Recommendations

In ΔRST, s = 7.3 inches, t = 3.1 inches and ∠R=138°. Find the area of ΔRST, to the nearest 10th of a square inch.

Oksana_A [137]

Answer:

5.1 inches

Step-by-step explanation:

Five triangles make up the pentagon.

The area of each is aside

The area of the pentagon is 5

Substitute values and calculate

8 0

2 years ago

An arithmetic sequence with a thrid term of 8 and constant difference of 5

olga nikolaevna [1]

$\bf n^{th}\textit{ term of an arithmetic sequence}\\\\
a_n=a_1+(n-1)d\qquad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
d=\textit{common difference}\\
----------\\
d=5\\
a_3=8\\
n=3
\end{cases}
\\\\\\
a_3=a_1+(3-1)5\implies 8=a_1+(2)5\implies 8=a_1+10
\\\\\\
\boxed{-2=a_1}
\\\\\\
a_n=-2+(n-1)5$

8 0

3 years ago

Which graph represents the inequality y>1-3x

slava [35]

Answer:

b............ .......... which one is a b c d

For this case we must indicate the graph of the following inequality:

y≥1−3x

It is observed that inequality includes equality, so the boundary line of the graph will not be dotted, so we discard options D and C.

We test option A, we substitute the point (0,0) in the inequality, if it is fulfilled then the graph corresponds to it.

It is not fulfilled

We test the last option B, we choose the point (3,1) that belongs to the graph:

1≥1−3(3)

\1≥1−9

1≥−8

it is fulfilled

5 0

2 years ago

Stefan is making new cushion covers for a chair. There are three sizes of cushions on the chair. What is the surface area of the

Valentin [98]

Answer:

990 square inches:)!

Step-by-step explanation:

i took the test >:).

8 0

2 years ago

I am having trouble with this relative minimum of this equation.<br>

Norma-Jean [14]

Answer:

So the approximate relative minimum is (0.4,-58.5).

Step-by-step explanation:

Ok this is a calculus approach. You have to let me know if you want this done another way.

Here are some rules I'm going to use:

$(f+g)'=f'+g'$ (Sum rule)

$(cf)'=c(f)'$ (Constant multiple rule)

$(x^n)'=nx^{n-1}$ (Power rule)

$(c)'=0$ (Constant rule)

$(x)'=1$ (Slope of y=x is 1)

$y=4x^3+13x^2-12x-56$

$y'=(4x^3+13x^2-12x-56)'$

$y'=(4x^3)'+(13x^2)'-(12x)'-(56)'$

$y'=4(x^3)'+13(x^2)'-12(x)'-0$

$y'=4(3x^2)+13(2x^1)-12(1)$

$y'=12x^2+26x-12$

Now we set y' equal to 0 and solve for the critical numbers.

$12x^2+26x-12=0$

Divide both sides by 2:

$6x^2+13x-6=0$

Compaer $6x^2+13x-6=0$ to $ax^2+bx+c=0$ to determine the values for $a=6,b=13,c=-6$ .

$a=6$

$b=13$

$c=-6$

We are going to use the quadratic formula to solve for our critical numbers, x.

$x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}$

$x=\frac{-13 \pm \sqrt{13^2-4(6)(-6)}}{2(6)}$

$x=\frac{-13 \pm \sqrt{169+144}}{12}$

$x=\frac{-13 \pm \sqrt{313}}{12}$

Let's separate the choices:

$x=\frac{-13+\sqrt{313}}{12} \text{ or } \frac{-13-\sqrt{313}}{12}$

Let's approximate both of these:

$x=0.3909838 \text{ or } -2.5576505$ .

This is a cubic function with leading coefficient 4 and 4 is positive so we know the left and right behavior of the function. The left hand side goes to negative infinity while the right hand side goes to positive infinity. So the maximum is going to occur at the earlier x while the minimum will occur at the later x.

The relative maximum is at approximately -2.5576505.

So the relative minimum is at approximate 0.3909838.

We could also verify this with more calculus of course.

Let's find the second derivative.

$f(x)=4x^3+13x^2-12x-56$