Suppose f(x)=2x-8, evaluate f(7) =

value of the sides of the triangle are given as follows;

shorter leg = 5

longer leg = 12

hypotenuse = 13

Pythagoras Theorem states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.

If the short leg = x

the longer length = x+7

the hypotenuse = x+7+1 = x+8

Using Pythagorean theorem

(x+8)² = x² + (x+7)²

x² +16x +64 = x²+ x² + 14x +49

collecting like terms

x²-2x²+16x -14x+64 -49= 0

-x² + 22x +15 = 0

x² -2x -15 = 0

x² -5x +3x -15 = 0

(x² -5x) (3x -15) = 0

x(x-5) +3(x-5)

(x+3)(x-5) = 0

x= -3 or +5

Since length is discreet we choose the positive answer

therefore x = 5

shorter leg = 5

longer leg = 5+7 = 12

hypotenuse = 5+7+1 = 13

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Equation [1] : a(n) = 3 + (n - 1)5 represents the step where he made the mistake.

We have,

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have a student who used the explicit formula a[n] = 5+3(n-1) for the sequence 3,8,13,18,23,...to find the 12th term.

The given sequence is -

3 , 8 , 13 , 18 , 23, ..

Here -

d = 8 - 3 = 13 - 8 = 5

a = 3

a(n) = a + (n - 1)d      {for arithmetic sequence}

a(n) = 3 + (n - 1)5     ...Eq[1]

a(n) = 3 + 5n - 5

a(n) = 5n - 2

Therefore, Equation [1] : a(n) = 3 + (n - 1)5 represents the step where he made the mistake.

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complete question:

A student uses the explicit formula an= 5+3(n-1) for the sequence 3,8,13,18,23,...to find the 12th term. Explain the error the student made.

The length of arc length s is 1152π² or 11358.26.

We have,

The arc length of a circle can be calculated using the formula:

Arc Length = 2πrθ/360

Where:

π is a mathematical constant approximately equal to 3.14159.

r is the radius of the circle.

θ is the central angle subtended by the arc, measured in degrees.

The arc length of a circle can be written as:

s = angles/360 x 2πr _______(1)

Now,

r = 4 cm

Angle = (2/5)π

Now,

Substitute in (1).
s = angles/360 x 2πr

s = (2/5)π/360 x 2π x 4

s = 2π x 72 x 2π x 4

s = 4π² x 288

s = 1152π²

or

s = 11358.26

Thus,

The length of arc length s is 1152π² or 11358.26.

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Using the conversion factor, we can convert the liters into the number of gallons of 1. 057 gallons.

A conversion factor is a mathematical ratio that is used to convert one unit of measurement to another. It is a multiplier or divisor that relates two different units of measurement for the same quantity.

To convert 4 liters into gallons using the conversion factor 1 gallon = 3.785 liters, you divide the given value (in liters) by the conversion factor.

This means that the number of gallons in 4 liters would be:

= 4 liters ÷ 3. 785 liters/gallon

= 1. 057 gallons

Therefore, 4 liters is approximately equal to 1. 057 gallons.

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The total cost of the meal if the meal costs $50 is $60

From the question, we have the following parameters that can be used in our computation:

Tip percent = 20%

From the question, we can use any value as the cost of the meal

So, we can use the following

Meal cost = $50

So, we have

Tip amount = Tip percent * Meal cost

This gives

Tip amount = 20% * 50

Tip amount = 10

Next, we have

Total meal cost = Tip amount + Meal cost

This gives

Total meal cost = 10 + 50

Evaluate

Total meal cost = 60

Hence, the total cost of the meal is $60

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If Each card corresponds to a sample point with a 1/52 probability then the  sample points in the event an ace is selected is S = {ace of clubs, ace of diamonds, ace of hearts, ace of spades}

In a standard deck of 52 playing cards, there are four aces.

Each ace corresponds to a different suit: clubs, diamonds, hearts, and spades.

So, when we talk about the event of selecting an ace, we are referring to the act of choosing one of these four specific cards from the deck.

The sample points in the event "an ace is selected" are the individual cards that match this criteria.

Therefore, the sample points in this event are:

S = {ace of clubs, ace of diamonds, ace of hearts, ace of spades}

These four cards are the possible outcomes when we randomly select a single card from the deck, focusing only on the event of selecting an ace.

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Answer: false

Step-by-step explanation:

Using DeMoivre’s theorem, the answer in regular form would be (5 + 5√3i)⁷ = -5000000 + 8660254.03i

The De Moivre's Theorem is used to simplify the computation of powers and roots of complex numbers and is used in together with polar form.

Convert the complex number to polar form. The polar form of a complex number is z = r(cos θ + isin θ),

r = |z|  magnitude of z

it becomes

r = √((5)² + (5√3)²) = 10

θ = arg(z) is the argument of z.

θ = atan2(b, a) = atan2(5√3, 5) = π/3

(5 + 5√3i) = 10 × (cos π/3 + i sin π/3)

De Moivre's theorem to raise the complex number to the 7th power

(5 + 5√3i)⁷

= 10⁷× (cos 7π/3 + i sin 7π/3)

= 10⁷ × (cos 2π/3 + i sin 2π/3)

Convert this back to rectangular form:

Real part = r cos θ = 10⁷× cos (2π/3) = -5000000

Imaginary part = r sin θ = 10⁷ × sin (2π/3) = 5000000√3 = 8660254.03i

∴  (5 + 5√3i)⁷ = -5000000 + 8660254.03i

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Answer:10^7 (1/2 - √3/2 i)

Step-by-step explanation:

To use DeMoivre's theorem, we first need to write the number in polar form. Let's find the magnitude and argument of the number:

Magnitude:

|5 + 5√(3i)| = √(5^2 + (5√3)^2) = √(25 + 75) = √100 = 10

Argument:

arg(5 + 5√(3i)) = tan^(-1)(√3) = π/3

So the number can be written in polar form as:

5 + 5√(3i) = 10(cos(π/3) + i sin(π/3))

Now we can use DeMoivre's theorem:

(5 + 5√(3i))^7 = 10^7 (cos(7π/3) + i sin(7π/3))

To simplify, we need to find the cosine and sine of 7π/3:

cos(7π/3) = cos(π/3) = 1/2

sin(7π/3) = -sin(π/3) = -√3/2

Explanation:

So the final answer in rectangular form is:

10^7 (1/2 - √3/2 i)

The constraints involve three variables (Y, I, and Z), it is not feasible to graphically represent the entire Feasible region in three dimensions.

The linear programming model for  decision variables, objective function, and constraints.

Decision Variables:the number of gallons of frozen yogurt purchased each week as Y and the number of gallons of ice cream purchased each week as I.

Objective Function:

The objective is to maximize the total profit. The profit from frozen yogurt can be calculated as 3.60Y, and the profit from ice cream can be calculated as 4.15I. Thus, the objective function is:

Maximize Profit: Z = 3.60Y + 4.15I

Constraints:

1. Budget constraint: The total cost of frozen yogurt and ice cream should not exceed the weekly budget of $90.

  Cost Constraint: 0.75Y + 0.93I ≤ 90

2. Freezer space constraint: The total gallons of frozen yogurt and ice cream should not exceed the available freezer space of 115 gallons.

  Space Constraint: Y + I ≤ 115

3. Ice cream sales constraint: The weekly ice cream sales should be at least twice the frozen yogurt sales.

  Ice Cream Sales Constraint: I ≥ 2Y

4. Non-negativity constraint: The number of gallons for both products cannot be negative.

  Non-negativity Constraint: Y ≥ 0, I ≥ 0

The model using graphical analysis, we can plot the constraints on a graph and find the feasible region. Then, we can evaluate the objective function at each corner point of the feasible region to determine the optimal solution.

Since the constraints involve three variables (Y, I, and Z), it is not feasible to graphically represent the entire feasible region in three dimensions.

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Lin's family has completed approximately 86.15% of the total Distance to her grandmother's house.

The percentage of the distance Lin's family has completed, the ratio of the distance they have traveled to the total distance.

The distance traveled is 325 miles, and the total distance to Lin's grandmother's house is 377 miles.

To calculate the percentage, we can use the following formula:

Percentage = (Distance Traveled / Total Distance) * 100

Plugging in the values, we have:

Percentage = (325 / 377) * 100

          = 0.8615 * 100

          = 86.15

Therefore, Lin's family has completed approximately 86.15% of the total distance to her grandmother's house.

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John William is entitled to purchase 15,000 shares before the offering is made to the public.

a. To calculate the percentage of the total vote John William will control, we need to find the proportion of shares he owns out of the total shares represented at the meeting.

John William owns 6,000 shares out of the 20,000 shares offered so far. Therefore, the proportion of shares he owns is 6,000/20,000, which simplifies to 3/10 or 0.3.

To convert this proportion to a percentage, we multiply by 100:

Percentage of the total vote = 0.3 * 100 = 30%

Thus, John William will control 30% of the total vote at the.         shareholder meeting.    

b. Preemptive rights allow existing shareholders to purchase new shares before they are offered to the public. To determine the number of shares John William is entitled to purchase, we need to calculate the proportion of his current ownership.

John William owns 6,000 shares out of the total shares offered so far, which is 20,000. Therefore, his ownership proportion is 6,000/20,000, or 3/10.

If Peixotto Media plans to issue 50,000 new shares, John William's entitlement would be:

Entitlement = (3/10) * 50,000 = 15,000 shares.

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The expression that is equivalent to [tex]\\\\\frac{60m^-2n^6\\}{5m^-4 n^-2}[/tex] for all values of m and n where the 5m-4n-2 expression is defined is [tex]12m^{2} n^{8}[/tex]

In mathematics, an expression or mathematical expression  can be described as the finite combination of symbols which is been analyzed and  well-formed according by following some set of rules which could be varies base on the kind of the symbol as ll as the operation  that are involved in the expression and it s been done  depending on the context so that another expression can be gotten.

This is given as   [tex]\\\\\frac{60m^-2n^6\\}{5m^-4 n^-2}[/tex]

Then we have it defined by;  [tex]12m^{2} n^{8}[/tex]

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The other information can the student use to establish the AA criterion is Angle LMN congruent angle LQR or angle LMN congruent angle LRQ

The student can use the following information to establish the AA criterion:

These two angles correspond to the two angles in the other triangle (LQR or LRQ) that are not congruent to the angle already known to be congruent (angle QLR).

Therefore, the AA congruent for similarity can be congruent .

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About 88.49% of cellphone plans have charges that are less than $83.60.

To determine the percentage of plans that have charges less than $83.60, we need to find the z-score (z) using the given mean and standard deviation, and then look up the corresponding area under the normal distribution curve.

z = (x – μ) / σ

where x = 83.60, mean, μ =  62 and standard deviation, σ = 18

Thus, the z-score of $83.60 is:

z = (83.60 - 62) / 18 = 1.2

Using a standard normal distribution table, we can find that the area to the left of z = 1.20 is 0.8849 or 88.49% (check image attached).

Therefore, about 88.49% of cellphone plans have charges that are less than $83.60.

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Answer:

45 degrees

Step-by-step explanation:

The 4 angles of a quadrilateral will add to 360.

We know 1 of them (angle B) is 90 degrees.

We can set up an equation to solve the others.

2x+3x+x+90 = 360

Now solve for x.

Start by combining the x terms together.

6x+90 = 360

6x = 360-90

6x = 270

(6x/6) = 270/6

x = 45 degrees

Check back to see if that makes sense and if the equation equals 360 when x is 45:

2x+3x+x+90 = 360

2(45)+3(45)+45+90=360.

The values of x for the tangent segments to the circles are: (25). x = 2 and (26). x = 4

A theorem of tangents to a circle states that if from one exterior point, two tangents are drawn to a circle then they have equal tangent segments.

(25). 2x - 1 = x + 1 {equal tangent segments}

2x - x = 1 + 1 {collect like terms}

x = 2

(26). 2x - 4 = x {equal tangent segments}

2x - x = 4 {collect like terms}

x = 4

Therefore, the values of x for the tangent segments to the circles are: (25). x = 2 and (26). x = 4

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Answer:

It is true that in algebra minus symbol represent two things

Step-by-step explanation:

And it is true that it depend on where it placed such as

8-2 this minus indicate the substraction of two terms

-3 this show that the number has negative quantity

The circle equation x² + 8x + y² -10y - 32 = 0​ can be graphed using (x + 4)² + (y - 5)² = 73

From the question, we have the following parameters that can be used in our computation:

x² + 8x + y² -10y - 32 = 0​

Add 32 to both sides of the equation

This gives

x² + 8x + y² -10y = 32

Group the terms in two's

So, we have

(x² + 8x) + (y² -10y) = 32

When we complete the square on each group, we have

(x + 4)² + (y - 5)² = 16 + 25 + 32

Evaluate the like terms

(x + 4)² + (y - 5)² = 73

Hence, the circle equation can be graphed using (x + 4)² + (y - 5)² = 73

See attachment for the graph

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The type of retirement account is an investment option for ANY young person is  401(k). option C

A 401(k) retirement account is described as an option for investing money, created and arrangement for youths with access to any lucrative job that pays a reasonable amount of money.

This retirement account creates room for  individuals to contribute a portion of their tax income towards retirement savings, and also  contributes to grow tax-deferred until withdrawal.

However, pensions are employer-funded retirement plans and may be unavailable to all young individuals

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answer: 5'6"

step by step: 1'5"+2"=1'7"+1'3"=3'0"+1'2"=4'2"+1'4"=5'6"

Answer: X = 8

Step-by-step explanation:

47 - 7 = 40

40 / 5 = 8

x = 8

Answer:

[tex]a_n=3n+4[/tex]

Step-by-step explanation:

If the common difference is d=3 and the first term is a₁=7, then we can create an arithmetic sequence:

[tex]a_n=a_1+(n-1)d\\a_n=7+(n-1)(3)\\a_n=7+3n-3\\a_n=3n+4[/tex]

Answer:

(d) 58

Step-by-step explanation:

Let's start with the equation:

6a+4b-3c

Now, since we got the values of a, b, and c, we can just plug them into the equation:

6(4)+4(7)-3(-2)

24+28+6=58

So the answer is d) 58

Option C (15 17 19) has a similar mean absolute deviation to the data set in the given dot plot.

The informational collection in the given speck plot has a mean of roughly 55 and a moderately little scope of values, with most of the information bunched around the mean. An informational index with a comparable mean outright deviation would have a comparative degree of variety in the information values.

Out of the given choices, the informational index that has a variety like the given informational collection is choice C: 15 17 19. This informational collection has a mean of roughly 17 and a little scope of values, with most of the information bunched around the mean.

The mean outright deviation of this informational collection is around 1.63, which is like the mean outright deviation of the given informational collection. Choice A (50 51 52 53 54 55 56 57 58 59 60 61) has a bigger scope of values and a bigger mean outright deviation contrasted with the given informational collection.

Choice B (4612) and Choice D (8 9 1011 and 55 57 59 61 63 65) have altogether unique mean qualities and scopes of values, and consequently their mean outright deviations are not quite the same as the given informational collection.

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The number of rides that one would expect to be less than `6.5` minutes long is 4 rides.

To determine the number of rides, we will first begin by classifying the quartiles. There are 4 quartiles that each constitute 25% of the ride timing.

The number of rides that one would expect to be less than 6.5 minutes can be gotten by finding 25% of 16, the total days recorded. This is 1/4 * 16 = 4. So, the number of rides that will be less than 6.5 minutes will be 4 rides.

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Answer:

width = 6

length = 9

Step-by-step explanation:

Perimeter = 2(length + width) or P = 2(l + w)

2(l + w) = 50

l + w = 25

l = 25 - w

Area = length x width or A = lw

lw = 114

Substitute l = 25 - w into the lw = 114

(25 - w)w = 114

25w - w^2 = 114

-w^2 + 25w - 114 = 0

=> w^2 - 25w + 114 = 0

we have x = [-b ± √(b^2 - 4ac)] / 2a

w = [-(-25) ± √((-25)^2 - 4(1)(114)))] / 2(1)

w = [25 ± √(625 - 456)] / 2

w = [25 ± √(169)]/2

w = [25 ± 13]/2

w = [25 + 13]/2 = 38/2 = 14

or

w = [25 - 13]/2 = 12/2 = 6

if width = 14, length = 25 - 14 = 11

then area = 14 x 11 = 154, this is incorrect answer

if width = 6, length = 25 - 6 = 19

then area = 6 x 19 = 114, this is correct answer

Answer:

zero product property

Step-by-step explanation:

To conclude that x+2=0 or x+6=0 from the equation (x+2)(x+6)=0, one must use the zero product property.

The zero product property states that if the product of two factors is equal to zero, then at least one of the factors must be equal to zero. In this case, if (x+2)(x+6)=0, it means that the product of (x+2) and (x+6) is zero. Therefore, we can conclude that either (x+2) = 0 or (x+6) = 0, based on the zero product property.