Answer:
The answers are below
Step-by-step explanation:
The greater sign is > and the less then symbol is <
Using the red arrows on the number line, you can tell which one is bigger or less. The dot is colored in so it has to have a line under it. So for the first one (top, left), The red arrow is pointing to the right side meaning x is bigger than 3. Therefore x ≥ 3.
In the next one (top, right) the arrow is pointing to the negative side so that one must be less than 3. The dot is also colored in meaning it is: x ≤ 3
In the next one (bottom, left) the arrow is pointing to the right, the dot not colored in, so it has no line. Therefore it is x > 3
Last one (bottom right) the arrow is pointing left, dot is white meaning that the answer is x < 3
If you're wondering what the open dots and closed dots mean:
An open dot is used to show that the ray's endpoint is not a component of the solution when the inequality is "strict" ( < or >).
A closed dot is used to denote that the endpoint is a component of the solution for the other types of inequalities (≥ and ≤ ).
to find the mode of the data set it's the number that occurs the most so 8 is the answer
Answer:
![\mathrm{Factor}\:4x^4-32x^3-60x^2:\quad 4x^2\left(x^2-8x-15\right)\\](https://tex.z-dn.net/?f=%5Cmathrm%7BFactor%7D%5C%3A4x%5E4-32x%5E3-60x%5E2%3A%5Cquad%204x%5E2%5Cleft%28x%5E2-8x-15%5Cright%29%5C%5C)
![\mathrm{Apply\:exponent\:rule}:\quad \:a^{b+c}=a^ba^c\\x^3=xx^2\\x^4=x^2x^2\\=4x^2x^2-32xx^2-60x^2\\\mathrm{Rewrite\:}60\mathrm{\:as\:}4\cdot \:15\\\mathrm{Rewrite\:}32\mathrm{\:as\:}4\cdot \:8\\=4x^2x^2-4\cdot \:8xx^2-4\cdot \:15x^2\\\mathrm{Factor\:out\:common\:term\:}4x^2\\=4x^2\left(x^2-8x-15\right)](https://tex.z-dn.net/?f=%5Cmathrm%7BApply%5C%3Aexponent%5C%3Arule%7D%3A%5Cquad%20%5C%3Aa%5E%7Bb%2Bc%7D%3Da%5Eba%5Ec%5C%5Cx%5E3%3Dxx%5E2%5C%5Cx%5E4%3Dx%5E2x%5E2%5C%5C%3D4x%5E2x%5E2-32xx%5E2-60x%5E2%5C%5C%5Cmathrm%7BRewrite%5C%3A%7D60%5Cmathrm%7B%5C%3Aas%5C%3A%7D4%5Ccdot%20%5C%3A15%5C%5C%5Cmathrm%7BRewrite%5C%3A%7D32%5Cmathrm%7B%5C%3Aas%5C%3A%7D4%5Ccdot%20%5C%3A8%5C%5C%3D4x%5E2x%5E2-4%5Ccdot%20%5C%3A8xx%5E2-4%5Ccdot%20%5C%3A15x%5E2%5C%5C%5Cmathrm%7BFactor%5C%3Aout%5C%3Acommon%5C%3Aterm%5C%3A%7D4x%5E2%5C%5C%3D4x%5E2%5Cleft%28x%5E2-8x-15%5Cright%29)
<em>Hope this helps and have a great day!!!</em>
<em>
</em>
Answer:
a) the numerator, <em>a</em>, would be a smaller number than the denominator, <em>b.</em>
b) the fraction a/b could be over or under the amount of 1/2.
c) the fraction could be over or under the amount of 1.
Step-by-step explanation:
examples:
a) 2/8
b)3/8 or 6/10
c) 8/9 or 1 1/8
Hope this helps :)