3. Select the angles that identify an obtuse triangle. Mark all

that apply.

A

acute, acute, acute

(B

acute, acute, obtuse

ll Publishing Company

©

right, acute, acute

D

obtuse, right, acute

1

The general formula for the nth term of the series is:an = 13 + 17² + 19² + ... + (n-2)pn² where p1, p2, ... are the first n-2 prime numbers.

This formula gives the nth term of the given series and not the partial sum of the series.

The given series is 13, 19, 127, 181, ... Let's analyze the given series.

Notice that the given series contains prime numbers. Also, each term of the series is obtained by adding the previous term to the square of the previous prime number.

With this observation, we can conclude that the nth term of the series can be represented by the formula:an = a1 + p1² + p2² + ... + (n-2)pn² where p1, p2, ... are the first n-2 prime numbers.

The first term a1 = 13, p1 = 17, p2 = 19 and so on.

To know more about prime number click on below link:

https://brainly.com/question/30210177#

#SPJ11

Answer:

25% increase

Step-by-step explanation:

Just do 250000/200000 you will find 1.25

And the one is the base 200000 and convert .25 to percentage, which is 25%

Brainliest maybe?

Answer:

25% or .25

Step-by-step explanation:

fist find the number it increased by minus 250000 from 200000

250000 - 200000 = 50000

then divide the increase by the original

50000/200000 = .25 or 25%

To find the exact value of the expression sec 0° + cot 45°, let's evaluate each term separately: sec 0°:

The secant function is the reciprocal of the cosine function. Since cosine is 1 at 0°, the reciprocal of 1 is also 1.

Therefore, sec 0° = 1.

cot 45°:

The cotangent function is the reciprocal of the tangent function. The tangent of 45° is equal to 1, so the reciprocal is also 1.

Therefore, cot 45° = 1.

Now, let's add the two terms together:

sec 0° + cot 45°

= 1 + 1

= 2

Therefore, the exact value of the expression

sec 0° + cot 45° is 2.

The correct choice is: A.

sec 0° + cot 45° = 2

To know more about secant function visit:

https://brainly.com/question/29044147

#SPJ11

Answer:

(2x+1) (2x-7)

Step-by-step explanation:

Multiply the coefficient of the first term by the constant   4 • -7 = -28

Find two factors of  -28  whose sum equals the coefficient of the middle term, which is   -12

(  -28    +    1    =    -27  

     -14    +    2    =    -12  )

Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -14  and  2  

                    4x2 - 14x + 2x - 7

Add up the first 2 terms, pulling out like factors :

                   2x • (2x-7)

             Add up the last 2 terms, pulling out common factors :

                    1 • (2x-7)

Add up the four terms :

                   (2x+1)  •  (2x-7)

Answer:

9

Step-by-step explanation:

4x2 + 8(3/4) - 5

8 + 6 - 5

14 - 5

9

Answer:

The expression (8-i)/(2+i) in standard form is, 3 - 2i

Step-by-step explanation:

The expression is,

(8-i)/(2+i)

writing in standard form,

\((8-i)/(2+i)\\\)

Multiplying and dividing by 2+i,

\(((8-i)/(2+i))(2-i)/(2-i)\\(8-i)(2-i)/((2+i)(2-i))\\(16-8i-2i-1)/(4-2i+2i+1)\\(15-10i)/5\\5(3-2i)/5\\=3-2i\)

Hence we get, in standard form, 3 - 2i

The expression (8-i)/(2+i) in standard form a+bi is (15 - 10i) / (3 + 4i).

To write the expression (8-i)/(2+i) in standard form a+bi, we need to eliminate the imaginary denominator. We can do this by multiplying the numerator and denominator by the conjugate of the denominator.

The conjugate of 2+i is 2-i. So, we multiply the numerator and denominator by 2-i:

(8-i)/(2+i) * (2-i)/(2-i)

Using the distributive property, we can expand the numerator and denominator:

(8(2) + 8(-i) - i(2) - i(-i)) / (2(2) + 2(i) + i(2) + i(i))

Simplifying further:

(16 - 8i - 2i + i^2) / (4 + 2i + 2i + i^2)

Since i^2 is equal to -1, we can substitute -1 for i^2:

(16 - 8i - 2i + (-1)) / (4 + 2i + 2i + (-1))

Combining like terms:

(15 - 10i) / (3 + 4i)

Therefore, the expression (8-i)/(2+i) in standard form a+bi is (15 - 10i) / (3 + 4i).

About complex numbers here:

https://brainly.com/question/20566728

#SPJ11

Using algebra, the necessary investment to earn $100,000 in one year with a desired rate of return of 8% is $1,250,000.

To calculate the necessary investment to earn $100,000 in one year with a desired rate of return of 8%, follow these steps:

Step 1: Define the variables.
Let P be the principal amount (the investment you want to find), R be the desired rate of return (8% or 0.08 as a decimal), and T be the time in years (1 year).

Step 2: Use the formula for simple interest.
The formula for simple interest is: Interest = P × R × T

Step 3: Set the Interest to $100,000.
$100,000 = P × 0.08 × 1

Step 4: Solve for P (the principal amount).
To find the necessary investment, P, divide both sides of the equation by 0.08:
P = $100,000 / 0.08

Step 5: Calculate the result and round to the nearest dollar.
P = $1,250,000

So, to earn $100,000 in one year with a desired rate of return of 8%, you would need to invest approximately $1,250,000.

Know more about algebra here:

https://brainly.com/question/6143254

#SPJ11

● < P=R " angles opp =sides"

●PQ =QR " Angles opposite = sides"

therefore PQR is an isosceles " 2 opp angles and sides are equal "

Answer:

The HCF of \(a=2^1 \cdot 3^4 \cdot 5^1\) and \(b = 2^3 \cdot 3^2 \cdot 5^2\) is \(90\).

Step-by-step explanation:

To calculate the HCF of two numbers given their prime factorization, we take the lowest exponent of every prime when comparing the two numbers.

So the HCF of \(a=2^1 \cdot 3^4 \cdot 5^1\) and \(b = 2^3 \cdot 3^2 \cdot 5^2\) is \(2^1 \cdot 3^2 \cdot 5^1 = 90\).

The credit card company has a balance of $1,000, a monthly interest rate of 1.5 percent, and an APR of 18 percent. If the credit card company allows Pierre to continue making no payments, then after 15 months, his balance will exceed $1,000.

Explanation:

Given that the credit card company has an APR of 18%, which means it charges an interest rate of 18/12 = 1.5% monthly, and the current balance is $800.

Let t be the time in months since Pierre's last payment, then we can use the formula to find the balance after t months:

B = P * (1 + r/100)^t

where P is the principal amount,

r is the interest rate per annum,

t is the time in years,

and B is the balance after t years.

Substituting the values of P, r, and t in the above formula, we get:

B = 800 * (1 + 1.5/100)^t

Simplifying, we get:

B = 800 * (1.015)^t

We need to find the value of t for which the balance B exceeds $1000. So, we can set up the following equation:

1000 = 800 * (1.015)^t

Dividing both sides by 800, we get:

1.25 = (1.015)^t

Taking the logarithm on both sides, we get:

log 1.25 = log (1.015)^t

Using the property of logarithms, we can simplify this as:

t = log 1.25 / log 1.015

t = 14.99

Hence, after about 15 months, Pierre's balance will exceed $1,000.

Complete Question: The credit card company has a balance of $1,000, a monthly interest rate of 1.5 percent, and an APR of 18 percent. If the credit card company were to allow Pierre to continue making no payments, after how many months would his balance exceed $ 1000 ?

To know more about interest refer here:

https://brainly.com/question/30393144

#SPJ11

Answer:

x = 5/2 is the answer to the question

An equation for a rational function with the given intercepts, vertical and horizontal asymptotes is \(f(x)=\frac{-6(x+5)(x-2)}{(x+2)(x-4)}\).

Any equation with at least one fraction in which both the numerator and denominator are polynomials is said to be rational. Let f(x) represent the required function. Given that x=1 and x=3 are vertical asymptotes. Therefore, the rational function's denominator includes the terms (x-1) and (x-3). Then, the required function is written as,

\(f(x)=\frac{g(x)}{(x+2)(x-4)}\)

Given that function f(x) has a horizontal asymptote, the degree of g(x), which is in the numerator, must match that of the denominator.

Also given that the x-intercepts are at (-5, 0) and (2, 0), the numerator can be expressed as \(f(x)=\frac{(x+5)(x-2)}{(x+2)(x-4)}\). Now substituting the horizontal asymptote at y=-6, we get, \(f(x)=\frac{-6(x+5)(x-2)}{(x+2)(x-4)}\).

To know more about asymptotes:

https://brainly.com/question/4084552

#SPJ4

Answer:

14.

Step-by-step explanation:

-67 - (-81)=14

The solution set of a homogeneous system of 18 linear equations in 20 variables lies in the null space of the coefficient matrix.

To know that every associated nonhomogeneous equation has a solution, we need to ensure that the homogeneous system has a nontrivial solution.

This means that we need to know whether the rank of the coefficient matrix of the homogeneous system is less than the number of variables, i.e., whether there exist free variables.

If the rank is less than the number of variables, then there are infinitely many solutions to the homogeneous system, and thus every associated nonhomogeneous equation has a solution.

However,

We also need to ensure that the particular solution to the nonhomogeneous equation does not lie in the null space of the coefficient matrix.

This is equivalent to checking whether the null space of the coefficient matrix is orthogonal to the vector on the right-hand side of the nonhomogeneous equation.

If it is, then the nonhomogeneous equation has a solution.

So, in summary, to know that every associated nonhomogeneous equation has a solution.

We need to know whether the rank of the coefficient matrix of the homogeneous system is less than the number of variables, and we need to check whether the particular solution lies in the null space of the coefficient matrix.

For similar question on coefficient matrix:

https://brainly.com/question/13127746

#SPJ11

Required value of s(4), s(7), s(5), s(9) are V(4) + C, V(7) + C, V(5) + C, V(9) + C respectively where c is the constant.

To determine the values of s(t) at different time points, we need to integrate the velocity function v(t) with respect to time. Based on the values you provided, it seems like you have already performed the integration correctly. However, since the values you provided are the definite integrals, we need to find the antiderivative or the indefinite integral of the velocity function to determine s(t) explicitly.

Let's assume the indefinite integral of v(t) is V(t). Then, we have:

s(t) = V(t) + C

where C is the constant of integration. To determine the constant C, we can use the initial condition s(0) = -3. Substituting t = 0 into the equation, we get:

s(0) = V(0) + C

-3 = V(0) + C

Since the constant of integration is the only unknown term, we can solve for C:

C = -3 - V(0)

Now, we can find the position function s(t) for different values of t using the indefinite integral and the constant C:

s(4) = V(4) + C

s(7) = V(7) + C

s(5) = V(5) + C

s(9) = V(9) + C

Learn more about integral here,

https://brainly.com/question/31497840

#SPJ4

Answer:

$11.56

Step-by-step explanation:

Let x = price of 1 cookbook.

Let y = price of 1 novel.

The total is

4x + y = 52.80

The novel cost $5 less than each cookbook.

y = x - 5

We have a system of equations.

4x + y = 52.80

y = x - 5

Substitute x - 5 for y in the first equation and solve for x.

4x + x - 5 = 52.80

5x = 57.80

x = 11.56

Answer: $11.56

Answer:

12, 17, 24

Step-by-step explanation:

To find the first 3 terms, substitute n = 1, 2, 3 into the rule, that is

T₁ = 1² + 2(1) + 9 = 1 + 2 + 9 = 12

T₂ = 2² + 2(2) + 9 = 4 + 4 + 9 = 17

T₃ = 3² + 2(3) + 9 = 9 + 6 + 9 = 24

Answer:

12, 17, 21 is the answer to the question

The expected loss without the generator ($495,000) is less than the cost of installing the generator ($800,000), it would not be economically justifiable for the bank to install the new power generator based on this decision tree analysis.

The management of First American Bank faces a decision regarding the installation of an emergency power generator to mitigate potential losses from physical catastrophes such as power failures or fires.

To evaluate this decision, we can use decision tree analysis.

Without the generator, there is a 10% chance of a power outage. In the event of an outage, there is a 0.05 probability of very large losses ($80 million) and a 0.95 probability of slight losses ($1 million). To calculate the expected loss from not installing the generator, we can use the following formula:

Expected loss = (probability of outage) x [(probability of large loss x large loss amount) + (probability of slight loss x slight loss amount)]

Expected loss = 0.1 x [(0.05 x $80 million) + (0.95 x $1 million)]
Expected loss = 0.1 x [$4 million + $950,000]
Expected loss = 0.1 x $4.95 million
Expected loss = $495,000

Now let's compare this expected loss to the cost of installing the emergency power generator, which is $800,000. Since the expected loss without the generator ($495,000) is less than the cost of installing the generator ($800,000), it would not be economically justifiable for the bank to install the new power generator based on this decision tree analysis.

To learn more about probability  click here

brainly.com/question/30034780

#SPJ11

By using multiplication, it can be calculated that

3 \(\times\) 9423 = 28269

What is multiplication of integers?

At first it is important to know about integers

Integers are those numbers which has no fractional part. Integer can be positive, negative and zero is also an integer.

Repeated addition is called multiplication. Multiplication is used to find the product of two or more integers.

Here the given multiplication is 3 \(\times\) 9423

3 \(\times\) 9423 = 28269

To learn more about multiplication of integers, refer to the link-

https://brainly.com/question/10873737

#SPJ1

Answer:

Parallel

Step-by-step explanation:

So if they have the same slope but different y-intercepts, it would be parallel because the slope stays the same so the line doesnt change, just the starting point

For example use the following equations

y = x + 2  

y = x + 3  

In the graph, these equations are parallel

Declan's reasoning does make sense. This is because 3/4 and 1/2 have the same denominator, and 3/4 is a larger fraction than 1/2.

Therefore, it is reasonable to assume that 3/4 is greater than 6/12 because 6/12 simplifies to 1/2. Simplifying fractions means dividing the numerator and denominator by the same number, in this case, 6 is divisible by 2, so we can reduce the fraction to 1/2.

So, Declan is correct in his reasoning that 3/4 is greater than 6/12. It is important to understand the relationship between fractions and their denominators to make such comparisons accurately.

3/4 = 9/12

1/2 = 6/12

6/12 = 6/12

Since 9/12 (which is equivalent to 3/4) is greater than 6/12 (which is equivalent to 1/2), we can say that 3/4 is indeed greater than 6/12.

Therefore, Declan's reasoning is correct.

Learn more about Fractions:

https://brainly.com/question/78672

#SPJ4

Answer:

171

Step-by-step explanation:

The data set that represented by the dot plot given is:

D. {145, 165, 165, 165, 165, 165, 175, 175, 175, 175, 175, 175, 185}

In a dot plot, each data point in a data set is represented by a dot.

To find out the data set that is represented in the dot plot, list out the data points as plotted on the dot plot given.

In the given dot plot that is showing the pulse rates of runners after finishing a marathon, it can be seen that,

There are 1 dot on 145, 5 dots on 165, 6 dots on 175 and 1 dot on 185.

Thus:

Therefore, the data set that represented by the dot plot given is:

D. {145, 165, 165, 165, 165, 165, 175, 175, 175, 175, 175, 175, 185}

To learn more about dot plots, visit the link:

brainly.com/question/25957672

#SPJ4

Answer:

The absolute difference is 1050

The relative percentage is 32.3076%

Step-by-step explanation:

We are given

The population of a town increased from 3,250 in 2008 to 4,300 in 2010

In 2008:

In 2010:

Absolute difference:

we know that

absolute difference =

absolute difference =

absolute difference is 1050

Relative increase:

we know that

Relative percentage is

now, we can plug values

=32.3076

So, the relative percentage is 32.3076%

Answer:

A,B,D

Step-by-step explanation:

right on edge

Answer:

A,B,D

Step-by-step explanation:

Therefore, Subscript indices must be real positive integers or logicals in MATLAB. This error message occurs when a user tries to access a non-existent element of an array using an index that is not a real positive integer or a logical value.

Subscript indices must be real positive integers or logicals is a MATLAB error message that occurs when a user tries to access a non-existent element of an array using an index that is not a real positive integer or a logical value. Subscripts must always be a positive integer, and not a floating-point number, character, or string.When the user tries to access an element in an array using an index that is not a real positive integer or logical value, the MATLAB interpreter throws this error message. It means that the user has tried to access an element in the array using a negative index or a non-numeric index, which is not permitted. This error message occurs when a user tries to access an array element that does not exist or is out of range. The user must ensure that the index is a real positive integer or a logical value. Logical values can be used as indices to select elements from an array. If the user tries to use a floating-point number or a string as an index, MATLAB will return an error message. In conclusion, subscript indices must be real positive integers or logicals.

Therefore, Subscript indices must be real positive integers or logicals in MATLAB. This error message occurs when a user tries to access a non-existent element of an array using an index that is not a real positive integer or a logical value.

To know more about statement visit :

https://brainly.com/question/27839142

#SPJ11

Just subtract the sum of 1/4 and 1/3 on 1

.

1 - [(1/3) + (1/4)]

Get the least common denominator. LCD = 12

= 12/12 - [(4/12) + (3/12)]

= 12/12 - (7/12)

= 5/12

.

Therefore, 5/12 of the tank is empty.

The Length of the conjugate axis is equal to 2b. The transverse axis is an essential feature of a hyperbola, as it determines the overall shape of the hyperbola.

In a hyperbola, the name of the green segment is called the transverse axis. The transverse axis is the longest distance between any two points on the hyperbola, and it passes through the center of the hyperbola. It divides the hyperbola into two separate parts called branches.

The transverse axis of a hyperbola lies along the major axis, which is perpendicular to the minor axis. Therefore, it is also sometimes called the major axis.

The other axis of a hyperbola is called the conjugate axis or minor axis. It is perpendicular to the transverse axis and passes through the center of the hyperbola. The length of the conjugate axis is usually shorter than the transverse axis.In the hyperbola above, the green segment is the transverse axis, and it is represented by the letters "2a". Therefore, the length of the transverse axis is equal to 2a.

The blue segment is the conjugate axis, and it is represented by the letters "2b".

Therefore, the length of the conjugate axis is equal to 2b.The transverse axis is an essential feature of a hyperbola, as it determines the overall shape of the hyperbola. In particular, the distance between the two branches of the hyperbola is determined by the length of the transverse axis.

If the transverse axis is longer, then the branches of the hyperbola will be further apart, and the hyperbola will look more stretched out. Conversely, if the transverse axis is shorter, then the branches of the hyperbola will be closer together, and the hyperbola will look more compressed.

For more questions on Length .

https://brainly.com/question/28322552

#SPJ8