The Pythagorean Theorem, given by the formula a² + b² = c², relates the
three sides of a right triangle. Solve the formula for the positive value of b in
terms of a and c.

Answer:

Step-by-step explanation:

Answer:

d = 9°

Step-by-step explanation:

When the sum of two angles is equal to 90 degrees, they are called complementary angles.

soln

27° + (8d – 9)° = 90°

27° + 8d – 9° = 90°

27°–9° + 8d = 90°

18° + 8d = 90°

8d = 90° – 18°

8d = 72°

divide both sides by (8)

d = 9°

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It is important to state the restrictions before simplifying rational expressions because the simplified expression may be defined for restrictions of the original.

What is rational expressions?

The ratio of two polynomials is a rational expression. F can be expressed in the form p/q, where p and q are polynomials, if f is a rational expression.

Fractional terms are seen in rational expressions. We include constraints because with some x values, the equation may become undefined. Undefined inquiries are hypothetical or ideal. The seven expressions for undefined words are  (∞-∞),∞^∞, N/0, 0⁰, 1^∞, ∞/∞ and 0×∞ respectively. N/0 is the most typical constraint on rational expressions. Any number divided by 0 is therefore undefined. For instance, if you substitute 0 for x in the case of the function f(x) = 6/x2, the outcome is 6/0, which is undefined. If you graphed this function, you would see a break at x=0.

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Answer:

The amount of goo remaining after 32 minutes is approximately 54.7 grams.

Step-by-step explanation:

The half-life of a substance is the amount of time it takes for half of the substance to decay. To find the half-life of the goo in the experiment, we need to solve the equation G ( t ) = G ( 0 ) / 2 for t , where G ( 0 ) is the initial amount of goo and G ( t ) is the amount of goo remaining after time t .In this case, G ( 0 ) = 176 grams and G ( 135 minutes ) = 11 grams, so we can write the equation as follows:11 grams = 176 grams / 2Solving for t , we get:t = 135 minutes * ( 1 / 2 ) = 67.5 minutesThis is the half-life of the goo in the experiment.To find the amount of goo remaining after time t , we can use the equation G ( t ) = G ( 0 ) * ( 1 / 2 ) ^ ( t / t1/2 ) , where G ( 0 ) is the initial amount of goo, t is the time at which we want to find the amount of goo remaining, and t1/2 is the half-life of the goo.In this case, G ( 0 ) = 176 grams, t = 32 minutes, and t1/2 = 67.5 minutes, so we can plug these values into the equation to find the amount of goo remaining after 32 minutes:G ( 32 minutes ) = 176 grams * ( 1 / 2 ) ^ ( 32 minutes / 67.5 minutes )This equation tells us that the amount of goo remaining after 32 minutes is approximately 54.7 grams.

Answer: It is an obtuse triangle.

Answer: No

Step-by-step explanation:

To know if a triangle is a right triangle, we can use Pythagorean Theorem to test.

Pythagorean Theorem: [tex]a^2+b^2=c^2[/tex]

[tex]4^2+6^2=8^2[/tex]                [exponents]

[tex]16+36=64[/tex]                [add]

[tex]52\neq 64[/tex]

Therefore, this is not a right triangle.

Answer:

10

Step-by-step explanation:

in the first one, 6 16 8, (6×8)/3=16

in the third one, 9 21 7, (9×7)/3=21

using the same comcept, 5 ? 6, (5×6)/3=10

so, ?=10

The given statements are:

We can then use the ASA congruence theorem to prove the triangles are congruent, aka they are mirror copies of one another.

Each "A" refers to facts (1) and (3) shown above. Fact (2) is the "S" of ASA.

ASA = angle side angle

Using the ti-83 plus/ti-84 plus calculator, the 25th percentile of x is equal to 47.25 with a mean of 48 and a standard deviation of 12, respectively.

A dataset's mean is calculated by dividing the sum of all values by the total number of values. The term "average" is frequently used to describe it because it is the most widely used central tendency metric.

calculation

a) µ =     48    

σ =     12    

n=    115    

X =    45    

Z =(X - µ )/(σ/√n)  =     (45-48)/(12/√115)=    -2.68

P(X<45) = P(Z<-2.68) =         0.0037

b) µ =     48.00    

σ =     12.00    

n=    115.00    

P(X ≤ x) =    0.2500    

z value at  0.25=    -0.674        (excel formula =NORMSINV(0.25))

z=(x-µ)/(σ/√n)        

X=z * σ/√n +µ= -0.674*12/√115+48=        47.25

Using the ti-83 plus/ti-84 plus calculator, the 25th percentile of x is equal to 47.25 with a mean of 48 and a standard deviation of 12, respectively.

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The domain the function is In interval notation [7,  ∞). The range of the function is in the interval  (-1, ∞).

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). A "vertical line test" can be used when examining a graph to determine whether a relation is a function. The relation is not a function if any point on the graph can be used to draw a vertical line that crosses the relation twice.

Here,

y=√(x-7)-1

x-7≥0

x≥7

at x=7

y=√(7-7)-1

y=-1

The function's domain is represented by the interval notation [7, ∞). The function's range falls within the range [-1, ∞).

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The speed of boat is 14 miles per hour and the speed of current 35 mile per hour

Speed:

The general formula to calculate the speed is written as

Speed = Distance/Time

Given,

A boat travel 42 mile uptream in 3 hour looking for a lot diver. It then travel downstream 70 mile in 2 hour.

Here we need to find the speed of boat and the speed of current.

While we looking into the given question, we have identified the following values,

Distance = 42 mile

time = 3 hour

Then the speed is calculated as,

=> speed = 42/3

=> speed = 14 miles per hour

Similarly, for the current is

distance = 70 miles

time = 2 hour

Then the speed is calculated as,

=> speed = 70/2 = 35 miles per hour.

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Answer:

1679 songs

Step-by-step explanation:

         23

       x73

----------------------------

            69

    +   1610

-------------------------------

         1679

Answer:

180-125 = x

x= 55 ( allied angle)

Point ( 0 , -27 ) on the line and  ( -9 , 0 ) are not on the line

Given :

Madison is reeling in her string at a steady rate the linear equation 3y - 9x = -81 can be used to find y the number of feet of kite string she still needs to reel in after x seconds .

Points ( 0 , -27 )

when x = 0

3y - 9 * 0 = -81

3y - 0 = -81

3y = -81

y = -81 / 3

y = -27

so point ( 0 , -27 ) on the line .

when y = 0

3 * 0 - 9x = -81

0 - 9x = -81

-9x = -81

x = 81/9

x = 9

so ( -9 , 0 ) are not on the line

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Hence, the slope which is perpendicular to the line to [tex]y = -x - 18[/tex] and passes through [tex](-6, 11)[/tex] is [tex]y=x+17[/tex].

What is the equation?

The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

Here given that,

The line in slope-intercept form that is perpendicular to [tex]y = -x - 18[/tex] and passes through [tex](-6, 11)[/tex].

As we know the slope of line is

[tex]y=mx+c[/tex]

where [tex]m[/tex] is the slope and [tex]c[/tex] is the y intercept.

Given points are [tex](-6,11)[/tex].

If we want to describe the perpendicular line to the original line then the slope of line is

[tex]m_2=-\frac{1}{m_1}[/tex]

In our given slope of line

[tex]y = -x -18[/tex]

where [tex]m_1=-1[/tex]

So,

[tex]m_2=-\frac{1}{m_1}\\\\m_2=-\frac{1}{-1}\\\\m_2=1[/tex]

Now for the slope of second line we use the point slope from the construct equation then,

[tex]y-y_1=m_2(x-x_1)\\\\y-11=1(x-(-6))\\\\y-11=x+6\\\\y=x+6+11\\\\y=x+17[/tex]

Hence, the slope which is perpendicular to the line to [tex]y = -x - 18[/tex] and passes through [tex](-6, 11)[/tex] is [tex]y=x+17[/tex].

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The monthly base fee of the situation is $0

From the question, we have the following parameters that can be used in our computation:

Charges per minute = $0.50 per minute

Number of minutes = 200 minutes

Total charges = $100

The above parameters mean that

Total charges = Monthly Base fee + Charges per minute x Number of minute

Substitute the known values in the above equation, so, we have the following representation

Monthly base fee + 0.50 * 200 = 100

This gives

Monthly base fee + 100 = 100

Subtract 100 from both sides

Monthly base fee = 0

Hence, the monthly base fee is $0

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It can be seen that the radius and circumferance are not proportional.

        y = mx

        m = y/x

        [m] is called constant of proportionality.

Given is a graph as shown in the figure.

For the proportional relationship -

(25 - 18)/(4 - 3) should be equal to (38 - 25)/(6 - 4)

7/1 = 13/2

7/1 = 6.5

7 ≠ 6.5

Therefore, it can be seen that the radius and circumferance are not proportional.

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Answer: 50 + 0.25 is less than 90

Step-by-step explanation:

The 16 miles out of 40 miles. Then the percentage will be 40%.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

The 16 miles out of 40 miles. Then the percentage is calculated as,

P = (16 / 40) x 100

P = 0.40 x 100

P = 40%

The 16 miles out of 40 miles. Then the percentage will be 40%.

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The missing part of the question is given below.

Determine the percentage.

Answer:

Step-by-step explanation:

Given f(x) = √(3+x) and g(x) = √(3-x), you want the domains of various combinations of f and g.

The domain of each of these functions is the interval on which it is defined. The domain of the square root function is all argument values greater than or equal to zero.

The argument of the square root will be non-negative when ...

  3 +x ≥ 0

  x ≥ -3 . . . . . . subtract 3

  -3 ≤ x . . . . . . written using left-pointing arrow

The argument of the square root will be non-negative when ...

  3 -x ≥ 0

  3 ≥ x . . . . . add x

  x ≤ 3 . . . . . written using left-pointing arrow

Any combination of functions f and g will only be defined on the domain where both f and g are defined. That is, the domain will be the intersection of the domains of f and g:

  (-3 ≤ x) ∩ (x ≤ 3) = -3 ≤ x ≤ 3

The domain of f+g is the intersection of the domains of f and g.

  [-3, 3]

The domain of f-g is the intersection of the domains of f and g.

  [-3, 3]

The domain of f ·g is the intersection of the domains of f and g.

  [-3, 3]

The domain of f/g is the intersection of the domains of f and g, excluding the value of x that makes g(x) = 0. That value is x=3.

  [-3, 3)

__

Additional comment

The graphs of the combinations of functions are attached. You notice the graph of f/g tends to infinity as x → 3. It is undefined at x=3.

[tex]\angle R \cong \angle STV[/tex]: Alternate interior angles theorem

[tex]\angle TSV \cong \angle U[/tex]: Alternate interior angles theorem

[tex]\angle R \cong \angle TSV[/tex]: Transitive property of congruence

[tex]\angle R \cong \angle U[/tex]: Transitive property of congruence

The two-column method can be used to prove that the triangles ΔACD and ΔBCD are congruent is presented as follows;

Statements [tex]{}[/tex]                                         Reasons

1. AC ≅ BC   [tex]{}[/tex]                                        1 Given

2 D is the midpoint of AB [tex]{}[/tex]                  2 Given

3. CD ≅ CD [tex]{}[/tex]                                         3 Reflexive property → CD = CD

4 ∠ACD ≅ ∠BCD [tex]{}[/tex]                               4 Median line of an isosceles triangle bisects the vertex angle

5 ΔACD ≅ ΔBCD  [tex]{}[/tex]                              5. SAS congruency postulate

The two-column method consists of two columns, including a statement column and a reasons column, in which each statement made is provided with an accompanying reason.

The reasons in the prove for the congruency of the triangles, ΔACD and ΔBCD are as follows;

Reflexive property

The reflexive property of equality indicates that the value of a number or measure is equal to itself, therefore, the length of the segment CD is the same as the length of the segment CD.

Median of an isosceles triangle

In an isosceles triangle, two sides are congruent. The median segment drawn from the altitude of an isosceles triangle forms two congruent segment at the base, such that the two triangles formed by the median line are congruent, by Side-Side-Side, SSS congruency postulate, therefore, the angles formed at the vertex of the triangle by the median segment are also congruent

SAS congruency postulate

The Side-Angle-Side congruency postulate states that two triangles are congruent if two sides and the included angle of one triangle are congruent to two sides and the included angle of the other triangle.

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The line's equation that is parallel to the given line is=  3x - 8

A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance.

Equations come in a variety of forms, including linear, quadratic, cubic, etc.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation.

To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. The statement is not an equation if there is no "equal to" symbol in it.

According to our question-

The line's equation in the form of the slope intercept is,

y = mx + c

m is the line's slope, and c is its y-intercept.

line equation provided that,

Therefore, the line's slope is

Finding the equation of the line that crosses (4,4) and runs parallel to the provided lines is necessary.

Because all parallel lines have the same slope.

Equation for the necessary line is,

Replace point (4,4) in the line above.

In order for the line equation to become,

3x - 8

Hence, The line's equation that is parallel to the given line is=  3x - 8

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If the equation x² + 16x + c = 0 has only one real solution, the value of c is equal to 64.

The quadratic formula includes the discriminant, which comes after the square root. The discriminant of a quadratic equation is important because it indicates the quantity and kind of solutions.  

The formula for the Discriminant of a Quadratic Equation ax²+bx +c = 0 is given by

Here we have

x² + 16x + c = 0 equation has only one real solution

Compare given equation with ax²+ bx + c = 0

=> a = 1, and b = 16  

As we know when an equation has only one real solution

then its Discriminant will be equal to zero

=> b² - 4ac = 0

By the above values,

=> 16² - 4(1)c = 0  

=> 256 - 4c = 0

=> 4c = 256

=> c = 256/4

=> c = 64

Therefore,

If the equation x² + 16x + c = 0 has only one real solution, the value of c is equal to 64.

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Answer:

C/25 + H/40 = 15

Step-by-step explanation:

Let's call C the number of city miles, and H the number of highway miles.

The total gas used is therefore:

C/25 + H/40

The fuel tank holds 15 gallons, so:

C/25 + H/40 = 15

Answer:

<AFC

Step-by-step explanation:

Vertical angles are pairs of opposite angles that are created by two intersecting lines. As an example, the other pair of vertical angles are <CFD and <AFE.

Answer:

[tex]y=\frac{1}{2} x-2[/tex]

The surface area, A, is changing at a rate of 288 km/min decreasing.

Given,

Base length, l = 6 km

Height, h = 10 km

dl/dt = -9 km/min

dh/dt = 12 km/min

Surface area of a prism, A = 2 × (lw + lh + wh)

For a square prism,

Length, l = width, w = 6km

A = 2 × (l² + lh + lh)

= 2(l²) + 4lh

A = 2(l²) + 4 lh

= 2 × (l² + 2lh)

dA/dt = 2 × (2I × dI/dt + 0 × dh/dt + 2 × 2h × dl/dt + 2l × dh/dt)

dA/dt = 2 × (2l × dl/dt + 0 + 2 × 2h × dl/dt + 2l × dh/dt)

= 2 × (2(6) × (-9) + 2(10) × (-9) + 2(6) × (12))

= 2 × (- 108 + -180 + 144)

= 2 × -144

= -288 km/min

The rate of change of the surface area, A is decreasing by 288 km/min.

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Question is incomplete. Completed question is given below;

The length s(t)s(t)s, (, t, )of the side of the base of a square prism is decreasing at a rate of 9 kilometers per minute and the height h(t)h(t)h, (, t, )of the prism is increasing at a rate of 12 kilometers per minute. At a certain instant t_0t 0 ​ t, start subscript, 0, end subscript, the base's side is 6 kilometers and the height is 10 kilometers. What is the rate of change of the surface area A(t)A(t)A, (, t, )of the prism at that instant?

The equation of the straight line is 2y + 21x = 10. The correct option is (D).

To represent a straight line on a graph consider two points namely x and y intercepts of the line. To find x-intercept put y = 0 and for y-intercept put x = 0. Then draw a line passing through these two points.

The given points are (-4, 47) and (2, -16) respectively.

The equation of the straight line passing through them can be written as,

(y - 47)/(x - (-4)) = (-16 - 47)/(2 - (-4))

=> (y - 47)/(x + 4) = -63/6

=> (y - 47)/(x + 4) = -21/2

=> 2(y - 47) = -21(x + 4)

=> 2y - 94 = -21x - 84

=> 2y + 21x = -84 + 94

=> 2y + 21x = 10

Hence, the standard form of the straight line passing through given points is 2y + 21x = 10.

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