What is the variable if


the trinomial a^2+7a+6 and the binomial a+1 have the same value?

Following are the measures of the angles given :∠ ABC = 180, ∠ BCD = 180, ∠ CDA = 270, ∠ DAB = 270.

What is parallel lines ?

Parallel lines are two or more lines that are always the same distance apart and never intersect, no matter how far they are extended.

Since AB is parallel to DC and AD is parallel to BC, we know that angles A and C are corresponding angles and angles B and D are also corresponding angles. Corresponding angles are congruent when two parallel lines are intersected by a transversal.

So, we have:

∠ A = ∠ C

∠ B = ∠ D

Given:

∠ D = 3x - 75

∠ B = x + 35

We can solve for x using the fact that the sum of the angles in a quadrilateral is 360 degrees:

∠ A + ∠ B + ∠ C + ∠ D = 360

Substituting the values we know, we get:

∠ A + (x + 35) + ∠ C + (3x - 75) = 360

Simplifying, we get:

4x - 40 = 360

4x = 400

x = 100

Now we can substitute x = 100 into the expressions for ∠ B and ∠ D to find their values:

∠ B = x + 35 = 100 + 35 = 135

∠ D = 3x - 75 = 3(100) - 75 = 225

Since angles A and C are corresponding angles, we know that:

∠ A = ∠ C = 180 - ∠ B = 180 - 135 = 45

Therefore, we have:

∠ ABC = ∠ A + ∠ B = 45 + 135 = 180

∠ BCD = ∠ B + ∠ C = 135 + 45 = 180

∠ CDA = ∠ C + ∠ D = 45 + 225 = 270

∠ DAB = ∠ D + ∠ A = 225 + 45 = 270\

So, we can see that angles ABC and BCD are straight angles (180 degrees) and angles CDA and DAB are reflex angles (more than 180 degrees).

Therefore, Following are the measures of the angles given :∠ ABC = 180, ∠ BCD = 180, ∠ CDA = 270, ∠ DAB = 270.

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The probability of rolling a dice less than 3 times is 17/100.

It is a branch of mathematics that deals with the occurrence of a random event.

The total no of times rolling = 200

The probability of rolling 1 = 17 times

And, The probability of rolling 2 = 17 times

So, the probability of rollng a dice less than 3 times is

17+17/200

34/200

17/100

Hence, the probability of rolling a dice less than 3 times is 17/100.

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Answer:

I think the answer is x= 5, -1

Answer:

i got x= 5,-1

Step-by-step explanation:

i hope this helps and have a good day

The final answer in simplest form is 7[tex]x^{2}[/tex] - 2x + 10/x.

To find the quotient of (28[tex]x^{5}[/tex]-8[tex]x^{4}[/tex]+40[tex]x^{(2)[/tex])/(4[tex]x^{3}[/tex]), we need to divide each term in the numerator by the denominator.

First, we divide 28[tex]x^{5}[/tex] by 4[tex]x^{3}[/tex]:

(28[tex]x^{5}[/tex])/(4[tex]x^{3}[/tex]) = (28/4)[tex]x^{(5-3)[/tex] = 7[tex]x^{2}[/tex]

Next, we divide -8[tex]x^{4}[/tex] by 4[tex]x^{3}[/tex]:

(-8[tex]x^{4}[/tex])/(4[tex]x^{3}[/tex]) = (-8/4)[tex]x^{(4-3)[/tex] = -2x

Finally, we divide 40[tex]x^{2}[/tex] by 4[tex]x^{3}[/tex]:

(40[tex]x^{2}[/tex])/(4[tex]x^{3}[/tex]) = (40/4)[tex]x^{(2-3)[/tex] = 10[tex]x^{(-1)[/tex] = 10/x

Putting it all together, we get:

(28[tex]x^{5}[/tex] - 8[tex]x^{4}[/tex] + 40[tex]x^{2}[/tex])/(4[tex]x^{3}[/tex]) = 7[tex]x^{2}[/tex] - 2x + 10/x

Therefore, the final answer in simplest form is 7[tex]x^{2}[/tex] - 2x + 10/x.

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Answer:

(3x + 5) and (x - 6).

Step-by-step explanation:

The height of the cylinder is approximately 2.45 inches.

Volume is the measure of the space occupied by a three-dimensional object. It is typically expressed in cubic units.

The volume of a cylinder is given by the formula V = πr²h, where V is the volume, r is the radius, and h is the height.

Substituting the given values, we get:

1 and 1/16 = π(1/4)²h

Simplifying and solving for h, we get:

h = (1 and 1/16) / (π(1/4)²)

h = (17/16) / (π/16)

h = 17/π

Approximating using π = 22/7, we get:

h ≈ 17 / (22/7)

h ≈ 2.45 inches (rounded to two decimal places)

Therefore, the height of the cylinder is approximately 2.45 inches

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Answer:

Step-by-step explanation:

Answer:

-1 and 0

Step-by-step explanation:

This is a set of simultaneous equations. To solve them, you need to substitute one into the other. The easiest way to do this would be to rearrange x - y = -6 to make x the subject:

x = -6 + y

x = y - 6

Now we can substitute this equation into y = -x^2 + 5x + 6:

y = -(y - 6)^2 + 5(y - 6) + 6

Now simplify this equation, and rearrange to make it equal to 0:

y = -y^2 + 12y - 36 + 6

y = -y^2 + 12y - 30

0 = -y^2 + 12y - y - 30

-y^2 + 11y - 30 = 0

Now solve this quadratic equation to obtain two solutions:

y = 5, y = 6

Now substitute these values back into one of the starting equations to find the respective values for x:

When y = 5:

x - 5 = -6

x = -1

When y = 6

x - 6 = -6

x = 0

Therefore, the x solutions are -1 and 0.

Answer:

70m3

Step-by-step explanation:

5:2

The 2 represents the smaller cylinder. The smaller cylinder=28

To find out how much 1 is we can divide 28 by 2 and that =14. So in the ratio 1=14 and as seen on the left side we have 5    1's. So 14 times 5= 70

Have a nice day :-)

The sum of the two polynomials is 12x^(5) - 5x^(3) - 5x^(2).

To find the sum of the two polynomials, we need to add the coefficients of the like terms. Like terms are terms that have the same variable and exponent.

Step 1: Identify the like terms in the two polynomials.
- The like terms are 8x^(5) and 4x^(5), -5x^(3) and 0 (since there is no x^(3) term in the second polynomial), x^(2) and -6x^(2).

Step 2: Add the coefficients of the like terms.
- 8x^(5) + 4x^(5) = 12x^(5)
- -5x^(3) + 0 = -5x^(3)
- x^(2) + -6x^(2) = -5x^(2)

Step 3: Combine the terms to get the sum of the two polynomials.
- 12x^(5) + -5x^(3) + -5x^(2)

Step 4: Simplify the expression if possible.
- There are no like terms that can be combined, so the expression is already simplified.

The sum of the two polynomials is 12x^(5) - 5x^(3) - 5x^(2).

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Answer:

If the relationship is proportional, we can use the proportionality constant, k, to relate the cost and number of climbs. The equation would be:

t = kc

We can find the value of k by using the given information that 5 climbs cost $52.50:

52.50 = k(5)

Solving for k, we get:

k = 10.50

Therefore, the equation that represents the total cost, t, of c climbs is:

t = 10.50c

The average percentage of time spent studying is 8.64%.

To find the average percentage of time spent studying, we need to first add up the total hours and total percentage of all the students. Then, we can divide the total percentage by the total hours to find the average percentage of time spent studying.

Total hours = 18 + 10 + 2 + 6 + 8 = 44 hours
Total percentage = 100% + 80% + 50% + 70% + 80% = 380%

Average percentage = Total percentage / Total hours = 380% / 44 hours = 8.64%
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Complete question

Find the average percentage of time spent on studying. data. Nina: 18 hours, 100%; Johannes: 10 hours, 80%; Al-Rahim: 2 hours, 50%; Caroline: 6 hours, 70%; Saul: 8 hours, 80%

Liabilities include student loans, money owed to parents, mortgage payments, and car payments, but investments and retirement funds are considered assets.

What is liability ?

Liability refers to an obligation or debt that an individual, company, or organization owes to another party. In accounting and finance, liabilities are generally classified as current or long-term and can include items such as loans, mortgages, accounts payable, taxes owed, and salaries payable.

The following options would be considered a liability:

Student loan

Money you owe your parents

Mortgage payment

Car payment

Investments and retirement funds would not be considered liabilities as they are assets.

Therefore, Liabilities include student loans, money owed to parents, mortgage payments, and car payments, but investments and retirement funds are considered assets.

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Answer:

45

Step-by-step explanation:

3² · (12-2) ÷ 2

= 9 · (10) ÷ 2

= 90 ÷ 2

= 45

So, the answer is 45

Answer: 135

Step-by-step explanation: use a calculator/online calculator

Answer:

III

Step-by-step explanation:

The option that would most likely contribute toward lowering the premium a policyholder pays for life insurance is III - maintaining good health.

Choosing whole instead of term insurance, decreasing the death benefit, and taking up smoking would increase the premium a policyholder pays for life insurance. Whole life insurance typically has higher premiums than term life insurance, decreasing the death benefit reduces the amount of coverage provided by the policy, and taking up smoking increases the risk of premature death and therefore increases the likelihood that the policy will need to pay out.

On the other hand, maintaining good health reduces the risk of premature death and lowers the likelihood that the policy will need to pay out. Therefore, insurance companies typically offer lower premiums to policyholders who maintain good health.

Answer:

answer is B

Step-by-step explanation:

II, III

The factored form of the polynomial is p(z) = (2z - 5)(z^(2) + 2z + 37).

To write the polynomial p(z) in factored form as a product of linear and quadratic expressions using integer coefficients only, we need to find the other zeros of the polynomial.

Since one of the zeros is a complex number, z = -1 + 6i, the other complex zero will be its conjugate, z = -1 - 6i. This is because complex zeros of polynomials with real coefficients always come in conjugate pairs.

Now, we can write the quadratic expression that has these two complex zeros as

(z - (-1 + 6i))(z - (-1 - 6i)) = (z + 1 - 6i)(z + 1 + 6i) = (z + 1)^(2) - (6i)^(2) = z^(2) + 2z + 1 - 36i^(2) = z^(2) + 2z + 37.

Since the polynomial p(z) is of degree 3, there must be one more zero, which we can find by dividing p(z) by the quadratic expression we just found:

p(z)/(z^(2) + 2z + 37) = 2z^(3)/(z^(2) + 2z + 37) - z^(2)/(z^(2) + 2z + 37) + 64z/(z^(2) + 2z + 37) - 185/(z^(2) + 2z + 37) = 2z - 5

So the other zero is z = 5/2.

Now,
p(z) = 2(z - 5/2)(z^(2) + 2z + 37) = (2z - 5)(z^(2) + 2z + 37)

So the factored form of the polynomial is p(z) = (2z - 5)(z^(2) + 2z + 37).

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Answer: A cup of coffee costs $2.50 and a bagel costs $3.50.

Step-by-step explanation: Let's use the following variables to represent the price of each item:

c: price of a cup of coffee (in dollars)

b: price of a bagel (in dollars)

From the problem statement, we know that:

b = c + 1 (a bagel costs $1 more than a cup of coffee)

We also know that you bought 4 cups of coffee and 6 bagels for a total of $31. This can be expressed as:

4c + 6b = 31

Now we can substitute the first equation into the second equation to eliminate b:

4c + 6(c + 1) = 31

Simplifying this equation, we get:

10c + 6 = 31

Subtracting 6 from both sides, we get:

10c = 25

Dividing both sides by 10, we get:

c = 2.5

Now we can use the first equation to find the value of b:

b = c + 1 = 2.5 + 1 = 3.5

Therefore, a cup of coffee costs $2.50 and a bagel costs $3.50.

Answer:  2+n

Step-by-step explanation:

Tn=T1 + (n-1) d

3+(n-1)1

3+n-1

3-1+n

2+n

y = 2.50 / (1 + 15.80^−x)

You can use technology to approximate the given data with a logistic regression curve y = N/(1 + Ab^−x).

To do this, you'll need to calculate the parameters A, N, and b. To calculate A and N, you can use the values of y at the extremes of x. At x = 0, y = 3.0 and at x = 150, y = 9.9. So, A = (9.9 - 3.0) / (1 - 0.003^150) and N = 9.9 - A*0.003^150. Then, b can be calculated using the average of the logarithm of all x values. The final logistic regression curve will be:

y = 2.50 / (1 + 15.80^−x)

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Answer: cos B-sin²A = cos²A-sin-B

Step-by-step explanation:

Answer: cos B-sin²A = cos²A-sin-B

Explanation:

Using the double angle identity, we can express the left side of the equation as:

cos(A + B).cos(A-B) = cos A.cos B - sin A.sin B

Now, using the Pythagorean identity, we can rewrite the right side of the equation as:

cos²A-sin-B = cos A.cos B - sin A.sin B

Hence, we can conclude that cos(A + B).cos(A-B) = cos B-sin²A = cos²A-sin-B

Answer: Read the step by step explanation for the answer.

Step-by-step explanation:

We can prove this trigonometric identity using the product-to-sum and Pythagorean identities as follows:

Starting with the left-hand side (LHS):

cos(A + B).cos(A - B)

Using the product-to-sum identity:

= [cos A cos B - sin A sin B][cos A cos B + sin A sin B]

= cos²A cos²B - sin²A sin²B

Using the Pythagorean identity:

= cos²A(1 - sin²B) - sin²A(1 - cos²B)

= cos²A - cos²A sin²B - sin²A + sin²A cos²B

= cos²A - sin²A + sin²A cos²B - cos²A sin²B

Using the Pythagorean identity:

= cos²A - sin²A + sin²A(1 - sin²B) - cos²A sin²B

= cos²A - sin²A + sin²A - sin²A sin²B - cos²A sin²B

= cos²A - sin²A + sin²A cos²B - sin²B cos²A

= cos²A - sin²A + cos²A sin²B - sin²B cos²A

Using the Pythagorean identity:

= cos²A - sin²A + cos²A - sin²B

= 2cos²A - sin²A - sin²B

= cos²A + cos²A - sin²A - sin²B

= cos²A + sin²A cos²B - sin²B

= RHS

Therefore, we have shown that (b) cos(A + B).cos(A-B) = cos B-sin²A = cos²A-sin-B.

Answer:0.1

Step-by-step explanation:

0.1

Answer:

Answer:

Most poison dart frogs are brightly colored, displaying aposematic patterns to warn potential predators. Their bright coloration is associated with their toxicity and levels of alkaloids. ... Poison dart frogs are an example of an aposematic organism.

Hostas for Full Sun

In general, yellow or gold hostas tolerate partially sunny location without losing their vibrant yellow color. About two hours of daily sun exposure will keep these yellow or golden beauties looking their best. Aim for morning sun to avoid burned leaves.

hope this helps

Step-by-step explanation:

Hope this is the right answer Have a good day!

have a good day

The likelihood function for a sequence of coin tosses x1, . . . , xn with P[H] = p is given by:

L(p) = P(x1, . . . , xn | p) = P(x1 | p) * P(x2 | p) * . . . * P(xn | p)

Using the notation that 1 denotes H and 0 denotes T, we can write the likelihood function as:

L(p) = p^k * (1-p)^(n-k)

where k is the number of heads in the sequence and n-k is the number of tails.

To find the maximum likelihood estimate for p, we need to take the derivative of L(p) with respect to p and set it equal to zero:

dL(p)/dp = k*p^(k-1)*(1-p)^(n-k) - (n-k)*p^k*(1-p)^(n-k-1) = 0

Solving for p, we get:

p = k/n
Therefore, the maximum likelihood estimate for p is the number of heads in the sequence divided by the total number of tosses.

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The value of the sample variance and the sample standard deviation for the given data is equal to 47.4 and 6.9 respectively.

Data values are,

23, 12, 5, 9,8

Number of observations 'n' = 5

Mean = ( sum of all the observations ) / ( number of observations)

         = (23 + 12 + 5 + 9 + 8) / 5

         = 57 /5

         = 11.4

Deviations of each data point from the mean,

(23 - 11.4) = 11.6

(12 - 11.4) = 0.6

(5 - 11.4) = -6.4

(9 - 11.4) = -2.4

(8 - 11.4) = -3.4

Square each deviation is equal to,

11.6² = 134.56

0.6² = 0.36

(-6.4)² = 40.96

(-2.4)² = 5.76

(-3.4)² = 11.56

Sample Variance = ( Sum of squared deviation )/ ( n - 1)

⇒Sample Variance = (134.56 + 0.36 + 40.96 + 5.76 + 11.56) / (5-1)

⇒Sample Variance = 47.35

⇒Sample Variance = 47.4(rounded to one decimal place)

Now,

Standard deviation = √variance

Substitute the value we get,

⇒ Standard Deviation = √(47.35)

⇒ Standard Deviation = 6.9 (rounded to one decimal place)

Therefore, the sample variance is 47.4 and the sample standard deviation is 6.9.

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The above question is incomplete, the complete question is:

Calculate the sample variance and the sample standard deviation for the given data. Provide your sample standard deviation answer precise to one decimal place.

23, 12, 5, 9,8

-13 is the  value of b in linear equation.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

                              Equations with variables of power 1 are referred to as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.

y = 6x + 4

 y = mx + c

is a straight line  of gradient of c.

  m = 6

y = 6x + c

the line passes through points(x,y) where x = 3 and y = 5

      5 = 6 * 3 + c

        c = 5 - 18

         c = -13

         y = 6x - 13

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Check the picture below.

Answer: Factors

Step-by-step explanation:

Triangle ABC and ADC are similar if BE is parallel to CD.

What does a triangle similarity mean?

Two triangles are comparable if the measurements of their corresponding sides are proportionate. The same is true if the lengths of two sides in one triangle are proportional to the lengths of the corresponding sides in another triangle and the included angles are congruent.

What is the triangle Theorem's similarity?

According to the fundamental theorem of similarity, a line segment can divide two triangle sides into proportionate segments if and only if it is parallel to the third side of the triangle.

We are given that BE is parallel to CD.

As per the theorem of similarity, the two triangles are similar when the a line segment of the triangle is parallel to that of another triangle.

So, from this we get that the Triangle ABC and ADC are similar.

Hence, Triangle ABC and ADC are similar.

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A company establishes a sinking fund to pay a debt of $150,000 due in 4 years. The required payment at the beginning of each six-month period is $6,235.54.

The sinking fund payment will earn interest at a rate of 9% per year, compounded semi-annually. This means the effective interest rate per six-month period is [tex](1 + 0.09/2)^2 - 1 = 0.045 = 4.5%[/tex]

Using the formula for the future value of an annuity, [tex]FV = R[((1+r)^n - 1)/r][/tex], where r is the interest rate per period and n is the number of periods, we can calculate the required payment R as:

[tex]150,000 = R[((1+0.045)^8 - 1)/0.045][/tex]

R = 6,235.54

Therefore, the company needs to make payments of $6,235.54 at the beginning of each six-month period to accumulate enough money in the sinking fund to pay off the $150,000 debt in 4 years.

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The number 19 is the solution of the equation n-7=12.

The equation given is n-7=12. To find the solution, we need to isolate the variable n on one side of the equation. We can do this by adding 7 to both sides of the equation. This gives us:

n-7+7=12+7

Simplifying the equation gives us:

n=19

Now, we can check which numbers in the set {17,19,21} are solutions of the equation. The only number that satisfies the equation is 19. Therefore, the solution of the equation is 19.

Answer: The number 19 is the solution of the equation n-7=12.

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