Answer:
G = M/3 + 2
Step-by-step explanaion
We can interpret the quotient of Myrons height and 3 as "M/3" and we add "+2" to account for the "2 in. taller" part of the problem. We can also represent George's height using "G"
The expression that represents George's height, in inches is G = M/3 + 2
What is algebra?
Algebra is the branch of mathematics that helps in the representation of problems or situations in the form of mathematical expressions. It involves variables like x, y, z, and mathematical operations like addition, subtraction, multiplication, and division to form a meaningful mathematical expression.
Given:
George is 2 in. taller than the quotient of Myron's height and 3.
let M represent Myron's height, in inches.
and, the quotient of Myrons height and 3 can be written as
=M/3
Now, add 2 to Myron's height.
Then George's height will be
G = M/3 + 2
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Choose h and k such that the system has (a) no solution, (b) a unique solution, and (c) many solutions.
x1 +hx2 = 3
5x1 + 15x2 = k
a. Select the correct answer below and fill in the answer box(es) to complete your choice. (Type an integer or simplified fraction.)
A. The system has no solutions only when k nothing and h is any real number.
B. The system has no solutions only when h nothing and k nothing.
C. The system has no solutions only when h nothing and k is any real number.
D. The system has no solutions only when h nothing and k nothing.
E. The system has no solutions only when h nothing and k nothing.
F. The system has no solutions only when k nothing and h is any real number.
G. The system has no solutions only when h nothing and k nothing.
H. The system has no solutions only when h nothing and k is any real number.
b. Select the correct answer below and fill in the answer box(es) to complete your choice. (Type an integer or simplified fraction.)
A. The system has a unique solution only when h and k
B. The system has a unique solution only when h =-and k is any real number.
C. The system has a unique solution only when k | and h is any real number.
D. The system has a unique solution only when h-U and k = 1
Answer:
a) C) The system has no solutions only when h=3 and k is any real number.
b) D) The system has a unique solution when [tex]h=(-\infty,3)U(3,\infty)[/tex] and k is any real number.
c) The system has may solutions when h=3 and k=15
Step-by-step explanation:
a) In order to determine when the system will have no solution, we can start by solving the equation by substitution. We can solve the first equation for x1:
[tex]x_{1}+hx_{2}=3[/tex]
so
[tex]x_{1}=3-hx_{2}[/tex]
Next we can substitute this into the second equation so we get:
[tex]5(3-hx_{2})+15x_{2}=k[/tex]
We distribute the 5 into the first parenthesis so we get:
[tex]15-5hx_{2}+15x_{2}=k[/tex]
and group like terms:
[tex]-5hx_{2}+15x_{2}=k-15[/tex]
we factor x2 so we get:
[tex]x_{2}(-5h+15)=k-15[/tex]
and solve for x2:
[tex]x_{2}=\frac{k-15}{-5h+15}[/tex]
this final answer is important because it tells us what value the system of equations is not valid for. That answer will not ve vallid if the denominator is zero, so we can set the denominator equal to zero and solve for h, so we get:
[tex]-5h+15= 0[/tex]
and solve for h:
[tex]-5h= -15[/tex]
[tex]h=\frac{-15}{-5}[/tex]
[tex]h= 3[/tex]
so it doesn't really matter what value k gets since all that matters is that the denominator of the answer isn't zero.
b)
For part b we need to know when the system of equations will have infinitely many answers. Generally, this will happen when both equations are basically the same, so we need to make sure to simplify the second equation so it looks like the first equation, compare them and determine the respective coefficients.
So we take the second equation and factor it:
[tex]5x_{1}+15x_{2}=k[/tex]
we start by factoring a 5 from the left side of the equation so we get:
[tex]5(x_{1}+3x_{2})=k[/tex]
Next, we divide both sides of the equation into 5 so we get:
[tex]x_{1}+3x_{2}=\frac{k}{5}[/tex]
we now compare it to the first equation:
[tex]x_{1}+hx_{2}=3[/tex]
[tex]x_{1}+3x_{2}=\frac{k}{5}[/tex]
In this case, every coefficient of the two equations must be the same for us to get infinitely many answers, so we can see that h=3 and [tex]\frac{k}{5}=3[/tex]
when taking the second condition and solving for k we get that:
[tex]k=3(5)[/tex]
so
k=15
Anything else than the specific combination h=3 and k=15 will give us unique solutions, so for b, the answer is:
D) The system has a unique solution when and k is any real number.
c)
We have already solved part c on the previous part of the problem, so the answer is:
The system has many solutions when h=3 and k=15
Write the equation of each line described in slope-intercept form (y = mx + b) with a slope of -6 and x-intercept of 4. (4,0)
Answer:
ill give u the answer if u do 73 divided by 2628
Step-by-step explanation:
A parachutists speed during a free fall reaches 153 miles per hour. What is this speed in feet per second? at this speed, how many feet will the parachutist fall during 15 seconds of free fall? in your computations, use the fact that 1 mile is equal to 5280 feet. do not round your answer
153 miles x 5280 feet per mile = 807,840 feet per hour.
1 hour = 3600 seconds.
The speed is 807,840 feet / 3600 = 224.4 feet per second.
Distance in 15 seconds = 224.4 x 15 = 3,366 feet.
The height of the rocket after t seconds is given by the equation h(t) = -16t² + 42t
What is an equation?An equation is an expression that shows the relationship between two or more variables and number.
1 mile = 5280 feet, 1 hour = 3600 seconds
153 miles per hour = (153 * 5280) / (3600) ft/s = 224.4 ft/s
After 15 seconds, height = 224.4 ft/s * 15 s = 3366 ft
The speed of the parachute is 224.4 ft/s, while after 15 seconds the distance fell was 3366 ft.
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I will give you branilest!
When you mix two colors of paint in equivalent ratios, the resulting color is always the same. Complete the table as you answer the questions.
cups of blue paint cups of yellow paint
2 10
1 5
3 15
.
4. What is the constant of proportionality in the table? (choose one)
a. 5
b. 8
c. 9
d. 1
Answer:
I believe it is 5 because when simplified they all simplify to 1/5
HELP ASAP I have no clue what to do here pls just click the picture and help :(
Answer: 3 Multiply
Step-by-step explanation: u would Multiply 4x7
2x + 3x = 60 for x = 12
True or false
Answer:
true
Step-by-step explanation:
Trust me
Answer:
True
Step-by-step explanation:
2(12)+3(12)=60
24+36=60
Three consecutive integers add up to 258. What is the smallest integer?
Answer:
Answer the three consecutive integers are 85, 86 and 87. Taxicab number 1729 is the smallest integer that can be expressed as a sum of two positive integer cubes in 2 distinct ways.
Answer:
85, 86, and 87
Step-by-step explanation:
85 + 86 + 87 = 258
Brainliest Please???
Which factor can cause secondary succession?
A. clear cutting
B. glacial melting
C. competition
D. predation
(Which one from these answers?)
Answer:
a
Step-by-step explanation:
sharon drops a rubber ball from a height of 160 feet every bounce sends the ball half as high as it was before what is the total vertical (up and down ) distance the ball has traveled from the mament it is dropped to the moment it hits the floor for the fourth time
Answer:
10 feet.
Step-by-step explanation:
First time: 160/2=80.
Second time: 80/2=40.
Third time: 40/2=20.
Fourth time: 20/2=10.
Boom.
why does the graph of a proportional relationship must pass through the origin (0,0)
Answer:
Directly proportional relationships always pass through the origin (0,0). There are other linear relationships that do not pass through the origin.
The graph of a proportional relationship must pass through the origin (0,0). Because of the value of k, the ordered pair (0, 0) satisfies this equation.
What is a graph?
The relation between lines and points is described by a graph, which is a mathematical description of a network. A graph is made up of some points and connecting lines. It doesn't matter how long the lines are or where the points are located. A node is specified for each element in a graph.
A ray is used to describe any proportional relationship using an equation of the form y = kx. The ordered pair (0, 0) satisfies this equation regardless of the value of k, hence the ray or line must traverse the origin.
Thus, the graph of a proportional relationship must pass through the origin (0,0). Because of the value of k, the ordered pair (0, 0) satisfies this equation.
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Please help it’s urgent!!!!!
Answer:
5 hours; Home Decor
Step-by-step explanation:
First thing you want to do is make an equation of the two to find when they'll be the same price. So it'll look something like this:
500+35x=600+15x
Get like terms together
100=20x
divide
x=5
After 5 hours, they'll be the same price.
For the second half, plug in the number 3 instead of 5 into the original equation
500+105 600+45
605 645
So he'd go with the first company
Three partners are investing a total of $700,000 to open a garden and landscaping store. The first partner wns 30% of the business, and the second partner owns 25% of the business. What percent does the third partner own? Just input the numerals for your answer -do not add a percent sign. hip
Answer: 45
Step-by-step explanation: The 3rd partner has 45% of the store. Which is also $315,000.
Answer: the third partner owns 45% or $315,000 of the business.
Step-by-step explanation:
30 percent of 700,000=210,00
25 percent of 700,000=175,000
175,000+210,000=385,000
700,000-385,000= 315,000
the third partner owns 315,000 and 315,000=45%
2,9,23,51,107
Determine the next terms of sequence
Answer:
answer is 142
Step-by-step explanation:
If jack age is 5 years, 4 months old and he is expected to live 79.7. years. How many more years is jack is expected to live?
Need help rn will give brainlyest if correct answer with explaining
unit ratio
Answer: The cost per bag is $27
Step-by-step explanation:
Divide 135 by 5 = 27
Unit ratio means that if you know the rate per unit, you can calculate the cost by multiplying the constant rate by the number of units. In this question, the rate is $27 and the unit is the bag.
The ratio looks like
1:27 as 2:54 as 3:81 as 4:108 as 5:135
They are all equivalent to 1/27
y = 27x is another way of writing an equation for this ratio.
Which situation can be represented by this inequality?
3 + 2.0 > 8x
Select one:
The cost of 2 candy bars plus a $3 bag of chips is greater than 8 candy bars.
The cost of 2 candy bars with a discount of $3 is greater than 8 candy bars.
o The cost of a $3 bag of chips plus 2 candy bars is at least as much as 8 candy bars.
The cost of a $3 bag of chips plus 2 candy bars is less than 8 candy bars.
Answer: D
Step-by-step explanation:
Steve drew line segments CDEF, GHI, ADH, and BEH as shown in the
diagram below. Scalene ADEH is formed.
If segment CDEF is parallel to segment GHI, which statement is true? *
Answer:
BEF=IHEStep-by-step explanation:
ADE=DHG
FEH=IHE
ADE=DHE
ADC=EHI
BEF=IHE <This would be the correct answer if segment CDEF is parallel to segment GHI.
I mark as brainliest
Answer:
.1
Step-by-step explanation:
Answer:
Point Q is represented by the ordered pair (-2,9)
Four times a number, added to 8, is 32
Answer: 6
Step 1: Subtract 8.
32 - 8 = 24
Step 2: Divide by 4, since the question is asking for 4 times the number.
24 ÷ 4 = 6
Answer = 6
The given table values represents a liner equation. What is the slope?
A. 2
B. 3
C. 1
D. 4
Answer:
A. 2
Step-by-step explanation:
[tex] slope (m) = \frac{y_2 - y_1}{x_2 - x_1} [/tex]
Use any two points given in the table of values. Let's use (1, 5), (3, 9)
Let,
[tex] (1, 5) = (x_1, y_1) [/tex]
[tex] (3, 9) = (x_2, y_2) [/tex]
Plug these values into the slope formula:
[tex] slope (m) = \frac{9 - 5}{3 - 1} [/tex]
[tex] slope (m) = \frac{4}{2} [/tex]
[tex] slope (m) = 2 [/tex]
What is the slope-intercept equation of the line below?
5
-5
H
O A. y = 2x+1
O B. y=-2x+1
O C. y= 2x-1
O D. y=-2x-1
Answer:
could I have a picture of the line
Given f(x) = -x + 7, find x when f(x)= -4
Answer:
x = 11
Step-by-step explanation:
f(x) = -x + 7
f(x) = -4
Using substitution, -x + 7 = -4
Then you can solve from there
-x + 7 = -4
-x = -11
x = 11
Hope this helps!
(I apologize if I'm incorrect)
Evaluate : (r - 3)³ + r² if r = -3 and s = -4. Show all the steps of working for this question.
I have a math test please give me the right answer!!
Answer:
-207
Step-by-step explanation:
Using r= -3, we can substitute r in the whole equation as (-3) which gives you: ((-3)-3)^3 +(-3)^2. Now you can calculate these values in a step by step manner. (-6)^3 +9 then to -216 +9 which brings you to the answer of -207.
Answer:
225
Step-by-step explanation:
(r - 3)³ + r² if r = -3 and s = -4
(-3 - 3)^3 + (-3)^2
(-6)^3 + (9)
(-6 x -6 x -6) + 9
-216 + 9
-207
There are 70 fish in the tank. Half of the fish have orange spots and 1/5 of the remaining fish have orange and black spots. How many fish have orange and black spots?
Answer:
7 orange and black fish
Step-by-step explanation:
a fifth of the remaining fish is 7 because you are doing 35*1/5. 35 is the remaining number of fish because already half of the other fish is 35 and they are orange
Alex would like to buy one pack of colored pencils
Answer:
good for alex
Step-by-step explanation:
Please help !! I am having trouble, I keep getting this question wrong.
Answer:
sure
Step-by-step explanation:
I will do that okay
Each student in the fifth grade at Bonchon elementary bought 15 to the book fair they bought 1245 altogether how many fifth grade students go to Boston elementary
Answer:
83 fifth grade students
Step-by-step explanation:
the total amount was 1,245
they each bought 15
equation is 1,245/15=?
answer is 83
Answer:
3 students went to the book fair
Step-by-step explanation
Doing inverse operations so you do 1245 divided by 15 and that would be your answer.
There are 24 marbles in a jar. 3 marbles are added to the jar when the class is good. How many times can the class be rewarded to get 100 marbles
What is the smallest value that x^(2)+6 can have?
Answer:
-56.9034
Step-by-step explanation:
prime factorization of 60 error
Answer:
2*2*3*5
Step-by-step explanation: