The front of a brush fire is moving through some dead grass at a rate of 3 miles per hour. Luckily, it is moving directly toward the fire station, which can dispatch a fire truck to fight the blaze. If the fire station is 1 mile away and the truck can travel straight to the fire's front at 44 miles per hour, how long will it be before the fire truck reaches the fire's front?

The domain and the range of the piece-wise function are given as follows:

The domain of a function is composed by the set that contains all possible input values of the function.

In this problem, the function is a piece-wise function, as it has two different definitions. However, for each definition, the function is a linear function, which has no input restrictions, hence the domain of the function is composed by all real values.

The range of a function is composed by the set that contains all possible output values of the function.

The outputs of the function are obtained as follows:

Linear functions have no open spaces on it's domain, hence the interval that describes the range is given by:

(-∞, 4].

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Answer

34.056 I'm pretty sure it's right. I took a test with the same question

Answer:

34.556

Step-by-step explanation:

= (3x10) + (4x1) + (5x1/10) + (5x1/100) + (6x1/1000)

= 30 + 4 + 0.5 + 0.05 + 0.006

The ratios of corn to lima beans are not equivalent.

What are equivalent ratios?

The ratios that are same when compared are called equivalent ratios. The equivalentity of two or more ratios can be determined by comparing them to one another. For instance, 1:2 and 2:4 have the same ratio.

In case of Gabby:

Ratio of corn to lima beans = 5/6 = 0.833

In case of Robert:

Ratio of corn to lima beans = 7/9 = 0.777

Notice that  0.833 ≠ 0.777

So, the ratios of corn to lima beans are not equivalent.

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(a) The respondents who chose silver 2.3 times more than red , and

(b) the respondents who chose either silver or black are 3.8 times more than who chose red .

In the question ,

a table is given which shows popular sports cars colors in North America .

Part(a)

portion of respondents who chose silver = 0.20  ,

portion of respondents who chose red = 0.09 ,

the number of times more respondents chose silver than red = 0.20/0.09

= 20/9

= 2.22222

On rounding to the nearest tenth

≈ 2.3

Part(b)

portion of respondents who chose black = 0.14 ,

portion of respondents who chose either black or silver = 0.20 + 0.14

= 0.34

number of times more respondents chose either silver or black than red

= 0.34/0.09

= 3.7777777

rounding to the nearest tenth

≈ 3.8

Therefore , (a) The respondents who chose silver 2.3 times more than red , and

(b) the respondents who chose either silver or black are 3.8 times more than who chose red .

The given question is incomplete , the complete question is

Use the table that shows popular sports cars colors in North America

(a) how many times more respondents to silver than red round to the nearest 10th if necessary.

(b) How many times more respondents chose either silver or black than red?   Round to the nearest tenth if necessary.

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Jeff would have had 10 cards to begin with.

Then, if Jeff sold half of his baseball cards, he would then have 5 cards.

It says that Jeff bought 16 more cards, so 16 + 5

Well, 16 + 5 = 21. The text says that he now has 21 cards, so this should be a correct answer.

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Joke: What is a snowman's favorite type of Mexican food?

Answer: Burr-itos!

Have a great day and God bless! :D

Answer:

Step-by-step explanation:

Answer:

1: 8

2: 5^4

3: 6^2 x 6^3

Step-by-step explanation:

(2^2x2)^3/(2^4x2^2)

(4x2)^3/(16x4)

8^3/64

512/64

8

2)

5^-2x5^5x5^1

5^-2+5+1

5^4

3)

6^2 x 6^3

Hopes this helps please mark brainliest

The ordered pairs that are on the graph of the linear equation are:

{(2,2), (3,5), (– 1,– 7), (0, -4)}

Here we have a list of ordered pairs and we want to see which ones are solutions for the given linear equation:

3x = y + 4

To check that, we can just replace the values of each ordered pair in the equation and see if the equation is true or false. If it is true, then the ordered pair is a point on the graph.

1) (7,– 1)

3*7 = -1 + 4

21 = 3  this is false.

2) (2,2)

3*2 = 2 + 4

6 = 6   this is true.

3) (3,5)

3*3 = 5 + 4

9 = 9  this is true.

4) (0,4)

3*0 = 4 + 4

0 = 8  this is false.

5) (– 1,– 7)

3*-1 = -7 + 4

-3 = -3  this is true.

6) (0, -4)

3*0 = -4 + 4

0 = 0  this is true.

So the correct options are:

{(2,2), (3,5), (– 1,– 7), (0, -4)}

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Answer: what grade is this

Step-by-step explanation:

[tex]{ \boxed{ \red{ \sf{y = 3 + 5x}}}}[/tex]

Step-by-step explanation:

[tex]{ \blue{ \tt{y - 5x = 3}}}[/tex]

Shift -5x to right side then,

[tex]{ \boxed{ \blue{ \tt{y = 3 + 5x}}}}[/tex]

The statements on the relations and whether they are proportional relationships is given as follows:

A proportional relationship is a linear function that has intercept of zero and slope as the constant of the proportionality k, as follows:

y = kx.

A relation represents a proportional relationship if the ratio of the output y by the input x is the same for all the points.

For the first relation, the constant for each point is given as follows:

Hence it represents a proportional relationship, and the equation is given as follows:

y = -1.5x.

For the second relationship, the constants are:

Different constants, hence it does not represent a proportional relationship.

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Answer:

infinite solutions

Step-by-step explanation:

both sides are identical

Answer:

1/6

Step-by-step explanation:

I just did the problem myself! Photo evidence included!

The greatest common factor for 36m(r+t) and 9p(r+t)6 is 18(r+t).

According to the question,

We have the following two expressions:

36m(r+t) and 9p(r+t)6

Now, we will first solve the second expression:

54p(r+t)

Now, the greatest common factor means the greatest number and variables which can divide both the terms completely.

So, the common variables in both the terms are (r+t).

In 36 and 54, the greatest common factor is 18 because their respective product of factors are 2*2*3*3 and 3*3*3*2.

Now, the common factors in their product are 2*3*3. So, the greatest common factor or highest common factor is 18.

Hence, the greatest common factor for 36m(r+t) and 9p(r+t)6 is 18(r+t).

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The required time taken by the sofia is 15.75 minutes.

Work is defined as the efficiency of the person to do a particular work in the certain period of time. Work is directly proportional to the efficiency and inversely proportional  to time.

Formula, work = efficiency/time

According to the given data in the question:

Let efficiency of sofia be 1, then efficiency of elsa is 3.

We have time for 21 minutes

total work =efficiency/time

time for sofia = 3x and that of elsa = 1x

then time= 4x = 21 = 5.25= x

time taken by sofia is 3(5.25) = 15.75 minutes

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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:

x = -4

The x+43 angle is 39 degrees

The x+66 angle is 62 degrees

======================================================

Explanation

Rule: The three inside angles of any triangle always add to 180 degrees.

In this case we can say the following

(x+43)+(x+66)+(79) = 180

2x+188 = 180

2x = 180-188

2x = -8

x = -8/2

x = -4

That leads us to

The three interior angles of this triangle are

They add to 39+62+79 = 180 to confirm the answer.

Answer:

4 and 4

Step-by-step explanation:

using the rule of logarithms

[tex]log_{b}[/tex] x = n ⇒ x = [tex]b^{n}[/tex]

(a)

let [tex]log_{3}[/tex] (81) = n , then

81 = [tex]3^{n}[/tex] = [tex]3^{4}[/tex] with n = 4

then [tex]log_{3}[/tex] (81) = 4

(b)

note that log(10,000) = [tex]log_{10}[/tex] (10,000)

let [tex]log_{10}[/tex] (10,000) = n , then

10,000 = [tex]10^{n}[/tex] = [tex]10^{4}[/tex] with n = 4

then log(10,000) = 4

The shares of $2.25 are 200 and the shares of $2.75 are 700.

According to the question,

We have the following information:

An investor bought 700 shares of stock, some at $2.25 per share and some at $2.75 per share. And the total cost was $1825.00.

Now, let's take the shares of $2.25 to be x and the shares of $2.75 to be y.

So, we have the following expression:

x+y = 700

x = 700-y ....(1)

2.25x+2.75y = 1825 ...(2)

Putting the value of x from equation 1:

2.25(700-y)+2.75y = 1825

1575-2.25y+2.75y = 1825

1575+0.5y = 1825

0.5y = 250

y = 250/0.5

y = 500

Now, putting the value of y in equation 1:

x = 700-y

x = 700-500

x = 200

Hence, the shares of $2.25 are 200 and the shares of $2.75 are 700.

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Answer:

Step-by-step explanation:

You can determine whether a function is increasing or decreasing by taking its derivative.

If the derivative is bigger than 0, then function is increasing.

If the derivative is less than 0, then the function is decreasing.

You can also graph the functions to determine whether they are increasing or decreasing.

Answer:-2.326

Step-by-step explanation:i believe it's that

Answer:

c. 11x + 4x = 180; x = 12

Step-by-step explanation:

If m||n, then angle 11x and angle 4x must be same-side interior angles, which means they are supplementary (adds up to 180 degrees). This means we can set up the equation

11x + 4x = 180

15x = 180

x = 12

Answer:

I do not see any answer to this problem besides only simplifying

Therefore, there is no solution, unless if your question was a typo error.

Thank you.

The value of the expression a^2 - 2ac + 5b is, 175.

What is the value of expression?

When the variables and constants in the expression are given values, the calculation that this expression describes yields the value. In an algebraic expression, letters can substitute for numbers.

Consider, the given expression,

a^2 - 2ac + 5b

The values of a, b and c are

a = -8, b = 3, c = 6.

Plug these values in the above expression,

So, the expression becomes

(-8)^2 - 2(-8)(6) + 5(3) = 64 + 96 + 15 = 175

Hence, the value of the expression is, 175.

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The answer for the part 1 I=1500, part 2: R = 2.5% and part 3: T=1year, using Simple interest, Rate and Time.

What is simple interest and Rate?

A quick and simple way to figure out interest on money is to use the simple interest technique, which adds interest at the same rate for each time cycle and always to the initial principal amount. Any bank where we deposit our funds will pay us interest on our investment. One of the different types of interest charged by banks is simple interest. Now, before exploring the idea of basic curiosity in further detail,

The formula for simple interest is:

S = p*t*r/100

where P is the principal amount of money, R is the interest rate as a decimal, T is the time.

Given part 1: P=$3000,R=10%,T=5 yrs.

I = 3000*10*5/100 = 1500

part 2: P=$8000,T=4 yrs,I=$800

R= 800*100/8000*4 = 2.5%

part3: P=$2000,R=20%,I=$400

So T = 400*100/2000*20 = 1 year

Hence the answer for the part 1 I=1500, part 2: R = 2.5% and part 3: T=1year

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5 qt of oil cost $6.25 when twelve quarts of oil cost $15.00.

The unitary approach is frequently helpful for multiplying and dividing by fractions because it is intuitive and, assuming the numbers add up, may be performed mentally. As a result, it might be a useful way to explain or introduce the often used written algorithms for fractions, especially division by a fraction. The unitary approach involves calculating the value of a single unit, from which we can calculate the values of the necessary number of units.

Given,

12 qt = 15.00

For one unit, we will use unitary method:

1 qt = 15/12

1 qt = 5/4

For 5 qt of oil:

5 qt = 5/4 × 5

5 qt = 25/4

Converting it in decimals:

5 qt = 6.25

5 qt of oil cost $6.25 when twelve quarts of oil cost $15.00.

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The dimensions which will give Margo the largest area is 6 m by 6 m

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.

Given that, Margo has 24 meters of wood to build a fence around her garden. She wants to create the largest area possible

Let the length  be L and the width be W

So the perimeter equation is

2L + 2W = 24

2(L+W) = 24

L+ W= 12

L= 12-W

To find the largest area

area = L×W

area = (12-W) ×W

area= 12W- W²

A= -W²+ 12W

The vertex of the parabola is the point (h, k) where h=

= 6

to find the k part

k= (-6)² + 12(6)= 108 m²

The largest possible area is  108 m²

putting the value of W  in

L= 12-W

L= 12-6 = 6 m

Hence, the length and width is same, 6 m by 6 m

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