Which statement is true?

Using the distance formula and the converse of the pythagorean theorem to determine whether the points are vertices of a right triangle :

22. The points (1,1), (4,4), and (1,4) form a right triangle.

23. The points (6,0), (6,4), and (2,4) form a right triangle.

24. The points (-2,1), (3,5), and (6,-2) does not form a right triangle.

The points (1,1), (4,4), and (1,4) form a triangle. We can use the distance formula to find the lengths of the three sides, and then use the converse of the Pythagorean theorem to determine whether it is a right triangle. The distance formula is:

d = √((x₂-x₁)² + (y₂-y₁)²)

So the lengths of the three sides are:

d₁ = √((4-1)² + (4-1)²) = √(27)

d₂ = √((1-1)² + (4-1)²) = √(9)

d₃ = √((1-4)² + (4-1)²) = √(18)

To check if it is a right triangle, we need to see if any of the sides squared equals the sum of the squares of the other two sides. If that is the case, then it is a right triangle. Otherwise, it is not. Checking the three possible combinations, we see that:

d₁² = 27

d₂² + d₃² = 9 + 18 = 27

Therefore, the triangle formed by the points (1,1), (4,4), and (1,4) is a right triangle.

Similarly for points (6,0), (6,4), and (2,4), the lengths of the three sides are:

d₁ = √((6-6)² + (4-0)²) = 4

d₂ = √((2-6)² + (4-4)²) = 4

d₃ = √((6-2)² + (0-4)²) = 4√2

To check :

d₁² + d₂² = 16 + 16 = 32

d₃² = 32

Therefore, the triangle formed by the points (6,0), (6,4), and (2,4) is a right triangle.

For points (-2,1), (3,5), and (6,-2) the lengths of the three sides are:

d₁ = √((3-(-2))² + (5-1)²) = √(41)

d₂ = √((6-3)² + (-2-5)²) = √(58)

d₃ = √((6-(-2))² + (-2-1)²) = √(73)

To check :

d₁² + d₂² = 41 + 58 = 99

d₃² = 73

Therefore, the triangle formed by the points (-2, 1), (3,5), and (6, -2) is not a right triangle.

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Answer: It is 180

Step-by-step explanation:

The vοlume οf the cοne is apprοximately 205.9 cubic inches.

A cοne is a shape fοrmed by using a set οf line segments οr the lines which cοnnects a cοmmοn pοint, called the apex οr vertex, tο all the pοints οf a circular base(which dοes nοt cοntain the apex). The distance frοm the vertex οf the cοne tο the base is the height οf the cοne.

The diameter οf the base is twice the radius, sο:

Diameter = 2 x Radius = 2 x 3.5 inches = 7 inches

The height οf the cοne is twice the diameter, sο:

Height = 2 x Diameter = 2 x 7 inches = 14 inches

The vοlume οf a cοne can be fοund using the fοrmula:

Vοlume = (1/3) x π x Radius² x Height

Substituting the given values, we get:

Vοlume = (1/3) x π x (3.5 inches)² x (14 inches)

Simplifying, we get:

Vοlume = (1/3) x π x 12.25 inches² x 14 inches

Vοlume = 205.9 cubic inches (rοunded tο οne decimal place)

Therefοre, the vοlume οf the cοne is apprοximately 205.9 cubic inches.

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The area of the composite shapes are:

1) A = 22 cm²

2) A = 91.5cm²

1) The formula for area of a trapezium is:

A = ¹/₂(sum of parallel sides) * height

Area of rectangle = Length * width

Thus:

Total Area of composite shape is:

A = (7 * 2) + ¹/₂(6 + 2)*2

A = 14 + 8

A = 22 cm²

2) Area of square = side * side

Area of semi circle = ¹/₂π(r²)

Total area of composite shape is:

A = (5 * 5) + (21 * 3) + ¹/₂π(1.5²)

A = 91.5cm²

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We can simplify the square root of 98 by factoring 98 into its prime factors:

98 = 2 * 7 * 7

Now, we can take out one factor of 7 from the square root and simplify it:

√98 = √(2 * 7 * 7)

√98 = √2 * √7 * √7

√98 = 7√2

Therefore, the simplified form of the square root of 98 is 7√2.

Answer:

33

Step-by-step explanation:

135/360 × 2 × 22/7 × 14

= 33

Answer:

1. 11s2 - 21st

2. 4st - t2

3. 2x² + x³

4. 2x + 2

5. 9x - 3s - 2t

6. 95x - 1

7. 9x - 2

8. 7s

9. 12 - 10x

10. 33x - 4

11. 10t

12. 26g

13. 13 + 13x

14. 17s

15. 3t

Answer:

53.  

Step-by-step explanation:

The cost increases by $10 for each ton of sugar being transported. This can be seen from the fact that for every 1 ton increase in weight, the cost increases by $10. And the slope of the line is $10/ton.

(a) To calculate the cost increase per ton of sugar being transported, we need to find the change in cost when the weight of sugar increases by 1 ton.

Looking at the graph, we can see that the cost increases from $20 to $30 as the weight of sugar increases from 1 ton to 2 tons. Therefore, the cost increase per ton of sugar is:

$30 - $20 = $10

So the cost increases by $10 for each ton of sugar being transported.

(b) The slope of the line can be calculated using the formula:

slope = (change in y) / (change in x)

where y is the cost and x is the weight of sugar being transported.

Since the line is perfectly horizontal, the change in y is zero for any change in x. Therefore, the slope is:

slope = 0 / (change in x) = 0

So the slope of the line is zero, which means that the cost does not change as the weight of sugar being transported changes.

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You need to use the formula

pi r squared times the height and all you need to do is plug it in and you’ll have your answer

After answering the provided question, we can conclude that So the ratio of red apples to all the apples in the basket is 5:14.

In mathematics, ratios show how frequently one number is contained in another. For example, if there are 8 oranges and 6 lemons in a fruit dish, the ratio of oranges to lemons is 8 to 6. In a similar vein, the orange-to-whole-fruit ratio is 8, while the lemon-to-orange ratio is 6:8. A ratio is an ordered pair of numbers a and b expressed as a / b, where b is not zero. A ratio is an equation that equates two ratios. For example, if there is one boy and three girls (for every boy she has three girls), 3/4 are girls and 1/4 are boys.

(a) The ratio of green apples to all the apples in the basket is:

Green apples : Total apples = 9 : (9+5) = 9 : 14

So the ratio of green apples to all the apples in the basket is 9:14.

(b) The ratio of red apples to all apples in the basket is:

Red apples : Total apples = 5 : (9+5) = 5 : 14

So the ratio of red apples to all the apples in the basket is 5:14.

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Answer:

Step-by-step explanation:

If a straight line falling on two other straight lines makes the interior angles on the same side less than two right angles

Answer:

Step-by-step explanation: ???

Answer:It would be 40•.25=10

Step-by-step explanation: which means 40-10=30 so it’d be .25 and you’d move the decimal over 2 spots so it’d be 25% off

Answer:8

Step-by-step explanation:

if x>7 it means x is have to be bigger than 7

in this case,

6<7

5<7

8>7

which is answer.

the acorn falls approximately 12.15 meters (to the nearest tenth of a meter) in 2.25 seconds.

the natural force  that makes things fall to the ground when you drop them.

The given function is:

d(t) = (1/2)a[tex]t^2[/tex]

where a = 4.8 m/[tex]s^2[/tex] is the acceleration due to gravity.

To find the distance an acorn falls in 2.25 seconds,  t = 2.25 seconds  

d(2.25) = (1/2)(4.8)[tex](2.25)^2[/tex]

= (1/2)(4.8)(5.0625)

= 12.15 meters (rounded to two decimal places)

Therefore, the acorn falls approximately 12.15 meters.

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Answer:

113.04cm2

Step-by-step explanation:

6cm is the radius, right?

If so, 12*3.14 = 37.68cm is the circumference and 6^2*3.14 = 113.04cm2 is the area.

HOPES THIS HELPS

If the average is 85 minutes, then on the seventh day he skated for 115 minutes.

For a set of N values {x₁, x₂, ..., xₙ} we define the average as:

A = (x₁ + ... + xₙ)/N

Here we know that for four days, he skated for 1hr + 25min = 85 min

Then for 2 days he skated for 1hr + 10min = 70 min

And the seventh day he skated x minutes.

We know that the average is 85 min, then we can write the equation:

(4*85 + 2*70 + x)/7 = 85

x = 85*7 - 2*70 - 4*85

x = 115

He scated for 115 minutes.

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Using the laws of exponents, we can simplify the given expression as:

-(¹/₂₇)(1/x¹²)y²¹

Some of the laws of exponents are:

1) When multiplying like bases, keep the base the same and add the exponents.

2) When raising a base with a power to another power, keep the base the same and multiply the exponents.

3) When dividing like bases, keep the base the same and subtract the denominator exponent from the numerator exponent.

The expression is given as:

(-3x⁴y⁻⁷)⁻³

Using the power to power rule of exponents, we have:

-3⁻³x⁻¹²y²¹

Using the reciprocal law of exponents, we have:

(-1/3³)(1/x¹²)y²¹

= -(¹/₂₇)(1/x¹²)y²¹

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The majority of the marina's bolts are white. The remaining bolts are divided into 4/7 blue and the remainder red. There are 84 vessels at the marina if there are nine red boats.

Let's start by finding the fraction of bolts that are not red:

Fraction of white bolts: 3/4

Fraction of bolts that are not white: 1 - 3/4

Fraction of bolts that are not white = 4-3/4

Fraction of bolts that are not white = 1/4

Fraction of blue bolts: 4/7 of 1/4

Fraction of blue bolts = 4/28

Fraction of blue bolts = 1/7

Fraction of red bolts: 1/4 - 1/7

Fraction of red bolts = 7-4/28

Fraction of red bolts = 3/28

We know that there are nine red boats, which is equal to 3/28 of the total number of bolts. So we can set up an equation to solve for the total number of bolts:

3/28x = 9

Multiplying both sides by (28/3), we get:

x = (28/3) * 9

x = 28 * 3

x = 84

Therefore, there are 84 boats in the marina.

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Answer:

the answer is very simple the answer would be, 5 giga horse power every hour, 5/60*360= 30, the answer is 30m/s2

Step-by-step explanation:

according to formula

The solution for the equation x^2 - 10x = -100 is

The solution for the equation x^2 + 7x - 16 = 0 is

To complete the square for the equation x^2 - 10x = -100, we need to add and subtract  (b/2a)^2 = (10/2)^2 = 25 to both sides of the equation:

x^2 - 10x + 25 = -100 + 25

(x - 5)^2 = -75

x - 5 = ±√75i

x = 5 ± √(75)i

x = 5 ± 5√3 i

Therefore, the solutions are x = 5 + 5√3i and x = 5 - 5√3i.

For the equation x^2 + 7x - 16 = 0, we need to add and subtract (7/2)^2 = 49/4 to both sides of the equation:

x^2 + 7x + 49/4 - 49/4 - 16 = 0

(x + 7/2)^2 = 81/4

x + 7/2 = ±9/2

x = -7/2 ± 9/2

x = -8 or x = 1

Therefore, the solutions are x = -8 and x = 1.

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Answer:

$5920.00

Step-by-step explanation:

1. (6% ÷ 100)×4000

=240.

2. 240 interest per year

240×8 years

= $1920

3. $1920 + $4000= $5920.00

The amount of money you'll have at the end of the indicated time period is $5920.

Given

You invest $4000 in an account that pays a simple interest of 6% for 8 years.

The amount of money you'll have at the end of 8 years.

We know the formula of simple interest, substitute the values in it,

[tex]\text{Simple interest}=\dfrac{\text{P}\times\text{R}\times\text{T}}{100}[/tex]

Substitute all the values in the formula

[tex]\text{Simple interest}=\dfrac{\text{P}\times\text{R}\times\text{T}}{100}[/tex]

[tex]\text{Simple interest}=\dfrac{\text{4000}\times\text{6}\times\text{8}}{100}[/tex]

[tex]\text{Simple interest}=40\times6\times8[/tex]

[tex]\text{Simple interest}=1920[/tex]

Therefore,

The amount of money you'll have at the end of the indicated time period is:

[tex]= \$1920 + \$4000 = \$5920[/tex]

Hence, the amount of money you'll have at the end of the indicated time period is $5920.

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After answering the provided question, we can state that As a result, 145.62 square feet of glass are required to cover the entire pyramid.

A pyramid is a polygon formed by connecting points known as bases and polygonal vertices. For each hace and vertex, a triangle known as a face is formed. A cone with a polygonal shape. A pyramid with a floor and n pyramids has n+1 vertices, n+1 vertices, and 2n edges. Every pyramid is dual in nature. A pyramid contains three dimensions. A pyramid is made up of a flat tri face and a polygonal base that come together at a single point known as the vertex. A pyramid is formed by connecting the base and peak. The base's edges form triangle faces known as sides that connect to the top.

To determine how much glass is required to cover the entire pyramid, we must first determine the total surface area of the pyramid, including the base.

The formula for calculating the surface area of each triangular face is:

(1/2) x width x height

27.31 square feet = (1/2) x 7 feet x 7.79 feet

24 square feet = (1/2) x 6 feet x 8 feet

Simply multiply the length and width to find the area of the rectangular base:

7 feet by 6 feet equals 42 square feet

As a result, the total surface area of the pyramid is:

145.62 square feet = 2 (27.31 square feet) + 2 (24 square feet) + 42 square feet

As a result, 145.62 square feet of glass are required to cover the entire pyramid.

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Answer: 102.53

Step-by-step explanation:  I calculated all the numbers you gave me and then added them to get 102.53

Answer: 18/27 or 2/3

Step-by-step explanation: trust me

1. To compare, we have to use the matched test.

2. n = 57

3. Sample mean difference = -0.4681

3b. Sample standard deviation of difference = 1.2824

In statistics, the null hypothesis is a statement that suggests there is no significant difference between two groups, samples, or variables being compared. It is a starting point for statistical analysis, and the goal is to either reject or fail to reject this hypothesis based on the evidence from the data.

The images below contains the histogram of differences, the comparison data and the calculation

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Answer:

Let age of mine be n years.

Age of my father is twice of mine -2 n years.

Find the sum of age of me and my father.

= n+2n

Step-by-step explanation:

if it helped you please mark me a brainliest :))

The expression n + 2n is an example of multiplication, where 2n is two times n. Adding n and 2n together results in 3n, which is three times n.

The original equation formed after factoring out [tex]$-\frac{1}{2}$[/tex] is [tex]$$(x-0)^2 - 2x - 8 = 0$$[/tex].

What is meant by factor?

In mathematics, a factor is a number or expression that divides another number or expression evenly without a remainder. Factoring is the process of finding the factors of a number or expression. In algebra, factoring is used to simplify expressions, solve equations, and find zeros of functions. By factoring, we can rewrite a complex expression or equation as a product of simpler expressions or factors.

To factor out [tex]$-\frac{1}{2}$[/tex] from the equation [tex]$-\frac{1}{2}(x-0)^2+x+4=0$[/tex], we can divide both sides of the equation by [tex]-\frac{1}{2}$:[/tex]

[tex]$-\frac{1}{2}(x-0)^2 \div -\frac{1}{2} + x \div -\frac{1}{2} + 4 \div -\frac{1}{2} = 0 \div -\frac{1}{2}$$[/tex]

Simplifying each term, we get:

[tex]$$(x-0)^2 - 2x - 8 = 0$$[/tex]

This is the factored form of the original equation, after factoring out [tex]-\frac{1}{2}$.[/tex]

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Using derivative of a function

The derivative of a function is its limit as the change in the independent variable tends to zero.

Now, since we have the [tex]\lim_{h \to 0}\frac{cos(\pi + h) - (- 1)}{h}[/tex].

We know that the definition of the derivative of  a function f(x) is

[tex]f'(x) =\lim_{h \to 0}\frac{f(x + h) - f(x)}{h}[/tex]

Now, comparing both equations, we see that

f(x + h) = cos(x + h), f(x) = -1

Now, since f(x + h) = cos(x + h), we notice that f(x) must be a cosine function.

So, f(x) = cosx

Now, f(a) = -1

cosa = -1

a = cos⁻¹(-1)

= π

So, substituting this into the derivative equation, we have

[tex]f'(x) =\lim_{h \to 0}\frac{f(x + h) - f(x)}{h}[/tex]

[tex]f'(x) =\lim_{h \to 0}\frac{cos(x + h) - (-1)}{h}\\=\lim_{h \to 0}\frac{cos(x + h) - cos(x)}{h}\\=\lim_{h \to 0}\frac{cos(\pi + h) - cos(\pi )}{h}\\= -sin\pi \\= 0[/tex]

So,

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