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DENIUS [597]
3 years ago
12

Find the perimeter of ABC with vertices A (1,1), B (7,1), and C (1,9)

Mathematics
1 answer:
Effectus [21]3 years ago
4 0

Answer:

24 unit

Step-by-step explanation:

Given,

The vertices of the triangle ABC are,

A (1,1), B (7,1), and C (1,9),

By the distance formula,

AB=\sqrt{(7-1)^2+(1-1)^2}=\sqrt{6^2}=6\text{ unit}

BC=\sqrt{(1-7)^2+(9-1)^2}=\sqrt{6^2+8^2}=\sqrt{36+64}=\sqrt{100}=10\text{ unit}

CA=\sqrt{(1-1)^2+(1-9)^2}=\sqrt{8^2}=8\text{ unit}

Thus, the perimeter of the triangle ABC = AB + BC + CA = 6 + 10 + 8 = 24 unit

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What it 33/7 divided by 4/6
lakkis [162]

Answer:99/14

Step-by-step explanation:

33/7÷4/6

33/7×6/4

(33×6)÷(7×4)

198/28

Reduce to lowest term

99/14

4 0
3 years ago
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Find the polynomial of minimum degree, with real coefficients, zeros at
drek231 [11]

Answer:

\huge\boxed{p(x)=4x^3-20x^2+4x+300}

Step-by-step explanation:

\text{If}\ x=4\pm3i\ \text{and}\ x=-3\ \text{are the zeros of a polynomial, then it has  a form:}\\\\p(x)=\bigg(x-(4-3i)\bigg)\bigg(x-(4+3i)\bigg)\bigg(x-(-3)\bigg)\bigg(r(x)\bigg)\\\\p(x)=(x-4+3i)(x-4-3i)(x+3)\bigg(r(x)\bigg)\\\\p(x)=\underbrace{\bigg((x-4)+3i\bigg)\bigg((x-4)-3i\bigg)}_{\text{use}\ (a+b)(a-b)=a^2-b^2}(x+3)\bigg(r(x)\bigg)\\\\p(x)=\bigg((x-4)^2-(3i)^2\bigg)(x+3)\bigg(r(x)\bigg)\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2

p(x)=(x^2-2(x)(4)+4^2-3^2i^2)(x+3)\bigg(r(x)\bigg)\qquad\text{use}\ i^2=-1\\\\p(x)=(x^2-8x+16-9(-1))(x+3)\bigg(r(x)\bigg)\\\\p(x)=(x^2-8x+16+9)(x+3)\bigg(r(x)\bigg)\\\\p(x)=(x^2-8x+25)(x+3)\bigg(r(x)\bigg)\qquad\text{use FOIL}:\ (a+b)(c+d)=ac+ad+bc+bd\\\\p(x)=\bigg((x^2)(x)+(x^2)(3)+(-8x)(x)+(-8x)(3)+(25)(x)+(25)(3)\bigg)\bigg(r(x)\bigg)\\\\p(x)=(x^3+3x^2-8x^2-24x+25x+75)\bigg(r(x)\bigg)\qquad\text{combine like terms}\\\\p(x)=(x^3-5x^2+x+75)\bigg(r(x)\bigg)

\text{The y-intercept is at 300}.\\\\\text{For}\ w(x)=a_nx^n+a_{n-1}x^{n-1}+a_{n-2}x^{n-2}+...+a_1x+a_0\\\\\text{y-intercept is}\ a_0\\\\\text{Therefore for}\ p(x)=(x^3-5x^2+x+75)\bigg(r(x)\bigg)\\\\\text{y-intercet is}\ 75\bigg(r(x)\bigg)\\\\75\bigg(r(x)\bigg)=300\qquad\text{divide both sides by 75}\\\\r(x)=4\\\\\text{Finally:}\\\\p(x)=(x^3-5x^2+x+75)(4)\qquad\text{use the distributive property}\\\\p(x)=(x^3)(4)+(-5x^2)(4)+(x)(4)+(75)(4)\\\\p(x)=4x^3-20x^2+4x+300

7 0
3 years ago
arts academy requires there to be 6 teachers for every 144 students and 3 tutors for every 24 students. How many students does t
jonny [76]

Answer:

the teachers would have 24 students per teacher. 10 students per tutor. There would need to be 11 tutors

Step-by-step explanation:

each tutor would have 10 students then if you do 11 times 10 you get 11

(hope this helps can I pls have brainlist (crown)☺️)

4 0
2 years ago
A dog is moving at a constant speed of 8 m/s. what is the dog’s acceleration
ozzi

\quad \huge \quad \quad \boxed{ \tt \:Answer }

\qquad \tt \rightarrow \: Acceleration_{dog} = 0

____________________________________

\large \tt Solution  \: :

A dog is moving at a constant speed of 8 m/s, that concludes that there's no change in its speed with respect to time.

And Acceleration is define as rate of change in velocity, but since velocity/speed is constant. change in velocity = 0

Henceforth, Acceleration of dog is 0 as well.

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

4 0
1 year ago
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LenKa [72]

Answer:

It should be $12168.75

Step-by-step explanation:

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then, solving our equation

I = 11000 × 0.0425 × 2.5 = 1168.75

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on a principal of $ 11,000.00

at a rate of 4.25% per year

for 2.5 years is $ 1,168.75.

1,168.75 + 11000 = 12168.75

5 0
3 years ago
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