Find the equation of a line that passes through (1,12) and is parallel to the graph of y=3x+4 . Write the equation in​ slope-intercept form.

Answer:

Step-by-step explanation:

3x = 90 + 46 - 14

3x = 122

x=\(\frac{122}{3}\)≈40,7

Answer: 40.6 repeated

Step-by-step explanation: combine -46 and 14 which is -32. then add 32 to 90. then divide 3 on both sides. 122/3 is 40.6 repeated

Explanation is in the file

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Answer:

X = 8

Step-by-step explanation:

A triangle's degrees always add up to 180, this is a right triangle meaning that one of the degrees is 90, and we see the other one is 54, so we add these together and subtract them from 180 and set that equall to 3x+12.  

Answer:

(10, 5π/3)

Step-by-step explanation:

To convert rectangular coordinates (5, -5√3) to polar form, we can use the following formulas:

r = √(x^2 + y^2)

θ = arctan(y/x)

Substituting the given values, we get:

r = √(5^2 + (-5√3)^2) = √(25 + 75) = √100 = 10

θ = arctan((-5√3)/5) = arctan(-√3) = -π/3

Note that the value of θ is in the fourth quadrant, which corresponds to a negative angle. However, we need to express the angle θ in the range 0 ≤ θ < 2π. To do this, we can add 2π to the angle if it is negative:

θ = -π/3 + 2π = (5π/3)

Therefore, the rectangular coordinates (5, -5√3) in polar form are (10, 5π/3).

Answer:

d) 1/12

Step-by-step explanation:

The Propositions are resulting

(a) ∀x∃y(x = y²) is False

(b) ∀x∃y(x² = y) is True.

(c) ∃x∀y(xy = 0) is True.

(d) ∀x∃y(x + y = 1) is True.

(a) ∀x∃y(x = y²)

This proposition states that for every x, there exists a y such that x is equal to y². To determine the truth value, we need to check if this statement holds true for every value of x.

If we take any positive value for x, we can find a corresponding value of y that satisfies the equation.

For example, if x = 4, then y = 2 satisfies the equation since 4 = 2². Similarly, if x = 9, then y = 3 satisfies the equation since 9 = 3².

Therefore, the proposition (a) is false.

(b) ∀x∃y(x² = y)

For any given positive or negative value of x, we can find a corresponding value of y that satisfies the equation.

For example, if x = 4, then y = 2 satisfies the equation since 4² = 2. Similarly, if x = -4, then y = -2 satisfies the equation since (-4)² = -2.

Therefore, the proposition (b) is true.

(c) ∃x∀y(xy = 0)

The equation xy = 0 can only be satisfied if x = 0, regardless of the value of y. Therefore, there exists an x (x = 0) that makes the equation true for every y.

Therefore, the proposition (c) is true.

(d) ∀x∃y(x + y = 1)

To determine the truth value, we need to check if this statement holds true for every value of x.

If we take any value of x, we can find a corresponding value of y that satisfies the equation.

For example, if x = 2, then y = -1 satisfies the equation since 2 + (-1) = 1. Similarly, if x = 0, then y = 1 satisfies the equation since 0 + 1 = 1.

Therefore, the proposition (d) is true.

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Answer:

Step-by-step explanation:

Hello,

Question 15

We can search x such that:

   \(x^2-4x+4=2x-5\\\\\text{*** subtract 2x-5 from both sides ***}\\ \\x^2-4x-2x+4+5=0\\ \\\text{*** simplify ***}\\ \\x^2-6x+9=0 \\ \\\text{*** we can notice a perfect square ***}\\ \\x^2 -2\cdot x \cdot 3 + 3^2=(x-3)^2=0\\\\\text{*** taking the root ***}\\\\x-3=0\\\\\large \boxed{\sf \ \ x=3 \ \ }\)

There is 1 solution.

Question 16

Again, we search x such that:

  \(x^2-8x+15=2x-6\\\\\text{*** subtract 2x-6 from both sides ***}\\\\x^2-8x-2x+15+6=0\\\\\text{*** simplify ***}\\\\x^2-10x+21=0 \\ \\\text{*** we are looking for two roots where the sum is 10 and the product is 21 = 7 x 3 ***} \\\\x^2-7x-3x+21=x(x-7)-3(x-7)=(x-3)(x-7)=0\\\\\large \boxed{\sf \ \ x= 3 \ or \ x =7 \ \ }\)There are two solutions.

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Starting with the given equation: 2 sin x cos x = cos x

By dividing both sides by cos x, we may simplify: 2 sin x = 1

Dividing both sides by 2:

sin x = 1/2

The values of x that fulfil sin x = 1/2 must now be found, and they are:

x = π/6 + 2πn or x = 5π/6 + 2πn, where n is any integer.

Therefore, the general solution is:

x = π/6 + 2πn or

x = 5π/6 + 2πn, where n is any integer.

