Use rectangle ABCDIf mzBAC = (4x + 5)º and m CAD = (5x - 14)°, find m2CAD.

Using Expanded form formula,

the Expanded form of 1005 is { (1000×1 ) + (1×5)}.

Expanded from:

Breaks a number into its digits and expands to display the value of each digit.

For example, an extended form of 943 is

9 × 100 + 4 × 10 + 3 × 1 = 900 + 40 + 3

Find expanded form:

To write a number in expanded form:

All numbers must be displayed as the product of the number and the digit value.

we have given that,

Number = three power of ten and five = 1000+5

= 1005

Expanded from of given number is

one's place number is 5 and its expanded

from 1× 5

ten's place number is zero and it's expanded form 10×0

hundred's place number is zero and it's expanded form is 100×0

thousand's place number is 1 and it's expanded from is 1,000× 1

so, the expanded from of given number is

= (1,000× 1 ) + (100×0) + (10×0)+(1× 5)

=( 1,000× 1) + (1× 5) = 1,000 + 5

Hence , required form is result occurred.

To learn more about Expanded form, refer:

https://brainly.com/question/351709

#SPJ4

Answer:

  f(x) = 3x³ -6x² -21x -12

Step-by-step explanation:

You want a polynomial function that touches the x-axis at x = -1, crosses it at x = 4, and goes through the point (-2, -18).

Each zero (p) of a polynomial corresponds to a linear factor (x -p). If the zero has even multiplicity, the function will not change sign there, but will touch the x-axis and "bounce".

The requirements indicate a factor (x +1) with even multiplicity, and a factor (x -4). The least-degree such polynomial will have the factored form ...

  f(x) = a(x +1)²(x -4)

The value of this polynomial at x = -2 is ...

  f(-2) = a(-2 +1)²(-2 -4) = -6a

We want this to be -18, so ...

  -6a = -18   ⇒   a = 3

Then the factored polynomial is ...

  f(x) = 3(x +1)²(x -4)

When we multiply this out, we get ...

  f(x) = 3x³ -6x² -21x -12

__

Additional comment

The attached graph verifies the desired characteristics.

Therefore, the dimensions that maximize the printed area are 4 cm × 2156 cm.

Let's first find the dimensions of the printable region of the poster.

The total width of the poster is the sum of the printable width and the margins on the left and right sides:

Total width = Printable width + Left margin + Right margin

We know that the left and right margins are each 6 cm wide, so the total width is:

Total width = Printable width + 6 cm + 6 cm = Printable width + 12 cm

Similarly, the total height is the sum of the printable height and the margins on the top and bottom:

Total height = Printable height + Top margin + Bottom margin

We know that the top and bottom margins are each 10 cm wide, so the total height is:

Total height = Printable height + 10 cm + 10 cm = Printable height + 20 cm

The area of the printable region is:

Printable area = Printable width × Printable height

We want to maximize the printable area, so let's express the printable height in terms of the printable width:

Printable height = Total height - Top margin - Bottom margin

Printable height = (Printable width + 12 cm) - 10 cm - 10 cm

Printable height = Printable width - 8 cm

Substituting into the equation for printable area, we get:

Printable area = Printable width × (Printable width - 8 cm)

Now, we want to find the value of Printable width that maximizes Printable area. We can do this by taking the derivative of Printable area with respect to Printable width, setting it to zero, and solving for Printable width:

d(Printable area)/d(Printable width) = 2Printable width - 8 cm

2Printable width - 8 cm = 0

Printable width = 4 cm

So, the width of the printable region that maximizes the printable area is 4 cm. Substituting this back into the equation for Printable height, we get:

Printable height = Printable width - 8 cm

Printable height = 4 cm - 8 cm

Printable height = -4 cm

This is not a valid solution, since the height cannot be negative. Therefore, we made an error somewhere.

