All categories

3 years ago

The product of three consecutive odd integers is 75.

Mathematics

2 answers:

Zigmanuir [339]3 years ago

4 0

1). 3X+6=75
75-6=69=23
Answer 23,25,27

Inessa [10]3 years ago

3 0

Answer:it’s A

Step-by-step explanation: I jus got it right

You might be interested in

Factor f(x)=x4-x3-7x2+13x-6 completely. Then Sketch the graph

Dennis_Churaev [7]

ANSWER TO QUESTION 1

$f(x)=(x-2)(x+3)(x-1)^2$ .

EXPLANATION

The function given to us is,

$f(x)=x^4-x^3-7x^2+13x-6$

According to rational roots theorem,

$\pm1,\pm2,\pm3,\pm6$ are possible rational zeros of

$f(x)=x^4-x^3-7x^2+13x-6$ .

We find out that,

$f(-3)=(-3)^4-(-3)^3-7(-3)^2+13(-3)-6$

$f(-3)=81+27-63-39-6$

$f(-3)=6-6$

$f(-3)=0$

Also

$f(2)=(2)^4-(2)^3-7(2)^2+13(2)-6$

$f(2)=16-8-28+26-6$

$f(2)=6-6$

$f(2)=0$

This implies that

$x-2 and x+3$ are factors of

$f(x)=x^4-x^3-7x^2+13x-6$ and hence $(x-2)(x+3)=x^2+x-6$ is also a factor.

We perform the long division as shown in the diagram.

Hence,

$f(x)=(x-2)(x+3)(x-1)^2$ .

ANSWER TO QUESTION 2

Sketching the graph

We can see from the factorization that the roots

$x=2$ and $x=-3$ have a multiplicity of 1, which is odd. This means that the graph crosses the x-axis at this intercepts.

Also the root $x=1$ has a multiplicity of 2, which is even. This means the graph does not cross the x-axis at this intercept.

Now we determine the position of the graph on the following intervals,

$x\le -3$

$f(-4)=(-4)^4-(-4)^3-7(-4)^2+13(-4)-6$

$f(-4)=150\:>0$

$-3\le x \le 1$

$f(0)=-6\:$

$1\le x\le 2$

$f(1.5)=-0.56\:$

$x \ge 2$

$f(3)=24\:>0$

We can now use these information to sketch the function as shown in diagram

4 0

3 years ago

PLEAS HELP ME

GarryVolchara [31]

$\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \stackrel{Table~A}{\begin{array}{ccll} x&y\\ \cline{1-2} 60&48\\70&56\\80&64 \end{array}}~\hspace{7em} \stackrel{Table~B}{\begin{array}{ccll} x&y\\ \cline{1-2} 20&24\\30&36\\40&48 \end{array}} \\\\[-0.35em] ~\dotfill$

$\bf \textit{for table A, we know that } \begin{cases} x=60\\ y=48 \end{cases}\implies 48=k60\implies \cfrac{48}{60}=k \\\\\\ \cfrac{4}{5}=k\qquad therefore\qquad \boxed{y=\cfrac{4}{5}x} \\\\\\ \textit{for table B, we know that } \begin{cases} x=30\\ y=36 \end{cases}\implies 36=k30\implies \cfrac{36}{30}=k \\\\\\ \cfrac{6}{5}=k\qquad therefore\qquad \boxed{y=\cfrac{6}{5}x}$

4 0

3 years ago

What's the alternate interior angles

NemiM [27]

<QRO and <SRP
<NOM and <POM
<QRT and <SRT

hope this helps!

6 0

3 years ago

Assume a quarter, diameter 0.96 inches, is centered at the point (–2, 5), where each unit represents one inch. Write the equatio

storchak [24]

If the diameter of this circle is .96, then the radius is .48. The h and k values of our center are (-2, 5), and the standard form of a circle is $(x-h)^2+(y-k)^2=r^2$ . We will fill in accordingly. $(x-(-2))^2+(y-5)^2=.48^2$ . That simplifies to $(x+2)^2+(y-5)^2=.2304$ . That's the equation of the circle that will completely enclose the quarter.

7 0

4 years ago

Read 2 more answers

Elisa puts $1,000 into each of 2 bank accounts.

Dafna1 [17]

Answer:

How much money will be in Account A at the end of 3 years? $ ⇒ 1092.73

How much money will be in Account B at the end of 3 years? $112

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers