Use the properties of operations to determine if each pair of expressions is equivalent for 1/2(4 - 2x); 2 - 2x

Answer:

242

Step-by-step explanation:

22=a/11

22*11= a

242 = a

a=242

Answer:

a=242

Step-by-step explanation:

Compound interest formula:

Amount = starting value x ( 1+ interest rate/compounds per year)^(compound per year x number of years)

Amount = 12,000,000 x (1+ 0.10/1)^(1x5)

Amount = 19,326,120.00

Answer:

Explanation:

The complete question is:

A sequence can be generated by using    [tex]a_n=4a_{(n-1)}[/tex]    where    [tex]a_1=6[/tex]     and n is a whole number greater than 1. What are the first four terms in the sequence.

The given rule     [tex]a_n=4a_{(n-1)}[/tex]     is a recursive formula, which means that  to find any term consecutive term, from the second one, you multiply the current term by 4.

Thus:

[tex]a_1=6\\ \\ a_2=4a_1=4\times 6=24\\\\ a_3=4a_2=4\times 24=96\\ \\ a_4=4a_3=4\times 96=384[/tex]

Answer:

The option (b) is correct as the sequence is generated as 6, 24, 94, 384,...

Step-by-step explanation:

Considering the sequence

[tex]a_{n} =4a_{n-1}[/tex]

As [tex]a_{1} =6[/tex]

So,

[tex]a_{n} =4a_{n-1}[/tex]

[tex]a_{2} =4a_{2-1}[/tex]

[tex]a_{2} =4a_{1}[/tex]

[tex]a_{2} =4.6[/tex]

[tex]a_{2} =24[/tex]

[tex]a_{3} =4a_{3-1}[/tex]

[tex]a_{3} =4a_{2}[/tex]

[tex]a_{3} =4.24[/tex]

[tex]a_{3} =96[/tex]

[tex]a_{4} =4a_{4-1}[/tex]

[tex]a_{4} =4a_{3}[/tex]

[tex]a_{4} =4a_{3}[/tex]

[tex]a_{4} =4.96[/tex]

[tex]a_{4} =384[/tex]

Therefore, the option (b) is correct as the sequence is generated as 6, 24, 94, 384,...

Keywords: sequence

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Answer:

Step-by-step explanation:

f(x) = 2x^3 - 4x.....find f(-2).....so sub in -2 for x

f(-2) = 2(-2^3) - 4(-2)

f(-2) = 2(-8) + 8

f(-2) = -16 + 8

f(-2) = -8 <==

We have [tex]f(x)=2x^3-4x[/tex], to find [tex]f(-2)[/tex] put -2 instead of x, [tex]f(-2)=2(-2)^3-4(-2)=-16+8=\boxed{-8}[/tex].

Hope this helps.

Step-by-step explanation:

Given data is 32,47,49,53,54,66,67,71,72

Median = [tex](\frac{n+1}{2}) ^{th}[/tex] term

            =[tex](\frac{9+1}{2} )^{th}[/tex] term

            =[tex]5^{th}[/tex] term

           =54

First quartile = [tex]\frac{1}{4} (n+1)^{th} term[/tex]

                     = [tex]\frac{47+49}{2}[/tex]

                     =48

Third quartile=[tex]\frac{3}{4} (n+1)^{th} term[/tex]

                     = [tex]\frac{67+ 71}{2}[/tex]

                     = 69

Interquartile range = (69- 48)

                                = 21

Answer:

27

Step-by-step explanation:

right on expo

Answer:

C

Step-by-step explanation:

A rhombus always has 4 sides, making it a quadrilateral.

Feel free to ask further questions..

Answer:

Step-by-step explanation:

We know:

1m = 100cm

therefore

1m 74cm = 1m + 74cm = 100cm + 74cm = 174cm

45cm + 1m 74cm = 45cm + 174cm = 219cm = 200cm + 19cm = 2m 19cm

Answer:its is 2m 19cm

Step-by-step explanation:

0.45+

1.74

______

2.19

Which is 2cm 19m. HOPE IT HELPS YOU!!!

Will is 29% taller than Wanda, so Will's height is 77.5% of Wanda's height.

Solution:

Let x be Will's height, and y be Wanda's height.

