You are given g(x)=4x^2 + 2x and
f(x) = the integral of g(t) from 0 to x.
How would you find f(6)?

Answer:

There is no answer.

0 is rational since it can be written as a fraction (0/5, 0/69)

1 is obviously rational. 7/8 is .875 and 5 1/4 is 5.25

Answer:

[tex] 3 {x}^{3} - 25 {x}^{2} + 35x - 23 = 0[/tex]

Step-by-step explanation:

We want to create an equation that will have the solution

[tex]x = \frac{1}{3},x = 4 + \sqrt{7}i,x = 4 - \sqrt{7}i[/tex]

This implies that:

[tex]3x -1= 0,x -( 4 + \sqrt{7}i) = 0,x - ( 4 - \sqrt{7}i) = 0[/tex]

We put the roots in factored form by reversing the zero product principle to get:

[tex](3x -1)(x -( 4 + \sqrt{7}i))(x - ( 4 - \sqrt{7}i)) = 0[/tex]

We expand the last two parenthesis to get:

[tex](3x - 1)( {x}^{2} - 4x + \sqrt{7}ix - 4x - \sqrt{7}ix + 16 - 7 {i}^{2}) = 0 [/tex]

We simplify to get:

[tex](3x - 1)( {x}^{2} - 8x + 23) = 0[/tex]

We expand further to obtain:

[tex]3 {x}^{3} - 25 {x}^{2} +35x - 23 = 0[/tex]

Answer: $4

Step-by-step explanation:

2d + 14 = 22

subtract 14

2d = 8

divide by 2

d = $4

each bag of Doritos costs $4

Elizabeth spent a total of $8 on 2 large bags of Doritos after spending $14 on soda, which means each bag costs $4.

To determine the price of each bag of Doritos, we need to subtract the amount spent on soda from the total amount spent. Elizabeth spent $14 on soda and had a total of $22 in expenses. So, the money spent on Doritos is the difference between the total amount and the soda amount.

Amount spent on Doritos = Total amount - Amount spent on soda

Amount spent on Doritos = $22 - $14

Amount spent on Doritos = $8

Since Elizabeth bought 2 large bags of Doritos, we can find the price per bag by dividing the total amount spent on Doritos by 2.

Price per bag of Doritos = Total spent on Doritos / Number of bags

Price per bag of Doritos = $8 / 2

Price per bag of Doritos = $4 per bag

Therefore, each large bag of Doritos costs $4.

Answer:

Step-by-step explanation:

Write a numerical expression that represents the number of increments it will take to reach -60 feet

Answer:

(-60) ÷ (-10)

Step-by-step explanation:

Answer:

m/d = V

Step-by-step explanation:

Answer:

m/d=V

Step-by-step explanation:

I did the quiz

Answer:

AB = 40 cm

Distance = [tex]10\sqrt{3}[/tex] cm

Step-by-step explanation:

Draw two heights DE and CF. These heights together with bases of trapezoid form rectangle DEFC. In this rectangle, DC=EF=20 cm.

Consider right triangle ADE. In this triangle, angle ADE has the measure of 30° (the sum of the measures of all interior angles is always 180°, so m∠ADE=180°-60°-90°=30°)

Leg opposite to 30° angle is equal to half of the hypotenuse, so

[tex]AE=\dfrac{1}{2}AD=\dfrac{1}{2}\cdot 20=10\ cm[/tex]

Similarly, in triangle CBF, BF=10 cm.

Hence,

[tex]AB=AE+EF+FB=10+20+10=40\ cm[/tex]

The height of the trapezoid (the second leg of triangle ADE) is the distance between DC and AB. By the Pythagorean theorem,

[tex]AD^2=AE^2+DE^2\\ \\DE^2=20^2-10^2=400-100=300\\ \\DE=\sqrt{300}=10\sqrt{3}\ cm[/tex]

Answer:

[tex]9\ pounds[/tex]

Step-by-step explanation:

Let

x ----> the number of pounds of a DVD player

we know that

The number of pounds of a DVD player multiplied by the cost per pound ($0.55) plus the charge of $6.99 must be equal to $11.94

so

The linear equation that represent this situation is

[tex]0.55x+6.99=11.94[/tex]

solve for x

subtract 6.99 both sides

[tex]0.55x=11.94-6.99[/tex]

[tex]0.55x=4.95[/tex]

divide by 0.55 both sides

[tex]x=9\ pounds[/tex]

Answer:

The median refer to the middle

value or number when arranged ascendingly or descendingly therefore the MEDIAN IS 36.8

Step-by-step explanation:

By arranging the numbers ascendingly we have

5.9, 11.2, 13.9, 16.6, 22.9, 36.8, 43.1, 43.7, 44.2, 45.1, 49

Therefore the median which is the number at the centre is 36.8

There are 6 balloons in small bouquet and 21 balloons in large bouquet.

Step-by-step explanation:

Let,

Number of balloons in small balloon bouquet = x

Number of balloons in large balloon bouquet = y

According to given statement;

2x+3y=75    Eqn 1

2x+y=33      Eqn 2

Subtracting Eqn 2 from Eqn 1

[tex](2x+3y)-(2x+y)=75-33\\2x+3y-2x-y=42\\2y=42[/tex]

Dividing both sides by 2

[tex]\frac{2y}{2}=\frac{42}{2}\\y=21[/tex]

Putting y=21 in Eqn 2

[tex]2x+21=33\\2x=33-21\\2x=12[/tex]

Dividing both sides by 2

[tex]\frac{2x}{2}=\frac{12}{2}\\x=6[/tex]

There are 6 balloons in small bouquet and 21 balloons in large bouquet.

Keywords: linear equation, subtraction

Learn more about subtraction at:

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Final answer:

In solving the system of linear equations, we determined that a small balloon bouquet contains 6 balloons and a large balloon bouquet contains 21 balloons.

Explanation:

Solving a System of Equations

Let's denote the number of balloons in a small bouquet as s and in a large bouquet as l. The given problem provides us with two equations based on the information about the graduation party and Father's Day celebration:

For the graduation party: 2s + 3l = 75

For the Father's Day celebration: 2s + l = 33

Now we solve this system of linear equations to find the values of s and l. Subtracting the second equation from the first gives us:

2s + 3l - (2s + l) = 75 - 33

Which simplifies to:

2l = 42

Dividing by 2 gives us:

l = 21

Now we can plug in the value of l into any of the original equations to find the value of s. Let's use the Father's Day equation:

2s + 21 = 33

Subtracting 21 from both sides gives us:

2s = 12

Finally, dividing by 2 gives us:

s = 6

Therefore, a small balloon bouquet contains 6 balloons and a large balloon bouquet contains 21 balloons.

Answer:

y=5/4x-5

Step-by-step explanation:

Perpendicular means negative reciprocal of the slope.

y-y1=m(x-x1)

y-(-5)=5/4(x-0)

y+5=5/4(x)

y+5=5/4x

y=5/4x-5

Answer:

A real number encompasses all numbers, whether it be irrational (irrational numbers go on forever) like pi or the square root of 5, an integer like a negative, a decimal, a fraction, 0, a whole number, a natural number etc.

Step-by-step explanation:

A real number encompasses all numbers, whether it be irrational (irrational numbers go on forever) like pi or the square root of 5, an integer like a negative, a decimal, a fraction, 0, a whole number, a natural number etc. (This doesn't include imaginary numbers however, like the square root of -1.)

Answer:

Step-by-step explanation:

A real number is a number that can be found on a number line. Numbers we use everyday. Real numbers include : natural numbers, whole numbers, integers, fractions, rational numbers, and irrational numbers. They do not include imaginary numbers, numbers that cannot be quantified, such as square root of -1.

Answer:

C) Y = -45

Step-by-step explanation:

Y/9 + 5 = 0

Y/9 = -5

y = -5 * 9

Y= -45

Answer:

The interest rate is 8% simple interest.

Step-by-step explanation:

Let the investment of $555 is getting r% simple interest for 6 years to become the balance of $821.4.

So, from the equation of the simple interest we can write

[tex]821.4 = 555(1 + \frac{6r}{100})[/tex]

⇒ [tex](1 + \frac{6r}{100}) = 1.48[/tex]

⇒ [tex]\frac{6r}{100} = 0.48[/tex]

⇒ r = 8%

Therefore, the interest rate is 8% simple interest. ( Answer )

The cost of each bush is $ 18.49

Let "f" be the cost of each flower

Let "b" be the cost of each bush

Given that Mrs. Kelly buys 15 flowers and 3 bushes for a total cost of $160.32

15 flowers x cost of each flower + 3 bushes x cost of each bush = 160.32

[tex]15 \times f + 3 \times b = 160.32[/tex]

15f + 3b = 160.32  ----- eqn 1

Each bush costs $11.50 more than each flower

Cost of each bush = 11.50 + cost of each flower

b = 11.50 + f  ------ eqn 2

Let us solve eqn 1 and eqn 2 to find values of "b" and "f"

Substitute eqn 2 in eqn 1

15f + 3(11.50 + f) = 160.32

15f + 34.5 + 3f = 160.32

18f = 160.32 - 34.5

18f = 125.82

Substitute f = 6.99 in eqn 2

b = 11.50 + 6.99 = 18.49

Thus the cost of each bush is $ 18.49

Answer:

Paul. He has made 60 pizzas after 9 days.

Step-by-step explanation:

Paul makes 12 pizzas the first day and 6 pizzas each day after that.

So, after 9 days Paul will make total [12 + (9 - 1)6] = 60 pizzas.

Now, Cindy makes 16 pizzas the first day and 4 pizzas each day after that.

So, after 9 days Cindy will make total [16 + (9 - 1)4] = 48 pizzas.

Therefore, after 9 days Paul will make more pizzas and the number is 60 pizzas. (Answer)

Answer:

B

Step-by-step explanation:

Answer:

Equation: y = 15x.

:)

Answer:

y = 15x

Step-by-step explanation:

The question asked,  what equation shows the line through the data points.  And it stated the equation needed to be in the form y = kx

Where

y represents the vertical axis

x represents the horizontal axis

k = constant

K is the constant interval and can be use to get the next points

y = kx

viewing the most visible points from the graph , let use the point where total saved is 90(y axis) and the time in weeks (x axis) is 6, the constant K can be gotten.

y = 90

x = 6

y = kx

90 = 6k

divide both sides by 6

k = 90/6

k = 15

Therefore,

y = 15x

Answer:

AC = 146

Step-by-step explanation:

Given that B  is the midpoint of AC, then

AB = BC, that is

9x + 1 = 6x + 25 ( subtract 6x from both sides )

3x + 1 = 25 ( subtract 1 from both sides )

3x = 24 ( divide both sides by 3 )

x = 8

Hence

AC = AB + BC = 9x + 1 + 6x + 25 = 15x + 26, thus

AC = (15 × 8) + 26 = 120 + 26 = 146

Answer:

146

Step-by-step explanation:

AB = BC (Definition of midpoint) so:

9x+1=6x+25.

Solve it as you would any other algebraic equation  >>>  9x+1=6x+25  >>>  9x+1-1=6x+25-1  >>>  9x=6x+24  >>>  -6x+9x=6x-6x+24  >>>  3x=24  >>>  3x/3=24/3  >>>  x=8

AB=9x+1  >>>  AB=9*8+1  >>>  AB=73

BC=6x+25  >>>  BC=6*8+25  >>>  BC=73

AC=AB+BC  >>>  AC=73+73  >>>  AC=146

To find the value after 20 years, use the future value of a series formula with the given parameters, resulting in an approximate amount of $9,321.

To find the value of $300 saved annually at 4.5% interest compounded annually after 20 years, we use the future value of a series formula:

FV = [tex]P * ((1 + r)^n - 1) / r[/tex]

Where:

Substituting the given values:

FV = $300 * ((1 + 0.045)^20 - 1) / 0.045

= $300 * ((1.045)^20 - 1) / 0.045

= $300 * (2.398 - 1) / 0.045

= $300 * 1.398 / 0.045

= $300 * 31.07

= $9,321

Therefore, after 20 years, the value will be approximately $9,321.

Answer:

x = 3

Step-by-step explanation:

Since all 3 sides of the triangle are congruent then the triangle is equilateral

The 3 angles are congruent and equal to 60°, thus

25x - 15 = 60 ( add 15 to both sides )

25x = 75 ( divide both sides by 25 )

x = 3

Answer:

[tex]\large\boxed{(1+2x^3)^2=4x^6+4x^3+1}[/tex]

Step-by-step explanation:

[tex](1+2x^3)^2\\\\\bold{METHOD\ 1:}\\\\(1+2x^3)^2=(1+2x^3)(1+2x^3)\qquad\text{use FOIL}\ (a+b)(c+d)=ac+ad+bc+bd\\\\=(1)(1)+(1)(2x^3)+(2x^3)(1)+(2x^3)(2x^3)\\\\=1+2x^3+2x^3+4x^6\qquad\text{combine like terms}\\\\=1+4x^3+4x^6[/tex]

[tex]\bold{METHOD\ 2:}\\\\\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\(1+2x^3)^2=1^2+2(1)(2x^3)+(2x^3)^2\\\\=1+4x^3+2^2(x^3)^2\\\\=1+4x^3+4x^6[/tex]

Answer:

The scale factor is 2

x=11 units

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

The ratio of its corresponding sides is called the scale factor

In this problem

Triangles RST and MNO are similar

so

[tex]\frac{NO}{ST}=\frac{MN}{RS}[/tex]

substitute the given values

[tex]\frac{x}{5.5}=\frac{6}{3}[/tex]

solve for x

[tex]\frac{x}{5.5}=2[/tex]

[tex]x=2(5.5)\\x=11\ units[/tex]

The scale factor of triangle RST to triangle MNO (enlargement) is equal to 2

Answer:

No, Mary is incorrect. If you turn the fractions into decimals, 1/4 would be 0.25 and 1/8 would be 0.12½. Since 0.25 is greater than 0.12½, Mary is incorrect.

