Patterns and lines for (0,0) (4,-12)

Answer:

[tex]\dfrac{\sqrt{40}\cdot \sqrt{40}}{2}[/tex]

Step-by-step explanation:

The length of the base is the distance between the points 4+2i and 10+4i, so

[tex]\text{Base}=|10+4i-(4+2i)|=|10+4i-4-2i|=|6+2i|=\sqrt{6^2+2^2}=\\ \\=\sqrt{36+4}=\sqrt{40}[/tex]

The middle point of the base is placed at point

[tex]\dfrac{4+2i+10+4i}{2}=\dfrac{6i+14}{2}=7+3i[/tex]

The length of the height is the distance between the points 5+9i and 7+3i

[tex]\text{Height}=|5+9i-(7+3i)|=|5+9i-7-3i|=|-2+6i|=\sqrt{(-2)^2+6^2}=\\ \\=\sqrt{4+36}=\sqrt{40}[/tex]

So, the area of the triangle is

[tex]A=\dfrac{1}{2}\cdot \text{Base}\cdot \text{Height}=\dfrac{\sqrt{40}\cdot \sqrt{40}}{2}[/tex]

Answer:

A

Step-by-step explanation:

did on edge

Answer:

2m^2 / n.

Step-by-step explanation:

4m^3/n^2 / 2m/n.

Invert the last term and multiply:

= 4m^3 / n^2 *  n/2m

= 4m^3 n / 2mn^2

= 2m^2 / n.

Answer:

2m^2 / n.

Step-by-step explanation:

Answer:

The equation of the parallel line is x + 2y = a

Step-by-step explanation:

* lets revise the general form of the linear equation

- The general form of the linear equation is ax + by + c = 0, where

 a , b , c are real numbers

- The linear equation represented by a line its slope = -a/b and

  intersects the y-axis at point (0 , -c/b) means y-intercept = -c/b

- The parallel lines have equal slopes and different y-intercepts

* Now lets solve the problem

- There is a line with equation x + 2y = 7

- Put the equation in the general form

∵ x + 2y = 7 ⇒ subtract 7 from both sides

∴ x + 2y - 7 = 0

∵ ax + by + c = 0 is the general form of the linear equation

∴ a = 1 , b = 2 , c = -7

∵ The slope of the line is -a/b

∴ The slope of the line -1/2

- We need to find the equation of the parallel line which has the

  same slope

∵ The two lines are parallel

∴ Their slopes are equal

∴ The slope of the line is -1/2

∵ The slope depends on a and b

∴ The line has the same value of a and b

∵ a = 1 and b = 2

∵ ax + by + c = 0

∴ The equation of the line is x + 2y + c = 0

- To find c substitute x and y in the equation by the coordinates of

  any point on the line

∵ The line passing through point (a , 0)

- Substitute x by a and y by 0

∴ a + 2(0) + c = =

∴ a + c = 0 ⇒ subtract a from both sides

∴ c = -a

- Substitute the value of c in the equation by - a

∴ The equation of the line is x + 2y - a = 0 ⇒ add a for both sides

∴ The equation of the line is x + 2y = a

* The equation of the parallel line is x + 2y = a

- They are equal in slopes and different in y-intercepts

Final answer:

The equation of the line passing through the point (a, 0) and parallel to x + 2y = 7 is y = -0.5x + 0.

Explanation:

To find the equation of a line parallel to the line x + 2y = 7 and passing through the point (a, 0), we need to determine its slope. This can be done by rearranging the given equation in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.

First, we rewrite the given equation as 2y = -x + 7 and then divide everything by 2 to get y = -0.5x + 3.5. Since the line we're looking for is parallel to this line, it will have the same slope of -0.5.

So, the equation of the line passing through (a, 0) and parallel to x + 2y = 7 is y = -0.5x + 0.

Answer:

Part 1) Option a. [tex]240\ dices[/tex]

Part 2) Option c. [tex]9.156.24\ pounds[/tex]

Step-by-step explanation:

Part 1)

step 1

Find the volume of one dice

The volume is equal to

[tex]V=b^{3}[/tex]

we have

[tex]b=2\ cm[/tex]

substitute

[tex]V=2^{3}=8\ cm^{3}[/tex]

step 2

Find the volume of the box

The volume is equal to

[tex]V=LWH[/tex]

we have

[tex]L=20\ cm[/tex]

[tex]W=12\ cm[/tex]

[tex]H=8\ cm[/tex]

substitute

[tex]V=20*12*8=1,920\ cm^{3}[/tex]

step 3

Find the number of dices

Divide the volume of the box by the volume of one dice

[tex]1,920/8=240\ dices[/tex]

Part 2)

step 1

Find the volume of the cylinder

The volume is equal to

[tex]V=\pi r^{2} h[/tex]

we have

[tex]r=9\ ft[/tex]

