Algebra 2
1) What is the multiplicative inverse of 300?
a) 300
b) 0.03
c) 1/300
d) None of the above
e) a and b
f) b and c
g) a and c

Answer:

x > - 3

Step-by-step explanation:

x + 2[tex]\frac{1}{2}[/tex] > - [tex]\frac{1}{2}[/tex]      First turn 2[tex]\frac{1}{2}[/tex] into an fraction since its easier. So it becomes [tex]\frac{5}{2}[/tex]

x + [tex]\frac{5}{2}[/tex] > - [tex]\frac{1}{2}[/tex]

  - [tex]\frac{5}{2}[/tex]     - [tex]\frac{5}{2}[/tex]         Do inverse operations, so subtract [tex]\frac{5}{2}[/tex] from both sides.

    x > - [tex]\frac{6}{2}[/tex]          Combine  - [tex]\frac{5}{2}[/tex] with - [tex]\frac{1}{2}[/tex], which gives us - [tex]\frac{6}{2}[/tex]

    x > - 3          Since we know that 6 divided by 2 is 3.

This would not allow me to attach an image so I am going to type a visual representation f what the graph would look like below)

<-------------O--------------------------------------------------->

-5    -4     -3      -2       -1     0     1     2    3    4     5

So, the number line would be a solid line rather than dashed (but I was not able to attach an image so I kind of had to improvise). When using ≥ ≤ sings the circle of the point is closed. When using < and > signs, the circle of the point is open. Thus, in this scenario since he sign is >, then the circle of the point is open. The direction of the arrow and ray for this equality is going to the right because the answer is that x is greater than - 3, Therefore any values greater than - 3 are a possibility which is why the arrow goes on indefinitely.

Answer:

B. 10°, 10°, 160°

Step-by-step explanation:

The rule with triangles is that the angles combined may only ever add to 180°

So, lets add to be sure.

A. 90° + 45° + 46° = 181°

B. 10° + 10° + 160° = 180°

C. 28° + 12° + 120° = 160°

Therefore, option B

Answer:

8.4 is 10% of 100

Step-by-step explanation:

84 is 100%

x is 10 %

x= 84*10/100= 8.4

The corresponding element in the range when 7 is an element  in the domain is f(7)=33

Step-by-step explanation:

Given that the 7 is an element in the domain of f(x)

The function f is defined by f(x)=6x-18/2

To find the corresponding element in the range:

That is put x=7 in the given function f(x)

Therefore f(x) becomes

f(7) = 6(7)-18/2

      =42-18/2

      =42-9

      =33

Therefore corresponding element in the range when 7 is an element  in the domain is f(7)=33

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Answer:

Surveying every 5th customer that enters the yogurt shop

Step-by-step explanation:

Answer:

5/12

Step-by-step explanation:

Add both fractions and divide by 2 to find the one right in between.

3/8+11/24=5/6

then divide by two

(5/6)/2=5/12

=5/12

Answer:

[tex]volume = \frac{1}{3} \pi {r}^{2} h \\ = \frac{1}{3} \times 3.14 \times {(14.3)}^{2} \times 3.9 \\ = 834.73 \: cubic \: in[/tex]

Answer:835.2

Step-by-step explanation:

Answer:

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Step-by-step explajyhgftdcsesdxqadfadrfswfeedfrsdx:

Answer:

Step-by-step explanation:

7,80

Answer:

The value of x is 2/7 or 0.285

Step-by-step explanation:

Here, we will make equivalent expressions in the equation that all have equal bases.

6²⁽⁶ˣ⁻¹⁾ = 6⁵ˣ

Since, The bases are the same i.e., 6. So, exponent are also same

2(6x - 1) = 5x

Solve for x

12x - 2 = 5x

12x - 5x - 2 + 2 = 5x - 5x + 2

7x = 2

7x/7 = 2/7

x = 2/7 = 0.285

Thus, The value of x is 2/7 or 0.285

For verification

36⁶ˣ⁻¹ = 6⁵ˣ

36⁶⁽⁰°²⁸⁵⁾ ⁻ ¹ = 6⁵⁽⁰°²⁸⁵⁾

36¹°⁷¹ ⁻ ¹ = 6¹°⁴²⁵

36⁰°⁷¹ = 6¹°⁴²⁵

12.7 = 12.7

Hence, L.H.S = R.H.S

VERIFIED!!

Answer: C

Step-by-step explanation:

Based on the graph, we know that it is negative if it is under the x-axis. It is also indicated by the negative labels.

A: incorrect

Looking at choice A, it says the interval is from -3<x<-2. This means we have to find x=-3 and x=-2. On the graph, that interval is above the x-axis, so it is positive, not negative.

B: incorrect

Looking at choice B, it says the interval is from 2<x<3. This means we have to find x=2 and x=3. On the graph, that interval is above the x-axis, so it is positive, not negative.

C: correct

Looking at choice C, it says the interval is from 4<x<5. This means we have to find x=4 and x=5. On the graph, that interval is under the x-axis, so it is negative.

Therefore, C is the correct answer.

Answer:

3x-2y+2z

Step-by-step explanation:

Answer:

[tex] \displaystyle M = ( 3,1 )[/tex]

Step-by-step explanation:

we are given the endpoint i.e P and Q of a line segment

we want to figure out the Midpoint of the Line segment

in order to do so we can use Midpoint formula given by

[tex] \displaystyle M = \bigg( \frac{ x_{1} + x_{2} }{2} , \frac{ y_{1} + y_{2}}{2} \bigg)[/tex]

so let

[tex]x_1=-2\\x_2=8\\y_1=-2\\y_2=4[/tex]

substitute

[tex] \displaystyle M = \bigg( \frac{ - 2 + 8}{2} , \frac{ - 2 + 4}{2} \bigg)[/tex]

simplify addition:

[tex] \displaystyle M = \bigg( \frac{ 6}{2} , \frac{ 2}{2} \bigg)[/tex]

simplify division:

[tex] \displaystyle M = ( 3,1 )[/tex]

hence,

the Midpoint of the line segment is (3,1)

Answer:

36°, 72°, and 72°

Step-by-step explanation:

The interior angles of a triangle will always add to 180°.

Let's say the smallest angle is x, then the other two angles are both 2x.

x+2x+2x=180

5x=180

x=36

If our angles are x, 2x, and 2x, and we know x is 36, then the answer is:

36°, (2*36)°, and (2*36)°, which equals

36°, 72°, and 72°

Check: 36+72+72=180

An indirect proof is an argument that begins with the assumption that a conclusion is false, then uses logical reasoning to show that the assumption leads to a contradiction.

a fact or assertion that contradicts what someone else said or that differs from another fact or assertion to the point where one of them must be incorrect.

A situation or set of ideas that contradict one another is called a contradiction. A contradiction would be saying out loud that you support the environment while never remembering to empty the recycling. A statement that contains opposing ideas is frequently referred to as a "contradiction in terms."

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Answer:

x = -1

y = -1

Step-by-step explanation:

This is a system of equations- the set up of the problem lends well to using the elimination method. There are always many ways of solving a system of equations, both in methods and different strategies within each method. The problem isn't necessarily complete but I can assume you're being asked to solve for x and y values.

divide the first equation by -2. this means we can use elimination to cancel out the y value, and is also our simplest option (rather than multiplying the second equation by -2.

-2x + 20y = -18 --> x - 10y = 9

x - 10y = 9

8x + 10y = -18

Using the elimination method to essentially add the parts of the equations together, this comes out to 9x = -9 , meaning x = -1 .

We can then return to our original equations, and substitute -1 for x (either equation will work, but the second one is simpler and therefore the better option).

8 (-1) +10y = -18

-8 + 10y = -18

10y = -10

y = -1

CHECKING

Substitute both x and y values back into the original equations to check them. the sides should be equal if our values are correct.

-2 (-1) + 20 (-1) = -18

Our first equation works: 2 - 20 = -18

8 (-1) + 10 (-1) = -18

The second equation works as well: -8-10= -18

Answer:

33 degrees

Step-by-step explanation:
Angle 1 and 2 add up to a right angle which is 90 degrees. To find 2, subtract 57 from 90

90-57=33

Therefore 33 degrees is the answer

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The Trigonometric inequality Sec (x)< cot(x) will hold true in π/2 < x < π.

How can a trigonometric inequality be expressed?

The intervals where the trigonometric inequality sec (x) cot (x) always holds true are what we are looking for.

