Darrion's car has a gas mileage of 30 miles per gallon. How many miles can Darrion travel on 13 gallons of gas?

Answer:

Quadratic Equations

A quadratic equation is one of the form ax2 + bx + c = 0, where a, b, and c are numbers, and a is not equal to 0.

Factoring

This approach to solving equations is based on the fact that if the product of two quantities is zero, then at least one of the quantities must be zero. In other words, if a*b = 0, then either a = 0, or b = 0, or both. For more on factoring polynomials, see the review section P.3 (p.26) of the text.

Example 1.

2x2 - 5x - 12 = 0.

(2x + 3)(x - 4) = 0.

2x + 3 = 0 or x - 4 = 0.

x = -3/2, or x = 4.

Answer:

90 dollars

Step-by-step explanation:

so first you need to solve for the rate of change or slope with the equation

y 2 - y1 / x2 - x1

here i think the independent variable is number of roses since the dollars rely on the number of roses (sorry for my explanation its kinda bad)

so since number of roses is independent we know that it is x and that the price in dollars is y

anyways we have to substitute two values into the equation

y 2 - y1 / x2 - x1

(3, 9) (6, 18)

18 - 9 / 6 - 3

9 / 3

3

knowing that the rate of change is 3, to find the price for 30 roses all we have to do is:

let p be price

p = 3x

p = 3(30)

p = 90 dollars

Answer:

$254.68

Step-by-step explanation:

145.80+252.95-44.32-15-84.75=$254.68

Answer:

function i think

Step-by-step explanation:

Answer:

(10 - x + y) units

Step-by-step explanation:

Perimeter of the triangle = (3 - 2x + x + 7 + y) units = (10 - x + y) units

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Answer:

Step-by-step explanation:

For step explanation:

1. write the problem

2. distinguishing the neg sign

3. distributing 3

4. moving like terms next to each other through commutative property

5.  Combining like terms

6. getting rid of parentheses

Answer:

63000 or 62400. Didn't specify whether to the thousandth or hundredth

The value of the given expression is 64ab.

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

Given a mathematical expression which includes the basic operations of multiplication and subtraction.

There are two terms for the expression, (-2a × 4b) and (-12a × 6b).

-2a × 4b = -8ab

-12a × 6b = -72ab

(-2a × 4b) - (-12a × 6b) = (-8ab) - (-72ab)

Two negatives become positive.

(-8ab) - (-72ab) = -8ab + 72ab

Both are like terms since the variables a and b are same. Just subtract it.

-8ab + 72ab = 64ab

Hence the solution of the difference of the expression is 64ab.

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Answer:

The radius is 8 inches

Step-by-step explanation:

The volume of a cylinder is given by

V = pi r^2 h

Assuming you mean 320 pi for the volume

320  pi = pi r^2 ( 5)

320 =5pi r^2

Divide each side by 5pi

320 pi / 5pi = 5 pi r^2 / 5pi

64 = r^2

Take the square root of each side

sqrt(64) = sqrt(r^2)

8 = r

The radius is 8 inches

Answer:

\(\Huge \boxed{\mathrm{4.51 \ inches}}\)

\(\rule[225]{225}{3}\)

Step-by-step explanation:

\(V=\pi r^2 h\)

The volume is 320 in³.

The height is 5 in.

\(320=\pi r^2 * (5)\)

Solving for \(r\).

Dividing both sides by 5.

\(64=\pi r^2\)

Dividing both sides by \(\pi\).

\(20.371833=r^2\)

Taking the square root of both sides.

\(r= 4.513517\)

The radius is 4.51 inches.

\(\rule[225]{225}{3}\)

Answer:

lol I rlly thought hahhahaha

The statements that are FALSE about the Outliners are

(b) all outliers are influential points  ,   and

(d) outliers should usually be removed from a data  .

The statement "(b) all outliers are influential points"  is false because not all outliers are influential points, meaning that they do not have a significant effect on the results of a statistical analysis.

Whether or not an outlier is influential depends on the specific situation and the type of analysis being performed.

The statement "(d) outliers should usually be removed from a data " is false because removing all outliers from a data set is not always appropriate.

Outliers can provide important information and removing them can sometimes lead to the loss of valuable information. In some cases, outliers can be valid observations and should be kept in the data.

The given question is incomplete , the complete question is

Which of the following statements are false? (select all responses that apply) group of answer choices

(a) Outliers can not be leverage points

(b) all outliers are influential points

(c) all outliers are leverage points

(d) outliers should usually be removed from a data  .

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The requreid we can reject the null hypothesis and conclude that at least one of the desserts is significantly more popular than the others.

To conduct an ANOVA analysis, we need to calculate the mean and variance for each group, as well as the overall mean and variance.

Pies: Mean = (5+2+7+4+3)/5 = 4.2
Variance =\(((5-4.2)^2 + (2-4.2)^2 + (7-4.2)^2 + (4-4.2)^2 + (3-4.2)^2)/4\)
               = 3.7

Similarly,

Cakes:
Mean =  5, Variance = 6.4

Cookies:
Mean =  6, Variance = 8.8

Overall mean =  5.1, Overall variance =5.1

To calculate the F-statistic, we need to use the formula,
F = (between-group variance)/(within-group variance).

Between-group variance \(= ((4.2-5.1)^2 + (5-5.1)^2 + (6-5.1)^2)*5 + ((5-5.1)^2 + (5-5.1)^2)*6 + ((6-5.1)^2)*7\) =5.3

Within-group variance = (3.7+6.4+8.8)/14 = 0.8

F = 5.3/0.8 = 6.6

The appropriate statistic for an ANOVA analysis is the F-statistic. we can reject the null hypothesis and conclude that at least one of the desserts is significantly more popular than the others.

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The completely factoring form of 6a^2 - 15a + 6 is 3(2a - 1)(a - 2).

To completely factor the expression 6a^2 - 15a + 6, the first step is to check if there is a common factor among the coefficients (6, -15, and 6) and the terms (a^2, a, and 1).

In this case, we can see that the common factor among the coefficients is 3, so we can factor out 3:

3(2a^2 - 5a + 2)

Now we need to factor the quadratic expression inside the parentheses further. We are looking for two binomials that, when multiplied, give us 2a^2 - 5a + 2. The factors of 2a^2 are 2a and a, and the factors of 2 are 2 and 1. We need to find two numbers that multiply to give 2 and add up to -5.

The numbers -2 and -1 fit this criteria, so we can rewrite the expression as:

3(2a - 1)(a - 2)

Therefore, the completely factored form of 6a^2 - 15a + 6 is 3(2a - 1)(a - 2).

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Answer:

The median of the numbers is 3.66 less than the mean

Step-by-step explanation:

To find the median, find the middle of the numbers

0.6, 0.7, 0.85, 1.5, 5.4

To find the mean, add all the numbers and divide by the number of numbers

0.6 + 0.7 + 0.85 + 15 + 5.4 = 22.55

22.55/5 = 4.51

To find how less, subtract the median from the mean

4.51 - 0.85 = 3.66

The height of the projectile after 4 seconds is 421.28 ft.

The projectile is in the air for 8.015 seconds.

The horizontal distance traveled by the projectile is 881.77 ft.

The maximum height of the projectile is 464.1 ft.

To solve this problem, we can use the kinematic equations of motion for a projectile.

Let's assume that the initial height of the projectile is zero.

What is the height of the projectile after 4 seconds:

We can use the equation:

\(y = yo + vot + 1/2at^2\)

where

y = height of the projectile

yo = initial height (zero in this case)

vo = initial vertical velocity = 220 sin(60°) = 190.53 ft/sec

a = acceleration due to gravity \(= -32.2 ft/sec^2\) ( negative since it acts downwards)

t = time = 4 sec

Plugging in the values, we get:

\(y = 0 + (190.53)(4) + 1/2(-32.2)(4)^2 = 421.28 ft\)

Therefore, the height of the projectile after 4 seconds is 421.28 ft.

Long is the projectile in the air:

The time of flight of a projectile can be calculated using the equation:

t = 2vo sinθ / g

where θ is the launch angle and g is the acceleration due to gravity.

Plugging in the values, we get:

t = 2(220 sin(60°)) / 32.2 = 8.015 sec

Therefore, the projectile is in the air for 8.015 seconds.

Horizontal distance traveled by the projectile:

The horizontal distance traveled by the projectile can be calculated using the equation:

\(x = xo + vot + 1/2at^2\)

where

x = horizontal distance traveled

xo = initial horizontal position (zero in this case)

vo = initial horizontal velocity = 220 cos(60°) = 110 ft/sec

a = acceleration due to gravity (zero in the horizontal direction)

t = time = 8.015 sec

Plugging in the values, we get:

\(x = 0 + (110)(8.015) + 1/2(0)(8.015)^2 = 881.77 ft\)

Therefore, the horizontal distance traveled by the projectile is 881.77 ft.

Maximum height of the projectile:

The maximum height of a projectile can be calculated using the equation:

\(ymax = yo + (vo^2 sin^2 \theta ) / 2g\)

Plugging in the values, we get:\(ymax = 0 + (190.53^2 sin^2(60\degree )) / (2)(32.2) = 464.1 ft\)

Therefore, the maximum height of the projectile is 464.1 ft.

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Answer:

Third answer.

Step-by-step explanation:

To simplify, we can factor 'x' from the equation, giving us:

\(\frac{x(1)}{x(4 + x)} = \frac{1}{x+4}\)

However, we must put a domain restriction to ensure that the denominator will not equal 0. This means that 'x+ 4' cannot equal zero. Therefore, x ≠ -4.

The third answer is correct.

The polynomial expression that represents the perimeter is (3x^3 +3x -148)ft and the value is 182ft

Polynomials are algebraic expressions that consist of variables and coefficients. Variables are also sometimes called indeterminates. We can perform arithmetic operations such as addition, subtraction, multiplication, and also positive integer exponents for polynomial expressions but not division by variable.

Perimeter of the triangle is the sum of the sides of the triangle which is = 2x^2 -120 + x^2 -5x +8x -28

Perimeter = (3x^2 +3x -148)ft

when x = 10

Perimeter = 3(10)^2 +3(10) -148 = 182ft

In conclusion the expression  (3x^2 +3x -148)ft is the expression for the perimeter of the triangle and the value is 182ft

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The value of the number is x = 34.

Let's break down the problem and solve it step by step.

1. "Five less than twice the value of a number": This can be represented as 2x - 5, where x is the number.

2. "Three times the quantity of 4 more than 1/2 the number": This can be represented as 3 * (x/2 + 4).

According to the problem statement, the two expressions are equal. We can set up the equation as follows:

2x - 5 = 3 * (x/2 + 4)

Now, let's solve the equation:

2x - 5 = 3 * (x/2 + 4)

Distribute the 3 to both terms inside the parentheses:

2x - 5 = (3/2)x + 12

Multiply through by 2 to eliminate the fraction:

2(2x - 5) = 2((3/2)x + 12)

4x - 10 = 3x + 24

Next, let's isolate the x term by moving the constant terms to the other side of the equation:

4x - 3x = 24 + 10

Simplify:

x = 34

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Answer:

b=–2

Step-by-step explanation:

we've got:

(3+bx)⁵===> b⁵x⁵+15b⁴x⁴+90b³x³+720b²x²+405bx+243

and we've also got the coefficient of x³ as –720

90b³=–720===> b³=–8===> b=–2

The value of piecewise function at x = -1 is f(-1) = 11, and the value of piecewise function at x = 9 is f(9) = 1.

what is piecewise function?

A piecewise-defined function in mathematics is one that is composed of several smaller functions, each of which has a specific interval of the domain it applies to. Instead of being a property of the function itself, piecewise definition is a way to express the function.

We have to evaluate the piecewise function for x = -1 and x = 9.

Let, function has value for x = -1 in the domain x ≤ 5 which is 11.

And function has value for x = 9  in the domain 6 < x which is 1.

⇒  f(-1) = 11 and f(9) = 1

Hence, the value of piecewise function at x = -1 is f(-1) = 11, and the value of piecewise function at x = 9 is f(9) = 1.

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ANSWER and EXPLANATION

f) The y-intercept of a graph is the point where the graph touches/intersects the y-axis of the coordinate grid.

Therefore, the y-intercept for the given graph is:

g) The domain of a function is the set of all input values for which the function is valid. In other words, it is the set of all x-values of the function.

From the given graph, we have that the domain of the function is:

h) The range of a function is the set of all output values for which the function is valid. In other words, it is the set of all y-values of the function.

From the given graph, we have that the range of the function is:

That is the answer.

Answer:

D. Bank charges a large fee for bouncing a check is not an example of overdraft protection.

Step-by-step explanation:

Overdraft protection is a service offered by banks that allows you to link your checking account to another account, such as a savings account or a line of credit. If you overdraw your checking account, the bank will automatically transfer funds from the linked account to cover the shortfall, which helps you avoid overdraft fees and other penalties.

Option A is not an example of overdraft protection as it refers to earning interest on money in your savings account, which is a separate service.

Option B refers to additional fees collected by the bank when you bounce a check, which is a penalty for not having sufficient funds in your account to cover the check.

Option C refers to an ATM machine providing you with cash, which is a basic function of an ATM and is not related to overdraft protection.

we have:

volume circular cone:

volume circular cylinder:

therefore volume of silo is:

answer: 1047.2 ft2

Step-by-step explanation:

bonjour quelqu'un peut-il se joindre à zo om Numéro d'identification 77974021488 le mot de passe 9taPHH

The correct expression which show the points Roopesh earns if two beanbags land on the board will be;

⇒ 2 × 2

or 2 + 2

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that,

In a bean bag toss game, players earn 2 points for each beanbag that lands on the game board and 5 points for each bean bag that lands in the hole.

Since, Roopesh dropped the bag on land for two times, and points for bag landing is 2.

Therefore, We get;

His score will be,

⇒ 2 × 2

or 2 + 2

Therefore, We get;

The correct expression which show the points Roopesh earns if two beanbags land on the board will be;

⇒ 2 × 2

or 2 + 2

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Mark needs a ladder that is 13 feet long in order to reach the second floor windows of the building.

Length is a measurement of distance or space from one point to another. It is typically measured in units such as meters, feet, or inches. Length is a scalar quantity, meaning it has magnitude but no direction. Length is a fundamental property of physical objects and can be used to measure the size of an object or the distance between two points.

To properly calculate the ladder length Mark needs, we must use the Pythagorean Theorem. The Theorem states that for the triangle formed by the ladder and the building, the square of the hypotenuse (the ladder length) is equal to the sum of the squares of the other two sides. Therefore, the ladder length Mark needs is equal to the square root of the sum of the squares of 5 feet and 12 feet, which is equal to the square root of 169, or 13 feet. Therefore, Mark needs a ladder that is 13 feet long in order to reach the second floor windows of the building.

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The three statements that are true include the following:

A. The radius of the circle is 3 units.

B. The center of the circle lies on the x-axis.

D. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

In Mathematics, the standard form of the equation of a circle is represented by this mathematical expression;

(x - h)² + (y - k)² = r²   .......equation 1.

Where:

h and k represents the coordinates at the center of a circle.

r represents the radius of a circle.

Based on the information provided, we have the following equation of a circle:

x² + y² – 2x – 8 = 0      ......equation 2.

In order to determine the true statements, we would rewrite the equation in standard form and then factorize by using completing the square method:

x² – 2x + y² = 8 = 0

x² – 2x + (2/2)² + y² = 8 + (2/2)²

x² – 2x + 1 + y² = 8 + 1

(x – 1)² + (y - 0)² = 9         .......equation 3.

By comparing equation 1 and equation 3, we have the following:

Center (h, k) = (1, 0)

Radius (r) = 3

Additionally, this line and the center of the given circle lies on the x-axis (x-coordinate) because the y-value is equal to zero (0).

(x - 0)² + (y - 0)² = 3²

x² + y² = 9.

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