On solving the expression for (y), we get two possible values, one real and one complex as -
y = √{ (a²x²/c² + a² + 2a²x/c) - (x² + c² + 2xc)} -- Real
y = i√{(a{x/c + 1})² + (x² + c² + 2xc)} -- Complex
What is expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is the expression as follows -
√{(x + c)² + y²} = x (a/c) + a
√{(x + c)² + y²} = xa/c + a
√{(x + c)² + y²} = a{x/c + 1}
√{x² + c² + 2xc + y²} = a{x/c + 1}
{x² + c² + 2xc + y²} = ± (a{x/c + 1})²
Now, we can write -
{x² + c² + 2xc + y²} = (a{x/c + 1})² ...... (1)
and
{x² + c² + 2xc + y²} = - (a{x/c + 1})² ......... (2)
Solving (1) as -
{x² + c² + 2xc + y²} = (a{x/c + 1})²
{x² + c² + 2xc + y²} = a²(x/c + 1)²
{x² + c² + 2xc + y²} = a²(x²/c² + 1 + 2x/c)
{x² + c² + 2xc + y²} = (a²x²/c² + a² + 2a²x/c)
y² = (a²x²/c² + a² + 2a²x/c) - (x² + c² + 2xc)
y = √{ (a²x²/c² + a² + 2a²x/c) - (x² + c² + 2xc)}
Solving (2) as -
{x² + c² + 2xc + y²} = - (a{x/c + 1})²
y² = - (a{x/c + 1})² - (x² + c² + 2xc)
y² = - {(a{x/c + 1})² + (x² + c² + 2xc)}
y = √- {(a{x/c + 1})² + (x² + c² + 2xc)}
y = i√{(a{x/c + 1})² + (x² + c² + 2xc)}
Therefore, on solving the expression for (y), we get two possible values, one real and one complex as -
y = √{ (a²x²/c² + a² + 2a²x/c) - (x² + c² + 2xc)} -- Real
y = i√{(a{x/c + 1})² + (x² + c² + 2xc)} -- Complex
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What is the solution to the system of equations 3x 2y 7 and Y 3x 11?
The solution to the system of equations is x = 4 and y = 5.
3x + 2y = 7
y = 3x - 11
Substitute 3x - 11 for y in the first equation:
3x + 2(3x - 11) = 7
Simplify:
3x + 6x - 22 = 7
Combine like terms:
9x - 22 = 7
Add 22 to both sides:
9x = 29
Divide both sides by 9:
x = 29/9
x = 4
Change x in the second equation to 4:
y = 3(4) - 11
Simplify:
y = 12 - 11
y = 1
The solution to the system of equations is x = 4 and y = 1.
The solution to the system of equations 3x + 2y = 7 and y = 3x - 11 is x = 4 and y = 1. To solve this system, we first substituted 3x - 11 for y in the first equation. We then simplified the equation and combined like terms to get 9x - 22 = 7. We then added 22 to both sides, divided both sides by 9, and got x = 29/9 which is x = 4. We then substituted 4 for x in the second equation, simplified, and got y = 1. Thus, the solution to the system of equations is x = 4 and y = 1.
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An automobile manufacturer has given its car a 48.3 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the actual MPG for this car since it is believed that the car has an incorrect manufacturer's MPG rating. After testing 150 cars, they found a mean MPG of 48.2. Assume the population variance is known to be 6.76. A level of significance of 0.02 will be used. Find the P-value of the test statistic. You may write the P-value as a range using interval notation, or as a decimal value rounded to four decimal places
The p-value of the test statistic is calculated as follows:
0.6386.
What are the hypothesis tested?At the null hypothesis, it is tested if the mean is actually of 48.3 miles per gallon, that is:
[tex]H_0: \mu = 48.3[/tex]
At the alternative hypothesis, it is tested if the mean is different of that, hence:
[tex]H_1: \mu \neq 48.3[/tex]
What is the test statistic?The population standard deviation is known, hence the z-distribution is used to obtain the test statistic.
The equation is given as follows:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.[tex]\sigma[/tex] is the standard deviation of the population.n is the sample size.The parameters for this problem are given as follows:
[tex]\overline{x} = 48.2, \mu = 48.3, \sigma = \sqrt{6.76} = 2.6, n = 150[/tex]
Hence the test statistic is obtained as follows:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{48.2 - 48.3}{\frac{2.6}{\sqrt{150}}}[/tex]
z = -0.47.
The p-value is found using a z-distribution calculator, with a two-tailed test, as we are testing if the mean is different of a value, with z = -0.47, hence it is of:
0.6386.
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PLEASEEE HELP ME!!!!
Answer:
girl I have the same question
What is the rule for translations?
Answer:
A translation is a type of transformation that moves each point in a figure the same distance in the same direction.
Step-by-step explanation:
Translations are often referred to as slides. You can describe a translation using words like "moved up 3 and over 5 to the left" or with notation.
An adult seal eats 48.5 pounds of food daily. how many full days would 785.7 pounds of food last?
16 full days will be covered by the 785.7 pounds of food.
What is unitary method?A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary technique.
We typically utilize this technique for math calculations.
This approach will be helpful to you while tackling problems involving ratio and proportion, algebra, geometry, etc.
We are able to locate the missing value using the unitary technique.
This technique allows us to calculate both the value of multiple units from the value of a single unit and the value of single unit from the value of multiple units.
According to our question-
1 pound of food will last = 1/48.5 day
Pounds equal 785.7*(1/48.5) = 785.7
= 785.7/48.5
= 16.2
Only full days will be counted, therefore
We'll only count up to 16.
So, the 785.
16 days will pass after 7 days.
The 785.7 pounds of food will therefore be plenty for 16 full days.
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1 kilogram is equivalent to about 2.2 pounds. An orangutan weighs 142 pounds. What is its mass in kilograms?
In response to the question, we may say that As a result, the orangutan's expression mass in kilogrammes is roughly 64.55 kg.
what is expression ?An expression in mathematics is a collection of representations, numbers, and conglomerates that mimic a statistical correlation or regularity. A real number, a mutable, or a mix of the two can be used as an expression. Mathematical operators include addition, subtraction, fast spread, division, and exponentiation. Expressions are widely used in arithmetic, mathematics, and shape. They are employed in the depiction of mathematical formulas, the solving of equations, and the simplification of mathematical relationships.
To convert pounds to kilogrammes, divide the pound weight by the conversion ratio of 2.2.
Hence, to calculate the orangutan's mass in kilos, do the following:
Divide the orangutan's weight in pounds by the conversion ratio of 2.2:
142 pounds divided by 2.2 is 64.54545... kilos (rounded to the nearest hundredth)
As a result, the orangutan's mass in kilogrammes is roughly 64.55 kg.
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A rectangle has a perimeter of 36 cm and an area of 72 cm2.
What is the length of the rectangle's shorter side?
O 2 cm
O 3 cm
04 cm
6 cm
8 cm
What is the length of the rectangle's longer side?
06 cm
O 8 cm
O 9 cm
O 12 cm
18 cm
The length of the rectangle's shorter side is 6cm and the of the rectangle's longer side is 12cm.
What is perimeter?
The total length of a shape's boundary, as used in geometry, is referred to as the shape's perimeter. Adding the lengths of all the sides and edges that surround a shape yields its perimeter. It is calculated using linear length units like centimeters, meters, inches, and feet.
Given:
A rectangle has a perimeter of 36 cm and an area of 72 cm^2.
Let the length of the rectangle's shorter side is 'a' and
the length of the rectangle's longer side 'b'.
As the perimeter is 36 cm.
⇒ Perimeter = 2(a + b)
36 = 2(a + b)
18 = a+ b
a = 18 - b
Now the area of rectangle is 72cm^2.
⇒ Area = ab
72 = (18 - b)*b
72 = 18b - b^2
b^2 - 18b + 72 = 0
b^2 - 12b - 6x + 72 = 0
b(b - 12) - 6(b - 12) = 0
(b - 12)(b - 6) = 0
(b - 12) = 0, (b - 6) = 0
b = 12, b = 6
When b = 12 ⇒ a = 18 - 12 = 6
When b = 6 ⇒ a = 18 - 6 = 12
Hence, the length of the rectangle's shorter side is 6cm and the of the rectangle's longer side is 12cm.
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You are planning to sell ice cream cones for a school sporting event . You plan to sell 300 ice cream cones. Before selling the ice cream, you give a survey to determine what flavors to sell. The results are below.
• 10% - Mint
• 25% - Strawberry
• 15% - Chocolate chip
• 50% - Vanilla
Based on the survey results, how much of each flavor will you sell at the sporting event
Answer: Based on the survey results, we can calculate the number of ice cream cones to sell for each flavor by multiplying the percentage of the flavor by the total number of ice cream cones to be sold.
Mint: 10% of 300 ice cream cones = 0.1 * 300 = 30 ice cream cones
Strawberry: 25% of 300 ice cream cones = 0.25 * 300 = 75 ice cream cones
Chocolate chip: 15% of 300 ice cream cones = 0.15 * 300 = 45 ice cream cones
Vanilla: 50% of 300 ice cream cones = 0.5 * 300 = 150 ice cream cones
So, based on the survey results, you should sell 30 ice cream cones of Mint flavor, 75 ice cream cones of Strawberry flavor, 45 ice cream cones of Chocolate chip flavor, and 150 ice cream cones of Vanilla flavor.
It's worth mentioning that the sum of the percentages provided, 10+25+15+50 = 100%. Which means that it is a proper survey and the total number of ice cream cones you expect to sell is equal to the survey results.
Step-by-step explanation:
Based on the survey results flavors sold at the sporting event are, 30 mint ice creams, 75 Strawberry icecreams, 45 Chocolate chip icecreams, and 150 Vanilla icecreams.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
The number of different types of ice creams can be obtained as follows,
10% - Mint.
= (10/100)×300.
= 30.
25% - Strawberry.
= (25/100)×300.
= 75.
15% - Chocolate chip.
= (15/100)×300.
= 45.
50% - Vanilla.
= (50/100)×300.
= 150.
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Do isosceles triangles have 3 congruent angles?
Yes, isosceles triangles have three congruent angles.
An isosceles triangle is a triangle with at least two congruent sides and two congruent angles. The two congruent sides and two congruent angles form an isosceles triangle. The two congruent angles are known as the base angles, and they are opposite to the two congruent sides. The third angle in an isosceles triangle must also be congruent to the two base angles in order for the triangle to be true. This is because the angles of a triangle must always sum up to 180 degrees. Therefore, isosceles triangles have three congruent angles. These angles are all equal in measure and have the same shape. The angles of each isosceles triangle can be different from other isosceles triangles, but the angles are still congruent to each other. Therefore, isosceles triangles have three congruent angles.
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5/6 long division from math
Answer: 0.8333
Step-by-step explanation:
Step 1: Finding the part-to-part and part-to-whole ratios
To make his special energy drink, Jerome uses 8 cups of water and 3 cups of drink mix.
a)What is the ratio of water to drink mix?
(b)What is the ratio of drink mix to water?
(c)What is the ratio of drink mix to mixed energy drink?
d)What is the ratio of water to mixed energy drink?
Answer: ummm B
Step-by-step explanation:
Answer: B
Step-by-step explanation: To make his special energy drink Jerome uses 8 cups of water and 3 cups of drink mix. So the ratio of drink mix to water is 3:8.
You work at an oil refinery and are in charge of draining a tank until the
are 635 gallons left inside. The tank starts with 859 gallons, and you can
drain it at a rate of 56 gallons per minute. How many minutes do you
need to drain the tank to the right level?
You need
minutes.
Answer:
To drain the tank to the right level, you need to remove 859 - 635 = <<859-635=224>>224 gallons.
So you need to work for 224 / 56 = <<224/56=4>>4 minutes.
Step-by-step explanation:
If 7/8 is multiplied by 4/5, will the product be greater than wait her of the two factors Explain.
Answer:
[tex] \frac{7}{8} \times \frac{4}{5} = \frac{7 \times 1}{2 \times 5} \\ = \frac{7}{10} [/tex]
GIVEN: GH (congruent JH and FH (congruent) HI
PROVE: FG (congruent) IJ
Hence proved that FG = IJ with CPCT theorem for ΔGHF ≅ ΔJHI by SAS Congruency rule.
What is Congruency of triangles?Triangle congruence: Two triangles are deemed to be congruent if all three of their corresponding sides and angles have the same magnitude. Slides, rotations, flips, and turns can be used to make these triangles appear identical. They would be in alignment if they were moved. Congruence is represented by the letter "≅".
When two figures are similar to one another in terms of their size and shape, this is what mathematicians mean by congruence. It can be demonstrated that two triangles are congruent using four congruence rules in general. Finding all six dimensions is necessary, though.
Given that,
GH ≅ JH
FH ≅ HI
And,
∠GHF = ∠JHI
Therefore,
ΔGHF ≅ ΔJHI (SAS Congruency)
∴ FG = IJ (CPCT theorem)
Hence proved that FG = IJ with CPCT theorem for ΔGHF ≅ ΔJHI by SAS Congruency rule.
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What is the value of x in 2 5 )= 14?
The value of x in 2(5x)=14 is 1 2/5.
Define mixed fraction.A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder. An amalgam of a whole number and a legal fraction is a mixed fraction.
How to convert mixed fraction to improper fraction?When converting a mixed fraction to an improper fraction, the denominator and the whole number are multiplied, the product is added to the numerator, and the sum is written as the numerator and denominator.
2(5x) = 14
10x = 14
x = 14/10
Simplify the fraction, by turning it into a mixed number.
x = 1 4/10
Simplify the equation by dividing it by 2, so that it is in simplest form.
x = 1 2/5
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Determine if the triangles can be proved congruent by SSS, SAS, ASA, AAS, or HL.
The triangle in the figure can be proved by ASA, SAS, and AAS
What is congruency of triangle?Triangles are said to be congruent when the sides and angles equal in accordance to to the triangle congruency rules
Some of the rules include
Side - Side - Side = SSS
Side - Angle - Side = SAS
Angle - Side - Angle = ASA
Angle - Angle - Side = AAS
Hypotenuse and one leg = HL
The problem requires the prove by ASA, SAS, and AAS to ensure that the the triangles are congruent.
Alternate angles in the figure are also equal
According to the ASA rule, two triangles are said to be congruent if any two angles and the side located between the angles of one triangle are equal to the corresponding two angles and side located between the angles of the second triangle.
The Angle-Angle-Side (AAS) Congruence Theorem states that two angles and a non-included side in one triangle must be congruent with two angles and the equivalent non-included side in another triangle for the triangles to be congruent.
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Angle A and Angle B are complementary angles. The measure of Angle A is twice the measure of Angle B.
Write and equation to represent the complementary angle relationship between Angle A and Angle B. Use the equation to find
the measure of Angle A and B. Show all of your work.
Answer:
Acc.to question,
A+B=90° (since,they are complementary angles)
or,A+ A/2=90°(since,A is. twice the measure of B)
or,3A/2=90°
or,A=(90°×2)/3
:.A=60°
Also,
B=A/2=60/2=30°
A wedding menu has 5 starters, 3 mains, and 4 desserts. The list gives the meal options each attendee must choose from. a starter and a main, a main and a dessert, a starter, a main, and a dessert. How many different ways of choosing a meal for this wedding are there
There are 60 different ways of choosing a meal for this wedding.
How many different ways of choosing a meal?There were five distinct main courses available for selection.
There are a total of 15 possible main dish and salad combinations when ordering these 5 distinct main meals together with any one of the 3 available salads.
A total of 60 distinct main dishes, salads, and dessert combinations are conceivable by ordering one of the four potential deserts for each of the 15 various main meals and salad combinations.
60 distinct main dishes might be purchased since.
There are 60 different ways of choosing a meal for this wedding
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a shopper purchased 8 t-shirts and 5 pairs of pants for $220. the next day, he purchased 5 t-shirts and 1 pair of pants for $112.How much does each t shirt and each pair of pants cost?
Answer:
Step-by-step explanation:
Let the costs of 1 t - shirt and 1 pair of pants be 'x' and 'y' respectively then:
Case 1 --> 8x + 5y = 220 ----------(1)
Case 2 --> 5x + y = 112 ----------(2)
Multiplying equation (2) by 5:
8x + 5y = 220
25x + 5y = 560 ------(3)
Subtracting equation (1) from equation (3) we get :
17x = 340
x = 20
Putting x in (2):
5 x 20 + y = 112
y = 12
therefore, cost of each t-shirt is 20 rupees and the cost of each pair of pants is 12 rupees
How do you write 5 more than a number?
x+5 is the way we can write 5 more than a number.
In a formula or equation involving mathematical operations, the representation of numbers by alphabet is referred to as algebra.
Using the knowledge provided above, we must translate the mathematical statement provided in the question into an algebraic expression. Let's say that number is "x". The result of adding 5 to the provided number is a number that is 5 greater than this number. Thus, a number that is 5 more than x is equal to x+5. As a result, "5 more than a number" is represented by the algebraic expression "x+5".
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Use the correct order of operations to solve the problem below.
14 - 8 + 6 - 10 ÷ 2
Answer: 7
Step-by-step explanation:
a 96 ounce container of juice cost 4.80. at what price should a 128 container be sold, in order for the unit rate for both items to be the same
Response is $6.40, a proportion is the relationship or equivalence between two ratios or fractions.
Is a proportion the same as a percentage?While the denominator of a percentage is always 100, a proportion is the relationship or equivalence between two ratios or fractions. Both proportion and percentage can be expressed as fractions.
A percentage is an equation in which two ratios are made equal to one another.
Out of a possible 100, the percentage is given.
Because 32 ounces is the difference between 128 and 96, making it 1/3 of 96, we can divide $4.80 by 3 to get $1.60, then add $1.60 to $4.80 to get $6.40.
Response is $6.40, a proportion is the relationship or equivalence between two ratios or fractions.
The complete question is,
It cost $4.80 for a 96-ounce bottle of orange juice. How much should be charged for a 128-ounce container in order to equalize the unit rates of the two sizes? Describe your thought process.
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Two players are stand on a basketball court. The angles of elevation from the foot of each player to the 3.5 meters high basket are 40° and 50°. How far apart are the players from each other?
Please try to answer it with a trigonometric function
Therefore, the players are 6.84 meters apart from each other.
What is a projectile?An item that is propelled by the application of an external force and then travels freely while being affected by gravity and air resistance is referred to as a projectile. Projectiles are generally used in sports and combat, despite the fact that every item traveling through space is a projectile.
What is tangent?The straight line that traverses a point with a slope equal to the derivative of the curve at that location is said to be the tangent line to a plane curve at that point in geometry. It was described by Leibniz as the path connecting two points on a curve that are infinitely near together.
If we let x be the distance between the players, then we can use the tangent function to relate the angle of elevation to the distance between the player and the basket:
tan(40°) = 3.5/x
tan(50°) = 3.5/(x+1)
We can solve for x in both equations, and set them equal to each other, we get x= 6.84m
Therefore, the players are 6.84 meters apart from each other.
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Use the following denomination (Ghana cedis 200,100,50 and 20)to find the quantities of notes
1.3584655000
2.85760000
3.146737000
4.5555627000
5.7777000
1) Number of 200 notes = 17,923,275
Number of 100 notes = 35,846,550
Number of 50 notes = 71,693,100
Number of 20 notes = 179,232,750
2) Number of 200 notes = 428,800
Number of 100 notes = 857,600
Number of 50 notes = 1,715,200
Number of 20 notes = 4,288,000
3) Number of 200 notes = 733,685
Number of 100 notes = 1,467,370
Number of 50 notes = 2,934,740
Number of 20 notes = 7,336,850
4) Number of 200 notes = 27,778,135
Number of 100 notes = 55,556,270
Number of 50 notes = 111,112,540
Number of 20 notes = 277,781,350
5) Number of 200 notes = 38,885
Number of 100 notes = 77,770
Number of 50 notes = 155,540
Number of 20 notes = 388,850
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
Ghana credits 200,100,50 and 20 notes.
Now,
Since, Ghana credits 200,100,50 and 20 notes.
1) Hence, To credit the amount 3584655000,
Number of 200 notes = 3584655000/200 = 17,923,275
Number of 100 notes =3584655000/100 = 35,846,550
Number of 50 notes =3584655000/50 = 71,693,100
Number of 20 notes = 3584655000/20 = 179,232,750
2) To credit the amount 85760000;
Number of 200 notes = 85760000/200 = 428,800
Number of 100 notes = 85760000/100 = 857,600
Number of 50 notes = 85760000/50 = 1,715,200
Number of 20 notes = 85760000/20 = 4,288,000
3) To credit the amount 146737000;
Number of 200 notes = 733,685
Number of 100 notes = 1,467,370
Number of 50 notes = 2,934,740
Number of 20 notes = 7,336,850
4) To credit the amount 5555627000;
Number of 200 notes = 27,778,135
Number of 100 notes = 55,556,270
Number of 50 notes = 111,112,540
Number of 20 notes = 277,781,350
5) To credit the amount 7777000;
Number of 200 notes = 38,885
Number of 100 notes = 77,770
Number of 50 notes = 155,540
Number of 20 notes = 388,850
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In a certain lottery, 5 numbers between 1 and 13 inclusive are drawn. These are the winning numbers. How many different selections are possible
1287 combinations are a way to calculate the total outcomes of an event where order of the outcomes does not matter.
How many different lottery combinations are there?You win the jackpot if you match all six numbers. You receive a lesser fixed prize if you partially match some of the numbers.
Divide the number of winning lottery numbers by the total number of available lottery numbers to discover the probability of winning any lottery. Use the formula if the numbers are picked from a set and the order of the numbers is unimportant.
To find the winning combination we use the following formula
n !/ r!( n – r ) !
Where n = total number of to be drawn
r = the number which are drawn
In this question, n = 13, and r = 5
from the formula
13 !/5!( 13 – 5 ) !
= 13! / 5! 8!
= 13*12*11*10*9*8! / 5*4*3*2*1*8!
= 154,440 / 120
= 1287
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Ana has bought 12 3/6 kg of flour. Mary has brought 14 2/8 kg of flour and Kristina has bought 11 8/12 kg of flour. Who bought the most flour?
Answer:
Mary bought the most flour
Step-by-step explanation:
Ana bought 12 3/6 kg of flour
12 3/6 = 75/6 = 12.5 kg of flour
Mary has brought 14 2/8 kg of flour
14 2/8 = 114/8 = 14.25 kg of flour
Kristina bought 11 8/12 kg of flour.
11 8/12 = 140/12 = 11.66 kg of flour
So, Mary bought the most flour.
What is the solution to the system of linear equations 3x 2y equals 14 5x y equals 32?
The solution to the system of linear equations 3x + 2y = 14 and 5x + y = 32 is (x, y) = (6, 10).
3x + 2y = 14
5x + y = 32
Subtracting 3x from both sides of the first equation:
2y = 14 - 3x
Substituting this into the second equation:
5x + (14 - 3x) = 32
Simplifying:
8x = 18
x = 18/8
x = 2.25
This x value is substituted into the first equation.:
2y = 14 - 3(2.25)
2y = 14 - 6.75y
= 7.25
The solution is (x, y) = (2.25, 7.25)
The solution to the system of linear equations 3x + 2y = 14 and 5x + y = 32 is (x, y) = (2.25, 7.25). To solve the system, we first subtracted 3x from both sides of the first equation and then substituted this into the second equation. After simplifying, we obtained a value of x, which we then substituted into the first equation to obtain a value of y. This gave us the solution (x, y) = (2.25, 7.25).
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A survey found the following number of pets in different households.
What is the mean absolute deviation for the number of pets?
Answer:
absolute deviation means distance between each data value and the mean of the data set.
Step-by-step explanation:
(MAD)
or
(Average)
The line has a slope 5 / 4 and passes through ( − 3, 4 ). What is the equation of the line ? Select one: a. 4x + 5y + 31 = 0 b. 5x − 4y + 31 = 0 c. 4x − 5y + 31 = 0 d. 5x − 4y − 31 = 0
Answer:
b: 5x-4y+31=0
Step-by-step explanation:
Let's look for an equation of the form y=mx+b, where m is the slope and b the y-intercept (the value of y when x=0).
We are given the slope, m, as (5/4), so we can write: y = (5/4)x+b.
To find b, just enter the given point, (-3,4), into the above equation and solve for b:
y=(5/4)x + b
4=(5/4)(-3) + b for (-3,4)
4 = -(15/4)+b
4 + (15/4) = b
4 + (3 3/4) = b
b = 7 3/4
The equation becomes y = (5/4)x + 7 3/4
Also written as: y = (5/4)x + (31/4)
To match this with one of the options, let's multiply by 4 to remove the two fractions:
y = (5/4)x + (31/4)
4y = (5)x + (31)
Rearrange so that the expression is = 0:
4y-5x-31 = 0
Now multiply by -1: -4y+5x+31=0
Rearrange and this will match option b: 5x-4y+31=0
write the rule x= 10, -4, 0, 5, -2
y= 29, -13, -1, 14, -7
10=29
-4=-13
0=-1
5=14
-2=-7 help asap!!
The rule for the given set of data is y = 3x - 1.
What is rule in function?The relationship between dependent and independent variables, expressed as an equation, is referred to as a function rule. In order to calculate the value of the dependent variable, say y, in terms of the independent variable, say x, one must follow a specific function rule.
A function rule can be defined as the procedure that transforms an input value into an output in plain English.
Lets put two of the points in slope formula
y - y₁ = m(x - x₁)
29 - (-13) = m(10 - ( -4))
42 = m14
m = 42/14
m = 3
Now lets make the equation
y - 29 = m(x - 10)
y = 3x - 30 + 29
y = 3x - 1
Thus, the rule for the given set of data is y = 3x - 1.
Learn more about function rule
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