Using the concept of scale, we find that the distance between Cleveland and Cincinnati on the first map (1 cm to 10 km) is 40 cm, equivalent to 400 km in real-world distance. On the second map with a scale of 1 cm to 50 km, the equivalent distance is calculated to be 8 cm.
To calculate the distance between Cleveland and Cincinnati on the second map, we use the concept of scale. On the first map, the scale is 1 cm to 10 km, and the distance is represented as 40 cm. Scaling this to the real-world distance gives us 40 cm × 10 km/cm = 400 km between the two cities.
Now, let's apply the second map's scale of 1 cm to 50 km. To find the corresponding map distance, we set up a proportion: 10 km/cm (first map) / 50 km/cm (second map) = 40 cm (distance on the first map) / X cm (distance on the second map). Simplifying this, we find that X = 40 cm ×(10 km/cm) / (50 km/cm) = 40 cm × 1/5 = 8 cm.
Therefore, the distance between Cleveland and Cincinnati on the second map, which has a scale of 1 cm to 50 km, would be 8 cm.
The order pair (5,6) is a solution of a direct variation equation.
The direct variation equation that is satisfied by this ordered pair is y = 6/5x
In order to find this, we start with the base equation for direct variation. We then plug in and solve for k.
y = kx
6 = k5
6/5 = k
And now we can use that to model all future direct variations with this.
y = 6/5x
Use this figure to find each ratio in simplest form.
We know that
triangles ADE and ABC are similar triangles
so, the ratios of their sides must be same
now, we will find value of sides
we are given
AD=12
DB=6
AE=14
EC=7
[tex]AB=AD+DB[/tex]
now, we can plug values
[tex]AB=12+6[/tex]
[tex]AB=18[/tex]
so, we can get ratio
[tex]\frac{DE}{BC} =\frac{AD}{AB}[/tex]
now, we can plug values
[tex]\frac{DE}{BC} =\frac{12}{18}[/tex]
So, the ratio in simplest form is
[tex]\frac{DE}{BC} =\frac{2}{3}[/tex]..............Answer
Theo had a balance of -$4 in his savings account. After making a deposit,he has $25 in his account. What is the overall change to his account?
the answer is $29 dollars! ! ! ! ! !
The overall change to theo's account was that he deposited 29$ to the account. Hope this helps :)
find the value of y if the line through the two given points is to have the indicated slope. (-3,y) and (-11,8), m = -2
[tex]\bf (\stackrel{x_1}{-3}~,~\stackrel{y_1}{y})\qquad(\stackrel{x_2}{-11}~,~\stackrel{y_2}{8})\\\\\\slope = m\implies\cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{8-y}{-11-(-3)}~~=~~\stackrel{m}{-2}\\\\\\\cfrac{8-y}{-11+3}=-2\implies \cfrac{8-y}{-8}=-2\implies 8-y=16\implies -8=y[/tex]
How do I round 24 and 80 percent to the nearest whole?
24 rounds to 25 and 80 stays the same
4. Part A. Find the value of x.
A) x=20
B) x=35
C) x=70
D) x=110
Part B. Find the measure of the unlabeled angle in the previous question.
A) 40°
B) 70°
C) 110°
D) 140°
Hey there!!
The measure of the unlabeled angle is ( x + y - 5 ) due to the vertically opposite angles.
We also know 2x = y due to vertically opposite angles
If we add up all the angles, we get 360 degrees.
Hence,
y + 2x + x + y - 5 + x + y - 5 = 360
4x + 3y - 10 = 360
Add 10 on both sides
4x + 3y = 370
We know 2x = y
Hence,
4x + 3y = 370 can be broken down as ,
4x + y + y + y = 370
4x + 2x + 2x + 2x = 370
10x = 370
x = 370 / 10
x = 37
The unknown angle = x + y - 5
x + 2x - 5
3x - 5
3 ( 37 ) - 5
111 - 5
106
Hence, the unknown angle is 106°
Hope my answer helps!!
Consider the following functions that represent cost and revenue for the band's sales of spirit mugs.
f(x)=100+3x
g(x)=8x
a. Which function represents the cost function?
b. Which function represents the revenue function?
c. How can the functions be combined to create profit function?
d. Write the profit function.
Answer(a):
We have been given two functions f(x)=100+3x and g(x)=8x.
Now we need to decide which one of them is cost function and which one is the revenue function.
We know that production usually involves fixed cost for operating the production so usually that is of the form y=mx+b.
Hence f(x)=100+3x is the cost function
Answer(b):
Then g(x)=8x is the revenue function.
Answer(c):
We know that profit function is the difference of revenue and cost
Profit = Revenue - Cost
P(x)= g(x) - f(x) =8x-(100+3x)
P(x)= 8x-100-3x
P(x)= 5x-100
Hence P(x)= 5x-100 is the profit function.
Answer(d):
P(x)= 5x-100 is the profit function.
How is a table helpful when constructing equations
Its helpful because it gives you the number to put in and to find the unit rate
Tables aid in constructing equations by facilitating the organization and visualization of mathematical data. This makes it easier to apply given parameters to equations and to understand their behavior. For instance, an equilibrium state can be visually represented in a table.
Explanation:A table is incredibly helpful when constructing equations because it aids in the organization and visualization of mathematical data. Through the usage of tables, one can clearly list and categorize known values that might be used in an equation, thereby making it easier to identify what needs to be solved. For instance, if you're given multiple variables and constants in a word problem, a table can be used to order these parameters systematically so they can be more easily applied into constructing equations.
Similarly, tables contribute to expressing equations visually as they can illustrate changes in variable values, which can further assist in understanding the behavior of the equation. An equilibrium state, for instance, can be clearly italicized in a table to visually represent the point where an equation balances, which would be harder to see in text form.
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Vertex of f(x)=x^2+12x+8
the vertex is (-6,-28). let me know if i'm wrong
I have a ring for each finger of both hands. I want to buy 4 more rings. How many rings will I have then?
you will
have 14 rings
you will have 14 rings, because you have ten fingers, and ten plus 4 is 14.
hope it helps.
the graph of a quadratic function has a vertex ar (3,-6). One point of the graph is (7,10). What is another point on the graph?
Answer:
y + 6 = (x -3)^2
Step-by-step explanation:
Let's use the general form of the vertex equation of a quadratic: y - k = a(x - h)^2.
Subst. 10 for y, 7 for x, -6 for k and 3 for h. Then, 10 + 6 = a(7 - 3)^2, or
16 = a(4)^2, or 16 = a(16). Thus, a = 1, and the equation of this particular parabola is:
y + 6 = (x -3)^2
Given a quadratic function with a vertex at (3,-6) and a point (7,10), by substituting the values into the equation, we find that another point on the graph is (4,-5).
The vertex form of a quadratic function is [tex]\(y = a(x - h)^2 + k\)[/tex], where (h, k) is the vertex of the parabola. In this case, the vertex is (3, -6), so the equation is [tex]\(y = a(x - 3)^2 - 6\).[/tex]
You're also given a point on the graph, which is (7, 10). You can use this point to find the value of a.
Substitute the point's coordinates into the equation and solve for a:
[tex]\(10 = a(7 - 3)^2 - 6\)[/tex]
[tex]\(10 = a(4^2) - 6\)[/tex]
10 = 16a - 6
Now, isolate a:
16a = 10 + 6
16a = 16
a = 1
Now that you know a = 1, you can use this information to find another point on the graph. Simply plug in a different value for x into the equation. Let's choose x = 4 for example:
[tex]\(y = 1(4 - 3)^2 - 6\)[/tex]
y = 1(1) - 6
y = 1 - 6
y = -5
So, another point on the graph is (4, -5).
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If the product ab is 0, then either a or b must be
i need help solving x^2-2=7 by factoring
x^2-2=7
Subtract 7 from both sides
x^2-2-7=7-7
x^2-9=0
x^2-3^2=0
Using a^2-b^2=(a+b)(a-b)
Where a=x and b=3
(x-3)(x+3)
Which is the equation of the graphed line written in standard form? y = x x – 1/2y = 0 x – y = 0 y =1/2x
The standard for of this equation is x – y = 0
Firstly, options A and D are not in standard form, so they are not options.
To decided between B and C, we choose a point on the line and see if it works. For example, we'll use (2, 2).
x – y = 0
2 - 2 = 0
0 = 0
This is true for option C. Therefore, it is correct.
Answer:
C.
Step-by-step explanation:
Edgen 2023
Devyn sold 15 boxes of cookies this week. This is 7 more than he sold last week. How many boxes did he sell last week?
8, 15 - 7 = 8 thats correct
multiply(-17)-(-6) i need this answer like now
If you mean -17 times -6 then the answer is a positive 102
Joanne is campaigning for class president and plans to distribute some campaign materials. 20 flyers and 16 buttons. She wants each classroom to receive an identical set of campaign materials without having any materials left over. What is the greatest number of classrooms Joanne can distribute materials to?
