The focus of a parabola is (3,-7) and the directrix is y = -4.
What is an equation of the parabola?

Answer:

Linear f(x) = 2·x + 3

Quadratic f(x) = x² + 2·x - 3

Exponential f(x) = 3ˣ - 2

Step-by-step explanation:

1) Linear function

The general form of the linear equation is of the form, f(x) = y = m·x + c

Where;

m = The slope

c = y-intercept (Constant)

The linear function is therefore, f(x) = 2·x + 3

2) Quadratic function

The general form of the quadratic function is f(x) = a·x² + b·x + c

Where;

a, and b are the coefficients of x² and x respectively and c is the constant term

Therefore,  f(x) = x² + 2·x - 3, is a quadratic function, with a = 1, b = 2, and c = -3

3) Exponential function

The general form of the exponential function is f(x) = a·bˣ + k

Where;

a = The initial

b = The multiplier (growth or decay value)

k = vertical shift

Therefore, the function f(x) = 3ˣ - 2 is an exponential function with the initial = 1, b= 3, and k = -2

Answer:

There are 3 ways

Step-by-step explanation:

The formula for a sector's area is:

1. A = (sector angle / 360 ) * (pi *r2)

2. A = (sector angle / (2*pi)) * (pi * r2)

3. A = (fraction of the circle) * (pi * r2)

[tex]\text{Solve for y:}\\\\-4.1=8(y-5)\\\\\text{Use the distributive property}\\\\-4.1=8y-40\\\\\text{Add 40 to both sides}\\\\35.9=8y\\\\\text{Divide by 8}\\\\\boxed{4.4875=y}\\\\[/tex]

Answer:

C(x)=3x³+4x²-11x-8

Step-by-step explanation:

The water usage is modeled by the equation W(x) = 4x³ + 6x² − 11x + 7

The amount of decrease in water used is modeled by D(x) = x³ + 2x² + 15

C(x)= W(x)-D(x)

C(x)=4x³ + 6x² − 11x + 7-(x³ + 2x² + 15)

C(x)=4x³ + 6x² − 11x + 7-x³-2x²-15

c(x)=3x³+4x²-11x-8

Answer:

the second option

Step-by-step explanation:

Answer:

10 centimeters

Step-by-step explanation:

formula for volume of a cylinder = πr² · h

1. Set up the equation

(3.14)(r²)(14) = 4,396

2. Simplify

(43.96)(r²) = 4,396

3. Solve

r² = 100

√r = √100

r = 10

6 cm from what im seeing

Answer: 7 cm

Step-by-step explanation:

Answer:

Man's present age: 32 years

Older son's present age: 8 years

Younger sons present age: 4 years

Step-by-step explanation:

Let their present ages be represented by:

Man = a

Older boy = b

Younger boy = c

A man has two sons, one twice as old as the other:

b = 2 × c

b = 2c......... Equation 1

The man is four times as old as the older boy:

a = 4 × b

a = 4b.......Equation 2

In three years he will be five times as old as the younger boy:

a + 3 = 5 (c + 3)

a + 3 = 5c + 15........Equation 3

Since b = 2c and a = 4b

Subtitute 2c for b in Equation 2

a = 4b

a = 4 × 2c

a = 8c

Subtitute 8c for a in Equation 3

a + 3 = 5c........Equation 3

8c + 3 = 5c + 15

Collect like terms

8c - 5c = 15 - 3

3c = 12

c = 4

Therefore since c, represents the present age of the younger son, the younger son is 4 years old

b = 2c

b = 2 × 4

b = 8

Since b is the present age of the older son, the older son is 8 years old

a = 4b

b = 8

a = 4 × 8

a = 32

Since a is the present age of the man, the man is 32 years old

Therefore,

Man's present age: 32 years

Older son's present age: 8 years

Younger sons present age: 4 years

[tex]2x \times x + 2x \times 5 - 9 \times x - 9 \times 5[/tex]

[tex] {2x }^{2} + 10x - 9x - 45 [/tex]

[tex] {2x}^{2} + x - 45 [/tex]

●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●

Hi my lil bunny!

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

[tex]\boxed{x=14}[/tex]

Reorder the terms:

[tex]-9 + 2x = 5 + x[/tex]

Solving

[tex]-9 + 2x = 5 + x[/tex]

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1x' to each side of the equation.

[tex]-9 + 2x + -1x = 5 + x + -1x[/tex]

Combine like terms: [tex]2x + -1x = 1x[/tex]

[tex]-9 + 1x = 5 + x + -1x[/tex]

Combine like terms: [tex]x + -1x = 0[/tex]

[tex]-9 + 1x = 5 + 0\\-9 + 1x = 5[/tex]

Add '9' to each side of the equation.

[tex]-9 + 9 + 1x = 5 + 9[/tex]

Combine like terms: [tex]-9 + 9 = 0[/tex]

[tex]0 + 1x = 5 + 9\\1x = 5 + 9[/tex]

Combine like terms: [tex]5 + 9 = 14[/tex]

[tex]1x = 14[/tex]

Divide each side by '[tex]1[/tex]'.

[tex]x = 14[/tex]

Simplifying

[tex]x = 14[/tex]

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●

Have a great day/night!

❀*May*❀

Answer:

Hey there!

4^2-2(3(5)+1)

16-2(15+1)

16-2(16)

-16

C is correct.

Let me know if this helps :)

Answer:

Step-by-step explanation:

[tex] \mathsf{ {4}^{2} - 2(3 \times 5 + 1)}[/tex]

Evaluate the power

⇒[tex] \mathsf{16 - 2(3 \times 5 + 1)}[/tex]

Multiply the numbers

⇒[tex] \mathsf{16 - 2(15 + 1)}[/tex]

Calculate the sum

⇒[tex] \mathsf{16 - 2 \times 16}[/tex]

Multiply the numbers

⇒[tex] \mathsf{16 - 32}[/tex]

Calculate

⇒[tex] \mathsf{ - 16}[/tex]

Hope I helped!

Best regards!

1. (ab + bc) (ab – bc) + (bc + ca) (bc – ca) + (ca + ab) (ca – ab) = 0

We know that (a+b)(a-b) = a²-b²

(ab + bc)(ab -bc) can be written as a²b² - b²c²

(bc + ca)(bc -ca) can be written as b²c² - c²a²

(ca + ab)(ca - ab) can be written as c²a² - a²b²

→ a²b² - b²c² + b²c² - c²a² + c²a² - a²b²

→ a²b² - a²b² - b²c² + b²c² - c²a² + c²a²

→ 0

2. (a + b + c) (a² + b² + c² – ab – bc – ca) = a³ + b³+ c³ – 3abc

→ a³ + ab² + ac² -a²b - abc -ca² + a²b + b³ + bc² - ab² - b²c - abc + a²c + b²c + c³ - abc - bc² - c²a

→ a³ + b³+ c³ + (- abc - abc - abc) + (ab² - ab² )+ (ac² - ca² ) -(a²b + a²b )+ (bc² - bc² )+ (a²c - c²a) + (b²c - b²c)

→ a³+b³+c³ - 3 abc .

3. (p – q) (p² + pq + q²) = p³ – q³.

→ p³ + p²q + pq² - p²q - pq² - q³

→ p³ - q³ +(p²q - p²q) + (pq² - pq²)

→ p³ - q³

Answer:

Below

Step-by-step explanation:

Let x be the measure in degrees

● x/180 = 1.2/Pi

Cross multiply the values

● x*Pi = 180×1.2

● x = 216/Pi

Take Pi = 3.14

● x = 68.78 wich is approximatively 69°

Answer:

Area= 97.9 km²

Step-by-step explanation:

Angle at w = 180-119-34

Angle at w = 27°

Side XV= x

x/sin27= 26/sin119

x= sin27(26/sin119)

x= 0.454(26/0.8746)

x= 13.5 km

Side WX = y

y/sin 34= 26/sin119

y= sin34(26/sin119)

y= 0.559(26/0.8746)

y= 16.6 km

S= (16.6+13.5+26)/2

S= 56.1/2

S=28.05

Area = √(28.05(28.05-26)(28.05-13.5)(28.05-16.6))

Area=√(28.05(2.05)(14.55)(11.45))

Area=√(9579.772744)

Area=97.8763

Area= 97.9 km²

Answer:

21 squares

Step-by-step explanation:

Here in this question, we are given a pattern and we want to determine what the values in that pattern will be at a specific step.

We proceed as follows;

What we can see in this pattern is that the difference in number of squares between a pattern and the next pattern increases by the addition of the next integer to the number of squares we have in the last pattern.

Thus for step 5, we shall be adding the next integer( 5) to the number of squares ;

That would be 10 + 5 = 15 squares

For step 6, we shall be adding the next integer (6) to the number of squares in step 5.

That would be 15 + 6 = 21 squares

How we got the initial next integer?

step 1 = 1 square

step 2 = 3 squares ( integer difference of 2)

step 3 = 6 squares ( integer difference of 3)

step 4 = 10 squares ( integer difference of 4)

so;

step 5 = 15 squares ( integer difference of 5)

step 6 = 21 squares( integer difference of 6)

Answer:

[tex]\huge \boxed{16}[/tex]

Step-by-step explanation:

4 raised to 2 is 4 squared or 4 to the power of 2.

[tex]4^2 =4 \times 4 = 16[/tex]

Answer:

See Explanation

Step-by-step explanation:

Given

[tex]a = b[/tex]

Required

Match proper type of equality

Each of the equality properties can easily be identified with their names; For multiplication property of equality, same term must be multiplied on both sides;

For addition, same term  must be added on both sides;

Same thing implies for division and subtraction

Multiplication:

[tex]a(c) = b(c)[/tex]

Subtraction

[tex]a - c = b - c[/tex]

Addition

[tex]a + c = b + c[/tex]

Division

[tex]a/c = b/c[/tex]

Answer:

Step-by-step explanation:

[tex]x^{2} -x-x<[/tex] 0

[tex]x^{2} -2x[/tex] < 0

x^2-2x+1<1

(x-1）^2<1

-1<x-1<1

0<x<2

[tex](x-1)^{2}[/tex][tex](x-1)^{2}[/tex]

Answer:

i couldnt find a solution to the equation all i could get is u +v

Step-by-step explanation:

what were you trying to say when you said "let u="

Answer:

4.8

Step-by-step explanation:

(-3,4) + (8,2) = 4.8

Answer:

D

Step-by-step explanation:

Since this is a right triangle, and we are given that one of the other angles is 30°, we have a 30°, 60°, 90° triangle.

In a 30°, 60°, 90° triangle, the side lengths are all related as shown below.

We should determine a first. a is the measure of the side opposite to the 30° angle. Thus:

[tex]a=11[/tex]

The side opposite to the 60° angle is given by a√3. Since a = 11, the side opposite to the 60° angle or x is:

[tex]x=(11)\sqrt{3}=11\sqrt3[/tex]

Finally, the hypotenuse will be 2a. Since a = 11, the hypotenuse or y will be:

[tex]y=2(11)=22[/tex]

Hence, x = 11√3 and y = 22.

Our answer is D.

Answer:

100.5 ft^2

Step-by-step explanation:

First find the area of the rectangle

A = l*w

A = 12.16 * 6

A =72.96 ft^2

Then find the area of the triangle

A = 1/2 bh

The base is 12 ft - 6ft = 6ft

The height is 9.16 ft

A = 1/2 ( 9.16) * 6

A = 27.48 ft^2

Add them together

27.48+72.96

100.44 ft^2

Round to the nearest tenth

100.5 ft^2

Answer:

[tex]\huge \boxed{\mathrm{100.4 \ ft^2 }}[/tex]

Step-by-step explanation:

To find the area of the shape, we can add the area of the rectangle with the area of the triangle.

Area of rectangle :

base × height

6 ft × 12.16 ft

72.96 ft²

Area of triangle :

base × height × 1/2

(12 ft - 6 ft) × 9.16 ft × 1/2

6ft × 9.16 ft × 1/2

27.48 ft²

Adding the areas.

72.96 ft² + 27.48 ft²

100.44 ft²

≈ 100.4 ft² (rounded to nearest tenth)

Answer:

x = -1

Step-by-step explanation:

the line of the simetry is x = -1

Answer:

Its x = -1 because it splits the diamond shape perfectly at x -1

Step-by-step explanation:

Answer:  x = 4/5

Step-by-step explanation:

[tex]\tan\ y=\dfrac{\text{side OPPOSITE y}}{\text{side ADJACENT to y}}=\dfrac{1}{6}\\\\\\.\qquad \qquad \qquad \qquad \qquad \qquad \dfrac{x}{x+4}=\dfrac{1}{6}\\\\\\\text{Cross multiply, distribute, and solve for x:}\\6(x)=1(x+4)\\6x=x+4\\5x=4\\\\\large\boxed{x=\dfrac{4}{5}}[/tex]

Answer:

Graph C.

Step-by-step explanation:

Hi there!

Well let’s first put,

7x + 2y < 8

We need to single out y.

7x + 2y < 8

-7x to both sides

2y < -7x + 8

Divide everything by 2,

y < -7/2x + 4

Well the shade on the graph should be going down because it is y is less than,

And the y intercept should be at 4 with a dotted line and a slope of -7/2.

So graph C. Is correct.

Hope this helps :)

The graph that represents the inequality 7x + 2y < 8 will be graph C.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The inequality is given as,

7x + 2y < 8

Simplify the equation in slope-intercept form, then we have

7x + 2y < 8

2y < 8 - 2x

y < (8 - 2x) / 2

The value of the variable 'y' is less. Then the graph that represents the inequality 7x + 2y < 8 will be graph C.

More about the inequality link is given below.

https://brainly.com/question/19491153

#SPJ2

Answer:

[tex]\boxed{10}[/tex]

Step-by-step explanation:

[tex]2x+5=8x[/tex]

[tex]\sf Subtract \ 8x \ from \ both \ sides.[/tex]

[tex]2x+5-8x=8x-8x[/tex]

[tex]-6x+5=0[/tex]

[tex]\sf Subtract \ 5 \ from \ both \ sides.[/tex]

[tex]-6x+5-5=0-5[/tex]

[tex]-6x=-5[/tex]

[tex]\sf Divide \ both \ sides \ by \ -6.[/tex]

[tex]\displaystyle \frac{-6x}{-6} =\frac{-5}{-6}[/tex]

[tex]\displaystyle x =\frac{5}{6}[/tex]

[tex]\sf Evaluate \ 12x.[/tex]

[tex]\displaystyle 12 \cdot \frac{5}{6} =\frac{60}{6} =10[/tex]

Answer:

10

Step-by-step explanation:

2x+5=8x: First, you are going to subtract 2x from both sides of the equation.

5=6x: Now divide 6x from each side of the equation.

x=5/6: now plug in 5/6 by multiplying this number by 12.

Your final answer should be 10.

Answer:

Anthropologists study human societies and cultures and the development of them from the past and present. They study this to analyze the differences and evolutions that us as humans have.

Answer:

[tex] 0.88^x [/tex]

Step-by-step explanation:

Exponential decay formula is given as [tex] a(1 - r)^x [/tex], where,

a is the initial amount

r is the decay rate

x is the time interval

Therefore, the multiplier that corresponds to 12% decay is [tex] (1 - r)^x = (1 - \frac{12}{100})^2 = (1 - 0.12)^x = 0.88^x [/tex]

Answer:  D

Step-by-step explanation:

To find how much time she need on each project divide the time by 3 because there are 3 projects and to get to 1 project you will need to divide by 3.

16 3/4 =  67/4

[tex]\frac{67}{4}[/tex] ÷ [tex]\frac{3}{1}[/tex]  = [tex]\frac{67}{12}[/tex]   = 5 7/12

Answer:

Step-by-step explanation:

Answer:

(3x-1) (x+1)

Step-by-step explanation:

3x^2 + 2x − 1

3x^2 factors into 3x and x

-1 factors into -1 and 1

We want a postive 2x

(3x-1) (x+1)

Answer:

(3x-1)(x+1)

Step-by-step explanation:

3x² + 2x − 1

when factorizing , first look at the constant number( in this case it is 1 prime number), then find the GCF if found.

(3x        )(x      )     first step : 3x*x=3x^2

(3x-      ) (x+   )      the sign for the constant is minus so the factoring has to be minus and plus on each side

(3x-1)(x+1)   look at the 2x it has positive sign, means the sign is plus:

3x-1

x+1

                        regular standard multiplication

3x(x)-1(x)+1(3x)-1

3x²+2x-1

Answer:

Toni's Tiles and Bob's Bathrooms are in a proportional relationship as they have the same unit rate

Step-by-step explanation:

The given parameters are;

,                                           Area Tiled (ft²)                                    Time (Hr:min)

,                                            

Toni's Tiles,                                   803                               2:12

Bob's Bathrooms,                         1,460                             4:00

Rhonda's Restroom Redos          753                                1:30

The unit rate for each tiler

Toni's Tiles = 803/2:12 = 803/(2×60 + 12) =  6.083 ft²/min

Bob's Bathrooms = 1460/(4×60) =  6.083 ft²/min

Rhonda's Restroom Redos  = 753/(60 + 30) = 8.37 ft²/min

Therefore we have;

The rates at which Toni's Tiles and Bob's Bathrooms tile are to one another = 6.083 to 6.083  = 1:1

The rates at which Toni's Tiles and Rhonda's Restroom Redos tile are to one another = 73/12×30/251 = 365:502

The rate at which Bob's Bathrooms  and Rhonda's Restroom Redos tile are to one another = 73/12×30/251 = 365:502

Therefore, Toni's Tiles and Bob's Bathrooms are in a proportional relationship as they have the same unit rate.

Answer:

90

Step-by-step explanation:

90 has 0 ones so it is already rounded.

Answer:

90

Step-by-step explanation:

Hey there!

Well 90.000 to the nearest tenth is just 90 because there is decimal places to round.

Hope this helps :)

Answer:

B. 2.7 g

Step-by-step explanation:

The half life of a substance is the time taken for the substance to reduce to half of its original amount. It is given by:

[tex]A=A_o*(\frac{1}{2})^\frac{t}{t_{1/2}}\\ Where\ A\ is \ the \ amount \ of \ substance\ remaining\ after\ t\ years, \\A_o \ is \ the\ initial\ value\ of \ the\ substance,\ t_{1/2} is\ the\ half\ life\ and\\t\ is\ the\ years\ spent[/tex]

Given that:

Ao = 4 g, t = 3 years, t(1/2) = 5.26 years. Therefore:

[tex]A=A_o*(\frac{1}{2})^\frac{t}{t_{1/2}}\\A=4*(\frac{1}{2} )^\frac{3}{5.26}=4*0.6735=2.7\\ A=2.7\ g[/tex]