Answers
Start with equation (1). Plug in (x,y) = (-10,-1)
x + 5y = -15
-10 + 5y = -15 ... replace x with -10
-10 + 5(-1) = -15 ... replace y with -1
-10 - 5 = -15
-15 = -15 ... true equation
So we've confirmed one equation so far. Let's check the other equation
--------------------
Start with equation (2). Plug in (x,y) = (-10,-1)
y = (1/5)*x + 1
y = (1/5)*(-10) + 1 ... replace x with -10
-1 = (1/5)*(-10) + 1 ... replace y with -1
-1 = -2 + 1
-1 = -1
Since both equations are true when (x,y) = (-10,-1), this confirms the answer. Nice work on getting the correct answer.
Visually we can see the two lines crossing at (-10,-1). See the attached image. Note: 1/5 = 0.2 so the second equation can be written as y = 0.2x+1
Related Questions
<ABD has a measure of 36 degrees. a)find the compliment of the angle b)find the supplement of that angle
Answers
b) The supplement of an angle is whatever number can be added to the original to add up to 180 degrees. The supplement of <ABD would be 180-36=144
What is the value of the expression 3^−4 ?
Answers
When there is a negative exponent, do the problem the same, but make it it’s reciprocal:
3^-4
1/3^4
1/81
Hope this helped!
The required simplified value for the expression [tex]3^{-4}[/tex] is 1 / 81.
Given that,
To determine the simplified value of the expression [tex]3^{-4}[/tex] .
The process in mathematics to operate and interpret the function or expression to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
Here,
[tex]3^{-4} = 1/3^4[/tex]
3 * 3 * 3 * 3 = 9 * 9 = 81
[tex]3^{-4} = 1 / 81[/tex]
Thus the required simplified value for the expression [tex]3^{-4}[/tex] is 1 / 81.
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1. Is it possible for a composite number to have more than one prime factorization? Is it possible for a number to have no prime factors? Why?
2.Give and example of how prime factorization could be used in the real world
Answers
Prime number are numbers that only has a factors of 1 and itself.
It is very possible for a composite number to have more than one prime factorization. But, it is not possible for a number to not have a prime factor.
When you factorize a number, you break it down into its most basic factors and these basic factors are all prime numbers.
Prime factorization is basically breaking down numbers to its most basic factors. It can be used in everyday living especially when we deal with numerical transactions like money and values.
Study the number 31,342. How many times less is the three in the hundreds place as compared to the three in the 10,000 place?
Answers
of the 150 people surveyed seven out of 10 said they owned at least one pet how many of the people surveyed owned pets
Answers
ax-x=c
solve the equation for x
Answers
Like last problem, group the x out.
x(a-1) = c
Now divide.
x = c/a-1
Hope this helps!
the school fun fair made 1,768 on games and 978 on food sales. how much money did the fun fair make on games and food.
Answers
(3 – 6y2)(y2 + 2) what is this
Answers
3(y^2 + 2) - 6y^2(y^2 + 2) =
3y^2 + 6 - 6y^4 - 12y^2 =
-6y^4 - 9y^2 + 6 <===
X to 2nd power equals 9/256
Answers
An airplane can travel at a speed of 550 mph. Write and solve an equation to find the time it will take to fly from London to Montreal, a distance of approximately 3300 miles
Answers
The time it will take for an airplane to fly from London to Montreal at a speed of 550 mph covering a distance of 3300 miles is approximately 6 hours.
Explanation:To find the time it will take for an airplane to fly from London to Montreal, we can use the equation for speed, which is:
Speed = Distance \u00f7 Time
Knowing that the plane can travel at a speed of 550 mph and the distance from London to Montreal is 3300 miles, we can rearrange the equation to solve for time:
Time = Distance \u00f7 Speed
Time = 3300 miles \u00f7 550 mph
After calculating, we find that:
Time = 6 hours
Therefore, it will take the airplane approximately 6 hours to fly from London to Montreal at a constant speed of 550 mph, ignoring any other factors such as wind or air traffic delays.
To find the time it will take, we can use the formula Time = Distance/Speed. In this case, it will take approximately 6 hours to fly from London to Montreal.
