First consider the system of equations y = -1/2 x + 1 and y = x - 5. Then consider the system of inequalities y > -1/2x+1 and y < x-5. When comparing the number of solutions in each of these systems, which statement is true?
Both systems have an infinite number of solutions.
The system of equations has more solutions.
The system of inequalities has more solutions.
Both systems have only one solution.​

36 students does not watch regularly the programme.

Lets simplify the problem,

Total students = 48

Regular students 1//4*48

=> 12 students

Through Simple Subtraction method,

Irregular students = Total students - regular students

Irregular students = 48-12

=36

Hence 36 students does not watch regularly the programme.

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Answer:

[tex]x=\frac{83}{36}[/tex]

Step-by-step explanation:

1) Convert [tex]2\frac{1}{4}[/tex] to  improper fraction. Use this rule: [tex]a\frac{b}{c} =\frac{ac+b}{c}[/tex].

[tex]x-\frac{2\times4+1}{4} = \frac{1}{18}[/tex]

2) Simplify [tex]2\times4[/tex] to 8.

[tex]x-\frac{8+1}{4} =\frac{1}{18}[/tex]

3) Simplify [tex]8+1[/tex] to 9.

[tex]x-\frac{9}{4} =\frac{1}{18}[/tex]

4) Add [tex]\frac{9}{4}[/tex] to both sides.

[tex]x=\frac{1}{18} +\frac{9}{4}[/tex]

5) Simplify [tex]\frac{1}{18} +\frac{9}{4}[/tex] to [tex]\frac{83}{36}[/tex].

[tex]x=\frac{83}{36}[/tex]

Decimal Form: 2.305556

Answer:

83/36

Step-by-step explanation:

x - 2 1/4 = 1/18

x = 1/18 + 9/4

L.C.M= 36,

x = 1x2/18x2 + 9x9/4x9

x = 2/36 + 81/36

x = 83/36

Decimal form = 2.305556

The example on direct variation is illustrated below based on the information given.

An example will be:

When x = 2, y = 10. Find the value of y when x is 6.

In this case, this will be calculated thus:

y = kx

10 = 2k

k = 10/2

k = 5

Since y = kx.

y = 5 × 6

y = 30

The value of y is 30.

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[tex]Answer: \displaystyle\left {{x^2+(y-3)^2=36} \atop {x^2+(y+8)^2=36}} \right. .[/tex]

Step-by-step explanation:

[tex]D=12\ \ \ \ O(0;b)\\\displaystyle\\R=\frac{D}{2}\\R=\frac{12}{2} \\ R=6.\\Circle \ equation\ is:\\(x-a)^2+(y-b)^2=R^2.\\a=0\ \ \ \ \ R=6\\x^2+(y-b)^2=6^2\\x^2+(y-b)^2=36\\Henese:\\\displaystyle\\\left {{x^2+(y-3)^2=36} \atop {x^2+(y+8)^2=36}} \right. .[/tex]

He needs to do 10 visits to earn a free ticket.

We know that he gets 30 points just for signing up, and he gets 8.5 points for each visit, then the amount of points as a function of v, the number of visits, is:

P(v) = 30 + 8.5*v

He will get a free movie ticket when he gets 115 points, then we need to solve the linear equation:

P(v) = 115 = 30 + 8.5*v

Solving for v:

v = (115 - 30)/8.5 = 10

He needs to do 10 visits to earn a free ticket.

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Answer:

140g

Step-by-step explanation:

One pencil box has a mass of 140g, to find out the weight of 4 pencil boxes we multiply 140 by 4: 140*4 = 560g

Let the mass of the notebook be x: 560+x = 700

560+x = 700

x = 140g

Answer:

91 in2

Step-by-step explanation:

11+15 over 2 , times by 7 equals 91 ??

Answer:

25 minutes

Step-by-step explanation:

If it takes 5 minutes to prepare one game we need to multiply 5 games by 5 minutes: 5*5 = 25 minutes

The simplified form of the expression is [tex]10 x^{18}[/tex].

What are indices in maths?

The given expression is [tex]\sqrt{100x^{36} }[/tex]

Applying the rule, [tex]\sqrt[n]{ab} = \sqrt[n]{a} \sqrt[n]{b}[/tex]

Now, [tex]\sqrt{100} \sqrt{x^{36} }[/tex]

Simplifying, we get;

[tex]10\sqrt{x^{36} }[/tex]

Applying the exponent rule, [tex]a^{bc} = (a^{b} )^{c}[/tex]

We get

[tex]10 \sqrt{(x^{18} })^{2}[/tex]

[tex]10 x^{18}[/tex]

Therefore, the simplified form of the expression is [tex]10 x^{18}[/tex].

