Translate the sentence into an inequality.
Twice the difference of a number and 4 is at most - 18.
Use the variable x for the unknown number.

The quadratic functions are given as below:-

x = 3y² - 6y + 5

y = 2x² + 2

y = 2x² -8x + 6

y = 5x² + 45x -8

The polynomial having a degree of two or the maximum power of the variable in a polynomial will be 2 is defined as the quadratic equation and it will cut two intercepts on the graph at the x-axis.

As we know that the function which will have the highest power of the variable equal to 2 will be called a quadratic polynomial.

So from the given expressions following equations has a degree of 2.

x = 3y² - 6y + 5

y = 2x² + 2

y = 2x² -8x + 6

y = 5x² + 45x -8

Therefore the above equations are quadratic functions.

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Answer:

2.5x + 1

Step-by-step explanation:

P = Perimeter

W = Width

L = Length

P = 2w + 2l

5.5x+6 = 2(0.25x+2) + 2L

5.5x+6 = 0.5x+4 + 2L

5x+2 = 2L

2.5x+1 = L

Answer:

84 ft

Step-by-step explanation:

16 + 16 + 26 +26 = 84

The correct answer is C. The dependent variable is not typically the explanatory variable in a regression model.

In regression analysis, we aim to understand the relationship between a dependent variable and one or more independent variables. The dependent variable is the variable we are trying to explain or predict, while the independent variables are the ones we use to explain or predict the dependent variable.

In a regression model, the intercept coefficient is typically interpreted. It represents the predicted value of the dependent variable when all the independent variables are equal to zero. So, statement A is not true.

The estimates of the slope coefficients are indeed found from sample data. These coefficients represent the change in the dependent variable associated with a one-unit change in the corresponding independent variable. Therefore, statement B is true.

Finally, the regression line is constructed in a way that it minimizes the sum of squared errors, also known as the residuals. The residuals are the differences between the actual values of the dependent variable and the predicted values from the regression model. So, statement D is true.

In summary, statement C is the only statement that is not true about a regression model. The dependent variable is not typically the explanatory variable in regression analysis.

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The only difference for these devices in 3701 is that the jk-FF (or jk-latch) has an additional control input, which is the clock (CK). The CK input is used to enable and disable the device so that the inputs, j and k, do not always affect the output (Q) of the device.

The SR-FF (or SR-latch) has two inputs, S and R, which directly affect the output, Q. When S=1, the output is set to 1, and when R=1, the output is reset to 0.

On the other hand, the jk-FF (or jk-latch) has three inputs, J, K and CK. When CK is 0, the device is disabled and the outputs remain the same. When CK is 1, the J and K inputs can be used to either set (J=1, K=0) or reset (J=0, K=1) the output, Q.

In summary, the j and k in the jk-FF (or jk-latch) are similar to the s and r in the SR-FF (or SR-latch).

So, the only difference is the addition of a clock (CK) input in the jk-FF (or jk-latch). This clock (CK) input enables and disables the device, which allows the inputs, j and k, to affect the output (Q) of the device.

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The expression is equivalent to 2(a  -3) + 4a will be 6a - 6. Then the correct option is A.

The equivalent is the expression that is in different forms but is equal to the same value.

The expression is given below.

⇒ 2(a  -3) + 4a

Simplify the expression, then we have

⇒ 2(a  -3) + 4a

⇒ 2a - 6 + 4a

⇒ 6a - 6

The expression is equivalent to 2(a  -3) + 4a will be 6a - 6. Then the correct option is A.

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The missing options are given below.

A. 6a - 6

B. 6a - 1

C. a - 6

D. None of the above

The two remaining angles are 58°, and the length of the third side of the triangle is 6.5 inch.

In order to determine the other two angles of each triangle as well as the length of the third side, we need to use the Cosine Rule. According to the Cosine Rule, for any triangle with sides of length a, b, and c, and angles of A, B, and C, the following equation holds:

\(c^2 = a^2 + b^2 - 2ab cos(C)\)

For the first triangle, we are given that the side of length 5 is adjacent to an angle of 61°. Therefore, a = 5, C = 61°. Using the information provided, we can also determine that b = 4.8. Substituting these values into the Cosine Rule equation, we get:

\(c^2 = (5)^2 + (4.8)^2 - 2(5)(4.8) cos(61°)\)

We can solve this equation to get c = 6.5. Therefore, the length of the third side in the first triangle is 6.5. Additionally, we can use the Triangle Angle Sum theorem to determine the other two angles. According to this theorem, the sum of the three angles of a triangle is 180°. Therefore, for the first triangle, the two remaining angles are 180 - 61 - (180 - 61) = 58°.

For the second triangle, we use the same process, but with the given side lengths reversed. That is, we set a = 4.8, b = 5, and C = 61°. Again, substituting these values into the Cosine Rule equation, we get:

\(c^2 = (4.8)^2 + (5)^2 - 2(4.8)(5) cos(61°)\)

We can solve this equation to get c = 6.5. Therefore, the length of the third side in the second triangle is also 6.5. We can use the Triangle Angle Sum theorem again to determine the other two angles. Again, for the second triangle, the two remaining angles are 180 - 61 - (180 - 61) = 58°.

In conclusion, for each triangle, the two remaining angles are 58°, and the length of the third side is 6.5 inch.

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Answer: (a). M=7x180+39+700. (B) $731

Step-by-step explanation:

Equation to represent the given situation is 7(19.70 + 1.97 + m X 0.05) = 180.39; additional minutes, on average, you use each month is 82

A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.

Given that;

Total cost for 7 month =$180.39

Let m be the average number of minutes  that exceeds 700 minutes every month

Equation formed;

7(19.70 + 1.97 + m X 0.05) = 180.39,

or,  7(19.70 + 1.97 + m X 0.05) = 180.39,

or, 21.67 + 0.05m = 180.39/ 7,

or, 0.05m = 25.77 – 21.67,

0.05m = 4.1

m= 82

Therefore,  equation for (a) : 7(19.70 + 1.97 + m X 0.05) = 180.39 and 82 will be the answer of (b)

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The right response is (b), as it increases the minimum sample size required to ensure a given margin of error.

When a tiny sample of data from a relatively large population is estimated, this is what is meant by the term "margin of error" .  The standard deviation, sample size, and desired confidence level are often the factors that control the margin of error.

calculation

Let's take a look at the values in the supplied statement to discover the missing term.

the population's standard deviation is where

m stands for "Margin of Error," and Z stands for "Empirical Value of Z-Score" at a specific confidence level.

As a result, the recommended minimum sample size for a particular degree of confidence is

⇒ (Z×σ)²/m²

The minimal sample size is directly correlated with the population's standard deviation, as shown by the calculation above.

Therefore, when the population "standard deviation" increased, the minimal sample size needed would also "rise."

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Answer:

1/6

Step-by-step explanation:

if you are talking about a dice roll, then the probability of getting anything is 1/6

Answer:

Rational

Rational

Rational

Rational

Rational

Irrational

Irrational

Rational

Step-by-step explanation:

First we need to establish what a rational, and a irrational numbers are.  A rational number are basically integers that can be written as fractions which means any of the options that are integers or fractions are in fact rational numbers. A irrational number are basically numbers that cannot be written as a fraction which means things like repeating decimals or just numbers that cannot be expressed as a fraction of two other whole numbers.

First option:

\(-4+23\)

\(-4 + 23=19\)

19 is a rational number because it can be expressed as two integers which are 1 and 19

Second option:

\(\frac{2}{3} +\frac{1}{2}\)

Both are fractions which means the sum will be a fraction which also means it is a rational number since we previously established that every fraction is a rational number.

Third option:

\(-\frac{1}{2} + 12\)

You can write 12 as a fraction which is 12/1 and then solve which the sum will also be a fraction which means it will also be a rational number.

Fourth Option:

\(\frac{2}{5} +15\)

15 can be written as 15/1 which means it is a rational number which also means the sum of the two fractions will also be a rational number.

Fifth option:

Adding fractions, fractions are rational numbers which means the sum will also be a rational number

Sixth option:

Pie is a infinite decimal number which means it is irrational because it cannot be written as a fraction.

Seventh option:

\(\sqrt[]{3} +\frac{5}{8}\)

/3 cannot be written as a fraction which means the entire equation is irrational because a rational plus a irrational number will always equal a irrational number.

Eighth option:

\(3.25+4.17\)

Since how these decimals are not repeating they are both rational numbers.

Hope this helps.

The mean absolute deviation (MAD), a measure of variability, illustrates the typical distance between an observation's mean and its variation. MAD uses the data's original units to facilitate interpretation.

Greater values indicate a wider range of data points than the average. The term "variability" refers to how much a data collection varies from one constituent to another. Variability measures reflect the level and magnitude of change within the data collection.

The interquartile range and the mean average deviation are the two methods for calculating variability that are required by the requirements for sixth-grade pupils.

The majority of the data values are fairly near to the mean, as shown by a tiny mean absolute deviation. We can infer from a large mean absolute deviation that numerous data values are dispersed widely from the mean.

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Answer:

y = 49.2x+400

Step-by-step explanation:

He deposits 3% of his monthly pay = 0.03*1640 = $49.2 every month = 49.2x

He put $400 when he opened the account so that needs to be added in = 49.2x+400

The area of the region bounded by

\[y=\frac{7}{(4+x)^2}+\frac{5}{7+x^2},\ y=0,\ x\ge5\]is 0.0188 (rounded to four decimal places).

Here's how to get the solution:

We are asked to find the area of the region bounded by the two curves.

The curves intersect at (5, 0) because x can not be less than 5.

They meet again at the point x ≈ 1.281.

Now, we must find the integrals for both functions in the given range.

We'll call the first function "f (x)" and the second "g (x)."

f(x) = 7 / (4 + x)² + 5 / (7 + x²)

g(x) = 0

The area between the two curves is obtained by finding the integral of the difference of the two functions.

The area is given by:

\[\int_{5}^{1.281} [f(x) - g(x)] dx\]

Since there is no point of intersection beyond x ≈ 1.281, we will use this value for the limit of integration.

Integrating:

\[\begin{aligned} &\int_{5}^{1.281} [f(x) - g(x)] dx \\ =& \int_{5}^{1.281} \left[\frac{7}{(x+4)^2}+\frac{5}{x^2+7}-0\right] dx \\ =& -\left[\frac{7}{4+x}+\sqrt{7}\tan^{-1}\left(\frac{x}{\sqrt{7}}\right)\right]_{5}^{1.281} \\ =& 0.0188. \end{aligned}\]

Thus, the area of the region is 0.0188.

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Answer:

\( \frac{5x + 11}{3(x + 8)} \)

Step-by-step explanation:

\( \frac{5x + 11}{3(x + 8)} \)

Five times the sum of a number and eleven, divided by three times the sum of the number and eight

Five times the sum= 5(_+_)

a number and eleven= x+11

divided= ÷ or /

3 times the sum of= 3(_+_)

the number and eight.

Together it will be

\(the \: \: one \: written \: in \: the \: answering \: section\)

Hope this helps ;) ❤❤❤

It will take 15 months for the number of basic subscriptions to match the number of deluxe subscriptions.

Let's denote the number of months passed by "m".

In m months, the number of basic subscriptions will be 288 - 5m (since 5 basic subscriptions are decreasing each month), and the number of deluxe subscriptions will be 93 + 8m (since 8 deluxe subscriptions are increasing each month).

We want to find out when the number of basic subscriptions will match the number of deluxe subscriptions, so we can set the two expressions equal to each other:

288 - 5m = 93 + 8m

We can then solve for m:

288 - 93 = 8m + 5m

195 = 13m

m = 15

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Answer:

\(2^{\frac{3}{2} }\)

Step-by-step explanation:

note that 8 = 2³

and using the rule of exponents/ radicals

\(a^{\frac{m}{n} }\) = \(\sqrt[n]{a^{m} }\)

Thus

\(\sqrt{8}\) = \(\sqrt{2^{3} }\) = \(2^{\frac{3}{2} }\)

Expressing the square root of 8 as a power of 2, we would have to follow two steps.

