Solution:
The slope-intercept form of a line with slope m and y-intercept b is given by the following formula:
[tex]y\text{ = mx+b}[/tex]On the other hand, the slope m is given by the following equation:
[tex]m\text{ = }\frac{Y2-Y1}{X2-X1}[/tex]where (X1,Y1) and (X2,Y2) are points on the line. In this case, we can take the points:
(X1,Y1) = (1,2)
(X2,Y2) = (-1,-1)
replacing this data into the slope equation, we get:
[tex]m\text{ = }\frac{-1-2}{-1-1}\text{ = }\frac{-3}{-2}\text{ = }\frac{3}{2}[/tex]thus, the slope of the line would be:
[tex]m\text{ = }\frac{3}{2}[/tex]now, replacing this into the slope-intercept form of the line we get:
EQUATION 1
[tex]y\text{ = }\frac{3}{2}x\text{ + b}[/tex]We only need to find the y-intercept b. For that, take any point on the line, for example (x,y) = (1,2), and replace it into the previous equation:
[tex]2\text{ = }\frac{3}{2}(1)\text{ + b}[/tex]this is equivalent to:
[tex]2\text{ = }\frac{3}{2}+\text{ b}[/tex]solving for b, we get:
[tex]b\text{ = 2- }\frac{3}{2}\text{ = }\frac{1}{2}[/tex]that is:
[tex]b\text{ = }\frac{1}{2}[/tex]finally, replacing this into the EQUATION 1, we get:
[tex]y\text{ = }\frac{3}{2}x\text{ + }\frac{1}{2}[/tex]then, the slope-intercept form of a line with the points (1,2) and (-1,-1) would be:
[tex]y\text{ = }\frac{3}{2}x\text{ + }\frac{1}{2}[/tex]
please i need help
Answer:
they both go up by 2
Complete the mapping of the vertices of ADEF. D(2,-4) - D E(1,-1) - E F(5, 1) - F >
The vertices of the ΔDEF are given by (-4, 2)D', (-1, 1)E' , (1, 5)F' through mapping.
what is mapping?
Any set, including all whole integers, all the points on a line, or all the objects inside a circle, can be mapped. A mapping of the set of all whole numbers onto the set of even numbers is defined by the expression "multiply by two," for instance. A rotation is an internal map of a plane or of all of space.
The vertices of ΔDEF are given by D(2,-4) - D E(1,-1) - E F(5, 1).
According to the rule defining a reflection across the line, y=x should be stated when reflecting a point across the line. Then, the x and y coordinates are switched as follows:
y(x, y) → (y, x)
Let's now use the aforementioned rule to finish mapping the vertices of DEF. Change the x and y coordinate locations as follows:
D(2, –4) gives (-4, 2)D'E(1, –1) gives (-1, 1)E'F(5, 1) gives (1, 5)F'The vertices of the ΔDEF are given by (-4, 2)D', (-1, 1)E' , (1, 5)F' through mapping.
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the recommended amount of meat to serve 1 and 1/2 dozzen people is 4 and 1/2 pounds. how many pounds of meat are recommended to feed 1 dozzen people? how many pounds are recommended to feed 4 people? and how many pounds are recommended to feed 1 person
First, 1 dozen is 12 units, so
[tex]1\frac{1}{2}\text{ dozen people }=\text{ 12 people + 6 people = 18 people}[/tex]Now, to solve the exercise you can use the rule of three. So, you have
*How many pounds of meat are recommended to feed 1 dozen people?
[tex]\begin{gathered} 18\text{ people}\rightarrow4.5\text{ pounds} \\ 12\text{ people}\rightarrow x\text{ pounds} \\ x=\frac{12\text{ people }\ast\text{ 4.5 pounds}}{18\text{ people}} \\ x=\frac{54}{18}\text{ pounds} \\ x=3\text{ pounds} \end{gathered}[/tex]Therefore, 3 pounds of meat is recommended to feed a dozen people.
*How many pounds are recommended to feed 4 people?
[tex]\begin{gathered} 18\text{ people}\rightarrow4.5\text{ pounds} \\ 4\text{ people}\rightarrow x\text{ pounds} \\ x=\frac{4\text{ people }\ast\text{ 4.5 pounds}}{18\text{ people}} \\ x=\frac{18}{18}\text{ pounds} \\ x=1\text{ pound} \end{gathered}[/tex]Therefore, 1 pound of meat is recommended to feed 4 people.
*How many pounds are recommended to feed 1 person
[tex]\begin{gathered} 18\text{ people}\rightarrow4.5\text{ pounds} \\ 1\text{ person}\rightarrow x\text{ pounds} \\ x=\frac{1\text{ person}\ast4.5\text{ pounds}}{18\text{ people}} \\ x=\frac{1}{4}\text{ pounds} \end{gathered}[/tex]Therefore, 1/4 pound of meat is recommended to feed 1 person.
a table shows the cost (in cents) of producing and distributing each coin for the years 2007 and 2014
which coin has a cost in 2014 that is less than 0.95 times the cost in 2007
2007. 2014
quarter. 9.78. 8.95
dime. 4.09. 3.91
nickel. 9.53. 8.09
penny. 1.67. 1.66
The dime has a cost in 2014 that is less than 0.95 times the cost in 2007.
To solve this problem by finding out the ratio. We can solve this problem by following a few steps.
According to the question, the cost in 2014 is less than 0.95 times the cost in 2007.
So the ratio is 1: 0.95. Which can be written as, 1/ 0.95 = 100/95 = 20/19 = 20: 19.
Now, we have to find among all those coins which follow the trend of 20: 19.
For the quarter, the ratio is 9.78: 8.95 = 9.78 / 8.95 ≠ 20 : 19For the dime, the ratio is 4.09: 3.91 = 4.09/3.91 ≈20: 19For the nickel, the ratio is = 9.53: 8.09= 9.53. 8.09 ≠ 20: 19For the penny, the ratio is = 1.67: 1.66 = 1.67/1.66 ≠ 20: 19Here only the price of a dime has declined 0.95 times.
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Write a quadratic equation in standard form with the given root(s) -7,3/4 and can you explain how you did it? i need it ASAP please and thank you
The equation of the quadratic equation is P(x) = x² + 23/4x - 21/4
What are quadratic equations?Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k
How to determine the quadratic equation?The given parameters are
Zeros = -7 and 3/4
The sum of multiplicities of the quadratic equation must be equal to the degree.
This means that the multiplicity of the zeros -7 and 3/4 is 1
The equation of the quadratic equation is then calculated as
P(x) = (x - zero)^ multiplicity
So, we have
P(x) = (x + 7)(x -3/4)
Expand
P(x) = x² + 7x - 3/4x - 21/4
This gives
P(x) = x² + 23/4x - 21/4
Hence, the equation is P(x) = x² + 23/4x - 21/4
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Describe the transformation of f(x)= x2 represented by g. then graph.
What would the simplified form be to-√12+3√3
Hello, I need some assistance with this precalculus homework question, please?HW Q2
Answer:
A. The solution set is {4096}.
Explanation:
Given the logarithmic equation:
[tex]\frac{1}{2} \log _{6} x=3 \log _{6} 4[/tex]Multiply both sides of the equation by 2:
[tex]\begin{gathered} \frac{1}{2}\times2\log_6x=3\times2\log_64 \\ \log_6x=6\log_64 \end{gathered}[/tex]Next, apply the power law of logarithms to the right side of the equation.
[tex]\begin{gathered} \log_6x=\log_64^6 \\ \implies\operatorname{\log}_6x=\operatorname{\log}_64096 \end{gathered}[/tex]Since the bases are the same, equate the numbers:
[tex]x=4096[/tex]The solution set is {4096}.
Find the greatest common factor (GCF) of 64 and 72.A. 8B. 9C. 4D. 12
Okay, here we have this:
Let's decompose each number and then we see their common factors:
64=2*2*2*2*2*2
72=2*2*2*3*3
The factors common to both are: 2*2*2, and by multiplying we obtain that the greatest common divisor is 8. The correct answer is option A.
In the figure, ABCD and DEFG are squares.AC:FD=7:5, find CE
Given:
The ratio of the diagonals of the squares ABCD and DEFG is:
[tex]AC:FD=7:5[/tex]Required-the value of CE.
Explanation:
Given that the ratio of the diagonals of the squares ABCD and DEFG is:
[tex]AC:FD=7:5[/tex]So, the sides will be in the same ratio.
[tex]AD:GD=7:5[/tex]Let the sides of the two triangles ABCD and DEFG be 7x and 5x.
Given that
[tex]AG=3cm[/tex]So, we can write AG as:
[tex]\begin{gathered} AG=AD-GD \\ 3=7x-5x \\ \\ 2x=3....(1) \end{gathered}[/tex]Now, we have to find CE, so we can write CE as:
[tex]\begin{gathered} CE=CD+DE \\ \\ CE=7x+5x \\ \\ CE=12x \\ \\ CE=6(2x) \\ \\ CE=6\times3 \\ \\ CE=18cm \end{gathered}[/tex]Final answer: The value of CE is 18 cm.
Write the following comparison as a ratio reduced to lowest terms 2 nickels to 27 dimes
The ratio of 2 nickels to 27 dimes is 27.
What is ratio?A ratio in mathematics demonstrates how many times one number is contained in another. For instance, the ratio of oranges to lemons in a dish of fruit is eight to six if there are eight oranges and six lemons present. Similarly, the ratio of oranges to the total amount of fruit is 8:14 while that of lemons to oranges is 6:8. A ratio is an ordered pair of numbers a and b, expressed as a / b, where b is not equal to 0. A percentage is an equation in which two ratios are made equal to one another. For instance, you could express the ratio as 1: 3 (one boy to three females), meaning that one in four of the population is male.
Nickel is equivalent to 0.05 dollars.
2 nickels are equivalent to (0.05 × 2) = 0.01 dollars.
1 dime is equal to 0.1 dollars.
27 dimes are equivalent to (27 × 0.01) = 0.27dollars.
Therefore, to compare 27 nickels to 2 dimes as a ratio reduced to lowest term will be 0.27 : 0.01
= 27
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A teacher was helping me but I got force quite the app due to lag can you help me with question C, D, and E !!!
Parts C, D and E
Answer:
Explanation:
C) The maximum height is the highest point on the graph. On the x axis of the graph, each small square is 0.25 units. Thus, the x coordinate of the maximum height is is 1.25. The ball reached maximum height after 1.25 seconds
D) There were two different times when the ball was at 10m.
When y = 10 m, x = 0.5
when y = 10, x = 2
At 0.5 and 2 seconds, the ball was at 10m
E) A the time the when the ball hit the ground, the height is 0. Thus, the time when the ball hits the ground is 3 seconds
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
d
Step-by-step explanation:
The number of years must be non-negative.
This eliminates all of the options except for d.
In a single throw of a fair die, what is the probability that an odd number or a perfect square greater than one shows up?
The probability that an odd number or a perfect square greater than one shows is 2/3.
Probability - The area of mathematics known as probability deals with numerical representations of the like that an event will occur or that a statement is true.
The probability of an event is a value between 0 and 1.total no. of outcomes - 1,2,3,4,5,6
odd number = 1,3,5
or a perfect square = 4
probability - dividing the favorable number of outcomes by the total number of possible outcomes.
probability = favorable outcomes / total no. of outcomes
= 4/6
= 2/3
The probability that an odd number or a perfect square greater than one shows is 2/3.
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5. Which equation is solved for the height of the cone based on theinformation given below ?
The equation for the Volume (V) of the cone given is,
[tex]V=\frac{1}{3}\pi r^2h[/tex]We are to isolate 'h' in the equation above
SOLUTION
Multiply both sides by 3
[tex]3V=3\times\frac{\pi}{3}r^2h[/tex]Simplify
[tex]3V=\pi r^2h[/tex]Divide both sides by πr²
[tex]\frac{3V}{\pi r^2}=\frac{\pi r^2h}{\pi r^2}[/tex]Simplify
[tex]h=\frac{3V}{\pi r^2}[/tex]Hence, the answer is
[tex]h=\frac{3V}{\pi r^2}\text{ (OPTION D)}[/tex]Write the equation of the line with the given information. Through (-1, -1) parallel to h(x)=-1+10
The equation of a line that passes through (-1, -1) and parallel to h(x) = -1x + 10 is y = -x -2
How to find equation of a line?The line passes through (-1, -1) and it is parallel to h(x) = -1x + 10
When lines are parallel, the slopes are the same.
Therefore, the equation of a line that passes through (-1, -1) and parallel to h(x) = -1x + 10 can be calculated as follows:
Hence,
y = mx + b
where
m = slopeb = y-interceptTherefore, let's find the y-intercept using (-1, -1)
y = -x + b
-1 = -(-1) + b
b = -1 - 1
b = -2
Therefore, the equation of the lines is y = -x -2
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Which inequality correctly compares 118%, 0.34, and two and one fifth?
0.34 < 118% < two and one fifth
118% < 0.34 < two and one fifth
0.34 < two and one fifth < 118%
two and one fifth < 0.34 < 118%
Which inequality correctly compares 118%, 0.34, and two and one fifth?
0.34 < 118% < two and one fifth
118% < 0.34 < two and one fifth
0.34 < two and one fifth < 118%
two and one fifth < 0.34 < 118%
118% = 118%
0.34 = 34%
2 and 1/5 = 200.2%
34% < 118% < 200.2%
A large pizza pie with 15 slices is shared among x students such that each student's share is 3 slices. Write it as a mathematical statement.
15/x = 3
Explanation:Total number of slices = 15
Number of students = x
Each student's share = 3
(Total number of slices)/(Number of students) = Each student's share
Therefore, the mathematical statement representing the illustration is:
15/x = 3
A ticket to see your favorite baseball team costs $30.86. That price decreases by $0.35 for every game lost during the regular season. What equation could you use to find the cost C of a ticket after L losses? Represent the total change in the cost of a ticket after the team loses 31 games. What is the price of a ticket after the team loses 31 games?
Answer:20.01
Step-by-step explanation:
0.35x31=10.85
30.86-10.85=20.01
Solve the following quadratic equation by the square root method. If needed, write your answer as a fraction reduced to lowest term
Solution
Solve the following quadratic equation by the square root method.
[tex]\begin{gathered} y^2-10y+25=-49 \\ y^2-10y+25+49=0 \\ y^2-10y+74=0 \end{gathered}[/tex]Therefore the correct answer for y are
[tex]y=5+7i,\text{ 5-7i}[/tex]A student is initially outside. He is given the choice with a probability of 0.4 of going to the playground, 0.3 of shopping in the mall and 0.3 of returning home. If he is in the playground, he takes 2 hrs of time and then decides to stay in the playground again or return back home. (he can continue to decide to stay in playground like a recursive process) Similarly, If he is in the mall, he takes 3 hrs of time and then decides to stay in the mall again or return back home. (he can continue to decide to stay in mall like a recursive process) For all cases, it takes 1 hr to return home. what is the expected hours the student was outside home?
Based on the probability values, it will take the student 2 hours to stay outside the home
How to determine the expected value of the student?The given parameters are:
Probabilities
P(1) = 0.4
P(2) = 0.3
P(3) = 0.3
Time
Time 1 = 2 hours
Time 2 = 3 hours
Time 3 = 1 hour
When the above are represented on a table, we have the following table of values
Time (x) | 2 3 1
Probability (P(x)) | 0.4 0.3 0.3
The expected value of the student is then calculated as
E(x) = ∑ x * P(x)
Substitute the known values in the above equation
E(x) = 2 * 0.4 + 3 * 0.3 + 1 * 0.3
Evaluate the products
E(x) = 0.8 + 0.9 + 0.3
Evaluate the sum
E(x) = 2
Hence, the expected value is 2
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Write an equation that represents the line.
Use exact numbers.
Answer:
y = 0.75x + 2
Step-by-step explanation:
Take two distinct points on the graph
Compute the slope m and y-intercept b
Equation of line in slope-intercept form is
y = mx + b
Take points (0, 2) and (4, 5)
Slope m = (5 - 2) /(4-0) = 3/4
y-intercept from the graph is 2
So y = 3/4 x + 2 =0.75x + 2
Which expression is equivalent to -4(2 - 6x) - 2.5x ?
Rewriting the expression, we have:
[tex]\begin{gathered} -4\mleft(2-6x\mright)-2.5x \\ =-8+24x-2.5x \\ =21.5x-8 \end{gathered}[/tex]So an equivalent expression is 21.5x - 8.
Find the tangent of
To find tan S, we will use the trigonometric ratio:
[tex]\text{tan}\theta=\frac{opposite}{adjacent}[/tex]From the question,
θ=S opposite=55 adjacent = 48
substitute the values into the formula
[tex]\tan S=\frac{55}{48}[/tex]Seven less than n is 11
MATHEMATICALLY THIS CAN BE WRITTEN AS:
[tex]n - 7 = 11 \\ n = 11 + 7 \\ n = 18[/tex]
THAT NUMBER n IS 18
HOPE THIS HELPS
If A={h,y,d,r,o,p,l,a,n,e,s} and U={a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z}, find A′
Answer:
A' = { b,c,f,g,i,j,k,m,q,t,u,v,w,x,z }
Step-by-step explanation:
11. Find the length of the missing side. 16 25 19
Answer:
x = 14.12
Explanation:
To find the missing side, we will use the cosine law:
[tex]c^2=a^2+b^2-2ab\cos (C)[/tex]Where a, b, and c are the length of the sides of the triangle and C is the measure of the angle formed by the sides a and b.
So, we can use the equation to find the angle formed by the side of length 35 and the side of length 44 (25 + 19 = 44). So, replacing a by 35, b by 44, and c by 16, we get:
[tex]16^2=35^2+44^2-2(35)(44)\cos (\theta)[/tex]Then, solving for θ, we get:
[tex]\begin{gathered} 256=1225+1936-3080\text{cos(}\theta) \\ 256=3161-3080\cos (\theta) \\ 256-3161=-3080\cos (\theta) \\ -2905=-3080\cos (\theta) \\ \frac{-2905}{-3080}=\cos (\theta) \\ 0.9432=\cos (\theta) \\ \cos ^{-1}(0.9432)=\theta \\ 19.41=\theta \end{gathered}[/tex]Now, we can calculate the length of the missing side, using the angle θ = 19.41°, the side with length 35 and the side with length 25 as:
[tex]x^2=35^2+25^2-2(35)(25)\cos (19.41)[/tex]Therefore, the value of x is:
[tex]\begin{gathered} x^2=1225+625-1650.56 \\ x^2=199.44 \\ x=\sqrt[]{199.44} \\ x=14.12 \end{gathered}[/tex]So, the length of the missing side is 14.12
Choose the equation of a circle with radius 9 and center (3,-4).
Choose the correct answer below.
○ A. (x+3)² + (y− 4)² = 81
○ B. (x − 3)² + (y+4)² = 81
○ C. (x+3)² + (y−4)² = 9
OD. (x-3)²+(y+4)² =
Answer:
B. (x − 3)² + (y+4)² = 81
Step-by-step explanation:
If a circle has center located at (a, b) and radius of r, the equation of this circle is
(x - a)² + (y-b)² = r²
We have a = 3, b = -4 and r = 9
So equation is
(x - 3)² + y - (-4))² = 9²
==> (x − 3)² + (y+4)² = 81
a survey survey asked 200 students to name their favorite fruit the table shows the results of a survey
Part A
Fraction of peach 2/5
Total = 200
number of students that pick peach as their favorite fruits
[tex]\begin{gathered} =\text{ }\frac{2}{5}\text{ x 200} \\ =\text{ }\frac{2\text{ x 200}}{5} \\ =\text{ }\frac{400}{5} \\ =\text{ 80 students} \end{gathered}[/tex]Part B
number of students that pick orange as their favorite fruits
[tex]\begin{gathered} =\frac{3}{8}\times200^{} \\ =\text{ }\frac{3\text{ x 200}}{8} \\ =\text{ }\frac{600}{8} \\ =\text{ 75} \end{gathered}[/tex]number of students that pick plum as their favorite fruits
[tex]\begin{gathered} =\text{ }\frac{1}{10}\text{ x 200} \\ =\text{ }\frac{200}{10} \\ =\text{ 20} \end{gathered}[/tex]There are 55 more students that chose orange rather than plum.
Line k is shown below.Vai4 321 (2, 1)x-5 -4 -3 -2I NON0 1 2 3 4 5k(-4,-2) 3-5Which ratio represents the slope of a line parallelto line k??221O-221
hello
to solve this problem, we have to use the formula of slope of a line
[tex]\begin{gathered} \text{slope(m)}=\frac{y_2-y_1}{x_2-x_1} \\ y_2=1 \\ x_2=2 \\ y_1=-2 \\ x_1=-4 \end{gathered}[/tex]substitute the values into the equation (formula)
[tex]m=\frac{1-(-2)}{2-(-4)}=\frac{1+3}{2+4}=\frac{4}{6}=\frac{2}{3}[/tex]from the calculations above, the slope of the line is equal to 2/3