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Pavlova-9 [17]
2 years ago
5

Which of the following is an equivalent form of the compound inequality −22 > −5x − 7 ≥ −33?

Mathematics
1 answer:
Finger [1]2 years ago
5 0

The equivalents of the given compound inequality are x > 3 and x ≤ 5.2 OR 3 < x ≤ 5.2

<h3>Solving inequalities </h3>

From the question, we are to determine the equivalent form of the compound inequality

We will solve the given compound inequality

The given inequality is

−22 > −5x − 7 ≥ −33

We can write that

−22 > −5x − 7 AND −5x − 7 ≥ −33

Solving  −22 > −5x − 7

5x > -7 +22

5x > 15

x > 15/5

x > 3

Also,

Solve −5x − 7 ≥ −33

−5x ≥ −33 +7

-5x ≥ -26

x ≤ -26/-5

x ≤ 5.2

Hence, the equivalents of the given compound inequality are x > 3 and x ≤ 5.2 OR 3 < x ≤ 5.2

Learn more on Inequalities here: brainly.com/question/20356565

#SPJ1

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<h3>Surface Area = 1,256 cm</h3>

<u>Solution:</u>

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They intersect at the point (p, q).<br> Which is greater, c or d? Explain how you know.
Natasha2012 [34]

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d is greater than c, since at x = 0, g(x) > f(x)

Step-by-step explanation:

We are given two exponential functions, f and g.

Since f has the higher base(3 instead of 2 in g), it increases faster, so initially, g is greater than f, and after point (p,q), f is greater than g.

The values of c and d are found when x = 0. At this point, we have that g is greater than f, so d is greater than c.

4 0
3 years ago
The polynomial $f(x)$ has degree 3. If $f(-1) = 15$, $f(0)= 0$, $f(1) = -5$, and $f(2) = 12$, then what are the $x$-intercepts o
Alex_Xolod [135]

Your calculator's cubic regression function can tell you the equation is

... f(x) = 2x³ + 5x² -12x = x(x +4)(2x-3)

The x-intercepts are -4, 0, +1.5.

_____

If you want to solve this "by hand", you can first of all recognize that since there is an x-intercept at 0, the cubic will only have three coefficients. That is, you can write the equation as

... f(x) = ax³ + bx² + cx

Substituting the given points (except (0, 0)) gives three linear equations in a, b, c.

... -a +b -c = 15 . . . . . for x=-1

... a + b + c = -5 . . . . for x=1

... 8a +4b +2c = 12 . . for x=2

adding the first two equations gives 2b=10, or b=5. Now, you can reduce the system to

... a + c = -10

... 4a +c = -4

Subtracting the first of these equations from the second gives 3a=6, or a=2. That tells you c=-12 (from a+c=10).

Then your equation is

... f(x) = x(2x² +5x -12)

Factoring by any of the usual techniques, or graphing, or using the quadratic formula will tell you the zeros (x-intercepts) are as above.

_____

Since the input values are sequential, you can also develop the function from differences of the output values. Those are 15, 0, -5, 12. First differences are -15, -5, +17. Second differences are +10, +22. The third difference is 12. Using the first of these differences in appropriate places in the interpolating polynomial formula, we have

... f(x) = 15 + (x+1)(-15 + (x)/2·(10 + (x-1)/3·(12))) = 2x³ +5x² -12x . . . . as above

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3 years ago
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