A parobola has the equation y=x²+2x-3
What are the coordinates of the turning point of the parabola? what is the equation of the axis of symmetry for this parabola?​

Answer: 1.2x

Step-by-step explanation:

Profit = Selling price - Cost

She bought the stock at a cost of x dollars

Her profit was 20% of that, which is 0.2x dollars

Selling price = Profit + Cost = x + 0.2x = 1.2x

Answer:

$2,000

Step-by-step explanation:

7,440/3.72

Answer:

Step-by-step explanation:

The formula for finding the volume of a triangular prims is:

0.5 * b * h * length, where b is the length of the base of the triangle, h is the height of the triangle and length is prism length.

So, let's substitute those variables with the base length, height length, and prism length

The base length is 6km, the height length is 8km, and the prism length is 9km

So, we get:

0.5 * 6 * 8 * 9

= 1/2 * 6 * 8 * 9

= 1/2 * 48 * 9

= 1/2 * 432

= 216

The volume of this prism is 216km.

If we make appropriate equation then we can find that there are 21 people and animals belong to the circus.

Given The number of acrobats and ballerinas, minus the number of clowns, is one fewer than the number of dogs. Double the combined number of acrobats and ballerinas is five more than three times the number of clowns.

We have to find total people and animals belong to the circus.

An equation is relationship between variables that are expressed in equal to form. It is solved to find the variables in equal to form Equations of two variables look like ax+ by=c.

let the number of acrobats be x, ballerinas be y, clowns be z, clowns be u.

According to given information in question the equations are:

x+ y-z=u-1-----------------------1

2(x+ y)=3z+5-------------------2

u=z+1----------------------------3

Put the value of u from 3 in 1

x+y- z=z+1-1

x+y-2z=0

from 2

z=2x+2y-5/3

put the value of z in x+y-2z=0

x+y-2(2x+2y-5/3)=0

-x-y+10=0

x+ y=10-------------------------4

put put the value of x+y=10 in 1

10-z=u-1

u+z=11-----------------------------5

solving 3

u-z=1------------------------6

Now add 5&6

u+z+u-z=11+12

2u=12

u=6

Put the value of u in 6

6-z=1

z=5

From above we get x+y=10, u=6, z=5

Add all three we get the total number of people and animals belong to circus.

x+y+u+z=10+6+5

=21

Hence there are total 21 people and animals belong to the circus.

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The general direction that Lin walked from the gym to his house is; B: Lin walked southwest, creating an obtuse triangle.

We are given;

Distance between the lecture hall and gym = 910 feet.

Distance between the gym and Lin apostrophe's house = 615 feet.

Distance between the lecture hall and Lin apostrophe's house = 651 feet.

Now, since this 3 distances form a triangle and the 3 distances are unequal, then we can call it an obtuse triangle since he walked west and then walked northwest.

Now, since he walked back to his house from the gym, we can say that he walked southwest if we picture the bearing of his first two directions.

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Answer:

vertex = (2, 64 )

Step-by-step explanation:

given a parabola in standard form

f(x) = ax² + bx + c ( a ≠ 0 ) , then the x- coordinate of the vertex is

x = - [tex]\frac{b}{2a}[/tex]

f(x) = - 16x² + 64x ← is in standard form

with a = - 16, b = 64, c = 0 , then

x = - [tex]\frac{64}{-32}[/tex] = 2

substitute x = 2 into f(x) for corresponding y- coordinate

f(2) = - 16(2)² + 64(2) = - 16(4) + 128 = - 64 + 128 = 64

vertex = (2, 64 )

Answer:

Step-by-step explanation:

The formula for the volume of a sphere of radius r is V = (4/3)(pi)r^3.

Here, with r = 3 in, the volume is

V = (4/3)(3.14)(3 in)^2, or  V  =  36(pi)(27 in)^3 = 36pi in^3

Answer:

300 meters per minute

Step-by-step explanation:

Step 1

Determine the fraction of the total distance for each part of the race.

Given:

1st part of race = 4/9 of total distance

2nd part of race = 2/5 of remaining distance

Step 2

Determine the distance of the third part of the race.

Given:

time = 15 minutes

speed = 300 meters per minute

Step 3

If the third part of the race (which is 1/3 of the total distance) is 4500m, then the distance of the whole race is:

Step 4

Determine the distance of the 1st part of the race:

Step 5

Determine the speed of the 1st part of the race:

Given:

time = 20 minutes

distance = 6000 m

Answer:

The inverse of the function f(x) = 64x³ - 1 is [tex]\frac{\sqrt[3]{x+1}}{4}[/tex]

Step-by-step explanation:

First replace x with y.

