3. What value of r makes this equation true?
2(r+ 8) = r + 10

Answer:

If you don't agree or there's an error, let me know so I can edit.

Step-by-step explanation:

f(x) = x⁴ + 2

differentiate

f(x) = 4x³ + 0 =0

x(4x²) = 0

at x= 0 f(x) = 0 points = (0,0)

at x= 1. f(x) = 3 points = (4,3)......

The ordered pair is (4,3).

An ordered pair is a composition of the x coordinate (abscissa) and the y coordinate (ordinate), having two values written in a fixed order within parentheses. It helps to locate a point on the Cartesian plane for better visual comprehension. The numeric values in an ordered pair can be integers or fractions.

Given:

f(x) = x⁴ + 2

Now, differentiate the above function for the small values

f(x) = 4x³ + 0 =0

x(4x²) = 0

When x= 0

f(x) = 0

So, the points = (0,0)

when x= 1

f(x) = 3

so, the points = (4,3).

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Answer:

The class 35 - 40 has maximum frequency. So, it is the modal class.

From the given data,

\( {\bf \:\: {By\:using\:the\: formula}} \\ \\ \)

\(\:\dag\:{\small{\underline{\boxed{\sf {Mode,\:M_{o} =\sf\red{x_k + {\bigg(h \times \: \dfrac{ ( f_k - f_{k-1})}{ (2f_k - f_{k - 1} - f_{k +1})}\bigg)}}}}}}} \\ \\ \)

\(\sf \:\:\:\:\:\:\:\:\:= 35+ {\bigg(5 \times \dfrac{(50 - 34)}{ ( 2 \times 50 - 34 - 42)}\bigg)} \\ \\ \)

\(\sf \:\:\:\:\:\:\:\:\:\:\:\:\:\:\:= 35 +{\bigg(5 \times \dfrac{16}{24}\bigg)} \\ \\ \)

\(\sf \:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:= {\bigg(35+\dfrac{10}{3}\bigg)} \\ \\ \)

\(\sf \:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:(35 + 3.33) =.38.33 \\ \\ \)

\(\:\:\sf {Hence,}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\ \large{\underline{\mathcal{\gray{ mode\:=\:38.33}}}} \\ \\ \)

\({\large{\frak{\pmb{\underline{Additional\: information }}}}}\)

MODE

MODAL CLASS

\({\bf{\underline{Formula\:for\: calculating\:mode:}}} \\ \)

\({\underline{\boxed{\sf {Mode,\:M_{o} =\sf\red{x_k + {\bigg(h \times \: \dfrac{ ( f_k - f_{k-1})}{ (2f_k - f_{k - 1} - f_{k +1})}\bigg)}}}}}} \\ \\ \)

Where,

\(\sf \small\pink{ \bigstar} \: x_{k}= lower\:limit\:of\:the\:modal\:class\:interval.\)

\( \small \blue{ \bigstar}\)\(\sf \: f_{k}=frequency\:of\:the\:modal\:class\)

\(\sf \small\orange{ \bigstar}\: f_{k-1}=frequency\:of\:the\:class\: preceding\:the\;modal\:class\)

\(\sf \small\green{ \bigstar}\: f_{k+1}=frequency\:of\:the\:class\: succeeding\:the\;modal\:class\)

\( \small \purple{ \bigstar}\)\(\sf \: h= width \:of\:the\:class\:interval\)

Answer:

y = 3x -5

Step-by-step explanation:

Use the slope-intercept form:

y = (slope)x + intercept

slope = 3

intercept = -5

Equation in slope-intercept form:

y = 3x -5

Answer:

first two boxs maybe -5, and 8?

-4, 3

Step-by-step explanation:

im not into this yet so thats js guess

\(sin60 = \frac{opp}{hyp} \\ sin60 = \frac{y}{12 } \\ \frac{ \sqrt{3} }{2} = \frac{y}{12} \\ 2y= 12 \sqrt{3} \\ y = 6 \sqrt{3} \)

\(cos60 = \frac{adj}{hyp} \\ cos60 = \frac{x}{12} \\ \frac{1}{2} = \frac{x}{12 } \\ 2x = 12 \\ x = 6\)

Hope it helps

Please give brainliest

\(\large\red{┈──┈──┈──┈──┈──┈──┈──┈──┈─}\)

The best option is letter C. t = 2h + 32

Answer:

0.2% as a decimal is 0.002, 3.71 as a percentage is 371%

Answer:

The answer to your problem is, 78

Step-by-step explanation:

Let’s divide in order to find the answer.

