Find the area of triangle ABC with vertices A(2,1), B (12,2), C (12,8). Hence, or otherwise find the perpendicular distance from B to AC.

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:

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]

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:

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:

each side is 21 inches long.

4x+3=21

subtract 3 from both sides

4x=18

x=4.5

Answer:

4.5

Step-by-step explanation:

Since its an equilateral triangle, all the sides are equal.

SO, you can set up the equation:

3 ( 4x + 3 ) = 63

Start by disributing

12x + 9 =63

Subtract 9 from each side to isolate the variable

12x = 54

Divide both sides by 12

x = 4.5

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°.

The values of x and y needs to be 39 degrees and 21 degrees respectively to show that ABCD is a parallelogram.

We know that opposite angles of a parallelogram are equal and we are asked to find the value of x and y.

We are given that angle A = 3y angle B = 3x , angle C = y + 78 and angle D = 4x - 21

Now as we know that the opposite angles are going to be equal.So,

angle A = angle C

3y = y + 78

2y = 78

y = 39

So, the value of y is going to be 39 degrees.

Similarly, we can also find the value of x.

angle B = angle D

3x = 4x - 21

-x = -21

x = 21

So, the value of x is going to be 21 degrees.

Hence, the values of x and y needs to be 39 degrees and 21 degrees respectively to show that ABCD is a parallelogram.

Answer:

Step-by-step explanation:

Provide problems and we're here to help.

Answer:

write the problem, decide whether you use add or sub.,add or sub. the constant on both sides, eliminate the coefficients of the variable, last solve for the variable.

Step-by-step explanation:

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:$18.00

Step-by-step explanation:

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

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

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

Learn more about division at:

#LearnwithBrainly

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:

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

Answer:

Step-by-step explanation:

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

7,015,000,000 <===

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:

[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:

Step-by-step explanation:

1/2 of 9

" of " in math means multiply

1/2 * 9 = 9/2 or 4 1/2 or 4.5

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.

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:

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.

Final answer:

The 5 in 11.205 is in the thousandths place and represents 0.005, while the 5 in 5.32 is in the units place, representing 5. The 5 in 5.32 is one thousand times the value of the 5 in 11.205, and vice versa.

Explanation:

The relationship between the 5 in 11.205 and the 5 in 5.32 can be described in terms of their place values. In the number 11.205, the 5 is in the thousandths place, which means it represents 5 thousandths or 0.005. In the number 5.32, the 5 is in the units place, which means it represents 5 ones or simply 5.

To compare their values, we can say that the 5 in 5.32 is one thousand times the value of the 5 in 11.205 because 5 divided by 0.005 equals 1000. Alternatively, we could say the 5 in 11.205 is one thousandth the value of the 5 in 5.32.

These comparisons are based on the understanding of place value in decimal numbers, where each position to the left or right of the decimal point represents a power of 10. Therefore, the value of a digit is determined by its position relative to the decimal point.

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:

-3x-16

Step-by-step explanation:

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

2x-6-5x-10

2x-5x-6-10

-3x-6-10

-3x-16

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).

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]

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.

The explicit equation for the nth term of the geometric sequence 3584, 896, 224 is:

[tex]a_n=3584(0.25)^{n-1}\\\\\text{Where } n\geq 1 \text{ ,n = 1, 2, 3, 4, .........}[/tex]

Solution:

Given that we have to find the explicit equation for nth term of geometric sequence

Given sequence is:

3584, 896, 224

A geometric sequence has a common ratio

Let us find the common ratio. Divide each term by the previous term.

[tex]r=\frac{896}{3584} = 0.25\\\\r = \frac{224}{896} = 0.25[/tex]

Thus the common ratio is 0.25

The formula for nth term of geometric sequence is given as:

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

Where,

[tex]a_n[/tex] is the nth term of sequence

a is the first term of sequence

r is the common ratio

Here in given sequence 3584, 896, 224

first term = a = 3584

common ratio = r = 0.25

Therefore,

[tex]a_n=3584(0.25)^{n-1}[/tex]

[tex]\text{Where } n\geq 1 \text{ ,n = 1, 2, 3, 4, .........}[/tex]

"n" is a natural positive number greater than or equal to 1

Thus the explicit equation to find nth term is found