The distance between car B's original point and the point where car A and car B pass each other is 20 miles, given the speed of car A is twice the speed of car B, and they are 60 miles apart initially.
We assume the speed of car B to be x miles/hour.
Given car A going at twice the speed of car B, the speed of car A = 2x miles/hour.
When moving toward each other, the relative speed of the cars is the sum of their speeds.
Therefore, the relative speed = x + 2x miles/hour = 3x miles/hour.
The total distance between the cars is given as 60 miles.
Therefore, the time taken by car A and car B to reach the same point = 60/3x hours = 20/x hours.
Therefore, the distance from car B's original point and the point where car A and car B pass each other = Speed of car B*Time = x*(20/x) miles = 20 miles.
Therefore, the distance between car B's original point and the point where car A and car B pass each other is 20 miles, given the speed of car A is twice the speed of car B, and they are 60 miles apart initially.
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what is -3 plus 1/2 ?
Answer:
-2.5
Step-by-step explanation:
Answer:
-5/2 or -2.5
you can type it in a calculator
Identify the domain and range of
each function.
y = 3.5x
The domain of this function is
The range of this function is
DONE
Answer:
Domain: [tex](-\infty, \infty)[/tex]Range: [tex](0, \infty)[/tex]Step-by-step explanation:
The domain of an exponential function is all real numbers.
The range of an exponential function that has not been vertically shifted is [tex](0, \infty)[/tex].
The domain of the function is all the real numbers and the range of the function is set of all positive real numbers
What are domain and range?The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.
The range is the set of outputs of a relation or function. In other words, it's the set of possible y values. Recall that ordered pairs are of the form (x,y) so the y coordinate is listed after the x. The output is listed after the input.
Given data ,
The domain of the given function is all real numbers. In other words, there are no restrictions on the possible values of x that we can plug into the function.
To see why, note that we can raise any real number to any power, so there are no values of x that are off-limits for this function.
The range of the function is all positive real numbers.
This is because the base of the exponential function is 5, which is positive, and raising 5 to any power results in a positive number. Multiplying a positive number by 3 also results in a positive number, so the function output is always positive.
Hence , we can write the domain and range of the function as:
Domain: all real numbers
Range: y > 0 (all positive real numbers)
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GD Simpinying Radicals Simplify the number into simplest radical form. Use the factor tree to help determine the factors. √96 Warm-Up √6 O 2√6 0 4√6 0 4√3 Intro O Select a composite number to break into factors. Continue factoring until all factors are prime. 96 Done GD Simpinying Radicals Simplify the number into simplest radical form . Use the factor tree to help determine the factors . √96 Warm - Up √6 O 2√6 0 4√6 0 4√3 Intro O Select a composite number to break into factors . Continue factoring until all factors are prime . 96 Done
Answer:
Step-by-step explanation:
What’s the sum of square root of square root of -2
The sum of the square root of -2 and -18 is 4i√2
How to determine the sum of square rootFrom the information given,
The sum square root of -2
√-2 + √-18
√-2 = √(-1*2) = √-1 * √2 = i√2 Note that the square root of -1 = i
√-18 = √(-1*18) = √-1 * √1`8 = i√18 Note that the square root of -1 = i
But we have that
√18 = √(9*2)
Using surd form. we have
= √9 * √2= 3√2
Then,
√-18 = i√18= i(3√2) = 3i√2
Let's add the sum of square root, we have
√-2 + √-18 = i√2 + 3i√2 = (i + 3i)√2 = 4i√2
Therefore, the sum of the square root of -2 and -18 is 4i√2
The complete question is;
What is the sum of square root of -2 and square root of -18?
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In a movie, a child who was 32 inches tall was ''blown up'' to be 160 feet tall. Find the scale factor (unitless) needed for the props in the movie. (12 inches:1 foot)
Answer:
60 or 60:1 (Depending on the answer choices)
Step-by-step explanation:
160 feet = 1920 inches (160 * 12)
[tex]\frac{1920}{32} = \frac{60}{1}[/tex]
The scale factor required will be 1:60 or 60:1 (actual:movie or movie:actual).
