What is the general form of the equation for the given circle centered at o(0, 0)? a. x2 y2 41 = 0 b. x2 y2 − 41 = 0 c. x2 y2 x y − 41 = 0 d. x2 y2 x − y − 41 = 0

The probability that a resident is female is 0.625.

Probability is a method for determining how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is.

We know that the probability of a function is the ratio of favorable cases to the total number of cases possible.

Given that,

Total number of females = 19+2+4 =25

total number of males=1+9+5 = 15

The probability that a resident is female is the Total number of females / total number of people

Hence total number of people = 25+15 = 40

So, Probability = 25/40 = 0.625

Therefore, the probability that a resident is female is 0.625.

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The probability that a resident is female = 0.625

The correct answer is an option (d)

The complete contingency table would be:

                      60-69         70-79          Over 79           Total

Male                  1                  9                 5                     15

Female              19                2                 4                      25

Total                  20               11                 9                     40

Here, sample space i.e., the total number of residents = 40

So, n(S) = 40

Let event A: a resident is female

From the contigency table, the number of favourable outcomes of the event A are 25

So, n(A) = 25

Using the definition of probability, the probability of event A would be,

p(A) = n(A)/n(S)

p(A) = 25/40

p(A) = 0.625

Therefore, the required probability is 0.625

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Answer:

(a)   width = (x - 1)

      length = (7x - 6)

(b)  Area = 350 cm²

     Perimeter = 114 cm

Step-by-step explanation:

Given equation:  \(7x^2-13x+6\)

⇒ a = 7,  b = -13,  c = 6

Find 2 two numbers that multiply to ac and sum to b:   -6 and -7

Rewrite b as the sum of these 2 numbers:

\(\implies 7x^2-7x-6x+6\)

Factorize the first two terms and the last two terms separately:

\(\implies 7x(x-1)-6(x-1)\)

Factor out the common term (x - 1):

\(\implies (7x-6)(x-1)\)

Therefore:

Substitute the given value of x = 8 into the equations to find the area and perimeter:

\(\begin{aligned}x=8cm \implies \textsf{Area} & = 7(8)^2-13(8)+6\\& = 448-104+6\\& = 350 \sf \:\: cm^2\end{aligned}\)

\(\begin{aligned}\textsf{Perimeter} & = 2(\sf width+length)\\& =2[(x-1)+(7x-6)]\\ & = 2[(8-1)+(7(8)-6)]\\ & = 2[7+(56-6)] \\& = 2(7+50)\\& = 2(57)\\ & = 114 \sf \:\: cm\end{aligned}\)

Answer:

See below ~

Step-by-step explanation:

\(\textsf {Question 15(A) :}\)

\(\textsf {Given :}\)

\(\implies \mathsf {7x^{2} - 13x + 6}\)

\(\textsf {Splitting the middle term :}\)

\(\implies \mathsf {7x^{2} - 7x - 6x + 6}\)

\(\textsf {Grouping common terms :}\)

\(\implies \mathsf {7x(x - 1) - 6(x - 1)}\)

\(\textsf {Dimensions are :}\)

\(\textsf {Question 15(B) :}\)

\(\textsf {Formula for perimeter :}\)

\(\implies \mathsf {2 \times (length + width)}\)

\(\implies \mathsf {2 \times (7x - 6 + x - 1)}\)

\(\implies \mathsf {2 \times (8x-7)}\)

\(\textsf {Substitute x = 8 :}\)

\(\implies \mathsf {2 \times [8(8)-7]}\)

\(\implies \mathsf {2 \times (64-7)}\)

\(\implies \mathsf {2 \times 57}\)

\(\implies \mathsf {Perimeter = 114 cm}\)

\(\textsf {Now substitute x = 8 in the area formula :}\)

\(\implies \mathsf {7(8)^{2} - 13(8) + 6}\)

\(\implies \mathsf {7(64) - 104 + 6}\)

\(\implies \mathsf {448 - 98}\)

\(\implies \mathsf {Area = 350 cm^{2}}\)

Answer:

answer A

Step-by-step explanation:

Hello,

\((fog)(x)=f(g(x))=f(2x-1)=3(2x-1)+14=6x-3+14=6x+11\)

so the correct answer is A.

hope this helps

Answer:

A.  6x + 11.

Step-by-step explanation:

(f o g)(x)

We replace the x in f(c) by g(x) and simplify:

= 3(2x - 1) + 14

= 6x - 3 + 14

= 6x + 11.

