ax+by=a−b .......... (1)
bx−ay=a+b .......... (2)
Multiply equation (1) with a and equation (2) with b ,
a
2
x+aby=a
2
−ab ..........(3)
b
2
x−aby=ab+b
2
......... (4)
Adding (3) and (4), we get,
(a
2
+b
2
)x=a
2
+b
2
⇒x=1
Now, from (1),
ax+by=a−b
a+by=a−b
by=−b
y=−1
Answer:
The equation represents a polynomial equation in which the variables X, y, and z are raised to the third power and are equal to a constant value "k".The degree of the polynomial is 3, meaning that the highest power of the variable is 3. The equation has no solution if k is not a sum of three cubes of real numbers.A polynomial equation is an equation that involves one or more variables raised to apower, or exponent, and can include constants and coefficients. The sum or difference of two or more such equations is also a polynomial equation. The degree of a polynomial equation is the highest power of the variable in the equation. For example, in the equation , the degree is 2 because the highest power of the variable X is 2.A polynomial equation of degree one is a linear equation, and a polynomial equation of degree two is a quadratic equation. The solutions of a polynomial equation of degree n will be n roots/solutions. The solutions can be real or complex numbers.
(ignore my answer i choose), but pls help me
the question says: sal graphed a circle on the grid below.
sal translated the circle 6 units to the left and 7 units up. Which grid shows the result of this translation?
A. B. C. or D.
Answer:
the third choice
Step-by-step explanation:
take the center of the circle of the graph (4, -2)
move it 6 units to the left and 7 units up
so basically subtract 6 from 4
and add 7 to -2
to get
the center is (2, 5)
Is it ever possible for the lateral area of a cylinder to equal the surface area of the cylinder? Justify your response.
.
Answer: No
Step-by-step explanation: That was a question on an assignment and I got it right
What is the ordered pair Pls hurry up !!!!!
y=3x +8
5x+8y=6
[tex]\frac{k}{-3}[/tex] + 3+-2 a two step equation
Answer:A two-step equation is an algebraic equation you can solve in two steps. Once you've solved it, you've found the value of the variable that makes the equation true. Example 1 We're given an equation and asked to solve for x x: 3 x + 2 = 14 3x + 2 = 14 We need to manipulate the equation to get x x by itself.
Step-by-step explanation: i took the test and got it right
Question is in picture down below
PLEASE include explaination
Answer: 3 units (look at the image for the solution)
Step-by-step explanation:
Answer:
109-5h
Step-by-step explanation:
Idek
Determine whether each relation is a function. If so, provide the domain and range.
Width (m) Area (m2)
1 6
5 10
10 150
11 176
14 266
Function? (Yes or No) ________________
If it is a Function what is the:
Domain = _____________
Range = _______________
Hours worked vs. Salary
Hours Worked
Salary
0 0
10 $300
20 $600
30 $900
40 $1200
Function? (Yes or No) ________________
If it is a Function what is the:
Domain = _____________
Range = _______________
Height vs. Age
Height (cm)
Age (years)
160 20
160 25
160 30
160 35
160 40
160 45
160 50
Function? (Yes or No) ________________
If it is a Function what is the:
Domain = _____________
Range = _______________
Answer:
Step-by-step explanation:
dont now
Which is equivalent to 2r⋅2r⋅2r⋅2r⋅2r⋅2r?
2r6, (2r)6, 12r6, or 12r
Answer:
Step-by-step explanation:
would be 64 r^6
Which expression is equivalent to x2+7y3−8z4?
x2−7y3+8z4, 7y3−x2+8z4, 7y3+x2−8z4, or 8z4+x2−7y3
Chau is a software salesman. His base salary is $2300, and he makes an additional $50 for every copy of Math is Fun he sells.
Let P represent his total pay (in dollars), and let N represent the number of copies of Math is Fun he sells. Write an equation relating P to N. Then use this equation to find his total pay if he sells 26 copies of Math is Fun.
Answer: hope this helps ♡
P = $3600
Step-by-step explanation:
P = total pay
N = num of 'Math is Fun'
P = $2300 + $50(N)
P = $2300 + $50(26)
P = $2300 + $1300
P = $3600
PLEASEEE HELPPP ILL GIVE 5 STARS
Answer:
[tex](7a \cdot 5b) \div 6c \cdot 2d[/tex]
Step-by-step explanation:
If there is both multiplication and division in an expression and no parentheses, you start solving from left to right. Since in the expression [tex]7a \cdot 5b \div 6c \cdot 2d[/tex] you would start by solving [tex]7a \cdot 5b[/tex], (because it's at the leftmost part of the expression) it won't matter whether you put parentheses around [tex]7a \cdot 5b[/tex] or not. Therefore, the expression [tex](7a \cdot 5b) \div 6c \cdot 2d[/tex] is equivalent to [tex]7a \cdot 6b \div 6c \cdot 2d[/tex].
HELP PLEASE A cylinder has a radius of 3 cm and a height of 5 cm. Please answer in either fraction, mixed number or decimal.
Answer:
45π
Step-by-step explanation:
V = πr^2h
3^2 = 9
9*5 = 45
45π
(2. 135)
(3. 22.5)
Answer: slay
Step-by-step explanation:
Break-Even Analysis: Popcorn
The business club is going to sell popcorn at hockey games. Since they are astute business men
and business women, they know that they will not make a profit right away because they have to
pay the cost of buying a popcorn machine. They need to know how many bags of popcorn they
must sell in order to cover the set-up costs. In other words, what is the break-even point for
their popcorn business?
The red and glass popcorn carts often seen at carnivals and fairs costs $450. This is the fixed
cost. Regardless of the number of bags of popcorn they make and sell, the machine cost will not
change.
1. The popcorn, butter, salt, and serving bags cost $15 for every 100 bags of popcorn. What is
the cost per bag for these consumables?
$15 per 100 bags = $.15 per bag
The variable cost changes depending on how many bags of popcorn they make. The more
popcorn they make, the more they spend on popcorn, butter, salt and bags. The variable cost is
$0.15 times the number of bags of popcorn.
The total cost is the variable cost plus the fixed cost.
Total Cost = Variable Cost+Fixed Cost
2. Write an equation for the Total Cost as a function of the number of bags of popcorn made.
Use the notation C(x) for total cost, and let x be the number of bags of popcorn they make.
((x) =115x+450
Each bag of popcorn sells for $1.00. The revenue is the amount of money they receive from
selling bags of popcorn. If they sell 20 bags of popcorn, they will receive $20, since each bag
sells for $1. The revenue they take in is the price per bag of popcorn multiplied by the number of
bags of popcorn sold.
(Price per Item) (Number of Items)
3. Write an equation for the Revenue as a function of the number of bags of popcorn sold. Label
the revenue function R(x).
Revenue =
Answer:
Step-by-step explanation:
here you go hit this link
Answer: Price per Bag * Number of Bags = $1 * x = R(x)
To find the break-even point for the popcorn business, you need to find the number of bags of popcorn that need to be sold in order to cover the total cost, which includes the fixed cost of the machine and the variable cost of the consumables.
Calculate the cost per bag of popcorn for the consumables:
$15 for every 100 bags of popcorn ÷ 100 bags = $0.15 per bag.
Write an equation for the total cost as a function of the number of bags of popcorn made:
Total Cost = Variable Cost + Fixed Cost
Variable Cost = $0.15 * Number of Bags
Total Cost = $0.15 * Number of Bags + $450
Let C(x) represent the total cost where x is the number of bags of popcorn.
C(x) = $0.15 * x + $450
Write an equation for the revenue as a function of the number of bags of popcorn sold:
Revenue = Price per Bag * Number of Bags
Price per Bag = $1
Revenue = $1 * Number of Bags
Let R(x) represent the revenue where x is the number of bags of popcorn.
R(x) = $1 * x
Set the revenue equation equal to the total cost equation and solve for x, the number of bags of popcorn that need to be sold to reach the break-even point:
R(x) = C(x)
$1 * x = $0.15 * x + $450
$0.85 * x = $450
x = $450 ÷ $0.85 = 529 bags
Therefore, the business club needs to sell 529 bags of popcorn in order to reach the break-even point and cover their costs.
Step-by-step explanation:
Need help ASAP please
The volume of this pyramid would be 630
At summer camp, 60 students are divided in two groups for swimming or hiking. Each camper flips a coin, where heads represents swimming and tails represents hiking.
Outcome Frequency
Swimming 26
Hiking 34
Compare the probabilities and determine which statement is true.
The theoretical probability of swimming, P(swimming), is one half, but the experimental probability is 34 over 60.
The theoretical probability of swimming, P(swimming), is 26 over 34, but the experimental probability is one half.
The theoretical probability of swimming, P(swimming), is 26 over 60, but the experimental probability is one half.
The theoretical probability of swimming, P(swimming), is one half, but the experimental probability is 26 over 60.
Answer:
The theoretical probability of swimming, P(swimming), is 26 over 60, but the experimental probability is one half.
Step-by-step explanation:
How to calculate the probability
The ratio between the number of favorable events and the total number of conceivable outcomes is known as the theoretical probability.
The experimental probability can be calculated mathematically using the following formula: Probability of an Event P(E) = Number of Times an Event Occurs / Total Number of Trials.
The experimental probability will be:
= Frequency for swimming / Total frequency
= 26 / 60
Kathy was building a bed for her dollhouse. She used her bed, which is 3 feet × 5 feet, as a guide. She scaled down the dimensions of her bed by a factor 1/5. What are the dimensions of the model bed she built? (1 point)
a
0.06 ft × 0.1 ft
b
0.3 ft × 0.5 ft
c
0.03 ft × 0.05 ft
d
0.6 ft × 01 ft
Please help I am le dum
Answer:
p = 2x + 14
Step-by-step explanation:
Perimeter
p = 2l + 2w
p = 2(x + 2) + 2(5)
p = 2x + 4 + 10
p = 2x + 14
Write an equation that you can use to find the value of x. Perimeter of triangle: 16 in. An equation that you can use is 16=
Answer:
3x =16 is the required equation.
Step-by-step explanation:
help me pls thank you
Answer:
36
Step-by-step explanation:
2x3=6
5x6=30
Width vs. Area
Width (m)
Area (m2)
1 6
5 10
10 150
11 176
14 266
Function? (Yes or No) ________________
If it is a Function what is the:
Domain = _____________
Range = _______________
Hours worked vs. Salary
Hours Worked
Salary
0 0
10 $300
20 $600
30 $900
40 $1200
Function? (Yes or No) ________________
If it is a Function what is the:
Domain = _____________
Range = _______________
Height vs. Age
Height (cm)
Age (years)
160 20
160 25
160 30
160 35
160 40
160 45
160 50
Function? (Yes or No) ________________
If it is a Function what is the:
Domain = _____________
Range = _______________
Answer:
yes
Step-by-step explanation:
help asap, pls and thanks :)
Answer:
34 cm^2
Step-by-step explanation:
The formula for the area of a trapezoid is (1/2) * (b1 + b2) * height, where b1 and b2 are the different base lengths. In this problem, b1 + b2 = 4 + 13 = 17cm. The height is given in the figure as 4 cm. Thus, the area is (1/2) * (17cm) * (4cm) = 34 cm^2
Help me with this cube surface area.
Step-by-step explanation:
[tex]a = 6 {x}^{2} [/tex]
Since the figure shows 1/3
[tex]a = (6) { \frac{1}{3} }^{2} [/tex]
Squaring fractions is pretty much squaring the numerator and denominator. 1 squared is 1. 3 squared is 9, so....
[tex]a = (6) \frac{1}{9} [/tex]
[tex]a = \frac{2}{3} [/tex]
Answer: 8 square foot
Step-by-step explanation:
[tex]A = 6a^{2},[/tex]
Convert: 1 ft = 12 in
Divide: 12in / 3 = 4 in
1 / 3 ft = 4 in
L X W = 4in X 4in = area on one side 16 in
Surface Area = 16in x 6 sides = 96 sq in
Convert to Sq Inches to Sq Foot
96 / 12 = 8 square foot
PLEASE HELP EASY QUESTION Which models represent the sum? AND WILL GIVE BRAINLIEST IF CORRECT
1.1 + 0.6
THERE IS MORE THEN ONE ANSWER
Select EACH correct answer. PICK MORE THEN ONE ANSWER
Answer:
C and D
Step-by-step explanation:
C and D both show 1.1 + 0.6
The others do not
What is Calculus? Give equations that are an example of calculus.
Answer:
the branch of mathematics that deals with the finding and properties of derivatives and integrals of functions, by methods originally based on the summation of infinitesimal differences. The two main types are differential calculus and integral calculus.
Step-by-step explanation:
Let f(y) = y2 and g(y) = ey.
please help if you know how to do this, show an explanation please
Answer:
a. 8, 3, 6, 10
b: 220
Step-by-step explanation:
surface area = bh + (b1 + b2 + b3) L
6(8) + (6+8+3) x 10
48 + (17)(10)
48 + 170 = 220
Answer:
96 ft²
Step-by-step explanation:
Surface area of triangular prism:A = 8 ft
B = 2 ft
C = 6 ft
D = 10 ft
[tex]\boxed{\bf Surface \ area \ of \ right \ triangular \ prism = (perimeter \ of \ triangle)*B + C*A }[/tex]
= (A + C + D)* B + C*A
= (8 + 6 + 10)*2 + 6*8
= 24*2 + 48
= 48 + 48
= 96 ft²
What is the interquartile range of the data displayed in this box-and-whisker plot?
A) 7
B) 12
C) 22
D) 49
Evaluate. 4² - 6 ÷ 2 + 3 =
Answer:
16-3+3= 16 is the answer.
4^2=16 then 6 divided by 2 equal 3 then plus 3= 16
Answer:
16
Step-by-step explanation:
(4²) - (6 ÷2)+3
(4²) - (6 ÷2)+3(16 - 3) + 3
(4²) - (6 ÷2)+3(16 - 3) + 313 + 3
(4²) - (6 ÷2)+3(16 - 3) + 313 + 316
Hence, the correct answer is 16
What is the circumference of the circle in terms of π?
circle with a segment drawn from one point on the circle through the center to another point on the circle labeled 6 yards
36π yards
18.84π yards
6π yards
3π yards
Answer:
Therefore, the circumference of the circle is 6π yards.
Step-by-step explanation:
The circumference of a circle can be calculated using the formula C = 2 * π * r, where r is the radius of the circle.
In this case, we have a segment drawn from one point on the circle through the center to another point on the circle labeled 6 yards, which is equal to the diameter of the circle. So, the radius of the circle is 6 yards / 2 = 3 yards.
Plugging this into the formula, we have:
C = 2 * π * 3 = 6 * π
Therefore, the circumference of the circle is 6π yards.
What is a possible explanation for why median and interquartile range are the preferred measures of center and variation when a data set contains outliers?
Answer: The median is the middle number in a data set, better than a mean because in a mean, those outliers are part of the average. The IQR is the middle 50% of a data set, better than a regular range because it excludes any outliers on either end.
(っ◔◡◔)っ ♥
Hope this helps.
MM4343
The median and interquartile range are often preferred measures of center and variation when a data set contains outliers because they are robust to outliers.
What is interquartile range?The interquartile range (IQR) is a measure of data set variability or spread. It is the difference between a distribution's third and first quartiles (Q3), and it represents the range of the middle 50% of the data.
When a data set contains outliers, the median and interquartile range are often preferred measures of center and variation because they are robust to outliers.
Outliers are extreme values that are far outside the range of the remaining data points and can have a significant impact on measures of center and variation such as the mean and standard deviation.
Thus, when there are outliers in a data set, using the median and IQR as measures of center and variation, respectively, can provide a more accurate representation of the data set's central tendency and variability than using the mean and standard deviation, which are more sensitive to outliers.
For more details regarding interquartile range, visit:
https://brainly.com/question/29204101
#SPJ2
i need help pls mathematics :)
Answer:
The solution is B. 2 2/10
Step-by-step explanation:
[tex]6 \frac{8}{10} - 4 \frac{6}{10} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ = (6 - 4) + ( \frac{8}{10} - \frac{6}{10} ) \\ = 2 + ( \frac{2}{10} ) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ = 2 \frac{2}{10} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
Lupita rides a taxi that charges a flat rate of $6. 75 plus $3. 20 per mile. If the taxi charges Lupita $40. 03 in total for her trip, how many miles is her ride?
Enter your answer in the box as a decimal to the nearest tenth of a mile.
_____ miles
Answer:
10.4 miles
Step-by-step explanation:
Write an equation for the total cost paid as a function of the # of miles driven:
L(x) = $6.75 + ($3.20/mile)x
and set this equal to $40.03 to determine the # of miles Lupita rode:
L(x) = $6.75 + ($3.20/mile)x = $40.03
Isolate the x term by subtracting $6.75 from both sides:
($3.20/mile)x = $40.03 - $6.75 = $33.28
Finally, divide both sides by ($3.20/mile):
x = $33.28 / ($3.20/mile)
= 10.4 miles
Lupita rode 10.4 miles in the taxi.
