What is the equation of the line that is perpendicular to the line defined by the equation 2y=3x+2 and goes through the point (3,2)

Considering a geometric sequence, the pattern is given as follows:

1, 2, 4, 8, 16, 32, 64.

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

The nth term of a geometric sequence is given by:

[tex]a_n = a_1q^{n-1}[/tex]

In which [tex]a_1[/tex] is the first term.

The first term and common ratio are given as follows:

[tex]a_1 = 1, q = 2[/tex].

Hence the remaining terms are:

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Answer:

[tex]x^4-20x^3 +175x^2 -750x+1250[/tex]

Step-by-step explanation:

By the conjugate root theorem, 5+5i is also a root.

[tex]f(x)=a(x-5)^2 (x-5-5i)(x-5+5i) \\ \\

= a(x^2 - 10x+25)((x-5)^2 - (5i)^2) \\ \\

= a(x^2 - 10x+25)(x^2 - 10x+25+25) \\ \\

= a(x^2-10x+25)(x^2-10x+50) \\ \\

= a(x^4- 10x^3 + 50x^2 - 10x^3 + 100x^2 - 500x + 25x^2 - 250x+1250) \\ \\

= a(x^4-20x^3 +175x^2 -750x+1250) \\ \\ [/tex]

Answer:

1050 masks per person.

Step-by-step explanation:

1) Create an equation to find the total number of masks

2) Solve equation and divide total by 2 to get the number of masks that can be given to both Mark and Paula so that they have equal number.

1) Since Paula has 70% of the total masks, it can be represented as 0.7 * t where t is the variable representing the total number of masks. Mark on the other hand has the remaining number of masks out of 100% which is 30%. We can express that as 0.3. We multiply that by t because he has 30% of the masks. The final equation we have is 0.3t + 840 = 0.7t. 840 because Paula has 840 more masks than Mark.

2) Solve by subtracting 0.3t from both sides leaving you with 0.4t = 840. We divide both sides by 0.4 to get 2100. That is the total number of masks. If we divide that number by 2, we get 1050.

The graph that represents the inequality is:

Number line with an open circle on 1, shading to the right and an open circle on 5, shading to the left.

The inequality is:

|2x - 6| < 4

Which means that the distance of 2x - 6 to the origin is less than 4, hence:

-4 < 2x - 6 < 4.

The solution is:

2x - 6 > -4

2x > 2

x > 1

2x - 6 < 4

2x < 10

x < 5

The solution has open circles at x = 1 and x = 5, as they are not part of the solution, and the shading is in the middle, as the solution is 1 < x < 5, hence the correct option is:

Number line with an open circle on 1, shading to the right and an open circle on 5, shading to the left.

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Paul's rent budget is $750, given that his food budget of $225, is 30 percent of his rent budget.

Fractions are representation of quantities as a part of a certain quantity.

Written as a/b, read as a by b, and functions as a divided by b, represents a fraction showing a parts of b equal parts.

a is called the numerator, and b is called the denominator.

Percentages are modified fractions where the whole quantity is represented by 100.

To convert a fraction into percentages we multiply it by 100, while to convert percentages to fraction divided by 100.

In the question, we are given that Paul's budget for food is 30% of the budget he has for rent.

We are asked if his budget for food is $225, what is his budget for rent.

We assume Paul's budget for rent to be $x.

We know that Paul's food's budget is 30 percent of his rent.

Hence, Paul's food budget = 30% of x.

or, Paul's budget for food = 30/100 * x {To convert percentages to fraction divided by 100}

But, we know that Paul's food budget is $225. Thus, we can show that:

225 = 30/100 * x,

or, x = (225*100)/30 = 750.

Thus, Paul's rent budget is $750, given that his food budget of $225, is 30 percent of his rent budget.

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The triangle ABC is shifted upwards by 3 units and towards the left by 4 units. After translation again it is rotated 90° counterclockwise. All these transformations are shown in the graph below.

The following are the basic transformation rules:

A triangle ABC is given in the graph with vertices as

A(-1, 2), B(1, 4), and C(4, -1)

The transformation to be applied is A"B"C" = Ro 90°(T(-4,3)(ABC))

Where -

T(-4, 3) represents the translation of 3 units upwards and 4 units towards the left

R0 90° represents the rotation of 90° (counterclockwise) of the translated triangle.

Step 1: applying translation (-4, 3):

The new vertices of the triangle ABC translated by (-4, 3) units are represented by A'B'C'. They are:

A' - (-1 - 4, 2 + 3) = (-5, 5)

B' - (1 - 4, 4 + 3) = (-3, 7)

C' - (4 - 4, -1 + 3) = (0, 2)

These are shown in the graph below.

Step 2: applying rotation 90° (counterclockwise): (x', y') → (-y, x)

Now the new triangle formed after the translation is ΔA'B'C'

So, on applying rotation, the vertices are changed to,

A'(-5, 5) → A"(-5, -5)

B'(-3, 7) → B"(-7, -3)

C'(0, 2) → C"(-2, 0)

These are shown in the graph below.

Therefore, Δ ABC → Δ A'B'C' (by T(-4, 3)) → Δ A"B"C" (by Ro 90°) i.e.,

Δ A"B"C" = Ro 90°(T(-4, 3) ABC).

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Cara has saved 1, 430 pennies. She needs to put the pennies in paper rolls so the bank can count them easily. Each penny roll holds 50 pennies. The number of pennies will be in the last roll is 30.

To find out the number of pennies will be in the last roll.

The branch of mathematics dealing with the properties and manipulation of numbers. a science that deals with the addition, subtraction, multiplication, and division of numbers. Fractions, decimals, percentages, fractions, square root, exponents, and other arithmetic operations are used to achieve mathematical simplifications.

Given that:

Cara has saved 1, 430 pennies.

Each penny roll holds 50 pennies.

1430 divides by 50 = 143/5≈29 roles and in last roll it will be 30 pennies.

So, the number of pennies will be in the last roll is 30.

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The solution to the given system of linear equations is x = 1, y = 2. That is (1, 2)

From the question, we are to solve the given system of equations

The given system of equations is

4x + y = 6     -----------(1)

2x - 3y = -4   -----------(2)

From the equation (1)

4x + y = 6

y = 6 - 4x      ----------(3)

Substitute the value of y into equation (2)

2x - 3y = -4

2x -3(6 - 4x) = -4

2x -18 +12x = -4

2x + 12x = -4 + 18

14x = 14

x = 14/14

x = 1

Substitute the value of x into equation (3)

y = 6 - 4x

y = 6 - 4(1)

y = 6 - 4

y = 2

Hence, the solution to the given system of linear equations is x = 1, y = 2. That is (1, 2)

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Hello.

sin²x + cos²x = 1

cos²x = 1 - sin²x

secx = 1/cosx

sec²x = tan²x + 1

Answer:

12 inches

Step-by-step explanation:

Perimeter refers to distance around the 2D shape.

A hexagon is a polygon with 6 sides. The formula for the perimeter of a hexagon is P=6s

72=6s

The hexagon is 12 inches long

A hexagon has 6 sides. This means that 72 divided by 6 sides = 12 in.

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Please remember to revise this and make it in your own words if you want! I hope this helps you. -Doodle

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Answer:

11

Step-by-step explanation:

try it and see, .........

Answer:

22222222222222222222222222+22222222

Answer:

(-1,7)

Step-by-step explanation:

Use elimination, x = -1, y = 7

Answer:

(-1, 7)

Step-by-step explanation:

Elimination: Step 1

Write in standard form (you can have negatives)

(standard form= Ax+By=C)

Elimination: Step 2

Create(find) opposites

Elimination: Step 3

Add to cancel one variable

Elimination: Step 4

Solve for variable

Elimination: Step 5

Substitute into other equation to find other variable

In a linear system of equations, substitution results in one equation with one variable. The solution to a linear system is an ordered pair, not just a single value.

Problem:

Solve 2x+y=5;x+y=6

Steps:

I will solve your system by substitution.

(You can also solve this system by elimination.)

