Find the 18th term of the arithmetic sequence whose common difference is d=-5 and whose first term is a₁ = 20.

Answer: (3/2,-6)

Step-by-step explanation:

Answer:

Formula for midpoint is given as [(x1+x2)÷2, (y1+y2)÷2] where x and y are the coordinates of the points.

Midpoint = [(8+(-5))÷2, (-3+(-9))÷2]

= (3/2, -12÷2)

= (3/2, -6)

Answer: E. The 20 plants in the two groups

Step-by-step explanation: experimental units are individuals on which the experiment is being performed. In this case the pepper plants are being used to test the effectiveness of the new fertilizer.

Slant height of the conical frustum, l = 5 units.

Total surface area of the conical frustum, a = 329.87 square units.

Volume of the conical frustum, v = 1394.87 cubic units.

Given,

Radii of bases of a conical frustum,

r₁= 9

r₂ = 12

Height = 4

We have to find the total surface area of the frustum and volume of the frustum.

Formula for total surface area, a = [tex]\pi l(r_{1} +r_{2}[/tex][tex])[/tex]

Volume of the frustum, v = [tex]\frac{1}{3} \pi h(r_{1} ^{2} +r_{2} ^{2} +(r_{1} r_{2} )} )[/tex]

Here l is the slant height.

Slant height, l = [tex]\sqrt{(r_{1} -r_{2} )^{2} +h^{2} }[/tex]

First we have to find the slant height.

l = [tex]\sqrt{(r_{1} -r_{2} )^{2} +h^{2} }[/tex]

l = [tex]\sqrt{(9-12)^{2}+4^{2} }[/tex]

l = [tex]\sqrt{(-3)^{2} +16}[/tex]

l = [tex]\sqrt{9+16}[/tex]

l = [tex]\sqrt{25}[/tex]

Slant height, l = 5 units

Now,

Total surface area, a = [tex]\pi l(r_{1} +r_{2}[/tex][tex])[/tex]

a = [tex]\pi[/tex] × 5 × ( 9 + 12)

a = [tex]\pi[/tex] × 5 × 21

a = 329.87 square units.

Then,

Volume of the frustum, v = [tex]\frac{1}{3} \pi h(r_{1} ^{2} +r_{2} ^{2} +(r_{1} r_{2} )} )[/tex]

v = [tex]\frac{1}{3}[/tex] × π × 4 × (9² + 12² + ( 9×12))

v = [tex]\frac{1}{3}[/tex] × π × 4 × (81 + 144 + 108)

v = [tex]\frac{1}{3}[/tex] × π × 4 × 333

v = 1394.87 cubic units.

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If two cyclists, 30 miles apart, start riding toward each other at the same time. one cycles 2 times as fast as the other. if they meet 2 hours later, The speed (in mi/h) of the faster cyclist is: 5 mph and 10 mph.

Let r represent the speed of one

Let 2r represent thee speed of the other

Total distance traveled by both the sisters = 30 miles

Time ×rate = Distance

Hence,

2(2r+r) = 30

2(3r)=30

6r=30

r=30/6

r=5 mph

Speed=5 mph and (5 mph×2)

Speed=5 mph and 10 mph

Therefore If two cyclists, 30 miles apart, start riding toward each other at the same time. one cycles 2 times as fast as the other. if they meet 2 hours later, The speed (in mi/h) of the faster cyclist is: 5 mph and 10 mph.

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The estimate for the side length of the square = the width of the rectangle (w) = √44.

Area of Rectangle = (length)(width)

Given the parameters below:

If this rectangle is divided to form two squares with equal areas, then the side length of each square would be equal to the length of the original rectangle = w.

(2w)(w) = 88

2w² = 88

w² = 88/2

w² = 44

√w² = √44

w = √44

Thus, an estimate of the side length of the square = the width of the rectangle (w) = √44.

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Answer:

-9.2 or -9 1/5

Step-by-step explanation:

Hope it helps!

Answer:

m = -40

Step-by-step explanation:

Solve for m by simplifying both sides of the equation, then isolating the variable.

Answer:

A. 0

Step-by-step explanation:

Slope tells you steepness or flatness of your line.

If you know two points on a line find slope by subtracting the y's and put that on top of a fraction. And subtract the x's and put that on the bottom of the fraction.

Subtract y's: 3 - 3

Put it on top: 0/...

Subtract x's: 5 - -4

same as 5+4

Put that on the bottom: 0/9

slope, usually called m, is 0/9, which is 0.

Notice if you graph these two points its a hOrizOntal line. HOrizOntal lines have zerO slope.

Answer:

B, 15 pencils

Step-by-step explanation:

Our equation: (5 x 42)/14

42 x 5 = 210

210/14= 15

The probability that Colleen selected a bottle of water and then a bottle of lemonade without replacement is 35/138

Probability is the measure of that how likely is an event can occur.

Probability of an event = Favorable outcomes of the event / total outcomes

Multiplication rule of probability states that probability of two events happening at the same time = (probability of one event )*(probability of another event )

Given that A cooler contains 14 bottles of water and 10 bottles of lemonade. Colleen randomly selects 2 bottles from the cooler

Total bottle = 14 +10 = 24

Let E be the event that Colleen selects a bottle of water first

Probability of E = 14/24

Let F be an event that Colleen selects bottle of lemonade when at the same time a bottle of lemonade is already taken out  

Probability of F = 10/23

Therefore , The probability that Colleen selected a bottle of water and then a bottle of lemonade without replacement is

= Probability of E * Probability of F = (14/24)*(10/23) =35/138.

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The required zeros of the polynomial f(x) are 1 and ±√-1.

What are zeros of the polynomial?

All the possible values of x that will make the polynomial zero are called the zeros of the polynomial, p(x). Zeros of a polynomial can either be negative or positive.

Solving for the zeros of a polynomial

y = x³ - x² + x - 1

Let, f(x) = 0

x³ - x² + x - 1 = 0

Using heat and trial method, we get,

x =1 as one of the zero of the polynomial

It implies that (x-1) is the root of polynomial

Thus, dividing x³ - x² + x - 1 by x - 1, we get

x² + 1, which is then equated to 0 to obtain the zeros of the given polynomial

i.e. x² + 1 = 0

x = 1, ±√-1

Hence, the required zeros of the polynomial y are 1 and ±√-1.

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Answer:

Super = 20 + 10x

Fance = 60 + 2x

Step-by-step explanation:

→ Start with the set fee for both

Super = 20 +

Fancy = 60 +

→ Assign a new variable to denote hours

x

→ Complete

Super = 20 + 10x

Fance = 60 + 2x

Answer:

Smaller

Step-by-step explanation:

When you multiply something by 1/3, basically what you are doing is multiplying that thing by one and dividing it by 3.

To put it in a better perspective, let's say you have something that is 5 inches long and you multiply it by a scale factor of 1/3. The equation would be: (5*1)/3.

*Please mark brainliest answer

The solving of fraction shows that there are 4 cups of lemonade use the table.

A fraction seems to be a part of a whole. The number is expressed in arithmetic as a quotient, which is the numerator divided by that of the denominator. Both are integers in a simple fraction. A complex fraction has a fraction in both the numerator and the denominator.

Fractions help children know the nature of numbers but instead their interactions (e.g., the meaning of division) (e.g., the meaning of division). If a child does not grasp how fractions work, he will struggle to understand algebra later in life.

Based on the given conditions, formulate:

= [tex]16 \times \frac{1}{2} \div\left(\frac{1}{2}+1 \frac{1}{2}\right)[/tex]

Convert the expression into a fraction:

= [tex]\frac{16}{2 \times\left(\frac{1}{2}+\left(\frac{1}{1}+\frac{1}{2}\right)\right)}[/tex]

Expand the fraction to get the least common denominator:

= [tex]\frac{16}{2 \times\left(\frac{1}{2}+\left(\frac{2}{1 \times 2}+\frac{1}{2}\right)\right)}[/tex]

Calculate the product or quotient:

= [tex]\frac{16}{2 \times\left(\frac{1}{2}+\left(\frac{2}{2}+\frac{1}{2}\right)\right)}[/tex]

Write the numerators over common denominator:

= [tex]\frac{16}{2 \times \frac{1+2+1}{2}}[/tex]

Write the numerators over common denominator:

= [tex]\frac{16}{2 \times \frac{3+1}{2}}[/tex]

Calculate the sum or difference:

= [tex]\frac{16}{2 \times \frac{4}{2}}[/tex]

Calculate the sum or difference:

= 16 /2

Cross out the common factor:

= 4

This shows that there are 4 cups of lemonade use the table.

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The solution of factorization of x ³ + 64 is ( x + 4 )( x ² - 4 x + 16 ) [ Option C ].

The question asks to factorize the given polynomial, that is, x ³ + 64.

The question clearly states that we need to use the sum of cubes formula to factor the given polynomial x ³ + 64.

Sum of cube formula is given as

a ³ + b ³  = ( a + b ) ( a ² - a b + b ² ).

Substitute the values of variable a and b from the given polynomial x ³ + 64

x³ + 64 can be written as x ³ + 4 ³

=> a = x and b = 4

=> x ³ + 4 ³ = ( x + 4 ) ( x ² - 4 x + 4 ² )

=>  x ³  + 4 ³ = ( x + 4 ) ( x ² - 4 x + 16 )

This matches with the option c among the multiple choices for this question.

Therefore, we get the solution of factorization of x ³ + 64 as ( x + 4 )( x ² - 4 x + 16 ).

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Triangle ABC is rotated 85° around the point D to create A'B'C'.

Rotation is a transformation in which a figure is turned around a point . This point is fixed and is called the center of rotation.

From the given diagram we can see that the triangle is rotated about the fixed point D with an angle of 85° such that A' is new location of A and B' and C' are new locations of B and C respectively.

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Answer:

z score

Step-by-step explanation:

The value of the composite function (h⁰ g)(x) calculated by  function operation is  2x+28 .

A function is described as the relationship between a set's domain and range and its elements. f, g, or h are frequently used to denote functions.

Each element of an algebraic function, denoted by the formula y=g(x), is connected to a single value of x.

(h ∘ g)(x) can also be expressed as h[g(x)] , which signifies that the value of x=g(x) will be replaced in the function h, is referred to as a composite function.

A composite function is produced by combining two existing functions to produce a third, distinct function.

In h of g of x, the output of one function becomes the input of another.

Given functions are:

f(x)=4 x and g(x)=1/2x+7

Therefore (f ∘ g)(x)=f[g(x)]

=f(1/2x+7)

=4×(1/2x+7)

=2x+28

Therefore the value of the function operation  (f⁰ g)(x) is  2x+28

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The expression to illustrate the information when Toby's seventh grade class is going on a field trip to a history museum will be 0.2 (10x + 30y).

It should be noted that there are x students and y teachers going on the trip. Tickets for students are $10 each and tickets for teachers are $20 each and the history museum gave the class 20% off as part of a group promotion.

Therefore, it should be noted that the expression to illustrate this will be:

= 20% × (10 × x) + (20 × y)

= 0.2 (10x + 30y)

Therefore, the expression to illustrate the information when Toby's seventh grade class is going on a field trip to a history museum will be 0.2 (10x + 30y).

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Toby's seventh grade class is going on a field trip to a history museum. There are x students and y teachers going on the trip. Tickets for students are $10 each and tickets for teachers are $20 each. The history museum gave the class 20% off as part of a group promotion. What expression will illustrate this?

Answer:

Step-by-step explanation:(2x+5)(2x+9)

      use foil method           ([tex]4x^{2}[/tex]+18x+10x+45)

                                            [tex]4x^{2}[/tex]+28x+45

The absolute value of the given modulus function are -1 and 7.

The given modulus function is;

|4x - 12| = 16

Removing modulus sign will provide two values;

4x - 12 = ±16

Solve for positive value of modulus function;

4x - 12 = 16

Add 12 on both side;

4x - 12 + 12 = 16 + 12

4x = 28

Dive both side by 4.

x = 7

Now, solve for negative value of modulus function.

4x - 12 = -16

Add 12 on both side;

4x - 12 + 12 = -16 + 12

4x = -4

Divide both side by 4;

x = -1

Thus, the two value of the given modulus function are -1 and 7.

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The function which f(2) = 3 is the function with the equation f(x) = x + 1

The function value is given as

f(2) = 3

The above means that the value of the function is 3 when x = 2

i.e., f(x) = 3 when x = 2 or we substitute 2 for x in f(x)

Next, we test the above function in the list of given options

So, we have

f(x) = x^2 + 1

Substitute 2 for x in f(x)

f(2) = 2^2 + 1

Evaluate the exponent in the above equation

So, we have

f(2) = 4 + 1

Evaluate the sum in the above equation

So, we have

f(2) = 5

f(x) = 2x + 1

Substitute 2 for x in f(x)

f(2) = 2 x 2 + 1

Evaluate the product in the above equation

So, we have

f(2) = 4 + 1

Evaluate the sum in the above equation

So, we have

f(2) = 5

f(x) = x + 1

Substitute 2 for x in f(x)

f(2) = 1 x 2 + 1

Evaluate the product in the above equation

So, we have

f(2) = 2 + 1

Evaluate the sum in the above equation

So, we have

f(2) = 3

Hence, the function which f(2) = 3 is the function with the equation f(x) = x + 1

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Possible question

Identify each function for which f (2) = 3

f(x) = x^2 + 1

f(x) = 2x + 1

f(x) = x + 1

f(x) = 2x^3 + 1

  Solving the problem by multiplying and simplifying we have as a result 16x¹⁵

Simplification is a process of reducing terms to expressions, which do not generate changes or values.

  Multiplication is also known as product, and it is a mathematical operation of a successive sum, this operation consists of adding a number a certain number of times:

a x b the number "a" will be added "b" times.

  The algebraic expression that we must simplify to its minimum expression is:

4√16 x⁸ . 4√x¹⁴

4×4x⁸ × 4x¹⁴/²  

16x⁸× 4x⁷  ; multiply power of equal base

16x⁸⁺⁷

16x¹⁵

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Answer:if A= [2 6] prove that (A')' = A

3 7

4 9​

Step-by-step explanation:

Answer:

I believe it's 25% .............

Answer:

40%

Step-by-step explanation:

The cash price = $4,250

If Steve rents the computer for $595 for 10 months he would have to spend $595 x 10 = $5,950

The difference in money = 5950 - 4250 =$1700

As a percentage of the cash price this would be
1700/4250 x 100 =  40%

Answer:
Rent option is  40% more than the cash price 40%

We can verify this by noting that if there is an increase of r% in the price of an item then
Increased price = Old price + Increase

= Old price + Old price x r/100

In this case, Old price = 4250
r = 40%, r/100 = 0.04

New price = 4250 + 4250 x 0.04  = 4250(1 + 0.04) = 4250(1.04) = 5950 which tallies with given figures

The correct answer for the given expression is 5.

Given,

evaluate the expression 4ˣ + 1

By putting x= 1,

we get 4¹ + 1

= 4+ 1

= 5

So, the the answer for the question, evaluate  4ˣ + 1 is 5.

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