PLEASE! 10 POINTS! For what number A does the equation 3Ax - 24 = 5x - 9 + x have no solutions for x?

Answer:

A. [tex] x \leq -16[/tex]  

B. b > 11

C. [tex] c \leq -13 [/tex]

D. [tex] x \geq -9[/tex]

Step-by-step explanation:

Given the following algebraic expression;

A. [tex] \frac {3x}{4} \leq 12 [/tex]

We would simplify the equation by multiplying all through by 4;

[tex] 4 * \frac {-3x}{4} \leq 12 * 4[/tex]

[tex] -3x \leq 48[/tex]

Divide both sides by -3;

[tex] x \leq -16[/tex]

B. 5b - 28 > 27

Rearranging the equation, we have;

5b > 27 + 28

5b > 55

Divide both sides by 5

b > 11

C. [tex] 13c \leq -169[/tex]

Divide both sides by 13

[tex] c \leq -13 [/tex]

D. [tex] 3x - 7 \geq 4x + 2[/tex]

Collecting like terms, we have;

[tex] 3x - 4x \geq 2 + 7[/tex]

[tex] -x \geq 9[/tex]

Divide both sides by -1

[tex] x \geq -9[/tex]

==========================================================

Explanation:

Let's focus on the x coordinates of each point for now.

The idea to find the midpoint's coordinates is to add up the endpoints coordinates and divide by 2.

So we'll add up -7 and x, then divide by 2 to get the midpoint x coordinate of -4

In short we have:  (-7+x)/2 = -4

Solving for x leads to...

(-7+x)/2 = -4

-7+x = 2*(-4)

-7+x = -8

x = -8+7

x = -1

This is the x coordinate of point N

-------------------------------

We'll repeat the same idea and steps for the y coordinates

So,

(4+y)/2 = -1

4+y = 2(-1)

4+y = -2

y = -2-4

y = -6

This is the y coordinate of point N.

------------------------------

In summary, we found that point N is located at (-1, -6)

Point A is (-7,4) and point N is (-1,-6)

If you apply the midpoint formula to those two points, you should find the midpoint to be M(-4,-1) which helps confirm the answer.

Another way to confirm the answer is to compute the distance from A to M, which finds the length of segment AM. Do the same for segment MN. You should find that both segments are the same length.

The diagram below is a visual way to check. Starting at point A and moving down to point B, we moved 5 units. Then go from B to M and you'll move 3 units to the right. This pattern "down 5, right 3" is applied again when we go from M to C to N in that order. This effectively creates two congruent triangles (ABM and MCN) which can lead to proving AM = MN.

In short: the red piece of the graph is the same length as the blue piece; this confirms we have the correct answer.

Step-by-step explanation:

According to Question , M is the midpoint of AN, A has coordinates (-7,4), and M has coordinates (-4, -1).

Figure :-

[tex] \setlength{\unitlength}{1 cm}\begin{picture}(20,12) \put(4,0.2){\line(0,-1){0.4}}\put(1,0){\line(1,0){6}} \put(3.8,-0.6){$\bf M(-4,-1) $} \put(1,-0.6){$\bf A (-7,4)$} \put(6.8,-0.6){$\bf N(x,y)$} \end{picture}[/tex]

Let the coordinates of N be ( x , y )

Now , according to Midpoint Formula , the midpoint of points say A(x , y) and B (x' , y') is given by ,

[tex]\boxed{\blue{ \bf Midpoint =\bigg( \dfrac{x+x'}{2} , \dfrac{y+y'}{2} \bigg) }}[/tex]

On using this formula ,

[tex]=> Midpoint = \bigg( \dfrac{x+x'}{2} , \dfrac{y+y'}{2} \bigg) \\ \\ => (-4, 1) = \bigg( \dfrac{x -7 }{2} , \dfrac{y + 4 }{2}\bigg) \\ \\ => -4 = \dfrac{x-7}{2} \\\\ => x - 7 = -8 \\\\ => x = 7 -8 \\\\ \boxed{\red{\sf=> x = -1 }} \\\\ => \dfrac{y+4}{2}=-1 \\\\=> y +4 = -2 \\ \\ y = -4-2 \\\\\boxed{\red{\sf=> y = -6 }}[/tex]

Note: The first point of the table should be (-2,-1) instead of (-1,-2). because (-1,-2) does not satisfy the relation.

Given:

Consider the table of values is

x      y

-2     -1

0     3

1      5

3     9

To find:

The equation that best describes the  relationship between the corresponding values of x and y.