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Answer:

10 x 18

Step-by-step explanation:

Answer:

3rd option

Step-by-step explanation:

8 - 3x ≥ - 4 ( subtract 8 from both sides )

- 3x ≥ - 12

divide both sides by - 3 , reversing the symbol as a result of dividing by a negative quantity.

x ≤ 4

since ≤ the circle on number line is solid ( not open )

since less than 4 then arrow points left away from 4

the solution is shown on the third graph

If this is the one you are talking about then:

horizontal translation of 3 units is:     y= f(x-3)

vertical stretch by a scale factor of 3 is:     y= 3f(x)

reflection over the x-axis is:     y= -f(x)

vertical translation of 3 units is:     y= f(x)+3

Step-by-step explanation:

Adding a value to f(x) translates the graph of f vertically. So, the equation that shows a vertical translation of 3 units is y = f(x) + 3.

Adding a value to the input, x, of f(x) translates the graph of f horizontally. So, the equation that shows a horizontal translation of 3 units is y = f(x − 3).

Multiplying f(x) by a negative value reflects the graph of f over the x-axis. So, the equation that shows a reflection over the x-axis is y = -f(x).

Multiplying f(x) by a constant, k, vertically stretches the graph of f by a scale factor of k. So, the equation that shows a vertical stretch by a scale factor of 3 is y = 3f(x).

2b^3 -5 b^2 +b+2. R 9/ b-4

Use synthetic division

Step-by-step explanation:

x³ - x² - 24x - 36

factors of -36 are 1, 2, 3, 4, 6, 9, 12, 18, 36 and negative equivalents.

1 - 1 - 24 - 36 != 0

8 - 4 - 48 - 36 != 0

27 - 9 - 72 - 36 != 0

64 - 16 - 96 - 36 != 0

216 - 36 - 144 - 36 = 0

So one factor is 6

x = 6

(x - 6) = 0

x²(x - 6) = x³ - 6x²

5x(x - 6) = 5x² - 30x

6(x - 6) = 6x - 36

x³ - 6x² + 5x² - 30x + 6x - 36

(x - 6)(x² + 5x + 6)

(x - 6)(x² + 3x + 2x + 6)

(x - 6)(x(x + 3) + 2(x + 3))

(x - 6)(x + 3)(x + 2)

x - 6 = 0

x = 6

x + 3 = 0

x = -3

x + 2 = 0

x = -2

x = -2, -3, 6.

One is the product of the other 2 as -2 x -3 = 6.

Graphic proof is shown above or below in the image

Answer:

167

Hope this helps you out

Answer:

167

Step-by-step explanation:

Break it into steps.

2+2+5 = 9

69 + 9 = 78

78 + 89 = 167

Hope this helps.

The fraction of the students in Siena's class are girls with brown eyes is 5/12.

Let the fraction of students in Siena's class with brown eyes be a=5/8.

And the fraction of students in Siena's class with brown eyes are girls be b=2/3.

Then, the fraction of students in Siena's class are girls with brown eyes be z=a×b

Therefore, by substituting the fraction values, we get

z=(5/8)×(2/3)

z=5/12.

Hence, 5/8 of the students in Siena's class have brown eyes. 2/3 of the students with brown eyes are girl. Then, the fraction of students in Siena's class are girls with brown eyes is 5/12.

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Answer:

B.6 is the significant digits of number 1.00250

I HOPE IT HELP YOU

The number of significant figures that are available in 1.00250 are; B: 6

Significant figures are defined as the number of digits in a value, often a measurement, that contribute to the degree of accuracy of the value.

Now, in the question we are given the decimal number 1.00250.

Now, it should be noted that when dealing with significant numbers as regards decimals, any zero digit to the left of the decimal is a non-significant figure while any zero digit to the right of the decimal is a significant figure.

Thus, the significant figures in the question are all the numbers which are 6 in number.

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(a) |-9| + 6 = 9 + 6 = 15

(b) |-9 + 6| = |-3| = 3

Hello, the solution of the problem is in this photo.

If the graph of the line falls from left to right, then the slope is negative.

The midpoint of point A and point B is (5, -2.5)

The coordinates are given as:

A = (3, -8)

B = (7, -3)

The midpoint is calculated as:

(x, y) = 0.5 * (x1 + x2, y1 + y2)

So, we have:

(x, y) = 0.5 * (3 + 7, -8 + 3)

This gives

(x, y) = 0.5 * (10, -5)

Evaluate

(x, y) = (5, -2.5)

Hence, the midpoint of point A and point B is (5, -2.5)

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The equation which expresses the number of bacteria, P, present at any time, t is P(t) = 4(2)^t

Check all options

When t = 1

P(t) = 8(4)^t

= 8(4)¹

= 8(4)

P(t) = 32

Not true

P(t) = 4(2)^t

= 4(2)¹

= 4(2)

= 8

True

P(t) = (2)^t

= (2)¹

= 2

Not true

P(t) = 8(2)^t

= 8(2)¹

= 8(2)

= 16

Not true

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Answer:

No

Step-by-step explanation:

Lets simplify both expressions:

We will start with Gloria's first expression:

[tex]1/4 (12x + 24) -9x[/tex]

Apply distributive property:

[tex](3x + 6) -9x[/tex]

Combine like terms, we are then left with:

[tex]6-6x[/tex]

Now lets simplify the second expression

[tex]-6(x+1)[/tex]

Apply distributive property

[tex]-6x-6[/tex]

Rearrange:

[tex]-6-6x[/tex]

Now we can see that the two equations are not equal, as the first is 12 greater than the second. Another way we could have tested this was plugging in a value for x and then solving.

The missing fraction is 7/9

The given equation is:

[tex]\frac{3}{4}+\frac{1}{2}+\frac{2}{9}+x=\frac{9}{4}[/tex]

This can be simplified as:

[tex]\frac{27+18+8+36x}{36} =\frac{9}{4} \\\\\frac{53+36x}{36} =\frac{9}{4}[/tex]

Cross multiply

[tex]9(36)=4(53+36x)\\\\324=212+144x\\\\144x=324-212\\\\144x=112\\\\x=\frac{112}{144} \\\\x=\frac{7}{9}[/tex]

Therefore, the missing value is [tex]\frac{7}{9}[/tex]

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The difference between the observed value of the dependent variable and the value predicted using the estimated regression equation is known as the Residual model.

Regression is the process used to predict the variation in one variable based on another variable.

The difference between the observed value of the dependent variable and the value predicted using the estimated regression equation is known as the residual model.

This value s predicted by the regression line.

Residual = Observed value - predicted value

Therefore, the difference is known as residual.

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Answer: [tex]y=5x+1[/tex]

Step-by-step explanation:

The slope of the given line is

[tex]\frac{1-0}{0-5}=-\frac{1}{5}[/tex]

Since perpendicular lines have slopes that are negative reciprocals, the slope of the line we want to find is 5.

Since the y-intercept is (0,1), the equation is [tex]y=5x+1[/tex].

Answer: the answer is c

The elements which must be contain in a body paragraph of a literary analysis are;

A strong body paragraph basically is characterized as a medium of stating facts regarding a viewpoint and these statements must be accompanied by supporting evidence and commentary.

On this note, the three elements which should be contained in a strong body paragraph are;

Remarks:

an introduction to a text

reasons that support a viewpoint

O a thesis statement

supporting evidence and commentary

Da summary of the main points

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Answer:

11

Step-by-step explanation:

Answer:

Infinite solutions.

Step-by-step explanation:

 y = 5 - 2x

 2x + y = 5  ---------(I)

 a₁ = 2  ; b₁ = 1  and c = 5

4x + 2y = 10

a₂ = 4  ; b₂ = 2   and c₂  = 10

[tex]\sf \dfrac{a_1}{a_2}=\dfrac{2}{4}=\dfrac{1}{2}\\\\\dfrac{b_1}{b_2}=\dfrac{1}{2}\\\\\dfrac{c_1}{c_2}=\dfrac{5}{10}=\dfrac{1}{2}[/tex]

⇒  [tex]\sf \dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}=\dfrac{c_1}{c_2}=\dfrac{1}{2}[/tex]

So, the line are coincident and has infinite solutions.

Using a linear function, the inequality is given by: 69.5 + 5x < 90.

The solution is: x < 4.1.

A linear function is modeled by:

y = mx + b

In which:

In this problem, we have that:

Hence the cost of using x gigabytes is:

C(x) = 69.5 + 5x.

The cost has to be under 90, hence the inequality is:

C(x) < 90

69.5 + 5x < 90.

Then the solution is:

5x < 90 - 69.5.

x < 20.5/5

x < 4.1.

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Answer:

Inequality: 5x+35<50

Answer: x<3

Step-by-step explanation:

Answer: Option (4)

Step-by-step explanation:

A quadrilateral with two pairs of opposite congruent sides must be a parallelogram.