Complete the two-column proof. Given: 3x+7=X-5 Prove: -6 = X​

Answer:

For the given graph the constant of proportionality is 6.

Step-by-step explanation:

Answer:

  (a)  p = 6

Step-by-step explanation:

You want the constant of proportionality if the point (1/2, 3) lies on the graph of the relationship.

The equation for a proportional relationship is ...

  y = px

The value of p can be found as ...

  p = y/x . . . . . divide by x

For the given relationship, the point (x, y) = (1/2, 3) tells ...

  p = 3/(1/2) = 3·(2/1) = 6

The constant of proportionality is p = 6, matching choice A.

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The meaning of the z-score of 2.8 for the past year's temperature is that the temperature is 2.8 standard deviations above the historical mean. Option B is correct

B) The past year's average temperature was 2.8 standard deviations above the historical mean.

The z-score also known as the standard score indicates the relationship of a value, within a set of value, with the mean of the set of values

Mathematically, the z-score can be presented as follows;

[tex]Z = \dfrac{x- \mu}{\sigma}[/tex]

Where;

x = The point score

μ = The mean score

σ = The standard deviation

The z-score indicates the number of standard deviations a score is from the mean

The z-score of the past year's temperature = 2.8

Therefore, the z-score of 2.8 for the past year's temperature indicates that the past year's temperature was 2.8 times the standard deviation away from (above) the mean of the local weather temperature, (the historical mean temperature) on record.

The correct option is option B)

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Answer:

y=7.5x-2

Step-by-step explanation:

y=mx+c

m is the gradient of the line so it has to be positive for a positive slope

c is the y intercept so it has to be negative for a negative y intercept

If the two functions be g(x) = x + 2 and h(x) = 3x - 3 then

(h - g)(x) = 2x - 5

(h + g)(x) = 4x - 1

(h . g)(1)  = 3x² + 3x - 6

A phrase is considered a mathematical expression if it contains at least two numbers or variables and one or more mathematical operations. Mathematicians can multiply, divide, add, or subtract. An expression is structured as follows: (Math Operator, Number/Variable, Math Operator) is an expression.

Mathematical expressions are built using the addition, subtraction, multiplication, and division operations.

Let the two functions be g(x) = x + 2 and h(x) = 3x - 3

(h - g)(x) = h(x) - g(x)

substitute the value expressions in the above equation, we get

= (3x - 3) - (x + 2)

= 2x - 5

(h + g)(x) = h(x) + g(x)

= (3x - 3) + (x + 2)

= 4x - 1

(h . g)(1) = h(1) . g(1)

= (3x - 3) . (x + 2)

= 3x² + 3x - 6

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The radical expression √16x² and ∛27x³ have the absolute value in the simplified form.

Absolute value of a number is the distance value from zero without considering sign of a number. It is also represented as |x|, where x is any number.

The simplified value of √16x² = 4x                {option 2}

And the simplified value of ∛27x³ = 3x              {option 3}

And the simplified value of [tex]\sqrt[5]{(-32)(x)^5}[/tex] = 2ix    {option 1}

Above expression does not have the absolute value. Since i have the value √-1.

And the simplified value of ∛27x = 3∛x               {option 4}

Therefore, only the option 2 and 3 get us the absolute value.

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Answer: 402

Step-by-step explanation:

The required cost of the sweater after sales tax is $31.96.

Given that,
Suzanne bought a sweater priced at $34 and the sales tax is 6%.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
While calculating the percentage it must be multiplied the number with the given percentage value.

Sale tax on sweater = 6% of 34

                              = 0.06 × 34
                              = $2.04

Thus, the required cost of the sweater after sales tax is $31.96.

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Answer:

Step-by-step explanation:

Newton's method is an iterative method for finding the roots of a function, which means that it can be used to find the values of x that make a function equal to zero. It can also be used to find the maximum or minimum values of a function, but to do so you will need to find the derivative of the function and use that to determine where the maximum or minimum values occur.

The derivative of the function f(x) = 7x cos(x) is f'(x) = 7 cos(x) - 7x sin(x), and you can use this to find the maximum value of the function. To do this, you would need to find the values of x that make the derivative equal to zero, since the maximum or minimum values of a function occur at the points where the derivative is equal to zero.

To find the values of x that make the derivative equal to zero, you can use Newton's method, which involves starting with an initial guess for the value of x, and then using the derivative to find a better approximation for the value of x. This process is repeated until the desired level of accuracy is reached.

In your case, you could start by making an initial guess for the value of x that makes the derivative equal to zero. For example, you could start with x = 0 and then use the derivative to find a better approximation. This process would involve calculating the derivative at the initial guess, and then using that value to find a better approximation for the value of x. This process would be repeated until the desired level of accuracy is reached.

Once you have found the values of x that make the derivative equal to zero, you can plug those values back into the original function to find the maximum value of the function. This will give you the absolute maximum value of the function f(x) = 7x cos(x), 0 ≤ x ≤ , correct to six decimal places.

Answer:

Hope this helps lol !

Step-by-step explanation:

This is how to calculate net price. Start with the list price and add any taxes and other government-mandated charges. Then subtract any discounts, negotiated prices. The result you get will be the net price.

Answer:17.95x=y

Step-by-step explanation just multiply 17.95 for each cookbooks he gets and that your y and your x is the amount of book he gets

Answer: x<_9

Step-by-step explanation:

subtract 15 from both sides then subtract 15 from 60 and get 45. Divide both sides by 5 since 5 is positive the inequality direction remains the same. divide 45 by 5 to get 9.

-7 ≥-10 follows the given condition because -7 is greater that -10. So the given point (10,-7) is a solution of y ≥-0.5x-5.

In the given question, we have to explain (10,-7) is a solution of y ≥-0.5x-5 or not.

The given point is (10,-7).

The given inequality is y ≥-0.5x-5.

To check whether the given point is solution of the given inequality or not we put the value of x and y from the given point.

As we know that in the given point one value is representing the value of x and one of y.

So, after putting the value we simplify the inequality. If it follows the given condition then the given point is the solution of the inequality else it is not.

Now putting the value of x and y in the inequality.

-7 ≥-0.5(10)-5

Simplifying

-7 ≥-5-5

-7 ≥-10

As we can see that it follows the given condition because -7 is greater that -10. So the given point (10,-7) is a solution of y ≥-0.5x-5.

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Answer:

x = 3

This equation has only one solution.  The only number that will make both sides of the equation equal is 3.

Step-by-step explanation:

2(4x -3) -8 = 4 + 2x  Distribute the 2

8x -6 -8 = 4 + 2x  Combine like terms

8x -14 = 4 + 2x  Subtract 2x from both sides S(Subtraction property of equality)

6x - 14 = 4  Add 14 to both sides (subtraction property of equality)

6x = 18  Divide both sides by 6 (division property of equality)

x = 3

Check:

2[4(3) - 3] - 8 = 4 + 2(3)

2(12 - 3) - 8 = 4 + 6

2(9) - 8 = 10

18 - 8 = 10

10 = 10

Answer:

The square root of 75 can be written as √75. To simplify this expression, we can use the property that the square root of a product is equal to the product of the square roots of the factors. In this case, we can factor 75 as the product of 25 and 3:

√75 = √(25 x 3)

We can then apply the property of the square root of a product to simplify the expression:

√75 = √(25 x 3) = √25 x √3

We can further simplify the expression by applying the property that the square root of a perfect square is equal to the number itself. Since 25 is a perfect square, we can simplify √25 to 5:

√75 = √(25 x 3) = √25 x √3 = 5 x √3

Therefore, the simplified form of √75 is 5 x √3. This means that the square root of 75 is equal to 5 times the square root of 3.

Step-by-step explanation:

Answer:

  C)  Always

Step-by-step explanation:

You want to know the values of x for which y is negative, given that y = -|x -2| -4.

The absolute value function always returns a non-negative value. Its minimum value is 0, which will occur for x=2 in this function.

When the absolute value function is negated, as here, the largest the result can be is zero—for any value of x. When 4 is subtracted from that, the largest the value of y can be is -4, again, for any value of x.

  y is always less than 0.

The attached graph should help you see the vertex (maximum) of the function is (2, -4), and it opens downward. It is negative for all values of x.

The irregular polygon has an area of 300 square inches.

Herein we find an irregular pentagon shown in the figure, whose area has to be found. This can be done by considering it a composite figure, whose area is the sum of areas of triangles and rectangles.

In that sense, the area of the irregular polygon is the sum of the areas of two triangles and a rectangles, whose formulas are shown below:

Triangle

A = 0.5 · b · h

Where:

Rectangle

A = b · h

Now we proceed to determine the area of the irregular polygon:

A = 0.5 · (20 in) · (6 in) + (12 in) · (15 in) + 0.5 · (8 in) · (15 in)

A = 300 in²

The area of the irregular polygon is equal to 300 square inches.

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It depends on the type of function, however there are patterns that can be found

A general rule of thumb to consider is as follows

f(x) + d shifts a function up d units

f(x) - d shifts a function down  d units

Ex. [tex]f(x) = x^{2} +3[/tex] shifts up 3 units, and [tex]f(x) = 2x - 4[/tex] shifts down four units

f(x+c) shifts a function left c units

f(x-c) shifts a function right c units

EX. [tex]f(x) = (x+2)^{2}[/tex] shifts left 2 units, and [tex]f(x) =(x-7)^{2}[/tex] shifts right 7 units

-f(x) is a reflection over the x-axis

EX. [tex]f(x) = x^{2}[/tex] opens up, while [tex]f(x) = -x^{2}[/tex] opens down

These guidelines can also be combined

EX. [tex]f(x) = -(x-4)^{2} + 3[/tex] opens down, is shifted right 4 units, and is shifted up 3 units from the parent function

Answer:

In rectangular form, a complex number is expressed as $x + yi$, where $x$ and $y$ are the real and imaginary parts, respectively. The conversion from polar form to rectangular form is done using the following equations:

$x = r \cos \theta$

$y = r \sin \theta$

where $r$ is the magnitude (or modulus) of the complex number and $\theta$ is the argument (or phase) of the complex number.

In the given problem, we are given the complex number $z = 3(cos(7pi/6)+ i sin (7pi/6))$. We can write this in polar form as $z = 3 \cdot cis(7pi/6)$, where $cis(x) = cos(x) + i \cdot sin(x)$. Thus, we have $r = 3$ and $\theta = 7pi/6$. Using the equations above, we can convert this to rectangular form to obtain:

$x = r \cos \theta = 3 \cos (7pi/6) = -\frac{3}{2}$

$y = r \sin \theta = 3 \sin (7pi/6) = \frac{\sqrt{3}}{2}$

Therefore, the rectangular form of the complex number is $-\frac{3}{2} + \frac{\sqrt{3}}{2} i$.

In the given right angled triangle ABC, the value of x is equal to 10.7 (round to the nearest tenths place).

As given in the question,

In the triangle ABC,

Triangle ABC is right angled triangle with ∠C = 90°

Measure of angle A = 68degrees

AC = 4 units

AB = x units

Using trigonometric ratio,

cos 68° = AC / AB

⇒cos 68° = 4 / x

⇒ 0.3746 = 4 / x

⇒ x = 4 / 0.3746

⇒ x = 10.68

⇒ x = 10.7 ( round to the nearest tenths place)

Therefore, in triangle ABC , the value of x is equal to 10.7(round to the nearest tenths place).

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(1/2)x - 4y = -1 is the necessary equation, and A = 1/2 is the value of the missing coefficient of the equation Ax - 4y = -1

The definition of an equation is a mathematical statement with at least two terms that contain variables or equal numbers.

According to the Given information

An equation has been provided to us as

Ax - 4y = -1 ...... (i)

The answer is given at point (6,1),

Replace the values of x = 6 and y = 1 in the equation above,

A(6) - 4(1) = -1

A×6 -4 = -1 (+4)

A×6 = 3 / 6

In the equation above, decrease the fraction.

A = 1/2

Replace A = 1/2 with its value in the equation (i),

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

As a result, (1/2)x - 4y = -1 is the necessary equation, and A = 1/2 is the value of the missing coefficient of the equation Ax - 4y = -1

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Answer: Yes

Step-by-step explanation:

4*10=40

3*10=30

Which means that they are of equal proportion.

The number of cookies Zahra made with 4/5 kilograms of butter is 1333.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given that, Zahra has 4/5 kilograms of butter to bake cookies.

Each batch of cookies requires 6/10 grams of butter

4/5 kilograms = 800 grams and 6/10 grams =0.6 grams

Number of cookies = Number of kilograms of butter ÷ Butter requires in each cookie

= 800 ÷ 0.6

= 800/0.6

= 1333

Therefore, the number of cookies are 1333.

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The statement which correctly identifies the intermolecular force which is represented by D and compares its strength relative to the intermolecular force represented by C is that: C. D represents ion-dipole forces, which are stronger than the force represented by C.

In Chemistry, there are different types of intermolecular force (chemical bonds) and these include the following:

In Chemistry, an ion-dipole force can be defined as an attractive force which arises from the electrostatic attraction between an ion and a neutral molecule that contains a dipole.

Additionally, an ion-dipole force is most commonly found in solutions because they are composed of polar molecules such as is represented by bond (letter) D.

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The value of x that makes the inequality true is: D. √0.02.

If we are given an inequality statement, the value of the variable of the inequality must be such that makes the statement true, which is the possible set of values of the variable.

Given that 1/8 < x < 18%, note the following:

1/8 = 0.125

18% = 0.18

This means that, 0.125 must be less than the value of x, while the value of x must be less than the value of 0.18, for the inequality to be true.

Considering the options given, 1/5 = 0.2. 0.2 is greater than 0.18 (18%).

1.6 is also greater than 0.18 (18%) and 1/8 (0.125).

1/8(0.125) is greater than 0.09.

Thus, √0.02 is approximately 0.14.

1/8 (0.125) < 0.14 < 18% (0.18). Therefore the value of x would be: D. √0.02.

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Exactly 5/12 of a full rotation is 150, where full rotation is 360.

A "full rotation," "revolution," "whole turn," or "full circle" describes this. It entails spinning around till you are once again pointing in the same direction. a rotational movement. In rotation, there is a fixed central point around which everything else revolves in a circle. 360° is a "Full Rotation." Each point in a figure is transformed into a rotation by rotating it a specific amount of degrees around another point.

Given,

Number = 5/12

Full rotation = 360

5/12 of full rotation

5/12 × 360

5 × 30

150

Exactly 5/12 of a full rotation is 150, where full rotation is 360.

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Solution of equation 3x² = -2x+ 4 using the quadratic formula x = -1± √13/3.

The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation has the general form ax² + bx + c = 0. where a, b, and c are numerical coefficients and x is an unknown variable. Due to the fact that the Latin word quadratum, which means "square," and the fact that the area of a square with side length x is equal to x², a polynomial equation with exponent two is referred to as a quadratic ("square-like") equation.

Given,

Equation

3x² = -2x+ 4

3x² + 2x - 4 = 0

Using quadratic formula,

x = -2 ± √2²- 4 × 3(-4)/ 2× 3

Simplifying:

x = -2 ± 2√13/6

Equations:

x = -2 + 2√13/6

x = -2 - 2√13/6

x = -1 + √13/3

x = -1 - √13/3

x = -1± √13/3

Solution of equation 3x² = -2x+ 4 using the quadratic formula x = -1± √13/3.

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The number of pizza expected to be eaten is equal to the number of persons that attends the party and this is equal to 0.8gp/s

From the problem it can be deduced that

number of people invited to the party = g

number of people attending

= 80% of people invited to the party

= 80% of g

and 80% = 80 / 100 = 0.8

therefore,

= 0.8g

You estimate that your guests will each eat p pieces of pizza

= 0.8g * p

= 0.8gp

and each pizza has s slices

the number of slices = s

the number of pizza to be taken is  0.8gp/s

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Answer:

Step-by-step explanation:

sorry, i'm not a college student, so i don't know how to answer this.

The 95% confidence interval for true average CO2 level in the population of all homes from which the sample was selected is given as follows:

(612.05, 696.27).

The interpretation is that we are 95% sure that the population mean is between these two values.

The confidence interval is obtained using the t-distribution, as we have the standard deviation for the sample instead of the standard deviation for the population.

The bounds of the interval are given by the equation presented as follows:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which the variables of the equation are presented as follows:

The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 60 - 1 = 59 df, is t = 2.0010.

The remaining parameters are given as follows:

[tex]\overline{x} = 654.16, s = 163.02, n = 60[/tex]

Hence the lower bound of the interval is of:

654.16 - 2.001 x 163.02/sqrt(60) = 612.05.

The upper bound of the interval is of:

654.16 + 2.001 x 163.02/sqrt(60) = 696.27.

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