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2 years ago

Please help 7th grade math

Mathematics

1 answer:

shtirl [24]2 years ago

4 0

Answer:

Step-by-step explanation:

The mode is the number that appears most in the data set.

8 appears twice while all the other only appear once.

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If x+a is a factor of 2x²+2ax+5x+10,find a.

vazorg [7]

If $x+a$ is a factor of the polynomial, it means that $-a$ is a root of the polynomial.

In fact, if a polynomial $p(x)$ has a root $x_0$ (i.e. $p(x_0)=0$ ), then the polynomial is divisible by $(x-x_0)$

In your case, you know that the polynomial is divisible by $(x+a)=(x-(-a))$ , so $-a$ is a solution.

Let's evaluate $p(-a)$ and set it to zero:

$2(-a)^2+2a(-a)+5(-a)+10 = 0 \iff 2a^2-2a^2-5a+10=0 \iff -5a+10 = 0 \iff a = 2$

We can check the answer: if $a=2$ the polynomial becomes

$2x^2+2(2)x+5x+10 = 2x^2+9x+10$

And we're claiming that $-a=-2$ is a root of this polynomial:

$2(-2)^2+9(-2)+10 = 2\cdot 4 - 18 + 10 = 0$

5 0

2 years ago

Solve this equation. 1+1 = ?

max2010maxim [7]

Answer:

Step-by-step explanation:

5 0

2 years ago

Mark put his dog on a diet. The dog's total weight change for the first two weeks was -3/4 pound. The dog lost the same amount o

saw5 [17]

The change in the first week is .375 pounds =. Divide 3/4 by 2

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3 years ago

What are the are and perimeter of the triangle?

fenix001 [56]

Answer:

First option is correct answer.

Step-by-step explanation:

Area = 4x - 10

Perimeter = x + 8

5 0

2 years ago

Use spherical coordinates. evaluate xyz dv e , where e lies between the spheres ρ = 4 and ρ = 6 and above the cone ϕ = π/3.

sergey [27]

Set

$x=\rho\cos\theta\sin\varphi$

$y=\rho\sin\theta\sin\varphi$

$z=\rho\cos\varphi$

so that the volume element is

$\mathrm dV=\mathrm dx\,\mathrm dy\,\mathrm dz=\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi$

The integral is then

$\displaystyle\iiint_Exyz\,\mathrm dV=\int_{\varphi=0}^{\varphi=\pi/3}\int_{\theta=0}^{\theta=2\pi}\int_{\rho=4}^{\rho=6}\rho^5\cos\theta\sin\theta\sin^3\varphi\cos\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\rho$

$=\displaystyle\left(\int_0^{\pi/3}\sin^3\varphi\cos\varphi\,\mathrm d\varphi\right)\underbrace{\left(\int_0^{2\pi}\cos\theta\sin\theta\,\mathrm d\theta\right)}_0\left(\int_4^6\rho^5\,\mathrm d\rho\right)$

and so evaluates to 0.

3 0

2 years ago