Factorise
15x²y³z+25x³y²z+35x²y²z²

Simplifying this equation gives: [tex](x - 1)^2+(y+5/8)^2=5[/tex].

A circle is a geometrical shape that consists of all the points in a plane that are equidistant from a fixed point called the center. The distance from the center to any point on the circle is called the radius, and the distance across the circle passing through the center is called the diameter. The circumference of a circle is the distance around the edge of the circle, and it is calculated as 2 times pi (π) times the radius. Circles are found in many areas of mathematics and the physical world, and they have important applications in geometry, trigonometry, calculus, physics, and engineering, among other fields.

The equation of a circle with center (a, b) and radius r is given by:

[tex](x - a)^2 + (y - b)^2 = r^2[/tex]

In this case, the center is (1, -5/8) and the radius is √5. So, the equation of the circle is:

[tex](x - 1)^2 + (y + 5/8)^2 = (\sqrt5)^2[/tex]

Simplifying this equation gives:

[tex](x - 1)^2+(y+5/8)^2=5[/tex]

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The area of the trapezoid is 70 square centimeters.

locating a right trapezoid's area. A = (a + b) x h/2 is the formula to calculate the area of a right trapezoid.

We must apply the following calculation to determine the area of the trapezoid:

A = (b1 + b2) * h/2

where A is the area, h is the height, b1 and b2 are the lengths of the parallel sides (or the distance between the parallel sides).

We can observe that in this instance, b1 = 12 cm, b2 = 8 cm, and h = 7 cm. When we plug these numbers into the formula, we get:

A is equal to (12 + 8) x 7 cm / 2.

A = 20 cm * 7 cm / 2

A = 70 cm²

Hence, the trapezoid has a surface area of 70 square centimetres.

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Answer:9/2

Step-by-step explanation:

Answer:

To convert mixed number 4 1/2 to improper fraction, you follow these steps: Multiply the whole number by the denominator 4 × 2 = 8 Add the product from Step 1 to the numerator

Step-by-step explanation:

First, note that 4 1/2 is a mixed number, also know as mixed fraction. It has a whole number and a proper fraction. The numbers in the mixed fraction are defined as follow:

4 = whole number

1 = numerator

2 = denominator

To convert mixed number 4 1/2 to improper fraction, you follow these steps:

Multiply the whole number by the denominator

4 × 2 = 8

Add the product from Step 1 to the numerator

8 + 1 = 9

Write answer from Step 2 over the denominator

9/2

The mixed number 4 1/2 converted to improper fraction is therefore :

9/2

Andy has 15 coins made up of quarters and half dollars, and their total value is $5.00.

He has 10 quarters and 5 half dollars.

To find this answer, we can set up the following equation: 0.25Q + 0.50H = 5.00, where Q represents the number of quarters and H represents the number of half dollars. Solving for Q, we get Q = 10. Therefore, Andy has 10 quarters and 5 half dollars.

To solve this equation, we can use algebra to isolate the variable Q. We can start by subtracting 0.50H from both sides, giving us 0.25Q = 5.00 - 0.50H.

Next, we can divide both sides by 0.25, giving us Q = (5.00 - 0.50H) / 0.25. Therefore, we can substitute the values for 5.00 and 0.50H and solve for Q, giving us Q = 10.

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The relation in which a college student is related to another if and only if they have attended class together is an example of an equivalence relation.

Reflexivity: Every element of the set is related to itself. In this case, every student has attended class with themselves, so the relation is reflexive.

Symmetry: If one element is related to another, then the second element is also related to the first. In this case, if student A has attended class with student B, then student B has also attended class with student A, so the relation is symmetric.

Transitivity: If one element is related to a second, and the second is related to a third, then the first is related to the third. In this case, if student A has attended class with student B, and student B has attended class with student C, then student A has also attended class with student C, so the relation is transitive.

Therefore, the relation in which a college student is related to another if and only if they have attended class together satisfies all three properties of an equivalence relation, and is an example of such a relation.

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The value 2,649 represents the estimated population of elephants in Northwestern Namibia and Etosha National Park in 1995 and the estimated population was 618.4.

The formula for population growth can be represented as:

P = P0ert

Here, P is the population of elephants, P0 is the initial population, e is the base of the natural logarithm, r is the rate of growth or decay, and t is the time in years.

Now, as per the given data, P = 2,649P0 = initial population r = 1.045 (as per the given expression)b = t - 1995 (as per the given formula)Now, putting these values in the population growth formula,

P = P0ert2,649 = P0e1.045(b-1995)Dividing by P0 on both sides, we get:e1.045(b-1995) = 2649/P0

Taking the natural logarithm on both sides,

ln e1.045(b-1995) = ln (2649/P0)

Applying the property of logarithm,1.045(b-1995) ln e = ln (2649/P0)1.045(b-1995) = ln (2649/P0)

vAs we need to find the value of P0, substitute the value of b = 0,1.045(0-1995) = ln (2649/P0)-1.045*1995 = ln (2649/P0)ln (2649/P0) = -2069.95

Taking anti-logarithm or exponentiation on both sides,2649/P0 = eln (2649/P0) = e^(-2069.95)2649/P0 = 4.29P0 = 2649/4.29P0 = 618.4

Therefore, the estimated population of elephants in Northwestern Namibia and Etosha National Park in 1995 was 618.4.


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Triangle DAC and triangle CAB are congruent triangles using the SAS criteria.

Both triangles are said to be congruent if the three sides and three angles of one triangle match those of the other triangle's corresponding angles and sides. Pairs of corresponding sides and corresponding angles in two triangles are said to be equal if they are congruent. They have a similar size and form. In triangles, there are several congruence criteria. The dimensions of the triangles' sides and angles determine whether two or more triangles are congruent. A triangle's size is determined by its three sides, and its form by its three angles.

Given that, AD = AB and AC bisects angle DAB.

As AC bisects DAB, it divides the angle in two half angles that is:

angle DAC = angle CAB

In triangle DAC and triangle CAB.

AD = AB (Given)

angle DAC = angle CAB (AC bisects DAB)

AC = AC

Thus, triangle DAC and triangle CAB are congruent triangles using the SAS criteria.

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Answer:

1. reduction

2.  scale factor of 1/2

Step-by-step explanation:

1. the second image is smaller than the original

2. 18*1/2= 9 and 6*1/2=3

Answer:

400

Step-by-step explanation:

480-80=400

Answer

x=6

Step-by-step explanation:

80*x=480

80*6=480

Answer:

20/52 or simplified to 5/13

Step-by-step explanation:

The Venn Diagram is provided

Let
n(A) =  number of customers who had syrup
n(B) =  number of customers who had sprinkles

n(A and B) = number of customers who had both syrup and sprinkles = 16
This would be the number in the overlapping region

n(A or B) = number of customers who had either syrup or sprinkles or both
= n(A) + n(B) - n(A and B)
= 48 + 28 - 16
= 60

Therefore number of customers who had neither topping = 80 - 60 = 20

This number is indicated outside both circles but within the rectangle

The number of customers who had only syrup is given by set difference

= No. of customers who had syrup - No. of customers who had both
= n(A) - n(A and B)
= 48 - 16
= 32

This is the figure inside the left circle

Let's consider the statement: Customers who didn't have sprinkles

This would be customers who had only syrup(32) + customers who had neither topping(20)
= 32 + 20 = 52

Number of customers who did not have either topping = 20
P(selected customer doesn't have either topping, given that they don't have sprinkles)
= 20/52
= 5/13

The expression g(f(x)) simplifies to -6x + 6, and we can see that the coefficient of x is -6 and the constant term is 6.

A function f(x) is a mathematical relationship that assigns a unique output value (or range value) for every input value (or domain value) from a specified set. In other words, a function takes one or more input values and produces a single output value based on a specific rule or set of rules.

To find g(f(x)), we need to substitute the expression for f(x) into g(x) wherever x appears, since g(x) is being evaluated at the value of f(x). That is, we need to substitute -2x+5 for x in the expression for g(x). This gives:

g(f(x)) = g(-2x+5)

         = 3(-2x+5) - 9

         = -6x + 15 - 9

         = -6x + 6

So, g(f(x)) = -6x + 6.

Therefore, the expression g(f(x)) simplifies to -6x + 6, and we can see that the coefficient of x is -6 and the constant term is 6. Thus, we can express the response as follows:

g(f(x)) = -6x + 6

         = [-6]x + [6]

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Answer:

Step-by-step explanation:

they're perpendicular

Answer:

No.

Step-by-step explanation:

Line XY will be tangent to Circle W when XY is perpendicular to the radius XW. We can test if it is perpendicular by using Pythagoras theorem as it only works on right angled triangle. If the angle WXY is 90 degrees (XY ⊥ WX) then the theorem should work.

[tex](XY)^2=(WX)^2+(XY)^2\\R.H.S = 66^2+54^2 = 7272\\L.H.S = 87^2 = 7569\\R.H.S \neq L.H.S[/tex]

Thus the angle is not 90 degrees since the Pythagoras theorem doesn't work thus the line is not tangent since it is not at 90 degrees with the radius WX.

Answer:

not a tangent

Step-by-step explanation:

if XY is a tangent to the circle then ∠ WXY = 90°

using converse of Pythagoras' identity.

if the square of the longest side is equal to the sum of the squares on the other 2 sides , then the triangle is right.

longest side is WY

WY² = 87² = 7569

WX² + XY² = 66² + 54² = 4356 + 2916 = 7272

since WY² ≠ WX² + XY² , then Δ WXY is not right

then XY is not a tangent to the circle

Answer: 63056$

Step-by-step explanation: i learned that in school 2 hours ago

Step-by-step explanation:

5x-2(x+1)=10

5x-2x+2=10

3x+2=10

3x=10-2

3x=8

8/3

2.7 if you do round it

2.666666667 before you do

x=2.7

(I think it's right Because I've already been taught this if not just tell me.)

Answer:

I believe the answer would be 30 people.

Step-by-step explanation:

To calculate the percentage out of a group of people or items, you just multiply the percent (in decimal form) by the amount of people you want it out of. For example: A 0.1% chance out of 1,000 people would be a chance and expectancy of 1 person out of those 1,000 people. In this case it's 3% for every person. 0.03 • 1,000 is 30.

Answer:

53°

Step-by-step explanation:

it’s vertical, verticals are always identical, I think  

Answer:

m(slope) = -1.8 or -1 and 4/5s

Step-by-step explanation:

To find the slope between any two points, a good equation to always remember would be the slope equation.

y2-y1

--------

x2-x1

Or in simple words, the difference of y divided by the difference of x.

-10-8= -18, so the difference in y= -18.

3- (-7)= 3+7= 10, so the difference in the x values= 10.

Finally, divide -18/10= -1.8 or -1 and 4/5s

3198 x 750 equals 2,398,500. We may use the distributive approach to solve 3198 x 750 without a calculator by multiplying each digit of one number by each digit of the other number, starting with the rightmost digit.

We may use the distributive approach to solve 3198 x 750 without a calculator by multiplying each digit of one number by each digit of the other number, starting with the rightmost digit.

markdown

3198 \s x 750

23970 (8 x 0), 319800 (9 x 0 + 9 x 5) and 2398500 (9 x 0 + 9 x 7 + 8 x 5) are the numbers.

Because of this, 3198 x 750 equals 2,398,500.

When a problem or question asks to be solved "without using a calculator," it signifies that the answer must be determined by hand without the aid of a calculator or any other electronic instrument. This is frequently used to assess a person's math prowess and to motivate them to hone their problem-solving and mental math ability.

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To get an output of 5 from a function, the second point must be at a distance of 5 units above the x-axis.

The function represents the relationship between the inputs and the outputs. The function's domain is the set of all possible input values, while the range is the set of all possible output values. The function's graph is the set of all ordered pairs (x, y), where x is the input and y is the output.To get an output of 5 from the function, the second point must be at a distance of 5 units above the x-axis. This implies that the y-value of the second point is 5. The x-value of the second point is arbitrary, and it can be any value. The point (0,5) is an example of a point that is 5 units above the x-axis.

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The value that makes the expressions equivalent is 6, as 5+6=11, 11+6=15 and 15+6=30.

Value is the worth of something in terms of the amount of other things for which it can be exchanged or in terms of some medium of exchange. It is also seen as a measure of the usefulness or desirability of something. Value is often subjective, based on personal opinion and preferences, and can change over time. Value can also be seen as an intangible quality of a product or service that makes it desirable, such as convenience, reliability, or customer service.

This is known as a linear sequence, where the difference between each number is the same. In this case, the difference is 6. To find the equivalent expression, you must add 6 to each number in the sequence.

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The value that makes the expressions equivalent is 6, as 5+6=11, 11+6=15 and 15+6=30.

Value is the worth of something in terms of the amount of other things for which it can be exchanged or in terms of some medium of exchange. It is also seen as a measure of the usefulness or desirability of something. Value is often subjective, based on personal opinion and preferences, and can change over time. Value can also be seen as an intangible quality of a product or service that makes it desirable, such as convenience, reliability, or customer service.

This is known as a linear sequence, where the difference between each number is the same. In this case, the difference is 6. To find the equivalent expression, you must add 6 to each number in the sequence.

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Complete questions as follows-
What value makes the expressions equivalent?
6(3x+5) and 15x+□+3x

A. 5
B.11
C.15
D.30

To find:-

Answer:-

We are here given that 1 gallon of paint can be used to paint 400 sq ft. of an area .

There are 4 walls in a room and the area of opposite walls are equal.

So let's find out the area of wall ABCD , its area would be equal to the area of the wall EFGH . So ,

Area of wall ABCD and EFGH :-

Area = lb

Area = 18ft * 8ft

Area = 144ft.²

Therefore area of wall EFGH will also be 144ft.² .

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

Again,

Area of wall DAHE and CBGF :-

Here both the areas of the wall would again be equal, as they have same dimensions of 14ft × 8ft .

Area = lb

Area = 14ft * 8ft

Area = 112ft.²

Therefore area of walls DAHE and CBGF is 112ft.²

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

Calculating total area of the four walls :-

Total area = 2( 112ft.² + 144ft.² )= 512ft.²

Hence total area of four walls is 512ft.²

Now since there will be two coats of paints , total area to be painted would become double that is 1024ft.²

Now we may use Unitary Method :-

To paint 400ft.² 1 gallon of paint is needed.

To paint 1ft.² 1/400 gallon of paint is needed.

To paint 1024ft.² , 1/400*1024 = 2.56 gallons of paint would be needed.

Hence the total paint required is 2.56 gallons.

and we are done!

Answer:

3 one-gallon containers of paint.

Step-by-step explanation:

First, find the total surface area that needs to be painted.

To find the surface area of the walls of a rectangular room, calculate the area of each of the four walls and then add them together.

The area of a rectangle is the product of its width and length.

For the walls of the given room, the "length" is the height of 8 ft, since we want to paint from the floor to the ceiling.

The room has four walls:

Therefore, the total surface area is:

[tex]\begin{aligned}\textsf{Total surface area}&=2(14 \times 8)+2(18 \times 8)\\&=2(112)+2(144)\\&=224+288\\&=512\;\sf ft^2\end{aligned}[/tex]

Since we want to apply two coats of paint, we need to double the surface area:

[tex]\implies 2 \times 512=1024 \; \sf ft^2[/tex]

Now, we can find how many gallons of paint are needed by dividing the total surface area by the coverage per gallon:

[tex]\implies \dfrac{1024}{400}=2.56\; \sf gallons[/tex]

Therefore, we need 2.56 gallons of paint to paint two coats of each wall of the rectangular room.

Since we cannot buy a fraction of a gallon, we need to round up to the nearest gallon. Therefore, we need to buy 3 one-gallon containers of paint.

The pizza would be covered by approximately 100.48 centimeters of the pizza cutter if it is rotated exactly 4 times.

The circumference of a circle can be calculated using the formula:

circumference = π x diameter

where π is approximately equal to 3.14.

Given that the diameter of the pizza cutter is 8 centimeters, we can calculate its circumference as:

circumference = π x diameter

circumference = 3.14 x 8

circumference = 25.12 centimeters

If the pizza cutter is rotated exactly 4 times, it will cover a distance equal to 4 times its circumference:

distance covered = 4 x circumference

distance covered = 4 x 25.12

distance covered = 100.48 centimeters

Therefore, approximately 100.48 centimeters of the pizza would be covered by the pizza cutter if it is rotated exactly 4 times.

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Complete question

The image shows a circular pizza cutter that has a diameter of 8 centimeters. Approximately how many centimeters would the pizza cutter cover if it is rotated exactly 4 times

Answer:

16%

Step-by-step explanation:

translation

x% times 2800 = 448

x% = 448 divided by 2800

x% = 0.16 = move decimal 2 spaces to the right = 16%

To find the commission rate we just have to divide the total commission by the total amount of merchandise sold. The commission was $448 and the amount of merchandise sold was $2800.

[tex]\dfrac{448}{2800}=0.16[/tex]

Then, to rewrite a decimal as a percentage, we just need to multiply the number by 100.

[tex]0.16=\dfrac{0.16\times100}{100} =\dfrac{16}{100} =16\%[/tex]

The commission rate is 16%.

The amount of money Mayte can spend on a daily basis is given by $ 111 .

Sellers and purchasers of products and services both accept money as a form of payment. When we purchase goods like food, clothing, a house, groceries, etc., we provide money in exchange. We exchange money for everything we buy. This is a straightforward swap.

In mathematics, division is the process of dividing a number into equal parts and calculating the maximum number of equal parts that can be made. For instance, dividing 15 by 3 results in the division of 15 into 3 groups of 5 each. The division sign, "," or occasionally "/," is used in computer code.

Mayte get a total money of  $977 from her parents so,

total = 977

She saves $200 for herself so now the remaining sum is

977 - 200 = 777

The rest she has to distribute in 7 days so, by using the simple dividation rule we get,

777/7 = 111

Therefore, much money can you spend daily is $111.

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Complete question:

Mayte is a foreign student and receives his parents $977 per week. She saves $200 and the rest is distributed among the 7 days of the week, How much money can you spend daily?​

To solve this problem, we can use the method of mixtures. Let x be the number of pounds of chocolate to be mixed with the trail mix. We can set up the following equation based on the given information:

(21.10x + 3.10(14)) / (x + 14) = 12.41

Simplifying and solving for x, we get:

21.10x + 43.40 = 12.41x + 173.54

8.69x = 130.14

x = 15

Therefore, the store owner should mix 15 pounds of chocolate costing $21.10 per pound with 14 pounds of trail mix costing $3.10 per pound to create a mixture worth $12.41 per pound.

To check this answer, we can verify that the total cost of the mixture equals the total cost of the chocolate and trail mix:

15(21.10) + 14(3.10) = 315 + 43.40 = 358.40

And the total weight of the mixture is:

15 + 14 = 29

So the cost per pound of the mixture is:

358.40 / 29 = 12.41

which matches the desired cost per pound.

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