find the derivative of the given function at the indicated point f(x)=1/x a=2

Answers

Answer 1

Final answer:

The derivative of the function f(x) = 1/x at x = 2 is -1/4, found using the power rule of differentiation.

Explanation:

To find the derivative of the function f(x) = 1/x at the point where a = 2, we employ the power rule of differentiation. The function can be rewritten as f(x) = x-1. Applying the power rule (f'(x) = n*xn-1) to this function, the derivative is f'(x) = -1*x-2 or f'(x) = -1/x2. To find the derivative at x = 2, we simply substitute x with 2, giving us f'(2) = -1/22 = -1/4.

Related Questions

Carl is boarding a plane. He has 2 checked bags of equal weight and a backpack that weighs 4 kg. The total weight of Carl's baggage is 35kg. Write an equation to determine the weight, w ww, of each of Carl's checked bags. Find the weight of each of his checked bags.

Answers

Let B equal how many bags

2+4b=35

35-2=33

33/4=8.25kgs

Answer:

15.5 kg (each)

Step-by-step explanation:

Let [tex]w[/tex] be the weight of each checked bag (there are 2). Thus, we can write, from the information given:

[tex]w+w+4=35\\2w+4=35[/tex]

Now we solve this equation for [tex]w[/tex] to find weight of each checked bag:

[tex]2w+4=35\\2w=35-4\\2w=31\\w=\frac{31}{2}\\w=15.5[/tex]

So, the weight of each of his checked bags is 15.5 kg.

Which inequality will have a shaded area above its graph?

a
x − 9y ≤ 1
b
4x + 3y < 6
c
2x − y ≥ 4
d
x − 3y > 4

Answers

x − 9y ≤ 1

Because If you solve the equation y will be greater than ...

x − 9y ≤ 1

Solve for y...

Subtract x from both sides...

- 9y ≤ - x + 1

Divide both sides by -9

REMEMBER WHEN DIVIDING OR MULTIPLYING BY A NEGATIVE NUMBER FLIP THE INEQUALITY SIGN....

y ≥ x/9 - 1/9

To find the inequality whose graph is shaded *above* the line, you’ll have to find the inequality in which y is greater than the right side of the inequality. This boils down to isolating y in each of these, but there’s a bit of a shortcut you can take if you know about how multiplying/dividing both sides of an inequality by a negative number flips the inequality.

If the coefficient of y is negative, you’ll have to flip the inequality sign around in the process of isolating y. Which of those options have negative coefficients for y, and how would flipping the inequality sign effect them? Try to find the one option where the inequality ends up facing the y.

does velocity or mass impact momentum more and why

Answers

as the mass of an object increases the object will be gaining more velocity and the impact of the object would be that the momentum will be very high... also its pretty much common sense bc since the mass of the car is so heavy it makes it more difficult to stop. so for example To understand this think about stopping a car. If the breaks are applied gently, the momentum of the car is changed gradually over a long period of time and the force on you the passenger is slight. If you STOMP on the breaks, the momentum of the car changes immediately and the force on the passenger is great. The impulse is the same for the two situations but the time and force are different.

Final answer:

Both mass and velocity equally affect momentum in classical physics. However, at relativistic speeds, velocity has a more significant effect on momentum due to relativistic mass increase.

Explanation:

The impact of mass and velocity on momentum depends on the context of the object's motion. In classical physics, momentum is defined as the product of an object's mass and velocity, thus both mass and velocity equally influence momentum. However, for objects moving at relativistic speeds—approaching the speed of light—the effect of velocity on momentum is more pronounced due to the relativistic mass increase. To illustrate, a football player with greater mass has a larger impact due to having more momentum when moving at the same velocity as a player with less mass. In contrast, at relativistic speeds, an increase in velocity would result in an exponentially greater momentum, surpassing the effect of just increasing mass.

What is a security deposit

Answers

ecurity deposit is any money a landlord takes from a tenant other than the advance payment of rent. The security deposit serves to protect the landlord if the tenant breaks or violates the terms of the lease or rental agreement. It may be used to cover damage to the property, cleaning, key replacement, or back rent.

