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bezimeni [28]
3 years ago
9

Show work only do those 32,34,36,38,40

Mathematics
1 answer:
Free_Kalibri [48]3 years ago
7 0

Answer:  see below

<u>Step-by-step explanation:</u>

32)\quad \dfrac{3}{5}(x-12)>x-24

        3(x - 12) > 5(x - 24)

        3x - 36 > 5x - 120

      <u> -5x       </u>   <u>-5x         </u>

        -2x - 36 >      -120

        <u>      +36</u>      <u>    +36 </u>

        -2x        >       -84

   <u>  ÷ -2        </u> ↓    <u>   ÷ -2  </u>

             x      <       42

Graph:   ←------------o

                             42

34)   6[5y - (3y - 1)] ≥ 4(3y - 7)

        6[5y - 3y + 1] ≥ 4(3y - 7)

        6{2y + 1]        ≥ 4(3y - 7)

         12y + 6        ≥ 12y - 28

        <u>-12y            </u>    <u>-12y       </u>

                  6        ≥         -28

                        TRUE  so the solution is All Real Numbers

Graph:   ←-----------------------→

36)   BC  +  AC      > AB

         4    + 8 - AB > AB

                12 - AB  > AB

       <u>             +AB  </u>  <u>+AB </u>

                12          > 2AB

      <u>         ÷2        </u>    <u>÷2     </u>

                 6           >  AB

                         AB < 6

38)\quad \dfrac{1}{2}(y-16)\geq y+2\quad ;\text{claim}\ y\leq 20

Check: let y = 16

           then \frac{1}{2}(16 - 16) ≥ 16 + 2

                            0    ≥ 18

                            FALSE  so the claim is wrong

40) question not provided in the image so I cannot give a solution.

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Basile [38]

Answer:

<em>The mass of the steel ball is 4,235.9 gr</em>

Step-by-step explanation:

<u>Density</u>

The density ρ of a substance is a measure of its mass per unit volume:

\displaystyle \rho=\frac{m}{V}

If the density and the volume are given, the mass can be calculated by solving the above formula for m:

m=\rho.V

We know the density of pure steel ρ=8.09 gr/cm3 and the diameter of a solid steel ball d=10 cm.

We need to calculate the volume of the sphere:

The volume of a sphere of radius r is given by:

\displaystyle V=\frac{4}{3}\cdot \pi\cdot r^3

The radius is half the diameter: r= 10/2 = 5 cm. Thus:

\displaystyle V=\frac{4}{3}\cdot \pi\cdot 5^3

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3 years ago
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Answer:

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Step-by-step explanation:

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Which expression could help you find the distance
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2.5 Finding the Distance Between Two Numbers - Math 7 CCSS

FlexBooks® 2.0  >  CK-12 Interactive Middle School Math 7 - Teacher's Edition  >  Finding the Distance Between Two Numbers - Math 7 CCSS

Last Modified: Sep 04, 2020

Common Core Standards

Focus Standards:  7.NS.A.1.c

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Show that the distance between two rational numbers on the number line is the absolute values of their difference.

Solve problems involving finding the difference between two rational numbers in a real-world context.

Agenda

Warm-Up: Diving Deeper 10 min

Activity 1: Along the Street 20 min

Activity 2: Getting Around Washington DC  15 min

Review Questions 5 min

(Students do not see text in purple)

Now that subtraction has been introduced, it is applied to finding the distance between two points in this lesson.  The distance between two points will first be introduced as counting units on a number line, but then formalized into a definition with subtraction and absolute value.  Review with students that distance is always positive and the definition of absolute value before beginning.

Warm-Up: Diving Deeper

The distance between two points can be defined as the number of units between them. Typically, this means we subtract the values, but what if one point is negative and the other is positive?

Example

Fatima’s friend, Tyler, is more daring than she and when he jumps into the water to scuba dive, he starts from 4 feet above the water, at the back of the boat.  After his first jump, he went 7 feet below the water. How many feet did he actually travel?

This interactive shows an application of how negative values are used; in this case, it is how deep a diver dives. Students will see a body of water, a diver on a cliff, boat and some fish. There are also two number lines; the horizontal line ranges from -20 to 5 and the vertical line ranges 5 feet to -20 feet. The horizontal line has a red point that students can click and drag to make the diver dive. While the student moves the point in the negative direction the father down the diver will go. The arrow on the vertical line will travel down with the diver showing the student how many feet down the diver is.

TRY IT

Inline Questions: Students see inline questions here. The questions are formative and have detailed instructional feedback. The questions and correct answers are printed below for your convenience as an instructor.

Which expression tells us the total distance Tyler travels to return to 5 feet above the water from a depth of 15 feet?

|-15 - 5|

|5 -15|

|5 - (-15)|

|-15 - (-5)|

Which expression can we use to find the total distance Tyler traveled?

|4 - (-7)|

4 - 7

|4 - 7|

-7 - 4

If Tyler started 5 feet above the water, jumped, then went 8 feet below the water, which of the following represent the total distance traveled?

|5 - (-8)|

|-8 - (-5)|

|5 - 8|

|-8 - 5|

Tyler is 7 feet below the water's surface and dives another 8 feet down. How can we determine how far below the water's surface he is now?

|-7 - (-8)|

|7 - 8|

|-7 - 8|

|8 - 7|

It is important to remember that when finding the total distance between two points on a number line, you may need to find the absolute value of those distances separately, depending on what the question is asking for.

Emphasize to students that when finding the total distance between two points on a number line, they need to use absolute value. As is the case with #3, you may need to draw a picture showing them that he starts at -7 feet down and goes down another -8 feet. His total distance from the surface is |-7| + |-8| or |-7 - 8|.

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This interactive is another application of how negative numbers may be used to show distance traveled. On the number lines there are five places Jason can travel: Jason’s house is the starting point and located at zero. The school is located at -8, the movies are at -5, his friend’s house is at 4 and the store is at 7. Students can move the red point along the number line to the different locations. Above the number line students can see the distance the location is from the starting point (Jason’s house).

TRY IT

Step-by-step explanation:

3 0
2 years ago
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Sever21 [200]

Answer:

x = -2.5

Step-by-step explanation:

→ Multiply both sides of the equation by the opposing denominator

8x = -20

→ Divide both sides by 8 to isolate x

x =  -\frac{20}{8} =-\frac{10}{4} =-\frac{5}{2}  or -2.5

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