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Oksi-84 [34.3K]
3 years ago
13

Enter a number into the blank to make the equation true.

Mathematics
2 answers:
yKpoI14uk [10]3 years ago
8 0

Answer:

779

Step-by-step explanation:

Allushta [10]3 years ago
5 0
Where is the equation?
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Christine is a software saleswoman. Her base salary is $2300, and she makes an additional $120 for every copy of History is Fun
slava [35]

Answer:

please give me brilliant answer

Boundless Algebra

Quadratic Functions and Factoring

Graphs of Quadratic Functions

Parts of a Parabola

The graph of a quadratic function is a parabola, and its parts provide valuable information about the function.

LEARNING OBJECTIVES

Describe the parts and features of parabolas

KEY TAKEAWAYS

Key Points

The graph of a quadratic function is a U-shaped curve called a parabola.

The sign on the coefficient aa of the quadratic function affects whether the graph opens up or down. If a<0a<0, the graph makes a frown (opens down) and if a>0a>0 then the graph makes a smile (opens up).

The extreme point ( maximum or minimum ) of a parabola is called the vertex, and the axis of symmetry is a vertical line that passes through the vertex.

The x-intercepts are the points at which the parabola crosses the x-axis. If they exist, the x-intercepts represent the zeros, or roots, of the quadratic function.

Key Terms

vertex: The point at which a parabola changes direction, corresponding to the minimum or maximum value of the quadratic function.

axis of symmetry: A vertical line drawn through the vertex of a parabola around which the parabola is symmetric.

zeros: In a given function, the values of xx at which y=0y=0, also called roots.

Recall that a quadratic function has the form

f(x)=ax2+bx+cf(x)=ax2+bx+c.

where aa, bb, and cc are constants, and a≠0a≠0.

The graph of a quadratic function is a U-shaped curve called a parabola.  This shape is shown below.



Parabola : The graph of a quadratic function is a parabola.

In graphs of quadratic functions, the sign on the coefficient aa affects whether the graph opens up or down. If a<0a<0, the graph makes a frown (opens down) and if a>0a>0 then the graph makes a smile (opens up). This is shown below.



Direction of Parabolas: The sign on the coefficient aa determines the direction of the parabola.

Features of Parabolas

Parabolas have several recognizable features that characterize their shape and placement on the Cartesian plane.

Vertex

One important feature of the parabola is that it has an extreme point, called the vertex. If the parabola opens up, the vertex represents the lowest point on the graph, or the minimum value of the quadratic function. If the parabola opens down, the vertex represents the highest point on the graph, or the maximum value. In either case, the vertex is a turning point on the graph.

Axis of Symmetry

Parabolas also have an axis of symmetry, which is parallel to the y-axis. The axis of symmetry is a vertical line drawn through the vertex.

yy-intercept

The y-intercept is the point at which the parabola crosses the y-axis. There cannot be more than one such point, for the graph of a quadratic function. If there were, the curve would not be a function, as there would be two yy values for one xx value, at zero.

xx-intercepts

The x-intercepts are the points at which the parabola crosses the x-axis. If they exist, the x-intercepts represent the zeros, or roots, of the quadratic function, the values of xx at which y=0y=0. There may be zero, one, or two xx-intercepts. The number of xx-intercepts varies depending upon the location of the graph (see the diagram below).



Possible xx-intercepts: A parabola can have no x-intercepts, one x-intercept, or two x-intercepts

Recall that if the quadratic function is set equal to zero, then the result is a quadratic equation. The solutions to the equation are called the roots of the function. These are the same roots that are observable as the xx-intercepts of the parabola.

Notice that, for parabolas with two xx-intercepts, the vertex always falls between the roots. Due to the fact that parabolas are symmetric, the 

7 0
3 years ago
A cylindrical tank of water as a radius of 1 foot, and a height of 2 feet. The tank is filled to the brim with water and a spher
tatyana61 [14]

Answer:

you need to find the volume of the cylinder 1rst

Step-by-step explanation:

3 0
3 years ago
For place values that occur to the left of the decimal point, each place value is ten times ______ than the place value to its r
Llana [10]
D. think about it this way. the closer it is to decimal, the closer it is to a whole number which is the "biggest"
8 0
3 years ago
What is the area of the trapezoid to the nearest tenth? <br> PICTURE BELOW ⬇⬇⬇⬇
Nastasia [14]

Answer:

  62.4 ft²

Step-by-step explanation:

The unmarked horizontal dimension at the bottom of the triangle is ...

  (8 ft)sin(30°) = 4 ft

The unmarked vertical dimension of the triangle (the height of the trapezoid) is ...

  (8 ft)cos(30°) ≈ 6.93 ft

Then the area of the trapezoid is given by the formula ...

  A = (1/2)(b1 +b2)h

  A = (1/2)((4 ft+7 ft) +(7 ft))(6.93 ft) ≈ 62.4 ft²

_____

The mnemonic SOH CAH TOA can remind you of the relationships between right triangle dimensions and angles.

  Sin = Opposite/Hypotenuse   ⇒   Hypotenuse×Sin = Opposite

  Cos = Adjacent/Hypotenuse   ⇒   Hypotenuse×Cos = Adjacent

6 0
3 years ago
When a water-cooled nuclear power plant is in operation, oxygen in the water is transmuted to nitrogen-17. After the reactor is
wolverine [178]

Answer:

The differential equation is \frac{dR}{dt} = -kR

Step-by-step explanation:

Differential equation for the rate of change in radiation level:

Radiation level is R.

Rate of change indicates that the radiation level R varies in function of time t, which mathematically means that we have:

\frac{dR}{dt}

After the reactor is shut down, the radiation from the nitrogen-17 decreases in such a way that the rate of change in the radiation level is directly proportional to the radiation level.

Rate of change is k. Decreases means that k is negative. Proportional to the radiation level of R means that -k multiplies R. So the differential equation is:

\frac{dR}{dt} = -kR

7 0
3 years ago
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