Any money a landlord takes from a tenant other than the advanced payment for rent . It's also protection for the landlord if the tenant violates the term of the lease agreement

Bill weighs 120 lbs and is gaining ten lbs each month. Phil weighs 150 lbs and is gaining four lbs each month. How many months will it take for bill to wiegh the same as phil?

Answers

First, let's write two expressions, letting x= the number of months which have elapsed:

Bill: 120 + 10x
Phil: 150 + 4x

If we set them equal to each other, then solve for x, that will be the number of months where their weights equal each other:

120+10x = 150 + 4x [starting equation]
-120 -4x -120 -4x [ subtract 120 from both sides, and 4x from both sides, to isolate the term with the variable]

6x = 30 [divide both sides by 5]
5 5

x=6. They will weigh the same in six months.

Algebraic equations are equations that contain variables that are unknown. These unknown variables are represented by any letters of the Alphabet.

it will take 5 months for Bill to weigh the same as Phil.

Let's represent the number of months they gain extra weight as: m

Step 1

Bill weighs 120 lbs and is gaining ten lbs each month. The algebraic equation for the above statement is :

120 ib + 10 ib x m

120 + 10m ........Equation 1

Phil weighs 150 lbs and is gaining four lbs each month. The algebraic equation for the above statement is :

150 ib + 4 ib x m

150 + 4m ........Equation 2

Step 2

We equate equations 1 and 2 to each other

Equation 1 = Equation 2

120 + 10m = 150 + 4m

Collect like terms

10m - 4m = 150 - 120

6m = 30

Divide both sides by 6

6m/6 = 30/6

m = 5

Therefore, it will take 5 months for Bill to weigh the same as Phil

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What is the value for ƒ(x) = 4²ˣ - 100 when x = 2 ?

Answers

The answer is: " 156 " .
__________________________________________
Given: f(x) = 4^(2x) - 100 ;
__________________________________________
When "x = 2" ;

f(2) =4^(2*2) - 100 = [4^(4) ] - 100 ;

= (4* 4 * 4 * 4) - 100 ;

= (16 * 4 * 4) - 100 ;

= (64 * 4) - 100 ;

= (256) - 100 ;

= 156 .
____________________________________

Answer:

f(x)=156

Step-by-step explanation:

Two lines that do not intersect are parallel.alwayssometimesnever

Answers

its always. When you have parallel lines, the lines never touch.

Divide. 42/−8 Enter your answer as a mixed number, in simplified form, in the box.

Answers

-5 and 1/4. hope it helps

How to solve more complex problems involving angles the backwards Method

Answers

What are you asking?

The game of clue involves 6 suspects, 6 weapons, and 9 rooms. one of each is randomly chosen and the object of the game is to guess the chosen three. (a) how many solutions are possible? in one version of the game, the selection is made and then each of the players is randomly given three of the remaining cards. let s, w, and r be, respectively, the numbers of suspects, weapons, and rooms in the set of three cards given to a specified player. also, let x denote the number of solutions that are possible after that player observes his or her three cards. (b) express x in terms of s, w, and r. (c) find e[x].

Answers

Part A:

Given that the game of clue involves 6 suspects, 6 weapons, and 9 rooms.

The number of ways that one of each is randomly chosen is given by:

[tex] ^6C_1\times{ ^6C_1}\times{ ^9C_1}=6\times6\times9=324[/tex]

Therefore, the number of solutions possible is 324.

Part B:

Given that a players is randomly given three of the remaining cards, let s, w, and r be, respectively, the numbers of suspects, weapons, and rooms in the set of three cards given to a specified player.

The number of suspects, weapons, and rooms remaining respectively after the player observes his or her three cards are: 6 - s, 6 - w, and 9 - r.

Let x denote the number of solutions that are possible after that player observes his or her three cards, then:

[tex]x={ ^{6-s}C_1}\times{ ^{6-w}C_1}\times{ ^{9-r}C_1}=(6-s)(6-w)(9-r)[/tex]

Therefore, x in terms of s, w, and r is given by x = (6 - s)(6 - w)(9 - r).

Part C:

The expected value E(x) of a data set [tex]x_i[/tex] with probabilities [tex]p(x_i)[/tex] is given by [tex]E(x)=\Sigma xp(x)[/tex]

There are [tex] ^{3+3-1}C_{3-1}={ ^5C_2}=10[/tex] possible combinations s, w and r. They are (3, 0, 0), (0, 3, 0), (0, 0, 3), (2, 1, 0), (0, 2, 1), (1, 0, 2), (2, 0, 1), (1, 2, 0), (0, 1, 2), (1, 1, 1)

Thus the expected value is given by

[tex]E(x)=3\cdot6\cdot9p(3, 0, 0)+6\cdot3\cdot9p(0, 3, 0)+6\cdot6\cdot6p(0, 0, 3) \\ 4\cdot5\cdot9p(2, 1, 0)+6\cdot4\cdot8p(0, 2, 1)+5\cdot6\cdot7p(1, 0, 2)+4\cdot6\cdot8p(2, 0, 1) \\ +5\cdot4\cdot9p(1, 2, 0)+6\cdot5\cdot7p(0, 1, 2)+5\cdot5\cdot8(1, 1, 1) \\ \\ = \frac{1}{ ^{21}C_3} (162\cdot{ ^6C_3}\cdot{ ^6C_0}\cdot{ ^9C_0}+162\cdot{ ^6C_0}\cdot{ ^6C_3}\cdot{ ^9C_0}+216\cdot{ ^6C_0}\cdot{ ^6C_0}\cdot{ ^9C_3} \\ \\ +180\cdot{ ^6C_2}\cdot{ ^6C_1}\cdot{ ^9C_0}+192\cdot{ ^6C_0}\cdot{ ^6C_2}\cdot{ ^9C_1}[/tex]

[tex]+210\cdot{ ^6C_1}\cdot{ ^6C_0}\cdot{ ^9C_2}+192\cdot{ ^6C_2}\cdot{ ^6C_0}\cdot{ ^9C_1}+180\cdot{ ^6C_1}\cdot{ ^6C_2}\cdot{ ^9C_0} \\ \\ +210\cdot{ ^6C_0}\cdot{ ^6C_1}\cdot{ ^9C_2}+200\cdot{ ^6C_1}\cdot{ ^6C_1}\cdot{ ^9C_1} \\ \\ =\frac{1}{1,330}(324\cdot20+216\cdot84+360\cdot90+384\cdot135+420\cdot216+200\cdot324) \\ \\ =\frac{1}{1,330}(6,480+18,144+32,400+51,840+90,720+64,800) \\ \\ =\frac{1}{1,330}(264,384) \\ \\ =\bold{198.78}[/tex]

Answer:

(a) 324 solutions are possible

(b) (6 - s)(6 - w)(9 - r)

Step-by-step explanation:

Just a pure guess and also give brainliest to the other person

The profits of a company are found by subtracting the company's costs from its revenue. If a company's cost can be modeled by 14x + 120,000 and its revenue can be modeled by 40x - 0.0002x^2, what is an expression for the profit?

Answers

The profit function is given by [tex]$ P(x) = -0.0002x^2 + 26x - 120,000 $.[/tex]

To find the expression for the profit, we need to subtract the cost function from the revenue function.

