QUESTION 1 1 POINT
Find the difference quotient
Provide your answer below:
f(a+h)-f(x)
h
f(x)=x²+x+2
Give a simplified expression involving and h, if necessary. For example, if you found that the difference quotient was
x+h, you would enter x + h.
Content attribution
for the function given below.
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The ratio of 50 hours to 30 hours is 1.33 hours.

What is ratio ?

ratio can be defined as the given value divided by the total value, called as the ratio.

Given ,

To find the ratio of 50 hours to 30 hours

let ratio of x to y is x/ y

similarly,

ratio = 50/30

ratio = 5/3

ratio = 1.33 hours.

in terms of minutes it is = (5/3) * 60

number of minutes = 100 minutes

so the ratio of 50 hours to 30 hours in terms of minutes = 100 minutes

Hence, The ratio of 50 hours to 30 hours is 1.33 hours.

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Answer:

To solve this problem, we need to use the concept of scale factor. The scale factor tells us how much larger or smaller an image is compared to the original image. In this case, the scale factor is 7/6, which means that the new image will be 7/6 times larger than the original image.

We can use the scale factor to find the dimensions of the new image. To do this, we simply multiply the dimensions of the original image by the scale factor.

Original dimensions: 24 cm x 12 cm

New dimensions: (24 cm x 7/6) x (12 cm x 7/6) = 28 cm x 14 cm

So, the dimensions of the photograph after it is sent through the photocopier are length 28 cm and width 14 cm.

Therefore, the correct answer is length 28 cm, width 14 cm.

This x = −8 value of x is included in x < 7.

What is the number line?

A number line is a type of line that can be used to show the positions of all numbers. It has two ends which start with -∞, and stops at +∞. A directed number is a number that is either negative or positive. Thus all directed numbers can be located on the number line.

The Real number line is just a number line. The point associated with the real number line is called the coordinate.

The number “0” represents the origin. All the positive numbers are represented on the right side of the origin, whereas all the negative numbers are represented on the left side of the origin.

The solution set x < 7 means all the values of x that are less than 7.

On a number line, all the values to the left of 7, including negative numbers and 7 itself are not included, are the solutions of the inequality x < 7.

Hence, This x = −8 value of x is included in x < 7.

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Answer:

Part A: [tex]T(t)=79e^{-0.015t}+19[/tex]

Part B: [tex]76.4^\circ \text{C}[/tex]

Step-by-step explanation:

Newton's law of cooling can be modeled with the general equation [tex]\displaystyle \frac{dT}{dt}=-k(T-T_a)[/tex] with solution [tex]\displaystyle T(t)=(T_o-T_a)e^{-kt}+T_a[/tex] for cooling. [tex]T(t)[/tex] represents the temperature of the coffee after [tex]t=45[/tex] minutes given the initial temperature [tex]T_o=98^\circ \text{C}[/tex] and room/air temperature of [tex]T_a=19^\circ \text{C}[/tex] with constant [tex]k[/tex].

Part A: Temperature of coffee after "t" minutes

[tex]T(t)=(T_o-T_a)e^{-kt}+T_a\\T(45)=(98-19)e^{-45k}+19\\60=79e^{-45k}+19\\41=79e^{-45k}\\\frac{41}{79}=e^{-45k}\\\ln(\frac{41}{79}) =-45k\\k\approx0.015\\T(t)=79e^{-0.015t}+19[/tex]

Part B: Average temperature of coffee after 45 minutes

[tex]\displaystyle T_{avg}=\frac{1}{b-a} \int\limits^b_a {T(t)} \, dt\\\\=\frac{1}{45-0}\int\limits^{45}_0 {(79e^{-0.015t}+19)} \, dt\\\\=\frac{1}{45}\biggr(\frac{79}{-0.015}e^{-0.015t}+19t\biggr)\biggr|_0^{45}\\ \\=\frac{1}{45}\biggr(\biggr(\frac{79}{-0.015}e^{-0.015(45)}+19(45)\biggr)+\frac{79}{0.015}\biggr)\\ \\\approx 76.4^\circ \text{C}[/tex]

Answer:

[tex](125)[/tex]

(5-2)(5_-1)2

The most money an individual is allowed to earn in accordance with the law is known as their maximum wage, also referred to as their wage ceiling.

The inequality be [tex]I=400 x+500y[/tex].

A maximum wage, often known as a wage ceiling, is the maximum amount of money an individual is permitted to make under the law.

The amount of money, property, and other transfers of value obtained over a predetermined period of time in return for services or goods are often referred to as "income." Income is defined in accordance with the context in which the word is employed; there is no single, universal definition.

Let x be the oak chairs produced

y be the walnut chairs produced

[tex]$$x+y \leq 20 \\ \\100 x+150 y \leq 2400 \\ \\x \geq 0 \\ \\y \geq 0 \\ \\ I=400 x+500 y\end{array}\right.$$[/tex]

The inequality be [tex]I=400 x+500y[/tex].

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Answer:

C

Step-by-step explanation:

Let x = number of toppings.

Pizza 4 U price:

14 + 1.25x

John's Pizza price:

10 + 1.5x

We want Pizza 4 U to be less expensive.

Pizza 4 U price < John's Pizza price

14 + 1.25x < 10 + 1.5x

-0.25x < -4

0.25x > 4

Answer: C

Answer:

C)  0.25x > 4

Step-by-step explanation:

Define the variable:

If Pizza 4 U charges $14 plus $1.25 per topping:

If John's Pizza charges $10 plus $1.50 per topping:

If Pizza 4 U is less than John's Pizza:

⇒ 14 + 1.25x < 10 + 1.5x

⇒ 4 + 1.25x < 1.5x

⇒ 4 < 0.25x

⇒ 0.25x > 4

Therefore, the inequality that could be solved to find the number of

toppings that makes Pizza 4 U less expensive than John's Pizza is:

There are 2 possible ways for Juan to pick exactly one purple counter.

The multiplication principle states that if there are m ways to perform one task and n ways to perform another task, then there are m x n ways to perform both tasks together.

We have two tasks from the question which are:

picking one purple counter from Box A and picking one purple counter from Box B.

To find the number of ways to pick one purple counter from Box A, we can use the formula for combination, which is: ⁿCᵣ = n! / (r! (n-r)!).

where n is the total number of counters in the box and r is the number of purple counters in the box.

we know that there are only green and purple counters in Box A, and since Juan wants to pick one purple counter, we can assume that there is one purple counter in the box.

so, the number of ways to pick one purple counter from Box A = 1.

Similarly, to find the number of ways to pick one purple counter from Box B

we know that there are green, purple and orange counters in Box B, and since Juan wants to pick one purple counter, we can assume that there are two purple counters in the box.

so, the number of ways to pick one purple counter from Box B = ²C₁ = 2.

Now, using the multiplication principle, we can find the total number of ways for Juan to pick exactly one purple counter:

1 x 2 = 2

Therefore, there are 2 possible ways for Juan to pick exactly one purple counter using the multiplication principle of counting

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Answer:

21.4 miles apart

Step-by-step explanation:

David calculations were wrong since the distance he measure were how far apart they both were together from the home and not from eachother.

simply just draw a line from the End point Jan is from Tim, you can see that it forms a third triangle to which you can use Pythagoras to figure the distance apart.

David already calculated the length of the two other sides being 13 and 17 so:

13^2 + 17^2 = c^2

458 = c^2

c = squareroot of 458

c = 21.4

therefore the distance between Jan and Tim was actually 21.4 miles

The proof that arc AB = arc CD is shown below

Given a circle with center O and chords AB and CD,

Such that AB = CD.

Considering a point P on arc AB and a point Q on arc CD

Such that AP = BP and CQ = DQ

Since OP = OQ and P and Q are on arcs AB and CD respectively,

It follows that angle POQ is equal to half the central angle of the circle that subtends the same arc as chord AB.

Similarly, arc AB is equal to the central angle of the circle that subtends arc CD.

Therefore:

POQ i= 1/2 * central angle of the circle and

Arc CD subtends twice the central angle as POQ.

Since the central angles subtended by arc AB and arc CD are equal, it follows that the arcs themselves are equal, i.e., AB = CD.

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The sprinkler's holes have to be 15mm apart and can have a 1mm allowance that space B is bigger than space A, and the notes in space B say "+2" while space A says "-3".

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Answer:

18

Step-by-step explanation:

y+17=35

y=18

The equation of the line that is parallel to y = 1/5(x + 4) is y = 1/5x + 37/5 or y = 1/5(x + 37). The graph is shown below.

Recall that when two lines are parallel to each other, they will have the same slope (m), and each can be expressed in slope-intercept form as y = mx + b.

Given the line, y = 1/5(x + 4), which can be rewritten as y = 1/5x + 4/5, the slope (m) = 1/5.

Substitute m = 1/5 and (x, y) = (3, 8) into y = mx + b:

8 = 1/5(3) + b

8 = 3/5 + b

8 - 3/5 = b

37/5 = b

b = 37/5

To write the equation of the parallel line, substitute m = 1/5 and b = 37/5 into y = mx + b:

y = 1/5x + 37/5

The graph of the lines are shown below.

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Answer: YESS

Step-by-step explanation: HOW DO WE HAVE THE SAME NAME? AND KOKUSHIBO IS THE UPPER MOON 1 DEMON I HAVE HIM AS MY PFP

Answer: Upper Moon 1

The second to strongest demon (technically third from Tanjiro.) Is the twin brother of Yoriichi.

On solving the provided question, we can say that the equation,  x² - 16x + 4 = 0 => ( x - 12)(x + 2) = 0 => x = 12, -2

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

the equation,

x² - 16x + 4 = 0

( x - 12)(x + 2) = 0

x = 12, -2

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Answer:

The relationship between Amy's age, a, and her sister's age is that her sister is 7 years less than twice Amy's age. To represent this relationship, we can use the equation:

2a - 7 = sister's age

This equation shows that the sister's age is equal to twice Amy's age minus 7.

Alternatively, we can use the equation:

a + (2a - 7) = 41

This equation shows that the sum of Amy's age and her sister's age is 41.

The correct equation is number 2. a + (2a - 7) = 41

0.45 names come to graduation.

Let's review the information given to us to answer the question correctly:

Rate of ceremony was observed was 66 feet, and 30 feet deep on both sides.

x = Number of feet both side

x + 30 =come to graduation

Solving for x:

66* (x + 30) = 30x/66

=0.45

x=0.45

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Answer:

12+4x

Step-by-step explanation:

multiply 3 by 4 and get 12.

then you multiply 4 by x and get 4x.

You then end up with 12+4x or 4x+12

Because there is only one intercept on the graph, the system of equations has a single solution.

When we have a system of equations, we can solve it graphically by graphing both equations on the same coordinate axis, and find the points where the graphs intercept.

Each one of these intercepts is a solution of the system of equations.

Here we can see that the system of equations is graphed, and there is a single intercept at the point (1, 3)

So the system has a single solution.

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Part (a)

[tex]D(1)=\frac{1000}{\sqrt{1}}-1=999 \\ \\ D(4)=\frac{1000}{\sqrt{4}}-1=499 \\ \\ \frac{D(4)-D(1)}{4-1}=\frac{499-999}{4-1}=\boxed{-\frac{500}{3}}[/tex]

Part (b)

[tex]D(100)=\frac{1000}{\sqrt{100}}-1=99 \\ \\ \frac{D(100)-D(4)}{100-4}=\frac{99-499}{100-4}=\boxed{-\frac{25}{6}}[/tex]

Answer:

Triangle NML

Step-by-step explanation:

Use the corresponding angles in the order they are stated and do the same for the other side. N corresponds to N on the other triangle. P corresponds to M on the other triangle, and Q corresponds to L on the other triangle. Now just say it as Triangle NML

If you still have any questions don't hesitate to ask!

Answer:

D

Step-by-step explanation:

Age and adress have quite less. In common

Answer:

A

Step-by-step explanation:

the number of pizzaordered

a) The angular speed is  1633 rad/min.

b) The speed is  1715 feet per minute.

We know that the angular speed would have to do with the speed with the object would move through a circular path. Let us note that in this case we have that the wheels turn at a rate of 260 revolutions per minute.

Now;

1 rev/min = 6.28 rad/min

260 revolutions per minute = 260 * 6.28/1

= 1633 rad/min

Given that;

v = rω

v = linear speed

r = radius

ω = angular speed

v = 1.05 feet *  1633 rad/min

v = 1715 feet per minute.

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[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

As we know, exterior angle of a triangle is equal to sum of the two internal angles that are not in linear pair with it (or opposite to that angle)

So, by using this property :

[tex]\qquad \sf  \dashrightarrow \: 4x + 80 \degree = 2x\degree + 108\degree[/tex]

[tex]\qquad \sf  \dashrightarrow \: 4x - 2x \degree = 108\degree - 80\degree[/tex]

[tex]\qquad \sf  \dashrightarrow \: 2x \degree = 28\degree [/tex]

[tex]\qquad \sf  \dashrightarrow \: x = (28 \div 2)\degree [/tex]

[tex]\qquad \sf  \dashrightarrow \: x = 14\degree [/tex]

Angle Q is equal to :

[tex]\qquad \sf  \dashrightarrow \: 2x [/tex]

[tex]\qquad \sf  \dashrightarrow \: 2 \times 14 \degree[/tex]

[tex]\qquad \sf  \dashrightarrow \: 28 \degree[/tex]

Answer:24

Step-by-step explanation:

75 percent *32

= (75/100)*32

= (75*32)/100

= 2400/100 = 24

Now we have: 75 percent of 32 = 24

The measure of the side b in the right triangle ABC is 8 units.

A right triangle is a triangle with one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees. The triangle ABC is a right angle triangle because it has one angle as 90 degrees.

Therefore, the side b can be found using trigonometric ratios.

Hence,

tan 45° = opposite / adjacent

tan 45° = b / a

tan 45° = b / 8

cross multiply

b = 8 tan 45°

b = 8 × 1

b = 8

Therefore,

length of b = 8 units.

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option c. 1 3/5

2/5 ÷ 2/8

= 2/5 × 8/2

= 8/5

= 1 3/5

Hence, option c. 1 3/5

Answer:

Step-by-step explanation:

Find 15 percent of 81.95 and add it to that.

The answer is 94.24 rounded.

The statement s(x) means that s is a function of x

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

s(x)

The above is a function notation

Generally, the expression f(x) means that f is a function of x

When f is replaced with s, we have

s is a function of x

Hence, the meaning is that "s is a function of x"

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