs.
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Use matrix method to find the point of intersection between the lines:
5x+3y-35=0 and 3x-4y=-8
Hello !
[tex]\begin{cases} 5x+3y - 35&=0 \\ 3x - 4y &= - 8 \end{cases}[/tex]
[tex]\Leftrightarrow\begin{cases} 5x+3y &=35 \\ 3x - 4y &= - 8 \end{cases}[/tex]
[tex]\Leftrightarrow AX = B [/tex]
With
[tex]A=\left[\begin{array}{ccc}5&3\\3& - 4\end{array}\right] [/tex]
[tex]X=\left[\begin{array}{ccc}x\\y\\\end{array}\right] [/tex]
[tex]B=\left[\begin{array}{ccc}35\\ - 8\\\end{array}\right] [/tex]
The solution is given by [tex]X=A^{-1}B[/tex].
[tex]X= {\left[\begin{array}{ccc}5&3\\3& - 4\end{array}\right] }^{ - 1} \left[\begin{array}{ccc}35\\ - 8\\\end{array}\right] [/tex]
[tex]X=\left[\begin{array}{ccc}4\\ 5\\\end{array}\right] [/tex]
The point of intersection between the lines is (4;5).
Have a nice day
Answer:
Point of intersection (4,5)
Step-by-step explanation:
5x + 3y - 35 = 0
3x - 4y = -8
⇒ 5x + 3y = 35
3x - 4y = -8
Matrix A will be formed by the coefficient of x and y. Matrix B will be formed by the constants.
[tex]\sf A = \left[\begin{array}{cc}5&3\\3&-4\end{array}\right][/tex]
[tex]\sf B = \left[\begin{array}{c}35&-8\end{array}\right][/tex]
AX = B
[tex]\sf X =A^{-1}B[/tex]
[tex]Now ,\ we \ have \ to \ find \ A^{-1}[/tex],
Find the workout in the document attached.
What is the completely factored form of 6 x squared minus 13 x minus 5? (2x - 5)(3x 1) (2x 5)(3x - 1) (2x - 1)(3x - 5) (2x 1)(3x 5)
Answer:
(2x - 5)(3x + 1)
Step-by-step explanation:
6x² - 13x - 5
ax² + bx + c
ac = 6 × (-5) = -30
-30 = -15 × 2
-13 = -15 + 2
6x² - 13x - 5 =
= 6x² - 15x + 2x - 5
= 3x(2x - 5) + 1(2x - 5)
= (2x - 5)(3x + 1)
Answer: its a.) (2x-5)(3x+1)
Step-by-step explanation:
6x² - 13x - 5ax² + bx + cac = 6 × (-5) = -30-30 = -15 × 2-13 = -15 + 26x² - 13x - 5 == 6x² - 15x + 2x - 5= 3x(2x - 5) + 1(2x - 5)= (2x - 5)(3x + 1)
and got it right on the test review.
Eden just bought a trough in the shape of a rectangular prism for her horses. She needs to know what volume of water to add to the trough. She knows that the height of the trough is 13 inches shorter than the width, and that the length is 33 inches longer than the width.
The volume of the trough, V(w), can be modeled by a polynomial function, where w is the width of the trough. Which of the following correctly models the situation and gives the rate of change of the volume over a width of 38 inches to 53 inches?
A. V(w)= w^3 + 20w^2 - 429w
Rate of Change: 2167 cubic inches per inch
B. V(w)= w^3 + 20w^2 - 429w
Rate of Change: 7658 cubic inches per inch
C. V(w)=w^2 + 429w
Rate of Change: 520 cubic inches per inch
D. v(w) = w^2 + 20w - 429
Rate of Change: 111 cubic inches per inch
The volume of the trough is V(w) = w³ + 20w² - 429w and the rate of change of the volume over a width of 38 inches to 53 inches is 4695 in³/in
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Let w represent the width, hence:
length = w + 33, height = w - 13
Volume (V) = w(w + 33)(w - 13) = w³ + 20w² - 429w
V(w) = w³ + 20w² - 429w
Rate of change = dV/dw = 3w² + 40w - 429
When w = 38, dV/dw = 3(38)² + 40(38) - 429 = 5423
When w = 53, dV/dw = 3(53)² + 40(53) - 429 = 10118
Rate = 10118 - 5423 = 4695 in³/in
The volume of the trough is V(w) = w³ + 20w² - 429w and the rate of change of the volume over a width of 38 inches to 53 inches is 4695 in³/in
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At what values of x, does f(x) = 0?
a. 0
b. -1
c. -8
d. 4.2
e. 4
f. 2
Answer:
B E F
Step-by-step explanation:
as the graphic shows, f(x) = 0 means that the y value is 0. and that means these are the points, where the curve intersects the x-axis.
they are already marked in the graphic :
for x = -1, 2, 4
HELP ASAP NO ROCKY!!!!!!!!
Answer:
○ The distance between a and b on the number line is 0.47 units.
Explanation:
The first statement is not true because the distance between a and b on the number line is not 0.47.
Distance between a and b = 5.25 - (-5.72)
= 10.97
• The second statement is true because the sum of a and b is negative:
Sum = a + b
= -5.72 + 5.25
= -0.47
• The third statement is true because the quotient of a and -b is:
a ÷ -b
⇒ -5.72 ÷ -5.25
⇒ 1
And the quotient of -a and b is:
-a ÷ b
⇒ -(-5.72) ÷ 5.25
⇒ 1
This shows that the quotients are the same.
• The fourth statement is true because the product of a and -b:
a × -b
⇒ -5.72 × -(5.25)
⇒ 30.03 ,
is positive.
Please help! Which is the solution set of the following inequality?
Answer:
x<3
Step-by-step explanation:
3x - 4 < 17 - 4x
So, the -4 shall cross to the other side and replace the -4x which will now take the place of where the -4 used to be and the signs of both digits will change to a positive (+)
Remember the inequality sign (<) shall not change
so now the equation shall appear like this;
3x + 4x < 17 + 4
add both sides and it will appear like this;
7x < 21
simplify both sides by 7 and you'll get
x < 3
You enter a room. 2 dogs, 4 horses, 1 giraffe and a duck lie on the bed. 3 hens fly over a chair. How many legs are there on the floor?.
Answer:
4 legs from the bed and 4 from the chair im guessing since not all have 4
Hope This Help
Answer:
4 legs from the bed and 4 from the chair
Step-by-step explanation:
im a math wizard fr
Sarah received scores of 85, 92 and 78 on her first three exams of the grading period. What is the lowest score Sarah can earn on the next exam for the exam average to be at least a 87 for the grading period.
Please help ill give whoever answers the best the brainliest answer :)))
Answer:
4th option
Step-by-step explanation:
L = larger softball and S = smaller softball ,then
L + S = 80 → (1) ← equation based on number of softballs ordered
2.75L + 3.25S = 245 → (2) ← equation based on cost
subtract S from both sides in (1)
L = 80 - S → (3)
substitute L = 80 - S into (2)
2.75(80 - S) + 3.25S = 245 ← distribute parenthesis and simplify left side
220 - 2.75S + 3.25S = 245
220 + 0.5S = 245 ( subtract 220 from both sides )
0.5S = 25 ( divide both sides by 0.5 )
S = 50
substitute S = 50 into (3)
L = 80 - 50 = 30
50 small softballs and 30 large softballs were ordered
Answer:
the 4th answer option
Step-by-step explanation:
L, S are the number of balls of that size.
so, L + S = 80. as we order a total of 80 balls.
then each large ball costs $2.75. and each small ball costs $3.25.
so, the total price is
2.75L + 3.25S = 245
as we order balls in total for $245.
so, this set of 2 equations with 2 variables allows us to find the solution.
one defines the total number of balls, and one defines the total amount of money spent by using the individual prices for each type of ball.
the advantage of variables is that we can define the rising and dependencies before we have to calculate any of them specifically.
and once we have all of them defined, then we can start solving the numbers.
A bird sits at the top of a 24 ft tall tree. A cat, 12 ft away from the base of the tree, sees the bird. To the nearest degree, what is the angle of elevation from the cat to the bird?
Answer:
https://brainly.com/question/14172055?referrer=searchResults
Step-by-step explanation:
Your question has already been answered.
Here is the link to the answer:
https://brainly.com/question/14172055?referrer=searchResults
Hope this helps!
If not, I am sorry.
A rectangular container with a square base, an open top, and a volume of 1,372 cm3 is to be made. What is the minimum surface area for the container
The minimum surface area for the rectangular container is [tex]588cm^{2}[/tex].
How to find the surface area?A solid object's surface area is a measurement of the overall space that the object's surface takes up. Compared to the definition of the arc length of a one-dimensional curve or the definition of the surface area for polyhedra (i.e., objects with flat polygonal faces), where the surface area is equal to the sum of the areas of its faces, the mathematical definition of surface area in the presence of curved surfaces is much more complex.
Let s be the side of the square base and h be the height.
Surface Area=[tex]s^{2}+4sh[/tex]
Volume=[tex]s^{2}h[/tex]
According to the question,
[tex]s^{2}h=1372\\ h=\frac{1372}{s^{2} }[/tex]
So, surface area=[tex]s^{2} +4s(\frac{1372}{s^{2} })[/tex]
=[tex]s^{2}+\frac{5488}{s}[/tex]
Differentiate with respect to s,
Surface area=[tex]2s-\frac{5488}{s^{2} }[/tex]
Now, [tex]2s-\frac{5488}{s^{2} }=0[/tex]
[tex]2s=\frac{5488}{s^{2} } \\2s^{3}=5488\\ s^{3}=2744\\ s=14[/tex]
Find the value of h from the volume.
[tex]14*14*h=1372\\h=\frac{1372}{14*14}\\ h=7[/tex]
Thus, the minimum surface area=[tex]14^{2}+4*14*7[/tex]
=[tex]588cm^{2}[/tex]
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Jarom is working for a landscaping company and is responsible for building the stone border around a rectangular pond. The pond measures 6 meters by 15 meters. The manager told Jarom that the budget only allowed enough stone for 46 square meters and to make the stone border as wide as possible. How wide can the border be
The width is 1 meter.
Given,
Jarom is working for a landscaping company and is responsible for building the stone border around a rectangular pond.The pond measures 6 meters by 15 meters. The manager told Jarom that the budget only allowed enough stone for 46 square meters
Let the border be width = x
then the area of the border will be
2(6x) + 2(15x) +4x2 = 46
= 12x +30x+ 4x2 = 46
= 4x2 + 42x - 46 = 0
=> x =( -42 +- √42² +4*4*46)/8
x =1 , x = -11.5
since the width is 1 meter.
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Terry runs a snowplowing business. income from snowplowing is given by the function f(x) = 35.5x 6, where f(x) is the income in dollars and x is the snowfall in inches received during a winter. if during the years 2006 to 2011, terry’s town received 53, 42, 55, 63, 58, and 47 inches of snowfall, what was his income (in dollars) during those years?
If the function is f(x)=35.5x+6 and snowfall in inches are 53,42,55,63,58,47 then the income received will be $1887.5,$1497,$1958.5,$2242.5,$2065$1674.5.
Given Snowfall received during the years:53,42,55,63,58,47 and f(x)=35.5x+6
We have to find the income in dollars received if f(x) shows the income.
Function is a relationship between variables and it have each value of y for each value of x.
To find the income we have to just put the values of x=53,42,55,63,58,47one by one and we will get income.
f(53)=35.5*53+6=1887.5
f(42)=35.5*42+6=1497
f(55)=35.5*55+6=1958.5
f(63)=35.5*63+6=2242.5
f(58)=35.5*58+6=2065
f(47)=35.5847+6=1674.5
Hence the income for snowfall 53,42,55,63,58,47 inches are 1887.5,1497,1958.5,2242.5,2065,2674.5.
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Which of the following is a fifth root of the given complex number?
Answer:
D
Step-by-step explanation:
This result is true by De Moivre's theorem.