The solution to system is x = 0 and y = -1
Solution:
Given system of equations are:
-8x + 2y = -2 ----------- eqn 1
4x + 4y = -4 ---------- eqn 2
We have to solve the system of equations
We can solve the equations by elimination method
Multiply eqn 2 by 2
8x + 8y = -8 ------ eqn 3
Add eqn 1 and eqn 3
-8x + 2y = -2
8x + 8y = -8
( + ) ---------------
0x + 2y + 8y = -2 - 8
10y = -10
Divide both sides by 10
y = -1
Substitute y = -1 in eqn 1
-8x + 2(-1) = -2
-8x - 2 = -2
-8x = -2 + 2
x = 0
Thus the solution to system is x = 0 and y = -1
Eighteen less than the quotient of twelve and a number
Eighteen less than the quotient of twelve and a number is written as:
[tex]\frac{12}{x} - 18[/tex]
Solution:
Given statement is:
Eighteen less than the quotient of twelve and a number
We have to translate the given sentence into algebraic expression
Let "x" be the number
Therefore,
Eighteen less than the quotient of twelve and "x"
Quotient means result of division
Therefore,
[tex]\frac{12}{x} - 18[/tex]
Which means, 18 less than quotient of 12 and x
Thus the given sentence is translated into algebraic expression
The phrase 'eighteen less than the quotient of twelve and a number' is mathematically expressed as 12/n - 18, where n represents the unknown number.
The expression 'eighteen less than the quotient of twelve and a number' translates to a mathematical operation. First, we find the quotient of twelve and a number, which is the result of dividing twelve by that number (let's call it n). Then, we subtract eighteen from that quotient. The algebraic representation of this expression is 12/n - 18.
It's important to follow mathematical rules and order of operations correctly when performing such calculations, similarly to how the rules of arithmetic must be applied correctly regardless of the context, as is described in the example of counting goats or students. Mathematics provides various methods to arrive at the correct answer, and in this case, simplifying the operation is straightforward. It is a demonstration of understanding the correct usage of mathematical operations as well as number fluency.
A rectangular table has a border of same-sized square tiles. The rectangle has 10 tiles along the length and 6 tiles along the width for a total of 28 total tiles. Notice that 10 + 10 + 6 + 6 ≠ 28. If the rectangular table has L tiles along the length and W tiles along the width, which of the following expressions represents the total number of tiles in the border?
l. 2l + 2w
II. 2l + 2w + 4
III. 2l + 2w - 4
IV. 2(1-2) + 2(w-2)+4
A. I only B. II and IV only C. III only D. III and IV only
Answer:
IV. 2(1-2) + 2(w-2)+4
Step-by-step explanation:
III. 2l + 2w - 4
1. If I have a car that cost 30,000 and every year it loses value at 20% a year, then what would the value of
the car be after 5 years?
Growth
rate
Answer:
$9,830.40
Step-by-step explanation:
1st year--$30,000.00 x .20=$6,000.00= $30,000.00 - $6,000.00 =$24,000.00
2nd year--$24,000.00 x .20=$4 800.00=$24,000.00 -$4,800.00=$19 200.00
3rd year---$19,200.00 x .20 =$3,840.00= $19,200.00 - $3,840.00 = $15,360.00
4th year---$15,360.00 x .20=$3,072.00=$15,360.00 - $3,072.00=$12,288.00
5th year $12,288.00 x .20=$2,457.60=$12,288.00 - $2,457.60 =$9,830.40
STATE -The Martins bought a condominium for $145,000. Assuming
that the value of the condo will appreciate at most 5% a year, how much
will the condo be worth in 5 years?
The future value of a condominium bought for $145,000 with a 5% annual appreciation over 5 years is calculated using the compound interest formula, resulting in a value of approximately $185,061.
The question is asking us to calculate the future value of an investment in real estate, specifically a condominium that was bought for $145,000 with an annual appreciation rate of 5% over a span of 5 years. To find the value of the condo in 5 years, we use the formula for compound interest, which is:
[tex]A = P(1 + r/n)^{nt}[/tex]
Where:
A is the amount of money accumulated after n years, including interest.
P is the principal amount (the initial amount of money).
r is the annual interest rate (decimal).
n is the number of times that interest is compounded per year.
t is the time the money is invested for in years.
Since the appreciation is compounded annually, n is 1. So, we can simplify the formula to:
[tex]A = P(1 + r)^t[/tex]
Substituting the given values:
[tex]A = $145,000(1 + 0.05)^5[/tex]
Now, let's calculate the future value:
[tex]A = $145,000(1.05)^5[/tex]
A = $145,000(1.2762825)
A ≈ $185,061
The condominium will be worth approximately $185,061 in 5 years.
The lawn is 30 yd long and 16 yd wide how much shorter is your walk if you walk diagonally
Check the picture below.
Round 86 to the nearest 10
Answer:
90
Step-by-step explanation:
"The answer is 90.
To round 86 to the nearest ten, one must look at the digit in the ones place, which is 6 in this case. Since 6 is greater than or equal to 5, the number in the tens place is increased by one. The digit in the tens place is 8, so when it is increased by one, it becomes 9. Therefore, 86 rounded to the nearest ten is 90."
The perimeter of a park is 0.251 meters the actual perimeter of the park is 1,000 times as large what is the actual perimeter of the park
The actual perimeter of the park is 251 meters
Solution:
Given that, perimeter of a park is 0.251 meters
The actual perimeter of the park is 1,000 times as large
To find: Actual perimeter of park
From given,
Actual perimeter of park = 1,000 times as large as perimeter of park
Here, "times" means multiplication
Actual perimeter of park = 1000 x perimeter of a park
Actual perimeter of park = 1000 x 0.251
Actual perimeter of park = 251
Thus the actual perimeter of the park is 251 meters
SOMEONE PLEASE HELP ME PLEASE
Answer
23. 180
24. congruent
25. transversal line
Showton Middle School has 840 students. Teresa surveys a random sample of 60 students and finds that 8 of them have more than 3 siblings, How many students at the school are likely to have more than 3 siblings?
Based on a sample of 60 students, where 8 have more than 3 siblings, approximately 112 students out of 840 at Showton Middle School are estimated to have more than 3 siblings.
If there are 840 students at the school, we can use this sample to estimate the total number of students likely to have more than 3 siblings across the entire school population. This is a problem related to proportions within a population.
To make this estimation, we need to set up a proportion based on the sample data:
Sample proportion of students with more than 3 siblings: 8 out of 60, or 8/60.Total number of students in the school: 840.Now we can set up a proportion:
(number of students with >3 siblings) / 840 = 8 / 60
We solve for the unknown number of students with more than 3 siblings by cross-multiplying:
(number of students with >3 siblings) * 60 = 8 * 840
(number of students with >3 siblings) = (8 * 840) / 60
(number of students with >3 siblings) = 112
Therefore, based on Teresa's sample, approximately 112 students at Showton Middle School are likely to have more than 3 siblings.
19.4mm what the lower bound correct to 1dp
Answer:
The lower bound of 19.4 is 19.35
The length of CD is 12 units C’D’ is the image of CD under a dilation with a scale factor of n.Which of these are true?
Answer: FIrst option, Fourth option and Fifth option.
Step-by-step explanation:
First it is important to know the definition of "Dilation".
A Dilation is defined as a transformation in which the Image (which is the figure obtained after the transformation) and the Pre-Image (this is the original figure, before the transformations) have the same shape, but their sizes are different.
If the length of CD is dilated with a scale factor of "n" and it is centered at the origin, the length C'D' will be:
[tex]C'D'=nCD=(n)(12\ units)[/tex]
Therefore, knowing this, you can determine that:
1. If [tex]n=\frac{3}{2}[/tex] , you get:
[tex]C'D'=(\frac{3}{2})(12\ units)=18\ units[/tex]
2. If [tex]n=4[/tex], then the length of C'D' is:
[tex]C'D'=(4)(12\ units)=48\ units[/tex]
3. If [tex]n=8[/tex], then:
[tex]C'D'=(8)(12\ units)=96\ units[/tex]
4. If [tex]n=2[/tex], then, you get that the lenght of C'D' is:
[tex]C'D'=(2)(12\ units)=24\ units[/tex]
5. If [tex]n=\frac{3}{4}[/tex], the length of C'D' is the following:
[tex]C'D'=(\frac{3}{4})(12\ units)=9\ units[/tex]
Terry shared an apartment with three other people. Each person paid an equal share of the rent. Together they paid $1495.00 per month. How much did Terry pay per month?
Answer:$493.33
Step-by-step explanation:
$373.75 Terry paid per month.
What is Division?A division is a process of splitting a specific amount into equal parts.
Given that Terry shared an apartment with three other people. .
The total number of people is 4.
Each person paid an equal share of the rent. Together they paid $1495.00 per month.
We have to find the Terry pay per month.
To find this we have to divide $1495.00/4
$373.75
Hence, $373.75 Terry paid per month.
To learn more on Division click:
https://brainly.com/question/21416852
#SPJ5
Tell if the slope is positive, negative, zero, or no slope.
Answer:
I think the slope is zero
Answer:
The slope is 0.
Step-by-step explanation:
If the slope line is straight with the x-axis, its 0.
If the slope isnt going straight on x nor y-axis, it had a slope of anything greater or less than 0, but not 0.
Need help please. Thanks so much.
Answer:
[tex](-1,\frac{17}{6})[/tex]
[tex](3,\frac{3}{2})[/tex]
[tex](-5,\frac{25}{6})[/tex]
Step-by-step explanation:
The given equation is [tex]2x+6y=15[/tex]
We substitute the ordered pairs to see which ones satisfies the equation.
For (-1,-8), we put x=-1 and y=-8 to get:
[tex]2(-1)+6(-8)=^?15[/tex]
[tex]-2+-48=^?15\\-50=^?15[/tex]
This is not true.
For [tex](-1,\frac{17}{6}))[/tex] we put x=-1 and [tex]y=\frac{17}{6}[/tex] to get
[tex]2(-1)+6*\frac{17}{6})=15\\ -2+17=15\\15=15[/tex]
This is true
For (3,3/2) we have 2(3)+6(3/2)=15
This implies 6+9=15
15=15
This is also True
For (-5,25/6), we have 2(-5)+6(25/6)=-10+25=15
This is also true.
please help me...... I need help
First, let us find out how many miles the hikers travel per day.
They walk at a rate of two mph for eight hours each day which means that they travel 16 miles per day (8x2).
Because the total distance of the great wall is 3948 miles to find out the amount of time needed...
3948/16 = 246.75 days (which is greater than 3 months)
answer: They can't cover the entire distance in three months.
Whats the square root of 4?
Answer:
2
Step-by-step explanation:
Answer: 2
Step-by-step explanation: The square root of 4 is 2.
4 is a perfect square which means that a whole number which in this case is 2 can be multiplied by itself to give us 4.
It's also on our perfect square list which I have attached below.
Suppose that 21 inches of wire costs 63 cents. At the same rate, how much (in cents) will 14 inches of wire costs?
See picture for solution and answer.
Caitlin is at the grocery store, and she’s trying to finthe unit price on a 6-pack of drinks on sale for $2.99.
Her younger brother says that at that
would cost just over $1.00. Is he correct, and how do
you know? If he were incorrect, how would Caitlin’s
brother find the correct price?
Well, first off, any ameteur who read the question once would know he is INCORRECT, this is because you can easily see he's dividing it by 3 not 6 like you should be, so 2.99 divided by 6 is 0.498333 ( continuing ) so since this must be rounded to the nearest hundredth, so, 50 cents per bottle.
So question 1: No, because he divided with the incorrect numbers.
Question 2:( I actually don't understand this question, cause we just established he was wrong ) so since I don't understand this one, imma say no, or meh.
CORRECT unit rate: 50 cents per bottle.
Hope this helps, if not, comment below please!!!!
81) The figure below is a trapezoid.
What appears to be true about this trapezoid's sides?
A) LM || NO
B) NO = LM
C) MN I NO
D) LO || MN
Answer:
A) LM || NO
Step-by-step explanation:
In a trapezoid one pair of opposite sides is always parallel.
Here, in the given figure, LM is parallel to NO
A) LM || NO is the correct answer.
Need the answer urgently
Shade the amount of pie given in the mixed number. There may be more pies than you need.
The table shows the mean monthly temperatures in Alcudia for the last 2 years in degrees Celsius. °C Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Last Year 9 10 11 14 19 22 27 29 21 18 11 6 2 Years Ago 7 11 10 13 17 23 25 25 20 18 12 9. What was the modal temperature last year?
Answer:
The modal temperature last year is 11 (March and November)
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
A year ago Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
9 10 11 14 19 22 27 29 21 18 11 6
2 years ago Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
7 11 10 13 17 23 25 25 20 18 12 9
2. What was the modal temperature last year?
Let's recall the mode of a data set is the number that occurs most frequently in the set. The number that occurs the most in the average temperatures last year is 11 (March and November) and 2 years ago is 25 (July and August)
Which expression is equal to (6•5)^4
Ise the terms 4, 12a, 6, 2a, and 24 to make equivalent expressions
Answer:
12a + 24 = 6(2a + 4) is the equivalent expressions
Step-by-step explanation:
Given the terms ; 4, 12a, 6, 2a, and 24
There are two terms with unknown = 12a and 2a
but 12a = 2a x 6 .........(1)
from the last term = 24 = 6 x 4 ...........(2)
add both equation 1 and 2 = 12a + 24
12a + 24 = 6(2a + 4) is the equivalent expressions .
to VERIFY; Use a = 2
substitute into the expression ; LHS = RHS
= 12(2) + 24 = 24 + 24 = 48 (LHS)
FOR RHS = 6(2a+4) = 6(2x2 + 4)
= 6(4+4) = 48
Hence LHS = RHS
Solve the equation 3x - 13y = 2 for x.
Hey there!
To solve for x, you must isolate the x term. To do so, first add 13y to both sides so you can leave 3x isolated on one side:
3x - 13y + 13y= 2 + 13y
3x= 2 +13y
Now, divide both sides by 3 to isolate the x variable and get your final answer:
(3x)/3 = (2 + 13y)/3
x = [tex]\frac{2 + 13y}{3}[/tex]
The equation could also be written as x= [tex]\frac{2}{3}+\frac{13y}{3}[/tex] if you choose to separate the 2 and 13y.
I hope this helps!
Answer:
[tex]x = \frac{2 + 13y}{3} \\ [/tex]
Step-by-step explanation:
[tex]3x - 13y = 2 \\ 3x = 2 + 13y \\ \frac{3x}{3} = \frac{2 + 13y}{3} \\ x = \frac{2 + 13y}{3} [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
What is the value of the expression (2)^6?
I need help on this please
Answer:
B. R/3
Step-by-step explanation:
720 = N + 315 + 240 what is it
Answer:
Note: N is represented by n instead.
Step-by-step explanation:
[tex]720 = n + 315 + 240[/tex]
Add the numbers
[tex]720 = n + 555[/tex]
Move the variable to the left-hand side and change its sign
[tex] - n + 720 = 555[/tex]
Collect like terms
[tex] - n = 555 - 720[/tex]
Calculate the difference
-N= - 165
N= 165
Hope this helps
Help ASAP!!! 3/8 of the seventh grade students were taking Advanced math at the beginning of the year, but Seven dropped out by the end of the year. If there were 140 students taking advanced math at the end of the year, how many total seventh grade students are there?
Answer:
There are 392 students in the seventh grade.
Step-by-step explanation:
Let us assume that there are x number of students in the seventh grade.
Now, 3/8 of the seventh grade students were taking Advanced math at the beginning of the year, but seven dropped out by the end of the year.
So, after the end of the year there were [tex](\frac{3}{8}x - 7)[/tex] number of students taking advanced math.
So, as per given condition, [tex](\frac{3}{8}x - 7) = 140[/tex]
⇒ [tex]\frac{3}{8}x = 147[/tex]
⇒ x = 392
Therefore, there are 392 students in the seventh grade. (Answer)
Pre-image point N(6,-3) was dilated to point N'(2, -1). What was the scale factor used?
Answer:
scale factor = [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
Consider the ratio of the x and y- coordinates, image to original, that is
scale factor = [tex]\frac{2}{6}[/tex] = [tex]\frac{-1}{-3}[/tex] = [tex]\frac{1}{3}[/tex]
What percent of the 2019 world population lives in Canada? Round the percentage to three decimal places.
Population in Millions
World: 7,691
Canada: 37.4
0.486 % of world population lives in canada
Solution:
From given,
World population = 7691 million
Canada population = 37.4 million
We have to find the percent of world population lives in canada
Let "x" be the percent of world population lives in canada
Therefore, from question,
x % of world population = canada population
x % of 7691 = 37.4
Solve the above equation for "x"
[tex]x \% \times 7691 = 37.4\\\\\frac{x}{100} \times 7691 = 37.4\\\\7691x = 3740\\\\Divide\ both\ sides\ by\ 7691\\\\x = \frac{3740}{7691}\\\\x = 0.486[/tex]
Thus 0.486 % of world population lives in canada