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3 years ago

Solve and graph on a number line -6x+5<-15.2

Mathematics

1 answer:

Kaylis [27]3 years ago

7 0

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Which expression has an equivalent value to x^2 + 9x + 8 for all values of x?

pochemuha

The first choice: <span>(x + 1)(x + 8)</span>.
1+8=9
1*8=8

6 0

3 years ago

A company makes paper labels for paint cans. As shown below, each can is in the shape of a cylinder

sineoko [7]

The company needs 41 labels on average, each minute.

<h3>What is the circumference of a circle?</h3>

The perimeter of a circle (circumference): 2 π radius

Replacing with the values given:

C = 2 (3.14) 2 = 12.56 cm

So, the area of one label is:

Area of a rectangle: length x width = 12.56 x 7 = 87.92 cm sq.

Now, the number of label be n

87.92 x n = 3612.64 cm2

n = 3612.64 / 87.92

n = 41.09

Hence, The company needs 41 labels on average, each minute.

Learn more about circumference;

brainly.com/question/4268218

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6 0

2 years ago

How to find the vertex calculus 2What is the vertex, focus and directrix of x^2 = 6y

son4ous [18]

Solution:

Given:

$x^2=6y$

Part A:

The vertex of an up-down facing parabola of the form;

$\begin{gathered} y=ax^2+bx+c \\ is \\ x_v=-\frac{b}{2a} \end{gathered}$

Rewriting the equation given;

$\begin{gathered} 6y=x^2 \\ y=\frac{1}{6}x^2 \\ \\ \text{Hence,} \\ a=\frac{1}{6} \\ b=0 \\ c=0 \\ \\ \text{Hence,} \\ x_v=-\frac{b}{2a} \\ x_v=-\frac{0}{2(\frac{1}{6})} \\ x_v=0 \\ \\ _{} \\ \text{Substituting the value of x into y,} \\ y=\frac{1}{6}x^2 \\ y_v=\frac{1}{6}(0^2) \\ y_v=0 \\ \\ \text{Hence, the vertex is;} \\ (x_v,y_v)=(h,k)=(0,0) \end{gathered}$

Therefore, the vertex is (0,0)

Part B:

A parabola is the locus of points such that the distance to a point (the focus) equals the distance to a line (directrix)

Using the standard equation of a parabola;

$\begin{gathered} 4p(y-k)=(x-h)^2 \\ \\ \text{Where;} \\ (h,k)\text{ is the vertex} \\ |p|\text{ is the focal length} \end{gathered}$

Rewriting the equation in standard form,

$\begin{gathered} x^2=6y \\ 6y=x^2 \\ 4(\frac{3}{2})(y-k)=(x-h)^2 \\ \text{putting (h,k)=(0,0)} \\ 4(\frac{3}{2})(y-0)=(x-0)^2 \\ Comparing\text{to the standard form;} \\ p=\frac{3}{2} \end{gathered}$

Since the parabola is symmetric around the y-axis, the focus is a distance p from the center (0,0)

Hence,

$\begin{gathered} Focus\text{ is;} \\ (0,0+p) \\ =(0,0+\frac{3}{2}) \\ =(0,\frac{3}{2}) \end{gathered}$

Therefore, the focus is;

$(0,\frac{3}{2})$

Part C:

A parabola is the locus of points such that the distance to a point (the focus) equals the distance to a line (directrix)

Using the standard equation of a parabola;

$\begin{gathered} 4p(y-k)=(x-h)^2 \\ \\ \text{Where;} \\ (h,k)\text{ is the vertex} \\ |p|\text{ is the focal length} \end{gathered}$

Rewriting the equation in standard form,

Since the parabola is symmetric around the y-axis, the directrix is a line parallel to the x-axis at a distance p from the center (0,0).

Hence,

$\begin{gathered} Directrix\text{ is;} \\ y=0-p \\ y=0-\frac{3}{2} \\ y=-\frac{3}{2} \end{gathered}$

Therefore, the directrix is;

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

3 0

1 year ago

What is the average rate of change for this exponential function for the interval from x=2 to x=4?

mario62 [17]

The equation to calculate the average rate of change is: y/x

y = f(x2) - f(x1)x = x2 - x1

x1: 1 (The smaller x value. It can be any number)x2: 2 (The larger x value. It also can be any number)f(x1): The value when you plug x1 into the function.f(x2): The value when you plug x2 into the function.

If we know this, the variables for this problem are assuming the function is 10(5.5)^x:

x2: 2x1: 1f(x2): 10(5.5)^(2) = 302.5f(x1): 10(5.5)^(1)= 55

This means:y = 302.5 - 55 = 247.5x = 2 - 1 = 1

Remember: the equation for avg rate of change is y/x

So, our average rate of change for the function on the interval [1,2] is 247.5 (y/x = 247.5/1)

5 0

3 years ago

Read 2 more answers

An arc on a circle measures 250 degrees. Within range which range is the radian measure of the central angle?

blondinia [14]

If the arc measures 250 degrees then the range of the central angle lies from π to 1.39π.

Given that the arc of a circle measures 250 degrees.

We are required to find the range of the central angle.

Range of a variable exhibits the lower value and highest value in which the value of particular variable exists. It can be find of a function.

We have 250 degrees which belongs to the third quadrant.

If 2π=360

x=250

x=250*2π/360

=1.39 π radians

Then the radian measure of the central angle is 1.39π radians.

Hence if the arc measures 250 degrees then the range of the central angle lies from π to 1.39π.

Learn more about range at brainly.com/question/26098895

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8 0

2 years ago