Answers
=========================================================
Explanation:
x = number of weeks
y = height of the plant (inches)
The first sentence of "plant is 4 inches tall on week 8" gives us the point (x,y) = (8,4)
The second sentence gives us the point (32,16)
To find the growth rate, compute the slope.
[tex](x_1,y_1) = (8,4) \text{ and } (x_2,y_2) = (32,16)\\\\m = \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{16 - 4}{32 - 8}\\\\m = \frac{12}{24}\\\\m = \frac{1}{2}\\\\m = 0.5\\\\[/tex]
The slope of 0.5 means the plant grows 0.5 inches per week.
Put another way, the plant grows 1 inch per every 2 weeks.
-----------------
Another approach:
The plant goes from 4 inches to 16 inches. It has grown 16-4 = 12 inches over the timespan of 24 weeks (since 32-8 = 24).
So its growth rate is 12/24 = 0.5 inches per week.
Notice how these values and calculations were mentioned in the previous section.
Related Questions
What is 2/3 plus 4/8 equal to please let me know and please explain, and this is 5th grade.
5th grade
Answers
Answer: 7/6
Step-by-step explanation:
Ok so first we must take these fractions and make them have a common denominator. The best way to do this is to take 2/3 and multiply the numerator and denominator by 8 giving us 16/24. Next take 4/8 and multiply the numerator and denominator by 3 giving us 12/24. Now we have both a common denominator. Now we add the numerators of both (16+12) to get 28/24 but now we have an improper fraction divide the numerator and denominator by 4 to get us 7/6.
Hope this Helps :)
Graph the image of the given triangle after the transformation that has the rule (x, y) −> (x - 1, y+5) .
Answers
Answer:
I do not see the original triangle, but you would take the original and move it one unit to the left and 5 units up.
Step-by-step explanation:
For example, if the three vertices (corners) of the triangle were points:
(0,0), (1,5) and (-2,3).
Point (0,0) would move to (-1, 5) 0-1 and 0+5
Point (1,5) would move to (0, 10)
Point (-2,3) would move to (-3, 8)
Answer:
To graph the image of the triangle after the transformation, we first need to have the coordinates of the vertices of the original triangle. Once we have those coordinates, we can apply the transformation to each vertex to obtain the coordinates of the corresponding vertex in the transformed image. Then, we can plot the three transformed vertices to obtain the image of the triangle.
Let's say the original triangle has vertices A, B, and C with coordinates A(x1, y1), B(x2, y2), and C(x3, y3), respectively.
To obtain the transformed coordinates of A, we apply the transformation rule (x, y) → (x - 1, y + 5) to the coordinates of A:
A' = (x1 - 1, y1 + 5)
Similarly, we can obtain the transformed coordinates of B and C:
B' = (x2 - 1, y2 + 5)
C' = (x3 - 1, y3 + 5)
Now that we have the transformed coordinates of the three vertices, we can plot them to obtain the image of the triangle.
Here's an example:
Suppose the original triangle has vertices A(2, 4), B(5, 6), and C(7, 3). Applying the transformation rule (x, y) → (x - 1, y + 5) to each vertex gives us:
A' = (2 - 1, 4 + 5) = (1, 9)
B' = (5 - 1, 6 + 5) = (4, 11)
C' = (7 - 1, 3 + 5) = (6, 8)
Plotting these three points gives us the image of the triangle after the transformation:
Before transformation:
B (5, 6)
/ \
/ \
A (2, 4) C (7, 3)
After transformation:
B' (4, 11)
/ \
/ \
A' (1, 9) C' (6, 8)
Here's what the image of the transformed triangle would look like on a graph:
|
|
C' | B'
|
---------|--------
|
A' |
|
6. According to Statistics Canada, the number of cable television subscribers increased from about 1 151 000 in 2002 to about 1 393 000 in 2003. What was the mean number of new subscribers per month during that year?
Answers
The mean number of new subscribers per month during that year is 242000.
What is a mean?A mean simply means the average of the numbers given.
The number of cable television subscribers increased from about 1 151 000 in 2002 to about 1 393 000 in 2003.
The mean number of new subscribers will be:
= Change in numbers / Number of years
= (1393000 - 1151000) / 1
= 242000 / 1
= 242000
Therefore, the mean is 242000.
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which proportion is equivalent to the original equation
Answers
Original equation (1/2) + (1/2x) = (x² -7x +10)/4x is equivalent to the proportion (x+1)/2x = (x² -7x +10)/4x.
