Each interior angle of a regular hexagon is 4x+24°. What is x?

Answer:

The actual answer is D

The point (a, b) lies in the second quadrant. Then the correct option is B.

Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.

If a < 0 and b > 0.

Then the point (a, b) is in Quadrant will be given as,

Thus, the point (a, b) lies in the second quadrant.

Then the correct option is B.

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Answer:

[tex]t\,=\,\frac{-3+\sqrt{9+4d}}{-8}\:\:and\:\:\frac{3+\sqrt{9+4d}}{8}[/tex]

Step-by-step explanation:

Given: d = -16t² + 12t

To find: t using quadratic formula

If we have quadratic equation in form ax² + bx + c = 0

then, by quadratic formula we have

[tex]x\,=\,\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Rewrite the given equation,

-16t² + 12t - d = 0

from this equation we have,

a = -16 , b = 12 , c = d

now using quadratic formula we get,

[tex]t\,=\,\frac{-12\pm\sqrt{12^2-4\times(-16)\times d}}{2\times(-16)}[/tex]

[tex]t\,=\,\frac{-12\pm\sqrt{144+64d}}{-32}[/tex]

[tex]t\,=\,\frac{-12\pm\sqrt{16(9+4d)}}{-32}[/tex]

[tex]t\,=\,\frac{-12\pm4\sqrt{9+4d}}{-32}[/tex]

[tex]t\,=\,\frac{4(-3\pm\sqrt{9+4d})}{-32}[/tex]

[tex]t\,=\,\frac{-3\pm\sqrt{9+4d}}{-8}[/tex]

[tex]t\,=\,\frac{-3+\sqrt{9+4d}}{-8}\:\:,\:\:\frac{-3-\sqrt{9+4d}}{-8}[/tex]

[tex]t\,=\,\frac{-3+\sqrt{9+4d}}{-8}\:\:and\:\:\frac{-(3+\sqrt{9+4d})}{-8}[/tex]

[tex]t\,=\,\frac{-3+\sqrt{9+4d}}{-8}\:\:and\:\:\frac{3+\sqrt{9+4d}}{8}[/tex]

Therefore, [tex]t\,=\,\frac{-3+\sqrt{9+4d}}{-8}\:\:and\:\:\frac{3+\sqrt{9+4d}}{8}[/tex]

Answer:

[tex]\frac{3-\sqrt{9-d}} {8}\text{ or }t=\frac{3+\sqrt{9-d}} {8}[/tex]

Step-by-step explanation:

Here, the given expression,

[tex]d= -16t^2+12t[/tex]

[tex]\implies -16x^2+12t-d=0[/tex] ------(1)

Since, if a quadratic equation is,

[tex]ax^2+bx+c=0[/tex] ------(2)

By using quadratic formula,

We can write,

[tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

By comparing equation (1) and (2),

We get, a = -16, b = 12, c = -d,

[tex]t=\frac{-12\pm \sqrt{12^2-4\times -16\times -d}}{2\times -16}[/tex]

[tex]t = \frac{-12\pm \sqrt{16\times 9-16\times d}}{-32}[/tex]

[tex]t = \frac{-12\pm \sqrt{16}\times \sqrt{9-d}} {-32}[/tex]

[tex]t = \frac{-12\pm 4\sqrt{9-d}} {-32}[/tex]

[tex]t = \frac{4(-3\pm \sqrt{9-d})} {4(-8)}[/tex]

[tex]t = \frac{-3\pm \sqrt{9-d}} {-8}[/tex]

[tex]t = \frac{-3+\sqrt{9-d}} {-8}\text{ or }t=\frac{-3-\sqrt{9-d}} {-8}[/tex]

[tex]\implies t = \frac{3-\sqrt{9-d}} {8}\text{ or }t=\frac{3+\sqrt{9-d}} {8}[/tex]

Which is the required solution.

Answer:

320 ft

Step-by-step explanation:

I'm not sure how the other person was awarded brainliest answer because that answer is pretty far off. But the work was good just they messed up. Also kinda sad he is a brainly teacher and still has incorrect answers.

if youre doing the vocab thing -- Distance

Answer:

USD 3,508.16

Step-by-step explanation:

Hello

Let´s see what happens the first year when the car depreciates 13.75% of 20700 USD

[tex]depreciation=20700*\frac{13.75}{100} =2846.25 USD\\[/tex]

at the end of the first year the car will have a price of 20700-2486.25=17853.75 USD,  and this will be the price at the beginning of the second year.

completing the data for the 12 years with the help of excel you get

                                          depreciation           New Value

end of year 1  USD 20,700.00   USD 2,846.25   USD 17,853.75  

end of year 2  USD 17,853.75   USD 2,454.89   USD 15,398.86  

end of year 3  USD 15,398.86   USD 2,117.34   USD 13,281.52  

end of year 4  USD 13,281.52   USD 1,826.21   USD 11,455.31  

end of year 5  USD 11,455.31   USD 1,575.10   USD 9,880.20  

end of year 6  USD 9,880.20   USD 1,358.53   USD 8,521.68  

end of year 7  USD 8,521.68   USD 1,171.73            USD 7,349.94  

end of year 8  USD 7,349.94   USD 1,010.62   USD 6,339.33  

end of year 9  USD 6,339.33   USD 871.66           USD 5,467.67  

end of year 10 USD 5,467.67   USD 751.80       USD 4,715.87  

end of year 11  USD 4,715.87   USD 648.43     USD 4,067.43  

end of year 12 USD 4,067.43   USD 559.27   USD 3,508.16

after 12 years the car will ha a value of USD 3508.16

you can verify this by applying the formula

[tex]v_{2} =v_{1} (1-\frac{depreciatoin}{100} )^{n} \\\\v_{2} =20700 (1-\frac{13.75}{100} )^{12} \\v_{2} = 20700*0.1694\\v_{2} = 3508.16 USD[/tex].

Have a great day.

The value of a new car, originally priced at $20,700 and depreciating at 13.75% per year will be approximately $1446.63 after 12 years. This is calculated using a compound interest formula with a negative rate.

In order to solve this, we are going to use the formula for compound interest. Although we're actually dealing with depreciation, the calculation is the same as for interest, we just use a negative rate. The formula is P(t) = P0 * (1 + r) ^t, where P(t) is the value of the car after time t, P0 is the initial price of the car, r is the rate of depreciation, and t is time.

Here P0 = $20,700, r = -13.75% = -0.1375 (remember to convert rate from percentage to a proportion), and t = 12 years.

Substituting these values into the formula, we get: P(t) = 20700 * (1 - 0.1375)^12. Using a calculator, the value of the car after 12 years, to the nearest cent, is approximately $1446.63.

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Answer: The answer is 5, 10, 20, 40 and 80.

Step-by-step explanation:  We are to write the first five terms of a sequence, along with the explicit and recursive formula for the general term of the sequence.

Let the first five terms of a sequence be  5, 10, 20, 40 and 80. These terms are taken from a geometric sequence with first term [tex]a_1 5[/tex] and common ratio [tex]r=2.[/tex]

Therefore, we have

[tex]a_2=a_1\times r,\\\\a_3=a_2\times r,\ldots[/tex]

Therefore, the recursive formula is

[tex]a_{n+1}=2a_n,~~a_1=5.[/tex]

And explicit formula is

[tex]a_n=a_1r^{n-1}.[/tex]

Answer:

Let the first five terms of a sequence be, 4,8,12,20,24

Ok, let me explain the meaning of term explicit and Recursive formula.

Explicit formula ,is the general formula to find any  term of the sequence.

And, Recursive formula, is the method by which, we can find the nth term of the sequence if (n-1)th term of the sequence is known.

So,the explicit formula for the sequence is,

y = 4 n, where , n is any natural number.

And the recursive formula is .

y = 4 (n-1), with the help of (n-1)th term we can find nth term.

First term =4=4 × 1

Second term =8 =4 × 2

Third term =12=4×3

Fourth term =16 =4 × 4

.....................

...........................

.................................

(n-1) th term =4 × (n-1)

nth term =4 × n

Applying the simple procedure by looking at the first , second and the way the next term goes , the general and recursive formula is obtained.

As, you said you don't want simpler sequence

Consider the first five terms of the sequence, 0, 3,8,15, 24.

Explicit formula =n² + 2 n

Recursive formula=(n-1)²+2(n-1)

If,you will look at the sequence, it is neither Arithmetic nor geometric .

First term =0=0²+0×0

Second term =3=1+2=1²+2 × 1

Third term =8=4+4=2²+2×2

Fourth term =15=9+6=3²+2×3

Fifth term =24=16 +8=4²+2×4

So, Explicit formula= n²+ 2 n, where n is a whole number.

Mary has 3 marbles.

To find out how many marbles Mary has, we can use the information that Joan has 45 marbles and Joan has 15 times as many marbles as Mary. So, we can set up an equation:

45 = 15m

To solve for m, we divide both sides of the equation by 15:

m = 45/15

Simplifying the expression, we get:

m = 3

Therefore, Mary has 3 marbles.

Answer:

28

Step-by-step explanation:

Square: 4 * 4 = 16

Small Triangle: 1 * 4 = 4  / 2 = 2

Large Triangle: 5 * 4 = 20  / 2 = 10

16 + 2 + 10 = 28

Number seven  Is B. -2/3

The equation of the parabola is y = – 5x² + 20. The time when an acorn is 5 m above the ground in 1.7 seconds. Then the correct option is C.

It is the locus of a point that moves so that it is always the same distance from a non-movable point and a given line. The non-movable point is called focus and the non-movable line is called the directrix.

The function graphed approximates the height of an acorn, in meters, x seconds after it falls from a tree.

We know that the equation of the parabola will be given as

y = a(x - h)² + k

where (h, k) is the vertex of the parabola and a is the constant.

We have

(h, k) = (0, 20)

Then

y = ax² + 20

The parabola is passing through (2, 0), then we have

0 = 4a + 20

a = -5

Then we have

y = – 5x² + 20

The time in seconds when the acorn is 5 m above the ground.

–5x² + 20 = 5

       –5x² = –15

             x = 1.7

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The remainder obtained when we carry out the operation (-6x³ + 3x² - 4) ÷ (2x - 3) is -17.5 (2nd option)

The following data were obtained from the question:

Using the remainder theorem, we can obtain the remainder as illustrated below:

Let

f(x) = -6x³ + 3x² - 4

2x - 3 = 0

From 2x - 3 = 0, make x the subject as shown below:

2x - 3 = 0

x = 3/2

Substitute the value of x into f(x). We have:

f(x) = -6x³ + 3x² - 4

f(3/2) = -6(3/2)³ + 3(3/2)² - 4

= -6(27/8) + 3(9/4) - 4

= -20.25 + 6.75 - 4

= -17.5

Thus, we can conclude that the remainder obtained when (-6x³ + 3x² - 4) is divided by (2x - 3) is -17.5 (2nd option)

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Answer : Distance will be 1507.2 feet .

Explanation :

Since we have given that

Radius of circle = 80 feet

So,

Circumference of circle is given by

[tex]2\pi r=2\times 3.14\times 80=502.4 \text{ feet}[/tex]

Since , a car travels 3 times around a traffic circle.

So,

[tex]\text{ Distance covered by the car will travel}= 3\times 502.4= 1507.2 \text{ feet }[/tex]

So, Distance will be 1507.2 feet .

A square is cut from a circle with a 14-foot diameter. Remaining circle area ≈ 53.86 sq ft here nearest round off option is c. 50 square feet.

To find the area of the remaining portion of the circle after a square with a side of 10 feet is cut out,

Find the area of the square:

Area of square

= side × side

= 10 feet × 10 feet

= 100 square feet

Find the radius of the circle:

The diameter is approximately 14 feet, so the radius is half of that:

Radius = 14 feet / 2 = 7 feet

Find the area of the entire circle:

Area of circle = π × radius²

Area of circle

= π × (7 feet)²

≈ 153.86 square feet (using π ≈ 3.14)

Subtract the area of the square from the area of the circle to find the remaining portion:

Remaining area = Area of circle - Area of square

Remaining area

≈ 153.86 square feet - 100 square feet

≈ 53.86 square feet

Therefore, the approximate area of the remaining portion of the circle is approximately 53.86 square feet nearest option is c. 50 square feet.

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The above question is incomplete , the complete question is:

A square is cut out of a circle whose diameter is approximately 14 feet. What is the approximate area of the remaining portion of the circle in square feet?

Attached figure

Answer: The correct option is third, i.e., [tex]y\geq \frac{3}{2} x+\frac{1}{5}[/tex].

Explanation:

From the figure it is noticed that the line passing through the points (0,0.2) and (3,2.2).

The equation of line passing through two points is,

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)[/tex]

[tex]y-0.2=\frac{2.2-0.2}{3-0}(x-0)[/tex]

[tex]y-\frac{1}{5} =\frac{2}{3} x[/tex]

[tex]y =\frac{2}{3} x+\frac{1}{5}[/tex]

The equation of the line is [tex]y =\frac{2}{3} x+\frac{1}{5}[/tex].

From the figure it is noticed that as the value of x increases the value of y is less.

he point (1,0) lies on the shaded reason it means this point must satisfy the equation.

[tex](0)=\frac{2}{3} (1)+\frac{1}{5}[/tex]

[tex](0)=\frac{2}{3} +\frac{1}{5}[/tex]

[tex](0)=\frac{10+3}{15}[/tex]

[tex](0)=\frac{13}{15}[/tex]

It is true of the sign is less than or equal to instead of equal.

[tex]y \leq \frac{2}{3} x+\frac{1}{5}[/tex]

Therefore, option third is correct.

The equation of the ellipse is required.

The required equation is [tex]\dfrac{x^2}{16}+\dfrac{(y+4)^2}{25}=1[/tex]

It can be see that the major axis is parallel to the y axis.

The major axis points are

[tex](h,k+a)=(0,1)[/tex]

[tex](h,k-a)=(0,-9)[/tex]

[tex]k+a=1[/tex]

[tex]k-a=-9[/tex]

Subtracting the equations

[tex]2a=10\\\Rightarrow a=5[/tex]

The foci are

[tex](h,k+c)=(0,-1)[/tex]

[tex](h,k-c)=(0,-7)[/tex]

[tex]k+c=-1[/tex]

[tex]k-c=-7[/tex]

Subtracting the equations

[tex]2c=6\\\Rightarrow c=3[/tex]

[tex]k+c=-1\\\Rightarrow k=-1-c\\\Rightarrow k=-1-3\\\Rightarrow k=-4[/tex]

Foci is given by

[tex]c^2=a^2-b^2\\\Rightarrow b=\sqrt{a^2-c^2}\\\Rightarrow b=\sqrt{5^2-3^2}=4[/tex]

The equation is

[tex]\dfrac{(x-h)^2}{b^2}+\dfrac{(x-k)^2}{a^2}=1\\\Rightarrow \dfrac{(x-0)^2}{4^2}+\dfrac{(y+4)^2}{5^2}=1\\\Rightarrow \dfrac{x^2}{16}+\dfrac{(y+4)^2}{25}=1[/tex]

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No, thanks to you, I got the question wrong it was hours.

The difference in payments from year 5 to year 6 is approximately $369.32 for the 5/1 ARM mortgage.

To calculate the payment difference from year 5 to year 6 for a 5/1 ARM (Adjustable Rate Mortgage) with a 3/12 cap structure, we need to understand how the ARM works and how the caps affect the adjustment.

1. Initial Mortgage Parameters :

  - Loan Amount: $265,000

  - Interest Rate: 5.25%

  - Term: 20 years

2. Adjustment Frequency : The 5/1 ARM adjusts after the initial 5-year fixed period, then annually.

3. Cap Structure :

  - Initial Adjustment Cap: 3%

  - Subsequent Adjustment Cap: Each year after the initial adjustment, the rate can adjust up to 3% from the previous rate.

4. Calculation Steps :

  a. Calculate the initial monthly payment using the loan amount, interest rate, and term.

  b. Determine the new interest rate for year 6 based on the cap structure.

  c. Calculate the monthly payment for year 6 with the new interest rate.

  d. Find the difference between the payments from year 5 to year 6.

Let's start the calculations:

a. Calculate the initial monthly payment  using the loan amount, interest rate, and term. We'll use the formula for a fixed-rate mortgage:

[tex]\[ P = \frac{P_r \cdot A}{1 - (1 + r)^{-n}} \][/tex]

Where:

- [tex]\( P \)[/tex] = Monthly Payment

- [tex]\( P_r \)[/tex] = Periodic Interest Rate (annual rate divided by 12)

- [tex]\( A \)[/tex] = Loan Amount

- [tex]\( r \)[/tex] = Periodic Interest Rate

- [tex]\( n \)[/tex] = Total number of payments (loan term in years multiplied by 12)

For the initial fixed period of 5 years:

[tex]\[ P_r = \frac{5.25\%}{12} = 0.004375 \][/tex]

[tex]\[ n = 20 \times 12 = 240 \][/tex]

Plugging these values into the formula:

[tex]\[ P = \frac{0.004375 \cdot 265000}{1 - (1 + 0.004375)^{-240}} \][/tex]

[tex]\[ P \approx 1645.80 \][/tex]

So, the initial monthly payment is approximately $1,645.80.

b. Determine the new interest rate for year 6 :

  - The initial rate can adjust up to 3% in year 6.

  - So, the new interest rate could be up to \( 5.25\% + 3\% = 8.25\% \).

c. Calculate the monthly payment for year 6 :

  - Use the formula for the monthly payment again with the new interest rate:

[tex]\[ P_r = \frac{8.25\%}{12} = 0.006875 \][/tex]

Plugging into the formula:

[tex]\[ P = \frac{0.006875 \cdot 265000}{1 - (1 + 0.006875)^{-240}} \][/tex]

[tex]\[ P \approx 1985.09 \][/tex]

So, the monthly payment for year 6 is approximately $1,985.09.

d. Find the difference in payments from year 5 to year 6:

[tex]\[ Difference = Payment_{Year6} - Payment_{Year5} \][/tex]

[tex]\[ Difference = 1985.09 - 1645.80 \][/tex]

[tex]\[ Difference \approx 339.29 \][/tex]

So, the difference in payments from year 5 to year 6 is approximately $339.29.

Therefore, the closest answer is C. $369.32 .

Answer:

The inequality is given to be :

[tex]\frac{3x+8}{x-4}\geq 0[/tex]

The inequality will be greater than or equal to 0 if and only if both the numerator and denominator of the left hand side will have same sign either both positive or both negative.

CASE 1 : Both positive

3x + 8 ≥ 0

⇒ 3x ≥ -8

[tex]x\geq \frac{-8}{3}[/tex]

Also, x - 4 ≥ 0

⇒ x ≥ 4

Now, Taking common points of both the values of x

⇒ x ∈ [4, ∞)

CASE 2 :  Both are negative

3x + 8 ≤ 0

⇒ 3x ≤ -8

[tex]x\leq \frac{-8}{3}[/tex]

Also, x - 4 ≤ 0

⇒ x ≤ 4

So, Taking common points of both the values of x we have,

[tex]x=(-\infty,-\frac{8}{3}][/tex]

So, The solution of the equation will be the union of both the two solutions

So, Solution is given by :

[tex]x=(-\infty,-\frac{8}{3}]\:U\:[4,\infty)[/tex]