(lesson 4.2.5) Find g(-5) given g(x) = x³ - 2​

The two solutions of the quadratic equation x² + 11x - 26 = 0 are x = 2 and x = -13

Here we have the quadratic equation:

x² + 11x - 26 = 0

A quadratic equation is a second-degree polynomial equation in one variable, where the highest power of the variable is two.

To solve it we need to use the quadratic formula, it will give:

[tex]x = \frac{-11 \pm \sqrt{11^2 - 4*1*-26} }{2*1}[/tex]

Now we can simplify that and we will get two solutions, these are:

[tex]x = \frac{-11 \pm \sqrt{11^2 - 4*1*-26} }{2*1}\\\\x = \frac{-11 \pm15}{2}[/tex]

Then the two solutions of the quadratic equation are:

x+ = (-11 + 15)/2 = 4/2 = 2

x- = (-11 - 15)/2 = -26/2 = -13

Learn moer about quadratic equations at:

https://brainly.com/question/1214333

#SPJ1

As a result, Plan 4's $38.89 monthly premium is the lowest.

The monthly premium you pay for health insurance. You typically have to pay additional fees for your health care in addition to your premium, such as a deductible, copayments, and coinsurance.

(P + Simple Interest) / (500 + 58.33) / 14 = $42.02 is the formula for the monthly payment.

Plan 4: P = $500

t = 18/12 years, and r = 0.12

Simple interest equals $500 * 0.12/* (18/12) = $90.

(P + Simple Interest) / t = ($500 + $90) / 18 = $38.89 is the monthly payment.

Plan 5: P = $500

t = 12/12 years, and r = 0.14.

Simple interest is equal to $500 * 0.14 * (12/12) = $70.

(P + Simple Interest) / t = ($500 + $70) / 12 = $47.50 is the amount due each month.

As a result, Plan 4's $38.89 monthly premium is the lowest.

To know more about premium visit:-

https://brainly.com/question/7511249

#SPJ1

Answer:

300/65

Step-by-step explanation:

Answer:

3 65/100 then the simplified version is 13/20

Step-by-step explanation:

Answer:

x > 35

Step-by-step explanation:

Let's denote the width of the picture frame as "x" inches.

According to the problem, the length of the picture frame is 7 inches more than the width, so it can be expressed as "x + 7" inches.

The perimeter of the picture frame can be found by adding up the lengths of all four sides, which is given by:

Perimeter = 2*(length + width)

Substituting the values of length and width in terms of x, we get:

Perimeter = 2*(x + 7 + x)

Perimeter = 4x + 14

Now we can set up an inequality to find the values of x for which the perimeter is greater than 154 inches:

4x + 14 > 154

Subtracting 14 from both sides, we get:

4x > 140

Dividing both sides by 4, we get:

x > 35

Therefore, the values of x for which the perimeter of the picture frame is greater than 154 inches are x > 35.

The volume of the rectangular prism is 210cm³.

A rectangular prism is a three-dimensional solid shape that has six rectangular faces. Each face of the prism is a rectangle, and the opposite faces are congruent and parallel. The rectangular prism is also known as a rectangular cuboid or a rectangular parallelepiped. The rectangular prism has eight vertices (corners), twelve edges, and six faces. It is a special case of a parallelepiped, which is a three-dimensional solid with six parallelogram faces.

The surface area of the rectangular prism is:

Surface Area = 2(lw + lh +  wh)

Surface Area = 2(7cm x 6cm) + 2(7cm x 5cm) + 2(6cm x 5cm)

Surface Area = 84cm² + 70cm² + 60cm²

Surface Area = 214cm²

Hence, the rectangular prism has a 214 cm² surface area.

We must multiply the rectangular prism's length, width, and height in order to get its volume.

The volume of the rectangular prism is:

Volume = lwh

Volume = 7cm x 6cm x 5cm

Volume = 210cm³

Hence, the rectangular prism has a 210 cm³ volume.

To know more about parallelepiped, visit:

https://brainly.com/question/29140066

#SPJ1

The standard deviation of the difference Y - X depends on the standard deviations of both X and Y, and is given by the formula below.

(b) (i) The mean of the difference Y - X is μY - μX, which is 0 since both X and Y have the same mean, μ.

(b) (ii) The standard deviation of the difference Y - X is √(σY^2 + σX^2), where σY and σX are the standard deviations of Y and X, respectively. Assuming that the values of X are independent of the value of Y, we can use the formula for the variance of the difference of two random variables to get:

Var(Y - X) = Var(Y) + Var(X) - 2Cov(Y, X)

where Cov(Y, X) is the covariance between Y and X. Since Y and X have the same mean, we have:

Cov(Y, X) = E[(Y - μ)(X - μ)] = E[(Y - μ)X] - μE[X] = E[(Y - μ)X] - μ^2

where E[] denotes the expected value. Since X and Y are independent, we have:

E[(Y - μ)X] = E[Y - μ]E[X] = 0

Therefore, we get:

Var(Y - X) = Var(Y) + Var(X) = σY^2 + σX^2

Taking the square root of both sides gives us the standard deviation of Y - X:

SD(Y - X) = √(σY^2 + σX^2)

Therefore, the standard deviation of the difference Y - X depends on the standard deviations of both X and Y, and is given by the formula above.

To know more about standard deviation:

https://brainly.com/question/29808998

#SPJ1

The test statistics do not lie in the rejection so the null hypothesis does not reject.

Here we have the following information:

[tex]\bar{x}_{1}=25.3, n_{1}=25, s_{1}=9, \bar{x}_{2}=20.5, n_{2}=23, s_{2}=8[/tex]

Here degree of feedom will be

[tex]df=n_{1}+n_{2}-2=25+23-2=46[/tex]

The critical values of t are: +/- 2.687

Rejection region:

If t < -2.687 and t > 2.687, reject H0

Pooled variance is :

[tex]s^{2}_{p}=\frac{(n_{1}-1)s_{1}^{2}+\left ( n_{2}-1 \right )s_{2}^{2}}{n_{1}+n_{2}-2}=72.8696[/tex]

The standard error is

[tex]s_{M_{1}-M_{2}}=s_{p}\sqrt{\frac{1}{n_{1}}+\frac{1}{n_{2}}}=2.4664[/tex]

and t-statistics will be

[tex]t=\frac{\bar{x}_{1}-\bar{x}_{2}}{s_{p}\sqrt{\frac{1}{n_{1}}+\frac{1}{n_{2}}}}=1.946[/tex]

The test statistics do not lie in the rejection so the null hypothesis does not reject.

You cannot conclude...

not

Read more about independent samples here:

https://brainly.com/question/29342664

#SPJ1

B is not the multiplicative inverse of A.

The multiplicative inverse matrix, also known as the inverse matrix or simply the inverse, is a matrix that when multiplied by a given matrix, results in the identity matrix. The identity matrix is a square matrix with ones on the diagonal and zeros elsewhere.

Here we have

[tex]A = \left[\begin{array}{cc}3&-2&\\0&-3&\end{array}\right][/tex]    [tex]B = \left[\begin{array}{cc}-1&2&\\0&-4&\end{array}\right][/tex]  

Product of A and B

[tex]AB = \left[\begin{array}{cc}3&-2&\\0&-3&\end{array}\right] \times \left[\begin{array}{cc}-1&2&\\0&-4&\end{array}\right][/tex]

[tex]AB = \left[\begin{array}{cc}3(-1) + (-2)(0) &3(2) + (-2)(-4)&\\0 + 0 &0 +(-3)(-4)&\end{array}\right][/tex]  

[tex]AB = \left[\begin{array}{cc}-3 &14&\\0 &12&\end{array}\right][/tex]  

Product of B and A

[tex]BA = \left[\begin{array}{cc}-1&2&\\0&-4&\end{array}\right] \times \left[\begin{array}{cc}3&-2&\\0&-3&\end{array}\right][/tex]

[tex]BA = \left[\begin{array}{cc}1(3) + 2(0)&-1(-2)+2(-3)\\0(3)+0 &0(-2)+(-4)(-3) \end{array}\right][/tex]

[tex]BA = \left[\begin{array}{cc}-3&-4\\0&12\end{array}\right][/tex]

Here AB ≠ BA ≠ I

Therefore,

B is not the multiplicative inverse of A.

Learn more about Matrix at

https://brainly.com/question/30968484

Complete Question given in the picture

Answer:

Step-by-step explanation:

9x-3=4x+7

             +3

9x=4x+10

-4x=-4x

5x=10

divide the 5 by 10 which equals 2.

x=2

The distance from point A to point B is 812 feet.

What is triangle?

A triangle is a form of polygon with three sides; the intersection of the two longest sides is known as the triangle's vertex. There is an angle created between two sides. One of the crucial elements of geometry is this.

Certain fundamental ideas, including the Pythagorean theorem and trigonometry, rely on the characteristics of triangles. The angles and sides of a triangle determine its kind.

