Answer:
Step-by-step explanation:
The equation of the line can be found using the point-slope form:
y - y1 = m (x - x1)
where m is the gradient, (x1, y1) is a point on the line.
For the given information:
m = 3, x1 = -1, y1 = 3
Plugging in the values into the point-slope form:
y - 3 = 3 (x - (-1))
Simplifying the equation:
y = 3x + 6
So, the equation of the line is: y = 3x + 6
How would you find x?
Answer:
1/3
Step-by-step explanation:
You want to find x in a Venn diagram with regions labeled (x(x-5)), x, 2x, and 20, when the total is ε = 100. And you want to know the probability that a British stamp is from the 20th century.
Sum of the partsThe whole is the sum of the parts:
ε = x(x-5) +x +2x +20
100 = x² -2x +20 . . . . . . . . simplify
81 = x² -2x +1 . . . . . . . . . subtract 19 to make a complete square
81 = (x -1)²
9 = x -1 . . . . . . . positive square root
x = 10 . . . . . . . . add 1
ProbabilityNow we know ...
P(B) = (x +2x)/ε = 30/100 = 0.3
P(T&B) = x/ε = 10/100 = 0.1
The probability that a British stamp is from the 20th century is ...
P(T|B) = P(T&B)/P(B) = 0.1/0.3
P(T|B) = 1/3
Type the correct answer in each box. If necessary, use / for the fraction bars,
Write the function for the parabola shown with its directrix in the graph.
f(x) =
4
3
2
→
&
تنا
2 3
(x-
y = -2.25
The equation of the parabola graphed is given as follows:
(x - 3)² = 5(y + 1)
How to obtain the equation of the parabola?The equation of a vertical parabola is given as follows:
(x - h)² = 4p(y - k)
In which:
(h,k) are the coordinates of the vertex.y = k - p are the coordinates of the directrix.(h, k + p) are the coordinates of the focus.The vertex is at the coordinate (3,-1), hence the parameters h and k are given as follows:
h = 3, k = -1.
The directrix is at the coordinate y = -2.25, hence the value of p is obtained as follows:
-1 - p = -2.25
p = 1.25.
Meaning that the equation of the parabola is given as follows:
(x - 3)² = 5(y + 1)
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determine whether the angle vector v makes with vector u is acute, obtuse, straight, a right angle, or whether v is a vector in the same direction as u. uv
The angle that the vector "v = 9i + 8j - 4k" makes with the vector "u = 6i - 4j - k" is Acute Angle .
To determine the angle between two vectors, we need to find the dot product of the vectors and divide it by the product of their magnitudes.
If the result is positive, the angle between the vectors is acute, if it's negative the angle is obtuse, and if it's zero, the angle is a right angle.
In this case, the dot product of vectors "u" and "v" is:
⇒ (6i - 4j - k) . (9i + 8j - 4k) = 54 - 32 + 4 = 26 ;
The magnitude of vector "u" is = √(6² + (-4)² + (-1)²) = √(36 + 16 + 1) = √53
The magnitude of vector "v" is = √(9² + 8² + (-4)²) = √(81 + 64 + 16) = √161
So, the Cosine (Cos) of angle between two vectors "u" and "v" is:
⇒ Cos(θ) = 26/(√37 × √145) = 26/√5365 .
Since the value of Cos(θ) is positive, the angle between the vectors is acute. This means the vectors "u" and "v" are pointing in somewhat similar directions, but not exactly the same direction.
The given question is incomplete , the complete question is
Determine whether the angle vector "v" makes with vector "u" is acute, obtuse, straight, a right angle, or whether "v" is a vector in the same direction as "u" . u=6i-4j-k and v=9i+8j-4k .
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[tex]\frac{x-4}{3}\leq 5[/tex]
Answer:
Hi, I'm Za'Riah! I will gladly assist you with your problem! (see explanation)
Step-by-step explanation:
Let's solve your inequality step-by-step.[tex]\frac{x-4}{3} \leq 5[/tex]
Step 1: Simplify both sides of the inequality.[tex]\frac{1}{3}x + \frac{-4}{3} \leq 5[/tex]
Step 2: Add 4/3 to both sides.[tex]\frac{1}{3}x+ \frac{-4}{3} + \frac{4}{3} \leq 5+ \frac{4}{3} \\\frac{1}{3}x\leq \frac{19}{3}[/tex]
Step 3: Multiply both sides by 3.[tex]3*\frac{1}{3}x\leq 3*( \frac{19}{3} )[/tex]
Answer:
x [tex]\leq[/tex] 19
(Hope this helped!)
(see image for number line graph)
c) Bhurashi can do part of a work in 1 day. She worked for 4 days and 20 left. If the remaining parts of the work was done by Rita, how much work did she do ?
Answer: the only clear answer i can think of would be, NO, the work she did was not clear i would say she did 4/10days she needed to work
Step-by-step explanation:
evalutate the espression I need help ASAP please don't answer incorrectly just for the points
The expressions are evaluated to 7 and -6
What are algebraic expressions?Algebraic expressions are mathematical expressions comprising of terms, coefficients, variables, constants and factors.
These expressions are also comprised of mathematical or arithmetic operations. These operations are;
MultiplicationSubtractionDivisionFloor divisionAdditionBracketParenthesesFrom the information given, we have that;
a. -4d + 3
b. k - m
Given that d= ,-1. k = 4 and m = -10
Now, substitute the values, we get;
a.-4(-1) + 3
expand the bracket
4 + 3 = 7
b. k - m
4 - 10
-6
Thus the values are 7 and -6
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if a cylinder with a 6 in. radius is spinning at 24 mph, find the angular velocity in rpm of a point on its rim ?
The angular velocity in rpm of a point on its rim is equals to the 4224 rad/min.
We have, a cylinder with Radius , R = 6 inch. Spining velocity, S = 24 miles per hour
We have to calculate the the angular velocity in rpm of a point on its rim. To calculate Angular and Linear Speed from Linear velocity :
Step 1: Identify which speed we are asked to calculate and Identify the radius and the velocity. We already identified all this in above.
Step 2: To calculate the angular speed when the linear speed and the radius of the circular object use : angular velocity = linear velocity/radius
First, we need to reconcile the unit of the radius of the wheel/rim and the unit of the speed of the car. Also, we are asked to give the answer in radians per minute. So, let's convert the speed to inches per minutes. So, the linear velocity of spining = 24 miles per hour × 5280 ft. per miles× 12 inches per ft. × 1 hour / 60 minutes
= 25,344 inches per minute
Now, the angular velocity is written as
angular velocity = linear velocity /radius
= 25,344 inches per minute / 6 inches
= 4224 /min. Hence, the angular velocity of the rim is 4224 rad/min.
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If a cylinder with a 6 in. radius is spinning at 24 mph, The angular velocity of a point on the rim of the cylinder is 672.27 rpm.
Angular velocity is a measure of the speed at which an object is rotating around a central axis. It is measured in units of radians per second (rad/s) or revolutions per minute (rpm). To find the angular velocity of a point on the rim of the cylinder, we need to first convert the linear velocity (24 mph) to linear velocity in feet per second (ft/s). We can use the formula:
v = r * ωwhere v is the linear velocity, r is the radius of the cylinder, and ω is the angular velocity.
