Which of the following points is a solution of the inequality y < -|x|?

a. (1,-2)

b. (1,-1)

c. (1,0)

Answer:  The required factored form of the given expression is [tex](x-6)(2y+5).[/tex]

Step-by-step explanation:  We are given to factorize the following expression :

[tex]E=2xy+5x-12y-30~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

We will be using the following property :

[tex]a(b+c)+d(b+c)=(a+d)(b+c).[/tex]

From expression (i), we have

[tex]E\\\\=2xy+5x-12y-30\\\\=x(2y+5)-6(2y+5)\\\\=(x-6)(2y+5).[/tex]

Thus, the required factored form of the given expression is [tex](x-6)(2y+5).[/tex]

Answer:

False

Step-by-step explanation:

If f(x) is a function , then for each value of x  there should be  a single y values

For input 0 there is a output 0

for input 10, the output is 2

for input 15, output is 3

For input 5, we have two output 1 and 3

for single input 5, the function cannot have two outputs 1  and 3

So this f(x) is not a function

The correlation coefficient r=0.23 will remain unchanged at 0.23 even after adding a constant to all x-variable values, doubling the y-variable values, and swapping the x and y variables, because the correlation coefficient is unaffected by such transformations.

The correlation between two variables is denoted by the symbol, r, and it measures the strength and direction of a linear relationship between two quantitative variables. When we add a constant to all values of the x-variable or multiply all values of the y-variable by a constant, the correlation coefficient does not change. However, interchanging the x and y variables also does not change the value of r since correlation is symmetrical. Therefore, if r=0.23 initially, after adding 0.14 to all values of x, doubling the y-variable values, and interchanging the two variables, the new correlation will still be 0.23.

Answer:

The boundary line should be solid because it have a 'great/less than or equal to' sign

Step-by-step explanation:

Answer:  The x-intercept and y-intercept of the given line are (3.6, 0) and (0, -1.2) respectively.  

Step-by-step explanation:  We are given to find the x-intercepts and y-intercepts of the line described by the following equation :

[tex]3x-9y=10.8~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

We know that

the x-intercept of a line is the point where the y co-ordinate is 0. Similarly, y-intercept is the point where the x co-ordinate is 0.

Substituting y = 0 in equation (i), we get

[tex]3x-9\times0=10.8\\\\\Rightarrow 3x-0=10.8\\\\\Rightarrow 3x=10.8\\\\\Rightarrow x=\dfrac{10.8}{3}\\\\\Rightarrow x=3.6.[/tex]

So, x-intercept is (3.6, 0).

And substituting x = 0 in equation (i), we get

[tex]3\times 0-9y=10.8\\\\\Rightarrow 0-9y=10.8\\\\\Rightarrow 9y=-10.8\\\\\Rightarrow y=-\dfrac{10.8}{9}\\\\\Rightarrow y=-1.2.[/tex]

So, y-intercept is (0, -1.2).

Thus, the x-intercept and y-intercept of the given line are (3.6, 0) and (0, -1.2) respectively.  

Answer:

The measure of length of equal side is 36 cm each.

B is correct.

Step-by-step explanation:

Isosceles triangle ABC has a perimeter of 96 centimeters.

The base of the triangle is BC and measures 24 cm

We need to find the length of equal side of triangle.

AB=AC

The perimeter of triangle is 96 cm

AB + AC + BC = 96

AB + AB + 24 = 96                          ( ∵ AB=AC)

              2AB = 96-24

              2AB = 72

                AB = 36

Hence, The measure of length of equal side is 36 cm each.

The answer is gas because gas particles move so fast they bounce off one another when they collide. Plasma has Negatively AND Positively charged particles within it.

Gases are the state of matter where neutral particles bounce off one another as they collide. This is due to their constant, random motion and the elastic nature of their collisions.

The state of matter that has neutral particles that bounce off one another as they collide is a Gas. This is due to the fact that gases are composed of a large number of particles that are in constant, random motion. These particles collide with each other and with the walls of their container. Importantly, these collisions are perfectly elastic, meaning they conserve both momentum and kinetic energy.

In Liquids and Solids, the particles are held together with stronger intermolecular forces which restrict their motion. In Plasma, the particles are ionized and hence, are not neutral.

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The value of x is 6.

Given,

3(3x-8)=4x+6

We need to solve for x and show steps by steps.

Distributive property of multiplication over addition.

: a ( b + c ) = a x b + a x c

Distributive property of multiplication over subtraction.

: a ( b - c ) = a x b - a x c

Combining like terms.

: cx + ax + b = x (c + a) + b

: cx - ax - b = x (c - a) + b

We have,

3(3x-8)=4x+6

Removing the brackets.

3x(3x) - 3x8 = 4x + 6

9x - 24 = 4x + 6

Subtracting 4x on both sides.

9x - 24 - 4x = 4x + 6 - 4x

5x - 24 = 6

Adding 24 on both sides.

5x - 24 + 24 = 6 + 24

5x = 30

Dividing 5 into both sides.

5x/5 = 30/5

x = 6

Thus the value of x is 6.

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If the discriminant in a quadratic equation is 16, a positive number, then the quadratic equation will have two distinct real solutions.

In mathematics, particularly in quadratic equations, the discriminant plays a vital role in determining the nature of the solutions. The discriminant in a quadratic equation is the part under the square root in the quadratic formula, and it is usually represented by the symbol Δ (Delta). The quadratic formula is given by x = [-b ± sqrt(Δ)] / 2a. Now, if the discriminant is 16 (a positive number), then the quadratic equation will have two distinct real solutions. This is because the square root of a positive number yields two real numbers (one positive and one negative) which provide the two solutions when substituted back into the quadratic formula.

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The average rate of change of the function over the interval is 2

Finding the average rate of change

From the question, we have the following parameters that can be used in our computation:

The graph

The interval is given as

From x = -3 to x = 3

The function is a quadratic function

This means that it does not have a constant average rate of change

From the graph

y = -8, when x = -3

y = 4, when x = 3

This means that

f(-3) = -8

f(3) = 4

The average rate is calculated using

Rate = (Change in y values)/(Change in corresponding x values)

So, we have

Rate = (4 + 8)/(3 + 3)

Evaluate

Rate = 2

Hence, the average rate of change is 2

A=6  YZ= 38

An expression is defined as a set of numbers, variables, and mathematical operations. An equivalent expression for 1.5(3x+4)+0.25(6x+8) is 7x+8.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The given expression can be simplified as,

1.5(3x + 4) + 0.25(6x + 8)

= 4.5x + 6 + 2.5x + 2

= 7x + 8

Hence, an equivalent expression for 1.5(3x+4)+0.25(6x+8) is 7x+8.

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Answer:

Step-by-step explanation:dhdjdbfbd

estimate  by rounded to the nearest dollars

2 +1 +5 +2 +3 +9 +1 =  $23

-2

23-2 = 21

 yes the amount is reasonable

Answer: 3+1+5+2+3+9+1-1-1=22

The total on the register is reasonable because if you estimate $21.77 to the nearest dollar you would get $22.00.

Step-by-step explanation:

The function that best represents the graph of the function which is given is:

               [tex]f(x)=(x-3)^2+1[/tex]

From the graph that is provided to us we observe that the graph passes through the point (3,1).

Hence, we will check which of the following function satisfies this point.

a)

[tex]f(x)=(x-3)^3-1[/tex]

when x=3 we see that:

[tex]f(x)=(3-3)^3-1\\\\i.e.\\\\f(x)=-1\neq 1[/tex]

Hence, option: a is incorrect.

c)

[tex]f(x)=(x+3)^3-1[/tex]

when x=3 we have:

[tex]f(3)=(3+3)^3-1\\\\i.e.\\\\f(3)=9^3-1\\\\i.e.\\\\f(3)=729-1\\\\f(3)=728\neq 1[/tex]

Hence, option: c is incorrect.

d)

[tex]f(x)=(x+3)^3+1[/tex]

when x=3 we have:

[tex]f(3)=(3+3)^3+1\\\\i.e.\\\\f(3)=9^3+1\\\\i.e.\\\\f(3)=729+1\\\\f(3)=730\neq 1[/tex]

Hence, option: d is incorrect.

Now we are left with option: b)

i.e.

b)

[tex]f(x)=(x-3)^2+1[/tex]

Also, when x=3 we have:

[tex]f(3)=(3-3)^2+1\\\\f(3)=0+1\\\\f(3)=1[/tex]

Hence, it passes through the point (3,1)

Also, when we will plot this function we observe that it matches the given graph.

Answer:

[tex]r=\frac{25-bh}{h}[/tex]

Step-by-step explanation:

Given : Consider the following equation, [tex]bh+hr=25[/tex]

To find : Solving for r ?

Solution :

The equation is [tex]bh+hr=25[/tex] solve for r,

Subtract 'bh' both side,

[tex]bh+hr-bh=25-bh[/tex]

[tex]hr=25-bh[/tex]

Divide both side by 'h',

[tex]\frac{hr}{h}=\frac{25-bh}{h}[/tex]

[tex]r=\frac{25-bh}{h}[/tex]

Therefore, [tex]r=\frac{25-bh}{h}[/tex]

Final answer:

To find the equation of the line perpendicular to 4x-3y=5 that passes through (3,1), we determine the negative reciprocal of the original line's slope, which is -3/4, and use the point-slope form to establish the new line's equation:

y = (-3/4)x + 13/4.

Explanation:

To write an equation of the line containing the point (3,1) and perpendicular to the line 4x−3y=5, first, we need to find the slope of the given line by rearranging the equation into slope-intercept form (y=mx+b), where m is the slope.

The line 4x - 3y = 5 can be rewritten as 3y = 4x - 5, or y = (4/3)x - 5/3. This gives us a slope of 4/3. The slope of a line perpendicular to this will be the negative reciprocal, hence the perpendicular slope is -3/4.

Next, given the point (3,1), we can use the point-slope form of a line's equation, which is y - y₁ = m(x - x₁), where (x₁,y₁) is the point the line passes through, and m is the slope. Substituting the values, we get y - 1 = (-3/4)(x - 3).

Finally, to express the equation in slope-intercept form (y=mx+b), we expand and simplify: y - 1 = (-3/4)x + 9/4, which gives us y = (-3/4)x + 13/4 as the equation of the line.

Answer: You could use straight angles as a counterexample for the argument all angles are either right obtuse or acute .

Final answer:

Louis spent a total of 3 hours practicing chords last week, which is 1/4 of the total 12 hours he dedicated to practicing guitar.

Explanation:

Louis spent 12 hours last week practicing guitar. To calculate the amount of time he spent practicing chords, we need to find 1/4 of 12 hours since 1/4 of the time was dedicated to chords.

Here is the calculation:

Divide the total time by 4 to find 1/4 of 12 hours: 12 hours ÷ 4 = 3 hours.

So, Louis spent 3 hours practicing chords last week.

The total number of sides in a polygon with n vertices is = n sides.

We have a Polygon with n vertices.

We have to determine the number of sides of this polygon.

In geometry, a polygon can be defined as a  plane, two-dimensional closed shape bounded with straight sides.

According to the question, we have -

A polygon with n vertices.

The total number of sides in a polygon with n vertices is = n sides.

The sides of the polygon are connected end to end in a cyclic order. The side with endpoints as nth and (n - 1)th vertices is connected to the side with endpoints as (n - 1)th and (n - 2)th vertices and so on.

Hence, the total number of sides in a polygon with n vertices is = n sides.

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