Here lines AC and ED are parallel. So alternate angles are equal. Now the corresponding angles in triangle ADC and BDC.

In Δ ADC ,

=> tan 9 = opposite / adjacent = 141/AC

=> AC = 141/ tan9= 890.2389.

Now In ΔBDC,

=> tan 61 = 141/BC

=> BC = 141/tan 61 = 78.1575

Now distance AB = AC - BC = 890.2389 - 78.1575 = 812 feet.

Hence the distance from point A to point B is 812 feet.

To learn more about triangle refer the below link

https://brainly.com/question/17335144

#SPJ1

The area of the rectangle is d. 54 square units.

A rectangle is a closed two-dimensional geometry with four sides, four corners, and four right angles (90°). A rectangle's opposite sides are equal and parallel. Because a rectangle is a 2-D form, it has two dimensions: length and width. The length of the rectangle is the longer side, while the width is the shorter side.

The rectangle has two pairs of parallel sides, so its area can be calculated by multiplying the length of one pair of parallel sides by the length of the other pair of parallel sides.

From the given points, we can see that the length of one pair of parallel sides of the rectangle is:

4 - (-5) = 9 units

And the length of the other pair of parallel sides of the rectangle is:

2 - (-4) = 6 units

Therefore, the area of the rectangle is:

9 units × 6 units = 54 square units.

So the area of the rectangle is d. 54 square units.

Learn more about area of rectangle on:

https://brainly.com/question/2607596

#SPJ1

The slope-intercept form of a line's equation is y = mx + b, where m is the slope of the line and b is the y-intercept. We can use the given slope and point to solve for the y-intercept and write the equation in slope-intercept form.

Given: Slope (m) = -2 and point (-2, -3)

The writer can best improve their organization by reordering sentences to keep related ideas together.

Who is called writer?

Writers are individuals who use written words to communicate ideas, stories, or information to a particular audience. They may work in various fields such as journalism, creative writing, copywriting, technical writing, or academic writing. Writers can be novelists, poets, essayists, screenwriters, playwrights, and more, and their work can take many forms, such as books, articles, blogs, scripts, and speeches. Writing is a skill that can be developed and honed through practice, and good writers are able to engage and captivate their readers with their words.

Here,

The writer can best improve their organization by reordering sentences to keep related ideas together. Here's a possible reorganization of the text:

Ponies and horses have significant differences. Horses are considered to be over fifty-eight inches tall and usually live to be twenty-five to thirty years old. In contrast, ponies are generally shorter than horses, with a height of less than fifty-eight inches, and they tend to live longer, often up to thirty-five or even forty years.

This revision keeps the sentences that relate to each other together, creating a clear and logical progression of ideas. Additionally, it removes the redundant statement of defining ponies as a type of horse, which is already well-known information.

Learn more about essay here,

https://brainly.com/question/30849680

#SPJ1

Answer:

Hurit Imala's gross annual pay is $17,680

Step-by-step explanation:

Hurit Imala works 40 hours a week, so her weekly pay would be:

40 hours/week x $8.50/hour = $340/week

To find her annual pay, we need to multiply her weekly pay by the number of weeks in a year:

$340/week x 52 weeks/year = $17,680/year

Therefore, Hurit Imala's gross annual pay is $17,680.

Step-by-step explanation:

If Debbie saves $900 each summer for four summers, she will have saved a total of:

$900 x 4 = $3600

Her parents have agreed to pay half the tuition, which is $8,500 / 2 = $4250.

Therefore, Debbie will need to come up with the remaining amount:

$8,500 - $4,250 = $4,250

Since Debbie will have saved $3,600 from her summer job, she will need an additional:

$4,250 - $3,600 = $650

Debbie will need $650 more to afford her first year's tuition.

PS I love you. And i asked the Ask AI app to write this for me. Get it for free --> https://get-askai.app

The amplitude is 2 units.

The period is 2π units.

f(x) = 2 sin(x - π/2)

An oscillation that repeats itself repeatedly in many natural events is described by the sine function, which is a mathematical function. It is described as the proportion of a right triangle's hypotenuse to the side that faces an angle. The typical notation for the sine function is sin(x), where x represents the angle.

Amplitude:

The distance between the graph's midline and its maximum or minimum point is known as the amplitude. The midline in the following graph is located at y=0, midway between the greatest value of 2, and the minimum value of -2. The amplitude is therefore 2 units.

Period:

The distance among two consecutive graph points with the same value and direction is known as the period. The above graph repeats itself every 2π units of x and has one complete cycle between x=0 and x=2π. The duration is therefore 2π units.

Midline:

The midline, also referred to as the average of the highest and minimum values, traverses the graph's centre horizontally. The x-axis or the line y=0 serves as the midline in the presented graph.

It is possible to write the sine function equation for the provided graph with a horizontal shift between 0 and 2 as:

f(x) = 2 sin(x - π/2)

The graph fluctuates up and down near the midline, hence the sine function is utilised. The highest value occurs at x=π/2, which is π/2 units to the right of x=0, and the graph continues every 2π units of x, therefore the horizontal shift is π/2. The sine function multiplies the amplitude of two units.

To know more about graph, visit:

brainly.com/question/15399633

#SPJ1

The complex fractions are simplified to;

(1/4 - 1/5)/(1/3)

To simplify this complex fraction, first simplify the numerator by finding a common denominator:

(1/4 - 1/5) = (5/20 - 4/20) = 1/20

Then, we can divide by the denominator by multiplying by its reciprocal:

1/20 ÷ (1/3) = 1/20 × (3/1) = 3/20

Therefore, the simplified complex fraction is 3/20.

(x-y)/(x⁻¹ - y⁻¹)

To simplify this complex fraction, use the formula for the difference of squares on the denominator:

x⁻¹ - y⁻¹ = (x - y)/(xy)

Then, we can rewrite the complex fraction as a division of two fractions:

(x-y)/(x⁻¹ - y⁻¹) = (x-y) × (xy)/(x - y) = xy

Therefore, the simplified complex fraction is xy.

((2x + 1)/(x- (1/x)) - (1/x))/(2x + (2x)/(1-1/x))

To simplify this complex fraction, first simplify each of the two fractions in the numerator and denominator separately:

(2x + 1)/(x- (1/x)) = [(2x² + x)/x]/[(x² - 1)/x] = (2x² + x)/(x² - 1)

(1/x) = (x⁻¹)

(2x + (2x)/(1-1/x)) = (2x + (2x)/(x-1))

= [(2x(x-1) + 2x)/ (x-1)] / [(x-1)/(x-1)]

= (2x² - 2x + 2x)/(x-1)

= (2x²)/(x-1)

Substituting these simplified fractions back into the original complex fraction:

[(2x² + x)/(x² - 1) - x⁻¹] ÷ [(2x²)/(x-1)]

= [(2x² + x)/(x² - 1) - (1/x)] × [(x-1)/(2x²)]

= [(2x² + x) - (x² - 1)]/[x(x² - 1)] × [(x-1)/(2x²)]

= (x² + x + 1)/[2x³(x-1)]

Therefore, the simplified complex fraction is (x² + x + 1)/[2x³(x-1)].

Find out more on complex fractions here: https://brainly.com/question/29015784

#SPJ1

Image transcribed:

60. (1/4 -1/5)/(1/3)

62. (x-y)/(x⁻¹ - y⁻¹)

64. ((2x 1)/(x- (1/x)) - (1/x))/(2x + (2x)/(1-1/x)

Answer:

  60. 3/20

  62.  -xy

  64.  (2x³ -x² +1)/(4x⁴ +2x³ -2x²)

Step-by-step explanation:

You want the simplified form of various complex fractions.

Fractions are added and divided in the usual ways:

  a +b/c = (ac +b)/c

  a/b +c/d = (ad +bc)/(bd)

  (a/b)/(c/d) = (ad)/(bc)

  (1/4 -1/5)/(1/3) = (5 -4)/(5·4)·(3/1) = 3/20

  (x -y)/(1/x -1/y) = (x -y)/((y -x)/(xy)) = xy(x -y)/(y -x) = -xy

  [tex]\dfrac{\dfrac{2x}{x-\dfrac{1}{x}}-\dfrac{1}{x}}{2x+\dfrac{2x}{1-\dfrac{1}{x}}}=\dfrac{\dfrac{2x^2}{x^2-1}-\dfrac{1}{x}}{2x+\dfrac{2x^2}{x-1}}=\dfrac{(2x^3-x^2+1)(x-1)}{x(x^2-1)(2x^2-2x+2x^2)}\\\\=\dfrac{2x^3-x^2+1}{2x^2(x+1)(2x-1)}=\boxed{\dfrac{2x^3-x^2+1}{4x^4+2x^3-2x^2}}[/tex]

__

Additional comment

The factored form in 64 is useful for many purposes. "Simplified" usually means that factors are multiplied out. Note that we used (x²-1) = (x-1)(x+1).

If you were to describe the domain of the expression in 64, it would exclude x=1 as well as those values of x that make the remaining denominator factors zero.

Answer:

up down

Step-by-step explanation:

 π/30 R is the radian measure of the central angle.

What is a circle, exactly?

The collection of all points in the plane that make up a circle are all equally spaced from a certain point known as the "centre," making the form a closed two-dimensional shape.

                       The reflection symmetry line is created by all lines that traverse the circle. Additionally, it is symmetrical in rotation around the centre at all angles.

Total circle circumference would be  π d  =   28 π

this arc is a fraction of the total

7π/15 / 28π  x  2π   =   π/30 R

Learn more about circle

brainly.com/question/29142813

#SPJ1

[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{11}\\ a=\stackrel{adjacent}{6}\\ o=\stackrel{opposite}{RT} \end{cases} \\\\\\ RT=\sqrt{ 11^2 - 6^2}\implies RT=\sqrt{ 121 - 36 } \implies RT=\sqrt{ 85 }\implies RT\approx 9.22[/tex]

Using trigonometric functions, we can find the value of the angles as:

Sinθ = 3/5

Cosθ = 4/5

Tanθ = 3/4

Six basic trigonometric operations are used in trigonometry. These operations are described by trigonometric ratios. The six basic trigonometric functions are the sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function. The foundation for trigonometric identities and functions is the ratio of the sides of a right-angled triangle. The sine, cosine, tangent, secant, and cotangent values are computed for the perpendicular side, hypotenuse, and base of a right triangle using trigonometric formulas.

Here as per the question,

Opposite side of the angle = 3 units.

Adjacent side of the angle = 4 units.

Hypotenuse of the triangle = 5 units.

Sinθ = opposite side/ hypotenuse

= 3/5

Cosθ = adjacent side/ hypotenuse

= 4/5

Tanθ = opposite side/adjacent side

= 3/4

To know more about trigonometric functions, visit:

https://brainly.com/question/6904750

#SPJ1

Answer:

  θ ∈ {π/4, π/2, 3π/4, 5π/4, 3π/2, 7π/4}

Step-by-step explanation:

You want the solutions to sin(2θ)sin(θ)=cos(θ) on [0, 2π).

We can use the identity for sin(2θ) to write the equation in terms of sine and cosine.

  (2sin(θ)cos(θ))·sin(θ) = cos(θ) . . . . replace sin(2θ)

  2sin(θ)²cos(θ) - cos(θ) = 0 . . . . . . . subtract cos(θ)

  cos(θ)(2 sin(θ)² -1) = 0

The zero product rule tells you a product will be zero only when one or more factors is zero. The zeros of the factors are ...

  cos(θ) = 0   ⇒   θ = π/2, 3π/2

  2sin(θ)² -1 = 0   ⇒   sin(θ) = ±√(1/2)   ⇒   θ = π/4, 3π/4, 5π/4, 7π/4

The solutions are θ ∈ {π/4, π/2, 3π/4, 5π/4, 3π/2, 7π/4}.

__

Additional comment

The solutions are the x-intercepts of the graph of sin(2θ)sin(θ) -cos(θ), the values of x where this expression is zero. A graphing calculator finds them nicely.

we are selecting 5 flavors out of 7 without regard to order. The number of combinations of 7 things taken 5 at a time is given by: C(7,5)  = 21

what is  combinations ?

Combinations, on the other hand, refer to the selection of objects from a set without considering their order. For example, the combinations of 2 letters from the set "ABC" are "AB", "AC", and "BC". The order of the letters in each combination does not matter, so "AB" and "BA" are considered the same combination.

In the given question,

This is a combination problem, since we are selecting 5 flavors out of 7 without regard to order. The number of combinations of 7 things taken 5 at a time is given by:

C(7,5) = 7! / (5! * 2!) = (76543) / (54321) = 21

Therefore, you can purchase 21 different combinations of 5 flavors of hot sauce

To know more about combinations , visit:

https://brainly.com/question/10525991

#SPJ1

The values of x and y for the right triangle are 4 and 7.21

The perpendicular height of the right triangle divides the triangle in two triangles with the same proportions as the original triangle.

by Pythagoras, the hypotenuse for the bigger of the two triangles is calculated as;

√(6² + 9²) = 10.82

the angle opposite the side length 6 for triangle with hypotenuse 10.82 and the angle opposite the side length x for triangle with hypotenuse y are the same by proportion, so:

x/6 = 6/9 {opposite/adjacent}

x = 36/9 {cross multiplication}

x = 4

also;

4/y = 6/10.52 {opposite/hypotenuse}

y = 42.08/6

y = 7.21

Therefore, the values of x and y for the right triangle are 4 and 7.21

Read more about right triangle here:https://brainly.com/question/2920412

#SPJ1

H0 is the null hypothesis stating with that the population proportion of

puppies who are spotted is less than or equal to 0.25,

H0: p <= 0.25

H1: p > 0.25

In a scientific setting, a hypothesis (plural: hypotheses) is a tested

claim regarding the causal connection between two or more variables

or a suggested explanation for a phenomenon that has been

observed.

where H0 is the null hypothesis stating that the population proportion

of puppies who are spotted is less than or equal to 0.25, and H1 is the

alternative hypothesis stating that the population proportion of puppies

who are spotted is greater than 0.25.

To know more about hypotheses Visit:

https://brainly.com/question/18064632

#SPJ1

Answer:

  a) sin(β) = 7/6 is false for any β

  b) angle β is not a real angle

Step-by-step explanation:

You want to use the Sine Law to show that a triangle with sides of lengths 6 and 10 and a smallest angle of 44.5° is impossible.

The Sine Law tells you side lengths are proportional to the sines of their opposite angles.

  sin(β)/10 = sin(44.5°)/6

  sin(β) = 10(0.7)/6

  sin(β) = 7/6

The angle β does not exist. The maximum value of the sine function is 1. There are no angles for which the sine is greater than 1.

The triangle is impossible because angle β cannot exist.

In effect, the angle 44.5° is too large, or side 10 is too long, or side 6 is too short for the figure to be a triangle.

__

Additional comment

In the realm of complex numbers, β ≈ π/2 -0.569618i radians, about (90 -32.64i)°. You cannot draw this complex angle with your real pencil.

a) For any, sin(β) = 1.17 is false.

b) Angle (β) is not a true angle.

In the branch of mathematics known as trigonometry, the relationships between the sides and angles of triangles are examined.

It involves the study of trigonometric functions like sine, cosine, tangent, cotangent, secant, and cosecant that describe the connections between the sides and angles of a right triangle.

(a) Using the Sine Law, we have:

sin(β)/10 = sin(44.5°)/6

Multiplying both sides by 10, we get:

sin(β) = (10/6)sin(44.5°)

sin(β) = 1.17

However, this is impossible since the sine of an angle can never be greater than 1. Therefore, there is no value of β that satisfies the equation, and we cannot find the value of B.

(b) The fact that the sine of β is greater than 1 means that there is no angle whose sine is equal to that value.

Therefore, there is no possible angle for β that can satisfy the given conditions of the triangle.

This means that the triangle is impossible and cannot exist with the given side lengths and angle measures.

To know more about Sine Law visit:

https://brainly.com/question/30760425

#SPJ1

6. Using Pythagoras Theorem the value of x = 99. 7, The value of x is 102.56. 8. The triangle is a right triangle. 9. The triangle is acute. 10. The triangle is acute. 11. The value of x is 32.28. 12. The value of x is 40.

The relationship between the sides of a right triangle is explained by the Pythagorean theorem, a fundamental mathematical theorem. The square of the hypotenuse's length, the longest side in a right triangle, is said to be equal to the sum of the squares of the lengths of the other two sides.

6. For a = 20, b = 99 using the Pythagoras Theorem we have:

x² = a² + b²

x² = 20² + 99²

x² = 9801

x = 99

7. For a = 60, b = 91 we have:

x² = 60² + 91²

x² = 10521

x ≈ 102.56

8. To determine whether the triangle is acute, obtuse, or right we check for using the Pythagoras Theorem.

a = 20, b = 21, and c = 29

Here,

20² + 21² = 841

29² = 841

Hence, the triangle is right.

9. For a = 15, b = 19, and c = 24. We have:

15² + 19² = 556

24² = 576

The triangle is acute.

10. For a = 11, b = 23, and c = 26. We have:

11² + 23² = 650

26² = 676

The triangle is acute.

11. Using the Pythagoras Theorem we have:

x² = 53² - 45²

x² = 1044

x ≈ 32.28

The value of x is 32.28

12. x² = 41² - 9²

x² = 1600

x = 40

The value of x is 40.

Learn more about Pythagoras Theorem here:

https://brainly.com/question/343682

#SPJ1

Answer:

Step-by-step explanation:

Answer:95

Step-by-step explanation: cause 320 - 225 = 95