Answer:
Rate of change = -3
Explanation:
Given the equation:
[tex]y=-3x+10[/tex]When x=1
[tex]\begin{gathered} y=-3(1)+10 \\ =-3+10 \\ =7 \end{gathered}[/tex]When x=2
[tex]\begin{gathered} y=-3(2)+10 \\ =-6+10 \\ =4 \end{gathered}[/tex]Observe that the value of y decreases by 3 as the x increases by 1.
Thus, the rate of change is -3.
Alternate Route
Another way is to express and compare the line with the slope-intercept form:
[tex]\begin{gathered} y=mx+b \\ y=-3x+10 \end{gathered}[/tex]The rate of change is the coefficient of x.
Coefficient of x = -3
Thus, the rate of change is -3.
A ball is thrown in the air. It's height, h (in meters).is given by h = -4.91 +306 + 6 where is thetime (in seconds). What is the height of the ballafter 3 seconds?
The given equation-
[tex]-4.9t^2+30t+6[/tex]After three seconds, we evaluate for t = 3.
[tex]-4.9(3)^2+30(3)+6=-4.9(9)+90+6=-44.1+96=51.9[/tex]Therefore, the height after 3 seconds is 51.9 meters.May I ask a question?if I have a 10 girls in a class and the total number of students in the class are 30, what's the percentage of the total amount of girls?
Given:
The number of girls =10 and the total number of students =30.
The percentage of the total amount of girls is
[tex]=\frac{The\text{ number of girls}}{\text{The total number of students}}\times100[/tex][tex]=\frac{10}{30}\times100[/tex][tex]=33.33[/tex]Hence the percentage of the total amount of girls is 33.33 %.
How many degrees was ABCDE rotated? (submit your answer as a number)
If a figure has a vertex, (x, y) and it is rotated 180 degrees counterclockwise, the corresponding vertex of the new image would have a coordinate of (- x, - y)
Looking at the given figure, we would compare the corresponding coordinates of a given vertex. Looking at vertex A,
For the original figure, the coordinate is (1, 3)
For the ratated figure, the coordinate of A' is (- 1, - 3)
This corresponds to what was we stated earlier
Thus, it was rotated 180 degrees in the counterclockwise direction
9. The exchange rate of a certain foreign currency with the Indian rupee is Rs 62.50.How much of the foreign currency can be had for Rs3125 ?
Answer
Rs. 3125 is equivalent to 50 units of the foreign currency.
Step-by-step Explanation
The exchange rate of the foreign currency in Indian Rupee is Rs. 62.50
This means that
1 unit of that foreign currency = Rs. 62.50
Or better written as
Rs. 62.50 = 1 unit of the foreign currency
So, we are then told to find how much Rs. 3125 is in the foreign currency
Let Rs. 3125 be equal to x units of the foreign currency
Rs. 62.50 = 1 unit of the foreign currency
Rs. 3125 = x units of the foreign currency
A simple mathematics relation obtained by cross multiplying will give us the value of x
After cross multiplying
62.50 × x = 3125 × 1
62.50x = 3125
Divide both sides by 62.50
(62.50x/62.50) = (3125/62.50)
x = 50
Therefore, Rs. 3125 is equivalent to 50 units of the foreign currency.
Hope this Helps!!!
Jason provided the following work when asked to convert 0.105 to its
simplest fraction form.
1. Why did Jason get the problem wrong?
2. Provide the work for properly writing the decimal in its simplest fraction
form.
Jason's Work:
0.105=
105/1000
21/200
Jason provided the work when asked to convert 0.105 to its simplest fraction form which is; 21/200
How to convert from decimal to fraction?For conversion from decimal to fraction, we write it in the form a/b such that the result of the fraction comes as the given decimal. To get the decimal of the form a.bcd, we will count the digits that are there after the decimal point; then we write 10 raised to that many power as the denominator and the considered number without any decimal point as the numerator.
Given that Jason's Work:
0.105
Jason provided the work when asked to convert 0.105 to its simplest fraction form which could be;
0.105 = 105/1000
= 21/200
Hence, Jason provided the work when asked to convert 0.105 to its simplest fraction form which is; 21/200
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I need help pls 1. Is this graph sine or cosine 2. What’s the amplitude of graph 3. What’s the equation of the midline 4. Whats the period of the function Whats the equation of the function Whats the domain and range?
