A driver's distance D in miles from a rest stop after x hours is given by D(x) = 72x.
a) How far is the driver from the rest stop
after 3 hours?
b) Find the slope of the graph of D. Interpret
this slope as a rate of change.

The difference of two numbers is 30. If the smaller number is two-third of the larger one, The smaller number is 60 and the larger number is 90.

Let's assume the smaller number is x and the larger number is y.

Two conditions exist given the information provided:

Between the two numbers, there is a 30 point difference:

y - x = 30

The smaller number is two-thirds of the larger number:

x = (2/3) * y

To find the values of x and y, we can solve this system of equations.

From equation 2, we can express y in terms of x:

y = (3/2) * x

Substituting this value of y in equation 1:

(3/2) * x - x = 30

(3/2 - 1) * x = 30

(1/2) * x = 30

x = (30 * 2) / 1

x = 60

Now, substituting the value of x in equation 2 to find y:

y = (3/2) * 60

y = 90

As a result, 60 is the smaller number while 90 is the larger number.

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Answer: The expression for the absolute value of x+2 when x is less than 2 is -(x+2).

Step-by-step explanation: When x is less than 2, x+2 is a negative number. The absolute value of a negative number is its opposite with the negative sign, so the absolute value of x+2 is -(x+2). Therefore, when x is less than 2, the expression for the absolute value of x+2 is -(x+2).

Based on the best-fit line, the prediction that is TRUE is option d.) Jack devoted 41 minutes to playing video games after 2 days.

1. Look at the scatterplot and identify the best-fit line, which represents the trend or pattern in the data points.

2. Locate the point on the x-axis corresponding to 2 days.

3. Follow the vertical line from that point until it intersects with the best-fit line.

4. From that intersection, move horizontally to the y-axis to find the predicted value for the amount of time Jack devoted to playing video games after 2 days.

5. Based on the best-fit line, the predicted value is approximately 41 minutes.

6. Compare the predicted value with the given options.

7. Among the options, option d.) states that Jack devoted 41 minutes to playing video games after 2 days, which matches the prediction from the best-fit line.

8. Therefore, the TRUE prediction is option d.) Jack devoted 41 minutes to playing video games after 2 days.

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Answer:

Step-by-step explanation:

The line of best fit can be used to get predictions. So if we look at a particular day, we can get a predicted time based on the corresponding value on the best-fit line. If we look at Day 8, then the predicted time looks to be about 64 minutes.

Answer:

Step-by-step explanation:

x+9

Let x, be 4

4+9=13

given condition,

x+9<4x

4+9<4(4)

13<16

The answer is:

Work/explanation:

Our inequality is:

[tex]\sf{x+9 < 4x}[/tex]

Flip it

[tex]\sf{4x > x+9}[/tex]

Solve

[tex]\sf{4x-x > 9}[/tex]

Combine like terms

[tex]\sf{3x > 9}[/tex]

Divide each side by 3

[tex]\sf{x > 3}[/tex]

The lengths of the other two sides of the right triangle are 24m and 25m, respectively.

Let's assume the consecutive integers representing the lengths of the other two sides of the right triangle are x and x + 1, where x is the smaller integer. We are given that the shortest side measures 7m. Now, we can use the Pythagorean theorem to solve for the lengths of the other two sides.

According to the Pythagorean theorem, in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

Using this theorem, we have the equation:

[tex]7^2 + x^2 = (x + 1)^2[/tex]

Expanding and simplifying this equation, we get:

[tex]49 + x^2 = x^2 + 2x + 1[/tex]

Now, we can cancel out [tex]x^2[/tex] from both sides of the equation:

49 = 2x + 1

Next, we can isolate 2x:

2x = 49 - 1

2x = 48

Dividing both sides by 2, we find:

x = 24

Therefore, the smaller integer representing the length of one side is 24, and the consecutive integer representing the length of the other side is 24 + 1 = 25.

Hence, the lengths of the other two sides of the right triangle are 24m and 25m, respectively.

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Using the binomial distribution, it is found that there is a 0.056 = 5.6% probability that exactly one of their three children will have that trait.

For each children, there are only two possible outcomes, either they have the trait, or they do not. The probability of a children having the trait is independent of any other children, hence, the binomial distribution is used to solve this question.

Binomial probability distribution

[tex]P(X=\text{x})=C_{n,\text{x}}\times p^{\text{x}}\times(1-p)^{\text{n}-\text{x}}[/tex]

[tex]C_{n,\text{x}}=\dfrac{n!}{\text{x}!(n-\text{x})!}[/tex]

The parameters are:

In this problem:

The probability is P(X = 1), hence:

[tex]P(X=\text{x})=C_{n,\text{x}}\times p^{\text{x}}\times(1-p)^{\text{n}-\text{x}}[/tex]

[tex]P(X=1)=C_{3,1}\times(0.83)^1\times(0.15)^2=0.056[/tex]

0.056 = 5.6% probability that exactly one of their three children will have that trait.

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The calculated value of the integral [tex]\int\limits^{\infty}_1 {(xe^{-x}) \, dx[/tex] is 0.7358

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

[tex]\int\limits^{\infty}_1 {(xe^{-x}) \, dx[/tex]

The above expression can be integrated using integration by parts method

When integrated, we have

[tex]\int\limits^{\infty}_1 {(xe^{-x}) \, dx = -\left(x+1\right)\mathrm{e}^{-x}[/tex]

Recall that the x values are from 1 to ∝

This means that

[tex]\int\limits^{\infty}_1 {(xe^{-x}) \, dx = -\left(\infty +1\right)\mathrm{e}^{-\infty} + \left(1+1\right)\mathrm{e}^{-1}[/tex]

So, we have

[tex]\int\limits^{\infty}_1 {(xe^{-x}) \, dx = 0 + \frac{2}{e}[/tex]

Solving further, we get

[tex]\int\limits^{\infty}_1 {(xe^{-x}) \, dx = 0 + 0.7358[/tex]

Evaluate

[tex]\int\limits^{\infty}_1 {(xe^{-x}) \, dx = 0.7358[/tex]

Hence, the value of the integral is 0.7358

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The correct option is C, ON is the normal to the surface.

Remember that when we have an incident ray on a surface, a reflected ray will be emmited such that the angle with respect to the normal is the same one for the incident ray.

For any plane surface, this normal is perpendicular to the surface.

Here, we can see that ON is normal to the sruface of reflection, thus, the correct option is C, segment ON is the normal.

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Answer:

1 5/8

Step-by-step explanation:

3 1/4 - 1 5/8 = 3 2/8 - 1 5/8 = (2 + 1 + 2/8) - 1 5/8 = 2 + 8/8 + 2/8 - 1 5/8 =

= 2 10/8 - 1 5/8 = 1 5/8

The degree of the given polynomial is 4.The given polynomial is 2x²y - 8xy³ + 5xy. Let us count the number of terms in this polynomial. We have 3 terms.Let us now calculate the degree of each of these terms.

The degree of the first term is (2 + 1) = 3, as there are two variables x and y, and both are raised to the power 2 and 1 respectively.The degree of the second term is (1 + 3) = 4, as there are two variables x and y, and x is raised to the power 1 and y to the power 3.

The degree of the third term is (1 + 1) = 2, as there are two variables x and y, and both are raised to the power 1 each. So the degree of this polynomial will be the highest degree among these 3 terms.

The highest degree is 4. Therefore, the degree of the given polynomial is 4.

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Dos kilos de arroz tiene un precio total de 533.332 pesos.

En este problema debemos determinar el precio total de dos kilos de arroz. Inicialmente, nosotros debemos construir el sistema de ecuaciones lineales correspondiente:

2 · x + y = 500

3 · x = 350

Donde:

Ahora determinamos los precios unitarios:

x = 350 / 3

x = 116.667

y = 500 - 2 · x

y = 500 - 2 · 116.667

y = 266.666

Finalmente, calculamos el precio total de los dos kilos de arroz:

C = 2 · 266.666

C = 533.332

El enunciado está incompleto. La forma completa es la siguiente:

Si tengo dos papas y un kilo de arroz y me sale 500 pesos. Y si compro tres papas con 350 pesos. ¿Cuánto valen dos kilos de arroz?

Asimismo, el enunciado y la respuesta están escritos en español.

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Answer:

(0,a)

Step-by-step explanation:

The y-intercept of a function is the point where the graph of the function intersects the y-axis.

To find the y-intercept of the function F(x) = (a)(b^x), we can substitute x = 0 into the equation and solve for F(0).

When x = 0, we have:

=> F(0) = (a)(b^0)

=>  F(0) = (a)(1)

=> F(0) = a

Therefore, the y-intercept of the function F(x) = a * b^x is the point (0, a).

The hypotenuse of the right triangle is 25

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

The right triangle

The hypotenuse of the right triangle can be calculated using the following Pythagoras theorem

h² = sum of squares of the legs

Using the above as a guide, we have the following:

h² = 15² + 20²

Evaluate

h² = 625

Take the square roots

h = 25

Hence, the hypotenuse of the right triangle is 25

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A point on the line is (0, 3).

Given equation of the line:y + 3 = 3/2 (x + 4)

It can be rewritten in slope-intercept form as: y = 3/2x + 6 - 3

Slope of the line can be determined by comparing with y = mx + b, where m is the slope and b is the y-intercept.

Therefore, comparing given equation with y = mx + b, we get Slope (m) = 3/2

To find a point on the line, we can substitute any arbitrary value of x or y and solve for the other variable.

Let's take x = 0:y + 3 = 3/2 (0 + 4)y + 3 = 6y = 3

Therefore, a point on the line is (0, 3).

Now, to graph the line, we need to plot this point and use the slope to find other points. We know that slope is rise over run, which means for every increase of 2 units in x, there is an increase of 3 units in y.

So, we can use this to find other points as follows:Starting from (0, 3), move 2 units to the right and 3 units up to get another point, say (2, 6).Then, move 2 units to the left and 3 units down to get another point, say (-2, 0).

Join all the points on the graph to get the line.

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Using this property on the given expression, we get:

[tex]{(x^3/4)^2/3} = x^(3/4*2/3)[/tex] {multiplying the exponents}= [tex]x^(1/2)[/tex]

Now, we can rewrite the expression in radical form as √x which is the required answer.

The given expression to rewrite with rational exponents as a radical expression by extending the properties of integer exponents is:

[tex]{(x^3/4)^2/3}[/tex]

To rewrite this expression with rational exponents as a radical expression by extending the properties of integer exponents, the general formula of the power rule of exponents can be used, which states that [tex](a^m)^n = a^(mn)[/tex].

Now applying this power rule of exponents on the given expression:

[tex]{(x^3/4)^2/3}={x^(3/4*2/3)}={x^(1/2)}[/tex]= √x

Hence, the required expression, when rewritten with rational exponents as a radical expression by extending the properties of integer exponents, is √x.
To understand the solution, let's understand the concepts and formulas used in it.

The given expression is {(x^3/4)^2/3}. Now, to rewrite this expression with rational exponents as a radical expression by extending the properties of integer exponents, we need to use the power rule of exponents.

The power rule of exponents is an important property of the exponents that states that when we raise a power to another power, we need to multiply the exponents.

That is (a^m)^n = a^(mn).

Using this property on the given expression, we get:

[tex]{(x^3/4)^2/3} = x^(3/4*2/3)[/tex] {multiplying the exponents}= [tex]x^(1/2)[/tex]

Now, we can rewrite the expression in radical form as √x which is the required answer. Hence, the given expression rewritten with rational exponents as a radical expression by extending the properties of integer exponents is √x.

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Its the second one.

2f+10=20

Answer:

x = 26

Step-by-step explanation:

Since s║t and r is a transversal, consecutive interior angles add to 180

⇒ 2(x + 15) + (3x + 20) = 180

⇒ 2x + 30 + 3x + 20 = 180

⇒ 5x + 50 = 180

⇒ 5x = 180 - 50

⇒ 5x = 130

⇒ x = 130/5

⇒ x = 26

Answer:

x=26

Step-by-step explanation:

Given:

s || t

2(x+15) + (3x+20) = 180°

Since the sum of co interior angle is 180°

Opening bracket

2x + 30 + 3x + 20 =180

Solving like terms

5x+50= 180

subtracting both side by 50

5x=180-50

5x = 130

dividing both side by 5.

[tex]\tt x=\frac{130}{5}[/tex]

x = 26

Therefore value of x is 26.

The distance that represents the distance from point Q to RS is: QT.

The distance between a point and a line, is usually defined as the shortest distance that exists between a fixed point and any point on the line. It is the length of the line segment that is perpendicular to the line and passes through the point.

In the given figure attached, we can see that among the lines drawn from point Q to line RS ,the line QT is perpendicular to RS and as such, it means that is represents the distance between the point and the line.

Therefore, we conclude that the distance that represents the distance from point Q to RS is: QT.

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Answer:

Part I:

The amplitude of the function F(x) is 2, since the coefficient of the cosine function is 2.

The amplitude of the function G(x) is not defined since it does not contain any trigonometric functions.

The period of the function F(x) is 2π since the period of the cosine function is 2π.

The period of the function G(x) is π since the function is a linear function with slope 2.

Part III:

To sketch the graph of F(x), we can start by plotting the maximum and minimum values of the cosine function, which are 2 and -2, respectively. Then, we can shift the graph downward by 2 units to obtain the graph of F(x). The resulting graph should look like a cosine graph with amplitude 2, but shifted downward by 2 units. We can repeat this pattern for one period of the function, which is 2π, to obtain the following sketch:

| /\

2 | / \

| / \

| / \

| / \

| / \

_____|_________________________

| 0 π 2π

To sketch the graph of G(x), we can start by plotting the y-intercept, which is 0. Then, we can use the slope of 2 to plot additional points on the graph. Since the period of G(x) is π, we can plot two periods by plotting points at x=0, π/2, π, 3π/2, and 2π. The resulting graph should look like a straight line with slope 2. Here is a sketch of the graph:

|

|

|

4 | /

| /

| /

|/________________________

| 0 π 2π

Note that the critical point of G(x) is at x=0, where the slope changes from positive to negative.

The statement "Yes, because every x-value corresponds to exactly one y-value" (A) is correct.

The given table represents a function. A function is a relationship where each input (x-value) is associated with exactly one output (y-value).

Looking at the table:

X | Y

2 | 1

4 | 3

6 | 4

8 | 6

10 | -

We can see that each x-value in the table corresponds to a unique y-value. There is no repetition or duplication of x-values, and each x-value has only one corresponding y-value.

Therefore, the statement "Yes, because every x-value corresponds to exactly one y-value" (A) is correct.

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Answer:

27

Step-by-step explanation:

[tex]2u-5=3\\2u=8\\u=4\\\\9u-9=9(4)-9=36-9=27[/tex]

Answer:

84

Step-by-step explanation:

A= [tex]\frac{1}{2}[/tex]b*h

A= [tex]\frac{1}{2}[/tex]14*12

A=84

Declarative sentences are those which state a fact, describe something, or make a statement. A declarative sentence is a simple statement that gives some information. It ends with a period and always has a subject and a predicate.

1. Example of a closed declarative statement: A closed declarative sentence is one that has only one answer and cannot be disputed.

An example of a closed declarative statement would be: The capital of France is Paris. This is a closed declarative statement because there is no other city that is the capital of France other than Paris.

2. Example of an open declarative statement: An open declarative sentence is one that may have many possible answers and may be disputed.

An example of an open declarative statement would be: The best pizza topping is pepperoni. This is an open declarative statement because some people may disagree and have their own preferences about pizza toppings.

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Answer: answer is C

Step-by-step explanation: If you take the value of greeting cards and divide by the amount of greeting cards you will get the rate per greeting card.

The estimated total cost of the project is $7,663.20.

We need to add up the costs of soil, sand, sod, and tree/shrubbery installation, including the contingency.

Soil: 8 cubic yards x $80/cubic yard = $640

Sand: 3 cubic yards x $100/cubic yard = $300

Sod: 3600 square feet / 30 square feet/roll x $100/roll = $1200

Tree and shrubbery installation: $2500

Contingency: 3% x $4640 = $139.20

Total cost: $640 + $300 + $1200 + $2500 + $139.20 = $7,663.20

Therefore, The estimated total cost of the project is $7,663.20

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9

This seems to be an isosceles triangle, which means that 2 sides are equal. In this case, that would be 9.