The interior angle of a triangle measures 32 degrees. What is the measure of the adjacent exterior angle?

Answer:

1. 8

2. 4

3. 16

4. 18

Step-by-step explanation:

Hope this helps!! <3

Answer:

15,625

Step-by-step explanation:

5 to the 6 power = 5 × 5 × 5 × 5 × 5 × 5 = 15,625

Answer: Andy is 35 and Mike is 21.

Step-by-step explanation:

Andy’s present age: Mike’s present age

= 5:3

Andy’s age in “if”: Mike’s age in “if”

=6:2

1 unit = 7

5 unit = 35 (Andy’s age)

3 unit = 21 (Mike’s age)

The answer is none of the above

The leading coefficient can be a number other than one

The quadratic function is increasing on the interval:

(-∞, 0)

Here we want to see on which intervals is the quadratic function increasing.

Or function is:

f(x) = 5 - 2x^2

Notice that we have a negative leading coefficient, which means that the parabola opens downwards.

Then the function will be increasing from negative infinity to the x-value of the vertex.

Remember that for the general quadratic:

y = a*x^2 + b*x + c

the x-value of the vertex is:

x = -b/2a

In this case we don't have a linear term, so b = 0, then the vertex is at x = 0.

Which means that the function is increasing on the interval (-∞, 0)

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Answer:

9

Step-by-step explanation:

ok so first if the place you're rounding to is 5 or more you round up and if the place is 4 or less then it stays the same

8.5

5 is 5 or more so you round up

to 9

9514 1404 393

Answer:

  see below

Step-by-step explanation:

Each vertex has a single-letter label.

Each edge joins two vertices, and is named by naming those two vertices.

Each polygon is named by listing the vertices at its corners. It is a plane figure.

The base is the polygon opposite the point where all of the triangles come together.

__

16. figure: pentagonal pyramid ABCDEF

17. base: ABCDE

18. faces: ABF, BCF, CDF, DEF, AEF, ABCDE (the bottom face, or base)

19. edges: AB, BC, CD, DE, AE, FA, BF, CF, DF, EF

20. vertices: A, B, C, D, E, F

a. The angle that the ship turn through when it headed back to the port is 6.4°.

b. The total area that the ship covered during its journey 80.3 miles.

a. Angle

Let p represent the angle

Sin(180°-15°)/139=SinP/60

Sin165°/139=SinP/60

P=Sin^-1 (60sin165°/139)

P=6.4°

b. Total area covered

Let x represent the Total area covered

Hence:

Sin8.6°/x=Sin165°/139

x=80.3 miles

Inconclusion the ship turn at angle 6.4° and the total area is  80.3 miles.

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Answer: 0.00002163799

Step-by-step explanation:

Answer:

46,215

Step-by-step explanation:

you just have to divide the bigger number first and then the smallest

The distance from the center of the Earth to the point where the net gravitational force is zero is one-ninth the distance from the Earth to the Moon.

Let's assume that the distance from the center of the Earth to this point is denoted as x.

Given:

Mass of the Moon (M\(_{moon}\)) = 1/81 × M\(_{earth}\)

Distance from Earth to Moon (d\(_{moon}\)) = distance on center

According to the principle of gravitational equilibrium, the gravitational force from the Earth and the gravitational force from the Moon acting on an object at that point must balance out. Mathematically, we can express this as:

F\(_{earth}\) = F\(_{moon}\)

The gravitational force between two objects can be calculated using Newton's law of universal gravitation:

F \(_{gravity}\)= G × (m₁ × m₂) / r²

Where:

G is the gravitational constant (approximately 6.67430 x 10⁻¹¹m²/kg/s²)

m₁ and m₂ are the masses of the two objects

r is the distance between the centers of the two objects

Considering the gravitational forces involved:

F\(_{gravity}\)\(_{earth}\) = G ₓ (M\(_{EARTH}\)  ₓ m\(_{OBJECT}\)) / (d\(_{earth}\))²

F\(_{gravity}\) \(_{moon}\) = G ₓ (M \(_{moon}\) ₓ m\(_{object}\)) / (d \(_{moon}\))²

Since we are looking for the point where the net gravitational force is zero, we set these two forces equal to each other:

G × (M\(_{earth}\) × m\(_{object}\)) / (d\(_{earth}\))²   =     G × (M \(_{moon}\) × m\(_{object}\)) / (d \(_{moon}\))²

Canceling out the common factors of G and m\(_object}\), and substituting the given values:

(M\(_{earth}\) × 1) / (d\(_{earth}\))² = (M \(_{moon}\) × 1) / (d \(_{moon}\))²

Rearranging the equation:

(d\(_{earth}\))²/ (M\(_{earth}\)) = (d \(_{moon}\))² / (M \(_{moon}\))

Taking the square root of both sides:

d\(_{earth}\) / √(M \(_{moon}\))) = d_moon / √(M \(_{moon}\))

Substituting the given values:

d\(_{earth}\) /√(M\(_{earth}\)) = d\(_{moon}\) / √(1/81 × M\(_{earth}\))

Simplifying further:

d\(_{earth}\)  / √(M\(_{earth}\)) =d\(_{moon}\)  / (1/9 × √(M\(_{earth}\)))

Multiplying both sides by √(M\(_{earth}\)):

d\(_{earth}\) = (1/9) × d\(_{moon}\)

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Answer:

If your solving for x then its x=3 because you combine liked terms then divide both sides by 3.

9514 1404 393

Answer:

  854.88 lb/yr

Step-by-step explanation:

It is effectively a units conversion problem. The conversion factors of interest are ...

  1000 W × 1 h = 1 kWh

  52 wk = 1 yr

__

  (1500 W)×(8 h/wk) × (52wk/yr) ÷ ((1000 W)(1 h))/(1 kWh) × (1.37 lb/kWh)

  = (1500×8×52×1.37)/(1000) lb/yr

  = 854.88 lb/yr

Answer:

Step-by-step explanation:

In this scenario, Octavia should buy at least 12 small milkshakes. At $2.50 each small milkshake, buying 12 would be a total of $30. Since she needs to buy atleast 20 total milkshakes, she would need to buy 8 large milkshakes which at $6 each would cost her a total of $48. Together this would sum up to be $78 for the 20 milkshakes which would mean that Octavia is still under her budget.

Answer:

2.5 hours

Step-by-step explanation:

The cost of the rental - the scooter rental = 30.50 - 16.75, which equals 13.75.

Divide the additional per hour by that number.

13.75 / 5.5 = 2.5

Therefore, the scooter was rented for 2.5 hours.

Answer:

2.5

Step-by-step explanation:

13.75 / 5.5 = 2.5

Answer:

-8x + 31

Step-by-step explanation:

Hope it helps, have a great day

Answer:

35 cm

Step-by-step explanation:

a. Slope of WZ = -2.25; Slope of WX = 5

b. WZ = √97; WX = √41

c. WXYZ is not a rectangle, rhombus, nor a square. We can conclude that: D. WXYZ is none of these.

Slope = change in y/change in x

Given:

W(-1, 2), X(-5, 7), Y(-1, -2), and Z (3, -7)

a. Slope of WZ and slope of WX:

Slope of WZ = (-7 - 2)/(3 -(-1)) = -2.25

Slope of WX = (7 - 2)/(-1 -(-1)) = 5

b. Use distance formula, \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\), to find WZ and WX:

\(WZ = \sqrt{(3 - (-1))^2 + (-7 - 2)^2}\\\\\mathbf{WZ = \sqrt{97} }\)

\(WX = \sqrt{(-5 -(-1))^2 + (7 - 2)^2}\\\\\mathbf{WX = \sqrt{41} }\)

c. The quadrilateral WXYZ have adjacent sides that are not perpendicular to each other and have different slopes and different lengths, so therefore, WXYZ is not a rectangle, rhombus, nor a square. We can conclude that: D. WXYZ is none of these.

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Step-by-step explanation:

A: If there are 2 modes, x can be either 1 or 2.

B: To find the mode of the data set, we need to count how many times each number appears.

- 0 appears 2 times

- 1 appears 4 times

- 2 appears 4 times

- 3 appears 3 times

- 4 appears 1 time

Since both 1 and 2 appear 4 times in the data set, there are two modes.

For x, if we add it to the data set, then the mode must be x plus either 1 or 2.

If we choose x to be 2, then the mode would be 2, since 1 and 2 each appear 4 times, and adding another 2 would make it the mode.

So a possible value for x could be 2, and the mode would be 2.

The length of Mid segment QT is 57.56 units.

The incenter of a triangle can be discovered by drawing the triangle's angle bisectors and then locating the location of their intersection. This is possible with the aid of a compass.

The three line segments and the three lines that include those segments are equally spaced from the incenter and constitute each of the three sides of the triangle.

the single point where the three internal angle bisectors of a triangle meet and which also serves as the circumference of the circle around which it is inscribed.

The three line segments and the three lines that include those segments are equally spaced from the incenter and constitute each of the three sides of the triangle.  

ΔQUT is right triangle

QU = 55

UT= 17

Using Pythagoras Theorem

QT² = QU² + UT²

QT² = 55² + 17²

QT = √3314

QT = 57.56

Thus, The length of Mid segment QT is 57.56 units.

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The circle on a graph by drawing the center point and then drawing a circle around it with a radius of 6.

To graph the circle with the equation (x - 3)² + (y + 3)² = 36, we can start by finding the center and radius of the circle.

The equation of a circle in standard form is (x - h)² + (y - k)² = r² (h, k) represents the center of the circle and r represents the radius.

Comparing the given equation with the standard form, we can see that the center of the circle is (3, -3) and the radius is √36 = 6.

Using this information, we can proceed to plot the circle on a graph:

Plot the center point: (3, -3).

From the center point, move 6 units in each direction (up, down, left, and right) to determine the points on the circle.

Up: (3, -3 + 6) = (3, 3)

Down: (3, -3 - 6) = (3, -9)

Left: (3 - 6, -3) = (-3, -3)

Right: (3 + 6, -3) = (9, -3)

Connect the plotted points to form a circle.

The resulting graph should look like this:

    |            • (3, 3)

    |  

    |    •

    |                     •

__|_____________________________

    |

    |

    |

    |  

    |    • (3, -3)

The center of the circle is denoted by a solid dot (•) in the graph and the other points lie on the circumference of the circle.

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The measure of the angle ∠ABC will be 40 degrees. Then the correct option is B.

It is the centre of an equidistant point drawn from the centre. The radius of a circle is the distance between the centre and the circumference.

In the diagram, the measure of the arc from A to B not passing through C is 80 degrees.

Then the measure of angle ACB will be

We know that Angles subtended by the very same arc at any position on the circular path are half of the angles subtended by the very same arc at the centre.

Then we have

2∠ABC = ∠AOB

2∠ABC = 80°

 ∠ABC = 40°

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When x = 5 and y = 4, the expression \(x + (x^2 - xy) - y\)  evaluates to 6.

To evaluate the expression \(x + (x^2 - xy) - y\) when x = 5 and y = 4, we substitute the given values into the expression and perform the

calculations:

\(x + (x^2 - xy) - y\\x= 5 + (5^2 - 5*4) - 4\\x= 5 + (25 - 20) - 4\\x= 5 + 5 - 4\\x= 10 - 4\\x= 6\\\)

It's crucial to remember that the expression in question is not an equation that represents a graph, nevertheless. It is merely an algebraic expression that, given the values of "x" and "y," evaluates to a single value. We need an equation that connects 'x' and 'y' and specifies the relationship between them if we are to construct a graph.

Therefore, when x = 5 and y = 4, the expression \(x + (x^2 - xy) - y\) evaluates to 6.

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Correct Question is:

Evaluate:  \(x + (x^2 - xy) - y\) if x = 5 and y = 4.

52s is the maximum time that she can take on her last lap and still make the team.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

Given that he mean pace a student needs to achieve on 5 laps of the pool is 60 seconds (s).

The student swims a lap in 63 s, 62 s, 65 s, and 58 s on her first four laps.

We need to find the maximum time (in seconds) that she can take on her last lap and still make the team

Let x be the maximum time (in seconds) that she can take on her last lap

60=(63+62+65+58+x)/5

300=63+62+65+58+x

300=248+x

Subtract 248 on both sides

300-248=x

x=52s

Hence, 52s is the maximum time that she can take on her last lap and still make the team.

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Answer:

The second length of the piece because 141 times 2 which is two times the amount of the second piece is 282.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The answer is 47.

The perimeter and the area of each composite figure are, respectively:

Case 1: p = 77.6 cm, A = 304 cm²

Case 2: p = 25.1 ft, A = 28 ft²

Case 3: p = 42 mi, A = 52.5 mi²

Case 4: p = 56.5 in, A = 179.424 in²

In this problem we need to determine the perimeter and the area of four composite figures, that is, figures formed by combining triangles and rectangles, whose area formulas are listed below:

Triangle

A = 0.5 · b · h

Rectangle

A = b · h

Where:

Now we find the perimeter and the area of each figure:

Case 1

p = 2 · (18.8 cm) + 2 · (20 cm)

p = 77.6 cm

A = (15.2 cm) · (20 cm)

A = 304 cm²

Case 2

p = 10 ft + 8.1 ft + 7 ft

p = 25.1 ft

A = 0.5 · (10 ft) · (5.6 ft)

A = 28 ft²

Case 3

p = 17.5 mi + 6 mi + 18.5 mi

p = 42 mi

A = 0.5 · (17.5 mi) · (6 mi)

A = 52.5 mi²

Case 4

p = 20 in + 13.9 in + 15 in + 7.6 in

p = 56.5 in

A = (7.6 in) · (13 in) + 0.5 · √[(13.9 in)² - (13 in)²] · (13 in) + 0.5 · √[(15 in)² - (13 in)²] · (13 in)

A = 98.8 in² + 31.982 in² + 48.642 in²

A = 179.424 in²

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Answer:

\(\frac{4(8-1)}{6}\)

6

Step-by-step explanation:

\(\frac{4(8 + 1) }{6}\)

\(\frac{4(9)}{6}\)

\(\frac{36}{6}\)

6

Answer:

The expression is:

4(8+1)/6

Simplify:

= 6

Step-by-step explanation:

The expression is:

4(8+1)/6

Simplify:

= 4(9) / 6

= 36/6

= 6

The equation for w(width of rectangle) is: W = (P - 2L)/2

The correct answer is an option (c)

We know that the formula for the perimeter of the rectangle is:

P = 2L + 2W

where P is the perimeter of the rectangle,

L is the length of the rectangle,

and W is the width of the rectangle.

We need to rearrange this equation for w.

Consider equation,

P = 2L + 2W

P - 2L = 2L + 2W - 2L      ......(subtract 2L from each side of equation)

P - 2L = 2W

(P - 2L)/2 = 2W/2             .....(divide each side by 2)

W = (P - 2L)/2

Therefore, the correct answer is  W equals the quantity P minus 2 times L all over 2

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The complete question is:

Makayla is taking a math course and is working with the perimeter of rectangles. She knows the perimeter and length of her rectangle but wants to solve for the width. Rearrange the following equation for W, where P is the perimeter, L is the length, and W is the width of the rectangle. P = 2L + 2W.

a) W = 2P − 2L

b) W = P/ 2-2 times L

c) W equals the quantity P minus 2 times L all over 2

d) W = 2P + 2L

Answer:

c) W equals the quantity P minus 2 times L all over 2

Step-by-step explanation:i just took the test

Answer:

2:5, 2/5, 2 to 5

Step-by-step explanation:

The ratio is 6 to 15, but you can simplify that to 2 to 5.

Answer:

a) v_avg = k

b) 0.034 km/h

Step-by-step explanation:

a) The average velocity is given by the displacement over the time:

\(v_{avg}=\frac{\Delta x}{\Delta t}\)   (1)

Δx is the area under the line. In this case you can consider two areas. Firs, from t=0 t0 t=30 and from t=30 to t=50:

S1 = 30k

S2 = 20k/2 = 10k

Then, the total surface is:

S = S1+S2 = 50k

The average speed is:

v_avg = (50k)/(50s)= k

b) The value of k can be determined by using the expression for the total area under the line, which is the total displacement of the car S=1.7 km:

S=50k=1.7km

k=(1.7km)/(50k)=0.034km/h = 34 m/h