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3 years ago

Factor x3 + x2 + x + 1 by grouping. What is the resulting expression?

Mathematics

2 answers:

Svet_ta [14]3 years ago

8 0

X^3 +x^2 +x +1 = x^2(x +1) + x +1 = (x^2 +1)(x +1)

hope helped

Salsk061 [2.6K]3 years ago

5 0

Answer:

$(x^2+1)(x + 1)$

Step-by-step explanation:

Factor $x^3 + x^2 + x + 1$ by grouping

Group first two terms and last two terms

$(x^3 + x^2) + (x + 1)$

Factor out GCF from each group . when we factor out GCF , divide each term by GCF

$x^2(x+1) + 1(x + 1)$

Factor out x+1

$(x^2+1)(x + 1)$

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A tower that is 166 feet tall casts a shadow 167 feet long. Find the angle of elevation of the sun to the

Ira Lisetskai [31]

Answer:

The angle is approximately $45^\circ$ .

Step-by-step explanation:

We should start with a diagram (like the one attached). Notice the length of the tower and the length of the shadow are the legs of a right triangle, and the angle of elevation is an acute angle of that triangle.

Since we are given the opposite and adjacent sides to the angle, we will use the tangent function:

$\tan{\theta}=\frac{\text{opposite side}}{\text{adjacent side}}$

In this case, the opposite side is the height of the tower, 166 ft. The adjacent side is the length of the shadow, 167 ft. So, we have:

$\tan{\theta}=\frac{166}{167}$

To get the angle, we need to use inverse tangent:

$\theta=\tan^{-1}(\frac{166}{167})\\\theta \approx 45$

The angle is approximated $45^\circ$ when rounded to the nearest degree.

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3 years ago

Cal's go cart has a gas tank with the dimensions shown below.

In-s [12.5K]

Answer: 2 cans.

Step-by-step explanation:

Calculate the volume of the go cart tank, which has the form of a rectangular prism. You can use the following formula:

$V=l*w*h$

Where:

l: is the lenght.

w: is the width.

h: is the height.

In this case:

$l=15.4in\\w=10in\\h=3in$

Substitute values into the formula. Then:

$V=(15.4in)(10in)(3in)=462in^3$

If a gas can holds 1 gallon of gas and $1\ gallon=231\ in^3$ , then the number of full gas cans that will take to fill the go cart's tank (whose volume is 462 in³) is: