Answer:
D. 0 ≤ x ≤ 10
Step-by-step explanation:
I took the quiz.
The domain of the function is 0 ≤ x ≤ 10 if the function is f(x) = 20(2)ˣ which represnts the exponential function option (D) is correct.
What is an exponential function?It is defined as a function that rapidly increases and the value of the exponential function is always positive. It denotes with exponent y = a^x
where a is a constant and a>1
It is given that:
A bacteria is growing by a factor of 2 every hour from 1 p.m. to 11 p.m.
The function is:
f(x) = 20(2)ˣ
The value of x represents the domain of the exponential function.
The domain of the function is:
0 ≤ x ≤ 10
Thus, the domain of the function is 0 ≤ x ≤ 10 if the function is f(x) = 20(2)ˣ which represnts the exponential function option (D) is correct.
Learn more about the exponential function here:
brainly.com/question/11487261
#SPJ5
I need help with this math problem
Answer:
AB = 4.5 cm
Step-by-step explanation:
the total area (A) of the 2 rectangles is calculated as
A = x(x - 4) + 3x(x - 2)
= x² - 4x + 3x² - 6x
= 4x² - 10x
Given A = 36 , then equating
4x² - 10x = 36 ( subtract 36 from both sides )
4x² - 10x - 36 = 0 ( divide through by 2 )
2x² - 5x - 18 = 0 ← as required
To factorise the equation
consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.
product = 2 × - 18 = - 36 and sum = - 5
the factors are + 4 and - 9
use these factors to split the x- term
2x² + 4x - 9x - 18 = 0 ( factor the first/second and third/fourth terms )
2x(x + 2) - 9(x + 2) = 0 ← factor out (x + 2) from each term
(x + 2)(2x - 9) = 0
equate each factor to zero and solve for x
x + 2 = 0 ⇒ x = - 2
2x - 9 = 0 ⇒ 2x = 9 ⇒ x = 4.5
but x > 0 , then x = 4.5
Then
AB = x = 4.5 cm
Answer:
AB = 4.5 cm
Step-by-step explanation:
[tex]\boxed{\textsf{Area of a rectange}=\sf width \times length}[/tex]
Area of the smaller rectangle:
[tex]\implies A=x(x-4)[/tex]
[tex]\implies A=x^2-4x[/tex]
Area of the larger rectangle:
[tex]\implies A=(2x+x)(x-2)[/tex]
[tex]\implies A=3x(x-2)[/tex]
[tex]\implies A=3x^2-6x[/tex]
The area of the compound shape is the sum of the areas of the two rectangles:
[tex]\implies A=(x^2-4x)+(3x^2-6x)[/tex]
[tex]\implies A=x^2+3x^2-4x-6x[/tex]
[tex]\implies A=4x^2-10x[/tex]
If the area of the compound shape equals 36 cm² then:
[tex]\implies 36=4x^2-10x[/tex]
[tex]\implies 36-36=4x^2-10x-36[/tex]
[tex]\implies 0=4x^2-10x-36[/tex]
[tex]\implies 4x^2-10x-36=0[/tex]
[tex]\implies \dfrac{4x^2}{2}-\dfrac{10x}{2}-\dfrac{36}{2}=\dfrac{0}{2}[/tex]
[tex]\implies 2x^2-5x-18=0[/tex]
The length of AB is x cm.
To find the value of x, factor the quadratic.
To factor a quadratic in the form [tex]ax^2+bx+c[/tex] find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex].
[tex]\implies ac=2 \cdot -18=-36[/tex]
[tex]\implies b=-5[/tex]
Therefore, the two numbers are: -9 and 4.
Rewrite [tex]b[/tex] as the sum of these two numbers:
[tex]\implies 2x^2-9x+4x-18=0[/tex]
Factor the first two terms and the last two terms separately:
[tex]\implies x(2x-9)+2(2x-9)=0[/tex]
Factor out the common term (2x - 9):
[tex]\implies (x+2)(2x-9)=0[/tex]
Apply the zero-product property:
[tex](x+2)=0 \implies x=-2[/tex]
[tex](2x-9)=0 \implies x=\dfrac{9}{2}=4.5[/tex]
As length is positive, x = 4.5 only.
Therefore, AB = 4.5 cm.
A person has a choice of receiving 3000 now or 4000 after she graduates from college in five years she decided to take the 3000 and the best add expected 10% annual rate of return. Did she make a wise decision?
Yes she made a wise decision as she will get an amount of 4500 after 5 years which is better than getting 4000 after 5 years.
Given that ,
Let us assume that the person takes the amount 3000 from the college, and invests it on a annual rate of 10% for a period of 5 years,
means,
Principal amount = 3000
Rate of Interest = 10%=0.1
Time = 5 years
What Is the Future Value Simple Interest ?The future value simple interest formula is the addition of the principal amount that we have in the beginning and the interest earned on that principal amount after the completion of the period. The Future Value Simple Interest Formula is given as,
F V = P + I or F V = P(1 + rt)
Here,
P is the principal amount,
I is the interest,
r is the rate, and
t is the time.
So, We know that
Simple Interest = Principal amount * Rate of Interest * Time
Simple Interest = 3000*0.1*5
Simple Interest = 1500
So, The person will have a Future value of
Principal amount + Simple Interest
= 3000+1500
=4500
Therefore, If the person invests after 5 years will get a amount of 4500 in return which is a wise decision than not investing and getting a amount of 4000 .
Learn more about Simple Interest here
https://brainly.com/question/25845758
#SPJ1
Write equations for the horizontal and vertical lines passing through the point (8,1)
Check the picture below.
Answer:
Step-by-step explanation:
Horizontal line is y = 1
Vertical lone is x = 8.
PLS HELP AND EXPLAIN pls
Check the picture below.
[tex]\stackrel{\measuredangle N}{(5x-8)}~~ + ~~\stackrel{\measuredangle O}{(x-5)}~~ + ~~\stackrel{\measuredangle P}{(6x+1)}~~ = ~~180 \\\\\\ 12x-12=180\implies 12x=168\implies x=\cfrac{168}{12}\implies x=14 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\measuredangle O}{(x-5)}\implies (14)-5\implies {\Large \begin{array}{llll} \stackrel{\measuredangle O}{9} \end{array}}[/tex]
find thesum using a number line
7t5=
Answer:
12
Step-by-step explanation:
Did you mean 7+5?
If so, then 7 + 5 = 12
Find X? x+14+x3=78 How can I find X? Please answer. Thanks so much! (This is my older sister's account btw)
The value of variable x in the equation is 16.
How to find the variable x in the equation?The equation represented as follows:
x + 14 + x³ = 78
The value x is the variable.
A variable is number represented with a letter in an equation.
Therefore,
x + 14 + 3x = 78
subtract 14 from both sides of the equation
x + 3x + 14 - 14 = 78 - 14
x + 3x = 64
Therefore,
4x = 64
divide both sides by 4
4x / 4 = 64 / 4
x = 16
learn more on variable(x) here: https://brainly.com/question/12574072
#SPJ1
SHOW YOUR WORK FOR BRAINLIEST
Solve for x. Assume that lines which appear to be diameters are actual diameters.
The Answer is -6
Answer:
if x = -6, r = 180/pi and D = 360/pi
without knowing the actual D or r, one cannot truly solve for x.
Step-by-step explanation:
looking at the angle, [tex]125^o[/tex], it is part of two supplementary parts of the circle, let us call the angle between [tex]55^o\ \&\ 125^o[/tex] y. given that 125 is supplementary to y:
125+y=180
and so...
y=55
now, let us call the angle associated with the arc-length, x+76 z.
Knowing that y+55 and z are supplementary (given the length is a diameter), we can write the equation:
y + 55 + z = 180
substituting y=55 gives:
55 + 55 + z = 180
combining like terms gives:
110 + z = 180
further simplifying gives:
z = 70
x + 76 is the arc-length of the section of the circle, whose angle is now denoted by z = 70.
