Subtract (3x^2 + 2x+4) - (x^2 +2x+1) =

Answer:

[tex]\frac{4x^2-3x}{(x+9)(x-4)}[/tex]

Step-by-step explanation:

The sum of two rational expressions is done in the following way:

[tex]\frac{a}{b}+\frac{c}{d} = \frac{a*d + c*b}{b*d}[/tex]

In this case we have the following rational expressions

[tex]\frac{3x}{x+9} + \frac{x}{x-4}[/tex]

So:

[tex]a=3x\\d=(x+9)\\c=x\\d=(x-4)[/tex]

Therefore

[tex]\frac{3x}{x+9} + \frac{x}{x-4}=\frac{3x(x-4)+x(x+9)}{(x+9)(x-4)}[/tex]

simplifying we obtain:

[tex]\frac{3x(x-4)+x(x+9)}{(x+9)(x-4)}=\frac{3x^2-12x+x^2+9x}{(x+9)(x-4)}\\\\\frac{3x^2-12x+x^2+9x}{(x+9)(x-4)}=\frac{4x^2-3x}{(x+9)(x-4)}[/tex]

Answer:

[tex]\frac{4x^2-3x}{(x+9)(x-4)}[/tex]

Step-by-step explanation:

We are given the following expression and we are to find the sum of this rational expression below:

[tex] \frac { 3 x } { x + 9 } + \frac { x } { x - 4 } [/tex]

Taking LCM of it to get:

[tex]\frac{3x}{x+9} =\frac{3x(x-4)}{(x+9)(x-4)}[/tex]

[tex]\frac{x}{x-4} =\frac{x(x+9)}{(x-4)(x+9)}[/tex]

[tex]\frac{3x(x-4)}{(x+9)(x-4)}+\frac{x(x+9)}{(x-4)(x+9)}[/tex]

[tex]\frac{3x(x-4)+x(x-9)}{(x+9)(x-4)}[/tex]

[tex]\frac{4x^2-3x}{(x+9)(x-4)}[/tex]

Answer:

x < -3

Step-by-step explanation:

using the distributive property, distribute 9(2x +1) so it's 18x + 9, subtract 9x from 18x, subtract 9 from -18, divide both sides by 9, x < -3

Inequality is a relationship between two numbers or two expressions.

The value of x in the solution set of 9(2x + 1) < 9x – 18 is

x < -3

i.e -2, -1, 0, 1, 2, 3, 4, ,,,,,,∞

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal =

Greater than and equal=

We have,

9(2x + 1) < 9x – 18

Remove the parenthesis.

9 x (2x) + 9 x 1 < 9x - 18

18x + 9 < 9x - 18

Subtract 9x on both sides.

18x + 9 - 9x < 9x - 18 - 9x

9x + 9 < -18

Subtract 9 on both sides.

9x + 9 - 9 < -18 - 9

9x < -27

Divide both sides by 9.

9x/9 < -27/9

x < -3

This means x is less than -3.

i.e -2, -1, 0, 1, 2, 3, 4, ,,,,,,∞

Thus,

The value of x in the solution set is x < -3.

i.e -2, -1, 0, 1, 2, 3, 4, ,,,,,,∞

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Answer: 120 people

Step-by-step explanation: To do this problem, you want to find common denominators. The lowest common denominator is 900. So to get the denominator to 900 from 30, multiply it by 30. 30 x 30=900. Multiply 4 by 30. 4 x 30=120. Another way to do this is to set up a proportion. It would be 4/30=x/900. Cross multiply and solve for x. 3600=30x. X=120.

Step-by-step explanation:

Given that line a is parallel to line b

∠6 = ∠2 = 36.5° (property of corresponding angles)

∠8 = 180° -∠6 (property of adjacent angles on a straight line)

∠8 = 180° - 36.5° = 143.5°  

Answer:

125-135

Step-by-step explanation:

The standard deviation is 7. This implies that the IQ scorings can be between 123 and 137. With a 90% confidence in these numbers, 125-135 is the closest interval to 90% confidence.

Answer: (129.04,130.96)

Step-by-step explanation:

Given : Sample size : n= 145

Mean IQ in the sample : [tex]\overline{x}=130[/tex]

Standard deviation : [tex]\sigma=7[/tex]

Significance level : [tex]\alpha=1-0.9=0.1[/tex]

Critical value : [tex]z_{\alpha/2}=1.645[/tex]

The confidence interval for population mean is given by :-

[tex]\overline{x}\pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}\\\\=130\pm(1.645)\dfrac{7}{\sqrt{145}}\\\\=130\pm0.96\\\\=(129.04,\ 130.96)[/tex]

Hence, the 90% confidence interval for the students' mean IQ score is (129.04,130.96)

Answer:

Graph 1: Consistent Dependent

Graph 2: Consistent Independent

Graph 3: Consistent Dependent

Graph 4: Inconsistent

Step-by-step explanation:

Consistent means they have at least one solution.  So lines that intersect once or lines that intersect infinitely many times are both consistent systems.

