AABC ~ AQRS
Find the missing side length, m.
R
3
A
B
2
C
10
m = [?]
4
S

-15.7

Step-by-step explanation:

2

-15

-12

-10

-12

-18

-20

-25

-------

-110

7 divide by -110=-15.7

By chain rule, the first derivative of the composite function f(x) = \(4^{5\cdot x - 9}\) is equal to  \(4^{u}\) · 5 · ㏑ 4.

Herein we have the case of a composite function, that is, a function of the form f[u(x)]. Chain rule is a derivative rule used to find the derivative of composite functions, which is now defined:

df / dx = (df / du) · (du / dx)

If we know that u(x) = 5 · x - 9 and f(u) = \(4^{u}\), then the derivative of the compond function is:

df / du = \(4^{u}\) · ㏑ 4

du / dx = 5

Then, by chain rule:

df / dx = \(4^{u}\) · 5 · ㏑ 4

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Answer:

Step-by-step explanation:

The the terms be x and y

The sum of the terms = x+y

Difference of terms = x-y

Product of the sun and differences will be expressed as:

(x-y)(x+y) = x²-xy+xy-y²

(x-y)(x+y) = x²-y²

Hence the product of the terms is equivalent to the difference of two squares of the terms

I’m sorry I tried my best but I didn’t get the correct answer

Expand.

-5x-10=8x

−5x−10=8x

2 Add 5x5x to both sides.

-10=8x+5x

−10=8x+5x

3 Simplify  8x+5x8x+5x  to  13x13x.

-10=13x

−10=13x

4 Divide both sides by 1313.

-\frac{10}{13}=x

−

13

10

​

=x

5 Switch sides.

x=-\frac{10}{13}

x=−

13

10

​

Answer: x=− 13/10

​

Given

Find

Rewrite in the form of

Explanation

Here , we use the identity

so , the given function becomes

Final Answer

Therefore , the new function is

The algebraic expression of the mentioned statement will be 5x-3.

According to the question,

An unknown number is thought of, multiplied by 5, and then subtracted by 3 from the result.

Let the unknown number be taken as x.

If we have to write the statement mathematically by taking x as a variable, the algebraic expression will be,

x* (5), which is equal to 5x, (by taking the variable x and multiplying it with 5).

For the second step, the expression will be 5x -3, (by subtracting 3 from the previous result, that is, 5x).

Hence, algebraically the final statement will be 5x -3.

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-17 is less than -89, so it's A.

Answer:

2x = 65 + 75

2x = 140

x = 140/2

x = 70

Step-by-step explanation:

Answer:

2x = 65 + 75

2x = 140

x = 140/2

x = 70

Chelsea sold:

Aubree sold:

Subtracting the first equation from the second equation, it follows that:

Substitute x=20 into the first equation:

Cheese: 5p + 3c = 160

Aubree: 5p + 10c = 300

Pecan Cheesecake: $ 20

Chocolate Marble Cheesecake: $ 20

Answer:

210

Step-by-step explanation:

Answer:

Simplify ans: 3 x^2 y^-4

a no = x( x+2)

b no = 2x(x- 3)

c no = 5x(3- 2x^2)

d no.= 3x^2( 3+ x)

Hope this helps you

Answer:

see explanation

Step-by-step explanation:

Using the rules of exponents

\(\frac{a^{m} }{a^{n} }\) ⇔ \(a^{(m-n)}\) ( m > n)

\(\frac{a^{m} }{a^{n} }\) ⇒ \(\frac{1}{a^{(n-m)} }\) ( n > m )

Given

\(\frac{21x^6y^5}{14x^2y^9}\)

= \(\frac{21}{14}\) × \(x^{(6-2)}\) × \(\frac{1}{y^{(9-5)} }\)

= \(\frac{3}{2}\) × \(x^{4}\) × \(\frac{1}{y^{4} }\)

= \(\frac{3x^4}{2y^4}\) ← with positive exponents

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

(a)

x² + 2x ← factor out x from each term

= x(x + 2)

(b)

2x² - 6x ← factor out 2x from each term

= 2x(x - 3)

(c)

15x - 10x³ ← factor out 5x from each term

= 5x(3 - 2x²)

(d)

9x² + 3x³ ← factor out 3x² from each term

= 3x²(3 + x)

Answer:

y- intercept = - 5, slope = 8

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + b ( m is the slope and b the y- intercept )

y = 8x - 5 ← is in slope- intercept form

with slope m = 8 and y- intercept b = - 5

Answer: slope: 8, intercept: (0, −5)

Step-by-step explanation:

Find the Slope and y-intercept

y = 8x − 5

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

y = mx + b

Find the values of m and b using the form y = mx + b.

m = 8

b = −5

The slope of the line is the value of m, and the y-intercept is the value of b.

Slope: 8

intercept: (0, −5)

Answer:

Below

Step-by-step explanation:

4 [x-3] + 2    = y    is not discontinuous anywhere

However    4 / [x-3]  + 2   DOES have a discontinuity at x = 3 because this would cause the denominator to be zero <===NOT allowed !!

Answer:

52°

Step-by-step explanation:

it should always add up to 180°

The amount of money accumulated by investing R8000 at a 7.2% annual interest rate compounded annually over 10 years is approximately R12,630.47.

To calculate the amount of money accumulated by investing R8000 at a 7.2% annual interest rate compounded annually over 10 years, we can use the formula for compound interest:

A = P * (1 + r/n)^(nt)

Where:

A is the amount of money accumulated

P is the principal amount (initial investment)

r is the annual interest rate (as a decimal)

n is the number of times the interest is compounded per year

t is the number of years

In this case, the principal amount (P) is R8000, the annual interest rate (r) is 7.2% or 0.072 (as a decimal), the interest is compounded annually (n = 1), and the investment period is 10 years (t = 10).

Plugging in these values into the formula:

A = 8000 * (1 + 0.072/1)^(1*10)

A = 8000 * (1 + 0.072)^10

A ≈ R12,630.47

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Answer:

x=4

Step-by-step explanation:

9+x=13

x=4

Answer:

The number is 4

Step-by-step explanation:

Let the number = x

Nine more than a number: x +9

x + 9 = 13

Subtract 9 from both sides

x + 9 -9 = 13 - 9

x = 4

Answer: 6

Step-by-step explanation:  25x0.24=6

Answer:

6 ,. ...................

Alessia spent $5,408 on entertainment in 2021.

To determine how much Alessia spent on entertainment in 2021, we need to work backward from the given information about her salary in 2022.

Let's assume Alessia's salary in 2021 was the same as in 2022, which is $26,000 after tax.

Since Alessia spends 35% of her after-tax salary on rent, we can calculate her rent expenditure:

Rent = 35% × $26,000

= $9,100

The remaining amount is split between food, petrol, and entertainment in the ratio 6:11:8.

To determine the ratio's total parts, we sum the individual parts:

Total parts = 6 + 11 + 8 = 25

Next, we calculate the value of one part of the ratio:

One part = ($26,000 - $9,100) / 25

= $16,900 / 25

= $676

Now, we can calculate how much Alessia spent on entertainment in 2021, which is 8 parts of the ratio:

Entertainment expenditure = 8 × $676

= $5,408

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Let, speed of car B is -x.

So, speed of car A is x + 10.

Relative speed of A w.r.t B is ,

\(v_{ab}=(x+10)-(-x)\\\\v_{ab}=2x+10\ mph\)

So, time taken by A to travel 300 miles relative to B given by 3 hours .

\(v_{ab}=2x+10\\\\\dfrac{300}{3}=2x+10\\\\x = 45 \ mph\)

Therefore, speed of car A is 45 + 10 = 55 mph.

Hence, this is the required solution.

Answer:

$2.5

Step-by-step explanation:

15 divided by 6 because its asking to split into groups equally

Answer:2.5

Step-by-step explanation:

Answer:

(7, -4)

Step-by-step explanation:

Answer:

32,29

Step-by-step explanation:

Answer:

(x,y) = (-3,-6)

Step-by-step explanation:

gm gn cgmcgmxgmgnx

312.5 μCi is equivalent to 0.3125 mCi.

Conversion factors refer to a relationship between the value in one unit to the value in another unit. It is used to convert a quantity expressed in one unit to another unit.