Arc-length = Circumference * percentage of circle
circumference is given as C = π * D OR C = 2r * π (because 2r = D)
percentage of circle is simply (number of degrees covered ÷ total degrees of a circle)
so, we have that the percentage = 70/360 [360 degrees in a circle, 70 degrees covered by the angle, z]
and the circumference is unknown without a radius or diameter length, so we will use the equation C = π * D
using the formula for arc-length:
Arc-length = π * D * 70/360
Arc-length also happens to equal x + 76, so:
x + 76 = π * D * 70/360
reduce:
x + 76 = π * D * 7/36
simplify by getting x alone:
x = π * D * 7/36 - 76
we can further simplify by creating one fraction:
[tex]x = \frac{7D\pi - 2736}{36}[/tex]
it can also be shown as:
[tex]x = \frac{7r\pi - 1368}{18}[/tex]
because, D = 2r and you could factor 2 from (7*2*r*pi - 2736) and then reduce by dividing top and bottom each by 2.
You can divide top and bottom by 2 because:
[tex]\frac{2}{36} = \frac{1}{18}[/tex]
which is because [tex]\frac{km}{ln}=\frac{k}{l} * \frac{m}{n}[/tex]
if we say km = 2 and ln = 36, then k = 2, m = 1 is the only options for k and m
and l and n can be any set of factors of 36, which include 2*18, 3*12, 6*6, 9*4.
if we choose l = 2 and n = 18, then k = l = 2 and:
[tex]\frac{k}l=\frac{2}2 = \frac{r}{r}[/tex]
which is to say that k = r = l = 2, which I only show to say generally that when k = l or you have r ÷ r, it is equal to 1.
1 * s = s
and if s = m ÷ n, then [tex]\frac{km}{ln} = \frac{m}{n}\ whenever\ k = l[/tex]
given that the answer to what is x, is -6, the arc length is therefore 70. we can plug in this 70 now to find r and therefore, D.
[tex]70 = \pi * D * \frac{70}{360}\\\\multiply\ by\ \frac{360}{70}\ on\ both\ sides\ to\ get:\\360=\pi * D\\divide\ by\ \pi\ on\ both\ sides\ to\ get:\\360/\pi = D\ OR\ 180/\pi=r[/tex]
Find the slope of the line represented
by the data below.
xl 0 2
y 15
4
9 3
6 8
-3 -9
Simplify completely.
Slope = [?]
Hint: The slane of lin
Change in y
Answer:
-3
Step-by-step explanation:
[tex] \frac{a - 15}{2 - 0} = \frac{ - 6}{2} = - 3 \\ \frac{3 - 9}{4 - 2} = - 3 \\ \frac{ - 3 - 3}{6 - 4} = - 3 \\ \frac{ - 9 - ( - 3)}{8 - 6} = - 3 \\ so \: slop \: is \: - 3[/tex]
Your answer is
Dante will run at least 33 miles this week. So far, he has run 15 miles. What are the possible numbers of additional miles he will run?
Use t for the number of additional miles he will run.
Write your answer as an inequality solved for t.
The number of possible additional miles that he needs to run will be 18.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
Dante will run at least 33 miles this week. So far, he has run 15 miles.
Then the number of possible additional miles that he needs to run.
Let t be the number of additional miles he will run. Then the inequality is given as,
15 + y ≤ 33
y ≤ 33 - 15
y ≤ 18
The number of possible additional miles that he needs to run will be 18.
More about the inequality link is given below.
https://brainly.com/question/19491153
#SPJ1
After 5 years, $8,000 deposited in a savings account with simple interest had earned $3,600 in interest. What was the interest rate?
Answer:
9%
Step-by-step explanation:
So first we need to find how much interest he got in a single year.
3600 ÷ 5 = 720
Now we find out how much 720 is compared to 8000.
720 ÷ 8000 = 0.09
Then we make that a percentage:
9%
Stephen hit the ball 12 times out of 16 bats in the first half of the season in six times out of the 14 at that in the second half of the season what is his batting average for the first full season written as a decimal
The average for the first full season when Stephen hit the ball is 0.60.
What is the average?The average for the first full season can be determined by adding the number of time he hit the ball in the first half and the second half of the season together and then dividing it by the total number of bats.
Average is a measure of central tendency. Average is also known as mean. Other measures of central tendency are mode and median.
Average = sum of the times he hit the ball / total number of bats
(12 + 6) / (16 + 14)
18 / 30 = 0.60
To learn more about average, please check: https://brainly.com/question/25842202
#SPJ1
help me out please i think it's correct but
Answer:
Step-by-step explanation:
your answer along with the work is down below please go and check it out also sorry I'm wrong have nice day:)
find both the number combinations in the number of permutations for 9 objects taken 7 at a time
Answer
There are 36 combinations and 181440 permutations
Explanation
The number of combinations of n object taking r at a time is given by the formula;
[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]From the question, n = 9 and r = 7, then substitute these values into the formula
[tex]^9C_7=\frac{9!}{7!(9-7)!}=\frac{9!}{7!\text{ }2!}=\frac{9\cdot8\cdot7!}{7!\times2}=\frac{72}{2}=36[/tex]The number of permutations of n object taking r at a time is given by the formula;
[tex]^nP_r=\frac{n!}{(n-r)!}[/tex]Also, n = 9 and r = 7, then substitute these values into the formula to get the number of permutations
[tex]^9P_7=\frac{9!}{(9-7)!}=\frac{9!}{2!}=\frac{9\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2!}{2!}=181440[/tex]Therefore, there are 36 combinations and 181440 permutations
(x^3-2x^2-13x) divided by (x+5)
Find the distance between each pair of points round to nearest tenth if needed
Answer: 3.6
20
8.25
Step-by-step explanation:
7 - 10 = 3
-6 - -8 = 2
[tex]\sqrt{3^{2} +2^{2} } =3.6[/tex]
Question 5
Point C is the midpoint of AB and point B is between points A and D. If AD = 15 and
BD = 7, what is CD?
CD
If C is the midpoint of AB then the length of CD is 11 units.
The midpoint of a line segment is referred to as the midpoint in geometry.
It functions as the centroid of the segment and the endpoints, and it is equally separated from both. It cuts the portion in half. As there is no distinguishing point to act as the point at infinity (any point in a geometric range may be protectively transferred into any other point in (the very same or some other) projective range), the midpoint is difficult to define in projective geometry. On the perception line in question, an affine structure can be defined by fixing a point at infinity and then using the aforementioned concept.Given C is the midpoint of AB.
AD = 15 and BD = 7
Now AB = 15 - 7 = 8
Again AC = BC
Therefore = BC = 8 / 2 = 4
Now CD = BC + BD = 4 + 7 = 11
Therefore the length of CD is 11 units.
To learn more about midpoint visit:
https://brainly.com/question/28224145
#SPJ1
Half a number increased by 15 is equal to the sum of five and the product of three and the number what is the number 
The number is (x/2)+15=5+3x if Half of Number augmented by 15 equals the sum of 5 and the product of 3 and the number.
Explain what a number system is?A system of writing numbers is known as a number system. It is the mathematical notation for consistently employing digits or other symbols to represent the numbers in a particular set. It represents the arithmetic and algebraic structure of the numbers and gives each number a distinct representation.
Which four different number systems are there?Decimal Number System is one of the four popular forms of number systems and other 3 are -
System of binary numbers.
System of Octal Numbers.
System of Hexadecimal Numbers.
From the given question,
X is the number. first we have to halve it , then we add 15.
Next ,set it equal to the other side . the second side is 5+ ( because it is the sum)
3x( the product of 3 and x means multiply them)
Hence the number is (x/2)+15=5+3x
Learn more about representation of number here:
https://brainly.com/question/28827977
#SPJ10
a function f(x) is defined by the set of coordinate pairs {(-3,8),(2,5),(7,-1),(11,3)} explain why it is impossible to give a value for f(-1)
It is impossible to give a value for f(-1) because -1 is not in the domain of the function f.
It is given in the question that function f(x) is defined by the set of coordinate pairs {(-3,8),(2,5),(7,-1),(11,3)}.
Here, the ordered pair (a,b) represents (x ,f(x))
Which means:-
f(-3) = 8 , f(2) = 5, f(7) = -1, f(11) = 3.
Here, the elements of domain are -3, 5, -1 and, 3 and the elements of range are 8, 5, -1 and, 3.
We cannot find the value of f(-1) because -1 is not present in the domain of the function.
To learn more about function, here:-
https://brainly.com/question/12431044
#SPJ1
exponential functions with radical bases: simplify: 64 1/4
The simplified form of the exponential expression [tex]64^{\frac{1}{4} }[/tex] is [tex]2\sqrt{2}[/tex]
The given expression = [tex]64^{\frac{1}{4} }[/tex]
The exponential function is the function in the form of f(x)= [tex]a^{x}[/tex], where x is the variable and a is the constant. The constant term is the base of the exponential function.
The given expression = [tex]64^{\frac{1}{4} }[/tex]
Here we have to use the power rule of the exponents
[tex](a^{m})^{n}=a^{mn}[/tex]
To increase a number with an exponent to the power, we have to multiply the exponent times the power
We know
64 = [tex]2^{6}[/tex]
Then
[tex]64^{\frac{1}{4} }[/tex] = [tex](2^{6})^{\frac{1}{4} }[/tex]
Apply the power rule of the exponent
[tex](2^{6})^{\frac{1}{4} }[/tex] = [tex]2^{(6)(\frac{1}{4} )}[/tex]
= [tex]2^{\frac{3}{2} }[/tex]
= [tex]2\sqrt{2}[/tex]
Hence, the simplified form of the exponential expression [tex]64^{\frac{1}{4} }[/tex] is [tex]2\sqrt{2}[/tex]
Learn more about exponent here
brainly.com/question/15993626
#SPJ1
portia can read 23 pages i 10 minutes. at this rate how many can she read in 55 minutes
The rate at which Portia reads is 2.3 pages per minute, at this rate, she can read 126.5 pages in 55 minutes.
How many pages can she read in 55 minutes?We know that Portia can read 23 pages in 10 minutes, so the number of pages she reads per minute is given by the rate:
R = (23 pages)/(10 minutes) = 2.3 pages per minute.
Now, the number of pages she can read in 55 minutes is given by the product between the rate and 55 min, so we will get:
(2.3 pages/min)*55 min = 126.5 pages
We conclude that Portia can read 125.6 pages in 55 minutes.
Learn more about rates:
https://brainly.com/question/19493296
#SPJ1
if anyone can help lmk brainly answer and 20 points
a)Midpoints are (-6.5,-4).
b)Midpoints are (-6.5,-4).
What are midpoints?In geometry, a line segment's midpoint is referred to as the midpoint. It serves as both the segment's and the ends' centroid, and it is equally spaced from both. The portion is halved by it. The midpoint formula is employed when it is important to pinpoint the exact intersection of two given points. The point that splits a line segment described by two points in half can thus be found using this method. The halfway is the precise numerical intersection of two integers. The two-number average computation and the midpoint calculation are equivalent. Consequently, you may get the halfway point between any two integers by adding any two numbers together and dividing by two.
Given Data
Mid point formula = [tex]\frac{x+x}{2}[/tex]¹ , [tex]\frac{y+y}{2}[/tex]¹
a) (2,-1) (-8,6)
Equating values in formula,
[tex]\frac{2-8}{2}[/tex] , [tex]\frac{-1+6}{2}[/tex]
(-4,2.5)
Midpoints are (-4,2.5)
b) (-8,-9) (-5,1)
Equating,
[tex]\frac{-8-5}{2}[/tex] , [tex]\frac{-9+1}{2}[/tex]
[tex]\frac{-13}{2}[/tex] , [tex]\frac{-8}{2}[/tex]
(-6.5,-4)
Midpoints are (-6.5,-4).
To learn more about midpoint, visit:
https://brainly.com/question/28224145
#SPJ13
Helppp pls asappp simple math
Answer:
D. reflection over the y-axis.
Step-by-step explanation:
Reflections are the samere same shapes, but mirrored and over a certain axis (x or y axis). In this case, we see a reflection over the y-axis.
please help only one question i don’t get ;( i will mark brainliest
The graph plotted represents a discrete data
The domain of the function is -2 ≤ x ≤ 2
The range of the function is 1 ≤ y ≤ 5
The graph plotted is represent circle functions
What is discrete data?This is a term used to represent data that can be estimated by counting. The circle graph is an instance of methods of representing discrete data.
What is domain and range?The term domain refers to the input variables on a graph, the domain is usually plotted on the x axis.
Range is a term that describes the output functions and are usually plotted on the y axis.
The function plotted is a circle with a radius of 2 units.
Read more on discrete data here: https://brainly.com/question/14812653
#SPJ1
A line is drawn so that it passes through the points (3, 4) and (4, 1)
What is the slope of the line?
A: 1/3
B: 3
C: -1/3
D: -3
Answer:
m=y2-y1/x2-X1 so the slope is equal to -3
3 1/4 x 1 1/6 as a mixed number in simplest form
Identify the constant term in the following polynomial
8x + 2x^3 - 5x^4 - 9
-9
Step-by-step explanation:Constants are terms that are only numbers, without any variables.
Terms
First, let's define what a term is. Within a polynomial, a term is an expression that is added to other terms to create a polynomial. It is important to note that terms are always added. So, if there is subtraction, that means one of the terms is negative.
Constants
The easiest way to identify constants is to look for terms without variables. In the polynomial above, the only constant is -9. All of the other terms have x to some power as a factor. Since they have variables, they cannot be a constant.
Numbers cannot be changed; this is why there are called constants. No matter the x-value, -9 will not change.
Geometry, if |AC| = |CD|, find angle x.
From the given figure the value of angle x is 40 degrees
How to find angle x|AC| = | CD |
Δ ( ACD ) = Δ ( DCB )
< ( BAC ) = 70 degrees
Since |AC| = | CD | then the base angles are equal, hence
< ( ADC ) = < ( BAC ) 70 degrees. ( base angles of isosceles triangle )
< ( ADC ) + < ( BAC ) + < ( ACD ) = 180 degree ( sum of angles in a triangle)
note < ( BAC ) = < ( DAC )
< ( ACD ) = 180 - 70 - 70
< ( ACD ) = 180 - 140
< ( ACD ) = 40 degrees
If Δ ( ACD ) = Δ ( DCB ) then the angles should be equal
Δ ( ACD ) has angles:
< ( ADC ) = 70
< ( DAC ) = 70
< ( ACD ) = 40
Then Δ ( DCB ) should have angles 70, 70, and 40. The figure did not give enough information to put the angles where it should be.
Comparing with the options, only angle 40 degrees is in the option, hence the correct answer
Read more on geometry here
https://brainly.com/question/19241268
#SPJ1
The ordered pair (a,b) satisfies the inequality y
The ordered pair that satisfies the inequality is (aₓ ,bₓ) .
In mathematics, an inequality is a link that compares two numbers or other mathematical expressions unfairly.
Size comparisons between two numbers on the number line are most usually made.Various types of inequalities can be represented using various notations.By definition, any monotonically growing function can be applied to both sides of an inequality without destroying their relationship (provided that both expressions are in the domain of that function). An inequality relation would be reversed if a monotonically dropping function were applied to both sides of the inequality. Examples of how to employ a monotonically declining function are the rules for the additive and multiplicative inverses for positive values.The notation a b c denotes "a b and b c," from which it also follows that a c, in accordance with the transitivity aspect discussed above. The aforementioned laws state that all three components can be changed by either adding or subtracting the same number, or by multiplying or dividing all three terms by a nonzero number, and reversing any inequalities if the number is negative. As a result, a + e + b + c is the same as a + b + e + c.Therefore we can conclude that (aₓ, bₓ) satisfies the inequality.
To learn more about inequality visit:
https://brainly.com/question/20383699
#SPJ1
Is 4.887888 a rational number
Answer:
Step-by-step explanation:
yes it is
2a + 3=7 and 6x +10y =40 what is the value of 6a+9b what is the value of 3x +5y
Using the given information, the value of 6a + 9b is 21 and the value of 3x + 5y is 20
Evaluating an expressionFrom the question, we are to determine the values of the given expressions.
From the given information,
2a + 3b = 7
and
6x + 10y = 40
To determine the value of 6a + 9b, multiply the first equation by 3.
That is
3 × [ 2a + 3b = 7
6a + 9b = 21
∴ The value of 6a + 9b is 21
To determine the value of 3x + 5y, we will divide the second equation by 2
That is,
6x + 10y = 40 ] ÷ 2
3x + 5y = 20
The value of 3x + 5y is 20
Learn more on Evaluating an expression here: https://brainly.com/question/15032611
#SPJ1