Answer:

Step-by-step explanation:

Let x represent the number of meters of shirt material that he bought.

Let y represent the number of meters of trouser material that he bought.

For every 3 metres of the shirt material, he buys 2 metres of the trouser material. It means that

2x = 3y

x = 3y/2

shirt material cost him ₹ 50 per metre and trousers material cost him ₹ 90 per metre. It means that the total cost is

50x + 90y

Selling price for the shirt material is

50x + (12/100 × 50x) = 56x

Selling price for the trouser material is

90y + (10/100 × 90y) = 99y

If his total sale is ₹ 36,600, it means that

56x + 99y = 36600- - - - - - - - 1

Substituting x = 3y/2 into equation 1, it becomes

56(3y/2) + 99y = 36600

Multiplying both sides by 2, it becomes

168y + 198y = 73200

366y = 73200

y = 73200/366

y = 200

x = 3y/2 = 3 × 200/2

x = 300

He bought 200 meters of trouser material

Answer:

5/6

Step-by-step explanation:

It might make the problem easier to understand if we were to rewrite it as:

  2

 ----

   3

======

   4

  ----

     5

In this expression, we're dividing by a fraction, the fraction 4/5.  We can get the same result by inverting this divisor fraction, 4/5, and then multiplying 2/3 by 5/4:

 5       2

----- * -----

  4       3

This reduces to

 5       1

----- * ----- = 5/6

 2       3

Answer: 16

Step-by-step explanation:

\(n^2-(n+a)(n-a)=\\n^2-(n^2-a^2)=\\n^2-n^2+a^2=\\a^2\)

\(326541829^2-326541833*326541825=\\32654129^2-(32654129+4)(326541129-4)=\\4^2=\\4*4=\\16\)

Answer : One of the following statements is not always true: uX (vtw) =uXv+uXw, (vtw) Xu =vXu+wXu.

The statement, "one of the following is not always true: points a. uX (vtw) =uXv+uXw b. (vtw) Xu =vXu+wXu c. v X u=uXv d. 0 X u = 0," is correct. The first statement, "uX (vtw) =uXv+uXw," is false because in general, the distributive law does not apply to vector multiplication. This means that the left-hand side of the equation, "uX (vtw)," cannot be rearranged to "uXv+uXw."

The second statement, "(vtw) Xu =vXu+wXu," is also false because vector multiplication is not commutative; the order of the vectors in a multiplication equation matters. Therefore, "(vtw) Xu" is not equal to "vXu+wXu." The third statement, "v X u=uXv," is true because vector multiplication is commutative. This means that the order of the vectors in a multiplication equation does not matter.

The fourth statement, "0 X u = 0," is also true. The zero vector is a special type of vector whose components all equal 0. When any vector is multiplied by the zero vector, the result is always the zero vector.

In conclusion, one of the following statements is not always true: uX (vtw) =uXv+uXw, (vtw) Xu =vXu+wXu.

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if the area of a rectangle is 80 square units, the perimeter must be lesser than or equal to 35. 9 units.

What is a conjecture?

A conjecture is a conclusion or a proposition that is made tentatively and without supporting evidence.

The conjecture for the given question is:

if the area of a rectangle is 80 square units, the perimeter must be lesser than or equal to 35. 9 units.

Greater than → Lesser than or equal to

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There are a few different ways you can determine whether a function is always positive:

1. Analyze the function's formula: If the function's formula includes only positive terms or is a product of positive factors, it is likely that the function will be positive for all input values.

2. Graph the function: Plotting the function on the coordinate plane can give you a visual understanding of the function's behavior. If the graph always lies above the x-axis, the function is always positive.

3. Consider the function's domain: If the domain of the function consists only of positive numbers, the function will be positive for all input values in its domain.

4. Use the function's properties: If the function is increasing, continuous, and has no zeros in its domain, it will always be positive. Similarly, if the function is decreasing, continuous, and has no zeros in its domain, it will always be negative.

5. Test the function for specific input values: You can also test the function for specific input values to see if the output is always positive. For example, if the function is defined for all real numbers, you could test it for a few small positive and negative values to see if the output is always positive.

Thus, above mentioned are used to determine if a function is always positive.

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Answer:

-2/3

Step-by-step explanation:

Add the first two then subtract

The answer to the equation is B, \(-\frac{2}{3}\)

First, you must add the the fractions. You add the numerator because all three fractions have like denominators.

\(-\frac{8}{9} +\frac{4}{9} -\frac{2}{9}=\frac{6}{9}\)

Then, you must simplify \(-\frac{6}{9}\)

\(-\frac{6}{9} =-\frac{2}{3}\)

The answer to the equation is \(-\frac{2}{3}\)

Answer:

Answer: LCM of 3 and 15 is 15. 2.

Step-by-step explanation:

Hope this helps

Answer:

4\(a^{9}\)\(b^{8}\)

Step-by-step explanation:

\(\frac{8a^{6}b^{12} x 4a b^{3} }{8x^{-2}b^{7} }\)

\(\frac{32a^{7} b^{15} }{8a^{-2} b^{7} }\)

4\(a^{9}\)\(b^{8}\)

Helping in the name of Jesus.

Answer:

The distance between the two is 465 meters

Step-by-step explanation:

We first need to set up a triangle that shows the relative position and distances of the two friends

Please check attachment for this

To get this distance, which represents the hypotenuse of the triangle, we make use of Pythagoras’ theorem

Mathematically;

Pythagoras’ theorem states that the square of the hypotenuse equals the sum of the squares of the two other sides

Thus;

D^2 = 256^2 + 388^2

D^2 = 216,080

D = √216,080

D = 464.84 which is approximately 465 m

Answer:

The video is blocked for me

Step-by-step explanation:

Answer:

Step-by-step explanation:

The length of one side of the equilateral triangle is 5x + 10 units

What is an equilateral triangle ?

An equilateral triangle is a triangle that has all of its sides equal. Let a, b and c be the sides of the equilateral triangle. Since all the sides are equal, then a = b = c.

The perimeter of the triangle is the sum of all the sides of the triangle.

P  = a + b+ c

GIVEN THE PERIMETER OF THE EQUILATERAL TRIANGLE AS P = 15 x + 30 units and a = b = c, then;

15 x + 30 = a + b + c

15 x + 30 = a + a + a (since all sides are equal)

15 x + 30 = 3a

3a = 15 x + 30

3a = 3(5x+10)

Dividing both sides by 3 will give;

3a/3 =   3(5x+10)/3

a = 5x+10

Hence, the length of one side of the equilateral triangle is 5x + 10 units.

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a) The formula that models this situation is: T(t) = 68 + 32\(e^{(-0.0152t)}\) .

b) To the nearest minute, it take 99 minutes for the soup to cool to 70° F.

c) To the nearest minute, it take 1.1 hours for the turkey to cool to 120° F.

a) Using Newton's Law of Cooling to model this situation we have:

T(t) = Troom + (T₀ - Troom)\(e^{(-kt)}\)

Where, T(t) is the temperature of the soup (or turkey) at time t

Troom is the room temperature

T₀ is the initial temperature k is a constant of proportionality

t is time measured in minutes

For the soup, we have:

T(t) = 68 + (100 - 68)\(e^{(-kt)}\)

After 20 minutes, the internal temperature of the soup was 91° F.

Therefore, when t = 20,

T(t) = 91.

Hence, we can substitute these values in the above equation and solve for k as follows:

91 = 68 + 32\(e^{(-20k)}\)

=> 23 = 32\(e^{(-20k)}\)

=> ln(23/32)

= -20k

=> k ≈ 0.0152

Therefore, the formula that models this situation is:

T(t) = 68 + 32\(e^{(-0.0152t)}\) (rounded to four decimal places)

b) To find the time it takes for the soup to cool to 70° F,

we need to solve the equation T(t) = 70.

Therefore:

70 = 68 + 32\(e^{(-0.0152t)}\)

=> 2 = 32\(e^{(-0.0152t)}\)

=> ln(1/16) = -0.0152t

=> t ≈ 98.60

Hence, it will take approximately 99 minutes for the soup to cool to 70° F. (rounded to the nearest minute)

c) 1.1 hours is equal to 66 minutes.

Therefore, to find the temperature of the soup after 1.1 hours, we need to evaluate T(66):

T(66) = 68 + 32\(e^{(-0.0152 \times 66)}\) ≈ 83.36

Therefore, after 1.1 hours, the soup's temperature will be about 83 degrees Fahrenheit. (rounded to the nearest degree)

For the turkey:

a) Using Newton's Law of Cooling to model this situation we have:

T(t) = Troom + (T₀ - Troom)\(e^{(-kt)}\)

Where, T(t) is the temperature of the turkey (or soup) at time t

Troom is the room temperature

T₀ is the initial temperature

k is a constant of proportionality

t is time measured in minutes

For the turkey, we have:

T(t) = 73 + (190 - 73)\(e^{(-kt)}\)

After half an hour, the internal temperature of the turkey was 150° F.

Therefore, when t = 30, T(t) = 150.

Hence, we can substitute these values in the above equation and solve for k as follows:

150 = 73 + 117\(e^{(-30k)}\)

=> 77 = 117\(e^{(-30k)}\)

=> ln(77/117) = -30k

=> k ≈ 0.0228

Therefore, the formula that models this situation is:

T(t) = 73 + 117\(e^{(-0.0228t)}\) (rounded to four decimal places)

b) To find the temperature of the turkey after 55 minutes, we need to evaluate T(55):

T(55) = 73 + 117\(e^{(-0.0228 \times 55)}\) ≈ 139.57

Therefore, after 55 minutes, the turkey's temperature will be about 140 degrees Fahrenheit. (rounded to the nearest degree)

c) To find the time it takes for the turkey to cool to 120° F,

we need to solve the equation T(t) = 120.

Therefore:120 = 73 + 117\(e^{(-0.0228t)}\)

=> 47 = 117\(e^{(-0.0228t)}\)

=> ln(47/117) = -0.0228t

=> t ≈ 92.61

Hence, it will take approximately 93 minutes for the turkey to cool to 120° F. (rounded to the nearest minute)

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1. The first number is equal to 2.

2. The second number is equal to 5.

3. The third number is equal to -3.

Translating the word sentence into an algebraic expression, we have;

The sum of three numbers is 4:

\(a+b+c=4\)   ....equation 1.

The second number is 1 more than twice the first:

\(b=2a+1\)    ....equation 2.

The sum of the first and third is –1:

\(a+c=-1\)    ....equation 3.

From eqn. 3, we have:

\(c=-1-a\)   ....equation 4.

Substituting into eqn. 1, we have:

\(a+2a+1+(-1-a)=4\\\\3a+ 1-1-a=4\\\\2a=4\\\\a=\frac{4}{2}\)

a = 2

To find the value of b:

\(b=2a+1\\\\b=2(2)+1\\\\b=4+1\)

b = 5

To find the value of c:

\(c=-1-a\\\\c=-1-2\\\\\)

c = -3

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The x- and y-coordinates of the center of mass are; (20, 0)

The center of mass is the location where the sum of the relative position of the masses in a mass distribution is zero. It is the point where force can be applied on the distributed mass without causing a rotation of the system.

The mas of the steel plate = 800 g = 0.8 kg

The base length of the isosceles triangular plate = 20 cm = 0.2 m

The height of the isosceles triangular plate = 30 cm = 0.3 m

Considering a small strip of height, dx and width, I, we get

Area of small strip, dA = I·dx

Density of the plate for a unit thickness, ρ = M/A

Density of the small strip of mass dm = dm/dA

Considering the density of the plate as uniform, we get;

\(\displaystyle {\frac{dm}{dA} =\frac{M}{A}\)

Therefore;

\(\displaystyle {dm=\frac{M}{A}\times dA}\)

The area of the triangular plate, A = (1/2) × 0.2 m × 0.3 m = 0.03 m²

Mass of the plate, M = 0.8 kg

Therefore;

\(\displaystyle {dm=\frac{0.8}{0.03}\times I\cdot dx}\)

The width of the small strip, I, located at a distance x from the vertex of the triangular plate, using similar triangles, indicates;

\(\dfrac{I}{20} = \dfrac{x}{30}\)

\(I=20\times \dfrac{x}{30} = \dfrac{2}{3} \cdot x\)

Therefore;

\(\displaystyle {dm=\frac{0.8}{0.03}\times I\cdot dx} = \frac{0.8}{0.03}\times \dfrac{2}{3} \cdot x\cdot dx}\)

The center of mass, \(x_{cm}\), can be obtained with the formula; \(\displaystyle {x_{cm} = \dfrac{1}{M} \cdot \int\limits {x} \, dm }\)

Therefore; \(\displaystyle {x_{cm} = \dfrac{1}{0.8} \cdot \int\limits {x} \cdot \frac{0.8}{0.03} \cdot \frac{2}{3}\cdot x\, dx }\)

\(\displaystyle {x_{cm} = \dfrac{1}{0.8} \cdot \int\limits {x} \cdot \frac{0.8}{0.03} \cdot \frac{2}{3}\cdot x\, dx } = \dfrac{1}{0.8} \times \frac{0.8}{0.03} \times \frac{2}{3}\cdot \int\limits^3_0 {x^2} \, dx\)

\(\displaystyle {x_{cm} = \dfrac{1}{0.8} \times \frac{0.8}{0.03} \times \frac{2}{3}\cdot \int\limits^3_0 {x^2} \, dx = \frac{200}{9} \cdot \left[\frac{x^3}{3} \right]^{0.3}_0\)

\(\displaystyle {x_{cm} = \frac{200}{9} \cdot \left[\frac{x^3}{3} \right]^{0.3}_0=\frac{200}{9} \times \frac{0.027}{3} =0.2\)

The location of the x-coordinate center of mass, \(x_{cm}\) = 0.2 m = 20 cm from the vertex, which is the same location as the x-coordinate of the centroid of the plate of uniform density.

The plate is symmetrical about the x-axis, therefore, the y-coordinate of the center of mass is along the x-axis, which is \(y_{cm}\) = 0

The coordinate of the center of mass = (0.2, 0)

Part of the question requires the location of the coordinate of the center of mass of the triangular plate

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Answer:

1. Incorrect because it's suppose to be -4/5, -1/10, 7/10

2. Incorrect because it's suppose to be -7/8, -3/8, -3/4

3. Correct -2/3, -5/9, 2/9

4. Incorrect because it's suppose to be -4/7, -5/14, 6/7

Answer:

63

Step-by-step explanation:

70x9=630, and that over 10 is the same as dividing it by ten, and 630 divided by 10 is 63

Rounding to four decimal places, the probability is approximately 0.1293.

Given that the weights of steers in a herd are normally distributed with a mean (µ) of 1400 lbs and a variance (σ²) of 40,000 lbs², we first need to find the standard deviation (σ). We can do this using the formula:

σ = sqrt(σ²)

In this case, σ = sqrt(40,000) = 200 lbs.

Now, we need to find the z-scores for the weights 1580 lbs and 1720 lbs. The z-score formula is:

z = (X - µ) / σ

For 1580 lbs:

z1 = (1580 - 1400) / 200 = 0.9

For 1720 lbs:

z2 = (1720 - 1400) / 200 = 1.6

Next, we need to find the probability between these two z-scores. We can use a standard normal distribution table or calculator to find the probabilities corresponding to the z-scores:

P(z1) = P(Z ≤ 0.9) ≈ 0.8159
P(z2) = P(Z ≤ 1.6) ≈ 0.9452

Now, we'll subtract the probabilities to find the probability that the weight of a randomly selected steer is between 1580 and 1720 lbs:

P(0.9 ≤ Z ≤ 1.6) = P(Z ≤ 1.6) - P(Z ≤ 0.9) = 0.9452 - 0.8159 = 0.1293

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The equation of the circle that meets the specified requirements is x^2 + y^2 = 89, with the center at the origin and going through P(5, 8).

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical phrase with two equal sides separated by an equal sign is called an equation. An example of an equation is 4 + 6 = 10.

Here,

The equation of a circle with center at the origin (0,0) and passing through the point (x1,y1) can be found using the distance formula.

The distance between a point (x1, y1) and the origin (0,0) is given by:

sqrt((x1-0)^2 + (y1-0)^2) = sqrt(x1^2 + y1^2)

Let's call the radius of the circle r. We know that the distance between the point (x1,y1) and the origin is equal to r. So, we can set up the equation:

sqrt(x1^2 + y1^2) = r

Substituting the values x1 = 5 and y1 = -8, we have:

sqrt(5^2 + (-8)^2) = r

Solving for r, we get:

r = sqrt(5^2 + (-8)^2) = sqrt(25 + 64) = sqrt(89)

Finally, we can write the equation of the circle in standard form using the center (0,0) and radius r:

(x - 0)^2 + (y - 0)^2 = r^2

x^2 + y^2 = r^2

x^2 + y^2 = 89

The  equation of the circle that satisfies the stated conditions that is center at the origin, passing through P(5, −8) is x^2 + y^2 = 89.

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Answer:

We will transform the equation to the vertex form:

y = x² + 8 x + 12 = x² + 8 x + 16 - 16 + 12 =

= ( x + 4 )² - 4

Vertex form is: y = a ( x - k )² + h

Vertex coordinates are: ( - 4, - 4 ).

Step-by-step explanation:

Answer: A rectangle is ALWAYS a parallelogram and not all parallelograms are rectangles. (ex. Rhombus, square are both parallelograms) So Ainsley is wrong.

Step-by-step explanation: Parallelograms is a quadrilateral shape with 2 pairs of parallel sides. So, a rectangle has to always be one.

Answer: (8,8)

Step-by-step explanation: because, you just need to do the math

The equation of line is y = ( 3/4 )x + 2

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P = P ( 8 , 8 )

Let the second point be Q = Q ( 4 , 5 )

Now , the slope of the line between the two points is

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 5 - 8 ) / ( 4 - 8 )

Slope m = -3/-4

Slope m = 3/4

Now , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 8 = 3/4 ( x - 8 )

On simplifying the equation , we get

y - 8 = ( 3/4 )x - 6

Adding 8 on both sides of the equation , we get

y = ( 3/4 )x + 2

Therefore , the value of A is y = ( 3/4 )x + 2

Hence , the equation of line is y = ( 3/4 )x + 2

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Answer:

The magnitude is sqrt((-4)^2 + (-9)^2) = 9.85. The angle is atan(-9/-4) = 180 deg + 66 deg = 246 deg = -114 deg.

Step-by-step explanation:

hope it help

Answer:

9.85

Step-by-step explanation:

|v|= √9²+(-4)²

=√81+16

=√97

|v|= 9.85

Answer:

Step-by-step explanation:

1.    n=6

2. n= no solution

3. n= no solution

something you should keep in mind is that all three angles in a triangle always add up to 180 degrees.

so, here, since you know the two other angles, you can find the third.

180 - 106 - 42 will give you the measure of that third angle.

your answer will be 32.

hope i helped, good luck!

Answer:

32

Step-by-step explanation:

as you triangle angle add up to 180 so you add 106 by 42 which gives you 148 then

you take 180 -148 which it will give you =32

The average rate of change per hour in the temperature is 0.83 degrees.

To find the average rate of change per hour, we need to divide the total change in temperature by the number of hours over which the temperature changed.

The temperature rose by 5 degrees from 6:00 am to 12:00 pm, which is a period of 6 hours.

Therefore, the average rate of change per hour can be calculated as follows:

average rate of change per hour = total change in temperature / number of hours

So, we have

average rate of change per hour = 5 degrees / 6 hours

average rate of change per hour = 0.83 degrees/hour (rounded to two decimal places)

So, the average rate of change per hour is 0.83 degrees.

Read more about rate of change at

https://brainly.com/question/17131025

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