What is a scale factor?The scale factor is the simplest ratio between the actual and the model's size of the same object.
How to solve the question?In the question, we are informed that in a movie, a child who was 32 inches tall was ''blown up'' to be 160 feet tall.
We are asked to determine the scale factor needed for the props in the movie.
To find the scale factor, we first find the size of the child in the movie in inches.
Size = 160 feet = 160*12 inches = 1920 inches.
Now, the scale factor is calculated as the ratio of the actual size to the size in the movie, that is,
Scale factor = 32:1920 = 32/1920 = 1:60.
Therefore, the scale factor required will be 1:60 or 60:1 (actual:movie or movie:actual).
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Sketch the region that is common to the graphs of x ≥ 2,
y ≥ 0, and x + y ≤ 6, and find its area.
a. Find the graph of their common region in the attachment
b. The area of the common region of the graphs is 8 units²
a. How to sketch the region common to the graphs?Since we have x ≥ 2, y ≥ 0, and x + y ≤ 6, we plot each graph separately and find their region of intersection.
The graph of x ≥ 2 is the region right of the line x = 2.The graph of y ≥ 0 is the region above the line y = 0 or x-axis.To plot the graph of x + y ≤ 6, we first plot the graph of x + y = 6 ⇒ y = -x + 6. Then the graph of x + y ≤ 6 is the graph of y ≤ - x + 6.So, the graph of x + y ≤ 6 is the region below the line y = - x + 6
From the graph, the regions intersect at (2, 0), (2, 4) and (6, 0)
Find the graph of their common region in the attachment
b. The area of the common regionFrom the graph, we see that the common region is a right angled triangle with
height = 4 units and base = 4 unitsSo, its area = 1/2 × height × base
= 1/2 × 4 units × 4 units
= 1/2 × 16 units²
= 8 units²
So, the area of the common region of the graphs is 8 units²
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Evaluate the function g (x)=6x^(2) at x=2. (need answer within 10 min)
Answer:
24
Step-by-step explanation:
If x were to be 2, then we need to substitute the 2 in for x
So, it would be 6(2)^2
2 times 2 is 4 and 4 times 6 is 24
Hope this helped! :)
f(x)
121x
10
8
co to
6-
**
--6-5-4-3-2-12
6449
-4
-6
-10-
-12-
geg
5 6 x
Which statement is true regarding the functions on the
graph?
Of(2)= g(2)
Of(0) = g(0)
Of(2)= g(0)
Of(0) = g(2)
Answer: f(2)=g(2)
Step-by-step explanation:
The graphs intersect at x=2.
The correct statement which is true regarding the functions on the graph is,
f (2) = g (2)
We have to given that,
Graph of functions f (x) and g (x) are shown in figure.
Now, From the graph,
At x = 2;
f (2) = 0
And, At x = 2;
g (2) = 0
Therefore, At x = 2,
f (2) = g (2) = 0
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Which statement is correct?
(2.06 times 10 Superscript negative 2 Baseline) (1.88 times 10 Superscript negative 1 Baseline) less-than StartFraction 7.69 times 10 Superscript negative 2 Baseline Over 2.3 times 10 Superscript negative 5 Baseline EndFraction
(2.06 times 10 Superscript negative 2 Baseline) (1.88 times 10 Superscript negative 1 Baseline) greater-than-or-equal-to StartFraction 7.69 times 10 Superscript negative 2 Baseline Over 2.3 times 10 Superscript negative 5 Baseline EndFraction
(2.06 times 10 Superscript negative 2 Baseline) (1.88 times 10 Superscript negative 1 Baseline) greater-than StartFraction 7.69 times 10 Superscript negative 2 Baseline Over 2.3 times 10 Superscript negative 5 Baseline EndFraction
(2.06 times 10 Superscript negative 2 Baseline) (1.88 times 10 Superscript negative 1 Baseline) = StartFraction 7.69 times 10 Superscript negative 2 Baseline Over 2.3 times 10 Superscript negative 5 Baseline EndFraction
The correct statement is [tex](2.06 * 10^{-2})(1.88 * 10^{-1}) < \frac{7.69 * 10^{-2}}{2.3* 10^{-5}}[/tex]
How to determine the correct statement?The proper form of the question is added as an attachment
The expressions are given as:
[tex](2.06 * 10^{-2})(1.88 * 10^{-1})[/tex]
[tex]\frac{7.69 * 10^{-2}}{2.3* 10^{-5}}[/tex]
Evaluate both expressions
[tex](2.06 * 10^{-2})(1.88 * 10^{-1}) = 2.06 * 1.88 * 10^{-2-1}[/tex]
[tex](2.06 * 10^{-2})(1.88 * 10^{-1}) = 3.87 * 10^{-3[/tex]
[tex]\frac{7.69 * 10^{-2}}{2.3* 10^{-5}} = \frac{7.69}{1.88} * 10^{5-2[/tex]
[tex]\frac{7.69 * 10^{-2}}{2.3* 10^{-5}} = 4.09 * 10^3[/tex]
By comparing both expressions, we have:
[tex]3.87 * 10^{-3} < 4.09 * 10^3[/tex]
This means that:
[tex](2.06 * 10^{-2})(1.88 * 10^{-1}) < \frac{7.69 * 10^{-2}}{2.3* 10^{-5}}[/tex]
Hence, the correct statement is [tex](2.06 * 10^{-2})(1.88 * 10^{-1}) < \frac{7.69 * 10^{-2}}{2.3* 10^{-5}}[/tex]
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Can someone help with this
The measure of angle B = 31 degrees, measure of angle C
= 121 degrees, and b = 9. Then a =
to the
nearest tenth.
A sports team came to town. the stadium filled all 10,000 seats at two-level pricing. level 1 tickets are $50 each, and level 2 tickets are $150 each. the stadium made $75,000 in ticket sales. the system of equations that models this scenario is: x + y = 10,000 50x + 150y = 75,000 what do the x and y represent in the system?
x represents the number of tickets of level 1 and y represents the number of tickets of level 2 in the system given that there are 10,000 seats, level 1 tickets are $50 each, and level 2 tickets are $150 each and equation representing the situation:x + y = 10,000, 50x + 150y = 75,000. This can be obtained by understanding the question and observing the equations.
What do the x and y represent in the system?Given that total number of seats is 10,000 and there are two levels pricing.
Thus by observing the equation, x + y = 10,000,
10,000 is the sum of 2 variable which obviously will be the number of tickets in level 1 and number of tickets in level 2.
Since there are two level pricing,
50x + 150y = 75,000 represent the addition of total cost of tickets of level 1 and 2.
Hence x represents the number of tickets of level 1 and y represents the number of tickets of level 2 in the system given that there are 10,000 seats, level 1 tickets are $50 each, and level 2 tickets are $150 each and equation representing the situation:x + y = 10,000, 50x + 150y = 75,000.
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(PLEASE HELP I WILL MARK BRAINLIEST)
Dilate the figure by the scale factor. Then enter
the new coordinates.
K = 3
C(-4,-2)
A' = ([?],
B' = ([],
B (3-1) C'=(,
A(1,2)
Hint: To calculate the
x-value of A', multiply the
x-value of A by 3.
Answer:
A' = (3, 6)
B' = (9, -3)
C' = (-12, -6)
Step-by-step explanation:
you can mulitply both the x and y coordinates of each point by the scale factor (3)
point (1, 2) becomes point (3, 6)
(3, -1) becomes (9, -3)
(-4, -2) becomes (-12, -6)
hope this helps!! have a lovely day :)
{this is why whoever wrote the problem gave that hint--you can follow through on that logic, but just remember that it has to be a scaled version of the original figure--so the ratios between points (and x/y values) must be consistent}
I am drinking beer and you are drinking light beer. Your light beer is 1/3 less filling than my regular beer. I drink 3 beers. How many do you have to drink to be equally full
Using proportions, it is found that you have to drink 9 beers to be equally full.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
Your drink is 1/3 less filling, hence you have to drink 3 times the amount I drink to be equally full. I drink 3 beers, hence the number you drink is given as follows:
N = 3 x 3 = 9 beers.
