Round to 2 decimal places 8.041

The vertex-form of the quadratic equation is given by y = (x + 4)² - 13, and the minimum value of y is of -13.

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient. If a > 0, k is the minimum value of y, and if a < 0, it is the maximum value.

In this problem, the equation is:

y = x² + 8x + 3.

Completing the squares, the function is:

y = (x + 4)² - 13

13 is subtracted as (x + 4)² = x² + 8x + 16, hence for the equations to be equal 13 has to be subtracted. k = -13 is also the minimum value of y.

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The minimum y-value of the function for the parabolic equation is -13.

The vertex for an up-down facing parabola of the form y = ax² + bx + c is [tex]\mathbf{x_v= -\dfrac{b}{2a}}[/tex]

From the given equation:

y = x² + 8x + 3

The parameters for the parabola are:

a = 1, b = 8, c = 3

[tex]\mathbf{x_v= -\dfrac{8}{2\times 1}}[/tex]

[tex]\mathbf{x_v= -4}[/tex]

If we replace the value of [tex]\mathbf{x_v= -4}[/tex] to find the minimum value of [tex]\mathbf{y_v}[/tex] value, we have:

[tex]\mathbf{y_v = -13}[/tex]

Thus, the parabola vertex is (-4,-13). If a< 0, the vertex is a maximum value and If a>0, the vertex is a minimum value.

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Step-by-step explanation:

a vertical asymptote goes up and down.

the horizontal ones (like the horizon) go left and right.

A

1 vertical asymptote at x = 0

B

2 vertical asymptotes at x = -1 and x = +1

C

no vertical asymptote (whatever vertical line you can think of, it will always really cross the graph in finite space)

D

1 vertical asymptote at x = 3

E

like A

F

2 vertical asymptotes at x = -1 and x = +4

Answer:

x: 98 y: 112

Step-by-step explanation:

Supplementary angles add up to 180 so:

x + 82 = 180

x = 98

And:

y + 68 = 180

y = 112

Answer:

supplementary, 98°, 112°

Step-by-step explanation:

Opposite angles of a quadrilateral inscribed in a circle are supplementary, i.e., they add up to 180°.

∴ x° + 82° = 180°

  x = 180° - 82°

       x = 98°

y° + 68° = 180°

y = 180° - 68°

    y = 112°

Answer:

Question 4: letter c

Question 3: letter c

Step-by-step explanation:

Based on the information provided, the equation of this new circle is equal to: B. (x - h)² + (y - k)² = r²

Mathematically, the equation of a circle can be derived by using Pythagorean theorem;

x² + y² = r²

Where:

After translating h units along the x-axis and k units along y-axis on a coordinate plane, the equation of this new circle is given by:

(x - h)² + (y - k)² = r²

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Answer: B) (x – h)2 + (y – k)2 = r2

Step-by-step explanation:

Answer:

18.88

Step-by-step explanation:

tan 42° = 17/x

x= 17/(tan 42°)

x = 17/(0.9004)

x = 18.88

Answer:

g(-2) = 0
g(4) = -4

Step-by-step explanation:

-2 works in the second equation because it is within the restrictions, therefore it is 0.
4 works in the third equation because it is within those restrictions, therefor it is -4.

Answer:

865

Step-by-step explanation:

if minus than answer

The slope and y-intercept will be the negative 5/2 and 4.

The complete question is attached below.

The equation of line is given as

y = mx + c

Where m is the slope and c is the y-intercept.

The equation is given below.

y > -(5/2)x + 4

The slope and y-intercept will be the negative 5/2 and 4.

The graph is also attached below.

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Answer: The measure of each angle is  105°, 50°, and 25°.

Step-by-step explanation: The first step in solving this is writing down what you know.

In the phrase it tells you that "one angle of a triangle measures 80 more than the smallest", so we can say that one angle = 80 + smallest angle.

This can be simplified more to x = 80 + y

x = One Angle

y = Smallest Angle

Then if we continue with the phrase it says "a third angle is twice the smallest", so we can say that a third angle = 2(Smallest Angle).

This can be simplified more to z = 2(y)

z = Third Angle

We also know that a triangles angles add up to 180°, so we know x + y + z = 180.

So, with these equations we can now solve for x, y, and z.

The easiest way would be to simply just plug in x and z straight into the 180 equation as follows.

x = 80 + y

z = 2(y)

180 = x + y + z

180 = (80 + y) + y + (2y)

180 = 80 + 4y

100 = 4y

y = 25

Then we can use y to solve for the other two equations.

z = 2(25)     x = 80 + 25

z = 50         x = 105

After completing that you are left with the three angles of the triangle, 25, 50, and 105.

[tex] \sf{\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Let's solve for x and z ~

[tex]\qquad \sf  \dashrightarrow \: z + 68 = 180[/tex]

[ they form co - exterior angle pair ]

[tex]\qquad \sf  \dashrightarrow \: z = 180 - 68[/tex]

[tex]\qquad \sf  \dashrightarrow \: z = 112 \degree[/tex]

now, it's time for x :

First angle z is equal to its vertical opposite angle, and then that angle forms co - interior angle pair with (3x - 28)

[tex]\qquad \sf  \dashrightarrow \: 3x - 28 + 112 = 180[/tex]

[tex]\qquad \sf  \dashrightarrow \: 3x + 84 = 180[/tex]

[tex]\qquad \sf  \dashrightarrow \: 3x = 180 - 84[/tex]

[tex]\qquad \sf  \dashrightarrow \: 3x = 96[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = 96 \div 3[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = 32 \degree[/tex]

That's all... let me know if you have questions ~

Answer:

the answer is $62

Step-by-step explanation:

if you subtract 110 by 98 you get 12 and the same for the rest so if you subtract 74 by 12 you get 62

Hope that help :)

Answer:

62

Step-by-step explanation:

The ordered pair that represents a function is {(0,0),(1,10),(10,4),(-1,-7)}.

A set of ordered pairs that defines a function will be the one that has exactly one y-value that assigned to every x-value. This means that none of its x-values can have two corresponding y-values.

All the sets of ordered pairs don't have exactly one y-value that corresponds to each of its x-value except {(0,0),(1,10),(10,4),(-1,-7)}.

Thus, we can say that the ordered pair that represents a function is {(0,0),(1,10),(10,4),(-1,-7)}.

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Answer:

F(x) = - [tex]\sqrt[3]{x}[/tex]  

Step-by-step explanation:

A square root can only have a positive input for the domain

(The domain is the input for the function)

The cube root can be either negative or positive as an input

F(x) = - [tex]\sqrt[3]{x}[/tex]  can have inputs from negative infinity to infinity

The number of diagonals drawn from the vertex of the polygon of n sides is (n−3).

The correct option is C)

⇒  A diagonal is a segment that connects two non-consecutive vertices in a polygon.

⇒  The number of diagonals in a polygon that can be drawn from any vertex in a polygon is three less than the number of sides.

A polygon is a plane figure enclosed by line segments called sides. Polygon is a 2d shape.

Regular polygons contain equal side lengths.

⇒  Let n be the number sides in the polygon.

⇒  So, the number of diagonals drawn from the vertex of the polygon of n sides is (n−3).

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Answer:

9 men

Step-by-step explanation:

If 6 men are required to complete a job in 8, than 9 men would be required for a 12 day job.

12-8=4 which is half of 8

Half of 6 is 3

6+3=9

Answer:

4 men

Step-by-step explanation:

• Let x be the number of men needed to do the work I need 12 days.

•• it’s clear that the two variables (number of men and number of hours are in inverse proportion)

•• Which means their product is always equal to a constant.

Therefore

12 × x = 6 × 8 = 48

Then

x = 48 ÷ 12

  = 4

Answer:

A. y = 3x + 1

Explanation:

Find slope:

[tex]\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} = \dfrac{\triangle y}{\triangle x} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]

Take two points: (0, 1), (1, 4)

[tex]\sf \rightarrow slope \ (m) : \dfrac{4-1}{1- 0 } = 3[/tex]

Equation:

[tex]\sf y - y_1 = m(x - x_1)[/tex]

[tex]\sf y - 1 = 3(x - 0)[/tex]

[tex]\sf y = 3x + 1[/tex]

Answer:

radius = 5

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

(x - 2)² + (y - 6)² = 25 ← is in standard form

with r² = 25 ( take the square root of both sides )

r = [tex]\sqrt{25}[/tex] = 5

Answer:

x = 2

Step-by-step explanation:

3x + 1 = 7

3x = 7 – 1

3x = 6

x = 6/3

x = 2

-------------------------------------------------------------------------------------------------------------

Answer:  [tex]\textsf{x = 2}[/tex]

-------------------------------------------------------------------------------------------------------------

Given:  [tex]\textsf{3x + 1 = 7}[/tex]

Find:  [tex]\textsf{Solve for x}[/tex]

Solution: In order to isolate x we need to subtract 1 from both sides and the divide both sides by 3.

Subtract 1 from both sides

Divide both sides by 3

Therefore, the value of x is equal to 2.

