Factorise and Simplify :

a) 6p - 7q/12p - 14q

b) 6x⁵ - 8x²/2x

c) 10a + 15b/5

d) p² - 6q + 8/3p - 6
​

guys please help! please

Answer:

A(8,9,10,11,12)

Step-by-step explanation:

A(8,9,10,11,12)

The equation of the conic represents a circle with an area of 36π square units.

In this problem we find the equation of the conic in general form, on which we need to determine what kind of conic it represents. This can be done by finding the standard form of the equation by means of algebra properties, using a strategy known as completing the square. The quadratic equation in general form is described by the quadratic equations of the form:

A · x² + B · y² + C · x + D · y + E · x · y + F = 0

Now we proceed to find the standard form of the equation. First, write the equation in standard form:

x² + y² - 3 · x + 6 · y = 7 · x + 2

x² + y² - 10 · x + 6 · y - 2 = 0

Second, complete the square:

(x² - 10 · x + 25) + (y² + 6 · y + 9) = 2 + 25 + 9

(x - 5)² + (y + 3)² = 36

The standard form of the quadratic equation indicates the equation of a circle with a diameter of 12 units and a center at (h, k) = (5, - 3). The area of the circle is calculated below:

A = 0.25π · D²

Where D is the diameter of the circle, in units.

A = 0.25π · 12²

A = 36π

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Answer:

(48b 2) 3

Step-by-step explanation:

The answer is  A) The simplified expression is a polynomial. & B)The simplified expression has a constant term.

Polynomials are sums of phrases of the form okay⋅xⁿ, where ok is any range and n is an effective integer. as an instance, 3x+2x-5 is a polynomial. Introduction to polynomials. This video covers commonplace terminology like phrases, diploma, fashionable form, monomial, binomial and trinomial.

Here, we have,

A polynomial is described as an expression that consists of variables, constants, and exponents, which can be mixed with the usage of mathematical operations including addition, subtraction, multiplication, and department (No department operation by way of a variable).

t³(8 + 9t) - (t² + 4)(2 - 3t)

=   8t³ + 9t⁴ - (2t² - 3t³ + 8 - 12t)

=   8t³ + 9t⁴ - 2t² + 3t³ - 8 + 12t

=   9t⁴ + 11t³ - 2t² + 12t - 8.

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complete question;

T^3(8 + 9t) - (t2 + 4) (2 – 3t)

The simplified expression is a polynomial.

The simplified expression has a constant term.

The simplified expression is cubic.

The simplified expression has four terms.

The simplified expression is a trinomial

Answer:

40%

Step-by-step explanation:

2/5=x/100

cross multiply and you get 5x=200

by isolation the variable you will get x=40

therefore, 40% of Canadians read at least 10 books a year

Step-by-step explanation:

the thing you need to do here is put the value of x and just simply the expression.....

= 3y + 78 + 6y + 13

= 3 × 3 + 78 + 6 × 3 + 13

= 9 + 78 + 18 + 13

= 118

\(....\)

Answer:

3×3+78+6×3÷13

9+78+18÷13

88.38

Step-by-step explanation:

i m not sure if it's correct since i didn't follow tye bodmas rule properly and it was bit tricky and it comes in decimal so not sure if it's correct

Answer:

2 2/5 = 9/

1

= 9

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

3/5(-20 · 3)(-2/3)

3/5(-60)(-2/3)

(-36)(-2/3) = 72/3 = 24

Answer:

the answer is five(5).

Steve is correct. Steve can find the difference in temperature between 7 AM and 12 PM on Wednesday by adding the distances from 0.

By using a number line, Steve can find the difference in temperature between 7 AM and 12 PM on Wednesday by adding the distances from 0. One temperature is negative and the other is positive, but by adding their distances, he can find the difference. Kelly's method of subtracting -5.1 from the temperature at 12 PM on Wednesday is not necessarily incorrect, but it does not give the exact difference in temperature between the two times. Therefore, using Steve's method, the change in temperature would be the sum of the distance from 0 to the temperature at 7 AM (which is 2.5) and the distance from 0 to the temperature at 12 PM (which is also 2.5), resulting in a difference of 5 degrees.

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Answer: Jim raised %8.3

Step-by-step explanation: Well the total amount raised was $120 dollars, Jim raised $10 of that $120. Therefore jim raised %8.3 percent of the earned income.

The order of the fraction from least of greatest are

The fractions in order from least to greatest.

7/15 3/11 13/5 4/2 4/3

converting to decimals

7/15 = 0.4667

3/11 = 0.2727

13/5 = 2.6

4/2 = 2

4/3 = 1.3333

The order is written as follows

3/11 = 0.2727

7/15 = 0.4667

4/3 = 1.3333

4/2 = 2

13/5 = 2.6

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Answer:

1

Step-by-step explanation:

Mark the "number" as x.

6 times x plus 10 = x minus 5.

6x + 10 = x - 5.

Put the x's together:

5x = 5

Divide each side by 5 to leave the x alone:

x = 1

The area of the rectangular shape is 77 square ft and the area of the trapezoidal shape is 154 square ft.

The size of a region on a surface is determined by its area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a shape or planar lamina.

The area of the rectangular shape is:-

Area = Length x Width

Area = 7 x 11

Area = 77 square ft

The area of the trapezoid is:-

Area = 1/2 x h x ( a + b )

Area = 1/2 x 11 x ( 8 + 20 )

Area = 154 square ft

Therefore, the rectangular shape's area is 77 square feet, while the trapezoidal shape's area is 154 square feet.

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Answer:

Step-by-step explanation:

The line y = x is the line of symmetry in the reflection, which means that the x-coordinate and y-coordinate of each point get swapped. Therefore, the x-coordinate of A becomes its y-coordinate in its reflection A', and the y-coordinate of A becomes its x-coordinate in A'. Thus, the coordinates of A' are (n, m).

Therefore, the correct answer is J. (n, m).

Answer:

A. 20

Step-by-step explanation:

We know that there are 8 eights in a whole, and a whole is equal to the number 1. The number 2 consists of two wholes, and so we multiply 8 by 2.

8 wholes in each 1 × 2 ones = 16 wholes

Now, we know that the number 2 is equal to 16 wholes, so now we need to find how much 1/2 of a whole is worth.

1 whole = 8 eights, so divided by 2, it would be 4 eights for a half of a whole.

So, we add 16 + 4 to get the result of 20.

Answer:

I think it is yes.

Step-by-step explanation:

The equation of the line that passes through (-4, 5) and (1, -4), in slope-intercept form, is: y = -9/5x - 11/5.

To find the equation of a line that passes through two points, first, use the two points to find the slope (m) of the line, then find the y-intercept (b) and plug in the values into the equation, y = mx + b, which is the slope-intercept form.

Given the two points:

Slope (m) = change in y / change in x = (-4 - 5) / (1 - (-4))

Slope (m) = -9/5

Find the y-intercept, b, by substituting m = -9/5 and (x, y) = (1, -4) into y = mx + b:

-4 = -9/5(1) + b

-11/5 = b

b = -11/5

To write the equation, substitute m = -9/5 and b = -11/5 into y = mx + b:

y = -9/5x - 11/5

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Answer:

(1)

compound amount = 802.5 $

invest earned = 52.5 $

Step-by-step explanation:

total amount = 10000 $

let amount x invested in ventures A and remaining (1000-x) on ventures B

now,

6x/100 +23/400(1000-x ) = 588.75

{24x+23(1000-x)}/400 =588.75

x=235500-230000

x=5500

Amount invested on A = 5500$

Amount invested on B = 4500$

(2)

principle=750$

time= 1 year

effective invest rate = 7%

a) compound amount = p(1+(r/w)^t

=750{1+(7/100)}^1

=802.5$

b) invest earned = 802.5-700 = 52.5$

a)

From a standard normal distribution table we have that:

b)

In this case we need to use the z-score defined as:

where mu is the mean, sigma is the standard deviation and x is the value we are looking for; in this case we would have:

Therefore:

c)

Using the method in the previous part and the probability properties we have:

To find how many teams we find the probability and multiply by the population:

Therefore approximately 25 teams have at least 76 points.

Answer:

B

Step-by-step explanation:

table B: because when x increases y increases at the same rate and stay the same . the graph has proportional relation when it is a straight line passes through origin

for B :25/20=30/24=40/32=5/4

y=5/4 x

The angle measures for this problem are given as follows:

The sum of the measures of the internal angles of a triangle is of 180º.

The triangle in this problem is ABC, hence the measure of a is obtained as follows:

a + 68 + 50 = 180

a = 180 - (68 + 50)

a = 62º.

c and d are corresponding angles to angle a, as they are on the same position relative to parallel lines, hence their measures are given as follows:

Angle b is a corresponding interior angle with angle a, hence they are supplementary and it's measure is given as follows:

a + b = 180

62 + b = 180

b = 118º.

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Answer:

its greater than 10 but lesser than 100 because simplifying them in fractional form indeed informs u that its greater than 10

The expected value of buying one scratch-off ticket will be $42,400.

Given that:

25,000 scratch-off lottery tickets are sold by the state. Each entry fee is $2. One hundred tickets will reward the player $10, twenty-five tickets will win the player $100, and one ticket will win the player $5000 out of the total of 25,000 tickets.

The expected value of buying one scratch-off ticket is calculated as,

Expected value = $2 x 25,000 - ($10 x 100 + $100 x 25 + $5,000 x 1)

Expected value = $50,000 - ($1,000 + $2,500 + 5,000)

Expected value = $50,000 - $7,600

Expected value = $42,400

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a. The number of red roses left t hours after the store opens \(R(t) = 400/2^{t/2}\)    

b. The number of boxes of chocolate left t hours C(t) = 200 - 0.15t

c. One possible solution is t ≈ 7.546 hours after the store opens.

d. there are 194 boxes of chocolates left.

e. you need to arrive at the store no later than 7.504 hours after it opens.

a. The proportion (relative frequency) of times an event is anticipated to occur when an experiment is repeated a large number of times under identical conditions is known as the probability of the event.:

\(R(t) = 400/2^{t/2}\)

b. Let C(t) be the quantity of boxes of chocolate left t hours after the store opens. At first, there are 200 boxes, of which 15% are purchased every hour. We can therefore write:

C(t) = 200 - 0.15t

c. We must solve the equation R(t) = C(t) in order to determine the time at which the number of boxes of chocolates and the number of roses are equal. We obtain: by substituting the formulas we discovered in parts a and b:

\(400/2^{t/2} = 200 - 0.15t\)

Simplifying this equation, we get:

\(2^{t/2 + 1} + 0.15t - 400 = 0\)

We can solve this equation numerically, using a calculator or a computer program. One possible solution is t ≈ 7.546 hours after the store opens.

d. At 12:30 in the early evening, which is 3.5 hours after the store opens, we can utilize the recipe we tracked down to some extent b to work out the quantity of boxes of chocolates left:

C(3.5) = 200 - 0.15(3.5) = 194.25

We ought to adjust this solution to appear to be legit with regards to the issue. Since we cannot have a fraction of a box, we can round to the nearest integer and state that there are 194 chocolate boxes remaining.

e. To buy 36 red roses, we need to solve the equation R(t) = 36. Substituting the formula we found in part a, we get:

\(400/2^{t/2}= 36\)

Simplifying this equation, we get:

2^(t/2) ≈ 11.111

Taking the logarithm of both sides, we get:

t/2 ≈ log2(11.111)

t ≈ 2 log2(11.111)

Using a calculator, we get:

t ≈ 7.504 hours after the store opens.

Therefore, you must arrive at the store no later than 7.504 hours after it opens in order to purchase 36 red roses.

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The correct answer for the average salinity of the estuary would be 22.235.

Given in the question,

Salinity of ocean water at the entrance to the estuary:  35.

Volume of ocean water in the estuary:  63% (or 0.63).

Volume of freshwater in the estuary:  37% (or 0.37).

Consider, salinity of freshwater as 0.5.

To calculate the average salinity of the estuary, the  formula know is:

Average Salinity = (Salinity of Ocean Water * Volume of Ocean Water + Salinity of Freshwater * Volume of Freshwater) / Total Volume of Estuary

\(= \dfrac{35*0.63 + 0.5 * 0.37}{1}\\\\= 22.05 + 0.185\\\\= 22.235\)

Therefore, Average salinity of the estuary would be approximately 22.235.

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Given that g(x) =f(kx). The graph of function g is graph Z Because the graph a function g is the result of a horizontal compression applied to the graph of function F.

A graph can be described  as a pictorial representation or a diagram that represents data or values in an organized manner.

The graph of the function g(x) = f(kx) is obtained from the graph of f(x) by a horizontal compression or stretching, depending on the value of k.

In conclusion, If k is greater than 1, then the graph of g(x) is obtained from the graph of f(x) by a horizontal compression.

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Answer:

217945728000 ways

Step-by-step explanation:

Given

\(Books = 12\) --- 1 dozen

\(Shelf = 4\)

The given condition implies that;

\(Book\ 1 = 4\) ---- any of the 4 shelves

\(Book\ 2 = 5\) --- any of the 4 shelves and either ways of book 1

\(Book\ 3 = 6\)  --- any of the 4 shelves and either ways of book 1 and 2

-----------------------

----------------

----------

So, the number of ways is:

\(Ways = 4 * 5 * 6 * 7 * 8 * 9 * 10 * 11 * 12 * 13 * 14 * 15\)

\(Ways = 217945728000\)

Answer:

10, 13, 3, 12, and 2

Step-by-step explanation:

Answer:

He got scammed for paying $2.50 for a Juice box

Answer:

Step-by-step explanation:

The equation for total cost:

Solve for x:

Jim did not buy any tickets (n_Jim = 0).

Larry bought 7 more tickets than Jim.

To determine the number of tickets Larry bought more than Jim, we need to find the values of n for Larry and Jim's ticket purchases.

For Larry:

Let's substitute C = $170 into the equation C = 24n + 2 and solve for n:

$170 = 24n + 2

Subtracting 2 from both sides:

$168 = 24n

Dividing both sides by 24:

n = 7

For Jim:

We can calculate the number of tickets Jim bought by subtracting 12 from Larry's number of tickets:

n_Jim = n_Larry - 12

n_Jim = 7 - 12

n_Jim = -5

Since we cannot have a negative number of tickets, we can conclude that Jim did not buy any tickets (n_Jim = 0).

To find the difference in the number of tickets bought, we subtract the number of tickets Jim bought from the number of tickets Larry bought:

n_difference = n_Larry - n_Jim

n_difference = 7 - 0

n_difference = 7

Therefore, Larry bought 7 more tickets than Jim.

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Question

The equation C=24n+2 represents the cost, C, in dollars, of buying n tickets to a play. J $170. How many more tickets did Larry buy than Jim? 12