Answers
Answer
Lake depth after 4 weeks: 343.6 ft
Lake depth after 9 weeks: 340.6 ft
Step-by-step explanation
The relation between time and lake depth is linear. Using the x-variable to represent time and the y-variable to represent the lake depth, we can use the next equation to relate these variables:
[tex]y=mx+b[/tex]where m is the slope and (0, b) is the y-intercept of the line.
The slope of the line that passes through the points (x₁, y₁) and (x₂, y₂) is calculated as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]From the table, this line passes through (0, 346) and (2, 344.8), then its slope is:
[tex]m=\frac{344.8-346}{2-0}=\frac{-1.2}{2}=-0.6[/tex]From the table, this line passes through (0, 346), then parameter b is 346.
Substituting m = -0.6 and b = 346, the equation of the line is:
[tex]y=-0.6x+346[/tex]Evaluating this line at x = 4, that is, when time = 4 weeks, we get the next depth:
[tex]\begin{gathered} y=-0.6(4)+346 \\ y=-2.4+346 \\ y=343.6\text{ ft} \end{gathered}[/tex]Evaluating the equation of the line at x = 9, that is, when time = 9 weeks, we get the next depth:
[tex]\begin{gathered} y=-0.6(9)+346 \\ y=-5.4+346 \\ y=340.6\text{ ft} \end{gathered}[/tex]Related Questions
whats the absolute value between the points -45 and -11
Answers
For two real numbers u and v, |u-v| is the absolute value between the points:
|-45-(-11)|=|-34|=34
Don José es un conocido comerciante. Al inicio de la semana tenía una suma de dinero, de la cual invirtió 2,000 pesos en mercancía. Al término de la semana, ingresó por ventas tres veces el capital con que contaba después de comprar la mercancía; de modo que su capital llegó al doble del inicial. Determina cuál es el capital inicial de Don José.
Seleccione una:
O a. 4,000
O b. 10,000
O c. 6,000
Answers
Answer:
The Initial capital is 6000 pesos
Step by step explanation:
x: initial capital of Don José
Start of the week:
I buy merchandise in 2000 pesos
At the end of the week:
Sales income twice the capital you had after buying the merchandise: 2(x-2000)
Income - purchases = Profit
Capital + Profit = Final capital
Capital + Income - purchases = Final Capital
x+ 2(x-2000) - 2000 = 2x
x+2x-4000-2000 = 2x
3x-6000 = 2x
x = 6000
The Initial capital is 6000 pesos
See more in Brainly - brainly.lat/tarea/10835657
Step-by-step explanation:
which answer shows the correct ratios for the problem? in the forest, the ratio of elm trees to oak trees is 5/7. of the 120 trees, how many are elms? a. 40...b. 85....c..50...d...60
Answers
Answer:
The number of elms tree in the forest is;
[tex]50[/tex]Explanation:
Given that the ratio of elm trees to oak trees is 5:7.
And there are 120 trees in total in the forest.
For the ratio of the elms tree to the total number of trees is;
[tex]=\frac{5}{5+7}=\frac{5}{12}[/tex]Let's now calculate the number elms tree in the forest;
[tex]\begin{gathered} n=\frac{5}{12}\times120\text{ tr}ees \\ n=50\text{ tre}es \end{gathered}[/tex]Therefore, the number of elms tree in the forest is;
[tex]50[/tex]what is the rate of change of the cube’s surface area when its edges are 50 mm long?
Answers
The first thing we are going to do is identify the volume and surface of the cube and their respective derivatives or rate of change
[tex]\begin{gathered} V\to\text{volume} \\ S\to\text{surface} \\ l=\text{side of a square} \end{gathered}[/tex][tex]\begin{gathered} V=l^3\to(1) \\ \frac{dV}{dt}=3l^2\frac{dl}{dt}\to(2) \end{gathered}[/tex][tex]\begin{gathered} S=6l^2\to(3) \\ \frac{dS}{dt}=12\cdot l\cdot\frac{dl}{dt}\to(4) \end{gathered}[/tex]From the exercise we know that:
[tex]\begin{gathered} \frac{dV}{dt}=300\frac{\operatorname{mm}^3}{s}\to(5) \\ 3l^2\frac{dl}{dt}=300\frac{\operatorname{mm}^3}{s}\to(2)=(5) \\ \frac{dl}{dt}=\frac{300}{3l^2}\frac{\operatorname{mm}^3}{s}\to(6) \end{gathered}[/tex]The exercise asks us to calculate the rate of change of the surface (4) so we substitute the differential of length (6) in (4)
[tex]\begin{gathered} \frac{dS}{dt}=12\cdot l\cdot(\frac{300}{3l^2}\frac{\operatorname{mm}^3}{s}) \\ \frac{dS}{dt}=\frac{1200}{l}\frac{\operatorname{mm}}{s} \end{gathered}[/tex]what is the rate of change of the cube’s surface area when its edges are 50 mm long?
[tex]\begin{gathered} l=50\operatorname{mm} \\ \frac{dS}{dt}=\frac{1200}{50\operatorname{mm}}\frac{\operatorname{mm}^3}{s} \\ \frac{dS}{dt}=24\frac{\operatorname{mm}^2}{s} \end{gathered}[/tex]The answer is 44mm²/sFind the missing side or angle.Round to the nearest tenth.b=15a=30c=29A=[ ? 1°
Answers
STEP 1
The given parameters are a=30, b=15 and c=29
The corresponding cosine rule needed to find the angle A is denoted below
[tex]A=\cos ^{-1}\mleft[\frac{b^2+c^2-a^2}{2bc}\mright]^{}[/tex]STEP 2
Substitute the given parameters into the equation.
[tex]\begin{gathered} A=\cos ^{-1}\mleft\lbrace\frac{15^2+29^2-30^2}{2\times15\times29}\mright\rbrace \\ A=\cos ^{-1}\mleft\lbrace\frac{225+841-900}{870}\mright\rbrace \\ A=\cos ^{-1}\mleft\lbrace\frac{166}{870}\mright\rbrace \\ A=\cos ^{-1}0.1908 \\ A=79.0^0 \end{gathered}[/tex]HELP HELP HELP PLEASE!!!!!!!!!!
Answers
The slope of the given table is m = 5/4 or 1.25
The given table has various values of x and y
So given : y₂ = 30 and y₁ = 45
likewise x₂ = 8 and x₁ = 4
Thus the points are
P₁ = ( 4, 45 ) and P₂ = ( 8, 30 )
Since both points are positive thus these points lie in the first quadrant
Also to calculate the slope of a graph we use the formula
m or slope = y₂ - y₁ / x₂ - x₁
On substituting the above mentioned values
we will get
m or slope = 45 - 30/ 8 - 4
this further implies that
m or the slope = 5 /4 = 1.25
Thus the slope of the given values is 1.25
To know more about slope and coordinate geometry you may visit the link which is mentioned below:
https://brainly.com/question/16302642
#SPJ1
graph the slope connecting (2,3) and (4,0)
Answers
SOLUTION
STEP 1: Write the given points
[tex](2,3)\text{ }and\text{ }(4,0)[/tex]STEP 2: Find the slope
[tex]\begin{gathered} \mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1} \\ \left(x_1,\:y_1\right)=\left(2,\:3\right),\:\left(x_2,\:y_2\right)=\left(4,\:0\right) \\ m=\frac{0-3}{4-2} \\ m=-\frac{3}{2} \end{gathered}[/tex]The graph of the slope is seen below:
Question 25.Show if given 1-1 functions are inverse of each other. Graph both functions on the same set of axes and show the line Y=x as a dotted line on graph.
Answers
Given:
[tex]\begin{gathered} f(x)=3x+1_{} \\ g(x)=\frac{x-1}{3} \end{gathered}[/tex]To check the given functions are inverses of each other,
[tex]\begin{gathered} To\text{ prove: }f\mleft(g\mleft(x\mright)\mright)=x\text{ and g(f(x)=x} \\ f(g(x))=f(\frac{x-1}{3}) \\ =3(\frac{x-1}{3})+1 \\ =x-1+1 \\ =x \end{gathered}[/tex]And,
[tex]\begin{gathered} g(f(x))=g(3x+1) \\ =\frac{(3x+1)-1}{3} \\ =\frac{3x+1-1}{3} \\ =\frac{3x}{3} \\ =x \end{gathered}[/tex]It shows that, the given functions are inverses of each other.
The graph of the function is,
Blue line represents g(x)
Red line represents f(x)
green line represents y=x
Hello can you assist me please i need to solo e and Identity sine cosine or tangent and identify opposite hypnose or adjeact #12
Answers
Solution (12):
Given the triangle;
The opposite side is labelled as x and the adjacent side is 17.
Using the tangent trigonometry ratio, we have;
[tex]\tan\theta=\frac{opposite}{adjacent}[/tex]Thus;
[tex]\begin{gathered} \tan(51^o)=\frac{x}{17} \\ \\ x=17\tan(51^o) \\ \\ x=20.99 \\ \\ x\approx21 \end{gathered}[/tex]In a coordinate plane, the midpoint of AB is (2,5) and A is located at (-5,10). If (x,y) are the coordinates of B, find x and y.
Answers
In a coordinate plane, the midpoint of AB is (2,5) and A is located at (-5,10). If (x,y) are the coordinates of B, find x and y.
Remember that
the formula to calculate the midpoint between two points is equal to
[tex]M=(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]In this problem we have
M=(2,5)
(x1,y1)=A(-5,10)
(x2,y2)=B(x,y)
substitute the given values
[tex](2,5)=(\frac{-5+x}{2},\frac{10+y}{2})[/tex]step 1
Find the x-coordinate of B
equate the x-coordinates
so
2=(-5+x)/2
solve for x
4=-5+x
x=4+5=9
step 2
Find the y-coordinate of B
equate the y-coordinates
5=(10+y)/2
solve for y
10=y+10
y=0
therefore
the coordinates of B are (9,0)What integer value of b would make this not factorable
Answers
Answer:
Any integer other than -14 or 14.
[tex](x - 1)(x - 3) = {x}^{2} - 14x + 13[/tex]
[tex](x + 1)(x + 3) = {x}^{2} + 14x + 13[/tex]
Find an equation of variation in which y varies directly as x and y=28 when x=7. Then find the value of y when x=16.
Answers
I need help with homework I got the picture with the questions and will send it to you
Answers
3a.
DVA + AVB = 180 (straight line), so
75 + Angle AVB = 180
Angle AVB = 180 - 75
Angle AVB = 105 degrees
3b.
Angle DVC and Angle BVA are vertical angles.
Vertical angles form when we have a geometrical "X".
Vertical angles are equal so,
DVC = BVA
60 = 60
BVA = 60 degrees
3c.
BVC and CVD are in a straight line, so
BVC + CVD = 180
2x + 35 + 3x + 45 = 180
Let's solve for x:
5x + 80 = 180
5x = 100
x = 100/5
x = 20
Angle BVC = 2x + 35 = 2(20) + 35 = 40 + 35 = 75 degrees
Angle CVD = 3x + 45 = 3(20) + 45 = 60 + 45 = 105 degrees
got a square thats 23cm and 57cm .what is the perimeter
Answers
The perimeter of the shape is obtained by summing up all its 4 sides
=> 23 + 23 + 57 + 57
Perimeter = 46 + 114
perimeter = 160 cm
How would you describe the graphs of the sine and cosine functions? The sine and cosine functions are periodic functions. What does it mean to be a periodic function?
Answers
The sine and cosine functions are wave-like functions that repeat themselves on the plane an infinite number of times. The fundamental difference between the two functions is that the valley of the sine function is intersected by the y-axis. In contrast, the crest of the cosine function intersects the y-axis.
Given a function f(x)
[tex]f(x)=\sin (ax)[/tex]We can find its period using the formula below
[tex]\text{period}=\frac{2\pi}{a}[/tex]where the 2pi term is in radians.
The period of the function is the x-distance needed for the function to complete a cycle.
A periodic function is a function that repeats its values at regular intervals (2pi/a as we found above)
Two monomials are shown below.18x³y 30x22What is the greatest common factor (GCF) of thesemonomials?
Answers
The given monomials are:
[tex]\begin{gathered} 18x^3y \\ 30x^2y^2 \end{gathered}[/tex]Factorizing each term, we get,
[tex]\begin{gathered} 18x^3y=2\times3\times3\times x^2\times y \\ 30x^2y^2=3\times2\times5\times x^2\times y^2 \end{gathered}[/tex]Therefore, the GCF is,
[tex]\text{GCF}=6x^2y[/tex]Use a calculator to find an angle θ on the interval [0∘,90∘] that satisfies the following equation.tanθ=3.54
Answers
Answer:
θ = 74.23°
Explanation:
The inverse function of the tangent is arctangent and it can be written as:
[tex]\arctan (x)=\tan ^{-1}(x)[/tex]So, if tan θ = 3.54, then:
[tex]\theta=\tan ^{-1}(3.54)[/tex]Then, using the calculator, we get:
[tex]\theta=74.23\text{ degrees}[/tex]So, the answer is θ = 74.23°
Learn A STORY OF UNITS Lesson 4 Homework Helper 4.2 5. Mikal's backpack weighs 4,289 grams. Mikal weighs 17 kilograms 989 grams more than his backpack. How much do Mikal and his backpack weigh in all?
Answers
We have that the backpack weighs 4,289 grams = 4.289 kg.
Since Mikal weigh 17.989, we have that the total weight is:
[tex]17.989+4.289=22.278[/tex]therefore, Mikal and his backpack weigh 22.278 kg
find the value of x in the figure given then find the measure of angle y
Answers
Answer:
x = 33
Angle Y = 105°
Explanation:
The sum of the interior angles of a polygon with 5 sides is equal to 540°. So, we can write the following equation:
4x + 113 + (3x+8) + (2x + 9) + 113 = 540
So, solving for x, we get:
4x + 113 + 3x + 8 + 2x + 9 + 113 = 540
9x + 243 = 540
9x + 243 - 243 = 540 - 243
9x = 297
9x/9 = 297/9
x = 33
Then, using the value of x, we can calculate the value of the angle with measure (2x + 9) as:
(2x + 9) = 2(33) + 9
(2x + 9) = 75
Finally, this angle and the angle Y are supplementary, the sum of them is equal to 180°, so the measure of angle Y can be calculated as:
(2x + 9) + Y = 180°
75° + Y = 180°
Y = 180° - 75°
Y = 105°
So, x is equal to 33 and the measure of angle Y is 105°
Triangle 1 has a 50 degree angle, a 60 degree angle and one side that is 15 cmlong. Triangle 2 has a 50 degree angle, a 60 degree angle, and one side that is 15cm long. Are the triangles guaranteed to be congruent? No Yes
Answers
Congruent triangles have exactly the same three sides and three angles. The triangles may be rotated to see the congruency between them. In other words congruent triangles has corresponding sides equal and corresponding angles equal.
The 2 triangles have equal corresponding
juan is mailing a box like the one pictured below to his sister
Answers
Given:
Given a rectangle with
[tex]\begin{gathered} h=5cm \\ l=12cm \\ w=6cm \end{gathered}[/tex]Required:
To find the volume.
Explanation:
The formula for surface area is
[tex]SA=2lw+2lh+2wh[/tex]Here
[tex]\begin{gathered} =2(12)(6)+2(12)(5)+2(6)(5) \\ =144+120+60 \\ =324 \end{gathered}[/tex]Final Answer:
[tex]324cm^2[/tex]What is the Slope of HI ? Justify your answer .Please help
Answers
Solution:
Given:
A coordinate plane with two similar triangles.
To get the slope of HI, because the two triangles are similar, their hypotenuses will always have the same slope.
Hence, the slope of HI is also the slope of DE.
[tex]\begin{gathered} \text{Considering }\Delta DEF,\text{ using the points (8,32) and (12,24)} \\ \text{where;} \\ x_1=8 \\ y_1=32 \\ x_2=12 \\ y_2=24 \end{gathered}[/tex]
Using the formula for calculating slope (m),
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Substituting the values of the points gotten from triangle DEF,
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{24-32}{12-8} \\ m=\frac{-8}{4} \\ m=-2 \end{gathered}[/tex]Since the slope of triangle DEF is the hypotenuse of the right triangle DEF, then the slope HI is also the hypotenuse of triangle HIJ and both hypotenuses have the same slope since both triangles are similar.
Therefore, the slope of HI is -2.
There are gallon of orange juice and gallon of cranberry juice in the refrigerator. How many gallons of juice are there in all? A 8 10 B. 112/2 C 8 12 17/12
Answers
Answer:
2 gallons of juice
Step-by-step explanation:
your welcome
13. Graph the inequality. xs-3 X>8 10 9
Answers
You have teh following inequality:
x ≤ -3
consider that the previous inequality includes all number lower and equal to -3, that is, -3,-4,-5,.., until - infinity.
Then, the graph is:
For the following inequality:
x > 8
consider that the solutions are all numbers greater than 8 without including it.
Then, for the graph, you have:
5.) The elements of f(x) are (-7,3).(-1, 6) and (8,-3). What is the range of the function?
Answers
The range of a function is all values of y the function have.
So, looking at the elements (-7, 3), (-1, 6) and (8, -3), the y-coordinates of these points are 3, 6 and -3.
So the range of f(x) is:
[tex]\text{range}=\mleft\lbrace-3,3,6\mright\rbrace[/tex]Perform a web search for images for the term graph of sales trends. Choose an image where there are both increasing and decreasing trends. Upload the image you found and discuss the time period(s) when the sales trend is increasing, and when it is decreasing. Also indicate any periods where the trend stayed constant (that is, it did not change).
Answers
Imagine you have a newsstand and you start to pay attention to how many magazines you sell each month for one year to understand which months you sell more and which months you sell less. So what you want is to understand the trends of your business.
So, after a year, you are able to draw a graph that represents all sales for this year per month as follows:
So, as we can see above, We have the sales of your newsstand from January to August. The x-axis indicates the months of the year and the y-axis indicate the number of magazines sold. We can see for January you sold 15 magazines and the number increased for February and Mars. Between Mars, April and May, it stayed constant and from May to August it decreased. It is represented by the line in red, where we have first an increasing trend, after a constant trend and finally a decreasing trend. So that is how it works, and now you can understand and explain how a graph of sales trends works and which kind of images you have to look for.
8 А 400 11 1200 С Which triangle can be proven congruent to AABC shown above? (G.6)(1 point) O A. 11 200 400 O B. 22 11 28 C. 1200 200 40° O D. 11 400 28
Answers
Answer:
Triangle A.
Explanation:
We need to look for a triangle which has the same angle measures and same side measurement of corresponding side lengths.
Now in the original triangle we know two angles and one side length; therefore, by AAS another triangle which has two angles and one side length given and they are congruent to that of the corresponding measurements of the first triangle, then the two triangles are congruent.
Now for choice A the problem is that we are given angle measurements different from those given in the original triangle. However, we can use the fact that the angles must sum to 180 degrees to find the third angle and it turns out to be 120.
Hence, at this point triangle A has the same angle and side length measurements as the original triangle; therefore, by AAS the two triangles are congruent.
Graph x + 4y = 8The y-intercept is ___ (I got this already its 8)
Answers
Answer
The y-intercept = 2
Explanation
The slope and y-intercept form of the equation of a straight line is given as
y = mx + b
where
y = y-coordinate of a point on the line.
m = slope of the line.
x = x-coordinate of the point on the line whose y-coordinate is y.
b = y-intercept of the line.
So, we just have to write the given equation in this form and the y-intercept will become apparent.
x + 4y = 8
4y = -x + 8
Divide through by 4
(4y/4) = (-x/4) + (8/4)
y = -0.25x + 2
Comparing this with y = mx + b
We can see that
b = y-intercept = 2
Hope this Helps!!!
geometry special parallelogramsSide LK = Side KO =Side OL = Side KM = Side NL =
Answers
KLMN is a square
NM = 8
Side LK = 8
Side KO = 8 * sqrt(2)/2 = 4 * sqrt(2)
Side OL = 8 * sqrt(2)/2 = 4 * sqrt(2)
Side KM = sqrt(KN² + NM²) = sqrt(8² + 8²) = sqrt(64 + 64) = sqrt(128) = sqrt(64*2) = 8 * sqrt(2)
Side NL = 8 * sqrt(2)
45°
90°
45°
90°
Answers in BOLD
The area of a square backyard is 79 ft?. The owner is looking to get fencing to enclose the yard, so they need to find the approximate length of each side of the backyard AND what is the perimeter of the backyard?
Answers
According to the given question we have the following:
The area of a square backyard is 79 ft
Therefore if the area of a square backyard is 79 ft that means that length of each side would be the following:
length of each side=area of a square backyard/2
length of each side=79 ft/2
length of each side=39.5
Therefore if 39.5 is lenght of each side, the perimeter of the backyard would be calculated as follows:
perimeter of the backyard=l+l+l+l
perimeter of the backyard=39.5+39.5+39.5+39.5
perimeter of the backyard=158