Round 3.55 to the nearest whole = 4

275 / 4

= 68.75

But if we instead of “ 4 “ we can add 3.55

275 / 3.55

= 77.46

Since it is a little over 77. We round it to 78. Due to it be measured in money

Thus the answer to your problem is, 78

Answer:

The answer is y = 7/x -6.

Step-by-step explanation:

A linear function is one where x and y are both to the first power.  Using this knowledge, let's look at the options that we are given.

y = 4x + 9

In the above equation, both x and y are raised to the first power, so we know that this equation is linear.

y = 7/x - 6

In the above equation, y is raised to the first power, but x is not.  Since x is in the denominator of a fraction, it actually has a power of -1, which makes this equation nonlinear.

y = x - 6/7

In the above equation, both x and y are raised to the first power, making the equation linear.

Therefore, the correct choice is y =7/x - 6.

Hope this helps!

Answer:

5

Step-by-step explanation: i created the list of numbers.

15: 1,3,5,15

20: 1,2,4,5,10,20

can i get branliest

Answer:

A. 2^4 . 2^-3 . 2^4 . 2

Step-by-step explanation:

Option A,

2^4 . 2^-3 . 2^4 . 2

= 2^4 . 2^-3 . 2^4 . 2^1

= 2^( 4 + 4 + 1 - 3 )

= 2^( 9 - 3 )

= 2^6

= 64

So, Option A is the correct answer.

Answer: 0.06

Also could you mark my answer as brainliest? It helps and doesnt hurt

Answer: 0.06

Step-by-step explanation:

By using the same logic and identity, we can also say that ¬(p∨¬q) is equivalent to q∧¬p.

a. To find the given series i.e.,  5∑n=0(9(2)n)−7(−3)nTo find 5∑n=0(9(2)n)−7(−3)n,

we need to find the first five terms of the series. The given series is,

5∑n=0(9(2)n)−7(−3)n5[(9(2)0)−7(−3)0] + [(9(2)1)−7(−3)1] + [(9(2)2)−7(−3)2] + [(9(2)3)−7(−3)3] + [(9(2)4)−7(−3)4]

After evaluating, we get:

5[(9*1) - 7*1] + [(9*2) - 7*(-3)] + [(9*4) - 7*9] + [(9*8) - 7*(-27)] + [(9*16) - 7*81]15 + 57 + 263 + 1089 + 4131= 5555b.

Given premises: p → q, ¬p → r, r → s.

We are to prove that ¬q → s. i.e.,

Premises: (p → q), (¬p → r), (r → s)

Conclusion: ¬q → s

To prove ¬q → s,

we need to assume ¬q and show that s follows.

Then we use the premises to derive s.

Proof:

1. ¬q        Assumption

2. ¬(¬q)    Double negation

3. p         Modus tollens 2,1 & p → q

4. ¬¬p      Double negation

5. ¬p        Modus ponens 4,3 (Conditional elimination)

6. r         Modus ponens 5,2 (Conditional elimination)

7. s         Modus ponens 6,3 (Conditional elimination)

8. ¬q → s     Conditional introduction (Implication)

Thus, ¬q → s is proven.

c. To show that ¬(p∨¬q) and q∧¬p are equivalent, we need to show that their negation is equivalent. i.e.,

we show that (p ∨ ¬q) ↔ ¬(q ∧ ¬p)Negation of (p ∨ ¬q) = ¬p ∧ q Negation of (q ∧ ¬p) = ¬q ∨ p

Thus, we are to show that (p ∨ ¬q) ↔ ¬(q ∧ ¬p) is equivalent to ¬p ∧ q ↔ ¬q ∨ p

Proof:

¬(q ∧ ¬p)  ≡  ¬q ∨ p       Negation of (q ∧ ¬p)(p ∨ ¬q)   ≡  ¬(q ∧ ¬p)  

De Morgan's laws ∴ (p ∨ ¬q) ≡ ¬q ∨ p

By using the same logic and identity, we can also say that ¬(p∨¬q) is equivalent to q∧¬p.

