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\(\mathtt{8}\) ÷ \(\mathtt{2(2\: + \:2)}\)

Explain into your own words.

Thanks~

Answer:

y = 5x-17

Step-by-step explanation:

point slope form would be

y- -2   =  5(x-3)        or  re-arrange to:    y = 5x -17

The equation that represents the total number of black and white squares on the chess board is 8 * 2² = 32

From the question, we have the following parameters that can be used in our computation:

The chess board

From the chess board, we have

Black squares = 32

White squares = 32

When factorized, we have

Black squares = 32 = 8 * 2²

White squared = 32 = 8 * 2²

Hence, the equation that represents the squares on the chess board is 8 * 2² = 32

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Answer: In that picture the slope is increasing

Step-by-step explanation: positive rise and positive run (uphill from left to right)

Solving a system of equations we can find the exponential function, then we can evaluate it to get:

f(10.4)= 1,427.2

We know that f(x) is a exponential function, then we can write it as:

f(x) = A*b^x

First, we know that:

f(3) = 11

f(5.5) = 57

Then we can write a system of equations:

11 = A*b^3

57 = A*b^5.5

Taking the quotient between the two equations we will get:

57/11 = (A*b^5.5)/(A*b^3)

5.18 = b^(5.5 - 3)

5.18 = b^2.5

Solving for b we will get:

(5.18)^(1/2.5) = b

1.93 = b

with that, we can get the value of b.

11 = A*(1.93)^3

A = 11/(1.93)^3

A = 1.53

So the function is:

f(x)= 1.53*(1.93)^x

Then:

f(10.4) = 1.53*(1.93)^10.4 = 1,427.2

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To calculate the 60% of 90, we need to understand what means 60% in terms of fractions. Converting a percentage into a fraction has a simple method: Dividing the percentage by 100. So 60% in fraction form is just

Now, to solve the problem, we only need to multiply our number 90 by this fraction; it gives us

Thus the 60% of 90 is 54.

The required image T of triangle ABC under the transformation (x,y) → (x-4, y+1) is formed by connecting the vertices A'(a-4, b+1), B'(c-4, d+1), and C'(e-4, f+1)

To find the image T of triangle ABC under the transformation (x,y) → (x-4, y+1), apply this transformation to each of the vertices of triangle ABC and then connect the new vertices to form the image T.

Let's assume that the coordinates of the vertices of triangle ABC are A(a,b), B(c,d), and C(e,f).

To find the image of vertex A under the transformation, we substitute x = a and y = b into the transformation equation:

(x,y) → (x-4, y+1)

(a,b) → (a-4, b+1)

Therefore, the image of vertex A is A'(a-4, b+1).

Similarly, we can find the images of vertices B and C:

B'(c-4, d+1)

C'(e-4, f+1)

Therefore, the image T of triangle ABC under the transformation (x,y) → (x-4, y+1) is formed by connecting the vertices A'(a-4, b+1), B'(c-4, d+1), and C'(e-4, f+1)

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The probability of a prime number or a number greater than 3 coming up is given as follows:

5/6.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

When a dice is thrown, there are six possible outcomes, ranging from 1 to 6, and the desired outcomes are given as follows:

Hence the probability is given as follows:

5/6.

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Part a

Setting \(x=6\), \(y=7.9(1.02)^6 \approx \boxed{8.9}\)

Part b

Setting \(x=14\), \(y=7.9(1.02)^{14} \approx \boxed{10.4}\)

Answer:

R = { ( 3 , 1 ) , (4 , 1) , (4 , 2) }

Step-by-step explanation:

Which ordered pairs are in the relation {(x, y) | x > y + 1} on the set {1, 2, 3, 4}

Assuming that:

R should be the set of real numbers such that:

R = { (x,y) | x > y + 1}  on the set {1, 2, 3, 4}

Then:

The ordered pairs for the relation can be computed as:

R = { ( 3 , 1 ) , (4 , 1) , (4 , 2) }

Example: (2x - 4) x=7 so (2x (x=7) - 4) =18

Answer:

942 square millimeters.

Step-by-step explanation:

The formula for the surface area of a cylinder is:

S = 2πr^2 + 2πrh

where S is the surface area, r is the radius, and h is the height.

Substituting the given values, we get:

S = 2 x 3.14 x 10^2 + 2 x 3.14 x 10 x 5

S = 628 + 314

S = 942

Therefore, the surface area of the cylinder is 942 square millimeters.

A name for the marked angle in 2 different ways include the following:

∠UST

∠TSU

In Mathematics and Geometry, a plane is sometimes referred to as a two-dimensional surface and it can be defined as a flat, two-dimensional surface with zero curvature and zero thickness, that extends indefinitely (infinitely). Additionally, two (2) planes intersect at a line.

Generally speaking, there are different characteristics of a plane and these include the following:

In this scenario, we can reasonably infer and logically deduce that a name for the marked angle is either ∠UST or ∠TSU.

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Phil would need to save for at least 6 weeks to have enough money to buy the bike.

Phil saves one-quarter of his pay each week, which is:

1/4 x £240 = £60

Let's assume it takes him n weeks to save enough to buy the bike. Then, the amount he saves in n weeks is:

n x £60 = £349

We can solve for n by dividing both sides by £60:

n = £349 / £60

n ≈ 5.82

Since we can't have a fraction of a week, Phil would need to save for 6 weeks to have enough money to buy the bike.

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Answer:

x = -2, y = -1, z = 1

Step-by-step explanation:

From (3), z = 2x + 5

From (2) y = (x - 2)/4

Sub them into (1):

5x - 6*(x - 2)/4 + 3(2x + 5) = -1

5x - 3x/2 + 3 + 6x + 15 = -1

19x/2 = -19

x/2 = -1

x = -2

y = (x - 2)/4 = (-2-2)/4 = -1

z = 2x + 5 = 2(-2) + 5 = 1

Answer:

$841.10

Step-by-step explanation:

To find the total cost of the TV with sales tax included, we need to add the tax to the listed price.

The tax amount is:

$787.95 × 0.0675 = $53.15

So the total cost with tax included is:

$787.95 + $53.15 = $841.10

Rounded to the nearest cent, the total cost is $841.10.

Answer:

length: 9cm

width: 9cm

Step-by-step explanation:

9×9=81

Answer:

i need a better picture reference to help you

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

28/n = n/7

cross multiply

n^2=196

n=14

Let's represent the number with the variable "x". According to the given property, we can write the following equation:

3(x + 4) < 7x

Now, let's solve this inequality to find the range of numbers that satisfy the property.

3x + 12 < 7x

Subtract 3x from both sides:

12 < 4x

Divide both sides by 4 (since the coefficient of x is 4):

3 < x

So, the range of numbers that satisfy the given property is x > 3.

Therefore, any number greater than 3 will satisfy the condition. For example, 4, 5, 6, 7, 8, etc.Step-by-step explanation:

Answer:

\(5x^4-\frac{25x^4}{x+8}+\frac{5x^5}{(x+8)^2}\)

Step-by-step explanation:

\(f(x)=x^5\\f'(x)=5x^4\\g(x)=1-\frac{5}{x+8}\\g'(x)=\frac{5}{(x+8)^2}\\\\\frac{d}{dx}f(x)g(x)\\\\=f'(x)g(x)+f(x)g'(x)\\\\=5x^4(1-\frac{5}{x+8})+x^5(\frac{5}{(x+8)^2})\\\\=5x^4-\frac{25x^4}{x+8}+\frac{5x^5}{(x+8)^2}\)

Answer: See step by step

Step-by-step explanation: Subtract f(x) from g(x) which gives us -2x-5. The domain of a linear function is all real numbers or (-∞,+∞) since we can plug any x-values into it to find the range.

Given triangle ABC as shown in the image below and the information given, the following conclusions can be made:

2. AD = DC

4. AD+DC = AC

The median of a triangle is a line segment that joins a vertex of a triangle to the midpoint of the opposite side of the vertex, thereby dividing the opposite side into two equal halves.

Thus, given triangle ABC as shown in the image below and the information given, the following conclusions can be made:

2. AD = DC

4. AD+DC = AC

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Answer:

72.3

Step-by-step explanation:

Given that:

The arithmetic sequence:

\(\sum \limits ^{14}_{k=0} (3 + 0.26k)\)

The first term of the sequence \(a_0\) = 3 since k = 0

i.e (3 + 0.26(0)) = 3

The last term of the sequence \(a_{14}\) = 6.64

i.e (3+ 0.26(14)

= (3 + 3.64)

= 6.64

Total no of terms = 15 i.e from 0 to 14

∴

The partial sum of the arithmetic sequence = \(\dfrac{Total \ no \ of \ terms }{2} \times (a_o+a_{15})}\)

\(=\dfrac{15 }{2} \times (3+6.64)}\)

= 72.3

Answer:

Step-by-step explanation:

4,15

The point (4, 3) is on the graph of this exponential model.

An equation contains one or more terms with variables connected by an equal sign.

Example:

2x + 4y = 9 is an equation.

2x = 8 is an equation.

We have,

We can use the given information to form two equations with two unknowns (a and b) and solve for them.

From the first data point (2, 3 km):

y = a b^x

3 = a b^2

From the second data point (3, 9 km):

y = a b^x

9 = a b^3

Dividing the second equation by the first equation:

9/3 = (a b³) / (a b²)

3 = b

Substituting b = 3 into the first equation:

3 = a x 3²

a = 1/9

So the exponential model is y = (1/9) x 3^x.

To find another point on the graph of this exponential model, we can choose a value for x and calculate y.

Let's try x = 4:

y = (1/9) x 3^4

y = 1 x 3/3 x 3/3 x 3/3 x 3/9

y = 3

Therefore,

The point (4, 3) is on the graph of this exponential model.

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Answer:

the two problems do not have the same answer. The first problem is dividing and has a quotient of 1. The second problem is multiplying which results in a quotient of -1.

If f(n) = f(n - 1) + 4, then

f(n - 1) = f(n - 2) + 4

and substituting this into the first equation gives

f(n) = f(n - 2) + 2•4

Similarly,

f(n - 2) = f(n - 3) + 4

so that

f(n) = f(n - 3) + 3•4

and so on.

Note the pattern:

f(n) = f(n - k) + k•4

so that when k = n - 1, we have

f(n) = f(n - (n - 1)) + (n - 1)•4

or

f(n) = f(1) + 4 (n - 1)

so that

[D] f(n) = -2 + 4 (n - 1)

The approximate height of the tree is given as follows:

45.6 ft.

The geometric mean theorem states that the length of the altitude drawn from the right angle of a triangle to its hypotenuse is equal to the geometric mean of the lengths of the segments formed on the hypotenuse.

The altitude segment for this problem is given as follows:

14.5 ft.

The bases are given as follows:

5.2 ft and x ft.

Hence the value of x is given as follows:

5.2x = 14.5²

x = 14.5²/5.2

x = 40.4 ft.

Hence the height of the three is given as follows:

5.2 + 40.4 = 45.6 ft.

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It can be concluded that triangle ABC and triangle CDE have the same shape, but possibly different sizes, and their corresponding sides are in proportion to each other.

In mathematics, a graph is a set of vertices (or nodes) and edges connecting pairs of vertices. Graphs can be used to represent relationships between objects or to visualize data. In a graph, the vertices usually represent the objects being studied, while the edges represent the connections or relationships between the objects. Graphs can be used to model a wide range of phenomena, from social networks to chemical reactions to the flow of traffic in a city. There are many different types of graphs, including directed graphs, undirected graphs, weighted graphs, and many others.

Slope is a measure of how steep a line is. It is the ratio of the change in the y-coordinates of two points on the line to the change in their x-coordinates. Symbolically, if (x1, y1) and (x2, y2) are two points on a line, then the slope of the line is given by:

slope = (y2 - y1) / (x2 - x1)

In other words, the slope is the amount by which the y-coordinate changes for every unit increase in the x-coordinate. It can be positive, negative, zero, or undefined depending on the direction and steepness of the line.

If the slopes of AC and CE are the same in the given graph, it means that the two sides are parallel to each other. By the corresponding angles theorem, angle C in triangle ABC is congruent to angle C in triangle CDE, as they are opposite angles formed by the intersection of parallel lines. Therefore, triangles ABC and CDE are similar by the angle-angle (AA) criterion.

This means that they have the same shape, but possibly different sizes, and their corresponding sides are in proportion to each other.

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