Jayden ran [tex]\frac{6}{25}[/tex] of a kilometers in one minute
Solution:
Given that Angel and Jayden were at track practice
The track is two-fifth kilometers around
[tex]\text{ track length } = \frac{2}{5} \text{ kilometers}[/tex]
Angel ran 1 lap in 2 minutes
Jayden ran 3 laps in 5 minutes
To find: distance ran by Jayden in 1 minute
3 laps were run by Jayden in 5 minutes
3 laps = 5 minutes
"x" laps = 1 minute
Therefore laps run by Jayden in one minute is:
On cross multiplication we get,
5x = 3
[tex]x = \frac{3}{5}[/tex]
Therefore Jayden ran [tex]\frac{3}{5}[/tex] laps in 1 minute
Distance covered is:
Total track length = [tex]\frac{2}{5} \text{ km}[/tex]
Distance ran in 1 minute = [tex]\frac{3}{5} \times \frac{2}{5} = \frac{6}{25}[/tex]
Thus Jayden ran [tex]\frac{6}{25}[/tex] of a kilometers in one minute
write 1/5 as a terminating decimal
Answer: The answer is 0.2
Step-by-step explanation:
1 divided by 5 is 0.2 because 1 goes into 5 0.2 times.
Hope this helps!
7/8÷2/8 equal gfffghgddth
Answer:
3.5
Step-by-step explanation:
Jamie has 1/10 yard of blue felt and 5/6 yard yard of green felt.
Which answer is the most accurate estimate for how much more green felt Jamie has than blue felt?
Answer:
Jamie has 11/15 yards of Green Felt more than Blue Felt
Step-by-step explanation:
Green felt- Blue felt
= 5/6- 1/10
= 25/30- 3/30 ( taking LCM)
= 25 - 3/30
=22/30
=11/15 yards
LCM= 2*3*5= 30
Factors of 6= 2*3
Factors of 10= 2*5
if the number 9,899,399 is increased by 2,082 the result will be
Answer:
Step-by-step explanation:
9,899,399+2082
=9901481
Final answer:
To find out what 9,899,399 increased by 2,082 is, add the two numbers together, resulting in 9,901,481.
Explanation:
The question asks what the result will be if the number 9,899,399 is increased by 2,082. To find the result, we simply need to add the two numbers together. This type of problem involves basic arithmetic operations and is fundamental in understanding how to manipulate and work with numbers.
To calculate the result:
Start with the original number: 9,899,399.
Add the increase: 2,082.
Perform the addition: 9,899,399 + 2,082 = 9,901,481.
Therefore, when the number 9,899,399 is increased by 2,082, the result is 9,901,481.
How do u solve
1×-2y=4
-1×+10y=8
Answer: x = -8 ; y = -6
Step-by-step explanation:
1*x-2*y=4
1*x = 4 + 2*y
x = 4 + 2*y
Now you replace the value of x on the following equation:
-1*x+10*y=8
-1*(4 + 2*y) = 8
-4 - 2*y = 8
-2*y = 8+4
-2*y = 12
y = -12/2
y = -6
You replace the value of y in the previous equation:
x = 4 + 2*y
x = 4 + 2*(-6)
x = 4 - 12
x = -8
the concept and full method
Answer:
Step-by-step explanation:
This kinda looks like the limiting definition of a derivative.
Anyway, what we are doing with the f(2 + h) is evaluating f(x) with 2+h in place for x. That looks like this:
f(2 + h) = 2(2 + h) - 3 which simplifies to
f(2 + h) = 4 + 2h - 3 which simplifies to
2h + 1
From that we are subtracting f(2). What we are doing with that is evaluating f(x) with 2 in place for x. That looks like this:
f(2) = 2(2) - 3 which simplifies to
f(2) = 4 - 3 which simplifies to
f(2) = 1. Now put those together over h to get:
[tex]\frac{f(2+h)-f(2)}{h}=\frac{2h+1-1}{h}=\frac{2h}{h}=2[/tex]
what is
7/4 times 10
Answer: 17.5 hope this helps
the answer is 17.5
:D
Which graph shows the system of equations 4x+y=3 and 2x-3y=3?
Answer:
The graph in the attached figure
Step-by-step explanation:
we have
[tex]4x+y=3[/tex] ----> Red line
[tex]2x-3y=3[/tex] ---> blue line
Solve the system by graphing
Remember that the solution is the intersection point both graphs
using a graphing tool
The solution is the point (0.857,-0.429)
The graph in the attached figure
Solve for a.
a-15=4a-3
Answer:-4
Step-by-step explanation:
a-15=4a-3
a-4a=-3+15
-3a=12
a=-4
Find the value of x that makes ABCD a parallelogram.
Answer:
x=70
Step-by-step explanation:
I'm pretty sure the sum of all angles has to be 360°
and 70+70+40+40=220
so 220+x=360
we figure this out by taking 360-220 which equals 140
and then we divide 140 by 2 which is 70.
To double check, if you add 70+70+40+40+70+70, it equals 360.
The value of x from the given parallelogram is 70°. Therefore, option B is the correct answer.
What is parallelogram?A parallelogram is a special kind of quadrilateral that is formed by parallel lines. The angle between the adjacent sides of a parallelogram may vary but the opposite sides need to be parallel for it to be a parallelogram. A quadrilateral will be a parallelogram if its opposite sides are parallel and congruent.
Given that, ABCD is a parallelogram.
Here, ∠A+∠B+∠C+∠D=360°
70°+x+40°+70°+x+40°=360°
220°+2x=360°
2x=360°-220°
2x=140°
x=70°
Therefore, option B is the correct answer.
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I WILL GIVE YOU A BRILLIANT
Jessica's hamster cage is shaped like a rectangular prism. The cage has a height of 24 inches and a volume of 6,480 cubic inches. Jessica puts a piece of paper on the bottom of the cage. The paper fits the bottom of the cage perfectly.
What is the area of the paper on the bottom of the cage?
Enter your answer in the box.
in²
Answer:
270
Step-by-step explanation:
I am not sure if i am correct but i think you should divide 6,480 by 24 which is 270
Answer:
270 in2
Step-by-step explanation:
Divide 6480 . by 24
Servey says!?: 270 is the awnser!
What is the value of x in the equation 3/4x+2=5/4x-6
Solving for x...
3/4x+2=5/4x-6
8=2/4x
8=1/2x
x=16
To find the value of x in the given equation, we can eliminate the fractions, combine like terms, and solve for x. The value of x is 16.
Explanation:To find the value of x in the equation 3/4x+2=5/4x-6, we need to isolate x on one side of the equation. We can do this by first getting rid of the fractions. Multiplying each term in the equation by the LCD (Least Common Denominator) of 4 will help us eliminate the fractions. Then, we can combine like terms and solve for x.
Multiplying both sides of the equation by 4, we get: 4(3/4x+2) = 4(5/4x-6), which simplifies to: 3x + 8 = 5x - 24.Next, we can subtract 3x from both sides to isolate the x terms: 3x + 8 - 3x = 5x - 24 - 3x, giving us: 8 = 2x - 24.Then, we can add 24 to both sides of the equation to further isolate x: 8 + 24 = 2x - 24 + 24, which simplifies to: 32 = 2x.
Finally, we can divide both sides by 2 to solve for x: (32/2) = 2x/2, resulting in x = 16.
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Write the expression that represents the phrase,
"two times the difference of a number and 17."
Use x as the variable.
Answer:
2x + 17
Step-by-step explanation:
Answer:
2(x-17).
Step-by-step explanation:
The given phrase is "two times the difference of a number and 17."
We need to find the expression for given phrase.
Let x be the unknown variable.
Difference is denoted by "-" symbol.
Time is denoted by "×" symbol.
Difference of a number and 17 = x-17
Two times the difference of a number and 17 = 2×(x-17) = 2(x-17)
Therefore, the required expression is 2(x-17).
consider the linear system of equations Y = 2/5x - 1 and 2x -3y + 1 = 0
Answer:
The solution is the point (-5,-3)
Step-by-step explanation:
The complete question is
Consider the linear system of equations y = 2/5x - 1 and 2x -3y + 1 = 0
The solution of the system of equations is?
we have
[tex]y=\frac{2}{5}x-1[/tex] ----> equation A
[tex]2x-3y+1=0[/tex] ----> equation B
Solve by substitution
substitute the equation A in equation B
[tex]2x-3(\frac{2}{5}x-1)+1=0[/tex]
solve for x
[tex]2x-\frac{6}{5}x+3+1=0[/tex]
[tex]2x-\frac{6}{5}x+4=0[/tex]
Multiply by 5 both sides to remove the fraction
[tex]10x-6x+20=0[/tex]
[tex]4x+20=0[/tex]
subtract 20 both sides
[tex]4x=-20[/tex]
divide by 4 both sides
[tex]x=-5[/tex]
Find the value of y
[tex]y=\frac{2}{5}(-5)-1[/tex]
[tex]y=-3[/tex]
The solution is the point (-5,-3)
The question involves solving a system of linear equations from high school algebra. Substituting Y from the first equation into the second and solving for x, we find that x = -5 and Y = -3.
Explanation:The student is asking about solving a system of linear equations, which is a concept in algebra that falls under high school mathematics. To find the solution to the given linear system, we can use either substitution or elimination methods. Let's use substitution since the first equation has Y isolated.
From the first equation Y = 2/5x - 1, we substitute for Y in the second equation, which gives us 2x - 3(2/5x - 1) + 1 = 0. Simplifying, we get 2x - 6/5x + 3 + 1 = 0, which further simplifies to 4/5x + 4 = 0. Solving for x gives x = -5. Substituting x back into the first equation to find Y yields Y = 2/5(-5) - 1, so Y = -3. Therefore, the solution to the system of equations is x = -5 and Y = -3, which is the point where the two lines intersect.
x-3=5 what does x equal
Answer:
8
Step-by-step explanation:
x-3=5
add the 3 to both sides of the equal sign
x-(3+3)=(5+3)
x=8
Answer: X = 8
Step-by-step explanation: To solve for x in this equation, we want to get x by itself on the left side of the equation. Since 3 is being subtracted from x, to get x by itself, we need to add 3 to the left side of the equation. If we add 3 to the left side, we must also add 3 to the right side.
Notice that on the left side -3 and +3 cancel each other out so we're simply left with x. On the right side, 5 + 3 gives us 8 so we have x = 8.
We can check our answer by substituting 8 back into the original equation. So we have (8) - 3 = 5 or 5 = 5 which is a true statement so our answer is correct.
evaluate
5/6 f for f=4/9
10/27
1 7/8
8/15
Answer:
The answer is 10/27
Step-by-step explanation:
5/6 times 4/9 is equal to 10/27
Please answer the 3 questions above and SHOW YOUR WORK!
If you reply me with something like “amdblwdbkw” or “I don’t know the answer” I’m going to report account.
Question # 1 Solution:
As the expression [tex]13v + 8f +6b+3m[/tex] represents her cost, in dollars for the arrangements when she buys
v vases, f stems of flowers, b stems of wood bark, and m packages of marbles for the bottom of the vasesWhich statement is true?
A.The term 13v represents the cost of 13 vases.
B.The coefficient 6 represents the cost of b stems of wood bark.
C.The term 8f represents the cost of f stems of flowers at $8 per stem.
D.The coefficient 3 represents the number of packages of marbles she buys.
Choosing the correct statement:
As the formula for cost of any item can be calculated by multiplying the cost of one item with the total number of items.
So, if f represents the stems of flowers, and the cost of f stems of flowers at $8 per stem. Then according to the formula for cost of any item, the statement C is true i.e. "The term 8f represents the cost of f stems of flowers at $8 per stem" is the correct statement.
Question # 2 Solution
As the inequality is given as:
12x + 9x - 3 ≤ 3(2x + 14)
and we have to find the value of x.
So,
12x + 9x - 3 ≤ 3(2x + 14)
Step 1: Simplify both sides of the inequality
21x - 3 ≤ 6x + 42
Step 2: Subtract 6x from both sides.
21x - 3 - 6x ≤ 6x + 42 - 6x
15x - 3 ≤ 42
Step 3: Add 3 to both sides.
15x - 3 + 3 ≤ 42 + 3
15x ≤ 45
Step 4: Divide both sides by 5
15x/5 ≤ 45/5
3x ≤ 9
x ≤ 9/3
So, x ≤ 9/3 is the right answer. Please note that x ≤ 9/3 can also be written as x ≤ 3.
Hence, option A i.e. x ≤ 9/3 is correct. The solution graph is also attached in figure a.
Question # 3 Solution
As we have to find the correct statements from the given graph that represents John's weight (in pounds) as a function of time t, measured in days since January 1, 2017.
So, here are the correct statements that validate the graph:
The statement 'The independent variable is t, the number of days since January 1, 2017' is correct as t represents the independent variable because John's weight (in pounds) being the function of time t depends on the time t. Hence, time t is independent variable. The statement 'f(t) = 160 means that John weighed 160 lbs. on day 12, 120, and 172 after January 1, 2017' is correct because the output value i.e. f(t) of graph is showing John's weight weighed 160 lbs. i.e. f(t)=160 on the input values of day 12, 120, and 172 i.e. t = 12,120 and 172 after January 1, 2017. The statement 'f(0) = 140 means that John weighed 140 lbs. on January 1, 2017' is correct because the output value i.e f(0) of graph is showing John's weight weighed 140 lbs. i.e. f(0)=140 right on the day January 1, 2017 because t = 0 on January 1, 2017. And the value of t increases after January 1, 2017. The statement 'f(40) = 180 means that John gained 40 lbs. since January 1, 2017' is correct because on t = 40, the graph reaches to 180 i.e. the output value i.e. f(40) = 180 on t = 40. As on January 1, 2017, John was already weighed 140 i.e. f(0) = 140 on t = 0. So, f(40) = 180 means that John gained 40 lbs. since January 1, 2017.The statement 'f(200) - f(160) = 30 means that John gained 30 lbs. from day 160 after January 1, 2017 to day 200' is correct because the difference of f(200) and f(160) is 30 lbs. So, it specifies that on days' intervals from 160 to 200, the constitute gain of John's weight was 30 lbs.The statement 'The most appropriate domain for this function is all integers' is incorrect because when we talk about all integers it means it must have consisted negative integers too. But, as we cannot have negative time or days, and his weight also cannot be negative. So, to say that 'The most appropriate domain for this function is all integers' is not correct.
Keywords: inequality, equation, graph, rate of change, function
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The circumference of a circle is 8.97cm.
Find the length of the diameter.
Give your answer rounded to 2 DP
The length of the diameter is 2.86 cm rounded to 2 DP
Step-by-step explanation:
The formula of the circumference of a circle is
C = 2πr, where r is the radius of the circleC = πd, where d is the diameter of the circle∵ The circumference of a circle is 8.97 cm
- We need to find the diameter of the circle, then we will use
the 2nd formula of circumference above
∵ The circumference = πd
- Substitute the value of the circumference in the formula
∴ 8.97 = πd
- Subtract both sides by π
∴ 2.855 = d
- Round it to 2 decimal places (to the nearest hundredth)
∴ d = 2.86 cm
The length of the diameter is 2.86 cm rounded to 2 DP
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The ages of three siblings combined is 27. The oldest is twice the age of the youngest. The middle child is 3 years older than the youngest. Write and solve an equation to find the ages of each sibling
Answer:
Youngest Age = 6
Middle Age = 9
Oldest Age = 12
Step-by-step explanation:
Let youngest age be x
Middle one age be y
Oldest age be z
So,
x < y < z
Now lets come up with the equations using the statements.
Three age combined is 27, so we can write:
x + y + z = 27
Oldest is TWICE youngest, so we can write:
z = 2x
Middle is 3 YEARS OLDER than youngest, so we can write:
y = x + 3
Now we replace first equation with 2nd and 3rd, to get:
x + y + z = 27
x + x + 3 + 2x = 27
We can solve this for x:
x + x + 3 + 2x = 27
4x + 3 = 27
4x = 24
x = 24/4
x = 6
Now finding y:
y = x + 3
y = 6 + 3
y = 9
Now finding z:
z = 2x
z = 2(6)
z = 12
Thus,
Youngest Age = 6
Middle Age = 9
Oldest Age = 12
If James borrows $4,200 to pay his college tuition. He signs a 5 year simple interest loan. If monthly payments are $78.40, what is the interest rate on the loan?
0.024 /yr
Step-by-step explanation:
Without interest, the monthly repayment would be;
5 yrs = 12 months * 5 = 60 months
$4200 / 60
= $70
James, however, pays $78.40 monthly. The interest therefore is;
Jmaes pays a total of $78 * 60 = $4704 at the end of the 5 years. The formula for finding simple interest is;
A = P(1 + rt)
Where:
A = Total Accrued Amount (principal + interest)
P = Principal Amount
I = Interest Amount
r = Rate of Interest per year in decimal; r = R/100
R = Rate of Interest per year as a percent; R = r * 100
t = Time Period involved in months or years
4704 = 4200 (1 + 5r )
4704 = 4200 + 21000r
504 = 21000r
r = 504/21000
r = 0.024
Interest rate = 0.024 /yr
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What is the line through the points (2,3) and (19,17)
Answer:
y-3=14/17(x-2)
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(17-3)/(19-2)
m=14/17
y-y1=m(x-x1)
y-3=14/17(x-2)
write two division equations for each multiplication equation.
a. 15 x 2/5=6
b. 6 x 4/3=8
c. 16 x 7/8=14
Two division equations were found for each given multiplication equation. The division equations are the inverse of the multiplication equations, essentially reversing the operation.
Explanation:The goal is to find two division equations that correspond to each given multiplication equation. Basically, we are undoing or reversing the multiplication operation.
a. 15 x 2/5 = 6
First Division Equation: 6 ÷ 15 = 2/5Second Division Equation: 6 ÷ 2/5 = 15b. 6 x 4/3 = 8
First Division Equation: 8 ÷ 6 = 4/3Second Division Equation: 8 ÷ 4/3 = 6c. 16 x 7/8 = 14
First Division Equation: 14 ÷ 16 = 7/8Second Division Equation: 14 ÷ 7/8 = 16Learn more about Division and Multiplication Equations here:https://brainly.com/question/32871453
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The frequency table shows the number of times some people visited a movie theater last year . which set could the frequency table represent?
Answer:
The frequency table shows the number of times some people visited a movie theater last year . which set could the frequency table represent?
Step-by-step explanation:
besides spectators the capacity limit of victory stadium includes players, news reporters and stadium workers.how many nonspectators could be at a sold-out game
Answer:
Victoria Stadium
Step-by-step explanation:
Answer:
whats the answer
Step-by-step explanation:
English muffins are on sale for $1.99 per package, but only if you buy five packages. This is a $1.00 discount per package. What percent do you save off the regular price when buying the English muffins on sale? Round the answer to the nearest tenth.
Answer:
50.3% of profit.
Step-by-step explanation:
English muffins are on sale for $1.99 per package, but only if you buy five packages.
Therefore, the price of five packages of muffins on sale is $(1.99 × 5) = $9.95.
There is a $1.00 discount per package on sale.
So, the ordinary price per package of muffins is $(1.99 + 1) = $2.99.
Therefore, the ordinary price of five packages of muffins is $(2.99 × 5) = $14.95.
Hence, the percentage of profit that I will make when I purchase the package of muffins in the sale is [tex]\frac{14.95 - 9.95}{9.95} \times 100\% = 50.25\%[/tex] ≈ 50.3 % (Answer)
Can someone help me with these problems? I'm in k12 and this assignment was in classkick, so if anyone already completed this and can help, please do. I also am going to be asking some more questions, if you can help with those too. Thanks! (Will give brainliest.)
PLEASE HELP ME!
SOLVING QUESTIONS FROM 1ST PAGE
Given the point B(-5, 0)y = -3x - 5
Putting x = -5, and y = 0 in y = -3x - 5
0 = -3(-5) - 5
0 = 15 - 5
0 = 10 ∵Putting B(-5, 0) in y = -3x - 5 does not equate the equation.
As L.H.S ≠ R.H.S
So,
Does this check?
Answer: no ∵ L.H.S ≠ R.H.S
Given the point C(-2, 1)y = -3x - 5
Putting x = -2, and y = 1 in y = -3x - 5
1 = -3(-2) - 5
1 = 6 - 5
1 = 1 ∵Putting C(-2, 1) in y = -3x - 5 rightly equates the equation.
As L.H.S = R.H.S
So,
Does this check?
Answer: yes ∵ L.H.S = R.H.S
Given the point D(-1, -2)y = -3x - 5
Putting x = -1, and y = -2 in y = -3x - 5
-2 = -3(-1) - 5
-2 = 3 - 5
-2 = -2 ∵Putting D(-1, -2) in y = -3x - 5 rightly equates the equation.
As L.H.S = R.H.S
So,
Does this check?
Answer: yes ∵ L.H.S = R.H.S
SOLVING QUESTIONS FROM 2ND PAGE
Given the point B(6, 18)y = -2x + 18
Putting x = 6, and y = 18 in y = -2x + 18
18 = -2(6) + 18
18 = -12 + 18
18 = 6 ∵Putting B(6, 18) in y = -2x + 18 does not equate the equation.
As L.H.S ≠ R.H.S
So,
Does this check?
Answer: no ∵ L.H.S ≠ R.H.S
Given the point C(9, 24)y = 2x + 6
Putting x = 9, and y = 24 in y = 2x + 6
24 = 2(9) + 6
24 = 18 + 6
24 = 24 ∵Putting C(9, 24) in y = 2x + 6 rightly equates the equation.
As L.H.S = R.H.S
So,
Does this check?
Answer: yes ∵ L.H.S = R.H.S
SOLVING QUESTIONS FROM 3RD PAGE
Given the point D(2, 7)y = 3x + 4
Putting x = 2, and y = 7 in y = 3x + 4
7 = 3(2) + 4
7 = 6 + 4
7 = 10 ∵Putting D(2, 7) in y = 3x + 4 does not equate the equation.
As L.H.S ≠ R.H.S
So,
Does this check?
Answer: no ∵ L.H.S ≠ R.H.S
SOLVING QUESTIONS FROM 4th PAGE
b. Which function could have produced the values in the table.
A. y = 3x + 4
B. y = -2x + 18
C. y = 2x + 6
D. y = x + 9
The Table:
x y
3 12
6 18
9 24
Checking A) y = 3x + 4
Putting (3, 12), (6, 18) and (9, 24) in y = 3x + 4
For (3, 12)
y = 3x + 4
12 = 3(3) + 4
12 = 13 ∵ L.H.S ≠ R.H.S
Does this check?
Answer: no ∵ L.H.S ≠ R.H.S
For (6, 18)
18 = 3(6) + 4
18 = 18 + 4
18 = 22 ∵ L.H.S ≠ R.H.S
Does this check?
Answer: no ∵ L.H.S ≠ R.H.S
For (9, 24)
24 = 3(9) + 4
24 = 27 + 4
24 = 31 ∵ L.H.S ≠ R.H.S
Does this check?
Answer: no ∵ L.H.S ≠ R.H.S
So, the equation y = 3x + 4 could have not produced the all values in the table as the the ordered pairs in table do not satisfy(equate) the equation.
Checking B) y = -2x + 18
Putting (3, 12), (6, 18) and (9, 24) in y = -2x + 18
For (3, 12) ⇒ y = -2x + 18 ⇒ 12 = -2(3) + 18 ⇒ 12 = 12 ⇒ L.H.S = R.HSFor (6, 18) ⇒ y = -2x + 18 ⇒ 18 = -2(6) + 18 ⇒ 18 = 6 ⇒ L.H.S ≠ R.HSFor (9, 24) ⇒ y = -2x + 18 ⇒ 24 = -2(9) + 18 ⇒ 18 = 0 ⇒ L.H.S ≠ R.HSSo, y = -2x + 18 could have not produced all the values in the table, as (6, 18) does not equate the equation.
Checking C) y = 2x + 6
Putting (3, 12), (6, 18) and (9, 24) in y = 2x + 6
For (3, 12) ⇒ y = 2x + 6 ⇒ 12 = 2(3) + 6 ⇒ 12 = 12 ⇒ L.H.S = R.HSFor (6, 18) ⇒ y = 2x + 6 ⇒ 18 = 2(6) + 6 ⇒ 18 = 18 ⇒ L.H.S = R.HSFor (9, 24) ⇒ y = 2x + 6 ⇒ 24 = 2(9) + 6 ⇒ 24 = 24 ⇒ L.H.S = R.HSSo, y = 2x + 6 could have produced the values of in the table as all the orders pairs in the table satisfy/equate the equation.
Checking D) y = x + 9
Putting (3, 12), (6, 18) and (9, 24) in y = x + 9
For (3, 12) ⇒ y = x + 9 ⇒ 12 = 3 + 9 ⇒ 12 = 12 ⇒ L.H.S = R.HSFor (6, 18) ⇒ y = x + 9 ⇒ 18 = 6 + 9 ⇒ 18 = 15 ⇒ L.H.S ≠ R.HSFor (9, 24) ⇒ y = x + 9 ⇒ 24 = 9 + 9 ⇒ 24 = 18 ⇒ L.H.S ≠ R.HSSo, y = x + 9 could have also not produced all the values in the table, as (6, 18) and (9, 24) do not satisfy/equate the equation.
So, from all the verification we conclude that:
HENCE, ONLY y = 2x + 6 COULD HAVE PRODUCED THE VALUES IN THE TABLE AS ALL THE ORDERED PAIRS OF THE TABLE SATISFY/EQUATE THE EQUATION.
SOLVING QUESTIONS FROM 5th PAGE
What is the domain and range of the relation?
{(-3, 7), (6, 2), (5, 1), (-9, -6)}
Domain: Domain is the set of all the x-coordinates of the ordered pairs of the relation, meaning the all first elements of the ordered pairs in a relation include in the domain of the relation. Range: Range is the set of all the y-coordinate of the ordered pairs of the relation, meaning the all second elements of the ordered pairs in a relation include in the range of the relation.As the given relation is {(-3, 7), (6, 2), (5, 1), (-9, -6)}
The domain is: {-3, 6, 5, -9}
Note: generally, we write the numbers in ascending order for both the domain and range.
The domain could also be written in order as: {-9, -3, 5, 6}
The range is: {7, 2, 1, -6}
The range could also be written in order as: {-6, 1, 2, 7}
Keywords: equation, point, ordered pair, domain, range
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You missed a monthly payment on your mortgage. Your monthly payment is $1,278. Your mortgage holder places a 5%
penalty on all late monthly payments. What is your total penalty cost?
Answer: $63.90
Step by Step explanation:
$1,278 + 5% = 63.90
What would be the answer to this? Would it be a rotation of 90 degrees counterclockwise followed by reflection over x- axis???help
A circle with a radius of 9cm sits inside of a circle with a radius of 11cm. What is the area of the shaded region? Round your answer to the nearest hundredth. PLEASE HELP DUE TOMORROW
Answer:
[tex]A=125.66\ cm^2[/tex]
Step-by-step explanation:
The complete question is
The area of the shaded region is the area inside the larger circle and outside the smaller circle
so
To find out the area of the shaded region subtract the area of the smaller circle from the area of the larger circle
Remember that
The area of the circle is
[tex]A=\pi r^{2}[/tex]
therefore
The area of the shaded region is
[tex]A=\pi [r_1^2-r_2^2][/tex]
where
[tex]r_1=11\ cm[/tex] ---> radius of the larger circle
[tex]r_2=9\ cm[/tex] ---> radius of the smaller circle
assume
[tex]\pi =3.1416[/tex]
substitute
[tex]A=3.1416 [11^2-9^2][/tex]
[tex]A=3.1416 [40][/tex]
[tex]A=125.66\ cm^2[/tex]
A dress costs p dollars. An 8% sales tax must be added to the cost of the dress. Martha wants to multiply the cost of the dress by 0.08 to find the tax and then add it to the cost of the dress. Esther thinks that the cost of the dress should be multiplied by 1.08. The expressions for the two methods are shown below.
Martha: p+0.08p
Esther: 1.08p
Are the two expressions equivalent? Explain.
What does this mean in terms of the methods outlined by Martha and Esther?
Answer:
Yes, both expressions for the two method are equivalent.
Step-by-step explanation:
Let the cost of the dress be p as given.
Marta want to evaluate the tax which is proportional to the cost.
8% sales tax will correspond to (8/100)*p=0.08p
Then she will add 0.08 p to p to obtain 0.08p+p= p(0.08+1)= 1.08p
On the other hand, Esther thinks that the cost of the dress, p, should be multiplied by 1.08 to obtain 1.08p at once!
Thus both expressions are equivalent. Only that Martha is wanting to pay much attention to the details , while Esther is a quick one :-)!