Explanation:To find the time it will take to fly from London to Montreal, we can use the formula Time = Distance/Speed. In this case, the distance is approximately 3300 miles and the speed is 550 mph.
Plugging in the values into the formula, we get Time = 3300 miles / 550 mph = 6 hours. So, it will take approximately 6 hours to fly from London to Montreal.
Therefore, the time it will take to fly from London to Montreal is 6 hours.
4,444,444 the digit in the hundreds thousands place is 10 times the value of the digit in the ten thousands place?
Answers
"true or false:
the digit in the hundreds thousands place is 10times the value of the digit in the ten thousands place"
then that would be true.
I'm not really sure what you're asking... sorry :|
So far, 37 miles of a new highway have been completed. This is one mile less than two thirds of the entire length. How long will the new highway be when complete?
Answers
37 + 1 = 2/3x
38 = 2/3x
38 / (2/3) = x
38 * 3/2 = x
114/2 = x
57 = x <=== when complete, the highway will be 57 miles
The total length of the new highway, when complete, will be 57 miles.
Explanation:The question states that 37 miles of a new highway have been completed and this distance is one mile less than two thirds of the entire length of the highway. To solve this problem, we need to write an equation using the given information and solve for the variable representing the total length of the highway.
Let's denote the total length of the highway as 'x'. According to the problem, two thirds of this length minus one mile equals 37 miles. Forming an equation, we can write (2/3)x - 1 = 37.
To solve for 'x', first add 1 to both sides of the equation to get rid of the '-1' on the left, that gives us (2/3)x = 38. After, to completely isolate 'x', multiply both sides of the equation by the reciprocal of 2/3, which is 3/2. Doing this results in 'x' = 38 * (3/2) = 57 miles.
Therefore, the new highway will be 57 miles long when complete.
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What is 40/3 simplified
Answers
40/3 can't be necessarily simplified, but it can be converted to a mixed number.
It would be 13 1/3
Hope this helps!
in which square is 25% not shaded
Answers
Which is the best estimate for the sum of 31,096 and
58,721?
Answers
how is 2.25 written as a fraction
Answers
So 25/100 is your answer.
Men in the age groups of 18-34 years need to be to run a marathon in 3 hours and 10 minutes to qualify for the boston marathon how many seconds is this?
Answers
You would take 3 hours to minutes which is 180 then add the following 10 minutes and convert it to seconds.
which number has a 2 in position where it represents 10 times as much as the 2 in 4,523 a. 241 d. 612 c. 928 b. 2,175
Answers
The 2 in 4,523 is 20.
20 times 10= 200.
So the answer has to have a 2 in the hundreds place.
The number 2,175 is the correct answer because its 2 is in the 'hundreds' place which is 10 times as much as the 2 in the 'tens' place of the number 4,523.
Explanation:In the provided options for numbers, we are to find a number which has a 2 that represents 10 times as much as the 2 in 4,523. In number 4,523, the number 2 represents '20', that is, it is in the 'tens' place. Therefore, we are looking for a number where 2 is in the 'hundreds' place as the 'hundreds' place is 10 times the 'tens' place. From the options given, only number 2,175 fits this criterion as in this number, 2 is in the 'hundreds' place which is 10 times as much as the 'tens' place.
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A crane cable can support a maximum load of 17,000 kg. If a bucket has a mass of 4,000 kg and gravel has a mass of 1,500 kg for every cubic meter, how many cubic meters of gravel (g) can be safely lifted by the crane? Enter any fractions as reduced improper fractions.
Answers
4000 + 1500x = 17,000
1500x + 4000 = 17,000
Now solve for x
1500x + 4000 = 17000
1500x + 4000 - 4000= 17000 - 4000
1500x = 13000
1500x / 1500 = 13000 / 1500
x = [tex]\frac{26}{3}[/tex]
How many shapes are in the world
Answers
To keep it short and simple, there are an infinite number of shapes in the world.
-4+6(-4x+3) combining like terms & distributive property
Answers
Disribute 6 into both numbers in the parenthesis. So that means...
6 x 4x = 24x
6x3 = 18
Your new expression is:
-4 +24x +18
Combine ALL like terms:
-4 + 18 = 14
New Expression:
14 + 24x
And since you don't have any equal sign, that's as much as you can do to simplify the expression.
What is the answer to -1 = 5+x divided by 6
Answers
-1=5+x
-1-5=5-5+x
x = -6
then, we will divide this answer by 6 as mentioned in the problem as follows:
-6/6 = -1
To do this, first we can solve the equation.
-1 = 5 + x
-5 -5
-6 = x, then divide -6 by 6 to get your answer.
Answer: x = -1
Avery and her friends attend a museum. It costs $5 to enter the main exhibit hall, with an added charge of $3 to view each special exhibit. Avery writes an equation that models the total price of visiting the museum as a function of the number of special exhibits they view. What is the slope and y-intercept of Avery’s model?
Answers
And y intercept =5+3x
Hence, slope = 3 and, y-intercept = 5.
What is function?
Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.
Here, given that,
Avery and her friends attend a museum. It costs $5 to enter the main exhibit hall, with an added charge of $3 to view each special exhibit.
Avery writes an equation that models the total price of visiting the museum as a function of the number of special exhibits they view.
Now, let the function be,
f(x)= 3x+5 = the total price of visiting the museum
[where, x= special exhibit & 5=the main exhibit hall]
Let, y = f(x)
So, w get, y=3x+5
Hence, slope = 3
and, y-intercept = 5.
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Segment PQ bisects segment ST at point R.
SR=2x+2 and ST=40
Find the length of segment SR.
a
SR=9
b
SR=40
c
SR=36
d
SR=20
Answers
2x+2, 2×9+2, 18+2, 20=sr
or simply 40÷2=20
Answer:
2(2x+2)=40, 4x+4=40, 4x=36, x=9..plug in 9..
2x+2, 2×9+2, 18+2, 20=sr
Step-by-step explanation:
(4.9 x 10^-2) (9.80 x 10^2) = _____
Answers
4.9×10^-2 and 9.80×10^2 ( find the scientific notation)
.0049 for the first one
980. for the second one
Then you multiply:
.0049×980.=4.802
Your answer is 4.802
4 divided by 10.2 =
Please help me
Answers
round to the nearest hundredth
0.39
Quinn runs 3 miles 3 times every week. How many miles does Quinn run in 6 weeks
Answers
Change the order and the grouping of the addends so that you can use mental math to find the sum. Then find the sum. 43+39+43+11=
Answers
Final answer:
By applying the commutative property of addition and rearranging the numbers for easier mental calculation, the sum of 43 + 39 + 43 + 11 can be found to be 136.
Explanation:
The question asks to change the order and the grouping of the addends for easier mental calculation, and then to find the sum of 43 + 39 + 43 + 11. By understanding the commutative property of addition, which states that numbers can be added in any order without changing the sum, we can rearrange these numbers for easier addition.
To use mental math effectively, grouping numbers that make round numbers or those that are easier to add can simplify the process. Here, we can group 43 and 43, which are identical, and 39 and 11, which sum up to a round number.
Therefore, by rearranging:
43 + 43 = 86
39 + 11 = 50
Adding these sums together:
86 + 50 = 136
By changing the order and grouping of the addends, we find that the sum is 136.
A water cooler fills 150 glasses in 30 minutes. How many glasses of water can the cooler fill per minute?
Answers
5x30=150
The teacher separated her class of twenty-eight student into two group. one group has 4 more than twice as many students as the other group. how many students are in each group?
Answers
x=group 1
y=group 2
x+y=28
2x+4=y
Isolate the variable in equation 1.
y=-x+28
Substitute it into equation 2.
-x+28=2x+4
Solve.
-3x=-24
x=8
Substitute it into one of the equations for y.
-x+28=y
-8+28=y
y=20
There are 8 students in one group and 20 students in the other.
Hope this helps!
x=28-y
x=4+2y
28-y=4+2y
28-4=2y+y
24=3y
24/3=y
y=8
x+y=28
x+(8)=28
x=28-8
x=20
(20)=4+2(8)
20=4+16
20=20
one group=20, other group=8