Mathematics College

What is the average rate of change of f(x) = −2x + 1 from x = −5 to x = 1?

Answers

Answer 1

by calculating the slope, the average rate of change is -2
-1-11
---------
1--5

Answer 2

Answer:-2

Step-by-step explanation:

Related Questions

Estimated 65% of 152

Answers

Here you're asked for an estimate, not an exact answer.

Note that 65% is close to 66.666...%, or 2/3, and that 152 is close to 150.

2/3 of 150 is 100 (answer)

Amy has 1/2 hour to do 3 chores. She plans to spend the same fraction of an hour on each chore. She wants to use the number line to help her determine what fraction of an hour she can spend on each chore. What is the correct number label for point A?

Answers

Point A would be zero; Point B, the end of the 1/2-hour time interval, would be 1/2 (representing 1/2 hour). Then Amy needs to subdivide the interval A to B into three equal time intervals and to determine the length of each of these subintervals.

I would begin with 1/2 and divide that by 3:

1
--
2
====
3
--
1

Inverting the fraction in the denom. and multiplying, we get

1 1 1
-- * ---- = -----
2 3 6

So Amy will spend 1/6 th of an hour, or 10 minutes, on each chore.

Note that 3 times 1/6 comes out to 1/2 (hour), which is were we started.

A number changed to 12.6 after it was rounded. To what place waa the number rounded? Explain how you know

Answers

12.6 ...if it was rounded, it was rounded to the nearest tenths.....because ur 6 is in the tenths place

if it was 12.67 rounded, then it would have been rounded to the nearest hundredths place because ur last digit is in the hundredths place

and if it was 12.678 rounded, then it would have been rounded to the nearest thousandths place because ur last number is in the thousandths place

u get it ?

Answer:

The number round to nearest tenths.

Step-by-step explanation:

Given : A number changed to 12.6 after it was rounded.

To find : To what place was the number rounded?

Solution :

The number round when the last digit place value is greater than 5, then before that number rounds by 1 and change the number.

In number 12.6 it was rounded to the nearest tenths.

Which means the hundredths place is greater than 5 either 6,7,8 or 9 and the tenths place is definitely 5.

So, the number can be 12.56, 12.57, 12.58, 12.59

If they all round we get the number 12.6.

60 bricklayers began a 16-day project to build a castle. After five days, five of the bricklayers quit the job. If they work the same amount each day, how many extra day(s) (beyond the original estimate of 16) will the remaining bricklayers need?

Answers

The concept of answer this item is the man-days equation. This means that the man-days of the original plan should be equal to that of the real activity. From the given,

(60)(16) = (5)(60) + (11 + x)(60 - 5)

where x is the number of extra days that the bricklayers will still have to work to complete the job. The value of x from the equation is 1

Answer: 1

which of the fallowing is a factor? EXPLAIN:

Answers

Find two numbers that multiply to -28 (last term) and add to -3 (middle term)

Those two values are -7 and 4
-7 plus 4 = -3
-7 times 4 = -28

Since the numbers are -7 and 4, this means the given expression factors to (x-7)(x+4)

The two factors are x-7 and x+4

The factor x+4 isn't listed in the list of answer choices, so we can ignore it. The factor x-7 is listed as choice B, so that is the only answer.

We can solve for x using a technique called successive approximations. step 1: if we assume that x is very small compared to 0.100 (such that 0.100 x ≈ 0.100) then our first approximation of x (let\'s call it x1) can be calculated as

Answers

Supposed that we are given the equation:

7.20 x 10^-5 = x(0.100+x)^2

So assuming that x is very small so that:

0.100 + x ~ 0.100

and calling it x1, so:

7.20 x 10^-5 = x1 (0.100)^2

Then we simply solve for x1:

x1 = 7.20 x 10^-5 / (0.100)^2

x1 = 7.20 x 10^-3

Final answer:

Successive approximations involve iterative guesses to find a solution, Newton's Method refines initial guesses using derivatives, and the Intermediate Value Theorem guarantees a solution in a given interval.

Explanation:

Successive Approximations: When solving for x using successive approximations, we make iterative guesses, refining our estimation with each step. The method involves making an initial guess, then refining it until a sufficiently accurate solution is obtained.

Newton's Method: Newton's method is a numerical technique used to find roots of a function. It involves making an initial guess and then iteratively improving upon it by using the function's derivative.

Intermediate Value Theorem: The intermediate value theorem states that a continuous function that takes on values of opposite signs at two points must have at least one root within that interval.

Use the normal approximation to find the indicated probability. the sample size is n, the population proportion of successes is p, and x is the number of successes in the sample. n = 86, p = 0.68: p(54 x 61) 9)

Answers

To find the indicated propability we will use the normal approximization. The sample size is;n= 86, The population proportion of successes is;p= 0.68: and the number of successes in the sample is x
P(54 ≤ X≤ 61)
0.6330 is the answer in this question which is the probability.

What is an a priori proposition? an a posteriori proposition?

Answers

a priori means as things were in the beginning or at the start.
a posteriori means as things are after any event.

Final answer:

An a priori proposition is knowledge known through reason alone, such as mathematical truths, while an a posteriori proposition requires empirical experience, like knowledge of a physical location.

Explanation:

An a priori proposition is a type of knowledge or statement that is known to be true independently of experience. It relies on reason or logical deduction rather than empirical evidence. For example, mathematical truths, such as the statement "The square root of 9 is 3," are considered a priori because they can be known through reason alone. In contrast, an a posteriori proposition is one that requires experience or sensory input to be known. Empirical knowledge, like knowing the best route to a location, is typically a posteriori because it is based on observations from the world around us.

The foundational philosophical debate revolves around the nature of these propositions, with some philosophers questioning whether any knowledge is genuinely a priori or if all understanding comes from some form of experience. However, in many cases, a priori knowledge is associated with necessity, certainty, and independence from experience, while a posteriori knowledge is empirical and grounded in sense perception.

If you are making a scale drawing of a giraffe that is 6m tall, and the height of the giraffe in your drawing is 3 cm, what is the scale of the drawing?

Answers

Ok so, 1/x = would = 6/3 so then convert to centimeters then it would be 600/3
The equation would look like 1/x = 600/3 then simplify so you would get 200
meaning the ratio would be 1:200 PLEASE MARK BRANLIEST!
HOPE IT HELPS!!!!!

Answer:

The scale of the drawing of girrafe is [tex]1:200[/tex].

Step-by-step explanation:

Given: scale drawing of a giraffe that is [tex]6\rm\;{m}[/tex] tall, and the height of the giraffe in your drawing is [tex]3\rm\;{cm}[/tex].

As per question,

Dimension of giraffe is [tex]6\rm\;{m}[/tex] tall and height is [tex]3\rm\;{cm}[/tex].

For scaling the drawing, the given unit must be same.

As we know that,

[tex]1\rm\;{m}= 100\rm\;{cm}\\6\rm\;{m}=600\rm\;{cm}[/tex]

Therefore, scale of the drawing is [tex]3\rm\;{cm}:600\rm\;{cm}=1:200[/tex].

Hence, the scale of the drawing is [tex]1:200[/tex].

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Only the Fahrenheit one plz

Answers

The formula given is:
F = 1.8C + 32
The temperature C is given as -20
So, all you have to do is plug the given C temperature in the formula to get the corresponding F temperature as follows:
F = 1.8(-20) + 32 = -36 + 32 = -4 degrees Fahrenheit

A box contains marbles of five different colors: red, green, blue, yellow, and purple. there is an equal number of each color. assign probabilities to each color in the sample space. (give your answers as fractions.)

Answers

P(red) = 1/5 [that says "probability of getting red is one fifth"
P(green) = 1/5
P(blue) = 1/5
P(yellow) = 1/5
P(purple) = 1/5

The reason the fractions are all the same is that there are equal numbers of each color. For example, if there were 7 marbles of each color, there would be a total of 35 marbles.

P(red) = 7/35 = 1/5
Similar for the other colors.

Final answer:

To assign probabilities to each color in the sample space of marbles in a box, you need to determine the total number of marbles and the number of marbles of each color. Assuming there is an equal number of each color, the probability of drawing each color is 1/5.

Explanation:

To assign probabilities to each color in the sample space, we need to determine the total number of marbles and the number of marbles of each color. Since there is an equal number of each color, let's assume there are n marbles of each color.

The total number of marbles is 5n. The probability of drawing a red marble is n/5n = 1/5. Similarly, the probability of drawing a green marble is n/5n = 1/5, the probability of drawing a blue marble is n/5n = 1/5, the probability of drawing a yellow marble is n/5n = 1/5, and the probability of drawing a purple marble is n/5n = 1/5.

A major stadium has 45,000 seats. If baseball fans have bought 5/8 of the seats for the next game, how many seats are available?

Answers

if 5/8 were bought then 3/8 are still available ( 5/8 +3/8 = 1)

45000 * 3/8 = 135000/8 = 16,875 seats are still available

Which of the following numbers is not part of the solution to x ≤ -2?

-2

-2.45

-8

-1.76

Answers

This question is asking how many numbers out of the four possible answers fulfill the rule that x must be less than or equal to -2. So try out each number and see whether or not this statement is true, that is: is the number in place of x less than or equal to -2, or not?

-2: -2 fulfills the statement, as it is equal to -2.
-2.45: Also fulfills the statement, since it is less than -2.
-8: Once again fulfills the statement, as it is less than -2.
-1.76: DOES NOT fulfill the statement, it is greater than -2.

The answer would be -1.76

Answer:

i think it is -1.76

A car travels down a highway at 45 m/s. An observer stands 200 m from the highway.

How fast is the distance from the observer to the car increasing when the car passes in front of the observer?

How fast is the distance increasing 40 s later?

Answers

check the picture below.

so, the left-side is when the car is right in front of the observer, at that point, notice the y-distance, is pancaked, so is 0, but increasing, we know dy/dt is 45 m/s, and notice the "r" distance, is the same as the "x" distance, keeping in mind that whilst "r" is increasing or moving about, "x" is static, is a constant.

[tex]\bf \stackrel{\textit{pythagorean theorem}}{r^2=x^2+y^2}\implies 2r\cfrac{dr}{dt}=\stackrel{constant}{0}+2y\cfrac{dy}{dt} \\\\\\ 2r\cfrac{dr}{dt}=0+2(0)(45)\implies \cfrac{dr}{dt}=0[/tex]

now, 40 seconds later, since the car is going at 45 m/s, in 40 seconds it has covered 40 * 45 meters, or 1800, so y = 1800, x = 200, what is "r"?

[tex]\bf r^2=x^2+y^2\implies r=\sqrt{200^2+1800^2}\implies r=\sqrt{3280000} \\\\\\ r=\sqrt{200^2\cdot 82}\implies r=200\sqrt{82}\\\\ -------------------------------\\\\ 2r\cfrac{dr}{dt}=0+2y\cfrac{dy}{dt}\implies \cfrac{dr}{dt}=\cfrac{y\frac{dy}{dt}}{r}\quad \begin{cases} r=200\sqrt{82}\\ y=1800\\ \frac{dy}{dt}=45 \end{cases} \\\\\\ \cfrac{dr}{dt}=\cfrac{1800\cdot 45}{200\sqrt{82}}\implies \cfrac{dr}{dt}=\cfrac{405}{\sqrt{82}}\implies \cfrac{dr}{dt}=\cfrac{405\sqrt{82}}{82}[/tex]

Describe the additive inverse of a vector in the vector space.

Answers

I dont know what you mean by describe but the inverse is -v

please help im really dumb lol

Answers

Haha I do K12 WAVA too! Sorry, I'm not 100% sure of the answer, though. :)

Jan has a 12 ounce milkshake four ounces in the milkshake are vanilla and the rest is chocolate what are two equivalent fraction of the milkshake is vanilla

Answers

four ounces out of 12 ounces would be 4/12, or simplified form that would be 1/3, and the rest is 8/12, or 2/3.

Answer:

In this item, we are given that out of 12 ounces of ingredients comprising the milkshake, there are 4 ounces vanilla. Expressing this into fraction will give us an answer of 4/12. This fraction can be one of the answers. Since we are asked for two fractions, we can simplify 4/12 such that we get an equivalent fraction that is equal to 2/6. Hence, the answers to this question are 4/12 and 2/6...

hope it helps

Baruka has gallon of milk left in the 1/2 fridge. How many 5/64 gallon (10-ounce) servings of milk does she have left? Show your work

Answers

The question is written oddly...If you mean she has 1/2 a gallon left then she has 64 oz left so she has 6.4 10 oz servings left... 64 divided by 10=6.4

Baruka has [tex]$ \frac{32}{64} $[/tex] gallons left. [tex]$ \frac{32}{5} $ servings of $ \frac{5}{64} $[/tex] gallons; she has 6 servings.

To find out how many [tex]$ \frac{5}{64} $[/tex] gallon servings of milk Baruka has left, we need to first convert the amount of milk she has in gallons to the same unit as [tex]$ \frac{5}{64} $[/tex] gallons.

Since [tex]$ 1 $[/tex] gallon is equivalent to [tex]$ \frac{64}{64} $[/tex] gallons, and she has [tex]$ \frac{1}{2} $[/tex] gallon left, she has [tex]$ \frac{1}{2} \times \frac{64}{64} = \frac{32}{64} $[/tex] gallons left.

Now, we can find out how many [tex]$ \frac{5}{64} $[/tex] gallon servings are in [tex]$ \frac{32}{64} $[/tex] gallons:

[tex]\[ \frac{\frac{32}{64}}{\frac{5}{64}} = \frac{32}{5} \][/tex]

Now, we divide [tex]$ 32 $ by $ 5 $[/tex] to find the number of servings:

[tex]\[ \frac{32}{5} = 6.4 \][/tex]

So, Baruka has [tex]$ 6.4 $[/tex] servings of [tex]$ \frac{5}{64} $[/tex] gallon servings of milk left. However, since she can't have a fraction of a serving, she has [tex]$ 6 $[/tex] servings left.

The hypotenuse of right triangle ABC, line segment AC, measures 13 cm. The length of line segment BC is 5 cm. What is the approximate difference between m∠C and m∠A?

Answers

check the picture below.

make sure your calculator is in Degree mode, if you need the angles in degrees, or Radian mode if you need them in radians.

and their difference is clearly just C - A.

Answer

Difference between m∠C and m∠A= 44.76

Step-by-step explanation:

The hypotenuse of right triangle ABC, line segment AC, measures 13 cm. The length of line segment BC is 5 cm.

Hypotenuse AC = 13 cm

So angle B is right angle = 90 degrees

AC is the hypotenuse

BC is the adjacent side for C

cos (c)= adjacent side / hypotenuse

C= cos^-1(BC/AC)

[tex]C= cos^{-1}(\frac{5}{13})= 67.38[/tex]

angle B is a right angle= 90 degree

Angle C= 67.38 degrees

Sum of angles in a triangle is 180°

A + B +C = 180

A + 90 + 67.38 = 180

A= 180 - 90 - 67.38=22.62

Difference between m∠C and m∠A= 67.38 - 22.62=44.76

help .. Solve the literal equation cy−7=5d+3y for y .

Answers

The literal equation cy - 7 = 5d + 3y can be solved for y by first bringing all the y terms to one side, and then factoring y out and dividing by the remaining coefficient to isolate y. The solution is y = (5d + 7) / (c - 3).

To solve the literal equation cy - 7 = 5d + 3y for y, we need to isolate y on one side of the equation. First, we want to bring all the terms containing y to one side and the rest to the other side. We achieve this by subtracting 3y from both sides of the equation and adding 7 to both sides, leading to cy - 3y = 5d + 7.

Now, we factor y out of the terms on the left side thus: y(c - 3) = 5d + 7. Finally, we divide both sides by (c - 3) to get y by itself: y = (5d + 7) / (c - 3). Therefore, we have isolated y and expressed it in terms of c and d.

A bag contains 5 red marbles, two orange marbles, one yellow marbles, and two green marbles. Two marbles are drawn from the bag. What is the approximate probability of choosing an orange marble and a green marble?

Answers

green marble- probability is 2 out of 10
orange-1 out of 10

Answer: 0.04444

Step-by-step explanation:

Francis gets 6 paychecks in 12 weeks how many paychecks does she get in 52 weeks

Answers

She gets about 25 paychecks

Well, lets find out how many weeks it takes for him to get one paycheck:

Divide the time (12 weeks) by the number of checks (6 paycheck)

12/6 = 2

Francis gets one paycheck every two weeks.

Now to get the answer, simply divide the total (52 weeks) by 2.

52/2 = 26

The final answer is Francis gets 26 paychecks in 52 weeks.

Hope this helps!

a tennis ball machine serves a ball vertically into the air from a height of 2 feet, with an inital speed of 120 feet per second. What is the maximum height, in feet, the ball will attain?

Answers

check the picture below.

[tex]\bf ~~~~~~\textit{initial velocity}\\\\ \begin{array}{llll} ~~~~~~\textit{in feet}\\\\ h(t) = -16t^2+v_ot+h_o \\\\ \end{array} \quad \begin{cases} v_o=\stackrel{\textit{initial velocity of the object}}{120}\\\\ h_o=\stackrel{\textit{initial height of the object}}{2}\\\\ h=\stackrel{}{\textit{height of the object at "t" seconds}} \end{cases} \\\\\\ h(t)=-16t^2+120t+2[/tex]

[tex]\bf \textit{ vertex of a vertical parabola, using coefficients}\\\\ \begin{array}{llll} h(t)= &{{ -16}}t^2&{{ +120}}t&{{ +2}}\\ &\uparrow &\uparrow &\uparrow \\ &a&b&c \end{array}\qquad \left(-\cfrac{{{ b}}}{2{{ a}}}\quad ,\quad {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}\right) \\\\\\ \left(-\cfrac{120}{2(-16)}~~,~~2-\cfrac{120^2}{4(-16)} \right)\implies \left( \cfrac{15}{4}~~,~~2+\cfrac{14400}{32} \right)[/tex]

[tex]\bf \left( \cfrac{15}{4}~~,~~2+450 \right)\implies \left( \stackrel{seconds}{3\frac{3}{4}}~~,~~\stackrel{feet}{452} \right)[/tex]

Find the total amount due on a simple-interest loan if the principal is $3000 with a rate of 5% for 10 years.

Answers

Final answer:

The total amount due on the simple-interest loan is $4500.

Explanation:

To find the total amount due on a simple-interest loan, we can use the formula:

Total Amount = Principal + (Principal x Rate x Time)

Given that the Principal is $3000, the Rate is 5%, and the Time is 10 years, we can substitute these values into the formula to calculate the total amount:

Total Amount = $3000 + ($3000 x 0.05 x 10)Total Amount = $3000 + $1500Total Amount = $4500

Therefore, the total amount due on the loan is $4500.

Which expression is equivalent to 14a + 8?

14(a + 4)
7(7a + 1)
2(7a + 4)
14(a + 1)

Answers

The answer is 2(7a+4) because using distributive property 2 times 7a is 14a and 2 times 4 is 8 so it equals 14a+8

The solution is Option C.

The value of the equation A = 14a + 8 can be simplified to A = 2 ( 7a + 4 )

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

A = 14a + 8 be equation (1)

Now , the equation (1) can be simplified as

Taking the common term as 2 in the equation , we get

A = 2 ( 7a + 4 )

The 2 is taken as common term , and the multiples are the values 7a and 4

So ,

The value of A = 2 ( 7a + 4 )

A = 2 ( 7a ) + 2 ( 4 )

The value of A = 14a + 8

Therefore , the value of A is 2 ( 7a + 4 )

Hence ,

The value of the equation A = 14a + 8 can be simplified to A = 2 ( 7a + 4 )

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John is 3 years older than jim. jim is 4 years less than twice david's age. how old are the three boys if their ages add up to 35?

Answers

Here you go, hope this helps

Find the nth term of the follwing sequences 7,13,19,25

Answers

n=1+6x
Hope this helps!

7,13,19,25,31,37,43,49,55

n=55

Write an equation of the line that passes through (18, 2) and is parallel to the line 3y - x = -12

Answers

Final answer:

To find the equation of a line parallel to 3y - x = -12 that goes through the point (18, 2), first find the slope of the given line, which is 1/3. Then, use the point-slope form with the given point and the slope to write the equation of the desired line, which is y = (1/3)x - 4.

Explanation:

To write an equation of the line that passes through the point (18, 2) and is parallel to the line 3y - x = -12, we first need to find the slope of the given line. For a line to be parallel, it must have the same slope as the line to which it is parallel. We start by putting the equation of the given line in slope-intercept form (y = mx + b).

First, isolate y:
3y = x - 12
y = (1/3)x - 4

The slope (m) of the given line is 1/3. Our parallel line should have the same slope, so we'll use this slope and the point (18, 2) in the point-slope form of a line equation, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line.

Now, plug in the values:
y - 2 = (1/3)(x - 18)

This is the point-slope form of the equation for our parallel line. To put it into slope-intercept form, we distribute and simplify:

y - 2 = (1/3)x - 6
y = (1/3)x - 4

whats the answer for 5x+14=k

Answers

= -14/5 + k/5
please give me brainliest.

Simplifying 5x + 14 = k

Reorder the terms: 14 + 5x = k

Solving 14 + 5x = k

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-14' to each side of the equation.

14 + -14 + 5x = -14 + k

Combine like terms: 14 + -14 = 0
0 + 5x = -14 + k
5x = -14 + k

Divide each side by '5'. x = -2.8 + 0.2k

Simplifying x = -2.8 + 0.2k

Hope this helps :)
Brainliest would be great! but its ok if u don't

Drag a statement or reason to each box to complete this proof. If 4x+5=17 , then x=3 .

Answers

The answer fam is........

Statement Reason

1) 4x + 5 = 17 Given

2) 4x + 5 - 5 = 17 - 5 Subtraction property of equality

3) 4x = 12 Simplifying

4) 4x/4 = 12/4 Division property of equality

5) x = 3 Simplifying

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Answer:

Here it is!

Step-by-step explanation:

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