Solution:

Consider any two points from the given table, i.e., (0,3) amd (1,5).

So, the equation of line is

[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

[tex]y-3=\dfrac{5-3}{1-0}(x-0)[/tex]

[tex]y-3=\dfrac{2}{1}(x)[/tex]

[tex]y-3=2x[/tex]

Adding 3 on both sides, we get

[tex]y=2x+3[/tex]

Therefore, the correct option is C.

Answer:

2 times

Step-by-step explanation:

The probability of 1/3 means that the spinner will land on a 2, 1/3 of the time:

We can predict how many times it will land on a 2 by finding 1/3 of 6:

6/3

= 2

So, the spinner will land on a 2, two times

Number of times probability of landing on a 2 is 2, when you spin the spinner 6 times.

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes

Given that, in a game, the probability that a spinner will land on a 2 is 1/3.

If you spin the spinner 6 times, probability of landing on a 2 is

1/3 ×6

= 2

Therefore, number of times probability of landing on a 2 is 2.

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#SPJ2

Answer:

61

Step-by-step explanation:

7a-9 = 7(10)-9 = 70-9 = 61

Answer:

quadrant 1 - (2,4)

quadrant 2 - (-3,4)

quadrant 3 - (-1, -5)

quadrant 4 - (6, -1)

Step-by-step explanation:

quadrant one consists of both x and y being positive.

quadrant two being the x is negative but the y is negative.

quadrant 3 has its x and y both negative.

finally, quadrant 4 has its x positive, but y is negative.

what r the tax amounts

Answe

number plus 14

fourteen more than a number

a number increased by 1

Step-by-step explanation:

Which phrases can be represented by the algebraic expression x + 14

Assuming the unknown number = x

Then,

a number plus 14

= x + 14

fourteen more than a number

= x + 14

a number increased by 14

= x + 14

Plus, more than and increased all means plus(+)

Answer:

number plus 14

fourteen more than a number

a number increased by 1

Step-by-step explanation:

Answer:

Difference between the two is $36.

Step-by-step explanation:

Pair of shorts costs $12. Shirt costs $48.

48-12=36

Answer:

d no 8 unit df parallel bc and 1by 2 bc

Step-by-step explanation:

(1x2+1) x -(6/15)

3/2 x -(6/15)

3/2 x -(2/5)

3/2 x (-2/5)

(-3/2)

Answer:

[tex]1 \frac{1}{2} \times ( - \frac{6}{15} ) = \frac{3}{2} \times ( \frac{ - 6}{15} ) \\ = \frac{ - 3}{5} [/tex]

Answer:

I think 35 pieces of candy for $12.24 because If you doubled the 14 pieces by money and you would get 28 pieces of candy for $10.98.

Step-by-step explanation:

35 pieces would be the best answer!

Answer:

15 % of usual price is a savings

Step-by-step explanation:

Given that tool set normally cost $80

During the sale this week the tools that cost $12 less than usual

To find: what percentage of the usual price is a savings

From given information,

Usual price of tool set = $ 80

Given that tools that cost $12 less than usual which means she saved $ 12

Savings = $ 12

To find what percentage of the usual price is a savings, we can solve by framing a expression,

Let "x" be the required percentage

Then x % of percentage is equal to savings price

x % of usual price = savings price

x % of 80 = 12

Therefore 15 % of usual price is a savings

Answer:

Answer is 15%

Step-by-step explanation:

You have to do a proportion

12. = x

80 100 and u have to cross multiply

80x = 1200

80. 80

then divide 1200÷80=15

Answer:

a)3^-2 = 1/3^2 =1/9

b)4^-3 = 1/4^3 = 1/64

c)2^-6 = 1/2^6 = 1/64

Answer:

Step-by-step explanation:

Imagine the numbers are plotted on the number line.

Order on the number line which is from least to greatest:

Answer:

m=3/2

look how many units go up and to the side between 2 points

As seen here, we go up 3 units and over 2 units from (0, -3) to (2, 0.) Therefore, slope is 3/2

Step-by-step explanation:

Step-by-step explanation:

a).6x^8y^5

b)4x^5z^8

c)12a^9b^7

d)6s^9t³

Answer: step 4

Step-by-step explanation:

Error in the proof starts with the first mistake done. The erroneous step in the proof is given by: Option B: Step 6.

Sign changing in equation does by multiplying -1 on both the sides.

So, if we had [tex]a + b = c[/tex]

Then, its signs are changed as:

[tex]-1(a + b) = -1 \times c\\-a -b = -c[/tex]

For the given case, the mistake occurred during transition from step 5 to step 6. Step 6 is wrong as when sign was changed, sin of cos(θ) remain same, which makes step 5 and step 6 not equal to each other.

The correct proof would be like:

[tex]\rm \cos(2x) = 1- 2\sin^2(x)\\Let\: 2x = \theta\\\\Then: x = \dfrac{\theta}{2}\\\\\cos(\theta) = 1 - 2\sin^2(\dfrac{\theta}{2})\\-1 + \cos(\theta) = -2\sin^2(\dfrac{\theta}{2})\\\\1 - \cos(\theta) = 2\sin^2(\dfrac{\theta}{2})\\\\\dfrac{1-\cos(\theta)}{2} = \sin^2(\dfrac{\theta}{2})\\\\\sin(\theta) = \pm \sqrt{\dfrac{1-\cos(\theta)}{2} }[/tex]

Thus, the erroneous step in the proof is given by: Option B: Step 6.

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Answer:

[tex](5p + 11) + (8p - 4) \\ = ( 13p + 7)[/tex]

Answer:

-2

Step-by-step explanation:

Substitute in the values

(2(3)-3(-2))/(-2)(3)

multiply

(6+6)/(-6)

(the second 6 became positive because it is a negative 3 times negative 2.)

add

12/-6

divide

-2

Answer:

k=-100

Step-by-step explanation:

Hope this helped have an amazing day!

Answer:

B

Step-by-step explanation:

Step-by-step explanation:

after you draw a unit circle you will find the answer

cosec(3pi)=1/sin(3pi)

sin3pi=sinpi=0

so cosec3pi=1/0 which is undefined.

The trigonometric functions [tex]csc(3\pi)[/tex] is undefined.

To understand more, check below explanation.

The value of given trigonometric function are show below,

            [tex]sec(-\pi)=sec(\pi)=-1\\\\csc(3\pi)=\frac{1}{sin(3\pi)}=1/0 =\infty\\\\cot(\frac{7\pi}{2} )=\frac{1}{tan(\frac{7\pi}{2} )} =\frac{1}{\infty} =0\\\\csc(-\frac{3\pi}{2} )=1\\\\cot(\frac{5\pi}{3} )=\frac{1}{\sqrt{3} }[/tex]

Hence, the trigonometric functions [tex]csc(3\pi)[/tex] is undefined.

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Answer:

Step-by-step explanation:

(28a+36ab)

Answer:

a) The height of the building is 12 metres.

b) The ball will take 6 seconds to hit the ground.

c) The maximum height of the ball is 16 metres and occurs 2 seconds after launch.

d) The ball have a height of 7 meters above the ground 5 seconds after launch.

Step-by-step explanation:

a) The roof of the building is represented by the initial height of the ball according to the function. If we know that [tex]t = 0\,s[/tex], the height of the building, measured in metres, is:

[tex]y = -(0\,s)^{2}+4\cdot (0\,s) + 12[/tex]

[tex]y = 12\,m[/tex]

The height of the building is 12 metres.

b) Let equalise the given polynomial and solve for [tex]t[/tex] to determine the time taken for the ball to hit the ground:

[tex]-t^{2}+4\cdot t +12 = 0[/tex] (1)

By the Quadratic Formula, we find the following solutions:

[tex]t_{1} = 6\,s[/tex] and [tex]t_{2} = -2\,s[/tex]

Since time is a positive variable, then the only solution that is physically reasonable is:

[tex]t = 6\,s[/tex]

The ball will take 6 seconds to hit the ground.

c) The maximum height of the ball occurs when speed is equal to zero. First, we differentiate the function and equalise to zero:

[tex]-2\cdot t + 4 = 0[/tex] (2)

[tex]t = 2\,s[/tex]

Lastly, we evaluate the function at given time:

[tex]y = -(2\,s)^{2}+4\cdot (2\,s)+12[/tex]

[tex]y = 16\,m[/tex]

The maximum height of the ball is 16 metres and occurs 2 seconds after launch.

d) We equalise the height formula to seven and solve the resulting polynomial:

[tex]-t^{2}+4\cdot t + 12 = 7[/tex]

[tex]-t^{2}+4\cdot t +5 = 0[/tex] (3)

By the Quadratic Formula, we get the following solutions:

[tex]t_{1} \approx 5\,s[/tex] and [tex]t_{2} \approx -1\,s[/tex]

The only solution that is physically reasonable is [tex]t = 5\,s[/tex].

The ball have a height of 7 meters above the ground 5 seconds after launch.