If two of the angles in a scalene triangle are 54° and 87°, what is the other angle?

The length of the hypotenuse in the isosceles 90-degree triangle is √(2).

In an isosceles 90-degree triangle, two legs are equal in length, and the third side, known as the hypotenuse, is longer. Let's denote the length of the legs as x and the length of the hypotenuse as 4x.

According to the Pythagorean theorem, in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse. In this case, we have:

[tex]x^2 + x^2 = (4x)^2.[/tex]

Simplifying the equation:

[tex]2x^2 = 16x^2.[/tex]

Dividing both sides of the equation by [tex]2x^2[/tex]:

[tex]1 = 8x^2.[/tex]

Dividing both sides of the equation by 8:

[tex]1/8 = x^2[/tex].

Taking the square root of both sides of the equation:

x = √(1/8).

Simplifying the square root:

x = √(1)/√(8),

x = 1/(√(2) * 2),

x = 1/(2√(2)).

Therefore, the length of each leg in the isosceles 90-degree triangle is 1/(2√(2)), and the length of the hypotenuse is 4 times the length of each leg, which is:

4 * (1/(2√(2))),

2/√(2).

To simplify the expression further, we can rationalize the denominator:

(2/√(2)) * (√(2)/√(2)),

2√(2)/2,

√(2).

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Answer:

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Step-by-step explanation:

w usually app all app all do all app so all rip so we rip do all do all app all do all do all do all do all rip trip we rip all app so all do all do all app all do all app all yep all app all app all app all app all app all app all app to

The values in the domain of fᵒg are all real numbers.

Therefore, the correct answer is: x - 6.

To determine the domain of the composite function fᵒg, we need to find the values of x that are valid inputs for the composition.

The composite function fᵒg represents applying the function f to the output of the function g. In this case, g(x) is equal to -9.

So, we substitute -9 into the function f(x) = √6x:

f(g(x)) = f(-9) = √6(-9) = √(-54)

Since the square root of a negative number is not defined in the set of real numbers, the value √(-54) is undefined.

Therefore, -9 is not in the domain of fᵒg.

To find the values in the domain of fᵒg, we need to consider the values of x that make g(x) a valid input for f(x).

Since g(x) is a constant function equal to -9, it does not impose any restrictions on the domain of f(x).

The function f(x) = √6x is defined for all real numbers, as long as the expression inside the square root is non-negative.

So, any value of x would be in the domain of fᵒg.

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The mean is the measure that gives the most accurate picture of the data's center. It is an essential measure of central tendency that represents the arithmetic average of a dataset.

It is calculated by summing up all the values in the dataset and dividing the sum by the total number of values. The mean is suitable for datasets that have a normal or symmetrical distribution.

The mean is highly sensitive to outliers, which can significantly influence the average value. When outliers are present, it is appropriate to use other measures of central tendency such as the median or mode to obtain an accurate picture of the data's center.

The median is the middle value in a dataset arranged in ascending or descending order. It is not affected by outliers and is suitable for datasets with skewed distributions.

The mode is the most frequent value in the dataset. It is suitable for categorical data but can also be used for continuous data.

In summary, the mean is the most accurate measure of central tendency, but its accuracy can be improved by using the median or mode in datasets with outliers or skewed distributions.

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Answer:

The answer is number 3

Y =-3/7X + 3

Step-by-step explanation:

Substitue with the value of the two points in all answers

The value of the left side must equal the value or the right side

For instance,

The two points are (0,3) & (7,0)

Substitue in the first answer with the point (0,3)

3 = - 3 (rejected)

Second answer

3 = 3 works for the point (0,3) then also Substitue with the other point (7,0)

0 = 6 (rejected)

sub. With point (0,3).

Sub. With point (7,0)

Then that's the right one

Answer:

Step-by-step explanation:

Answer:

[tex](x +5)^2+(y-1)^2=25[/tex]

Step-by-step explanation:

To determine the equation of the graphed circle, we need to find the coordinates of its center and the length of its radius.

The center of the circle is a single point that lies at an equal distance from all points on the circumference of the circle.

From inspection of the graphed circle, we can see that its domain is [-10, 0] and its range is [-4, 6].  The x-coordinate of the center is the midpoint of the domain, and the y-coordinate of the center is the midpoint of the range.

[tex]x_{\sf center}=\dfrac{-10+0}{2}=-5[/tex]

[tex]y_{\sf center}=\dfrac{-4+6}{2}=1[/tex]

Therefore, the center of the circle is (-5, 1).

The radius of the circle is the distance from the center to all points on the circumference of the circle. Therefore, to calculate the length of the radius, find the distance between x-coordinate of the center and one of the endpoints of the domain.

[tex]r=0-(-5)=5[/tex]

Therefore, the radius of the circle is r = 5.

To determine the equation of the circle, substitute the center and radius into the standard formula.

[tex]\boxed{\begin{minipage}{4 cm}\underline{Equation of a circle}\\\\$(x-h)^2+(y-k)^2=r^2$\\\\where:\\ \phantom{ww}$\bullet$ $(h, k)$ is the center. \\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}[/tex]

As h = -5, k = 1 and r = 5, then:

[tex](x - (-5)^2+(y-1)^2=5^2[/tex]

[tex](x +5)^2+(y-1)^2=25[/tex]

Therefore, the equation of the graphed circle is:

[tex]\boxed{(x +5)^2+(y-1)^2=25}[/tex]

Answer:

-x + 20(8) = 147 -x + 10(8) = 67

-x + 160 = 147 -x + 80 = 67

x = 13 x = 13

A. The system has exactly one solution. The solution is (13, 8).

B. All three colonies had a population of 8 thousand people in 2013.

Answer:

chemical reaction that releases heat energy to the surroundings is known as endothermis reaction

Answer:

1

Step-by-step explanation:

The degree of a polynomial is the exponent of the varieble x. So the exponent of x in that function is 1.

Answer:

f^(-1)(x) = ±√(x - 5).

Step-by-step explanation:

Replace f(x) with y: y = x^2 + 5.

Swap the x and y variables: x = y^2 + 5.

Solve the equation for y. To do this, we'll rearrange the equation:

x - 5 = y^2.

Take the square root of both sides (considering both positive and negative square roots):

±√(x - 5) = y.

Swap y and x again to express the inverse function:

f^(-1)(x) = ±√(x - 5).

The expression is completed as (x-4)(x -7)

From the information given, we have that the polynomial is given as;

x² - 11x + 28

Using the factorization method, we have;

First, find the product of the coefficient of x squared and the constant value

Then, we have;

1(28) = 28

Now, find the pair factors of the product that adds up to -11, we have;

-7x and -4x

Substitute the values, we have;

x² - 7x - 4x + 28

Group in pairs, we get;

x(x-7) - 4(x - 7)

Then, we have the expressions as;

(x-4)(x - 7)

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Statement that is always true about obtuse triangles:

An obtuse triangle always has one angle that measures more than 90 degrees.

In the given tree diagram, the "Obtuse" category represents triangles with at least one obtuse angle.

An obtuse angle is an angle that measures more than 90 degrees. Since an obtuse triangle is defined as having one obtuse angle, it will always have an angle that measures more than 90 degrees.

Therefore, the statement that an obtuse triangle always has one angle that measures more than 90 degrees is always true.

Statement that is sometimes true about obtuse triangles:

An obtuse triangle can have different side lengths.

In the given tree diagram, the "Obtuse" category represents triangles with at least one obtuse angle.

The "Scalene" category represents triangles with different side lengths. Therefore, it is possible for an obtuse triangle to have different side lengths, making the statement "An obtuse triangle can have different side lengths" sometimes true.

However, it is also possible for an obtuse triangle to have two or more sides with the same length, which would make it an isosceles or equilateral triangle.

Hence, the statement is only sometimes true and not always true.

In summary, an always true statement about obtuse triangles is that they always have one angle that measures more than 90 degrees.

A sometimes true statement about obtuse triangles is that they can have different side lengths.

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The number we're looking for, which when added to 24/5 results in 9, is 21/5 or 4.2 in decimal form.

Let's solve the equation: 24/5 + x = 9, where x represents the unknown number we're trying to find.

To isolate x, we'll start by subtracting 24/5 from both sides of the equation:

x = 9 - 24/5

To add these two fractions, we need a common denominator. The denominator of 9 is 1, and the denominator of 24/5 is 5. To find a common denominator, we multiply 1 by 5:

x = (9 * 5)/5 - 24/5

This gives us:

x = 45/5 - 24/5

Now we can combine the fractions with the same denominator:

x = (45 - 24)/5

Simplifying the numerator:

x = 21/5

Therefore, the number we're looking for is 21/5. In decimal form, it can be written as 4.2.

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Answer:

volume=60cm3, surface area=96cm2

Step-by-step explanation:

volume=1/3×(6×6)×5

=60cm3

surface area= 4(1/2×6×5)+(6×6)

=96cm2

Answer:

29. 59.06°

30. 10.6

Step-by-step explanation:

29.
By using the Tangent angle rule, we can find the angle of elevation,

We know that

Tan Angle = opposite/adjacent

Tan x=AB/BC

Tan x=20/12

Tan x=5/3

[tex]x=Tan^{- }(\frac{5}{3})[/tex]

x=59.06°

30.

The law of sine is a formula that can be used to find the lengths of the sides of a triangle, or to find the angles of a triangle, when two sides and the angle between them are known. The formula is:

a / sin(A) = b / sin(B) = c / sin(C)

Here taking

a / sin(A) = c / sin(C)

here A=75°, C=180-75-50=55° and c -9 and

we need to find a,

substituting value

a/Sin(75°)=9/Sin(55°)

a=9*Sin(75°)/Sin(55°)

a=10.61

Therefore, the value of a is 10.6

Answer:

        tan (θ) = 20/12, and solve for θ

       We then get the equation tan (θ) =  20/12

        θ = arctan(5/3)

        Tan θ  =  opp/adj

        Tan θ  = 20/12

         θ  =  Tan^-1 (20/12)

          θ  =  59.03624346 degrees

           θ = 59.0 degrees

       Hence, the Angle of Elevation is ------->  59.0°

       m < C = 180 degrees - m<A - m<B

       m<C  = 180 degrees - 75 degrees  -  50 degrees

      m<C  =  55 degrees

       a/sin A  =  c/sin C

       a/sin 75 degrees  =  9/sin 55 degrees

        a  =  9 * sin 75 degrees/sin 55 degrees

        a  =  10.3

Therefore, The length of side A in --------> △ABC is approximately 10.3

Hope this helps you!

Answer: [-2,7]

Step-by-step explanation: The range of a graph is just the range of minimum and maximum outputs of the y axis. The minimum y axis value is -2, while the maximum is 7. Putting your answer in brackets means that the endpoints (-2 and 7) are inclusive, which is the case since the dots are filled in. If the dots are hollow, the range does not include those endpoints and you would use parentheses instead.

Answer: 28

Step-by-step explanation:

If [tex]a = 7[/tex] and [tex]b = 2[/tex], then [tex]2ab[/tex] can be worked out as follows:

[tex]\Large 2ab = 2 \times a \times b[/tex]

Substituting the values of [tex]a[/tex] and [tex]b[/tex], we get:

[tex]2 \times 7 \times 2 = 28[/tex]

Therefore, [tex]2ab[/tex] is equal to 28 when [tex]a = 7[/tex] and [tex]b = 2[/tex].

________________________________________________________

The answer is:

Work/explanation:

To evaluate the expression [tex]\sf{2ab}[/tex], I begin by plugging in 7 for a and 2 for b:

[tex]\large\pmb{2(7)(2)}[/tex]

Simplify by multiplying.

[tex]\large\pmb{2*14}[/tex]

[tex]\large\pmb{28}[/tex]

The correct expression to calculate the area of a triangle with a base of 21 inches and height of 12 inches is (21 × 12) ÷ 2.

The subject of your question is Mathematics, specifically dealing with the topic of how to calculate the area of a triangle. The formula to calculate the area of a triangle is 1/2 multiplied by the base multiplied by the height. So, in your question where the base of the triangle is 21 inches and the height is 12 inches, the correct choice would be D. (21 × 12) ÷ 2 which applies the formula correctly.

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The ordered pair that is a solution for both inequalities is (-2, 2).

Here we have the system of inequalities:

y < -x + 1

y > x

And we want to see which one of the given points makes both of them true.

To find that, just replace the values in both inequalities and see if both become true or not.

For example, for the first point:

(-3, 5)

We will get:

5 < -(-3) + 1 = 4

5 > -3

The first one is false, and the second one is true.

The correct option is the second point:

2 < -(-2) +1 = 3

2 > -2

Both are true.

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The coordinates of the reflected quadrilateral A'B'C'D' are:

A' = (6, 4)

B' = (-3, 2)

C' = (-1, 23)

D' = (-x, 12)

To find the coordinates of the reflected quadrilateral A'B'C'D', we need to apply the transformation Ty = x to each vertex of the original quadrilateral ABCD. The transformation Ty = x reflects each point across the y-axis.

Given the coordinates of the original quadrilateral ABCD as:

A = (-6, 4)

B = (3, 2)

C = (+1, 23)

D = (x, 12)

Applying the transformation Ty = x to each vertex, we can determine the coordinates of the reflected quadrilateral A'B'C'D':

A' = (-(-6), 4) = (6, 4)

B' = (-3, 2)

C' = (-1, 23)

D' = (-x, 12)

The reflected quadrilateral A'B'C'D' thus has the following coordinates:

A' = (6, 4)

B' = (-3, 2)

C' = (-1, 23)

D' = (-x, 12)

Therefore, the x-coordinate for point D' will be represented as -x in the reflected quadrilateral.

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The correct Option is D. 45÷3= 15 . The equation that best shows that 45 is a multiple of 15 is 45 ÷ 3 = 15.

A multiple is a product that results from multiplying two or more numbers.

A common multiple is a multiple that is common to two or more numbers.

A multiple of a number can be expressed as an integer multiple of the number.

If the result is a whole number, the first number is a multiple of the second.

An equation that shows 45 is a multiple of 15 is as follows: 45 ÷ 3 = 15.

A multiple is a number that can be divided by another number without leaving a remainder.

As a result, we divide 45 by 3 to find out whether 45 is a multiple of 15.

If the result is a whole number, 45 is a multiple of 15.

Here is the equation that shows this: 45 ÷ 3 = 15

Thus, we can conclude that the equation that best shows that 45 is a multiple of 15 is  45 ÷ 3 = 15.

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Answer:

C-351

Step-by-step explanation:

Answer:

y^10 + (5/8xy^5 - 5/8xy^6) - (25/64x^2)

Step-by-step explanation:

To simplify the given expression, we can expand it using the distributive property:

(5/8x + y^5)(y^5 - 5/8x)

Expanding the expression yields:

= (5/8x * y^5) + (5/8x * -5/8x) + (y^5 * y^5) + (y^5 * -5/8x)

= (5/8xy^5) - (25/64x^2) + y^10 - (5/8xy^6)

Combining like terms, we have:

= y^10 + (5/8xy^5 - 5/8xy^6) - (25/64x^2)

Hope this help! Have a good day!

The tangent and normal lines of the curve:

Case (i): y = (4 / 5) · x + 13 / 5

Case (ii): (x, y) = (0, 13 / 5)

Case (iii): y = - (5 / 4) · x + 35 / 4

In this problem we have the representation of a curve whose equations for tangent and normal lines must be found. Lines are expressions of the form:

y = m · x + b

Where:

Both tangent and normal lines are perpendicular, the relationship between the slopes of the two perpendicular lines is:

m · m' = - 1

Where:

The slope of the tangent line is found by evaluating the first derivative of the curve at intersection point.

Case (i) - First, determine the slope of the tangent line:

y = √(8 · x + 1)

y' = 4 / √(8 · x + 1)

y' = 4 / √25

y' = 4 / 5

Second, determine the intercept of the tangent line:

b = y - m · x

b = 5 - (4 / 5) · 3

b = 5 - 12 / 5

b = 13 / 5

Third, write the equation of the tangent line:

y = (4 / 5) · x + 13 / 5

Case (ii) - Find the coordinates of the intercept of the tangent line:

(x, y) = (0, 13 / 5)

Case (iii) - First, find the slope of the normal line:

m' = - 1 / (4 / 5)

m' = - 5 / 4

Second, determine the intercept of the normal line:

b = y - m' · x

b = 5 - (- 5 / 4) · 3

b = 5 + 15 / 4

b = 35 / 4

Third, write the equation of the normal line:

y = - (5 / 4) · x + 35 / 4

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Answer:

550 gallons

Step-by-step explanation:

Let [tex]x[/tex] be the number of gallons for the 90% antifreeze solution and [tex]x+100[/tex] be the total number of gallons that will contain 80% antifreeze solution:

[tex]\displaystyle \frac{0.90x+0.25(100)}{x+100}=0.80\\\\0.90x+25=0.80x+80\\\\0.10x+25=80\\\\0.10x=55\\\\x=550[/tex]

Therefore, you would need 550 gallons of the 90% antifreeze solution.

The rates of change of the two functions that compare correctly is A. The rate of change of function A is 6, and the rate of change of function B is -10/9.

To compare the rates of change of the two functions, we can calculate the slope of each function. The slope represents the rate of change of a linear function.

For Function A, the equation is y = 6x - 1. The coefficient of x, which is 6, represents the slope. The rate of change of Function A is 6.

For Function B, we are given three points: (13, 0), (4, 10), and (6, 15). We can calculate the slope using the formula: slope = (change in y) / (change in x). Taking the first two points, we have: slope = (10 - 0) / (4 - 13) = 10 / (-9) = -10/9.

Comparing the rates of change, we have:

A. The rate of change of function A is 6.

The rate of change of function B is -10/9.

The correct option is A. The rate of change of function A is 6, and the rate of change of function B is -10/9.

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Hello!

x² - 5x + 6

= (x² - 2x) + (-3x + 6)

= x(x - 2) - 3(x - 2)

= (x - 2)(x - 3)