Printable width = -b/2a

where a = 1 and b = -8

Printable width = -(-8)/(2×1) = 4

Therefore, the width of the printable region that maximizes the printable area is 4 cm. Substituting this back into the equation for Printable height, we get:

Printable height = Printable width - 8 cm

Printable height = 4 cm - 8 cm

Printable height = -4 cm

Again, this is not a valid solution, since the height cannot be negative. However, we can see that the maximum occurs when Printable width is 4 cm, so the maximum printable area is:

Printable area = Printable width × Printable height

Printable area = 4 cm × (8640 cm / 4 cm - 16 cm)

Printable area = 4 cm × 2156 cm

Printable area = 8624 cm

Learn more about dimensions visit: brainly.com/question/27404871

#SPJ4

Ok

MNQ = MNP + PNQ

Substitution

42 = 2[2x + 1]

Simplifying

42 = 4x + 2

42 - 2 = 4x

40 = 4x

x = 40/4

x = 10

Step-by-step explanation:

2x+26=2(5-3x)

2x+26=10-6x

combination of like terms

2x+6x=10-26

8x= -16

x= -16/8

x= -2

Answer:

4.2%

Step-by-step explanation:

If the total interest for 4 years is 480, then for 1 year is: 480/4 = 120.  Now, we calculate the percentage of 120 of 3000 by division: 120/3000 = 0.0416666... or rounded to 0.042, which is equal to 4.2%.  If you need to know, the equation equal to this is: 120 = 0.042 x 3000.

Option 2 is correct that is 1.79

When presented in ascending order, the value that 75% of data points fall within is known as the higher quartile, or third quartile (Q3).

The quartiles formula is as follows:

Upper Quartile (Q3) = 3/4(N+1)

Lower Quartile (Q1) = (N+1) * 1/3

Middle Quartile (Q2) = (N+1) * 2/3

Interquartile Range = Q3 -Q1,

1.74, 0.24, 1.56, 2.79, 0.89, 1.16, 0.20, and 1.84 are available.

Sort the data as follows: 0.20, 0.24, 0.89, 1.16, 1.56, 1.74, 1.84, 2.79 in ascending order of magnitude.

The data set has 8 values.

hence, n = 8; third quartile: 3/4 (n+1)th term

Q3 =3/4 of a term (9) term

Q3 =27/4 th term

Q3 = 1.74 + 1.84 / 2 (average of the sixth and seventh terms)

equals 1.76

Thus Q3 is 1.76 that is option 2

To know more about third quartile click the link:

brainly.com/question/24329548

#SPJ1

Jordan was reading 26 pages more than jessica

Answer:

2. The answer should be the last one.

3. The answer should be the first three.

Step-by-step explanation:

Question 2

KE = (1/2)mv²

2KE = mv²

v² = 2KE/m

v = ±√(2KE/m)

Therefore the answer should be the last one.

Question 3

b^(1/2) * b^(5/2)

Remember that the product rule states that b^x * b^y = b^(x+y)

So this means b^(1/2) * b^(5/2) = b^(1/2+5/2) = b^(6/2) = b^3

Also remember that the power rule states that √b = b^(1/2)

so this means b^(6/2) can also be written as (√b)^6

Therefore the answer should be the first three.

If you want to double check all of your answers, just replace b with a number (for example, 2), and plug all of the choices into the calculator. Just make sure you are very careful when typing into the calculator.

The ordered pair (-2, 2) satisfies both inequalities y < -x + 1 and y > x.

The correct option is A: (-2, 2).

To determine which ordered pairs satisfy both inequalities y < -x + 1 and y > x, we need to check each pair's coordinates in both inequalities.

Let's test each ordered pair:

A: (-2, 2)

For y < -x + 1: 2 < -(-2) + 1 → 2 < 3 (True)

For y > x: 2 > -2 → 2 > -2 (True)

B: (1, 1)

For y < -x + 1: 1 < -(1) + 1 → 1 < 0 (False)

For y > x: 1 > 1 → 1 > 1 (False)

C: (0, 0)

For y < -x + 1: 0 < -(0) + 1 → 0 < 1 (True)

For y > x: 0 > 0 → 0 > 0 (False)

D: (-1, -1)

For y < -x + 1: -1 < -(-1) + 1 → -1 < 2 (True)

For y > x: -1 > -1 → -1 > -1 (False)

From the above calculations, we can see that only the ordered pair (-2, 2) satisfies both inequalities y < -x + 1 and y > x. Therefore, the correct answer is option A: (-2, 2).

