Answer:
{x,y} = {-2,2}
Step-by-step explanation:
Solve equation [2] for the variable y
7y = 7x + 28
y = x + 4
Plug this in for variable y in equation [1]
-8x + 4•(x +4) = 24
-4x = 8
Solve equation [1] for the variable x
4x = - 8
x = - 2
By now we know this much :
x = -2
y = x+4
Use the x value to solve for y
y = (-2)+4 = 2
Solution :
{x,y} = {-2,2}
and this intersects at only one point so your answer is A
The correct answer is: [tex]\[ \text{C. Infinitely many solutions} \][/tex].
To determine the number of solutions for the given system of equations, let's analyze it:
1. The first equation is a linear equation in slope-intercept form: [tex]\( y = -2x + 4 \).[/tex]
2. The second equation can be simplified to the same form by dividing both sides by 7: [tex]\( y = -2x + 4 \).[/tex]
Comparing the two equations, we can see that they represent the same line. In other words, the equations are equivalent.
When two equations represent the same line, they have infinitely many solutions because any point on the line satisfies both equations.
37 A recreation center ordered a total of 15 tricycles and bicycles from a sporting goods store
The number of wheels for all the tricycles and bicycles totaled 38.
Write a linear system of equations that models this scenario, where represents the number of
tricycles and b represents the number of bicycles ordered
Answer:
1) The system of linear equations is equal to
b+t=15 and 2b+3t=38
2) The number of bicycles ordered was 7 and the number of tricycles ordered was 8
Step-by-step explanation:
Let
b----> the number of bicycles ordered
t----> the number of tricycles ordered
we know that
b+t=15 -----> equation A
2b+3t=38 ---> equation B
Solve the system of equations by graphing
Remember that the solution of the system of equations is the intersection point both graphs
The solution is the point (7,8)
see the attached figure
therefore
The number of bicycles ordered was 7
The number of tricycles ordered was 8
The number of bicycles ordered was 7 and the number of tricycles ordered was 8.
What is the system of equations?
Systems of equations are sets of equations where the solution is the intersecting point(s) between the equations.
Let, the number of tricycles and b represent the number of bicycles ordered.
A recreation center ordered a total of 15 tricycles and bicycles from a sporting goods store.
[tex]\rm b+t=15[/tex]
The number of wheels for all the tricycles and bicycles totaled 38.
[tex]\rm 2b+3t=38[/tex]
From equation 1
[tex]\rm b+t=15\\\\b=15-t[/tex]
Substitute the value of b in equation 2
[tex]\rm 2b+3t=38\\\\ 2(15-t)+3t=38\\\\30-2t+3t=38\\\\t=38-30\\\\t=8[/tex]
Substitute the value of t in equation 1
[tex]\rm b+t=15\\\\b=15-t\\\\ b = 15-8\\\\b=7[/tex]
Hence, the number of bicycles ordered was 7 and the number of tricycles ordered was 8.
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The point (-2, -1) satisfies which of the following inequalities?
A) 5x - 2y + 1 > 0
B) -5x + 2y + 1 > 0
C) -2x + 5y - 1 > 0
D) 2x + 5y - 1 > 0
Ik for s fact the awnser not a
Answer:
B) [tex]-5x + 2y + 1 > 0[/tex]
Step-by-step explanation:
Given point is (-2,-1)
to find out which inequality satisfies this point we plug in x and y value of the given point in each inequality
A) [tex]5x - 2y + 1 > 0[/tex]
x=-2 and y=-1
[tex]5(-2) - 2(-1) + 1 > 0[/tex]
[tex]-10+2+1>0[/tex]
[tex]-7>0[/tex] is False
B) -5x + 2y + 1 > 0
[tex]-5(-2) +2(-1) + 1 > 0[/tex]
[tex]10-2+1>0[/tex]
[tex]9>0[/tex] is True
C) -2x + 5y - 1 > 0
[tex]-2(-2) +5(-1) -1 > 0[/tex]
[tex]4-5-1>0[/tex]
[tex]-2>0[/tex] is False
D) 2x + 5y - 1 > 0
[tex]2(-2) +5(-1) - 1 > 0[/tex]
[tex]-4-5-1>0[/tex]
[tex]-10>0[/tex] is False
g(1)=51 g(n)=g(n-1)+2 fina an explicit formula for g(n)
Answer:
g(n) = 2n+49
Step-by-step explanation:
Since g(1) = 51, then g(1)+2=g(2) or g(2)=53. So the formula for g(n) is
g(n) = 49+2n
The explicit formula for g(n) will be g(n) = 2n + 49.
What is a function?Functions are found all across mathematics and are required for the creation of complex relationships.
g(1) = 51 and g(n) = g(n – 1) + 2
Since g(1) = 51, then g(1) + 2= g(2) or g(2) = 53.
So the formula for g(n) will be
g(n) = 49 + 2n
More about the function link is given below.
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what is the approximate area of the circle shown (please help first answer gets brainliest)
Answer:
The answer is B.
Step-by-step explanation:
One lap around a track is equal to 1/8 of a mile. A horse ran a distance of 9 laps in 2 minutes and 30 seconds. What was the horse's average speed in miles per minute?
12,450 so yeah your welcome have a fantasist day
which of the following quadratic equations has the solution (1/2,5)
(x-5)(2x-1) (-2x+1)(-x+5)=0 and (-2x+1)(x-5)=0 quadratic equation have as solution set.
Answer:
well i got some HOPE THIS WILL HELP
Step-by-step explanation:
To find the solution set of a factored quadratic equation, you should set each one of the factors equal to zero and solve for .
Lets take our first quadratic equation (x+1/2)(x-5)=0 and apply this. First we are our factors equal to zero and ; next we are going to sole for in each factor to find the solution set:
and , so the solution set for the quadratic equation (x+1/2)(x-5)=0 is
Lets do the same for our next one (x-5)(2x-1)=0
and
So, the solution set for the quadratic equation (x-5)(2x-1)=0 is
Next one (x+5)(2x-1)=0
and
So, the solution set for the quadratic equation (x+5)(2x-1)=0 is
Next one (-2x+1)(-x+5)=0
and
So, the solution set for the quadratic equation (-2x+1)(-x+5)=0 is : therefore, we are going the select this one.
Next one (x+1/2)(x+5)=0
and
So, the solution set for the quadratic equation (x+1/2)(x+5)=0 is
Finally, our last one (-2x+1)(x-5)=0
and
So, the solution set for the quadratic equation (-2x+1)(x-5)=0 is ; this is also a correct answer, make sure to select this one too.
We can conclude that both (-2x+1)(-x+5)=0 and (-2x+1)(x-5)=0 quadratic equation have as solution set.
Express the polynomial 5a^2 + 3a^3 + 1 in standard form and then classify it.
A.
A. cubic binomial
B. quadratic monomial
C. cubic trinomial
D. linear trinomial
Answer: OPTION C
Step-by-step explanation:
To express a polynomial in Standard form, you need to see the exponent of each term of the polynomial and then order the polynomial from highest exponent to lowest exponent.
Therefore, for the polynomial [tex]5a^2 + 3a^3 + 1[/tex], you get:
[tex]3a^3 +5a^2 +1[/tex]
The highest exponent gives you the degree of the polynomial. In this case, the highest exponent is 3, then it is a polynomial of degree 3 or a cubic polynomial.
When a polynomial has three terms, is called "trinomial". Since this polynomial has three terms, it is a trinomial.
Therefore, the you can classify it as:
Cubic trinomial
Answer:
C
Step-by-step explanation:
Does 2x-5y=-15 represent a linear relationship? please explain
ANSWER
Yes
EXPLANATION
The given relation is
2x-5y=-15
We solve for y to obtain:
-5y=-2x-15
Divide through by -5.
[tex]y = \frac{2}{5}x + 3[/tex]
This is linear relation.
There is a positive linear relationship between the two variables x and y.
