Answer:
![The\:number\:is\:-35](https://tex.z-dn.net/?f=The%5C%3Anumber%5C%3Ais%5C%3A-35)
Step-by-step explanation:
![Let\:x\:be\:the\:number,\:we\:have\:an\:equation:\\\frac{3x}{5}=-21\Leftrightarrow 3x=-105\Rightarrow x=-35](https://tex.z-dn.net/?f=Let%5C%3Ax%5C%3Abe%5C%3Athe%5C%3Anumber%2C%5C%3Awe%5C%3Ahave%5C%3Aan%5C%3Aequation%3A%5C%5C%5Cfrac%7B3x%7D%7B5%7D%3D-21%5CLeftrightarrow%203x%3D-105%5CRightarrow%20x%3D-35)
Answer:
Any [a,b] that does NOT include the x-value 3 in it.
Either an [a,b] entirely to the left of 3, or
an [a,b] entirely to the right of 3
Step-by-step explanation:
The intermediate value theorem requires for the function for which the intermediate value is calculated, to be continuous in a closed interval [a,b]. Therefore, for the graph of the function shown in your problem, the intermediate value theorem will apply as long as the interval [a,b] does NOT contain "3", which is the x-value where the function shows a discontinuity.
Then any [a,b] entirely to the left of 3 (that is any [a,b] where b < 3; or on the other hand any [a,b] completely to the right of 3 (that is any [a,b} where a > 3, will be fine for the intermediate value theorem to apply.
Answer: i don’t know
Step-by-step explanation:
Firstly, solve the inequality for y using subtraction:
y > -6 - 4x
Then plug in the x and y values from the answer until the inequality proves true:
-12 > -6 -4(1)
-12 > -10 (false)
Then the next choice:
-9 > -6 - 4(0)
-9 > -6 (false)
Next choice:
-1 > -6 -4(-1)
-1 > -6 + 4
-1 > -2 (true)
Therefore, C is the correct answer. Hope this helps and let me know if you need more help!