If they are the system that has one solution they are considered independent.

If they are the system that has infinitely many solutions then are considered dependent.

Inconsistent means they won't intersect at all.

First graph shows the same line graphed onto itself.  That means they have infinitely many solutions and is therefore a consistent dependent system.

Second graph shows the lines intersecting once.  That means they have one solution and therefore is a consistent independent system.

Third graph shows the same description of graph one and is therefore a consistent dependent system.

The last graph shows parallel lines. Parallel lines do not intersect and therefore do not have a solution.  So this system is inconsistent.

Answer:

125.59 feet

Step-by-step explanation:

(see attached)

For this case we must factor the following expression:[tex]x ^ 2-12x-20[/tex]

We have that the expression cannot be factored with rational numbers.

On the other hand, we can find the zeros, applying the quadratic formula we have:[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2 (a)}[/tex]

Where:

[tex]a = 1\\b = -12\\c = -20[/tex]

[tex]x = \frac {- (- 12) \pm \sqrt {(- 12) ^ 2-4 (1) (- 20)}} {2 (1)}\\x = \frac {12 \pm \sqrt {144-4 (1) (- 20)}} {2 (1)}\\x = \frac {12 \pm \sqrt {144 + 80}} {2}\\x = \frac {12 \pm \sqrt {224}} {2}\\x = \frac {12 \pm \sqrt {16 * 14}} {2}\\x = \frac {12 \pm4 \sqrt {14}} {2}[/tex]

Thus, the roots would be:

[tex]x_ {1} = 6 + 2 \sqrt {14}\\x_ {2} = 6-2 \sqrt {14}[/tex]

Answer:

the expression cannot be factored with rational numbers.

The factors of the given quadratic expression are: (x - 2) and (x - 10)

The quadratic expression is given as:

x² - 12x - 20

Now, to get the factors, we need to write as follows:

x² - 10x - 2x + 20

This can be factorized to get:

x(x - 10) - 2(x - 10)

= (x - 2)(x - 10)

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Answer:

A = 95.03in² or 95.03 ( rounded to the nearest hundredth )

Step-by-step explanation:

The approximate area of a circle that has a diameter of 11 inches, rounded to the nearest hundredth is 95.03.

Formula: A=1/4πd²

A=1

4πd^2=95.03.

4·π·11^2≈95.03318in²

Answer:

611.04 mm³

Step-by-step explanation:

The area (A) of a parallelogram is calculated as

A = bh ( b is the base and h the perpendicular height )

here b = 30.4 and h = 20.1, hence

A = 30.4 × 20.1 = 611.04 mm³

Answer:

611.04 mm³

Step-by-step explanation:

Formula for finding the area of a parallelogram: A = B * H

B is base, H is height, * is multiply.

_________________________________________________

The area of the parallelogram pictured: 611.04 mm³

A=bh=30.4·20.1=611.04

_________________________________________________

Answer:

10a-4b+2c

Step-by-step explanation:

Answer:

10a -4b +2c

Step-by-step explanation:

6a-4b+c and 4a+c

6a-4b+c + 4a+c

Combine like terms

6a+4a   + (-4b) + c+c

10a -4b +2c

ANSWER

a. 12 units

EXPLANATION

According to the altitude theorem, RT which is the altitude, is equal to the geometric mean of TQ and TS, the segments created by the foot of the altitude on the hypotenuse.

This implies that:

[tex]x = \sqrt{TQ \times TS} [/tex]

From the diagram, TQ=16 and TS=9.

We substitute these values and solve for x.

[tex]x = \sqrt{9 \times 16} [/tex]

[tex]x = \sqrt{144} [/tex]

[tex]x = 12[/tex]

Therefore x is 12 units.

The correct answer is A

Answer:

Step-by-step explanation:

In each parallelogram opposite sides have the same length.

Therefore we have the equations:

2x - 4 = x + 12 and 3y - 2 = y + 6

2x - 4 = x + 12         add 4 to both sides

2x = x + 16         subtract x from both sides

x = 16

3y - 2 = y + 6            add 2 to both sides

3y = y + 8           subtract y from both sides

2y = 8            divide both sides by 2

y = 4

AB = 3y - 2 → AB = 3(4) - 2 = 12 - 2 = 10

BC = x + 12 → BC = 16 + 12 = 28

Answer:

D

Step-by-step explanation:

Answer:

[tex]\large\boxed{x=\dfrac{1}{2}-\sqrt2\ or\ x=\dfrac{1}{2}+\sqrt2}[/tex]

Step-by-step explanation:

[tex]\text{The quadratic formula of}\ ax^2+bx+c=0:\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

[tex]\text{We have:}\\\\4x^2-7=4x\qquad\text{subtract}\ 4x\ \text{from both sides}\\\\4x^2-4x-7=0\\\\a=4,\ b=-4,\ c=-7\\\\b^2-4ac=(-4)^2-4(4)(-7)=16+112=128\\\\\sqrt{b^2-4ac}=\sqrt{128}=\sqrt{64\cdot2}=\sqrt{64}\cdot\sqrt2=8\sqrt2\\\\x=\dfrac{-(-4)\pm8\sqrt2}{(2)(4)}=\dfrac{4\pm8\sqrt2}{8}\qquad\text{simplify by 4}\\\\x=\dfrac{1\pm2\sqrt2}{2}\to x=\dfrac{1}{2}\pm\sqrt2[/tex]

Answer:

f(x) = -1.25

Step-by-step explanation:

Substitute x with -5, so our equation would look this:

Note: We were already given the value of x

f(x) = 1/4(-5)

Multiply 1/4 and -5:

1/4 * -5 = -1.25

So, our answer would be -1.25

-1.25

In order to find the answer to your question, we're going to need to plug in a number to the variable x.

We know that x = -5

This means that whenever you see x, you would replace it with what it equals to. In this case, we would plug in -5 to x, since that's what it equals to.

Your equation would look like this:

[tex]\frac{1}{4}( -5)[/tex]

Now, you would solve to get your answer.

[tex]\frac{1}{4} (-5)=-1.25\\\\\text{1/4 is the same as 0.25} \\\\0.25(-5)=-1.25[/tex]

Once you're done solving, you should get -1.25

This means that f(x) = -1.25

Answer: B

Step-by-step explanation:

Because m<7 and m<6 share a vertex and doesn’t share any common sides and they are across from each other which means they are vertical and vertical angles are congruent

The missing reason for the 3rd step will be vertical angles are congruent. Then the correct option is B.

The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.

Corresponding angle - If two lines are parallel then the third line. The corresponding angles are equal angles.

Vertically opposite angle - When two lines intersect, then their opposite angles are equal.

The diagram is given below.

Then the missing reason for the 3rd step will be vertical angles are congruent.

Thus, the correct option is B.

More about the angled link is given below.

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[tex]\huge{\boxed{y=\frac{1}{2} x+1}}[/tex]

First, we must find the slope of the graphed line. We can use the formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are known points on the line.

Plug in the values. [tex]\frac{4-2}{-1-0}[/tex]

Subtract. [tex]\frac{2}{-1}[/tex]

Simplify. [tex]-2[/tex]

To find the slope of the perpendicular line, we must find the opposite inverse slope. This means we first need to multiply it by [tex]-1[/tex], then we need to swap the numerator and denominator.

[tex]-2*-1=2[/tex]

Now, swap the numerator and denominator. The numerator is [tex]2[/tex], and the denominator is [tex]1[/tex] by default.

[tex]\frac{1}{2}[/tex]

The only answer choice with a slope of [tex]\frac{1}{2}[/tex] is [tex]\boxed{y=\frac{1}{2} x+1}[/tex]

Answer:

It shows that  h varies directly with V and inversely with l and w.

Step-by-step explanation:

The given equation is:

h = V/lw

It shows that  h varies directly with V and inversely with l and w.

Inversely means if the value of one entity increases, the value of second entity decreases or vice versa. Directly related means as one quantity increases, another quantity increases at the same rate

We can show it as h=1/lw which means  h is in inverse relation with l and w and in direct relation with V....

Answer:

There will be 96 lemmings in 7 years

Step-by-step explanation:

we have

[tex]f(x)=200(0.901)^{x}[/tex]

This is a exponential function

where

x ------> the time in years

f(x) ----> lemming population

so

For x=7 years

substitute in the function

[tex]f(7)=200(0.901)^{7}[/tex]

[tex]f(7)=96.4[/tex]

There will be 96 lemmings in 7 years

ANSWER

[tex]y = 2( {x - 4)}^{2} - 3[/tex]

EXPLANATION

The function equation of a parabola that opens up in vertex form is given by

[tex]y = a( {x - h)}^{2} + k[/tex]

where (h,k) is the vertex and 'a' is the leading coefficient.

The given graph is a parabola that opens up and has its vertex at (4,-3).

This implies that, h=4 and y=-3

We substitute these values into the vertex form to obtain,

[tex]y =a( {x - 4)}^{2} + - 3[/tex]

This simplifies to,

[tex]y =a( {x - 4)}^{2} - 3[/tex]

The graph also contains (3,-1). We plug x=3 and y=-1 into the equation to find the value of 'a'.

[tex] - 1=a( {3 - 4)}^{2} - 3[/tex]

[tex] - 1 + 3 = a( { - 1})^{2} [/tex]

[tex]2 = a[/tex]

We substitute this value to get:

[tex]y = 2( {x - 4)}^{2} - 3[/tex]

The last choice is correct.

Answer:

A

Step-by-step explanation:

The graphs of two functions y=f(x) and y=g(x) intersect at one point. The coordinates of this point are (0,-2). This means

f(0)=-2

g(0)=-2

Thus,

f(0)=g(0)

Note that the blue line passes through the point (-2,4), so

f(-2)=4

and the red line passes through the point (-2,-4), so

g(-2)=-4

Hence,

f(-2)≠g(-2)

and f(0)≠g(-2)

Answer:

First Option

Step-by-step explanation:

It can be seen in the graph that the two plotted functions are linear, which means that if the lines are not parallel or not lying on each other, then the lines will intersect at most one point in the plane. It can be clearly seen that both the lines intersect at the point (0,-2). As far as the functions are concerned, there is an input and an associated output. The term f(0) means that 0 is the input and f(0) is the functional value, which is the output. In the graph, both lines have the y-intercept of -2. Y-intercept is the point where the value of the input (i.e. the value of x) is 0. Since both lines are intersecting at (0,-2), this implies that f(0) = g(0). This essentially means that the the functional value of f, which is -2, is equal to the functional value of g!!!

Answer:

Mechanic A worked for 5 hours and Mechanic B worked for 15 hours

I hope my answer and explanation helped!

okay to get started you need to make a system of equations:

x= number of hours worked by mechanic A

y= number of hours worked by mechanic B

x + y= 20

95x + 60y= 1375

substitute in an equation:

x + y= 20

y= 20- x

95x + 60(20-x)=1375

Solve for x

95x + 1200 - 60x=1375

35x =175

x= 5

plug in x to solve for y

x + y= 20

5 + y= 20

y=15

Check work

then you're done :D

Given a quadratic equation [tex]ax^2+bx+c=0[/tex], the two solution (if they exist) are given by the formula

[tex]x_{1,2}=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

In your case, the coefficients are

[tex]a=3,\quad b=5,\quad c=2[/tex]

So the quadratic formula becomes

[tex]x_{1,2}=\dfrac{-5\pm\sqrt{25-24}}{6} = \dfrac{-5\pm 1}{6}[/tex]

So, the two solutions are

[tex]x_1 = \dfrac{-5+1}{6}=-\dfrac{4}{6}=-\dfrac{2}{3}[/tex]

[tex]x_2 = \dfrac{-5-1}{6}=-\dfrac{6}{6}=-1[/tex]

Answer:

D. Y+5=-(1/2)*(x+3)

Step-by-step explanation:

Perpendicular Lines are those with the following condition:

y=a*x+b (1)

y=c*x+d (2)

Where 'a' and 'c' are the respective slope

If These two lines are perpendicular, then

a=- 1/c

Equation (1) for our case is written as y=2x-8, meaning that a=2 and b = -8

Using those principles we have that the slope for our needed line ('c') has to be -(1/2).

Now we most use the given point to find the remaining term of the equation (d) so, evaluate (-3,-5) in eq (2) to have this:

-5=(-1/2)*(-3)+d

resulting that d=-5-(3/2)

Eq (2) is written now as the following: y= (-1/2)*x - (5+3/2)

Rearranging terms, we have the following:

y+5=(-1/2)*x-(3/2)

where you can obtain a more pretty expression:

y+5=(-1/2)*(x+3)

Answer:

1/34 or 2.94%

Step-by-step explanation:

There is only one paper that has your name on it out of 34 papers. So there is a 1 out of 34 chance your name is drawn.

You have write this as a fraction 1/34 or as a percentage 2.94%

Final answer:

The probability that your name will be drawn first in a contest with 34 entrants is 1 in 34, based on the principle of equally likely outcomes in a random selection process.

Explanation:

The probability of any one person being chosen first in a random draw from a group of 34 people is based on the principle that each person has an equal chance of being selected. To determine this probability, we use the concept of equally likely outcomes, which suggests that each person has 1 chance in the total number of people competing. Therefore, the probability that your name will be drawn first from a group of 34 people is 1 in 34.

[tex]

-3(2x-5)<5(2-x) \\

-6x+15<10-5x \\

-x<-5 \\

\boxed{x>5}

[/tex]

Hope this helps.

r3t40