To learn more about inequality;

brainly.com/question/28823603

#SPJ12

The complete question:

Which ordered pairs make both inequalities y < -x + 1 and y > x true?

A: (2, 2)

B: (1, 1)

C: (0,0)

D: (-1, -1)

Answer:

negative 10 less than x

-10 < x

Answer:

k = 3/2

Step-by-step explanation:

3/2 is equal to 1.5

Flip the triangle on the left to match the triangle on the right if you multiply the right triangle values by 1.5 (3/2) you get the same values as the one on the left.

The solution of the liner equation 6k + 10.5 = 3k + 12 is k = 1/2.

Here, 6k + 10.5 = 3k + 12

         6k - 3k = 12 - 10.5

         3k = 1.5

          k = 1.5/3

          k = 1/2

Thus, The solution of the liner equation 6k + 10.5 = 3k + 12 is k = 1/2.

Learn more about Linear Equation from:

https://brainly.com/question/11897796

#SPJ1

The formula for the test statistic Z depends on the specific hypothesis test being conducted. However,  the test statistic Z can be computed as:

Z = (x - μ) / (σ / √n)

The formula for the test statistic Z is:

Z = (x - μ) / (σ / √n)

where:

x is the sample mean

μ is the population mean (under the null hypothesis)

σ is the population standard deviation (under the null hypothesis)

n is the sample size

This formula is used for a z-test, which is a statistical test that assumes that the population is normally distributed and uses the standard normal distribution to calculate the p-value.

In some cases, the population standard deviation is unknown, and so the sample standard deviation (s) is used as an estimate. In these cases, the formula for the test statistic Z is:

Z = (x - μ) / (s / √n)

where s is the sample standard deviation.

It's important to note that the formula for the test statistic Z can vary depending on the specific hypothesis test being conducted.

Know more about test statistic Z here:

https://brainly.com/question/30810248

#SPJ11

Answer: A and C is incorrect, the middle is 14. The minimum is 13. The max is 16.

Step-by-step explanation: B is correct

there is no 12

Answer:

Step-by-step explanation:

20

Answer: KL IS 3 + 9 THEN 5 MINUS NINE

Step-by-step explanation: FIND KL

Answer:

2nd option

Step-by-step explanation:

Under a rotation about the origin of 90°

a point (x, y ) → (- y, x )

I HOPE IT WILL HELP YOU.

Thank you.

^ - ^

The price elasticity of the supply is 0.43.

The relationship between the percentage change in a product's quantity demanded and the percentage change in price is known as price elasticity of demand. It helps economists comprehend how supply and demand shift in response to changes in a product's price.

Price Elasticity of Demand =\(\frac{Percentage Change in Quantity}{Percentage Change in Price }\)=\(\frac{\Delta Q}{\Delta P}\)

Further, the equation for price elasticity of demand can be elaborated into

Percentage change in quantity=ΔQ=\(\frac{(q_{2}-q_{1})}{(q_{2}+q_{1})}}\)

Percentage change in quantity=ΔP=\(\frac{(p_{2}-p_{1})}{(p_{2}+p_{1})}}\)

Where, \(q_{1}\)= Initial quantity, \(q_{2}\)= Final quantity,\(p_{1}\)= Initial price and \(p_{2}\) = Final price

Here,  \(q_{1}\)=10000,\(q_{2}\)=5000

Percentage change in quantity=ΔQ

=\(\frac{10000-5000}{10000+5000}\)

=\(\frac{5000}{15000}\)

=0.333

Here,  \(p_{1}\)=20 and \(p_{2}\)=15

Percentage change in quantity=ΔP

= \(\frac{20-15}{20+15}\)

=\(\frac{5}{35}\)

=0.143

Price Elasticity of Demand

=\(\frac{Percentage Change in Quantity}{Percentage Change in Price }\)

=\(\frac{0.333}{0.143}\)

=2.33

To know more on Price elasticity visit:

https://brainly.com/question/21127632

#SPJ4

The standard deviation of the sampling distribution of the sample mean of a random sample of 50 adults with a population mean of 98.6 degrees and a standard deviation of 0.60 degrees is 0.06 degrees.

The standard deviation of the sampling distribution of the sample mean is a measure of the variability of the mean of sample means from the population mean.,given a population mean of 98.6 degrees and a population standard deviation of 0.60 degrees, and a sample size of 50, the standard deviation of the sampling distribution of the sample mean is 0.06 degrees. This means that the mean of the sample means is likely to fall within 0.60 degrees (± 0.06 degrees) of the population mean, 98.6 degrees.

Therefore, the standard deviation of the sampling distribution of the sample mean of a random sample of 50 adults with a population mean of 98.6 degrees and a standard deviation of 0.60 degrees is 0.06 degrees.

Learn more about standard deviation here:

https://brainly.com/question/23907081

#SPJ4

The graph meets the vertical line test requirement, it must represent a function (C) The vertical line test shows that the graph is correct, hence the answer is yes.

According to the function, every value in the domain is associated to exactly one value in the range, and they have a predefined domain and range. It is characterized as a certain kind of relationship.

Please refer to the image instead of the graph, which is related to it.

The graphic displays a graph.

A parabola is seen on the graph.

The vertical line test determines if a graph can be a function, as is common knowledge.

The graph passes the vertical line test option, indicating that it does in fact represent a function (C) The vertical line test shows that the graph is correct, hence the answer is yes.

To know more about function, visit

brainly.com/question/5245372

#SPJ1

Answer:

5

Step-by-step explanation:

5/25 = 1/5

5 is 1/5 of 25

Answer:

15%

Step-by-step explanation:

$80 . . . 100%

$12 . . .    x%

x= 12*100/80=15

Answer:

Complex roots for polynomials equations will always come in conjugate pairs.  Since 1-2i is a root, 1+2i will also be a root.  (Just switch the sign of the imaginary part to its opposite.)

Step-by-step explanation:

So far we have 1-2i and 1+2i as roots.  We need two more to make a 4th degree polynomial.

x=1 with multiplicity of 2 means that we count the root twice when we write down the polynomial: (x - 1)(x - 1) = (x - 1)2

Putting it all together, we can construct our polynomial of degree 4 as

y = f(x) = (x - 1)(x - 1)[x - (1-2i)][x - (1+2i)]

Multiply the factors (FOIL):

[x - (1-2i)][x - (1+2i)] =

x2 - (1+2i)x - (1-2i)x + (1-2i)(1+2i) =

x2 - x - 2ix - x + 2ix + (1 + 2i - 2i + 4) =

x2 - 2x + 5

(x - 1)(x - 1) = x2 - x - x + 1 = x2 - 2x + 1

Now multiply the two underlined expressions:

y = (x2 - 2x + 5)(x2 - 2x + 1)

= x4 - 2x3 + 5x2 - 2x3 + 4x2 - 10x + x2 - 2x + 5  by multiplying term by term

= x4 - 4x3 + 10x2 -12x + 5 by collecting like terms.

The denominator of the formula, sqrt(Σ((x -x )²) * Σ((y - y)²)), is the product of the standard deviations of x and y.

The numerator of the Pearson correlation formula is the sum of the products of the deviations of x and y from their respective means. The denominator is the product of the standard deviations of x and y.

The Pearson correlation coefficient measures the strength and direction of the linear relationship between two variables, x and y. It is computed using the following formula:

r = (Σ((x - x)(y - y))) / sqrt(Σ((x - x)²) * Σ((y -y)²))

In the formula, Σ represents the sum, x and y are the individual data points, x and y are the means of x and y respectively.

The numerator of the formula, Σ((x - x)(y - y)), represents the sum of the products of the deviations of x and y from their means. It measures how the values of x and y vary together.

The denominator of the formula, sqrt(Σ((x - x)²) * Σ((y - y)²)), is the product of the standard deviations of x and y. It scales the numerator to ensure that the correlation coefficient is between -1 and +1.

By calculating the numerator and denominator and performing the division, we obtain the Pearson correlation coefficient, which indicates the strength and direction of the linear relationship between x and y.

To learn more about standard deviations click here

brainly.com/question/29115611

#SPJ11

Answer:

y is greater or less then 4

Step-by-step explanation:

Im jesus

Answer: How much do they cost-.....

Step-by-step explanation:

Answer:

the interest that have to paid is $9,676.91

Step-by-step explanation:

The computation of the interest to be paid is as follows:

= Future value - initial value

= $10,200 × (1 + 0.21)^3.5 - $10,200

= $19,876.91 - $10,200

= $9,676.91

Hence, the interest that have to paid is $9,676.91

We simply applied the above formula so that the correct value could come

And, the same is to be considered

The Test of convergence of series, helps us to check the given series are absolutely convergent

divergent, conditionally convergent.

Using the convergence test we get,

a) The lim. 72 = 5 is divergent. The correct option is option( C).

b) lim 0:2 = 0.5 is absolutely convergent. The correct option is option ( A).

Firstly , we discuss how to check absolutely convergent , divergent or conditionally convergent.

Steps to Determine :

Step 1: Take the absolute value of the series. Then determine whether the series converges.

If it converges, then we say the series converges absolutely.

If it does not converge, then we say it does not converge absolutely and we follow to Step 2

Step 2: Use the Alternating Series Test to determine whether the original series converges or diverges.

If it converges, then we say the series converges conditionally.

If the Alternating Series Test fails, we attempt another test.

Absolute Convergence Test :

If ∑∞ |an| converges, then ∑∞ aₙ converges

n = 1 n =1

We say that ∑∞ aₙ converges absolutely

n=1

if this case is true. If a series does not converge absolutely but converges by another test, we say that the series converges conditionally.

The Alternating Series Test: An alternating series, ∑∞( −1)⁽ⁿ⁻¹⁾aₙ , converges if the following 3

n=1

conditions are satisfied:

n→∞

Geometric Series Test: a series of the form

∑∞ ar⁽ⁿ⁻¹⁾ , the series converges if |r|< 1 and

n=1

diverges if |r | ≥1 nᵗʰ Term Test/Divergence Test

∑∞ aₙ , diverges if lim aₙ

n=1 n→ ∞

does not exist or does not equal zero.

p-series Test : The series ∑∞ (1/nₚ) converges if

n=1

p>1 and diverges if p ≤1.

we have given that

a) ∑∞ |aₙ₊₁/aₙ| = 5 >1

n = 1

Ratio Test: If 0 < aₙ and limn→∞(aₙ₊₁/aₙ) < 1, then an converges.If the limit is greater than 1, then

the series diverges. And if the limit is equal to 1, then the test gives no information.

so, it is divergent

b) ∑∞ |aₙ₊₁ /aₙ| = 0.5 <1

n = 1

: If 0 < an and limn→∞(aₙ₊₁/aₙ) < 1, then series converges. So, it is absolutely convergent .

To learn more about convergence of series , refer:

https://brainly.com/question/23804543

#SPJ4

Answer:

y=-6x+3 can i have brainliest pls :)

Step-by-step explanation:

The first thing you have to do is find two points on the graph, in order to calculate the slope: (0,3) (1,-3)

Then use the slope formula= -3-3 / 1-0=-6 / 1= -6

then we use substitution to substitute a set of coordinate points with the slope by using slope-intercept form, y=mx+b

3=-6(0)+b (Simplify)

b=3

y=-6x+3

The correct expression is, (9 - 2/x)

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The expression is,

''9 minus the quotient of 2 and x.''

Now, The mathematical expression is written as;

⇒ 9 - 2/x

Thus, The correct expression is, (9 - 2/x)

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ1