3) Calculate the area of this trapezium
D
A
11 cm
¹9 cm
19 cm
B
10 cm
C

Answer:

a) (in order) {-1, 0, 1, 2, 3}
b) {-1, 0, 1, 2, 3}

Step-by-step explanation:

I will use the law of exponent below

⇒if you re multiplying powers of them same base, keep  one base and add the exponents mathematically we say:

[tex]x^{n} *x^{n} \\=x^{n+n}[/tex]

[tex]=m^{9+(-3)} \\=m^{9-3} \\=m^{6}[/tex]

OPTION D is the solution

Answer:

$19.6

Step-by-step explanation:

B=20.50-0.06.x

B=20.50-0.06*15

B=20.50-0.9

B=19.6

The constant of proportionality in the equation:

P = 0.45*n

Is k = 0.45, so we can conclude that Julie is correct.

A proportional relationship between two variables x and y is written as:

y = k*x

Where k is the constant of proportionality.

In this case, we have the variables P and n, and the proportional relationship is:

P = 0.45*n

So we can see that the value of the constant of proportionality is k = 0.45, so yes, Julie is correct.

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The equation of the line that passes through point (-3,1) and perpendicular to y=-5x+2 is y = (1/5)x + 8/5.

Given the data in the question;

First we determine the slope of the initial line using the slope intercept-form. y = mx + b

y = -5x + 2

Compared with the slope intercept form,

Slope m = -5

Now, for the equation of line perpendicular to the initial line, its slope must be a negative reciprocal of the initial slope.

Hence, slope of the perpendicular line is;

Slope m = -1/(-5) = 1/5

To find the equation of the perpendicular line, we use the point slope formula.

y - y₁ = m( x - x₁ )

Plug in the slope m ( 1/5) and point (-3,1).

y - 1 = (1/5)( x - (-3) )

y - 1 = (1/5)( x + 3 )

Convert to slope-intercept form.

y - 1 = (1/5)( x + 3 )

y - 1 = x/5 + 3/5

y = x/5 + 3/5 + 1

y = x/5 + 3/5 + 1

y = x/5 + 8/5

y = (1/5)x + 8/5

Therefore, the equation of the perpendicular line is y = (1/5)x + 8/5.

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The bacterial cell is 6.25 x 10 times smaller than the amoeba cell.

The length of the Bacterial cell is 4 x 10⁻⁶ meters.

The length of the Amoeba cell is 2.5 x 10⁻⁴ meters.

The length L of the bacterial cell can be written as,

L = 0.000004 meters.

Also, the length L' of the amoeba cell can be written as,

L' = 0.00025 meters.

Let us say that the bacterial cell is N times smaller than the amoeba cell.

So. we can write,

Length of bacterial cell x N = length of amoeba cell.

LN = L'

0.000004(N) = 0.00025

N = 0.00025/0.000004

N = 62.5  

So, now we can say that the length of the bacterial cell is 62.5 times smaller than he amoeba cell.

As we have to state our answer in scientific notation,

We can write 62.5 as 6.25 x 10.

Now the number of significant figure is has are three.

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Pythagoras's theorem - The two teachers are both seated at a distance of 15 meters from each other.

What is Pythagoras' theorem?

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic Euclidean geometry relationship between a right triangle's three sides. According to this rule, the area of the square with the hypotenuse (the side across from the right angle) is equal to the sum of the areas of the squares with the other two sides. The Pythagorean equation, which generally refers to the relationship between the lengths of the legs a, b, and the hypotenuse c, can be used to represent this theorem.

We are given,
the distance between Krysta and her math teacher to be 12 meters, and the distance between Krysta and her science teacher to be 9 meters

for simplicity, we'll let  
the distance between Krysta and her math teacher to be KM =12 meters
and the distance between krysta and her science teacher to be KS =9 meters we need to find the distance between the maths teacher and the science teacher, i.e. MS.

all three people's sitting arrangement makes a triangle, with them sitting on the vertex of it.

Using Pythagoras' theorem,

(KM)² + (KS)² = (MS)²

(12)² + (9)² = (MS)²

144 + 81 = (MS)²

225 = (MS)²

√225 = (MS)

thus, MS = 15 meters

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Answer:

d

Step-by-step explanation:

1 = 1 cup

1/2 can be 2/4

2/4+1/4=3/4

1+3/4 = 1 3/4

Answer:

f(-3)=10

Explanation:

Given the function:

When x = -3

The dimensions that would guarantee that the garden has the greatest possible area is 190 feet on the shorter side and 380 feet on the longer side to produce an area of 72,200 square feet.

A dimensions of a rectangle is the length of each side.

Let x = length of the shorter side

y = length of the longer side

If one side of the garden is bordered by a river and so it does not need any fencing, and assume that the longer side is this side, then the perimeter that only needs to be fenced by 760 feet of fencing materials is

2x + y = 760

y = 760 - 2x

The area of the rectangular garden is the product of the shorter side and the longer side of the garden. Hence,

A = xy

A = x(760 - 2x)

A = 760x - 2x²

To obtain the largest area possible, the first derivative of the area should be equal to zero.

A(x) = 760x - 2x²

A'(x) = 0

760 - 4x = 0

Solve for x.

760 - 4x = 0

4x = 760

x = 190

length of the shorter side = 190 feet

y = 760 - 2x

y = 760 - 2(190)

y = 380

length of the longer side = 380 feet

Solve for the greatest possible area.

A = xy

A = 190 feet(380 feet)

A = 72,200 square feet

" A gardener has 760 feet of fencing to fence in a rectangular garden. One side of the garden is bordered by a river and so it does not need any fencing. What dimensions would guarantee that the garden has the greatest possible area? "

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Any point satisfying the relation y = -[1 - (∛x²)]²(1/(∛x)) will be points on the graph where the tangent line has slope 1.

What is the slope of a given line?
A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate. Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively.
Consequently, the formula for the change in y-coordinate with respect to the change in x-coordinate is the slope of a line is represented by the expression m = change in y/change in x =Δy/Δx.
Additionally, the slope of the line can be shown as tan θ = Δy/Δx
So, the slope of a line is tan θ.

The given equation is: (∛x²) + (∛y²) = 1
Therefore, (∛y²) = 1 - (∛x²) ⇒ y² = [1 - (∛x²)]³
Differentiating the equation formed with respect to x, we get
2y(dy/dx) = 3[1 - (∛x²)]²(-2/3)(1/(∛x)) ⇒ dy/dx = (-1/y)[1 - (∛x²)]²(1/(∛x)) -(i)
Given, the slope of the tangent line is = 1 -(ii)
Thus, equating (i) and (ii), we get,
(-1/y)[1 - (∛x²)]²(1/(∛x)) = 1 ⇒ y = -[1 - (∛x²)]²(1/(∛x))
Therefore any point satisfying the relation y = -[1 - (∛x²)]²(1/(∛x)) will be points on the graph where the tangent line has slope 1.

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Answer:

By using commutative property, if a = b and b = c, then a = c.

Step-by-step explanation:

Answer:

translative property

Step-by-step explanation:

All the points are P1=(0, 2), P2= (1,3), P3(2,4), P4(3,5 ), and P5(4,6).

y=x+2 is obtained function through the equation y-x=2.

Consider the value of X=0 for P1.

Y= 0+2

Y=2

If X=0, then Y=2.

∴ (0, 2)

Consider the value of X=1 for P2.

Y=1+2

Y=3

If X=1, then Y=3

∴ (1,3)

Consider the value of X=2for P3.

Y=2+2

Y=4

If X=2, then Y=4

∴ (2,4)

Consider the value of X=3for P4.

Y=3+2

Y=5

If X=3, then Y=5.

∴ (3,5 )

Consider the value of X=4 for P5.

Y=4+2

Y=6

If X=4, then Y=6.

∴ (4,6)

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Answer: 30

Step-by-step explanation:

The load each should get to maximize the profit is $67,500, $78,700 and $90,000

What Is Profit?

In accounting, a profit is an income that is given to the owner throughout a successful market producing process. Profitability, which is the owner's primary interest in the income-formation process of market production, is measured by profit. There are various profit metrics that are frequently used.

Let x represent the total number of laptops and y represent the total number of desktop computers.

A laptop computer occupies 2 cubic feet, hence x laptops each use 2x cubic feet. Desktop computers take up 5 cubic feet of space, hence 5y cubic feet of room is required for 5y desktop computers.

They require 2x + 5y cubic feet in total.

Since the delivery truck's maximum capacity is 800 cubic feet,

2x + 5y <= 800.

They must load at least 300 laptops because of the demand,

hence, x >= 300

They make $225 on each laptop, which translates to $225 times as many computers. They make a profit of $280 on each desktop computer, or $280y on y desktops.

Total profit is:

P=$(225x + 280y)

Draw the inequality system (see attached diagram)

2x + 5y <= 800.

x >= 300

One of the common region's three vertices will have the most profit:

P(300,0) = 225(300) + 280(0) = $67,500

P(300,40) = 225(300) + 280(40) = $78,700

P(400,0) = 225(400) + 280(0) = $90,000

Hence, each should load $67,500, $78,700 and $90,000 on the truck to maximize profit

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The size of the population of mosquito follows an exponential model.

the size of the population in 10 days is 1370

The size of the population in 10 days is 1370

The given parameters are:

p(0) = 574

p'(0)= 50

An exponential function is represented as:

p(t) =p(0) * e^ rt

So, we have:

p(t)=574*e^rt

Differentiate

p'(t)=574*r*e^rt

Substitute 0 for t

50=574 r

Divide both sides by 574

r=0.087

The function becomes

p(t)= 574*e^rt

   = 574*e^0.087 t

In 10 days, t = 10.

So, we have:

p(10)=574*e^0.87

Solve

p(0)=1370

Hence, the size of the population in 10 days is 1370

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Answer:

0.75

Step-by-step explanation:

in the pic

goodluck

Using mathematical operations, Maury bought 6 tickets at the Ticket Outlet if he paid $77 at $12 each.

The basic mathematical operations are addition, subtraction, multiplication, and division.

These basic operations are used to manipulate numbers and variables in mathematical expressions to produce mathematical results.

The first mathematical operation used here is the subtraction operation.  

After subtracting the fixed cost from the total cost, the difference is the total variable cost.

This difference is then divided by the unit variable cost to get the number of tickets.

The unit cost of the ticket = $12

The service charge (fixed cost) = $5

The total cost = $77

The number of tickets bought = 6 ($77 - $5)/$12

Thus, using mathematical operations, Maury did buy 6 tickets for $77.

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Answer:

f(x)=(x-4)^2-4

The parent function (x^2) is shifted to the right 4 times (x-4) and down 4 times (-4).

Answer:

1 unit

Step-by-step explanation:

- 1 1/2 - (- 2 1/2)

= 1 unit

The height of an "angry bird" shot into the sky as a function of time (seconds) is h = 8.65 ft.

The height of the bird is given by the following equation

h(t)= -0.25t2 + 1.9t + 17

t= 1

   = -0.25 + 1.9 + 17

   = -8.35 + 17

h   = 8.65 ft.

The following are the three equations:

-First equation of motion: v = u + at

-Second equation of motion: s = u t + 1/2 at2

Third equation of motion: v2 = u2 + 2as

t is the time, in seconds.

h(t) is the height, in feet, which is dependent of the time.

h(t) is height in feet and t is time in seconds

then h = 8.65 ft.

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The expression shows the product of the number of ladder rungs that Yan climbed is D. (Negative 4) + (negative 4) + (negative 4) + (negative 4) + (negative 4) + (negative 4) + (negative 4) + (negative 4)

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

We have been given that each time Yan descends 4 rungs on the ladder.

SInce, each time the number of ladder rungs that Yan climbed is negative 4, where negative sign represent descends.

Yan made eight stops with no extra steps.

-4 x 8 = -32

It can also written as; (-4) + (-4)+(-4)+(-4)+(-4)+(-4)+(-4)+(-4)

The correct answer is D. (Negative 4) + (negative 4) + (negative 4) + (negative 4) + (negative 4) + (negative 4) + (negative 4) + (negative 4)

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Answer:

B

Step-by-step explanation:

it shows that it doesn't go anywhere in the interval of 2 and 5, other ones would be wrong bcs it's either go up or down

Answer: 8 weeks

Step-by-step explanation:

Answer: Yes they do.

Answer: 56.25 = u

Step-by-step explanation:

1) Multiply 3 on both sides to leave u by itself

18.75 = u/3

18.75*3 = u

56.25 = u

A. A short word problem about a purchase made to illustrate the equation is that John bought six pens and bought books for $18. The total amount is $72. Find the cost of each pen.

B. The cost of each pen is $9

C. The variable is x.

A. The problem is that John bought six pens and bought books for $18. The

B. The equation to illustrate this will be:

6x + 18 = 72

Collect like terms

6x = 72 - 18

6x = 54

Divide

x = 54 / 6.

x = $9

The cost of each pen is $9.

C. The variable is x = 9. This is the cost of the pen.

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The graph of the linear inequality can be seen in the image at the end.

Here we have the linear inequality:

y  ≥ 2x + 1

To graph this, we first need to graph the line.

y = 2x + 1

With a solid line, because we have the symbol ≥, which means that the points on the line are solutions.

Once we graphed that line, we look at our inequality:

y  ≥ 2x + 1

It says that y is larger than or equal to the values on the line, so once the line is graphed we need to shade all the region above that line.

The shaded region (and the line itself) represent all the solutions of the linear inequality.

And the graph can be seen below.

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