In the space provided below, solve the equation 4x² 768 = 0 for x algebraically. Write your answer in simplest radical form. Show all work. ​

An integer between 1000 and 9999 inclusive is called balanced if the sum of its two leftmost digits equals the sum of its two right most digit. Therefore, there are 615 balanced integers .

If the common sum of the first two and last two digits is n ,

such that 1 ≤n ≤ 9 , there are n choices for the first two digits and n +1 choices for the second two digits (since zero may not be the first digit).

This gives:

            ∑⁹ₙ₋₁ n(n+1) balanced numbers.

If the common sum of the first two and last two digits is n, such that:

                   10≤ n ≤ 18

there are 19 - n choices for both pairs.

This gives : ∑ₙ ₁₀¹⁸ ( 19 - n)²

               = ∑₁⁹ n²

               = 285balanced numbers.

Thus, there are in total 330 + 285 = 615 balanced numbers.

Both summations may be calculated using the formula for the sum of consecutive squares, namely:

        ∑₁ⁿ k² = n (n+1) (2n + 1) / 6

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Answer: 0.555555556

Step-by-step explanation:

15/27=0.555555556

Checking work by plugging it in: 27x0.555555556=15

======================================================

Work Shown:

a = old value = 15

b = new value = 27

c = change in values

c = b-a

c = 27-15

c = 12

The positive c value tells us that we have an increase.

Then divide over the starting value a = 15

c/a = 12/15 = 0.80

Move the decimal point two spots to the right to go from 0.80 to 80%

Or multiply 0.80 with 100% to get 0.80*100% = 80%

We have a percent increase of 80%

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

Check:

80% of 15 = 0.80*15 = 12

If the stock increases by 80%, then it has increased by $12 to go from $15 a share to 15+12 = 27 dollars a share. This confirms the answer.

A slight shortcut would be to say 1.80*15 = 27

The multiplier 1.80 represents an increase of 80% since 100% + 80% = 1 + 0.80 = 1.80

The equations that represent the left side, right side, top side and bottom side are y = 3x+2, y = 3x-10, y = 5 and y = -1 respectively

The slope-intercept form of the equation of a line is y =mx+c,

where m is the slope and c is the y-intercept

slope(m) = y2-y1 / x2-x1

Left side

The line moves from point 1 (-1, -1) to point 2 (1,5)

x1 = -1, y1 = -1 and x2 = 1, y2 = 5

Slope(m) = 5-(-1) / 1-(-1)  = 6/2 = 3

Using the equation of a line for 2 points:

y-y1 = m(x-x1)

y-(-1) = 3(x-(-1))

y+1 = 3(x+1)

y+1 = 3x+3

y = 3x+2

Right side

The line moves from point 1 (3, -1) to point 2 (5,5)

Slope(m) = 5-(-1) / 5-3  = 6/2 = 3

y-(-1) = 3(x-3)

y+1 = 3x -9

y = 3x-10

Top side

y = 5

Bottom side

y = -1

Therefore, equation for the left side : y = 3x+2, equation for the right side: y = 3x-10, equation for the top side: y = 5 and equation for the bottom side: y = -1

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Answer:

Neither, Perpendicular, Parallel, Neither

Step-by-step explanation:

Parallel lines have the same slope.

Perpendicular lines have slopes that are negative reciprocals.

Marcelo will have to take 50 shots in order to miss 30 shots because the ratio of shots to missed shots is 5:3

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls.

To solve this question, we can simply compare the ratio or proportion of shots to the number of missed shots.

In every 25 shots taken, he made 10 shots. This implies he lose 15 shots.

So, for every 25 shots, he lost 15 shots.

How many shots did he take to miss 30 shots.

25 shots = 15 missed shots

x shots = 30 missed shots

crossed multiply both sides and solve for x

x = (30 * 25) / 15

x = 50 shots.

Marcelo took 50 shots.

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Answer:

$16.28

Step-by-step explanation:

44.%

Move the decimal up by two numbers to get a whole number, .44

and multiply .44 by $37

Answer:( 3.5 , -2 )

Step-by-step explanation:

Lenny's total wage is $7000

In this question, Lenny works a basic week of 32 hours. His basic rate of pay is $1,750. During a certain week he worked 9 hours overtime for which he was paid triple time.

32 hours of work = $1750

In a certain week, we work 9 hours as over time

For this overtime which he was paid triple time.

1750 * 3 = $5250

So, Lenny's total wage would be,

$1,750 +  $5250 = $7000

Therefore,  Lenny's total wage is $7000

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Answer:

c) [-16, 4]

Step-by-step explanation:

Given equation,

→ 2 + |t + 6| = 12

Now the value of t will be,

→ 2 + |t + 6| = 12

→ 2 + t + 6 = 12 || → 2 -(t + 6) = 12

→ t + 8 = 12 || → -t - 4 = 12

→ t = 12 - 8 || → -t = 12 + 4

→ [ t = 4 ] || → [ t = -16 ]

Hence, value of t is 4 (or) -16.

Answer:

Step-by-step explanation: I don’t know if this is what your asking for but 26, 37, 48.

The r - values that represents the weakest linear correlation is ;

-0.312 is the weakest negative correlation and 0.558 is the weakest positive correlation.

Given,

The r- values;-

- 0.904, -0.312, 0.558, 0.870

We have to find the r - values that represents the weakest linear correlation;

r- values represents correlation between two variables. The r- value lies from -1 to 1.

So, here.

-0.904 is close to -1, so it represents strong negative correlation.

-0.312 is close to -0.5, so it represents weak negative correlation.

0.558 is close to 0.5, so it represents weak positive correlation

0.870 is close to 1, so it represents strong positive correlation.

Therefore,

The r - values that represents the weakest linear correlation is ;

-0.312 is the weakest negative correlation and 0.558 is the weakest positive correlation.

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Answer:

-0.312

Step-by-step explanation:

−0.312

The size of the correlation, r  indicates the strength of the linear relationship between x and y. Values of r which are closer to −1 or to +1 indicate a stronger linear relationship between x and y.

There doesn't seem to be enough information to answer problem 1.

I would ask your teacher for clarification.

=============================================

Problem 2

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

Explanation

x = number of cards, which is some positive whole number.

Your teacher has provided these facts:

which I'll call "fact 1", "fact 2", "fact 3" in that order.

For now I'll focus on fact 3.

Recall that multiples of 5 either end with 0 or 5. Example: 25 is a multiple of 5, and so is 60.

Fact 3 says that we get a remainder 2 when dividing by 5. Therefore, x must be something like 25+2 = 27 or 60+2 = 62. I added 2 to each previous example mentioned earlier.

In short, the value of x must end with 2 or 7.

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

Now focus on fact 1.

The multiples of 4 are {4, 8, 12, ...} all of which are even since 2 is a factor of each.

Add remainder 3 to each item to get {7, 11, 15, ...} and it should be fairly obvious that all of these items are odd.

What does this mean? It means we know 100% that x ends with 7 in the units digit. If x has 2 in the units digit, then x would be even, but it's not in the set {7, 11, 15, ...}

So this is very useful info that x ends with 7.

x could be any of these: {7, 17, 27, 37, ...}

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

We've looked at facts 1 and 3 so far. The only thing left is fact 2.

List the multiples of 3 to get

{3, 6, 9, 12, 15, 18, ...}

then add on the remainder 2 giving this new updated set

{5, 8, 11, 14, 17, 20, ...}

We see that 17 is in that set which fits the criteria of "the number ends with 7". So it's possible that 17 is the answer.

But 17/4 = 4 remainder 1 which doesn't fit fact 1 (since we want remainder 3 instead).

But we can add on multiples of 3*5 = 15 to extend to this new set of

{17, 32, 47, 62, 77, ...}

then erase stuff that ends with 2 to get

{17, 47, 77, ...}

Through guess and check, 47 will work out as shown in the next section below. Therefore, 47 is the final answer.

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

Check:

We get the proper remainders mentioned earlier, so the answer has been confirmed.

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

Side note: The convention for problems like this is to use the Chinese Remainder Theorem. However, I decided not to use it because I wasn't sure if your teacher has covered modulo arithmetic yet or not. If s/he has covered it, then I recommend using that method instead of what I posted above. It's a much more efficient option.

Answer:

A = ₤500

B = ₤420

C = ₤340

D = ₤260

See Image 1 attached for the plot.

Step-by-step explanation:

The bank account starts with ₤500, so that is the amount at 0 months on the chart.

After one month, ₤80 is withdrawn, and the total becomes:

[tex]500-80=420[/tex]

After two months, another ₤80 is withdrawn from the account:

[tex]420-80=340[/tex]

Finally, after 3 months, ₤80 is withdrawn again:

[tex]340-80=260[/tex]

The monthly installment to be paid is $17.85.

Given:

A washing machine is priced at $450. A man buys the washing machine on HP according to the following terms: A deposit of 15% and the remaining to be paid in monthly installment over 2 years at a simple interest rate of  12 % per annum.

Remaining amount = 450 - 450*15/100

= 450 - 9*15/2

= 450 - 67.5

= $382.5

1 month amount = 382.5 + 382.5*0.12 / 24

= 428.4/24

= $17.85.

Therefore the monthly installment to be paid is $17.85.

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The classification of each game as fair or not, using probabilities, is given as follows:

1. Fair.

2. Fair.

A fair game is a game in which each competitor will have the same chance of winning the game.

These changes are calculated using probabilities, which is the number of desired outcomes in the context of the experiment divided by the number of total outcomes.

The probability of two tails when two fair coins are tossed is:

p = 1/2 x 1/2 = 1/4.

The probability of one head and one tail when two fair coins are tossed is:

p = 1/2 x 1/2 = 1/4.

In game 1, the two players have the same probability of winning, hence it is a fair game.

When two dice are thrown, there are 36 possible outcomes. The number of outcomes regarding the sums are given as follows:

Same probabilities, hence game 2 is also fair.

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Answer:

361

Step-by-step explanation:

By using the box plots, the statement that is most appropriate comparison of the spread is option D. The interquartile range (IQR) for brand A, $10, is less than the IQR for brand B, $25.

Box plot

A box plot refers the a type of chart often used in explanatory data analysis and it visually show the distribution of numerical data and skewness through displaying the data quartiles (or percentiles) and averages.

Given,

Here we have the box plot that contains the details about the comparison of spread.

Now, we have to find the statement is the most appropriate comparison of the spreads

In the given box plots, we have identified that the

Lower quartile of A = 70

Upper quartile of A = 80

Similarly,

Lower quartile of B = 25

Upper quartile of B = 50

Then the inter quartile is calculated as,

Brand A has interquartile range = 80- 70 =10,

Where as

Brand B has interquartile range = 50 - 25 = 25.

Therefore, the option D is correct.

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Answer: 0

Step-by-step explanation:

8x-4=4(2x+1)

8x-4=8x+4

0= 8

This isn't true as 0 can't equal to 8 so there are 0 solutions

Answer:

===========================

Sum of interior angles of a regular polygon is:

Find the measure of interior angle a:

Equate the values of angle a and solve for z:

Correct choice is B.

Answer:

z = 12

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{5.4 cm}\underline{Interior angle of a regular polygon}\\\\$\dfrac{180^{\circ}(n-2)}{n}$\\\\where $n$ is the number of sides.\\\end{minipage}}[/tex]

Given that the regular polygon has 5 sides, then the measure of one interior angle is:

[tex]\implies \dfrac{180^{\circ}(5-2)}{5}=\dfrac{180^{\circ}(3)}{5}=\dfrac{540^{\circ}}{5}=108^{\circ}[/tex]

If "a" is the measure of one angle, and m∠a = (3z + 72)° then:

[tex]\implies m \angle a=108^{\circ}[/tex]

[tex]\implies (3z+72)^{\circ}=108^{\circ}[/tex]

[tex]\implies 3z+72=108[/tex]

[tex]\implies 3z+72-72=108-72[/tex]

[tex]\implies 3z=36[/tex]

[tex]\implies \dfrac{3z}{3}=\dfrac{36}{3}[/tex]

[tex]\implies z=12[/tex]

The height of a cylinder is D. 7 halves inches

The volume of a cylinder is calculated as:

V = πr²h

r = radius = 1/3

h = height = ?

v = volume = 1 2/9

We will slot the value info the formula. This will be:

V = = πr²h

1 2/9 = 22/7 × 1/3 × 1/3 × h

1 2/9 = 22/63h

Divide through by 22 / 63

h = 1 2/9 ÷ 22/63

h = 11/9 × 63/22

h = 7/2

The correct option is D.

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Answer:

7/2 is your answer i have the same test :)))

Step-by-step explanation:

The volume of a cylinder is calculated as:

V = πr²h

r = radius = 1/3

h = height = ?

v = volume = 1 2/9

We will slot the value info the formula. This will be:

V = = πr²h

1 2/9 = 22/7 × 1/3 × 1/3 × h

1 2/9 = 22/63h

Divide through by 22 / 63

h = 1 2/9 ÷ 22/63

h = 11/9 × 63/22

h = 7/2

The correct option is D.

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The slope of a line that is parallel to the line y = x + 2 is 1.

What is slope?

A line's steepness is determined by its slope. In mathematics, the slope is determined by "rise over run" (change in y divided by change in x).

Given the equation of line: y = x + 2

We have to find the slope of a line that is parallel to the given line.

Since any line parallel to the given line  y = x + 2  will have the same slope as that of a given line

The general equation of line is given as y = mx + c

where. m is the slope of the line and c is y-intercept.

Thus for given equation of line y = x + 2

Comparing , we get

slope is m=1

Thus, any line with slope 1  is parallel to the given line y = x + 2

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Answer:

6×6

Step-by-step explanation:

6×6=36 and so it would be 6 rows and 6 columns.

Answer:

[tex]l=\frac{A}{W}\\[/tex]

Step-by-step explanation:

Sometimes we have to manipulate a variable this is often easier to do when we solve for the variable we want and input numbers into the rest of the equation

Let's say A=16 and w=8

Solving for l would me using the A=lw and inputing those values

A=lw

16=l(8)

[tex]\frac{16}{8}=\frac{8l}{8}[/tex]

[tex]l=\frac{16}{8} \\[/tex]  or [tex]l=2[/tex]

If A = 16 and w = 8, we could substitute those values into the original equation(A=lw) and say that

[tex]l=\frac{A}{W}[/tex]

Sometimes we have to manipulate a variable.

This is often easier to do when we solve for the variable we want and input numbers into the rest of the equation.

I hope this explanation is helpful :)

Answer:

h(3)=4

Step-by-step explanation:

Answer:

y=-x+16

Step-by-step explanation:

let’s put this equation in slope intercept form: y=mx+b

2x+2y=-8

-2x.      -2x

2y=-2x-8

/2.  /2.  /2

y=-x-4

We know parallel lines have the same slope as each other so let’s fill in the equation with the given point

10=-(6)-4

10=-10

We need to add 20 more to the y intercept to make this true like this

y=-x-4+20

y=-x+16

Now let’s see if it works

10=-(6)+16

10=10

It works so this is the equation

Hopes this helps please mark brainliest

Answer: y = -x +16

Step-by-step explanation:

rearrange the equation to make y the subject

2y = -2x -8

y = -x-4

equation of line parallel to the line (gradient will be the same)

y = -x +c

Substitute the x and y values into the parallel line equation

10 = -6 + c

10 + 6 = c

16 = c

Therefore, the equation of the line parallel to 2x + 2y = -8 is y = -x +16