The measures of the exterior angles of a quadrilateral are x°, 4x°, 6x°, and 7x°. Find the measure of the smallest exterior angle.

Answer:

p= -11.2

Step-by-step explanation:

-112.74 = 9.2p - 9.7

-103.04 = 9.2p (added 9.7 to both sides because its the inverse operation)

\(\frac{-103.04}{9.2}\) = \(\frac{9.2p}{9.2}\)

-11.2 = p

Answer:

40

Step-by-step explanation:

\(180 - 116 = 64\)

\(180 - 64 \times 2 = 52\)

\(180 - 52 - 88 = 40\)

1) 2(x + 7)

2x + 14

2) 8 (x - 3)

8x - 24

3) -4 (y - 6)

-4y + 24

4) -5 (2x + 3)

-10x - 15

The set of expressions that is NOT an example of the associative property is B. (8 - 2) + 3 and 8 + (-2 + 3).

The associative property states that the way you group numbers when adding or multiplying does not change the result. For example, (8 + 2) + 3 is the same as 8 + (2 + 3). However, the associative property does not apply to subtraction or division. Therefore, (8 - 2) + 3 is not the same as 8 + (-2 + 3).

Besides associative property, there are 3 other mathematical properties that only works on adding and multiplying. They are:

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Answer:

Here is your answer

((6 * 5) ^ 10) ^ 8 =

(30 ^ 10) ^ 8 =

590490000000000 ^ 8 = 14780882941434592331608321020638329760100000000000000000000000000000000000000000000000000000000000000000000000000000000

Step-by-step explanation:

Answer:

I'm not really sure but I think it's 2

Step-by-step explanation:

So here's what I did;

x³+3x-9=x - 1 +2x

x³+3x - x -2x = 9 - 1

x³= 8

x = ³√8

x = 2

I hope this helps

Answer:

  6.9

Step-by-step explanation:

You want half the side length of an equilateral triangle with an altitude of 12.

The altitude shown divides the base into equal parts. If one of those parts is x, then the full side length is 2x. The Pythagorean theorem relates the side lengths of the right triangle:

  (2x)² = x² +12²

  3x² = 144 . . . . . . . . subtract x²

  x² = 48 . . . . . . . . divide by 3

  x = √48 = 4√3 . . . take the square root

  x ≈ 6.9

__

Additional comment

You should be familiar with the fact that a 30°-60°-90° triangle has side lengths in the ratio 1 : √3 : 2. This means the shortest side (x) will have a length of 12/√3 ≈ 6.9, since the middle-length side is shown as having a length of 12.

The correct answer is A.\(\((5 \frac{1}{\overline{9}}) \times (-0.\overline{3})\)\), as it involves the multiplication of two rational numbers, resulting in a rational number.

Therefore, the product of these two rational numbers in option A will yield a rational number.

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Answer:

p = 16x² + 38y

Step-by-step explanation:

x + 10y + x + 10y + 8x² - x + 9y + 8x² - x + 9y

Simplify:

16x² + 38y

good luck, i hope this helps :)

nonhomogeneous equation y(x) = C_1e^(√(2/11)x) + C_2e^(-√(2/11)x) + cot(x)

To find the general solution of the nonhomogeneous equation 11y'' = 2y + 11cot(x) given a particular solution y_p(x) = cot(x), we need to find the complementary solution y_c(x) and then combine it with y_p(x) to obtain the general solution.

First, let's find the complementary solution by solving the homogeneous equation 11y'' - 2y = 0. We assume the solution has the form y_c(x) = e^(rx), where r is a constant to be determined. Substituting this into the equation, we get:

11(r^2)e^(rx) - 2e^(rx) = 0

Factoring out e^(rx), we have:

e^(rx)(11r^2 - 2) = 0

For this equation to hold true, either e^(rx) = 0 (which is not a valid solution) or 11r^2 - 2 = 0. Solving the quadratic equation, we find two possible values for r:

r_1 = √(2/11)

r_2 = -√(2/11)

The complementary solution is then given by:

y_c(x) = C_1e^(√(2/11)x) + C_2e^(-√(2/11)x)

where C_1 and C_2 are arbitrary constants.

The general solution of the nonhomogeneous equation is obtained by combining the complementary solution with the particular solution:

y(x) = y_c(x) + y_p(x) = C_1e^(√(2/11)x) + C_2e^(-√(2/11)x) + cot(x)

Here, C_1 and C_2 are arbitrary constants representing the coefficients of the complementary solution, and cot(x) represents the particular solution.

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.

The applicants that would have to apply in order to meet the target is 52. Option 4 is correct.

We have to define x as the applications to meet target

The number of persons to hire is 30

10 percent do not meet requirements. Hence 90 meets the requirements. 90% of x

= 0.9X

12% fail the pre screening stage. Hence 88% have passed it. This would be 88% of 0.9x. = 0.792x

23% Did not come for the interview, hence 77% showed up. This would be 0.77*0.792x = 0.60984x

then 5% are said to have failed the background test. This means that 95% passed the test.

0.95 * 0.60984x = 0.579348X

We have to equate this to 30 in order to get the value of x

0.579348X = 30

divide through by 0.579348

X = 30 / 0.579348

X = 51.78

X ~ 52

The number of applicants is 52

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The cyclist needs to ride approximately 23.21 km in the direction of 23.13° W of North to get back to the starting point.

We can use trigonometry to find the x and y components.

x3 = 12 * cos(15°) ≈ 11.59 km (east)

y3 = -12 * sin(15°) ≈ -3.10 km (south, hence the negative sign)

Leg #4: 14 km [South]

x4 = 0 km (no east/west movement)

y4 = -14 km (south, hence the negative sign)

Now, let's find the total x and y displacements:

x_total = x1 + x2 + x3 + x4 ≈ 0 + 10 + 11.59 + 0 ≈ 21.59 km

y_total = y1 + y2 + y3 + y4 ≈ 8 + 0 - 3.10 - 14 ≈ -9.10 km

Now, we can find the distance and direction he needs to ride to get back to the starting point:

Distance=  

\(\sqrt{21.59^2 + (-9.10)^2}\))

23.21 km

Direction:

angle =

arctan(9.10 / 21.59)

= 23.13°

The cyclist needs to ride approximately 23.21 km in the direction of 23.13° W of North to get back to the starting point.

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The mean fill in ounces should be set at 5.068 to ensure that 98% of 6 oz cups will not overflow.

To determine the value of mean that will ensure that 98% of 6 oz cups will not overflow, we can use the following steps:

Calculate the z-score corresponding to the desired percentile (98%):

Using a standard normal distribution table or calculator, we can find that the z-score corresponding to the 98th percentile is approximately 2.33.

Convert the given cup size (6 oz) to a z-score using the formula:

z = (x - μ) / σ

where x is the given cup size, μ is the mean fill in ounces, and σ is the standard deviation in ounces. Solving for μ, we get:

μ = x - z × σ

= 6 - 2.33 × 0.4

= 5.068

Therefore, the mean fill in ounces should be set at 5.068 to ensure that 98% of 6 oz cups will not overflow.

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Answer:

-2/8

-3/12

-4/16

-5/20

-6/24

-7/28

-8/32

a great equivulent of -1/4 would be...

(fraction)

-2/8, -4/16, -16/64

(decimiel)

-.25

Answer:

Area of a rectangle = 7/12 of an inch

Step-by-step explanation

Area of a rectangle = Length × width

In this case, the length is represented by height

Height = 2/3 of an inch

Width = 7/8 of an inch

Area of a rectangle = Length × width

= 2/3 × 7/8

= (2 * 7) / (3 * 8)

= 14 / 24

= 7 / 12

Area of a rectangle = 7/12 of an inch

$1.09 x 2 = $2.18. $2.18 + $3.99 = $6.17. $6.17 + $5.25 = $11.42. So, the best estimate of total cost (excluding tax) equals $11.42.

Answer:

Notebook: 3.99

Pencils: 1.09 x 2 = 2.18

Markers: 5.25

$11.42 = not estimated/exact

Estimated: $11.50

The slope in this scenario is 12 and , starting at $30 the cost will increase by $12 per month .

In the question ,

it is given that

the average bowling league has  one time registration fees

and

a monthly fees .

let the number of months the training continues be "x" .

the equation is given as y = 12x + 30

since the one time registration fees is fixed so , it will be 30 .

and the monthly fees varies with the number of months of training , so monthly fees will be 12x  .

On comparing the given equation y = 12x + 30 with slope intercept form of the line y = mx + c  ,
we get ,

slope (m) = 12 .

and starting cost = $30 and the increase in cost by $12 per month .

Therefore , The slope in this scenario is 12 and , starting at $30 the cost will increase by $12 per month , the correct option is (c) .

The given question is incomplete , the complete question is

A professional bowler wanted to gather data about the cost of local bowling leagues in the area. After collecting and plotting the data, it was determined that the average bowling league consists of a one-time registration fee and a monthly fee modeled by the equation y = 12x + 30.

Identify and interpret the slope in this scenario.

(a) The slope is 30. Starting at $12, the cost will increase by $30 per month.

(b) The slope is 30. Starting at $12, the cost will decrease by $30 per month.

(c) The slope is 12. Starting at $30, the cost will increase by $12 per month.

(d) The slope is 12. Starting at $30, the cost will decrease by $12 per month.

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Hope it helps........................

A person of interest has been identified by the police, the appropriate location of the person of interest is D(5, -4). Therefore, option D is the correct answer.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let (x, y) be the coordinates of the person of interest. Then, we can set up three equations based on the distances between the person and the three known locations:

√((x-(-2))²+(y-9.9)²)=6

√((x-(-8))²+(-(-4.7))²)=10

√((x -(-12))²+(y-4)²)=9

Squaring both sides of each equation and simplifying, we get:

(x+2)²+(y-9.9)²=36

(x+8)²+(y+4.7)²=100

(x+12)²+(y-4)²=81

Expanding the squared terms and simplifying, we get a system of three linear equations in two variables:

x²+4x+y²-19.8y=4

x²+16x+y²+9.4y=52.59

x²+24x+y²-8y=21

We can solve this system of equations to find the values of x and y that satisfy all three equations.

y = (-11.94 + 6x)/19.8

Substituting this expression for y into the first equation, we get a quadratic equation in x:

x²+4x+((-11.94+6x)/19.8)²-19.8((-11.94+6x)/19.8)-4=0

Simplifying and solving for x, we get:

x=-0.217 or x=5.184

Substituting these values of x into the expression for y, we get:

y=1.283 or y=-3.772

So, x=5 and y=-4

Therefore, option D is the correct answer.

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Answer:

Step-by-step explanation:

-2.8, -13/9, .25, 2/3, 1 7/8, 2.16

Answer:

30 feet of chain link and 50 feet of rope

Step-by-step explanation:

Let's call the amount of chain link as x and the amount of rope as y. We can write:

x + y = 80 -- Equation 1

2x + 1.5y = 135 -- Equation 2

2x + 2y = 160 -- Equation 3 (Multiply Equation 1 by 2)

0.5y = 25 (Subtract Equation 2 from Equation 3)

y = 50 (Divide by 2)

x + 50 = 80 (Substitute y = 50 into Equation 1)

x = 30 (Subtract 50)

Answer:

\(\sqrt{85}\) or 9.21954

Step-by-step explanation:

Use the distance formula to determine the distance between the two points.

\(d = \sqrt{(x_{2} -x_{1})^{2} + (y_{2} - x_{1})^{2} }\)

d = distance

\((x_{1}, y_{1})\) = coordinates of the first point

\((x_{2}, y_{2})\) = coordinates of the second point

Answer:

The perimeter of the figure as a function of the number of triangles is \(y = 6 + 4\cdot x\).

Step-by-step explanation:

According to the diagram, we get the following facts:

i) For one triangle (\(x=1\)), the total perimeter is (\(y=2\cdot 3 + 1\cdot 4 = 10\)).

ii) For two triangles (\(x = 2\)), the total perimeter is (\(y = 2\cdot 3 +2\cdot 4 = 14\))

iii) For three triangles (\(x = 3\)), the total perimeter is (\(y = 2\cdot 3 +3\cdot 4 = 18\))

iv) For four triangles (\(x = 4\)), the total perimeter is (\(y = 2\cdot 3 +4\cdot 4 = 22\))

From these information we conclude that the equation that determines the perimeter of the figure as a function of the number of triangles is \(y = 6 + 4\cdot x\).

Answer:

sqrt(1/m+4)

Step-by-step explanation:

n^2-1/m=4

n^2=1/m+4

n=sqrt(1/m+4)

The value of the equation is n = √ ( 4 + 1/m )

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

n² - 1/m = 4   be equation (1)

On simplifying the equation , we get

Adding 1/m on both sides of the equation , we get

n² = 4 + 1/m

Taking square roots on both sides of the equation , we get

n = √ ( 4 + 1/m )

Therefore , the value of n is √ ( 4 + 1/m )

Hence , the equation is n = √ ( 4 + 1/m )

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Answer:

7

Step-by-step explanation:

(2t+3r) divide 4

so if r=2 and t=11 the new equation will be :

(2times11 + 3times 2) divide 4

(22+6) divide 4

= 28 divide 4 = 7