As per given by the question,
There are given that a graph.
Now,
1. The given graph is cosine graph.
2. The aplitute of the given graph is,
From the graph, it is lie between -2 to 2.
So,
The amplitude of the given graph is 2.
Now,
3. The equation of the midline is,
[tex]y=-2[/tex]Now,
4.The period of the fumction is,
[tex]P=\frac{2\pi}{3}[/tex]Now,
The equation of the function.
First the general form of cosine graph function is,
[tex]y=A\cos (bx+c)+d[/tex]Then,
[tex]y=2\cos (3x+c)+d[/tex]Now,
[tex]y=2\cos (3x-1)+3[/tex]Where, D is vertical shift.
Hence, the equation of the function is,
[tex]y=2\cos (3x-1)+3[/tex]Two students are painting strips of wood to make scenery for the school play. Henry has painted 14 strips of wood. He can paint 3½ strips of wood per minute. Sandy has painted 10 strips of wood. She can paint 4 strips of wood per minute. After how many minutes will both students have painted the same number of strips of wood? Let m represent the number of minutes. Select the correct values to write an equation to represent the situation.
The number of minutes when they would both paint the same strip of wood is 8 minutes.
In how many minutes would they paint the same strip of wood?The linear equation that represents the total strip of wood that is painted by Henry is: amount of strips already painted + (strips painted per minute x minute)
14 + (3½x m)
14 + 3½m
The linear equation that represents the total strip of wood that is painted by Sandy is: amount of strips already painted + (strips painted per minute x minute)
10 + (4 x m)
10 + 4m
When both people paint the same strip of wood, the two above equations would be equal.
10 + 4m = 14 + 14 +3½m
4m - 3½m = 14 - 10
0.5m = 4
m = 4 / 0,5 = 8
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Please help and no I cannot show a picture of it. 5+5×0+5
Answer:
Solving the expression gives;
[tex]5+5\times0+5=10[/tex]Explanation:
Given the expression;
[tex]5+5\times0+5[/tex]Applying the rule of BODMAS or PEMDAS;
multiplication comes first;
[tex]\begin{gathered} 5+5\times0+5 \\ 5+0+5 \end{gathered}[/tex]Then we can do the addition;
[tex]\begin{gathered} 5+0+5 \\ =5+5 \\ =10 \end{gathered}[/tex]Therefore, solving the expression gives;
[tex]5+5\times0+5=10[/tex]Find the value of x assume the triangles are the same
1) In this problem, we need to find the constant of proportionality assuming these triangles are similar. So let's divide each corresponding leg:
[tex]\frac{22}{18}=\frac{33}{27}\Rightarrow\:k=\frac{11}{9}[/tex]2) So, based on that constant of proportionality (k) we can find the missing leg.
[tex]\begin{gathered} x\div\frac{11}{9}=36 \\ \\ x\cdot\frac{9}{11}=36 \\ \\ 11\times\frac{9}{11}x=36\times11 \\ \\ 9x=396 \\ \\ \frac{9x}{9}=\frac{396}{9} \\ \\ x=44 \end{gathered}[/tex]Note that since the triangle on the top is larger than the one on the bottom, we can tell that x must be larger than 36.
