A line passes through the given points. Write an equation for the line in
point-slope form. Then rewrite the equation in slope-intercept form.
(4, -2), (9, -8)

Answer:

-4,-4,-4,-4,-2,-2,-2,-2,3,3,3,3,3,|5|,|5|,|5|,5,|6||6||-6||-6|

Numbers' absolute values are outputted as non-negative numbers. The arrangement of given numbers from least to greatest is: Option A: -4, -2, 3, |5|, |-6|

Modulus of a real number, also called absolute value, is non-negative result of the input value.

This is defined as:

[tex]|x| = x ; \text{ (x is non-negative)}\\\\|x| = -x ; \text{ (x is negative)}[/tex](so that the outer negative makes the negative number positive).

Example:

[tex]|5| = 5\\|-5| = -(-5) = 5[/tex]

A number has both magnitude(its absolute value) and its sign(positive or negative).

If numbers are negative, the more their magnitude increases, the lesser they become.

If numbers are positive, the more their magnitude increases, the greater they become.

Thus, for -5, the magnitude is 5, and sign is –ve.

Also, positive numbers > 0 > negative numbers.

For given case, we get:

Arranging, we get:

-4 < -2 < 3 < 5 < 6

or

-4 < -2 < 3 < |5| < |-6|

Thus,

The arrangement of given numbers from least to greatest is: Option A: -4, -2, 3, |5|, |-6|

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Answer:

( A )

Step-by-step explanation:

To solve this problem you must apply the procedure shown below:

1. You have the following equation given above:

2. The negative four will pass as a positive four to the right member.

3. Te sum of 7 and 4 will be divided by , as following:

Answer:

Step-by-step explanation:

The given equation is :

Cx-4=7.

To solve for x we isolate the x term .

Adding 4 both sides:

Cx=7+4

Cx=11

To x term C is multiplied ,performing  the opposite operation that is dividing both sides by C we have :

x=[tex]\frac{11}{C}[/tex]

Answer:

C. 6 equilateral triangles

6 Equilateral triangles needed to construct the hexagon option (C)  6 Equilateral triangles is correct.

A hexagon is a six-sided polygon with six inner angles totalling 720° and six outside angles totalling 360° in geometry. Regular, irregular, concave, convex, and complicated hexagons are two-dimensional shapes.

We have a given a hexagon in the figure.

As we know hexagon is a polygon made up from six sides also hexagon can be made using six equilateral triangles by joining them.

Thus, 6 Equilateral triangles needed to construct the hexagon option (C)  6 Equilateral triangles is correct.

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Answer:

2.507* 10^-4

Step-by-step explanation:

0.0002507

We need to have one number to the left of the decimal

We move the decimal 4 places to the right

Since we moved the decimal to the right, the exponent on the power of 10 is negative

2.507* 10^-4

Answer:

y=-2

Step-by-step explanation:

y+3y+5y=−18

Combine like terms

9y = -18

Divide each side by 9

9y/9 = -18/9

y = -2

The equation y + 3y + 5y = -18 simplifies to 9y = -18; solving for y, we find y = -2.

The equation presented is y + 3y + 5y = −18. To find the value of y, we first need to simplify the left-hand side of the equation by adding the similar terms together. In this equation, all terms on the left-hand side are multiples of y. Thus, y + 3y + 5y simplifies to 9y.

Our equation then becomes 9y = -18. To solve for y, we divide both sides of the equation by 9, yielding y = -2.

So, the value of y in this equation is -2.

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Answer:

the correct answer is C

Step-by-step explanation:

Number of favorite outcomes=5

Total Number of outcomes=9

5/9 = 0.56

The probability that the next Tucker family vacation lasts less than 333 days is about 0.560.560, point, 56.

1: n+5

2: n-5

3: x+8

4: x-8

5: 8-x

6: 5-n

7: x+(5+7)

8: x+(8+2)

9: x+(8-2)

10: x+x

Answer:

[tex]\large\boxed{\left(7,\ \dfrac{13}{3}\right)}[/tex]

Step-by-step explanation:

You must use the algebraic method: substitution or elimination.

I will solve a given system of equations the substitution method.

[tex]\left\{\begin{array}{ccc}y=\dfrac{1}{3}x+2&(1)\\\\y=\dfrac{4}{3}x-5&(2)\end{array}\right\qquad\text{substitute (2) to (1)}\\\\\dfrac{4}{3}x-5=\dfrac{1}{3}x+2\qquad\text{multiply both sides by 3}\\\\3\!\!\!\!\diagup^1\cdot\dfrac{4}{3\!\!\!\!\diagup_1}x-(3)(5)=3\!\!\!\!\diagup^1\cdot\dfrac{1}{3\!\!\!\!\diagup_1}x+(3)(2)\\\\4x-15=x+6\qquad\text{add 15 to both sides}\\\\4x=x+21\qquad\text{subtract x from both sides}\\\\3x=21\qquad\text{divide both sides by 3}\\\\x=7\\\\\text{put the value of x to the first equation}\\\\y=\dfrac{1}{3}\cdot7+2\\\\y=\dfrac{7}{3}+\dfrac{6}{3}\\\\y=\dfrac{13}{3}[/tex]

Answer:

[2, 1]

Step-by-step explanation:

By the Elimination method, you are left with 8x = 16 because -8 and 8 are what are called Additive Inverses, meaning they result in 0⃣; x = 2, plug 2⃣ back into both equations, and you will see that y = 1, making the solution above.

Answer:

Option D 37.5 miles

Step-by-step explanation:

we know that

The scale on a map is [tex]\frac{1}{5}\frac{in}{mi}[/tex]

so

using proportion

Find the actual distance for a length on a map of 7.5 in

Let

x ----> the actual distance

[tex]\frac{1}{5}\frac{in}{mi}=\frac{7.5}{x}\frac{in}{mi}\\ \\ x=7.5*5\\ \\x=37.5\ mi[/tex]

Answer:

y=ln(x/(1-x))

Step-by-step explanation:

y=e^x/(1+e^x)

Cross multiply

y(1+e^x)=e^x

Distribute

y+ye^x=e^x

Put anything with x on with side and everything without x on opposing side:

y=e^x-ye^x

Factor right hand side

y=(1-y)e^x

Divide both sides by (1-y)

y/(1-y)=e^x

Use natural log.

ln(y/(1-y))=x

The inverse is

y=ln(x/(1-x))

Answer:

Step-by-step explanation:

[tex]\text{The slope}[/tex]

[tex]m=\dfrac{rise}{run}[/tex]

[tex]rise=-4\\\\run=-1[/tex]

[tex]m=\dfrac{-4}{-1}=4[/tex]

The required slope of the graph exists 4.

The graph exists in a straight line.

The line passes through the points (0, -3) and [tex]$\left(\frac{3}{4}, 0\right)$[/tex].

We know the slope of a straight line passing through the points (a, b) and (c, d) is given by

[tex]$m=\frac{d-b}{c-a} .$$[/tex]

Therefore, the slope of the given line is

[tex]$m=\frac{0-(-3)}{\frac{3}{4}-0}$$[/tex]

[tex]$&\Rightarrow m=\frac{3}{\frac{3}{4}} \\[/tex]

[tex]$&\Rightarrow m=3 \times \frac{4}{3}\end{aligned}$$[/tex]

[tex]$\Rightarrow m=4 \text {. }$$[/tex]

The required slope of the graph exists 4.

Therefore, the correct answer is option D. 4

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255 square centimeters

First, break this into two shapes: a triangle and a rectangle.

The rectangle is 22 cm by 10 cm.  [tex]22 * 10 = 220[/tex] square centimeters

The triangle's base is 10 cm ([tex]22-12=10[/tex]) and its height is 7 cm ([tex]17-10=7[/tex]).  [tex]\frac{1}{2} * 10 * 7 = 5 * 7 = 35[/tex] square centimeters

Add the areas together. [tex]220 + 35 = 255[/tex] square centimeters

Answer:

The corresponding point is (5,8)

Step-by-step explanation:

In this problem we know that

The rule of the transformation is equal to

(x,f(x)) ------> (x,f(x)+4)

so

for the point (5,4)

x=5, f(x)=4

substitute

(5,4) ------> (5,4+4)

(5,4) ------> (5,8)

therefore

The corresponding point is (5,8)

Answer:

x=18y+5

Step-by-step explanation:

Answer:

x = 5 + 18y

Step-by-step explanation:

Equation: [tex]\frac{4(x - 5)}{8}[/tex] = 9y

Multiply and distribute: 4x - 20 = 72y

Add: 4x = 20 + 72y

Divide: x = 5 + 18y

Answer:

8x^2 +14x +3

Step-by-step explanation:

(2x + 3)* (4x + 1)​

FOIL

first 2x *4x = 8x^2

outer  2x*1 = 2x

inner  3*4x =12x

last = 3*1 =3

Add them together

8x^2 +2x+12x +3 = 8x^2 +14x +3

Answer:

$6.88

Step-by-step explanation:

We are trying to compare two options: Buying a magazine for 12 months or for just 1 year.

To solve this, we can multiply the monthly rate by 12 because there are 12 months in a year.

5.99 x 12 = 71.88

The other option is to just pay $65 dollars for a whole year (12 months).

Comparing the two options, we see paying for the whole year is cheaper than paying for each month individually. Because of this, we can subtract $65, the cheaper option, from $71.88 to get $6.88

Chris will save $6.88 by paying for the whole year instead of purchasing for each month.

Answer:

[tex]\frac{83}{186}[/tex]

Step-by-step explanation:

In probability, "OR" means "+" and "AND" means "*".

The total amount of people is:

32 + 54 + 78 + 112 + 96 = 372

Number of diabetic patients are 54

Number of eye patients are 112

Since we want "OR", we will add the two probabilities:

P(diabetic or eye problem) = 54/372 + 112/372 = 83/186

Answer:

yes

Step-by-step explanation:

a

The answer is:

Yes, the given equation is also a function. (it's a quadratic function)

We know a function exists when there is only one value of y (output) for each x (input).

We can easily know if an equation (relation) is also a function using the graphic method:

To know if a relation is a function, we need to graph it a draw a vertical line, if the line cut the graph in only one point, the relation is a function, otherwise, if the vertical line cuts the graph in two or more points, the relation is a not a function. Remember, the condition for a function is that there is only one output for each input.

Note: I have attached a picture for better understanding.

Have a nice day!

Answer:

17 is the missing the number

Step-by-step explanation:

Pattern: +1, +3, +5, +7, etc.

The most appropriate description ascribed to the meaning of definition from the options given is ; A precise statement of the qualities of an idea, object or process.

Therefore, since the definition ascribed to a process or phenomenon as to be original and precise, then the most appropriate statement is the option C.

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Answer:

There is an association because the relative frequencies by column are different.

Step-by-step explanation:

For checking the association of a two-way table we have to calculate the relative frequency of the table. Here we see that there is an association between timing and day pf watching the movie. Also here relative frequencies of both columns are similar.

[tex]\bf \begin{array}{ccll} grams&people\\ \cline{1-2} 480&4\\ x&14 \end{array}\implies \cfrac{480}{x}=\cfrac{4}{14}\implies \cfrac{480}{x}=\cfrac{2}{7}\implies 3360=2x \\\\\\ \cfrac{3360}{2}=x\implies 1680=x[/tex]

Solving for  b  by simplifying both sides of the equation, then isolating the variable.

b  =  −y  +  6x

----

Choosing three values for  x  and substitute in to find the corresponding  y  values.

(0,−3)  ,  (1,0)  ,  (2,3)

____

I hope this helps, as always. I wish you the best of luck and have a nice day, friend..

Answer:

Step-by-step explanation:

y = 6x -b

and -3x +y =-3

on simplifying equation 2 ,we have y = 3x -3

System of equation has infinite number of solution if one equation can be obtained by multiplying by suitable non zero number

if we multiply equation by 2 we get y =6x -6

Since coefficient of x and y is same therefore comparing the value of x b with constant in another equation which is 6 .

therefore b =6

Answer:

√'xy/y

Step-by-step explanation:

1. [x*y^(1/2)] / [y * x^(1/2)]  

= [x^(1/2) * y^(1/2)] / y  

= (xy)^(1/2) / y  

You'll get your answer as :  √'xy/y

Step-by-step explanation:

Let the total amount of salary be X, then

3/10X + 2/3X + amount left= his salary(X)

(9X + 20X)/ 30 + 2100 = X

29X/30 - X = -2100

(29X - 30X)/30 = -2100

by cross multiplying

-X = -2100×39

-X = -81900

divide both side by -1

X = 81900.

therefore his salary = 81900

Answer:

Muli's salary = 62,000

Step-by-step explanation:

Let Muli's salary  be x.

Money spent on food = 3/10 of x = 3x/10

Money spent on rent = 2/3 of x = 2x/3

Money left with him = 2100

(3x/10) + (2x/3) + 2100 = x

x - (3x/10) - (2x/3) = 2100             ( LCM = 30)

30x/30 - 9x/30 - 20x/30 = 2100

(30x - 9x - 20x ) / 30 = 2100

x/30 = 2100

x = 2100 * 30 = 62,000

Answer:

x(x + 1) ≤ 0

-1 ≤ x ≤ 0

{x | x ≥ -1 and x ≤ 0}

Follow steps:

Solving the Inequality x(x+1)≤0

To solve x(x+1)≤0, we need to find values of x where the product is negative or zero. X can be split into the regions x < 0 and x > 0. As x approaches zero from either direction, x(x+1) approaches zero as well. The function is zero at the roots of the equation x(x+1) = 0, which are x = 0 and x = -1. These two roots divide the real line into three intervals: (-∞, -1), (-1, 0), and (0, ∞). Analyzing each interval:

For x in (-∞, -1), x < -1 and x+1 < 0, so the product x(x+1) is positive.

For x in (-1, 0), x is negative and x+1 is positive, so the product x(x+1) is negative.

For x in (0, ∞), both x and x+1 are positive, and thus, the product x(x+1) is positive.

The inequality is only satisfied in the interval where the product is negative or zero. Therefore, the solution is [{-1}, 0], which can be written in interval notation as (-1, 0]. This is a single continuous interval that includes the root x = 0 and excludes the root x = -1.

Finally, using interval notation, we express the solution to the inequality x(x+1)≤0 as (-1, 0].