Make t the subject of the formula 2(t-5) = y

Final answer:

△RST is a right triangle because the slope of line RS is 3/2 and the slope of line RT is 0, indicating that RS is perpendicular to RT.

Explanation:

To determine whether △RST is a right triangle, we can calculate the slopes of the sides to check for perpendicularity. A right triangle will have one pair of sides that are perpendicular to each other, meaning their slopes will be negative reciprocals.

The slope of line RS is calculated using the coordinates R(-3,1) and S(-1,4) as:

Slope of RS = (4 - 1) / (-1 + 3) = 3 / 2

The slope of line RT is calculated using the coordinates R(-3,1) and T(3,1) as:

Slope of RT = (1 - 1) / (3 + 3) = 0 / 6 = 0

Since the slope of RS is a non-zero finite number and the slope of RT is zero, they are perpendicular to each other because the slope of a line perpendicular to a horizontal line (slope of 0) is undefined, which is the negative reciprocal of 0.

Therefore, the correct statement is:

△RST is a right triangle because RS‾ is perpendicular to RT‾.

Final answer:

Upon calculating the slopes of the sides of △RST, it is concluded that none of the sides are perpendicular to one another, which means that △RST is not a right triangle.

Explanation:

To determine if △RST is a right triangle, we need to calculate the slopes of the sides to check for perpendicularity because perpendicular lines have slopes that are negative reciprocals of each other. Let's calculate the slopes of line segments RS, ST, and RT.

Slope of RS is given by (4 - 1)/(-1 + 3) = 3/2.
Slope of ST is (4 - 1)/(-1 - 3) = 3/-4 = -3/4.

Slope of RT is (1 - 1)/(3 + 3) = 0/6 = 0.

Since the slope of RT is 0, it means that RT is a horizontal line. The slope of RS is 3/2, and the slope of ST is -3/4. These slopes are not negative reciprocals of each other. Hence, none of the lines are perpendicular to each other, and we can conclude that △RST is not a right triangle because no two of its sides are perpendicular.

Answer:

The exact value is [tex]\cfrac{\sqrt{3}}3[/tex]

Step-by-step explanation:

Since 60 degrees is an angle we can find on the unit circle, the goal to get an exact value is to use the elements of the unit circle, which are exact values of sine and cosine.

Writing cotangent in terms of sine and cosine

We can use the trigonometric identity

[tex]\cot \theta = \cfrac{\cos \theta }{\sin \theta }[/tex]

Thus for the exercise we will have

[tex]\cot 60^\circ = \cfrac{\cos 60^\circ }{\sin 60^\circ }[/tex]

Identifying the known exact values.

From the unit circle that you can see on the attached image below, we have to identify the exact values of cosine and sine of 60  degrees.

So first try to look for the angle 60 degrees, there you will see a point that has a pair of values,  those represent (cosine, sine), thus we get:

[tex]\cos 60^\circ=\cfrac 12 \\\\\sin 60^\circ = \cfrac{\sqrt3}2[/tex]

Finding the exact value of cot 60 degrees.

We can replace the exact values of sine and cosine on the trigonometric identity for cotangent.

[tex]\cot 60^\circ = \cfrac{\cfrac 12 }{\cfrac{\sqrt 3}2 }[/tex]

Working with the reciprocal we get

[tex]\cot 60^\circ = \cfrac 12\times \cfrac2{\sqrt 3}[/tex]

Simplifying we get

[tex]\cot 60^\circ = \cfrac 1{\sqrt 3}[/tex]

Rationalizing since we usually do not want square roots on the denominator we get

[tex]\cot 60^\circ = \cfrac 1{\sqrt 3} \times \cfrac{\sqrt 3}{\sqrt 3}\\\boxed{\cot 60^\circ = \cfrac {\sqrt 3}3}[/tex]

And that is the exact value of cotangent of 60 degrees.

The exact value of cot(60°) is √3 / 3.

To find the exact value of cot(60°), we can use the identity:

cot(θ) = 1 / tan(θ)

Since tan(θ) = sin(θ) / cos(θ), we need to find the values of sin(60°) and cos(60°).

In a 30-60-90 degree triangle, the sides are in the ratio 1 : √3 : 2. Since the angle is 60°, the opposite side (opposite the 60° angle) has length √3 and the adjacent side (adjacent to the 60° angle) has length 1.

Using these values, we can calculate the sine and cosine of 60°:

sin(60°) = opposite/hypotenuse = √3/2

cos(60°) = adjacent/hypotenuse = 1/2

Now, we can find cot(60°):

cot(60°) = 1 / tan(60°)

= 1 / (sin(60°) / cos(60°))

= 1 / (√3/2 / 1/2)

= 1 / (√3/1)

= 1 / √3

= √3 / 3

Therefore, the exact value of cot(60°) is √3 / 3.

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a. Probability density function (pdf) of X: 0.247 for 0.20 < x < 4.25.

b. Probability that diameter exceeds 2 mm: 0.556.

c. Probability that diameter is within 2 mm of the mean diameter: 0.988.

(a) Probability density function (pdf) of X:

For a uniform distribution with A = 0.20 and B = 4.25, the pdf is constant within the range A to B and 0 elsewhere. Therefore:

f(x) = 1 / (B - A) = 1 / (4.25 - 0.20) = 1 / 4.05 ≈ 0.247 for 0.20 < x < 4.25

(b) Probability that diameter exceeds 2 mm:

P(X > 2) = (4.25 - 2) * f(x) = 2.25 * 0.247 ≈ 0.556

(c) Probability that diameter is within 2 mm of the mean diameter:

The mean of a uniform distribution is (A + B)/2 = (0.20 + 4.25)/2 = 2.225.

So, we need to find P(2.225 - 2 < X < 2.225 + 2), which is P(0.225 < X < 4.225).

P(0.225 < X < 4.225) = (4.225 - 0.225) * f(x) = 4 * 0.247 ≈ 0.988

Complete question:

An article considered the use of a uniform distribution with

A = 0.20 and B = 4.25

for the diameter X of a certain type of weld (mm).

(a) Determine the pdf of X. (Round your answers to three decimal places.)

0.2<x<4.25

(b) What is the probability that diameter exceeds 2 mm? (Round your answer to three decimal places.)

(c) What is the probability that diameter is within 2 mm of the mean diameter? (Round your answer to three decimal places.)

Answer:

She bought 6 bag of chips.

Step-by-step explanation:

Let the price of bag of chips be s.

Each sandwich cost three times as much as a bag of chips.

Cost of sandwich = 3s

She bought 5 sandwiches for $6.

That is cost of sandwich = 3s = 6

                      s = 2$

Cost of bag of chips = s = 2$

Price of 5 sandwiches = 5 x 6 = 30 $.

She spent $42, remaining money = 42 - 30 =12 $

Number of bag of chips can be bought with 12 $

                 [tex]n=\frac{12}{2}=6[/tex]

She bought 6 bag of chips.

Answer:

The required equation is [tex]C=\frac{5}{9}(F-32)[/tex]

Step-by-step explanation:

Consider the provided equation.  

[tex]F= \frac{9}{5}C+32[/tex]

Solve the formula for C.

Subtract 32 from both sides.

[tex]F-32= \frac{9}{5}C+32-32[/tex]

[tex]F-32= \frac{9}{5}C[/tex]

Multiply both the sides by 5/9.

[tex]\frac{5}{9}(F-32)= \frac{9}{5}C\times \frac{5}{9}[/tex]

[tex]C=\frac{5}{9}(F-32)[/tex]

Hence the required equation is [tex]C=\frac{5}{9}(F-32)[/tex]

The formula to convert Fahrenheit to Celsius is C = 5/9( F - 32 ).

Given the equation in the question:

F = (9/5)C + 32

To solve for C (Celsius) in the conversion formula F = (9/5)C + 32, first, isolate the terms that contain C on one side of the equation.

F = (9/5)C + 32

Subtract 32 from both sides of the equation:

F - 32 = (9/5)C + 32 - 32

F - 32 = (9/5)C

Next, multiply both sides by the reciprocal of the coefficient of C: 5/9:

5/9( F - 32 ) = 5/9 × (9/5)C

5/9( F - 32 ) = C

C = 5/9( F - 32 )

Therefore, C equals C = 5/9( F - 32 ).

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The expression 64c¹⁵-d²⁷ having a difference of cube will be (4c⁵)³ - (d⁹)³. The correct option is D.

The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

The given expression is 64c¹⁵-d²⁷. the expression will be written in the power of a cube as below:-

64c¹⁵-d²⁷ = (4c⁵)³ - (d⁹)³

Therefore, the expression 64c¹⁵-d²⁷ having a difference of cube will be (4c⁵)³ - (d⁹)³. The correct option is D.

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Answer:

The equation that models this situation : [tex]4\times (6+x)=48[/tex]

Duration of bicycle rented on Sunday was of 6 hours.

Step-by-step explanation:

Cost of per hour to rent the bicycle = $4

Duration of bicycle rented on Saturday = 6 hours

Duration of bicycle rented on Sunday = x

Total mount paid = $48

[tex]\$4\times (6+x)=$48[/tex]

[tex]4\times (6+x)=48[/tex]

For solving for x:

[tex]x=\frac{48}{4}-6= 6[/tex]

Duration of bicycle rented on Sunday was of 6 hours.

The optimal least squares fit for the given data is y = 0.2732x² - 0.6452. This curve minimizes the sum of squared errors, providing an accurate representation of the data.

The provided data points are (-1, 0), (5, 5), and (6, 10), denoted as {x} = [-1, 5, 6] and {y} = [0, 5, 10]. The goal is to find the least squares fit for the curve y = ax² + b. To minimize the sum of squared errors between the data and the curve, the normal equations are derived.

The normal equations are given by:

(x₁⁴ + x₂⁴ + x₃⁴)a + (x₁² + x₂² + x₃²)b = x₁²y₁ + x₂²y₂ + x₃²y₃ (Equation 1)

(x₁² + x₂² + x₃²)a + 3b = y₁ + y₂ + y₃ (Equation 2)

By substituting the given data, the equations become:

1922a + 62b = 485

62a + 3b = 15

Solving these equations yields the values: a = 0.2732 and b = -0.6452. Therefore, the curve of the best least squares fit is y = 0.2732x² - 0.6452.

In conclusion, the curve that minimizes the sum of squared errors for the provided data points is y = 0.2732x² - 0.6452. The graph of this curve, along with the given data, visually represents the accuracy of the least squares fit.

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To find the initial number of chocolates Jenny had, we solve the equation (x - 2)/2 = 6, which results in x = 14. Therefore, Jenny had 14 chocolates initially.

The question asks to determine how many chocolates Jenny had in the beginning if she eats two and gives half of the remainder to Lisa, who ends up with six chocolates. To solve this, we let x represent the initial number of chocolates Jenny had. After eating two chocolates, Jenny has x - 2 left. She gives half of this remainder to Lisa, which means Lisa receives (x - 2)/2 chocolates. Since Lisa has six chocolates, we set up the equation (x - 2)/2 = 6. Solving this gives us x - 2 = 12 and therefore, x = 14. Hence, Jenny had 14 chocolates in the beginning. The correct answer is option C. 14.

Answer:

the anwser is A

Step-by-step explanation:

if you didnt understand the top

Answer:

g>5

Step-by-step explanation:

g-6>-1

+6 to both sides

g is left alone :)

To find the cost of the love seat, couch, and chair, set up a system of equations and solve for the variables.

To find the cost of the love seat, the couch, and the chair, we need to set up a system of equations based on the given information. Let's represent the cost of the chair as x. Since the couch costs twice as much as the chair, its cost will be 2x. The love seat costs $400 more than the couch, so its cost will be 2x + $400. The sum of the costs of all three pieces of furniture is $1565. Using these equations, we can solve for x, and then find the costs of the love seat, the couch, and the chair.

Equations:

Cost of the Chair: $233

Cost of the Couch: 2x = 2($233) = $466

Cost of the Love Seat: 2x + $400 = 2($233) + $400 = $466 + $400 = $866

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Answer:

(3,3)

Step-by-step explanation:

Answer:     4 1/2 in

Step-by-step explanation: correct on gradpoint

Answer:

P is True and q true is , so the statement, "A square root of 16 is 4 or a square root of 9 is -3" is false .

Explanation:

The table of conjunctions show:

The first statement, "A square root of 16 is 4," (p), is true.

The second statement, "a square root of 9 is -3," (q), is true.

The amount of water flowing each second is:

rate = 5.2 x 10^5 gallons / second

Since we know that:

1 hour = 3600 seconds

Therefore:

rate = (5.2 x 10^5 gallons / second) * (3600 seconds / hour)

rate = 1.872 x 10^9 gallons / hour

Final answer:

The average volume of water that flows over the falls in an hour is 1.89 x 10^9 gallons/hour.

Explanation:

To calculate the amount of water that flows over the falls in an hour, we need to convert the given flow rate from gallons per second to gallons per hour.

There are 3600 seconds in an hour, so we can multiply the flow rate (5.25 x 105 gallons per second) by 3600 to find the flow rate in gallons per hour.

The calculation would be: 5.25 x 105 gallons/s * 3600s/hour = 1.89 x 109 gallons/hour.

The result, in scientific notation, is 1.89 x 109 gallons/hour.

Answer:

As Given :The coordinates of the vertices of △JKL are J(3, 0) , K(1, −2) , and L(6, −2) . The coordinates of the vertices of △J′K′L′ are J′(−3, 1) , K′(−1, 3) , and L′(−6, 3) .

⇒As we can see the two triangles are congruent because length of sides are equal.i.e By SSS  ΔJKL and ΔJ'K'L' are congruent.

⇒ As you can see from the figure depicted below the triangle JKL is rotated by an angle of 180° then translation of y coordinate by 1 unit up has taken place.

So , Option (3) is correct which is :△JKL is congruent to △J′K′L′ because you can map △JKL to △J′K′L′ using a rotation of 180° about the origin followed by a translation 1 unit up, which is a sequence of rigid motions.

Final answer:

The two-digit number where the tens digit is three more than the units digit and the number is seven times the sum of its digits is 74.

Explanation:

The question involves finding a two-digit number that fits two conditions: it is seven times the sum of its digits, and its tens digit is three more than the units digit. To solve this, we set up the following equations. Let x represent the tens digit and y represent the units digit.

Substituting x from the second equation into the first equation, we get 10(y + 3) + y = 7(y + 3 + y). Solving this, we find y = 4 and therefore x = 4 + 3, which gives x = 7. Thus, the number is 74.