From the power rules, the matching of  each expression with its result is:

[tex](8.6*10^7)(9.1*10^{-8})=7.8[/tex]

[tex](6.9*10^5)(4.8*10^{-3})=3.3*10^3[/tex]

[tex]\frac{(3.7*10^2)*(4.6*10^{-3})}{(1.4*10^{-6})*(5.7*10^{8})} =2.1*10^{-3}[/tex]

[tex]\frac{(3.1*10^5)*(5.3*10^{-9})}{(7.3*10^{2})*(6.1*10^{-7})}=3.7[/tex]

There are different power rules, see some them:

1. Multiplication with the same base: you should repeat the base and  add the exponents.

2. Division with the same base: you should repeat the base and  subctract the exponents.

3.Power. For this rule, you should repeat the base and multiply the exponents.

4. Zero Exponent. When you have an exponent equals to zero, the result must be 1.

From this for your question, you have:

[tex]\frac{(3.7*10^2)*(4.6*10^{-3})}{(1.4*10^{-6})*(5.7*10^{8})} =\frac{(3.7*4.6)*(10^2*10^{-3})}{(1.4*5.7)*(10^{-6}*10^{8})} =\frac{17.02*10^{-1}}{7.98*10^2} =2.13*10^{-3}=2.1*10^{-3}[/tex]

[tex]\frac{(3.1*10^5)*(5.3*10^{-9})}{(7.3*10^{2})*(6.1*10^{-7})}=\frac{(3.1*5.3)*(10^{5}*10^{-9})}{(7.3*6.1)*(10^{2}*10^{-7})} =\frac{16.43*10^{-4}}{44.53*10^{-5}}=0.36896*10^1=3.7[/tex]

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2x - y = 8

3x + y = 17

2x - y = 8

3x + y = 17

________ +

5x = 25

x = 5

2(5) - y = 8

10 - y = 8

-y = -2

y = 2

The equivalent expression of [tex](\frac{x^{-4}y}{x^{-9}y^5})^{-2}[/tex] is [tex]x^{-10}y^8[/tex]

Which expression is equivalent to [tex](\frac{x^{-4}y}{x^{-9}y^5})^{-2}[/tex]

The expression is given as:

[tex](\frac{x^{-4}y}{x^{-9}y^5})^{-2}[/tex]

Apply the exponent law of indices

[tex](\frac{x^{-9}y^5}{x^{-4}y})^{2}[/tex]

Next, we apply the common base law of indices

[tex](x^{4 -9}y^{5-1})^2[/tex]

Evaluate the difference

[tex](x^{-5}y^4)^2[/tex]

Remove bracket

[tex]x^{-10}y^8[/tex]

Hence, the equivalent expression of [tex](\frac{x^{-4}y}{x^{-9}y^5})^{-2}[/tex] is [tex]x^{-10}y^8[/tex]

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Answer:

y^8/x^10

Step-by-step explanation:

The guy above me is right but just forgot to distribute the negative out of x. :)

Step-by-step explanation:

please mark me as brainlest

Answer:

slope = 2

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 )

y = - [tex]\frac{1}{2}[/tex] x + 5 ← is in slope- intercept form

with slope m = - [tex]\frac{1}{2}[/tex]

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{1}{2} }[/tex] = 2

The value of the variable x = 6 and y = 5. Then the position vector of P will be 6i + 5j.

The equation of line is given as

y = mx + c

Where m is the slope and c is the y-intercept.

PQRS is a parallelogram. the position vector of Q R and S are 5i +7j, -3i-8j and -4i-6j.

Then the point of Q, R, and S will be (5, 7), (-3, -8), and (-4, -6).

Let the point P be (x, y).

We know that the slope of the line QS and PQ will be same and line is passing through (-3, -8).

y = 1.444x + C

-8 = 1.444 (-3) + C

C = -3.667

Then the equation will be

y = 1.444x – 3.667  …1

The slope of the line PQ and RS will be same and line is passing through (5, 7).

y = -2x + D

7 = -2 (5) + D

D = 17

Then the equation will be

y = -2x + 17  …2

By solving equation 1 and 2, we have

x = 6 and y = 5

Then the position vector of P will be

⇒ 6i + 5j

The graph is given below.

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Answer:

5m-3

Step-by-step explanation:

Answer:

5m-3

Step-by-step explanation:

Answer:

y = 4x

Step-by-step explanation:

Equation of line in point -y intercept form:

    [tex]\sf \boxed{\bf y-y_1=m(x- x_1)}[/tex]

[tex]\sf x_1 = 1 \ ; \ y_1=4 \ \& \ m = 4[/tex]

  y - 4 = 4(x -1)

  y - 4 = 4*x - 4*1

  y - 4 = 4x - 4

Add 4 to both sides

       y = 4x - 4 + 4

      y =4x