Find the measure x of an angle that is complementary to a 67° angle.
O 32°
O 23°
O 13°
O 63°

Answer:

f(x) = x⁴ + 2x³ - 3x² - 4x + 4

Step-by-step explanation:

we have 3 turnarounds and no negative y values (so, it should be a function based on x⁴), 2 of these turnarounds are also directly on the x-axis (y=0).

f(0) = 4

f(1) = 0

f(-2) = 0

an equation based on x⁴ would have 4 interceptions with the x-axis. since we have only 2 here, then there must be 2 pairs of equal interceptions.

based on the known x-interceptions (x=1, x=-2) we can start with the approach

(x-1)(x+2)

this world give us a quadratic equation (based on x²).

the trick is now to get this to x⁴ without adding additional x-interceptions. that is done by simply "reusing" the ones we already used.

(x-1)(x+2)(x-1)(x+2) = (x-1)²(x+2)²

(x-1)²(x+2)² = (x² - 2x + 1)(x² + 4x + 4) =

x⁴ - 2x³ + x² + 4x³ - 8x² + 4x + 4x² - 8x + 4 =

x⁴ + 2x³ - 3x² - 4x + 4

Answer:

X1 = 2 Y1 = -5

Step-by-step explanation:

math simple slope

Answer:

m∠CDA=65°

Step-by-step explanation:

This is because an isosceles trapezoid has both pairs of base angles that are equivalent to one another.

This is because angles 1 and 4 are vertical angles. Such angles form whenever we have an X shape like this. Vertical angles are always opposite one another and they are always the same measure. The fact that lines k and l are parallel has no relevance (so they could easily be not parallel and the two angles mentioned are still congruent).

Answer:

83 spins

Step-by-step explanation:

Number of red spins = n

Number of orange spins = 8n

Number of yellow spins = 3n

Total number of trials = 240

Total number of spins :

(n + 8n + 3n) = 240

12n = 240

n = 240 / 12

n = 20

Number of red spins = 20

(1000/240) * n

4.1666666 * 20

= 83.333

= 83 spins

Answer:

A scatter plot can show a positive relationship, a negative relationship, or no relationship. If the points on the scatter plot seem to form a line that slants up from left to right, there is a positive relationship or positive correlation between the variables.

Answer:

A is ur answer

Step-by-step explanation:

Answer:

4/8 or 1/2

Step-by-step explanation:

Answer:

The answer is C!

Step-by-step explanation:

Answer:

D

NOTE: the answer "C" is NOT correct... see the image the green is "C" the purple is "D"

Step-by-step explanation:

no. of even factora of 120 which are greater than 20 and less than 120 are = 6

Answer:

54 and 36

Step-by-step explanation:

84

45% of 120 students chose the amusement park , then

45% of 120 = 0.45 × 120 = 54

54 students chose the amusement park

85

45% of 180 = 0.45 × 180 = 81

25% of 180 = 0.25 × 180 = 45

81 - 45 = 36

36 more students chose the amusement park than the water park

Answer:

54, 36

Step-by-step explanation:

84

45% of 120 students chose the amusement park

45% of 120 = 0.45×120=54

54 students chose the amusement park

85

45% of 180 = 0.45 × 180 = 81

25% of 180 = 0.25 × 180 = 45

81 - 45 = 36

36 students chose the amusement park than the water park

Answer:

sin θ = (√119)/12

tan θ = (√119)/5

csc θ = 12/(√119)

cot θ = 5/(√119)

Five trigonometric functions of θ are

sinθ = [tex]\frac{\sqrt{119} }{12}[/tex]cosθ = [tex]\frac{5}{12}[/tex]tanθ = [tex]\frac{\sqrt{119} }{5}[/tex]cosecθ = [tex]\frac{12}{\sqrt{119} }[/tex]secθ = [tex]\frac{12}{5}[/tex]cotθ = [tex]\frac{5}{\sqrt{119} }[/tex]

"The trigonometric functions of θ are functions of an angle. sine, cosine, and tangent are familiar trigonometric functions. The trigonometric functions relates the angles of a triangle to the length of its side."

Let θ be an acute angle of a right angle triangle

"An acute angle ("acute" meaning "small") is an angle smaller than a right angle. The range of an acute angle is between 0 and 90 degrees."

"A right angled triangle is a triangle in which one angle is a right angle (that is, a 90-degree angle).

"The side opposite the right angle is called the 'hypotenuse'. The hypotenuse is always the longest side. The sum of the other two interior angles is equal to 90°."

"An 'opposite' side is the one across from a given angle."

"An 'adjacent' side is next to a given angle. We use special words to describe the sides of right triangles."

we have,

cosθ = [tex]\frac{5}{12}[/tex]

secθ = [tex]\frac{12}{5}[/tex]

Hypotenuse side = 12

Adjacent side = 5

∴ Opposite side = [tex]\sqrt{hyp^{2}-adj^{2} }[/tex]= [tex]\sqrt{12^{2}-5^{2} }[/tex] = [tex]\sqrt{119}[/tex]

sinθ = [tex]\frac{opp}{hyp}[/tex] = [tex]\frac{\sqrt{119} }{12}[/tex]

tanθ = [tex]\frac{opp}{adj}[/tex] = [tex]\frac{\sqrt{119} }{5}[/tex]

cosecθ = [tex]\frac{hyp}{opp}[/tex] = [tex]\frac{12}{\sqrt{119} }[/tex]

cotθ  = [tex]\frac{adj}{opp}[/tex] = [tex]\frac{5}{\sqrt{119} }[/tex]

Learn more about trigonometric functions, acute angle and right angle triangle here

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Answer:

D

Step-by-step explanation:

Pythagorean

[tex]x^{2} + 9^{2} = 15^{2}[/tex] (x>0)

=> [tex]x=\sqrt{15^{2}-9^{2} }[/tex] [tex]=12[/tex]

Answer:

340 miles per hour

Step-by-step explanation:

To find the speed, take the distance and divide by the time

510 miles / 1.5 hours

340 miles per hour

Answer:

340 miles

Step-by-step explanation:

Speed= Distance/ Time=

510/ 1.5= 340 miles

Answer:

[tex]\sqrt{41}[/tex]

Step-by-step explanation:

think of this triangle being made up of 2 triangles with the lengths of 5, 4, and x.

x being the hypotenuse, 5 being one of the legs, and 4 being one of the legs. (8/2).

pythagorean theorem:

a^2 + b^2 = c^2

5^2 + 4^2 = x^2

25 + 16 = x^2

41 = x^2

x = sqrt 41

9514 1404 393

Answer:

  -8x +12

Step-by-step explanation:

The distributive property can help you simplify the product.

  (4)(-2x +3) = (4)(-2x) +(4)(3) = -8x +12

Answer:

192

Step-by-step explanation:

3(pi) x 4^2 x 12 ÷ 3 = 192

Answer:

A: n/100 = 15/30 is the correct option

The given transformations are rigid transformations, such that

the image and the preimage have the same dimensions.

Correct responses:

Given;

The images of triangle 1 are; Triangle 2, and triangle 3

Taking the image of line m as line m, we have;

Required:

The degree of the intersection of lines m and n

Solution:

Triangle 2 is the reflection of triangle 1 across line m, and

triangle 3 is the reflection of triangle 2 across line n

The distance of triangles 1 and 2 from line m are equal

The distance of triangle 2 and 3 from line n are equal.

Whereby the degree of rotation of triangle 1 to triangle 2, θ₁ is

equal to the degree of rotation of triangle 2 to triangle 3, θ₂,

we have;

θ₁ = θ₂

100° = θ₁ + θ₂ = 2·θ₁

θ₁ = θ₂ = 100° ÷ 2 = 50°

The angle of rotation of line m to line n = Rotation of triangle 1 to triangle 2 = θ₁ = 50°

The transformation to give triangle 2 from triangle 1 is a reflection about line m.

Similarly, the transformation that gives triangle 3 from triangle 2 is a reflection about line n.

Therefore;

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19 Step-by-step explanation:

Answer:

3.45 sqft

Step-by-step explanation:

Calculate all the areas individually, the 3 lateral sides are the same and using the formula for area we have 1/2 base times height. The height is 2 ft and the base is 1 ft so the area of one of the lateral sides is 1 ft.

There are three lateral sides so you multiply 1 by 3 to get 3.

The base is done the same way. It's base is 1 ft and it's height is 0.9ft so the area is 0.45.

3 + 0.45 = 3.45

The surface area is 3.45 sqft.

I could be wrong but the formula and process is the same, calculate the sides individually using the base height formula for area.

Answer: pi/6

explanation: took test

The value of θ on a unit circle where the terminal point of θ is (1/2,square root 3/2), is 60°.

The measure of the angle in degrees or radians over the circle, at the endpoint on the coordinate plane is known as terminal point

Thus the value of θ at terminal point on a unit circle (1/2,square root 3/2) is 60 degrees.

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Answer: No

Step-by-step explanation:

Add 2 sides together. If the sum of greater than the length of the 3rd side for all 3 options it can form a right triangle if it doesn’t than it can’t:

9 + 12 = 21 which is not greater than the 3rd side length of 21 so this cannot form a right triangle.

Answer:

120 / 561

Step-by-step explanation:

An automobile manufacturing plant produced 34 vehicles today: 16 were motorcycles, 9 were trucks, and 9 were vans. Plant managers are going to select two of these vehicles for a thorough inspection. The first vehicle will be selected at random, and then the second vehicle will be selected at random from the remaining vehicles.What is the probability that two motorcycles will be selected

16/34 X 15 X 33

Answer:

3.16, 3.16, 3.16

3.16, 3.16, 3.16

1.41, 1.41, 1.41

3.16, 3.16, 3.16

Step-by-step explanation:

Answer:

Length Length  Length

3.16         3.16   3.16

3.16 3.16   3.16

1.41   1.41   1.41

3.16  3.16  3.16

Step-by-step explanation:

Answer:

I think the sum of the measures of the interior angles of an octagon =(8−2)180° . The sum of the measures of the interior angles of an octagon is 1080° .

I hope this help!:)

Answer:

[tex]135^{\circ}[/tex]

Step-by-step explanation:

The sum of the interior angles of a polygon with [tex]n[/tex] sides is equal to [tex](n-2)180[/tex]. Since an octagon has 8 sides, the sum of its interior angles is equal to:

[tex](8-2)180=6\cdot 180=1,080^{\circ}[/tex]

By definition, a regular polygon is a polygon with equal sides and angles. An octagon has 8 sides and 8 angles. Therefore, a each interior angle of a regular octagon must be equal to:

[tex]\frac{1,080}{8}=\boxed{135^{\circ}}[/tex]

Answer:

y = (-7/3)x - 26/3

Step-by-step explanation:

To find the equation of a line given two points, we can first define an equation of a line to be y= mx +b, with m being the slope and b being the y intercept.

To calculate the slope, we can use the formula (change in y)/(change in x), or

(y₂-y₁)/(x₂-x₁). If we define (-2, -4) as point 1 (meaning -2 is x₁ and -4 is y₁) and (-8, 10) as point 2 (it doesn't matter which point is point 1/2), we can say that the slope is equal to

(10-(-4)) / (-8-(-2)

= 14/(-6)

= -7/3

Therefore, our formula so far is

y = (-7/3)x + b

To figure out b, we can plug in a point, e.g. (-8, 10) and solve for b. Plugging this in, we get

10 = (-7/3)(-8) + b

10 = 56/3 + b

subtract 56/3 from both sides

10 - 56/3 = b

= 30/3 - 56/3

= -26/3

Therefore, our equation is

y = (-7/3)x - 26/3

Answer:

I think 5x is the answer

stay safe

Answer:

[tex]\sqrt{40\\}[/tex], [tex]2\sqrt{10}[/tex], or 6.3 (rounded).

Step-by-step explanation:

Use the distance formula, [tex]\sqrt{(x_1-x_2)^2+(y_1-y_2)^2} \\x_1 is -8, y_1 is 6, x_2 is -6, y_2 is 0.[/tex]

Answer:

x > 20

Step-by-step explanation:

5x + 20 > 120

Divide 5 on both sides,

x + 4 > 24

x + 4 - 4 > 24 - 4

x > 20