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The solution to the system of linear equations is (x, y, z) = (64/11, 37/11, 9/11). The system has exactly one solution.

Let's solve the system of linear equations correctly.

The given system of linear equations is:

x = y + 3z = 6

x - 2y = 5

2x - 2y + 5z = 9

To determine the number of solutions, we can analyze the system using the method of elimination or substitution. Let's use the method of elimination:

From equation 1, we have:

x = y + 3z

Substituting this value of x in equation 2:

(y + 3z) - 2y = 5

y + 3z - 2y = 5

-z + 3z = 5 - y

2z = 5 - y

Now, let's substitute the value of x in equation 3:

2(y + 3z) - 2y + 5z = 9

2y + 6z - 2y + 5z = 9

11z = 9

Simplifying the equation, we find:

z = 9/11

Now, substituting this value of z back into the equation 2z = 5 - y, we get:

2(9/11) = 5 - y

18/11 = 5 - y

18/11 - 5 = -y

18/11 - 55/11 = -y

-37/11 = -y

y = 37/11

Finally, we can substitute the values of y and z into equation 1 to find the value of x:

x = y + 3z

x = 37/11 + 3(9/11)

x = 37/11 + 27/11

x = 64/11

Therefore, the solution to the system of linear equations is (x, y, z) = (64/11, 37/11, 9/11).

The system has exactly one solution.

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Answer: \(C. \frac{125}{7}\)

Step-by-step explanation:

1. Find the sum of the infinite geometric sequence:

\(S = \frac{125}{7}\)

2. Find the correct option:

C

Answer:

B. 56

Step-by-step explanation:

28 pounds converted to ounces is 448 ounces

so 448/8=56

Answer:

15.59 square inches

Step-by-step explanation:

In the required given diagram, the slant height of the cone was given as 3.6 inches.

The least amount of paper required would be equal to the curved surface area of the cone.

curved surface area of a cone = \(\pi\)rl

where r is the radius and l the slant height.

circumference of the top rim = 8.66 inches

circumference = 2\(\pi\)r

⇒ 8.66 = 2\(\pi\)r

4.33 = \(\pi\)r

r = 4.33/\(\pi\)

curved surface area = \(\pi\) x  4.33/\(\pi\) x 3.6

                                 = 4.33 x 3.6

                                = 15.588 square inches

Thus, the least amount of paper that can form the cone shaped cup is 15.59 square inches.

The least amount of paper should be 15.59 square inches

We know that

the curved surface area of a cone =πrl

And, the circumference is 2πr

So here radius should be

8.66 = 2πr

r = 4.33/π

Now

curved surface area should be

= π(4.33/π) ( 3.6)

= 4.33 (3.6)

=  15.59 square inches

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The probabilities in these cases are 0.125, 0.375, 0.58, 0.16, 0.5  and the only prime and even number is 2.

The probability is defined by the formula: specific outcome/ total possible outcomes. Based on this, let's calculate the probability in each case:

A prime number can be defined as a number that can be divided only by 1 and the number itself. On the opposite, a composite number can be divided by at least another number than 1 and itself.

The only prime and even number is 2.

Note: Here is the question in English:

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Answer:

The grandfather collected  2,379,682,122 more

Step-by-step explanation:

3,297,000,014 - 917,317,892 = 2,379,682,122

On solving the providewd question we can say that, public static double solve(double a, double b, double c, boolean flag )

A quadratic equation is a quadratic polynomial in one variable that looks like this: x = ax2 + bx + c. a 0. This polynomial has at least one solution since it is a second-order polynomial, according to the Fundamental Theorem of Algebra. The answer can actually work or be difficult.

public static double solve(double a, double b, double c, boolean flag)

{     double d = Math.sqrt(b*b - 4*a*c);     if(flag)

{         return (-b + d) / (2*a);     }

else {         return (-b - d) / (2*a);     } }

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Answer: D 28

Step-by-step explanation:

use the formuls x= -b/2a

the maximum is 28 and the minimum is 2

Answer:

1. 29.67°

2. 68.96°

3. 89.85°

Step-by-step explanation:

1. Reference angle = x

Opposite = 45 cm

Adjacent = 79 cm

Therefore:

\( tan(x) = \frac{45}{79} \)

\( tan(x) = 0.569620253 \)

\( x = tan^{-1}(0.569620253) \)

\( x = 29.67 \) (nearest hundredth)

2. Reference angle = B

Opposite = 14

Hypotenuse = 15

Therefore:

\( sin(B) = \frac{14}{15} \)

\( sin(B) = 0.93333 \)

\( B = sin^{-1}(0.93333) \)

\( B = 68.96 \) (nearest hundredth)

3. Reference angle = x

Adjacent = 238,900 mi

Hypotenuse = 92,955,807 mi

Therefore:

\( cos(x) = \frac{238,900}{92,955,807} \)

\( x = cos^{-1}(\frac{238,900}{92,955,807}) \)

\( x = 89.85 \) (nearest hundredth)

Answer:

Choice A

Step-by-step explanation:

End of the question states it, and I did it on Khan :)

Kara finds that the top 200200200 longest streaks in the world in June had an average of about 636363 so option (A) will be correct.

The mean is the average of a data set. Mean gives us the idea of that how much amount of overall data have.

In other words, the mean is the foundation of the deviation of data from all data sets.

Mean = sum of data / Number of data

For example, if you have marks in 5 subjects like 40,45,44,46,48 then the mean will be

( 40 + 45+ 44 + 46 + 48) /5 = 44.6.

Given that,

Kara finds that the top 200200200 longest streaks in the world in June had an average of about 636363 wins in a row

It means the top 200200200 longest streaks worldwide in June have an average longest streak of 636363.

Hence " Kara finds that the top 200200200 longest streaks in the world in June had an average of about 636363".

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The area and arc length of each piece can be found using the

relationship between a circle and a sector of the circle.

Responses (b, c, and d are approximated):

a. 120°

b. 10.6 square inch

c. 28.3 in.

d. Area: 15.8 in.², Central angle: 89.1°

Given:

Diameter of the pan, d = 9-inch

Number pie pieces cut from the apple pie = 6

The pie pieces are sectors of a circular pie.

a. The central angle of one pie pieces = \(\dfrac{360^{\circ}}{6}\) = 60°

Therefore;

b. Area of circular pie = π·r²

Where;

\(r = \mathbf{\dfrac{d}{2}}\)

Therefore;

\(r = \dfrac{9}{2} = \mathbf{ 4.5}\)

\(The \ area \ covered \ by \ each \ pie \ piece = \dfrac{\pi \times 4.5^2}{6} \approx \mathbf{10.6}\)

c. The circumference of a circle = 2·π·r

The circumference of the original pie = 2 × π × 4.5 in. ≈ 28.3 in.

d. Let the arc length of the pie piece = 7 inches

\(\mathbf{Area} \ of \ the \ \mathbf{pie \ piece}= \dfrac{7}{2 \cdot \pi \cdot 4.5} \times \pi \times 4.5^2 = \dfrac{7}{2 } \times 4.5 = 15.75 \approx 15.8\)

\(The \ central \ angle \ of \ the \ pie \ piece = \dfrac{7}{2 \cdot \pi \cdot 4.5} \times 360^{\circ} \approx \underline{ 89.1^{\circ}}\)

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Answer:

16 hours

Step-by-step explanation:

14 hours + 1 hour + 1 hour = 16 hours

Answer:

Step-by-step explanation:

x = 10 - 5/2y

The statement "In both cases, subtract 6 from both sides, but reverse the inequality sign when doing that for the inequality" best describes the process used to solve the equations.

In the equation -3x + 6 = 21, to isolate the variable x, we subtract 6 from both sides of the equation, which yields -3x = 15. Then, we divide both sides by -3 to solve for x, resulting in x = -5. This process is applicable to equations where we aim to find the exact value of the variable.

Similarly, in the inequality -3x + 6 < 21, we want to find the range of values for x that satisfy the inequality. By subtracting 6 from both sides, we obtain -3x < 15.

However, since we performed the same operation on both sides of the inequality, the direction of the inequality sign remains the same.

Thus, the correct inequality is -3x < 15. To isolate x, we divide both sides by -3. However, since we reversed the inequality sign, we must also reverse it again, resulting in x > -5.

This process allows us to determine the range of values for x that satisfy the inequality.

Therefore, the statement accurately describes the process for solving both the equation and the inequality, highlighting the significance of reversing the inequality sign when manipulating inequalities.

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Answer:

x = -10

Step-by-step explanation:

62 = 12 - 5x

-12 .   -12

62 - 12 = -5x

50 = -5x

__ .  __

-5 .    -5

-10 = x    

Answer:

x + x - 45 = 90

2x - 45 = 90

2x = 135

x = 67.5, so x - 45 = 22.5

The other two angles measure 22.5° and 67.5°.

Answer:

Step-by-step explanation:

18900 divided by 10 = 1890

1890 divided by 2 is 945

945 is 5 percent of 18900

18900 + 945 = 17955

Answer = 19845

Answer:

N= 5

Step-by-step explanation:

Solve for N by cross multiplying

Answer:

A = 35 cm²

Step-by-step explanation:

the area (A) of a rectangle is calculated as

A = length × width

by counting the squares on the sides

length = 7 cm and width = 5 cm , then

A = 7 × 5 = 35 cm²

−7 < x – 3 ≤ 6 is just a regular inequality, neither conjunction nor disjunction are involved.

x + 5 < -1 or x + 2 > 5 is a disjunction.

3 > x – 4 and x + 8 ≥ 2 is a conjunction.