3.17Using substitution, identify the ordered pair that is an element of the solution set of thesystem of equations.3x + y = 2y-x= -6
Answers
Hello
To solve this question, we are asked to use substitution method.
The given equation is
\(\begin{gathered} 3x+y=2\ldots\text{equ(i)} \\ y-x=-6\ldots\text{equ(}ii) \end{gathered}\)From equation (ii), let's make y the subject of formula
\(\begin{gathered} y-x=-6 \\ y=x-6\ldots\text{equ(}iii) \end{gathered}\)Put equation (iii) into equation (i)
\(\begin{gathered} 3x+y=2 \\ y=x-6 \\ 3x+(x-6)=2 \\ 3x+x-6=2 \\ \text{collect like terms} \\ 4x=2+6 \\ 4x=8 \\ \text{divide both sides by the coefficient of x} \\ \frac{4x}{4}=\frac{8}{4} \\ x=2 \end{gathered}\)We have the value of one of the ordered pair and we can use it to find the other one.
Put x = 2 in either equation (i) or (ii)
Using equation (ii)
\(\begin{gathered} y-x=-6 \\ x=2 \\ y-(2)=-6 \\ \text{collect like terms} \\ y=-6+2 \\ y=-4 \end{gathered}\)The value of x and y is (2, -4) and the ordered pair can be written as (2, -4)
Related Questions
a. NewBank started its first day of operations with $155 million in capital. A total of $92 million in checkable deposits is received. The bank makes a $28 million commercial loan and lends another $23 million in mortgage loans. If required reserves are 5.4%, what does the bank balance sheet look like?
b. Suppose NewBank decides to invest $273 million in 30-day T-bills. The T-bills are currently trading at $4,981 (including commissions) for a $4,940 face value instrument. How many T-bills do they purchase? What does the balance sheet look like?
Answers
The balance sheet attached shows the Total Assets to be $55.968M and Total Liabilities and Capital to be $252M respectively.
Understanding Balance Sheet1. Assets:
a. Cash in Reserves:
The required reserves are 5.4% of checkable deposits.
Therefore, the required reserves amount to 5.4% of $92 million, which is:
(0.054 * $92 million) = $4.968 million.
This amount is considered a liability for the bank, but it is held as an asset in the form of cash reserves.
b. Loans: The bank made a $28 million commercial loan and a $23 million mortgage loan. Therefore, the total loans amount to:
total loan = $28 million + $23 million
= $51 million.
2. Liabilities:
a. Checkable Deposits:
The bank received $92 million in checkable deposits.
b. Required Reserves:
As mentioned above, the required reserves amount to $4.968 million.
3. Capital:
The bank started with $155 million in capital.
Based on the above information, the bank's balance sheet would look as attached.
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Simplify: 3√5⋅√10+11√5⋅√10−√5
26√50
14√15−√5
14√50−√5
6√35
Answers
Answer:
When multiplying radical expressions with the same index, we use the product rule for radicals. If a and b represent positive real numbers,
Example 1: Multiply:
√2⋅√6
Solution: This problem is a product of two square roots. Apply the product rule for radicals and then simplify.
Step-by-step explanation:
Hope this helps . ;)
Calculate the volume of a container that is 10ft high, 3ft wide, and
6ft long.
Answers
Answer:
180 cubic feet
Step-by-step explanation:
10 * 3 * 6 = 180 feet
Use formula V = lbw for a container or cuboid
Enter values to write the function that matches the graph shown.
Answers
Answer:
The roots of this function are at -4 and -1.
f(x) = (2x + 8)(-2x - 2)
= (2x + 8)(-2x + (-2))
Answer: 90,000x6,899
1: Don't Che.at
2:Have a wonderful day!!!!!!!
XD
Answers
Answer:
The answer is 620,910,000 I worked it out By the way:)
Answer:
620,910,000 - Number form
620.9M+ - Short form
Six hundred twenty million, nine hundred, and ten thousand - Word form
Step-by-step explanation:
1. If you want me to go in full detail, I'll just say that I used a bit of internet search for the word form because I'm dyslexic, but yet I'm here in brainly answering other people's questions.
2. Have a wonderful day to you too!!
Hope this helped! :^)
- ✨7272033Alt✨
39. From the top of a vertical cliff 50 meters high, the angles of depression of an object that is levelled with
the base of the cliff is 30°. How far is the object from the base of the cliff?
A. 50 meters
B. 50-√3 meters
C. 100 meters
D. 100-√3 meters
40. What expression is used to answer: "A 4-m tall man stands on horizontal ground 43 m from a tree.
The angle of depression from the top of the tree to his eyes is 22°. Estimate the height of the tree."
A. sin 22
B. cos 22
C. tan 22
D. cot 22
41. From the top of the building of a food chain, the angle of depression from where Miguel stands is
45°. If the building is 12 meters high, how far is he from it?
A. 11 meters
B. 12 meters
C. 13 meters
D. 14 meters
42. A plane, at an altitude of 3,000 feet, observes the airport at an angle of 27°. What is the
horizontal distance between the plane and the airport to the nearest foot?
A. 3,000 feet
B. 4,000 feet
C. 5,000 feet
D. 6,000 feet
43. An escalator has an angle of elevation of 10° and a vertical rise of 6 m. Find the length of the
escalator.
C. 34.55 m
D. 36 m
A. 6,09 m
B. 34,03 m
Answers
Answer: cos4
Step-by-step explanation: 50 meters
B. 50-√3 meters
C. 100 meters
D. 100-√3 meters
40. What expression is used to answer: "A 4-m tall man stands on horizontal ground 43 m from a tree.
The angle of depression from the top of the tree to his eyes is 22°. Estimate the height of the tree."
A. sin 22
B. cos 22
C. tan 22
D. cot 22
What values of x solve the equation f (x) = 1
Answers
What is the midline equation for the function h(x)=−3cos(πx+2)−6?
Answers
Answer:
y = -6
Step-by-step explanation:
y=acos(bx+c)+d
d = -6 .. vertical shift
midline: y = -6
Describe the slope of the line
Find the slope
m=??
Answers
Slope formula (y2-y1)/(x2-x1) ride over run (4+3)/(5-2) = answer: 7/3 or 2 1/3
Answer: 2.333333...
Step-by-step explanation:
If we apply rise over run, we see that it rises 3.5 spaces, and runs 1.5, which means that \(m = \frac{rise}{run} = \frac{3.5}{1.5} = 2.33333...\)
The box plots display data collected when two teachers asked their classes how many pencils they lose in a school year.
A box plot uses a number line from 5 to 47 with tick marks every one unit. The box extends from 8 to 14 on the number line. A line in the box is at 11. The lines outside the box end at 7 and 45. The graph is titled Mr. Johnson's Class, and the line is labeled Number Of Pencils.
A box plot uses a number line from 0 to 51 with tick marks every one unit. The box extends from 12 to 21 on the number line. A line in the box is at 14.5. The lines outside the box end at 0 and 50. The graph is titled Mr. Simpson's Class, and the line is labeled Number Of Pencils.
Which class lost the most pencils overall based on the data displayed?
Mr. Simpson's class; it has a larger median value 14.5 pencils
Mr. Johnson's class; it has a larger median of 11 pencils
Mr. Simpson's class; it has a narrow spread in the data
Mr. Johnson's class; it has a wide spread in the data
Answers
Answer:
A) Mr. Simpson's class; it has a larger median value 14.5 pencils.
Step-by-step explanation:
A box plot is a visual display of the five-number summary:
Minimum value = The value at the end of the left whisker.Lower quartile (Q₁) = The left side of the box.Median (Q₂) = The vertical line inside the box.Upper quartile (Q₃) = The right side of the boxMaximum = The value at the end of the right whisker.From inspection of the box plots (attached), the measures of central tendency (median) and dispersion (range and IQR) are:
Mr Johnson's class:
Median = 11IQR = Q₃ - Q₁ = 14 - 8 = 6Range = max - min = 45 - 7 = 38Mr Simpson's class:
Median = 14.5IQR = Q₃ - Q₁ = 21 - 12 = 9Range = max - min = 50 - 0 = 50In a box plot, the median is a measure of central tendency and tells us the location of the middle value in the dataset. It divides the data into two equal halves, with 50% of the values falling below the median and 50% above it.
The median number of pencils lost in Mr Simpson's class is greater than the median number of pencils lost in Mr Johnson's class. Therefore, Mr. Simpson's class has a larger median value.
The spread of data in a dataset can be measured using both the range and the interquartile range (IQR).
As Mr Simpson's class has a greater IQR and range than Mr Johnson's class, the data in Mr Simpson's class is more spread out than in Mr Johnson's class.
In summary, as Mr Simpson's class has a larger median 14.5 and a wider spread of data, then Mr Simpson's class lost the most pencils overall.
What is the sum of 1.4 +2.37?
03.31
0 3.41
O 3.71
O 3.77
Answers
1.4+2.37=3.77
Step-by-step explanation:
1.4+2.37=3.77
One way you can find the answer is by using fact families
3.77 subtracted by 1.4 = 2.37
y=(-2)/4+5
y=(-1)/4+5
solve for y
Answers
Step-by-step explanation:
For y=(-2)/4 +5
y=-1/2 +5
y=9/2
For y=(-1)/4 +5
y= - 1/4 +5
y=19/4
You can use the equation A =(HW/3600)^1/2
to approximate a person's body surface area A (in square meters), where H
is height (in centimeters) and W is weight (in kilograms). Approximate the body surface area of a person with a height
of 160 centimeters and a weight of 64 kilograms.
Body surface area:______
m²
Answers
The body surface area is given by the equation A = 1.6865 m²
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the body surface area be represented as A
Now , the equation will be
A = ( HW / 3600 )^1/2
A = √( HW / 3600 ) be equation (1)
where H is the height in centimeters and W is the weight in kilograms
Now , the value of H = 160 cm
The value of W = 64 kg
Substituting the values in the equation , we get
A = √ [ ( 160 x 64 ) / 3600 ]
On simplifying the equation , we get
A = √ ( 10240/3600 )
A = √ ( 2.8444 )
A = 1.6865 m²
Therefore , the body surface area is 1.6865 m²
Hence , the equation is A = 1.6865 m²
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Find the value of f(4) for the function.
f(a) = 2(a + 4)-4
Answers
Step-by-step explanation:
4a=2a+4
C.L.T
4a-2a=4
2a=4
=2
Please please answer
Answers
Answer:
thanks for your support of the personal information on the direction of economics class
Whenever Deven and Laura owe each other money, they "pay" each other using stickers. They've agreed that a Harry Potter sticker is worth 49 dollars and a Twilight sticker is worth 35 dollars. They can even use stickers as "change" if one person overpays the other. For example, if Deven owes Laura 189 dollars, he can give her 6 Harry Potter stickers ($6 \cdot 49 = 294$ dollars), and she can return 3 Twilight stickers ($3 \cdot 35 = 105$ dollars). This trade is like a transfer of $294-105=189$ dollars. What is the smallest positive debt, in dollars, that can be paid off using sticker trading?
Answers
The smallest positive debt that can be paid off using sticker trading is $7$ dollars.
To find the smallest positive debt that can be paid off using sticker trading, we need to consider the values of the stickers (in dollars) and find the smallest positive amount that can be reached through a combination of these values.
Given that a Harry Potter sticker is worth $49 and a Twilight sticker is worth $35, we can approach this problem using the concept of the greatest common divisor (GCD) of these two values.
The GCD of $49$ and $35$ is $7$. This means that any multiple of the GCD can be represented using these sticker values.
In other words, any positive multiple of $7$ dollars can be paid off using sticker trading.
Therefore, the smallest positive debt that can be paid off using sticker trading is $7$ dollars.
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Lisa paid $43.95 for 16.1 gallons of gasoline. What was the cost per gallon rounded to the nearest hundredth?
Answers
Answer$ 2.73 per gallon
Step-by-step explanation:
Find the slope of identity function using points (0,0) and ( 3,3) then from two points (0,0) and (-3,-3). Is there any change in its slope?
Answers
There is no change in its slope as initial and final slope is 1.
What is slope?
In arithmetic, the slope or gradient of a line may be a variety that describes each the direction and therefore the abruptness of the line.
Main body:
formula for slope with two points form is =
y -y₁ =( y₂-y₁ /x₂-x₁ )(x - x₁)
according to question ,
points are (0,0) and (3,3)
y - 0 = (3-0/3-0)(x -0)
y = 3/3 *x
y = x
hence slope of line is 1.
Now points are (0,0) and (-3,-3).
y - 0 = (-3-0/-3-0)(x -0)
y =- 3/-3 *x
y = x
hence slope of line is 1.
So there is no change in its slope.
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-1.3125 as a fraction in simplest form
Answers
Answer: - 21/16 = 15/16 (simplified)
= - 1.3125 convert decimal to fraction
= - 13125/10000
= - 21/16 = 15/16 (simplified)
find the circumference of each circle. use 3.14 for
15 cm
Answers
Answer:
To find the circumference of a circle, you can use the formula: circumference = 2 * π * radius.
Given that the radius of the circle is 15 cm, we can substitute this value into the formula to calculate the circumference.
Circumference = 2 * 3.14 * 15 cm
Circumference = 94.2 cm
Therefore, the circumference of a circle with a radius of 15 cm is 94.2 cm.
The answer is:
C = 94.2 cmWork/explanation:
The formula for the circumference is:
\(\sf{C=2\pi r}\)
where:
C = circumference
\(\pi\) = pi (3.14)
r = radius
Plug in the value of the radius:
\(\sf{C=2\times3.14\times15}\)
Simplify:
\(\sf{C=94.2\:cm}\)
27 Answer:
Given the simple interest formula, I = Prt, solve for t
28 Answer:
Rewrite the equation so that y is a function of x:
7x + y = 13
29 Answer:
Rewrite the equation so that y is a function of x:
3x + 5y = 15
30 Answer:
Use the result in question #28 to find y when x = -1.
31 Answer:
Use the result in question #29 to find y when x = -1.
32 Answer:
Find the unit rate: 3 tablespoons for 1.5 servings.
33 Answer:
Find the unit rate: $10.99 for 12 slices of pizza.
34 Answer:
Convert the measure. Round your answer to the nearest tenth.
15 teaspoons to tablespoons (1 tablespoon = 3 teaspoons).
35 Answer:
Find the percent. Round to the nearest whole percent.
159 people in favor out of 350 people surveyed.
Answers
28. t = I / (Pr)
29. y = -(3x / 5) + (15 / 5)
30. y = -3/5 x + 3
31. y = -3/5 * -1 + 3 = 3 + 3/5 = 3.6
32. 2 tablespoons per serving
33. $0.92 per slice
34. 5 tablespoons
35. 45% (159 / 350 = 0.45 and 0.45 * 100 = 45)
What is a simple interest?Simple interest is a method of calculating the interest charge on a loan or deposit based on a constant interest rate and the original principal amount. The formula for simple interest is I = Prt, where P is the principal amount, r is the interest rate as a decimal, t is the time period in years, and I is the interest amount. In simple interest, the interest amount is calculated only on the original principal, not on any accumulated interest from prior periods.
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What is the image point of (1, 4) after a translation left 5 units and down 5
units?
Answers
Answer:
(-4,-1)
All you have to do to find it is subtract x by 5 and subtract y by 5. :)
At a speed of 22 revolutions per minute, how long will it take a wheel with radius 10",
rolling on its edge to travel 10 feet?
Answers
Answer:
0.4 seconds or
0.00667 minutes
Step-by-step explanation:
https://brainly.com/question/517612
pi times radius times 2 = circumference
pi times 10 inches times 2 = 62.83 inches = circumference
In one revolution, the wheel covers a distance equal to its circumference. So, at a speed of 22 revolutions per minute, the wheel covers a distance of:
22 x 62.83 inches inches per minute
1382.26 revolutions per minute
The wheel travels 1383.8 ft. in 60 seconds.
The wheel travels 1 ft. in (60 / 1383.8) seconds.
The wheel travels 10 ft. in (60 / 1383.8) * 10 seconds = 0.4 seconds
= 0.4 seconds divided by 60 = 0.00667 minutes
Please Help! I will give you the brainiest and a lot of points!
-Show work (You only have to do the odd numbers)
Answers
#19
\(\\ \sf\longmapsto \dfrac{7}{5}\)
#20
\(\\ \sf\longmapsto \dfrac{9}{5}\)
#21
\(\\ \sf\longmapsto \dfrac{11}{7}\)
#22
\(\\ \sf\longmapsto \dfrac{12}{7}\)
#23
\(\\ \sf\longmapsto \dfrac{2}{2}=1\)
#24
\(\\ \sf\longmapsto \dfrac{3}{2}\)
#25
\(\\ \sf\longmapsto \dfrac{5}{2}\)
#26
\(\\ \sf\longmapsto \dfrac{6}{2}=3\)
#27
\(\\ \sf\longmapsto \dfrac{8}{2}=4\)
#28
\(\\ \sf\longmapsto \dfrac{9}{2}\)
#29
\(\\ \sf\longmapsto \dfrac{13}{4}\)
#30
\(\\ \sf\longmapsto \dfrac{19}{4}\)
#31
\(\\ \sf\longmapsto \dfrac{37}{6}\)
#32
\(\\ \sf\longmapsto \dfrac{25}{6}\)
Answer:
19. 7 to base five => 12
21. 11 to base seven => 14
23. 2 to base two=> 10
25. 5 to base two => 101
27. 8 to base two => 1000
29. 13 to base four => 31
31. 37 to base six => 101
33. 87 to base five => 322
35. 108 to base four => 1230
37. 19 to base two => 10011
What is the meaning of conditionally promoted in school
Answers
After training Naruto went to a ramen shop for dinner. Since Naruto eats ramen for lunch and dinner daily, the shopkeeper gives him a 33.33% discount. If ramen costs 45 cents, how much does Naruto spend in 15 days?
Points given: 20
Answers
To calculate how much Naruto spends on ramen in 15 days, we need to determine the total cost of ramen per day and then multiply it by 15.
Since Naruto receives a 33.33% discount, he pays 100% - 33.33% = 66.67% of the original price.
66.67% of 45 cents is (66.67/100) * 45 = 30 cents.
So, Naruto spends 30 cents on ramen per day.
To find out how much he spends in 15 days, we multiply the daily cost by the number of days:
30 cents * 15 = 450 cents.
Therefore, Naruto spends 450 cents, which is equivalent to $4.50, on ramen in 15 days.
Simplify: -12- (–17)
Answers
Given the expression:
\(-12-(-17)\)You can simplify it as follows:
1. Multiply the signs applying the Sign Rules for Multiplication:
\(\begin{gathered} -\cdot-=+ \\ +\cdot-=- \\ +\cdot+=+ \\ -\cdot+=- \end{gathered}\)Then:
\(=-12+17\)2. Notice that the signs of the numbers are different. Therefore, you have to subtract them. The result will have the same sign of the number with the greatest absolute value (in this case, it will be positive:
\(=5\)Hence, the answer is:
\(=5\)Equation A
Х
Y
-2
6
2
1
0
2
-2
-9
Equation B
х
Y
-2
-1
-6
0
-3
1
0
What is the solution to this system of equations?
0 (-1,-5)
0 (0,2)
O (-2, 6)
O (1,0)
Answers
its c
Step-by-step explanation:
What is 8÷783 ???????? ?
Answers
Please answer this correctly
Answers
Answer:
50%
OR
1/2
Step-by-step explanation:
The box and whisker plot shows the time spent from 4 to 6 hours is Quartile 1 to 3 which makes it 50%.