How many positive integer pairs (x,y) satisfy 4x+12y=640?

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

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

The figures are congruent and the corresponding sides are AC = KM, AB = KL and BC = LM

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:

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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!

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.

Hence, we are expected to have 1,201 people aged under 18 in the sample.

For those aged 18 - 44,

Hence, we are expected to have 1,827 people aged 18-44 in the sample.

For those aged 45 - 64,

The expected number of samples for people aged 45-64 is 1,320.

Lastly, for aged 65 and over,

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

.

By using differentials the error in the volume estimation is 7.29 cubic centimeters.

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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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

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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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

Answer:

261 500

Step-by-step explanation:

450x670-80x500
301500-80x500

301500-40000

261500

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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======================================================

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

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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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.

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.

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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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

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:

The 14.2 cm correct 1 decimal place is 14.2 after rounding to the nearest 0.1 or the tenth place.

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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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

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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Answer:

it's 0

Step-by-step explanation:

i hope this helps you

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.

We have that the tangents which meet at the same point outside the circle have the same length:

Then, in this case:

Now 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

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

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.

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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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

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

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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The approximate length and width of this rectangle to the nearest tenth are 15.6 feet and 31.2 feet respectively.

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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