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umka21 [38]
3 years ago
8

−6x + 14 < −28 OR 9x + 15 ≤ −12. solve for x.

Mathematics
1 answer:
sasho [114]3 years ago
4 0

Answer:

x>7 or x ≤ -3

Step-by-step explanation:

Solving the 1st inequality

-6x +14 < -28 --------------- (Collect like terms)

-6x < -28 - 14

-6x < - 42 -------------------- (Divide both sides by -6)

Note: If you decide an inequality expression by a negative value, the inequality sign changes)

-6x/-6 > -42/-6

x > 7

Solving the 2nd inequality

9x + 15 ≤ −12 ----------- (Collect like terms)

9x ≤ −12 - 15

9x ≤ −27 ------------------(Divide both sides by 9)

9

9x/9 ≤ −27/9

x ≤ -3

Bring both results together, we get

x>7 or x ≤ -3

The final result is complex (i.e. can't be combined together).

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Convert the following percent into common fractions in simplest form:<br> 5 1/3%
Tomtit [17]

Answer:

4/75

Step-by-step explanation:

you will get 5 and 1/3 percent equals (5 + 1/3) / 100 which is equal to 5/100 + (1/3) / 100 which is equal to 5/100 + 1/300. place both fractions under a common denominator. you will get 5/100 + 1/300 = 15/300 + 1/300 = 16/300. simplify the fraction to get 16/300 = 8/150 = 4/75

6 0
3 years ago
Cookies are on sale! Today each cookie costs \$0.75$0.75dollar sign, 0, point, 75 less than the normal price. Right now if you b
TEA [102]

Answer:

The equation to determine the normal price of each cookie is

7(x - 0.75) = 2.80

The normal price of each cookie = $1.15

Step-by-step explanation:

Let us represent the normal price of a cookie as : x

We are told that:

Today each cookie costs \$0.75less than the normal price.

The price of a cookie today is

x - 0.75

Right now if you buy 7 of them it will only cost you \$2.80$

Hence:

7(x - 0.75) = 2.80

Solving for x

7x - 5.25 = 2.80

7x = 2.80 + 5.25

7x = 8.05

x = 8.05/7

x = $1.15

The normal price of each cookie = $1.15

8 0
2 years ago
Read 2 more answers
The side lengths of triangle ABC are 3, 4, and 5. Which set of ordered pairs form a triangle that is congruent to triangle ABC?
Ludmilka [50]
FORMULA:
AREA=     AC x h
        ----------------------
                    2
PERIMETER= AB+BC+CA

AREA   =   SQUAREROOT       
                  S(S-AB)(S-BC)(A-CA)


S= AB+BC+CA=   P
     -----------------   -----
               2             2


FOR THE COMPLETE SOLUTION PLEASE SEE THE PICTURE. THANKS.

6 0
3 years ago
Can someone help me with these? ​
kati45 [8]

Answer:

no they're not congruent angle side side No,no son congruents angle side side

6 0
3 years ago
Pat wishes to fence in a rectangular area, using the wall of her garage as one side, so only three sides need to be fenced. If s
natali 33 [55]

Answer:

The maximum area is 800 ft².

Step-by-step explanation:

Lets call L the length of the side parallel to the garage and M the length of the other two sides. The total amount to fence is 2M+L and the area is L*M.

Since Pat got 80ft of fence, then 2M+L = 80, hence L = 80-2M. By replacing the value of L in the formula of the area, we get that

A(M) = M*(80-2M) = -2M² + 80M

The maximum of this function can be obtaining throught derivation, but since it is a quadratic with negative main coefficient, we know that the maximum is the vertex. The x-coordinate of the vertex is '-b/2a' = -80/2*(-2) = 20. The y-coordinate (which represents the maximum area),  as a result, is A(20) = -2*20²+80*20 = 800.

800 is the maximum area that can be fenced. Note that M = 20 and L = 80-2L = 40.

8 0
3 years ago
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