Which ordered triple is a solution of this system?
2x + y - z = 7
-x - 2y + 4z = -15
x + 2y - 5z = 17
a) (3, 1, 0)
b) (1, 3, -2)
c) (2, 5, 2)
d) (-2, 6, -5)
Answers
Answer:
b) (1, 3, -2)
Step-by-step explanation:
A suitable calculator can give you the answer to this right away. Or, you can try the answer choices in the equations to see which works.
The answer choice that works is choice B.
2·1 +3 -(-2) = 7
-1 -2(3) +4(-2) = -15
1 +2(3) -5(-2) = 17
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[tex] \frac{3000}{1000}=3 [/tex]
Answer: 3 km
Ind the perimeter and area of the sandbox. Make sure your answers have the correct number of significant digits. A children's sandbox measures 7.8 feet by 5.23 feet.
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area: 40.794
WHAT IS THE EQUATION OF POINT SLOPE FORM
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y-y2= m(x-x2)
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A rectangle has length x+9 and width 2x-1 what are the areas of the rectangle
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a=(x+9)(2x-1) <--- Use FOIL
a=2x²-x+18x-9
a=2x²+17x-9
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the length of a rectangle is 2 cm less than 7 times the width.the perimeter is 60 cm. find the width and length
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length = 26
4 and 26 are the width and length
Which number produces a rational number when added to 1/5?
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If w= the weight of trout. Which algebraic expression represents the phrase below?
Answers
Product means multiplication.
Given w= weight of a trout.
So, we need to convert "product of 16 and weight of trout: w " into an algebraic expression.
So, product of 16 and w can be written as 16*w or simply 16w.
Hence, B is the correct choice.
Answer:
B
Step-by-step explanation:
Hope this helps!
Which postulate or theorem proves that △ RNM and △ QNP are congruent?
A) HL congruence theorem
B) SAS congruence postulate
C) AAS congruence theorem
D) SSS congruence postulate
Answers
Answer:
B) SAS congruence postulate
Step-by-step explanation:
We have marked that RN and NQ are congruent. We also have marked that MN and NP are congruent.
∠MNR≅∠QNP because they are vertical angles. Vertical angles are opposite angles that share only a vertex; these are vertical angles so they are congruent.
This gives us two sides and an included angle; this is SAS.
B) SAS congruence postulate proves that △ RNM and △ QNP are congruent
What is a triangle?A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.
We know two triangles are congruent when we have at least three respective sides or angles or both that are same as the other sides or angles of a triangle.
We also know that vertically opposite angles have the same measures.
here the vertically opposite angles are ∠RNM and ∠PNQ.
It is given that side RN is congruent to side NQ and side PN is congruent to side MN.
∴ It is proven by SAS congruence postulate.
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How to solve nonlinear equations using iteration method?
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PART A: Maria rented a coat at $285 for 3 days. If she rents the same coat for 60 days, she has to pay a total rent of $510. Write an equation in standard form to represent the total rent (y) that Maria has to pay for renting the coat for x days.
PART B: Write the equation obtained in Part A using function notation.
PART C: Describe the steps to graph the equation obtained above on the coordinate axes. Mention the labels on the axes and the intervals.
Answers
Number of days: x
rent: y
2) state the initial points
x y
days $
3 285
60 510
3) assume linear relation:
=> (y - yo) / (x - xo) = (y1 - yo) / (x1 - xo)
=> (y - 285) / (x - 3) = (510 - 285) / (60 - 3)
=> (y - 285) / (x - 3) = 225 / 57 = 75 / 19
=> 19 (y - 285) = 75 (x - 3)
=> 19y - 19*285 = 75x - 75*3
=> 19y - 75x = 5415 - 225
=> 19y - 75x = 5190
=> standar form = -75x + 19y = 5190
PART B: Write the equation obtained in Part A using function notation.
-75x + 19y = 5190
=> 19y = 5190 + 75x
=> y = 5190/19 + (75/19)x
=> function notation = f(x) = (75/19)x + 5190 / 19
PART C: Describe the steps to graph the equation obtained above on the coordinate axes. Mention the labels on the axes and the intervals.
1) Coordinate axes:
x: number of days
y: rent
2) draw the two given points: (3,285) and (60, 510)
3) draw the line that joins those points from the interception of the y-axis until some points further (60, 510).
Evaluate the expression -6×2×(-2)×(-5)×(-3)
Answers
A hexadecimal number is a number written in the base 16 number system.â
a. True
b. False
Answers
its made out of 16 characters
from 1-16 and from A-F
A hexadecimal number is a number written in the base 16 number system which is true.
What is the number system?A way of writing numbers is known as a number system. It is the mathematical notation for consistently employing digits or other symbols to represent the numbers in a particular set. It describes the mathematics and algebraic structure of the numbers and gives each number a distinct representation.