The following conversion factors are needed to convert 312.5 μCi to millicuries (mCi):1 mCi = 1000 μCiUsing the above conversion factor, we can write the given value of 312.5 μCi as:312.5 μCi = (312.5/1000) mCi= 0.3125 mCi

Therefore, the value of 312.5 μCi can be converted to millicuries (mCi) using the above conversion factor. We can rearrange the formula as shown below.312.5 μCi × 1 mCi / 1000 μCi= (312.5/1000) mCi= 0.3125 mCi

Therefore, 312.5 μCi is equivalent to 0.3125 mCi. The calculation can be summarized in a sentence as follows: To convert 312.5 μCi to millicuries (mCi), we use the conversion factor 1 mCi = 1000 μCi.

The calculation shows that 312.5 μCi is equivalent to 0.3125 mCi. The answer can be expressed as follows: 312.5 μCi = 0.3125 mCi.

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Answer:

..........

..........

....

x

i

an

Answer:

119.1

Step-by-step explanation:

Pt+1=1.06x100

P3=106^3x100

=119.1016

The volume of octahedron when centers of adjacent faces of a unit cube are connected to form a regular octahedron is 1/16 unit ³.

Let the side length of a cube is 1unit.

Therefore length of all edges of the regular octahedron =2√2 unit .

Now the base of the pyramids is a square are will be (2√2)² =12 unit.

Now clearly the height of the pyramid is half the height of the cube, i.e.,1/2.

So volume of the Pyramid will be ⇒ 1/3× (Base area) × (height) = 1/3×1/2×1/2 = 1/12.

Therefore, the volume of the octahedron= 2 × volume of Pyramid= 2 ×1/12=1/6 unit³.

Hence, the volume of octahedron when centers of adjacent faces of a unit cube are connected to form a regular octahedron is 1/16 unit ³.

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(a) The mean value of the current over the range t = 0 to t = 10 ms is 1/100.

(b) The RMS value of the current over the range t = 0 to t = 10 ms is sqrt(25 - (25/2n) * sin(2n)), where n = 100.

To find the mean value and root mean square (RMS) value of the current over the range t = 0 to t = 10 ms, we need to perform the necessary calculations using integral calculus.

The given current function is:

i = 50 sin(100nt)

(a) Mean value of the current:

The mean value of a function over an interval is given by the integral of the function divided by the length of the interval.

Mean value of current (I_mean) = (1 / T) * ∫[0, T] i dt

In this case, T = 10 ms = 0.01 seconds.

I_mean = (1 / 0.01) * ∫[0, 0.01] 50 sin(100nt) dt

= 100 * ∫[0, 0.01] sin(100nt) dt

= 100 * [-1/100n * cos(100nt)]|[0, 0.01]

= -cos(100n(0.01))/n + cos(100n(0))/n

= -cos(n) / n + cos(0) / n

= 1/n

Therefore, the mean value of the current is 1/n, where n = 100.

(b) RMS value of the current:

The RMS value of a function over an interval is the square root of the mean of the square of the function.

RMS value of current (I_rms) = sqrt((1 / T) * ∫[0, T] i^2 dt)

I_rms = sqrt((1 / 0.01) * ∫[0, 0.01] (50 sin(100nt))^2 dt)

= sqrt(5000 * ∫[0, 0.01] sin^2(100nt) dt)

= sqrt(5000 * (1/2) * ∫[0, 0.01] (1 - cos(200nt)) dt)

= sqrt(2500 * [t - (1/200n) * sin(200nt)]|[0, 0.01])

= sqrt(2500 * (0.01 - (1/200n) * sin(2n)))

= sqrt(25 - (25/2n) * sin(2n))

Therefore, the RMS value of the current is sqrt(25 - (25/2n) * sin(2n)), where n = 100.

Please note that in both cases, the values of n and T are substituted to reflect the specific range of t = 0 to t = 10 ms given in the problem statement.

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The general convention is to reject a hypothesis if your data analysis indicates that there is a probability that a hypothesis is incorrect. This is False.

Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1.

After a performing a test, scientists can reject the null hypothesis meaning there is a definite, consequential relationship between the two phenomena

In this case, the convention is to accept a hypothesis if your data analysis indicates that there is a probability that a hypothesis is incorrect.

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Answer:

\( {2}^{12} \)

Step-by-step explanation:

\( {16}^{3} \\ = (2 \times 2 \times 2 \times 2) ^{3} \\ = ( {2}^{4} {)}^{3} \\ = {2}^{4 \times 3} \\ = {2}^{12} \)

Hope it helps.

If you have any query, feel free to ask.