Joanne can distribute her campaign materials to 4 classrooms. Each classroom would get 5 flyers and 4 buttons.
Explanation:The subject of this question is Mathematics, specifically it deals with the topic of finding the greatest common divisor (GCD). In this scenario, Joanne has 20 flyers and 16 buttons she wants to distribute evenly amongst classrooms. The greatest number of classrooms she can distribute materials to is found by determining the GCD of 20 (the number of flyers) and 16 (the number of buttons). The GCD of 20 and 16 is 4. Therefore, Joanne can distribute her campaign materials to a maximum of 4 classrooms without any materials being left over. It is important to note that, in each classroom, there would be 5 (20/4) flyers and 4 (16/4) buttons.
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What is the distance (in units) between points C and D round your answer to the nearest hundredth
Coordinates of C: (-5,-1)
Coordinates of D: (0,3)
Distance formula:
[tex]d = \sqrt({x2 - x1)^2 + (y2 - y1)^2}[/tex]
--> [tex]\sqrt{(0 - (-5))^2 + (3 - (-1))^2}[/tex]
---> [tex]\sqrt{5^2 + 4^2}[/tex]
----> [tex]\sqrt{25 + 16} = \sqrt{41}[/tex]
The distance rounded to the nearest tenth is 6.40 units.
FIND THE MEAN OF THE DATA SET ROUND TO THE NEAREST TENTH IF NEED BE
15.8 14.9 16.7 17.6 13.4
First add all the numbers in the data:
15.8 + 14.9 + 16.7 + 17.6 + 13.4 = 78.4
Divide by how many numbers are in the data set there is 5 so:
78.4 ÷ 5 = 15.7
The mean is 15.7
Angle (<) E and <F are vertical angles. If m<E = 17x+1 and m<F =20x-14, find m<F.
The vertical angles theorem states that vertical angles are congruent to each other. Since angles E and F are vertical angles, this means you can make them equal to each other in an equation.
m∠E = m∠F
17x + 1 = 20x - 14
Subtract 20x from both sides.
-3x + 1 = -14
Subtract 1 from both sides.
-3x = -15
Divide both sides by -3.
x = 5
Substitute 5 for x in m∠F (20x - 14).
20(5) - 14 = 86
m∠F = 86°
A toll collector on a highway receives $8 for trucks and $3 for sedans. At the end of a 2 hour period, she collected $128. How many trucks and sedans passed through the toll booth during that period?
There are infinitely many combinations of trucks and sedans that could have passed through the toll booth to collect a total of $128 in 2 hours.
Let's assume the number of trucks that passed through the toll booth in the 2-hour period is represented by 't', and the number of sedans is represented by 's'.
According to the given information, the toll collector received $8 for each truck and $3 for each sedan. We can write two equations based on the total amount collected and solve them simultaneously.
The total amount collected from the trucks:
Amount from trucks = $8 × number of trucks = 8t
The total amount collected from the sedans:
Amount from sedans = $3 × number of sedans = 3s
We are also given that the toll collector collected a total of $128 in 2 hours. So we can write the equation:
Amount from trucks + Amount from sedans = $128
8t + 3s = 128
Now, we need to solve the above two equations simultaneously to find the values of 't' and 's'.
To solve these equations, we can use a method called substitution. Let's solve for 't' in terms of 's' using the first equation:
8t = 128 - 3s
t = (128 - 3s)/8
Now we substitute this value of 't' in the second equation:
8(128 - 3s)/8 + 3s = 128
128 - 3s + 3s = 128
128 = 128
We see that both 's' and 't' have been eliminated from the equation, and we are left with 128 = 128. This means the value of 's' can be any number, as long as it satisfies the equation.
Therefore, there are infinitely many combinations of trucks and sedans that could have passed through the toll booth to collect a total of $128 in 2 hours.
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Nick and Adam workout together. Nick weighs 160 pounds and is gaining 3 pounds per week. Adam weighs 195 pounds and is losing about 2 pounds each week. write an equation that can be used to find the number of weeks that it will take them to weigh the same amount.
Answer:
7
Step-by-step explanation:
assign the amount of weeks to x. then we write the equation 160+3x=195-2x which is 7
The equation that can be used to find the number of weeks it will take them to weigh the same amount is 160 + 3w = 195 - 2w , and it will take them 7 weeks to weigh the same amount.
Determining the equation and time for the weight to be equalLet's take w as the weight,
Nick's weight after w weeks: 160 + 3w
Adam's weight after w weeks: 195 - 2w
Since they will weigh the same after w weeks, you can set up the equation:
160 + 3w = 195 - 2w
Now, solve for w:
Combine like terms:
3w + 2w = 195 - 160
5w = 35
Divide both sides by 5 to isolate w:
w = 35 / 5
w = 7
So, it will take them 7 weeks to weigh the same amount.
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What’s the product of -2(-3.4)
Find the measure of two supplementary angles, ∠A and ∠B, if m∠A = (3x – 7)° and m∠B = (2x + 2)°. =180
Answers:
Angle A = 104 degrees
Angle B = 76 degrees
=================================
Supplementary angles add to 180 degrees.
A+B = 180
(3x-7)+(2x+2) = 180
5x-5 = 180
5x-5+5 = 180+5 ... add 5 to both sides
5x = 185
5x/5 = 185/5 .... divide both sides by 5
x = 37
Use x =37 to find
Angle A = 3x-7 = 3*37-7 = 111-7 = 104 degrees
Angle B = 2x+2 = 2*37+2 = 74+2 = 76 degrees
As a check: A+B = 104+76 = 180 so that helps confirm the answer
The measure of supplementary angle ∠A is 107 degrees and the measure of supplementary angle ∠B is 76 degrees. We get these values by setting up an equation based on the fact that the sum of the measures of two supplementary angles is 180 degrees, solving for x, and then substituting x back into the original equations.
Explanation:In this problem, we're asked to find the values of the supplementary angles ∠A and ∠B. The measure of a supplementary angle is based on the concept that the sum of the measures of two supplementary angles is 180 degrees. We can form an equation since we know m∠A + m∠B = 180°. This translates to (3x – 7)° + (2x + 2)° = 180°. To solve the equation, consolidate like terms, so 5x - 5 = 180. Add 5 to both sides of the equation to find that 5x = 185. Dividing both sides of the equation by 5, we find that x = 37. Substitute x = 37 back into the original equations for m∠A and m∠B to find m∠A = 3*37 - 7 = 107 degrees, and m∠B = 2*37 + 2 = 76 degrees.
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Drag each figure to show if it is similar to the figure shown or why it is not similar
Answer:
this box will show you the answer
Step-by-step explanation:
Thank Natalie222 for the answer its 6x10 not 6x3 :3
What’s the square root of pie
Answer:
l
Step-by-step explanation:
write the equation for the inverse of the function y=Cos^-1(x-pi)
we are given
[tex]y=cos^{-1}(x-\pi)[/tex]
Since, we have to find inverse function
step-1:
Set y=f(x)
It is already there
step-2:
Switch x and y
[tex]x=cos^{-1}(y-\pi)[/tex]
step-3: Solve for y
We can take cos on both sides
[tex]cos(x)=cos(cos^{-1}(y-\pi))[/tex]
we can simplify it
[tex]cos(x)=y-\pi[/tex]
now, we can solve for y
[tex]cos(x)+\pi=y-\pi+\pi[/tex]
[tex]cos(x)+\pi=y[/tex]
[tex]y=\pi +cos(x)[/tex]..............Answer
Answer:
The answer is C
Step-by-step explanation:
Kelsey has saved $35 towards the cost of A $390 video game in the weeks to come she plans to save in additional $10 per week use unit analysis to represent them out just saved after W weeks and identify the units for the expression
390-35=355
355-10w
355/10=35.5
355-10(35.5)
35 and a 1/2 weeks
36 weeks to have the full amount needed
Answer:
36th weeks
Step-by-step explanation:
Kelsey has saved $35 to buy a video game worth $390.
She plans to save additional $10 per week.
Let w represents number of week.
Let s represents total saving in w weeks.
Addition saving per week = $10
In w weeks saving = 10w
Previous saving amount = $35
Total saving in w week, s = 35 + 10w
Expression which represents total saving in w weeks
s = 35 + 10w
Now find number of weeks to save $390
So, put s=390 and solve for w
35 + 10w = 390
10w = 390 - 35
w = 355÷10
w = 35.5
Hence, Kelsey will save $390 in 36th weeks.
What fractions are equivalent to 10/14
The answer to your question is,
5/7.
-Mabel <3
0.38 times 15 1/3 in the simplest form . Explain how you got the answer you got
You get 1 9/10. You can change 0.38 to 38/100 which simplifies to 19/50. Then u can change 15 1/3 to an improper fraction. You get 46/3. Then multiply 19/50 by 46/3 and you get 19/10 which simplifies to 1 9/10.