Evaluate 3x for x = −2, x = 1, and x = 3. Question 18 options: A) 1∕3, 0, 9 B) 1∕9, 3, 27 C) 9, 3, 27 D) 1∕9, 9, 27

Answer:

Step-by-step explanation:

d = √(x₂ - x₁)² + (y₂ - y₁)²

x₂ = 1

x₁ = - 2 1/2 = - 5/2

y₂ = - 3

y₁ = - 3

d = √( 1 + 5/2)² + (- 3 + 3)²

= √(2/2 + 5/2) + 0

= √(7/2)²

= 7/2

= 3  1/2

Answer:

D

Step-by-step explanation:

(-2 1/2, -3) = (-5/2 , -3)    &  (1, -3)

[tex]Distance=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}\\\\ =\sqrt{(1-[\frac{-5}{2}])^{2}+(-3-[-3])^{2}}\\\\ =\sqrt{(1+\frac{5}{2})^{2}+(-3+3)^{2}}\\\\ =\sqrt{(\frac{7}{2})^{2}} \\\\=\frac{7}{2}\\\\=3\frac{1}{2}[/tex]

Answer:

25.12

Step-by-step explanation:

round pi to first 2 digits after decimal point.

3.14 x 8 =25.12

Answer:

The A) ΔABC ≅ ΔEDC

Step-by-step explanation:

The AAS congruence method requires 2 angles and their un-included side to be congruent. ∠A ≅ ∠E due to the markings, ∠C ≅ ∠C because they are vertical angles, and AB ≅ ED due to the markings. 2 angles and their un-included side are congruent.

As for the congruence statement, A is the correct answer because ∠A ≅ ∠E, ∠B ≅ ∠D, and ∠C ≅ ∠C. The order of the naming of the triangles aligns to the angle's congruence.

Answer:

A) triangle ABC is congruent to triangle EDC

Step-by-step explanation:

The AAS method of proving congruence of triangles uses two angles and a non-included side of the triangle. If two angles and the non-included side of a triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.

Let's see what we have in this problem:

<ACB and <ECD are congruent since they are vertical angles.

<A and <E are congruent by given.

Sides AB and ED are non-included sides and are congruent.

Since we have two angles and a non-included side of a triangle and the corresponding parts of another triangle, the triangles are congruent by AAS.

Now we need the statement of congruence.

Angles ACB and ECD are corresponding angles, so the letter C must appear in both triangles in the same position.

Angles A and E are corresponding angles, so the letters A and E must appear in both triangles the same position.

We already have CA and CE. The last angles left are corresponding angles B and D, so we get triangle CAB and triangle CED. Since a triangle may be named using any order of the vertices, we can rename the triangles ABC and EDC and maintain the same corresponding vertices.

Answer: A) triangle ABC is congruent to triangle EDC

Answer:

interpretation: -- 1/9 1/3 2/9 2/3

Input:

-(-1)/9×1/3×2/(9 + 2/3)

Exact result:

2/261

Answer:

I think there is an error in the question because

(f-g) = -4

(f-g) (7) = NO SOLUTION

Step-by-step explanation:

[tex]f(x) = -9x + 2 \\g(x) = -9x + 6\\(f - g)(7)\\(f - g) = -9x + 2 - (-9x+6)\\(f - g) = -9x +2 +9x-6\\(f - g) = -9x +9x+2-6\\(f - g) = -4[/tex]

Answer:

x=-3

Step-by-step explanation:

3x+2=x+4x+8

3x+2=5x+8

-2x+2=8

-2x=6

x=-3

Answer:

[tex]x=-3[/tex]

Step-by-step explanation:

[tex]3x + 2 = x + 4(x+2)[/tex]

Expand the brackets.

[tex]3x + 2 = x + 4x+8[/tex]

[tex]3x + 2 = 5x+8[/tex]

Subtract [tex]-5x[/tex] and [tex]-2[/tex] from both sides of the equation.

[tex]3x-5x=8-2[/tex]

[tex]-2x=6[/tex]

[tex]\frac{-2x}{-2}=\frac{6}{-2}[/tex]

Divide [tex]-2[/tex] on both sides of the equation.

[tex]x=-3[/tex]

Answer:

a) 5.83 cm

b) 34.4 deg

Step-by-step explanation:

a)

AC is the hypotenuse of a right triangle with legs measuring 3 cm and 5 cm.

c^2 = a^2 + b^2

c^2 = 3^2 + 5^2

c^2 = 9 + 25

c^2 = 34

c = sqrt(34) cm = 5.83 cm

b)

Triangle ACD is a right triangle with right angle DAC.

AD = 4 cm

AC = 5.83 cm

tan <ACD = opp/adj

tan <ACD = AD/AC

tan <ACD = 4/5.83

m<ACD = tan^-1 (0.68599)

m<ACD = 34.4 deg

The side length AC is 5.83 cm and angle ACD is 34.5 degrees

(a) Length AC

To do this, we make use of the following Pythagoras theorem in triangle ABC

[tex]\mathbf{AC^2 = AB^2 + BC^2}[/tex]

So, we have:

[tex]\mathbf{AC^2 = 3^2 + 5^2}[/tex]

[tex]\mathbf{AC^2 = 9 + 25}[/tex]

[tex]\mathbf{AC^2 = 34}[/tex]

Take square roots

[tex]\mathbf{AC = 5.83}[/tex]

(b) Angle ACD

To do this, we make use of the following tangent ratio

[tex]\mathbf{tan(C) = \frac{AD}{AC}}[/tex]

So, we have:

[tex]\mathbf{tan(C) = \frac{4}{5.83}}[/tex]

[tex]\mathbf{tan(C) = 0.6861}[/tex]

Take arc tan of both sides

[tex]\mathbf{C= 34.5}[/tex]

Hence, side length AC is 5.83 cm and angle ACD is 34.5 degrees

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Answer:

113.1 square mm

Step-by-step explanation:

A=πr2=π·62≈113.09734

Answer:

[tex]= 36\pi \: {mm}^{2} \\ [/tex]

Step-by-step explanation:

[tex]area = \pi {r}^{2} \\ = \pi \times 6 \times 6 \\ = 36\pi \: {mm}^{2} [/tex]

Answer:

Both lines are equal (they are the same)

Step-by-step explanation:

Given

[tex]3y - 8 = -5x[/tex]

[tex]6y = -10x + 16[/tex]

Required

What is true about graph of both lines

Questions like this are better solved when there's option(s) to select from. However, some of the properties of line equation that I'll consider are to check  if both lines are either parallel or perpendicular

To do this,

The first thing to do is to calculate the slope of both lines

[tex]3y - 8 = -5x[/tex]

Add 8 to both sides

[tex]3y - 8 + 8 = -5x + 8[/tex]

[tex]3y = -5x + 8[/tex]

Divide both sided by 3

[tex]\frac{3y}{3} = -\frac{5x}{3} + \frac{8}{3}[/tex]

[tex]y = -\frac{5x}{3} + \frac{8}{3}[/tex]

The slope of the line is the coefficient of x;

[tex]Slope = -\frac{5}{3}[/tex]

Solve for the y intercept; Let x = 0

[tex]y = -\frac{5 * 0}{3} + \frac{8}{3}[/tex]

[tex]y = 0 + \frac{8}{3}[/tex]

[tex]y = \frac{8}{3}[/tex]

Solve for the x intercept; Let y = 0

[tex]0 = -\frac{5x}{3} + \frac{8}{3}[/tex]

Subtract [tex]\frac{8}{3}[/tex] from both sides

[tex]0 - \frac{8}{3} = -\frac{5x}{3} + \frac{8}{3} - \frac{8}{3}[/tex]

[tex]- \frac{8}{3} = -\frac{5x}{3}[/tex]

Subtract both sides by [tex]-\frac{3}{5}[/tex]

[tex]-\frac{3}{5}*- \frac{8}{3} = -\frac{5x}{3} * -\frac{3}{5}[/tex]

