The solution of the equation 3x + 4 =1 is a) 1 b) 0 c) -1 d) 2​

Since AB is parallel to CD, we have alternate interior angles forming when transversal CE intersects the parallel lines. Therefore,

mZDCE = mZECB (Alternate Interior Angles)

(7x + 2) = (x + 8) (Substitute in the given angle measures)

Solving for x, we get:

7x + 2 = x + 8

6x = 6

x = 1

Now, we can use x to find the measure of angle ZDCE:

mZDCE = (7x + 2)

= (7*1 + 2)

= 9

Therefore, the measure of angle ZDCE is 9 degrees.

Answer:

Step-by-step explanation:

-4(y+9)

The rational function graphed in this problem is defined as follows:

y = -2(x - 1)/(x² - x - 2).

The vertical asymptotes of the rational function for this problem are given as follows:

x = -1 and x = 2.

Hence the denominator of the function is given as follows:

(x + 1)(x - 2) = x² - x - 2.

The intercept of the function is given as follows:

x = 1.

Hence the numerator of the function is given as follows:

a(x - 1)

In which a is the leading coefficient.

Hence:

y = a(x - 1)/(x² - x - 2).

When x = 0, y = -1, hence the leading coefficient a is obtained as follows:

-1 = a/2

a = -2.

Thus the function is given as follows:

y = -2(x - 1)/(x² - x - 2).

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The intersection of sets M and F contains the elements "c" and "d".

To find the intersection of sets M and F, we need to identify the elements that are common to both sets.

M = {a, b, c, d}

F = {c, d, e, f}

The intersection of M

and F is denoted by M ∩ F, which represents the set containing elements that are present in both M and F.

Looking at the elements in M and F, we can see that the common elements between the two sets are "c" and "d".

Therefore, the intersection of M and F can be expressed as:

M ∩ F = {c, d}

So, the intersection of sets M and F contains the elements "c" and "d".

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[tex]13 \leqslant 4x - 3 \leqslant 29 \\ 13 + 3 \leqslant 4x \leqslant 29 + 3 \\ 16 \leqslant 4x \leqslant 32 \\ 16 \div 4 \leqslant x \leqslant 32 \div 4 \\ 4 \leqslant x \leqslant 8[/tex]

Alexei's monthly payment is approximately $18.56.

Alexei finances her purchase of a $900 television with a one-year loan that has a fixed annual interest rate of 2.5%. To find Alexei's monthly payment, we can use the formula for calculating monthly loan payments.
The formula for calculating monthly loan payments is:
M = (P * r * (1 + r)^n) / ((1 + r)^n - 1)
Where:
M = monthly payment
P = principal loan amount
r = monthly interest rate (annual interest rate divided by 12)
n =number of monthly payments
In this case, the principal loan amount (P) is $900, the annual interest rate (r) is 2.5% (or 0.025 when expressed as a decimal), and the number of monthly payments (n) is 12 (since it is a one-year loan).
First, we need to calculate the monthly interest rate (r) by dividing the annual interest rate by 12: r = 0.025 / 12 = 0.002083.
Next, we can substitute the values into the formula:
M = (900 * 0.002083 * (1 + 0.002083)^12) / ((1 + 0.002083)^12 - 1)
Simplifying the formula gives us:
M = (900 * 0.002083 * 1.002083^12) / (1.002083^12 - 1)
Calculating the values inside the formula gives us:
M = (900 * 0.002083 * 1.026260) / (1.026260 - 1)
Further simplifying the formula gives us:
M = (900 * 0.002083 * 1.026260) / 0.026260
Finally, calculating the expression gives us:
M ≈ 18.56
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The probability that four batteries connected in series will have a combined voltage of 60.8 or more volts is approximately 0.0228 or 2.28%.

To find the probability that four batteries connected in series will have a combined voltage of 60.8 or more volts, we need to use the concept of the Central Limit Theorem.

In this case, we know that the mean voltage of a single battery is 15 volts and the standard deviation is 0.2 volts. When batteries are connected in series, their voltages add up.

The combined voltage of four batteries connected in series is the sum of their individual voltages. The mean of the combined voltage will be 4 times the mean of a single battery, which is 4 * 15 = 60 volts.

The standard deviation of the combined voltage will be the square root of the sum of the variances of the individual batteries. Since the batteries are connected in series, the variance of the combined voltage will be 4 times the variance of a single battery, which is 4 * (0.2)^2 = 0.16.

Now, we need to calculate the probability that the combined voltage of four batteries is 60.8 or more volts. We can use a standard normal distribution to calculate this probability.

First, we need to standardize the value of 60.8 using the formula:

Z = (X - μ) / σ

Where X is the value we want to standardize, μ is the mean, and σ is the standard deviation.

In this case, the standardized value is:

Z = (60.8 - 60) / sqrt(0.16)

Z = 0.8 / 0.4

Z = 2

Next, we can use a standard normal distribution table or calculator to find the probability associated with a Z-score of 2. The probability of obtaining a Z-score of 2 or more is approximately 0.0228.

Therefore, the probability that four batteries connected in series will have a combined voltage of 60.8 or more volts is approximately 0.0228 or 2.28%.

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Answer:

Step-by-step explanation:

3.6*

It is very easy to find the perimeter of a square when its area is given in the question. For that, you only ned to know one fomula. That formula is: Area = side^2

For this particular question, the given value for the area of the square is 36 sq.cm. So, we can solve for the side(s) by substituting the given value in the above mentioned formula.

We get

36 = s^2

Now, we need to get the square root of both sides, which gives us

s = √36 s = 6 cm

Since all the sides of a square are equal in length, the side length is 6 cm. Now to determine the perimeter, we must multiply the side length by 4 (because there are 4 equal sides in a square). That gives us Perimeter = 4 x side length Perimeter = 4 x 6 cm.

Therefore, the perimeter of the square is 24 cm.

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Hello!

7x² - 14x + 7

7(x² - 2x + 1)

= 7(x(x - 1) - 1(x - 1))

= 7((x - 1)(x - 1))

= 7(x - 1)²

The amount (present value at age 60) that Sandro would neet in his retirement savings account in order to have a monthly income of $1,500 until he is 90 years old, compounded at 4.5% monthly is $296,041.74.

The present value is computed using an online fiance calculator that discounts the future withdrawals (monthly income) for a 360-months period.

End of withdrawal period = 90 years old

Beginning of withdrawal period = 60 years old

The number of years between 60 and 90 = 30 years

N (# of periods) = 360 months (30 years x 12)

I/Y (Interest per year) = 4.5%

PMT (Periodic Payment) = $-1,500

FV (Future Value) = $0

Results:

Present Value (PV) = $296,041.74

Sum of all periodic payments = $540,000 ($1,500 x 360 months)

Total Interest = $243,958.26

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The mean absolute deviation is $106.6.

Given the table shows the amount Bill spent on 5 days last week.

DayAmount12622313126534To find the mean of the amount he spent: The formula for calculating the mean of a given set of values is mean=∑x/n where x represents the values, n represents the number of values, and ∑x represents the sum of the values.

Mean=total sum of values/total number of values Mean=(26+23+31+26+534)/5Mean=640/5Mean=128So,

the mean of the amount he spent is $128.To find the mean absolute deviation: The mean absolute deviation (MAD) is the average distance between each data value and the mean. MAD shows how much the data set deviates from the mean. The formula for calculating the MAD is MAD=∑|xi−m|/n where xi represents the values, m represents the mean, and n represents the number of values. So, the calculation for each day is:

Day Amount Absolute deviation from mean1 26 |128-26|=102 23 |128-23|=105 31 |128-31|=974 26 |128-26|=102 534 |128-534|=406

The sum of all absolute deviations is:

10+10+97+10+406=533The mean absolute deviation (MAD) is: MAD=533/5=106.6So.

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Answer:

1.5926

Step-by-step explanation:

-We need to first convert the height in feet to inches: Since there are 12 inches in a foot, that means there are 74 inches in a height of 6 foot 2 inches.

-Since the observed height is 74 inches and the mean height is 69.7 inches, we can find the z score by using the following formula:

z = (x-mean) / standard deviation

-We would fill this out like this:

z = (74-69.7) / 2.7

-This equals = 1.592592593

-Rounded to 4 decimal places, this equals 1.5926

Answer:

y = [tex]\sqrt{55}[/tex]

Step-by-step explanation:

using the Altitude- on- Hypotenuse theorem

(altitude)² = product of parts of hypotenuse

then

y² = 11 × 5 = 55 ( take square root of both sides )

y = [tex]\sqrt{55}[/tex]

Step-by-step explanation:

this is physics (not math per se).

the first moves to the left, because the distance to the positive charge on the left is shorter than the distance to the positive charge on the right.

the second moves to the right, because the positive charge is greater there and the distance to the positive charge is shorter too.

the third stays where it is. the -2 charge moves to the left until it hits the first +2 charge. there they neutralize each other, and nothing else is happening. also before -2 and +2 meet, they are neutralizing each other already for an outside observer (like the green ringed +2).

but - it depends how picky your teacher tries to be here.

because when you look at the very fine details, until -2 and the right +2 meet and really neutralize each other, there is a tiny little overhang of positive charges the green ringed +2 charge would "feel". simply because the +2 is a little bit closer than the -2.

and when we consider this, the green ringed +2 would move very little to the left (repelled by the other positive overhanging charge on the right) until -2 and +2 actually meet.

Step-by-step explanation:

21x²-2x +1/2 = 0

x² - 2x ×21 + 1/2× 21 = 0

Answer:

triangle XYZ is similar to triangle RPQ

scale factor = 2/5

Step-by-step explanation:

Angles X and R are given as congruent.

Angles Z and Q are right angles, so they are congruent.

Then, angles Y and P must be congruent.

The similarity statement is

triangle XYZ is similar to triangle RPQ

To find the scale factor, divide the length of a side of the image by the length of the corresponding side in the original.

10/25 = 2/5

The scale factor is 2/5.

Cliff pays a total interest of approximately $679.90 on his $5,000 loan.

To calculate the total interest paid on the loan, we need to use the formula for compound interest:

[tex]A = P(1 + r/n)^{(nt)}[/tex]

Where:

A is the final amount (loan amount + interest)

P is the principal (loan amount)

r is the annual interest rate (in decimal form)

n is the number of times interest is compounded per year

t is the number of years

Given that Cliff takes out a $5,000 loan with a fixed annual interest rate of 7% compounded monthly, we can substitute the values into the formula:

P = $5,000

r = 7% = 0.07

n = 12 (monthly compounding)

t = 2 years

[tex]A = 5000(1 + 0.07/12)^{(12 \times 2)[/tex]

Calculating this expression:

A ≈ 5000[tex](1.00583)^{(24)[/tex]

A ≈ 5000(1.13598)

A ≈ 5679.90

The final amount (A) is the loan amount plus the total interest paid. Therefore, to find the total interest paid, we subtract the principal (P) from the final amount (A):

Total Interest = A - P

Total Interest = 5679.90 - 5000

Total Interest ≈ $679.90

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