Due to the 6 in. = 0.5 feet,
ω = v χ 1 r = 24 miles hr 1 0.5 ft χ 5280 ft mile = 253,440 (rad) hr
Then, 672.27 rpm at 253,440 (rad) hr 1 2pi rev rad 1 60 hr min
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Rewrite each of the following expressions in expanded form. All of your answers should be in the form ax^² + bx + c for numbers a, b, and c. a. (x + 1)(2x + 4) =b. (2x + 3)(4x + 8) =c. (x + 12)^2 =
The given expressions in the expanded form are 2x² + 6x + 4, 8x² + 28x + 24 and x² + 24x + 144.
a. (x + 1)(2x + 4) =
Expanding the product:
2x² + (2 × 1 + 4 × 1)x + 4 × 1 = 2x² + 6x + 4
b. (2x + 3)(4x + 8) =
Expanding the product:
8x² + (4 × 3 + 8 × 2)x + 8 × 3 = 8x² + 28x + 24
c. (x + 12)² =
Expanding the square:
x² + 2 × x × 12 + 12² = x² + 24x + 144
So, for each expression, the expanded form is given by ax² + bx + c.
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Alejandro Associates is an accounting firm that provides audit and tax services to its clients. Each tax return is considered a "job" for the firm, just like a manufacturing company considers a customer order as a "job."
Alejandro has direct costs related to Tax Return 8405 as follows:
7 hours of staff labor $96 per hour
4 hours of assembly labor $172 per hour
$62 of materials
In addition, Alejandro Associates estimates its overhead related to the manufacture of tax returns to be $57,230 for the year. The company expects to do 10,217 returns for the year. The company also expects to use 59,712 staff hours for the year. If Alejandro allocates overhead to jobs based on staff hours, what is the total cost of Tax Return 8405? *Hint, make a job order cost sheet for Job 454. It should include materials, labor, and overhead. *Round each step to the nearest 2 decimal places. For your final answer, round to the nearest dollar
if r(x) is a rational function in simplest form where the degree of the numerator is 2 and the degree of the denominator is 2, then
Here, the degree of the numerator, 2, is equal to the degree of the denominator, 2, so r(x) has a nonzero horizontal asymptote
Asymptote is a line taken in relation to curve. The line is always far apart from the curve irrespective of distance. Taking the definition in sense of curve, then the curve tries to reach this line while moving towards infinity. Horizontal asymptote indicates the behaviour of function at graph edge.
The equation to be considered for formation of horizontal asymptote is y = mx + b, where u is y-axis, m is slope, x is axis and b is constant. If the two values, that are numerator and Denominator are equal, then y = b.
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Find the angle DEF
A. 158
B. 90
C. 39.5
D. 360
The measure of the angle DEF is 39.5 and thus option C is correct.
What is a circle simple definition?A circle is simply a round shape that has no corners or line segments. It is a closed curve shape in geometry. The points of circle are at a fixed distance from the center.
Given here: The arc angle as 79
But we know The measure of the angle is equal to half the sum of the intercepted arcs. The angle x is equal to half the sum of the intercepted arcs.
∴∠ DEF= 79/2
=39.5°
Hence, The measure of the angle is 39.5
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Janet unfolded a cardboard box. The figure of the unfolded box is shown below:
Which calculation will give the total surface area of the cardboard, in square inches, that was used to make the box? (1 point)
A. 5 × 6 × 6
B. 6 × 5 × 5
C. 10 × 6 × 6
D. 6 × 10 × 10
The total surface area of the cardboard in square inches is option B. 6 × 5 × 5.
What is Surface Area?The area of a three dimensional object on it's outer surface is called the surface area of the object.
From the given figure, there are 6 squares with each square having the side length equals 5 inches.
Area of a square = a × a, where a is the length of a side.
Area of a 5 inch square = 5 × 5
There are total of 6 squares.
Total surface area = 6 × 5 × 5
Hence the total surface area of the given figure is option B. 6 × 5 × 5.
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all ball can bounce to 95% of its original height what is the total vertical distance that it will travel if it is dropped from 20 feet
If dropped from a height of 20 feet, the ball will travel a vertical distance of 39 feet.
We know that a ball if dropped will bounce back to 95% of its original height.
This means that when a ball is dropped from a distance of 100 m, it will travel 95 meters up.
Here we have been given that the ball is dropped from a height of 20 feet.
Hence, it will bounce back to a height of
95% of 20 = 19 feet.
Hence, the total vertical distance traveled by the ball is
The height at which it was dropped from + distance it bounced back to
20 feet + 19 feet
= 39 feet.
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Shows the path of a beam of light through several layers with different indices of refraction. (a) If $\theta_{1}=30.0^{\circ}$, what is the angle $\theta_{2}$ of the cmerging beam? (b) What must the incident angle $\theta_{1}$ be to have total internal reflection at the surface between the medium with $n=1.20$ and the medium with $n=1.00 ?$
(a) If θ(1) = 26.0 degree, the angle θ(2) of the emerging beam is 41.3 degree.
(b) The smallest incident angle θ(1) to have total internal reflection at the surface between the medium with n(4) = 1.20 and the medium with n(4) = 1.06 is 62.01.
(a) The path of a beam of light through several layers with different indices of refraction.
Using the Snell's law
n(1) sinθ(i) = n(2) sinθ(r)
The two medium's refractive indices are n(1) and n(2), and the angles of incidence and refraction are θ(i) and θ(r).
The preceding can be revised as
sinθ(r) = sinθ(i)(n(1))/(n(2))
sinθ(r) = sin 26 × 1.60/1.40
sinθ(r) = 0.50
Going from n2 to n3 .
The above calculated will become angle of incidence made with the normal at n(2) and n(3) interface.
The angle of refraction at n(3) medium
sinθ(r3) = sinθ(r) × n(2)/n(3)
sinθ(r3) = 0.50 × 1.40/1.20
sinθ(r3) = 0.58
The angle of incidence for interfaces n(3) and n(4) is now θ(r3).
sinθ(2) = (sinθ(r3) × n(3))/n(4)
sinθ(2) = (0.58 × 1.2)/1.06
sinθ(2) = 0.66
Taking square root on both side, we get
θ(2) = [tex]\sin^{-1}[/tex](0.66)
θ(2) = 41.3 degree
(b) It is possible to calculate the critical angle at the n3 to n4 interface as
θ(c) = [tex]\sin^{-1}[/tex](n(4)/n(3))
θ(c) = [tex]\sin^{-1}[/tex](1.06/1.20)
θ(c) = 62.01
The angle at which 100% internal reflection takes place is known as the critical angle.
Total internal reflection will happen if the beam is incident at an angle of 62.01 at n(3).
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The complete question is:
The figure below shows the path of a beam of light through several layers with different indices of refraction. (Assume n(4) = 1.06.)
(a) If θ(1) = 26.0 degree, what is the angle θ(2) of the emerging beam?
(b) What is the smallest incident angle θ(1) to have total internal reflection at the surface between the medium with n(4) = 1.20 and the medium with n(4) = 1.06?
The function h is given by h(x) = 5x+13/ x-7 a) Write an expression for h−¹(x). b) For what value of x can h-¹(x) not be found? Give your answer as an integer or as a decimal.
Step-by-step explanation:
a) h−¹(x) = (x-13)/ (5x+7)
b) h-¹(x) cannot be found when x = 7.
Select the graph of the system of inequalities. –x + y ≤ –1 x + 2y ≥ 4
The common region to both the inequalities would be the solution region.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is the compound inequality as -
–x + y ≤ –1
x + 2y ≥ 4
Refer to the graph of the inequalities attached. The common region to both the inequalities would be the solution region.
Therefore, the common region to both the inequalities would be the solution region.
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There were 35 gallons of water in a tank and 4.5 gallons of water in a pail. An equal amount of water was poured into the tank and the pail. The ratio of the water in the tank to that pail became 7:2.
a. how much water was in the pail at the end?
b.how much water was poured into the pail?
please show work as well ty :)
Answer: A: 9 galloons and then
Step-by-step explanation:
A car rental agency has 20 cars. Of those cars, 4 are
luxury sedans and all the other cars are midsize sedans.
Each luxury sedan rents at a daily rate 50% greater
than the daily rate for the midsize sedans. If the luxury
sedans rent for $45 per day, what is the average daily
rental fee, to the nearest dollar, of all 20 cars at this
agency?
A. $27
B. $33
C. $38
D. $42
E. $56
Answer:
[tex]\Huge \boxed{\textbf{B. \$33}}[/tex]
Step-by-step explanation:
To solve this problem, we first need to find the daily rental rate for the midsize sedans. Since the luxury sedans rent for $45 per day and their daily rate is 50% greater than the midsize sedans, we can set up the following equation:
[tex]\Large \boxed{\texttt{45 = 1.5 $\times$ Midsize daily rate}}[/tex]
Now, we can solve for the midsize daily rate:
[tex]\texttt{Midsize daily rate} = \tt{\frac{45}{1.5}}[/tex][tex]\texttt{Midsize daily rate} = \tt{30}[/tex]So, the midsize sedans rent for $30 per day. There are 16 midsize sedans (20 total cars - 4 luxury sedans) and 4 luxury sedans. To find the average daily rental fee for all 20 cars, we can use the following formula:
[tex]\Large\boxed{\texttt{Average daily rental fee} = \frac{\texttt{Total rental fees}}{\texttt{Total number of cars}}}[/tex]
The total rental fees can be calculated as follows:
[tex]\texttt{Total rental fees} = \tt{(16 \times 30) + (4 \times 45) }\\[/tex][tex]\texttt{Total rental fees} = \tt{480 + 180}[/tex][tex]\texttt{Total rental fees} = \tt{660}[/tex]Now, we can find the average daily rental fee:
[tex]\texttt{Average daily rental fee} = \tt{\frac{660}{20}} \\[/tex][tex]\texttt{Average daily rental fee} = \tt{33}[/tex]So, the average daily rental fee for all 20 cars at this agency is $33, which corresponds to option B.
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________________________________________________________
Please find the answer to A B and C show work if possible please
Answer:um it dose not show the thing i downloded the file if u try again i will anser it for tho
Step-by-step explanation:
Circle A has center of −2, −2 and a radius of 4, and circle B has a center of 3, 3 and a radius of 2. What steps will help show that circle A is similar to circle B
Dilate circle A by a scale factor of 0.5
Reflect circle A over the line y = x
Translate circle A using the rule (x − 5, y − 5)
Rotate circle A 90° clockwise about the origin
The required steps to show that circle A is similar to circle B are,
1. Dilate circle A by a scale factor of 0.5.
2. Translate circle A using the rule (x − 5, y − 5).
The circle is the locus of a point whose distance from a fixed point is constant i.e center (h, k). The equation of the circle is given by
(x - h)² + (y - k)² = r²
where h, k is the coordinate of the center of the circle on the coordinate plane and r is the radius of the circle.
Here,
Circle A = Center of −2, −2 and a radius of 4,
Circle B = Center of 3, 3, and a radius of 2.
Steps to show circle A is similar to circle B
1. Dilate circle A by a scale factor of 0.5
2. Translate circle A using the rule (x − 5, y − 5)
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84 ×7=( + 4)x = 80 x || + 28 + x 7
Answer:
The expression "84 × 7 = ( + 4) × = 80 × || + 28 + x 7" is not a valid mathematical equation and has errors in syntax. I suggest rephrasing it to a clear and well-formed equation for me to help solve.
g a researcher is looking at the effect of drinking alcohol on the ability to play darts. he recruits 20 dart players from the nearby pub and has them come to a lab where he flips a coin for each player. if the coin comes up heads, he has the player drink a pint of beer. if the coin comes up tails, he has the player drink a pint of soda. each player then throws three darts at a dartboard and the score is recorded. the researcher calculates that the soda-drinkers score, on average, 2.5 points more than the beer-drinkers.
The paragraph above describes a/an c. controlled experiment.
The participants who drink beer are the b. control group, the participants who drink soda are the a. treatment group.
Flipping a coin to decide which player gets which drink is an example of g. randomization.
A controlled experiment is a type of study in which the researcher manipulates one or more independent variables to observe the effect on a dependent variable. In this case, the independent variable is the type of drink (beer or soda) and the dependent variable is the score achieved in a dart-throwing task.
The purpose of randomly assigning the players to drink either beer or soda is to control for any other factors that could affect the scores, such as the individual's dart-playing ability or the amount of alcohol consumed.
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Complete Question:
A researcher is looking at the effect of drinking alcohol on the ability to play darts. He recruits 20 dart players from the nearby pub and has them come to a lab where he flips a coin for each player. If the coin comes up heads, he has the player drink a pint of beer. If the coin comes up tails, he has the player drink a pint of soda. Each player then throws three darts at a dartboard and the score is recorded. The researcher calculates that the soda-drinkers score, on average, 2.5 points more than the beer-drinkers.
The paragraph above describes a/an _____________.The participants who drink beer are th_____________, the participants who drink soda are the _____________. Flipping a coin to decide which player gets which drink is an example of _____________.
Choose from the list below to fill in the blanks.
a. treatment group
b. control group
c. controlled experiment
d. observational study
e. placebo
f. confounding factor
g. randomization
Find the volume of each prism and match the volume to the correct prism. The units are understood to be square units, but are not included on the numeric answer.
Answer:
To find the volume of a prism, use the formula V = A * h, where A is the area of the base of the prism and h is its height. For example, for the first prism, the area of the base is 8 and the height is 4, so the volume is 8 * 4 = 32. For the second prism, the area of the base is 6 and the height is 9, so the volume is 6 * 9 = 54. The first prism has a volume of 32 and the second prism has a volume of 54.
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Let F be a function defined for all the nonnegative integers by thefollowing recursive definition.
F(0) = 0, F(1) =1
F(n+2) = 2F(n) + F(n+1),n Image for Let F be a function defined for all the nonnegative integers by thefollowing recursive definition. F(0) = 0, 0
Compute the first six values of F;that is, write the values of F(n) for n = 0, 1, 2, 3, 4, 5.
I started off just plugging in 0 andgot
F(0+2) = 2F(0) + F(0+1)
= 2 = 2(0) + 1
= 2 = 3
How do I do this?
For the recursive definition F(0) = 0, F(1) =1 , F(n+2) = 2F(n) + F(n+1) , n ≥ 0 ; the first six values are 0 , 1 , 1 , 3 , 5 and 11 .
The first six values of the function F can be computed step by step as follows:
the recursive definition is F(0) = 0, F(1) =1 , F(n+2) = 2F(n) + F(n+1) , n ≥ 0 ;
it is already known that : F(0) = 0 and F(1) = 1 ;
So , F(2) = 2×F(0) + F(1) = 2×0 + 1 = 1 ;
Similarly ; F(3) = 2×F(1) + F(2) = 2×1 + 1 = 3 ;
⇒ F(4) = 2×F(2) + F(3) = 2×1 + 3 = 5 ;
⇒ F(5) = 2×F(3) + F(4) = 2×3 + 5 = 11 .
Therefore , first six values of F are 0 , 1 , 1 , 3 , 5 and 11 .
The given question is incomplete , the complete question is
Let F be a function defined for all the nonnegative integers by the following recursive definition.
F(0) = 0, F(1) =1 , F(n+2) = 2F(n) + F(n+1) , n ≥ 0 .
Compute the first six values of F .
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Which of the following is equivalent to 5(a + 3) + 12?
5a + 15
5a + 27
5a + 36
15a + 12 please help me
If vector B is added to vector A, which two of the following choices must be true in order for the resultant vector to be equal to zero? and B are equal and opposite directions Aand B are perpendicular and B are equal and in the same direction and B are nJOt equal and in the sanie direction None of these'
If vector B is added to vector A and the resultant is a null vector then A and B are equal and have opposite directions
We are given two vectors, vector A and vector B.
Now, vector B is added to vector A and it is said that the resultant of this addition is a null vector. It can be written as
vector B + vector A = 0
It can also be written as
vector A = 0 - vector B
vector A = - vector B
We can see that the magnitude of both the vectors, vector A and vector B are equal. The minus sign here represents that the direction of vector B is opposite to vector A
Hence, we can conclude that if vector B is added to vector A and the resultant is a null vector then A and B are equal and have opposite directions
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Last socer season, Trish scored g goals , Alexa scored
4 more goals than Trish, write an expression that
shows how many goals Alexa scored.
Alexa scored g + 4 goals in the last soccer season.
What is expression in math?Expression in mathematics is a combination of symbols, such as numbers and operators, which produces a mathematical result. An expression can involve a single term or multiple terms and usually consists of a combination of constants, variables, operators, functions and parentheses. In an expression, operators are used to perform operations on terms, allowing one to solve equations and other problems. Examples of mathematical expressions include 3 + x = 5, sin(x) + 4, and (x + 2y)^2.
The expression that shows how many goals Alexa scored is: Alexa scored (g + 4) goals.
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Which of the following numbers is one-fifth of a given number if one-fourth of that same number is 20? Select the single best answer: A 10 B. 15 C. 20 D. 16 E. 25 usuan West >>
16 is the number which is one-fifth of a number when one-fourth of that same number is 20.
As per the given data:
One-fourth of the number is resulted to 20.
Here we have to determine the result of one-fifth of the same number from the given options.
An expression for a portion of a whole is a fraction.
For any real numbers, the fractional component of x is defined.
Let the number be X.
One-fourth of a number is 20 which means:
Multiply the one-fourth fraction with an unknown number which results in the number 20.
[tex]$\frac{1}{4}[/tex] (X) = 20
X = 20 × 4
X = 80
Now we have to determine that one-fifth of the same number.
Multiply the one-fifth fraction by 80.
We get:
= [tex]$\frac{1}{5}[/tex] (80)
= [tex]$\frac{1}{5}[/tex] × 5 × 16
= 16
One-fifth of the number 80 is 16
Therefore Option (D) - 16 is the correct answer.
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what is the approximate solution of the linear system represented by the graph below
The approximate solution of the linear system represented by the graph is, (5, 6)
What is the equation of line?The equation of a straight line is a relationship between x and y coordinates, The general equation of a straight line is y = mx + c, where m is the slope of the line and c is the y-intercept.
Given that,
A graph in which two lines are intersecting each other,
basically solution of linear system means where both the lines will intersect,
So, in the graph it can be seen that lines are intersecting around x coordinate 5 and y coordinate 6,
Therefore, the solution is (5, 6)
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according to car and driver, an alfa romeo going 70 mph requires 177 feet to stop. assuming that the stopping distance is proportional to the square of the velocity, find the stopping distance required by an alfa romeo going at 25 mph and at 110 mph.At 25 mph, stopping distance =At 110 mph, stopping distance =
At 25 mph, stopping distance = 22.56 feet
At 110 mph, stopping distance = 436.81 feet
Now, According to the question:
Let d represents the stopping distance required by an alfa romeo.
The stopping distance is proportional to the square of velocity is equivalent to the equation,
[tex]d = kv^2[/tex]
Here, k is proportionality constant.
We have,
d = 177 feet and v = 70 mph.
So, proportionality constant
[tex]k =\frac{177}{(70mph)^2}[/tex] ≈ 0.0361
Thus, the stopping distances required by an alfa Romeo going at 25 mph and at 110 mph,
[tex]d_2_5=0.0361[/tex] × [tex](25mph)^2[/tex] = 22.56 feet
[tex]d_1_1_0[/tex] = 0.0361 × [tex](110mph)^2[/tex] = 436.81 feet
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