[tex]x=64y^3-1[/tex]

Then solve for y.

[tex]y^3=\frac{x+1}{64}[/tex]

Cube root both sides.

[tex]y=\frac{\sqrt[3]{x+1}}{4}[/tex]

Hence, the inverse is [tex]\frac{\sqrt[3]{x+1}}{4}[/tex]

The value of a is -5 if the provided polynomial is divided by (3x + 2) option first -5 is correct.

Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.

[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have a polynomial:

3x² + 5x - 3

Which is divided by (3x + 2)

= (3x² + 5x - 3) ÷ (3x + 2)

[tex]\rm = \dfrac{\left(3x^2+5x-3\right)}{\left(3x+2\right)}[/tex]

[tex]\rm =x+\dfrac{3x-3}{3x+2}[/tex]

[tex]\rm =x+1+\dfrac{-5}{3x+2}[/tex]

[tex]\rm =x+1-\dfrac{5}{3x+2}[/tex]

By comparing with the given remainder.

a = -5

Thus, the value of a is -5 if the provided polynomial is divided by (3x + 2) option first -5 is correct.

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The solution to the value of x in the given equation is x = 0.00212658 or x = -0.00213958

The process of solving the unknown value of an algebraic equation involves equating the values of the unknown to the constant value.

Given that:

[tex]\mathbf{\dfrac{x^2}{0.35-x}= 1.3 \times 10^{-5} }[/tex]

[tex]\mathbf{x^2 = 1.3 \times 10^{-5} (0.35-x) }[/tex]

x² = 4.725 × 10⁻⁶ - 1.3 × 10⁻⁵x

= [tex]x^2 + 1.3\times10^{-5}x - 4.725 \times 10^{-6}[/tex]

= x²+0.000013x-0.000004725

x = 0.00212658 OR x = -0.00213958

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Given :

Multiply Equation #1 by 3 :

Add Equations 2 and 3 :

Now, input x in Equation #3 to find y :

∴ Hence, the point of intersection is (2/3, 5/6).

Answer:

  x = 5

Step-by-step explanation:

The equality of bases property says powers of the same base will be equal if and only if the powers are equal. This property is used to solve exponential equations.

  [tex]\dfrac{(2)^x}{2}=16\qquad\text{copy of the original equation}\\\\2\times\dfrac{(2)^x}{2}=2\times16\qquad\text{multiply by 2 to isolate the base}\\\\2^x=32\qquad\text{simplify}\\\\2^x=2^5\qquad\text{rewrite the constant as a power of 2}\\\\\boxed{x=5}\qquad\text{use the Equality of Bases Property}[/tex]

__

Additional comment

Equating the exponents is fully equivalent to taking the logarithm of both sides of the equation, to that base.

  [tex]\log_2(2^x)=\log_2(2^5)\ \Longrightarrow\ x=5[/tex]

Answer:

∠ ACB = 128° and ∠ABC = 32°

Step-by-step explanation:

∠ ADC = ∠ CAD (base angles theorem)

∠ ACD = 82° (angles in a triangle add to 180°)

∠ ACB = 128° (angles around a point add to 360°)

∠ ABC = 32° (angles in a triangle add to 180°)

Answer:

-9w^2-90w

Step-by-step explanation:

You just use the distributive property and watch the negatives and positives.

[tex]\huge\boxed{-9w^2-90w}[/tex]

Distribute [tex]-9w[/tex] to both [tex]w[/tex] and [tex]10[/tex] as shown in the attached image. Then, just simplify the terms with multiplication.

[tex](-9w)\cdot w+(-9w)\cdot10\\\boxed{-9w^2-90w}[/tex]

Answer:

Step-by-step explanation:

What is the solution to the equation?

[tex]2^{x}[/tex] + 4 - 12 = 20

[tex]2^{x}[/tex] = 20 - 4 + 12

[tex]2^{x}[/tex] = 16 + 12

[tex]2^{x}[/tex] = 28

Answer:

x-1

Step-by-step explanation:

because i said so

Option 3. The effect that it has when there are exceptions to the overall trend between two variable is that It is irrelevant to the relationship.

This is used in statistics to show that there is the existence of two variables that are positively correlated.

These two variables would then have a positive slope trend line. Hence the answer to the question is option 3.

What effect does it have when there are exceptions to the overall trend in a relationship between two variables?

O It increases the relationship

O It decreases the relationship

O It is irrelevant to the relationship.

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The given points of the expression is not a function because there are two different y-values for a single x-value.

Given The points are : (-2,-5), (-1,3), (1,-2) , (3,0) ,(4,-2) (4,4)

Function refers to a relation or expression involving one or more variables. In a function each value of x corresponds to each value of y. A relation which is having two or more values of y for x values is not a function.

We have been given points  (-2,-5), (-1,3), (1,-2) , (3,0) ,(4,-2) (4,4).

These are not points of a function because of a simple reason that it has two values of y for each one value of x.

Value of relation at x=-2 is -5.

Value of relation at x=-1 is 3.

Value of relation at x=1 is -2.

Value of relation at x=3 is 0.

Value of relation at x=4 is -2.

Value of relation at x=4  also equal to  4.

It has two values at x=4 one is -2 and other one is 4.

Hence the relation is not a function because there are two different y-values for a single x-value.

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The given points of the expression is not a function because there are two different y-values for a single x-value.

Given The points are : (-2,-5), (-1,3), (1,-2) , (3,0) ,(4,-2) (4,4)

Function refers to a relation or expression involving one or more variables. In a function each value of x corresponds to each value of y. A relation which is having two or more values of y for x values is not a function.

We have been given points  (-2,-5), (-1,3), (1,-2) , (3,0) ,(4,-2) (4,4).

These are not points of a function because of a simple reason that it has two values of y for each one value of x.

Value of relation at x=-2 is -5.

Value of relation at x=-1 is 3.

Value of relation at x=1 is -2.

Value of relation at x=3 is 0.

Value of relation at x=4 is -2.

Value of relation at x=4  also equal to  4.

It has two values at x=4 one is -2 and other one is 4.

Hence the relation is not a function because there are two different y-values for a single x-value.

Answer:

Option (2)

Step-by-step explanation:

The angle opposite the shortest side is the smallest and the angle opposite the longest side is the largest.

Since m is greater than or equal to 6, we know that:

2m+3 > m+8 > m-3

Answer:479

Step-by-step explanation:470+9=479

We can write the system of equation that determines the number of commercials and the number of movies on which Mason's songs were played as →  30x + 80y = 470   and    x + y = 9. The variables used in the system of equations are -

x - Number of times his song played in a commercial

y - Number of times his song played in a movie.

Equation modelling is a method of writing a mathematical relation from a mathematical statement for mathematical analyses of the problem given.

Given is Mason who collects royalties on his songs whenever they are played in commercials or movies.

Assume that his song played in 'x' commercials and 'y' movies.

Cost per song when played in commercial = $30

Then for 'x' commercials, total cost will be = $30x

Cost per song when played in movie = $80

Then for 'y' movies, total cost will be = $80y

Total money earned through both = $470

We can write the system of equation that determines the number of commercials and the number of movies on which Mason's songs were played as -

30x + 80y = 470

The total number of commercials and movies combined -

x + y = 9

The variables used in the system of equations are -

x -   Number of times his song played in a commercial

y - Number of times his song played in a movie.

Therefore, We can write the system of equation that determines the number of commercials and the number of movies on which Mason's songs were played as →  30x + 80y = 470   and    x + y = 9. The variables used in the system of equations are -

x - Number of times his song played in a commercial

y - Number of times his song played in a movie.

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Hello,

Answer:

for k = 4/9

Step-by-step explanation:

a = 9 ; b = 4 ; c = k

we search Δ = 0 (because 1 real root)

Δ = b² - 4ac = 4² - 4 × 9 × k = 16 - 36k

Δ = 0 ⇔  16 - 36k = 0 ⇔ 36k = 16 ⇔ k = 16/36 = (4 × 4)/(4 × 9) = 4/9

⇒ k = 4/9

Answer:

[tex]\{\frac{4}{9} \}[/tex]

Step-by-step explanation:

First off, we are given a parabola by definition:

[tex]f(x) = 9x^2 + 4x + k \\ a = 9, b = 4, c = k;[/tex]

Since [tex]a > 0[/tex], our parabola has an upward opening.

Should we think about it graphically, it will be no wonder that we should pay our attention to the points of the parabola intersecting the abscissa axis. In other words, we need our vertex to intersect the x axis only once per se.
The vertex:

[tex]V_{x} = \frac{-b}{2a} = \frac{-4}{2 * 9} = - \frac{2}{9} \\ V_{y} = 9V_{x}^2 + 4V_{x} + k = 9(- \frac{2}{9})^2 + 4(- \frac{2}{9}) + k = 9 * \frac{4}{9^2} - \frac{8}{9} + k = \frac{4}{9} - \frac{8}{9} + k = - \frac{4}{9} + k[/tex]

As a result, our [tex]V_{y}[/tex] is parametric. [tex]k = \frac{4}{9}[/tex] suits us because [tex]V_{y} = - \frac{4}{9} + \frac{4}{9} = 0[/tex]. If [tex]k > \frac{4}{9}[/tex], we do not have any roots at all. We have two roots if [tex]k < \frac{4}{9}[/tex].

A) The solution to m² + (1/m²) is gotten as; 14

B) The solution to m³ + ¹/₃ is gotten as; 52.312

We are given the algebraic equation;

(m² + 1)/m = 4

Multiply through by m to get;

m² + 1 = 4m

m² - 4m + 1 = 0

From online quadratic equation calculator, we have;

m = 3.732 or 0.268

A) Thus;

m² + (1/m²) = 3.732² + (1/3.732²)

⇒ 14

B) m³ + ¹/₃ gives;

3.732³ + (1/3) = 52.312

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Answer:

f(x)

Step-by-step explanation:

This question isn't to difficult, since all you need to know is: [tex](\frac{a}{b})^x=\frac{a^x}{b^x}[/tex]. If the you're not quite sure why this is true, I'll try to express this in another way. [tex](\frac{a}{b})^x=\frac{a}{b}*\frac{a}{b}*\frac{a}{b}...\text{ x amount of times}[/tex], and as you may know when multiplying fractions, you simply multiply the numerators by the numerators and the denominators by the denominators, this means that you can simplify it to: [tex]\frac{a*a*a...\text{ x amount of times}}{b*b*b...\text{ x amount of times}}[/tex] this is literally what an exponent is which is why you can distribute the exponent as such: [tex](\frac{a}{b})^x=\frac{a^x}{b^x}[/tex]. The next thing you need to know is that: [tex]1^x=1[/tex] for any real number. This is you can express this as: [tex]1*1*1...\text{ x amount of times} = 1[/tex], since 1 times 1 times 1, will always remain 1. You may think this will not apply for rational exponents, but it still does since: [tex]1^{\frac{a}{b}}=\sqrt[b]{1}^a[/tex], and no matter what b is, it's going to be 1. The square root of 1, is 1..., the cube root of 1 is 1.... This is because the very definition of a radical is what number times times it self index amount of times is equal to the number under the radical, and no matter how many times you multiply 1, you're going to get 1. If that's a bit confusing what I'm saying is: [tex]\sqrt[n]{b}\implies\text{?}^n=b[/tex].

Anyways hopefully you understand that, if not I'm sorry if I went a bit overboard trying to explain it. Anyways all you need to really know is that: [tex](\frac{1}{3})^x=\frac{1^x}{3^x}=\frac{1}{3^x}[/tex]. So this means as x increases, all you're really doing is increasing the denominator which is decreasing the number. The f function has an integer as a base, so the function will overall be increasing. This is not true for g(x) since as x increases the y-value decreases. So this means that f(x) has a faster rate. This is because the g(x) has a horizontal asymptote, since as x approaches infinity, g(x) approaches 0, since the denominator is increasing towards infinity. So the rate of change will be slowing down as x increases, since there is only so much the g(x) can change, since it has a horizontal asymptote. This is not true for f(x) as it has no horizontal asymptote and just goes towards infinity. So the f(x) has a faster rate.

Answer:

a) $7.50

Step-by-step explanation:

The total cost of $85.50 includes a 5% discount, so 95% of what price is $85.50?

[tex].95x = 85.50[/tex]

[tex]x = 90[/tex]

So the original price is $90. Divide this by 12, obtaining $7.50.

Answer:

a)$7.5

Step-by-step explanation:

Solution:

Let X represents socks

Given,

Selling price (SP) of 12x=$85.50

Discount precent (d%)=5%

So,

SP=(100-d)% of MP. [this formula really exist believe it or not]

85.50= (100-5)/100 ×MP

or, 85.50×100 =95×MP

or, 8550/95=MP

So,MP=$90

Now At last ,

cost of 1 shocks before discount is 90/12

which is $7.50 ans√

Answer: A 1/2 ^4

Step-by-step explanation:

Answer:

a)1/2^4

Step-by-step explanation:

First solve 2^-4.

Use negative power rule: x^-a = 1/xa

⇒ 1/2^4

Simplify 2^4 to 16

⇒ 1/16

Just evaluate the other options.

The first one is correct.

Here's why:

⇒ Simplify 2^4 to 16.

⇒ 1/16

They have the same steps, therefore making Option A correct.

Note: This is the longer way, there is a easier way of dealing with these types of problems. Example: Without using a calculator problem.

Answer: A

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The range is just the y-values. You don't have to write any of the repeated values. You do need to write them in numerical order.

4, 4, 2, 5

becomes

2,4,5

Answer:

Can u please upload more clearer pictures ?