How many positive integer pairs (x,y) satisfy 4x+12y=640?
Answers
The number of positive pairs that satisfy the given linear function is given by: 161.
When a function is positive and when it is negative?We have to look at the graph of the function relative to the x-axis, more specifically if the function is above or below the x-axis, as follows:
A function is positive when it is above the x-axis.A function is negative when it is below the x-axis.In the context of this problem, the function is defined as follows:
4x + 12y = 640.
Which is a linear function, as both x and y have exponents of 1. The ordered pairs on the function are the values above the line. With integer numbers, that is, numbers that have no decimal parts, from the graph of the function given at the end of the answer, the values of x for which the function is positive is given by:
0 ≤ x ≤ 160.
Containing 161 values of x. Since this represents a function, each of the 161 values of x is associated to a value of y, meaning that there are 161 positive integer pairs (x,y) that satisfy the equation 4x + 12y = 640.
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Related Questions
The right arrow symbol used to show the transition from a point to its image after a transformation is not contained within the Equation Editor. If such a symbol is needed, type "RightArrow." For example: P(0, 0) RightArrow P′(1, 2).
Write a translation rule that maps point D(7,-3) onto point D'(2,5)
PLLS HELP if you do it in simple words and step by step i will give brainliest
Answers
Answer:
translates up 8 and 5 left
Step-by-step explanation:
To find the distance (x) it translate up, -3 + x = 5 where x = 8
To find the distance (x) it translate left, 2 + x = 7 where x = 5
Answer:
(x, y) → (x-5, y+8)
Step-by-step explanation:
A translation is a type of transformation that moves a figure up, down, left or right.
Calculate the change in the coordinates by subtracting the coordinates of point D from the coordinates of point D':
[tex]\implies (x_{D'}-x_D, y_{D'}-y_D)[/tex]
[tex]\implies (2-7, 5-(-3))[/tex]
[tex]\implies (-5, 8)[/tex]
Therefore, to map point D onto point D', move 5 units left and 8 units up.
Therefore, the translation rule that maps point D(7, -3) onto point D'(2, 5) is:
(x, y) → (x-5, y+8)I need help with this.
Answers
The approximate length and width of this rectangle to the nearest tenth are 15.6 feet and 31.2 feet respectively.
How to calculate the area of a rectangle?Mathematically, the area of a rectangle can be calculated by using this formula:
A = LW
Where:
A represents the area of a rectangle.
W represents the width of a rectangle.
L represents the length of a rectangle.
Making length (L) the subject of formula, we have:
L = A/W
Substituting the given parameters into the formula, we have;
3x = 489/6x
3x × 6x = 489
18x² = 489
x² = 489/18
x² = 27.2
x = √27.2
x = 5.2
Now, we can determine the length and width of this rectangle as follows:
Width = 6x
Width = 6 × 5.2
Width = 31.2 feet.
Length = 3x
Length = 3 × 5.2
Length = 15.6 feet.
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There are integers that are not rational
numbers. (True or false)
There are whole numbers that are not rational
numbers. (True or false
There are integers that are not whole numbers.(true or false)
All rational numbers are integers. (True or false)
Answers
A number that contains both positive and negative integers, including zero, is called an integer. There are no fractional or decimal parts in it. Here are a few instances of integers: -5, 0, 1, 5, 8, 97, and 3,043
Explain about the integers?Integers, as opposed to fractions or decimals, are all whole numbers plus their antipodes. For instance, numbers include -3, -2, -1, 0, 1, 2, 3,... On a number line, positive numbers are those to the right of zero. Negative numbers are those to the left of 0
An integer, pronounced "IN-tuh-jer," is a whole number that can be positive, negative, or zero and is not a fraction. Integer examples include: -5, 1, 5, 8, 97, and 3,043.
False. An integer is a whole number.
False. For instance, 1/2 is not a whole number but is a rational number.
False. For instance, -3 is not a whole number but is an integer.
True. Rational numbers include all integers.
Answers:
False
False
False
True
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You bring 1.5 dozen bagels to school.
A dozen bagels cost $5.98.
You used a coupon that took $1.00 off the total.
Answers
Because you do 5.98 plus half of 5.98 and then minus a dollar
7 more than half on Eli's age is Sydney's age, 11. How old is Eli?
Answers
Answer:
8 years8 years
Explanation:
Let Eli's age be represented as x
Sydney's age = 11
half on Eli's age = x/2
7 more than half on Eli's age = x/2 + 7
If 7 more than half on Eli's age is Sydney's age, then;
x/2 + 7 = 11
Subtract 7 from both sides
x/2 + 7 - 7 = 11-7
x/2 = 4
Multiply both sides by 2;
x/2 * 2 = 4 * 2
x = 4 * 2
x = 8
Hence Eli is 8 years old
2
Write the decimal as a percent. .065
A
65%
B
650%
C
6.5%
D
.65%
Answers
The value of percent of the decimal .065 is 6.5 %.
We are provided with the value .065 .
The ratio or a number expressed as a fraction of 100 is referred to as percentage. It is denoted using the percent sign % .
We have, .065 . We need to convert this value in the percentage. certain steps need to be followed to convert this value in the percentage. These steps are mentioned below;
.065
Multiply this above mentioned value by 100 to convert it into percent.
.065 × 100
= 6.5 %
So, percent of the decimal value is 6.5 %.
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c) Suppose that you take a random sample of 5,000 people from the U.S. population.Make a table that shows the expected number of people in your sample who come fromeach of the four age groups
Answers
In order to determine the number of people in the sample for each age group, here are the steps:
1. Determine what proportion in the entire population the population of each group. To get the proportion, simply divide the population of each respective group by the entire population.
2. To get the number of samples for each group, multiply the proportion by 5,000 and round the answer to the nearest whole number.
Now, let's apply the steps above in each group.
Let's start with ages under 18.
[tex]\begin{gathered} Proportion:74,181,467\div308,745,538=0.240267333 \\ Number\text{ }of\text{ }Samples:0.240267333\times5,000=1,201.33\approx1,201 \end{gathered}[/tex]Hence, we are expected to have 1,201 people aged under 18 in the sample.
For those aged 18 - 44,
[tex]\begin{gathered} Proport\imaginaryI on:112,806,642\div308,745,538=0.3653709224 \\ Number\text{ }of\text{ }Samples:0.3653709224\times5,000=1,826.85\approx1,827 \end{gathered}[/tex]Hence, we are expected to have 1,827 people aged 18-44 in the sample.
For those aged 45 - 64,
[tex]\begin{gathered} Proportion:81,489,445\div308,745,538=0.2639372395 \\ Number\text{ }of\text{ }Samples:0.2639372395\times5,000=1,319.68\approx1,320 \end{gathered}[/tex]The expected number of samples for people aged 45-64 is 1,320.
Lastly, for aged 65 and over,
[tex]\begin{gathered} Proportion:40,267,984\div308,745,538=0.1304245051 \\ Number\text{ }of\text{ }Samples:0.1304245051\times5,000=652.12\approx652 \end{gathered}[/tex]The expected number of samples for people aged 65 and over is 652.
To summarize, we have:
Age under 18 ⇒ 1,201 samples
18 - 44 ⇒ 1,827 samples
45 - 64 ⇒ 1,320 samples
65 and over ⇒ 652 samples
.
14.2 cm correct 1 decimal place
Answers
The 14.2 cm correct 1 decimal place is 14.2 after rounding to the nearest 0.1 or the tenth place.
What is rounding off the number?Rounding is a technique to reduce a large number to a smaller, more approachable figure which is very similar to the actual. Rounding numbers can be achieved in a variety of ways.
It is given that:
14.2 cm correct 1 decimal place
14.2
Rounded to the nearest 0.1 or
the Tenths Place.
Rounded to the nearest tenth place. The 2 in the tenth place rounds down to 2 or stays the same because the digit to the right in the hundredth place is 14.2
Thus, the 14.2 cm correct 1 decimal place is 14.2 after rounding to the nearest 0.1 or the tenth place.
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Please help I'm struggling and this is due tomorrow morning
Explain how to solve this equation I know it's 16 but I don't know how to solve it
In picture
Answers
16/2=8
Answer: to solve this equation, multiply both sides of the equation by 2.
Step-by-step explanation: by multiplying both sides of the equation by 2, you are effectively eliminating the fraction on the left, making the answer x = 16.
State the law of logic that is illustrated.
4
Statement: If x > 12, then x +9>20. The value of x is 14. Therefore, x +9>20.
Answers
The given statement " If x > 12, then x +9>20. The value of x is 14. Therefore, x +9>20" is Hypotesis of a true conditional statement is true, so the conclusion is also true. This is Law of Detachment.
What is the hypothesis and conclusion of a conditional statement?The Hypothesis is the first or “If” portion of the conditional statement or p. The Conclusion is the second or “then” part of the conditional statement or q.
What is the truth of the conditional statement when the hypothesis true and the conclusion in true?If the hypothesis is true and the conclusion is true, the conditional statement if p, then q is true. If the hypothesis is true but the conclusion is false, the statement is false.
The following assertion "X + 9 > 20 if x > 12. X has a value of 14. Thus, x + 9 > 20 "The conclusion follows logically from the hypothesized truth of the conditional statement. This is the Detachment Law.
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help me wwqưqưeqưeqưeqưeqưeqư
Answers
Answer:
Step-by-step explanation:
So, what you need to do is find out the formula for this question. And your answer will come out to be x=32
Given f(x)= -6x+7, what are f(3) and f(-5). show your work please!!
f (3)=
f (-5)=
Answers
Answer:
f(3) = -11
f(-5) = 37
Step-by-step explanation:
f(x) = -6x + 7
We want to find f(3) and f(-5)
To do so we substitute the input with any x in the equation and evaluate.
f(3) = -6x + 7
==> substitute all x's with the input, 3
f(3) = -6(3) + 7
==> multiply -6 and 3
f(3) = -18 + 7
==> add -18 and 7
f(3) = -11
f(-5) = -6x + 7
==> substitute all x's with the input -5
f(-5) = -6(-5) + 7
==> multiply -6 and -5
f(-5) = 30 + 7
==> add 30 and 7
f(-5) = 37
Question 2 of 10Classify the following triangle. Check all that apply.
Answers
Given -
To Find -
Type of Triangle =?
Step-by-Step Explanation -
As we can see we have an obtuse angle in the triangle and also, the two sides are equal.
So,
It is an Obtuse angle triangle.
It is also an isosceles triangle
Final Answer -
B. Obtuse
E. Isoseceles
Q.4 Find the median class.
Size of the shoe No. of pair sold
3 4
4 18
5 25
6 12
7 5
8 1
Answers
Answer: Median = 5
=====================================================
Explanation
Given Table of Data
[tex]\begin{array}{|c|c|} \cline{1-2}\text{Size of the shoe} & \text{No. of pair sold}\\\cline{1-2}3 & 4\\\cline{1-2}4 & 18\\\cline{1-2}5 & 25\\\cline{1-2}6 & 12\\\cline{1-2}7 & 5\\\cline{1-2}8 & 1\\\cline{1-2}\end{array}[/tex]
The second column is the set of frequencies. Adding up those frequencies gets us
4+18+25+12+5+1 = 65
There are 65 total shoes.
Divide this in half
65/2 = 32.5
There are 32 values below the median, and 32 values above it. That's 32+32 = 64 values so far. When including the median value itself we have 32+1+32 = 65 values total. This only works when the sample size is odd.
---------------------------
What we'll do is add up the partial sums of the frequency values.
The goal is to get to a sum of 33, or larger, because the median is in the 33rd slot.
Adding the first two frequencies gets us 4+18 = 22. This is not 33 or larger, so we move on.
Adding the first three frequencies gets us 4+18+25 = 22+25 = 47 which is 33 or larger.
What this tells us is that the median corresponds to the third row of the table, since we added the first three frequencies to get to 33 or larger.
The median must be 5.
450 x 670 - 80 x 500 = ?
Answers
Answer:
261 500
Step-by-step explanation:
450x670-80x500
301500-80x500
301500-40000
261500
suppose that your boss must choose three employees in your office to attend a conference in jamaica. because all 18 of you want to go, he decides that the only fair way is to draw names out of a hat. what is the probability that you, sharon, and robert are chosen? enter a fraction or round your answer to 4 decimal places, if necessary.
Answers
The probability that I, Sharon, and Robert are chosen is 0.0012
What is the formula for calculating combinations?
The equation [tex]^{n}C_{r}=\frac{n!}{(n-r)! r!}[/tex] will be used to calculate combinations, where n is the overall number of things and r is the number of items that are being chosen at a time.
The total number of employees=18
The Boss must choose 3 employees to attend the conference.
The number of possible ways to choose 3 employees from the total of 18 employees is [tex]^{18}C_{3}[/tex] .
The equation [tex]^{n}C_{r}=\frac{n!}{(n-r)! r!}[/tex] will be used to calculate combinations,.
So, [tex]^{18}C_{3}=\frac{18!}{(18-3)! 3!}[/tex]
[tex]^{18}C_{3}=\frac{18!}{(15)! 3!}[/tex]
[tex]^{18}C_{3}=\frac{18 \times 17 \times 16 \times 15}{3 \times 2}[/tex]
[tex]^{18}C_{3} =816[/tex]
The probability that I, Sharon, and Robert are chosen is [tex]\frac{1}{816}[/tex] = 0.0012
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The probability that I, Sharon, and Robert are chosen is 0.0012
What is the formula for calculating combinations?
The equation [tex]^{n}C_{r}=\frac{n!}{(n-r)! r!}[/tex] will be used to calculate combinations, where n is the overall number of things and r is the number of items that are being chosen at a time.
The total number of employees=18
The Boss must choose 3 employees to attend the conference.
The number of possible ways to choose 3 employees from the total of 18 employees is [tex]^{18}C_{3}[/tex] .
The equation [tex]^{n}C_{r}=\frac{n!}{(n-r)! r!}[/tex] will be used to calculate combinations,.
So,
[tex]^{18}C_{3}=\frac{18!}{(18-3)! 3!}^{18}C_{3}=\frac{18!}{(15)! 3!}^{18}C_{3}=\frac{18 \times 17 \times 16 \times 15}{3 \times 2}[/tex]
[tex]^{18}C_{3}=816[/tex]
The probability that I, Sharon, and Robert are chosen is = 0.0012
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A car has 15 gallons of gas in its tank. The car travels 35 miles per gallon of gas. It uses 1/35 of a gallon of gas to go 1 mile
Answers
Answer:
525 miles is that was what was being asked
Step-by-step explanation:
sorry I don't know the quest but the car can travel a total of 525 miles with 15 gallons in the tank
15 times 35=525
A coin box contains $26.50 in dimes and quarters. There are 157 coins altogether. How many of each
type of coin are in the box?
Answers
======================================================
Work Shown:
x = number of dimes
y = number of quarters
x+y = 157 coins total
-------------------------------
$26.50 = 2650 cents
1 dime = 10 cents
x dimes = 10x cents
1 quarter = 25 cents
y quarters = 25y cents
total value = 10x+25y = 2650 cents
-------------------------------
We have this system of equations
x+y = 157
10x+25y = 2650
Let's solve for y in the first equation
x+y = 157
y = 157-x
Then plug this into the second equation and solve for x.
10x+25y = 2650
10x+25(157-x) = 2650
10x+25(157)+25(-x) = 2650
10x+3925-25x = 2650
-15x+3925 = 2650
-15x = 2650-3925
-15x = -1275
x = -1275/(-15)
x = 85 is the number of dimes
Then use this to find the value of y
y = 157-x
y = 157-85
y = 72 is the number of quarters
-------------------------------
Check:
85 dimes + 72 quarters = 157 coins total
85 dimes = 85*10 = 850 cents
72 quarters = 72*25 = 1800 cents
850 cents + 1800 cents = 2650 cents = $26.50
This confirms the answers.
Answer:
so 85 dimes and 72 quarter coins are in the box
Step-by-step explanation:
Given; Total number of coin =1557 Total amount money =26.50 To find Number of dimes and quarters in the box. In order to find the solution, make equation of number of coin and amount money. solve for unknown.Let, Number of dimes = x Number of quarters = y As, it is given that total number of coin is 157. x + y = 157 ......(a) Also, the total money is $ 26.50. .. 0.10x+0.25y = 26.50 ..(b)To, solve equation (a) & (b), put value of y from (a) to (b); From (b); From (a); y= 157 0.10x+0.25(157 - x) = 26.50 0.10x+39.25 - 0.25x = 26.50 0.15x+39.25 = 26.50 39.25 26.50 = 0.15x 12.75 = 0.15x 12.75 0.15 = x 85 = x Now, put value of x in equation (a); x + y 85+ y = y= 72
Find x so that q || r.
X =
Answers
Answer:
x = 12
Step-by-step explanation:
To justify q || r :
11x - 28 + 7x - 8 = 180 because they would be supplementary angles and their sum would be equal to 180°
add like terms
18x - 36 = 180 add 36 to both sides
18x = 216 divide both sides by 18
x = 12
Please help ASAP, will mark brainliest!
These triangles are congruent by the triangle congruence postulate:
Answers
Answer:
SAS
Step-by-step explanation:
SAS is side, angle, side so two sides are congruent and one angle is congruent.
If you look at the picture the side that is shared by both triangles is equal.(side)
The two sides with the line through them means they're equal.
(side)
The picture shows the two angles are equal.
(angle)
=SSA or SAS
suppose the side length of a cube is measured to be 9 cm with an accuracy of 0.03 cm. use differentials to estimate the error in the computed volume of the cube.
Answers
By using differentials the error in the volume estimation is 7.29 cubic centimeters.
What is the error of the computed volume of the cube?
The volume of a cube (V), in cubic centimeters, is equal to the cube of the side length (L), in centimeters, whose formulas are:
V = L³
Now we proceed to estimate the volume differential by using first derivatives:
dV = 3 · L² · dL
Where dL is the length differential, in centimeters.
If we know that L = 9 cm and dL = 0.03 cm, then the error in the computed volume of the cube is:
dV = 3 · (9 cm)² · (0.03 cm)
dV = 7.29 cm³
The error in the volume estimation is 7.29 cubic centimeters.
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What is the value of this expression when x = -4 and y = 64?
-4+x²
A.
B. -8
C. -16
D. -48
Answers
Answer:
it's 0
Step-by-step explanation:
i hope this helps you
The first of two numbers is twice the second. Seven more than the second number is equalto 6 less than the first number. Find the numbers.
Answers
Let's call x to the first number ans y to the second number.
The first of two numbers is twice the second:
x = 2y
Seven more than the second number is equal to 6 less than the first number:
7 + y = x - 6
Isolating x:
7 + y + 6 = x
13 + y = x
Combining last equation with first equation:
2y = 13 + y
2y - y = 13
y = 13
Then:
x = 2*13
x = 26
The figures below are congruent. Name the corresponding sides.
Answers
The figures are congruent and the corresponding sides are AC = KM, AB = KL and BC = LM
How to find congruent figures?Congruent figures in geometry are identical in shape and size.
In other words, congruent figures are geometric figures that have the same shape and size.
If the figures are polygons, then they are congruent if all the corresponding sides and corresponding angles are congruent.
Therefore, the polygons above are triangles, they are congruent if the corresponding sides and angles are equal.
Therefore, the figures(triangles) are congruent by the following rules:
Side AC is congruent to side KMSide AB is congruent to side KLSide BC is congruent to side LMlearn more on congruent figures here: https://brainly.com/question/3453193
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Simplify the expression (2 − 5i)(3 + 7i) − (4 + 3i) and please be sure to explain your steps!
Answers
Answer:
2-33i
Step-by-step explanation:
(2 − 5i)(3 + 7i) − (4 + 3i) |Set up equation|
6+14i-15i-35i-(4+3i) |Multiply the numbers in the parentheses together using the distributive property|
6-1i-35i-(4+3i) Subtract like terms
6-36i-(4+3i) Subtract like terms
6-4-36i+31 Open parentheses and put like terms together
2-33i Answer
Hope this helped!
assume that all the lines that appear tangent are tangent. Find the perimeter.
Answers
We have that the tangents which meet at the same point outside the circle have the same length:
Tangents in this caseThen, in this case:
PerimeterNow that we have all the measures, we find the perimeter just by adding them:
6 + 6 + 9 + 9 + 12+ 12 = 54
Answer: the perimeter of the figure is 54
Mayumi rides her bike around a park. Each lap around the park is 2/3 mi. Mayumi rides a total of 3 mi. how many laps around the park does Mayumi ride?
Answers
Mayumi took 4.5 laps by riding her bike around the park
Distance of each lap around the park = 2/3 miles
Distance covered by Mayumi = 3 miles
Fractions: The components of a whole or group of items are represented by fractions. A fraction consists of two components. The numerator is the figure at the top of the line. It specifies the number of equal portions of the whole or collection that are taken.
Laps took by Mayumi:
Distance covered by Mayumi on her bike/Distance of each lap around the park
= 3/(2/3)
= 3*3/2
= 9/2 or 4.5 laps
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R obery and dora need to write 4,300,000,000 using scentific notation robert wrote 4,300,000,000=4.3 10 9 whick descrbes. Whose number is correct and the reason it is
Answers
The number 4,300,000,000 in scientific notation is 4.3x10⁹.
What is a number?
A number is a quantitative entity that may be used to tally, measure, and name things. The natural numbers 1, 2, 3, 4, and so on are the original instances. Number words can be used to represent numbers in language. Individual numbers can be represented more generically by symbols known as numerals; for example, "5" is a numeral that represents the number five. Because only a small number of symbols can be memorized, fundamental numerals are often structured in a numeral system, which is a systematic method of representing any number. The most prevalent numeral system is the Hindu-Arabic numeral system, which allows any number to be represented using a combination of 10 fundamental numeric symbols known as digits.
The number 4,300,000,000 in scientific notation is 4.3x10⁹.
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HELP PLEASE!!!!
10 points!!
Answers
So the slope is 0
Select all sequence(s) of translations and reflections that were performed to show the two figures in each pair are
congruent. Image is shown with dashed lines.
*Remember to map the pre-image to the image. Select all that apply.
Answers
The sequence(s) of translations and reflections that were performed to show given two figures are congruent:
- Translate triangle ABC down and then reflect across vertical line.
- Reflect triangle ABC across vertical line and then translate down.
- ΔABC ≅ ΔDEF
In this question, we have been given a triangle and its image.
We need to select all sequence of translations and reflections that performed to show given figures in each pair are congruent.
From figure, we can see that the image of vertex A is vertex D, the image of vertex B is vertex E and the image of vertex C is vertex F.
In we translate the triangle ABC down and then reflect across vertical line then the image would be DEF.
We can do the same transformation by reflecting triangle ABC across the vertical line and then translating it down.
From above, we can conclude that, ΔABC ≅ ΔDEF
Therefore, the sequence(s) of translations and reflections that were performed to show given two figures are congruent:
- Translate triangle ABC down and then reflect across vertical line.
- Reflect triangle ABC across vertical line and then translate down.
- ΔABC ≅ ΔDEF
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