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3 years ago

Please help me with this

Mathematics

2 answers:

Fynjy0 [20]3 years ago

7 0

-5 is the base and the exponent is 6

You’re welcome (-◼️_◼️)

user100 [1]3 years ago

6 0

Answer:

Your base is -5 and your exponent is 6.

Step-by-step explanation:

Mark me as Brainliest plz!!!

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Solve the given inequality :

tigry1 [53]

Answer:

x < -5 or x = 1 or 2 < x < 3 or x > 3

Step-by-step explanation:

Given rational inequality:

$\dfrac{(x-1)^2(x-2)^3}{(x^2-5x+6)^2(x+5)}\geq 0$

$\textsf{Factor }(x^2-5x+6):$

$\implies x^2-2x-3x+6$

$\implies x(x-2)-3(x-2)$

$\implies (x-3)(x-2)$

Therefore:

$\dfrac{(x-1)^2(x-2)^3}{(x-3)^2(x-2)^2(x+5)}\geq 0$

Find the roots by solving f(x) = 0 (set the numerator to zero):

$\implies (x-1)^2(x-2)^3=0$

$\implies (x-1)^2=0\implies x=1$

$\implies (x-2)^3=0 \implies x=2$

Find the restrictions by solving f(x) = undefined (set the denominator to zero):

$\implies (x-3)^2(x-2)^2(x+5)=0$

$\implies (x-3)^2=0 \implies x=3$

$\implies (x-2)^2=0 \implies x=2$

$\implies (x+5)=0 \implies x=-5$

Create a sign chart, using closed dots for the roots and open dots for the restrictions (see attached).

Choose a test value for each region, including one to the left of all the critical values and one to the right of all the critical values.

Test values: -6, 0, 1.5, 2.5, 4

For each test value, determine if the function is positive or negative:

$f(-6)=\dfrac{(-6-1)^2(-6-2)^3}{(-6-3)^2(-6-2)^2(-6+5)}=\dfrac{(+)(-)}{(+)(+)(-)}=+$

$f(0)=\dfrac{(0-1)^2(0-2)^3}{(0-3)^2(0-2)^2(0+5)}=\dfrac{(+)(-)}{(+)(+)(+)}=-$

$f(1.5)=\dfrac{(1.5-1)^2(1.5-2)^3}{(1.5-3)^2(1.5-2)^2(1.5+5)}=\dfrac{(+)(-)}{(+)(+)(+)}=-$

$f(2.5)=\dfrac{(2.5-1)^2(2.5-2)^3}{(2.5-3)^2(2.5-2)^2(2.5+5)}=\dfrac{(+)(+)}{(+)(+)(+)}=+$

$f(4)=\dfrac{(4-1)^2(4-2)^3}{(4-3)^2(4-2)^2(4+5)}=\dfrac{(+)(+)}{(+)(+)(+)}=+$

Record the results on the sign chart for each region (see attached).

As we need to find the values for which f(x) ≥ 0, shade the appropriate regions (zero or positive) on the sign chart (see attached).

Therefore, the solution set is:

x < -5 or x = 1 or 2 < x < 3 or x > 3

As interval notation:

$(- \infty,-5) \cup x=1 \cup (2,3) \cup(3,\infty)$

4 0

2 years ago

A man earns$140 in 5 day week. What is his pay for 3 days?

Flura [38]

Answer:

$84

Step-by-step explanation:

Do 3/5*140 which will give you 84 dollars

4 0

3 years ago

-8(-8+2)-4 solve please

Anvisha [2.4K]

Answer:

Step-by-step explanation:

-8(-8+2)-4

1) Simplify inside the parenthesis: (-8+2)

-8(-6)-4

2) Multiply -8 and -6:

48-4

3) Simplify:

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3 years ago

What is JL? pls help

mrs_skeptik [129]

Answer:

It should be option a 4.5

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3 years ago

Read 2 more answers

Which of the following circles lie completely within the fourth quadrant? Check all that apply.

arlik [135]

Remember that the circle formula is (x – h)2 + (y – k)2 = r2 where h and k represents the center of the circle. We determine as follows:

A.(x - 2)2 + (y + 7)2 =64
 (h,k) = 2,-7 QUADRANT 4

B.(x - 5)2 + (y + 5)2 = 9
 (h,k) = 5,-7 QUADRANT 4

C.(x - 9)2 + (y + 9)2 = 16
(h,k) = 9,-9 QUADRANT 4

D.(x - 12)2 + (y + 0)2 = 72
 (h,k) = 12,0 QUADRANT 4

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3 years ago