Since Will is 29% taller than Wanda we have,

[tex]x=1.29y \rightarrow(y+29\% \text{ of y }\rightarrow1y+.29\rightarrow y\rightarrowy(1+.29)\Rightarrow1.29y)[/tex]

Then solving for y we get,

[tex]\Rightarrow y=\frac{x}{1.29}\rightarrow y=\frac{100x}{129}[/tex]

[tex]\Rightarrow y\approx0.7752x[/tex]

Therefore, Will is 77.5% of Wanda's height.

Will's height is 129% of Wanda's height.

To calculate the percentage of Will's height compared to Wanda's height, we need to determine how much taller Will is than Wanda. If Will is 29% taller, it means his height is 129% of Wanda's height. This can be calculated by adding 29% to 100%: 100% + 29% = 129%. Therefore, Will's height is 129% of Wanda's height.If Will is 29% taller than Wanda, then he is 100% of Wanda's height (which is Wanda's total height) plus an additional 29% of Wanda's height. Therefore, if you combine these percentages, you will find that Will's height is 129% of Wanda's height.

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Answer:

p+q = -2 ----- equation 1

p-q = 8 ------ equation 2

Adding both equations

p+q+p-q = -2+8

2p = 6

p = 6/2

p = 3

Subtracting equation 2 from equation 1

p+q - (p-q) = -2 - 8

p+q-p+q = -10

2q = -10

q = -10/2

q = -5

p= 3

q = -5

Step-by-step explanation:

Final answer:

The solution to the system of equations using the elimination method is p = 3 and q = -5.

Explanation:

The student is requesting assistance with solving a system of linear equations using the elimination method. The system given is:

p + q = -2

p - q = 8

We can eliminate the variable q by adding both equations together:

p + q + p - q = -2 + 8

2p = 6

p = 3

Now we can substitute p back into one of the original equations to find q:

3 + q = -2

q = -2 - 3

q = -5

The solution to the system is p=3 and q=-5.

Answer:

Therefore x = 33° , y = 40° and z = 109°.

Step-by-step explanation:

i) from properties of parallel lines a pair of alternate interior angles are equal

  Therefore x = 33°

ii) from properties of parallelogram that a pair of opposite angles are equal, Therefore z = 109°.

iii) from the law of triangle that the sum of all angles in a triangle is 180° and also using the property of parallel lines that a pair of alternate interior angles is equal we can say that x° + y° + z° = 180°                                           ⇒ 31° + y° + 109° = 180°, therefore   y° =  180° - 140° = 40°.

Therefore x = 33° , y = 40° and z = 109°.

The values of x, y and z in the parallelogram is 52°, 38° and 90° respectively.

The angles on the same side of the transversal of a parallelogram are supplementary, that is, 180°

So,

33° + 109° + y° = 180°

142 + y = 180

y = 180 - 142

y = 38°

x° + y° = 90°

x + 38 = 90

Subtract 38 from both sides

x = 90 - 38

x = 52°

x° + y° + z° = 180°

52 + 38 + z = 180

90 + z = 180

z = 180° - 90°

z = 90°

Hence,

x = 52°

y = 38°

z = 90°

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The first step to solve the equation 11-3x=44 is to isolate the variable x by subtracting 11 from both sides of the equation.

To solve the equation 11-3x=44, the first step is to isolate the variable x.

To do this, we need to get rid of the constant term on the left side of the equation. We can do this by subtracting 11 from both sides:

Now we have -3x = 33 as our new equation.

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Answer:

-$110

Step-by-step explanation:

An overdrawn bank account would be -$180. you would have to add $70 .

given 70 is not large enough to fully bring the balance to 0. long story short, subtract 70 from 180. since 70 is < 180 the number is therefore negative since 180 is negative in this problem

I hope this helps!!^^

Answer:

He is overdrawn by $110

Step-by-step explanation:

-180+ -70=110

Step-by-step explanation:

To go from A to M you need to go 4 to the right and 3 down. If M is the middle you'll need to do the same to get from M to B. So (2+4,-2-3)=(6,-5)

Answer:

OPTION C: 2x - y = -1

Step-by-step explanation:

Equations of two straight lines do not have a solution when they do not meet. Also, two parallel lines never meet.

Given the equation of the first line is: 2x - y = 1. So, the line parallel to this line should be the answer.

Note that the equations of two parallel lines only differ by a constant.

i.e, If ax + by + c = 0 is an equation of a line then the equation of the line parallel to this would be ax + by + k = 0.

Hence, the required answer is: 2x + y = -1, which is OPTION C.

Answer:

The function to represent the area a of the section inside the border is [tex]A=12x-x^2[/tex]

Step-by-step explanation:

Given section inside the border is [tex]x[/tex] inches and [tex](12-x)[/tex] inches.

We need to write the function to represent the area of the section inside the border.

We can see the length of border is [tex]x[/tex] and width of the border is [tex](12-x)[/tex].

So, the area of the rectangle will be [tex]length\times width[/tex]

The area [tex](A)[/tex] will be

[tex]A=x(12-x)\\\\A=12x-x^2[/tex]

So, the function to represent the area a of the section inside the border is [tex]A=12x-x^2[/tex]

Answer:

orange : cranberry : apple : orange

9 : 5 : 6

Step-by-step explanation:

Given the following ratios (fraction):

[tex]\frac{apple}{total} =\frac{1}{4}[/tex]

[tex]\frac{orange}{total} =\frac{3}{10}[/tex]

in order to add/subtract fractions, we have to ensure that the denominators are the same, we can see that for the denominators listed above, the least common multiple for 4 and 10 = 20, hence we can re-write the above as :

[tex]\frac{apple}{total} =\frac{1}{4} =\frac{5}{20}[/tex]

[tex]\frac{orange}{total} =\frac{3}{10} =\frac{6}{20} [/tex]

Hence,

Fraction of cranberry juice of the total is,

1 - [tex]\frac{5}{20}[/tex] - [tex]\frac{6}{20}[/tex]

= [tex]\frac{20}{20}[/tex] - [tex]\frac{5}{20}[/tex] - [tex]\frac{6}{20}[/tex]

= [tex]\frac{9}{20}[/tex]

Because all the denominators are the same, we can assemble the ratios of each component by taking the ratios of the numerators

cranberry : apple : orange

= ratios of their numerators

= 9 : 5 : 6

Answer:

y = -5/12

Step-by-step explanation:

−3(y+3)=2y+3 (multiply -3 with inside the parenthesis)

➡

-3y -9 = 2y +3

➡

-3y -2y = 3+9 add like terms

➡

-5y = 12

➡

y = -5/12

Answer:

The volume of Solid A is 120 cm³.

Step-by-step explanation:

Given the area of the solids are in the ratio: 4 : 9

Let their actual areas be 4x² and 9x². We have assumed the common ratio as x² for easier computation.

We have area: [tex]$ A_A : A_B = $[/tex]    4x²       :     9x²

This implies, the length should have been of the ratio of the square root of these numbers.

Therefore, the ratios of the lengths is: [tex]$ \sqrt{4x^2} : \sqrt{9x^2} $[/tex]

[tex]$ L_A : L_B = 2x : 3x $[/tex]

Now, volume is cube of lengths. Therefore, the ratio of volumes would be:

[tex]$ V_A : V_B = 8x^3 : 27x^3 $[/tex]

Given [tex]$ V_B = 405 cm^3 $[/tex]

[tex]$ \implies 27x^3 = 405 \hspace{1mm} cm^3 $[/tex]

[tex]$ \implies x^3 = \frac{405}{27} = 15 $[/tex]

Hence, the volume of solid A, [tex]$ V_A = 8x^3 = 8 \times 15 = \textbf{120} \hspace{1mm} cm^3 $[/tex].

Hence, the answer.

Answer:

IT'S B

Step-by-step explanation:

i actually got it! i looked up this answer for 3 hours and never found it, but i got it, it's B on edge!!!

The system of linear inequalities that includes the point (3, -2) in its solution set is y less-than-or-equal-to two-thirds x minus 4.

The system of linear inequalities that has the point (3, -2) in its solution set is y less-than-or-equal-to two-thirds x minus 4.

The first dashed line in the coordinate plane represents the inequality y = -3, where everything below the line is shaded. The second solid line, with a positive slope and passing through (0, -4) and (3, -2), represents the inequality y ≤ (2/3)x - 4, where everything below the line is shaded.

Therefore, the correct option is y less-than-or-equal-to two-thirds x minus 4.

Answer:

-26a - 25a^7

Step-by-step explanation:

Answer:

P ≡ [tex](- \frac{5}{4}, \frac{15}{4})[/tex]

Step-by-step explanation:

The point P divides the line segment from A(-2,3) and B(1,6) in the ratio of 1 : 3.

So, AP : PB = 1 : 3.

Now, the coordinates of point P will be given by [tex](\frac{1 \times 1 + 3 \times (- 2)}{1 + 3}, \frac{1 \times 6 + 3 \times 3}{1 + 3})[/tex]

= [tex](- \frac{5}{4}, \frac{15}{4})[/tex] (Answer)

Note: Let there are two points with known coordinates [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] and another a point having coordinates (h,k) divides the line joining the two above points internally in the ratio m : n, then (h,k) is given by

(h,k) ≡ [tex](\frac{mx_{2} + nx_{1}}{m + n}, \frac{my_{2} + ny_{1}}{m + n})[/tex]

Step-by-step explanation:

(208/409)*100%

50.85%

Answer:

1.625

Step-by-step explanation:

25% or 6.50 is 1.625 so multiply 25 times 6.50 then divide it by 100

Answer:

x = 4 OR 1x + 0y = 4

Step-by-step explanation:

so if it is a line parallel to the y axis, it is a vertical line. A vertical line has an undefined slope, so it cant be written in y = mx + b form.

ur equation would be : x = 4....because no matter what y is, x will always be 4.

but if u need it in standard form Ax + By = C it is :

1x + 0y = 4

The equation representing a line that is parallel to the y-axis and passes through the point (4,3) is x = 4.

The question is asking for an equation of a line that is parallel to the y-axis and goes through the point (4,3). In a coordinate system, a line parallel to the y-axis is a vertical line. The equation for a vertical line in the coordinate plane is of the form x = c, where 'c' is the x-coordinate of any point the line passes through. In this case, since the line passes through the point (4,3), the x-coordinate is 4. Therefore, the equation of the line parallel to the y-axis that passes through (4,3) is x = 4.

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Answer:

12

Step-by-step explanation:

x/3-9=-5

x/3=-5+9

x/3=4

x=4*3

x=12

Answer:

eight and one thousandth.

Answer:

Eight and one thousandth

Step-by-step explanation:

Writing 8.001 in words is eight and one thousandth.

OR

Eight point zero zero one.

Note that the place value of the numbers are as follow:

8= units; 0 = tenth; 0 = hundredth and 1 = thousandth.

Immediately after the decimal point are tenth, hundredth and thousandth.

Question:

Suppose we want to choose 3 colors, without replacement, from the red, blue, green, and purple.

(a)How many ways can this be done, if the order of the choices is taken into consideration?  

(b)How many ways can this be done, if the order of the choices is not taken into consideration?

Answer:

(a) 6 choices

(b) 3 Choices

Step-by-step explanation:

Given:

3 Colors

Order of choice : Red, Blue, Green

(a) Order of the choices taken into consideration :

When we are picking  the first colour there are 3 color choice.

When we are picking second colour there are 2 choice and so on.

Therefore, total choices are = 3*2 = 6 choices

(b) Order of the choices not taken into consideration :

When to take this option we choose as [tex]3 \times 2[/tex]  and the remove the duplicates

Therefore, choices are = [tex]\frac{(3 \times 2)}{(1 \times 2)}[/tex] =[tex]\frac{6}{2}[/tex] = 3 Choices

The concept of choosing colors without replacement has to do with probability, it means that once an item is selected, it is not put back in the set, thus changing the probability for the next selections.

The question involves the concept of probability in Mathematics, particularly in choosing colors without replacement. This refers to the situation where you are picking something out of a set (like colors or marbles in a bag) and you don't put it back again. This changes the probability for future picks.

For instance, consider a bag containing three colors - red, green and blue. If you want to pick any two colors without replacement, we have three options for the first pick and then two for the second pick as one color is already taken out from the bag and not replaced. These options are (red, green), (red, blue), (green, red), (green, blue), (blue, red), and (blue, green).

The same concept applies when dealing with different scenarios like picking cards from a deck or marbles from a bag. Each subsequent pick after the first pick without replacement has one less option to choose from resulting in changes in probabilities with each step.

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