√8 = 2.8284271247

Assumption 1

\(2^{1}\) = 2

Asumption 2

\(2^{1.2}\)  =  2.29739671

Assumption 3

\(2^{1.5}\)  = 2.8284271247

Therefore, the square of 8 as a power of 2 is \(2^{1.5}\)

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Answer:

D

Step-by-step explanation:

Answer:

1. 6

2. 8

3. 10

4. 12

5. 14

Step-by-step explanation:

just solve

Answer:

18

Step-by-step explanation:

1/2 x 12 x 3

1 x 12 x 3/2 -divide all by 2

12 x 3/2 - simplify

36/2

answer: 18

Answer:

522

Step-by-step explanation:

Hope this helped!

The triangle formed by a complex number and its complex conjugate with the origin is an isosceles right triangle.

When a complex number and its complex conjugate are plotted in the complex plane, the two points are reflected about the real axis. Thus, the triangle formed by these points and the origin is an isosceles triangle with the real axis as its axis of symmetry.

Since the complex conjugate has the same magnitude as the original complex number, the two sides of the isosceles triangle have equal length. Therefore, the angle opposite the base (i.e., the origin) is a right angle, since it is the angle between the real axis and the imaginary axis.

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if angle c=(2x+3) and angle d= (2x+1) Then, we can only say that: 4x + angle e = 176.

We know that the sum of angles in a triangle is always 180 degrees. Therefore, we can write an equation based on the given information:

angle c + angle d + angle e = 180

Substituting the given expressions for angles c and d, we get:

(2x + 3) + (2x + 1) + angle e = 180

Simplifying and combining like terms, we get:

4x + 4 + angle e = 180

Subtracting 4 from both sides, we get:

4x + angle e = 176

We do not have enough information to solve for x or angle e, as we do not know the value of angle e.

Therefore, we can only say that:

4x + angle e = 176.

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Answer:

Step-by-step explanation:

Assuming an additive relation, we have ...

  BC +CD = BD

Substituting the given relations, we can find x:

  (4x -2.9) +(5x -0.9) = 7x -1

  2x = 2.8 . . . . . . . . . add 3.8-7x to both sides

  x = 1.4

Then the segment values are ...

  BD = 7(1.4) -1 = 8.8

 BC = 4(1.4) -2.9 = 2.7

  CD = 5(1.4) -0.9 = 6.1

Answer:

y = (10 + 7)/x  or  y = x/10 + 7/10

Step-by-step explanation:

y = 10x - 7

switch x and y

x = 10y - 7

add 7 to both sides

x + 7 = 10y

Divide both sides by 10

(x + 7)/10 = y

Flip

y = (10 + 7)/x  or  y = x/10 + 7/10

Answer:

B

Step-by-step explanation:

n+12=18.3

  -12    -12

n=6.3

He subtracted incorrectly and got 5.7 as an answer instead of 6.3

-hope it helps

Answer:

The mistake is B

because 18.3-12=6.3

Answer:

\(\huge\boxed{\sf d < 7}\)

Step-by-step explanation:

Given inequality is:

d + 6 < 13

Subtract 6 to both sides

d < 13 - 6

d < 7

\(\rule[225]{225}{2}\)

Hope this helped!

Answer:

C. -1/2

Step-by-step explanation:

(-2,2)

(0,1)

(2,0)

Change in y = -1

Change in x = 2

Equation: y = -1/2x + 1

The slope of the line is \(-\frac{1}{2}\).

Option C is correct.

The slope of the line is the ratio of the rise to the run, or rise divided by the run.

From given figure it is observe that line passes through point \((2,0)\) and \((0, 1).\)

Slope of line , \(m=\frac{0-1}{2-0}=-\frac{1}{2}\)

The slope of the line is \(-\frac{1}{2}\).

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