11 less than the quotient of
4
44 and
�
xx.

Answer: B. (1, 8)

Step-by-step explanation:

Hope this helps! :)

The values of the variables x and y are;

1, x = -y and y = 5. Option D

2. x= 1 and y = -1. Option A

Using the substitution method of solving simultaneous equations, we have;

4x + 7y = 19

y - x = 9

Now, make 'y' the subject from equation 2

y = 9 + x

Substitute the equation into equation 1

4x + 7(9 + x)= 19

expand the bracket, we have;

4x + 63 + 7x = 19

collect the like terms

11x = -44

x = -4

then,

y = 9 - 4 = 5

-3x + y = -4

4x + 3y = 1

make y' the subject from equation 1

y =-4 + 3x

Substitute the value

4x + 3(-4 + 3x) = 1

expand the bracket

4x - 12 + 9x = 1

13x = 13

x = 1

Substitute the value

y = -4 + 3

y = -1

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Answer: 3.1

Step-by-step explanation: they are giving you the diameter so you halve it then you multiply it my 3.14 (pi) then you round it to the nearest tenth which is the 1 so you look to the left and it's not bigger than 5 so you round down so it stays as a 1

Step-by-step explanation:

well, the combination of all set elements.

FYI : if some elements appear in both sets, we only use these once for the result set (this is not the case here, but it might be in other questions).

the combination of both sets is then

{b, c, d, e, g, h}

The effect of increasing the distance e between charged object is that , the electric force decreases because the distance has an indirect relationship to the force.

Coulomb's law states that the force between two charged bodies is directly proportional to the product of the charge and inversely proportional to the square of the distance between them.

Coulomb's law can therefore be expressed mathematical as;

F = Q1Q2/r²

where r is the distance between charge Q1 and Q2

This means that since the force is inversely proportional to the square of distance, force will decrease as distance is increasing.

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The box and whisker plot that has the greatest interquartile range is option 3..

The interquartile range of a data set can be found by finding the difference of the data at the beginning and end of the edges of the rectangular box in a box and whisker plot.

It is also the difference between the third and first quartile.

The box and whisker plot in option 3 has the greatest interquartile range because the difference of the Q3 and Q1 is close to 9, which is the highest compared to the other data.

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One of the stages in Cooley's looking-glass self theory is A. We imagine how we look to other people.

As per Cooley's theory, our self-concept is shaped through a social interchange in which we envision how others perceive us, evaluate that perception and then deliberate on how those assessments influence our self-esteem.

All these components are part of the "looking-glass self" process, consisting of three stages: 1) fantasising about how one appears to others 2) pondering over the judgments made based on appearance and 3) evolution of the self-image influenced by such judgements. Notably, imagining one's outward persona forms an integral element of this psychological principle.

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The coupon rate of the bonds by King of Diamonds Industries would be 7 %.

The formula for the bond price shows the coupon payment and so can be used to find the coupon rate:

= (Coupon payment  x ( 1 - ( 1 + r ) ^ ( - number of years till maturity ) ) ) / r + Face value /  (1  + rate )^ number of years

1,482.01 = (C x (1 - (1 + 0.07 )^ (- 14) ) ) / 0.07 + F / (1 + 0.07 ) ^ 14

103.7407 - 0.07 x (F / (1 + 0.07) ^14 ) = C x  (1 - ( 1 + 0.07) ^ ( - 14) )

Using a calculator, C is $ 70.

This means that the coupon rate is:

= 70 / 1, 000

= 7 %

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Answer:

In 8th grade math, it's essential to know the following words: variable, coefficient, expression, equation, absolute value, function, slope, y-intercept, x-intercept, exponent, rational number, irrational number, proportion, ratio, and statistic. It's also crucial to have a solid understanding of basic arithmetic operations, including addition, subtraction, multiplication, and division, as well as properties of fractions, decimals, and percentages. Understanding geometric principles such as area, perimeter, and volume is also vital. Mastery of these terms and concepts will help your nephew excel in 8th grade math.

Answer: variable, coefficient, expression, equation, absolute value, function, slope, y-intercept, x-intercept, exponent, rational number, irrational number, proportion, ratio, and statistic. It's also crucial to have a solid understanding of basic arithmetic operations, including addition, subtraction, multiplication, and division, as well as properties of fractions, decimals, and percentages

Im Proud of you Bryson :)

Answer:

C

Step-by-step explanation:

To find the sum of the rational expressions, we need to add the two expressions and simplify if possible:

(2x-1)/(7x+x+2) + (x-2)/(8x-2)

Simplifying the denominators, we get:

(2x-1)/(8x+2) + (x-2)/(8x-2)

Now, we need to find the LCD, which is (8x+2)(8x-2) = 64x²-4:

[(2x-1)(8x-2) + (x-2)(8x+2)] / (64x²-4)

Simplifying the numerator, we get:

[16x²-4x-16x+4+8x²-2x+16x-4] / (64x²-4)

Combining like terms, we get:

(24x²-2) / (64x²-4)

Factoring out a 2 from the numerator and denominator, we get:

2(12x²-1) / 2(32x²-2)

Simplifying further, we get:

(12x²-1) / (16x²-1)

Therefore, the sum of the rational expressions is:

12x²-1

-----------

16x²-1

So, the answer is option C.

