What are the domain and range of the real-valued function f(x) = -3 + √√4x - 12?The domain is x ≥ 3, and the range is f(x) ≤ - 3.The domain is x ≥ 3, and the range is f(x) > - 3.The domain is x ≤ 3, and the range is f(x) ≥ - 3.O The domain is x ≥ 3, and the range is all real numbers.

Answer: x=-18

Step-by-step explanation:

Solve for x by simplifying both sides of the equation, then isolating the variable.

Answer:

\( \huge{ \fbox{ \sf{x = - 18}}}\)

Step-by-step explanation:

\( \text{4(7x + 3) = - 3(2 - 9x)}\)

\( \text{Step \: 1 \: : Distribute \: 4 \: through \: the \: parentheses}\)

\( \hookrightarrow{ \sf{28x + 12 = - 3(2 - 9x)}}\)

\( \text{Step \: 2 \: : Distribute \: - 3 \: through \: the \: parentheses}\)

\(\hookrightarrow{ \sf{28x + 12 = - 6 + 27x}}\)

\( \text{Step \: 3 \: : Move \: 27x \: to \: left \: hand \: side \: and \: change \: its \: sign}\)

\( \hookrightarrow{ \sf{28x - 27x + 12 = - 6}}\)

\( \text{Step \: 4 \: : Move \: 12 \: to \: right \: hand \: side \: and \: change \: its \: sign}\)

\( \hookrightarrow{ \sf{28x - 27x = - 6 - 12}}\)

\( \text{step \: 5 \: : Collect \: like \: terms}\)

\( \text{Like \: terms \: are \: those \: which \: have \: the \: same \: base.}\)

\( \hookrightarrow{ \sf{x = - 6 - 12}}\)

\( \text{step \: 6 \: : Calculate}\)

\( \text{ \underline{ Remember!}} : \sf{ \: The \: negative \: integers \: are \: always \: added \: but \: posses \: the \: negative \: ( - ) \: sign.}\)

\( \hookrightarrow{ \boxed{ \sf{x = - 18}}}\)

Hope I helped!

Best wishes ! :D

~\( \text{TheAnimeGirl}\)

The equation for the sentence below is x - 23 = 28.

The solution to the equation is x = 5.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Therefore, the sum of a number(x) and - 23 is 28 can be represented with an equation as follows:

The unknown number is x.

Hence,

x + (-23) = 28

Therefore, the equation from the sentence above is  x - 23 = 28.

Now, let's solve the equation for x as follows;

x - 23 = 28

add 23 to both sides of the equation

x - 23 + 23 = 28 - 23

x = 5

Therefore, the value of x is 5

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Answer:

a + c = 125 & 12a + 6c = 1140

Step-by-step explanation:

adult ticket total + child ticket total = 125 total tickets

($12 x adult ticket total) + ($6 x child ticket total) = $1140

Answer: irrational and real numbers

A second-degree polynomial takes the form

\(f(x) = ax^2 + bx + c\)

for some constants a, b, and c. Such a function is continuous and differentiable everywhere in its domain.

Differentiating f(x) with respect to x gives

\(\dfrac{df}{dx} = 2ax + b\)

We're told that

• f(x) is increasing on [0, 8]

• f(x) is decreasing on ]-10, 0]

and since df/dx is continuous, this tells us that df/dx = 0 when x = 0. It follows that b = 0, and we can write

\(f(x) = ax^2 + c\)

We're also given that the curve passes through the point (-8, 4), which gives rise to the constraint

\(f(-8) = 64a - 8b + c = 4 \implies 64a + c = 4\)

Since f(x) is decreasing on ]-10, 0], we have df/dx < 0 when x = -8, so

\(2ax+b < 0 \implies -16a < 0 \implies a > 0\)

This means f(x) is minimized when x = 0, with min{f(x)} = c, so the co-domain of f(x) is the set {f(x) ∈ ℝ : f(x) ≥ c}.

Without another condition, that's all we can say about the co-domain. There are infinitely many choices for the constants a and c that satisfy the given conditions. For example,

a = 1, c = -60   ⇒   f(x) = x² - 60   ⇒   f(-8) = 4

⇒   co-domain = {f(x) ∈ ℝ : f(x) ≥ -60}

a = 2, c = -124   ⇒   f(x) = 2x² - 124   ⇒   f(-8) = 4

⇒   co-domain = {f(x) ∈ ℝ : f(x) ≥ -124}

etc.

The probability that the mean of a sample of 40 families will be between 17.1 and 18.1 pounds is given as follows:

0.5874 = 58.74%.

The z-score of a measure X of a variable that has mean symbolized by \(\mu\) and standard deviation symbolized by \(\sigma\) is obtained by the rule presented as follows:

\(Z = \frac{X - \mu}{\sigma}\)

The parameters for this problem are given as follows:

\(\mu = 17.2, \sigma = 2.5, n = 40, s = \frac{2.5}{\sqrt{40}} = 0.3953\)

The probability that the mean of a sample of 40 families will be between 17.1 and 18.1 pounds is the p-value of Z when X = 18.1 subtracted by the p-value of Z when X = 17.1, hence:

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem:

\(Z = \frac{X - \mu}{s}\)

Z = (18.1 - 17.2)/0.3953

Z = 2.28

Z = 2.28 has a p-value of 0.9887.

Z = (17.1 - 17.2)/0.3953

Z = -0.25

Z = -0.25 has a p-value of 0.4013.

Hence:

0.9887 - 0.4013 = 0.5874 = 58.74%.

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Answer:

\(20x+240y/y\)

Step-by-step explanation:

1. Subtract the numbers

2. Evaluate the exponents

3. Subtract the numbers, again

4. Have a great day and thx for your inquiry :)

Answer: x=3

Step-by-step explanation: you can rewrite -(3x-9) as -1*(3x-9). as the negative sign is the same as -1. Now if you distribute you get -3x+9. then set this equation equal to zero and subtract 9 from both sides and you'll get -3x=-9. next divide both sides by -3 and you should get the answer x=3.

-(3x-9)

-1*(3x-9)

-3x-9=0

-3x=-9

x=3

Answer:

The table does not show the proportional relationship.

Step-by-step explanation:

When y varies directly with x, then the equation is

y ∝ x

y = kx

Where 'k' is called the proportionality constant.

Given the table

x         3        6      9      12

y         12      24    45    60

Let us check from the table whether the proportionality constant 'k' remains constant or not.

FOR (3, 12)

y = kx

k = y/x

   = 12 / 3 = 4

FOR (6, 24)

k = y/x

   = 24 / 6 = 4

FOR (9, 45)

k = y/x

   = 45 / 9 = 5

FOR (12, 60)

k = y/x

   = 60 / 12 = 5

From the above calculations, it is clear that the value of 'k' does not remain constant.

This means the value of 'k' for the points (6, 24) and (9, 45) is 4, while the value of 'k' for the points (9, 45) and (12, 60) is 5.

Hence, the table does not show the proportional relationship.

Answer:

1 kilometre is 0.621 mile

Answer:

1 Kilometer = 0.621 mile

Step-by-step explanation:

The distance d in miles (mi) is equal to the distance d in kilometers (km) divided by 1.609344

The completed blanks in Nyala's solution that is used to prove that the measure of angle x is 40° is as follows;

If we perform a 180° rotation about the point O the following happens

Ray \(\overleftrightarrow{EF}\) maps unto ray \(\overleftrightarrow{GH}\)

Ray \(\overleftrightarrow{GH}\) maps unto ray \(\overleftrightarrow{FE}\)x

\(\overleftrightarrow{FG}\) maps unto itself

Therefore, the image of angle x will be exactly where the pre-image of 40° was. Since rotation preserve angle measure, the measure of angle x must be 40°.

The measure of an angle is the degree of rotation between the initial side and the terminal side of the angle.

The details of the method Nyala used to prove that the measure of the angle x is 40° can be found as follows;

The rotation of a line 180° about the center of the line maps onto itself, and the rotation of a line about a non colinear point, is parallel to the original line.

Whereby the center of rotation of the line \(\overleftrightarrow{EF}\) is equidistant from both the line \(\overleftrightarrow{GH}\) which is parallel to the line \(\overleftrightarrow{EF}\), the image of the line \(\overleftrightarrow{EF}\) maps to the line \(\overleftrightarrow{GH}\) following a 180° rotation about the point O, and the rotation of the line \(\overleftrightarrow{FG}\) about the point O maps unto itself, such that the angle x maps to the angle 40°, therefore;

∠x ≅ 40° (A rotation transformation is a rigid transformation)

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Answer:

it would be 5.41 x 10^2

Step-by-step explanation:

the reason it would be this is because when you have it ^2 you love the decimal that many places the same goes for the number was negative then you would move it backwards.

Answer:

The answer is 5.41 × 10^2

Step-by-step explanation:

To make sure the answer is right, picture a decimal on the right of the 1 in the numeral. Then, picture it going to the left until it's next to the 5. Since it moved twice, the exponent is 2 and the decimal is 5.41. Hope this helps!

Answer: 0.3125.

Step-by-step explanation:

Outcome 1: all boys

boy  boy  boy  boy

0.5 * 0.5 * 0.5 * 0.5 = 0.0625

Outcome 2: first child is a girl, all others are boys

girl   boy   boy   boy

0.5 * 0.5 * 0.5 * 0.5 = 0.0625

Outcome 3: second child is a girl, all others are boys

boy   girl   boy   boy

0.5 * 0.5 * 0.5 * 0.5 = 0.0625

Outcome 4: third child is a girl, all others are boys

boy   boy   girl   boy

0.5 * 0.5 * 0.5 * 0.5 = 0.0625

Outcome 5: fourth child is a girl, all others are boys

boy   boy   boy   girl

0.5 * 0.5 * 0.5 * 0.5 = 0.0625

Therefore,

0.0625 + 0.0625 + 0.0625 + 0.0625 + 0.0625 = 0.0625 * 5 = 0.3125

Answer:

Step-by-step explanation this is a tough one but i know everything the answer is 69

The inequality expression that corresponds to the solution of the inequality graph is x² + 3x - 3 < 0.

option B.

The inequality expression that corresponds to the solution of the inequality graph is determined by simplifying the equations as follows;

The solution of the graph,

x > -4 and x < 1

The first equation with "≥" is ruled out because the graph doesn't have a thick dot.

Let's simplify the second expression;

x² + 3x - 3 < 0

solve using quadratic formula;

x > -3.79 or x < 0.79

The third expression is ruled out since its solution will be complex.

For the last expression;

x² + 3x - 3 > 0

x < -3.79 or x > 0.79

Thus, the correct inequality expression is x² + 3x - 3 < 0.

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Answer:

4 1/2 quarts.

Step-by-step explanation:

So 5 1/2 quarts to start. 4 left over.

Theres 4 cups in a quart.

So theres be 4 1/2 quarts used.. as 4 cups left would be a quart and 1 quart taken away from 5 1/2 quarts in 4 1/2.

The value of cos ø, for the given coordinates (8, 6), is 4/5 in the lowest terms.

To find the value of cosine (cos) ø, we need the coordinates (8, 6) of a point on the unit circle.

The unit circle is a circle with a radius of 1, and the coordinates (8, 6) do not lie on the unit circle. However, we can use these coordinates to calculate the cosine value indirectly.

First, we need to find the hypotenuse (r) of the right triangle formed by the coordinates (8, 6). We can use the Pythagorean theorem:

r = √(8² + 6²) = √(64 + 36) = √100 = 10

Now, we can find the cosine value by dividing the adjacent side length (x-coordinate) by the hypotenuse:

cos ø = 8 / 10 = 4/5.

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Using proportions, it is found that due to the smaller division of the exchange rate by the cost, the souvenir would be less expensive in Egypt.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

The souvenir would be less expensive in the country in which the division of the exchange rate by the cost is smaller.

In Britain, the cost is of 17, with an exchange rate of 0.83, hence the cost in US dollars is:

c = 17/0.83 = $20.48.

In Egypt, the cost is of 288, with an exchange rate of 18, hence the cost in US dollars is:

c = 288/18 = $16.

16 < 20.48, hence the souvenir would be less expensive in Egypt.

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Based on the given information, the second brand, Cola, is the more affordable option in terms of cost per milliliter compared to Co Fizz.

To determine which brand of cola is more expensive, we need to compare the cost per unit volume for each brand.

For the first brand, Co Fizz, a pack contains 4 bottles, and each bottle has a volume of 500 ml. The cost of the pack is $2.50. Therefore, the total volume in a pack is 4 * 500 ml = 2000 ml. To find the cost per milliliter (ml), we divide the total cost by the total volume: $2.50 / 2000 ml = $0.00125 per ml.

For the second brand, Cola, a pack contains 10 bottles, and each bottle has a volume of 330 ml. The cost of the pack is $2. Therefore, the total volume in a pack is 10 * 330 ml = 3300 ml. To find the cost per milliliter (ml), we divide the total cost by the total volume: $2 / 3300 ml ≈ $0.000606 per ml.

Comparing the two brands, we can see that the cost per milliliter for Co Fizz is $0.00125, while the cost per milliliter for Cola is approximately $0.000606.

Since the cost per milliliter for Co Fizz is higher than the cost per milliliter for Cola, it can be concluded that Co Fizz is more expensive in terms of price per unit volume.

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The probability that more than 2 students have blue eyes is 0.149, the expected number of students out of the 4 with blue eyes is 0.4, the variance is 0.36, and the standard deviation is 0.6.

a) P(X = 3) = (4 choose 3) * \((0.10)^3 * (0.90)^1\) = 0.0036

So the probability that exactly 3 of them have blue eyes is 0.0036.

b) P(X = 2) = (4 choose 2) * \((0.10)^2 * (0.90)^2\) = 0.0386

So the probability that exactly 2 of them have blue eyes is 0.0386.

c) P(at least 1) = 1 - P(none) = 1 - \((0.90)^4\) = 0.3439

So the probability that at least 1 of them has blue eyes is 0.344.

d) P(X > 2) = P(X = 3) + P(X = 4) = (4 choose 3) * \((0.10)^3 * (0.90)^1\) + (4 choose 4) * \((0.10)^4 * (0.90)^0\) = 0.0001

So the probability that more than 2 have blue eyes is 0.0001.

e) E(X) = n * p = 4 * 0.10 = 0.4

So the expected number of students out of the 4 with blue eyes is 0.4, not 0.291 as provided.

f)Var(X) = n * p * (1 - p) = 4 * 0.10 * 0.90 = 0.36

So the variance is 0.36.

g) SD(X) = sqrt(Var(X)) = sqrt(0.36) = 0.6

Standard deviation is 0.6.

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Answer:

Steps 4 and 5

Step-by-step explanation:

Paula divided both sides in 4 and 5 to keep the equations equal.

Hope that this helps!

Answer:3

Step-by-step explanation:

C = 2()r

2*3.14 = 6.28

18.84 / 6.28

=3

If correct pls give brainly

Answer:

\(x=7-2y\)        \((1,3)\)

\(3x+6y=-9\)      \((-1,-1)\)

\(4x-2y-3\)       \(\text{no solution}\)

\(2x+4y=7\)      \(\text{infinite number of solutions}\)

\(x=-2y-3\)     \((1,-2)\)

Step-by-step explanation:

1:   \(x=7-2y\)

    \(\Rightarrow x+2y=7\)

    \(\Rightarrow (1,3)\;\text{is a solution of the above equation}.\)

2:    \(3x+6y=-9\)

      \(\Rightarrow 3(-1)+6(-1)=-3-6=-9\)

      \(\Rightarrow (-1,-1)\; \text{is a solution of the equation 3x+6y=-9}.\)

3:    \(4x-2y-3\)

      \(\Rightarrow \;\text{It is not an equation}\\ \text{So, 4x-2y-3 has no solution.}\)

4:    \(2x+4y=7\)

     \(\Rightarrow 2x+4y=7\;\text{have an infinite number of solutions.}\\\text{Because for every x there exists a value of y which satisfies the equation.}\)

5:    \(x=-2y-3\)

     \(\Rightarrow x+2y=-3\)

     \(\Rightarrow 1-2(-2)=1-4=-3\)

    \(\Rightarrow (1,-2)\; \text{is a solution of the equation x=-2y-3}.\)

Answer:

  (d)  (1, 2)

Step-by-step explanation:

You want to know which of the given points satisfies the inequality.

We find it easiest to plot the given points on a graph of the solution. This shows us that (1, 2) is a solution to the inequality. (It lies in the solution area.)

__

Additional comment

Another way to choose the answer is to try each of the points in the inequality.

If you can visualize the boundary line (without plotting it) as a line with positive slope and a y-intercept of 2, you can more readily reject the first choice and accept the last choice. (0, 3) is above the y-intercept, and (1, 2) is to the right of it (in the solution space).

You may also recognize the x-intercept will be -3, so the second choice lies above the boundary line.

The triangle with side lengths √35 , √14 , 7 is a right triangle.

What is the right triangle?

A right-angle triangle is a triangle that has one of its angles 90 degrees. The sum of angles in a right triangle is 180 degrees.

p² + b² = h² ( In a right-angled triangle)

p = perpendicular of the triangle

b = base of the triangle

h = hypotenuse of the triangle

According to the Pythagoras theorem:

p² + b² = h² (In a right-angled triangle)

In Option D

(√35)² + (√14)² = 7²

49 = 49

Pythagoras theorem is followed in this triangle, hence it is a right angled triangle.

Hence, The triangle with side lengths √35, √14, 7 is a right triangle.

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Answer: $28.50

Step-by-step explanation:

(a) 20% of $32.99 = 6.598 so the discounted price is $32.99 - $6.60 (rounded) = $26.39 then 8% of $26.39 = $2.11 so the sales tax is $2.11. (b) the total amount Andre paid for the video game is $26.39 + $2.11 = $28.50.

Pls Brainliest?

Answer:

Step-by-step explanation:

part A $32.91         $32.99-8% = 32.91

part B $32.71         ($32.99-20%)-8% = 32.71

Answer:

Ryan: (100/13)(1/1,609.34)(3,600) =

17.21 miles per hour

Ryan is faster than Juan, by about 2.21 miles per hour

The linear model that could be used to calculate cost of mailing a large envelope is L(x) = 0.88 + 0.2(x – 1) and used to calculate cost of mailing a package is P(x) = 1.71 + 0.17(x – 3). The weight at which the cost a large envelope and a package will cost the same amount to mail is 17 ounces.

Linear models are used to describe a continuous response variable as a function of one or more predictor variables. Let x be the weight in ounces and L be the cost of mailing a large envelope. Based on the provided information, the cost of mailing a large envelope increases with increasing weight. The cost of mailing one ounce is $0.88 and increased by $0.2 for each additional weight. Hence,

L(x) = 0.88 + 0.2(x – 1)

Let x be the weight in ounces and P be the cost of mailing a package. Based on the provided information, the cost of mailing a package remains the same for weight of 1 to 3 ounces at the cost of $1.71, and then increases by $0.17 for each additional weight. Hence,

P(x) = 1.71 + 0.17(x – 3)

The weight at which a large envelope and a package will cost the same amount to mail is determined by equating the two models.

L(x) = P(x)

0.88 + 0.2(x – 1) = 1.71 + 0.17(x – 3)

0.88 + 0.2x – 0.2 = 1.71 + 0.17x – 0.51

0.68 + 0.2 x = 0.17 x + 1.2

0.2x – 0.17x = 1.2 – 0.68

0.03x = 0.52

x = 17.33 ≈ 17 ounces

Note: The question is incomplete. The complete question probably is: Provided table indicates the U.S. Postal Rates for large envelopes and packages of different weights. a) Create a linear model that could be used to calculate the cost to mail a large envelope, given its weight in ounces. Use L to represent the cost to mail a large envelope and x to represent the envelope weight in ounces. Create a linear model that could be used to calculate the cost to mail a package, given its weight in ounces. Use P to represent the cost to mail a package and x to represent the package weight in ounces. Find the weight at which a large envelope and a package will cost the same amount to mail, assuming your linear models still apply to higher weights.

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Complete Question:

The correlation between years of education and salary in a sample of 20 people from a certain company is .4. Is this correlation statistically significant at the .05 level?

Answer:

We accept \(H_o\) hence no significant  evidence

Step-by-step explanation:

From the question we are told that

sample correlation n= 20

population correlation  = 4

level of significance \(\alpha =0.05\)

Generally we are task to understand existing difference between  sample correlation and population correlation

Generally null hypothesis  is given by \(H_o : p=0\)

alternative hypothesis \(H1_1 : p\neq 0\)

generaly the mathematical representation of test statics

        \(t= r\sqrt{\frac{n-2}{1-r^2} }\)

        \(t= 0.04\sqrt{\frac{20-2}{1-0.4^2} }\)

        \(t= 1.85\)

Generally for table the p value is given by \(p= 0.08056\)

p value > the null hypothesis

Therefore

We accept \(H_o\) hence no significant  evidence

Answer:

To find the value of "a" when you know the perimeter of a shape, you need to know the specific shape you're referring to. Please provide more information about the shape in question, such as whether it's a rectangle, triangle, or another geometric figure. Additionally, if you have any specific measurements or relationships between the sides of the shape, please provide them as well.