What’s the axis of symmetry for the quadratic equation y=3x^2+5x-2? Would really appreciate it if someone knew! :)

I think the answer is n-20- first choice.

ANSWER

n-20

EXPLANATION

The terms of the sequence are:

-19,-18,-17,-16,-15,...

The first term of the sequence is

a=-19 and the common difference is d=-18--19=1

The rule is given by:

f(n)=a+d(n-1)

f(n)=-19+1(n-1)

f(n)=-19+n-1

f(n)=n-20.

Therefore the rule for the given sequence is n-20.

The first option is correct.

Answer:

10th term of the sequence 64,16,4... = 1/4096

Step-by-step explanation:

Points to remember

nth term of GP is given by.

Tₙ = ar⁽ⁿ⁻¹⁾

Where r is the common ratio and a is the first term

To find the 10th term of given GP

It is given that,

64, 16, 4,......

a = 64 and 6 = 1/4 Here

T₁₀ = ar⁽ⁿ⁻¹⁾

 = 64 * (1/4)⁽¹⁰⁻¹⁾ = 64 * (1/4⁹)

 = 4³/4⁹ = 1/4⁶ = 1/4096

Answer:

Part 1) The simple interest earned when you invest $1,000 for 3 years at 10 % is $300

Part 2) The interest compounded when you invest the same sum for 2 years at 5 % is $102.50

Part 3) [tex]f(t)=7(2)^t[/tex]

Part 4) [tex]f(t)=3,000(0.93)^t[/tex]

Part 5) [tex]f(t)=300(1.015)^t[/tex]

Part 6) [tex]f(t)=300(0.985)^t[/tex]

Step-by-step explanation:

Part 1) What will be the simple interest earned when you invest $1,000 for 3 years at 10 percent

we know that

The simple interest formula is equal to

[tex]I=P(rt)[/tex]

where

I is the Final Interest Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

in this problem we have

[tex]t=3\ years\\ P=\$1,000\\r=0.10[/tex]

substitute in the formula above

[tex]I=\$1,000(0.10*3)=\$300[/tex]

Part 2) What will be the compound interest earned when you invest $1,000 for 2 years at 5 percent ?

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]  

where  

I is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

[tex]t=2\ years\\ P=\$1,000\\ r=0.05\\n=1[/tex]  

substitute in the formula above  

[tex]A=\$1,000(1+\frac{0.05}{1})^{1*2}[/tex]  

[tex]A=\$1,000(1.05)^{2}=\$1,102.50[/tex]  

The interest is equal to

[tex]I=\$1,102.50-\$1,000=\$102.50[/tex]  

Part 3) There are 7 trout fish in a pond,  and the population doubles every year.

Find the population after t years.

we know that

This question is about exponent function of the form

[tex]f(x)= a(b)^t[/tex]

where

a is the initial value

b is the base of the exponent.

In this problem we have

There are 7 trout fish in the pound ----> initial value a=7

The population is double every year ------> the base is b=2

substitute

[tex]f(t)= 7(2)^t[/tex]

Part 4) A company buys a machine for $3,000.  The value of the machine depreciates  by 7% every year. Find the value of  the machine after t years.

we know that

This question is about exponent function of the form

[tex]f(x)= a(b)^t[/tex]

where

a is the initial value

b is the base of the exponent.

we have

Company buys a machine for $3,000 --> initial value is a=3,000

The value depreciate 7% a year

Since it was decreased by 7% every year, it will become: 100%-7%=93%

the base is 93%, b=0.93

substitute

[tex]f(t)=3,000(0.93)^t[/tex]

Part 5) The initial population of a colony of ants  is 300. The number of ants increases  at a rate of 1.5% every month. Find the  population of ants after t months.

we know that

This question is about exponent function of the form

[tex]f(x)= a(b)^t[/tex]

where

a is the initial value

b is the base of the exponent.

we have

Initial population of ants is 300----> initial value is a=300

The number of ants increases 1.5% per month.

