Simplify
4a + 5b – 3b + a
2 marks)

The flat fee of $25 is added to the product of $7.50 and the number of months.

a) To determine the slope of the line that has an x-intercept of -8 and a y-intercept of 5, we can use the formula for slope:

Slope (m) = (change in y) / (change in x)

The x-intercept is the point where the line crosses the x-axis, so the coordinates of this point are (-8, 0).

The y-intercept is the point where the line crosses the y-axis, so the coordinates of this point are (0, 5).

Using these two points, we can calculate the slope:

m = (5 - 0) / (0 - (-8)) = 5 / 8

The slope of the line is 5/8.

b) To determine the slope of a line perpendicular to the line passing through (-11, -8) and (6, 16), we can use the property that perpendicular lines have slopes that are negative reciprocals of each other.

First, calculate the slope of the given line:

m = (16 - (-8)) / (6 - (-11)) = 24 / 17

The negative reciprocal of this slope is:

m_perpendicular = -1 / m = -1 / (24 / 17) = -17 / 24

The slope of a line perpendicular to the given line is -17/24.

c) The total cost for a cheese of the month club is a flat fee of $25, plus $7.50 per month. We can represent this relationship with the equation:

C = 25 + 7.50m

Where C represents the total cost in dollars and m represents the number of months of membership. The flat fee of $25 is added to the product of $7.50 and the number of months.

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Answer:

seven hundred sixty-eight thousand six hundred seventy-six

hope this answer correct :)

Answer:

I believe that the answer is 13 degrees.

Step-by-step explanation:

Let's call the angle opposite 85 degrees y. y must be 85 degrees as vertically opposite angles must be equal.Let's call the third angle of the triangle which contains x, z. The angle next to z must be 98 degrees, as the rule of corresponding angles proves this if you look at the 98 degrees at the bottom of the digram, helping us find that angle z is 82, as angles on a straight line add to 180, so 180-98 is 82. y+z+x=180. We can simplify this now to 85 degrees+82 degrees+x is 180 degrees. 85 plus 82 is 167, and 180-167 is 13, so x is 13 degrees.

Answer:

2) 486 ft²

4) 38 ft²

5) 27 ft²

6) 149 ft²

Step-by-step explanation:

Just subtract the area of the unshaded part from the shaded part (as if the unshaded part wasn't there)

2) [shaded] (18 • 31.5) – [unshaded] (9 • 9) = 567 – 81 = 486

4) [shaded] (9 • 6) – [unshaded] (4 • 4) = 54 – 16 = 38

5) [shaded] (6 • 6) – [unshaded] (3 • 3) = 36 – 9 = 27

6) [shaded] (14 • 14) – [unshaded] (7 • 7)

= 196 – 49 = 149

The interest for Part 1 is approximately $385.10.

The interest for Part 2 is approximately $709.31.

The formula is as follows:

Interest is calculated as follows: Principal * Rate * Time

Where

Part 1:

$132,000 is the principal.

(Decimal) Rate = 12% = 0.12

Time = 8 days/365 days.

How much interest is there in Part 1?

Interest is calculated as follows : $132,000 * 0.12 * (8/365) = $385.10

Therefore, the interest for Part 1 is approximately $385.10.

Part 2:

$106,750 as the principal

(Decimal) Rate = 12% = 0.12

Time = 20 days / 365 days.

How much interest will there be in Part 2

Interest is calculated as follows : $106,750 * 0.12 * (20/365) = $709.31

Therefore, the interest for Part 2 is approximately $709.31.

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Answer:

Step-by-step explanation:

Look at the position of the letters in your similarity statement.

1. Corresponding angles are in the same position.  PAT - JEN. P is in the first position, so is J.  They are corresponding.

2. Proportional sides can be done the same way.  PA is in the first and second position, so is JE, so PA and JE are corresponding sides.

Answer:

-8,  -2, 10

Step-by-step explanation:

So our formula is y = 3x - 2, so to find out the y value given the x value, we input the x to find the y

x = -2, y = 3(-2) - 2 ; y = -8

x = 0, y = 3(0) - 2 ; y = -2

x = 4, y = 3(4) - 2 ; y = 10

Answer:

D

Step-by-step explanation:

1 + 4x and 57° are corresponding angles and are congruent , so

1 + 4x = 57 ( subtract 1 from both sides )

4x = 56 ( divide both sides by 4 )

x = 14

Answer:

x² + y² = 74

Step-by-step explanation:

given

(x - y) = 8 ( square both sides )

(x - y)² = 8² ← expand left side using FOIL

x² - 2xy + y² = 64 ← substitute xy = 5

x² - 2(5) + y² = 64

x² - 10 + y² = 64 ( add 10 to both sides )

x² + y² = 74

When the matrices A and B commute, or when they fulfill AB=BA, this is a significant exception.

A matrix is a rectangular array or table of numbers, symbols, or formulae used to represent mathematical objects or qualities of such things. It is often arranged in rows and columns. For instance, a matrix contains two rows and three columns. a group of integers organized in a rectangular array in rows and columns. Matrix elements or entries refer to numbers. In several disciplines of engineering, physics, economics, statistics, and mathematics, matrices have a wide range of applications.

The eigenvalues and eigenvectors of the sum of two matrices are typically not the same as the sums of the eigenvalues and eigenvectors of the individual matrices. In actuality, there is no way to separate the eigenvalues of A and B from one another.

When a vector v is an eigenvector of both A and B, it is also an eigenvector of A+B, with an eigenvalue equal to the sum of its eigenvalues for A and B, respectively. There is, however, no reason to anticipate that two matrices will share an eigenvector in general. There is no method to create an eigenvector of A+B from two random eigenvectors of A and B alone.

When the matrices A and B commute, or when they fulfill AB=BA, this is a significant exception. In this situation, their invariant spaces coincide, and if both of them are diagonalizable, they are concurrently diagonalizable, which means that their eigenvectors do as well. As was already noted, in this specific instance, the eigenvectors of A+B are likewise the same.

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The ordered pair that solves the system of equation is (0, 0).

To solve this system, we can substitute the first equation into the second equation to eliminate y:

x = 2x

Solving for x, we get x = 0.

Substituting x = 0 into the first equation, we get y = 0.

Therefore, the ordered pair that solves the system is (0, 0).

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Answer:

20

Step-by-step explanation:

20 yenara they hain aahe aahe

my answer is 20 i guess........

Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522

Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.

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Answer:

Step-by-step explanation

1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.

Now let's check if this result is correct:

1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.

So we have shown that each family paid **Rs 13,522** for the trip

Answer:

x = 10

m angle 2 = 77

m angle 4 = 77

m angle 5 = 103

Step-by-step explanation:

you can equate angle 2 to angle 4, solve for x. then plug in the x value. a angle 2 and 4 will both be 77. angle 5 will be 180-77since angle 2 and 6 are congruent, and angle 6 forms a straight line with angle 5.

Answer:

Let the father’s age be x and the son’s age be y . The first statement can be expressed as x−3=y×4 . The second statement can be expressed as x×y=430 . From there, it’s pretty easy to solve — although it involves some annoying algebra. x=y×4+3 which you can substitute into the second equation to get 4y2+3y=430 . Use the quadratic formula to solve for y . Solve for x . Calculate x+y .

Answer:

55

Step-by-step explanation:

\(\displaystyle MOE = z\biggr(\frac{\sigma}{\sqrt{n}}\biggr)\\\\4=1.96\biggr(\frac{15}{\sqrt{n}}\biggr)\\\\4=\frac{29.4}{\sqrt{n}}\\\\\sqrt{n}=\frac{29.4}{4}\\\\\sqrt{n}=7.35\\\\n=54.0225\\\\n\approx55\uparrow\)

Make sure to always round up the required sample size to the nearest integer!

Answer:

  (-∞, -3] or [-3, ∞)

Step-by-step explanation:

You want the largest domain interval(s) on which the function shown in the graph could be one-to-one.

A one-to-one function must pass the horizontal line test. That is, no horizontal line can intersect its graph in more than one place.

For that to be true of the given function, the interval on which it is defined cannot include values on both sides of x=-3, where the graph has a minimum. That is, the domain must be either x ≤ -3, or x ≥ -3, (or some subset of either of these).

The largest intervals on which the function has an inverse are ...

  (-∞, -3]  or  [-3, ∞)

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To make the given function one-to-one and have an inverse, we can restrict its domain to (-∞, a) or (a, ∞), where 'a' is the x-coordinate of the highest or lowest point on the graph.

To make the given function one-to-one and have an inverse, we need to restrict its domain. The largest domains, in interval notation, that can be used are: (-∞, a) or (a, ∞) where 'a' is the x-coordinate of the highest or the lowest point on the graph, depending on the function type.

If the graph has a highest point, the domain is restricted to (a, ∞), where 'a' is the x-coordinate of the highest point. If the graph has a lowest point, the domain is restricted to (-∞, a), where 'a' is the x-coordinate of the lowest point.

For example, if the graph has a highest point at (3, 5), the domain would be restricted to (3, ∞) to make the function one-to-one and have an inverse.

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Answer:

b=17

Step-by-step explanation:

b=(45+6)/3

b=51/3

b=17

she bought 17 books since the original price of evereything was 51 dollars before the discount of 6 dollars.

Answer:

Step-by-step explanation:

1. The possible amounts of time for which the chemistry club could rent the meeting room are 1 to 5 hours.

2. Solving the inequality for t is 39 + 6.80t ≤ 73, where the maximum time is 5 hours.

Inequality is a mathematical statement that two or more mathematical expressions are unequal.

Inequalities are depicted using the following symbols:

The total budget of the chemistry club for renting a meeting room = $73.60

The reservation fee charged by the college = $39

The additional fee (variable cost) per hour = $6.80

The number of hours the club can rent the meeting room = t

The inequality representing the situation is:

39 + 6.80t ≤ 73.

39 + 6.80t ≤ 73

6.8t ≤ 73 - 39

6.8t ≤ 34

t ≤ 5 (34/6.8)

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The ordered pairs that represents a function y in terms of x are  {(-2, -3),(1, 3),(1, 6) (9, 8}, (12, 11)) and {(-3, -5), (3, 2), (6, 5), (7, 9), (10, 16)}

A set of ordered equation represents a linear function if the domain of the coordinates are not repeated.

For instance, the ordered pairs that is a function are the coordinates that do not have any repeated y-coordinates.

From the given linear functions, the ordered pairs that represents a function y in terms of x are  {(-2, -3),(1, 3),(1, 6) (9, 8}, (12, 11)) and {(-3, -5), (3, 2), (6, 5), (7, 9), (10, 16)}

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The transformation of the function is illustrated below

Parent function is: f(x) = 2x - 6

Transformations are:

shifts f(x) 4 units down

f(x) → f(x) - 4 ⇒ g(x)= 2x - 6 - 4 = 2x - 10

stretches f(x) by a factor of 4 away from the x-axis

f(x) → 4*f(x) ⇒ g(x) = 4(2x - 6) = 8x - 24

shifts f(x) 4 units right

f(x) → f(x - 4) ⇒ g(x) = 2(x - 4) - 6 = 2x - 14

compresses f(x) by a factor of toward the y-axis (must be 4)

f(x) → f(4x) ⇒ g(x) = 2*4x - 6 = 8x - 6

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Answer:

CAB is 37 degrees

Step-by-step explanation:

90 + 53 = 143

180 - 143 = 37

After the second stop, there are 10 fewer people on the bus compared to the number of people on the bus before the 2:30 stop.

Before the 2:30 stop, the bus let off 15 people and let on 9 people. The total change in the number of people at that stop is -15 (let off) + 9 (let on) = -6.

Therefore, there are 6 fewer people on the bus after the 2:30 stop compared to before that stop.

Ten minutes later, the bus makes another stop and lets off 4 more people. This additional change needs to be considered.

Since the previous calculation only accounted for the changes up until the 2:30 stop, we need to adjust the total change by including the subsequent stop.

Adding the change of -4 (let off) to the previous total change of -6, we get a new total change of -10.

Therefore, after the second stop, there are 10 fewer people on the bus compared to the number of people on the bus before the 2:30 stop.

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Answer:

-9

Step-by-step explanation:

set y to 0

-2x + 1/2y = 18

-2x +1/2(0)=18

-2x / -2 = 18 /-2

x = -9

Answer:

-9

Step-by-step explanation:

−2x+1/2 y =18

-2x + 1/2 (0) = 18

-2x + 0 = 18

-2x = 18

then divide -2x by 18

then u get -9

Answer:

explanation below

Step-by-step explanation:

so in order for all 19 drivers to not be in a car accident the probability is

.93 ^ 14 which is around 0.362,

next for 18 of the drivers no accident its

.93^13 x .07 x 19 = around .518

for 17 drivers,

.93^12 x .07^2 x 171 = around .350

for 16 drivers,

so on and you can do the rest

Last one!!!! A = 0.5h(b1 + b2)

I hope this helps, have a good day!

Answer: the awnser is the last one to find the area of a trapizoid you have to add the 2 side so a + b then divide by 2 then multiply by the height

Step-by-step explanation:

Answer:

Step-by-step explanation:

geometric progresion formula:

\(a_n=a_1*r^{n-1}\\a_1=0.5\\r=10\\a_n=0.5*10^{n-1}\)

The algebraic rule describes the translation of quadrilateral HIJK to quadrilateral H'I'J'K' is (x, y) => (x+1, y-8)

What in mathematics is a quadrilateral?

A quadrilateral, a two-dimensional shape, is made up of four sides, four vertices, and four angles. The most prevalent shapes are concave and convex. Also included in the list of convex quadrilateral subgroups are trapezoids, parallelograms, rectangles, rhombuses, and squares.

Given: quadrilateral HIJK to that translated H'I'J'K'

To determine the algebraic rule, we need to get the coordinates of  HIJK and H'I'J'K' and then subtract them to get the translation:

H => (x, y) = (4, 6)  |  H' => (x, y) = (5, -2)

I =>  (x, y) = (6, 4)   |  I' =>  (x, y) = (7, -4)

J => (x, y) = (4, 2)   |  J' => (x, y) = (5, -6)

K => (x, y) = (4, 2)  |   K' => (x, y) = (3, -6)

Using points H and H' (you can use any point):

The difference in x is 5-4 = +1 => x+1

The difference in y is -2-6 = -8 => y-8

Therefore, the algebraic rule describes the translation is (x, y) => (x+1, y-8). Option C is the answer

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