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3 years ago

15

The top of a round table is 4 feet in diameter. The top splits to allow two extra boards to be inserted. The expansion boards ar

e 4 feet by 1 1/2 feet. What is the area of the expanded table?

1 answer:

Nutka1998 [239]3 years ago

8 0

The answer will be 6

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What is the solution to the following system of equations 2x+3y=3 and -3x-2y=8

SpyIntel [72]

<span>2x+3y=3
</span><span>-3x-2y=8

3y=3-2x
-2y = 8+3x

y = 1 - 2x/3
y = -4 - 3x/2

</span>1 - 2x/3 = -4 - 3x/2

5 = - 3x/2 + 2x/3

5 = -9x/6 + 4x/6

5 = -5x/6

x = 5 * 6/-5

x = -6

No plug it in.

<span>2x+3y=3 ; x = -6

-12 + 3y = 3

3y=3+12

3y=15

y = 5

So </span>x = -6 and y = 5

3 0

3 years ago

Solve the inequality. q - 1 1/3 > -2 1/2

ioda

$\Leftrightarrow q>1\frac{1}{6}$

Step-by-step explanation:

$q-\frac {11}{3}>-2\frac{1}{2}$

$\Leftrightarrow q>-2\frac{1}{2}+\frac {11}{3}$

$\Leftrightarrow q>\frac{7}{6}$

$\Leftrightarrow q>1\frac{1}{6}$

6 0

3 years ago

What are the exact solutions of x2 − 5x − 1 = 0 using x equals negative b plus or minus the square root of the quantity b square

geniusboy [140]

Answer:

$x=2.5+\frac{\sqrt{29}}{2}\\\\x=2.5-\frac{\sqrt{29}}{2}$

Step-by-step explanation:

So the question here is asking you to use the quadratic formula which is expressed as: $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\$

A quadratic can generally be expressed as: $y=ax^2+bx+c$

So using the equation you gave: $0=x^2-5x-1$

We can identify the following values: a=1, b=-5, c=-1

Btw the equation explicitly write "1" as the coefficient of x, but since it's not provided it's implied that it's 1.

So plugging in the known values, we get the following equation:

$x=\frac{5\pm\sqrt{(-5)^2-4(1)(-1)}}{2(1)}\\\\x=\frac{5\pm\sqrt{25+4}}{2}\\\\x=\frac{5\pm\sqrt{29}}{2}\\\\x=2.5+\frac{\sqrt{29}}{2}\\\\x=2.5-\frac{\sqrt{29}}{2}$

The last step just consists of taking the + and - solution, and since it asks for exact solutions you leave the 29 under the radical, and you don't approximate. There is no further simplification that can be done here.

5 0

2 years ago

Lesson: 1.08Given this function: f(x) = 4 cos(TTX) + 1Find the following and be sure to show work for period, maximum, and minim

Ber [7]

The given function is

$f(x)=4\cos \text{(}\pi x)+1$

The general form of the cosine function is

$y=a\cos (bx+c)+d$

a is the amplitude

2pi/b is the period

c is the phase shift

d is the vertical shift

By comparing the two functions

a = 4

b = pi

c = 0

d = 1

Then its period is

$\begin{gathered} \text{Period}=\frac{2\pi}{\pi} \\ \text{Period}=2 \end{gathered}$

The equation of the midline is

$y_{ml}=\frac{y_{\max }+y_{\min }}{2}$

Since the maximum is at the greatest value of cos, which is 1, then

$\begin{gathered} y_{\max }=4(1)+1 \\ y_{\max }=5 \end{gathered}$

Since the minimum is at the smallest value of cos, which is -1, then

$\begin{gathered} y_{\min }=4(-1)+1 \\ y_{\min }=-4+1 \\ y_{\min }=-3 \end{gathered}$

Then substitute them in the equation of the midline

$\begin{gathered} y_{ml}=\frac{5+(-3)}{2} \\ y_{ml}=\frac{2}{2} \\ y_{ml}=1 \end{gathered}$

The answers are:

Period = 2

Equation of the midline is y = 1

Maximum = 5

Minimum = -3

3 0

1 year ago

If Jenny has 20 donuts and she gives away 10 how many does she have left?

stiks02 [169]

10 donuts to be exact

8 0

3 years ago

Read 2 more answers