Since it will increases by 1.5% every month, it will become: 100%+1.5%=101.5%

the base is 101.5%, b=1.015

substitute

[tex]f(t)=300(1.015)^t[/tex]

Part 6) A research laboratory is testing a new  vaccine on 300 infected cells. The decay  rate is 1.5% per minute. Find the  number of infected cells after t minutes.

we know that

This question is about exponent function of the form

[tex]f(x)= a(b)^t[/tex]

where

a is the initial value

b is the base of the exponent.

we have

A research laboratory is testing new vaccine on 300 infected cells

 initial value is a=300

The decay/decrease rate is 1.5% per minute

Since it will decrease by 1.5% every min, it will become: 100%-1.5%=98.5%  

the base is 98.5%, b=0.985

substitute

[tex]f(t)=300(0.985)^t[/tex]

Answer:

100°

Step-by-step explanation:

The sum of angles in a quadrilateral is 360°, so the missing angle has measure ...

360° -44° -89° -127° = 100°

Answer:

100°

Step-by-step explanation:

Total angle measure of a quadrilateral is 360°

Add all the angles first.

44° + 89° + 127° = 260°

Quadrilateral has only four angle measures. And you need to find the fourth angle so,

360° - 260° = 100°

The fourth angle is measured 100°

since height to base ratio is tan73 so approx ratio is 3.27

The approximate height-to-base ratio is 3.27: 1

Given,

A 20-foot ladder is set up against a building so that the ladder makes an angle of 73° with the ground.

The height, h, is the vertical distance from the top of the ladder to the base of the building.

The base, b, is the horizontal distance from the bottom of the ladder to the base of the building.

We need to find what is the approximate height-to-base ratio.

Sin Ф = Perpendicular / Hypotenuse

Cos Ф = Base / Hypotenuse

Tan Ф = Perpendicular / Base

Find the height in the figure.

Sin 73 = h / 20 ft

Sin 73 = 0.9563

So,

0.9563 = h / 20 ft

h = 0.9563 x 20 ft

h = 19.126 ft

Find the base in the figure.

Cos 73 = b / 20 ft

Cos 73 = 0.2924

0.2924 = b / 20 ft

b = 0.2924 x 20 ft

b = 5.848 ft

Find the approximate height-to-base ratio.

= h : b

= 19.126 : 5.848

= 3.27 : 1

Thus the approximate height-to-base ratio is 3.27: 1

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For this case we must build a quotient, such that when multiplied by the divisor and then change the sign, go eliminating the terms of the dividend until you reach the remainder.

It must be fulfilled that:

Dividend = Divider * Quotient + Remainder

ANswer:

Option D

See attached image

Answer:

b = √c²-a²

Step-by-step explanation:

b² = c² - a²

b = √c²-a²

The Pythagorean theorem, denoted as a² + b² = c², can be rearranged as b = √(c² - a²) to solve for one of the sides of a right triangle. Once the lengths for a and c are known, they can be substituted into the formula to find the length of b.

The Pythagorean theorem, a key geometric principle, can be used to solve for one of the sides in a right triangle given the lengths of the other two. Usually, it's denoted as a² + b² = c², where a and b are the lengths of the triangle's legs, and c is the length of the hypotenuse. In the question, you want to solve for b.

First, let's isolate b in the formula. Rewrite the formula as b² = c² - a². To find the length of b, take the square root of both sides, resulting in b = √(c² - a²).

Now, once you have the values for a and c, you can substitute them into the formula to find b. This application of the Pythagorean theorem can be very useful in various situations where you have a right triangle, and you know the lengths of two of its sides but need to find the length of the third side.

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Answer:

A. What figures?: Hexagonal prism topped by a hexagonal cone

B. 246 sq cm

Step-by-step explanation:

A. What figures?

Imagine you're rolling up all 6 vertical pointy pieces around the base hexagon.  Then you'll have like a crown top with all the triangles.  You can fold these triangles to have their tips meet and form a hexagonal cone...

So, you'll have a hexagonal prism, topped with a hexagonal cone.

B. Surface area.

That's just a matter of calculating the areas of all triangles, rectangles and hexagon of the assembly.

Triangles: base: 4 cm, height: 5 cm, quantity: 6

A = (b * h) / 2 = (4 * 5) / 2 = 10 sq cm

AT = 6 * V = 6 * 10 = 60 sq cm

Rectangles: base: 4 cm, height: 6 cm, quantity: 6

A = b * h = 4 * 6 = 24 sq cm

AR = 6 * V = 6 * 24 = 144 sq cm

Hexagon: side: 4 cm, quantity: 1

Since it's a regular hexagon and we know its side length...

AH =  (3√3 * s²)/2 = (3√3 * 16)/2 = 24√3 = 41.57 sq cm

Then we add everything together:

A = AT + AR + AH

A = 60 + 144 + 41.57 = 245.57 sq cm

Rounded answer: 246 sq cm

Answer:

246 cm²

Step-by-step explanation:

The composite space figure consists of:

The surface area is the sum of all the areas of each figure.

Area of a hexagon = ½√(27) s²

Area of a rectangle = wl

Area of a triangle = ½ bh

So the total area is:

A = ½ √(27) (4)² + 6(4×6) + 6(½×4×5)

A = 8√(27) + 204

A ≈ 246 cm²

Answer:

1

Step-by-step explanation:

Answer:

+/- 6

A squared number can be from both a positive and negative number to make a positive square.

Answer:

  (37/360)π cm² ≈ 0.322886 cm²

Step-by-step explanation:

The area of a sector is given by the formula ...

  A = (1/2)r²θ . . . . . where r represents the radius and θ is the central angle is radians

Here, you have r = 1 cm, and θ = (37°·π/180°), so the area is ...

  A = (1/2)(1 cm)²·(37π/180) = 37π/360 cm²

  A ≈ 0.322886 cm²

Answer:

see explanation

Step-by-step explanation:

The meaning of n factorial → n !

n ! = n(n - 1)(n - 2)........ × 3 × 2 × 1

For example

7 !

= 7 × 6 × 5 × 4 × 3 × 2 × 1

Answer:

5. mCD is 27.8°  |  7. mAFC 52.3° |

Step-by-step explanation:

Answer:

10/12x100%= 83.3%

Step-by-step explanation:

Answer:

83.3%

Step-by-step explanation:

Charlie worked 10 of the 12 months so

[tex]\frac{10}{12}[/tex] × 100 = 83.3333

g(x) =f(x) +3

given f(x) =3x

i.e. g(x) =3x+3

For F(x) to be same as g(x)

3 must be added to f(x)

i.e. h(x) =3x+3

->h(x)= 3x +3(1)

-> h(x) = f(x) +f(1)

-> h(x) =f(x+1)

Hence Option (a) is your answer...

Hope it helps...

Regards

Leukonov/Olegion

Answer:

A) h(x) =  f(x +1).

Step-by-step explanation:

Given : f(x) = 3x and g(x) = 3x + 3.

To find : Which transformation of f(x) will produce the same graph as g(x).

Solution : We have given

f(x) = 3x

For x = 1.

f(1) = 3 (1)

f(x) = 3.

Plug the value of f(x) =3x and f(1) = 3 in g(x).

g(x) = 3x + 3.

g(x) = f(x) + f(1).

We can write  f(x) + f(1) = f(x +1).

g(x) = f(x +1)

h(x) = f(x +1)

So, it is a new function produce the same graph as g(x).

h(x) =  f(x +1).

Therefore, A) h(x) =  f(x +1).

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange - 3x + 4y = 5 into this form

Add 3x to both sides

4y = 3x + 5 ( divide all terms by 4 )

y = [tex]\frac{3}{4}[/tex] x + [tex]\frac{5}{4}[/tex] ← in slope- intercept form

with slope m = [tex]\frac{3}{4}[/tex]

• Parallel lines have equal slopes, thus

y = [tex]\frac{3}{4}[/tex] x + c ← is the partial equation of the parallel line

To find c substitute (2. 1) into the partial equation

1 = [tex]\frac{3}{2}[/tex] + c ⇒ c = - [tex]\frac{1}{2}[/tex]

y = [tex]\frac{3}{4}[/tex] x - [tex]\frac{1}{2}[/tex] ← equation of parallel line

Answer: a cube

(you could have looked this up on google that's what I did)

They are making me write an answer with at least 20 characters sorry

Answer:

cube

lol true about the 20 characters

Answer:

Distributive Property

Step-by-step explanation:

6(2 + x) = 12 + 6x illustrates the distributive property.

An algebraic property called the distributive property is utilized to multiply a single value by two or more values contained between parenthesis.

The distributive property of binary operations generalizes the distributive law, which declares that equality exists always accurate in elementary algebra.

Given

6(2+x )

[tex]= 6*2 + 6*x[/tex]

= 12+6x

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Answer: Approximately 3799 or 3800 cubic inches

Step-by-step explanation:

To find the volume of a cylinder I imagine I'm first finding the area of one of the circular "bases" (top or bottom) using the formula: Area = pi x radius squared. Once you have the area of a base, imagine you "stack" as many of them on top of each other until you get to the given height (here, it's 10 in. tall).

So . . . pi (3.14) x 11 (radius)^2 (3.14 x 11 squared) = 3.14 x 121 = 379.94 x 10 in. tall = 3799.4 cubic inches (in^3)

Answer:

d. Set A and Set B

Step-by-step explanation:

We have been given three sets:

Set A: (5, 2), (4, 3), (3, 4), (2, 5)

Set B: (-1, -6), (0, 2), (1, 2), (3, 6)

Set C: (2, 1), (4, 2), (2, 3), (8, 4)

Now we need to state about which of the following sets of ordered pairs represent a function.

We know that a function can't have repeated values in domain that is x-value can't repeat.

we see that set C has repeated x-value "2".

Then set C is not a function.

Hence correct choice is:

d. Set A and Set B

Answer:

A and B represent functions.

Step-by-step explanation:

In a function, any input (x-) value may have only one associated y value.  If the same input appears more than once, we know immediately that the data do not represent a function.

A:  The inputs are unique:  {5, 4, 3, 2} so this is a function.

B:   The inputs are unique:  {-1, 0, 1, 3}, so this is a function.

C:   2 is used twice as input, so this is not a function.

Answer:

The 3rd choice: 2/3 tank - 1/6 tank = 1/2 tank

Step-by-step explanation:

I assume those numbers are fractions.

The gas tank of Wendy’s car was 2/3 full. She used 1/6 of a tank of gas when driving to and from work. Which equation shows how full the gas tank is now?

We subtract 1/6 from 2/3. We need to use the common denominator 6.

2/3 - 1/6 = 4/6 - 1/6 = 3/6

Now we reduce 3/6.

2/3 - 1/6 = 1/2

Answer: 2/3 tank - 1/6 tank = 1/2 tank

Answer: No Solution

Step-by-step explanation:

When you subtract p on both sides, you get -4=-9 and that is not a true statement.

Hope this helps!

Answer:

S = 2((12(8) + 8(2) + 12(2))

= 2(96 + 16 + 24)

= 2(136)

= 272 square feet

Answer:

3 points, I believe.  

Step-by-step explanation:

ANSWER

[tex] \sqrt{5} [/tex]

EXPLANATION

The given points are (1,0) and (0,2).

We use the distance formula:

[tex]d = \sqrt{(x_2-x_1)^2 +(y_2-y_1)^2} [/tex]

We substitute the given points into the formula to get:

[tex]d = \sqrt{(0-1)^2 +(2-0)^2} [/tex]

We simplify to get:

[tex]d = \sqrt{1+4} [/tex]

[tex]d = \sqrt{5} [/tex]

Therefore the distance between the two points is √5 units.

Answer: Third option

[tex]u = -\frac{5\sqrt{29}}{29}i -\frac{2\sqrt{29}}{29}j[/tex]

Step-by-step explanation:

A unit vector [tex]u[/tex] is a vector that has magnitude 1.

To find a unit vector in the direction of the vector v we must first calculate the magnitude of v and then divide the vector v by its magnitude

The vector v is:

v = -5i - 2j

The magnitude of the vector is:

[tex]| v | =\sqrt{(-5)^2 +(-2)^2}\\\\|v|= \sqrt{29}[/tex]

Now we divide the vector v by its magnitude

[tex]u = \frac{1}{\sqrt{29}}v[/tex]

[tex]u = -\frac{5}{\sqrt{29}}i -\frac{2}{\sqrt{29}}j[/tex]

Simplifying we have to

[tex]u = -\frac{5\sqrt{29}}{29}i -\frac{2\sqrt{29}}{29}j[/tex]

Final answer:

To find the unit vector u in the direction of v = -5i - 2j, compute the magnitude of v and then divide each component of v by this magnitude. The result is u = (-5/√(29))i + (-2/√(29))j.

