What is the vertex of the parabola whose equation is y = (x + 1)2 + 3?

Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the corre

Margaret [11]

In getting the area of and equilateral triangle, you must first consider that all of its sides are congruent and that is 3 inches, so the formula in getting the area is height form its base so in getting its height you must use the pythagorean theorem by dividing the triangle so the hypotenuse of it is 3 and the base of 1.5inches, so the height is 4.77 inches then the area is 7.15 sqr.inch

4 0

2 years ago

Consider a circle whose size can vary. The circumference of the circle is always 2 π 2π times as large as its radius. Let r r re

Alenkasestr [34]

Answer: $C=2\pi r$

Step-by-step explanation:

Let be "C" the circumference of the circle (in feet) and "r" the radius of the circle (in feet).

Based on the information provided in the problem, you know that the circumference of the circle is always $2\pi$ as large as its radius.

Notice that this indicates a multiplication. Then, this means that the circumference of the circle is always equal to $2\pi$ by "r".

Based on this, you can write the following formula that expresses the circumference "C" in terms of the radius "r":

$C=2\pi r$

4 0

2 years ago

Find all solutions of the given system of equations (If the system is infinite many solution, express your answer in terms of x)

lisov135 [29]

Answer:

(a) The system of the equations $\left \{ {2x-3y\:=3} \atop {4x-6y\:=3}} \right.$ has no solution.

(b) The system of the equations $\left \{ {4x-6y\:=10} \atop {16x-24y\:=40}} \right.$ has many solutions $y=\frac{2x}{3}-\frac{5}{3}$

Step-by-step explanation:

(a) To find the solutions of the following system of equations $\left \{ {2x-3y\:=3} \atop {4x-6y\:=3}} \right.$ you must:

Multiply $2x-3y=3$ by 2:

$\begin{bmatrix}4x-6y=6\\ 4x-6y=3\end{bmatrix}$

Subtract the equations

$4x-6y=3\\-\\4x-6y=6\\------\\0=-3$

0 = -3 is false, therefore the system of the equations has no solution.

(b) To find the solutions of the system $\left \{ {4x-6y\:=10} \atop {16x-24y\:=40}} \right.$ you must:

Isolate x for $4x-6y=10$

$x=\frac{5+3y}{2}$

Substitute $x=\frac{5+3y}{2}$ into the second equation

$16\cdot \frac{5+3y}{2}-24y=40\\8\left(3y+5\right)-24y=40\\24y+40-24y=40\\40=40$

The system has many solutions.

Isolate y for $4x-6y=10$

$y=\frac{2x}{3}-\frac{5}{3}$

3 0

2 years ago

Bernite is selling candy bars for a school fundraiser. The school paid $20.00 for a box of 15 king-size candy bars and Bernite s

irina1246 [14]

Answer:

Step-by-step explanation:

candy sold vs money earned

money earned = 2 dollars * number of bars sold- cost of bars

money earned = 2 b -20

this is an equation of a line

(y= 2x-20)

A.The relationship is linear true

B.The relationship is nonlinear false

C.The relationship is always results in a negative profit false

it crosses the x axis at 10 candy bars

D.The relationship always result in a positive profit false

it crosses the x axis at 10 candy bars

E.The relationship is proportional false

F.The relationship is non-proportional true it is a line that does not cross the origin

1jaiz4 and 21 more users found this answer helpfulcandy sold vs money earned

money earned = 2 dollars * number of bars sold- cost of bars

money earned = 2 b -20

this is an equation of a line

(y= 2x-20)

A.The relationship is linear true

B.The relationship is nonlinear false

C.The relationship is always results in a negative profit false

it crosses the x axis at 10 candy bars

D.The relationship always result in a positive profit false

it crosses the x axis at 10 candy bars

E.The relationship is proportional false

F.The relationship is non-proportional true it is a line that does not cross the origin

3 0

2 years ago

Five years from now, the sum of the ages of a women and her daughter will be 40 years. The difference in their present age is 24

CaHeK987 [17]

Answer:

Her daughter is 3 years old now.

Step-by-step explanation:

Given:

Five years from now, the sum of the ages of a women and her daughter will be 40 years.

The difference in their present age is 24 years.

Now, to find how old is her daughter now.

Let the age of daughter be $x\ years$ .

And the age of mother be $y\ years$ .

According to question:

$(x+5)+(y+5)=40$

⇒ $x+y+10=40$

Subtracting both sides by 10 we get:

⇒ $x+y=30$

⇒ $x=30-y$ ............( 1 )

Now, as given in question:

The difference in their present ages is 24 years.

$x-y=24$

Putting the equation ( 1 ) in the place of $x$ we get:

⇒ $(30-y)-y=24$

⇒ $30-2y=24$

Moving variable on one side and the numbers on the other:

⇒ $30+24=2y$

⇒ $54=2y$

Dividing both sides by 2 we get:

⇒ $27=y$

So, the age of the mother is 27 years.

Now, putting the value of $y$ in equation( 1 ) we get:

$x=30-27$

⇒ $x=3$

The age of daughter is 3 years.

Therefore, her daughter is 3 years old now.

4 0

2 years ago