Find the exponential function in the form y=a*b^x that passes through the point (0,10) and (3,80).
[tex]{\Large \begin{array}{llll} y = ab^x \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=0\\ y = 10 \end{cases}\implies 10=ab^0\implies 10=a(1)\implies 10=a~\hfill \underline{y = 10b^x} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x = 3\\ y = 80 \end{cases}\implies 80=10b^3\implies \cfrac{80}{10}=b^3\implies 8=b^3 \\\\\\ \sqrt[3]{8}=b\implies 2=b~\hfill \underline{y = 10(2)^x}[/tex]
5. The elevation of the Dead Sea is -1,286 feet. (The Dead Sea is below sea level.) Mt.
McKinley has an elevation of 20,320 feet. What is the difference in the elevation between
the Dead Sea and Mt. McKinley?
22-13 You add
Answer:
21606 ft
Step-by-step explanation:
get difference between elevations with subtraction
20320 - - 1286
20320 + 1286
21606 ft
f(x) = 3 x + 1 and g (x) = 2x - 3. find f (g(x)) and g (f(x))
Step-by-step explanation:
f(x} = 3x + 1
g(x} = 2x -- 3
f(g(x)) = 3x + 1. (Calm down right?)
Let the x in the expression be (2x -- 3)
N.B x = g{x}
f(g(x)) = 3(2x --3} + 1
Open bracket
f(g(x)) = 6x -- 9 + 1
f(g(x)) = 6x -- 8...
2... Solve for g(f(x)), using the same strategy
g(f(x)) = 2x -- 3
x = f(x)
g(f(x)) = 2(3x + 1) -- 3
g(f(x)) = 6x + 2 -- 3
g(f(x)) = 6x -- 1
#AllonGod
Answer:
Step-by-step explanation:
f(g(x)) means substituting g(x) in f(x)
ie, 3(2x-3)+1 = 6x-9+1 = 6x - 8
g(f(x)) means substituting f(x) in g(x)
ie, 2(3x+1)-3 = 6x2-3 = 6x - 1
True or false? A corollary is a statement that can be easily proved using a
theorem.
O A. True
OB. False
SUBMIT
answer to this question for anyone who needs it
The theorem can be used to readily show the corollary because, according to its statement, it considerably depends on it. Consequently, the assertion is accurate.
The given statement is True.
Is the meaning of corollary?The term "corollary" refers to an outcome that follows logically from another action. You could claim that your rediscovered passion of reading is a corollary to the recent opening of a bookstore in your area. The term corollary describes the result of an action, such as the need to study more as a corollary to receiving a poor grade.
Briefing:A theorem states that two angles that add up to 180° and form a straight line are regarded as "supplementary."
A corollary of this is known as the "Vertical Angle Theorem," which asserts that where two lines intersect, their angles across from each other are equal (in the diagram, a=c and b=d).
The theorem can be used to readily show the corollary because, according to its statement, it considerably depends on it. Consequently, the assertion is accurate.
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Find the x intercept and y intercept x + 18 = 9y
Answer:
x = 72 and y = 0 im just guessing so dont be completey
PLEASEEEEE HELP IDEK WHAT TO DO
The evaluated value of the function is as follows:
g(10) = - 29f(3) = 16h(-2) = -6j(7) = 23h(a) = 12 / ag(b) + g(c) = -3b - 3c + 2x = -5x = -6x = 4How to evaluate a function?The functions can be evaluated as follows:
To evaluate a function is to replace (substitute) its variable with a given number or expression.
In other words, evaluating a function means to substitute a variable with its given number or expression.
Therefore,
g(x) = -3x + 1
f(x) = x² + 7
h(x) = 12 / x
j(x) = 2x + 9
Hence,
a.
g(10) = -3(10) + 1
g(10) = -30 + 1
g(10) = - 29
b.
f(3) = (3)² + 7
f(3) = 9 + 7
f(3) = 16
c.
h(-2) = 12 / -2
h(-2) = -6
d.
j(7) = 2(7) + 9
j(7) = 14 + 9
j(7) = 23
e.
h(a) = 12 / a
h(a) = 12 / a
f.
g(b) + g(c) = -3(b) + 1 + -3(c) + 1
g(b) + g(c) = -3b + 1 - 3c + 1
g(b) + g(c) = -3b - 3c + 2
h.
find x when g(x) = 16
16 = -3x + 1
16 - 1 = -3x
15 = -3x
x = 15 / -3
x = -5
j.
find x when h(x) = -2
-2 = 12 / x
-2x = 12
x = 12 / -2
x = -6
k.
find x when f(x) = 23
23 = x² + 7
23 - 7 = x²
x² = 16
square root both sides
x = √16
x = 4
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let’s review some basics of probability. a bag of skittles has 9 reds, 10 oranges, 7 yellows, 8 purples, and 6 greens. what is the probability of a red skittle if one is selected at random?
Answer:
7/20
Step-by-step explanation:
is always right use without the s
which numbers are my Ys (-8-6) and (-1,0)
The numbers which correctly represents the y-coordinates of the given pairs; (-8-6) and (-1,0) as in the task content are; -6 and 0 respectively.
What is the xy- coordinate plane?It follows from simple definition that the x -y plane, is a two dimensional plane which contains the x and y axis. The x and y axis happen to be used in the description of plane shapes which are two- dimensional in nature.
Also, it is noteworthy that each point on the xy-coordinate is described by a pair of coordinates and takes the form; (x, y).
In which case, the x-coordinate is written first and y-coordinate is written second as indicated above.
On this note, the y's of the pair of coordinates, (-8-6) and (-1,0) as given in the task content by convention can be observed to be; -6 and 0 respectively.
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Alfred is picking up chicken and steak to grill at a party
later that day. He has $60 to spend on the 30 pounds of
meat he needs for the party. The chicken is $1.50 per lb,
and the steak is $2.40 per lb.
Which graph models this situation, where cis pounds of
chicken, and s is pounds of steak?
Answer:
The graph should look like the one below.
Step-by-step explanation:
C is lbs of chicken
S is pounds of steak
Alfred spent 30 pounds of meat for the party:
c + s [tex]\leq[/tex] 30
Alfred spend $60 on the 30 lbs of meat.
The chicken is $1.50 per pound and the steak is $2.40 per lb then
1.5c + 2.50 [tex]\leq[/tex] 60
0.5c + 0.85 [tex]\leq[/tex] 20
The linear inequalities system that models situation is:
0.5c + 0.85 [tex]\leq[/tex] 20
c + s [tex]\leq[/tex] 30
c [tex]\geq[/tex] 0
s [tex]\geq[/tex] 0
The Graph:
If Aaron buys 5 watermelons for 9 how much would 4 cost at the same rate?
Answer: $ 7.20
Step-by-step explanation:
(9x4)/5
36/5
= 7.2
= $7.20
the daily useage time on the apple iphone is normally distributed with mean 5.4 hours and standard deviation 1.2 hours. suppose you survey 5 of your friends who have iphones. what is the probability that their mean useage time is between 4 and 7 hours? round your answer to three decimal places.
0.868 is the probability that their mean useage time is between 4 and 7 hours.
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.Given, population mean (μ) = 5.4
population standard deviation (σ) = 1.2
Sample size (n) = 5
Probability that the sum of their useage time is less than 30
= Probability that the sample mean is less than (30/5 = 6)
= p(x<6)3
Z score
= x - μ/σ/√n
= 6 - 5.4/1.2/√5
= 0.6/1.2/2.236068
= 0.6/0.536656
= 1.11803
Area to the left of (Z = 1.11803) = 0.86822 = 0.868
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Given the equation 13.25y = 79.5, determine the value of y.
6.00
66.25
92.75
1053.38
Given the equation 13.25y = 79.5, the value of y is A. 6.00.
What is an equation?An equation is a mathematical statement that states that two mathematical expressions are equal in value.
Equivalent values are also expressed as algebraic equations sharing the same root.
We depict equations by using the equation symbol (=).
13.25y = 79.5
y = 6 (79.5/13.25)
Check:
13.25y = 79.5
13.25(6) = 79.5
79.5 = 79.5
Thus, given the equation 13.25y = 79.5, the value of y cannot be 66.25, 92.75, or 1,053.38 but Option A.
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Which set of ordered pairs does not represent a function?
{(8,-2), (6,-1), (4,1), (0,1)}
{(8,4), (1,5), (-7,7), (9,5)}
{(4,-6), (-3,2), (7,-1), (-6, -4)}
{(-9,3), (8,7), (-9, -9), (2, 4)}
{(-9,3), (8,7), (-9, -9), (2, 4)}
=======================================================
Explanation:
To find an example of a non-function, we look for (x,y) points where x repeats itself. That occurs in choice D where we have (-9,3) and (-9,-9) in the same function set.
The input x = -9 leads to multiple outputs y = 3 and y = -9 simultaneously. This is not allowed if we wanted a function.
A function is only possible if each input x leads to exactly one y output.
So this is why we look for repeated x values when trying to find non-functions. Choices A, B and C all have unique x values that don't repeat, which means those choices represent functions.
Side note: The y values can repeat, but the function won't be one-to-one.
find the unit rate if suzie reads 45 books in 15 days
Step-by-step explanation:
she reads 45 books in 15 days.
so, the reading rate is 45/15.
now, a ratio is just a fraction with a special meaning, but calculations, simplifications and so on are all the same.
so,
45/15 = 9/3 = 3/1 = 3
that means she reads 3 books in 1 day.
Can somebody help me with this please?
From the given figure < BAC = 180 - ( < ABC + < BCA ) because they are sum of angles in a triangle
How to find < BACgiven data
< ABC = 52 degrees
< BCA = 88 degrees
calculation for angle BAC
< ABC + < BCA + < BAC = 180 degrees ( sum of angles in a triangle )
< BAC = 180 - ( < ABC + < BCA )
< BAC = 180 - < ABC - < BCA
plugging in the values gives
< BAC = 180 - 52 - 88
< BAC = 180 - 140
< BAC = 40 degrees
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Use the expression 11 + 9k + 6n. Tell whether each statement is True or False. T or F: the expression has 3 terms. T or F: In the expression, 11 is a coefficient. T or F: In one of the terms, 6 is a factor. T or F: The expression has two variables.
The classification of the terms in the expression is given as follows:
True: the expression has 3 terms.True: in the expression, 11 is a coefficient.True: In one of the terms, 6 is a factor.True: The expression has two variables.First statementIn an addition, each term involved in the addition is called a term. Hence, the expression has three terms, which are given as follows:
11.9k.6n.Hence the first statement is correct.
Second statementThe coefficients of the expression are:
11.9.6.Hence the second statement is correct.
Third statementIn the third term, 6n is divisible by 6, hence six is a factor of the term, and the third statement is correct.
Fourth statementThe variables of the expression are k and n, hence two variables, and the fourth statement is correct.
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The graph of a function f(x) passes through the following points:
(0,-2), (1,0), (-1,0)
Which of the following could be f(x)?
> f(x) = -2x - 2
> f(x) = 2x - 2
> f(x) = (2\sqrt[x])-2
> f(x) = 2x^2 - 2
*109
eight feral 103721
Write an equation in point-slope form of the line that passes through the given points, then write the equation in slope-intercept form.
(-9,7) (9,1)
What is the point-slope form of the equation of the line?
Answer:
Equation of line is given as y = mx + c, where m is the slope and c is the y-intercept.
First find the slope.
Formula for slope is given as (y2-y1)÷(x2-x1) or (y1-y2)÷(x1-x2).
Slope = (7-1)÷(-9-9)
= -6/18
= -1/3
Equation of line is y = -1/3 + c.
Substitute either one of the points into the equation to find c.
1 = -1/3(9) + c
c = 4
Hence equation of line is y = -1/3x + 4
What is the vertex of the graph of 3x^2 - 6x + 7?
Answer: (1,4)
Step-by-step explanation:
y = 3x^2 - 6x + 7
Flora is buying dog food for her dog. She wants to buy enough to last five weeks (35 days). If her dog eats 2 cups in a day, and there are 24 cups in each bag, how many bags of dog food does Flora need to buy to last 5 weeks? ⛔️ SOLVE USING A PROPORTIONAL RELATIONSHIP GRAPH! ⛔️
When the second number in the ordered pair, b, is not equal to 0, the ratio is expressed as a/b.
Flora needs 3 bags of dog food.
How to find the food bags needed?When the second number in the ordered pair, b, is not equal to 0, the ratio is expressed as a/b.
An equation in which two ratios are made equal is known as a percentage.
As an illustration, you could express the ratio as 1: 3 if there is 1 guy and 3 girls.
Given,
Dog eats 2 cups in a day
There are 24 cups in each bag
Solution:
Dog eats one bag of food in 24 cups/2 cups = 12 days
One food bag is sufficient to feed the dog for 12 days
For 35 days, the number of food bags needed is
1/x = 12/35 where x be the number of food bags needed for the dog.
x = 2.92
That is 3 bags of dog food are needed for 35 days to feed the dog.
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Darcie wants to simplify 20 over 24 fully.
What number should she divide both the
numerator and the denominator by in order
to simplify the fraction fully in one step?
Answer: 4
Step-by-step explanation:
This simplifies to 5/6.
So 20 / 5 = 4
and 24 / 6 = 4
if a circle has a radius of 7 m then what is the circumference exactly
If the measure of angle 2 is 70 degrees, what is the measure of angle 7?
A. 70; Ls 2 and 7 corresponding angles
B. 70; Ls 2 and 7 are alternate exterior angles
C. 120; 2s 2 and 7 are supplementary angles
D. Unable to determine
Answer:
B
Step-by-step explanation:
∠ 2 and ∠ 7 are alternate exterior angles and are congruent, then
∠ 7 = ∠ 2 = 70°
x/16 = 7/10
FIND X PLEASE
Answer:
x=11.2
Step-by-step explanation:
x/16=7/10
x=7/10×16
x= 11.2
Step-by-step explanation:
First, let's write down the equation properly:
[tex] \frac{x}{16} = \frac{7}{10} [/tex]
Then we follow these simple steps to solve the equation to find the value of x.
Cross multiply fractions.10x = 112
Divide both sides by 10.x = 11.2
EASY POINTS WILL GIVE BRAINLIST TO BEST ANSWER
Determine if the sequence is arithmetic. If it is, find the common difference, the 21st term, the explicit rule, the recursive rule, and the three terms in the sequence after the last one given.
33, 35, 37, 39
Answer:
Common difference = 2
21st term = 73
Explicit rule : a(n) = 31 + 2n
Three terms in the sequence after 73: 77,77,79
Step-by-step explanation:
Given:
33, 35, 37, 39
If the sequence is arithmetic it has a common difference ( same difference on each value)
d= Common difference = 35 - 33 = 37 - 35 = 39 - 37 = 2
d = 2
Explicit formula:
a(n) = a1 + d (n - 1 )
Where:
a1= first term = 33
d = common difference = 2
Replacing:
a(n)= 33 + 2 (n - 1 )
a(n) = 33 + 2n - 2
a(n) = 31 + 2n
21st term:
a(21) = 31 + 2 (21) = 31+ 42 = 73
To obtain the three terms in the sequence after 73, add the common difference 3 times.
73 + 2 = 75
75+2= 77
77 + 2 = 79
Answers:
Common difference = 2
21st term = 73
Explicit rule : a(n) = 31 + 2n
Three terms in the sequence after 73: 77,77,79
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a 13-foot ladder is leaning against a wall. if we pull the ladder away from the wall at a rate of 1ft/s, how fast is the top of the ladder moving down the wall when the bottom of the ladder is 12ft from the wall?
After solving the question using Pythagoras' theorem we get, The ladder moving down the wall at 8 feet per second.
According to the question,
The bottom(base) of the ladder is 12 feet,
the height of the ladder is 13 feet.
Now, We have to find the top of the ladder moving down the wall
by using Pythagoras' theorem,
hypotenuse ^2 = base^2 + perpendicular ^2
13^2 = x^2 + y^2
169 = x^2 + y^2
After using Pythagoras' theorem
we have this equation and now we will differentiate both sides:
0 =2x*dx/dt + 2y*dy/dt
0 =24*1 + 3* dy/dt
dy/dt = - 8 feet per second
Positive whole number we have to take.
So, dy/dt = 8 feet per second
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g(x)=1/4x+1
what is g(-16)?
When we're solving with functions, it's no different than solving from a regular equation.
In most cases, we only need to substitute x with a given value.
Solving the Question
[tex]g(x)=\dfrac{1}{4}x+1[/tex]
⇒ To find g(-16), plug in -16 as x:
[tex]g(-16)=\dfrac{1}{4}(-16)+1\\\\g(-16)=-4+1\\\\g(-16)=-3[/tex]
Answer-3
help fast i need to get this answer
Answer:
x = 3
Step-by-step explanation:
Plug in 1 for x:
- | 1 + 1 | + 5 = - |2| + 5 = -2 + 5 = 3
Question 4 of 10
What is the solution to the equation below? Round your answer to two
decimal places.
log₂ (2x-1)=3
O A. x=5
B. x = 4
O C. X=9/2
O D. X=7/2
The value of x from the given equation is 9/2
The given equation is
log₂(2x - 1) = 3
The general form of logarithm with base 2 is
log₂ N = x
Conversion of the logarithm to exponential form is
2ˣ = N
where x is the log₂ of N
x is the number of times number '2' should be multiplied by intself to obtain n
Using this conversion in the above equation,
log₂(2x - 1) = 3
(2x - 1) = 2³
(2x - 1) = 8
2x - 1 = 8
2x = 8 +1
2x = 9
x = 9/2
Therefore the value of x is 9/2
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