Answer:
With? I dont see an image if you attached one
Step-by-step explanation:
Answer:
16.97 ft
Step-by-step explanation:
According to the scenario, computation of the given data are as follows,
Side B = 21 ft
Side c = 27 ft
As we know, formula for right triangle is as follows,
![a^{2} + b^{2} = c^{2}](https://tex.z-dn.net/?f=a%5E%7B2%7D%20%2B%20b%5E%7B2%7D%20%3D%20c%5E%7B2%7D)
![a^{2} = c^{2} - b^{2}](https://tex.z-dn.net/?f=a%5E%7B2%7D%20%3D%20c%5E%7B2%7D%20-%20b%5E%7B2%7D)
So, by putting the value in the formula, we get,
![a^{2} = 27^{2} - 21^{2}](https://tex.z-dn.net/?f=a%5E%7B2%7D%20%3D%2027%5E%7B2%7D%20-%2021%5E%7B2%7D)
= 729 - 441
= 288
a = 16.97 ft
Hence, the length of the side for the right triangle is 16.97ft.
If you would like to know what was his total pay last week, you can calculate this using the following steps:
a base salary ... $400.00
an additional 11% commission on everything Ben sells
11% of $6050.00 = 11% * 6050 = 11/100 * 6050 = $665.5
$400 + $665.5 = $1065.5
Result: His total pay was $1065.5.
Answer:
The modulus of the complex number 6-2i is:
![|z|\:=2\sqrt{10}](https://tex.z-dn.net/?f=%7Cz%7C%5C%3A%3D2%5Csqrt%7B10%7D)
Step-by-step explanation:
Given the number
![6-2i](https://tex.z-dn.net/?f=6-2i)
We know that
where x and y are real and ![\sqrt{-1}=i](https://tex.z-dn.net/?f=%5Csqrt%7B-1%7D%3Di)
The modulus or absolute value of z is:
![|z|\:=\sqrt{x^2+y^2}](https://tex.z-dn.net/?f=%7Cz%7C%5C%3A%3D%5Csqrt%7Bx%5E2%2By%5E2%7D)
Therefore, the modulus of
will be:
![z=6-2i](https://tex.z-dn.net/?f=z%3D6-2i)
![z=6+(-2)i](https://tex.z-dn.net/?f=z%3D6%2B%28-2%29i)
![|z|\:=\sqrt{x^2+y^2}](https://tex.z-dn.net/?f=%7Cz%7C%5C%3A%3D%5Csqrt%7Bx%5E2%2By%5E2%7D)
![|z|\:=\sqrt{6^2+\left(-2\right)^2}](https://tex.z-dn.net/?f=%7Cz%7C%5C%3A%3D%5Csqrt%7B6%5E2%2B%5Cleft%28-2%5Cright%29%5E2%7D)
![=\sqrt{6^2+2^2}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B6%5E2%2B2%5E2%7D)
![=\sqrt{36+4}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B36%2B4%7D)
![=\sqrt{40}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B40%7D)
![=\sqrt{2^2}\sqrt{2\cdot \:5}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B2%5E2%7D%5Csqrt%7B2%5Ccdot%20%5C%3A5%7D)
![=2\sqrt{2\cdot \:5}](https://tex.z-dn.net/?f=%3D2%5Csqrt%7B2%5Ccdot%20%5C%3A5%7D)
![=2\sqrt{10}](https://tex.z-dn.net/?f=%3D2%5Csqrt%7B10%7D)
Therefore, the modulus of the complex number 6-2i is:
![|z|\:=2\sqrt{10}](https://tex.z-dn.net/?f=%7Cz%7C%5C%3A%3D2%5Csqrt%7B10%7D)
Answer:
is the function of the least degree has the real coefficients and the leading coefficients of 1 and with the zeros -1, 5, and 2.
Step-by-step explanation:
Given the function
![f\left(x\right)=x^3-6x^2+3x+10](https://tex.z-dn.net/?f=f%5Cleft%28x%5Cright%29%3Dx%5E3-6x%5E2%2B3x%2B10)
As the highest power of the x-variable is 3 with the leading coefficients of 1.
- So, it is clear that the polynomial function of the least degree has the real coefficients and the leading coefficients of 1.
solving to get the zeros
![f\left(x\right)=x^3-6x^2+3x+10](https://tex.z-dn.net/?f=f%5Cleft%28x%5Cright%29%3Dx%5E3-6x%5E2%2B3x%2B10)
∵ ![f(x)=0](https://tex.z-dn.net/?f=f%28x%29%3D0)
as
![Factor\:x^3-6x^2+3x+10\::\:\left(x+1\right)\left(x-2\right)\left(x-5\right)=0](https://tex.z-dn.net/?f=Factor%5C%3Ax%5E3-6x%5E2%2B3x%2B10%5C%3A%3A%5C%3A%5Cleft%28x%2B1%5Cright%29%5Cleft%28x-2%5Cright%29%5Cleft%28x-5%5Cright%29%3D0)
so
Using the zero factor principle
if ![ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0\:\left(\mathrm{or\:both}\:a=0\:\mathrm{and}\:b=0\right)](https://tex.z-dn.net/?f=ab%3D0%5C%3A%5Cmathrm%7Bthen%7D%5C%3Aa%3D0%5C%3A%5Cmathrm%7Bor%7D%5C%3Ab%3D0%5C%3A%5Cleft%28%5Cmathrm%7Bor%5C%3Aboth%7D%5C%3Aa%3D0%5C%3A%5Cmathrm%7Band%7D%5C%3Ab%3D0%5Cright%29)
![x+1=0\quad \mathrm{or}\quad \:x-2=0\quad \mathrm{or}\quad \:x-5=0](https://tex.z-dn.net/?f=x%2B1%3D0%5Cquad%20%5Cmathrm%7Bor%7D%5Cquad%20%5C%3Ax-2%3D0%5Cquad%20%5Cmathrm%7Bor%7D%5Cquad%20%5C%3Ax-5%3D0)
![x=-1,\:x=2,\:x=5](https://tex.z-dn.net/?f=x%3D-1%2C%5C%3Ax%3D2%2C%5C%3Ax%3D5)
Therefore, the zeros of the function are:
![x=-1,\:x=2,\:x=5](https://tex.z-dn.net/?f=x%3D-1%2C%5C%3Ax%3D2%2C%5C%3Ax%3D5)
is the function of the least degree has the real coefficients and the leading coefficients of 1 and with the zeros -1, 5, and 2.
Therefore, the last option is true.