Consider the sequence of steps to solve the equation:
X-3
—— = x +3
3

Step 1 = X-3 = 3(x + 3)
Step 2 = X-3 - 3x + 9
Step 3 = x= 3x + 12
Step 4 = -2x = 12
Step 5 = x= -6
Identify the property of equality which yields Step 1.
A)
Division Property
B)
Addition Property
C)
Subtraction Property
D)
Multiplication Property

Therefore, cos(K) = √(17)/9, sin(L) = 8/9, and cos(K) and sin(L) together are (√(17)/9, 8/9) are trigonometric ratios as fractions in simplest terms.

It is possible to calculate trigonometric ratios for various orientations. However, we memories the trigonometric ratios of a few particular angles, such as 0°, 30°, 45°, 60°, and 90°, to make computations easier. The numbers of the ratios at these angles can be found in the trigonometric ratios table.

The Pythagorean formula can be applied to the illustration to determine the length of the third side:

c²= a²+ b²

c²= 8² + √(17)²

c²= 64 + 17

c² = 81

c = 9

We can now calculate the trigonometry ratios of angles K and L:

cos(K) = adjacent/hypotenuse = √(17)/9

sin(L) = opposite/hypotenuse = 8/9

Using the same hypotenuse number of 9, we can calculate both cos(K) and sin(L) as follows:

cos(K) = adjacent/hypotenuse = √(17)/9

sin(L) = opposite/hypotenuse = 8/9

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The values of x and y after solving this system of equations will be 32/35 and -88/105 respectively.

System of equations are a set of two or more equations that contain variables. The values of the variables can be calculated using either method of elimination or substitution. The values of the variables must then satisfy all the equations.

For a set of two equations, in elimination we make the coefficient of any one variable equal to the coefficient of the same variable in the other equation. This can be done by multiplying or dividing the whole equation accordingly. Then we subtract the equations from each other and solve for one variable.

6x - 3y = 8 (multiplying this equation by -2 to make the coefficient of y equal to that of in the equation 23x + 6y = 16)

Now are equations are

-12x + 6y = -16 and 23x + 6y = 16

subtracting eq 1 from eq 2 gives,

35x = 32 (Note that y has now been eliminated)

x = 32/35

Substituting this value of x in any one of the equations will then give the value of y to be -88/105

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Answer:

45 degrees

Step-by-step explanation:

There are 8 sides and assuming the figure is regular, 360/8 = 45 degrees

Answer:

45°

Step-by-step explanation:

360/8=45°

Answer:

1 and 52 chance

Step-by-step explanation:

In order to solve this, we have to formulate two equations, the first one can represent the total acres of the farm, as mentioned in the question, the farm has 500 acres of land allotted for cultivating corn and wheat, then by adding the acres corn and the acres of wheat, x and y, we should get 500, lilke this:

x + y = 500

The Jhonson family can spend as much as $17,600, then by adding the cost of cultivating corn and the cost of cultivating the wheat we should get 17,600, like this:

corn costs + wheat costs = 17,600

The corn and wheat costs are calculated by multiplying the cost per acre cultivated by the number of acres of each product since an acre of corn costs $40 and an acre of wheat costs 28, we can rewrite the above equation to get:

40x + 28y = 17,600

Then, we have two equations

x + y = 500

40x + 28y = 17,600

By solving for y from the first equation, we get:

x + y = 500

x - x + y = 500 - x

y = 500 - x

By replacing 500 - x for y into 40x + 28y = 17,600, we get:

40x + 28y = 17,600

40x + 28(500 - x ) = 17,600

40x + 28×500 - 28x = 17,600

40x - 28x + 28×500 = 17,600

12x + 14,000 = 17,600

12x + 14,000 - 14,000 = 17,600 - 14,000

12x = 3600

x = 3600/12

x = 300

By replacing 300 for x into y = 500 - x, we get:

y = 500 - 300

y = 200

Then, x = 300 and y = 200. This means he should plant 300 acres of corn and 200 acres of wheat.

The distance between Bloemfontein and Upington is a distance of 582 kilometers. The distance between two cities may vary depending on the route taken, traffic, and other factors. The distance between these two cities is measured in a straight line, which may not be the actual road distance.

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Answer:

your answer is y = 8/3

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

slope (k) is the rise over run of the line

a way of finding the slope if you have two dots of the line is:

\(k \: = \frac{y2 - y2}{x2 - x2} \)

here the dots that belong to the line that you can most easily see are:

A(-6,0)

B(0,6)

by inserting the values into the euquation you get:

\( \frac{6 - 0}{0 - ( - 6)} = \frac{6}{6} = 1\)

good luck with your maths solving

Therefore , the solution of the given problem of equation comes out to be factor is (5b)(-5b+3).

A formula for connecting two statements using the equal sign (=) to denote equivalence is known as a mathematical equation. A mathematical equation in algebra is a statement that proves the equality of two mathematical expressions. For instance, the formula 3x + 5 = 14 places an equal sign between the variables 3x + 5 and 14. The mathematical relationship between the two sentences on either side of a letter is established. Most of the time, the symbol serves as both the one and only variable. for instance, 2x – 4 = 2.

Here,

the two numbers' primary factors are as follows:

-25\(b^{2}\) + 15b

Common prime factors can be multiplied to determine the GCF:

=> -25\(b^{2}\)  = -(5)(5) * \(b^{2}\)

=> 15b = (5)(3)b

The expression can be factored in the following fashion because the GCF is 5b:

=> -(5)(5) * \(b^{2}\) +  (5)(3)b

=> (5b)(-5b+3)

Therefore , the solution of the given problem of equation comes out to be factor is (5b)(-5b+3).

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Answer:

Following are the solution to the given equation:

Step-by-step explanation:

Please find the complete question in the attachment file.

In point a:

\(\to \mu=\frac{\sum xi}{n}\)

       \(=22.8\)

\(\to \sigma=\sqrt{\frac{\sum (xi-\mu)^2}{n-1}}\)

       \(=\sqrt{\frac{119.18}{16-1}}\\\\ =\sqrt{\frac{119.18}{15}}\\\\ = \sqrt{7.94533333}\\\\=2.8187\)

In point b:

\(\to \mu=\frac{\sum xi}{n}\)

       \(=20.6875\)  

\(\to \sigma=\sqrt{\frac{\sum (xi-\mu)^2}{n-1}}\)

       \(=\sqrt{\frac{26.3375}{16-1}}\\\\=\sqrt{\frac{26.3375}{15}}\\\\ =\sqrt{1.75583333}\\\\ =1.3251\)

In point c:

 \(\to \mu=\frac{\sum xi}{n}\)

         \(=21\)  

\(\to \sigma=\sqrt{\frac{\sum (xi-\mu)^2}{n-1}}\)

       \(=\sqrt{\frac{2.62}{16-1}}\\\\ =\sqrt{\frac{2.62}{15}} \\\\= \sqrt{0.174666667}\\\\=0.4179\)

In point d:

\(\to \mu=\frac{\sum xi}{n}\)

       \(=20.8375\)  

\(\to \sigma=\sqrt{\frac{\sum (xi-\mu)^2}{n-1}}\)

       \(=\sqrt{\frac{8.2975}{16-1}}\\\\ =\sqrt{\frac{8.2975}{15}} \\\\ =\sqrt{0.553166667} \\\\ =0.7438\)

Answer:

A, B, and E. Hope this helps!

Answer:

the third and fifth answers are correct

Step-by-step explanation:

π is a constant which equals 3.14 or 22/7

The shaded area under the normal curve is determined using the 68 - 95 - 99.7 rule to be 68.27%

The 68 95 99 rule, also known as the empirical rule in statistics, states that given normal distributions,

considering the figure and using the 68 - 95 - 99 rule, the shaded part is the reads 68% of the population and falls under the mean's 1 standard deviation.

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Answer:

1/720

Step-by-step explanation:

Multiply 60 times 60 because there are 60 seconds in a minute and 60 minutes in an hour.

now you have 3600 and if you put 5 over it it equals 1/720.

Answer:

To solve this, you would multiply -3 by x, which gives you -3x, and multiply -3 by -8. This would give you -3x+24.

Then, you would add 0.5x.

The answer would be -2.5x +24.

Whichever expressions below are equivalent to this answer are correct.

Hope this helps!

To solve this problem, we need to use vector addition to find the resultant velocity of Julia.

Let's assume that the east direction is the positive x-axis and the south direction is the negative y-axis.

The velocity of Julia in still water is 8 km/hr in the positive x-axis direction.

The velocity of the river is 3 km/hr in the negative y-axis direction.

To find the magnitude and direction of Julia's velocity, we need to find the resultant velocity vector, which is the vector sum of her velocity in still water and the velocity of the river.

Using the Pythagorean theorem, the magnitude of the resultant velocity can be calculated as:

|V| = √(Vx² + Vy²)

where Vx is the x-component of the resultant velocity and is equal to Julia's velocity in still water, and Vy is the y-component of the resultant velocity and is equal to the velocity of the river.

Vx = 8 km/hr

Vy = -3 km/hr

|V| = √(8² + (-3)²) = √(64 + 9) = √73 km/hr

The direction of the resultant velocity can be calculated as:

θ = tan⁻¹(Vy / Vx)

θ = tan⁻¹(-3 / 8) = -20.56°

The negative sign indicates that the resultant velocity vector makes an angle of 20.56° below the positive x-axis (east direction).

Therefore, the magnitude of Julia's velocity is approximately 8.54 km/hr, and the direction of her velocity is 20.56° below the positive x-axis (east direction).

The equation of the line that passes through points (5, 8) and
(-2.2, -6.4) is y = 2x - 2.

Option D is the correct answer.

We have,

We can use the point-slope form of the equation of a line, which is:

y - y1 = m(x - x1)

where (x1, y1) is a point on the line and m is the slope of the line.

Slope.

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

= (-6.4 - 8) / (-2.2 - 5)

= (-14.4) / (-7.2)

= 2

Next, we can use one of the two given points and the slope to write the equation of the line in the point-slope form:

y - 8 = 2(x - 5)

Expanding the right side and simplifying.

y - 8 = 2x - 10

y = 2x - 2

Therefore,

The equation of the line that passes through points (5, 8) and
(-2.2, -6.4) is y = 2x - 2.

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The coordinate of the point F which is midway from C to D as required in the task content is; +9.

The coordinate of the point C and D as given in the task content is; -6 and +24 respectively.

Therefore, it can be inferred that the midpoint F between points C and D is;

F = (-6+24)/2

F = 18/2

F = 9.

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Answer:

$5.30 :DDD

Step-by-step explanation:

SO WHAT YOU DO IS 26.50 X 0.20 AND YOU WILL GET 5.30 SO BAM

The value of y is 4√3

Similar triangles have the same corresponding angle measures and proportional side lengths. The corresponding angles of similar triangles are congruent or equal.

Also , the ratio of corresponding sides of similar triangles are equal.

There are two triangles that are similar

Therefore;

y /16 = 4/y

y² = 48

y = √48

y = √16 × √ 3

y = 4√3

Therefore, the value of y is 4√3

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Answer:

Slope - intercept form    \(y = \frac{14}{3} x + 34\)

Step-by-step explanation:

Explanation:-

Given points are ( -9 ,-8 ) and (-6,6)

slope of given two points

    \(m = \frac{y_{2} -y_{1} }{x_{2}-x_{1} } = \frac{6-(-8)}{-6-(-9)} = \frac{14}{3}\)

The equation of the straight line passing through the points and having slope

          \(y - y_{1} = m ( x - x_{1} )\)

        \(y - (-8) = \frac{14}{3} ( x - (-9) )\)

          3 y + 2 4 = 14 x + 126

           3 y = 14 x + 126 - 24

          3 y = 14 x + 102

            \(y = \frac{14}{3} + \frac{102}{3}\)

           \(y = \frac{14}{3} x + 34\)

Slope - intercept form  y= mx +C

Slope - intercept form    \(y = \frac{14}{3} x + 34\)

According to the given data we have the following:

measure of three angels of a triangle are 43, 70, x

x?

The sum of the measures of the three angles of the triangle is 180

Therefore, to calculate the value of x we would have to make the following calculation:

43 + 70 + x = 180

113+ x=180

x=180-113

x=67

Therefore, the value of the angle of x would be 67

The coordinates in the solution to the systems of inequalities graphically is (6, 2)

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

x + y > 3

x - 3y < 2

Next, we plot the graph of the system of the inequalities

See attachment for the graph

From the graph, we have solution to the system to be the shaded region

The coordinates in the solution to the systems of inequalities graphically is (6, 2)

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The simplified expression in mathematical form is -45.36.

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

The expression given is -

(-15 + (-1.6 + 9.34) / 6) × (3² - 5.7)

Simplifying the terms inside the parentheses first, we get -

(-15 + 7.74 / 6) × (9 - 5.7)

Next, we simplify 7.74 / 6 by dividing the numerator by the denominator -

(-15 + 1.29) × (9 - 5.7)

We add -15 and 1.29 inside the first set of parentheses -

(-13.71) × (9 - 5.7)

We subtract 5.7 from 9 inside the second set of parentheses -

(-13.71) × 3.3

Multiplying these two terms, we get -

-45.363 ≈ -45.36

Therefore, the value is obtained as -45.36.

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Answer:

the product of the decimal equivalents of all discount in the series

The pedagogical tool to support the development of students' understanding that fractions are numbers and that they expand the number system beyond whole numbers is number line.

What is meant by pedagogical tool?

In math, pedagogical tool refers designed to convey important lessons and allow people to improve their understanding of a problem or undertaking.

Here we need to find the research recommends that teachers use the following pedagogical tool to support the development of students' understanding that fractions are numbers and that they expand the number system beyond whole numbers.

While we looking into the given question, here we need to find the tool that is used to find the development of students' understanding that fractions are numbers and that they expand the number system beyond whole numbers that is none other than number line because it uses the visual representation of the number that gives better understanding of number.

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Answer:

(First answer option)

Step-by-step explanation:

General form of an exponential function

\(y=ab^x+c\)

where:

Given exponential function:

\(y=4(10)^x-3\)

The x-intercept is the point at which the curve crosses the x-axis, so when y = 0.  To find the x-intercept, substitute y = 0 into the given equation and solve for x:

\(\begin{aligned}& \textsf{Set the function to zero}:& 4(10)^x-3 &=0\\\\& \textsf{Add 3 to both sides}:& 4(10)^x &=3\\\\& \textsf{Divide both sides by 4}:& 10^x &=\dfrac{3}{4}\\\\& \textsf{Take natural logs of both sides}:& \ln 10^x &=\ln\left(\dfrac{3}{4}\right)\\\\& \textsf{Apply the power log law}:&x \ln 10 &=\ln\left(\dfrac{3}{4}\right)\\\\& \textsf{Divide both sides by }\ln 10:&x&=\dfrac{\ln\left(\dfrac{3}{4}\right)}{\ln 10} \\\\& \textsf{Simplify}:&x&=-0.1\:\:\sf(1\:d.p.)\end{aligned}\)

Therefore, the x-intercept is (-0.1, 0) to the nearest tenth.

An asymptote is a line that the curve gets infinitely close to, but never touches.

The parent function of an exponential function is:

\(f(x)=b^x\)

As x approaches -∞ the function f(x) approaches zero, and as x approaches ∞ the function f(x) approaches ∞.

Therefore, there is a horizontal asymptote at y = 0.

This means that a function in the form  \(f(x) = ab^x+c\) always has a horizontal asymptote at y = c.  

Therefore, the horizontal asymptote of the given function is y = -3.

A graph representing exponential growth will have a curve that shows an increase in y as x increases.

A graph representing exponential decay will have a curve that shows a decrease in y as x increases.

The part of an exponential function that shows the growth/decay factor is the base (b).  

The base of the given function is 10 and so this confirms that the function is increasing since 10 > 1.

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The vague pronoun "it" can be replaced by -

Option D: the spaceship

What is a pronoun?

An alternative to a noun is a pronoun. In order to avoid using the noun more than once in a paragraph or piece of writing, it replaces. Singular and plural pronouns can be used. The verb in the sentence should be utilised in keeping with the specific pronoun form that is being employed.

The sentence is "Did you see it in the sky last night?".

"The spaceship" is the most appropriate option to replace the ambiguous pronoun reference in this statement.

Did you see it in the sky last night? is a vague question because "it" could refer to a variety of sky-observed objects.

The language becomes clearer and more precise by swapping "it" for "the spaceship," referring specifically to a particular item observed in the sky.

Therefore, the spaceship is the correct choice.

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