This can also be expressed as: 1/cos (x) < 1/tan (x)

Now, this is only possible in the fourth quadrant, where cos x is positive and tan (x) is negative, where: π/2 < x < π.

The values for sin, cos, and tan are all positive in the first quadrant.

Only positive values for sin are present in the second quadrant.

The tan values in the third quadrant are all positive.

Only positive values for cos are present in the fourth quadrant.

Therefore the inequality Sec(x) < cot(x) will hold true in π/2 < x < π.

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Answer:

X=8

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

17x−30+7x+18=180

17x+−30+7x+18=180

(17x+7x)+(−30+18)=180(Combine Like Terms)

24x+−12=180

24x−12=180

Step 2: Add 12 to both sides.

24x−12+12=180+12

24x=192

Step 3: Divide both sides by 24.

X=8

Answer:

x = 15

y = -26

Step-by-step explanation:

x + y = -11

x - y = 41

let x = 41 + y

substitute:

41 + y + y = -11

2y = -52

y = -26

x -26 = -11

x = 15

Answer:

4/8

Step-by-step explanation:

The equation 3x - 9 = 0 has 3 as a solution out of all the given equations in the options.

Check the solution of equation 3x - 9 = 0

3x - 9 = 0

3x = 9

x = 3

Check the solution of equation 4x - 3 = 0

4x - 3 = 0

4x = 3

x = 3/4

Check the solution of equation 5x - 10 = 0

5x - 10 = 0

5x = 10

x = 10/5

x = 2

Check the solution of equation 7x - 49 = 0

7x - 49 = 0

7x = 49

x = 49/7

x = 7

Thus, only 3x - 9 = 0 satisfy the solution x = 3.

Hence, the correct option is A.

--The given question is incomplete, the complete question is

''Which equation has 3 as a solution set?

A. 3x - 9 = 0

B. 4x - 3 = 0

C. 5x - 10 = 0

D. 7x - 49 = 0''--

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The Ball Rolls Downhill, It's Kinetic Energy Increases And It's Potential Energy Maximum.

Hope Helps! :)

[tex] \: \: [/tex]

No, triangle ABC is not a right triangle. The equation of a line BC "y=x-11" is a line with slope of 1, which means it has an angle of 45 degrees with respect to the x-axis. The segment AB has a slope of 0, which means it is parallel to the x-axis. A right triangle's legs must be perpendicular, therefore a line with a slope of 1 and a line with a slope of 0 cannot be the legs of a right triangle.

A right triangle is a triangle in which one of the angles is 90 degrees. In order for a triangle to be a right triangle, the two sides (or legs) that form the 90-degree angle must be perpendicular to each other. Perpendicular lines have slopes that are negative reciprocals of each other.

In this case, the equation of the line segment AB is "y = -6", which means it is parallel to the x-axis. The slope of a line parallel to the x-axis is 0. On the other hand, the equation of the line BC is "y = x - 11", which means it has a slope of 1. A slope of 1 means that the line is at a 45 degree angle with respect to the x-axis.

Since the slopes of the two lines are not negative reciprocals of each other (0 and 1), the legs of the triangle cannot be perpendicular. Therefore, triangle ABC cannot be a right triangle.

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Answer:

184cm

Step-by-step explanation:

to find the area of the triandles

4 times (half of 6 ) 3 = 12 divided by 2 = 6 + 6 ( because there are two right triangles making up one side ) so one side is 12cm add the other side 12 +12 = 24cm

To find the left and right sides mutipy length times width 10 x 5 = 50 add the oher side 50 + 50 = 100

To fide the bottom rectangle do the same thing but 10 x 6 = 60

so add everything together 24+100+60 = 184cm

The temperature at midnight as required to ve determined in the task content is; 14°C.

According to the task content; the temperature was 11.2°C at 2 : 00am.

However, since the temperature dropped 1.4 °c each hour; we have that;

In the two hours between midnight and 2:00am, the total temperature drop is; 2 × 1.4°C = 2.8°C.

On this note, the temperature at midnight can be evaluated as; 11.2°C + 2.8°C = 14°C.

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Answer:

2,302,63

Step-by-step explanation:

................

Answer:

942.50

Step-by-step explanation:

First, multiply 2334.50 by 3 to get 7003.50. Then multiply 1437x3= 4311

7003.50-4311=2692.50 Then take away 1750. 2692.50-1750=942.50

I hope this helps! UWU