Work out the equation of the line which has a gradient of 2 and passes through the point (1, 4)

On solving the provided question, we can say that Therefore, the function has an average rate of change of -1.

The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.

The function has an average rate of change of -1.

R = 4-5/1-0

R = -1

Therefore, the function has an average rate of change of -1.

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The required area of the shaded region is 11.5 sq. units

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.

Given is a circle with center T and radius 3 units. there is a region in the circle which is shaded, we need to find that area.

So, the shaded part is composed of a right triangle and a minor sector of the circle.

To find the area of the shaded portion, we will add the area of right triangle and a minor sector

Now, area of a triangle = 1/2 × base × height

Here, base = height = radius = 3 units

And,

Area of a sector = θ/360° × π × radius²

Where, θ is the central angle.

θ = 90°

Area of the shaded region = 1/2 × 3 × 3 + 90°/360° × 3.14 × 3²

= 9/2 + 7.065

= 11.565

Hence, the required area of the shaded region is 11.5 sq. units

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Answer: The mass of one mole of a substance is equal to its molar mass in grams. The molar mass of a substance is the mass of one mole of that substance and is usually expressed in atomic mass units (amu) or grams per mole (g/mol).

One mole of a substance contains Avogadro's number of particles, which is approximately 6.022 x 10^23.

Since the mass of one doughnut is given in grams (74 g), we can assume that this is the molar mass of the substance in question. So, the mass in grams of one mole of the substance is:

Mass of one mole = 74 g

So, the answer to two significant figures is:

Mass of one mole = 74 g (rounded to two significant figures).

Step-by-step explanation:

The correct value of the measure of the exterior angle is 72 degrees

You should understand that when one side of a polygon is produced, the angle so formed is called an exterior angle

Note also that two opposite interior angles equal to one exterior angle

This implies that

x+30=2x-12

Collecting like terms

x-2x=-12-30

-x=-42

the value of x is 42

Then substitute x for the exterior angle

2(42)-12

84-12 = 72

The exterior angle is 72 degrees

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Answer:

x<-5

Step-by-step explanation:

-(2+2x)-2>6

-(2+2x)>8

2+2x<-8

2x<-10

x<-5

When triangle ABC is dilated to triangle A'BC then the line A'B' has the equation 2z+ 3y = 10.

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. No matter how far we extend a parallel line, it will never meet another parallel line.

Given that the triangle ABC is dilated to get the triangle A'BC.

If the triangle is dilated then, AB is parallel to A'B'.

So, the slopes of the two line are equal.

The equation of the AB is 2x + 3y = 5.

Converting into the standard equation of line:

y = - 2/3 x + 5/3

The slope of the line is -2/3.

From the given options, the line that has slope -2/3 when converted to standard form is:

2z+ 3y = 10

Hence, when triangle ABC is dilated to triangle A'BC then the line A'B' has the equation 2z+ 3y = 10.

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Answer:

f(x)= (X+5)^2

Step-by-step explanation:

pls, tell me if wrong have a good day/night<3

The value of {x} is equivalent to +55.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is that -

" - {-(x)} is 55 units to the right of 0".

It is given that -

- {-(x)} = {x}                                 ..... ( 1 )

We can rewrite -

{x} is 55 units to the right of 0.

As an equation, we can write -

0 + 55 = {x}

{x} = + 55

Therefore, the value of {x} is equivalent to +55.

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Answer:350

Step-by-step explanation: 280/4=70

280+70=350

Answer:

350

Step-by-step explanation:

The percentage is converted to decimal place and then multiplied by 280

[tex]280(\frac{125}{100} )=280(1.25)=350[/tex]

Hope this helps.

Answer: 7.34375

Step-by-step explanation:

Answer step bby step:

1. Isolate the variable:

1/5(4x - 2.5) = 5(0.4x + 10) + 3 1/2

5(0.4x + 10) + 3 1/2 = 1/5(4x - 2.5)

2. Multiply both sides by 5:

2(0.4x + 10) + 3 1/2 = 4x - 2.5

3. Subtract 2(0.4x + 10) from both sides:

3 1/2 = 4x - 2(0.4x + 10)

4. Subtract 3 1/2 from both sides:

0 = 4x - 2(0.4x + 10) - 3 1/2

5. Distribute the -2 to the parentheses:

0 = 4x - 0.8x - 20 - 3 1/2

6. Combine like terms:

0 = 3.2x - 23.5

7. Divide both sides by 3.2:

x = 7.34375

The statement "the sum of measures of angles B and A is 130 degrees" is  correct. Therefore, option A, B and E are the correct answer.

An isosceles trapezoid can be defined as a trapezoid in which non-parallel sides and base angles are of the same measure. In other words, if two opposite sides (bases) of the trapezoid are parallel, and the two non-parallel sides are of equal lengths, then it is an isosceles trapezoid.

