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2 years ago

given f(x)=3x^2-9x+k, and the remainder when f(x) is divided by x+1 is 14, then what is the value of k?

Mathematics

1 answer:

bazaltina [42]2 years ago

6 0

Answer:

Step-by-step explanation:

compare the divisor x+1 with x-a which will get you -1 and then use remainder theorem

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A 236 inch board is cut into two pieces. one piece is three times the length of the other. find the length of the two pieces

kirill [66]

let length of one piece = x

length of other piece = 236-x

one piece is three times the length of the other

x=3(236-x)

x=708-3x

4x=708

x=177

so first piece is 177 inches long and second piece is (236-177)= 59 inches long

7 0

2 years ago

Write an equation that illustrates a number with two decimal places multiplied by a number with one decimal place. The product h

Vilka [71]

Step-by-step explanation:

Let the number with two decimal places be 1.23

Let the number with one decimal place be 4.5

Then 1.23 multiplied by 4.5

= 1.23 × 4.5

= 5.535

The result has more than two nonzero digits.

Note: When you multiply two decimal numbers, the decimal place(s) of the result is the addition of the decimal places of each of the numbers being multiplied.

8 0

2 years ago

Josef's closet is 5 feet wide and 3 feet deep. What is the area of his closet floor?

choli [55]

Answer:

15f^2

Step-by-step explanation:

multiply lenghtxwidth

always make sure to square your answer when doing area

6 0

2 years ago

Solve the equation on the interval [0,2π]

WARRIOR [948]

$\bf 16sin^5(x)+2sin(x)=12sin^3(x)
\\\\\\
16sin^5(x)+2sin(x)-12sin^3(x)=0
\\\\\\
\stackrel{common~factor}{2sin(x)}[8sin^4(x)+1-6sin^2(x)]=0\\\\
-------------------------------\\\\
2sin(x)=0\implies sin(x)=0\implies \measuredangle x=sin^{-1}(0)\implies \measuredangle x=
\begin{cases}
0\\
\pi \\
2\pi 
\end{cases}\\\\
-------------------------------$

$\bf 8sin^4(x)+1-6sin^2(x)=0\implies 8sin^4(x)-6sin^2(x)+1=0$

now, this is a quadratic equation, but the roots do not come out as integers, however it does have them, the discriminant, b² - 4ac, is positive, so it has 2 roots, so we'll plug it in the quadratic formula,

$\bf 8sin^4(x)-6sin^2(x)+1=0\implies 8[~[sin(x)]^2~]^2-6[sin(x)]^2+1=0
\\\\\\
~~~~~~~~~~~~\textit{quadratic formula}
\\\\
\begin{array}{lcccl}
& 8 sin^4& -6 sin^2(x)& +1\\
&\uparrow &\uparrow &\uparrow \\
&a&b&c
\end{array} 
\qquad \qquad 
sin(x)= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a}
\\\\\\
sin(x)=\cfrac{-(-6)\pm\sqrt{(-6)^2-4(8)(1)}}{2(8)}\implies sin(x)=\cfrac{6\pm\sqrt{4}}{16}
\\\\\\
sin(x)=\cfrac{6\pm 2}{16}\implies sin(x)=
\begin{cases}
\frac{1}{2}\\\\
\frac{1}{4}
\end{cases}$

$\bf \measuredangle x=
\begin{cases}
sin^{-1}\left( \frac{1}{2} \right)
sin^{-1}\left( \frac{1}{4} \right)
\end{cases}\implies \measuredangle x=
\begin{cases}
\frac{\pi }{6}~,~\frac{5\pi }{6}\\
----------\\
\approx~0.252680~radians\\
\qquad or\\
\approx~14.47751~de grees\\
----------\\
\pi -0.252680\\
\approx 2.88891~radians\\
\qquad or\\
180-14.47751\\
\approx 165.52249~de grees
\end{cases}$

3 0

3 years ago

The Chicago Cubs have played in 28 less than twice the number of World Series Champion Than the St. Louis Cardinals. The cubs pl

aev [14]

The answer to your question is 11 world championships

8 0

2 years ago