2x+y=5;x+y=6

Step: Solve 2x+y=5 for y:

2x+y+−2x=5+−2x(Add -2x to both sides)

y=−2x+5

Step: Substitute −2x+5 for yin x+y=6:

x+y=6

x+−2x+5=6

−x+5=6(Simplify both sides of the equation)

−x+5+−5=6+−5(Add -5 to both sides)

−x=1

-x/-1 = 1/-1 (Divide both sides by -1)

x=−1

Step: Substitute −1 for x in y=−2x+5:

y=−2x+5

y=(−2)(−1)+5

y=7(Simplify both sides of the equation)

Answer:

x=−1 and y=7

The average cost per issue of magazine is $3

The given parameters are:

Cost = $36

Issue = 12

The cost per issue is calculated as:

Average = Cost/issue

This gives

Average = 36/12

Evaluate

Average = 3

Hence, the average cost per issue of magazine is $3

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The process needs to meet the following criterion:The process must make large amounts of product at a low cost. That is option A.

Ammonia is defined as a gas compound that is made up of nitrogen and oxygen in the ratio of 1:3 respectively.

The industrial and modern method constructed by Engineers for ammonia production is called steam reforming.

The natural resources used for industrial production of ammonia can be gotten from natural gas such as methane.

To make profit, natural products are used which costs less to acquire but will lead to the production of large ammonia quantity.

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The conclusion that they would arrive at based on the rejection region would be to reject the null hypothesis.

This is the region that tells us that we are not to accept the null. The conclusion would be to reject the null.

This happens when the rejection region is found to be around the area that is in the critical value.

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The value of x is 2 and the length of JK is 4

The given parameters from the circle are:

The lines SR and SQ are the radii of the circle P

This means that lines JK and JL are congruent

So, we have:

JK = KL

Substitute LK = 2x + 4 and JK = 4

4 = 2x + 4

Rewrite the above equation as:

2x + 4 = 8

Subtract 4 from both sides

2x + 4 - 4 = 8 - 4

Evaluate the difference

2x = 4

Divide both sides by 2

2x = 4/2

This gives

x = 2

Substitute x = 2 in LK = 2x + 4

LK = 2*2 + 4

Evaluate the product of 2 and 2

LK = 4 + 4

This gives

LK = 8

The point N divides JK into 2 equal segments

So, we have

JN = JK/2

JN= 8/2

JN = 4

Hence, the value of x is 2 and the length of JK is 4

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Answer:24

Step-by-step explanation:

Answer:

Step-by-step explanation:

Use the power rule,

[tex]\displaystyle \int x^n \, dx = \frac{x^{n+1}}{n+1} + C[/tex]

with [tex]n=-8[/tex]. It follows by the fundamental theorem of calculus that

[tex]\displaystyle \int_1^7 \frac{dx}{x^8} = -\frac1{7x^7} \bigg|_{x=1}^{x=7} = -\frac17 \left(\frac1{7^7} - \frac1{1^7}\right) = \boxed{\frac17 - \frac1{7^8}}[/tex]

The width and height of the rectangle inscribed in the right triangle have a measure of 3.529 units.

In this problem we must use critical values and algebraic methods to determine to determine the dimensions of the rectangle such that the area is a maximum. The equation of the quadrilateral is formed by definition of the area of a rectangle:

A = w · h    (1)

Where:

And the area of the entire triangle is:

0.5 · (5) · (12) = w · h + 0.5 · w · (12 - h) + 0.5 · (5 - w) · h

30 = w · h + 6 · w - 0.5 · w · h + 2.5 · h - 0.5 · w · h

30 = 6 · w + 2.5 · h

2.5 · h = 30 - 6 · w

h = 12 - 2.4 · w    (2)

The quadrilateral of maximum area is always a square, then we must  solve for w = h:

w = 12 - 2.4 · w

3.4 · w = 12

w = 3.529

Then, the width and height of the rectangle inscribed in the right triangle have a measure of 3.529 units.

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For the number line, an open circle will be drawn on the value of 6 and the arrow pointing to the right side.

Given the inequality expression as shown

-2x + 9 < x − 9

Collect the like terms

-2x - x < -9 - 9

-3x < -18

Divide through by -3

x > -18/-3

x > 6

For the number line, an open circle will be drawn on the value of 6 and the arrow pointing to the right side.

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The correct product of (6x - 2)(6 x + 2) is 36x^2 - 4

The expression is given as:

(6x - 2)(6 x + 2).

The above expression is a difference of two squares.

And this is represented as

(a - b)(a + b)= a^2 - b^2

So, we have

(6x - 2)(6 x + 2) = (6x)^2 - 2^2

Evaluate

(6x - 2)(6 x + 2) = 36x^2 - 4

Hence, the correct product of (6x - 2)(6 x + 2) is 36x^2 - 4

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Complete question

What is the product?

(6x - 2)(6 x + 2).

The inverse of the demand function is; P = 9 - 0.25Q

The profit-maximizing price and quantity are; $8.5 and 2 units.

The maximum profit is; $1

A) The demand function we are given is;

Q = 36 - 4P

Making P the subject gives the inverse demand function;

P = (36 - Q)/4

P = 9 - Q/4

P = 9 - 0.25Q

B) The profit-maximization point is the point at which MR = MC.

MR refers to the marginal revenue and MC is the marginal cost.

MC can be calculated as the first derivative of the cost function:

C(Q) = 4 + 4Q + Q²

MC = C'(Q) = 2Q + 4

Total Revenue = Price * Quantity

Total Revenue = (9 - 0.25Q) * Q

Total Revenue = 9Q - 0.25Q²

MR is gotten by differentiating Total Revenue to get;

MR = 9 - 0.5Q

Applying the condition MR = MC, we have;

9 - 0.5Q = 4 - 2Q

Solving for Q gives Q = 2

Thus, profit maximizing quantity is 2.

Thus, profit maximizing price will be;

P(2) = 9 - 0.25(2)

P(2) = $8.5

C) Formula for Maximum Profit is;

Profit = Total Revenue - Total Cost

Total Revenue = 8.5 * 2

Total revenue = $17

Total Cost is;

C(2) = 4 + 4(2) + 2²

C(2) = $16

Thus;

Maximum Profit = 17 - 16 = $1

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Answer:

141; 6526; 28d.

Step-by-step explanation:

try this option, all the details are in the attachment.

If each collection consists of at most 3 books on each subject, the number of collection that can be made of 3 English, 4 Economics, and 5 Business Mathematics books are 40.

A combination, as a mathematical technique, determines the number of possible arrangements in a collection of items.

In the combination, the order of the selection does not matter.

The implication is that in combinations, one can select the items in any order, unlike permutations, where the order of selection matters.

English books on shelf = 3

Economics books on shelf = 4

Business Mathematics books on shelf = 5

Collections to be made = 3 books on each subject

The solution can be set up as a combination problem, as follows:

3 C 3 x 4 C 3 x 5 C 3

3! / 3! (3 – 3)! The solution is 1.

4! / 3! (4 – 3)! The solution is 4.

5! / 3! (5 – 3)! The solution is 10.

1 x 4 x 10

= 40

Thus, if each collection consists of at most 3 books on each subject, the number of collections that can be made of 3 English, 4 Economics, and 5 Business Mathematics books is 40.

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Answer: [tex]\sqrt{407}[/tex]

Step-by-step explanation:

In this triangle, we know that [tex]IJ=46, IK=24, JK=36[/tex].

So, using the Law of Cosines in triangle IJK,

[tex]36^2 = 46^2 + 24^2 - 2(46)(24) \cos (\angle JIK)\\\\-1396=-2(46)(24) \cos(\angle JIK)\\\\\cos (\angle JIK)=\frac{349}{552}[/tex]

Using the Law of Cosines in the triangle LIK,

[tex](KL)^2 = 23^2 + 24^2 - 2(23)(24) \cos (\angle JIK)\\\\(KL)^2 = 23^2 + 24^2 - 2(23)(24)\left(\frac{349}{552} \right)\\\\(KL)^2 = 407\\\\KL=\sqrt{407}[/tex]

Answer:

1. 30

Step-by-step explanation:

∠H + ∠T = 180

(2x+60)+(x+30)=180

3x+90=180

3x=90

x=30