estimate the percent that is shaded

The length of the third side is 2√34 + 6.

We can use the triangle inequality theorem to solve this problem. According to the theorem, the sum of any two sides of a triangle must be greater than the length of the third side.

Let x be the length of the third side. Then we have:

2√34 + 6 > x

Subtracting 6 from both sides, we get:

2√34 > x - 6

Adding 6 to both sides, we get:

x < 2√34 + 6

Therefore, the length of the third side must be less than 2√34 + 6.

To find the exact length of the third side, we need to check if the triangle inequality is satisfied for an equality. In other words, we need to check if:

2√34 + 6 = x

If this is true, then the given sides can form a triangle.

Simplifying the equation, we get:

x = 2√34 + 6

The exact length is 2√34 + 6 if the triangle inequality is satisfied for an equality.

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Answer:

y=a\((x-h)^{2}\)+h

Step-by-step explanation:

equation for vertex form of a parabola is,

y=a\((x-h)^{2}\)+h

Answer:

y=a+h

Step-by-step explanation:

The equivalent decimal and mixed number for given letter C is,

⇒ C = 8.2 ; 8 2/10

We have to given that,

A number line is shown in image.

Since,

A number lines are the horizontal straight lines in which the integers are placed in equal intervals.

And, All the numbers in a sequence can be represented in a number line. This line extends indefinitely at both ends.

Now, By given number line,

Point C is two point left from point 8.

Hence, The point C is denoted as,

⇒ C = 8.2

⇒ C = 82/10

⇒ C = 8 2/10

Therefore, the equivalent decimal and mixed number for given letter C is,

⇒ C = 8.2 ; 8 2/10

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Answer: We need we need 10 pints of the second fruit juice (85% pure fruit juice). Therefore, we need

(60-10 = 50) pints of the first fruit juice (55% pure fruit juice).

Step-by-step explanation:

Let x be number of pints of the first fruit drink which is ( 55% pure fruit juice), while y will be the number of pints of second fruit drink (85% pure fruit juice).

We know that there are 60 total pints. Therefore:

x + y = 60

We also know that 60% of the 60 pints will be pure fruit juice, and the pure fruit juice will either come from

x or y.

For x pints of first juice, there is 0.55x pure fruit juice while for y pints of first juice, there is 0.85y pure fruit juice. Therefore, we get:

0.55x + 0.85y = 60 × 0.6

0.55x + 0.85y = 36

We will get rid of the decimals by multiplying through by 100. This will be:

55x + 85y = 3600

Combining both equations

x + y = 60 .......... i

55x + 85y = 3600 ........ ii

Multiply equation i by 55

Multiply equation ii by 1

55x + 55y = 3300

- 55x + 85y = 3600

Then subtract

-30y = -300

y = 10

Therefore, we need we need 10 pints of the second fruit juice (85% pure fruit juice). Therefore, we need

(60-10 = 50) pints of the first fruit juice (55% pure fruit juice).

Answer:a

Step-by-step explanation:

The length of the side P is 15 cm. And the right option is C.

Pythagoras theorem states that “In a right-angled triangle,  the square of the hypotenuse side is equal to the sum of squares of the other two sides.

To calculate the length of side P we use Pythagoras theorem's formula

Pythagoras formula:

Where:

From the diagram,

Given:

Substitute these values into equation 1

Hence, the right option is C 15 cm.

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Answer:

x = -15

Step-by-step explanation:

In fractional equations we cross multiply the expressions:

In cross multiplying the denominator of the first fraction is multiplied with the numerator of the second fraction and vice versa:

-2x = 30 divide both sides by -2

x = -15

Answer:

S= 1.301

Step-by-step explanation:

5.313-4.012=S

The equation of the sphere with center (8, 4, 6) are\((x-8)^{2} + (y -4)^{2} + (z-6)^{2} = 36\), \((x-8)^{2} + (y -4)^{2} + (z-6)^{2} = 16\), \((x-8)^{2} + (y -4)^{2} + (z-6)^{2} = 64\)

Given that, center of the sphere of sphere is (8, 4, 6)

a) If the sphere is touching the xy- plane , its radius is same as the magnitude of z- coordinate of the center which is 6.

The equation of the required sphere is

\((x-8)^{2} + (y -4)^{2} + (z-6)^{2} = 6^{2}\)

b) If the sphere is touching the yz- plane , its radius is same as the magnitude of x- coordinate of the center which is 8.

The equation of the required sphere is

\((x-8)^{2} + (y -4)^{2} + (z-6)^{2} = 8^{2}\)

c) If the sphere is touching the xz- plane , its radius is same as the magnitude of x- coordinate of the center which is 4.

The equation of the required sphere is

\((x-8)^{2} + (y -4)^{2} + (z-6)^{2} = 4^{2}\)

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The complete statement is,

The function g(x) is 3 units stretch Response area , and undergoes a vertical translated 5 unit right Response area compared to its cube root parent function.

Reflection is a type of transformation that flip a shape in mirror line, so that each point is the same distance from the mirror line as its reflected point.

We have to given that;

The function is,

⇒ f (x) = ∛(5x+ 3) - 5

This is a transformation of the cube root parent function.

Now, The parent function is,

⇒ f (x) = ∛x

After 5 units stretch Response area, we get;

⇒ g (x) = ∛5x

And, After translated 3 units right Response area,

⇒ g (x) = ∛ (5x + 3)

And, After translated 5 unit down, we get;

⇒ f (x) = ∛(5x+ 3) - 5

Thus, The complete statement is,

The function g(x) is 3 units stretch Response area , and undergoes a vertical translated 5 unit down Response area compared to its cube root parent function.

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Your response's numerical variable is x=-13.

Variable, A symbol (often a letter) used in algebra to represent an unknowable numerical value in an equation. X and Y (real-number unknowns), z (complex-number unknowns), t (time), r (radius), and s are examples of frequently used variables (arc length).

Mathematical expressions are used to represent situations or problems in algebra, a branch of mathematics. We use integers with fixed or definite values in algebra, such 2, 7, 0.068, etc. In algebra, we mix variables like x, y, and z with numbers.

accordance with the data provided;

the equation is 9+x=-4

x+9=-4

(x+9)+(-9)=-4+(-9)

x+9-9=-4-9

x=-13

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The exam scores , that will lead to the better grade is

(a) the score of "X=40" in exam with μ = 50 , σ = 20 ;

(b) the score of "X=51" in exam with μ = 45 , σ = 2 ;

(c) Both the score will lead to better grades .

Part(a) : In order to find which score leads to better grade, we calculate the z-scores for both scores and compare :

The score of X = 74 on the first exam is :

⇒ z = (74 - 82)/8 = -1  ;

The score of X = 40 on the second exam is :

⇒ z = (40 - 50)/20 = -0.5  .

The z-score of -0.5 is > -1,

So , the score of X = 40 on the second exam lead to better grade because the score of 40 is closer to mean of second exam (50) and has a smaller deviation from mean (20) than score of 74 on first exam .

Part(b) :

The score of X = 51 on the first exam is :

⇒ z = (51 - 45)/2 = 3  ;

The score of X = 90 on the second exam is :

⇒ z = (90 - 70) / 20 = 1  .

The z-score of 3 is > 1 ,

So , the score of X = 51 on the first exam should lead to the better grade.

Part(c) :

The score of X = 62 on the first exam is :

⇒ z = (62 - 50) / 8 = 1.5  ;

The score of X = 23 on the second exam is :

⇒ z = (23 - 20) / 2 = 1.5  .

Both scores have the same z-score of 1.5, they should lead to the same grade.

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Answer:

The mode of this set of numbers is 12. If that is what you are looking for.

The approximate height of the tree is given as follows:

45.6 ft.

The geometric mean theorem states that the length of the altitude drawn from the right angle of a triangle to its hypotenuse is equal to the geometric mean of the lengths of the segments formed on the hypotenuse.

The altitude segment for this problem is given as follows:

14.5 ft.

The bases are given as follows:

5.2 ft and x ft.

Hence the value of x is given as follows:

5.2x = 14.5²

x = 14.5²/5.2

x = 40.4 ft.

Hence the height of the three is given as follows:

5.2 + 40.4 = 45.6 ft.

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Answer:

hope it helps you..........

Answer:

60

Step-by-step explanation:

g(x)= x^2 +8x - 24

Substitute x for 6 in the equation

g(6)= 6^2 + 8(6) - 24

= 36+48-24

= 60

Answer: B) 31.4 inches

Step-by-step explanation:

5 x 2 = diameter

10 x 3.14 (pie)

= 31.4

Answer: c) 31.4 inches

Step-by-step explanation:

5 x 2 = diameter

10 x 3.14 (pie)

= 31.4

(-3, 3) and (4, -1) are the points that can be used to form a right triangle to derive the distance formula to find the length of the line segment

Given the line on the xy-plane, we are to determine the points on the line that can be used to determine the distance between the two points.

The required points on the line will be the two endpoints on the line. The end points are (-3, 3) and (4, -1). The distance between this points is expressed as:

D = √(-1-3)²+(4+3)²
D = √14 + 49
D = √63

Hence the points that can be used to form a right triangle to derive the distance formula are (-3, 3) and (4, -1)

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Answer: It’s -1,-3

Step-by-step explanation:

got 100 on the test

The given number is °:

To write it as a decimal, start by placing the integer part the same, now to find the decimal part, let's take the minutes 21' and divide it by 60 (because there are 60 minutes in 1°):

Now, let's divide the seconds 47" by 3600 (because there are 3600 seconds in 1°):

Thus, the number is:

Answer:

A. quadratic function; quadratic term: 6x2; linear term: x; constant term: −12

Step-by-step explanation:

We have been given the equation

The degree of the given polynomial is 2.

Hence, the function is quadratic.

The term with exponent 2 on x is called the quadratic term. The term with exponent  1 on x is called linear and the term without any variable is a constant term.

Therefore, we have

Quadratic term= 6x^2

Linear term= x

Constant term= -12

9514 1404 393

Answer:

  A. quadratic function; quadratic term: 6x²; linear term: x; constant term: −12

Step-by-step explanation:

The squared term (6x^2) is also called the "quadratic" term. The term with x to the first power (no exponent) is the "linear" term. The term with no variable at all is the "constant" term.

It should be no mystery that the quadratic term is 6x^2; the linear term is x; and the constant term is -12.

_____

Additional comment

As with much of algebra, this is about vocabulary and pattern recognition.

Answer:

makes no sense

Step-by-step explanation:

Answer:

10 times

Step-by-step explanation:

If you are talking about division, then we would do 87/8=10

Answer:

It can go 10.875  times.

Step-by-step explanation:

87/8 = 10.875

≈ 11

Hope this helps; have a great day!

a)The value of acceleration will be 4.8 m/s²

b)The total distance travelled is 505 m.

a) As all the movement happens along a straight line, we need to define an axis only, which we call x-axis, being the positive direction the one followed by the car.

We can choose to place our origin at the location where the motorcycle was stopped at the side of the road (assuming that it is the same point  for the car when it passes him), so our initial position is 0.

We can also choose our time origin to be the same as the instant that the motorcycle starts from rest, so t₀ = 0.

With these assumptions, and assuming also that the acceleration is constant, we can write two equations, one for the car (at constant speed) and the another one for the motorcycle, as follows:

xc = vx*t

xm= 1/2*a*t²

When the motorcycle passes the car, both distances traveled from the origin will be equal each other, i.e., xc = xm :

⇒ vx*t = 1/2*a*t²

We have as givens vx=35 m/s and t = 14.5 sec when both equations are equal each other.

⇒ 35 m/s* 14.5 s = 1/2*a*(14.5)²(s)²

Solving for a:

a = (2* 35 m/s) / 14.5 s = 4.8 m/s²

b) Replacing the value of a in the equation for xm, we have:

xm = 1/2*4.8 m/s²* (14.5)²s² = 505 m.

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Answer:

no because the two smallest sides have to be bigger that the third side

Easy way to do this, divide 24 with 3, you will get 8. That means 8 is 1/3 of 24. To get 2/3 you just add 8+8 which equals to 16

The circumference of a circle with one-third the curvature of a circle of radius 1 is 18.85 units

What is circumference ?

The perimeter of a circle is known as its circumference. It is the length of the circle's whole perimeter. The diameter of a circle and the constant are multiplied to get the circumference of the circle. This measurement of a circle's circumference is necessary for someone to cross a circular park or for a circle-shaped table to have a border. The units of the circumference are the same as the units of length and it is a linear value.

If a circle has a radius of 1,

the curvature is inversely proportional to this

So, the curvature= 1

A circle with a curvature of 1/3 :

radius=3

Thus, the circumference of the circle  =  2 *π * radius

                                                               =  2*π * 3

                                                               =  6π

                                                               ≈ 18.85 units

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The parametric equations are mathematically given as

(x(t), y(t), z(t))= (2-4t, 1-t, t)

Generally, To express the parametric point from A (2,1,0) to B(-2,0,1) in parametric form, we can use the following equation:

P(t) = (2-4t, 1-t, t)

To find the parametric equations for a point moving from A to B, we can use the following formula:

x = x₁ + t(x₂ - x1)

y = y₁ + t(y₂ - y₁)

z = z₁ + t(z₂ - z₁)

Where (x₁, y₁, z₁) is the starting point (A), (x₂, y₂, z₂) is the ending point (B), and t is a parameter that varies from 0 to 1.

Using this formula, the parametric equations for a point moving from A (2,1,0) to B(-2,0,1) are:

x = 2 + t(-2 - 2)

= 2 - 4t

y = 1 + t(0 - 1)

= 1 - t

z = 0 + t(1 - 0)

= t

These equations describe the motion of a point that starts at A, moves along the line segment from A to B, and arrives at B when t = 1.

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The complete Question was found

Find parametric equations for the line. (Use the parameter t.)

The line through points A (2,1,0) to B(-2,0,1)

(x(t), y(t), z(t))= \((\square)\)

Answer:

5(2a -5 + b)

Step-by-step explanation:

(10a - 25 + 5b) = 5( 2a - 5 + b)

5(b +  2a  - 5) = 5(2a - 5 + b)

Answer:

5(2a -5 + b)

Step-by-step explanation: