Equation line L is y=5x+1
The equation of line, L^2 is 2y-10x+3=0
Shows that these two lines are parallel

The length of the remaining sides is a = 57.50 and b = 61.93.

The law of sines specifies how many sides there are in a triangle and how their individual sine angles are equal. The sine law, sine rule, and sine formula are additional names for the sine law.

The side or unknown angle of an oblique triangle is found using the law of sine. Any triangle that is not a right triangle is referred to as an oblique triangle.

Given a triangle ABC, and ∠B = 90°

∠A = 68.2° and c = 23.0

so ∠C = 90 - ∠A

∠C = 90 - 68.2

∠C = 21.8°

according to the law of sines,

sinA/a = sinB/b = sinC/c

for a,

sinA/a = sinC/c

substitute the values

sin(68.2)/a = sin(21.8)/c

a = 23(sin68.2)/(sin21.8)

a = 57.50

and for b,

sinB/b = sinC/c

substitute the values

b = csinB/sinC

b = 23(sin90/sin21.8)

b = 61.93

Hence a = 57.50 and b = 61.93.

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The exponential grows at the same rate as the quadratic in the interval

0 ≤ x ≤ 1.

The average Rate of Change function is defined as the average rate at which one quantity is changing with respect to something else changing. In simple terms, an average rate of change function is a process that calculates the amount of change in one item divided by the corresponding amount of change in another.

The average rate of change of a function A = [tex](f(a) - f(b))/(b-a)[/tex]

Given an exponential function, say f(x), such that f(0) = 1 and f(1) = 2.

A quadratic function, say g(x), such that g(0) = 0 and g(1) = 1.

The rate of change of a function f(x) over an interval a ≤ x ≤ b is given by

[tex](f(a) - f(b))/(b-a)[/tex].

Thus, the rate of change (growth rate) of the exponential function, f(x) over the interval 0 ≤ x ≤ 1 is given by

 = (2-1)/1 = 1

Similarly, the rate of change (growth rate) of the quadratic function, g(x) over the interval 0 ≤ x ≤ 1 is given by

=(1 - 0)/1  = 1

Therefore, the exponential grows at the same rate as the quadratic in the interval 0 ≤ x ≤ 1.

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Answer: The area of the base of the triangular pyramid is given as 15.6 in² and each side of the base is 6 in, so we can use the formula for the area of an equilateral triangle to find the height of the base:

A = (s^2 * sqrt(3)) / 4

where s is the side length of the triangle. Plugging in the values, we get:

15.6 = (6^2 * sqrt(3)) / 4

Solving for the height of the base, h:

h = (4 * 15.6) / (6^2 * sqrt(3)) = 4 / sqrt(3)

Next, we can use the Pythagorean theorem to find the height of the pyramid, since the slant height is given:

h^2 + (base/2)^2 = slant height^2

where base is the length of one side of the base of the pyramid. Plugging in the values, we get:

h^2 + (6/2)^2 = 8^2

Solving for h:

h = sqrt(64 - 9) = sqrt(55)

Finally, the surface area of the pyramid can be found using the formula:

SA = base area + (perimeter * slant height) / 2

where perimeter is the total length of the sides of the base. Plugging in the values, we get:

SA = 15.6 + (3 * 6 * 8) / 2 = 15.6 + 36 = 51.6 in²

So, the surface area of the triangular pyramid is 51.6 in².

Step-by-step explanation:

The angle of least positive measure coterminal with -40 degrees is 320°

Coterminal angles are angles that share the same initial side and the same terminal side.

Since we have our initial angle as -40 degrees.

Let x be the angle of least positive measure coterminal with -40 degrees

We know that to get coterminal angles, we add or subtract 360° to the angle.

So, for a positive coterminal angle, we add 360° to it.

So, x = (-40°) + 360°

Which gives

x = -40° + 360°

x = 320°

So, tha angle is 320°

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Answer:

Option: 4

Step-by-step explanation:

It is in the form of ar^n-1.

For eg:

2nd term/1st term=3rd term/2nd term=4th term/3rd term

There's no need to turn it into a mixed number since 378/9 = 42 is entirely a whole number.

I suppose you could write  42  0/9 or 42 & 0/9 or [tex]42 \frac{0}{9}[/tex], but that isn't really necessary.

The fraction of their money remains for other expenses each month is 5/12.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

Given:

Williams spend 1/3 of their total monthly income for rent and 1/4 for food.

The fraction of their money remains for other expenses each month,

= 1 - 1/3 - 1/4

= 5/12

Therefore, 5/12 is the remaining money.

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The slope of the line represented by the graph of a linear function is  -5/2

The general equation of a straight line is -

y = mx + c

where -

m → slope of line

c → y - intercept of line

here, we have,

Given in a question a linear function that decreases from left to right passing through the coordinates A(0,3) and B(2, -2).

A linear function is a function of general equation → y = ax + b which is same as y = mx + c.

So, it represents a straight line.

The line passes through the points A (0,3) and  B (2, -2).

The Slope of the given line can be calculated using the following formula -

m = (y[2] - y[1]) / (x[2] - x[1])

m = (- 2 - 3) / (2 - 0)

m = -5/2

Therefore, the slope of the line represented by the graph of a linear function is  -5/2.

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(-5, -3), in slope-intercept form, is parallel to the equation -3x - 7y = 10.

Therefore, we must first determine this's slope.

-3x - 7y = 10

To both sides, add three.

-7y = 3x + 10

Add -7 to both sides.

y = -3/7x - 10/7

Our slope is thus -3/7.

The slopes always remain the same when searching for a line that is parallel to something.

Remember that y = mx+b is the slope-intercept form as well.

Where b is the y-intercept and m is the slope.

Our y-intercept is -3 since the coordinates (-5,-3) are available.

The slope here is -3/7.

Put those numbers into the slope-intercept form equation, then, to solve.

y = mx + b

y = -3/7x - 3

(-5, -3), in slope-intercept form, is parallel to the equation -3x - 7y = 10.

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The equation of the line parallel to the given line is y = -3x/7 + 47/7

The equation of the perpendicular will be  y = 7x/3 -13/3

The formula for a straight line is y=mx+c where c is the height at which the line intersects the y-axis, often known as the y-intercept, and m is the gradient.

A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept. Y = mx + c represents the equation of a straight line with gradient m and intercept c on the y-axis.

The slope of a line that is perpendicular to another line is equal to the negative reciprocal of that line's slope. The slope of the original line's perpendicular line is -2, which is the original line's negative reciprocal.

The equation of the line is 3x + 7y = 8

The slope of the line is = -3/7

so the equation of the line parallel to the given line is y = -3x/7 + c

the point given as (4,5)

The line is 5 = -3*4/7 + c

or, c = 5 + 12/7 = 47/7

the equation of the line parallel to the given line is y = -3x/7 + 47/7

The slope of the line perpendicular to the given line is 7/3

So, the equation of the line is y = 7x/3 + c

The intercept is 5 = 7*4/3 + c

or, c = 5 - 28/3 = -13/3

The equation of the perpendicular will be  y = 7x/3 -13/3

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Answer:

A

Step-by-step explanation:

have great day

The required solution of the given differentiation is given as y'(2) = 135/16. Option A is correct.

The method of determining the derivative of an implicit function is by differentiating each term separately, expressing the derivative of the dependent variable as a symbol, and solving the resulting expression for the symbol.

here,
y = [x - 1/x]³
y' = 3[x - 1/x]² × [1 + 1/x²]

put x = 2
y'(2) = 3 [2 - 1/2]² × [1 + 1/4]
y'(2) = 3[3/2]²[5/4]
y'(2) = 27/4 × 5/4
y'(2) = 135/16

Thus, the required solution of the given differentiation is given as y'(2) = 135/16.

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Given that a, b, and c are all equal in a cube, we can calculate the length of each side of the cube by taking the square root of 192, which is 64, and multiplying it by three to get 8.

Add the areas of each of the six rectangular sides of a cuboid to determine its surface area. The cuboid's length, width, and height can also be labelled, and the surface area (SA) can be calculated using the formula SA=2lw+2lh+2hw.

Volume is a three-dimensional measurement that accounts for the sum of a figure's length, breadth, and height. Planes, polygons, and other two-dimensional figures have no volume because they lack a vertical dimension.

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The change will be approximately $100 million by solving through simple algebra.

The use of percentages is widespread and diverse. For instance, percentages are used to convey discounts in stores, bank interest rates, inflation rates, and various statistics in the media. For comprehending the financial aspects of daily life, percentages are crucial.

Divide the whole number by 100, then multiply the result by the requested percentage to find a percentage of the given number: For instance, 12% of 250 equals (250 100) x 12 = 30.

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Answer:

4 4/10 is greater.

Step-by-step explanation:

4 = 40/10

then:

4 4/10 = 4 + 4/10 = 40/10 + 4/10 = (40+4)/10 = 44/10

Then:

44 > 32

44 is greater.

The exponential grows at the same rate as the quadratic in the interval

0 ≤ x ≤ 1.

The average Rate of Change function is defined as the average rate at which one quantity is changing with respect to something else changing. In simple terms, an average rate of change function is a process that calculates the amount of change in one item divided by the corresponding amount of change in another.

The average rate of change of a function A = [tex](f(a) - f(b))/(b-a)[/tex]

Given an exponential function, say f(x), such that f(0) = 1 and f(1) = 2.

A quadratic function, say g(x), such that g(0) = 0 and g(1) = 1.

The rate of change of a function f(x) over an interval a ≤ x ≤ b is given by

[tex](f(a) - f(b))/(b-a)[/tex].

Thus, the rate of change (growth rate) of the exponential function, f(x) over the interval 0 ≤ x ≤ 1 is given by

 = (2-1)/1 = 1

Similarly, the rate of change (growth rate) of the quadratic function, g(x) over the interval 0 ≤ x ≤ 1 is given by

=(1 - 0)/1  = 1

Therefore, the exponential grows at the same rate as the quadratic in the interval 0 ≤ x ≤ 1.

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Answer:

B

Step-by-step explanation:

The politician experience 16% of actual change and 47% relative change in his support.

Actual change refers to the simple difference between the ending and initial condition. In this case, actual change is the gap of the politician's support increase. The actual change of the politician's support is:

Actual change = Ending% - Initial %

Actual change = 50% - 34%

Actual change = 16%

Relative change is the percentage change between ending and initial condition based on the perspective of the initial condition. Relative change measures the gap between the ending and initial conditions compared to the initial condition. Relative change can be calculated by dividing the gap of 2 conditions with the initial condition.

The relative change of politician's support is:

Relative change = Ending% - Initial %

                                    Initial %

Relative change = 50% - 34%

                                    34%

Relative change = 47%

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The equation of line having a slope of 2 and passing through the point (1,4) is y = 2x + 2.

The formula for equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

Given that the line has a gradient of 2 and passes through the point (1, 4).

Plug the given values into the point-slope formula and solve for y.

y - y₁ = m( x - x₁ )

y - 4 = 2( x - 1 )

y - 4 = 2x - 2

Add 4 to both sides of the equation

y - 4 + 4 = 2x - 2 + 4

y = 2x - 2 + 4

y = 2x + 2

Therefore, the equation of the line is y = 2x + 2.

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Answer:

5/2 or 2.5

Step-by-step explanation:

Divide both sides by 2.

The line could contain A'B' is 3x+2y=10, so correct option is (a).

It usually consists of variables, coefficients, and constants, connected by operations such as addition, subtraction, multiplication, and division. Equations are used to model relationships between different quantities and to solve problems in various fields such as physics, engineering, and economics. For example, the equation y = mx + b represents a straight line in two-dimensional space, where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept.

The line 2x + 3y = 5 contains AB, so AB lies on the line 2x + 3y = 5. To dilate triangle ABC to A'B'C, the center of dilation is a fixed point and the scale factor is a constant. Since AB lies on the line 2x + 3y = 5, the line containing A'B' after dilation must be parallel to the line 2x + 3y = 5, so the correct answer is (a) 3x + 2y = 10.

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The total number of students in the class given the percentage of unhappy students is 263 students.

Percentage of unhappy students= 7.23%

Number of unhappy students= 19

Total number of students in class= x

Number of unhappy students = Percentage of unhappy students × Total number of students in class

19 = 7.23% × x

19 = 0.0723 × x

19 = 0.0723x

divide both sides by 0.0723

x = 19/0.0723

x = 262.7939142461964

Approximately,

x = 263 students

Therefore, there are 263 students in the class.

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Answer: i don't know give me more info

Step-by-step explanation:

The value of x is 11 for the given condition that m||n.

Parallel lines are any two or more lines that all lie in the same plane and never cross one another. They are equally spaced apart and have the same incline.

Numerous pairs of angles are created whenever any two parallel lines are intersected by a third line known as a transversal. The other angles are supplementary while some are congruent (equal).

Angles on a straight line sum up 180°

Let us take the line t as our straight line

(7x – 1)° + (9x + 5)° = 180°

(7x + 9x + 5 – 1) = 180

16x + 4 = 180

16x = 180 – 4

16x = 176

(16x)/16 = (176/16)

x = 11

Hence, the value of x is 11.

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Algebraic Expression for the table of Nora, Nora's brother and Mother would be x, x-4 and 4x.

What is Algebraic Expression?

An algebraic expression is when we use numbers and words in solving a particular mathematical question.

Let x be Nora's age. Then Nora's brother is x - 4 years old, and Nora's mother is 4 * x years old.

The algebraic expression for the table is:

Nora: x

Nora's Brother: x - 4

Nora's Mother: 4x

Therefore, The Algebraic Expression for the table of Nora, Nora's brother and Mother would be x, x-4 and 4x.

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The equations are 4x - y - 2 = 0 and x + 3y + 6 = 0. The solution has been obtained using two-point form.

What is two-point form?

One of the crucial forms for algebraically representing a straight line is the two-point form. Each and every point on a line fulfils the equation for that line, making it the representation of the entire line.

We are given two lines on the graph

Both the lines meet on the y-axis at (0,-2)

This means (0,-2) is the common solution.

Another point of the steeper line is (1,2)

Another point of the flatter line is (3,-3)

Now, as we know the two points of the line, using the two-point form, we get

[tex]\frac{y - y_{1}}{x-x_{1} } = \frac{y_{2} - y_{1}}{x_{2} -x_{1} }[/tex]

⇒ (y+2)/(x-0) = (2+2)/(1-0)

⇒ y+2 = 4x

⇒ y = 4x-2

⇒ 4x - y - 2 = 0

Similarly,

⇒ (y+3)/(x-3) = (-2+3)/(0-3)

⇒ (y+3)/(x-3) = -1/3

⇒ (y+3) = -(x-3)/3

⇒ y+3 = -x/3 + 1

⇒ y = -x/3 - 2

⇒x + 3y + 6 = 0

Hence, the equations are 4x - y - 2 = 0 and x + 3y + 6 = 0.

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Since there are multiple questions so, the question answered above is attached below

Answer: n= 4

Step-by-step explanation:

n+10=2(n+6) where n represents the number

you solve this.

n+10=2n+6

n+10-6=2n

n+4=2n

n=4

Answer:

b=8

Step-by-step explanation:

5(b-1)=30

5b-5=35

5b=40

b=8

The value for b is 7.

A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:

Given:

Darryl had 5 boxes of books with b books in each box.

If one 1 book remove from each box then total number of books

= (b-1) +  (b-1) +  (b-1) +  (b-1) +  (b-1)

= 5(b-1)

and, After giving away 1 book from each box, he had 30 total books left.

Then, 5(b-1)= 30

b-1 = 6

b = 7

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The total surface area painted black = 56.5 square feet to the nearest tenth.

A cone is a three-dimensional geometric form with a flat base and a smooth, tapering apex or vertex. A cone is made up of a collection of line segments, half-lines, or lines that link the base's points to the apex, which is a common point on a plane that does not include the base.

Given that, three large cones hang from the ceiling in an office building in front of a bank of windows.

The height of each cone is 12 feet, and the circumference of the base of each cone is 8π feet.

The base and 40% of the lateral surface of each cone is painted red, and the rest of each cone is painted black.

Circumference of the base of the cone = 8π feet.

2πr = 8π

πr = 4π

The surface area of the cone = πr x slant height

Slant height = [tex]\sqrt{radius^2+height^2}[/tex]

= √12²+4² = 12.6 ft

The surface area of the cone = 12.6 x 4π

The surface area of the cone = 60π.

The lateral surface area painted black = 30% of 60π.

Therefore, The total surface area painted black = 56.5 square feet to the nearest tenth.

Hence, the required area is 56.5 square feet.

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Answer:

Well, it depends, but I'd reckon kilograms.

Step-by-step explanation:

2.2 pounds is approximately 0.998 kg, which can be rounded off to 1 kg. However, you really do have to be precise, you may measure it in grams (that's, 998 grams).

So, the most appropriate way is to use 1 kilogram, as a hailstone can be considered quite heavy and we may not be keen on looking for a really precise measurements, as they're measured in hundreds of grams!
Hope this helps :)

From the graph, the coordinates of the points of the equation y=(x-1)(x-3): (1,0) (4,0), P(0,3) and turning point (2.5,2)

You should know that these are possible reading from the graph

The scale of the graph is [laced at 1 com to 1 unit on both axes

From the graph, the coordinates of A are (1, 0) This is where x=1 and y=0

The coordinates of B = (4, 0) This is where x=4 and y=0

b)  The coordinates of point P are (0,3) This is where x=0 and y= 3

c) The coordinates of the turning point are (2.5, 2) This is the minimum value of the curve

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