Mary's reasoning is incorrect because in fractions, the larger the denominator, the smaller the fraction's value, making 1/4 greater than 1/8.

Mary's reasoning that 1/8 is greater than 1/4 because 8 is greater than 4 is not correct. In the context of fractions, the larger the denominator (the bottom number), the smaller each part of the whole it represents. Thus, 1/4 is actually greater than 1/8 because dividing something into 4 parts results in larger parts than dividing it into 8 parts. This can be further understood by transforming both fractions into equivalent fractions with a common denominator or by converting them into decimal form (0.25 for 1/4 and 0.125 for 1/8) to directly compare their sizes.

Answer:

4m

Step-by-step explanation:

since it is not multiplication, there would be no power.

think of it as 2m + 1m + 1m

The answer is 4m

I hope this helped! If so, please mark brainliest!

The y intercept is (0, 12)

Solution:

Given function is:

[tex]f(x) = 8x^5 - 3x^3 + 12[/tex]

To find: y intercept

y-intercept or vertical intercept is a point where the graph of a function or relation intersects the y-axis of the coordinate system.

To find the y intercept using the equation of the line, plug in 0 for the x variable and solve for y

Substitute x = 0 in given function

[tex]f(0) = 8(0) -3(0) + 12[/tex]

y = 0 - 0 + 12

y = 12

Thus y - intercept is (0, 12)

Answer:

0.033

Step-by-step explanation:

Use binomial probability:

P = nCr pʳ (1−p)ⁿ⁻ʳ

where n is the number of trials,

r is the number of successes,

p is the probability of success,

and q is the probability of failure (1-p).

Here, p = 0.5, q = 0.5, and n = 11.

We need to find P when r is 0, 1, and 2, then add up the results to get the total probability.

r = 0:

P = ₁₁C₀ (0.5)⁰ (0.5)¹¹⁻⁰

P ≈ 0.0005

r = 1:

P = ₁₁C₁ (0.5)¹ (0.5)¹¹⁻¹

P ≈ 0.0054

r = 2:

P = ₁₁C₂ (0.5)² (0.5)¹¹⁻²

P ≈ 0.0269

Therefore, the total probability is:

P = 0.0005 + 0.0054 + 0.0269

P = 0.0328

Round to the thousandths place, the probability is 0.033.

Answer:

The sum would be a₅ = 506.25!

Step-by-step explanation:

Given that,

first term a₁ = 1600

common ratio (r) =

We need to find the fifth term of the geometric progression

We know that the nth term formula

aₙ = a₁rⁿ-¹

where a₁ is first term and r is the common ratio

n is the number of terms

So, n = 5

a₅ = 1600

a₅ = 1600*

a₅ = 1600*81/256

a₅ =

a₅ = 506.25                  

Answer:

116.64

Step-by-step explanation:

116.64 is the correct answer

when a1 = 1500 the a6 = 116,64

Answer:

12.8

Step-by-step explanation:

Answer:

The "I" figure is 13 years old. Her brother is 16. Her Sister is 11. Her mother is 47.

Step-by-step explanation:

13+16=29

29+11=40

40+47=87

By using the fact of supplement angles of congruent angles are congruent, we proved that ∠2 ≅ ∠3

Step-by-step explanation:

The supplementary angles are:

∵ ∠1 and ∠2 are supplementary

∴ m∠1 + m∠2 = 180° ⇒ (1)

∵ ∠3 and ∠4 are supplementary

∴ m∠3 + m∠4 = 180° ⇒ (2)

We can equate the left hand sides of (1) and (2) because the right hand sides are equal

∴ m∠1 + m∠2 = m∠3 + m∠4 ⇒ (3)

∵ ∠1 ≅ ∠4

∴ m∠1 = m∠4

- Substitute m∠4 by m∠1 in (3)

∴ m∠1 + m∠2 = m∠3 + m∠1

- Subtract m∠1 from both sides

∴ m∠2 = m∠3

∴ ∠2 ≅ ∠3

By using the fact of supplement angles of congruent angles are congruent, we proved that ∠2 ≅ ∠3

Learn more:

You can learn more about supplementary angles in brainly.com/question/10483199

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