find an equation of the line passing through the given points (1,-3) and (3,3)

The nth term of the quadratic sequence 1, 12, 29, 52, 81 is T(n) = 2n² - n - 2.

1. Check for a Quadratic Sequence:

To determine if a sequence is quadratic, we look at the differences between consecutive terms, and then the differences between those differences (second differences).

First differences: 11, 17, 23, 29

Second differences: 6, 6, 6

The sequence is quadratic since the second differences are constant.

2. General Form of a Quadratic Sequence:

The quadratic sequence formula in general is:

T(n) = an² + bn + c

Where:

T(n) is the nth term

a, b, and c are constants to be determined

3. Forming Equations:

We can use the first three terms of the sequence to create three equations:

For n = 1: a(1)² + b(1) + c = 1

For n = 2: a(2)² + b(2) + c = 12

For n = 3: a(3)² + b(3) + c = 29

Simplifying these equations, we get:

a + b + c = 1

4a + 2b + c = 12

9a + 3b + c = 29

4. Solving the Equations:

By concurrently solving this set of equations, we arrive at:

a = 2

b = -1

c = -2

5. Finding the nth Term:

Substituting the values of a, b, and c into the general formula, we get: T(n) = 2n² - n - 2

Answer:

-3x-16

Step-by-step explanation:

(2x-6)-(5x+10)

2x-6-5x-10

2x-5x-6-10

-3x-6-10

-3x-16

Answer:

12x-8y

Step-by-step explanation:

10x+2x=12x

-5y-3y=-8y

Answer: 12x-8y

Step-by-step explanation: add like terms 10x and 2x, and -3-5= 8 so 8y

m∠S = 45°

Solution:

Given ∠R = 3x°, ∠S = 2x°, ∠T = 3x°.

Sum of the angles of a triangle = 180°

⇒ m∠R + m∠T + m∠S = 180°

⇒ 3x° + 3x° + 2x° = 180°

Adding all the angles.

⇒ 8x° = 180°

Divide both sides of the equation by 8, we get

⇒ x° = 22.5°

Substitute x = 22.5° in m∠S.

⇒ m∠S = 2 × 22.5°

⇒ m∠S = 45°

Hence, m∠S = 45°.

Answer:

4850 students

Step-by-step explanation:

if 2619 women make up 54% of the entire student body, then we know that 0.54x=2619, since 54%=0.54 and we can call x the entire student body. solve:

0.54x=2619

÷0.54    ÷0.54

x=4850

henceforth, the total enrollment is 4850 students.

hope this is helpful!

Answer:

4850 students

Step-by-step explanation:

Let b = total enrollment.

Then 54% of b = 2619.  Find b by dividing both sides of

0.54b = 2619 by 0.54:

b = 4850

The total enrollment is 4850.

Answer:

35

Step-by-step explanation:

Final answer:

To determine the least number of years from 2023 until the year rounds to 2060, subtract 2023 from 2055, the first year that rounds to 2060, resulting in 32 years.

Explanation:

The question is asking for the least number of years it will take for the current year to be rounded to nearest ten to become 2060. To answer this, we consider the year closest to 2060 that when rounded will result in exactly 2060. We are considering that the current year is 2023, optimizing the rounding rule of being closer to or equal to the next multiple of ten (2055-2064 would round to 2060). Following this logic, the first year that rounds to 2060 is 2055, therefore the least number of years from 2023 until we reach a year that rounds to 2060 is 2055 minus 2023, which is 32 years.

Answer: 23x305 = n , n = 7,015 square feet

Step-by-step explanation:

1 office = 305 square feet

If we want to calculate the area of 23 offices, we just need to multiply the area of one office, by the number of total offices.

That's 305 square feet * 23 = 7015 square feet

The correct answer is 23x305 = n , n = 7,015 square feet

Hope I helped!

Answer:

23 over 3 will give you a mixed number / whole number of 8

Step-by-step explanation:

your answer is 8

Answer:

the answer to this is

24/3= 8 ( edited again as I TOOK THE wrong values )

Answer:

18.7 feet far

Step-by-step explanation:

Based on the information given we can conclude that our set up will be a Right triangle (i.e. one angle is 90°), where the hypotenuse will be denoted by the guy wire of [tex]20ft[/tex]  and angle of 21° is the angle formed between then hypotenuse and the base (i.e. ground).

