By forming and solving equations, we know that the speed of the runner is 4 miles per hour.
What are equations?The equals sign is a symbol used in mathematical formulas to denote the equality of two expressions. An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values. As in 3x + 5 = 15, for example. There are many different types of equations, including linear, quadratic, cubic, and others. The three primary forms of linear equations are point-slope, standard, and slope-intercept.So, we need to form an equation to get the speed of the runner:
2 × (18 + x) = 44'x' is the speed of the runner. Now, solve for x as follows:
2 × (18 + x) = 4418 + x = 44/218+x = 22x = 22 - 18x = 4 miles per bourTherefore, by forming and solving equations, we know that the speed of the runner is 4 miles per hour.
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20 hours and earns $210.00
Answer:
$10.5/hr
Step-by-step explanation:
210/20=10.5
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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Y=-3|x+2|+8 Slope of the rays
The slopes of the rays of the absolute value function, y = -3·|x + 2| + 8 are 3 and -3
What is an absolute value function?In an absolute value function, an algebraic expression is contained within an absolute value symbol.
The given absolute value function is; y = -3·|x + 2| + 8
The slope of the rays are found as follows;
The general form of the absolute value function is; f(x) = a·|x - h| + k
The vertex of the function is the point (h, k)
The slope of the function is a
Comparing the specified function, y = -3·|x + 2| + 8, to the general function, we get;
The vertex of the function is (h, k) = (-2, 8)
The slope of the rays of the function are; a = 3
Slope of the ray 1 = (8 - (-19))/(-2 - (-11)) = 3
Slope of ray 1 is therefore; 3
Slope of ray 2 = (8 - (-19))/(-2 - 7) = -3
The slope of the ray 2 is therefore; -3
The slope of the rays are; 3 and -3
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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.
which relation is not a function?
Answer:
D
Step-by-step explanation:
Two of the same X's
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.
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.
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.
How do I solve this?
10-7(3 + 2) +7²
Answer:
24
Step-by-step explanation:
10 - 7(3 + 2) + 7²
10 - 7(5) + 49
10 - 35 + 49
10 - 35 = -25
-25 + 49 = 24
I hope this helps!
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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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]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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What is the product of 54 and 2.2 \times 10^62.2×10 6 expressed in scientific notation?
The given expression is represented in scientific notation as (1.77 × 10⁶).
What do we mean by scientific notation?
Numbers that are either too large or too little to be conveniently stated in decimal form can be expressed using scientific notation. It is also known as the standard form in the UK and scientific form, standard index form, and standard form.When a number between 1 and 10 is multiplied by a power of 10, the result is represented in scientific notation. For instance, 650,000,000 can be represented as 6.5 × 10⁸ in scientific notation.So, the given expression in scientific notation:
= (2.2 × 10^6) - (4.3 × 10^5)= (2.2 × 1000000) - (4.3 × 100000)= 2200000 - 430000= 1770000= 177 × 10^4= 1.77 × 10⁶Therefore, the given expression is represented in scientific notation as (1.77 × 10⁶).
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Correct question?
2.2⋅10^6 −4.3⋅10^5 scientific notation
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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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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Cassandra has a tangler panto in her backyard the panto is 12.74 m long and 5.45 m wide round the length and width to the nearest whole number then estimate the perimeter of cassandra is panto write an equation to show your work
The perimeter measures around 36 metre.
Describe a perimeter?The perimeter refers to the area surrounding an object. For instance, your house has a fenced-in yard. The perimeter is the length of the fence. If the yard is 50 feet by 50 feet, your fence is 200 feet long.
While 12.74 rounds up to 13, 5.45 rounds down to 5. Recatangle created a total of four sides, two of which are identical in length to the other two (which is a poor way to explain it). There are two sides that are 13 inches long and two sides that are 5 inches long, which is the solution to this question. When added together, the perimeter would be 13+13+5+5.
As an expression,
2(13)+2(5)
=26+10
=36.
The perimeter is approximately 36 meters.
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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]
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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Air pressure may be represented as a function of height (in meters) above the surface of the Earth, as shown below. P(h) =P. e-0.00012h In this function, Po is the air pressure at the surface of the Earth, and his the height above the surface of the Earth, measured in meters. At what height will the air pressure equal 65% of the air pressure at the surface of the Earth?
A. 0.65 m
B. 5416.7 m
C. 3587.4 m
D. 3589.9 m
3589.9 m is the height at which air pressure equals 65% of the air pressure at the surface of the Earth
How to find the height at which air pressure equals 65% of P₀?
Given: the function P(h) =P₀ e^(-0.00012h)
When air pressure equals 65% of the air pressure at the surface of the Earth. That means P = 0.65P₀
Substitute P = 0.65P₀ into the function:
P(h) = P₀ e^(-0.00012h)
0.65P₀ = P₀ e^(-0.00012h)
Dividing both sides by P₀ gives:
0.65 = e^(-0.00012h)
Take ln of both sides (ln is the inverse of e):
ln 0.65 = -0.00012h
h = ln 0.65/ (-0.00012)
h = 3589.9 m
Therefore, the height at which air pressure equal 65% of the air pressure at the surface of the Earth is 3589.9 m. Option D is the answer
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Is y-8= -x a linear equation?
Find the rate of change for each interval solve 2
we will use the next formula to find the rate of change of the given interval
[tex]r=\frac{f(b)-f(a)}{b-a}[/tex]in our case
a=-3
b=6
[tex]f(-3)=10\log (-3+4)+2=2[/tex][tex]f(6)=10\log (6+4)+2=12[/tex]then we substitute the values in the formula
[tex]r=\frac{12-2}{6-(-3)}=\frac{10}{6+3}=\frac{10}{9}[/tex]The average rate of change is 10/9=1.11
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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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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HELP ME QUICKLY!!!
What is the equation of a line with a slope of 6 and à
y-intercept of 8.
A) y=6x+8
B) y=8x+6
C) y=48x
D) y=6x-8
Answer:
Equation of the line is 6x−y+8=0.
So I think Its A
Step-by-step explanation:
I rlly hope it helps u lol
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.
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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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
More after...............................
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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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]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]