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a. The formula given is, ∑n=0(9(2)n)−7(−3)n. Let’s find out the first five terms of the given formula as follows:

First term at n = \(0:9(2)^0-7(-3)^0= 9 + 7= 16\)

Second term at n = \(1:9(2)^1-7(-3)^1= 18 + 21= 39\)

Third term at n = \(2:9(2)^2-7(-3)^2= 36 + 63= 99\)

Fourth term at n = \(3:9(2)^3-7(-3)^3= 72 + 189= 261\)

Fifth term at n = \(4:9(2)^4-7(-3)^4= 144 + 567= 711\)

Therefore, the first five terms of the given formula are: 16, 39, 99, 261, 711.

b. To prove that ¬q→s from p→q, ¬p→r, and r→s,

we need to use the law of contrapositive for p→q as follows:

¬q→¬p       (Contrapositive of p→q)¬p→r         (Given)

∴ ¬q→r        (Using transitivity of implication) r→s           (Given)

∴ ¬q→s        (Using transitivity of implication)

Therefore, ¬q→s is proved.

c. To show that ¬(p∨¬q) and q∧¬p are equivalent,

we need to use the De Morgan’s laws as follows:

¬(p∨¬q) ≡ ¬p∧q     (Using De Morgan’s law)      

≡ q∧¬p     (Commutative property of ∧)

Therefore, ¬(p∨¬q) and q∧¬p are equivalent.

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Answer: 2 one number 2

Step-by-step explanation:

It's is number 2

The required solution of the quadratic equation  (4y - 3)² = 72 is y = 3 ± 6√2/4. Option A is correct.

What is simplification?

Simplification involves applying rules of arithmetic and algebra to remove unnecessary terms, factors, or operations from an expression.

Here,
Given expression, (4y - 3)² = 72

Simplifying the above expression:
(4y - 3)² = 72

4y - 3 = ±√72
4y - 3 = ±6√2
y = 3 ± 6√2/4

Thus, the required solution of the quadratic equation  (4y - 3)² = 72 is y = 3 ± 6√2/4. Option A is correct.

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The equation for the plane consisting of all points that are equidistant from the points (−7, 1, 1) and (3, 3, 5) is 20x + 4y + 8z = -9.

In order to determine the distance of this plane (x, y, z) with the given points, we would use the distance formula.

Mathematically, the distance between three (2) points that are on a coordinate plane can be calculated by using this formula:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²]

For these points (x, y, z) and (−7, 1, 1), the distance is given by:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²]

Distance = √[(x₂ - (-7))² + (y₂ - 1)² + (z₂ - 1)²]

Distance = √[(x₂ + 7)² + (y₂ - 1)² + (z₂ - 1)²]

By using the algebraic formulas, the expanded expression is given by:

(a - b)² = a² - b² - 2ab

(a + b)² = a² + b² + 2ab

Distance = √[(x² + 14x + 49) + (y² - 2y + 1) + (z² - 2z + 1)]   .......equation 1.

For these points (x, y, z) and (3, 3, 5), the distance is given by:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²]

Distance = √[(x - 3)² + (y - 3)² + (z - 5)²]

Distance = √[(x² - 6x + 9) + (y² - 6y + 9) + (z² - 10z + 25)]    .....equation2.

Since both distances are equidistant, we would equate eqn. 1 and eqn. 2 and then simplify:

√[(x² + 14x + 49) + (y² - 2y + 1) + (z² - 2z + 1)] = √[(x² - 6x + 9) + (y² - 6y + 9) + (z² - 10z + 25)]

(x² + 14x + 49) + (y² - 2y + 1) + (z² - 2z + 1) = (x² - 6x + 9) + (y² - 6y + 9) + (z² - 10z + 25)

x² + 14x + 49 + y² - 2y + 1 + z² - 2z + 1 = x² - 6x + 9 + y² - 6y + 9 + z² - 10z + 25

14x + 6x - 2y + 6y - 2z + 10z + 52 - 43 = 0

20x + 4y + 8z + 9 = 0

20x + 4y + 8z = -9.

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what type of math is that?

Graphing the equation 3x - 2y = -6 over the range x = -10 to x = 10:

To graph the equation 3x - 2y = -6, we need to rearrange it in the form y = mx + b, where m is the slope and b is the y-intercept.

3x - 2y = -6

-2y = -3x - 6

Divide both sides by -2:

y = (3/2)x + 3

Now we have the equation in slope-intercept form.

To graph the equation, we can plot a few points and draw a line through them. Let's choose some x-values from the range -10 to 10 and find the corresponding y-values.

For x = -10:

y = (3/2)(-10) + 3

y = -15 + 3

y = -12

For x = 0:

y = (3/2)(0) + 3

y = 0 + 3

y = 3

For x = 10:

y = (3/2)(10) + 3

y = 15 + 3

y = 18

Plotting these points (-10, -12), (0, 3), and (10, 18) on the graph and drawing a line through them, we get the graph of the equation 3x - 2y = -6.

Using the graphical method to solve the pair of equations:

The given equations are:

10x = 5y

-3x + y = 1

To solve these equations graphically, we need to plot their graphs on the same coordinate plane and find the point where they intersect, which represents the solution.

Rearranging the second equation in slope-intercept form:

y = 3x + 1

Now we have the equations in the form y = mx + b.

Plotting the graphs of the equations 10x = 5y and y = 3x + 1, we can find the point of intersection, which represents the solution to the system of equations.

The point of intersection is the solution to the system of equations.

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Answer:

10x - 6y = 30

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

d=-4 , f = 3

so, [8-(-4)]/4 × 3

= (8+4)/12

= 12/12

=1

Hope it helps

Answer:

1 is the answer

Step-by-step explanation:

8-(-4) / 4(3) = 1

Answer:

#carry on learning

Mark me as brainliest

(f + g)(x) = f(x) + g(x), where x is in the domain of both f and g. = 2x3 + x2 + 2. The domain of (f + g)(x) consists of all x-values that are in the domain of both f and g.

An osteoblast is referred to as an osteocyte when it is entirely encircled by the secretions of its own matrix.

Osteocyte is a specific kind of bone cell that develops when the osteblast, which produces the bone's structural material, is surrounded by material that it has released on its own. Osteocytes, which make up 90–95% of the cells in bone tissue as opposed to osteoclasts and osteoblasts, which make up just 5%, are the longest-living bone cells. (40). Osteoblasts develop into osteoocytes when they are implanted in the mineral matrix of bone and acquire unique properties.

Osteocytes function as endocrine cells, emitting hormones to regulate local deposit of minerals and chemistry at the cellular level of the bone matrix as well as phosphate transport to other organs like the kidney. Osteocytes appear to be principally responsible for many bone activities.

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Mu has walked 15 laps to raise a total of $105. Mu is walking laps to raise money for charity.

For each lap, her sponsors will donate $7. Mu has walked lll laps and raised a total of $105.

To write an equation that can describe the situation, we can use the formula \(y = mx\),

where y represents the total amount raised, m represents the amount raised for each lap, and x represents the number of laps walked.

Therefore, the equation that describes the situation is:

y = 7x (Mu's sponsors will donate $7 for each lap she walks).

Since Mu has walked lll laps and raised a total of $105,

we can substitute these values into the equation and solve for x. 105 = 7 × lll

To find lll, we can divide both sides by 7.

This gives us: lll = 15

Therefore, Mu has walked 15 laps to raise a total of $105.

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Answer:

Therefore, the book value of the equipment at the end of year four (including year four) is $2,880.

Step-by-step explanation:

To calculate the book value of the equipment at the end of year four using the MACRS method with GDS recovery period of five years, we can use the following steps in Excel:

1. Open a new Excel spreadsheet and create the following headers in row 1: Year, Cost, Depreciation Rate, Annual Depreciation, Cumulative Depreciation, and Book Value.

2. Fill in the Year column with the years 1 through 6 (since the truck has a life of six years).

3. Enter the cost of the truck, $12,000, in cell B2.

4. Use the following formula in cell C2 to calculate the depreciation rate for each year:

=MACRS.VDB(B2, 5, 5, 1, C1)

This formula uses the MACRS.VDB function to calculate the depreciation rate for each year based on the cost of the truck (B2), the GDS recovery period of five years, the useful life of six years, the salvage value of $2,000, and the year (C1).

5. Copy the formula in cell C2 and paste it into cells C3 through C7 to calculate the depreciation rate for each year.

6. Use the following formula in cell D2 to calculate the annual depreciation for each year:

=B2*C2

This formula multiplies the cost of the truck (B2) by the depreciation rate for each year (C2) to get the annual depreciation.

7. Copy the formula in cell D2 and paste it into cells D3 through D7 to calculate the annual depreciation for each year.

8. Use the following formula in cell E2 to calculate the cumulative depreciation for each year:

=SUM(D$2:D2)

This formula adds up the annual depreciation for each year from D2 to the current row to get the cumulative depreciation.

9. Copy the formula in cell E2 and paste it into cells E3 through E7 to calculate the cumulative depreciation for each year.

10. Use the following formula in cell F2 to calculate the book value of the equipment for each year:

=B2-E2

This formula subtracts the cumulative depreciation for each year (E2) from the cost of the truck (B2) to get the book value.

11. Copy the formula in cell F2 and paste it into cells F3 through F7 to calculate the book value for each year.

12. The book value of the equipment at the end of year four (including year four) is the value in cell F5, which should be $2,880.

Answer:

B

Step-by-step explanation:

When you add 2 of the sides together, they are always greater than the other

Answer:

y=42 degree

Step-by-step explanation:

90+y+48=180

138+y=180

y=180-138

y=42

Answer:

Step-by-step explanation:

In the lower triangle, the top angle is also 90 degrees, so just add 90 +48 = 138 and subtract from 180. Y= 42 degrees.

The equation T = 2π√(L/g) satisfies dimensional consistency, indicating that it is a valid relationship for the periodic time T of a simple pendulum.

To test the validity of the equation x = x₀ + v₀t + (1/2)at², we can check if the dimensions on both sides of the equation are consistent.

Breaking down the dimensions of each term:

x: Displacement has dimensions of length (L).

x₀: Initial displacement has dimensions of length (L).

v₀t: Velocity times time has dimensions of (L/T) * T = L.

(1/2)at²: Acceleration times time squared has dimensions of (L/T²) * T² = L.

Since the dimensions on both sides of the equation are consistent (L = L), the equation x = x₀ + v₀t + (1/2)at² is valid.

Now, let's use dimensional analysis to find the relationship of the periodic time T of a simple pendulum using the factors affecting it: mass of the bob (m), length (L) of the pendulum, and acceleration due to gravity (g).

The factors affecting the periodic time T of a simple pendulum are:

Mass (m): Denoted by [M].

Length (L): Denoted by [L].

Acceleration due to gravity (g): Denoted by [LT⁻²].

The periodic time T of a simple pendulum is expected to depend on these factors in some way.

By applying dimensional analysis, we can determine the relationship between these factors. The equation is given as T = 2π √(L/g), where T is the periodic time, π is a constant, L is the length, and g is the acceleration due to gravity.

Breaking down the dimensions of each term:

T: Periodic time has dimensions of time (T).

2π: A constant, so it is dimensionless.

√(L/g): The square root of the ratio of length to acceleration due to gravity has dimensions of √([L]/[LT⁻²]) = √(T²) = T.

Therefore, the equation T = 2π√(L/g) satisfies dimensional consistency, indicating that it is a valid relationship for the periodic time T of a simple pendulum.

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Answer:

Using a system of equations, it is found that he has 2 dimes, 5 nickels and 12 pennies.

In the system of equations, I am going to say that:

x is the number of dimes.

y is the number of nickels.

z is the number of pennies.

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

Two more nickels than dimes, thus:

Three times as many pennies as nickels, thus:

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

A dime is worth $0.1, a nickel is worth $0.05, and a penny is worth $0.01. Total of $0.52, thus:

Solving for x:

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

Solving for y and z:

He has 2 dimes, 5 nickels and 12 pennies.

Answer:

\(12x^3+2x\)

Step-by-step explanation:

The perimeter of a polygon is equal to the sum of its sides.

The sides in the triangle shown have lengths \(2x^3+6x\), \(4x^3-5x\), and \(6x^3+x\) in no specific order.

Since its perimeter is given by the sum of its sides, the perimeter is equal to:

\(2x^3+6x+4x^3-5x+6x^3+x\)

Combine like terms:

\(\boxed{12x^3+2x}\)

Answer:

A

Step-by-step explanation:

Answer:

when I finish the test I will tell you the right answerer

Step-by-step explanation: