The function which grows or decreases at a constant % growth rate is known as an exponential function, and further discussion can be defined as follows:
This equation can be written as [tex]\bold{ f(x) = a(1 + r)^x\ or\ f(x) = ab^x}[/tex], where [tex]\bold{b = 1 + r}[/tex].These functions were frequently used to represent real-world applications.These bacterial growth & decay, demographic growth or decline, and compound interest.Growth curve modeling is a statistical technique for examining change over time using observational studies.Learn more:
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Which equation represents a population of 320 animals that decreases at an annual rate of 19%
Population of 320 animals decreases at rate of 19 % = P = 320(0.81)t
What is percentage ?
Percentage means how much per hundredth.
we can write 20% as `1/5 in fraction. when we multiply a fraction by 100 we get the result in percentage.
In the given question
Population (P) = 320
Annual rate or per year decreasing percentage = 19%
As it decreases each year by 19% it retains (100 - 19)%= 81% of 320 animals
So in t years it will be P = 320([tex]\frac{81}{100}[/tex])t animals
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The instructor’s friend also plans to rent an apartment in the same complex. Use the graph to identify the y-intercept and the slope used to write the equation in slope intercept form. y-intercept = Slope = Linear equation =
Answer:
A graph has month on the x-axis and saved (money) on the y-axis. Points are at (0, 3,000), (2, 2,450), and (5, 1,625).
The instructor’s friend also plans to rent an apartment in the same complex. Use the graph to identify the y-intercept and the slope used to write the equation in slope intercept form.
y-intercept =
✔ 3000
Slope =
✔ –275
Linear equation =
✔ y = -275x + 3000
Step-by-step explanation:
The linear equation which models the data represented by the graph written is slope - intercept form is :y= - 275x + 3000
General form of a slope - intercept equation :
y = bx + cSlope = Rise / Run
Rise = y2 - y1 = (3000 - 1625) = 1375Run = x2 - x1 = (0 - 5) = - 5The slope, b:
Slope = (1375 ÷ -5) = - 275
The intercept, c:
This is the point on the graph where the trend line crosses the y-axis.
Hence, the intercept is 3000
Therefore, the slope - intercept equation is y= - 275x + 3000
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What is the solution set of the quadratic inequality x2-5<0?
Answer:
-\sqrt{5}< x < \sqrt{5}[/tex]
Step-by-step explanation:
[tex]x^{2} <5 => -\sqrt{5}< x < \sqrt{5}[/tex]
Answer:
[tex]-\sqrt{5} <x<5[/tex]
Step-by-step explanation:
The given expression is
[tex]x^{2} -5<0[/tex]
To solve this quadratic inequality, we need to isolate the variable and then apply the quadratic root at each side of the inequality, as follows
[tex]x^{2} <5\\x<\±\sqrt{5}[/tex]
Remember that a quadratic root has two results, one positive and one negative, which in this case would be
[tex]x<\sqrt{5}\\ x>-\sqrt{5}[/tex]
Remember that a negative factor changes the direction of the inequality relation to the opposite.
Therefore, the solution is
[tex]-\sqrt{5} <x<5[/tex]
That is, all values between [tex]-\sqrt{5}[/tex] and [tex]\sqrt{5}[/tex].
For the given true statements, what can you conclude?
If points A, B, and C are collinear, and B is between A and C, then AB + BC = AC.
Points Q, R, and S are collinear and R is between Q and S.
SQ + RS = QR
QR + QS = RS
RS + QS = SR
QR + RS = QS
Answer:
D:QR+RS=QS
Step-by-step explanation:
We are given that
If point A, B and C are collinear, B is between A nd C, then AB+BC=AC
Points Q, R and S are collinear and R is between Q and S.
We have to find the conclusion about given statement.
If R lie between Q and R
Then, QR+RS=QS (segment addition property)
Because point Q, R and S are collinear.
Therefore, option D is true.
Answer:D:QR+RS=QS
distance between -6.2 and -9.1
Step By Step
Answer:
[tex]D=\sqrt{10}=3,16...[/tex]
Step-by-step explanation:
[tex]A(x_{1},y_{1})[/tex]
[tex]B(x_{2};y_{2})[/tex]
[tex]D=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]
[tex]A(-6,2)[/tex]
[tex]B(-9;1)[/tex]
[tex]D=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]
[tex]D=\sqrt{[-9-(-6)]^{2}+(1-2)^{2}}[/tex]
[tex]D=\sqrt{[-9+6]^{2}+(1-2)^{2}}[/tex]
[tex]D=\sqrt{[-3]^{2}+(-1)^{2}}[/tex]
[tex]D=\sqrt{9+1}[/tex]
[tex]D=\sqrt{10}=3,16...[/tex]
Answer:
The distance between -6.2 and -9.1 is 2.9.
Step-by-step explanation:
Given : Two numbers -6.2 and -9.1.
To find : What is the distance between the numbers ?
Solution :
Let A=-6.2
B=-9.1
The distance between two number is [tex]d=|B-A|[/tex]
Substitute the values,
[tex]d=|-9.1-(-6.2)|[/tex]
[tex]d=|-9.1+6.2|[/tex]
[tex]d=|-2.9|[/tex]
[tex]d=2.9[/tex]
Therefore, The distance between -6.2 and -9.1 is 2.9.
Name two planes that intersect in the given line 19.QU 20.TS 21.XT 22.VW
Answer: 19. UQTX and UQRV
20. TSWX and TSRQ
21. XTQU and XTSW
22. VWXU and VWSR
Step-by-step explanation:
The planes are the faces of the box.
19) QU intersects the left side and the front of the box, which is planes UQTX and UQRV
20) TS intersects the back and the bottom of the box, which is planes TSWX and TSRQ
21) XT intersects the left side and the back of the box, which is planes XTQU and XTSW
22) VW intersects the right side and the top of the box, which is planes VWXU and VWSR
The two planes that intersect in the given line are QTS and TUV.
Explanation:In order to determine two planes that intersect in a given line, we can start by looking at the notation provided. Here, the given line is represented by the points 19.QU, 20.TS, 21.XT, and 22.VW. We can identify two planes that intersect in this line by observing the common points shared between them.
By analyzing the given line notation, we can see that the points U, T, and V are common to all four pairs of points, indicating that these points lie on the intersection of two planes. Therefore, the two planes that intersect in the line 19.QU 20.TS 21.XT 22.VW are the planes containing points QTS and TUV.
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Need help! what is 3√12 + √27 ?
Answer:
8√3
Step-by-step explanation:
3√12 = 3√4 x 3 = 5√3
√27 = 3√3
5√3 + 3√3 = 8√3
help please!!!!;;;;;;;;;;;;;;;;;;;;
Hey!
-----------------------------------------------
Solution:
= (-18) - (4)
= -18 - 4
= -22
When you subtract a positive to a negative number the end result will always be negative.
-----------------------------------------------
Answer:
B. 22
-----------------------------------------------
Hope This Helped! Good Luck!
The center of the dilation that transforms rectangle WXYZ into rectangle W'X'Y'Z' is origin___. (0,0) (0,-2) (-2,-2) (-2,1)
Answer:
It's C (-2,-2)
Step-by-step explanation:
The given line passes through the points (0, ) and (2, 3). On a coordinate plane, a line goes through (0, negative 3) and (2, 3). A point is at (negative 1, negative 1). What is the equation, in point-slope form, of the line that is parallel to the given line and passes through the point ()?
Option 2 is correct.
[tex]\[ y = \frac{1}{5}x + \frac{12}{5} \][/tex]
To find the equation of a line that is parallel to the given line and passes through the point (-2, 2), we follow these steps:
1. Determine the slope of the given line. Parallel lines have the same slope.
2. Use the point-slope form of a line equation with the given point and the determined slope to find the equation of the parallel line.
From the graph, we can see that the given line passes through points (0, -3) and (-5, -4). To find the slope (m) of the line, we use the slope formula:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Substituting the given points, we get:
[tex]\[ m = \frac{-4 - (-3)}{-5 - 0} \][/tex]
[tex]\[ m = \frac{-4 + 3}{-5} \][/tex]
[tex]\[ m = \frac{-1}{-5} \][/tex]
[tex]\[ m = \frac{1}{5} \][/tex]
Now we have the slope of the parallel line, which is[tex]\( \frac{1}{5} \)[/tex]. The point-slope form of the line equation is [tex]\( y - y_1 = m(x - x_1) \)[/tex]. Plugging in the slope and the point (-2, 2), we get:
[tex]\[ y - 2 = \frac{1}{5}(x - (-2)) \][/tex]
[tex]\[ y - 2 = \frac{1}{5}(x + 2) \][/tex]
Now we simplify and solve for y to put it in slope-intercept form ( y = mx + b ):
[tex]\[ y - 2 = \frac{1}{5}x + \frac{2}{5} \][/tex]
[tex]\[ y = \frac{1}{5}x + \frac{2}{5} + 2 \][/tex]
[tex]\[ y = \frac{1}{5}x + \frac{2}{5} + \frac{10}{5} \][/tex]
[tex]\[ y = \frac{1}{5}x + \frac{12}{5} \][/tex]
So the equation of the line that is parallel to the given line and passes through the point (-2, 2) is:
[tex]\[ y = \frac{1}{5}x + \frac{12}{5} \][/tex]
A rectangle has an area of 90 square centimeters and a height of 12.5 centimeters. What is the length of the base?
A.
7.2 centimeters
B.
72 centimeters
C.
112.5 centimeters
D.
1125 centimeters
Answer:
A. 7.2 centimeters
Step-by-step explanation:
The length of the base is 7.2 centimeters. The area of a rectangle is length*width
The length is unknown but the area is known. To find the length, all we have to do is divide the area from the height.
The working is as follows :
Area = 90 cm²
Height = 12.5 cm
Length = ?
Length = Area ÷ Height
= 90 ÷ 12.5
= 7.2cm
The length of the base of the rectangle is found by dividing the area by the height, which gives 7.2 centimeters.
Explanation:The subject is about finding the length of the base of a rectangle given its area and height. The formula to find the area of a rectangle is Area = Length x Width. From the question, we know the Area is 90 square centimeters and the height (which can also be considered as the Width) is 12.5 centimeters. Therefore, we can arrange the formula to solve for Length: Length = Area / Width.
Substituting the given numerical values we find: Length = 90 / 12.5 = 7.2 centimeters. So, the correct answer is 7.2 centimeters (Option A).
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Mary weighs n kg while her sister weighs 15 kg less. How many times is Mary heavier than her sister?
For this case we have to:
n: Represents the weight of Mary in Kg.
If your sister weighs 15 kg less we have:
[tex]y = n-15[/tex]
Where "y" represents the weight of his sister in kg.
To find how many times Mary is heavier than her sister, we must divide Mary's weight by her sister's weight.
We have then:
[tex]N= \frac{n}{n-15}[/tex]
Answer:
Mary is [tex]N= \frac{n}{n-15}[/tex] times heavier than her sister.
Answer:
Mary weighs[tex]\frac{n}{(n-15)}[/tex]heavier than her sister.
Explanation:
As we have given the data in the question that
Weight of marry = n kg
Weight of Marry sister = n-15 kg
Let Marry be ‘K' times heavier than her sister then it means that
K=[tex]\frac{n}{(n-15)}[/tex]
And we can write the above equation as
K(n-15) = n
K=[tex]\frac{n}{(n-15)}[/tex]
which completely explains the above statement that Weight of the marry is K times the weight of her sister.
So the correct answer is K=[tex]\frac{n}{(n-15)}[/tex]
(-14) = ((-2) – (3 + (+2))] - 7
Help me
Answer:
The equation above has no question, but if there was, then yes, the equation above does equal -14
Step-by-step explanation:
Answer:
-14
Step-by-step explanation:
(−2) − (3+(2))−7
= - 2 - ( 3 + 2 ) - 7 = − 2 − ( 3 + 2 ) − 7
= - 2 - 5 - 7 = − 2 − 5 − 7
- 14
A
B
C
D
Help much appreciate
Answer:
D
Step-by-step explanation:
A is 4, which is rational,
B is just 1/3, which is rational,
C is -8, which is rational,
leaving D, which is 3.1415926535...
For f(x) = 4x + 2 and g(x) = x2 - 6, find (f+ g)(x).
O A. x +4x- 4
O B. x2 + 4x+8
O c. 4x2 - 16
O D. 4x3 - 4
Answer:
A
Step-by-step explanation:
(f + g)(x) = f(x) + g(x)
f(x) + g(x) = 4x + 2 + x² - 6 = x² + 4x - 4 → A
What is 18 - 8x = -6x.
PLEASE DO IT RIGHT IT IS MY HOMEWORK
Answer:
Step-by-step explanation:
18 - 8x = -6x.
Add 8x from the left side to the right
18=2x
18/2 = 9
x=9
(2a+5b-7)+(a-9b-6) need help
Answer:
[tex]3a-4b-13[/tex]
Step-by-step explanation:
Given: [tex](2a+5b-7)+(a-9b-6)[/tex]
Since we are adding, there is no real use for the parenthesis. This may help you visualize it better.
[tex]2a+5b-7+a-9b-6[/tex]
Combine like terms:
[tex]3a-4b-13[/tex]
It is the answer shown below
3a-4b-13
Without graphing, classify each system as independent, dependent, or inconsistent
y = 4x+6
1-8x+2y=12
a. independent
b. dependent
c. inconsistent
please help
The system of equations provided is classified as inconsistent because the equations have equal slopes but different y-intercepts, indicating they are parallel lines without any intersection point.
Explanation:
To classify the system as independent, dependent, or inconsistent without graphing, we need to rearrange the equations into a common linear form, typically y = mx + b, where m is the slope and b is the y-intercept.
The given equations of the system are y = 4x + 6 and 1 - 8x + 2y = 12. Let's rewrite the second equation in the form y = mx + b, which results in y = 4x - 5.
Now, let's compare. The first equation has a slope of 4 (m1 = 4) and the second equation also has a slope of 4 (m2 = 4). However, the y-intercepts of the two lines (b1 = 6, b2 = -5) are different.
Since the slopes are equal and the y-intercepts are different, the system is inconsistent. In other words, the two lines are parallel and do not intersect, so there is no solution to the system.
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What power of 10 can you multiply 0.02 by to get a product of 20?
Answer:
10^{3\\}
Step-by-step explanation:
10x10x10x0.02
=20
Have a nice day!!!!
KA
I need to know what x is
What is 73.04 times 1.2
Answer:
87.648
this is the answer
Answer:
87.648 should be your answer
Subtract 2 1/8- 1 7/8
Answer:
2/8 or 1/4
Step-by-step explanation:
2 1/8 - 1 7/8 - Make improper fractions
17/8 - 15/8 - subtract them
2/8 - simplify
1/4 - final
In order to get the answer to this question you will have to change the mixed numbers into improper fractions and then subtract by finding the common denominator and then subtracting the numerators and reduce if needed to get your answer.
[tex]2\frac{1}{8} - 1\frac{7}{8}[/tex]
Convert into improper fractions:
[tex]2\frac{1}{8} =\frac{17}{8}[/tex]
[tex]1\frac{7}{8} = \frac{15}{8}[/tex]
[tex]\frac{17}{8} - \frac{15}{8}[/tex]
Find the common denominator:
[tex]CD=8[/tex]
[tex]17-15=2[/tex]
[tex]=\frac{2}{8}[/tex]
Reduce:
[tex]\frac{2}{8} \div2=\frac{1}{4}[/tex]
[tex]=\frac{1}{4}[/tex]
Therefore your answer is "1/4."
Hope this helps
What number does stand for in this equation? 6x3=(x5)-(x2)
Answer:
the answer is 6
Step-by-step explanation:
6×3=18
So 6×5=30, 6×2=12
30-12=18
18=18
Which ordered pair is a solution to the linear system? (2x + y = 5) (x – y = 13)
Answer:
The solution is {6, -7}.
Step-by-step explanation:
2x + y = 5
x – y = 13 Adding these 2 equations eliminates y:
3x + 0 = 18
x = 6.
Substituting for x in equation (1):
2(6) + y = 5
y = 5 - 12 = -7.
The ordered pair that is a solution to the linear system of equations, (2x + y = 5) and (x - y = 13), is (6, -7). The solution was found by using the elimination method.
Explanation:You can solve this linear system by using the substitution or elimination method. Here, I will use the elimination method, which involves adding or subtracting the equations to eliminate one of the variables.
First, add the two equations together. (2x + y) + (x – y) equals 5 + 13. This simplifies to 3x = 18. Second, divide both sides of the equation by 3 to solve for x. This gives x = 6. Substitute this value back into either of the original equations. By substituting into the first equation, it becomes 2*6 + y = 5. Simplifying it, gives y = -7.So the
ordered
pair that is a solution to the linear system is (6, -7).
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25 000,000/10,000
No calculator
25 000,000/10,000
Cross out equal amounts of 0's from both numbers:
There are 4 0's in 10,000, so remove 4 0's from both numbers to get:
2500/1
Any number over 1 is that number:
2500/1 = 2500
What is 6.02 nearest tenth
Answer:
6
Step-by-step explanation:
The digit in the hundredth place value of 6.02 is 2, so it rounds down.
The number 6.02, when rounded to the nearest tenth, results in 6.0, as '2' in the hundredths place is less than '5' and requires rounding down.
Explanation:Given the number 6.02, rounding to the nearest tenth means identifying what tenth it is closest to. The number in the tenths place is '0'. For rounding, we look at the digit following the tenths place, which is the hundredths place. Here, the number is '2'. If this number is 5 or more, we round up. If it's 4 or less, we round down. So, 6.02 to the nearest tenth, would be 6.0 because 2 is less than 5, so we round down.
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According to the 2010 census The state with the fewest people is Wyoming with a population of 563,626. Write the number that is 10,000 greater than 563,626
Answer:
573,626
Step-by-step explanation:
563626 + 10000 = 573626
IF YOU SOLVE FIRST YOU GET BRAINLIEST
Solve for x: 2/5(x − 2) = 4x. x = 2/9 x = −2 x = -2/9 x = -9/2
I solved 2/5(x − 2) = 4x. I don't know why you included those extra numbers.
-2/9
Which addition sentence could help solve this problem 3 + 5 + 7 =15
2+3=5
5+5=10
3+7=10
5+2=7
The required sentence are 3 + 7 = 10 could help solve this problem 3 + 5 + 7 =15. Option C is correct.
Given that,
Which additional sentence could help solve this problem 3 + 5 + 7 =15 is to be determined.
The technique in computation to use and analyze the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
What is arithmetic?In mathematics, it vends on a number of procedures according to the declarations. There are four primary arithmetic operators, addition, subtraction, multiplication, and division,
Here,
The sentence could help solve this problem 3 + 5 + 7 =15
3 + 7 + 5 = 15 - - - - - - -(1)
3 + 7 = 10
Put it in equation 1
10 + 5 = 15
Thus, the required sentence are 3 + 7 = 10 could help solve this problem 3 + 5 + 7 =15. Option C is correct.
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2(4-8x)+6=1 in distributive property
Answer:
x =13/16
Step-by-step explanation:
2(4-8x)+6=1
2*(4-8x) + 2*3 =1
2 ( 4 - 8x + 3 ) = 1
2 * ( 7- 8x ) = 1
2* 7 - 2 * 8x = 1
14 - 16x = 1
- 16x = 1-14
-16x = -13
x = -13 /- 16
x =13/16