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Fynjy0 [20]
3 years ago
12

What is the answer to this? −1.3≥2.9−0.6r

Mathematics
1 answer:
Karolina [17]3 years ago
6 0

Answer:

Inequality Form:

r ≥ 7

Interval Notation:

[7, ∞)

Step-by-step explanation:

−1.3 ≥ 2.9 − 0.6r

Rewrite so r is on the left side of the inequality.

2.9 − 0.6r  ≤ −1.3

Move all terms not containing r to the right side of the inequality.  

Subtract 2.9 from both sides of the inequality.

−0.6r  ≤ −1.3 − 2.9

Subtract 2.9 from −1.3.

−0.6r  ≤ −4.2

Divide each term by −0.6 and simplify.

      Divide each  term in −0.6r  ≤ −4.2 by −0.6. When multiplying or dividing both sides of an

      inequality by a negative value, f lip the direction of the inequality sign.

       −0.6r /−0.6 ≥  −4.2 /−0.6

       Cancel the common factor of −0.6.

                  −4.2

          r ≥    ______

                  −0.6

 Divide −4.2 by −0.6.

r ≥ 7

The result can be shown in multiple forms.

Inequality Form:

r ≥ 7

Interval Notation:

[7, ∞)

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A chemist needs to obtain a 75% acid solution. How many Ounces of a 20% acid solution must be mixed with 20 ouncesof an 90% acid
Tju [1.3M]

Answer: 5.4545 ounces

Step-by-step explanation:

Given the following :

Acid solution required = 75% acid solution

Let the number of ounces of 20% acid solution required = s

Then total ounces acid required can be expressed as :

=0.20s + 0.90 x 20

= 0.20s + 18

While the total ounces required is :

s + 20

Hence, (total ounces of acid / total ounces) = 75% acid solution

= (0.2 + 18) / (s + 20) = 0.75

= 0.2s + 18 = 0.75( s + 20)

0.2s + 18 = 0.75s + 15

18 - 15 = 0.75s - 0.2s

0.55s = 3

S = 3 / 0.55

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8 0
3 years ago
Given that KJ = MN and that L is the midpoint of JN, prove JKL = NML.
Semmy [17]
Let's follow the statements in the figure you provide and give the corresponding reason for each.

1. KJ is congruent to MN ---> GIVEN (That means that you were told this is true when the problem was posed. Read the problem...everything before the word "prove" is given to you).

2. JL is congruent to LN --> You were told that L is the midpoint of JN. A midpoint divides a segment into two congruent parts. So, the fact that L is a midpoint means that JL and LN are congruent. Here we do not say given because you were given that L is the midpoint and you had to now what a midpoint does to get to the fact that JL and LN are congruent. So here we say DEFINITION OF A MIDPOINT

3. angle JKL is congruent to angle NLM --> GIVEN. Here the information was given to you in the diagram. These angles are both drawn with a red curved line. Since these are the same (both a single red curve) it means that the angles are congruent.

PROVING TRIANGLES CONGRUENT
We are asked to prove that triangle JKL and triangle NML are congruent. There are various ways to prove that two triangles are congruent. These are:
SSS (each side in one triangle is congruent to a side in the other triangle)
SAS (two sides and the angle between them in one triangle are congruent to two sides and the angle between them in the other triangle)
ASA (two angles and the side between them in one triangle are congruent to two angles and the side between them in the other triangle)
AAS Two angles and a side not between them in one triangle is congruent to two angles and a side not between them in the other triangle.
HL (the hypotenuse and a leg of a right triangle is congruent to the hypotenuse and a leg in another right triangle)

OUR TRIANGLES
Attached is a diagram for this problem. In it since KJ and MN are congruent I have marked each with a single hashmark. Since JL and LN are congruent I have marked each of these with two hashmarks. You will notice that both triangles have a side with one hashmark and another with two hashmarks Also, there is an angle congruent in each. However, the angle is not BETWEEN the sides so we cannot use SAS. None of the other methods of proving two triangles congruent work because what we have is two sides and an angles not between them. That would be SSA but SSA is NOT one of the ways of proving triangles congruent. The triangles we are given might be congruent but they also might not be.

The answers is D --> There is not enough information to prove the triangles congruent.

7 0
2 years ago
Which of these is most likely a pair of independent and dependent variables?
prisoha [69]

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Semenov [28]

Answer:

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Step-by-step explanation:

3.8 x 104 = 395.2

2 x 103 = 206

395.2 - 206 = 189.2

hope this helps (:

3 0
3 years ago
What is the additive inverse of the complex number 9 – 4i?
stiks02 [169]

Answer:-(9 - 4i) =

Step-by-step explanation:

Given the complex number 9 - 4i, the additive inverse is the number that when added to the original number, would equate to zero. Another term this may be known as is the additive identity. The additive inverse is simply:

(a + bi) = -(a + bi)

Given: 9 - 4i

-(9 - 4i) = -9 + 4i

8 0
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