Explanation:

The question involves finding a unit vector in the direction of a given vector v = -5i - 2j. A unit vector is a vector with a magnitude of 1 that points in the direction of a given vector. To find the unit vector u in the direction of v, we first calculate the magnitude of v and then divide each component of v by its magnitude.

Upon calculating, the magnitude of v is sqrt(29), so the unit vector is u = (-5/√(29))i + (-2/√(29))j.

Answer:

x = 8

Step-by-step explanation:

Using Pythagoras' identity in the right triangle

The square on the hypotenuse is equal to the sum of the squares on the other two sides, that is

x² + 6² = 10²

x² + 36 = 100 ( subtract 36 from both sides )

x² = 64 ( take the square root of both sides )

x = [tex]\sqrt{64}[/tex] = 8

The answer is in the pic below and good luck,!

Hey there! :)

-7x - 4y = -8

To find the slope, we must turn this equation into slope-intercept form.

Slope-intercept form is : y=mx+b ; where m=slope, b=y-intercept

To get here, we must isolate y by adding 7x to both sides of our original equation.

-7x + 7x - 4y = 7x - 8

Simplify!

-4y = 7x - 8

Then, divide both sides by -4.

-4y ÷ -4y = (7x - 8) ÷ -4y

Simplify!

y = -7/4x + 2

Congrats, we got y isolated! Now, review the slope-intercept form equation to figure out what our slope & y-intercept are.

After reviewing our slope intercept form equation, we can come to the conclusion that -7/4 is our slope because it's in the "m" value slot, and 2 is our y-intercept because it's in the "b" spot.

So, our answer is :

Slope = -7/4

Y-intercept = 2

Hope this helped! :)

Check the picture below.

so notice,  in a cone the height and radius are always at a ratio of each other in a right-triangle, since the water level, in red, makes a similar triangle with the cone's volume, let's use proportions to get "x".

[tex]\bf \cfrac{21}{7}=\cfrac{x}{3}\implies 3=\cfrac{x}{3}\implies 9=x \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{volume of a cone}}{V=\cfrac{\pi r^2 h}{3}}~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} r=3\\ h=\stackrel{x}{9} \end{cases}\implies V=\cfrac{\pi (3)^2(9)}{3}\implies \stackrel{V=27\pi }{V\approx 84.823}[/tex]

The volume of water in a conical water reservoir can be calculated using the formula for the volume of a cone, substituting the values for the radius and height of the water.

In this problem, we are trying to calculate the volume of water in a water reservoir that is shaped as a right circular cone. We are told that this cone has a depth of 21ft and a radius of 7ft, while the water in the cone has a depth of x ft and a radius of 3ft.

In order to solve this problem, we first need to understand that the volume V of a cone is calculated using the formula, V = 1/3πr²h, where r is the radius and h is the height of the cone. This formula can be applied to determine the volume of water in the cone.

Substituting the given values into the formula, the volume of the water would be as follows: V = 1/3 * π * (3ft)² * x ft.

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Answer:

x = 4 ± [tex]\sqrt{13}[/tex]

Step-by-step explanation:

Given

x² - 8x + 3 = 0 ( subtract 3 from both sides )

x² - 8x = - 3

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 4)x + 16 = - 3 + 16

(x - 4)² = 13 ( take the square root of both sides )

x - 4 = ± [tex]\sqrt{13}[/tex] ( add 4 to both sides )

x = 4 ± [tex]\sqrt{13}[/tex]

The value of equation  x² - 8x + 3 = 0 using the completing the square method is found as  x = 4 ± √13.

To solve the equation x² - 8x + 3 = 0 using the completing the square method, follow these steps:

To solve the equation x² - 8x + 3 = 0 using the completing the square method, follow these steps:

Answer:

Yes.

Step-by-step explanation:

The vertex is 1,3. The vertex is in quad 1. The graph is shifted 1 to the right and up 3.