fine one value of x for which f(x) = 4 and find f(0)look at the graph below
To find the value of x for which f(x) = 4 we must find the point (x, 4), first, let's draw a horizontal line at y = 4:
As we can see the horizontal line touches the graph, then it touches the graph we draw a vertical line until we reach the x-axis, where we reach it, it's the value of x:
As we can see, the vertical line reaches x = -4, therefore, f(-4) = 4
[tex]f(-4)=4[/tex]Our final answer will be x = -4
b)
Now for f(0) = ?, we must do the same logic, but now we start with a vertical line at x = 0, and goes up until we reach the graph
As we can see it touches the graphic at y = 2, hence, f(0) = 2
[tex]f(0)=2[/tex]To find the value of x for which f(x) = 4 we must find the point (x, 4), first, let's draw a horizontal line at y = 4:
As we can see the horizontal line touches the graph, then it touches the graph we draw a vertical line until we reach the x-axis, where we reach it, it's the value of x:
As we can see, the vertical line reaches x = -4, therefore, f(-4) = 4
[tex]f(-4)=4[/tex]Our final answer will be x = -4
b)
Now for f(0) = ?, we must do the same logic, but now we start with a vertical line at x = 0, and goes up until we reach the graph
As we can see it touches the graphic at y = 2, hence, f(0) = 2
[tex]f(0)=2[/tex]The table gives a set of outcomes and their probabilities. Let A be the event "the outcome is less than 2". Let B be the event "the outcome is greater than 4". Find P(A or B). Outcome Probability 1 0.15 2 0.31 3 0.35 4 0.08 5 0.11
The general rule of P(A or B) is given by the formula
[tex]undefined[/tex]Mr. Baker wants to divide his class into smaller, equal-sized groups of students.
However, he finds that his class cannot be divided evenly into any size group except for individual groups of 1.
Complete the statements below about the number of students in Mr. Baker's class.
The completion of the statements about the number of students in Mr. Baker's class is as follows:
The number of students in his class must be a prime number.The quotient from the division of the students into equal-sized groups is not even because there must be a remainder.What is a prime number?A prime number is a number divisible by itself and 1 only.
When a prime number is divided by another number except by itself and 1, there is always a remainder in the quotient.
Some examples of the prime numbers in Mr. Baker's class include 19, 23, 29, 31, or 37 students.
Thus, these numbers of students cannot be divided by another number without a remainder because they are prime numbers.
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Question Completion:1. The number of students in his class must be a --- number.
2. The quotient from the division of the students into equal-sized groups is .... because there must be a .....
PLEASE HELP
A survey team is trying to estimate the height of a mountain above a level plain. From one point on the plain, the team observes that the angle of elevation to the top of the mountain is 25o. From a point 1,000 feet closer to the mountain along the plain, the team finds that the angle of elevation is 29o. How tall (in feet) is the mountain? Round to two decimal places.
The height of the mountain is 2936.39 feet.
Given,
In the question:
The angle of elevation to the top of the mountain is 25°.
To find the height of the mountain, we can draw triangles as in the image attached.
Now, According to the question:
Let's call the height of the mountain 'h', and the distance from the first point (25degrees) to the mountain 'x'.
Then, we can use the tangent relation of the angles:
tan(29) = h/x
tan(25) = h/(x+1000)
tan(25) is equal to 0.4663, and tan(29) is equal to 0.5543, so:
h/x = 0.5543 -> x = h/0.5543
using this value of x in the second equation:
h/(x+1000) = 0.6009
h/(h/0.5543 + 1000) = 0.4663
h = 0.4663 * (h/0.5543 + 1000)
h = 0.8412h + 466.3
0.1588h = 466.3
h = 466.3 / 0.1588 = 2936.39 feet
Hence, the height of the mountain is 2936.39 feet.
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Graph the functions on the same coordinate plane.f(x) = −5g(x) = x^2 + 2x − 8What are the solutions to the equation f(x) = g(x)? Select each correct answer.−5−3−113
ANSWER
[tex]\begin{equation*} -3,1 \end{equation*}[/tex]EXPLANATION
The graphical solution to the given equation is obtained at the points where the two graphs of the two functions intersect each other on the coordinate plane.
To graph f(x), we simply draw a straight horizontal line at the point y = -5.
To graph g(x), we have to find coordinate points by substituting values of x into the function and obtaining values for g(x).
Let us find the value of g(x) when x = -3, -1, 1:
[tex]\begin{gathered} x=-3: \\ g(-3)=(-3)^2+2(-3)-8=9-6-8 \\ g(-3)=-5 \\ x=-1: \\ g(-1)=(-1)^2+2(-1)-8=1-2-8 \\ g(-1)=-9 \\ x=1: \\ g(1)=(1)^2+2(1)-8=1+2-8 \\ g(1)=-5 \end{gathered}[/tex]Now, we have three points to plot the graph with: (-3, -5), (-1, -9), (1, -5)
Let us now plot the graphs of the functions:
Therefore, the solutions to the equation f(x) = g(x) are:
[tex]\begin{gathered} x=-3,x=1 \\ \Rightarrow-3,1 \end{gathered}[/tex]find the area of each. use your calculator's value of pi. round your answer to the nearest tenth.
We are asked to find the area of the given circle.
Recall that the area of a circle is given by
[tex]A=\pi r^2[/tex]Where π is a constant and r is the radius of the circle.
From the figure, we see that the diameter is 22 km
Recall that the radius is half of the diameter.
So, the radius of the circle is
[tex]r=\frac{D}{2}=\frac{22}{2}=11\: km[/tex]So, the area of the circle is
[tex]A=\pi r^2=\pi(11)^2=\pi\cdot121=380.1\: km^2[/tex]Therefore, the area of the circle is 380.1 square km (rounded to the nearest tenth)
Pls help! No ive asked 5 tutors and they cant do it!
The sampling distribution can be approximated to follow the normal distribution if the sample size is large, and the values of 'np' and 'n(1-p)' are much greater than 10.
Consider option A,
[tex]\begin{gathered} np=30\times0.3=9 \\ n(1-p)=30\times(1-0.3)=21 \end{gathered}[/tex]Consider option B,
[tex]\begin{gathered} np=22\times0.4=8.8 \\ n(1-p)=22\times(1-0.4)=13.2 \end{gathered}[/tex]Consider option C,
[tex]\begin{gathered} np=30\times0.8=24 \\ n(1-p)=30\times(1-0.8)=6 \end{gathered}[/tex]Consider option D,
[tex]\begin{gathered} np=22\times0.5=11 \\ n(1-p)=22\times(1-0.5)=11 \end{gathered}[/tex]It is observed that only the values in option D, give that 'np' and 'n(1-p)' are greater than 10. Therefore, option D will be the correct choice.
Give the equation of the line parallel to a line through (-3, 4) and (-5, -6) that passes through the origin. y = 5x y = 5x + 1 y=-1/5x + 1 y = -1/5x y
To solve for the equation of the line parallel :
[tex]\begin{gathered} (-3,4)\Longrightarrow(x_1,y_1) \\ (-5,-6)\Longrightarrow(x_2,\text{y}_2) \end{gathered}[/tex]For parallel line equation:
Slope-intercept form: y=mx+b, where m is the slope and b is the y-intercept
First let's find the slope of the line.
To find the slope using two points, divide the difference of the y-coordinates by the difference of the x-coordinates.
[tex]\begin{gathered} \text{slope =}\frac{y_2-y_1}{x_2-x_1} \\ \text{slope}=\frac{-6-4}{-5--3} \\ \text{slope=}\frac{-10}{-5+3}=\frac{-10}{-2} \\ \text{slope =5} \end{gathered}[/tex]Slope= 5
[tex]\begin{gathered} y=mx+c \\ y=5x+c \\ \text{where c = y-intercept} \end{gathered}[/tex]The y-intercept is (0, b). The equation passes through the origin, so the y-intercept is 0.
[tex]\begin{gathered} y=5x+0 \\ y=5x \end{gathered}[/tex]Hence the
Need to find the domain, range, x-intercept, y-intercept, and rate of change from the graph
Explanation
Step 1
Domain:The domain of a function is the complete set of possible values of the independent variable, by the graph is it a continuous line, so the domain is
[tex](-\infty,\infty),[/tex]Step 2
Range:The range is the set of all second elements of ordered pairs (y-coordinates), by the graph is it a continuous line, so the range is
[tex](-\infty,\infty),[/tex]Step 3
x-intercept
it is when y= 0 , by the graph :
[tex](-2,0)[/tex]Step 4
y-intercept
it is when x= 0 m by the graph:
[tex](0,4)[/tex]Step 5
rate of change
Let
P1(-2,0) P2(0,4)
[tex]\begin{gathered} rate\text{ of change=}\frac{y_2-y_1}{x_2-x_1}=\frac{4-0}{0-(-2)}=\frac{4}{2}=2 \\ \end{gathered}[/tex]rate of change:2
For the rotation 707°, find the coterminal angle from 0° ≤ 0 < 360°, thequadrant and the reference angle
Explanation
We are required to determine the coterminal, quadrant and reference angle of 707°.
