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Elina [12.6K]
2 years ago
12

Complete the square for x2 - 4x + Then write the resulting expression as a binomial squared.

Mathematics
1 answer:
alekssr [168]2 years ago
4 0

Answer:

x(x-4)

Step-by-step explanation:

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What is 24 + 100 then times it by two is there more than 120
MatroZZZ [7]
24 + 100 is 124, and 124 x 2 = 248. So yes it is more than 120
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3 years ago
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An arithmetic sequence with a third term of 8 and a constant difference of 5
Vanyuwa [196]

\bf n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad  \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ d=\textit{common difference}\\ \hrulefill\\[0.5em] a_3=8\\ n=3\\ d=5 \end{cases} \\\\\\ a_3=a_1+(3-1)5\implies 8=a_1+(2)5 \\\\\\ 8=a_1+10\implies -2=a_1 \\\\\\ \begin{cases} a_1=-2\\ d=5 \end{cases}\implies a_n=-2+(n-1)d

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3 years ago
Convert Зcis 180° to rectangular form.<br> А. -3<br> в. -3i<br> с. з<br> D. Зі.
Sunny_sXe [5.5K]

Answer:

-3

Step-by-step explanation:

3 cis(180^\circ) means 3(\cos(180^\circ)+i \sin(180^\circ))

What is the x-coordinate value that corresponds to \theta=180^\circ. That value is -1.

What is the y-coordinate value that corresponds to \theta=180^\circ. That value is 0.

So this implies \cos(180^\circ)=-1 \text{ and } \sin(180^\circ)=0.

3 cis(180^\circ)  

3(\cos(180^\circ)+i \sin(180^\circ))

3(-1+i (0))

3(-1+0)

3(-1)

-3

5 0
3 years ago
1.) What is the equation of the path of firework #1? Write your equation in general form.
valina [46]

1. I'm assumig that the paths are perfect parabolas

this means that their general forms can be written in y=ax^2+bx+c

it's easier to find vertex form first then expand to get general form

vertex form is y=a(x-h)^2+k where the vertex is (h,k) and a is a constant


firework #1

vertex is (10,50), so (h,k)=(10,50) and h=10, k=50

h_1=a(t-10)^2+50

to find the value of a, subsitute another point

(0,0)

0=a(0-10)^2+50)

0=100a+50

a=\frac{-1}{2}

so the equation in vertex form is h_1=\frac{-1}{2}(t-10)^2+50

expand to get general form

h_1=\frac{-1}{2}(t^2-20t+100)+50

h_1=\frac{-1}{2}t^2+10t-50+50

h_1=\frac{-1}{2}t^2+10t





2.

same as last time

vertex is (10,72) so (h,k)=(10,72) so h=10 and k=72

equation is h_2=a(t-10)^2+72

find a

use another point

(0,22)

22=a(0-10)^2+72

22=100a+72

-50=100a

a=\frac{-1}{2}

so the equation in vertex form is h_2=\frac{-1}{2}(t-10)^2+72




3.

range is the numbers that h is allowed to be

think about what h represents. it represents the height of the rocket

from the graph, we can see that the lowest possible height is 0yd and the highest height is 50yd

so range is 0 to 50 or 0≤h≤50


domain is the numbers that t is allowed to be

think about what t represents. it represents how long the rocket has been flying

it will stop flying when it hits the ground or at t=20

it starts flying at t=0

so domain is from 0 to 20 or 0≤t≤20

3 0
3 years ago
Find the area<br> top/bottom: 10.8<br> sides: 8.7
mihalych1998 [28]
93.96. You multiply them together to get the answer.
4 0
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