Simplify the expression –3(x + 3)2 – 3 + 3x. What is the simplified expression in standard form?

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: 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.

Answer:

The correct answer is first option

u² - 11u + 24 = 0

When u = (x² - 1)

Step-by-step explanation:

It is given that,

(x² - 1)² - (x² - 1) + 24 = 0

To find the correct answer

Substitute u = x² - 1

The equation becomes,

u² - 11u + 24 = 0 Where u = (x² - 1)

Therefore the correct answer is first option

u² - 11u + 24 = 0

When u = (x² - 1)

Answer:

u² - 11u + 24 = 0 is equivalent to (x²-1)² - 11(x²-1) + 24 = 0

Step-by-step explanation:

(x²-1)² - 11(x²-1) + 24 = 0

Evaluate each equation by substituting the value of u to match the equation above.

1) u² - 11u + 24 = 0 where u = (x² - 1)

(x²-1)² - 11(x²-1) + 24 = 0

This equation matches (x²-1)² - 11(x²-1) + 24 = 0

2) (u²)² - 11(u²) + 24 where u = (x² - 1)

[(x²-1)²]² - 11(x²-1)² + 24

This equation does not match (x²-1)² - 11(x²-1) + 24 = 0

3) u² + 1 - 11u +24 = 0 where u = (x² - 1)

(x² - 1)² + 1 - 11(x²-1) + 24 = 0

This equation does not match (x²-1)² - 11(x²-1) + 24 = 0

4) (u² - 1)² - 11(u² - 1) + 24 where u = (x² - 1)

[(x²-1)²-1]² - 11(u² - 1)² + 24

This equation does not match (x²-1)² - 11(x²-1) + 24 = 0

Therefore, the first quadratic equation is equivalent to (x²-1)² - 11(x²-1) + 24 =0.

!!

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:

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:

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:

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

Put the given y-intercept b = 7 and the coordinates of the point (-2, 1) to the equation:

[tex]1=-2m+7[/tex]          subtract 7 from both sides

[tex]-6=-2m[/tex]       divide both sides by (-2)

[tex]3=m\to m=3[/tex]

We have the equation:

[tex]y=3x+7[/tex]

Convert it to the general form [tex]Ax+By+C=0[/tex]:

[tex]y=3x+7[/tex]              subtract 3x and 7 from both sides

[tex]-3x+y-7=0[/tex]           change the signs

[tex]3x-y+7=0[/tex]

Answer:

QT = RT

Step-by-step explanation:

When drawing triangle PQR the perpendicular bisector cuts the triangle in half, which results in two sides that are congruent. This makes QT and RT congruent.

Based on the triangle QPR  option C) PQ = PR and A) QT = RT

Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure.

In QPR

∠Q = ∠R (∵ PT is a bisector)

∴QT = RT (∵ PT is a bisector of QR)

PT is a common  between PQT and RQT

∴PQ = PR ( by congruent part of congruent triangle)

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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

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:

C. (4y -1)(3y+2)

Step-by-step explanation:

12 y^2 + 5 y - 2

12 y^2 + (-3+8) y - 2

12 y^2 - 3y + 8y - 2

3y(4y-1)+2(4y-1)

(4y-1)(3y+2)

[tex]

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

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

-x<-5 \\

\boxed{x>5}

[/tex]

Hope this helps.

r3t40

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:

[tex]a_{20} = 12+3(20-1)[/tex]

Step-by-step explanation:

Answer:

its a)the first sequence is geometric bc of the common ratio of 2. the second sequence is arithmetic bc of the common difference of 7.

Option (A) the first sequence is geometric because there is a common ratio of 2 and the second sequence is arithmetic because there is a common difference of 7 is the correct answer.

Number pattern is a pattern or sequence in a series of numbers. This pattern generally establishes a common relationship between all numbers. A recursive pattern rule is a pattern rule that tells you the start number of a pattern and how the pattern continues.

For the given situation,

First sequence: 5, 10, 20, 40..

Second sequence: 8, 15, 22, 29, ...

Now consider the first sequence: 5, 10, 20, 40..

Here, when we divide the second number by first number, we get the common ratio as 2.

⇒ [tex]\frac{10}{5}=2[/tex]

⇒ [tex]\frac{20}{10}=2[/tex]

⇒ [tex]\frac{40}{20}=2[/tex]

Thus the first sequence follows a geometric progression with common ratio 2.

Now consider the second sequence: 8, 15, 22, 29, ...

Here, when we subtract the first term is subtracted from the second term, the common difference is 7.

⇒ [tex]15-8=7[/tex]

⇒ [tex]22-18=7[/tex]

⇒ [tex]29-22=7[/tex]

Hence we can conclude that option (A) the first sequence is geometric because there is a common ratio of 2 and the second sequence is arithmetic because there is a common difference of 7 is the correct answer.

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Answer:

C. anus

Step-by-step explanation:

The digestive system ends at the anus.

Therefore, it does not end in the colon, large intestine, or small intestine.

The digestive system starts when you take in food and ends in the anus.

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:

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:

The distance between the Earth and the Moon is equal to the distance between the Sun and the Moon multiplied by the sine of angle x

Step-by-step explanation:

Let

EM -----> the distance between the Earth and the Moon.

y -----> the distance between the Sun and the Moon.

we know that

In the right triangle of the figure

The sine of angle x is equal to divide the opposite side to angle x (distance between the Earth and the Moon.) by the hypotenuse ( distance between the Sun and the Moon)

so

sin(x)=EM/y

Solve for EM

EM=(y)sin(x)

therefore

The distance between the Earth and the Moon is equal to the distance between the Sun and the Moon multiplied by the sine of angle x

Answer:

6

Step-by-step explanation:

Because AD and BC Are congruent so when you add them that would equal the diameter of the rapper.

Option D is correct. The smallest diameter of wrapper that will fit the candy bar is 6

According to the attached figure - the cross-sectional view of candy bar ABC. If a cylindrical container is created from the cross-section, then the diameter of the cylindrical container formed from the cross-section will be the side AC.

From the figure, AD = DC and AC = AD + DC

Given the segment AD = 3cm

AC = AD + AD (Since AD = DC)

AC = 2AD

AC = 2(3)

AC = 6

This shows that the smallest diameter of wrapper that will fit the candy bar is 6. Option D is correct

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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]

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:

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:

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:

[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:

125.59 feet

Step-by-step explanation:

(see attached)

Answer:

that the linear scale factor is  4:3 which can be written as 4/3

the volume scale factor will be:

(4/3)^3

D. 64:27

Step-by-step explanation:

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.