Find the product of the binomial: <br> (x-1)(x+4)(x-3)

For the inverse variation equation xy = k, what is the value of x when y = 4 and k = 7? 3 28

Oliga [24]

Answer:

The value of x is $\frac{7}{4}$ .

Step-by-step explanation:

It is given that the inverse variation equation is

$xy=k$ ..... (1)

The value of y is 4 and the value of k is 7.

Substitute y=4 and k=7 in equation (1).

$x\times 4=7$

Divide both sides by 4.

$\frac{x\times 4}{4}=\frac{7}{4}$

$x=\frac{7}{4}$

Therefore the value of x is $\frac{7}{4}$ .

7 0

3 years ago

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50 POINTS!!! In rectangle ABCD, AB = 6 cm, BC = 8 cm, and DE = DF. The area of triangle DEF is one-fourth the area of rectangle

aalyn [17]

Answer:

$EF=4\sqrt{3}$

Step-by-step explanation:

In rectangle ABCD, AB = 6, BC = 8, and DE = DF.

ΔDEF is one-fourth the area of rectangle ABCD.

We want to determine the length of EF.

First, we can find the area of the rectangle. Since the length AB and width BC measures 6 by 8, the area of the rectangle is:

$A_{\text{rect}}=8(6)=48\text{ cm}^2$

The area of the triangle is 1/4 of this. Therefore:

$\displaystyle A_{\text{tri}}=\frac{1}{4}(48)=12\text{ cm}^2$

The area of a triangle is half of its base times its height. The base and height of the triangle is DE and DF. Therefore:

$\displaystyle 12=\frac{1}{2}(DE)(DF)$

Since DE = DF:

$24=DF^2$

Thus:

$DF=\sqrt{24}=\sqrt{4\cdot 6}=2\sqrt{6}=DE$

Since ABCD is a rectangle, ∠D is a right angle. Then by the Pythagorean Theorem:

$(DE)^2+(DF)^2=(EF)^2$

Therefore:

$(2\sqrt6)^2+(2\sqrt6)^2=EF^2$

Square:

$24+24=EF^2$

Add:

$EF^2=48$

And finally, we can take the square root of both sides:

$EF=\sqrt{48}=\sqrt{16\cdot 3}=4\sqrt{3}$

6 0

2 years ago

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Does this graph below represent a function? (Yes or no)

Whitepunk [10]

Answer:yes

Step-by-step explanation: it represents a function

4 0

2 years ago

Triangle ABC is translated 3 units to the left and downward 10 units to form triangle A'B'C', then dilated by a factor of 2 to f

11Alexandr11 [23.1K]

Triangle A"B"C" are similar triangles to triangle ABC and all corresponding angles are congruent. Also, triangle A"B"C" is twice the size of triangle ABC.

<h3>What is transformation?</h3>

Transformation is the movement of a point from its initial location to a new location. Types of transformations are<em> reflection, rotation, translation and dilation.</em>

Translation is the movement of a point either <em>up, left, right or down</em> in the coordinate plane.

Triangle ABC is translated 3 units to the left and downward 10 units to form triangle A'B'C', then dilated by a factor of 2 to form triangle A''B''C''.

Hence:

Triangle A"B"C" are similar triangles to triangle ABC and all corresponding angles are congruent. Also, triangle A"B"C" is twice the size of triangle ABC.

Find out more on transformation at: brainly.com/question/4289712

#SPJ1

8 0

1 year ago

Twice the complement of angles A is 40 less than the supplement of angle A. Find the measure of angle A

Serggg [28]

Complement adds to 90
complement of A is 90-A

supplement is adds to 180
supplemetn of A is 180-A

2(90-A) is -40+180-A

2(90-A)=-40+180-A
2(90-A)=140-A
distribute
180-2A=140-A
add 2A to both sides
180=140+A
minus 140 both sides
40=A

A=40 degres

4 0

3 years ago

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Find the product of the binomial: (x-1)(x+4)(x-3)