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3 years ago

7

Cameron is creating a garden. He designs a rectangular garden with a length of (x+6) feet and a width of (x+2) feet. When x=5, w

hat is the area of the garden ?

1 answer:

Zolol [24]3 years ago

6 0

(5+6) multiplied by (5+2)
11 x 7
77
The area of the garden is 77 square feet.

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2. Factor f(x) = x4 + 10x3 + 35x2 + 50x + 24 completely showing all work and steps with synthetic division. Then sketch the grap

telo118 [61]

We need to use rational root theorem to find out roots here.

The rational root theorem states that if p(x) is a polynomial with integer coefficients and if $\frac{p}{q}$ is a zero of p(x) then p is a factor of constant term and q is a factor of leasing term coefficient.

Here factors of constant term are 1,2,3,4,6,8,12,24,-1,-2,-3,-4,-6,-8,-12, and -24.

And factors of leading coefficient is -1,1.

Hence possible roots may be -1,1,-2,2,-3,3,-4,4,-6,6,-8,8,-12,12,-24 and 24.

Let us plugin these in f(x) to find zeroes.

$f(-1)=(-1)^{4}+10(-1)^{3}+35(-1)^{2}+50(-1)+24 =1-10+35-50+24=0$

Hence x=-1 is a zero which means x-(-1)=x+1 is a factor.

Let us use synthetic division to find quotient.

-1 | 1 10 35 50 24

<u>| 0 -1 -9 -26 -24</u>

<u> 1 9 26 24 0</u>

Hence quotient is $x^{3} +9x^{2} +26x+24$

Since all coefficients are positive, root must be negative. Let's plugin all remaining negative numbers in the quotient.

$(-2)^{3}+9(-2)^{2}+26(-2)+24 = 0$

Hence x+2 is another factor.

Let us find quotient again using synthetic division.

-2 | 1 9 26 24

<u>| 0 -2 -14 -24</u>

<u> 1 7 12 0</u>

Hence quotient is $x^{2} +7x+12$

Again we got quotient with all positive coefficients, let us plugin remaining negative numbers from rational root theorem.

$(-3)^{2}+7(-3)+12=-9-21+12=0$

Hence x+3 is also a factor.

Let us find quotient using synthetic division.

-3 | 1 7 12

<u>| 0 -3 -12</u>

<u> 1 4 0</u>

Hence quotient is x+4.

So, $f(x)=x^{4}+10x^{3}+35x^{2}+50x+24 =(x+1)(x+2)(x+3)(x+4)$

Please have a look at the graph attached.

4 0

3 years ago

Pls help ik mark brainliest

PolarNik [594]

4^4square root 2 is the answer

7 0

3 years ago

25 Points! Show ALL Work! Image Attached.

SVEN [57.7K]

Answer:

a) x = 13

b) x = 7

Step-by-step explanation:

A) Since they have the same base of 2 so

x + 4 + (-5) = 12

x - 1 = 12

x = 13

b) Since they have the same base of -3 so

8 + x + 4 = 19

x + 12 = 19

x = 7

4 0

3 years ago

If the range of f(x)= square root mx and the range of g(x)=m square root x are the same, which statement is true about the value

AveGali [126]

M can be any positive real number.

Explanation:

From f(x) = √(mx) ; if x is posive m has to be positive; if x is negative m has to be negative; if x is cero m can have any value, and the range will always be 0 or positve

From g(x) = m √x; x can only be 0 or positive and the range will have the sign of m.

Given we concluded that the range of f(x) can only be 0 or positive, then me can only be 0 or positive.

3 0

3 years ago

Given the diagram below what is tan 60?

Contact [7]

Answer:

A) √3

Step-by-step explanation:

The tangent of an angle can be found by dividing the leg opposite the angle over the leg adjacent to it.

So, we have to find them.

The 30-60-90 rule says that in a right triangle with the angles 30°, 60° and 90°, the sides opposite those angles will have the ratio of 1:√3:2.

That means the side adjacent to 60° is 2 units long and the one opposite is 2√3 units long.

Dividing those two gives us (2√3)/2, which can be simplified to √3.

3 0

3 years ago

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