What is the average rate of change of f over the interval [3,4]?

Answer:

[tex]2 {x}^{2} + 5x - 3 = 0 \\ 2( {x}^{2} + \frac{5}{2} x - \frac{3}{2} ) = 0 \\ 2( {x}^{2} + \frac{5}{2} x + {( \frac{5}{4} )}^{2} ) - \frac{3}{2} - {( \frac{5}{4} )}^{2} ) = 0 \\ ( {(x + \frac{5}{4} )}^{2} = \frac{49}{16} \\ x + \frac{5}{4} = ± \frac{7}{4} \\ x = 0.5 \: \: and \: \: 3[/tex]

Answer:

x= [tex]\frac{1}{2}[/tex]     or     x= -3

Step-by-step explanation:

[tex]\boxed{x^{2} +kx=(x+\frac{k}{2})^{2} -(\frac{k}{2})^{2} }[/tex]

First ensure that the coefficient of x² is 1.

x² +[tex]\frac{5}{2}[/tex]x -[tex]\frac{3}{2}[/tex]= 0

[x +([tex]\frac{5}{2}[/tex] ÷2)]² -([tex]\frac{5}{2}[/tex] ÷2)² -[tex]\frac{3}{2}[/tex]= 0

(x +[tex]\frac{5}{4}[/tex])² -([tex]\frac{5}{4}[/tex])² -[tex]\frac{3}{2}[/tex]= 0

(x +[tex]\frac{5}{4}[/tex])²- [tex]\frac{25}{16}[/tex] -[tex]\frac{3}{2}[/tex]= 0

(x +[tex]\frac{5}{4}[/tex])² -[tex]\frac{49}{16}[/tex]= 0

(x +[tex]\frac{5}{4}[/tex])²= [tex]\frac{49}{16}[/tex]

x +[tex]\frac{5}{4}[/tex]= [tex]\sqrt{\frac{49}{16} }[/tex]                (square root both sides)

x +[tex]\frac{5}{4}[/tex]= ±[tex]\frac{7}{4}[/tex]

x= -[tex]\frac{5}{4}[/tex] +[tex]\frac{7}{4}[/tex]       or       x= -[tex]\frac{5}{4}[/tex] -[tex]\frac{7}{4}[/tex]

x= [tex]\frac{1}{2}[/tex]             or       x= -3

Answer:

Solution given:

perpendicular[p]=x

base[b]=11.6m

hypotenuse[h]=19.2m

by using Pythagoras law

h²=p²+b²

19.2²-11.6²=x²

x=[tex]\sqrt{234.08}[/tex]

x=15.3m

option

a.

15.3 m

Answer:

15.3 m

Step-by-step explanation:

c refers to the longest side (hypotenuse) whereas a and b referes to the two other smaller sides of atriangle.

pythagoras theorem

a^2 + b^2 = c^2

11.6^2 + x^2 = 19.2^2

134.56 + x^2 = 368.64

x^2 = 368.64 - 134.56

x^2 = 234.08

x=[tex]\sqrt{234.08[/tex]

x=15.29

x=15.3 m

Answer:

i think c

Step-by-step explanation:

Answer:

5.0625 is 1.5 to the fourth power

Answer:

8

Step-by-step explanation:

4 to the power of 3 is 64.

64 ÷ (7 − 3) × 2

64 ÷ (4) × 2

64 ÷ 8

8

Your answer is 8.

I hope this helps, have a nice day.

Me too. It's the third option. :)

Answer:

I think its the third bubble. Hopefullly this helps. im pretty sure its correct.

Step-by-step explanation:

1st. add rt to both sides so that it cancels out. That should give you xy= s+rt.

2nd. Then divide x from both sides to single out the y. since x is multiplying with y you must use the inverse operation and divide by X. This should leave you with y= (s+rt)÷x

Answer:

Step-by-step explanation:

Adding two rational numbers results in a positive sum.

Answer:

d

Step-by-step explanation:

dddddddddddddddddddd

Step-by-step explanation:

diamonds and hearts are red cards

spades and clubs are black cards

15+11=26

26/52 is the probability of selecting a black card, 50%

Answer:

6. Base

Step-by-step explanation:

In Mathematics, a power involves the multiplication of factors repeatedly. Thus, it's simply a multiplication (product) of repeated factors.

The base of a power is the common factor. When working with a power, the base is the number that is the common factor.

For example;

10⁴ = 10 * 10 * 10 * 10

Therefore, the base in the above expression is 10.

Additionally, the exponent is 4 and it represents the number of times the base "10" was used as a factor.

Answer:

I'm not the best at explaining but I'll try my best. The x value to the bottom right is 61 degrees because the two sides are equal. Knowing that, there are 180 degrees in a triangle and 61 degrees plus 61 degrees adds up to 122. So, the value for x at the top is 58 degrees.

Answer:

Step-by-step explanation:

Do this by making this 2-part function into one all-in. Do this by finding a common denominator and then writing the function as one, over the common denominator, x. When we do this we get the function:

[tex]y=\frac{3x^3-2}{x}[/tex] and we will use the rule for quotients, which is the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all over the denominator squared. For us, that is, in steps:

[tex]y'=\frac{x(9x^2)-(3x^3-2)(1)}{x^2}[/tex] which simplifies to

[tex]y'=\frac{9x^3-3x^3+2}{x^2}[/tex] which simplifies finally to

[tex]y'=\frac{6x^3+2}{x^2}[/tex]. Nothing else you do can make this any more simplified.

Answer:

x = 5/26

Hope this helps! GL!

Answer:

[tex]let \: total \: distance \: be \: x \\ 30\% \: of \: x = 9 \\ \frac{30}{100} \times x = 9 \\ 30x = 900 \\ x = 30 \\ total \: distance = 30 \: miles[/tex]

The total distance Mira plan to run is 30 miles.

Percentage is a way of expressing a number as a fraction of 100. It is often denoted using the symbol ‘%’. For example, 25% is the same as 25/100 or 0.25. Percentages are used to express how large or small one quantity is relative to another quantity.

Given that, Mira has run 9 miles.

Let the total distance be x miles.

Distance is 30% of the total distance she plans to run

Here, 30% of x =9

30/100 ×x=9

30x=900

x=900/30

x=30

Therefore, the total distance Mira plan to run is 30 miles.

To learn more about the percentage visit:

brainly.com/question/24159063.

#SPJ3

Answer:

I'll setup the problem and you can do the calculations

Step-by-step explanation:

Total length of straw - L

Length of piece 1 - x

Length of piece 2 - y

Length of piece 3 - z

What's given and the answer to (i)

y = x - 3

z = 2x

(ii) L = x + y + z = x + x - 3 + 2x

L = 4x-3

(iii) x = (21+3)/4 = 24/4

leaving you to calculate x

then substitute x into expressions for y & z above and you will have the answer

comment if you have questions

Answer:

(1,1)

Step-by-step explanation:

Graph: y = -x^2 + 2x

Answer:

The input for the method is a continuous function f, an interval [a, b], and the function values f(a) and f(b). The function values are of opposite sign (there is at least one zero crossing within the interval). Each iteration performs these steps: Calculate c, the midpoint of the interval, c = a + b2.

Step-by-step explanation:

---------------------------

Answer:

60 bacteria

Step-by-step explanation:

c on edge 2022

Answer:

{15, 16} or {-15, -16}

Step-by-step explanation:

Quick solution:

take half of the sum (approx. 240), sqrt(240)=15.5

So the numbers are 15 and 16.  and also the negative equivalents since squares are always positive.

Exact method:

Let

x=smaller integer,

x+1 = next integer.

sum:

x²⁺(x+1)^2 = 481

2x^2 + 2x + 1 = 481

2x^2 + 2x - 480 = 0

x^2 + x -240 = 0

x = 15 or x = -16

so the integers are

either

{15, 16} or {-15, -16}

The sum of the squares of two consecutive integers is 481 will be -15 & -16 and 15 and 16.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Successive numbers are those that follow one another continually, from lowest to biggest. For instance, the numbers 1, 2, 3, 4, 5, and so on are all consecutive.

Assume 'x' is the number and the successive number is (x + 1).

The sum of the square of the consecutive number is 481. Then the equation of the number is given as,

x² + (x + 1)² = 481

Simplify the equation, then we have

x² + (x + 1)² = 481

x² + x² + 2x + 1 = 481

2x² + 2x - 480 = 0

x² + x - 240 = 0

x² + 16x - 15x - 240 = 0

x(x + 16) - 15(x + 16) = 0

(x + 16)(x - 15) = 0

x = 15, -16

Then the successive numbers are given as,

x + 1 = 15 + 1

x + 1 = 16

x + 1 = - 16 + 1

x + 1 = - 15

More about the solution of the equation link is given below.

https://brainly.com/question/545403

#SPJ2

Answer:

x ≈ 7.7

Step-by-step explanation:

Using the sine ratio in the right triangle

sin69° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{HI}{GI}[/tex] = [tex]\frac{7.2}{x}[/tex] ( multiply both sides by x )

x × sin69° = 7.2 ( divide both sides by sin69° )

x = [tex]\frac{7.2}{sin69}[/tex] ≈ 7.7 ( to the nearest tenth )

Answer:

ST is 12 meters

Step-by-step explanation:

The given triangle ΔRST = An equilateral triangle

The altitude of ΔRST = SV

The length of segment RV = 6 meters

Given that ΔRST is an equilateral triangle, the base angles of the triangles = 60°, therefore, in the formed triangles, ΔRSV, and ΔTSV, ∠RSV = ∠TSV = 90° - 60° = 30°

∴ ΔRSV, and ΔTSV are congruent, based on ASA rule of congruency

∴ Side VT in ΔTSV is congruent to side RV in triangle ΔRSV  

The midpoint of side ST

VT ≅ RV

Therefore, VT = RV = 6 meters

RT = RV + VT = 6 + 6 = 12 By segment addition property

In equilateral triangle, ΔRST, all the sides are equal, therefore;

RT = RS = ST = 12 m

ST = 12 meters.

Answer:

dkfjrjdjcjejxjxjwjjxjdjcjxjxjsjbebebdndnd

Answer:

what do you want to ask about i will answer

Answer:

r = V^2/a

Step-by-step explanation:

Here, we want to write the formula for r

What this simply mean is that we want to make r the formula subject

We have this as follows;

a = V^2/r

r = V^2/a

Answer:

second option is correct

Step-by-step explanation:

[tex]\frac{x^0y^-3}{x^2y^-1}[/tex]

=x^0-2 *y-3-(-1)

=x^-2*y^-3+1

=x^-2*y-2

=[tex]\frac{1}{x^2y^2}[/tex]

Answer:

(-12x - 25) / (x + 3) (x - 5)

Step-by-step explanation:

1 - 2x/(x+3) + (x+3)/(x - 5)

= {(x + 3)(x - 5) - 2x(x - 5) + (x + 3)(x - 3)} / (x + 3) (x - 5)

= {(x² -5x + 3x - 16) - (2x² + 10x) + (x² - 3x + 3x - 9)} / (x + 3) (x - 5)

= x² - 2x - 16 - 2x² - 10x + x² - 9 / (x + 3) (x - 5)

= x² - 2x² + x² - 2x - 10x - 16 - 9 / (x + 3) (x - 5)

= (-12x - 25) / (x + 3) (x - 5)

Answer:

the answer is #1

Step-by-step explanation:

Answer:

1:2.25

12/12 = 1

27/12 = 2.25

Hope this helps!

Answer: It is a 3% chance

Answer:

David is six times older than Janet. If David is 48 years old, how old is Janet? Janet is 8 years old.

Step-by-step explanation:

48÷6=8

Answer:

(1,1)

Step-by-step explanation:

In the equation f(x), you are plugging in the x coordinate which in this case is one. That means in 1/4f(x), x will remain the same, because you are still plugging in the same thing. What will change is the y coordinate. 1/4f(x) is saying that the y coordinate will be a fourth of the original y coordinate(4). 4 times 1/4 is equal to one.

If the x coordinate stays the same, and the y coordinate is a fourth of 4, the corresponding points in the function f(x) will be (1,1)