Also we can see that the highest degree of the variables is unity.
Hence it represents a linear relationship between x and y.
find the volume of a cylinder with diameter 8 inches and height 9 1/2 inches
Answer:
[tex]V=152\pi in^{2}[/tex] in terms or pi
[tex]V=477.52in^{2}[/tex] simplified
Step-by-step explanation:
To solve this, we are using the Cylinder's volume formula:
[tex]V=\pi r^{2} h[/tex]
where
[tex]V[/tex] is the volume of the cylinder
[tex]r[/tex] is the radius of the cylinder
Remember that radius is half the diameter, so we can divide the diameter of our cylinder by 2 to find its radius: [tex]r=\frac{d}{2} =\frac{8in}{2} =4in[/tex]. Now, 9 1/2 inches is 9 and a half inches, so [tex]h=9.5in[/tex].
Replacing values:
[tex]V=\pi (4in)^{2} (9.5in)[/tex]
[tex]V=\pi (16in^{2})(9.5in)[/tex]
[tex]V=152\pi in^{2}[/tex]
[tex]V=477.52in^{2}[/tex]
We can conclude that the volume of our cylinder is [tex]V=152\pi in^{2}[/tex] in terms of pi, or [tex]V=477.52in^{2}[/tex] simplified.
Answer:
[tex]V=477.5in^3[/tex]
Step-by-step explanation:
The volume of a cylinder can be calculated using the formula;
[tex]V=\pi r^2h[/tex]
where the radius is half of the diameter of the circle.
[tex]r=\frac{8}{2} =4in.[/tex]
The height of the cylinder is
[tex]h=9\frac{1}{2}=\frac{19}{2}in.[/tex]
We substitute the values into the formula to obtain;
[tex]V=\pi\times 4^2\times \frac{19}{2}[/tex]
[tex]V=477.5in^3[/tex]
correct to the nearest tenth
what is the quotient when x^3 -5x^2 + 3x -8 is divided by x-3 ?
For this case, when making the division of polynomials, we must build a quotient that when multiplied by the divisor of the same as the terms of the dividend, the sign is changed and they are eliminated until reaching the remainder of the division.
It must be fulfilled that:
[tex]Dividend = Quotient * Divider + Remainder[/tex]
When observing the attached figure, the quotient is:
[tex]x ^ 2-2x-3[/tex]
Answer:
[tex]x ^ 2-2x-3[/tex]
See attached image
Bottled apple juice is sold in four different different sizes. Which is the best to buy?
Answer:
the bigger one ;)
Step-by-step explanation:
Answer:
C 24-ounce bottle
Step-by-step explanation:
Evaluate and simplify the following complex fraction
Answer:
[tex]\frac{24}{5}[/tex]
Step-by-step explanation:
To evaluate division of fractions, that is
[tex]\frac{9}{-5}[/tex] ÷ [tex]\frac{-3}{8}[/tex]
Leave the first fraction, change division to multiplication and turn the second fraction upside down
[tex]\frac{9}{-5}[/tex] × [tex]\frac{8}{-3}[/tex] ( cancel the 9 and 3) giving
[tex]\frac{3}{-5}[/tex] × [tex]\frac{8}{-1}[/tex]
= [tex]\frac{3(8)}{-5(-1)}[/tex] = [tex]\frac{24}{5}[/tex]
To simplify a complex fraction, multiply both the numerator and the denominator by the same factor to eliminate fraction in the denominator, cancel common factors and follow rules of algebra to maintain equality.
Explanation:To evaluate and simplify a complex fraction, we can use a strategy that involves multiplying the numerator and denominator by the same factor. For example, if our complex fraction had a denominator of 1/2, we could multiply both the numerator and the denominator by 2 to eliminate the fraction in the denominator. This approach ensures the units or variables cancel out where appropriate, leaving us with a simpler expression. When working with fractions, common factors can be identified and cancelled to simplify the fraction further. Always remember that fractions represent division, so when simplifying, divide the digit term of the numerator by that of the denominator and subtract the exponentials accordingly. This process is governed by the rules of algebra, maintaining the equality of the expression.
Ms Redmond gave her theater students an assignment to memorize a dramatic monologue to present to the rest of the class. The graph shows the times, rounded to the nearest half minute, of the first 10 monologues presented
Answer:
The mean will decrease.
Answer:
The correct option is B.
Step-by-step explanation:
From the given dot plot we can create a frequency table.
x f
1.5 2
2 1
2.5 3
3 1
3.5 2
4 1
This data can be written as
1.5, 1.5, 2, 2.5, 2.5, 2.5, 3, 3.5, 3.5, 4
The mean of the data is
[tex]Mean=\frac{\sum x}{n}=\frac{1.5+1.5+2+2.5+2.5+2.5+3+3.5+3.5+4}{10}=2.65[/tex]
The number of terms is 10 which is an even number. So, the median of the data is
[tex]Median=\frac{(\frac{n}{2})th+(\frac{n}{2}+1)th}{2}=\frac{5th+6th}{2}=\frac{2.5+2.5}{2}=2.5[/tex]
If next student presents a monologue that is about 0.5 minutes long, then the new data is
0.5, 1.5, 1.5, 2, 2.5, 2.5, 2.5, 3, 3.5, 3.5, 4
The mean of the new data is
[tex]Mean=\frac{\sum x}{n}=\frac{0.5+1.5+1.5+2+2.5+2.5+2.5+3+3.5+3.5+4}{11}=2.4545..\approx 2.45[/tex]
The number of terms is 11 which is an odd number. So, the median of the new data is
[tex]Median=(\frac{n+1}{2})th=6th=2.5[/tex]
Median of given data and new data is same but the mean of new data is less than the mean of original data. It means the mean will decrease.
Therefore the correct option is B.
Write an equivalent expression for 4.5x(2 - 6)
[tex]4.5x(2 - 6) \\ \\ 1. \: 4.5x \times - 4 \\ 2. \: = - 18x[/tex]
[tex]\text{Hey there!}[/tex]
[tex]\text{You could solve this equation by distributing}[/tex]
[tex]\text{The Algebraic I formula for distribution is: a(b + c) = ab + ac}[/tex]
[tex]\text{4.5x(2 - 6)}\\\text{4.5x(2) = 9x}\\\text{4.5x(-6)= -27x}[/tex]
[tex]\text{Combine like terms: 9x - 27x = ?}[/tex]
[tex]\text{Solve that}\uparrow\text{you should get the rest of -18x}[/tex]
[tex]\boxed{\boxed{\text{Answer: -18x}}}\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
Jennifer's bill for 6 cans of grape juice and 4 cans of apple juice was $13.10. When she got home she found out that she should have bought 4 cans of grape juice and 6 cans of apple juice. Although she mixed up the order, she did save 60 cents. What is the cost per can of apple and grape juice
Solve the problem using substitution and elimination.
Convert your equations to slope intercept form and identify the variables for your x and y axes. Then graph.
SHOW ALL WORK
Answer:
Part 1) The system is solved using elimination
The cost per can of grape juice is [tex]\$1.19[/tex] and the cost per can of apple juice is [tex]\$1.49[/tex]
Part 2) The system is solved using substitution
The cost per can of grape juice is [tex]\$1.19[/tex] and the cost per can of apple juice is [tex]\$1.49[/tex]
Part 3) The system is solved by graphing
The graph in the attached figure
Step-by-step explanation:
Part 1) Solve the system by elimination
Let
x----> the cost per can of grape juice
y----> the cost per can of apple juice
we know that
[tex]6x+4y=13.10[/tex] -----> equation A
[tex]4x+6y=13.10+0.60[/tex]
[tex]4x+6y=13.70[/tex] -----> equation B
Solve the system by elimination
Multiply the equation A by -6 both sides
[tex]-36x-24y=-78.6[/tex] -------> equation C
Multiply the equation B by 4 both sides
[tex]16x+24y=54.8[/tex] -------> equation D
Adds equation C and equation D
[tex]-36x-24y=-78.6\\16x+24y=54.8\\----------\\-36x+16x=-78.6+54.5\\-20x=-23.8\\x=1.19[/tex]
Substitute the value of x in the equation A
[tex]6(1.19)+4y=13.10[/tex]
[tex]4y=5.96[/tex]
[tex]y=1.49[/tex]
therefore
The cost per can of grape juice is [tex]\$1.19[/tex]
The cost per can of apple juice is [tex]\$1.49[/tex]
Part 2) Solve the system by substitution
Let
x----> the cost per can of grape juice
y----> the cost per can of apple juice
we know that
[tex]6x+4y=13.10[/tex]
[tex]4y=-6x+13.10[/tex]
[tex]y=-1.5x+3.275[/tex] -----> equation A
[tex]4x+6y=13.10+0.60[/tex]
[tex]4x+6y=13.70[/tex]
[tex]6y=-4x+13.70[/tex]
[tex]y=-(4/6)x+13.70/6[/tex]
[tex]y=--0.67x+2.28[/tex] -----> equation B
Substitute equation B in equation A and solve for x
[tex]-0.67x+2.28=-1.5x+3.275[/tex]
[tex]1.5x-0.67x=3.275-2.28[/tex]
[tex]0.83x=0.995[/tex]
[tex]x=1.19[/tex]
Find the value of y
Substitute the value of x in the equation A
[tex]y=-1.5(1.19)+3.275=1.49[/tex]
therefore
The cost per can of grape juice is [tex]\$1.19[/tex]
The cost per can of apple juice is [tex]\$1.49[/tex]
Part 3) Solve the system by graphing
we have
[tex]y=-1.5x+3.275[/tex] -----> equation A
[tex]y=-(4/6)x+13.70/6[/tex] -----> equation B
Remember that
The solution of the system of equations is equal to the intersection point both lines
The solution is the point [tex](1.19,1.49)[/tex]
see the attached figure
therefore
The cost per can of grape juice is [tex]\$1.19[/tex]
The cost per can of apple juice is [tex]\$1.49[/tex]
PLEASE HELP IT'S TIMED
The 3rd one.....................
Answer:
Fourth option
Step-by-step explanation:
An m×n matrix is a matrix with m rows (horizontal lines) and n columns (vertical lines).
By definition, the multiplication of two matrices [tex]m_1[/tex]×[tex]n_1[/tex] and [tex]m_2[/tex]×[tex]n_2[/tex] can be done only if:
[tex]n_1 = m_2[/tex]
In the first option:
[tex]n_1 = 2\\m_2 = 1[/tex]
In the second option
[tex]n_1 = 1\\m_2 = 2[/tex]
In the third option
[tex]n_1 = 2\\m_2 = 1[/tex]
In the fourth option
[tex]n_1 = 1\\m_2 = 1[/tex]
[tex]n_1 = m_2[/tex] Multiplication can be done
What is the arithmetic mean of the following numbers? 8,10,10,10,6,7,8
Answer:
Step-by-step explanation:
To find the arithmetical mean, add all the numbers togther and divide by the number of numbers.
The sum of all the numbers is ... 59.
There are 7 numbers.
59/7 which is about 8.43 is the arithmetic mean.
Arithmetic mean is 8.42 (Approximately)
Given that;
Values = 8,10,10,10,6,7,8
Find:
Arithmetic mean
Computation:
Arithmetic mean = Sum of all number / Number of term
Arithmetic mean = [8 + 10 + 10 + 10 + 6 + 7 + 8] / 7
Arithmetic mean = 59 / 7
Arithmetic mean = 8.42 (Approximately)
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What is the measure of angle b
A) 98°
B)108°
C)118°
D)128°
Answer:
The correct answer is option B). 108°
Step-by-step explanation:
Points to remember
Sum of angles of hexagon is 720°
From the figure we can see a hexagon.
To find the m<B
m<B = 720 - ( m<A + m< C + m<D + m<E + m<F)
= 720 - ( 170 + 133 + 102 + 117 + 90)
= 720 - 612
= 108°
Therefore m<B = 108° Option B is the correct answer
Answer:
B. 108 degrees
Step-by-step explanation:
You are shown either nets or top and side view of three dimensional figures. Match the three dimensional figure to the correct views.
cone
cylinder
rectangular prism
sphere
triangular pyramid
Answer:
1. rectangular prism
2. cylinder
3. cone
4. triangular pyramid
5. sphere
Step-by-step explanation:
99/3 = Z/5 what is the value of z in this equation
The value 1/5 becuse you simplify
Answer:
165=z
Step-by-step explanation:
99/3 = z/5
We can solve this using cross products.
99*5 = 3z
495 = 3z
Divide each side by 3
495/3 = 3z/3
165 = z
Which is the equivalent of 6 14’ 48” written in decimal form ?
Answer:
Option A. 6.247°
Step-by-step explanation:
we know that
1°=60'
1'=60"
we have
6° 14' 48"
Convert to decimal form
Convert seconds to minutes
48"=48/60=0.8'
so
6° 14' 48"=6° + 14' +0.8'=6° 14.8'
Convert minutes to degrees
14.8'=14.8/60=0.247°
so
6° 14.8' =6° + 0.247°=6.247°
Answer:
6.247
Step-by-step explanation:
What is the volume of a cylinder to the nearest whole number? r=7.5 h=20
Answer:
V = 3533
Step-by-step explanation:
Volume of a cylinder is given by
V = pi r^2 h
Using 3.14 for pi
V = (3.14) (7.5)^2 * 20
V = 3532.5
To the nearest whole number
V = 3533
Over a 30-day period, the mean temperature in Capetown was 98°F with a standard deviation of 1.4°F and the mean
temperature in Three Rivers was 95°F with a standard deviation of 6.5°F.
What statement best describes the data?
A.the temperature was more Consistent in three Rivers
B. The temperatures were more consistent in Cape Town
C. The temperatures were of similar consistency and Cape Town and three rivers
Answer:
B. The temperatures were more consistent in Cape Town
Step-by-step explanation:
A low standard deviation indicates less variation away from the mean.
Since Cape Town has a lower standard deviation than Three Rivers, it is more consistent
Tariq designed the pool shown. The owner of the pool has one square cover to use. Find the area of the space that needs to be covered. (The four corners are squares.)
The area that needs to be covered is
___ ft2.
Step 1: Find the total area. Since it is a square all the sides are 12 ft so multiply 12 by 12
12 x 12 = 144
^^^This is the total area including the area around the pool. We just need the are of the pool
Step 2: Outside of the pool there are four little 2 ft by 2 ft squares that aren't part of pool, and therefore won't need to be covered. The area of these 2 ft by 2 ft square is 4ft (2 times 2 is 4). Since there are 4 of these squares we multiply 4 by 4 to get 16. This means that 16 ft of the 144 ft we found previously are not part of the pool and we must subtract 16 from 144 to get the total pool area
144 - 16 = 128
This means that the area of the pool is 128 ft
Hope this helped and made sense! Let me know!
Answer:
128
Step-by-step explanation:
pls help!! 5star and brainliest
Answer:
C, A, C
Hope This Helps!
Polygon Y is a scaled copy of Polygon X using a scale factor of \dfrac13 3 1 start fraction, 1, divided by, 3, end fraction. Polygon Y's area is what fraction of Polygon XXX's area?
Answer:
Polygon Y's area is one ninth (1/9) of Polygon X's area
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its areas is equal to the scale factor squared
In this problem
Let
z-----> the scale factor
a-----> Polygon Y's area
b----> Polygon X's area
[tex]z^{2}=\frac{a}{b}[/tex]
we have
[tex]z=\frac{1}{3}[/tex]
substitute
[tex](\frac{1}{3})^{2}=\frac{a}{b}[/tex]
[tex]\frac{1}{9}=\frac{a}{b}[/tex]
[tex]a=\frac{1}{9}b[/tex]
therefore
Polygon Y's area is one ninth (1/9) of Polygon X's area
Answer:
1/9
Step-by-step explanation:
whats the mode, median, mean and range of 24, 31, 12, 38, 12, 15
here is your answer young man/lady
The mode is 12, the median is 18.5, the mean is 23.6667, and the range is 26.
The mode is 12 because it appears twice in the list. The median is 18.5 because it is the middle value when the numbers are arranged in ascending order. The mean is 23.6667 which is the sum of all the numbers divided by the total count. The range is 26 which is obtained by subtracting the smallest value (12) from the largest value (38).
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simplify the expression -3/6 - 5/7
Rewrite both fractions so they have a common denominator:
-3/6 = -21/42
-5/7 = -30/42
Now you have -21/42 - 30/42
Now subtract to get:
-51/42 which reduces to -17/14 = -1 3/14
The simplification of the expression is,-17/14. The simplification is done by applying the mathematical operation step by step.
What does it mean to simplify an expression?Simplification usually entails doing out the expression's pending processes.
The given expression is
(-3/6) –(5/7)
The LCM of the 6 and 7 is 42 so rewrite the equation as;
(-3×7)/42 – (5×6)/7
(-21/42)-30/42
-51/42
Divide by 3 from the numerator and denominator we get;
-17/14
Hence, the simplification of the expression is,-17/14
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Two cars simultaneously left Points A and B and headed towards each other, and met after 2 hours and 45 minutes. The distance between points A and B is 264 miles. What is the speeds of the cars, if one of the cars travels 14 mph faster than the other?
Please help
This is the only problem of my homework that I don't understand
The answers are:
[tex]FirstCarSpeed=41mph\\SecondCarSpeed=55mph[/tex]
Why?To calculate the speed of the cars, we need to write two equations in order to create a relation between the two speeds and be able to calculate one in function of the other.
So, let be the first car speed "x" and the second car speed "y", writing the equations we have:
For the first car:
[tex]x_{FirstCar}=x_o+v*t[/tex]
For the second car:
We know that the speed of the second car is the speed of the first car plus 14 mph, so:
[tex]x_{SecondCar}=x_o+(v+14mph)*t[/tex]
Now, we already know that both cars met after 2 hours and 45 minutes, and the distance between A and B is 264 miles, so, we can calculate the relative speed between both cars.
If the cars are moving towards each other the relative speed will be:
[tex]RelativeSpeed=FirstCarSpeed-(-SecondCarspeed)\\\\RelativeSpeed=x-(-x-14mph)=2x+14mph[/tex]
So , since we know that they covered a combined distance equal to 264 miles in 2 hours + 45 minutes, we have:
[tex]2hours+45minutes=120minutes+45minutes=165minutes\\\\\frac{165minutes*1hour}{60minutes}=2.75hours[/tex]
Writing the equation:
[tex]264miles=(2x+14mph)*t\\\\264miles=(2x+14mph)*2.75hours\\\\2x+14mph=\frac{264miles}{2.75hours}\\\\2x=96mph-14mph\\\\x=\frac{82mph}{2}=41mph[/tex]
Therefore, the speed of the first car is equal to 41 mph.
Now, for the second car we have that:
[tex]SecondCarSpeed=FirstCarSpeed+14mph\\\\SecondCarSpeed=41mph+14mph=55mph[/tex]
We have that the speed of the second car is equal to 55 mph.
Hence, the answers are:
[tex]FirstCarSpeed=41mph\\SecondCarSpeed=55mph[/tex]
Have a nice day!
This week laptops are 25% off. If a laptop costs $340, what is its sale price?
Answer:
$25
Step-by-step explanation:
i have an odd method of solving these types of equations
25x=100
x=4
340/4 = 85
85 x 3 = 255
Answer:
13.6
Step-by-step explanation:
so i did 340 devided by 25 and thats how i got it i hope this is helpful