Answer:
1. 0.90m + 3 > 0.60m + 4; 2. 4.50v + 8.50 < 6.00v
Step-by-step explanation:
1. Taxis
Let A = cost of Taxi A
and B = cost of Taxi B
Then A = 0.60m + 4
and B = 0.90m +3
If B > A, then
0.90m + 3 > 0.60m + 4
2. Video games
Let A = monthly cost at Store A
and B = monthly cost at Store B
Then A = 4.50v + 8.50
and B = 6.00v
If A < B, then
4.50v + 8.50 < 6.00v
What is the sum or difference 2/3(7w+4) - 1/3(2w-1)
Answer:
4w+3
Step-by-step explanation:
2/3(7w+4)-1/3(2w-1)
14/3w+8/3-2/3w+1/3
14/3w-2/3w+8/3+1/3
12/3w+9/3
4w+3
Linear programming subjected to constraints
Answer:
The maximum value of C is 14
Step-by-step explanation:
we have the following constraints
[tex]x\geq 0[/tex] ----> constraint A
[tex]y\geq 0[/tex] ---> constraint B
[tex]2x+2y\leq 10[/tex] ---> constraint C
[tex]3x+y\leq 9[/tex] ---> constraint D
Determine the area of the feasible region using a graphing tool
see the attached figure
The vertices of the feasible region are
[tex](0,0),(0,5),(2,3),(3,0)[/tex]
To find out the maximum value of the objective function C, substitute the value of x and the value of y of each vertices in the objective function an then compare the results
we have
[tex]C=4x+2y[/tex]
For (0,0) ----> [tex]C=4(0)+2(0)=0[/tex]
For (0,5) ----> [tex]C=4(0)+2(5)=10[/tex]
For (2,3) ----> [tex]C=4(2)+2(3)=14[/tex]
For (3,0) ----> [tex]C=4(3)+2(0)=12[/tex]
therefore
The maximum value of C is 14
Is 7- y=5x+11 a standard form
Answer:
No.
Step-by-step explanation:
Because standard form is ax+by=c.
A coin toss is based on what type of probability?
Answer:
50/50 chance
Step-by-step explanation:
Answer: Classical Probability (also know as priori or theoretical probability)
Step-by-step explanation:
what is 2940 divided by 8
367.5, there are 367.5 8's in 2,940.
Hope this helps, if not, comment below please!!!!
Answer:
365.7
Step by step solving:
What is the slope of a line that is parallel to the line containing (-11, 5) and (-6, 1)?
Answer:
(5-1)/-11-(-6) = -4/5
Step-by-step explanation:
since the lines are parallel they have same slope/gradient
Answer:
-4/5
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(1-5)/(-6-(-11))
m=-4/(-6+11)
m=-4/5
if the sales tax rate is 7.25% in california, then how much would u pay in los angeles for a coat that cost $120.00
Answer:
The amount to be pay for coat is $128.70.
Step-by-step explanation:
Given:
The sales tax rate is 7.25% in California.
The cost for a coat in Los angeles is $120.00.
Now, to find amount to be paid.
Sales tax = 7.25%.
Cost = $120.00.
So, amount to be paid = $120 + 7.25% of $120.00.
[tex]=120+\frac{7.25}{100} \times 120.[/tex]
[tex]=120+\frac{870}{100}.[/tex]
[tex]=120+8.70[/tex]
[tex]=\$128.70[/tex]
Therefore, the amount to be pay for coat is $128.70.
the measure of an angle and it’s supplement are given. Determine the measures of the two angles
Answer:
The sum of any two supplementary angles is 180⁰. If you have been given a task to that one angle measures 120⁰ and have to find its supplement, you will compute as ⇒ 180⁰ - 120⁰ = 60⁰. So, the missing will be 60⁰.
Step-by-step explanation:
As we know that the sum of any two supplementary angles is 180⁰.If we have to get the supplement, all we need is to subtract a given angle from 180.A straight line measure 180⁰.If you have been given a task to that one angle measures 120⁰ and have to find its supplement, you will compute as ⇒ 180⁰ - 120⁰ = 60⁰. So, the missing will be 60⁰.Let us consider the m∠MON = 45⁰, as shown in figure a. As straight line measure 180⁰, and the sum of any two supplementary angles is 180⁰. So, 180⁰ - 45⁰ = 135⁰ ⇒ m∠MOL = 135⁰.
So, the supplement of m∠MON = 45⁰ is m∠MOL = 135⁰.
Keywords: supplementary angle, angle measure
Learn more about supplementary angle from brainly.com/question/12919127
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what could be the function for this graph in factored form?
Answer:
OPTION A
Step-by-step explanation:
Roots of a function can be determined from the graph by the point which cuts the x - axis.
Here, (-4, 0) and (2, 0) are the points that cut the x - axis.
That means, the roots should have been x = -4, 2.
So, from the options, we see that OPTION A has roots f(x) = (x + 4)(x - 2)².
Since, it is a parabola, we have (x - 2)².
Note that f(-4) = 0 and
f(2) = 0.
Hence, OPTION A is the answer.
first term 2 common difference 13
Answer:
With the first term is 2 and common difference is 13 then the series is 2,15,28,...
Step-by-step explanation:
Given first term is 2 and common difference is 13.
Arithmetic progression:
[tex]a_{1}=2[/tex] and d=2 [given]
Therefore we can find arithmetic series [tex]a_{1},a_{2},a_{3},...[/tex] with [tex]a_{1}=2[/tex] and d=2
d can be written as [tex]d=a_{2}-a_{1}[/tex]. Therefore we can write [tex]a_{2}[/tex] as below:
[tex]a_{2}=a_{1}+d[/tex]
Now substitute the values [tex]a_{1}=2[/tex] and d=2
[tex]a_{2}=2+13[/tex]
[tex]a_{2}=15[/tex]
Similarly we can find [tex]a_{3}[/tex]
d can be written as [tex]d=a_{3}-a_{2}[/tex]. Therefore we can write [tex]a_{3}[/tex] as below:
[tex]a_{3}=a_{2}+d[/tex]
[tex]a_{3}=15+13[/tex]
[tex]a_{3}=28[/tex]
and so on.
Therefore the series is 2,15,28,...
The ratio of two complementary angles is 7:2. What is the measure, in degrees, of the larger angle?
Answer:
The larger angle is 70°
And The smaller angle is 20° .
Step-by-step explanation:
Given as :
The ratio of two complementary angles = 7 : 2
Let The larger angle = 7 x
And The smaller angle = 2 x
Now, According to question
Complementary angle is define as when two angles were added to make right angle i.e 90° are complementary to each other .
So, here
7 x + 2 x = 90°
Or, 9 x = 90°
∴ x = [tex]\dfrac{90^{\circ}}{9}[/tex]
i.e x = 10°
Now, putting the value of x
So, The larger angle = 7 × 10° = 70°
And The smaller angle = 2 × 10° = 20°
Hence, The larger angle is 70°
And The smaller angle is 20° . Answer
Final answer:
The larger angle in a pair of complementary angles with a ratio of 7:2 measures 70 degrees, found by figuring the common ratio as 10 and multiplying it by 7.
Explanation:
To find the measure of the larger angle when two angles are complementary and their ratio is 7:2, we first need to understand that complementary angles add up to 90 degrees. If the ratio of the angles is 7 to 2, we can express this as 7x and 2x for some number x. By adding these two expressions, 7x + 2x, we get the total amount of degrees in complementary angles, which is 90 degrees. Therefore, we have the equation 9x = 90, which we can solve for x by dividing both sides by 9 to get x = 10.
The larger angle, which is 7 parts of the ratio, will be 7x which is 7 times 10, so it is 70 degrees.
Find x in the given figure.
Answer:
Step-by-step explanation:
7x + 95+2x + x+25 + 90 = 360
10x + 210 = 360
10x = 360 -210
10x = 150
x = 150/10
x = 15
Solve the system of equations algebraically. Verify your
answer using the graph.
y = 4x - 5
y=-3
What is the solution to the system of equations?
(1, -3)
in
Answer:
The solution is the point (0.5,-3)
Step-by-step explanation:
we have
[tex]y=4x-5[/tex] ----> equation A
[tex]y=-3[/tex] ----> equation B
Solve the system by substitution
Substitute equation B in equation A
[tex]-3=4x-5[/tex]
Solve for x
Adds 5 both sides
[tex]-3+5=4x[/tex]
[tex]2=4x[/tex]
Divide by 4 both sides
[tex]x=0.5[/tex]
therefore
The solution is the point (0.5,-3)
Verify your answer using the graph
using a graphing tool
Remember that the solution of the system of equations is the intersection point both graphs
The intersection point is (0.5,-3)
therefore
The solution is the point (0.5,-3)
see the attached figure
Answer:
Since y= -3, just put that in the equation.
-3 = 4x - 5
+5 +5
2 = 4x
/4 /4
x=1/2
The 10th term from the end of the ap 7,10,13....154;157 is?
Answer:
The 10th term from the end of the AP is 39 th term
[tex]\therefore a_{39} =114[/tex]
Step-by-step explanation:
Given:
Arithmetic Sequence as
7 , 10 , 13........154,157
∴ First term = a₁ = 7
Second term = a₂ = 10
∴ Common Difference = d = a₂ - a₁ = 10 - 7 = 3
∴ d = 3
[tex]a_{n} = 157[/tex]
To Find:
[tex]a_{10} = ?[/tex]
Solution:
An equation for the nth term of the arithmetic sequence is given by
[tex]a_{n} =a_{1} + (n-1)\times d[/tex]
Substituting a₁ and d and we get
[tex]157=7+(n-1)\times 3\\150=3n-3\\\\3n=147\\n=\frac{147}{3}\\\\n=49\\[/tex]
There are 49 terms in given AP
Therefore the 10th term from the end will be 39th term
[tex]a_{39} =a_{1} + (39-1)\times 3=7+38\times 3=114[/tex]
[tex]\therefore a_{39} =114[/tex]
Brian has money in two savings accounts. One rate is 5% and the other is 10%. If he has $900 more in the 10% account and the total interest is $273, how much is invested in each savings account?
Answers:
1220 dollars invested at 5% interest rate.
2120 dollars invested at 10% interest rate.
===============================================
Explanation:
Label the two accounts A and B.
Account A earns 5% interest
Account B earns 10% interest
Brian invests x dollars in account A and x+900 dollars in account B.
Using the formula, i = P*r*t, we can compute the simple interest for both accounts
----------
Start with account A over the course of t = 1 year.
i = P*r*t
i = x*0.05*1
i = 0.05x
then compute the interest for account B (use t = 1 also).
i = P*r*t
i = (x+900)*0.10*1
i = 0.10x + 90
---------
Over the course of 1 year, Brian earns 0.05x dollars in interest with account A and also 0.10x+90 dollars in interest with account B.
In total he earns 0.05x+0.10x+90 = 0.15x+90 dollars in interest.
We're told this amount of interest he earns is $273, so,
0.15x+90 = 273
0.15x+90-90 = 273-90
0.15x = 183
0.15x/0.15 = 183/0.15
x = 1220
This means $1220 was invested at 5% interest.
x+900 = 1220+900 = 2120
and $2120 was invested at 10% interest.
---------
Check:
If you invested $1220 in account A, then you earn
i = P*r*t
i = 1220*0.05*1
i = 61 dollars in interest
If you invest $2120 in account B, then you earn
i = P*r*t
i = 2120*0.10*1
i = 212 dollars in interest
So you get a total of 61+212 = 273 dollars in interest from both accounts. This confirms the two answers.
Final answer:
The question involves setting up a system of equations to find out how much Brian has invested in each of his savings accounts — one with a 5% interest rate and the other with a 10% rate, given that the total interest earned is $273 and the difference in the amount in each account is $900.
Explanation:
Brian has money in two different savings accounts, one with a 5% interest rate and the other with a 10% interest rate. He has $900 more in the account with the higher interest rate, and the total interest earned from both accounts is $273. To solve the problem, we need to set up a system of equations.
Let x be the amount in the 5% account, therefore x + $900 will be the amount in the 10% account. Using the formula Interest = Principal × Rate × Time, and assuming the time is 1 year, we get two equations:
0.05x (interest from the 5% account)0.10(x + $900) (interest from the 10% account)The sum of these two interests is $273, so we have:
0.05x + 0.10(x + $900) = $273Solving the equation, we find that x = $1,220 and x + $900 = $2,120. Therefore, Brian has $1,220 in the account with a 5% interest rate and $2,120 in the account with a 10% interest rate.
Tony’s fish weighs five pounds more than three times the weight of Mary’s fish. Let t represent the weight of Tony’s fish, and let m represent the weight of Mary’s fish.
Which expression below best represents the weight of Tony’s fish?
t = 5 + 3m is the required expression that represents weight of Tony fish
Solution:Let "t" represent the weight of Tony’s fish, and let "m" represent the weight of Mary’s fish
To find: expression that represents the weight of Tony's fish
According to given information,
Tony’s fish weighs five pounds more than three times the weight of Mary’s fish
Here the word "times" represents multiplication and "more than" represents addition
Weight of Tony fish = 5 + three times the weight of Mary’s fish
Weight of Tony fish = 5 + 3(m)
t = 5 + 3m
Thus the required expression is found out
Which pairs of triangles are similar? Check all that
apply.
AABC - ADEF
ADEF - AGHI
Ο ΔGHI - ΔABC
O AGHI - AJKL
AJKL - AABC
Answer:
JKL and ABC
DEF and GHI
Step-by-step explanation:
we know that
If two triangles are similar, then the ratio of its corresponding angles is proportional and its corresponding angles are congruent
so
In this problem
1) triangles JKL and ABC are similar
because
[tex]\frac{KL}{BC} =\frac{JL}{AC}[/tex]
substitute the given values
[tex]\frac{10}{20} =\frac{7}{14}[/tex]
Simplify
[tex]\frac{1}{2} =\frac{1}{2}[/tex] ---> is true
therefore
The ratio of the corresponding sides is proportional
That means----> The triangles are similar
2) triangles DEF and GHI are similar
because
[tex]\frac{HI}{EF} =\frac{GI}{DF}[/tex]
substitute the given values
[tex]\frac{15}{10} =\frac{12}{8}[/tex]
Simplify
[tex]1.5=1.5[/tex] ---> is true
therefore
The ratio of the corresponding sides is proportional
That means----> The triangles are similar
The pairs of triangles that are similar to each other are:
B. ΔDEF ~ ΔGHI
E. ΔJKL ~ ΔABC
Similar TrianglesCorresponding angles of two triangles that are similar are always congruent, however, their corresponding sides are proportional to each other. This means, their ratio is equal.
Thus, triangles KJL and ABC are similar triangles because:
BC/KL = AC/JL = 2
Also, triangles DEF and GHI are similar triangles because:
GI/DF = HI/EF = 1.5
Therefore, the pairs of triangles that are similar to each other are:
B. ΔDEF ~ ΔGHI
E. ΔJKL ~ ΔABC
Learn more about similar triangles on:
https://brainly.com/question/2644832
solve for x:3x=5x -8
Answer:
4
Step-by-step explanation:
3x = 5x - 8 is your equation. To solve for x, you want to get all the x's on the same side. You first subtract 5x from each side to get -2x = -8, and multiply both by 1- to get 2x = 8, and then divide both sides by 2 to find x = 4.
Answer:
Step-by-step explanation:
3x=5x -8
3x - 5x = - 8
-2x = -8
x = -8/-2
x = 4
twice the difference of a number and 8 is less than -20
Answer:
2(x-8) < -20
Step-by-step explanation:
Answer:
x = a number
2(x - 8) < -20
Write the general equation for the circle that passes through the points (-1,2)(4,2)(-3,4)
Answer:
x² + y² - 3x - 13y + 18 = 0
Step-by-step explanation:
Recall that the general equation of a circle looks something like this:
x² + y² + Ax + By + C = 0
substituting each of the points into the equation we get:
for (-1,2)
(-1)² + (2)² + A(-1) + B(2) + C = 0
1 + 4 -A+2B + C = 0
-A + 2B + C + 5 = 0 ------------ eq 1
for (4,2)
(4)² + (2)² + A(4) + B(2) + C = 0
16 + 4 + 4A + 2B + C = 0
4A + 2B + C + 20 = 0 ------------- eq 2
for (-3,4)
(-3)² + (4)² + A(-3) + B(4) + C = 0
9 + 16 -3A + 4B + C = 0
-3A + 4B + C + 25= 0 ----- eq 3
Now we have a system of equations with 3 equations and 3 unknowns.
Solving for A, B and C, we eventually get:
A = -3, B = -13, C = 18
Substituting these into the general equation:
x² + y² + Ax + By + C = 0
x² + y² - 3x - 13y + 18 = 0
The function f(x) = −x2 + 44x − 384 models the hourly profit, in dollars, a shop makes for selling coffee, where x is the number of cups of coffee sold, and f(x) is the amount of profit. Part A: Determine the vertex. What does this calculation mean in the context of the problem? (4 points) Part B: Determine the x-intercepts. What do these values mean in the context of the problem? (4 points) Part C: Determine the y-intercept. What does this value mean in the context of the problem? (2 points) (10 points)
Answer:
Part A) The vertex is the point (22,100) see the explanation
Part B) The x-intercepts are the points (12,0) and (32,0 see the explanation
Part C) The y-intercept is the point (0,-384) see the explanation
Step-by-step explanation:
Let
x ----> the number of cups of coffee sold
f(x) ---> the amount of profit
we have
[tex]f(x)=-x^{2} +44x-384[/tex]
This is a vertical parabola open downward (the leading coefficient is negative)
The vertex represent a maximum
Part A) Determine the vertex. What does this calculation mean in the context of the problem?
Convert the quadratic equation in vertex form
Factor -1
[tex]f(x)=-(x^{2}-44x)-384[/tex]
Complete the square
[tex]f(x)=-(x^{2}-44x+22^2)-384+22^2[/tex]
[tex]f(x)=-(x^{2}-44x+484)+100[/tex]
Rewrite as perfect squares
[tex]f(x)=-(x-22)^{2}+100[/tex]
The vertex is the point (22,100)
That means ----> The maximum profit of $100 is when the number of cups of coffee sold is 22
Part B) Determine the x-intercepts. What do these values mean in the context of the problem?
we know that
The x-intercepts are the values of x when the value of the function is equal to zero
so
we have
[tex]f(x)=-(x-22)^{2}+100[/tex]
For f(x)=0
[tex]0=-(x-22)^{2}+100[/tex]
solve for x
[tex](x-22)^{2}=100[/tex]
take square root both sides
[tex](x-22)=\pm10[/tex]
[tex]x=22\pm10[/tex]
so
[tex]x=22+10=32[/tex]
[tex]x=22-10=12[/tex]
The x-intercepts are the points (12,0) and (32,0)
That means -----> When the number of cups of coffee sold is 12 or 32 the profit is equal to zero
Part C) Determine the y-intercept. What does this value mean in the context of the problem?
we know that
The y-intercept is the value of the function when the value of x is equal to zero
so
For x=0
[tex]f(x)=-x^{2} +44x-384[/tex]
substitute the value of x
[tex]f(x)=-(0)^{2} +44(0)-384[/tex]
[tex]f(x)=-384[/tex]
The y-intercept is the point (0,-384)
That means ----> When the number of cups of coffee sold is zero the profit is negative -$384 (the cost is greater than the revenue)
I will mark brainliest for answering this question.
On a trip to visit relatives you drive 1,115.625 miles over the course of 21
hours and 15 minutes. What was the unit rate of the speed of your vehicle in miles
per hour? Round to the nearest tenth of a mile.
The unit rate of speed is 52.5 miles per hour
Solution:
Given that On a trip to visit relatives you drive 1,115.625 miles over the course of 21 hours and 15 minutes
We know that, 1 hour = 60 minutes
21 hours and 15 minutes = 21 hours + (15/60) hours = 21 + 0.25 = 21.25 hours
So they drive 1115.625 miles in 21.25 hours
To find the unit rate of speed of your vehicle in miles per hour, divide the total miles by time taken
unit rate of speed means miles driven in 1 hour
[tex]\rightarrow \frac{1115.625}{21.25} = 52.5[/tex]
So the unit rate of speed is 52.5 miles per hour
Is 7- y=5x+11 a standard form
Answer:
No.
