We are given an arithmetic progression and are requested to find the 100th term of the progression. We need to find the value of x from the question by equating differences.
[tex]\begin{gathered} T_2-T_1=T_3-T_2 \\ 3x+4-2x=13x-1-(3x+4)=13x-1-3x-4 \\ x+4=10x-5 \\ \text{Collecting like terms gives us:} \\ 10x-x=4+5 \\ 9x=9 \\ x=1 \end{gathered}[/tex]Now we will find the actual value of our terms.
[tex]\begin{gathered} T_1=a=2(1)=2 \\ T_2=3(1)+4=7 \\ T_3=13(1)-1=12 \\ \text{Therefore,} \\ \text{ d = }T_2-T_1=T_3-T_2 \\ d=7-2=12-7=5 \end{gathered}[/tex]Common difference, d = 5
Lastly, we employ our AP formula to find the 100th term.
[tex]\begin{gathered} Tn=a+(n-1)d \\ T_{100}=2+(100-1)5 \\ T_{100}=2+(99)5=497 \end{gathered}[/tex]The 100th term is 497
A can of diced tomatoes has a height of 11.5 cm and a diameter of 10 cm. What is the volume of the can? Use 3.14 for pie.DO NOT round your answer.
Answer:
902.75 cubic cm.
Explanation:
Given a can with:
• Height, h = 11.5 cm
,• Diameter = 10 cm
A can is in the shape of a cylinder; and the volume of a cylinder is calculated using the formula:
[tex]V=\pi r^2h[/tex]First, find the radius by dividing the diameter by 2.
[tex]r=\frac{10}{2}=5\;cm[/tex]Next, substitute r=5, h=11.5 and π=3.14 into the formula given above:
[tex]\begin{gathered} V=3.14\times5^2\times11.5 \\ =902.75\text{ cubic cm} \end{gathered}[/tex]The volume of the can is 902.75 cubic cm.
Given the parametric equations x = 7cos θ and y = 5sin θ, which of the following represents the curve and its orientation?
We have the following parameters
[tex]\begin{gathered} x=7cos\theta \\ y=5sin\theta \end{gathered}[/tex]the general equation of a circle with center (0,0) is the following,
[tex]x^2+y^2=r^2[/tex]Let's use the following tigonometric identity,
[tex]sin^2\theta+cos^2\theta=1[/tex]solving for cos and sin in the equations we are given,
[tex]cos\theta=\frac{x}{7},sin\theta=\frac{y}{5}[/tex]replace,
[tex](\frac{y}{5})^2+(\frac{x}{7})^2=1[/tex]Since we have two different numbers in the denominator, this is not a circle equation but an elipse, of the form,
[tex]\frac{y^2}{a^2}+\frac{x^2}{b^2}=1[/tex]where,
a is the vertex and,
b is the covertex
thus, in the x axis, the vertex is 7 and the y-axis the covertex is 5
Now, let's determine the direction by replacing
when Θ = 0 , then x = 7*cos0 = 7*1 = 7 , and y = 5*sin0 = 5*0 = 0
when Θ = 90° or π/2 , then x = 7*cos90° = 7*0 = 0 , and y = 5sin90° = 5*1 = 5
If we draw this, we can see that the direction is counterclockwise as in the bottom right image.
Consider the following word problem:Two planes, which are 1180 miles apart, fly toward each other. Their speeds differ by 40 mph. If they pass each other in 2 hours,what is the speed of each?Step 1 of 2: Use the variable x to set up an equation to solve the given problem. Set up the equation, but do not take steps to solve it.
So we have two planes flying toward each other. Let's use v for the speed of the slower plane. Then the speed of the faster plane is v+40. If we pass to the reference system of the slower plane we have that its speed is 0 and the speed of the other plane is v+v+40=2v+40. So basically we have a problem where one of the planes is stationary whereas the other approaches at 2v+40mph and it takes it 2 hours to travel 1180 miles. Remember that the speed is equal to the distance traveled divided by the time it took the plane to travel that distance. Then we get:
[tex]\begin{gathered} 2v+40\frac{mi}{h}=\frac{1180mi}{2h}=590\frac{mi}{h} \\ 2v=590\frac{mi}{h}-40\frac{mi}{h}=550\frac{mi}{h} \\ v=\frac{550\frac{mi}{h}}{2}=275\frac{mi}{h} \end{gathered}[/tex]Then we get:
[tex]v+40\frac{mi}{h}=275\frac{mi}{h}+40\frac{mi}{h}=315\frac{mi}{h}[/tex]Then the speeds of the planes are 275mph and 315mph.
Write the equation for the trigonometric graph.y= 8cos(pi/40x)y= –8sin(pi/40x)y= –8cos(pi/40x)y= 8sin(pi/40x)
Solution
For this case we can verify the answer using the point x= 0 if we replace we got:
y=8 cos (pi/40* 0) = 8 cos (0) = 8
y= -8 sin (pi/40 *0)= -8 sin(0) = 0
y= -8cos(pi/40*0)= -8 cos (0)= -8
y= 8 sin (pi/40 *0)= 8 sin(0) = 0
Then the correct option would be:
y= -8cos(pi/40*0)
What would you have to divide 584,900 by in order to have the 4 shift to the onesplace Explain your answer on the lines below.
in order to shift the 4 to the ones place, divide the given number 584,900 by 100. After dividing the the number 584,900 by 100, the new number is 584.900. It is clear that 4 is at ones olace.
what is 3/8 * 1/5 and 6/10 * 3/4
Answer
(3/8) × (1/5) = (3/40)
(6/10) × (3/4) = (9/20)
Explanation
We are asked to solve the given expressions
(3/8) × (1/5)
And
(6/10) × (3/4)
For (3/8) × (1/5)
[tex]\frac{3}{8}\times\frac{1}{5}=\frac{3\times1}{8\times5}=\frac{3}{40}[/tex]For (6/10) × (3/4)
[tex]\begin{gathered} \frac{6}{10}\times\frac{3}{4}=\frac{6\times3}{10\times4}=\frac{18}{40} \\ We\text{ can now reduce this to the simplest form} \\ \text{Divide numerator and denominator by 2} \\ \frac{18}{40}=\frac{9}{20} \end{gathered}[/tex]Hope this Helps!!!
20. Write the slope-intercept form of the line described in the followingPerpendicular to -2+3y=-15and passing through (2, -8)
The equation of a line in Slope-Intercept form is:
[tex]y=mx+b[/tex]Where "m" is the slope and "b" is the y-intercept.
Solve for "y" from the equation given in the exercise in order to write it in Slope-Intercept form:
[tex]\begin{gathered} -2+3y=-15 \\ 3y=-15+2 \\ y=-\frac{13}{2} \end{gathered}[/tex]You can notice that the equation has this form:
[tex]y=b[/tex]Where "b" is the y-intercept.
Then, it's a horizontal line, which means that its slope is:
[tex]m=0[/tex]Since it is a horizontal line, the lines perpendicular to that line is a vertical line, whose slope is undefined and whose equation is:
[tex]x=k[/tex]Where "k" is the x-intercept.
Knowing that the x-coordinate of any point on a vertical line is always the same, and knowing that this line passes through this point:
[tex]\mleft(2,-8\mright)[/tex]You can determine that the equation of the line is:
[tex]x=2[/tex]There were 18 students in a class taking a test. 4 students did pass the test. What percent did not pass the test.
Answer
Percent of students who did not pass the test = 77.8%
Explanation
The percent of an event is given as
[tex]\begin{gathered} \text{Percent of an event} \\ =\frac{\text{Number of elements in the event}}{Total\text{ number of elements}}\times100 \end{gathered}[/tex]For this question,
Percent of the event = Percent who did not pass the test = ?
Number of elements in the event
= Number of students who did not pass the test
= (Total number of students) - (Number of students who passed the test)
= 18 - 4
= 14
Total number of elements = Total number of students in the class = 18
Percent of students who did not pass the test
= (14/18) × 100%
= 0.778 × 100%
= 77.8%
Hope this Helps!!!
polynomials - diving polynomialssimplify the following expression with divisionbare minimum of steps
Which expression would be easier to simplify if you used the associativeproperty to change the grouping?
In option A, if expression is simplify with out using associative property then addition of 4/9 and -2/9 is easy, as compare to addition 6 and 4/9. So no need to apply associateive property to option A.
In option B, 60 and 40 can be easily add as compare to 40 and -27 so this expression do not need to apply associative property.
In option C, the expression is easier to simplify if 5/2 and -1/2 is added, which is possible if associative is apply to the expression.
[tex]\begin{gathered} (2+\frac{5}{2})+(-\frac{1}{2})=2+(\frac{5}{2}-\frac{1}{2}) \\ =2+(\frac{5-1}{2}) \\ =2+2 \\ =4 \end{gathered}[/tex]Thus option C use associative property to make the simplification easier.
Answer: Option C.
write the following basic forms in their single form
2√3
The expression which represents the written form of the basic form expression; 2√3 as a single form is; √12.
What is the single form expression which is equivalent to the basic form expression; 2√3?It follows from the task content that the basic form expression be written as it's equivalent single form expression.
Since the given radical expression is; 2√3; it follows that the expression can be written as a single form expression as follows;
First, the square of 2, 2² is equal to 4;
Hence, by the converse;
2 = √4.
The given expression can therefore be written as; √4 • √3.
The expression above can therefore be written in its single form as; √(4 × 3) = √12.
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Please help 100 points
Answer:
y = - 6x² - 12x + 2======================
GivenVertex of parabola = (- 1,8),Point on the graph = (0, 2).To findThe equation of the parabola in standard form.SolutionWe can represent the quadratic equation in vertex or standard forms.
Vertex form:
y = a(x - h)² + k, where (h, k) is the vertex, a- coefficientStandard form:
y = ax² + bx + c, where a and b are coefficients and c- constantUse the vertex form with given coordinates of the vertex:
y = a(x - (-1))² + 8 ⇒y = a(x + 1)² + 8Use the other point to find the value of a:
2 = a(0 + 1)² + 82 = a + 8a = - 6The equation is:
y = - 6(x + 1)² + 8Convert it to standard form:
y = - 6x² - 12x - 6 + 8y = - 6x² - 12x + 2Answer:
[tex]y=-6x^2-12x+2[/tex]
Step-by-step explanation:
Vertex form of a quadratic equation:
[tex]y=a(x-h)^2+k[/tex]
where (h, k) is the vertex.
Given:
Vertex = (-1, 8)Point on the curve = (0, 2)Substitute the given values into the vertex formula and solve for a:
[tex]\implies 2=a(0-(-1))^2+8[/tex]
[tex]\implies 2=a(1)^2+8[/tex]
[tex]\implies 2=a+8[/tex]
[tex]\implies a=-6[/tex]
Substitute the vertex and the found value of a into the vertex formula, then expand to standard form:
[tex]\implies y=-6(x-(-1))^2+8[/tex]
[tex]\implies y=-6(x+1)^2+8[/tex]
[tex]\implies y=-6(x^2+2x+1)+8[/tex]
[tex]\implies y=-6x^2-12x-6+8[/tex]
[tex]\implies y=-6x^2-12x+2[/tex]
Therefore, the quadratic function in standard form whose graph has the given characteristics is:
[tex]y=\boxed{-6x^2-12x+2}[/tex]
help 25 points
A line includes the points (10,6) and (2,7). What is its equation in point-slope form?
Use one of the specified points in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
Answer:
y = (-1/8)x + (29/4)
Step-by-step explanation:
(10, 6), (2, 7)
(x₁, y₁) (x₂, y₂)
y₂ - y₁ 7 - 6 1 -1
m = ------------ = ----------- = ----------- = ---------
x₂ - x₁ 2 - 10 -8 8
y - y₁ = m(x - x₁)
y - 6 = (-1/8)(x - 10)
y - 6 = (-1/8)x + (5/4)
+6 +6
-------------------------------
y = (-1/8)x + (29/4)
I hope this helps!
I need help question
Solution
- The first integral is bounded by the x-values of [6, 22]
- The second integral is bounded by the x-values of [6, 14]
- When we are asked to find the difference between the two integrals, since, they both begin at 6, it implies that, when the second integral is taken away from the first integral, there must be some extra x-values.
- The extra values are from 14 to 22.
- Thus, we have:
[tex]\int_6^{22}f(x)-\int_6^{14}f(x)=\int_{14}^{22}f(x)[/tex]Final Answer
[tex]\begin{gathered} b=22 \\ a=14 \end{gathered}[/tex]Tell whether the sequence is arithmetic. If it is what is the common difference? Explain.
{1, 5, 9, 13, …}
The sequence is arithmetic because the common difference is 4.
Answer:
the sequence is arithmetic. the cd is 4
Step-by-step explanation:
1 + 4 = 5
5 + 4 = 9
9 + 4 = 13
A baseball stadium has 50,100 seats. Each ticket for a seat costs $30. Tara created a function to model this situation and drew the graph of the function, where y represents profit from ticket sales, in dollars, given the number of tickets sold, x.
Is the graph function correct? why or why not?
The graph as shown in the image is the correct graph of the function.
What is the correct graph of the function?A function shows a mathematical relationship. We would need to look at the graph very closely so as to know weather or not the graph as it has been shown is the correct graph that is befitting of the function must be a straight line graph.
Clearly, the slope of the graph would be positive and beginning from the origin because the number of tickets that is sold is increasing just and the amount of the tickets is increasing. Thus the graph follows the general equation of a straight line; y = mx + c
All these goes to show that what we have befits the function.
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9(11 - x) = 3(3x -9) what is x
x = 7
Explanation:9(11 - x) = 3(3x -9)
Expanding the expression:
9(11) - (9x) = 3(3x) -3(9)
99 - 9x = 9x - 27
collect like terms:
99 + 27 = 9x + 9x
126 = 18x
Divide both sides by 18:
126/18 = 18x/18
x = 7
solve the following d. be sure to take into account whether a letter is capitalized or not .3y^3 ×m=5Qd
Step 1: Write out the equation.
[tex]3g^3+m=5Qd[/tex]Step 2: Divide both sides of the equation by 5Q, we have
[tex]\frac{3g^3+m}{5Q}=\frac{5Qd}{5Q}[/tex]this implies that
[tex]d=\frac{3g^3+m}{5Q}[/tex]Lesson 6.07: In a random sample of 74 homeowners in a city, 22 homeowners said they wouldsupport a ban on nonnatural lawn fertilizers to protect fish in the local waterways. The samplingmethod had a margin of error of +3.1%. SHOW ALL WORK!A) Find the point estimate.B) Find the lower and upper limits and state the interval.
Confidence interval is written in the form,
(point estimate +/- margin of error)
The given scenario involves population proportion
The formula for the point estimate is
p' = x/n
where
p' = estimated proportion of success. p' is a point estimate for p which is the true proportion
x represents the number of success
n represents the number of samples
From the information given,
n = 74
x = 22
p' = 22/74 = 0.297
The formula for finding margin of error is expressed as
[tex]\begin{gathered} \text{margin of error = z}_{\frac{\alpha}{2}}(\sqrt[]{\frac{p^{\prime}q^{\prime}}{n}} \\ q^{\prime}\text{ = 1 - p'} \\ q^{\prime}\text{ = 1 - 0.297 = 0.703} \end{gathered}[/tex]A) The point estimate is 0.297
B) margin of error = +/-3.1% = 3.1/100 = +/- 0.031
Thus,
the lower limit would be 0.297 - 0.031 = 0.266
Expressing in percentage, it is 0.266 x 100 = 26.6%
the upper limit would be 0.297 + 0.031 = 0.328
Expressing in percentage, it is 0.328 x 100 = 32.8%
Thus, the confidence interval is between 26.6% and 32.8%
-353-0-- * GR-35-21-2700-3s 6 - 2y-6- - +28+82-80 -592-35-07-2+27-35-30 9815+ Seesters << RB- --3-1-1-12) 6-5-3= LG - 5+13-2225 SVE -3-5y+6=-24 -*- 4y +50=-21 5r - 55 - 5 = 3r-S-=
Explanation:
5x - 4y + 2z = 21 ...equation 1
-x - 5y + 6z = -24 ....equation 2
-x - 4y + 5z = -21 ...equation 3
Using elimination method:
multiply equation 2 by 5:
-5x - 25y + 30z = -120 ....equation 2a
add equation 2a from 1:
5x - 5x -4y -25y + 2z + 30z = 21 - 120
0 - 29y + 32z = -99
-29y + 32z = - 99 ....equation 4
multiply equation 3 by 5:
-5x - 20y + 25z = -105 ...equation 3a
add equation 1 and 3a
5x - 5x - 4y - 20y + 2z +25z = 21 - 105
0 - 24y + 27z = -84
-24y + 27z = -84 ...equation 5
-29y + 32z = - 99 ....equation 4 (×-24)
-24y + 27z = -84 ...equation 5 (×-29)
696y - 768x = 2376 ...(4a)
696y -783x = 2436 ...(5a)
subtract 5a from 4a
696y - 696y -768x -(-783x) = 2376 - 2436
0 - 768x + 783x = -60
15x = -60
x = -60/15
x = -4
substitute for x in equation 4a:
696y - 768(-4) = 2376
696y + 3072 = 2376
696y = 2376 -3072
696y = -696
y = -696/696
y = -1
substitute for y in equation 4:
-29(-1) + 32z = -99
29 + 32z = -99
32z = -99 - 29
32z = -128
z = -128/32
z = -4
Help 20 points (show ur work)
There are 2 questions
The length of the trail is equal to 3mi and the selling price of the item is equal to $120.
RatioIn mathematics, a ratio shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six. Similarly, the ratio of lemons to oranges is 6:8 and the ratio of oranges to the total amount of fruit is 8:14.
In this question, we have to use the ratio given to determine the length of the trail.
Given that the ratio is 5in : 2mi, we have to convert the values to uniform units.
[tex]1mi = 63360in\\2mi = x\\x = 126720[/tex]
The ratio is now 5in : 126720in
Given that on the map, the length is 7.5in
[tex]5 = 126720\\7.5 = x\\x = 190080in[/tex]
Let's convert this into mi.
[tex]190080in = 3mi[/tex]
The actual length of the trail is 3in.
b)
To find the selling price of the item, let's use the percentage given to do that.
discount = 40%actual price = $200We can find 40% of 200 and then subtract the value from 200.
[tex]40\% of 200 = 0.4 * 200 = 80[/tex]
The discount price is $80 and we can find the selling price here.
[tex]selling price = actual price - discount price\\selling price = 200 - 80\\selling price = 120[/tex]
The selling price of the item is $120
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A boutique in Lanberry specializes in leather goods for men. Last month, the company sold 56 wallets and 63 belts, for a total of $3,920. This month, they sold 94 wallets and 22 belts, for a total of $3,230. How much does the boutique charge for each item?
Let w represent the cost of each wallet.
Let b represent the cost of each belt.
Last month, the company sold 56 wallets and 63 belts, for a total of $3,920. This means that
56w + 63b = 3920
This month, they sold 94 wallets and 22 belts, for a total of $3,230. This means that
94w + 22b = 3230
We would solve the equations by applying the method of elimination. To eliminate w, we would multiply the first equation by 94 and the second equation by 56. The new equations would be
5264w + 5922b = 368480
5264w + 1232b = 180880
Subtracting the second equation from the first, we have
5264w - 5264w + 5922b - 1232b = 368480 - 180880
4690b = 187600
b = 187600/4690
b = 40
Substituting b = 40 into 56w + 63b = 3920, we have
56w + 63(40) = 3920
56w + 2520 = 3920
56w = 3920 - 2520 = 1400
w = 1400/56
w = 25
Thus, the boutique charges $25 for each wallet and $40 for each belt
The inequality 3x +2> x+8 is equivalent to
A. x>-12
C. x > 3
B. x > 2/2/1
D. x <3
Answer: C
Step-by-step explanation:
3x + 2 > x +8
= 3x + 2 -2 > x + 8 -2
= 3x > x + 6
= 3x - x > x - x + 6
= 2x/2 > 6/2
= x > 3
Answer:
C
Step-by-step explanation:
It is the only one that makes sense.
pls mark brainlest with the crown
suppose s is between r and t use the segment addition postulate to solve for each variable RS equals 2z plus 6 St equals 4z - 3 RT = 5z + 12
If s is between r and t, then:
RS + ST = RT
Where RS = 2z + 6
ST = 4z - 3
RT = 5z + 12
So, we get:
(2z + 6) + (4z - 3) = 5z + 12
Solving for z, we get:
2z + 6 + 4z - 3 = 5z + 12
6z + 3 = 5z + 12
6z + 3 - 5z = 12
z + 3 = 12
z = 12 - 3
z = 9
Answer: z = 9
Sam rides at a rate of 14.5 miles per 1 hour. If he rides at a constant rate, how many miles would he ride in 1 hour and 15 minutes?
Sam would ride 18.125 miles when hw would ride at the rate of 14.5 miles/hour.
According to the question,
We have the following information:
Speed of Sam = 14.5 miles/hour
Distance to be covered = ?
Time taken to cover the distance = 1 hour and 15 minutes
Now, we will convert the time given in minutes into hour.
We have 15 minutes.
We know that 1 hour is equal to 60 minutes.
So, we will convert 15 minutes into hour:
15/60 hour
0.25 hour
So, the total time taken = (1 + 0.25) hour
Time taken = 1.25 hour
We know that the following formula is used to find the speed:
speed = distance/time
Distance = speed*time
Distance = 14.5*1.25
Distance = 18.125 miles
Hence, the distance covered by Sam in 1 hour and 15 minutes is 18.125 miles.
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Solving linear systems graphicallySolving 3 x 3 linear systemsModeling with linear systemsLinear programmingMixed degree systems
ANSWER:
The system can only be consistent and independent
STEP-BY-STEP EXPLANATION:
We have to:
• If a system has at least one solution, it is said to be consistent.
,• If a consistent system has exactly one solution, it is independent.
,• If a consistent system has an infinite number of solutions, it is dependent
,• If a system has no solution, it is said to be inconsistent
We know that the system has 2 solutions, and we know that the system is only inconsistent when it has no solution, therefore the correct answer is:
The system can only be consistent and independent
The sum of two numbers is 51. One number is 15 more than the other. What is the smaller number. Try solving this by writing a system of equations and substitution.
Let's convert the given relationships into an equation.
Let's name the two number x and y.
The sum of the two numbers is 51: x + y = 51
One number is 15 more than the other: x = y + 15
Using the equations that we generated from the given relationships, let's determine the value of the two numbers by substitution.
Let's substitute x = y + 15 to x + y = 51.
[tex]\text{ x + y = 51 }\rightarrow\text{ (y + 15) + y = 51}[/tex][tex]\text{ y + 15 + y = 51 }\rightarrow\text{ 2y = 51 - 15}[/tex][tex]\text{ 2y = 36 }\rightarrow\text{ y = }\frac{36}{2}[/tex][tex]\text{ y = 18}[/tex]Since we now get the value of y, y = 18, let's determine the value of x.
[tex]\text{ x = y + 15 }\rightarrow\text{ x = 18 + 15}[/tex][tex]\text{ x = 33}[/tex]Therefore, the value of the two numbers is 18 and 33.
A straight driveway is 87.0 ft long, and the top is 11.0 ft above the bottom. What angle does it make with the horizontal? ( Round to the nearest tenth
Let us begin by illustrating the problem using a diagram:
Here we have represented the angle that the driveway makes with the horizontal to be x
Step 1: Label the sides as shown:
Step 2: Using the sides given, find the required angle
The formula that relates the angle, opposite side and hypothenuse side is:
[tex]sin\theta\text{ = }\frac{opposite}{hypothenuse}[/tex]Applying the formula:
[tex]\begin{gathered} sinx\text{ = }\frac{11}{87} \\ sin\text{ x = 0.126437} \\ x\text{ }\approx\text{ 7.3}^0 \end{gathered}[/tex]Hence, it makes an angle of 7.3 degrees with the horizontal
Question 1-3
The distance traveled by car, for a duration of time, can be modeled with the equation s= 45t, where s is the distance, in miles, and it is
the time, in hours. Which graph represents this proportional relationship correctly?
120
105
90
Distance (mi)
Distance (mi)
75
60
45
120
30
105
90
15
75
60
45
30
0
15
2
Time (hr)
Time (hr)
100
lon
3
+X
X
120
105
90
Distance (mi)
75
60
45
30
15
0
1
2
Time (hr)
co
X
The equation s = 45t, where s is the distance in miles and it is the time in hours, can be used to simulate the distance driven by a car over a period of time then the car will travel 135 hours in 3 hours.
What is meant by the constant of proportionality?The ratio connecting two given numbers in what is known as a proportional relationship is the constant of proportionality. Constant ratio, constant rate, unit rate, constant of variation, and even rate of change are other names for the constant of proportionality.
Given: The distance traveled by car at a constant rate is proportional to the time spent driving.
In the equation d = 45 t, d denotes the distance (in miles) and t denotes the time (in hours).
d / t = 45 miles per hour
The constant of proportionality = 45 miles per hour.
Also, the distance traveled by car in 1 hour = 45 miles
The distance traveled by car in 3 hours = 3 × 45 = 135 miles
Therefore, a car will travel 135 hours in 3 hours.
The complete question is:
The distance traveled by car at a constant rate is proportional to the time spent driving. In equation d = 45t, d represents the distance (in miles) and t represents the time (in hours).
A. What is the constant of proportionality? _____ miles per hour
B. How far will the car travel in 3 hours? _______ miles
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which of the following properly describes "slope"? select all that apply. A. y2 - y1/ x2 - x1 B. x2-x1/y2-y1 C. run/rise D. rise/run E. ratio of change in y values (rise) for a segment of the graph to the corresponding change in x values (run)
The formula to calculate the slope is
[tex]m=\frac{y2-y1}{x2-x1}[/tex]A is right
also, the slope can be calculated with rise and run
[tex]m=\frac{rise}{run}[/tex]the correct formula is D.
and also apply E
the answer will be A,D and E