The angle of Z is 63.2 degree.

The word isosceles comes from the Ancient Greek term isosceles which literally means "equal-legged." An isosceles triangle has two of its sides of equal length, which means that the angles opposite these sides would also be of equal measure.

In Triangle ΔXYZ,

∠Y = 83°, XY = 9 and XZ = 10

To find the angle of Z

Using Sine rule :-  sine rule relates the sine of each angle to length of        opposite side.

[tex]\frac{Sin A}{a} =\frac{SinB}{b} =\frac{SinC}{c}[/tex]

Where, A, B , C are the angles of the triangles and a, b, c are the side of the triangles

Then, Apply it:

[tex]\frac{Sin83}{10}=\frac{SinZ}{9}[/tex]

Using cross multiplication:-

Sin 83 × 9 = Sin Z × 10

Sin Z = (Sin 83 × 9)/10

Sin Z = 0.893

∠Z = [tex]Sin^-^1(0.893)[/tex]

∠Z =  63.2°

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Answer: F

Step-by-step explanation:

Answer: correct answer is A

Step-by-step explanation:

Remember that the coordinates (−2,−5π3) tell us the radius r=−2 and the angle θ=−5π3. So the point should be on the circle labeled 2 and form an angle of −5π3 with the negative x-axis. Point A is the correct point.

Since the graph was obtained by transforming the graph of the square root function, an equation for the function the graph represent is: [tex]g(x) = -\sqrt{9(x - 1)} + 2[/tex]

In Mathematics and Geometry, a square root function is a type of function that typically has this form f(x) = √x, which basically represent the parent square root function i.e f(x) = √x.

In Mathematics and Geometry, a horizontal translation to the right is modeled by this mathematical equation g(x) = f(x - N) while a vertical translation to the positive y-direction (upward) is modeled by this mathematical equation g(x) = f(x) + N.

Where:

In this context, the required square root function can be obtained by applying a set of transformations to the parent square root function as follows;

f(x) = √x

g(x) = -√9(x - 1) + 2

[tex]g(x) = -\sqrt{9(x - 1)} + 2[/tex]

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5√2 is the value of x in the given triangle. Therefore, the correct option is option A among all the given options.

A polygon having three edges & three vertices is called a triangle. It can be considered one of the fundamental geometric shapes. A unique triangle and plane (i.e., the two-dimensional Euclidean space) are determined by any three non-collinear points in Euclidean geometry. In other words, every triangle has a location in a plane, and there is just one level that contains that triangle.

√2×√50 = √100 = 10.

1×√50 = √50 = 5√2

5√2 since √50 = √25×√2 = 5√2

Therefore, the correct option is option A among all the given options.

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Your question is incomplete but most probably your full question was,

The evaluation of the function gives 16.

A function is an expression that shows the relationship between the independent variable and the dependent variable.  A function is usually denoted by letters such as f, g, etc.

To evaluate the  function f(x) =80/4x-3, we need to substitute the value of the input (i.e. x = 2). Thus:

f(x) = 80/(4x-3)

f(2) = 80/(4*2 - 3)

f(2) = 80/(8 - 3)

f(2) = 80/5

f(2) = 16

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Answer:r=3sinθ/4cos^2 θ.

Step-by-step explanation:

To convert to polar coordinates, we use the relationships

xy=rcosθ=rsinθ.

Substituting these into the given equation, we find

3y3rsinθ3rsinθ=4x2=4(rcosθ)2=4r2cos2θ

Divide each side of the equation by the common factor r to get

The larger cube is made up of 384 small cubes, each with a volume of 1/4.

We have,

If we assume that 96 is the total volume of a larger cube made up of smaller cubes, and each small cube has a volume of 1/4.

We can make the following calculation:

Let x be the number of small cubes that make up the larger cube.

The volume of the larger cube = Volume of each small cube x Number of small cubes

96 = (1/4) x

Solving for x.

Multiply 4 on both sides.

96 x 4 = x

x = 384

Therefore,

The larger cube is made up of 384 small cubes, each with a volume of 1/4.

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Note that the graph of WXY when reflected to W'X'Y' is attached accordingly.

A reflection in mathematics is a mapping from a Euclidean space to itself that is an isometry with a hyperplane as a fixed point set; this set is known as the axis or plane of reflection. A figure's reflection image is its mirror image in the axis or plane of reflection.

A line of reflection is required to accomplish a geometric reflection; the resulting orientation of the two figures is opposite.

The distance between the corresponding portions of the figures is the same. Ordered pair rules reflect along the x-axis (x, -y), the y-axis (-x, y), and the line y=x (y, x).