Given:

Cost function: [tex]$ C(x) = 14x + 120,000 $[/tex]

Revenue function: [tex]$ R(x) = 40x - 0.0002x^2 $[/tex]

The profit function, ( P(x) ), is given by:

[tex]\[ P(x) = R(x) - C(x) \][/tex]

Substitute the given functions into the profit function:

[tex]\[ P(x) = (40x - 0.0002x^2) - (14x + 120,000) \][/tex]

Now, let's simplify:

[tex]\[ P(x) = 40x - 0.0002x^2 - 14x - 120,000 \][/tex]

[tex]\[ P(x) = 26x - 0.0002x^2 - 120,000 \][/tex]

This is the expression for the profit:

[tex]\[ {P(x) = -0.0002x^2 + 26x - 120,000} \][/tex]

So, the profit function is given by [tex]$ P(x) = -0.0002x^2 + 26x - 120,000 $.[/tex]

Simplify 2y^2-7y-15/3y^2-8y-2 9y^2-1/4y^2-9 / y^2+3y-10/2y^2-9y+9

Answers

2y2−7y−‌153‌y2−8y−29y2−‌14‌y2−‌9y2‌+3y−‌102‌y2−9y+9=‌‌−1494‌y4−21y3+9y2−9y2‌=‌−149y4−84y3+36y2−364yy‌=‌−149y4−84y3+36y2−364y2

MARTIN CHARGES $10 FOR EVERY 5 BAGES OF LEAVES HE RAKES. LAST WEEKEND, HE RAKED 24 BAGES OF LEAVES. HOW MUH MONEY DID HE AERN

Answers

I think it would be $240 because you would multiply 10 ×24... at least I'm pretty sure

A clinical trial was conducted to test the effectiveness of the drug zopiclone for treating insomnia in older subjects. before treatment with zopiclone, 16 subjects had a mean wake time of 102.8 minutes. after treatment with zopiclone, the 16 subjects had a mean wake time of 98.9 minutes and a standard deviation of 42.3 minutes (based on data from cognitive behavioral therapy vs zopiclone for treatment of chronic primary insomnia in older adults," by silverstein et al., journal of the american medical association, vol. 295, no. 24). assume that the 16 sample values appear to be from a a normally distributed population and construct a 98% confidence interval estimate of the mean wake time for a population with zopiclone treatments. what does the result suggest about the mean wake time of 102.8 minutes before the treatment

Answers

Final answer:

To construct a 98% confidence interval estimate of the mean wake time for a population with zopiclone treatments, use the formula: Confidence interval = sample mean ± (critical value * standard deviation / square root of sample size).

Explanation:

To construct a 98% confidence interval estimate of the mean wake time for a population with zopiclone treatments, we can use the formula:

Confidence interval = sample mean ± (critical value * standard deviation / square root of sample size)

Given that the sample mean after treatment with zopiclone is 98.9 minutes, the standard deviation is 42.3 minutes, and the sample size is 16, we need to find the critical value for a 98% confidence level. The critical value can be found using a t-distribution table or calculator.

Once the critical value is obtained, we can plug in the values into the formula to calculate the confidence interval estimate.

What is the perimeter of a polygon with vertices at (−2, 1) , (−2, 4) , (2, 7) , (6, 4) , and (6, 1) ?

Enter your answer in the box. Do not round any side lengths.

Answers

Let A, B, C, D, E be the given points in order.
AB=4-1=3
BC=√((7-4)²+(2-(-2))²)=√(9+16)=√25=5
CD=BC=5
DE=4-1=3
AE=6-(-2)=8
Perimeter=3+5+5+3+8=24.

Using the distance formula, the perimeter of the polygon that has the given vertices is calculated as: 24 units.

What is the Perimeter of a Polygon?

Perimeter = sum of all sides of the polygon.

Name the vertices as follows:

A(−2, 1)B(−2, 4)C(2, 7)D(6, 4) E(6, 1)

Perimeter of the polygon = AB + BC + CD + DE + EA

Use the distance formula, [tex]d = \sqrt{x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex], to find the length of each segment:

AB = |1 - 4| = 3 units

BC = √[(2−(−2))² + (7−4)²]

BC = 5 units

CD = √[(2−6)² + (7−4)²

CD = 5 units

DE = |4 - 1| = 3 units

EA = |6 - (-2)| = 8 units

Perimeter of the polygon = 3 + 5 + 5 + 3 + 8

Perimeter of the polygon = 24 units

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Graph each line y -7 = x + 4

Answers

Given the the equation: y − 7 = x + 4 ;

