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2 years ago

6

mr albernathy perchases a selection of wrenches for his shop. his bill was $78. he buys the same number of $1.50 wrenches and $2

.50 wrenches, and half as may $4 dollars wrenches. the number of $3 wrenches is one more than the number of $4 dollars wrenches. how many of each did he purchase?

1 answer:

ICE Princess25 [194]2 years ago

6 0

Answer:

Mr. Abernathy purchased 10 of $1.50 wrenches, 10 of $2.50 wrenches, 5 of $4 wrenches and 6 of $3 wrenches.

Step-by-step explanation:

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Step-by-step explanation:

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Reporting Stockholders' Equity

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The total stockholders equity based on the information given will be $8285000.

<h3>How to compute the equity?</h3>

The stockholders equity will be calculated thus:

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Paid in capital = $5632000

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1 year ago

HELP what's the distance for this question?

jeyben [28]

Answer:

$Distance = 38.57ft$

Step-by-step explanation:

Given

$Base = 60$

$\theta = 50$

Required

The distance between the top and John

The distance is calculated using:

$sin\alpha = \frac{Distance}{Base}$

Where

$\alpha = 90 - \theta$ --- the angle between the diagonal line and the vertical line

$\alpha = 90 - 50$

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So, we have:

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3 years ago

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

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$f(2)=6-6$

$f(2)=0$

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,

$x\le -3$

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

$-3\le x \le 1$

$f(0)=-6\:$

$1\le x\le 2$

$f(1.5)=-0.56\:$

$x \ge 2$

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

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

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3 years ago