Classify the triangle described below.
A triangle with measures of x°, 4x°, and 4x° is a(n) triangle.

Answer:

Step-by-step explanation:

A full revolution on a circle/radians is 2[tex]\pi[/tex], so keep adding or subtracting 2[tex]\pi[/tex] til you get a base angle, that's when the sign changes.  Then decide which quadrant your in.

For this one the equivalent of 2[tex]\pi[/tex] is [tex]6\pi /3[/tex]

-29[tex]\pi[/tex]/3 + [tex]6\pi /3[/tex]

= -23[tex]\pi[/tex]/3 + [tex]6\pi /3[/tex]

= -17[tex]\pi[/tex]/3 + [tex]6\pi /3[/tex]

= -11[tex]\pi[/tex]/3 + [tex]6\pi /3[/tex]

= -5[tex]\pi[/tex]/3 + [tex]6\pi /3[/tex]

= 1[tex]\pi[/tex]/3            sign changed it's equavalent to [tex]\pi /3[/tex]  Which is in the first quadrant.   See unit circle.

-5[tex]\pi[/tex]/6 + [tex]12\pi /6[/tex]

=[tex]7\pi /6[/tex]              third quadrant,  i count quadrants by know [tex]\pi[/tex]/6 is 30°, so every 30° line is 1/6 of the unit circle.  when i count 7 of them that's in the 3rd quadrant.  Don't forget to count the axis's

2[tex]\pi[/tex]/3 is in the 2nd quadrant.  Count my pi/3's which is 60°

45[tex]\pi[/tex]/7 - 14[tex]\pi[/tex]/7

= 31[tex]\pi[/tex]/7 - 14[tex]\pi[/tex]/7

=17[tex]\pi[/tex]/7 - 14[tex]\pi[/tex]/7

=3[tex]\pi[/tex]/7 - 14[tex]\pi[/tex]/7

= -11[tex]\pi[/tex]/7      1/7th's is not your typical unit circle angle

This one i think of logically.  this is -1 4pi/7  

1 pi going backwards is 180

keep going backards 4/7 is bigger than 1/2 so it's in the 1st quadrant

The points are not at a distance of 6 units from each other.

Given that the distance between point (2, 2) and point (8, 2) is 6 units a coordinate plane.

We need to find which other pairs of points are also 6 units apart.

The distance between two points (x₁, y₁), (x₂, y₂) are 6 if and only if either

( x₂ - x₁ = 6 and y₂ = y₁ )or ( x₂ = x₁ and y₂ - y₁ = 6 ).

If either of the conditions is satisfied, then only we can say that the two points has distance of 6 units between them.

Now, As given

Let (x₁, y₁) = ( 2, 2) , (x₂, y₂) = (8, 2)

Check whether the conditions are satisfied or not .

Here x₁ = 2 , x₂ = 8, y₁ = 2, y₂ = 2

Now,

x₂ - x₁ = 8 - 2 = 6 , y₂ - y₁ = 2 - 2 = 0

∴ we get

1st condition is satisfied, So the points have a distance of 6 units between them.

Now,

Let us suppose another point (x₁, y₁) = ( 4, 3) , (x₂, y₂) = (3, 3)

Here x₁ = 4 , x₂ = 3, y₁ = 3, y₂ = 3

Now,

x₂ - x₁ = 4 - 3 = 1 , y₂ - y₁ = 3 - 3 = 0

Here neither of the conditions are satisfied.

So, the points are not at a distance of 6 units from each other.

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The perimeter of the shape above is 22.22 units

the area of the shape above is 26 square units

We can see from the diagram shown, that the shape is made up of a semicircle below and a triangle above.

Now, the formula for calculating the area of a triangle is expressed as;

A = 1/2bh

Such that the parameters are;

Now, substitute the values

Area = 1/2 × 7 ×6

Multiply the values

Area = 42/2

Area = 26 square units

The formula for perimeter of a triangle is;

Perimeter = (a + b + c)

Perimeter = 6 + 7 + 9. 22

Add the values

Perimeter = 22. 22 units

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The recipe will need 21 cups of sauce and three and a half teaspoons of oregano for 7 servings. The correct option is C.

The sauce to oregano ratio for five servings is equal to 15 cups and 2.5 teaspoons, respectively. For a single portion of the recipe, this computes to 3 cups and 0.5 teaspoons.

It should be noted that to attain the correct amount needed for seven servings, simply multiply each part of the ratio by seven. Consequently, you should use 21 cups of sauce and three and one-half teaspoons of oregano. All together, this recipe requires 21 cups of sauce and three and a half teaspoons of oregano for 7 servings.

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The equation for contribution for each student is 185.5/14 = 13.25.

Price of new easel= $129

Set of blank canvases = $ 46

Sales tax = $ 10.50

So, the total amount is

= 129 + 46 + 10.5

= 185.5

Then, each student contribute

= 185.5 / 14

= 13.25

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Answer:

To solve m^2 - 6m = 3 using the quadratic formula, we first need to put the equation in standard form, which is ax^2 + bx + c = 0.

m^2 - 6m - 3 = 0

Now we can identify a, b, and c:

a = 1, b = -6, c = -3

Next, we can plug these values into the quadratic formula:

m = (-b ± sqrt(b^2 - 4ac)) / 2a

m = (-(-6) ± sqrt((-6)^2 - 4(1)(-3))) / 2(1)

m = (6 ± sqrt(48)) / 2

Simplifying the square root of 48, we get:

m = (6 ± 4sqrt(3)) / 2

Now we can simplify by factoring out a 2 from the numerator:

m = 3 ± 2sqrt(3)

So the solutions to the equation are:

m = 3 + 2sqrt(3) or m = 3 - 2sqrt(3)

Step-by-step explanation:

Answer: 3±2√3

Step-by-step explanation:

see image for explanation

Let me know if you more explanation with simplifying the root.  That is a whole lesson in itself.

The probability that you will get a 15-inch monitor = 1/3

We know that probability of event is the ratio of number of possible outcomes of event A and the total number of outcomes.

Let us assume that event A = you will get a 15-inch monitor

The number of favourable outcomes for event A are 2

So, n(A) = 2

The sample space for this experiment would be,

n(S) = 6

Using the definition of probability, the required proabability would be,

P(A) = n(A) / n(S)

P(A) = 2/6

P(A) = 1/3

Therefore, the required probability = 1/3

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Answer:

[tex]\huge\boxed{\sf x = 10\°}[/tex]

Step-by-step explanation:

According to the statement,

92° + x + 78° = 180°

170° + x = 180°

x = 180° - 170°

[tex]\rule[225]{225}{2}[/tex]

Answer: the tangent of the smaller acute angle in this right triangle is 8/15.

Step-by-step explanation:

Since the side lengths of the correct triangle are given as 8, 15, and 17, able to see that the sides with lengths 8 and 15 are the legs of the proper triangle, and the side with length 17 is the hypotenuse.

We know that the littler intense point θ is inverse the shorter leg of length 8. Hence, the digression of θ is:

tan(θ) = opposite/adjacent = 8/15

Answer:θ ≈ 2.57 radians

θ ≈ 0.58 radians

Step-by-step explanation:We can solve this quadratic equation in sin(θ) by factoring:

4sin^2(θ) + 7sin(θ) - 5 = 0

(4sin(θ) - 1)(sin(θ) + 5) = 0

Therefore, either:

4sin(θ) - 1 = 0

sin(θ) = 1/4

or:

sin(θ) + 5 = 0

sin(θ) = -5 (not possible, since sin(θ) is between -1 and 1)

So, we have sin(θ) = 1/4. Since 0 ≤ θ < 2π, we can find the two solutions in the interval [0, 2π) by using the inverse sine function:

θ = arcsin(1/4)

Using a calculator, we find:

θ ≈ 0.2531 or θ ≈ 2.8887

Therefore, in radians, the solutions for θ are approximately:

0.2531 (which is less than 2π)

2.8887 (which is greater than 2π)

So the only answer that satisfies 0 ≤ θ < 2π is:

The equation x² + y - 36 = 0 is symmetry about the y - axis.

We have to given that;

The equation of graph is,

⇒ x² + y - 36 = 0

Now, We get;

⇒ x² + y - 36 = 0

⇒ y = - x² + 36

By plotting the equation in graph we get;

The equation x² + y - 36 = 0 is symmetry about the y - axis.

Thus, The equation x² + y - 36 = 0 is symmetry about the y - axis.

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The graph is a function: yes

The domain of this function is: x ≥ -3.

The range of this function: all real numbers.

In Mathematics and Geometry, a domain is the set of all real numbers for which a particular function is defined.

Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = {-3, ∞}, x ≥ -3, or -3 ≤ x ≤ ∞.

Range = {-∞, ∞} or all real numbers.

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Answer:

C. complementary

Michel-Eugène Chevreul discovered that placing complementary colors next to each other can create the greatest contrast and vibrancy in color perception. This is because complementary colors are located opposite each other on the color wheel and, when placed side by side, they enhance each other and create a strong visual impact. For example, placing yellow next to violet or blue next to orange can create a dynamic and eye-catching effect. In contrast, placing tertiary colors (colors made by mixing primary and secondary colors) or arbitrary colors next to each other may not create as much contrast or visual interest. Overall, understanding color theory and the relationships between different colors can be helpful for creating visually appealing designs, artworks, or other color-based projects.

The surface area of the rectangular prism is 82 square cm.

Given that:

Length, L = 3 cm

Width, W = 7 cm

Height, H = 2 cm

Let the prism with a length of L, a width of W, and a height of H. Then the surface area of the prism is given as,

SA = 2(LW + WH + HL)

The surface area of the rectangular prism is calculated as,

SA = 2 x (3 x 7 + 7 x 2 + 2 x 3)

SA = 2 x (21 + 14 + 6)

SA = 2 x 41

SA = 82 square cm

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The correct solution of the expression is,

⇒ 16 / e¹²ˣ

We have to given that;

The value of Expression is,

⇒ (2e⁻³ˣ)⁴

Now, We can simplify as;

⇒ (2e⁻³ˣ)⁴

⇒ 2⁴ × e⁻¹²ˣ

⇒ 16e⁻¹²ˣ

⇒ 16 / e¹²ˣ

Thus, The correct solution of the expression is,

⇒ 16 / e¹²ˣ

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The unknown angle in the cyclic quadrilateral is as follows:

m∠DGF = 75 degrees

A cyclic quadrilateral is a quadrilateral which has all its four vertices lying on a circle.

The sum of angles in a cyclic quadrilateral is 360 degrees.

Therefore, let's the angle m∠DGF as follows:

The opposite angles of a cyclic quadrilateral have a total of 180°.

4x + 7 + 8x - 31 = 180

12x  - 24 = 180

12x = 180 + 24

12x = 204

divide both sides by 12

x = 204 / 12

x = 17

Hence,

m∠DGF = 4x + 7 = 4(17) + 7 = 68 + 7 = 75 degrees

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Answer:

Put your calculator in degree mode.

sin(13°) = 500/x

x sin(13°) = 500

x = 500/sin(13°) = 2,222.7 miles

Using a trigonometric relation we can see that x =  2,222.7 ft

We can see a right triangle, there we can see that one of the angles has a measure of 13°.

The opposite cathetus has a measure of 500ft, and we want to find x, which is the hypotenuse.

Then we can use the relation:

sin(a) = (opp cathetus)/hypotenuse

Replacing what we know, we will get:

sin(13°) = 500/x

Solving that for x:

x = 500/sin(13°) = 2,222.7 ft

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Answer:

The equation that describes a vertical translation of the square root parent function is A. y = x − 4−−√ + k where k is the vertical shift.

The square root parent function is f(x) = √x. To perform a vertical translation of this function, we add or subtract a constant value to the function. In this case, the function y = x − 4−−√ represents a vertical translation of the square root parent function by 4 units downwards.

Option B, y = x−−√−6 represents a vertical translation of the square root parent function by 6 units downwards. Option C, y = x−−√, represents the square root parent function without any vertical shift. Option D, y = −x−−√, represents a reflection of the square root parent function about the y-axis.

2. The side AC corresponds to side AE of the other triangle.

3. The length of side BC is 15.

Two or more triangles are said to be similar if on comparing their properties, there exist some common relations. Some of the common relations are; measure of internal angles, scale factor etc.

From the diagram given, we have;

2. Given that the triangles are similar, thus:

The side AC corresponds to side AE of the other triangle.

3. On comparing the corresponding length of the triangles, we have;

15/ 25 = 9/ BC

15BC = 9 x 25

         = 225

BC = 225/ 15

     = 15

The length of side BC is 15.

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Answer:

[tex]f(x)=\dfrac{1}{20}x^5+\sinh(x)-\dfrac{1}{2}\sinh(2)x+6[/tex]

Step-by-step explanation:

Given:

    [tex]\phantom{ww} \bullet\;\;\;f''(x)=x^3+\sinh(x)[/tex]

    [tex]\phantom{ww} \bullet\;\;\;f(0)=6[/tex]

    [tex]\phantom{ww} \bullet\;\;\;f(2)=7.6[/tex]

To find f'(x), integrate f''(x):

[tex]\begin{aligned}\displaystyle f'(x)=\int f''(x)\; \text{d}x&=\int \left(x^3+\sinh(x)\right)\; \text{d}x\\\\&=\int x^3\;\text{d}x+\int \sinh(x)\; \text{d}x\\\\&=\dfrac{1}{4}x^4+\cosh(x)+\text{K}\end{aligned}[/tex]

To find f(x), integrate f'(x):

[tex]\begin{aligned}\displaystyle f(x)=\int f'(x)\; \text{d}x&=\int \left(\dfrac{1}{4}x^4+\cosh(x)+\text{K}\right)\;\text{d}x\\\\&=\int \dfrac{1}{4}x^4\; \text{d}x+\int \cosh(x) \; \text{d}x + \int \text{K}\; \text{d}x\\\\&=\dfrac{1}{20}x^5+\sinh(x)+Kx+\text{C}\end{aligned}[/tex]

Substitute f(0) = 6 to determine the value of the constant C:

[tex]\begin{aligned}f(0)=\dfrac{1}{20}(0)^5+\sinh(0)+K(0)+\text{C}&=6\\\\0+0+0+\text{C}&=6\\\\\text{C}&=6\end{aligned}[/tex]

Substitute f(2) = 7.6 and C = 6 to determine the value of the constant K:

[tex]\begin{aligned}f(2)=\dfrac{1}{20}(2)^5+\sinh(2)+K(2)+6&=7.6\\\\1.6+\sinh(2)+2K+6&=7.6\\\\\sinh(2)+2K&=0\\\\2K&=-\sinh(2)\\\\K&=-\dfrac{1}{2}\sinh(2)\end{aligned}[/tex]

Therefore, function f(x) is:

[tex]\boxed{f(x)=\dfrac{1}{20}x^5+\sinh(x)-\dfrac{1}{2}\sinh(2)x+6}[/tex]

[tex]\textsf{As}\;\;\sinh(2)=\dfrac{e^4-1}{2e^2},\;\textsf{we can also write the equation as:}[/tex]

[tex]f(x)=\dfrac{1}{20}x^5+\sinh(x)-\dfrac{1}{2}\left(\dfrac{e^4-1}{2e^2}\right)x+6[/tex]

[tex]f(x)=\dfrac{1}{20}x^5+\sinh(x)-\left(\dfrac{e^4-1}{4e^2}\right)x+6[/tex]

The ratio of the sides of the medium box to the small box is 3:1, the ratio of the area of the bases is 9:1, and the ratio of the volumes is 27:1 and the volume of the medium box is 5832 cubic inches.

Let's denote the side length of the small cube as "s". Since it is a cube, all sides are equal.

Given that the volume of the small box is 216 cubic inches, we can set up the equation;

Volume of small box = s³ = 216

Taking the cube root of both sides, we get;

s = ∛216 = 6 inches

So, the side length of the small cube is 6 inches.

For the medium box, the length, width, and height are all tripled, so the new side length of the medium cube is 3 times the side length of the small cube:

Side length of medium cube = 3s = 3 × 6 = 18 inches

Now, let's calculate the ratio of the sides, area of the bases, and volumes of the small and medium boxes;

Ratio of sides: Side length of medium cube / Side length of small cube = 18 / 6 = 3

Ratio of area of bases: (Side length of medium cube)² / (Side length of small cube)² = (18)² / (6)² = 9

Ratio of volumes: (Volume of medium box) / (Volume of small box) = (Side length of medium cube)³ / (Side length of small cube)³ = (18)³ / (6)³ = 27

So, the ratio of the sides of the medium box to the small box is 3:1, the ratio of the area of the bases is 9:1, and the ratio of the volumes is 27:1.

The volume of the medium box is given by;

Volume of medium box = (Side length of medium cube)³ = 18³

= 5832 cubic inches

Therefore, the volume of the medium box is 5832 cubic inches.

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Check the picture below.

Answer:

a. The given equation is (y - 3)^2 -10 = 71. To determine the number and type of solutions, we need to use the discriminant, which is given by b^2 - 4ac, where a, b, and c are the coefficients of the quadratic equation in standard form (ax^2 + bx + c = 0). In this case, the equation can be rewritten as (y - 3)^2 = 81, which is in the form of (y - k)^2 = r^2, where k = 3 and r = 9. Therefore, the equation can be written as (y - k)^2 - r^2 = 0, which is a quadratic equation with a = 1, b = -6, and c = -72. The discriminant is then b^2 - 4ac = (-6)^2 - 4(1)(-72) = 300. Since the discriminant is positive, there are two real solutions.

b. To solve the equation (y - 3)^2 -10 = 71, we first add 10 to both sides to get (y - 3)^2 = 81. Then, we take the square root of both sides to get y - 3 = ±9. Adding 3 to both sides, we get y = 3 ± 9, which gives us two solutions: y = 12 and y = -6.

Therefore, the equation (y - 3)^2 -10 = 71 has two real solutions, which are y = 12 and y = -6.

Step-by-step explanation:

Answer:  type: real   number of solutions:2   y=12,-6

Step-by-step explanation:

see images for explanations

Answer:

Suppose X ~ N(12,2) represents a normal distribution with mean 12 and standard deviation 2. According to the empirical rule, about 68% of the x values lie within one standard deviation of the mean .

We can calculate the endpoints of the interval that represents one standard deviation from the mean as follows:

Lower endpoint: 12 - 2 = 10

Upper endpoint: 12 + 2 = 14

Therefore, about 68% of the x values lie between 10 and 14 1.

Step-by-step explanation:

The addition of the given fraction expression is 7/8.

In mathematics, an expression is a combination of numbers, symbols, and/or operators that represents a mathematical quantity or relationship. It can be a simple combination of numbers or a more complex combination involving variables, functions, or other mathematical constructs.

When adding fractions with the same denominator, you simply add the numerators and keep the denominator the same.

In this case, both fractions have a denominator of 8, so we can add their numerators:

5/8 + 2/8 = (5 + 2)/8 = 7/8

Thus, the sum of 5/8 and 2/8 is 7/8.

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Answer:

5

Step-by-step explanation:

use the table, when it asks f(2) that says what is the output *y) when the input is 2. Find when x=2 your answer is the y value, f(2)=5

Answer: Option B, the outcomes of a fair die rolled 100 times, is likely to be normally distributed.

Step-by-step explanation:

Answer: Option B, The outcomes of a fair die rolled 100 times

Step-by-step explanation:

that would most likely be normally distributed.

hope it helped! Good luck!!! :)

Answer: He would be spending $15.25 for each person including himself

Step-by-step explanation:

step 1. you need to find out how many people are getting food

step 2. divide that number (5) by how much the total cost is ($76.25) to get 15.25