[tex]-\frac{3}{5}*- \frac{8}{3} = x[/tex]

[tex]\frac{3}{5} * \frac{8}{3} = x[/tex]

[tex]\frac{8}{5} = x[/tex]

[tex]x = \frac{8}{5}[/tex]

------------------------------------------------------------------------------------------------------

[tex]6y = -10x + 16[/tex]

Divide both sides by 6

[tex]\frac{6y}{6} = -\frac{10x}{6} + \frac{16}{6}[/tex]

[tex]y = -\frac{10x}{6} + \frac{16}{6}[/tex]

Simplify fractions to lowest term

[tex]y = -\frac{5x}{3} + \frac{8}{3}[/tex]

The slope of the line is the coefficient of x;

[tex]Slope = -\frac{5}{3}[/tex]

Solve for the y intercept; Let x = 0

[tex]y = -\frac{5 * 0}{3} + \frac{8}{3}[/tex]

[tex]y = 0 + \frac{8}{3}[/tex]

[tex]y = \frac{8}{3}[/tex]

Solve for the x intercept; Let y = 0

[tex]0 = -\frac{5x}{3} + \frac{8}{3}[/tex]

Subtract [tex]\frac{8}{3}[/tex] from both sides

[tex]0 - \frac{8}{3} = -\frac{5x}{3} + \frac{8}{3} - \frac{8}{3}[/tex]

[tex]- \frac{8}{3} = -\frac{5x}{3}[/tex]

Subtract both sides by [tex]-\frac{3}{5}[/tex]

[tex]-\frac{3}{5}*- \frac{8}{3} = -\frac{5x}{3} * -\frac{3}{5}[/tex]

[tex]-\frac{3}{5}*- \frac{8}{3} = x[/tex]

[tex]\frac{3}{5} * \frac{8}{3} = x[/tex]

[tex]\frac{8}{5} = x[/tex]

[tex]x = \frac{8}{5}[/tex]

-------------------------------------------------------------------------------------------------------

By comparing the slope, x intercept and y intercept of both lines;

It'll be observed that they have the same slope, x intercept and y intercept

This implies that both lines are equal; in other words, they are the same.

Answer:

240; 24

Step-by-step explanation:

Given that:

Sum of two numbers = 264

One number ends with '0'

Second number = first number without '0'

Let the first number be 'a'

Since the second number is the first number with '0' erased, then,

Second number = (a ÷ 10)

Therefore, the expression becomes :

a + a/10 = 264

Multiply the equation by 10

10a + a = 2640

11a = 2640

a = 2640/11

a = 240

Therefore ;

a = 240 ;

a/10 = 240/10 = 24

The numbers are 240 and 24

Answer:

A

Step-by-step explanation:

We need to find two numbers that have a sum of 5 and a product of 6. These numbers are 2 and 3 so x² + 5x + 6 factored is (x + 2)(x + 3). Since x + 2 is a factor the answer is A.

The binomials below are a factor of A. X+ 2 this trinomial.

It is easy to remember binomials as bi means 2 and a binomial will have 2 terms. A classic example is the following: 3x + 4 is a binomial and is also a polynomial, and 2a(a+b) 2 is also a binomial (a and b are the binomial factors). The above are both binomials.

A trinomial is an algebraic expression that has three non-zero terms. Examples of a trinomial expression: x + y + z is a trinomial in three variables x, y, and z. 2a2 + 5a + 7 is a trinomial in a single variables a. xy + x + 2y2 is a trinomial in two variables x and y.

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Answer:

I'm pretty sure its c

Answer:

[tex]W(x)=30x+70[/tex]

Step-by-step explanation:

First, we will find the weight of the table. We know that 8 boxes weighs a total of 240 kg since each box weights 30 kg. Then to find the weight of the table, we can subtract the total weight from the weight of the boxes. Thus:

[tex]W_{\text{table}}=310-240=70\text{ kg}[/tex]

So, the weight of the table is 70 kg.

Now, we can write our function. Let [tex]x[/tex] equal the amount of boxes.

The table is a set weight, so that would be our constant.

Thus, we will have:

[tex]W(x)=30x+70[/tex]

Where W(x) represents the weight of the table after adding x boxes.

30x represents the weight each box of book adds to the total. One box equals 30 kg, two boxes equal 60 kg, etc.

The 70 represents the unchanging weight of the table.

Answer:

Step-by-step explanation:

Well first, we need to find the weight of the table. We know that 8 boxes weighs a total of 240kg (since each box weights 30kg). Thus, we can conclude that the table weighs 70kg by doing 310-240=70.Now, we can write our function. Let  equal the amount of boxes.

The table is a set weight, so that would be our constant so, we will have: 30x represents the weight each box of book adds to the total. One box equals 30kg, 2 boxes equal 60kg, etc.The 70 represents the unchanging weight of the table.In terms of W(x), it will be:

Answer:

n(n +1) is the Total number of seats in the corner section.

Step-by-step explanation:

We are given that:

Number of seats in first row = 2

Number of seats in second row = 4

Number of seats in third row = 6

:

Number of seats in [tex]n^{th}[/tex] row = [tex]2n[/tex]

We can clearly see that it is an Arithmetic progression with

First term, a = 2

Common Difference, d = 2

[tex]n^{th}[/tex] term, [tex]a_n=2n[/tex]

To find: Total number of seats in corner sections with n rows.

i.e. Sum of n terms of above AP.

Formula for sum of n terms of an AP:

[tex]S_n=\dfrac{n}{2}(2a+(n-1)d)\\[/tex]

Putting the values:

[tex]\Rightarrow \dfrac{n}{2} ({2 \times 2 +(n-1)2})\\\Rightarrow \dfrac{n}{2} (4 +2n-2)\\\Rightarrow \dfrac{n}{2} (2n +2)\\\Rightarrow \dfrac{n}{2} \times 2(n +1)\\\Rightarrow n(n +1)[/tex]

n(n +1) is the Total number of seats in the corner section.

Answer:

Yes the new method if sample size was less than 20 than that of old method or identical sample numbers of old and new the differences still prove the new operation is better. As 88 patients minus 1% still shows us 76.7475 significance of  old method being low point 67.5 = 30% of 225 and proved a 65.25 low point and 69.75 high point which is also a 20% jump to new methods low point significance.

You cna show this as workings to prove or follow any of the below statements.

Where new method of 88 patients -0.01 significance rate stands at 76.7475. This figure has reduced by 11.2525 from 88 patients to 76.7 we compare this to the old method if reversing significance we find  = 62.5 and it's 30% standing value of 67.5  as +1% increase shows us 31% = 69.7  ( 0.31 x 225 = 69.74)

Step-by-step explanation:

88/225  = 0.39111111111 = 39.11%%

P value 01 = 1%  =  225.225 or 5% range of alternative hypotheses.

To graph the P value we take the distance between the sample mean and the null hypothesis value (225 + 1% of sample - x nhv) = y ). We can graph the probability of obtaining a sample mean  (225 +/- ( x +1% of sample) where nhv has a decimal if needed to utilize the 1% added). we would replace nvp in this example with  Ha or H1 which means the alternative hypotheses as the data shows less than or equal to.

We can then show 225.225 -  Ha or H1  then graph the probability of obtaining a sample mean that is at least extreme in both tails  Ha or H1

However it would be the other way round where you take the first set of data and use the sample as the 30% significance of that sample indicates it may be a larger sample or a higher significance. Therefore this would be used in the graphing - 1%

We prove that 30-1 =29  where 29% of 225 = 225 x 0.29 = 65.25

this way we have proved that the new set of data being equal to 88 patients regaining their eyesight is <23 and can be written like this 65.25< x <88

This means that sample mean has taken the 1% to show on the graph we can show 225> 33.11 +1 .

We can prove that both indifference of significance would reduce when 1% is added and close based on being a higher percentage to begin with.

34.11 = 0.3411 x 225 = 76.7475 for second surgeon = 33.11% +1

Where as shown

30 = 0.3 x 225 = 67.5

76.5475 - 67.5 = 9.04 difference when comparing old method = +1%

where new method stands at 76.7475 has reduced by 11.2525 from 88 patients and where old method if reversing = 62.5 and has reduced from 67.5  as +1% and 31% = 69.7  ( 0.31 x 225 = 69.74)

You would therefore graph each higher methods first if comparing both by 0.01 or show 88 on graph and 76.7475 = +1%

NB/ if sample size was 20 more in the old data then 225+20 = 245 x 0.29 = 71.05 and would still be lower than new data. = 2.0 increase level of significance and not relevant unless you are looking for the decrease which means new is greater than 20% success than that of old method findings where 30% = 67.5.

Answer:

1/3

Step-by-step explanation:

When a line is perpendicular, to find the slope, you take the negative reciprocal of the other slope.

The slope of a perpendicular line is going to be the opposite and reciprocal of the original slope.

Opposite: -3 -> 3

Reciprocal: 3 -> 1/3

Therefore, the answer is 1/3

Best of Luck!

Answer:

Approximately 43.30 miles

Step-by-step explanation:

We use the given formula:

[tex]d=\sqrt{1.5\,h}[/tex]

replacing "h" with the value of the height of the Empire State Building (1250 feet):

[tex]d=\sqrt{1.5\,*1250} \\d= 43.30 \,\,\,miles[/tex]

Answer:

a) is -7

Step-by-step explanation:

8=2048[tex](2)^{n-1}[/tex]

[tex]\frac{8}{2048} =\frac{2048^{n-1} }{2048}[/tex]

8/2048=0.00390625 = [tex](2)^{n-1}[/tex]

[tex]2^{-8}[/tex] = 0.00390625

-8-1=-7

and do the rest with the same equation which is tn=a[tex]r^{n-1}[/tex]

Answer:

54 = 2 x 27

the cube root of 27 is 3.

the answer is C

Step-by-step explanation:

Answer:

The perfect cube is 27 and the perfect cube root is 3

Step-by-step explanation:

( 54) ^ 1/3

( 27*2) ^ 1/3

(27) ^1/3 * (2)^1/3

3 * (cube root of 2)

The perfect cube is 27 and the perfect cube root is 3

Answer:

62.363°

Step-by-step explanation:

The decimal form of degree is 62.363°.

Geographic coordinates for latitude and longitude can be expressed as decimal fractions of a degree using the notation decimal degrees (DD). Many geographic information systems (GIS), web mapping tools like OpenStreetMap, and GPS units all employ DD.

Latitudes that are positive are north of the equator and those that are negative are south of the equator. Longitudes that are positive are east of the Prime Meridian and those that are negative are west of the Prime Meridian.

Given 62°21'47"

A DMS value is converted to decimal degrees using the formula:

[tex]{\displaystyle \mathrm {D} _{\text{dec}}=\mathrm {D} +{\frac {\mathrm {M} }{60}}+{\frac {\mathrm {S} }{3600}}}[/tex]

D = 62°

M = 21'

S = 47"

substitute the values,

[tex]{\displaystyle \mathrm {D} _{\text{dec}}[/tex] = 62 + 21/60 + 47/3600

[tex]{\displaystyle \mathrm {D} _{\text{dec}}[/tex] = 62 + 0.35 + 0.01305

[tex]{\displaystyle \mathrm {D} _{\text{dec}}[/tex] = 62.3630

[tex]{\displaystyle \mathrm {D} _{\text{dec}}[/tex] = 62.363°

Hence the decimal form is 62.363°.

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Answer:

D

Step-by-step explanation:

Perfect square trinomials can be written as (a + b)² = a² + 2ab + b². In this case, we know that a = x so we can write this as x² + 2bx + b². Since we know that 2bx = 24x we can conclude that b = 12, so that means b² = 12 * 12 = 144.

Answer:

Answer D

Step-by-step explanation:

Take half of the coefficient of x:  Take half of +24, obtaining 12.  Now square this 12, obtaining 144.  This is the desired value.  Answer D is correct.

Answer:

0.015625

Step-by-step explanation:

.5x.5x.5x.5x.5x.5

Answer:

x= 70

Step-by-step explanation:

This question needs an attachment; see attached

Given

ABD = 55

Required

Find x?

In the figure shown in the attachment, angle b and ABD are alternate interior angles;

From parallel and perpendicular line theorems; alternate interior angles are equal.

This implies that <b = 55

Also; when a rectangle is divided by two diagonals, the resulting triangles are isosceles triangles;

where 2 sides and 2 angles are equal;

This implies that <b = <c = 55

Sum of angles in a triangle  = 180;

So,

<x + <b + <c = 55

x + 55 + 55 = 180

x + 110 = 180

Subtract 110 from both sides

x + 110 - 110 = 180 - 110

x = 180 - 110

x = 70

Answer:

Step-by-step explanation:

hello,

I understand that there are only 4 cards  and then the player draw a card out of the 4 cards, replace it so the second draw is still out of the 4 cards

How many ways can you draw two cards?

as the first card is replaced, this is 4*4=16

so there is 16 possibles ways

hearts hearts

hearts clubs

hearts diamonds

hearts spades

clubs hearts

clubs clubs

clubs diamonds

clubs spades

diamonds hearts

diamonds clubs

diamonds diamonds

diamonds spades

spades hearts

spades clubs

spades diamonds

spades spades

out of these 16 ways, how many have same colour for both cards?

I assume that there are only two colours Red and Black, so we can have

only 8 ways so the first probability is 8/16 = 1/2

out of these 16 ways, how many are red ace first and black ace?

There are 4 ways so the probability is 4/16 = 1/4

hope this helps

Standard deck has aces in four colors

Player draws one from four so the probability of drawing any first card is 1/4 (in the first drawing)

We replace the card so in second drowing its the same

So the probability of drawing two card of one chosen color is 1/4*1/4, and we have four colors

The probability of drawing two card of the same color is:

There are 2 red aces and 2 black aces

(sorry for coments - not reading carefully)

So a probability of drawing red ace in first drawing is 2/4=1/2

a probability of drawing black ace in second drowing is the same ('cause we replace the one drawn first)

So the probability that a red ace is drawn first and then the black ace is:

Answer:

[tex]\dfrac{2}{11}[/tex]

Step-by-step explanation:

It is given that a card is drawn one at a time from a well-shuffled deck of 52 cards.

Total repetitions of this experiment = 11

Number of kings in the experiment = 2

Let E is the event in which a king is drawn in the 11 trials. So

[tex]P(E)=\dfrac{\text{Number of kings in the experiment}}{\text{Total repetitions of this experiment}}[/tex]

[tex]P(E)=\dfrac{2}{11}[/tex]

Therefore, the experimental probability P(E) is [tex]\dfrac{2}{11}[/tex].

Answer:

The first one!

Step-by-step explanation:

the others don't work since there could be more possibilitys than just b and c.

D is just wrong (as you creati)

I seriously cited the sources you fool>;/

plagiarism, what joke is that! is it a joke? don't be crazy please! thanks!

Answer:

the scale factor whould be 1/2 because 3 divided by 6 is 0.5 and if you compare the corrdinate the ultimate awnser would be 1/2

Step-by-step explanation:

Answer: a scale factor is a number which multiplies ("scales") a quantity. For example,the "C" in y=Cx is the scale factor for x. If the equation were y=5x, then the factor would be 5.

Step-by-step explanation:

Hope that help

Answer:

yes their parallel

Step-by-step explanation:

their the same equation just one is negative they go the go next to each other but never touch

Answer:

64.21

Step-by-step explanation:

After performing some simple mathematical operations, we know that 6.421 x 10 = 64.21.

So, 6.421 x 10 = ?:

Evaluate as follows:

Therefore, after performing some simple mathematical operations, we know that 6.421 x 10 = 64.21.

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The correct question is given below:

Multiply. 6.421 x 10 = _____

A. 0.6421

B. 64.21

C. 642.10

D. 6,421