A complementary pair of angles have a measure of 37∘ and (5x+3)∘. solve for x and the missing angle.

x= the missing angle is ___

6x/2 = 12

Cancel out the common factor 2:

3x = 12

Divide both sides by 3:

x = 4

hope this helped!

Answer:The solution is x= +6, -6.

Step-by-step explanation:

What is Quadratic equation?

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.

The first condition for an equation to be a quadratic equation is the coefficient of x2 is a non-zero term(a ≠ 0). For writing a quadratic equation in standard form, the x2 term is written first, followed by the x term, and finally, the constant term is written.

Roots of a Quadratic Equation

The roots of a quadratic equation are the two values of x, which are obtained by solving the quadratic equation. These roots of the quadratic equation are also called the zeros of the equation.

Given:

x² - 36 =0

x² = 36

x= √36

x= ±6

hence, the solution is x= +6, -6.

Answer:

Joanie is correct. Each second sweater is sold at 40% off. If you divide this by 2 each sweater is sold by 20% off.

Joanie buys 4 sweaters and saves 20% total.

Drop downs:

John will clean the house for 5/2 = 2.5 hours.

What is quadratic equation?

The polynomial equation whose highest degree is two is called a quadratic equation or sometimes just quadratics. It is expressed in the form of:

ax² + bx + c = 0

where x is the unknown variable and a, b and c are the constant terms.

Given, that John cleans the house 2 hours more than Jane.

Let x be the time taken by the Jane and x +2 be the time taken by John.

Total they work for 2 hours 24 minutes

first we will convert minutes into hours, 24/60

= 2.4 hours

Let time taken by John = 1/x+2

time taken by Jane = x

1/x + 1/(x+2) = 2.4

Taking lcm,

x+x+2 = 2.4(x)(x+2)

2x +2 = 2.4\(x^{2}\) +4.8x

2.4x\(x^{2}\)+2.8x -2 = 0

On solving it,

x = \(\frac{b-\sqrt{b^{2-4ac} } }{2a}\)

x = 1/2 and x = -5/3

only x = 1/2 is possible value.

Time taken by John = 1+1/2

=5/2

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Answer:

717.25 that's the answer

5738 divided by 8 but you only want the R and the R is 2869

The terms with "x" cancel out, and we're left with:

0 = 12

6 + 10 + x + (12 - (6 + 10 + x)) = 12

Simplifying the equation, we have:

16 + x - (16 + x) = 12

The terms with "x" cancel out, and we're left with:

0 = 12

Let's denote the number of slices with both pepperoni and mushrooms as $x$. We are given that there are 6 slices with pepperoni and 10 slices with mushrooms.

Since every slice has at least one topping, the total number of slices is 12. We can break down the slices into the following categories:

Slices with only pepperoni: 6 slices

Slices with only mushrooms: 10 slices

Slices with both pepperoni and mushrooms: $x$ slices

Slices with neither pepperoni nor mushrooms: 12 - (6 + 10 + x) slices

We know that the total number of slices is 12, so we can write an equation:

6 + 10 + x + (12 - (6 + 10 + x)) = 12

Simplifying the equation, we have:

16 + x - (16 + x) = 12

The terms with "x" cancel out, and we're left with:

0 = 12

This equation is not possible to satisfy. Therefore, there must be an error or inconsistency in the given information. Please check the information provided again.

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There will be a nail clip tool when you press the + button. Then you will be able to access your file you need to enter.

The complete true mathematical statement is 4 4/5 + 3 2/3 < 8 1/2

From the question, we have the following parameters that can be used in our computation:

4 4/5 + 3 2/3 ________ 8 1/2

Evaluate the sum of the integer parts of the fractions

So, we have the following representation

7 4/5 + 2/3 ________ 8 1/2

Next, we take the LCM of 5 and 3 and evaluate the sum

This gives

7 (12 + 10)/15  ________ 8 1/2

Evaluate the sum of 12 and 10

So, we have

7 (22)/15  ________ 8 1/2

Simplify

7 + 1 7/15  ________ 8 1/2

Add 7 and 1

8 7/15  ________ 8 1/2

7/15 is less than 1/2

So, we have

8 7/15  < 8 1/2

Hence, the operator that completes the statement is <

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In the triangle Megan constructed, option A, B, and D are correct:  m∠A = x°, m∠B = (4x)°, and m∠C = (5x – 30)° respectively.

In Megan’s triangle, m∠A is represented by x°, m∠B is 4 times greater than m∠A, and m∠C is 30° less than 5 times m∠A. Therefore:

m∠A = x°

m∠B = 4x°

m∠C = 5x° - 30°

To find the sum of all angles in a triangle, we use the formula:

m∠A + m∠B + m∠C = 180°

Substituting the values we get:

x + 4x + (5x - 30) = 180

10x - 30 = 180

10x = 210

x = 21

Therefore:

m∠A = x° = 21°

m∠B = 4x° = 84°

m∠C = 5x° - 30° = 75°

So the following statements are true about the triangle Megan constructed:

m∠A = x° is true

m∠B = (4x)° is true

m∠C = (5x - 30)° is true

The sum of all angles in a triangle is always equal to 180 degrees.

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Complete question is:

Megan constructed triangle ABC. In Megan’s triangle, m∠A is represented by x°, m∠B is 4 times greater than m∠A, and m∠C is 30° less than 5 times m∠A.

Choose the statements that are true about the triangle Megan constructed. Select all that apply.

A) m∠A = x°

B) m∠A = (5x)°

C) m∠B = (4x)°

D) m∠C = (5x – 30)°

E) m∠A + m∠B + m∠C = 360°

Answer:

A half is not a unit of measure for weight, so it is not possible to answer this question.

The slope of the tangent to the curve \(y = 6 + 5x^2 - 2x^3\) at the point where x = a is given by the derivative of the equation, which is obtained by differentiating the equation with respect to x.

To find the slope of the tangent to the curve \(y = 6 + 5x^2 - 2x^3\) at the point where x = a, we need to take the derivative of the equation with respect to x. Differentiating each term of the equation, we get:

dy/dx = \(d(6)/dx + d(5x^2)/dx - d(2x^3)/dx\)

The derivative of a constant (6) is zero, and for the other terms, we apply the power rule of differentiation. The power rule states that the derivative of \(x^n\) with respect to x is \(nx^{(n-1)\). Applying the power rule, we obtain:

dy/dx = \(0 + 2(5x) - 3(2x^2)\)

Simplifying this expression, we get:

dy/dx = \(10x - 6x^2\)

Now, to find the slope of the tangent at the point where x = a, we substitute a for x in the derivative:

m = \(10a - 6a^2\)

Therefore, the slope of the tangent to the curve \(y = 6 + 5x^2 - 2x^3\) at the point where x = a is given by the expression \(10a - 6a^2\).

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The company can maximize its revenue by charging the price of $73 per phone.

Changing the price and monitoring how many phones are sold in reaction to the price change allows for trial-and-error in determining accuracy.

With 520 phones sold each week at $73, the corporation will make a total of $38,160 in revenue. There are 20 more phones than when it was charging $75, thus the business will make an additional $1,500 every week.

Due to the increased number of phones sold, the corporation may increase revenue by merely $2 by lowering the price, leading to an increase in both total revenue and profit.

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The expected number of heart cards in 60 trials is given as follows:

15 heart cards.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is then calculated as the division of the number of desired outcomes by the number of total outcomes.

Out of 52 cards in a deck, 13 are heart cards, hence the probability is given as follows:

p = 13/52

p = 1/4.

Hence, out of 60 trials, the expected number is given as follows:

E(X) = 60 x 1/4 = 15.

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Answer: 15 degrees.

Step-by-step explanation:

A bisector divides an angle in half. So, we know the total angle of ABC is 20 degrees, as show in blue. We draw the bisector BD in the middle, meaning each side is 10 degrees, show in green. This means angle ABD is 10 degrees and angle CBD is is 10 degrees. We bisect angle CBD with BE, shown in red. This means that we have two 5 degree angles on either side,  angle CBE and angle EBD. Lastly, we need to find angle ABE, highlighted in orange. We add the components, which are angle DBA, measuring 10 degrees, and angle EBD, measuring 5 degrees. When added together, this equals 15 degrees, which is our final answer for angle ABE.

Stacy can varnish 4 dining sets with the given amount of varnish.

To determine how many dining sets Stacy can varnish, we need to divide the total amount of wooden varnish she has by the amount of varnish required for each dining set.

Stacy has 14/3 cans of wooden varnish.

This means she has 14/3 units of varnish available.

Each wooden dining set requires 7/6 cans of varnish.

To find out how many dining sets Stacy can varnish, we need to divide the total varnish available by the varnish required per set.

Let's set up the division:

(14/3) / (7/6)

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:

(14/3) × (6/7)

Multiplying the numerators gives us 14 × 6 = 84, and multiplying the denominators gives us 3 × 7 = 21.

So, (14/3) / (7/6) simplifies to 84/21, which further simplifies to 4.

Stacy can varnish 4 dining sets using the 14/3 cans of wooden varnish she has, with each dining set requiring 7/6 cans.

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The aim when choosing the model parameters:

Find the parameters that minimize he squared distances, in the y direction, from each point up/down to the regression line

The correct option is (b)

This is incomplete question

Complete question is this:

With a linear regression, what is the aim when choosing the model parameters (aka the slope and coefficient(s))?

Choose the correct option:

Now, According to the question:

Hence, The aim when choosing the model parameters:

Find the parameters that minimize he squared distances, in the y direction, from each point up/down to the regression line

The correct option is (b).

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Answer:

<U=70

Step-by-step explanation:

Straight line=180 degrees

180-120

=60

So, we have 2 angles.

60 and 50

180=60+50+x

180=110+x

70=x

So, U=70

Hope this helps! :)

The height of the balloon is 21.33

According the the question the relation between height and surface area of balloon is

H=pA

where ,

H is height

p is proportionality constant

A is surface area

Surface area = 81

Height = 12

By Replacing the given values we get,

12=p x 81

p=12/81

Using it in given conditions,

H=(12/81)x144

H=21.33

So the height of the balloon in the given condition is 21.33

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total cost if the books= $32351

each book= $17

the number of books the library purchased.

to find the total number of books the library has purchased you'll have to divide the total cost of the books by cost of one book.

\( \frac{32351}{17} \)

\( = 1903\)

therefore, the library purchased 1903 books in total.

The Markov chain model for this system can be represented as follows:

State 0: Neither broker is on the phone

State 1: Broker 1 is on the phone, and Broker 2 is not

State 2: Broker 2 is on the phone, and Broker 1 is not

State 12: Both brokers are on the phone

The transition rates between states are as follows:

From state 0, a transition to state 1 occurs at rate λ1 = 1 per hour.

From state 0, a transition to state 2 occurs at rate λ2 = 1 per hour.

From state 1, a transition to state 0 occurs at rate μ1 = 3 per hour (call serviced).

From state 2, a transition to state 0 occurs at rate μ2 = 3 per hour (call serviced).

From state 1, a transition to state 12 occurs at rate λ2 = 1 per hour.

From state 2, a transition to state 12 occurs at rate λ1 = 1 per hour.

From state 12, a transition to state 0 occurs at rate μ1 = 3 per hour (call serviced) if Broker 1 finishes the call first.

From state 12, a transition to state 0 occurs at rate μ2 = 3 per hour (call serviced) if Broker 2 finishes the call first.

(b) To find the stationary distribution, we solve the system of equations:

π0λ1 = π1μ1 + π2μ2

π0λ2 = π2μ2 + π1μ1

π1λ2 = π12μ1

π2λ1 = π12μ2

π0 + π1 + π2 + π12 = 1

Solving these equations will give us the stationary distribution (π0, π1, π2, π12).

(c) With the upgraded telephone system, a call on one line that is busy is forwarded to the other phone and lost if that phone is busy. This implies that the system can no longer be in state 12 since both brokers cannot be on the phone simultaneously.

(d) To compare the rate at which calls are lost in the two systems, we need to analyze the transition rates and the probability of being in state 12 in the original system versus the upgraded system.

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The monthly bill is an illustration of linear functions

The function  that relates the number of gallons of water consumed in a month, x, to the total cost of the bill is \(c(x) = 22 + 0.003998x\)

The given parameters are:

\(Service\ Fee = \$22\)

\(y= \$31.02\) ---- Total Charge

\(x= 2256\) --- number of gallons

The expression for the total monthly charge (y) is:

\(y = Service\ Fee + r\times x\)

Where

r represents the rate per gallon

Substitute known values

\(31.02 = 22 + 2256\times r\)

Collect like terms

\(31.02 - 22 = 2256\times r\)

\(9.02 = 2256\times r\)

Solve for r

\(r = \frac{9.02}{2256}\)

\(r = 0.003998\)

So, the expression for the total monthly charges is:

\(y = Service\ Fee + r\times x\)

Substitute values for Service Fee and r

\(y = 22 + 0.003998x\)

Express as a function

\(c(x) = 22 + 0.003998x\)

Hence, the required function is: \(c(x) = 22 + 0.003998x\)

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Answer:

Step-by-step explanation:

Answer:

Our calculator limits your interest deduction to the interest payment that would be paid on a $1,000,000 mortgage. Interest rate: Annual interest rate for this

Step-by-step explanation:

Answer:

x=5.0

Step-by-step explanation:

First, figure out which trig function you are going to use.

In this problem you are dealing with the opposite side to the angle and the hypotenuse, and if you remember SOH CAH TOA, this requires sine.

sin (46) =opposite/hypotenuse

sin (46) =x/7

multiply both sides by 7 to get 7 * sin (46) = x

7 * sin (46) = 5.0

Hence x = 5.0

By finding out the HCF, we can infer that the maximum number of groups that can be formed will be 32.

The number that divides two or more numbers exactly is said to be the highest common factor (HCF) of those numbers.

Given data:

Number of girls = 128.

Number of boys = 96.

In order to find the maximum number of groups that can be formed, we need to find highest common factor of 96 and 128.

To find HCF, we have to divide each number into it's prime factors.

Prime factors of 128 are 2×2×2×2×2×2×2

Prime factors of 96 are 2×2×2×2×2×3

Out of those two groups (2×2×2×2×2×2×2) and ( 2×2×2×2×2×3), the only thing in common is 2⁵. So, 2⁵ is the highest common factor.

Hence, the maximum number of groups that can be formed is 32.

Now, to find out the number of pupil in each group, we divide the total by 2⁵, so:

128/32 = 4

96/32 = 3

So, there will be 4 girls and 3 boys in each group.

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Each bag of lemons costs $3.99

Let m represents the cost of eggs and n represents the cost of each bag of lemons.

He buys 6 bags of lemons that each cost the same amount.

so, the cost of six bags of lemons would be 6n

He pays a total of $29. 33

so, we get an equation,

m + 6n = 29. 33               ............(1)

Levi pays a total of $5. 39 for the eggs

So, m = 5.39

We need to find the value of n.

substitute above value of m in equation (1)

m + 6n = 29. 33

5.39 + 6n = 29. 33

6n = 23.94

n = 23.94 / 6

n = 3.99

Thus, the cost of each bag of lemon = 3.99 dollars

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Answer:

(-1,6)

Step-by-step explanation:

use the midpoint formula

\((\frac{x1 +x2}{2} , \frac{y1+y2}{2} )\)

plug in the given values

you should get

(-1,6)

Statistics & Data

For this data set, there is an outlier. The outlier is four.

This is representing a small number of assignments required in math class that month.

This means that the correct answer is B.

Answer:

B

Step-by-step explanation:

The answer should be B or the second choice because the number 4 is unusually low compared to the rest of homework assignments given in the other math classes for that month. I made a graph to show how the number 4 is not near the number of homework assignments given in the other math classes.

If you think I missed something or made a mistake, please let me know.