Step-by-step explanation:
Because standard form is ax+by=c.
Linear system word problem
Answer:
1 year
Step-by-step explanation:
Create two equations to represent each tree. Linear equations are written in the form y = mx + b. "m" is the slope or rate. "b" is the constant or starting value.
In this problem, "m" is the rate of growth in inches per year.
"b" is the starting height.
let "x" be the number of years
let "y" be the height in inches
Tree A: y = 8x + 3
Tree B: y = 9x + 2
Solve the system of equations. Since both are equal to "y", you can equate them to each other and solve for "x". Isolate by doing reverse operations.
8x + 3 = 9x + 2
8x + 3 - 3 = 9x + 2 - 3 Subtract 3 from both sides
8x = 9x - 1
8x - 9x = 9x - 9x - 1 Subract 9x form both sides
-x = -1 Divide both sides by -1 to isolate
x = 1 Number of years for the trees to be the same height
Therefore it will take 1 year for the trees to be the same height.
If you wanted to know how tall the trees will be at the same height, find y. You can substitute x=1 in one of the equations.
y = 8x + 3
y = 8(1) + 3
y = 11 Number of inches when trees are the same height
What is the slope of (-3,-1) (1,-13)
Answer:
-3
Step-by-step explanation:
Answer:
-3
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(-13-(-1))/(1-(-3))
m=(-13+1)/(1+3)
m=-12/4
m=-3
8.25+1/4w=10.75 round to nearest 10
The value of w is 10
Solution:
Given equation is:
[tex]8.25 + \frac{1}{4}w = 10.75[/tex]
We have to solve above given equation for "w"
[tex]8.25 + \frac{1}{4}w = 10.75[/tex]
We know that 1 divided by 4 gives 0.25
8.25 + 0.25w = 10.75
Moving 8.25 from L.H.S to R.H.S
0.25w = 10.75 - 8.25
0.25w = 2.5
[tex]w = \frac{2.5}{0.25}[/tex]
w = 10
Thus value of w is 10
A circle with a radius of 2 cm sits inside a circle with radius of 4 cm. What is the area of the shaded region? Round your final answer to the nearest hundredth.
Answer:
The area of the shaded region is 37.70 cm2
Step-by-step explanation:
hoped this helped ;3
Answer:
Area of smaller circle is a = pi times 2^{2} = 4 pi
Area of larger circle is A = pi times {4}^{2} = 16 pi
The area of the shaded region is: 16 pi - 4 pi = 12 pi
and 12 times pi= 37.70 cm2
10. Alex is writing a number in scientific
notation. The number is greater than one
million and less than ten million. Which
number will Alex use as the exponent
of 10?
A 8
B 7
C 6
D 5
Answer:
C. 6
Step-by-step explanation:
Since the number is greater than one million and less than ten million, the number is seven digit which ranges from two million to nine million
Therefore, Alex will use 6 as the exponent
For the equations given below, which statement is true?
-3x-8=19
-3x-2=25
A. The equations have the same solution because the second equation can be obtained by subtracting 6 from both sides of the first equation.
B. The equations have the same solution because the second equation can be obtained by adding 6 to both sides of the first equation.
C. The equations have the same solution because the second equation can be obtained by subtracting 19 from both sides of the first equation.
OD. The equations do not have the same solution because the second equation can be obtained by adding 6 to both sides of the first equation.
Answer:
B
Step-by-step explanation:
If you add 6 to both sides, you get -3x-8+6=19+6 which is then -3x-2=25
PLEASE HELP!!! 15 POINTS AND WILL GIVE BRAINLIEST!!!
Two functions are represented in different formats.
Function 1:
x y
−2 −1
0 1
2 3
5 6
Function 2:
Graph of a line passing through the origin and the point begin ordered pair 1 comma 3 end ordered pair.
Which statements are true?
Select each correct answer.
Function 1 has a greater rate of change than function 2.
Function 2 has a greater rate of change than function 1.
Function 1 has a greater y-intercept than function 2.
Function 2 has a greater y-intercept than function 1.
Function 1 has a greater y-intercept than function 2
Step-by-step explanation: