In triangle XYZ, m∠Y = 57.35° and m∠Z = 65.4°. Determine the measure of the exterior angle to ∠X.

The distance between Basti and Cian is approximately 138.2 ft. Option D

To find the distance between Basti and Cian, we can use the Law of Sines, which relates the lengths of sides to the sines of their opposite angles in a triangle.

Let's label the points: A, B, and C. Ali is at point A, Basti is at point B, and Cian is at point C.

Given:

Angle ABC = 50 degrees (angle opposite side AC)

Angle BAC = 60 degrees (angle opposite side BC)

Ali is 150 ft away from Basti (side AB)

We want to find the distance between Basti and Cian, which is side BC.

Using the Law of Sines, we have:

BC/sin(50) = AB/sin(60)

Substituting the known values:

BC/sin(50) = 150/sin(60)

To find BC, we can rearrange the equation:

BC = (150/sin(60)) * sin(50)

Using a calculator to evaluate the expression:

BC ≈ 138.2 ft

Option D is correct.

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Assuming that you want this to be expanded, simply multiply each term in the first set of parentheses with each term in the second parentheses:

(-2x + 10) (-9x + 5)

18x^2 - 10x - 90x + 15

18x^2 - 100x + 15

If the question, instead, is asking you to find the x-intercepts, set the expression to zero and solve:

0 = (-2x + 10) (-9x + 5)

0 = -9x + 5 <- divide -2x+10 on all sides

5/9 = x

OR

0 = -2x + 10

5 = x

Answer:

(-2x + 10) (-9x + 5) is a polynomial expression that represents the product of two binomials. To solve this expression, you can use the FOIL method, which stands for First, Outer, Inner, Last.

FOIL method:

First: multiply the first terms of each binomial (-2x and -9x) to get 18x^2

Outer: multiply the outer terms of each binomial (-2x and 5) to get -10x

Inner: multiply the inner terms of each binomial (10 and -9x) to get -90x

Last: multiply the last terms of each binomial (10 and 5) to get 50

Then, combine like terms to get the final expression:

(-2x + 10) (-9x + 5) = 18x^2 - 100x - 90x + 50 = 18x^2 - 190x + 50

Step-by-step explanation:

Brainliest Plss

The expression (-9x)^4 can be represented as -6561x^3 without using exponents.

To express the expression (-9x)^4 without using exponents, we can expand it by multiplying the base (-9x) four times using the multiplication property.

(-9x)^4 = (-9x) * (-9x) * (-9x) * (-9x)

To simplify this expression, we can multiply the terms together, taking care to apply the rules of multiplication:

(-9x) * (-9x) = (-9 * -9) * (x * x) = 81 * x^2 = 81x^2

So, by substituting this result back into the original expression, we get:

(-9x)^4 = 81x^2 * (-9x) = -6561 x^3

Therefore, the expression (-9x)^4 can be represented as -6561x^3 without using exponents.

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Answer:

C

Step-by-step explanation:

x + [tex]\frac{3}{4}[/tex] y = 5 ( multiply through by 4 to clear the fraction )

4x + 3y = 20 → (1)

x - [tex]\frac{1}{2}[/tex] y = 0 ( multiply through by 2 to clear the fraction )

2x - y = 0 → (2)

multiplying (2) by 3 and adding to (1) will eliminate y

6x - 3y = 0 → (3)

add (1) and (3) term by term to eliminate y

(4x + 6x) + (3y - 3y) = 20 + 0

10x + 0 = 20

10x = 20 ( divide both sides by 10 )

x = 2

The measure of angle D of the given Kite is: 127°

From the diagram, the figure represents a kite.

Properties of a kite are:

- Two pairs of adjacent sides are equal.

- Two diagonals intersect each other at right angles.

- The longer diagonal bisects the shorter diagonal.

- The angles opposite to the main diagonal are equal.

Thus:

The angle B = the angle D

The sum of all angles of a quadrilateral = 360

Given: ∠A = 36 and ∠C = 70

Thus:

2∠D = 360 - (36 + 70)

2∠D = 254

∠D = 127°

So, the measure of angle D = 127°

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(a) | BD | bisects | AC | (reason : Given)

(b) |AD| ≅ |CD| (reason: |BD| is the perpendicular bisector of segment AC).

(c) ∠ABD ≅ ∠CBD (reason: | BD |  bisects angle ABC)

(d) ∠A ≅ ∠ C (reason: complementary angles of a right triangle)

Congruent angles are the angles that have equal measure. So all the angles that have equal measure will be called congruent angles.

From the first statement, we will complete the flow chart as follows;

line BD bisects line AC (reason : Given)

line AD is congruent to line CD (reason: line BD is the perpendicular bisector of segment AC)

Angle ABD is congruent to angle CBD (reason: line BD bisects angle ABC)

Angle A is congruent to angle C (reason: angle ABD = angle CBD, and both triangles ABD and CBD are right triangles).

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The simplified expression is m^1 or simply m.

To simplify the expression −m^(-8) * m^9 without using negative exponents, we can utilize the properties of exponents.

First, let's deal with the negative exponent. A negative exponent indicates that the term should be moved to the denominator. So, we can rewrite −m^(-8) as 1/m^8.

Now, we can simplify the expression further: 1/m^8 * m^9.

When multiplying terms with the same base, we add the exponents. In this case, we have m^(-8) * m^9, which becomes m^(-8 + 9) = m^1 = m.

Finally, multiplying 1/m^8 by m gives us (1/m^8) * m = 1/m^(8-1) = 1/m^7.

Therefore, the simplified expression is 1/m^7, where m is the variable restricted to those numbers for which the expression is defined. By eliminating the negative exponent and combining like terms, we've simplified the expression without using negative exponents.

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Answer: 1/ 3 ^9

Step-by-step explanation:

Answer:

1/39

Step-by-step explanation:

3-9=1/39

The answer is 0ne over three exponent nine

[tex]\cos(A )=\cfrac{\stackrel{adjacent}{47}}{\underset{hypotenuse}{61}} \implies \cos^{-1}(~~\cos( A )~~) =\cos^{-1}\left( \cfrac{47}{61} \right) \\\\\\ A =\cos^{-1}\left( \cfrac{47}{61} \right)\implies A \approx 39.60^o[/tex]

Make sure your calculator is in Degree mode.

Answer:

-6

Step-by-step explanation:

Simply substitute x = 2 & y = -1 into the function:

[tex]f(2,-1) =[/tex] [tex]\\\sf{3x + 4y - 8[/tex]

               [tex]3(2) + 4(-1) - 8[/tex]

                [tex]6 - 4 - 8[/tex] = -6

Therefore, the value of f(2, -1) for the function f(x, y) = 3x + 4y - 8 is -6.

-------------------------------------------

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Answer:

Step-by-step explanation:

4 dozen = 48 cupcakes

The number must be odd over 48

Number must be multiple of 3 + 2

so:

With the number x:
x = 2a + 1 = 3b + 2 = 4c + 3 =?

2a + 1 = 3b + 2 = 4c + 3

2a + 1 = 59

3b + 2 = 59

4c + 3 = 59

Answer: 59

Step-by-step explanation:

48/2=24

24-3=21

21/7=3

3*19.9999999999997=59

Answer:  the temperature drop from day to night in the city is 31°C.

Step-by-step explanation:

o calculate the temperature drop from day to night, we need to find the difference between the average daily high temperature and the average nightly low temperature.

Temperature drop = Average daily high temperature - Average nightly low temperature

Temperature drop = (-9°C) - (-40°C)

Temperature drop = -9°C + 40°C

Temperature drop = 31°C

The measure of angel BDC in this problem is given as follows:

m < BDC = 43º.

The angle measures for this problem are given as follows:

As the figure is a rectangle, these two angles are complementary, hence the value of x is given as follows:

7x + 1 + 9x - 7 = 90

16x = 96

x = 6.

Then the measure of angle BDC is given as follows:

m < BDC = 7(6) + 1

m < BDC = 43º.

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Note that  the new triangle will have a base of 10 inches and the same side lengths as the given triangle (13 inches).

The perimeter of the new triangle is the sum of all three sides is 36 inches.

To construct another isosceles triangle with the same area as the given triangle, we can use the formula for the area of a triangle  -  

A =  (base x height)/2

In the   given triangle,the base is 10 inches.

Let's assume the height of the given triangle is h.

The area of the given triangle is

A = (1/2) * 10 * h

= 5h in²

To construct another isosceles triangle with the same area, we need to find a different base, let's call it x, such that

(1/2) * x * h = 5h.

Simplifying the equation, we get

x = 10.

Therefore, the new triangle will have a base of 10 inches and the same side lengths as the given triangle (13 inches).

The perimeter of the new triangle is the sum of all three sides: 10 + 13 + 13 = 36 inches.

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Based on the analysis, the equations that are equivalent to the original equation A = h(b1 + b2) are options A and B

To determine which equations are equivalent to the equation A = h(b1 + b2), we need to simplify and compare each equation to the original equation. Let's go through each option:

A. A = h(b1 + b2)

This is the original equation, so it is equivalent to itself.

B. 2Ahb1 + 52

To check if this equation is equivalent to the original, we can simplify it:

2Ahb1 + 52 = 2A(hb1) + 52 = 2Ahb1 + 52

The equation is equivalent to the original equation.

C. b1 - 24 - b2

To check if this equation is equivalent to the original, we can simplify it:

b1 - 24 - b2 = b1 - b2 - 24

This equation is not equivalent to the original equation since it does not involve the variable A or the term hb1.

D. A - hb2

To check if this equation is equivalent to the original, we can simplify it:

A - hb2 = h(b1 + b2) - hb2 = hb1 + hb2 - hb2 = hb1

This equation is not equivalent to the original equation since it only involves the variable b1 and not A.

E. bl

This equation is not equivalent to the original equation since it only involves the variable bl, which is not present in the original equation.

Based on the analysis, the equations that are equivalent to the original equation A = h(b1 + b2) are options A and B.

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Given statement solution is :- The final answer, in its simplest form as a mixed number, is 8 5/6.

To subtract mixed numbers, we need to find a common denominator for the fractions involved. In this case, the common denominator is 12.

Converting the whole numbers to fractions:

4 = 4/1

2 = 2/1

Now let's convert the mixed numbers to improper fractions:

7/12 = (7 * 12 + 1) / 12 = 85/12

1/4 = 1 * 4 / 4 = 4/4 = 1

So, the problem becomes: 4/1 + 85/12 - 2/1 - 1/4

To combine the fractions, we need to have a common denominator, which is 12:

(4/1) + (85/12) - (2/1) - (1/4) = (48/12) + (85/12) - (24/12) - (3/12)

Now we can subtract the fractions:

(48/12) + (85/12) - (24/12) - (3/12) = (48 + 85 - 24 - 3) / 12 = 106/12 = 53/6

The result is 53/6. To express it as a mixed number, we divide the numerator (53) by the denominator (6):

53 ÷ 6 = 8 remainder 5

Therefore, the final answer, in its simplest form as a mixed number, is 8 5/6.

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Therefore, we can conclude that the value of h(x) varies with the change in the value of x. In other words, the function h(x) is a variable function.

The given function is h(x) = 2x² - 4x - 10. To determine the value of h(x) for different values of x, we need to substitute x in the given expression. Let's evaluate the given function for some values of x.

h(0) = 2(0)² - 4(0) - 10h(0) = -10

This implies that if x is zero, the value of

h(x) is -10. h(1) = 2(1)² - 4(1) - 10h(1) = -8

This implies that if x is 1, the value of

h(x) is -8. h(-1) = 2(-1)² - 4(-1) - 10h(-1) = -12

This implies that if x is -1, the value of

h(x) is -12. h(2) = 2(2)² - 4(2) - 10h(2) = -10

This implies that if x is 2, the value of

h(x) is -10. h(3) = 2(3)² - 4(3) - 10h(3) = 4

This implies that if x is 3, the value of

h(x) is 4. h(-2) = 2(-2)² - 4(-2) - 10h(-2) = 16

This implies that if x is -2, the value of h(x) is 16.

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Answer:

Part A: To find the x-intercepts of the graph of f(x), we set f(x) equal to zero and solve for x:

2x² - x - 10 = 0

To factor this quadratic equation, we look for two numbers that multiply to give -20 and add up to -1 (the coefficient of the x-term). The numbers -5 and 4 satisfy these conditions:

2x² - 5x + 4x - 10 = 0

x(2x - 5) + 2(2x - 5) = 0

(x + 2)(2x - 5) = 0

Setting each factor equal to zero gives us:

x + 2 = 0 or 2x - 5 = 0

Solving these equations, we find:

x = -2 or x = 5/2

Therefore, the x-intercepts of the graph of f(x) are -2 and 5/2.

Part B: To determine whether the vertex of the graph of f(x) is a maximum or minimum, we can look at the coefficient of the x² term. Since the coefficient is positive (2), the parabola opens upwards, and the vertex represents a minimum point.

To find the coordinates of the vertex, we can use the formula x = -b / (2a), where a and b are the coefficients of the x² and x terms, respectively.

In this case, a = 2 and b = -1:

x = -(-1) / (2 * 2) = 1/4

To find the corresponding y-coordinate, we substitute this x-value back into the equation:

f(1/4) = 2(1/4)² - 1/4 - 10

f(1/4) = 1/8 - 1/4 - 10

f(1/4) = -81/8

Therefore, the vertex of the graph of f(x) is a minimum and has coordinates (1/4, -81/8).

Part C: To graph f(x), we can use the information obtained in Part A and Part B.

1. Plot the x-intercepts: Mark -2 and 5/2 on the x-axis.

2. Plot the vertex: Mark (1/4, -81/8) as the lowest point on the graph.

3. Determine additional points: Choose a few more x-values, calculate the corresponding y-values using the equation f(x) = 2x² - x - 10, and plot these points.

4. Draw a smooth curve: Connect the plotted points with a smooth curve, keeping in mind that the parabola opens upward.

Using these steps, you can graph f(x) and accurately represent the x-intercepts, vertex, and overall shape of the parabolic curve.

The measure of the angle B is 32. 0 degrees

To solve the given triangle, we need to know the different trigonometric identities and their ratios.

We have that these identities are;

From the information given, we have that;

Opposite side of angle B = 5

Hypotenuse side = 9.43

Using the sine identity, we get that;

sin B = 5/9.43

Divide the values, we have;

sin B= 0.5302

Find the inverse value of the sine identity and then substitute

B = 32. 0 degrees

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Answer:

6 Hrs 33 mins 49 sec

Step-by-step explanation:

For first we need to do it from second.

35-47

since 35 is less than 45 taking 1 min or 60 seconds from 9 min

new equation will be

(36+60)-47

=49 seconds

Secondly subtracting Mins

since we gave 60 sec or 1 min so

we have 9 min

equation will be

8-35

since 8 is less than 8 borrowing 60 min from hour

new equation will be

(8+60)-35

33 mins

Thirdly

subtracting hours

since we gave 60 min or 1 hour so

we have 13 hrs

equation will be

13-7

6 hours

Therefore Answer is 6 Hrs 33 mins 49 sec

Hello!

So the 2 angles of the base are equal, so:

(180 - 74)/2 = 53° one of the 2 angles

          74°

          /\
        /    \
      /        \
    /            \

53°             53°

180 - 74*2 = 32°

          32°

          /\
        /    \
      /        \
    /            \

74°             74°

So the others angles can be:

- 74° and 53°

- 74° and 32°

Answer:

Assuming that a movie has strong marketing and positive reviews, it is reasonable to expect that it could earn $16 million in its opening weekend.

Step-by-step explanation:

The question of when a movie will earn $16 million is a complex one that depends on a variety of factors. The success of a film is influenced by its marketing, critical reception, and competition from other movies in the marketplace. However, there are some general trends that can be observed when it comes to box office performance.

Typically, the first week of a movie's release is the most important for earning revenue. This is because theaters often give priority to new releases and allocate more screens to them.

The first five terms of the sequence are 2, 6, 12, 20, and 30.

The sequence can be simply represented using the equation [tex]\(a_n = n^2 + n\)[/tex]. We will substitute values of [tex]n[/tex] from 1 to 5 into the equation to find the first five terms:

[tex]\(a_1 = 1^2 + 1 = 2\),\\\(a_2 = 2^2 + 2 = 6\),\\\(a_3 = 3^2 + 3 = 12\),\\\(a_4 = 4^2 + 4 = 20\),\\\(a_5 = 5^2 + 5 = 30\).[/tex]

The concept used in this problem is that of a sequence, which is nothing but simply an ordered list of numbers or terms. In this question, the sequence is defined by the equation [tex]\(a_n = n^2 + n\)[/tex], where [tex]\(a_n\)[/tex] represents the nth term of the sequence.

In order to find specific terms of the sequence, we will substitute different values of [tex]\(n\)[/tex] into the equation and then further evaluate the expression. This will allow us to generate a list of values that form the sequence.

Therefore, the first five terms of the sequence are 2, 6, 12, 20, and 30.

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Answer:

12 km (565m)

Step-by-step explanation:

Note tha the   surface area of the toy box is 390cm².

To find the surface area of the toy box, we need to calculate the areas of all the faces and then sum them up.

The toy box is in the shape of a rectangular prism with dimensions:

Length = 15 cm

Width = 5 cm

Height = 6 cm

The surface area of a rectangular prism can be found using the formula  

Surface Area = 2(LW + LH + WH)

Substituting the values we have  -

Surface Area = 2(15 * 5 + 15 * 6 + 5 * 6)

= 2(75 + 90 + 30)

= 2(195)

= 390 cm²

Hence, the surface area of the toy box is 390 square centimeters.

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Analyzing the graph, we can see that initially, as the quantity of bagels increases, the cost decreases due to spreading the fixed cost over more units.

To complete the table and plot the data in one graph, we will calculate the average fixed cost, average variable cost, average total cost, and marginal cost based on the given fixed cost and variable cost information.

Quantity of Bagels represents the number of units produced, while Total Cost represents the sum of Fixed Cost and Variable Cost.

Now, let's plot the data on a graph:

The x-axis represents the Quantity of Bagels, and the y-axis represents the costs.

   |

$14 |                                                     Marginal Cost

   |                                                     -

   |                                                    |

$12 |                                                ----

   |                                              /

   |                                           ---

$10 |                                         /

   |                                      ---

   |                                  ----

$8  |                                /

   |                              --

   |                          ---

$6  |                        /

   |                      --

   |                   ---

$4  |                 /

   |               --

   |           ---

$2  |         /

   |       --

   |  ---

$0  |-----------------------

    0   5   10   15   20

             Quantity of Bagels

The graph shows the different cost curves:

Average Fixed Cost (AFC) curve starts high but decreases as the quantity of bagels increases, as the fixed cost is spread over more units.

Average Variable Cost (AVC) curve starts low but increases as the quantity of bagels increases, indicating diminishing returns.

Average Total Cost (ATC) curve is the sum of AFC and AVC and exhibits a U-shaped curve.

Marginal Cost (MC) curve intersects the AVC and ATC curves at their minimum points, indicating the change in cost for producing one additional unit.

Analyzing the graph, we can see that initially, as the quantity of bagels increases, the cost decreases due to spreading the fixed cost over more units. However, after a certain point, the diminishing returns of variable cost start to outweigh the benefit of spreading fixed costs, causing the average cost to increase.

Understanding cost behavior is essential for decision-making in business, such as pricing, production planning, and profit analysis. The graph provides insights into the relationship between the quantity produced and the associated costs, allowing businesses to optimize their production levels and pricing strategies to maximize profitability.

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The temperature drops by [tex]31\°C[/tex] from day to night in this city.

To calculate the temperature drop from day to night in [tex]\°C[/tex], we subtract the average nightly low temperature from the average daily high temperature.

Given:

Average nightly low temperature: [tex]-40\°C[/tex]

Average daily high temperature: [tex]-9\°C[/tex]

The temperature drop can be calculated as:

Temperature drop = Average daily high temperature - Average nightly low temperature

Substituting the given values:

Temperature drop = [tex]-9\°C - (-40\°C)[/tex]

Simplifying the equation:

Temperature drop = [tex]-9\°C + 40\°C[/tex]

Temperature drop = [tex]31\°C[/tex]

The concept of temperature drop refers to the difference in temperature between two specific periods or conditions. In this case, we are looking at the temperature drop from day to night in a city in China known for its cold climate.

Therefore, the temperature drops by [tex]31\°C[/tex] from day to night in this city.

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Answer:

----------------------

We have two similar triangles:

The ratio of corresponding sides of similar figures is same.

Set up equal ratios and find the missing side:

Hello!

[tex]\sf 89x - 135 = 24\\\\89x = 24 + 135\\\\89x = 159\\\\\boxed{\sf x = \dfrac{159}{89}} \\\\[/tex]