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Goshia [24]
3 years ago
12

You are taking a​ multiple-choice test that has 8 questions. each of the questions has 5 answer​ choices, with one correct answe

r per question. if you select one of these choices for each question and leave nothing​ blank, in how many ways can you answer the​ questions?
Mathematics
1 answer:
Murrr4er [49]3 years ago
8 0
5^8 = 390625 ways tp d
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Five times the sum of a number and 27 is greater than or equal to six times the sum of that
AleksAgata [21]

The complete version of question:

<em>Five times the sum of a number and 27 is greater than or equal to six times the sum of that number and 26. What is the solution of this problem.</em>

Answer:

5\left(x+27\right)\ge \:6\left(x+26\right)\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\le \:-21\:\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:-21]\end{bmatrix}

Step-by-step explanation:

As the description of the statement is:

'<em>Five times the sum of a number and 27 is greater than or equal to six times the sum of that number and 26'.</em>

<em />

As

  • <em>Five times the sum of a number and 27  </em>is written as: 5(x + 27)
  • <em>greater than or equal </em>is written as:  \geq
  • <em>six times the sum of that number and 26'  </em>is written as: 6(x + 26)

so lets combine the whole statement:

<em />5\left(x\:+\:27\right)\ge \:6\left(x\:+\:26\right)<em />

solving

<em />5\left(x\:+\:27\right)\ge \:6\left(x\:+\:26\right)<em />

<em />5x+135\ge \:6x+156<em />

<em />5x+135-135\ge \:6x+156-135<em />

<em />5x\ge \:6x+21<em />

<em />5x-6x\ge \:6x+21-6x<em />

<em />-x\ge \:21<em />

<em />\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}<em />

<em />\left(-x\right)\left(-1\right)\le \:21\left(-1\right)<em />

<em />x\le \:-21<em />

Therefore,

5\left(x+27\right)\ge \:6\left(x+26\right)\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\le \:-21\:\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:-21]\end{bmatrix}

6 0
3 years ago
Los 2/9 de mis lapices son blancos y los 21 restantes azules. ¿Que fracción de lapices son azules? ¿Cuantos lapices en total ten
Gelneren [198K]

Answer:

7/9 son azules. hay 27 en total y hay 6 lapices de blanco

Step-by-step explanation:

8 0
3 years ago
The feet of a commemorative parabolic steel arch 100m high are 200m apart. Determine whether the focus of the arch is above or b
Neko [114]
<span>First of all, there should be coherence for the units of measurement -- either they are all meters or they are all ft. I would assume they are all ft. The correct answer is 75 ft above. T The explanation is the following: suppose the ground level is the x-axis, the 2 feet of the arch lie respectively on (0,0) and (100,0) on the ground level. Since the arch is 100ft high, the vertex of the parabola will be the point (100,100). Thus, we can find the equation describing the parabola by putting the three points we know in a system and we find that the equation of the parabola is y=(-1/100)x^2+2 To find the focus F, we apply the formula for the focus of a vertical axis parabola, i.e. F(-b/2a;(1-b^2+4ac)/4a). By substituting a=-1/100, b=2 and c=0 into the formula, we find that the coordinates of the focus F are (100,75). So we conclude that the focus lies 75ft above ground.</span>
7 0
3 years ago
Read 2 more answers
The x axis is<br> vertical<br> horizontal<br> diagonal
Harman [31]

Answer:

Horizontal

Step-by-step explanation:

The x-axis is horizontal while the y-axis is vertical.

5 0
2 years ago
Read 2 more answers
Cuales son las raíces solución de la ecuación x^2-5x+4=0
Pepsi [2]
2x - 5x + 4 = 0
- 3x = - 4
x = 4/3
7 0
4 years ago
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