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3 years ago

Look at this set of 8 numbers:

Mathematics

2 answers:

Nastasia [14]3 years ago

5 0

the mode would change because 83 replaced 99

(idk sorry i wish i could help you but i really dont know)

meriva3 years ago

5 0

Answer:

it wouldnt change it will still be 8 numbers

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If f ( x ) = 5x^2 - 2x + 6 and g ( x ) = 4x^2 + 6x - 1,<br> then find f ( x ) + g ( x )

musickatia [10]

Answer:

9x^2+4x+5

Step-by-step explanation:

f ( x ) = 5x^2 - 2x + 6

g ( x ) = 4x^2 + 6x - 1,

Add the functions together

f(x)+ g(x) = 5x^2 - 2x + 6 + 4x^2 + 6x - 1

Combine like terms

=9x^2+4x+5

4 0

2 years ago

Evgen [1.6K]

The system of equations represented by the graph is:

y = x - 6

y + x = -2

And the solution is (2, -4), then the correct option is the first one.

<h3>What system is represented by the graph?</h3>

On the graph, we can see a system of linear equations, we can see a line with a positive slope and a line with a negative slope.

The line with a positive slope intercepts the y-axis at y = -6, then that line is:

y = a*x - 6

with a > 0.

The other line passes through the y-axis at y = -2, then the linear equation is:

y = b*x - 2

Where b < 0.

Also, remember that the solution for the system of equations is the point where the two lines intersect, so we can see that the solution is at (2, -4)

The only option that meets all the criteria is the first option:

y = x - 6

x + y = -2

And the solution is (2, -4)

Learn more about systems of equations:

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5 0

1 year ago

A baker purchased 13 lb of wheat flour and 14 lb of rye flour for a total cost of $14.85. A second purchase, at the same prices,

postnew [5]

An equation is formed when two equal expressions. The cost per pound of wheat flour is $0.55 and the cost of per pound of rye flour is $0.55.

<h3>What is an equation?</h3>

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Let the cost of a pound of wheat flour be x and the cost of a pound of rye flour be y.

A baker purchased 13 lb of wheat flour and 14 lb of rye flour for a total cost of $14.85.

13x + 14y = $14.85

x = (14.85-14y)/13

A second purchase, at the same prices, included 15 lb of wheat flour and 12 lb of rye flour.

15x + 12y = $14.85

Substitute the value of x from the above equation and solve for y,

$\dfrac{15(14.85-14y)}{13} + 12y = 14.85\\\\222.75-210y+156y = 193.05\\\\y = 0.55$

Substitute the value of y in any one of the equations formed,

13x + 14(0.55) = 14.85

13x = 7.15

x = 0.55

Hence, the cost per pound of wheat flour is $0.55 and the cost of per pound of rye flour is $0.55.

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8 0

2 years ago

A ball is thrown into the air from a height of 4 feet at time t = 0. The function that models this situation is h(t) = -16t2 + 6

galina1969 [7]

<h2>Hello!</h2>

The answers are:

a) The height of the ball after 3 seconds is 49 feet.

b) The maximum height of the ball is 66 feet.

c) That the ball hit the ground after 4 seconds.

d) The domain would be only the positive real numbers, from 0 to 4, since we found that the ball hit the ground at t equal to 4 seconds. However, if we were talking about a quadratic function with no time involved, the domain would be all the real numbers.

Since we are working with a quadratic function which describes the ball's motion in function of the time, we need to remember the following:

- The general equation of the parabola is:

$y=ax^{2} +bx+c$

- We can calculate the coordinates of the vertex of the parabola using the following formula:

$x_{vertex}=\frac{-b}{2a}$

- Evaluating a function means replacing the variable with the given value to evaluate.

The given function is:

$h(t)=-16x^{2}+63t+4$

Where,

$a=-16\\b=63\\c=4$

Now, calculating we have:

a) What is the height of the ball after 3 seconds?

We need to evaluate the time of 3 seconds into the function, so:

$h(3)=-16(3)^{2} +63(3)+4=49feet$

So, the height of the ball after 3 seconds is 49 feet.

b) What is the maximum height of the ball?

Since the function is describing the motion of a ball thrown into the air, we can find the maximum height by finding the y-coordinate of the vertex. If the parabola opens downward or upward, the vertex will be always the highest or the lowest point of the parabola.

So, calculating the vertex we have:

$x_{vertex}=\frac{-b}{2a}=\frac{-63}{2*-16}\\\\x_{vertex}=\frac{-63}{2*-16}=\frac{-63}{-32}=1.97$

Then, replacing "x" into the equation of the parabola, we find the y-coordinate of the vertex:

$y=-16(1.97)^{2}+63(1.97)+4=-16*3.88+63*1.97+4\\y=-16*3.88+63*1.97+4=-62.08+124.11+4=66.03$

So, if the y-coordinate is 66.03, the maximum height of the ball is 66.03 feet, or 66 feet (rounded to the nearest foot).

c) When will the ball hit the ground?

We can find the time when the ball hit the ground by making equal to 0 the function and finding the roots (zeroes)

Since it's a quadratic function, we can find the zeroes using the quadratic equation:

$\frac{-b+-\sqrt{b^{2}-4ac } }{2a}$

Substituting a, b and c, we have:

$\frac{-b+-\sqrt{b^{2}-4ac } }{2a}=\frac{-63+-\sqrt{63^{2}-4*(-16)*(4)} }{2*(-16)}\\\\\frac{-63+-\sqrt{63^{2}-4*(-16)*(4)} }{2*(-16)}=\frac{-63+-\sqrt{3969+256} }{-32}\\\\\frac{-63+-\sqrt{3969+256} }{-32}=\frac{-63+-\sqrt{4225} }{-32}=\frac{-63+-(65)}{-32}\\\\t1=\frac{-63-(65)}{-32}=4\\\\t1=\frac{-63+(65)}{-32}=-0.06$

Now, since negative time does not exists, we can conclude that the ball hit the ground after 4 seconds.

d) what domain makes sense for the function?

Since the function represents the motion of the thrown ball at "t" time, the domain would be only the positive real numbers, from 0 to 4, since we found that the ball hit the ground at t equal to 4 seconds. However, if we were talking about a quadratic function with no time involved, the domain would be all the real numbers,

Note: I've attached the graph of the function.

Have a nice day!

5 0

3 years ago

Sofia's parents gave her an allowance for summer camp of $125.if she is going to be at camp for 6 weeks,what is the most she can

professor190 [17]

Sofia can spend at most $20.83 each week.

Step-by-step explanation:

Given,

Amount of given by Sofia's parent = $125

Number of weeks = 6

Let,

x represent the amount that Sofia can spend each week.

As Sofia has $125, therefore, she can spend maximum $125 or less than that.

$6x\leq 125$

Dividing both sides by 6

$\frac{6x}{6}\leq \frac{125}{6}\\x\leq 20.83$

Sofia can spend at most $20.83 each week.

Keywords: inequality, division

Learn more about inequalities at:

#LearnwithBrainly

8 0

4 years ago