We should rewrite the equation in "slope-intercept form" ; that is:

" y = mx + b " ;
______________________
in which: "y" remains an isolated variable on the "left-hand side" of the equation (with "no coefficients"—except the "implied coefficient of "1"
{since "1" , multiplied by any value, results in that same value} ;

"m" refers to the "slope" of the line;
and "m" is the coefficient of "x" ;

"b" refers to the "y-intercept" of the graphed (linear) equation; or more precisely, the value of "y" of the coordinate of the [ point on the graphed line of the equation—where the line crossed the "y-axis" ] ; that is; the "y-coordinate of the "y-intercept" ; that is, the value of "y" when "x = 0" ;
______________________________________________________
{Note that: "m" (the slope) may be a negative value; & that: "y" may be a negative value; as regard to the "slope-intercept form" equation:
that is:
"y = mx + b" . }.
______________________________________________________
So; given the equation:
______________________________________________________
" y − 7 = x + 4 " ;
______________________________________________________
Add "7" to each side of the equation;
to isolate "y" on one side of the equation;
→ {specifically, the "left-hand-side" of the equation} ;

and to rewrite the equation in "slope-intercept form" ; that is;
→ to rewrite the equation in the format:
" y = mx + b " ;
_______________________________________________________
As such: "y − 7 = x + 4 " ;
_______________________________________________________
→ Add "7" to each side of the equation:
_______________________________________________________
→ y − 7 + 7 = x + 4 + 7 ;

to get:
_______________________________________________________
  → y = x + 11 ;
_______________________________________________________
Now, let us graph the equation:
_______________________________________________________
Let us make a table:
_______________________________________________________
x ║ (x + 11) ║ y ║
_______________________________________________________
-20 ║ (-20 + 11) ║ -9 ║

-19 ║ (-19 + 11) ║ -8 ║

-18 ║ (-18 + 11) ║ -7 ║

-17 ║ (-17 + 11) ║ -6 ║

-16 ║ (-16 + 11) ║ -5 ║

-15 ║ (-15 + 11) ║ -4 ║

-14 ║ (-14 + 11) ║ -3 ║

-13 ║ (-13 + 11) ║ -2 ║

-12 ║ (-12 + 11) ║ -1 ║

-11 ║ (-11 + 11) ║ 0   ║

-10 ║ (-10+ 11) ║ 1 ║

-9 ║ (-9 + 11) ║ 2 ║

-8 ║ (-8 + 11) ║ 3 ║

-7 ║ (-7 + 11) ║ 4 ║

-6 ║ (-6 + 11) ║ 5 ║

-5 ║ (-5 + 11) ║ 6 ║

-4 ║ (-4 + 11) ║ 7 ║

-3 ║ (-3 + 11) ║ 8 ║

-2 ║ (-2 + 11) ║ 9 ║

-1 ║ (-1 + 11) ║ 10 ║

0 ║ (0 + 11) ║ 11 ║

1 ║ (1 + 11) ║ 12 ║

2 ║ (2 + 11) ║ 13 ║

3 ║ (3 + 11) ║ 14 ║

4 ║ (4 + 11) ║ 15 ║

5 ║ (5 + 11) ║ 16 ║
_________________________________________________

Now, we plot these points on a graph, and draw a line through these points; the slope is "1" ; since the equation is:
" y = x + 11 " ; Note: The slope, "m", is "1", since there is an "implied coefficient of "1" ; i.e. " y = 1x + 11 " .
___________________________________
Graph of: "y = x + 11 " ;
_____________________________________

Final answer:

To graph y - 7 = x + 4, rewrite the equation in slope-intercept form as y = x + 11. Plot the y-intercept at (0, 11), choose another value for x to find a second point, like (1, 12), and draw the line through these points to visualize the dependence of y on x.

Explanation:

To graph the line given by the equation y - 7 = x + 4, we first need to write it in the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. So, we add 7 to both sides of the equation to get y = x + 11. This tells us the slope of the line is 1 (since for every increase by 1 in x, y increases by 1) and the y-intercept is 11 (this is where the line crosses the y-axis).

We can then plot the y-intercept on the graph by putting a point at (0, 11). To find another point, we can choose any value for x and solve for y. For example, if we choose x = 1, then y = 1 + 11 = 12, so another point on the line is (1, 12). By plotting these two points and drawing a line through them, we create the graph of the equation.

For more accurate results, plotting more points using various x values and connecting them would be ideal. This graphical representation illustrates the dependence of y on x.

It took Leo 3.5 hours to complete a route walking at a rate of 4.2 mph. How long would it take Leo to complete the same route walking at a rate of 2.8 mph?
plz give exact answer

Answers

Hope this helps! It's the equation in the middle of picture! Comment for any questions!

S = V*t
3.5 hrs * 4.2 mph = 14.7 mi
t = S/V
14.7 mi/ 2.8 mph = 5.25 hrs

Help

simply. this math problem

Answers

- 4 1/5 = -21/5 = -42/10

-13 1/10 = -131/10

-42/10 - -131/10=

-42/10 + 131/10 = 89/10 = 8 9/10

answer is A

−42/10+131/10=−42/10+131/10=−42+131/10=8910(Decimal: 8.9)Answer: A

Find the specific formula for the sequence. [−3,1,5,9,13,...]

Answers

x+4 is the specific formula for sequence [−3,1,5,9,13,...]

What is Sequence?

A sequence is defined as an arrangement of numbers in a particular order.

The given sequence is

−3,1,5,9,13,...

-3+4=1

1+4=5

5+4=9

9+4=13

As we can see above, to get from one number to the next it is simply adding 4. So the formula for sequence is x + 4.

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If an employer spends $30,000 for weight-lifting equipment for the company gym. The company charges $100 a year to each employee who wants to buy a gym pass. The pass is for an unlimited amount of uses. There are 50 employees that work for this company. How many years will it take to pay off the weight-lifting equipment if half of the employees buy the gym pass each year?

Answers

half of 50 is 25

25 *100 = 2500 a year

30,000 / 2500 = 12

it will take 12 years

Round 256 and 321 ( need to when rounding in the hundreds place do we not change the entire number?

Answers

Is it a decimal? If you mean 2.56 and 3.21, they are 2.6 and 3.2 rounded to the nearest tenth. To the nearest whole number, they would both be 3.

If they are whole numbers, rounded to the hundreds place would be 300 for both. Rounded to two digits would be 260 and 320, respectively.

Please clarify what you mean.

If 15% of x is 42, what is x?

Answers

"x" is 100%, and 42 is 15% of that, so, what's "x"?

[tex]\bf \begin{array}{ccll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ x&100\\ 42&15 \end{array}\implies \cfrac{x}{42}=\cfrac{100}{15}\implies x=\cfrac{42\cdot 100}{15}[/tex]

Write 15% as a fraction= 15/100= 3/20 times x=42 thats one equation.
3/20x=42
x= 42* 20/3 (reciprocal)
x=14*20
x=406

In triangle JKL, if line JK is equal to line JL, angle J equals 23x-4, angle K equals 4x-1, and angle L equals 9x-31, find x and the measure of each angle.

Answers

Based on the information about side JK = side JL, then we know it is at least an isosceles triangle. Furthermore, ∡K =∡L because they are the base angles in an isosceles triangle.
Equation: 4x - 1 = 9x - 31
Solved: x = 6
Angle measures: ∡J = 23(6) - 4 = 138 - 4= 134
∡K = ∡L = 23

m(∠J) = 134°, m(∠K) = 23° and m(∠L) = 23° is the answer.

From the figure attached,

JK and JL are equal sides of the triangle.m(∠J) = 23x - 4m(∠K) = 4x - 1m(∠L) = 9x - 31

Since, two sides JK and JL of ΔJKL are equal in measure,

Therefore, ΔJKL is an isosceles triangle.

By the property of an isosceles triangle, opposite angles of the equal sides are equal.

Therefore, m(∠K) = m(∠L)

4x - 1 = 9x - 31

9x - 4x = 31 - 1

5x = 30

x = 6

By substituting the value of 'x' in the measures of each angle,

m(∠J) = 23x - 4

= 23(6) - 4

= 138 - 4

= 134°

m(∠K) = 4x - 1

= 4(6) - 1

= 24 - 1

= 23°

m(∠L) = 9x - 31

= 9(6) - 31

= 23°

Therefore, m(∠J) = 134°, m(∠K) = 23° and m(∠L) = 23° will be the answer.

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Write an additional word problem in which the estimated sum is 14,000

Answers

10,000 + 4,000 = 14,000
7,000 + 7,000 = 14,000

Final answer:

The problem is about estimating the total sales sum of 7 TVs sold in a day, each priced at approximately $2,000, which gives us a total estimate of $14,000.

Explanation:

The mathematics problem could be something along the lines of this: In a local electronics store, 7 high-definition smart TVs were sold in one day. If each TV is approximately priced at $2,000, what is the estimated total sales sum for that day?

First, analyze the problem. We want to find the estimated total sales sum for the smart TVs.Then, we use estimation to solve it. We know each TV costs around $2,000 and that 7 TVs were sold.Just multiply $2,000 by 7. Thus, $2,000 * 7 = $14,000So, the estimated sum is $14,000

This estimation gives us a total sum of $14,000, which is close to the actual total if each TV is priced at $2,000.

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How many gallons is 15 percent of 55 gallons?

Answers

15% of 55 gallons is 46.75 gallons

Solve 4(c + 2) < 4c + 10.

Answers

4(c + 2)< 4c + 10
4c + 8 < 4c + 10
4c - 4c < 10 - 8
0 < 2...no variables
this inequality has no solution

[tex]4(c + 2) \ \textless \ 4c + 10[/tex]

[tex]4c+8\ \textless \ 4c+10 [/tex]

[tex]8\ \textless \ 10 [/tex] [tex]\text{Cancel 4c on both sides}[/tex]

[tex]\text{Since}[/tex] [tex]8\ \textless \ 10 [/tex] [tex]\text{is always true, there are infinitely many solutions}[/tex]

Choose the abbreviation of the postulate or theorem that supports the conclusion that the triangles are congruent.

Given:
∠C, ∠F are rt.∠'s; AC = DF; BC = EF

Answers

We're given two right triangles (since we're told that angle C and angle F are right angles)

The two legs, ie the sides adjacent to the right angle, for the two triangles are also given to be congruent to one another
leg AC = leg DF
leg BC = leg EF

Because we have two pairs of legs congruent for these two triangle triangles, we use the Leg Leg Theorem which abbreviates to the LL Theorem, or simply LL.

This is why the answer is choice B) LL

Answer:

Step-by-step explanation:

Odyssey

Determine the axis of symmetry the vertex and the x-and y intercepts f(x)=x2+2x-3

Answers

the axis of symmetry is: x=-1
The x- and y intercepts is: x- intercept: (1,0),(-3,0)
y intercept: (0,-3)

Hope this helps!:)

the axis of symmetry is: x=-1
The x- and y intercepts is: x- intercept: (1,0),(-3,0)
y intercept: (0,-3)

Write the following statement as a conditional. All flowers are beautiful.

Answers

If something is a flower, then it is beautiful.

Deshawn has several dimes and quarters that total $2.05. he has 3 fewer quarters than dimes. how many of each doe he have

Answers

Let
x = the number of dimes
y = the number of quarters

The total sum is $2.05, therefore
0.10x + 0.25y = 2.05
Divide through by 0.05 to obtain
2x + 5y = 41 (1)

There are 3 fewer quarters than dimes, therefore
y = x - 3 (2)

Substitute (2) into (1).
2x + 5(x - 3) = 41
2x + 5x - 15 = 41
7x = 56
x = 8
y = x - 3 = 5

Answer: 8 dimes, 5 quarters

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