1. Consider the following system of equations.
x+y=5
2x-y=-2
The solution to the system of equations: (12,7)
Create a third equation that could be added to the system so that the solution does not change.

False. Line charts are best suited for representing data that follows a sequential order, such as time series data. Nonsequential data is better represented by other types of charts, like scatter plots or bar graphs.

Line charts are graphical representations of data points connected by lines. They are commonly used to display trends over time or sequential data. For example, they are often used to show the change in stock prices over a period of time or the temperature variations throughout the day. This sequential order is the key feature of line charts.

However, for data that does not follow a sequential order, line charts may not be the best choice. Nonsequential data, such as categorical or unrelated data points, are better represented by other types of charts. Scatter plots, for instance, are useful for showing the relationship between two variables that are not necessarily ordered. Bar graphs can also be used to compare nonsequential data points in different categories.

In summary, line charts are not best suited for representing data that follows a nonsequential order. They are most effective when used to display data that has a clear sequential relationship, allowing for easy interpretation of trends and patterns.

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Answer:

x(5x²-7)

Step-by-step explanation:

5x³-7x

=x(5x²-7)

To prove your answer,let's multiply x by each term in the bracket

=x X 5x²=5x³

x X -7 =-7x

Graph △RST with vertices R(4, 1), S(7, 3), and T(6, 4) and its image after the glide reflection is shown in figure.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

In △RST;

The vertices are, R(4, 1), S(7, 3), and T(6, 4)

Here, Translation: (x, y) → (x, y−1)

And, Reflection in the y-axis.

Hence, New coordinate of the image of △RST are,

⇒ R' = (- 4, 1 - 1) = (- 4, 0)

⇒ S' = (- 7, 3- 1) = (- 7, 2)

⇒ T' = (- 6, 4 - 1) = (- 6, 3)

Thus, Graph △RST with vertices R(4, 1), S(7, 3), and T(6, 4) and its image after the glide reflection is shown in figure.

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The Orthocentre is one of the four (4) most common centres of a triangle.

It is located at the point where the triangle's three(3) altitudes intersect called a point of concurrency.

The Orthocentre is located inside an acute triangle, on a right triangle and outside an Obtuse triangle.

Hence, the correct option is Option C

Answer:

47

Step-by-step explanation:

The missing angle is complementary to the angle shown and together they from 90.

Your missing angle is 90 - 43

Answer:

1) 5
the smallest integer besides one that both sides are divisible by is 5
2) 2

make both denominators the same 35/40, and 16/40. because 16 can only go into 35 twice the answer is 2

However, we need to substitute a with s since that is the value we have calculated. Therefore, we get \(A(s) = (1/4)(5 + sqrt(5))s^2.\) This is the function notation that represents the area of a regular pentagon whose perimeter is 140 cm.

Let's consider that s be the length of a side of the regular pentagon.

The perimeter of the regular pentagon will be 5s. Therefore, we have the equation:5s = 140s = 28 cm

Also,

we have the formula for the area of a regular pentagon as:

\($A=\frac{1}{4}(5 +\sqrt{5})a^{2}$,\)

where a is the length of a side of the pentagon.

In order to represent the area of a regular pentagon whose perimeter is 140 cm, we need to substitute a with s, which we have already calculated.

Therefore, we have:\(A(s) = $\frac{1}{{4}(5 +\sqrt{5})s^{2}}$\)

Now, we have successfully used function notation (with the appropriate functions above) to represent the area of a regular pentagon whose perimeter is 140 cm.

The area of a regular pentagon can be represented using function notation (with the appropriate functions above). The first step is to calculate the length of a side of the regular pentagon by dividing the perimeter by 5, since there are 5 sides in a pentagon.

In this case, we are given that the perimeter is 140 cm, so we get 5s = 140, which simplifies to s = 28 cm. We can now use the formula for the area of a regular pentagon, which is\(A = (1/4)(5 + sqrt(5))a^2\), where a is the length of a side of the pentagon.

However, we need to substitute a with s since that is the value we have calculated. Therefore, we get\(A(s) = (1/4)(5 + sqrt(5))s^2.\) This is the function notation that represents the area of a regular pentagon whose perimeter is 140 cm.

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The maximum percentage of individuals who own a bike is 21.5%.

Margin of error is the percentage points a researcher's value would differ from the real population's value. The maximum percentage is the sum of the margin of error and the true value.

The maximum percentage = margin of error + true value

(1/5) x 100 + 1.5% = 21.5%

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Answer:

See image

Step-by-step explanation:

Plato

The cost of the leather used to make 100 bicycle seats is assigned to a custom order to be shipped to a bike retailer. This indicates that the custom order was for 100 bicycle seats and that they will be sold to a bike retailer. When it comes to the assignment of cost, the cost of the leather is an indirect cost.

The cost of the leather used to make 100 bicycle seats is assigned to a custom order to be shipped to a bike retailer. This indicates that the custom order was for 100 bicycle seats and that they will be sold to a bike retailer. When it comes to the assignment of cost, the cost of the leather is an indirect cost. Since it cannot be directly traced to the product, it must be allocated to the cost of production based on the percentage of production cost.
When 100 bicycle seats are being produced, and the cost of the leather used in their production is $400, then the cost per bicycle seat is $4. This is calculated by dividing the total cost of the leather ($400) by the number of bicycle seats (100). If the custom order is for 100 bicycle seats, the cost of the leather used to produce the seats will be $400.
The bike retailer, who will purchase the custom order, will be charged a retail price that is higher than the production cost.

The amount of the retail price will be higher than $4 per seat, and it will be based on several factors such as profit margin, overhead, and other expenses associated with the production and sale of the bicycle seats.
In conclusion, the cost of the leather used to make 100 bicycle seats will be assigned to a custom order to be shipped to a bike retailer. The cost of production is an indirect cost, and it will be allocated based on the percentage of production cost. The bike retailer will be charged a higher retail price that takes into account the production cost, profit margin, overhead, and other expenses.

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Answer:

no

Step-by-step explanation:

$1.50×8=12$ US$ so 12$ for 8ap or 6.50$ for 8ap

Answer:

\(Here,length=36 \: cm\)

\(breadth=24 \: cm\)

\(Perimeter=?\)

\(We \: know,\)

\(Perimeter=2(l+b)\)

\( = 2 \times 60\)

\( = 120.\)

Answer:

Perimeter=120 cm

Step-by-step explanation:

length=36cm

breadth=24cm

Perimeter=2(length+breadth)

Substitiute values in fomula above:

Perimeter=2(36+24)cm

Perimeter=2(60) cm

Perimeter=120 cm

The evaluation of the fraction, \(\dfrac{x^3-5\cdot x^2+ 2\cdot x-6}{x - 1}\), using the long division method is the option;

The expression can be presented as follows;

\(\dfrac{x^3-5\cdot x^2+ 2\cdot x-6}{x - 1}\)

The numerator x³ - 5·x² + 2·x - 6  does not have (x - 1) as a factor
However, dividing x³ - 5·x² + 2·x - 6 by (x - 1), gives;

        x² - 4·x -2

(x - 1)|x³ - 5·x² + 2·x - 6

  \({}\)      x³ - x²

\({}\)             -4·x² + 2·x - 6

\({}\)             -4·x² + 4·x

\({}\)                        -2·x - 6

\({}\)                      -2·x  + 2

\({}\)                                 -8

The quotient from the division is x² -4·x  -2, the remainder is -8, therefore, the result from the division x³ - 5·x² + 2·x - 6 by (x - 1) is the option;

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The correct expansion of the given expression would be = 2x 2x²+2x (-5)+3.2x²+3• (-5). That is option C.

The given expression of equations;

(2x + 3)(2x² - 5). That is the product of 2x+3 and 2x²-5

= 2x *2x² + 2x*(-5) + 3*2x²+3×(-5)

= 4x³ - 10x+ 6x²-15

= 10x⁵ -10x-15.

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Answer:c

Step-by-step explanation:

did it

Answer:

A

Step-by-step explanation:

Area of a circle = \(A = \pi r^{2} \\\)

R = 1/2 diameter

R = 14 / 2 = 7

A = π(7)²

A = 153.86

Answer:

a

Step-by-step explanation:

Answer 2,4 are all described as unit rates  a unit rate is anything that has per or each in it so a certain type of boat travels at 7 hours PER mile so we know question 2 is correct and 3 is a unit rate because it has each in it A summer camp provides 3 meals for EACH camper. That’s why the answer is 2 and 4

Answer:

answer is a

Step-by-step explanation:

zeros are x intercepts

Answer:

A

Step-by-step explanation:

(2x+1)(x+2)

so

2x=-1

x=-1/2

x=-2

A

Answer:

Order the numbers from least to greatest.

75, 83, 89, 94, 98, 101, 105, 108, 111, 122, 125, 130

Minimum is 75

Q1 is 91.5

The median is 103.

Q3 is 116.5

Maximum is 130

Now, look at the answer choices.

B has the incorrect median

D has incorrect Q1.

A has incorrect Q3.

C is the answer.

The number of beads of each type that are on each necklace will be 6 beads.

It should be noted that the jewelry maker will use 24 jade beads and 30 teak beads to make necklaces. each necklace will have the same number of necklaces she can make.

Therefore, it van be seen that the highest common factor between 24 and 30 is 6.

Therefore, the number of beads of each type that are on each necklace will be 6 beads.

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Answer:

If AB and CD are perpendicular, (slope of AB) x (slope of CD) = -1

9/a = -1

a = -9

Answer:

-9

Step-by-step explanation:

flip and change the sign of \(\frac{3}{4}\)

\(\frac{4}{-3}\)

set equal to each other

\(\frac{4}{-3}\) = \(\frac{12}{a}\)

cross multiply

4a = -36

divide by 4

a = -9

the graph of the function g(x) = |x + 3|  will not have a negative value. graph of the given function is attached below.

A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.

Given a function  g(x) = |x + 3|.

Since the modulus of a function is a function that gives the absolute value of a number or variable. It produces the magnitude of the number of variables. It is also termed an absolute value function. The outcome of this function is always positive, no matter what input has been given to the function.

Thus,

The domain of this function g(x) is - infinite to  + infinite

And range will be [0, ∞)

So the graph of the function g(x) = |x + 3|  will not have a negative value.

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Answer:

134 :)

Step-by-step explanation:

\(( ~~ \csc(\theta )-\cot(\theta ) ~~ )^2=\cfrac{1-\cos(\theta )}{1+\cos(\theta )} \\\\[-0.35em] ~\dotfill\\\\ ( ~~ \csc(\theta )-\cot(\theta ) ~~ )^2\implies \csc^2(\theta )-2\csc(\theta )\cot(\theta )+\cot^2(\theta ) \\\\\\ \cfrac{1^2}{\sin^2(\theta )}-2\cdot \cfrac{1}{\sin(\theta )}\cdot \cfrac{\cos(\theta )}{\sin(\theta )}+\cfrac{\cos^2(\theta )}{\sin^2(\theta )}\implies \cfrac{1}{\sin^2(\theta )}-\cfrac{2\cos(\theta )}{\sin^2(\theta )}+\cfrac{\cos^2(\theta )}{\sin^2(\theta )}\)

\(\cfrac{\cos^2(\theta )-2\cos(\theta )+1}{\sin^2(\theta )}\implies \cfrac{[\cos(\theta )-1][\cos(\theta )-1]}{\sin^2(\theta )} \\\\\\ \cfrac{[\cos(\theta )-1][\cos(\theta )-1]}{1-\cos^2(\theta )}\implies \cfrac{[\cos(\theta )-1][\cos(\theta )-1]}{-[\cos^2(\theta )-1]}\)

\(\cfrac{[\cos(\theta )-1][\cos(\theta )-1]}{-[\cos^2(\theta )-1^2]}\implies \cfrac{[\cos(\theta )-1][\cos(\theta )-1]}{-[\cos(\theta )-1][\cos(\theta )+1]} \\\\\\ \cfrac{\cos(\theta )-1}{-[\cos(\theta )+1]}\implies \cfrac{-[\cos(\theta )-1]}{\cos(\theta )+1}\implies \cfrac{1-\cos(\theta )}{1+\cos(\theta )}\)

The domain and range of f(x) = -24 are given as follows:

The domain and range of f(x) = 0.5(x + 4)² - 11 are given as follows:

The range of y = -2x² + 12x - 13 is given as follows:

y <= 5.

The domain of a function is the set that contains all the input values that can be assumed by the function.

As neither of the functions in this problem have any restriction, the domain is all real values for the two of them.

The range of a function is the set that contains all the output values that can be assumed by the function.

The ranges are given as follows:

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The value of the integral ∫∫∫ e²(x² + y²) dV in cylindrical coordinates is h (e²a - 1) π.

To evaluate the integral ∫∫∫ e²(x² + y²) dV in cylindrical coordinates, to express the integral in terms of cylindrical coordinates and determine the appropriate limits of integration.

In cylindrical coordinates, the variables are represented as (ρ, θ, z), where ρ is the radial distance, θ is the angle in the xy-plane, and z is the vertical coordinate.

The region e can be described as the volume inside the cylinder x² + y² ≤ a², where a is the radius of the cylinder.

In cylindrical coordinates, the equation of the cylinder x² + y²= a² becomes ρ² = a².

Therefore, the limits of integration for ρ are 0 to a, the limits for θ are 0 to 2π (covering a complete revolution), and the limits for z depend on the height of the cylinder.

If the height of the cylinder is h, then the limits for z would be -h/2 to h/2.

express the integral in cylindrical coordinates:

∫∫∫ e²(x² + y²) dV = ∫(0 to 2π) ∫(0 to a) ∫(-h/2 to h/2) e²(ρ²) ρ dz dρ dθ the integrand e²(ρ²)  depend on the angle θ,  factored out of the θ integration.

∫∫∫ e²(x² + y²) dV = ∫(0 to 2π) ∫(0 to a) e²(ρ²) ρ ∫(-h/2 to h/2) dz dρ dθ

The innermost integration with respect to z simply evaluates to h:

∫∫∫ e²(x² + y²) dV = ∫(0 to 2π) ∫(0 to a) e²(ρ²) ρ h dρ dθ

The integration with respect to ρ can be done by substitution. Let u = ρ², then du = 2ρ dρ:

∫∫∫ e²(x² + y²) dV = ∫(0 to 2π) ∫(0 to a) e²u/2 h (1/2) du dθ

= (h/2) ∫(0 to 2π) ∫(0 to a) e²u du dθ

= (h/2) ∫(0 to 2π) [e²u] (0 to a) dθ

= (h/2) ∫(0 to 2π) (e²a - 1) dθ

= (h/2) (e²a - 1) ∫(0 to 2π) dθ

= (h/2) (e²a - 1) [θ] (0 to 2π)

= h (e²a - 1) π

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