4. The first term in the sequence is 5 and the fifth term is 17. What is the common difference?
(1) 2.4
(2) 12
(3) 3
(4) 4

Answer:

49u² - 154u + 121  factored is  (7u - 11)²

Step-by-step explanation:

To factor the given quadratic expression, 49u² - 154u + 121, rewrite in the form a² - 2ab + b².

Rewrite 49 as 7² and 121 as 11²:

[tex]\implies 7^2u^2-154u+11^2[/tex]

[tex]\textsf{Apply the exponent rule} \quad a^n \cdot c^n=(ac)^n:[/tex]

[tex]\implies (7u)^2-154u+11^2[/tex]

Rewrite 154u as 2 · 7u · 11 :

[tex]\implies (7u)^2-2 \cdot 7u \cdot 11+11^2[/tex]

Compare with the form a² - 2ab + b²:

Apply the perfect square formula: a² - 2ab + b² = (a - b)²

[tex]\implies (7u)^2-2 \cdot 7u \cdot 11+11^2=(7u-11)^2[/tex]

If you are 25yr old and single with no kids/dependents.  The total Federal Income Taxes is $11,218 and FICA paid is $6,478.

First, you need to determine your taxable income.

Gross income: $84,649

Itemized deductions: $10,211

Tax-deferred retirement contributions: $3,288

Taxable income: $71,150

Next, you can use the tax brackets and rates for the 2023 tax year to calculate your federal income tax liability.

The first $10,950 is taxed at 10%: $1,095

The next $32,250 is taxed at 12%: $3,870

The next $28,425 is taxed at 22%: $6,253

The remaining $0 is taxed at 24%: $0

Total federal income tax liability: $11,218

b. For 2023, the Social Security tax rate is 6.2% on the first $147,000 of income, and the Medicare tax rate is 1.45% on all income.

Social Security tax: $5,240.80

Medicare tax: $1,237.20

Total FICA taxes: $6,478

Therefore the total Federal Income Taxes is $11,218 and FICA paid is $6,478.

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Using the unitary method, we found that the unit rate of slime is 0.2 cups per container.

What is meant by the unitary method?

The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, and then multiplying that value to determine the required value. Recognizing the units and values is crucial when using the unitary technique to a problem.

Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things. The unitary approach must be applied whenever we need to determine the ratio of one quantity to another.

Given,

 Number of cups of slime = 7.2

  Number of containers = 36

 Unit rate = Amount of slime in each container

Using the unitary method we can find the unit rate.

7.2 cups = 36 containers

1 container = 7.2/36 = 0.2 cups.

Therefore using the unitary method, we found that the unit rate of slime is 0.2 cups per container.

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C - this equation is simplified to a numeric identity. the variable has infinite solutions.

8k - 14 = -4k + 10 + 12(k - 2) --> use distributive property

8k - 14 = -4k + 10 + 12k -24 --> combine like terms

8k - 14 = 8k -14 --> combine like to each side

8k - 8k = -14 + 14 --> simplify

0 = 0

note, the variable cancels out, therefore there is no identity and ANY numeroc value can be used, as ant value will cancel itself out.

this means there is an infinite numbers of solutions.

The amount of radioactive material that would remain by the 7th hour of decay is 0.12 grams.

The exponential function is a mathematical function denoted by f(x)=\exp or e^{x}. Unless otherwise specified, the term generally refers to the positive-valued function of a real variable, although it can be extended to the complex numbers or generalized to other mathematical objects like matrices or Lie algebras.

here, we have,

An exponential function is in the form:

y = abˣ

where y,x are variables, a is the initial value and b is the multiplicative factor.

Let y represent the amount of substance remaining after x hours. Hence:

a = 9375, at x = 4, y = 15:

15 = 9375(b)⁴

b = 0.2

y = 9375(0.2)ˣ

For the 7th hour, x = 7:

y = 9375(0.2)⁷

  = 0.12

The amount of radioactive material that would remain by the 7th hour of decay is 0.12 grams.

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Shipping Central charges $0.51 more than Globe Delivery for any given weight of the package.

The cost for shipping a package that weighs x pounds from Boise to Los Angeles is shown below.

Company                    Cost ($)

Shipping Central        3x+3.50

Globe Delivery          2x + 2.99

To determine the amount more Shipping Central charges than Globe Delivery, you can subtract the cost function for Globe Delivery from the cost function for Shipping Central.

The difference between the two cost functions is:

3x + 3.50 - (2x + 2.99) = x + 0.51 = $0.51 + x

This means that, for any given weight of the package, Shipping Central charges $0.51 more than Globe Delivery.

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Triangle is a polygon with 3 sides. The record of the letters in your triangle from left to right is EGFBIHDCA.

A triangle is a polygon with 3 sides. Also, It has three vertices.

As the example is given to us, ABCDEFGHI is the record of the letters that are when seen from top to bottom, therefore, if we rotate the triangle such that the left side of the triangle is on the upper side, then the triangle we will get is given below.

Thus, the record of the letters in your triangle from left to right is EGFBIHDCA.

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The angle measure m<T is equivalent to 78 degrees

Similar triangles are triangles that have similar sides and angles.

From the given triangle

<A = <R

<B = <S

<C = <T

Since the sum of angle in a triangle is 180 degrees, hence;

<A + <B + <T = 180

24 + 78 + <T = 180

102 + <T = 180

<T = 180 - 102
<T = 78 degrees

Hence the measure of m<T from the triangle is 78 degrees

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Answer:

ummmm i would say unbiased fam only bc i love ice cream and i always wonder whichwtch one does people like more.

Step-by-step explanation:

Using their unit rates, the 12-ounce bottle costs lesser per ounce than the 8-ounce bottle of stay clean shampoo.

The unit rate is the cost per unit.

The unit rate is computed as the quotient of the total cost and the number of units.

The cost of a 12-ounce bottle of stay clean shampoo = $8

The unit rate per ounce of the 12-ounce bottle = $0.67 ($8/12)

The cost of an 8-ounce bottle of stay clean shampoo = $6

The unit rate per ounce of the 8-ounce bottle = $0.75 ($6/8)

Thus, comparing the unit rate of the 12-ounce bottle with the 8-ounce bottle, we can conclude that it costs more per ounce to buy the 8-ounce bottle than the 12-ounce bottle.

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Size of the house should be 2900 ft².

Correct option is B.

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation.

Given,

Equation for the line that expresses price of house

y = 0.06x + 60.5

where y is the price in thousand dollars, x is area in square feet.

Price of the house = $235000

⇒ y = 235

Then,

235 = 0.06x + 60.5

0.06x = $235 - 60.5

0.06x = 174.5

x = 174.5/0.06

x = 2908.33 ≈ 2900

Hence, 2900 ft² should be the size of the house.

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Answer:

54 and 47

Step-by-step explanation:

Lets first number be "x" and second number be "y"

x = y + 7

x + y = 101

(y + 7) + y = 101

2y + 7 = 101

2y = 94

y = 47

x = 47 + 7

x = 54

Answer:

C. 5x²-7x-8

Step-by-step explanation:

(-3x²-5x +1 ) + (8x²-2x-9)

Grouping like terms:
(- 3x² + 8x²)  + (- 5x - 2x) + (1 - 9)

=> (5x²) + (-7x) + (-8)

=> 5x² - 7x - 8

That's correct. The rate in the portion formula can be expressed as a decimal, fraction, or percentage, depending on the context and what is most convenient for the problem being solved.

How do you calculate ratio and proportion? Ans: The ratio formula is written as a: b a/b for any two numbers. Contrarily, the percentage formula is written as a:b::c:da:b::c:da:b=cd.

An equation in which two ratios are made equal is known as a percentage. As an illustration, you could express the ratio as 1: 3 if there is 1 guy and 3 girls (for every one boy there are 3 girls) 1 out of 4 are boys, and 3/ 4 are girls.

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Answer:

76

Step-by-step explanation:

(16x3)+28

Its 16x3 because there's 3 half hours in 1.5hrs  

To find the x-intercept of the equation 3x + 5y = 9, we set y = 0 and solve for x.When y = 0, the equation becomes 3x + 5(0) = 9, which simplifies to 3x = 9.Solving for x, we get x = 3.The x-intercept of the equation 3x + 5y = 9 is (3, 0).

What is x-intercept ?

An x-intercept is a point where a graph or a line crosses the x-axis. It is the value of the independent variable (x) when the dependent variable (y) is equal to zero. In other words, it is the point at which a function or equation intersects the x-axis, and its coordinates are of the form (x, 0). To find the x-intercept of a graph or equation, you can set y=0 and solve for x.

To find the x-intercept of the equation 3x + 5y = 9, we need to set y = 0 and solve for x.

So, we have:

3x + 5(0) = 9

3x = 9

x = 3

Therefore, the x-intercept of the equation 3x + 5y = 9 is (3,0), which means the point where the line intersects the x-axis is (3,0).

To verify, we can graph the equation and see that the point (3,0) is indeed on the x-axis.

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Answer:

Step-by-step explanation:

The formula for calculating the future value of a continuously compounded investment is:

FV = PV * e^(rt)

where PV is the present value, r is the annual interest rate as a decimal, t is the time in years, and e is the mathematical constant approximately equal to 2.718.

Plugging in the given values, we get:

FV = 5100 * e^(0.08 * 13) = 5100 * e^1.04 = 5100 * 2.856116786 = 14536.86

So, the future value of the investment after 13 years at an 8% interest rate compounded continuously would be approximately $14,536.86. Rounded to 2 decimal places, this is $14,536.86.

Answer:

2) 47 snow globes (51+8-12) 23) 130 snowballs (46+59+25) 4) 92 penguins (83+69-55)

Answer:

Step-by-step explanation:

The balance of the savings account after 48 months can be calculated using the formula for compound interest:

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

where:

A is the balance after t years

P is the principal (initial amount)

r is the interest rate (as a decimal)

n is the number of times compounded per year

t is the number of years

Step-by-step, the calculation is as follows:

Convert the interest rate from a percentage to a decimal:

r = 7% = 0.07

Determine the number of times compounded per year:

n = 2 (compounded semi-annually)

Determine the number of years:

t = 48 months / 12 months/year = 4 years

Plug the values into the formula:

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

A = $3500 * (1 + 0.07/2)^(2 * 4)

Calculate the balance using the formula:

A = $3500 * (1.035)^8

A = $3500 * 1.306769

A = $4588.72

So, the balance in the savings account after 48 months is $4588.72.

The measure of angle that is an exterior angle to B is 95°.

The angle created by any extended side of a triangle and its neighboring side is referred to as the external angle of a triangle. A triangle has three external angles. It should be noticed that every outside angle and corresponding interior angle constitute a linear pair. We are aware that a triangle's internal angle is created when its sides come together at its apex.

Given that,

The measure of angle 4 is 120°, and the measure of angle 2 is 35°.

Triangle A B C. Angle A is 2, angle B is 1, and angle C is 3. The exterior angle to angle B is 5, and the exterior angle to angle C is 4.

The sum of an interior and exterior angle is 180°,

∠4 + ∠3 = ∠1 + ∠5 = ∠2 + ∠6 = 180°

and ∠2+ ∠1 +∠3 = 180°

Also, ∠3 = 180 - ∠4

∠3 = 180 - 120 = 60°

Substitute the values,

∠2+ ∠1 +∠3 = 180°

35 + ∠1 + 60 = 180

∠1 = 180 - 95

∠1  = 85°

Now, ∠1 + ∠5 = 180

∠5 = 180 - 85

∠5 = 95°

Hence, the measure of angle that is an exterior angle to B is 95°.

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The correct question is:

Answer: A) 95 Degrees

Step-by-step explanation:

When x changes from 2 to 5, the average velocity (or average rate of change of y with respect to x) is 9.33 m/s. When x changes from 2 to 2 + h, the average velocity is 2 + hm/s.

Average speed is determined by dividing the total distance you travelled by the total time, whereas average velocity is determined by dividing your displacement (a vector Throughout the entire period, position to your finish position).

(A) The following formula is used to get the average velocity when x changes from 2 to 5:

value of y at x = 2

= 2²+2 = 6 m

value of y at x = 5

= 5²+5 = 30 m

displacement equals 30 – 6 = 24 m.

Time is 5 - 2 = 3 seconds.

average velocity

= displacement /Time duration

= 24/3 = m/s

B) Value of y at x = 2 = 5 for x changing from x to x plus ie for minimal change in x.

Displacement during a little change in x will be 0 because the value of y will once again be 5.

C )  

y(x) = x² + x

dy / dx = 2x + 1

dy / dx  represents instantaneous  velocity

so when x = 2

instantaneous velocity = 2 x 2 +1

= 5 m /s

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The values of x and y would be   [tex]x=\frac{20 \sqrt{3}}{3}[/tex] and [tex]y=\frac{40\sqrt{3}}{3}[/tex].

What are trigonometric ratios?

Trigonometric ratios are mathematical functions that describe the relationship between the angles and sides of a right triangle. The three main trigonometric ratios are the sine, cosine, and tangent.

In the given figure, by using trigonometric ratios, we can find x

tan60° = 20/x

√3 = 20/x

x = 20/√3

=> [tex]x=\frac{20 \sqrt{3}}{3}[/tex]

Now by using the ratio sin60°

sin60° = 20/y

√3/2  = 20/y

y = 40/√3

[tex]y=\frac{40\sqrt{3}}{3}[/tex]

Hence, the values of x and y would be   [tex]x=\frac{20 \sqrt{3}}{3}[/tex] and [tex]y=\frac{40\sqrt{3}}{3}[/tex].

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Answer:

12756pi km

Step-by-step explanation:

Circumference = pi * diameter

Diameter = radius * 2

kilometer = meter/1000

6378000*2= 12756000

diamter = 12756000 meters

12756000/1000 = 12756 kilometers

diameter = 12756 kilometers

12756pi km= circumference

Answer:

simple interest is $6.8

Miguel pay the amount to Julio at the end of 6​ months was $206.8

Step-by-step explanation:

Given : Miguel Rodriguez borrowed ​$200 from his brother Julio to pay for books and tuition. He agreed to pay Julio in 6 months with simple annual interest at 6.8​%.

To Find : ​a) How much will the interest amount​ to?

​b) What amount must Miguel pay Julio at the end of 6​ months?

Solution :

Formula for simple interest :

Where rate is in decimal

Time is in years

So, rate of interest = 6.8 % = 0.068

Time = 6 months = 6/12=0.5

Principal = $200

Thus= 200x0.068x0.5=6.8

An absolute value inequality that expresses the actual temperature in your city, given that the average January temperature is 45° F and the temperature can vary up to 5° F warmer or colder, would be: | x - 45 | ≤ 5.

Where x represents the actual temperature in degrees Fahrenheit.

An inequality with an absolute value expression is referred to as an absolute value inequality. A quantity is enclosed in vertical bars (| |), which stand for the distance between that quantity and zero on the number line, to indicate an absolute value statement. The absolute value of an integer is always positive, hence regardless of the sign of x, |x| indicates the distance of x from zero.

Finding all feasible values of the variable that meet the inequality is the goal when resolving an absolute value inequality. To accomplish this, we first isolate the expression defining the absolute value, and then divide the inequality into two cases, one for positive and one for negative expressions defining the absolute value. Then, we resolve each case separately and combine the solutions.

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Rounded to the nearest hundredth of an inch, the distance is 310.91 inches.

How far apart or how far away items or locations are from one another is measured numerically as distance. A physical quantity, it is typically stated in terms of meters, kilometers, miles, or feet. Given that it simply has magnitude and no direction, distance is a scalar quantity.

Usually, a formula is used to determine the distance between two points. One example is the distance formula in Euclidean geometry, which includes computing the square root of the sum of the squares of the coordinate differences between the two points.

Distance can be measured in a variety of contexts, including physics, where it is used to describe an object's displacement through time, and geography, where it is used to define the separation between two points on the surface of the Earth. It is also frequently used in daily life when people go for walks or runs or when they drive from one area to another to calculate the distance they travel.

There are no holes in the first and last 2 inches of the metal strip, leaving 3410 inches (3414 - 2 - 2) as the remaining length.

We can divide the total remaining length by the number of gaps between the holes to determine the distance between the centers of two adjacent holes. The distance between the 12 holes is determined by the fact that there are 11 gaps between them.

distance = (total length - length of 2 end pieces) / (number of gaps)

distance = (3410 in.) / 11

distance ≈ 310.91 in.

Rounded to the nearest hundredth of an inch, the distance is 310.91 inches.

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The equation for the graphed quadratic function is:

y = -1*(x - 3)^2 + 2

Here we have the graph of a quadratic equation. Remember that if the leading coefficient is a and the vertex is (h, k) then we can write:

y = a*(x - h)^2 + k

Here the vertex is at (3, 2) then we can write:

y = a*(x - 3)^2 + 2

We can see that it also passes through the point (1, -2), replacing these values we will get:

-2 = a*(1 - 3)^2 + 2

-2 = a*4 + 2

-2 - 2 = a*4

-4/4 = a = -1

Then the quadratic equation is:

y = -1*(x - 3)^2 + 2

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Step-by-step explanation :

Sum of first 50 terms for the AP:

[tex]\dashrightarrow { \boxed{\sf S = \dfrac{n}{2} (2a + (n - 1)d )}}[/tex]

where ,

On substituting the values , we get :

[tex]\dashrightarrow \sf S = \dfrac{50}{2}(2 \times 8 + (50 - 1) \times 12) \ \\ \\ \dashrightarrow \sf S = 25(16 + 49 \times 12 ) \\ \\ \dashrightarrow \sf S = 25(16 + 588 )\\ \\ \dashrightarrow \sf S = 25(604 )\\ \\ \dashrightarrow \sf S = 15100 \\ [/tex]

[tex] \therefore[/tex] Sum of the first 50 terms is 15100