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2 years ago

Which of the following could be the sum of exactly three consecutive even integers?

Mathematics

1 answer:

OLEGan [10]2 years ago

8 0

Answer: 198 is your answer:65+66+67 = 198 Hope I helped!

Step-by-step explanation:

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Solve the formula for the indicated variable <br> A=1/2bh solve for h

vfiekz [6]

Answer:

h=A*2b

Step-by-step explanation:

A=1/2bh

1/2bh=A

1/2bh÷1/2bh=A÷1/2bh (the 1/2b will cancel with the 1/2b on the left leaving h)

h=A*2b

7 0

3 years ago

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

Write an equation to match each graph:

Makovka662 [10]

Answer:

y=-|x+1|+1

Step-by-step explanation:

It's an absolute value function vertically flipped and shifted 1 unit to the left, 1 unit to the the top.

8 0

2 years ago

Write the verbal sentence as an equation. let y represent the number

viktelen [127]

Answer:

Marcus is picking songs to play during a slideshow. The songs are each 3\dfrac123

3, start fraction, 1, divided by, 2, end fraction minutes long. The slideshow is 31\dfrac1231

31, start fraction, 1, divided by, 2, end fraction minutes long.

Step-by-step explanation:

8 0

2 years ago

Mr. Jones eats out at his favorite buffet restaurant every Friday night. If the cost is $9 and he budgets $42 for the month, how

alexandr402 [8]

Answer:

He will be able to eat nine times.

Step-by-step explanation:

Because nine times nine is 91 which is on one less then what he has, so that means he will be able to eat there nine times. Hope I helped

7 0

2 years ago