a. The key features of the exponential function y = 1000(2)^(0.3x) is given as follows:
y-intercept: y = 100.Domain: all real values.Range: y ≥ 1000.b. The relevant domain and range are given as follows:
Domain: x ≥ 0.Range: y ≥ 1000.What are the features of the exponential function?The exponential function for this problem is modeled as follows:
y = 1000(2)^(0.3x).
The features are given as follows:
Initial value, when x = 0, of y = 1000, representing the y-intercept.Rate of change of 2 for each period of 0.3 units.The domain of the function is the set that composes all input values of the function, and as the exponential function does not have any restrictions such as a fraction or an even root, it is composed by all real values.
However, the relevant domain is x ≥ 0, as the number of days does not assume negative values.
The range is the set containing all output values of the exponential function. As the initial value of the exponential function is of 1000 and the function is increasing, the range is y ≥ 1000.
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PLEASE HELP !!
What is the missing reason for line 6 in this proof?
CPCTC
This acronym stands for "corresponding parts of congruent triangles are congruent". The triangles being congruent leads to their corresponding pieces being the same length. It's like saying if two houses are identical, then the front doors must be identical as well. Notice how this builds off the fact the triangles are proven congruent in line 5.
Find the lengths of the diagonals of rectangle WXYZ.
WY = 14x + 10
XZ = 11x + 22
The length of each diagonal is
units.
The length of each diagonal is √(196x^2 + 816x + 324) units.
What is the formula for diagonal length?The diagonal of a rectangle can be estimated using the hypotenuse formula, such as using the Pythagorean theorem calculator.
WX^2 = WY^2 + XZ^2
Given that WY = 14x + 10 and XZ = 11x + 22, we can substitute those values in the equation:
WX^2 = (14x + 10)^2 + (11x + 22)^2
WX^2 = 196x^2 + 816x + 324
WX = √(196x^2 + 816x + 324)
The same goes for the other diagonal, WZ.
WZ = √(196x^2 + 816x + 324)
So, the length of each diagonal is √(196x^2 + 816x + 324) units.
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At the candy store, Julie found a special scale that would measure the number of pounds, p, of candy and then calculate the cost, c, when you typed in the name of the candy. For her favorite candy, chocolate gummy bears, she wrote this table.
p c
0.25 1.69
0.45 3.04
0.75 5.06
1.25 11.81
Choose all of the following statements that are true.
Select one or more:
a.
A reasonable domain is [-1, 100]
b.
A reasonable domain is (0, 50] .
c.
c = 6.75p
d.
none of these
e.
A reasonable range is [0, 20].
The true statement about the function in the list of options is (d) none of these
How to determine the true statements in the list of optionsFrom the question, we have the following parameters that can be used in our computation:
p c
0.25 1.69
0.45 3.04
0.75 5.06
1.25 11.81
Where
the number of pounds of candy = p the cost of candy = cThe values in the p column represent the domain
In this case, the domain is
Domain = [0.25, 1.25]
The values in the c column represent the range
In this case, the range is
Range = [1.69, 11.81]
This means that the options (a), (b) and (e) are false
For option (c), we have
c = 6.75p
This means that
c = 6.75 * 0.25 = 1.69
c = 6.75 * 0.45 = 3.04
c = 6.75 * 0.75 = 5.06
c = 6.75 * 1.25 = 8.43 -- false
This means that the option (d) is false
Hence, none of the options is true
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How do you know if its logarithmic or exponential?
The difference between logarithmic and exponential functions can be determined by looking at the form of the equation and by performing a calculation.
A logarithmic equation is written as log_b(x) = y, where b is the base and x and y are variables. An exponential equation is written as b^x = y, where b is the base and x and y are variables.
To determine if an equation is logarithmic or exponential, begin by comparing the form of the equation to the two equations above. If the equation is written in the form of log_b(x) = y, then it is a logarithmic equation. If the equation is written in the form of b^x = y, then it is exponential.
To perform a calculation, plug in a known value for x and then solve for y. For example, if the equation is log_2(x) = 4, then plug in x = 8. The calculation would then be:
log_2(8) = 4
This is a logarithmic equation, as the form of the equation matches log_b(x) = y.
If the equation is b^x = 16, then plug in x = 4. The calculation would then be:
2^4 = 16
This is an exponential equation, as the form of the equation matches b^x = y.
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What is the equation of the line graphed below?
Answer: -2/3x is the slope and the beginning amount is 5 so the equation would be -2/3x+5.
Step-by-step explanation:
Once you find the slope using the formula rise/run you will get 2/3 but since the slope is going downwards it would be -2/3 which gives you the mx. Now to find the beginning amount look where the line intersects the graph which will give you the equation.
Use polar coordinates to find the volume of the given solid. Inside the sphere x^2 + y^2 + z^2 = 36 and outside the cylinder x^2 + y^2 = 1.
The required volume of the given solid is (√16 - r²) -(-√16 - r²).
What is volume?The measurement of three-dimensional space is volume. It is frequently expressed quantitatively using SI-derived units, as well as several imperial or US-standard units.
Volume and the notion of length are connected.
Volume, which is measured in cubic units, is the 3-dimensional space occupied by matter or encircled by a surface.
The cubic meter (m3), a derived unit, is the SI unit of volume.
So, the integrand often takes the form z upper z lower, where z stands for the solid's lower and upper borders.
We are treating the sphere as a hemisphere as of right now, with the XY-plane serving as its lower boundary. Consequently, you must multiply by 2.
The solid's volume is (√16 - r²) -(-√16 - r²).
Therefore, the required volume of the given solid is (√16 - r²) -(-√16 - r²).
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Correct question:
Use polar coordinates to find the volume of the given solid: Inside the sphere x^2 + y^2 + z^2 = 16 and outside the cylinder x^2 + y^2 = 4.
Lin makes her favorite juice blend by mixing cranberry juice with apple juice in the ratio shown on the double number line. complete the diagram to show smaller and larger batches that would taste the same as lin's favorite blend. please
help it's due tomorrow
Answer:
that is the persons username I got it from
Step-by-step explanation:
3 and 7
6 and 14
9 and 21
12 and 28
15 and 35
Step-by-step explanation:
If the two numbers they give you are 9 and 21, then the cranberry's are 3 ounces and the apples are 7 fliud ounces, then you can divide and multiply them to your will.
CORRECT ANSWER WITH **STEPS** GETS BRAINLIEST
for the following questions, determine what values of x makes the rational expression equal to zero.
1. x+6 / x-4
2. (x+4)(x-2) / (x+6)
3. 2x+10 / 3x-12
thanks.
If p(x) = b² - 16b +32 and q(x) = -32b-32 what values of x does p(x)=q(x)?
The functions are p(x) = b² - 16b +32 and q(x) = -32b-32 the x value when the functions are equivalent to each other is 8.
Given that,
The functions are p(x) = b² - 16b +32 and q(x) = -32b-32
We have to find the x value when the functions are equivalent to each other.
We know that,
Take the functions
p(x) = b² - 16b +32 and q(x) = -32b-32
When the function are equivalent
p(x) = q(x)
b² - 16b +32 = -32b-32
b² - 16b +32 +32b+32=0
b² + 16b +64 = 0
Now find the factors for 64
64 = 8×8
b² + 8b + 8b +64 = 0
Taking common terms
b(b + 8) + 8(b + 8)=0
(b + 8)(b + 8)=0
b=8
Therefore, The functions are p(x) = b² - 16b +32 and q(x) = -32b-32 the x value when the functions are equivalent to each other is 8.
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THIS IS A TEST!!!
HOW DO YOU SOLVE FOR X?
If you get this right, or you give an explanation. ill mark you as blranliest.
Answer:
[tex]x = \frac{9}{5} [/tex]
Step-by-step explanation:
[tex] - 7( - 7 \times ( - x - 1)) = 6 (- \times ( - 2x - 3))[/tex]
[tex] - 7 + 7x + 7 = 6 + 2x + 3[/tex]
[tex]7x - 2x = 6 + 3 + 7 - 7[/tex]
[tex]5x = 9[/tex]
[tex] \frac{5x}{5} = \frac{9}{5} [/tex]
[tex]x = \frac{9}{5} [/tex]
50 POINTS!! Pls make sure the answers are correct and the work is shown
Answer all pls and show work
Answer:
it 33 pts not 50
What is the slope of the line that passes through the points (-7,-8) and
(-5, 6)?
[tex](\stackrel{x_1}{-7}~,~\stackrel{y_1}{-8})\qquad (\stackrel{x_2}{-5}~,~\stackrel{y_2}{6}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{6}-\stackrel{y1}{(-8)}}}{\underset{\textit{\large run}} {\underset{x_2}{-5}-\underset{x_1}{(-7)}}} \implies \cfrac{6 +8}{-5 +7} \implies \cfrac{ 14 }{ 2 } \implies \text{\LARGE 7}[/tex]
what is f for 1/8f = 3
Answer:
F = 24
Step-by-step explanation:
simplify 1/8
(1/8 x F) - 3 = 0
3 = 3/1 = 3 x 8/ 8
F x (3 x 8) / 8 F - 24/ 8
F - 24/ 8 = 0
F - 24/ 8 = 0 x 8
Answer:
24
Step-by-step explanation:
You want to know f for 1/8f = 3.
UndoMultiply the given equation by 8 to undo the multiplication by 1/8:
8(1/8f) = 8(3)
f = 24 . . . . . . . . simplify
The value of f is 24.
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2 1/3 grams of spice A was mixed with 4 1/7 grams of spice B. The ratio of spice A to spice B is 1:
The ratio of spice A to spice B is : 49/87
Here, 2 1/3 grams of spice A was mixed with 4 1/7 grams of spice B.
First we convert the improper fraction into a proper fraction.
For improper fraction2 1/3,
2 1/3
= (2 × 3)/3 + 1/3
= 6/3 + 1/3
= (6 + 1)/3
= 7/3 which is a proper fraction.
and for 4 1/7
= (4 × 7)/7 + 1/7
= 28/7 + 1/7
= (28 + 1)/7
= 29/7
The ratio of spice A to spice B would be,
(2 1/3) / (4 1/7 )
= (7/3) / (29/7)
= (7/3) × (7/29)
= (7 × 7)/(3 × 29)
= 49/87
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Please help
me find the product
Answer:
cant answer sorry i didnt realize it was an equation
Step-by-step explanation:
Write a system of linear inequalities represented by the graph.
Inequality 1:
Inequality 2:
By using the unitary approach to answer the given question, we may conclude that total 28 + 40 = $68.
Unitary method: what is it?The unit technique is a strategy for addressing issues that entails first figuring out the value of a single unit, then multiplying that value to figure out the needed value. Simply expressed, the unit technique is used to extract a single unit value from a multiple that is provided. For example, 40 pens would cost 400 rupees, which is equal to the cost of one pen. This procedure could follow a regular procedure. a single nation. something has a distinct identity. Its adjoint and reciprocal are equal in terms of mathematics, algebra, linear algebra, mathematical analysis, or mathematics of matrices or operators.
One package of chicken costs = $7
steaks cost = $4 per pound.
cost of 4 chicken = 4 * 7 < $28
cost of 10 steaks = 4*10 < $40
total 28 + 40 > $ 68
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11. Solve the inequality.
g-6> -1
Answer:
g>5
Step-by-step explanation:
Simply add 6 to both sides to get g>5
Suppose that 15 inches of wire costs 90 cents. At the same rate, how many inches of wire can be bought for 72 cents?
Answer:
12 inches-----------------------------
15 inches of wire costs 90 cents, then 1 inch of wire costs:
90/15 = 6 centsThe length of wire for 72 cents:
72/6 = 12 inchesThe sum of three palm tree heights range from 32 to 42 feet. The height of two of the trees are 8 feet and 16 feet. If the height of the third tree is x feet, write and solve a compound inequality to show the possible heights of the third tree.
A. 8 ≤ x ≤ 16
B. 8 ≤ x ≤ 18
C. 32 ≤ x ≤ 42
D. 56 ≤ x ≤ 66
The compound inequality that shows the possible heights of the third tree is 8 ≤ x ≤ 18
What is an equation?An equation shows how two or more numbers and variables are related to each other.
The height of two of the trees are 8 feet and 16 feet. If the height of the third tree is x feet, hence:
Sum of three palm tree heights = x + 8 + 16 = x + 24
The sum of three palm tree heights range from 32 to 42 feet. Hence:
32 ≤ x + 24 ≤ 42
32 - 24 ≤ x ≤ 42 - 24
8 ≤ x ≤ 18
The solution to the compound inequality is 8 ≤ x ≤ 18
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What is the x-intercept of 2x y =- 4?
The x-intercept will be -2.
Now, According to the question:
How do you find the x-intercept?
To find the x-intercept we set y = 0 and solve the equation for x. This is because when y=0 the line crosses the x-axis. When an equation is not in y = mx + b form, we can solve for the intercepts by plugging in 0 as needed and solving for the remaining variable. To find y-intercept: set x = 0 and solve for y.
Here the equation is 2x-y = -4.
For finding the x-intercept
let us put the value of y as 0 we get,
2x−0=−4
⇒2x=−4 .
Dividing both sides by 2 we get,
2x2=−4/2⇒x=−2 .
Therefore, the x-intercept is -2.
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how do i find the unit rate for 30 inches per 5 years
per year unit rate becomes 6 inches. This can be solved using the concept of unit rate.
What is an unit rate?A unit rate is a price for one of anything. This is expressed as a proportion with such a base of one. For instance, you would cover 7 yards on average every second if you covered 70 yards in 10 seconds. The ratios of 70 yards in 10 seconds and 7 yards in 1 second are both rates, however, the latter is a unit rate.
A rate is the ratio of two different measurement units, whereas a unit rate seems to be the ratio of two different units of measurement for just a single object.
unit rate for 30 inches per 5 years:
= 30 inches / 5 years
= 6 inches / 1 year
Thus, per year unit rate becomes 6 inches.
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For two weeks the highest temp each day was recorded in four different cities. Line L, M, N, & P are graphs of the temp over time in Lubbock, Memphis, New Orleans, & Phoenix. Which statement is true?
A. the high temp in Lubbock increased as time passed
B. the high temp in Memphis decreased steadily
C. Initially, the high temp was warmer in Phoethen in Memphis
D. The high temp in Phoenix rose faster than the temp in New Orleans
Find the equation for the line running
to y = -5x + 5 and passes through the
perpendicular
point (10,7).
let's reword this a bit differently, since it looks jumbled
let's find the equation of a line that is perpendicular to y = -5x + 5, and it also passes through (10 , 7), well, keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]y=\stackrel{\stackrel{m}{\downarrow }}{-5}x+5\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ -5 \implies \cfrac{-5}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{-5}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{-5} \implies \cfrac{1}{ 5 }}}[/tex]
so we're really looking for the equation of a line with a slope of 1/5 and that it passes through (10 , 7)
[tex](\stackrel{x_1}{10}~,~\stackrel{y_1}{7})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{7}=\stackrel{m}{ \cfrac{1}{5}}(x-\stackrel{x_1}{10}) \\\\\\ y-7=\cfrac{1}{5}x-2\implies {\Large \begin{array}{llll} y=\cfrac{1}{5}x+5 \end{array}}[/tex]
Give your answer in the form y=ma + c, where m and c are integers or
fractions in their simplest forms.
Bookwork code, $79
Canalda
allowst
What is the equation of line H?
33
Line
Watch video
Answer? Helllppo
What does log () do in mathematics?
Log () helps to determine the single number to be multiplied.
Log stands for logarithm in algebra. The inverses of equations using exponents are called logarithms. Logs can be used to determine how many times one number needs to be multiplied to get another in its most basic form. For instance, to get 100 in the base-10 system, 10 must be multiplied by 10. In a base-10 system, the logarithm of 100 is therefore 2.
Log () expresses the power or exponent that a base number must be raised to or multiplied by in order to create another number in an ideal world. In situations where the user has data values that are significantly greater or lower than the other values, log scales are quite helpful. When displaying major percentage variations between data points, the user can also utilize a log scale.
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How many real solutions does the system X² y² 25 and ay 10 have?
The system X² y² 25 and ay 10 has no real solutions.
To solve this system, we need to solve each equation for y.
For the first equation, X² y² 25, we can divide both sides by X² to get:
y² = 25/X²
Then, take the square root of both sides to get:
y = ± √(25/X²)
For the second equation, ay = 10, we can divide both sides by a to get:
y = 10/a
To find out if the system has real solutions, we need to compare the two equations. Since the two equations are not equal, the system has no real solutions.
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Last year at a certain high school, there were 75 boys on the honor roll and 120 girls on the honor roll. This year, the number of boys on the honor roll increased by 24% and the number of girls on the honor roll increased by 10%. By what percentage did the total number of students on the honor roll increase
The total number of students on the honor roll increased by 20%.
Given that, 75 boys and 50 girls on the honor roll
=> boys increased by 24% = 75*24/100 = 18
So, the number of boys is increased by 18.
=> girls increased by 14% = 50*14/100 = 7
So, the number of girls is increased by 7.
After the increment, the number of boys and girls on the honor roll is 93 and 57, respectively.
Thus, the total number of students increased = 18+7 = 25
Therefore, the percentage increment in total = 25 / 125 * 100 = 20%
Hence, The total number of students on the honor roll increased by 20%.
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During a science experiment, a chemist boils a liquid and then sets it on the lab table and records the temperatures as it cools. The graph shows , the temperature in degrees Centigrade, and is the number of after the liquid is set on the table. Liquid Temperature Time () Which equation is the best model for this data?
The exponential function that best models this data is given as follows:
C. y = 80(0.75)^x + 20.
How to define the exponential function?An exponential function, considering it's asymptote, is defined as follows:
y = a(b)^x + c.
In which the parameters are given as follows:
a is used to define the initial value.b is the rate of change.c is the horizontal asymptote.From the graph, the horizontal asymptote is at y = 20, hence the parameter c is defined as follows:
c = 20.
When x = 0, y = 100, hence the parameter a is obtained as follows:
100 = a(b)^0 + 20
a + 20 = 100
a = 80.
When x = 5, y = 40, hence the parameter b is obtained as follows:
40 = 80b^5 + 20
80b^5 = 20
b^5 = 1/4
b = (1/4)^(1/5)
b = 0.75. (approximately).
Hence the function is defined as follows:
y = 80(0.75)^x + 20.
Meaning that the correct option is given by option C.
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How do you tell if a graph is linear quadratic or exponential?
A linear graph is one whose equation is in the form y = mx + b, where m and b are constants. A quadratic graph is one whose equation is in the form y = ax^2 + bx + c, where a, b, and c are constants.
To determine if a given graph is linear, calculate the equation of the line by finding two points on the graph and plugging them into the equation y = mx + b.
For example, if the two points on the graph are (2, 3) and (5, 7), then plugging these values into the equation gives us:
y = mx + b
3 = m*2 + b
7 = m*5 + b
Solving this system of equations gives m = 2 and b = -1, so the equation of the line is y = 2x - 1.
A quadratic graph is one whose equation is in the form y = ax^2 + bx + c, where a, b, and c are constants. To determine if a given graph is quadratic, calculate the equation of the parabola by finding three points on the graph and plugging them into the equation y = ax^2 + bx + c.
For example, if the points on the graph are (1, 6), (2, 13), and (3, 24), then plugging these values into the equation gives us:
y = ax^2 + bx + c
6 = a*1^2 + b*1 + c
13 = a*2^2 + b*2 + c
24 = a*3^2 + b*3 + c
Solving this system of equations gives a = 4, b = -5, and c = 6, so the equation of the parabola is y = 4x^2 - 5x + 6.
An exponential graph is one whose equation is in the form y = a*b^x, where a and b are constants. To determine if a given graph is exponential, calculate the equation of the line by finding two points on the graph and plugging them into the equation y = a*b^x.
For example, if the two points on the graph are (2, 16) and (3, 24), then plugging these values into the equation gives us:
y = a*b^x
16 = a*b^2
24 = a*b^3
Solving this system of equations gives a = 2 and b = 2, so the equation of the line is y = 2*2^x.
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For what value of k is 4x 2 8xy k * y 2 9 The equation of a pair of straight lines?
The value 'k' for which '4x^2 + 8xy + ky^2 = 9' is the second degree equation of a pair of straight lines is 4.
Therefore the answer is 4.
A general second-degree equation of a pair of straight lines is given by:
ax² + 2hxy + by² + 2gx + 2fy + c = 0
Where a, b, c, d, e, and f are constants, x and y are variables.
For the equation to represent a pair of straight lines, the following conditions must be met :
abc + 2fgh - af² - bg² - ch² = 0
In the equation 4x^2 + 8xy + ky^2 = 9, a = 4, h = 4, b = k, g = f = 0 and c = -9.
That is 4×k×(-9) + 2×0×0×4 - 4×0² - k×0² + 9×4² = 0
4×k×9 = 9×4²
k = 4
--The question is incomplete, complete question is given below--
"For what value of k is 4x^2 + 8xy + ky^2 = 9 the equation of a pair of straight lines?"
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