[tex]h=12\ ft[/tex]

assume

[tex]\pi =3.14[/tex]

substitute

[tex]V=(3.14)(9)^{2}(12)[/tex]

[tex]V=3,052.08\ ft^{3}[/tex]

step 2

Find how many pounds of sand will fit into the cylinder

using proportion

[tex]\frac{3}{1}\frac{pounds}{ft^{3}}=\frac{x}{3,052.08}\frac{pounds}{ft^{3}}\\ \\x=3,052.08*3\\ \\x=9.156.24\ pounds[/tex]

Answer:

see explanation

Step-by-step explanation:

letting u = x - 4 means the equation can now be expressed as a quadratic

u² - u - 6 = 0 ← quadratic equation in u

Answer:

[tex]u^2 - u - 6 = 0[/tex]

Step-by-step explanation:

We are given [tex](x - 4)^2 - (x -4) -6 = 0[/tex] and u = x - 4

Now we have to replace (X - 4) by "u".

So, we get

[tex]u^2 - u - 6 = 0[/tex]

Here the highest degrees of the equation is 2. Which is called a quadratic equation.

The general form of quadratic equation is [tex]ax^2 + bx + c = 0[/tex], where a≠ 0.

Therefore, the answer is [tex]u^2 - u - 6 = 0[/tex]

Answer:

x^1/12

Step-by-step explanation:

Hope this helped!

Answer:

7512 hours

Step-by-step explanation:

There are 8760 hours in a year.

There are 52 hours on Thursdays and Saturdays in a year.

The number of hours for Thurdays and Saturdays in a year is 1248.

8760-1248= 7512

thursdays and saturdays are the best days

The measures of angle POS and angle POQ cannot be determined without further information.

The measures of angle POS and angle POQ can vary depending on the context of the problem or the given information. Without specific details, we cannot determine the exact measures of these angles.

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[tex](100\%-15\%-25\%)\cdot240=60\%\cdot240=144[/tex]

Answer:

C) 144

Step-by-step explanation:

Somewhat Dissatisfied is 15%, and Completely Dissatisfied is 25%. The two dissatisfied parts add to 40%.

That means the two satisfied parts add to 60%.

60% were either Somewhat Satisfied or Completely Satisfied.

240 customers responded to the survey.

60% of 240 = 0.6 * 240 = 144

Answer: C) 144

Answer: Max should read 22 full pages a day, and he will have 16 pages left to read.

Step-by-step explanation:

First, divide 676 by 30. The answer you get is 22.53.

This means that Max should read 22 pages a day.

Next, you should multiple 22 by 30. The answer you get is 660.

Finally, subtract 660 from 676. You will end up with 16.

Answer:

22 R 16

Step-by-step explanation:

log₁₆64 is3/2

The logarithm is exponentiation's opposite function in mathematics. This indicates that the exponent to which a fixed number, base b, must be raised in order to create a specific number x, is represented by the logarithm of that number.

Given

log₁₆(64) = x

16ˣ=64

(2⁴)ˣ=2⁶

2⁴ˣ=2⁶

4x=6

x=3/2

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The log₁₆64 exists 3/2. Therefore, the correct answer is option c.3/2.

The logarithm exists as exponentiation's opposite function in mathematics. This signifies that the exponent to which a fixed number, base b, must be presented to make a specific number x, exists characterized by the logarithm of that number.

Given:

log₁₆(64) = x

16ˣ = 64

Simplifying the above equation, we get

(2⁴)ˣ = 2⁶

2⁴ˣ = 2⁶

4x = 6

x = 3/2

log₁₆(64) = 3/2.

Therefore, the correct answer is option c.3/2.

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Answer:

(x + 2)(x - 8)

Step-by-step explanation:

You had your signs altered. You want your B to result in -6, not 6.

I am joyous to assist you anytime.

[tex]\bf \textit{recall that }i^2=-1 \\\\[-0.35em] ~\dotfill\\\\ x^2+25\implies x^2+5^2\implies x^2-(-5^2)\implies x^2-(-1\cdot 5^2)\implies x^2-(i^2\cdot 5^2) \\\\\\ \stackrel{\textit{difference of squares}}{x^2-(5i)^2}\implies (x-5i)(x+5i)[/tex]

Answer:

The correct option is A.

Step-by-step explanation:

The given expression is

[tex]x^2+25[/tex]

[tex]x^2+5^2[/tex]

[tex]x^2-(-5^2)[/tex]

We know that [tex]i^2=-1[/tex].

Using this value the given expression can be written as

[tex]x^2-(i^25^2)[/tex]

[tex]x^2-(5i)^2)[/tex]              [tex][\because a^mb^m=(ab)^m][/tex]

[tex](x-5i)(x+5i)[/tex]             [tex][\because a^2-b^2=(a-b)(a+b)][/tex]

The given expression is equal to the expression (x-5i)(x+5i).

Therefore the correct option is A.

Answer:

45

Step-by-step explanation:

every term in the sequence is 3 more than the last, so:

12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45

1 2 3 4 5 6 7 8 9 10 11 12

45 is the 12th term

Answer:

Option b - 45

Step-by-step explanation:

Given : Sequence 12,15,18,21,...

To find : What is the 12th term in the sequence?

Solution :

Sequence 12,15,18,21,... is an arithmetic progression.

Where, first term is a=12

Common difference is d=15-12=3

The nth term of the sequence is

[tex]a_n=a+(n-1)d[/tex]

The 12th term is

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

[tex]a_{12}=12+(11)(3)[/tex]

[tex]a_{12}=12+33[/tex]

[tex]a_{12}=45[/tex]

Therefore, The 12th term of the sequence is 45.

So, Option b is correct.

Answer:

1st box ⇒ perpendicular

2nd box ⇒ B and E

3rd box ⇒ congruent

Step-by-step explanation:

* Lets revise the case SAS of similarity

- SAS similarity : In two triangles, if two sets of corresponding sides  

   are proportional and the included angles are equal then the two  

   triangles are similar.

- Example : In triangle ABC and DEF, if m∠A = m∠D and  

  AB/DE = AC/DF then the two triangles are similar by SAS

* Lets solve the problem

- In Δ ABC and Δ DEF

∵ AB/DE = BC/EF = 1/2

- That means two sets of corresponding sides are proportion

∵ AB is a vertical side and BC is a horizontal side

∵ DE is a vertical side and EF is a horizontal side

∵ Horizontal and vertical lines are perpendicular

∴ AB ⊥ BC and DE ⊥ EF

- So angles B and E are right angles by definition of perpendicular

   lines

∵ All right angles are congruent

∴ m∠B = m∠D

∵ The two triangles have two sets of corresponding sides are

  proportion and the included angles are equal then the two

  triangles are similar

∴ △ABC ~ △DEF by the SAS similarity theorem

Answer:

1. Perpendicular

2. B and E

3. Congruent

Step-by-step explanation:

Horizontal and vertical lines are always perpendicular. So, the answer for the first gap is PERPENDICULAR.

Line BC is horizontal line, line AB is vertical line, so lines BC and AB are perpendicular and, therefore, angle B is right angle. Line EF is horizontal line, line ED is vertical line, so lines EF and ED are perpendicular and, therefore, angle E is right angle. So, answer for the second option is angles B and E.

Every two right angles are congruent.

Having two pairs of proportional sides and a pair of congruent adjacent angles, you can apply SAS similarity Postulate.

Answer:sanjay

Step-by-step explanation:

Answer:

Joseph will have to pay $133.20 for the television.

Step-by-step explanation:

740 x 0.6 = 444

444 x 0.3 = 133.2

Answer:

133.20

Step-by-step explanation:

First we need to find the cost of the tv on sale

The discount is 740 * 40%

740 *.4

296

The new price is the original price minus the discount

740 -296

444

Joseph has to pay 30% of the cost

444* 30%

444 *.3

133.2

He will have to pay 133.20

[tex]\bf 3\sqrt{8\frac{1}{4}}~\hfill \stackrel{mixed}{8\frac{1}{4}}\implies \cfrac{8\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{33}{4}} \\\\\\ 3\sqrt{\cfrac{33}{4}}\implies 3\cdot \cfrac{\sqrt{33}}{\sqrt{4}}\implies 3\cdot \cfrac{\sqrt{33}}{\sqrt{2^2}}\implies \cfrac{3\sqrt{33}}{2}[/tex]

Answer:

Step-by-step explanation:

[tex]\text{The formula of volumes of:}\\\\a\ cone:\ V_{cone}=\dfrac{1}{3}\pi r_1^2H_1\\\\a\ cylinder:\ V_{cylinder}=\pi r_2^2H_2\\\\\text{If cone and cylinder are with the same radius and height, then:}\\\\r_1=r_2=r\ \text{and}\ H_1=H_2=H\\\\V_{cone}=\dfrac{1}{3}\pi r^2H,\ V_{cylinder}=\pi r^2H\to V_{cone}=\dfrac{1}{3}V_{cylinder}[/tex]

Step-by-step explanation:

refer the attachment......

ANSWER

C. x=2

EXPLANATION

The given equation is

[tex] \frac{x + 4}{6x} = \frac{1}{x} [/tex]

Cross multiply to get,

[tex]6x = x(x + 4)[/tex]

Expand to get:

[tex]6x = {x}^{2} + 4x[/tex]

[tex] {x}^{2} + 4x - 6x = 0[/tex]

[tex] {x}^{2} - 2x = 0[/tex]

[tex]x(x - 2) = 0[/tex]

[tex]x = 0 \: or \: x = 2[/tex]

But the domain is

[tex]x \ne0[/tex]

Therefore the solution is x=2.

ANSWER

He did not square 40, he just multiplied by 2.

EXPLANATION

According to the Pythagoras Theorem, the sum of the square of the shorter legs equals the square of the Hypotenuse.

Hans correctly applied the Pythagoras Theorem to obtain:

[tex] {9}^{2} + {40}^{2} = {c}^{2} [/tex]

The next correct step is to evaluate the squares to obtain:

[tex]9 \times 9+ {40} \times 40= {c}^{2} [/tex]

Which gives

[tex]81+1600= {c}^{2} [/tex]

But Hans mistakenly multiplied the exponent of the second square by the base to get

[tex]9 \times 9+ {40} \times2= {c}^{2} [/tex]

Which simplifies to;

[tex]81+ 80= {c}^{2} [/tex]

Therefore the error is that,he did not square 40, he just multiplied by 2.

The first choice is correct.

Answer:

Error: He did not square 40, he multiplied by 2

In calculation of 40² ( Correct was 1600 but he did 80)

The length of hypotenuse is 41 cm

Step-by-step explanation:

Given: In the given right angle triangle.

The two legs are 40 and 9.

The hypotenuse is c

Using Pythagoras theorem,

[tex]c^2=a^2+b^2[/tex]

where, a and b are legs and c is hypotenuse

a=40 , b=9

Substitute into formula

[tex]c^2=40^2+9^2[/tex]

[tex]c^2=1600+81[/tex]     Error        

Hans did mistake here to calculate square of 40.

instead of square Hans multiply 40 and 2.

[tex]c^2=1600+81[/tex]  

[tex]c^2=1681[/tex]

Taking square root

[tex]c=\sqrt{1681}[/tex]

[tex]c=41[/tex]

Hence, The length of hypotenuse is 41 cm

Error: In calculation of 40²

Answer:

Improper fraction (-81t/ 4s)

Mixed number (-20 1/4) (t/s)

Step-by-step explanation:

Multiply the numerators

9(9t) = 81t

Multiply the denominators

4s* (-1) = -4s

Put the numerator over the denominator

81t / -4s

If they want the answer as an improper fraction  -81t/4s

If they want a mixed number

81/4 = 20 with 1 left over

20 1/4

Then multiply by (-t/w)

(-20 1/4) (t/s)

ANSWER

[tex]{(x + 1)}^{2} =12(y - 2)[/tex]

EXPLANATION

The original parabola has equation

[tex] {x}^{2} = 12y[/tex]

This parabola has its vertex at the origin:

If the parabola is shifted one unit left and two units up, then its new vertex is at (-1,2).

The equation of the new parabola is now of the form:

[tex] {(x - h)}^{2} =1 2(y - k)[/tex]

where (h,k) is the vertex.

Substitute the vertex to get:

[tex] {(x - - 1)}^{2} =12(y - 2)[/tex]

[tex]{(x + 1)}^{2} =12(y - 2)[/tex]

Answer:

C, D, A

Step-by-step explanation:

[tex]a_n=4n+16[/tex]

Answer:

+4

Step-by-step explanation:

36-4=32

32-4=28

28-4=24

24-4=20

20+4=24

24+4=28

28+4=32

32+4=36

Answer: B

Step-by-step explanation:

x^1/2 is equal to √x meaning that the denominator will be the number in front of the √ sign.

so...

x^5/3 y^1/3 will be right

Answer: 4. The graph of f(2) will be above the graph of g(2) for all values of x

1. y is always 22 no matter what x value, g(2) = 22. However f(x) is a linear equation which increases vertically right up, so the y = (-∞, ∞ )

So not accurate

2. f(x) meets y axis at (0,50) while g(x) meets at (0,22), however, g(2) is (2,22) while f(x) is 190.

So not accurate

3. graph g(x) is not above f(2)

4. It is accurate

Answer:

Step-by-step explanation:

(4/5)n = (2/3)

move 4/5 to the right

n = (2/3)/(4/5)

n = 5/6

Answer:(–8, 8) and (2, 2) (–2, 1) and (3, –2)

Step-by-step explanation:

Answer:

Option B is correct.

Step-by-step explanation:

[tex]\sqrt[5]{32x^5y^10z^15}[/tex]

We need to solve the above expression.

32 = 2x2x2x2x2 = 2^5

and we know 5√ = 1/5

solving

[tex]=\sqrt[5]{2^5x^5y^{10}z^{15}}\\=(2^5)^{1/5}(5x^5)^{1/5}(y^{10})^{1/5}(z^{15})^{1/5}\\=2xy^2z^3[/tex]

So, simplified form is 2xy^2z^3

So, Option B is correct.