Thus we want to find the base length (lets call it [tex]x[/tex] ) of this triangle, so we can use trigonometry as we have one angle and the hypotenuse, as follow:

[tex]cos(21)=\frac{adjacent side}{hypotenuse}=\frac{baselength}{guywire}\\\\ cos(21)=\frac{x}{20} \\x=20cos(21)\\x=18.671\\x=18.7ft[/tex]

So the base is approximately 18.7 feet far from the tree of the anchored wire.

The distance from the base of the tree to the stake anchoring a guy wire that is 20 ft long and makes a 21-degree angle with the ground is approximately 18.8 ft, found using the cosine function of trigonometry.

The student asked for help in determining the distance from the base of the tree to the stake anchoring a guy wire that is 20 ft long and makes a 21-degree angle with the ground. To solve this problem, we need to employ trigonometry, specifically the cosine function which relates the adjacent side of a right triangle (the distance we're looking for) to the hypotenuse (the length of the guy wire) and the angle between them.

Using the formula cosine(angle) = adjacent/hypotenuse, we can set up our equation as cos(21°) = distance/20 ft. Rearranging the equation to solve for the distance, we get distance = 20 ft * cos(21°). After calculating, we find that the distance from the base of the tree to the stake is approximately 18.8 ft.

Answer:

[tex]p\leq 4[/tex]

Step-by-step explanation:

we know that

The solution of the graph shows the interval (-∞,4]

All real numbers less than or equal to 4

In a number line the shaded area is at left of x=4 (closed circle)

The number 4 is included in the solution

therefore

the inequality that represent the graph is

[tex]p\leq 4[/tex]

Answer:

The rule of translation (x,y) → (x+6 , y-8)

Step-by-step explanation:

The rest of the question is the coordinates of the ΔABC and ΔA'B'C'

The coordinates of the ΔABC: A(-6,2) , B(-5,5) , C(-1,3)

The coordinates of the ΔA'B'C': A'(0,-6) , B'(1,-3) , C'(5,-5)

It is required the rule of translation.

By Comparing between any of the points and its image

For example between A and A'

Let A(-6,2) = (x,y)  and  A'(0,-6) = (x+h , y+k)

So, x = -6 and y = 2

And x+h = 0 , y+k = -6

Substitute with x and y to find h and k

So, -6 + h = 0 ⇒ h = 6

And 2 + k = -6 ⇒ k = -8

So, the rule of translation (x,y) → (x+6 , y-8)

Answer:

9

Step-by-step explanation:

12x+40 = 7x + 85

12x - 7x = 85 - 40

5x = 45

x=9

so designing 9 shirts will take for the 2 stores to cost the

same.

Final answer:

To find the number of shirts, set up a system of equations and solve for the cost of each store. It will take 9 shirts for the two stores to cost the same.

Explanation:

To find the number of shirts it will take for the two stores to cost the same, we need to set up a system of equations. Let's assume the number of shirts needed is 'x'.

For Stylish Shirts: Total Cost = (Price per shirt * Number of shirts) + Design Fee = ($12 * x) + $40.

For Decatur Clothing: Total Cost = (Price per shirt * Number of shirts) + Design Fee = ($7 * x) + $85.

Setting the two total costs equal to each other, we have: ($12 * x) + $40 = ($7 * x) + $85. Solving this equation gives us x = 9. Therefore, it will take 9 shirts for the two stores to cost the same.

Answer:

right 2, down 9

Step-by-step explanation:

move point A' two places to the right, and down nine to get to point A

Answer:

270 miles

Step-by-step explanation:

Let the total distance be d.

Then (2/3)d = 180 miles.

Solve for d by multipying both sides by (3/2):

(3/2)(2/3)d  = (3/2)(180 miles) = 270 miles

The total distance is 270 miles.

Using Pythagorean theorem

[tex]\\ \sf\longmapsto P^2=H^2-B^2[/tex]

[tex]\\ \sf\longmapsto P^2=17^2-11^2[/tex]

[tex]\\ \sf\longmapsto P^2=289-121[/tex]

[tex]\\ \sf\longmapsto P^2=168[/tex]

[tex]\\ \sf\longmapsto P\approx 13[/tex]

Answer:

H=17B=11P=?Using Pythagorean theorem

Step-by-step explanation:

Answer:

70

Step-by-step explanation:

To evaluate k( -5), substitute x = - 5 into k(x)

k(−5)=(6×-5)+100=−30+100=70

Answer:

1246 sq cm

Step-by-step explanation:

you can break this shape into two rectangles, find the area of each, and then add them together

Answer:

First we need to find the area of the whole shape which would be the length times width

Length= 39

Width= 34

39*34=1,326

This is the area if the shape were shaded in

Now we want to find the area of the missing section which is again length times width

Length=10

Width=8

10*8=80

This is the area of the missing section, so to find the area of the shape you would take your total area minus your missing section area

1,326-80= 1,246

Your final answer would be 1,246 sq. cm

Hope this helps ;)

Step-by-step explanation:

Answer:

Step-by-step explanation:

10=z+6

subtract 6 from both sides

4=z

z=4

Answer:

The answer is 4

Step-by-step explanation:

To get the answer for this equation, take 6 and subtract from both sides.. meaning 6-6 and they will cancel and then subtract 6 from 10 and that will give you your answer of 4.

Answer:

[tex]\dfrac{x^2}{4}+\dfrac{y^2}{16}=1[/tex]

Step-by-step explanation:

If the ellipse has its x-intercepts at points (2, 0) and (-2, 0) and y-intercepts at points (0, 4) and (0, -4), then its symmetric across the y-axis and across the x-axis.

Moreover,

[tex]a=2\\ \\b=4[/tex]

The equation of such ellipse is

[tex]\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1[/tex]

Hence, the equation of the ellipse is

[tex]\dfrac{x^2}{2^2}+\dfrac{y^2}{4^2}=1\\ \\ \\\dfrac{x^2}{4}+\dfrac{y^2}{16}=1[/tex]

Answer:$18.00

Step-by-step explanation:

120% is "x" is 50, meaning "x" must be the 100%.

if 50 is 120% of "x", and "x" is the 100%, what is "x"?

[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} x&100\\ 50&120 \end{array}\implies \cfrac{x}{50}=\cfrac{100}{120}\implies \cfrac{x}{50}=\cfrac{5}{6}\implies 6x=250 \\\\\\ x = \cfrac{250}{6}\implies x = \cfrac{125}{3}\implies x = 41\frac{2}{3}\implies x = 41.\overline{6}[/tex]

Answer:

Step-by-step explanation:

7,014,999,999 rounded to the nearest hundred thousand

7,015,000,000 <===

Answer:

I think it is option B. and option C.

Step-by-step explanation:

an instance of a form of reasoning in which a conclusion is drawn from two given or assumed propositions. a common or middle term is present in the two premises but not in the conclusion, which may be invalid.

Answer:

C, B

Step-by-step explanation:

4x * 1 = 4x

4x * y = 4xy

4x + 4xy

Next

5 * x = 5x

5 * 3 = 15

5x + 15

Answer:

17(c)

18(b)

Step-by-step explanation:

17) (4x*1)+(4x*y)

4x+4xy

18) (x+3)5

(5*x)+(3*5)

5x+15

Brady bought items totaling $42.13 from the hardware store. After giving a hundred-dollar bill, he received $57.87 in change.

To calculate the change Brady gets back from the hardware store, we need to add up the cost of the items he purchased and then subtract this total from the amount of the hundred-dollar bill he provided to the owner. First, we add the cost of the wrench ($9.63), the nail gun ($28.01), and the dozen nails ($4.49) to find the total spending. Once we have the total, we subtract it from $100 to find out how much change Brady should receive.

Let's calculate:

Brady will receive $57.87 in change from the hardware store.

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Answer:

80.4

Step-by-step explanation:

To remember all of the ratios for trigonometry, using the acronym "SohCahToa". You always divide two sides for trig. ratios.

'S' is sine or sin for short.

'C' is cosine or cos for short.

'T' is tangent, or tan for short.

'h' means hypotenuse, the longest side in the triangle.

'o' means the side that's opposite, or not touching the angle of reference.

'a' means the side that's adjacent, or touching the angle of reference.

The angle of reference means the angle you are talking about (use the symbol θ to mean angle). In this question, the angle of reference is 15°.

We have the adjacent side, 300, and we need to find the opposite side, x.

The trig. ratio that has the side adjacent and opposite is tangent or 'tan'.

tanθ = opposite / adjacent     Trig. ratio for tangent

tan15° = x / 300     Substitute what we know. Isolate 'x'.

x = 300tan15°     This means 300 times tan15°. Use a calculator.

x = 80.3847..... Exact decimal answer on your calculator

x ≈ 80.4       Answer rounded to nearest tenth (first decimal)

When rounding, you decide to round up or down using the decimal place after where you will cut off.

In 80.3847..... '8' tells us to round up because it is 5 or greater.

If  the second decimal place was 4 or less, we round down (the answer would be 80.3).

The solution of this system of linear equations is [tex](x,y,z) = (1,2,4)[/tex]. (Correct choice: C)

The system of equations is represented by the following augmented matrix:

[tex]\left[\begin{array}{cccc}2&1&4&16\\5&-2&2&-1\\1&2&-3& -9\end{array}\right][/tex] (1)

Where the fourth column represents the vector column of independent coefficients. After making some operations, we find that the reduced row-echelon form of the augmented matrix is:

[tex]\left[\begin{array}{cccc}1&0&0&1\\0&1&0&2\\0&0&1& 4\end{array}\right][/tex]

The solution of this system of linear equations is [tex](x,y,z) = (1,2,4)[/tex]. (Correct choice: C) [tex]\blacksquare[/tex]

To learn more on augmented matrices, we kindly invite to check this verified question: https://brainly.com/question/4945755

Final answer:

To solve the system of equations, we need to find the reduced row-echelon form of the augmented matrix. Applying row operations, we can reduce the matrix to row-echelon form. Then, using backward substitution, we can find the values of x, y, and z. The solution to the system of equations is (-10, 2, 8.5).

Explanation:

To solve the system of equations, we can represent it as an augmented matrix and find its reduced row-echelon form. The augmented matrix for the given system of equations is:

[2 1 4 | 16]
[5 -2 2 | -1]
[1 2 -3 | -9]

Next, we need to apply row operations to reduce the matrix to its row-echelon form. Following the Gaussian elimination method, we perform the row operations:

R2 → R2 - 5R1, and
R3 → R3 - R1

The resulting matrix in row-echelon form is:

[2 1 4 | 16]
[0 -7 -18 | -81]
[0 0 0 | 0]

Now, we can apply backward substitution to find the values of x, y, and z. From the last row of the row-echelon form, we know that 0z=0. We can assign any value to z, such as 1, and then solve for x and y. Plugging in z=1, we get:

2x + 1y + 4(1) = 16

x + 2y - 3(1) = -9

Simplifying these equations, we get:

2x + y + 4 = 16 → 2x + y = 16 - 4 → 2x + y = 12

x + 2y - 3 = -9 → x + 2y = -9 + 3 → x + 2y = -6

Using these equations, we can solve for x and y by setting up a system of linear equations:

2x + y = 12
x + 2y = -6

Solving this system, we can find the values of x and y: x = -10 and y = 2. Finally, substituting these values back into one of the original equations, we can find z:

2(-10) + 1(2) + 4z = 16 → -20 + 2 + 4z = 16 → 4z = 34 → z = 8.5

So, the solution to the system of equations is (-10, 2, 8.5).

Final answer:

The cube root of 27x18 is 3x6, determined by taking the cube root of each term, with 27 yielding 3 and the x18 exponent reduced by a factor of 3 to x6.

Explanation:

The question posed is, "What is the cube root of 27x18?" To solve this, we need to break down the expression and compute the cube root of both terms separately. The cube root of 27 is 3 because 33 = 27. For the variable x raised to the 18th power, taking the cube root means we divide the exponent by 3, which gives us x6. Therefore, the cube root of 27x18 is 3x6.

It will take 6 years for the trees to be same height.

Step-by-step explanation:

Given,

Initial height of Type A = 7 feet = 7*12 = 84 inches

Growth rate = 2 inches per year

Let,

x be the number of years

Total height = T

T = 2x+84      Eqn 1

Initial height of Type B = 5 feet = 5*12 = 60 inches

Growth rate = 6 inches per year

T = 6x+60     Eqn 2

For same height;

Eqn 1 = Eqn 2

[tex]2x+84=6x+60\\84-60=6x-2x\\24=4x\\4x=24[/tex]

Dividing both sides by 4

[tex]\frac{4x}{4}=\frac{24}{4}\\x=6[/tex]

It will take 6 years for the trees to be same height.

Keywords: linear equation, division

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