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The angles and percentages have been calculated as shown below.

A pie chart for the information about the different make of cars is shown below.

For the total number of car makes, we have the following:

Total make of cars = 12 + 8 + 8 + 2 + 10

Total make of cars = 40.

Next, we would determine the angles and percentage as follows;

Toyota

12/40 × 360 = 108°

12/40 × 100 = 30%.

Nissan

8/40 × 360 = 72°

8/40 × 100 = 20%.

Datsun

8/40 × 360 = 72°

8/40 × 100 = 20%.

Volvo

2/40 × 360 = 18°

2/40 × 100 = 5%.

Peugeot

10/40 × 360 = 90°

10/40 × 100 = 25%.

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Answer:

Answer = 30° , 90° , 150°

Step-by-step explanation:

Hope it helps you

The appropriate measure of variability for this data set is the IQR, and its value is 2. The mean and median are measures of central tendency, not measures of variability. The range may not be the best measure of variability for this data set because it is influenced by extreme values.

The given data set is:

2, 10, 10, 12, 12, 20

To determine the appropriate measure of variability, we need to consider the spread or dispersion of the data. In this case, we can see that the range,

20 - 2 = 18.

A better measure of variability for this data set is the interquartile range (IQR), which is the range of the middle 50% of the data. To find the IQR, we first need to find the median of the data:

2, 10, 10, 12, 12, 20

The median is the middle value when the data set is arranged in order, which is 11. We can then divide the data set into two halves:

2, 10, 10 and 12, 12, 20

The lower half has a median of 10, and the upper half has a median of 12. The IQR is the difference between these medians:

IQR = 12 - 10 = 2

Therefore, the appropriate measure of variability for this data set is the IQR, and its value is 2. The mean and median are measures of central tendency, not measures of variability. The range may not be the best measure of variability for this data set because it is influenced by extreme values.

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The mean temperature of orange juice is 5 degrees greater than the mean temperature of water.

The mean is a measure of central tendency that represents the average value of a dataset. It is calculated by adding up all the values in the dataset and then dividing by the total number of values.

According to the graph, the different temperatures of water and orange juice on different time can be taken into consideration.

Sum of Temperature of Water at different time

= 55 + 62 + 69 + 71 + 79 + 75

= 441 degrees

Mean Temperature of Water

= 441/6

= 68.5 degrees

Sum of Temperature of Orange juice at different time

= 59 + 65 + 72 + 79 + 85 + 81

= 441 degrees

Mean Temperature of Orang juice

= 441/6

= 73.5 degrees

Difference = 73.5 - 68.5 = 5 degrees

Hence, the mean temperature of orange juice is 5 degrees greater than the mean temperature of water.

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The solution to the equation is x = 10 or x = -2.

An equation refers to a mathematical expression showing that two expressions are equal.

It must have variables (e.g. a, c, x, y), constants (like 1, 13, 50, etc), and mathematical operations (like +, -, *, /).

To solve for x, we shall start with the given equation:

x + 6 = √(2x + 29) + 9

Subtract 9 from both sides:

x - 3 = √(2x + 29)

Square both sides:

[tex](x - 3)^2[/tex] = 2x + 29

Expand the left side:

[tex]x^2[/tex] - 6x + 9 = 2x + 29

We then subtract 2x and 9 from both sides:

[tex]x^2[/tex] - 8x - 20 = 0

Next, actor the quadratic equation:

(x - 10)(x + 2) = 0

Therefore, the equation x = 10 or x = -2

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Rhys will have to pay £6 interest after the first year.

To calculate the interest, we can use the formula:

Interest = Principal x Rate

Where:

Principal = £200

Rate = 3% = 0.03 (in decimal form)

So, the interest Rhys will have to pay after the first year is:

Interest = £200 x 0.03 = £6

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The solution of the differential equation is y + e²ˣ = Ceˣ, if Ceˣ > 0

or -y - e²ˣ = Ceˣ, if Ceˣ < 0.

The solution of the differential equation is calculated as follows;

dy/dx = e²ˣ + y

Apply the method of separating viables;

dy/dx = e²ˣ + y

dy/(y + e²ˣ) = dx

Integrate both sides;

∫ dy/(y + e²ˣ) = ∫ dx

ln|y + e²ˣ| = x + C

To solve for y, we need to exponentiate both sides;

|y + e²ˣ| = e^(x+C) = Ceˣ

The final solution becomes;

y + e²ˣ = Ceˣ, if Ceˣ > 0

or

-y - e²ˣ = Ceˣ, if Ceˣ < 0

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Answer:

a = 3

Step-by-step explanation:

Collect like-terms:

[tex] - 16 = a - 19[/tex]

[tex]a = - 16 + 19[/tex]

[tex]a = 3[/tex]

Answer: 3

Step-by-step explanation: you take 19 from 3 giving you -16