Use the quadratic function to predict f(x) if x equals 2. f(x) = −3x2 + 180x − 285

3+5 = 8

240/8 = 30

30*3 = 90 red cars

Ella sold 37 necklaces for $20 each at the craft fair. She is going to donate half of the money she earned to charity. Use the Commutative Property to mentally find how much money she will donate. Explain the steps you used.

Solution:

Earning from 1 necklace=$20

Earning from 37 necklaces=$20*37

Half of the earnings= [tex] \frac{20*37}{2} =\frac{20}{2}*37=10*37 [/tex]

Half of the earnings=$10*37

Now, Applying Commutative Propert, a*b=b*a

So, Money she need to donate= Half of the earnings= 10*37 =37*10

So, Money she donates=$370

money she will donate=$370

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 .

Final answer:

To convert 2 2/3 to an improper fraction, multiply the whole number by the denominator and add the numerator, resulting in 8/3. The question lacks details to provide another specific quotient to compare this with. In dividing fractions, multiplication by the reciprocal is used to find equivalent quotients.

Explanation:

To find which quotient is equivalent to the mixed number 2 2/3, we must first convert the mixed number to an improper fraction. A mixed number is composed of a whole number and a fraction, which can be converted into an improper fraction by multiplying the denominator by the whole number and then adding the numerator to this product.

For the mixed number 2 2/3, we multiply the whole number 2 by the denominator 3, giving us 6, and then add the numerator 2, resulting in 8. Therefore, 2 2/3 as an improper fraction is 8/3.

However, without context, it's unclear what other quotient we are being asked to compare with the mixed number 2 2/3. Quotients can refer to the result of any division. Nonetheless, in contexts of dividing fractions, we use the multiplication of the inverse to find equivalent quotients. For example, if dividing by 3/1 (which is the same as dividing by 3), we would multiply by its reciprocal, 1/3.

In cases of conversion factors, we could use a factor that equals 1 to convert units without changing the value. For instance, 1 m / 100 cm is a conversion factor that equals 1, allowing us to convert meters to centimeters without changing the quantity.

Remember, multiplication and division in fractions can be seen as interconnected operations, where dividing by a number is the same as multiplying by its reciprocal.

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.

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.

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:

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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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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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.

Final answer:

To write a quadratic equation with roots −4 and 3 and a leading coefficient of 1, we start with the factored form (x - root1)(x - root2) = 0, substitute the given roots, and simplify to x² + x - 12 = 0.

Explanation:

The question asks us to write the quadratic equation whose roots are −4 and 3, and whose leading coefficient is 1. To find a quadratic equation given its roots, we can use the factored form of a quadratic equation, which is (x - root1)(x - root2) = 0, where root1 and root2 are the roots of the equation.

Given that the roots are −4 and 3, we substitute these values into the equation to get (x - (−4))(x - 3) = 0. Simplifying this, we first eliminate the double negative to get (x + 4)(x - 3) = 0. Multiplying these two binomials gives us the expanded form, which is x² + x - 12 = 0. This is the quadratic equation with roots −4 and 3, and a leading coefficient of 1.

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]

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

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:

B) Area of triangle =  149.4 square units.

Step-by-step explanation:

Given : A triangle with sides 16 , 19, 27 .

To find : Area of a triangle.

Solution : We have given that triangle with sides 16 , 19, 27 .

Using heron's formula :

Area of triangle:  [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex].

Where, s = [tex]\frac{a+b+c}{2}[/tex] and a,b,c are sides of triangle.

Then s = [tex]\frac{16+19+27}{2}[/tex].

s = 31 units.

Area of triangle =  [tex]\sqrt{31(31-16)(31-19)(31-27)}[/tex].

Area of triangle =  [tex]\sqrt{31(15)(12)(4)}[/tex].

Area of triangle =  [tex]\sqrt{22320)}[/tex].

Area of triangle =  149.39 square units.

Area of triangle =  149.4 square units. ( nearest tenth)

Therefore, B) Area of triangle =  149.4 square units.

Locating -1.5 and 1.5 on a number line involves measuring 1.5 units from the origin, but in opposite directions; -1.5 is to the left and 1.5 is to the right.

Locating -1.5 on a number line is similar to locating 1.5 in that you measure the same distance away from the origin (0 point), which is 1.5 units. The main difference is the direction in which you measure from the origin. For -1.5, you would move 1.5 units to the left of the origin since negative numbers are represented to the left on a number line. On the other hand, for 1.5, you would move 1.5 units to the right of the origin because positive numbers are placed to the right.

Another perspective of understanding this concept comes from the coordinate system. If you stand on a straight line and choose a point as the origin, moving to the left will give you the negative coordinates, whereas moving to the right will give you the positive coordinates. Regardless of which side you choose, the absolute value of your position from the origin remains the same; only the sign changes to reflect the direction.