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Which rectangular equation represents the parametric equations x =t superscript one-half and y = 4t?
2 dogs, 4 horses 1 giraffe and a duck are lying on the bed. 3 chickens are flying over a chair. How many legs are on the ground?.
(x + 2)*(x^2 -2*x+4) - (x^3 -12)
Answer:
[tex] \large{ \boxed{ \tt{20}}}[/tex]- Please see the attached picture for full solution!:)
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If Colorado Springs, Colorado, has 1.2 times as many days of sunshine as Boston, Massachusetts, how many days of sunshine does each city have if there are a total of 482 days of sunshine between the two in a year?
Colorado and Boston have 263 and 219 days of sunshine respectively.
What is the solution to the Equation?Let the number of days of sunshine in Colorado is x and the number of days of sunshine in Boston is y.
Total number of days of sunshine=482
Also, the number of days of sunshine in Colorado is 1.2 times the number of days of sunshine in Boston.
So, the equation is formed as follows:
x+y=482 -(1)
The other equation is formed as:
x=1.2y -(2)
Substitute the value x from equation (2) in (1),
1.2y+y=482
2.2y=482
y=482/2.2
y=219
Substitute the value of y in equation (1),
x+219=482
x=482-219
x=263
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The large rectangle below represents one whole.
What percent is represented by the shaded area?
Answer:
40%
Step-by-step explanation:
so have 5 rectangles in a whole.we also have 2 shaded potions in that whole which represents 2/5 shaded potions.2/5 in fraction =0.4Now Change 0.4 to percentage by multiplying 0.4 by 1000.4 x 100 = 40Therefore the percentage represented by the shaded area is 40% Hope this helps.Good luck ✅.jurgen cuts 5 metre-long timber beam into 3 pieces,first piece 2.34metres second piece 1.85 work out the length of the third piece
The length of the third piece is 0.81 m if the Jurgen cuts 5 meter-long timber beam into 3 pieces, the first piece 2.34metres second piece 1.85.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
We have:
Jurgen cuts 5 meter-long timber beam into 3 pieces, first piece 2.34metres second piece 1.85.
Let the length of the third piece is x m.
2.34 + 1.85 + x = 5
4.19 + x = 5
x = 0.81 m
Thus, the length of the third piece is 0.81 m if the Jurgen cuts 5 meter-long timber beam into 3 pieces, the first piece 2.34metres second piece 1.85.
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Leslie has 24 coins. They are all nickels and dimes. The total value of the coins is $1.85. How many dimes does Leslie have? Which of the following systems is correct for
this situation?
The number of dimes is 13.
The system of equation for the situation is as follows;
x + y = 24
0.1x + 0.05y = 1.85
How to solve system of equation?The coins are 24.
Therefore, they are all dimes and nickel.
Total value of the coins is $1.85.
Hence, let
x = number of dimes
y = number of nickels
Therefore,
x + y = 24
0.1x + 0.05y = 1.85
0.1x + 0.1y = 2.4
0.1x + 0.05y = 1.85
0.05y = 0.55
y = 0.55 / 0.05
y = 11
x = 24 - 11
x = 13
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How many revolutions will a car wheel of diameter 22 in. make as the car travels a distance of one mile
It would be take upto 999 revolutions.
Let try to solve it,
Let n represent number of revolutions.
We are asked to find the number of revolutions it will take for a car wheel of diameter 30 in. to travel a distance of one mile.
1 mile = 63360 inches.
We will use circumference of circle formula to solve our given problem.
Circumference = pi*d , where, D represents diameter of circle.
Now, we will set the product of n and circumference of circle equal to 63360 inches as:
pi*22*n= 63360
n= 63360*7/ 22*22
n= 443520/444
n= 998.91
Therefore It would be take upto 999 revolutions.
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The atmospheric pressure at sea level is 14.7lb / i * n ^ 2 This pressure is reduced by half for each 3.6 miles above sea level Which graph correctly identifies the amount of atmospheric pressure based on height, in miles, above sea level?
Answer:graph b
Step-by-step explanation:
Joe used random numbers to select boys from the alphabetized
version of the list shown to make a sample. The random numbers
were 17, 5, 1, and 12, so he selected the 17th, 5th, 1st, and 12th
names. Who was selected?
Alan, Craig, Dale, Eddie, Eugene, Glenn, Herbert, Howard, Jeremy,
Loren, Louis, Martin, Nathan, Randy, Ray, Russell, Sam, Steve, Victor,
Vincent
OA) Glenn, Howard, Nathan, Steve
OB) Craig, Eugene, Loren, Vincent
OC) Jeremy, Martin, Steve, Victor
OD) Alan, Eugene, Martin, Sam
Based on the numbers that Joe selected, the people selected were D) Alan, Eugene, Martin, Sam.
Who was selected?The 17th person was selected and if we assigned numbers from 1 to 20 to the alphabetized list, we would find that number 17 is Sam.
The 5th person is Eugene and the 1st person is Alan. The 12th person is Nathan.
In conclusion, option D is correct.
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Identify the type of function represented by f(x)=1/2(3)^x
A. increasing linear
B. exponential decay
C. decreasing linear
D. exponential growth
The function represented by f(x) = (1/2)(3)ˣ is an exponential growth
What is an equation?An equation is an expression that shows the relationship between two numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.
The independent variable in the function f(c) = 2c + 9 is c whereas the dependent variable is f.
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The independent variable in the function f(c) = 2c + 9 is c whereas the dependent variable is f.
What is an equation?An equation is an expression that shows the relationship between two numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.
An exponential function is in the form:
y = abˣ
Where a is the initial value and b is the multiplication factor.
If b > 1, it is an exponential growth but if b < 1, it is an exponential decay.
Given the function:
f(x) = (1/2)(3)ˣ
since 3 > 1, it is an exponential growth.
The function represented by f(x) = (1/2)(3)ˣ is an exponential growth
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A bicycle manufacturing company makes a particular type of bike. Each child bike requires 4 hours to build and 4 hours to test. Each adult bike requires 6 hours to build and 4 hours to test. With the number of workers, the company is able to have up to 120 hours of building time and 100 hours of testing time for a week. If c represents child bikes and a represents adult bikes, can the company build 10 child bikes and 12 adult bikes in a week. (2 points) Group of answer choices No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100 No, because the bike order does not meet the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100 Yes, because the bike order meets the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100 Yes, because the bike order meets the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100
The company cannot build 10 child bikes and 12 adult bikes No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100 , Option A is the correct answer.
What is System of Inequality ?System of inequality represent system of inequalities that satisfies common condition.
It is given that
Each child bike requires 4 hours to build and 4 hours to test.
Each adult bike requires 6 hours to build and 4 hours to test.
Total building hours = 120
Total testing hours = 100
If c represents child bikes and a represents adult bikes, can the company build 10 child bikes and 12 adult bikes in a week.
6a + 4c ≤ 120
4a +4c ≤100
On solving this system of Inequality
a ≤ 10
which is less than required , and so
No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100
Therefore Option A is the correct answer.
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how does the distance you determined in part c change if the radius of the small gear is 1.5 inches and the radius of the large gear is 45 inches?
If the radius of the smaller gear is 1.5 inches and the radius of the large gear is 4.5 inches then the bicycles can travel a distance of 62.83 inches.
Given radius of the small gear=1.5 inches and radius of the larger gear=4.5 inches.
Number of rotation of the small gear for each rotation of the larger gear=4.5/1.5=3
Distance which the bicycle can travel=3*2πr.
=3*2*π*10
=60π inches.
Difference in distance travelled=60π inches-40π inches.
=20π inches
put π=3.14
=20*3.14
=62.83 inches.
Hence the distance that the bicycle travels is 62.83 inches if the radius of smaller gear is 1.5 inches and radius of the larger gear is 4.5 inches.
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Question is incomplete as it should includes:
Description about the question that person is travelling through bicycle. That's why radius of gears has been given.
Question 4 I need help to solve all 3
Answer:
[tex]x^{2} +12x+36[/tex] [tex]\\[/tex]----- factors [tex](x+6)^{2}[/tex][tex]4x^{2} +24x+36[/tex] ----- factors [tex](2x+6)^{2}[/tex][tex]2x^{2} +10x+8[/tex] ------ factors (2x+2)(x+4)[tex]y^{2} -4[/tex] --------- factor (y+2)(y-2)Step-by-step explanation:
First bullet is called Perfect Square Trinomial (PST), the first and last is a perfect square and the middle is twice the product of the squared first and last term. To factor, just copy the middle sign and square the first and last term.
---
2nd bullet is also a PST with a value on a. Likewise you just need to square the first and last term. Then, copy the middle sign.
--
3rd bullet is a trinomial. To get the factor, get the prime factor of the value of a. Then, find the factors of 8 that when add up results to the value of b.
-
4th bullet is a special case. First get the square root of the first and last term, and copy the sign, Then, copy the factors and change it to the opposite sign.
Which is a stretch of an exponential decay function?
ofx= [*
O
○ f(x) = -—-—-(5)*
|_ f(x) = 5(---)*|
O
Of(x) = 5(5)*
Enter the correct answer in the box. Write your answer in the form y - mx + b, using the appropriate inequality symbol in place of
the equal sign.
What inequality is shown in the graph?
Hello and Welcome to Brainly!
Let's take this problem step-by-step:
The problem wants the final answer to be in the form ⇒ y = mx + b
m ⇒ value of the slopeb ⇒ y-interceptLet's find both of these values first
[tex]slope = \frac{y_2-y_1}{x_2-x_1}[/tex](x₁,y₁), (x₂,y₂) are any two points on the line
⇒ let's use (-4,0) and (0,-4)
[tex]Slope = \frac{-4-0}{0--4} =\frac{-4}{4} =-1[/tex]
the y-intercept is any coordinate whose x-coordinate equals '0'⇒, therefore, the y-intercept is -4
Our equation as of now: y __ -x - 4
Now let's use some points to test:
⇒ what way inequality should face:
test with (0,0) (within the shaded region)[tex]0 _._._. -(0) - 4\\0 _._._. -4\\0 \geq -4[/tex]
Therefore our equation is [tex]y\geq -x-4[/tex]
* we use '≤' since the line is solid
⇒ if the line were dotted, we would use '>'
Answer: y ≥ -x - 4
Hope that helps!
#LearnwithBrainly
Answer:
y ≥ -x − 4.
Step-by-step explanation:
On the average, 1.8 customers per minute arrive at any one of the checkout counters of a grocery store. What probability distribution can be used to find the probability that there will be no customers arriving at a checkout counter in the next minute
The probability that there will be no customers arriving at a checkout counter in the next minute is 0.16530.
The number of customers arriving per minute at the checkout counter of a grocery store is following Poisson Distribution.
A Poisson Distribution over a variable X, having a mean λ, has a probability for a random variable x as [tex]P(X = x) = e^{-\lambda} \frac{\lambda^{x}}{x!}[/tex] .
In the question, we are asked to find the probability that no customer arrives at the checkout, hence we put x = 0, and the mean number of customers per minute (λ) = 1.8.
Substituting the values of x and λ in the equation, we get:
[tex]P(X = 0) = e^{-1.8} \frac{1.8^{0}}{0!}[/tex] ,
or, [tex]P(0) = e^{-1.8} = 0.16530[/tex] .
Therefore, the probability that there will be no customers arriving at a checkout counter in the next minute is 0.16530.
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