The types of the number system are as follows:
Decimal Number System - There are only ten numbers and the base is 10.Binary Number System - There are only two numbers and the base is 2.Octal Number System - There are only eight numbers and the base is 8.Hexadecimal Number System - There are only sixteen numbers and the base is 16.A hexadecimal number is a number written in the base 16 number system which is true.
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) the admission fee at a small fair is $1.50 for children and $4 for adults. on a certain day 2,200 people enter the fair and $5,050 is collected. how many children and how many adults attended?
Answers
where
let x represent children
and y represent adult
therefore
x+y=2200
1.5x+4y=5050
solving using substitution method
y=2200-x
substituting this in the second equation we get
1.5x+4(2200-x)=5050
1.5x+8800-4x=5050
3750=2.5x
x=1500
so we had 1500 children and 700 adults
The flag of a country contains an isosceles triangle. (Recall that an isosceles triangle contains two angles with the same measure.) If the measure of the third angle of the triangle is 35° more than three times the measure of either of the other two angles, find the measure of each angle of the triangle. (Recall that the sum of the measures of the angles of a triangle is 180°.)
Answers
I hope this helps.
YOU'RE WELCOME :D
The admission fee at an amusement park is $2.00 for children and $5.60 for adults. On a certain day, 352 people entered the park, and the admission fees collected totaled 1280 dollars. How many children and how many adults were admitted?
Answers
solve for v
160=11-v
Answers
v = -149
Hope this helps
Explain how to write and evaluate an algebraic expression that represents the situation. The blueberries were divided equally into six bowls. Evaluate when b = 210.
Answers
The variable is the number of blueberries, the operation is division, and the constant is 6. Write the division expression as the fraction, b/6 . To evaluate, substitute 210 in for the variable, b, and simplify. 210 divided by 6 is 35. So each bowl has 35 blueberries.
The algebraic expression can be written in terms of the variable b and and evaluated as b/6 = 210/6 = 35
According to the question;
The blueberries were divided equally into six bowls;Hence, the algebraic expressions is;
b/6where, b = total number of blueberries
Hence, when b= 210
The number of blueberries in each bowl is; 210/6 = 35
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Doris put $4000 in a 2-year CD paying 6% interest, compounded monthly. After 2 years, she withdrew all her money. What was the amount of the withdrawal?
a. 4000.00
B. $4214.41
C. $4508.64
D. $4448.13
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A bakery makes donuts at the rate of 225 per hour. How long will it take the bakery to fill an order of 500 donuts?
Answers
I hope you found this helpful! C:
It will take them ~2.22 hours to make 500 donuts.
Karen's penny bank is 1/3 full. After she removes 240 pennies, it is 1/9 full. How many pennies can Karen's bank hold?
Answers
2/9 of the capacity if 240 pennies
2/9 * x=240
x=240*(9/2)=1080
the penny bank can hold 1080 pennies
The difference between the bank being 1/3 and 1/9 full equals 240 pennies, so 1/9 of the bank's capacity equals 120 pennies. So, Karen's bank can hold a total of 1080 pennies.
Explanation:This is a mathematics problem dealing with fractions and subtraction. From the problem, we understand that after Karen removes 240 pennies, the bank is 1/9 full from previously being 1/3 full. So, the difference between 1/3 and 1/9, which is 2/9, accounts for the 240 pennies that were removed.
To find out the total capacity of the penny bank, you need to consider that 1/9 (the fraction representing the bank's fill level after removal of the 240 pennies) is equivalent to 120 pennies (half of 240, as 2/9 of the capacity is 240 pennies). This means that the total capacity of the bank (comparable to 9/9 of the fraction) is 120 pennies times 9, which equals to 1080 pennies.
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If Dominik completes a project by himself, it will take him 8 hours. Working with Katarina, it will take them 5 hours. If they work together, what is the missing value from the table that represents the part of the project Dominik will complete? 8r 8(5) r (5)
Answers
Time for Katarina = (Dominick's Time * Total Time) / (Dominick's Time - Total Time)
Time for Katarina = (8 * 5) / (8 -5)
Time for Katarina = 40 / 3
Katarina's Time = 13.3333 hours
Answer:
answeerits (D) on ed
Step-by-step explanation:
Cafe A offers 2 free bottled waters or juices for every 20 purchased.Cafe B offers 3 bottled waters or juices for every 25 purchased. A) What is Cafe A's ratio of free drinks to purchased drinks? B) What is Cafe B's ratio of free drinks to purchased drinks? C) If you purchased 50 drinks at each cafe how many free drinks would you get?
PLEASEEEEE HELPPPPPPPPPP
Answers
3: 25, or for every 100 bottles you purchase, you get 12
you get 22 free drinks in all if you purchase 100 bottles from each store.
hope this helps
Complete the equation of the line through (4,-8) and (8,5).
Use exact numbers.
y=_______ Topic:
Slope-intercept from two points.
Answers
y = mx + b
b= y - mx
b = -8 - (13/4) (4)
b = -8 -13
b = -21
equation
y = 13/4x - 21
The equation of the line that passes through (4, -8) and (8, 5) in slope intercept form is y = 13 / 4 x - 21
Slope intercept form of a lineThe slope intercept form of a line is represented as follows;
y = mx + b
where
m = slopeb = y-interceptTherefore,
(4, -8) and (8, 5)
m = 5 + 8 / 8 - 4
m = 13 / 4
Therefore, using (8, 5)
5 = 13 / 4(8) + b
5 = 26 + b
b = 5 - 26
b = -21
Hence, the equation is as follows:
y = 13 / 4 x - 21
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What would '6 meters to 60 meters' be in a ratio
Answers
A female grizzly bear weighs 500 pounds. after hibernating for 6 months, she only weighs 200 pounds. what is the mean change in weight per month
Answers
Mean change is the average change over an entire data set.
The mean change in weight per month is 50 pounds.
What is mean change?Mean change is the average change over an entire data set.
We have,
The weight of the bear = 500 pounds
After 6 months the weight of the bear = 200 pounds
The change in weight of the bear in 6 months = 300 pounds
We can write it as:
6 months = 300 pounds
We need to find the weight change in one month so we need to make 6 months into 1 month by dividing both sides by 6.
So,
6/6 month = 300/6 pounds
1 month = 50 pounds
Thus the mean change in weight per month is 50 pounds.
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Jasmine has $15 dollars and saves $2.50 every month. Radha has $0 and saves $3.50 every month. Jasmine’s savings after x months can be represented by the function f(x) = 2.5x + 15. Radha’s savings after x months can be represented by the function g(x) = 3.5x. a. After how many months will they both have the same amount in savings? Find the values of x for which f(x) = g(x). b. Explain how to check your work. c. Explain what the graph of the two functions would look like.
Answers
2.5x+15 = 3.5x
subtract 2.5x from both sides
15 =x
15 months
If ABC DEC, what is the value of x?
x = 8
x = 5
x = 4
x = 1
x = 2
Answers
4(4)-1 (4)+ 2 4 can not be the answer
16-1 =6
=15
4x-1 x + 2
4(5)-1 (5)+ 2 5 can not be the answer
20-1 =7
=19
4x-1 x + 2
4(1)-1 (1)+ 2 X= 1 is the answer!!!
4 - 1 1 + 2
=3 =3
Answer:
Option D. x = 1
Step-by-step explanation:
If the two triangles Δ ABC and ΔDEC are similar then there corresponding sides will be in the same ratio.
Now using this theorem in these triangles
[tex]\frac{AB}{DE}=\frac{BC}{EC}[/tex]
Now it has been given
AB = (4x - 1)
BC = 4
EC = 4
DE = x + 2
By putting these values in the formula
[tex]\frac{4x-1}{x+2}=\frac{4}{4}=1[/tex]
We cross multiply on both the sides
(4x - 1) = (x + 2)
4x - x = 1 + 2
3x = 3
x = 1
Option D. x = 1 is the answer.
What is the value of X
Answers
180 - 70 - 42 = 68
x = 68 degrees
Use long division to determine the quotient of the polynomials. (x3 – 7x – 6) ÷ (x – 4) Which of the following options best describes the relationship between the polynomial division and the remainder? The quotient has a remainder of zero. Therefore, the divisor is a factor of the dividend. The quotient has a remainder of 9. Therefore, the divisor is not a factor of the dividend. The quotient has a remainder of 30. Therefore, the divisor is not factor of the dividend. The quotient has a remainder of 36. Therefore, the divisor is a factor of the dividend.
Answers
Using long division of polynomials, when we divide (x³ - 7x - 6) by (x - 4), the quotient is x² + 4x + 16 with a remainder of -70. This implies that the divisor (x - 4) is not a factor of the dividend (x³ - 7x - 6), since a non-zero remainder exists.
Explanation:To perform the task, we first note down the dividend (x³ - 7x - 6) and divisor (x - 4). We divide the first term of the dividend by the first term of the divisor to find the first term of the quotient and continue this process as required in polynomial division. Solving this using long division of polynomials, we get:
Dividend: x³ - 7x - 6
Divisor: x - 4
The quotient after performing long division is x² + 4x + 16 and the remainder is -70. This shows that the divisor (x - 4) is not a factor of the dividend (x³ - 7x - 6), since a remainder exists after the division is performed.
So, the correct option is: The quotient has a remainder of -70. Therefore, the divisor is not a factor of the dividend.
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Vectors...
Let u = <-3, -5>, v = <-3, 1>. Find u + v.
Answers
-5 + 1 = -4
vector = < 0,-4 >
Answer:
u + v = <-3 + -3, -5 + 1> = <-6 , -4>
u + v = <-6 , -4>
Step-by-step explanation:
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