In right triangle ABC, side AC is longer than side BC. The boxed numbers represent the possible side
lengths of triangle ABC.

Answer:

a) 75

b) 360 students

c) 56 ; 57 ; 58

d) 134 inches

e) 27°

Step-by-step explanation:

a)

[tex]5x = 375 \\ x = \frac{375}{5} \\ x = 75[/tex]

b)

[tex] \frac{x}{3} = 120 \\ x = 120 \times 3 \\ x = 360[/tex]

c)

[tex]x + x + 1 + x + 2 = 171 \\ 3x = 168 \\ x = 56 \\ (x + 1 = 57) \\ (x + 2 = 58)[/tex]

d)

[tex]2x + 2 \times 70 = 408 \\ 2x = 408 - 140 \\ x = \frac{268}{2} \\ x = 134[/tex]

e)

[tex]180 = 90 + 63 + x \\ x = 180 - 90 - 63 \\ x = 27[/tex]

Answer:

$11.50

Step-by-step explanation:

57.50 in 5 hours

→ Divide 57.50 by 5

$11.50

Step-by-step explanation:

Did you mean :

sin(x + 75°) = sin(15°)

x + 75° = 15°

x = 15° - 75°

x = -60°

Answer:

C. a = 3/2b

Step-by-step explanation:

7a - 2b = 5a + b

7a = 5a + 3b

7a - 5a = 3b

2a = 3b

a = 3/2b

Answer:

C. a = 3/2b

Step-by-step explanation:

7a - 2b = 5a + b

7a = 5a + 3b

7a - 5a = 3b

2a = 3b

a = 3/2b

f(n)=2.55+3.75(n), n>0

Answer:

SR= 2.55

GC=3.75

n=?

n rep number of games

SR shoe rental

GC Game cost

f(n)=2.55+3.75n

2.55=3.75n

n=2.55÷3.75

n=0.68

Answer:

angles

Step-by-step explanation:

the angles of these triangles are same

z  is equivalent to p

w is equivalent to h

x is equivalent to r

Answer:

so do

24.50-13=11.50

11.50-12.00=  answer

Step-by-step explanation:

I think so

Answer:

5f

Step-by-step explanation:

Answer:

Here is the answer and explanation all together

The largest area of an isosceles triangle that is inscribed in a circle of radius 3 units is 3.897 sq. units approx.

To find the maximum of a continuous and twice differentiable function f(x), we can firstly differentiate it with respect to x and equating it to 0 will give us critical points.

Putting those values of x in the second rate of function, if results in negative output, then at that point, there is maxima. If the output is positive then its minima and if its 0, then we will have to find the third derivative (if it exists) and so on.

For this case, we can construct a general circle and a variable isosceles triangle in it.

Let the radius of the circle be 'r' units.

For isosceles triangle inscribed in that circle, its vertex(intersection of two congruent sides) be fixed, and other two vertex are allowed to move equally on both the sides of that first vertex.

Those rest two vertices make a chord in that circle. Let the perpendicular distance from the center be 'd' units of that chord.

Then, by Pythagoras theorem for triangle OBD, we get:

[tex]|OB|^2 = |OD|^2 + |BD|^2\\|BD| = \sqrt{|OB|^2 - |OD|^2}\\|BD| = \sqrt{r^2 - d^2} \: \rm units[/tex]

Thus, as perpendicular from center to a chord bisects it, we get:

[tex]|BC| = |BD| + |DC| = |BD| + |BD| = 2\sqrt{r^2 - d^2}[/tex]

The distance from the first vertex (A) to the mid of the line segment BC is: r - d units.

Thus, area of the considered isosceles triangle is:

[tex]A = f(r,d) = \dfrac{1}{2} \times (r - d) \times 2\sqrt{r^2 - d^2} = (r-d)^{1.5}(r+d)^{0.5}[/tex]

At r = 3 units, we get:

[tex]f(3,d) = g(d) = (3-d)^{1.5}(3+d)^{0.5}[/tex]

Finding the value of 'd' for which the function g(d) becomes maximum will give us the maximum area.

Finding first and second derivative of g(d) with respect to 'd', we get:

[tex]g(d) = (3-d)^{1.5}(3+d)^{0.5}\\g'(d) = -1.5(3-d)^{0.5}(3+d)^{0.5} + 0.5(3+d)^{-0.5}(3-d)^{1.5}\\g''(d) = -1.5[-0.5(3-d)^{-0.5}(3+d)^{0.5}] + 0.5[-0.5(3+d)^{-1.5}(3-d)^{1.5}]\\[/tex]

Putting first rate = 0 to find the critical points, we get:

[tex]g'(d) =- 1.5(3-d)^{0.5}(3+d)^{0.5} + 0.5(3+d)^{-0.5}(3-d)^{1.5} = 0\\3(3-d)^{0.5}(3+d)^{0.5} = (3+d)^{-0.5}(3-d)^{1.5}\\3(3+d) = (3-d)\\9 + 3d = 3 - d\\d = 1.5[/tex]

At d = 1.5,  the second rate of g(d) evaluates to:

[tex]g''(1.5) = -1.5[-0.5(3-1.5)^{-0.5}(3+1.5)^{0.5}] + 0.5[-0.5(3+1.5)^{-1.5}(3-1.5)^{1.5}]\\g''(5) = 0.75(1.5)^{1.5}(4.5)^{0.5} -0.25(4.5)^{-1.5}(1.5)^{1.5}\\g''(5) =[/tex]

The area of the isosceles triangle is maximum, and is evaluated as:

[tex]A_{max} = f(3,1.5) = g(1.5) = (3-1.5)^{1.5}(3+1.5)^{0.5} \approx 3.897 \: \rm unit^2[/tex]

Thus, the largest area of an isosceles triangle that is inscribed in a circle of radius 3 units is 3.897 sq. units approx.

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Answer:

Dont know

Dont know

Dont know

Dont know dont know dont knowwwwwwwwwwwwwww

Answer:

60,000

Step-by-step explanation:

hope this helps x

The variables are the alphabets which can have any value depending on the relationship with the other numbers and variables in the equations.

To create the graph, select the correct relationship and then enter the values for the variables.

The graph is the representation of the equation in the form of lines or shapes.

The correct method to create a graph is to find the relationship of the variables and put their values to get the exact points.

The points are joined together to draw the required line or shape formed.

The best option of the given question is:

To create the graph, select the correct relationship and then enter the values for the variables.

For example in the given graph we see that the rate is increasing as the mass is decreasing.

The mass is plotted along x-axis and the rate along the y-axis.

Their relationship that they are inversely proportional i.e.  one increases as the other decreases can be seen in the given graph.

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Answer:

7-(-5)

Step-by-step explanation:

The other answers are all equal to -2. However, the answer for c is 12 which is the odd one out. Hope this helps :)

Answer: x = 81, y = 17

Step-by-step explanation:

x + y = 98

x/y = 4/13/y

x/y = 4y + 13/ y

x = 98 - y

(98 - y) / y = (4y+ 13) / y

Therefore

98 - y = 4y + 13

Collect like terms

-4y - y = 13 - 98

-5y = -85

Divide both sides by-5

y = 17

x = 98 - y

x = 98 - 17

x = 81

The two numbers​ x and y are 81 and 17 respectively.

Quotients are the number that is obtained by dividing one number by another number.

Dividend ÷ Divisor = Quotients

Given that the sum of two numbers is 98.

Let x and y be the two numbers

x + y = 98

Thus, the larger number is divided by the smaller quotient is 4 with a remainder of 13.

x/y = 4/13/y

x/y = 4y + 13/ y

x = 98 - y

(98 - y) / y = (4y+ 13) / y

Therefore,

98 - y = 4y + 13

Collect like terms;

-4y - y = 13 - 98

-5y = -85

Divide both sides by-5;

y = 17

x = 98 - y

x = 98 - 17

x = 81

Therefore, the two numbers​ x and y are 81 and 17 respectively.

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Answer:

x=1, y=6

Step-by-step explanation:

Answer:

73.33333 Yards = 74 Yards

Step-by-step explanation:

1 yard = 3 feet

220 ft * 1 yard / 3 ft

73.33333 = 74 yd

Step-by-step explanation:

the other answer is essentially correct but wrong for rounding.

again, 1 yd = 3 ft

220/3 = 73.3333... yd

rounded to the nearest tenth this is

73.3 yd

Answer:

I think its 14

hope its right

Step-by-step explanation:

Answer:

3.1

3.2

3.3

3.4

3.5

Step-by-step explanation:

Here are the five decimals between 3 and 4:

3.2, 3.6, 3.7, 3.8, and 3.9

One of the number types in algebra that has a whole integer and a fractional portion separated by a decimal point is a decimal. The decimal point is the dot that appears between the parts of a whole number and a fraction.

The accepted method for representing both integer and non-integer numbers is the decimal numeral system. It is the expansion of the Hindu-Arabic numeral system to non-integer values. Decimal notation is the term used to describe the method of representing numbers in the decimal system.

A decimal is a number that is divided into two parts: a whole and a fraction. Between integers, decimal numbers are used to express the numerical value of complete and partially whole quantities.

Therefore, the five decimals between 3 and 4 are 3.2, 3.6, 3.7, 3.8, and 3.9

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[tex] \Large{\boxed{\sf z= -\dfrac{59}{\: 34} + \dfrac{19}{34}i}} [/tex]

[tex] \\ [/tex]

To express the given complex number in a + bi form, also known as algebraic form, we will need to define what the conjugate of a complex number is.

[tex] \\ [/tex]

[tex] \\ [/tex]

[tex] \textsf{Let z be our complex number, and} \: \overline{\sf z} \: \textsf{its conjugate.} [/tex]

[tex] \\ [/tex]

The conjugate of z, [tex] \overline{ \sf z}, [/tex] is the complex number formed of the same real part as z but of the opposite imaginary part.

Since a is the real part of z, and b is its imaginary part, this can be expressed as:

[tex] \sf If \: z = a + ib \:, then \: \overline{ \sf z} = a - ib [/tex]

[tex] \\ [/tex]

[tex] \\ [/tex]

[tex] \sf z = \dfrac{7 - 8i}{ - 5 + 3i} \\ \\ \\ \diamond \sf Multiply \: both \: the \: numerator \: and \: the \: denominator \: by \: the \: conjugate \: of \: - 5 + 3i. \\ \\ \\ \sf z = \bigg(\frac{7 - 8i }{ - 5 + 3i \: } \bigg) \times \bigg( \frac{ - 5 - 3i}{ - 5 - 3i} \bigg) = \dfrac{(7 - 8i)( - 5 - 3i)}{( - 5 + 3i)( - 5 - 3i)} \\ \\ \\ \diamond \: \sf Expand \: knowing \: that \: (a + b)(c + d) = ac + ad + bc + bd. \\ \\ \\ \\ \sf z = \dfrac{7( - 5) + 7( - 3i) + ( - 8i)( - 5) + ( - 8i)( - 3i)}{( - 5)( - 5) + ( - 5)( - 3i) + 3i( - 5) + 3i ( - 3i)} \\ \\ \\ \sf z = \dfrac{ - 35 - 21i + 40i + 24 {i}^{2} }{25 + 15i - 15i - 9 {i}^{2} } = \dfrac{24 {i}^{2} + 19i - 35 }{25 - 9{i}^{2} } \\ \\ \\ \diamond \sf \: Substitute \: {i}^{2} = - 1. \\ \\ \\ \sf \: z = \dfrac{24( - 1) + 19i - 35}{25 - 9( - 1)} = \dfrac{ - 24 + 19i - 35}{25 - ( - 9)} = \dfrac{ - 59 + 19i}{34} \\ \\ \\ \diamond \: \sf Simplify \: the \: expression. \\ \\ \sf \: z = \dfrac{ - 59 + 19i}{34} = \dfrac{ - 59}{ \: \: 34} + \dfrac{19i}{34} \\ \\ \\ \\ \implies \boxed{ \boxed{ \sf z = - \dfrac{59}{34} + \dfrac{19}{34}i }} [/tex]

[tex] \\ \\ [/tex]

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Answer:

I think its Factor

Step-by-step explanation: (x-4) (x+1)

And for the equation x=4,-1

Sorry about that.

(21 - 17)² + 3⁴ =

4² + 81 =

16 + 81 =

Answer: 97

Answer:

97

Step-by-step explanation:

(21-17)²+3⁴=4²+81

=16+81

=97

Answer:

Step-by-step explanation:

4x-3y=18

3y=4x-18

  y=4/3x-6

By y=mx+c , Slope of line 4x-3y=18 is 4/3

Since the required line is perpendicular to the line 4x-3y=18 ,

slope of required line * Slope of line 4x-3y=18 = -1

slope of required line = -1/(4/3) = -3/4

Since the required line passes through (8,-8)

By point-slope form,

y-(-8)= -3/4(x-8)

      y= -3/4x-2

Answer:

Option 3: (5, 1)

Step-by-step explanation:

There are several ways of solving for systems of linear equations, either through graphing, substitution, or elimination.  

The graphing method is the easiest, as you only need to plot points on the graph using the y-intercepts and the slopes.  

I will be demonstrating the graphing method.  

Given the systems of linear equations:  

Equation 1:  y = x - 4

where the slope, m = 1, and y-intercept (0, -4).

Equation2: y = -x + 6

where the slope, m = -1, and y-intercept (0, 6).

The y-intercept is the point on the graph where it crosses the y-axis, and has coordinates of (0, b).

For Equation 1, plot the y-intercept, (0, -4) on the graph. Then use the slope, m = 1 (rise 1 unit, run 1 unit) to plot other points on the graph. Repeat this process until you have enough points to connect a line with.  

Repeat these same procedures for graphing Equation 2, start by plotting its y-intercept at (0, 6), and its slope, m = -1 (down 1 unit, run 1 unit).

The intersection of both lines occurs at point, (5, 1), which is solution to the given systems of linear equations.  Therefore, the correct answer is the third option, (5, 1).

Attached is the screenshot of the graphed systems of linear equations, where it shows the point of intersection at (5, 1).  

Answer:

4.712 radians

Step-by-step explanation:

Answer:

6999999

Step-by-step explanation:

Funny Number.

Answer:

Yes they are similar yes I think there is a ratio in which one is larger

Step-by-step explanation:

I hope this help

Answer:

oh! thanks for points

but this is yr question or what????

Answer:

20

Step-by-step explanation:

because it would stay the same

C. Brooke finished in 115 minutes, so she was faster.