As given in the question,
Given equation is :
Original equation (1/2) + (1/2x) = (x² -7x +10)/4x
Simplify the original equation to get the equivalent equation
Least common multiple is 2 and 2x is equal to 2x
Original equation (1/2) + (1/2x) = (x² -7x +10)/4x is Equivalent to the proportion is given by:
( x + 1) / 2x = (x² -7x +10)/4x
Therefore, original equation (1/2) + (1/2x) = (x² -7x +10)/4x is equivalent to the proportion (x+1)/2x = (x² -7x +10)/4x.
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Find the quadratic using the graph.
Answers
Step-by-step explanation:
the standard form is
f(x) = y = a(x - h)² + k
(h, k) are the vertex coordinates. here (-2, -9).
a is the stretch factor.
since the parabola opens upwards, a is positive.
so, we see already :
y = a(x + 2)² - 9
to get a we need an additional point on the curve. we see e.g. (1, 0) :
0 = a(1 + 2)² - 9 = a×3² - 9 = 9a - 9
9a = 9
a = 1
so, our standard form is
f(x) = (x + 2)² - 9
¿Cuál será el monto que se pagará por un préstamo de $200,000 a una tasa de interés del 36% si se negocia pagarlo en 2 años? C = $200,00
Answers
El interés junto con el préstamo de $ 200,000 tiene un monto de $ 8,080.
¿Cuánto debe pagar el usuario por un préstamo tras un plazo de dos años?En este problema tenemos el caso de una persona que pide prestado $ 200,000 a una tasa de interés anual de 36 %, cuyo pago se realiza tras un plazo de dos años de realizarse el préstamo. Asumimos, que la deuda se genera por interés compuesto, esto es, un interés acumulativo. El interés compuesto es descrito mediante la siguiente fórmula:
I = C' · [(1 + r / 100)ⁿ - 1]
Donde:
C' - Dinero prestado, en unidad monetaria.I - Intereses a pagar, en unidad monetaria.r - Tasa de interés, en porcentaje.n - Número de plazos, en años.Si sabemos que C' = 200,000, r = 36 y n = 2, entonces el interés a pagar al final del plazo es:
I = 200,000 · [(1 + 2 / 100)² - 1]
I = 8080
El interés a pagar es $ 8080, además del préstamo de $ 200,000.
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in the simple linear regression equation , the term b0 represents: a. estimated or predicted response b. estimated intercept c. estimated slope d. explanatory variable
Answers
In the simple linear regression equation , the term b0 represents b) Estimated intercept
Define estimated intercept.The expected mean value of Y when all X=0 is the intercept, also referred to as the constant. Create a regression equation with X as the only predictor to begin. The expected mean value of Y at that value is the intercept in the event that X occasionally equals 0. When x is 0, the projected value for y—the intercept of the regression line—is simply 0. A line's slope and intercept can be expressed in terms of the equation y = slope x x + intercept. The Value of Interception The point where the function crosses the y-axis is known as the intercept and is frequently denoted as a constant. In some analyses, removing the intercept and reducing the regression line to Y = bX + error causes the regression model to only become significant.
Given,
In the simple linear regression equation , the term b0 represents:
b) Estimated intercept
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I need help like asap !!!
only numbers and decimal points
Answers
Answer:
a = 6.63 cm
Step-by-step explanation:
Formula we use,
→ (AC)² = (BC)² + (AB)²
Now the value of a will be,
→ (12)² = a² + (10)²
→ 144 = a² + 100
→ a² = 144 - 100
→ a = √44
→ [ a = 6.63 cm ]
Hence, value of a is 6.63 cm.
You spent less than $75. They purchased three pitchers of soda for $12.99 and pizzas for $6 each. How
many pizzas could the group purchase?
Answers
Answer:
6 pizzas
Step-by-step explanation:
12.99 times 3 which is the 3 pitchers of soda is 38.97
38.97 subtracted from 75 which is our total amount is 36.03
36.03 which is what we have left divided by 6 since each pizza is 6$ is 6.
A line is drawn through (–7, 11) and (8, –9). The equation y – 11 = y minus 11 equals StartFraction negative 4 Over 3 EndFraction left-parenthesis x plus 7 right-parenthesis.(x + 7) is written to represent the line. Which equations also represent the line? Check all that apply.
y = y equals StartFraction negative 4 Over 3 EndFraction left-parenthesis x plus StartFraction 5 Over 3 EndFraction.x +
3y = –4x + 40
4x + y = 21
4x + 3y = 5
–4x + 3y = 17
Answers
The equivalent linear equation in standard form is 4x + 3y = 5
How to determine the equivalent equations?From the question, we have the following parameters that can be used in our computation:
Points = (-7, 11) and (8, –9)
Point-slope form is y - 11 = -4/3(x + 7).
Recall that the point-slope form is y - 11 = -4/3(x + 7).
So, we have
y - 11 = -4/3(x + 7).
Multiply through both sides by 3
This gives
3y - 33 = -4(x + 7).
Open the brackets
3y - 33 = -4x - 28
Evaluate the like terms
3y = -4x + 5
Add 4x to both sides
4x + 3y = 5
Hence, the equation is 4x + 3y = 5
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What are the like terms in the expression 8 + x squared minus 4 x cubed + 5 x + 2 x squared?
8, 5 x
x squared, 2 x squared
8, 5 x 2 x squared
x squared, Negative 4 x cubed, 2 x squared
Answers
In the expression, 8 + x squared minus 4 x cubed + 5 x + 2 x squared.
2x^2 and x^2 are the like terms
How to find the like terms in the expressionThe given expression is 8 + x squared minus 4 x cubed + 5 x + 2 x squared
This is rewritten as
8 + x^2 - 4x^3 + 5x + 2x^2
The terms in the expression are grouped as
constant terms: 8
terms with x variable : 5x
terms with x^2 variables: 2x^2 and x^2
terms with x^3 variables: 4x^3
Like terms refers to terms that are similar either as a constants or have same variables
Hence the like terms in the expression is 2x^2 and x^2
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A line passes through point (-2, 8) and has a slope of -5. Write an equation in Ax + By =C form for this line. Use integers for A, B, and C.
25 points
Answers
The equation of line with a slope of -5 and which passes through point (-2, 8) is 5x + y = -2.
What is the equation of line with the given point and slope?The formula for equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
Given the data in the question;
Point (-2,8)
x = -2y = 8Slope m = -5First, we determine the y-intercept 'b'. Plug the coordinates and slope into the equation of line formula and solve for b.
y = mx + b
8 = (-5)(-2) + b
8 = 10 + b
b = 8 - 10
b = -2
Now, plug values of slope m and y-intercept b into y = mx + b to determine the equation of the line.
y = mx + b
y = (-5)x + (-2)
y = -5x - 2
Convert to standard form; Ax + Bx = C
y = -5x - 2
Reorder the equation
5x + y = - 2
Therefore, the equation of the line is 5x + y = - 2.
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A garden designer designed a square decorative pool. The pool is surrounded by a walkway. On two opposite sides of the pool, the walkway is 8 feet. On the other two opposite sides, the walkway is 10 feet. The final design for the pool and walkway covers a total area of 1,440 square feet. ---------- a. The side length of the square pool is x. Write an expression that represents: 1. The total length of the rectangle (including the pool and walkway) 2. The total width of the rectangle (including the pool and walkway) 3. The total area of the pool and walkway b. Write an equation of the form: your expression = 1,440. What does a solution to the equation mean in this situation?
Answers
Part 1: The total length of the rectangle; 20 + x (Expression).
Part 2: The total width of the rectangle; 16 + x (Expression).
Part 3: The total area of the pool along with walkway; (20 + x)(16 + x).
Define the term area of the rectangle?The area a rectangle occupies is the space it takes up inside the limitations of its four sides. The dimensions of a rectangle determine its area. In essence, the area of a rectangle is equal to the sum of its length and breadth.The data for the question is given as-
The boardwalk around the pool is 8 feet long and on two different sides. The walkway is 10 feet wide on either two opposite sides. The pool and walkway's final design takes up a total of 1,440 square feet.The side length of the square pool is x.The expressions for the given cases are-
Part 1: The total length of the rectangle;
The total length of the rectangle = 10 + 10 + x
The total length of the rectangle = 20 + x (Expression)
Considering; 10 + 10 > 8 + 8
Part 2: The total width of the rectangle;
The total width of the rectangle = 8 + 8 + x
The total width of the rectangle = 16 + x (Expression)
Part 3: The total area of the pool along with walkway.
Area = length x breadth
Area = (20 + x)(16 + x).
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cómo se saca el porcentaje
Answers
Answer:
Step-by-step explanation:
Para determinar el porcentaje, tenemos que dividir el valor por el valor total y luego multiplicar el resultado por 100.
What two numbers = -48 (multiply) and does the two numbers = -13
Answers
Answer:
The two numbers are [tex]3[/tex] and [tex]-16[/tex].
Step-by-step explanation:
Two numbers that, when multiplied, result in a product of [tex]-48[/tex]:
[tex]x \cdot y = -48[/tex]
Same two numbers when added get a sum of [tex]-13[/tex]:
[tex]x + y = -13[/tex]
Solve for x in the summation identity:
[tex]y = -13 - x[/tex]
Plug the value back into the product identity and solve for [tex]x[/tex]:
[tex]x \cdot (-13-x) = -48\\-13x - x^2 = - 48\\x^2 + 13x = 48\\x^2 + 13x - 48 = 0\\(x-3)(x+16) = 0[/tex]
The roots we found for [tex]x[/tex] were:
[tex]x = 3\\x = -16[/tex]
Our two numbers are [tex]3[/tex] and [tex]-16[/tex]. We can test this:
[tex]3 + (-16) = -13\\3 * -16 = -48[/tex]
Factor x^2-x-72 Please
Answers
Answer:
(x+8)(x-9)
Step-by-step explanation:
1. Use the sum-product pattern
x²-x-72
x²+8x-9x-72
2. Find the common factor from the 2 pairs
x²+8x-9x-72
x(x+8)-9(x+8)
3. Rewrite in factored form
x(x+8)-9(x+8)
(x-9)(x+8)
Solution to problem: (x-9)(x+8)
A group of friends wanted to compare their average running speeds. They recorded the distance and amount of time each person ran one Saturday morning.
Select all the runners whose speeds are in a proportional relationship with each other.
Name Time (seconds) Distance (miles)
Liam 306.6 0.5
Taylor 756.36 1.2
Sarah 504.35 0.7
Ashley 459.9 0.75
Connor 600.5 1
Nathan 942.75 1.5
Juan 827.82 1.35
Katie 429.48 0.6
Answers
The runners whose speeds are in a proportional relationship with each other:
the running speed of Liam, Taylor, Ashley, Nathan, Juan are equal (0.0016) whereas the running speed of Sarah and Katie are equal.
In this question, we have been given the data for the distance and amount of time each person ran one Saturday morning.
We need to select all the runners whose speeds are in a proportional relationship with each other.
We find the speed using formula, speed = distance / time
Name Time (seconds) Distance (miles) Speed(mps)
Liam 306.6 0.5 0.5/306.6 = 0.0016
Taylor 756.36 1.2 1.2/756.36 = 0.0016
Sarah 504.35 0.7 0.7/504.35 = 0.0014
Ashley 459.9 0.75 0.75/459.9 = 0.0016
Connor 600.5 1 1/600.5 = 0.0017
Nathan 942.75 1.5 1.5/942.75 = 0.0016
Juan 827.82 1.35 1.35/827.82 = 0.0016
Katie 429.48 0.6 0.6/429.48 = 0.0014
Therefore, the runners whose speeds are in a proportional relationship with each other:
the running speed of Liam, Taylor, Ashley, Nathan, Juan are equal (0.0016) whereas the running speed of Sarah and Katie are equal.
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im stumped please help
Answers
Because the starting position is 0 and add 90 degrees for each square so it will be 270
Ada lives 12 4/5 miles from her aunt's house. she lives 17 3/8 miles from her grandmother's house. how many more miles does jada live from her grandmother's house than her aunt's house?
Answers
Answer:
[tex]4 \frac{23}{40}\; \rm miles[/tex]
Step-by-step explanation:
To find how many more miles Ada lives from her grandmother's house than her aunt's house, we need to subtract the distance to her aunt's house from the distance to her grandmother's house.
Ada lives 17 3/8 miles from her grandmother's house.
Ada lives 12 4/5 miles from her aunt's house.
Convert both mixed numbers into improper fractions by multiplying the whole number by the denominator of the fraction, adding this to the numerator of the fraction, and placing the answer over the denominator:
[tex]17 \frac{3}{8}=\dfrac{17 \cdot 8+3}{8}=\dfrac{139}{8}[/tex]
[tex]12 \frac{4}{5}=\dfrac{12 \cdot 5+4}{5}=\dfrac{64}{5}[/tex]
As both improper fractions have a different denominator, we need to change both fractions into equivalent fractions with the same denominator. To do this, find the least common multiple (LCM) of the denominators, 8 and 5.
The LCM of 8 and 5 is 40. Therefore, convert the fractions into their equivalent fractions (with 40 as their denominator) by multiplying the numerator and denominator by the same number:
[tex]\dfrac{139}{8}=\dfrac{139 \cdot 5}{8 \cdot 5}=\dfrac{695}{40}[/tex]
[tex]\dfrac{64}{5}=\dfrac{64 \cdot 8}{5 \cdot 8}=\dfrac{512}{40}[/tex]
Now the fractions have the same denominator, we can carry out the subtraction by simply subtracting the numerators:
[tex]\dfrac{695}{40}-\dfrac{512}{40}=\dfrac{695-512}{40}=\dfrac{183}{40}[/tex]
Finally, convert the improper fraction into a mixed number by dividing the numerator by the denominator:
[tex]183 \div 40=4\;\rm remainder \;23[/tex]
The mixed number answer is the whole number and the remainder divided by the denominator:
[tex]4 \frac{23}{40}[/tex]
Therefore, Ada lives 4 23/40 miles more from her grandmother's house than her aunt's house.
simplify
2√3/16-√75/16+2√27/16
Answers
Answer:
3.24759526401
Step-by-step explanation:
divide that
How do I find the missing angle of an intersecting line?
Answers
Answer:
Read the given problem, look at the given figure of intersecting lines, and identify the angle given and the unknown angles.
Step-by-step explanation:
List the independent and dependent variables
H(x)=3+0.5x
Answers
x is the independent variable and H(x) is the dependent variable
How to determine independent and dependent variables?
A dependent variable is a variable whose value depends upon independent variables.
An independent variable is a variable that does not depend on any other variable for its value.
For example, in an expression, y = 3x + 2, x is an independent and y is a dependent variable because y depends on x for its value
Given: H(x) = 3+0.5x
Therefore, x is the independent variable and H(x) is the dependent variable because it is a function of x
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Someone help me with this please
Answers
Answer:
C
Step-by-step explanation:
C has a directly proportional relationship. 27 glasses are in 9 cases, and 81 glasses are in 27 cases. Directly proportional since 9×3=27 (cases) and 27×3=81 (glasses)
As the diameter (d) of a circle increases in size, the circumference (C)
increases Likewise, as the diameter decreases in size, so does the circumference,
The constant of variation between Cand dist. Describe the kind of variation
between eireumference and diameter Write the equation.
Answers
The equation of direct proportion is y=kx, where is the constant of proportionality. When we input variables c (circumference) and d (diameter), we can write the equation as c=kd / d=kc
Robin's bank account has $1,876. Every month she withdraws $30 for her phone payment. Create an equation to describe how
much money she will have after a certain amount of months. Write the equation for this problem in function notation. Then
interpret how much money Robin will have after 6 months of payments. Make sure to define your variables and show all of your
work.
Answers
Answer: M = 1876 - 30n will give the amount of Money (M) remaining after n months of withdrawing exactly $30 per month, PROVIDED NOTHING ELSE IS EVER ADDED TO OR WITHDRAWN FROM THE ACCOUNT. (Not very realistic.)
Use n=6 to provide the balance after 6 months.
Step-by-step explanation:
passes through A (2, "-5)" parallel to BC with (1, 3) and ( 4, 5) PLS HURRRY!!!!!
Answers
The equation for the linear equation parallel to BC is:
y = (2/3)*x - 19/3
How to get the linear equation?
A general linear equation is written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
If the line passes through two points (x1, y1) and (x2, y2), then the slope is:
slope = (y2 - y1)/(x2 - x1)
And two lines are parallel if both lines have the same slope and different y-intercept.
So if we want to et a line parallel to BC whose endpoints are (1, 3) and ( 4, 5), the slope should be:
slope = (5 - 3)/(4 - 1) = 2/3
So our line is like:
y = (2/3)*x + b
And this must pass through (2, -5)
Replacing these values we get:
-5 = (2/3)*2 + b
-5 - 4/3 = b
-15/3 - 4/3 = b
-19/3 =b
Then the linear equation is:
y = (2/3)*x - 19/3
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2x + 4y < 20 what is the inequality simplifies
Answers
Answer:
x < 10 - 2y
Step-by-step explanation:
simplify the following
2²y + 3x² + 4y + 3x²y + 2y
Answers
Answer:
10y+3x^2+3x^2y
Step-by-step explanation:
^2 means square
2^2 is 4 and different variable cannot be added.
PLEASE HELP!!!!!!!!!!
I WILL NAME YOU THE BRAINLIEST!
The thing is in the photo.
I do not understand it because it looks like it has "!" Please help
Answers
A (8,4)
B (4,3)
C (4,-9)
D(2,-1)
please explain your answer!!!
Answers
Neither.
Parallel lines (when the line continues), never intersects. Perpendicular lines intersect and create a 90 degree angle.
The angle created by the lines intersect but do not create a 90 degree angle.
