[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{-1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-1}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{7}-\underset{x_1}{2}}} \implies \cfrac{ -5 }{ 5 } \implies - 1[/tex]
[tex]\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}{4}=\stackrel{m}{- 1}(x-\stackrel{x_1}{2}) \\\\\\ y-4=-x+2\implies {\Large \begin{array}{llll} y=-x+6 \end{array}}[/tex]
Solve the problem involving probabillities withindependent events.A single die is rolled twice. Find theProbability of getting a 6 the first time anda 3 the second time.
Solution
If a single die is rolled twice, we would have
[tex]P((6,3))=\frac{1}{36}[/tex]Contestants in a dance-a-thon rest for the same amount of time every hour. A couple rests for 8 minutes in 2 hours. How long did they rest in 3 hours?
The couple rests for 12 minutes in 3 hours in the dance-a-thon.
Given that the couple rests for 8 minutes in 2 hours and also it is given that the contestants rests for the same amount of time every hour.
We will divide the 8 minutes by 2 to get the hourly rest time.
=8/2
=4 minutes per hour.
The couple rests for 4 minutes every hour. For 3 hours they will rest for 3x4 minutes. As they rest for same amount of time every hour.
= 12 minutes for 3 hours.
Therefore, the contestants in a dance-a-thon rests for 12 minutes in 3 hours.
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A vendor sells h hotdogs and s sodas. If a hotdog costs twice as much as a soda, and if the vendor takes in a total of d dollars, how many cents does a soda cost?.
Given, there are hotdogs and sodas as items. Each hotdog costs twice the cost of soda.
Let's assume the cost of soda is x dollars. Then, the cost of a hotdog would be 2x dollars. Then, h hotdogs cost 2xh dollars, and simultaneously, s sodas cost xs dollars.
Given, the vendor takes a total of d dollars, then
d = 2xh + xs
Therefore, if the price of a soda is x dollars, then
x = [tex]\frac{d}{2h + s}[/tex] dollars
And also, since 1 dollar is 100 cents, therefore, 1 cent would be 0.01 dollars.
So finally, x, the price of a soda in cents would be
x = [tex]100(\frac{d}{2h+s})[/tex] cents
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Adrianna’s football team ran some warm up laps with a total distance of 6125 centimeters. There are 7 players on her football team. If they all ran the same number of laps, what is the distance each player ran? At the end of practice, each player ran to the store, which was 10.31 meters from the field. What is the total distance each of them ran?
The distance each player ran for warm up laps is 875 cm and the distance each player ran for the store is 1.47 meters.
According to the question,
We have the following information:
Adrianna’s football team ran some warm up laps with a total distance of 6125 centimeters. There are 7 players on her football team.
The distance to the store = 10.31 meters
Now, we can find the distance ran by each player by dividing the total distance by number of players.
Distance for warm up laps = 6125/7
Distance ran by each player = 875 cm
Distance for the store = 10.31/7
Distance for the store = 1.47 m
Hence, the distance each player ran for warm up laps is 875 cm and the distance each player ran for the store is 1.47 meters.
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Which line matches the equation belowF(x)=-3^xA RedB blueC greenD purple
The function is given as,
[tex]F(x)=-3^x[/tex]The graph representing the above equation is green colour.
Find the distance d between 21 and 22.Express your answer in exact terms and simplify, if needed.d=ImCO876-543+2+1+orA++ ++-9 -8 -7 -6 -5 -4 -3 -2+ Re1 2 3 4 5 6 7 8 9Cnu-2 +-3+-4-5+-6+
From the graph provided, the coordinates of the two points are;
[tex]\begin{gathered} z_1=(7,1) \\ z_2=(2,-7) \end{gathered}[/tex]The distance between two points is;
[tex]\begin{gathered} d=\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2} \\ \text{Where;} \\ x_1=7,y_1=1,x_2=2,y_2=-7 \end{gathered}[/tex]Then, we substitute the values into the formula, we have;
[tex]\begin{gathered} d=\sqrt[]{(-7-1)^2+(2-7)^2} \\ d=\sqrt[]{(-8)^2+(-5)^2} \\ d=\sqrt[]{64+25} \\ d=\sqrt[]{89} \end{gathered}[/tex]The distance d, between the points is;
[tex]d=\sqrt[]{89}=9.4340[/tex]natalie is organizing textbooks on her bookshelf. she has a spanish textbook, a biology textbook, a physics textbook, and a health textbook. how many different ways can she line the textbooks up on her bookshelf?
Natalie can line up her textbooks in 24 different ways on her bookshelf.
Natalie has a Spanish book, a biology book, physics book, and a health text book.
So, she has a total of 4 books in her book shelf.
So, the number of positions in which the books have to be put are four.
As we can see,
The books are only one in number each. So, the choices are not repeatable.
So,
In first position we have four choices, in third we will be left with three choices, in the seconds position we will have a total of two books as choice and in the last positive we have to put the book that is left.
So, the total different ways in which she can line up her books in the bookshelf are,
= 4×3×2×1
= 24
So, there are 24 different ways possible.
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Factorise the following x^2-8x-9
answer:
(x-9)(x+1)
step-by-step explanation:
this expression can be solved by grouping. hope that helps!
Han finds an expression for S(r) that gives the surface area in square inches of any cylindrical can with a specific fixed volume, in terms of its radius r in inches. This is the graph Han gets if he allows r to take on any value between -1 and 5.
What would be a more appropriate domain for Han to use instead?
What is this asking I don't understand
The more appropriate domain for Han is values between 0 and 4, while the minimum surface area is 20.
Given that,
Han discovers an equation for S(r) that, in terms of the radius r in inches, yields the surface area in square inches of any cylindrical container with a particular fixed volume. If Han lets r to take on any value between -1 and 5, he will obtain the graph shown above.
The more appropriate domain to use
The function's finishing graph is added as an attachment.
We can make the following observations based on the graph.
Minimum x value = 0
Maximum x value = 4
The following is a representation of the domain of the function's graph:
Minimum x value <= x <= Maximum x value
Substitute the known values in the above equation
So, we have
0 <= x <= 4
0 and 4 are represents a more appropriate domain.
The minimum surface area
The graph that completes the function is added as an attachment
From the graph, we have the following observation
Minimum y value = 20
20 is the minimum surface area of the cylindrical can.
Therefore, The more appropriate domain for Han is values between 0 and 4, while the minimum surface area is 20.
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carlos swam to the bottom of a pool that is 12 feet deep. what is the opposite of carlos's elevation relative to the surface ?
A -12 C 12 feet
B 0 feet D 1/12 foot
The opposite of Carlo's elevation is 12 feet
Carlos is said to have submerged himself in a 12-foot-deep swimming pool.
Carlos' elevation will be -12 feet with regard to the surface because he submerged himself to the pool's bottom.
The elevation of Carlos as it relates to the ground would be opposite of -12 feet, or -(- 12) feet.
12 feet
Carlos' elevation in relation to the ground is therefore 12 feet higher than it should be.
Thus the opposite of Carlo's elevation is 12 feet .
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What is the equation of the line that passes through the point (5,3) and has a slope of 3/5
The equation of the line that passes through the point (5,3) and has a slope of 3/5 is y = 3 / 5x .
How to write equation of a line in slope intercept form?The equation of a line in slope intercept form can be represented as follows:
y = mx + b
where
m = slopeb = y-interceptThe equation of the line passes through the point (5,3) and has a slope of 3/5. Therefore, let's find the y-intercept of the line using (5, 3)
y = 3 / 5 x + b
3 = 3 / 5 (5) + b
3 = 3 + b
b = 3 - 3
b = 0
Therefore, the equation of the lines is y = 3 / 5x
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Can sum1 pls help me asap
The correct answer is reflection. Option B.
Metamorphosis is a dramatic change in shape or appearance. Big events like getting a driver's license, going to college, or getting married can change your life. He has three basic fixed transformations of reflection rotation and translation. There is a fourth common transformation called expansion.
Simple Transformations is the SAP programming language for describing transformations between ABAP data and XML formats. ST is limited to ABAP data serialization and deserialization, the two most important modes of data integration. Transformation means change. A geometric transformation, therefore, means making some changes to a particular geometric shape. Transformation is a specific process by which exogenous genetic material is taken up and integrated directly into cells through the cell membrane.
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I need help with this math hw its' in the image
Answer:
x = 7y = 37Step-by-step explanation:
You want to know the values of x and y that make the angle measures consistent with the triangles being congruent in the given figure.
CongruenceThe side markings show congruent triangles with corresponding vertices (and angles) ...
L (3x+24)° ⇔ P (8x -11)°
M 84° ⇔ Q 84°
N (2x +y)° ⇔ R (no marking)
Corresponding angles L and P have the same measure, so ...
3x +24 = 8x -11
35 = 5x . . . . . . . . add 11-3x
7 = x . . . . . . . . . divide by 5
The measures of these angles are ...
(3(7) +24)° = 45°
Angle sum theoremThe sum of the angles in each triangle is 180°, so the measure of angle N is found to be ...
L +M +N = 180°
45° +84° +N = 180°
N = 51°
This lets us find the value of y from ...
(2x +y)° = 51°
2(7) +y = 51
y = 37 . . . . . . . . subtract 14
The value of x is 7. The value of y is 37.
1.9 worksheet Name: Veronica is fertilizing her backyard. The total weight of fertilizer varies rectly with the number of bags.
The rate of cahne of rate with respect to bags is.
[tex]\begin{gathered} R=\frac{120-90}{4-3} \\ =\frac{30}{1} \\ =30 \end{gathered}[/tex]Therfore, the rate is 30.
Since, the slope of the graph is positive. The variation is direct.
select all pairs of ratios that form a proportion.
A. 1/6,4/20
B.7/9 ,28/36
C. 14/18 ,21/27
D. 30/80 , 6/18
All the pairs of ratios that form a proportion are;
B. 7/9, 28/36
C. 14/18, 21/27
What is Proportional?
Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.
Given that;
All the ratio are,
A. 1/6,4/20
B.7/9 ,28/36
C. 14/18 ,21/27
D. 30/80 , 6/18
Now,
Solve the ratio in simplest form as;
A. 1/6, 4/20
1/6 = 1 / 6
And, 4 / 20 = 1 / 5
Thus, It is not form a proportion.
B. 7/9, 28/36
7 / 9 = 7 / 9
And, 28 / 36 = 7 / 9
Thus, It is form a proportion.
C. 14/18 ,21/27
14 / 18 = 7 / 9
And, 21 / 27 = 7 / 9
Thus, It is form a proportion.
D. 30/80 , 6/18
30 / 80 = 3 / 8
And, 6 / 18 = 1 / 3
Thus, It is not form a proportion.
Therefore, All the pairs of ratios that form a proportion are;
B. 7/9, 28/36
C. 14/18, 21/27
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i'm stuck on this problem!
7x-7;x=4
Answer:
7x-7 ;x=4
we will just substitute for the values
=7(4)-7
=28-7
=21
Step-by-step explanation:
award as brainliest
Can someone help me ill award 30 points
Answer:
The answer is Cai.
Step-by-step explanation:
2 1/4 is 9/4 as an improper fraction. 9/4 as a decimal is 2.25.
2/3 as a decimal is 0.666666666667.
2.25 is great than 0.666666666667, therefore Cai collected the most.
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Equation of line having passing points (-6,0) and (0,-24) is 4x + y + 24 = 0
What do you mean by equation of line?
The general equation for every straight line is y = mx + c, where m is the gradient (or degree of steepness) of the line and c is the y-intercept (the point in which the line crosses the y-axis).
The variables x and y are related to coordinates on the line in the linear equation y = mx + c.
The formula y = mx + c yields a result for y when we enter a value for x.
As y depends on the value of x, it follows that x is an independent variable and y is a dependent variable.
Two passing points of line are (-6,0) and (0,-24)
Equation of line having two passing points as (a,b) and (c,d) is
[tex](y-b) = \frac{d-b}{c-a} (x-a)[/tex]
So, here equation of line become ,
[tex](y - 0) = \frac{-24-0}{0+6}(x+6)[/tex]
⇒ [tex]y = \frac{-24}{6}(x+6)[/tex]
⇒ y = -4(x+6)
⇒ y = -4x - 24
⇒ 4x + y + 24 =0
Hence, equation of line having passing points (-6,0) and (0,-24) is 4x + y + 24 = 0
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walks 3/4 mile in 1/5 hour. whats the speed in miles per hour
The speed in miles per hour for the given situation is 3.75 miles per hour.
Given that, walks 3/4 mile in 1/5 hour.
What is the speed?The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.
We know that, Speed = Distance/Time
= 3/4 ÷ 1/5
= 3/4 × 5/1
= 15/4
= 3.75 miles per hour
Hence, the speed in miles per hour for the given situation is 3.75 miles per hour.
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Ten years ago, you could buy a loaf of bread for $1.21. Twenty years ago, you could buy a loaf of bread for $0.92.
Answer:
$0.29 is the price difference
Step-by-step explanation:
Ten years ago, you could buy a loaf of bread for $1.21. Twenty years ago, you could buy a loaf of bread for $0.92.
You borrow $6,191 from a bank which charges you 8.4% simple interest. Howamuch will you owe (total) after 6 and a half years?DO NOT ROUND ANY NUMBERS UNTIL YOUR FINAL ANSWER!Round your answer to the nearest cent.
The formula for simple interest is given by:
Simple Interest = Principal x interest rate x time period
SI = 6,191*0,084*6.5
SI= 3,380.286
Total amount: 3,380.286 + 6,191 = 9,571.286
Answer: $9,571.3
6x10^9/5x10^ write your answer in scientific notation
Answer:
1.2*10^4 or 12*10^3
Step-by-step explanation:
(6*10^9)/(5*10^5)=12000
12000=12*10^3
12000=1.2*10^4
Select all the pairs of equivalent expressions.
3^5\
3^8 and 3^-3
4^-3 and
4^3
(5^2)^-6 and 5^8
5^4\
5^9 and 5^13
Answer:
I don't know gh6y6y6yytthttrth3th
I don't have a diagram, but here's the key info:
There is a sector of a circle:
The radius is 5.2
The arc length is 6π
You are not given the angle of the sector
Find the area of the sector, and give your answer in terms of pi I got 49π, let me know if I'm right ty. I've attached my working out
Answer:
Area of sector is 15.6π========================
Let the central angle be α.
Arc length equations = 2πr × α/360, if α in degreess = 2πr × α/2π = αr, if α in radiansWe have s = 6π and r = 5.2Find the central angles = αr6π = 5.2αα = 6π/5.2Area of sectorA = r²α/2, when α in radiansSubstitute the value of αA = 5.2² × 6π/5.2 × 1/2 = 5.2 × 3π = 15.6πNote: You could get it more easily if considered 360° = 2π in your calculations.
Answer:
[tex]\dfrac{78}{5} \pi = 15.6 \pi[/tex]
Step-by-step explanation:
Given values:
Radius (r) = 5.2Arc length = 6πAs the arc length is given in terms of pi, use the formulas where the angle is measured in radians.
[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Arc length}\\\\Arc length $=r \theta$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $\theta$ is the angle measured in radians.\\\end{minipage}}[/tex]
Substitute the given values into the arc length formula to calculate the central angle (in radians):
[tex]\implies 6\pi=5.2\; \theta[/tex]
[tex]\implies \theta=\dfrac{6\pi}{5.2}[/tex]
[tex]\implies \theta=\dfrac{15}{13}\pi[/tex]
[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Area of a sector of a circle}\\\\Area of a sector = $\dfrac12 r^2 \theta$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $\theta$ is the angle measured in radians.\\\end{minipage}}[/tex]
Substitute the radius and the found angle into the formula and solve for area:
[tex]\begin{aligned}\implies \textsf{Area of the sector}&=\dfrac{1}{2}(5.2)^2 \left(\dfrac{15}{13}\pi\right)\\\\&=\dfrac{1}{2}(27.04) \left(\dfrac{15}{13}\pi\right)\\\\&=(13.52) \left(\dfrac{15}{13}\pi\right)\\\\&=\dfrac{78}{5}\pi \\\\&=15.6 \pi\end{aligned}[/tex]
the skills inWhat is the volume of the following figure?Front viewBack viewiş 1 cubic unitcubic unitsReport a problem
Given that each cube represents 1 cubic units, we need to count how many cubes are in the figure.
From the front view, we count 2 cubes.
From the back view, we count 5 cubes.
There are 5 + 2 = 7 cubes in total, so the volume of the figure is 7 cubic units.
не 22° K What is the measure of angle HJI? O 389 0 68° 112 1589
As, from the figure :
Angle HJK = 90 and IJK =22
Substitute the value :
Angle HJK = Angle HJI and the angle IJK
So, equations will be :
[tex]\begin{gathered} \angle HJK=\angle HJI\text{ + }\angle IJK \\ 90=\angle HJI+22 \\ \angle HJI\text{ = 90 -22} \\ \angle HJI=68 \end{gathered}[/tex]Answer : Angle HJI = 68 degrees
Answer B) 68 degrees
can yall help me with this
Answer:
C is correct.
Step-by-step explanation:
[tex] \sqrt[4]{ \frac{16}{81} } = \frac{ \sqrt[4]{16} }{ \sqrt[4]{81} } = \frac{2}{3} [/tex]
Yuvia works in a computer store, where she earns a commission of 8 percent of her sales. On monday, her sales were $2,500. She calculates the amount she made on commission: ($2,500)(0. 08) = yuvia also earns a base salary of $45 per day. What is the total amount she earned that day? [total salary = base pay + commission].
If Yuvia also earns a base salary of $45 per day. The total amount she earned that day will be $245.
What is percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
The usage of percentages is widespread and diverse. For instance, numerous data in the media, bank interest rates, retail discounts, and inflation rates are all reported as percentages. For comprehending the financial elements of daily life, percentages are crucial.
It is given that, Yuva works in a computer store, where she earns a commission of 8 percent of her sales. On Monday, her sales were $2,500.
Commission = 8 % of sales
Commission =($2,500)(0. 08)
Commission =$ 200
If yuvia also earns a base salary of $45 per day,
Total salary = base pay + commission].
Total salary =45 +200
Total salary =$245
f Yuvia also earns a base salary of $45 per day. The total amount she earned that day will be $245.
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Please help with linear equations See attached pic to understand problem more clearly
Given the system of equations. We have:
- For (5,0)
Substitute x = 5 and y = 0 in the equations:
[tex]\begin{gathered} 5(5)+4(0)=-1 \\ 25+0=-1 \\ 25\ne-1 \end{gathered}[/tex]Answer: No
- For (-7, -8)
x = -7 and y = -8
[tex]\begin{gathered} 5(-7)+4(-8)=-1 \\ -35-32=-1 \\ -67\ne-1 \end{gathered}[/tex]Answer: No
- For (3, -4)
[tex]\begin{gathered} 5(3)+4(-4)=-1 \\ 15-16=-1 \\ -1=-1 \\ \text{and} \\ 3(3)-2(-4)=-5 \\ 9+8=-5 \\ 17\ne-5 \end{gathered}[/tex]This is satisfied for the first equation but not for the second. Therefore it is not a solution to the system.
Answer: No
- For (-2, -2)
[tex]\begin{gathered} 5(-2)+4(-2)=-1 \\ -10-8=-1 \\ -18\ne-1 \end{gathered}[/tex]Answer: No
Need help asap!!!!!!
The county fair charges $1.25 per ticket for the rides. Jermaine bought 25 tickets for the rides and spent a total of $43.75 at the fair. Jermaine spent his money only on ride tickets and fair admission. The price of the fair admission is the same for everyone. Use y to represent the total cost and x to represent the number of ride tickets.
Define your variables.
Write a linear equation that can be used to determine the cost for anyone who only pays for ride tickets and fair admission.
What is the slope of the line? Show your work
Write the equation of the line in point-slope form. Show your work
Write the equation of the line in slope-intercept form. Show your work.
The equation of the line in point-slope form is; y=1.25 x+12.5 The slope of the line is 1.25.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let y is the total cost at the county fair and x is the number of tickets per ride
The variable in the linear equation;
y=mx+c
m=Cost per ticket ride
c= fair admission price
Given that;
y=$43.75
m=$1.25 per ticket ride
x=25 tickets
c=unknown
Now replacing;
43.75=(1.25×25)+c
c=43.75-31.25
c=12.5
The fair admission price will be; 12.5 dollar
The equation of the line in point-slope form is; y=1.25 x+12.5
The slope of the line is 1.25.
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