This can be achieved as:
Therefore, the reference angle can be gotten as:
[tex]720\degree-707\degree=13\degree[/tex]Hence, the reference angle is 13°.
The angle lies in the fourth quadrant.
The cotermi
If the m< P is 65 degrees, then what is the measure of Arc XY
Answer:
[tex]\text{ArcXY}=115\text{ degrees}[/tex]Step by step explanation:
We can solve this situation by the theorem of the angle formed outside of a circle by intersection:
*For two tangents:
[tex]mThen, if m
[tex]\begin{gathered} 65=\frac{1}{2}((360-mXY)-mXY) \\ 65=\frac{1}{2}(360-\text{mXY-mXY)} \\ 65=\frac{1}{2}(360-2\text{mXY)} \\ 65=180-\text{mXY} \\ \text{mXY}=180-65 \\ \text{mXY}=115 \end{gathered}[/tex]
Mrs. Smith stores water in different size bottles. she has 4 containers that are 2 1/2 quarts each and 3 containers that are 425 cups each. how many fluid ounces of water does she have?
Answer:
The total volume of fluid ounces of water she have is;
[tex]422\text{ ounces}[/tex]Explanation:
Given that she has 4 containers that are 2 1/2 quarts each
[tex]\begin{gathered} V_1=4\times2\frac{1}{2}\text{ quarts} \\ V_1=10\text{ quarts} \end{gathered}[/tex]Recall that to convert quarts to ounce;
[tex]1\text{ quart }=32\text{ ounces}[/tex][tex]\begin{gathered} V_1=10\text{ quarts }=10\times32\text{ ounces} \\ V_1=320\text{ ounces} \end{gathered}[/tex]Also, she has 3 containers that are 4.25 cups each;
[tex]\begin{gathered} V_2=3\times4.25\text{ cups} \\ V_2=12.75\text{ cups} \end{gathered}[/tex]To convert cups to ounces;
[tex]1\text{ cup}=8\text{ ounces}[/tex]So;
[tex]\begin{gathered} V_2=12.75\text{ cups }=12.75\times8\text{ ounces} \\ V_2=102\text{ ounces} \end{gathered}[/tex]The total volume of fluid ounces of water she have is;
[tex]V=V_1+V_2[/tex]substituting the values;
[tex]\begin{gathered} V=320+102\text{ ounces} \\ V=422\text{ ounces} \end{gathered}[/tex]Therefore, the total volume of fluid ounces of water she have is;
[tex]422\text{ ounces}[/tex]Maria used a hundred chart to find a sum. She started at 57 then she moved down 3 rows and back 2 spaces which number did she land on
She landed on the number 25 on the hundred chart.
What is an 100 chart?
It consists of the numbers to 100 in sequential order, with ten numbers per row across ten rows.
We are given that she was on 57th number
Then she moved down 3 rows
Each row contains 10 elements Hence we subtract 30 for 3 rows
57-30=27
Then also she took 2 steps back
Hence we again subtract 2 from 27
We get 27-2=25
Hence she is at 25th number
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The graph of f (in blue) is translated a whole number of units horizontally and vertically to obtain the graph of k (in red).The function fis defined by f(x) = fx/.Write down the expression for k(x).
Solution
We have the original function defined as:
[tex]f(x)=-\sqrt[]{x}[/tex]And we want to obtain the new red line so then we need to check how many units down and right the function moves:
And we have 3 units to the right and 2 units down then the answer is:
[tex]h(x)=-\sqrt[]{x-3}-2[/tex]Then the final answer is:
h(x) = -sqrt(x-3) -2
Look at this graph: 100 90 80 60 50 20 10 10 20 30 50 60 70 80 90 100 What is the slope? Simplify your answer and write it as a proper fraction, improper fraction or integer. Submit Not feeling yet These con heo
To find the slope of the line we have to use this equation:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Now we have to replace two coordiantes in the line, so I was able to see the coordinates: (0,40) and (20,50), sothe equation become:
[tex]m=\frac{50-40}{20-0}[/tex]and we simplify so:
[tex]m=\frac{10}{20}=\frac{1}{2}[/tex]So the slope is 1/2
In Exercises 25–26, the domain of each piecewise function is (-⬁,⬁). a. Graph each function. b. Use the graph to determine the function’s range.
We have to graph this piecewise function.
It will be two horizontal lines that change when x = -1: to the left it will be y = 5, as x ≤ 1, and to the right, it will be y = -3.
We can see it graphed as:
b) The range is the set of values that f(x) takes for the domain for which it is defined.
We can see that f(x) only takes two values: y = -3 and y = 5, so the set {-3,5} is the range of f(x).
Answer:
a) Graph
b) Range = {-3, 5}
See attached for the problem
The areas and volumes are given as follows:
a) Area of the four sides to be painted: 2448 m².
b) Area to be covered with shingles: 1140 m².
c) Volume of concrete needed to pour a floor 16 cm deep: 174.72 m³.
d) Total surface area: 5878.4 m².
Area -> Four sides paintedThe sides painted are divided as follows:
Two rectangles of dimensions 26 m and 18 m.Two rectangles of dimensions 42 m and 18 m.Hence the total area to be painted is found as follows:
Total area = 2 x 26 x 18 + 2 x 42 x 18 = 2448 m².
(Area rectangle = base x height)
Area to be covered with shinglesThis part of the problem seems incomplete, however the answer is correct.
Volume of concreteThe volume is given by:
Volume = base area x height.
Hence:
The base area is a rectangle of dimensions 26 m and 42 m.The height is of 16 cm = 0.16 m.Hence the volume is given by:
V = 26 x 42 x 0.16 = 174.72 m³.
Surface areaThe base is a rectangular prism of dimensions 26 m, 42 m and 18m, hence:
Surface area base = 2 x (26 x 42 + 26 x 18 + 42 x 18) = 4632 m².
The top is composed by:
Two rectangles of dimensions 13.6 m and 42 m.Two triangles of base 26 m and height 4 m.Hence:
Surface area top = 2 x 13.6 x 42 + 2 x 0.5 x 26 x 4 = 1246.4 m².
Then the total surface area is:
Total surface area = 4632 + 1246.4 = 5878.4 m².
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Name a postulate or theorem that can be used with the given information to prove that the lines are parallel<3 ~ <7
Postulates and Theorems of Parallel Lines
First, we need to know what type of angles are <3 and <7. Following the definition:
If two lines are crossed by another line, the angles in matching corners are called Corresponding Angles.
Angles 3 and 7 are corresponding angles and they are told to be congruent.
Now we apply the postulate that reads:
The Converse of the Corresponding Angles Postulate. If two lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel.
The postulate that can be used to prove that the lines are parallel is The Converse of the Corresponding Angles Postulate
A triangle has two sides of length 13 and 17. What is the largest possible whole numberlength for the third side?
Given two sides of a triangle, x, and z, such that
[tex]x\le z[/tex]then the third side y must satisfy the following condition
[tex]z-xIn our case,x =13, and z = 17
Then, the third side y
lies in
17-13 < x < 17 +13
4 < x < 30
Hence the largest possible whole number of the third side is 29
b. Solve the system of linear equations y = x + 2 and y = 3x – 4 by graphing.
To find the solution we need to graph both lines on the plane. To do this we need to find two points for each line.
First we graph the line y=x+2. To find a point we give x a value, whichever value we like, and then find y.
Let x=0, then:
[tex]\begin{gathered} y=0+2 \\ y=2 \end{gathered}[/tex]Then we have the point (0,2).
Let x=1, then:
[tex]\begin{gathered} y=1+2 \\ y=3 \end{gathered}[/tex]Then we have the point (1,3).
Then we plot this points in the plane and join them with a line:
Now let's plot eh second line, y=3x-4.
Let x=0, then:
[tex]\begin{gathered} y=3(0)-4 \\ y=-4 \end{gathered}[/tex]So we have the points (0,-4).
Let x=1, then:
[tex]\begin{gathered} y=3(1)-4 \\ y=3-4 \\ y=-1 \end{gathered}[/tex]so we have the point (1,-1).
Now we plot this points and join them with a line:
Once we have both lines graph in the plane the solution is the intersection of the lines. Looking at the graph we conclude that the solution of the system is x=3 and y=5.
what is 2x2 and 3x0 and 3x3 and 4x4