Given that, an isosceles trapezoid ABCD has two parallel sides AB and CD and m∠A = 65°.

Correct statements are

The sum of measures of angles B and A is 130 degrees.

The measure of angle D is 115 degrees.

The sum of measures of angles B and C is 180 degrees.

Therefore, option A, B and E are the correct answer.

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Answer:

9:8

Step-by-step explanation:

We know that 72:64

If you multiply 9 by 8 you get 72, so you know that the answer will have to be simplified by 8.

64/8 = 8

Therefore your answer for this will be 9:8

The given trigonometric equation is csc²x-1 =cotx/tanx is proved LHS=RHS.

A trigonometric equation is one that involves one or more of the sixs sine, cosine, tangent, cotangent, secant, and cosecant. Some trigonometric equations, like x = cos x, can be solved only numerically, through successive approximations.

The given trigonometric equation is csc²x-1 =cotx/tanx.

Here, csc²x-1 =cosx/sinx ÷ sinx/cosx

csc²x-1 =cosx/sinx × cosx/sinx

csc²x-1 =cos²x/sin²x

csc²x-1 =cot²x

We know that, cot²x+1=csc²x

So, cot²x=cot²x

Hence, proved LHS=RHS.

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The updated median is 56.37 and the updated IQR is 17.66.

The median is the value in the middle of a data set, meaning that 50% of data points have a value smaller or equal to the median and 50% of data points have a value higher or equal to the median. For a small data set, you first count the number of data points (n) and arrange the data points in increasing order.

Given that, one employee recorded the measurements for the lengths of 55 different wood boards.

Median =58.37 and IQR=19.66

Someone discovers the measuring tape used started at 2 inches instead of 0.

The interquartile range is given by the difference between the 75th percentile(value that is greater than 75% of the measures) and the 25th percentile.

This means that each piece of wood is actually 2 inches shorter than the value recorded by the employee.

This means that the length of each wood is less than 5. However, the difference between the 75th percentile and the 25th percentile will stay the same, since both were subtracted by 2.

So, IQR=19.66-2 =17.66

Therefore, the updated median is 56.37 and the updated IQR is 17.66.

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[tex]\displaystyle \lim_{x\to -4}~\cfrac{~~ \frac{1 }{4 }+\frac{1}{x} ~~}{4+x} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{~~ \frac{1 }{4 }+\frac{1}{x} ~~}{4+x}\implies \cfrac{~~ \frac{4+x}{4x} ~~}{4+x}\implies \cfrac{~~ \frac{4+x}{4x} ~~}{\frac{4+x}{1}}\implies \cfrac{4+x}{4x}\cdot \cfrac{1}{4+x}\implies \cfrac{1}{4x} \\\\[-0.35em] ~\dotfill\\\\ \displaystyle \lim_{x\to -4}~\cfrac{1}{4x}\implies \cfrac{1}{4(-4)}\implies -\cfrac{1}{16}[/tex]

The boat speed in still water is 2 km/hr.

Speed is a measure of how fast an object is moving. It is defined as the distance traveled by an object in a given amount of time. Speed is a scalar quantity, meaning it only has magnitude and does not have direction. It is typically expressed in units of distance per time, such as meters per second (m/s) or miles per hour (mph). The formula for speed is speed = distance / time. It is important to distinguish speed from velocity, which is a vector quantity that includes both magnitude (speed) and direction.

The formula to calculate the speed of the boat in still water is:

speed = distance / (time up + time down)

To use this formula, we first need to find the distance traveled upstream and downstream. Let's assume that the distance traveled upstream and downstream is the same, so we can use the average of the two times: (30 min + 10 min) / 2 = 20 min.

Next, we need to convert the time to hours. 20 minutes is equal to 20/60 = 1/3 hours.

Now, let's calculate the distance using the current speed of 2 km/hr:

distance = current speed * time

distance = 2 km/hr * 1/3 hours = 2/3 km

Finally, we can use the formula to calculate the boat speed:

speed = distance / time = 2/3 km / (1/3 hours) = 2 km/hr

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The point (-2 3/4, -4 1/2) is plotted below.

Coordinates are the set of points in a geometrical plane or space, which is used to denote the exact point in the coordinate plane or space.

The given point is (-2 3/4, -4 1/2).

Both the coordinates are in the mixed number form.

-2 3/4 = -(2 × 4 + 3) / 4 = -11/4 = -2.75

-4 1/2 = -(4 × 2 + 1) / 2 = -9/2 = -4.5

So the point is (-2.75, -4.5).

Hence the given point is (-2.75, -4.5) which is marked in the coordinate plane as shown below.

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An equation of the line that passes through the point (1, -3) and has a slope of -3 in slope-intercept form is y = 2x + 3.

Mathematically, the standard form of the equation of a straight line is given by this mathematical expression;

y = mx + c

Where:

Next, we would determine the slope of this straight line by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (15 - 3)/(2 - (-4))

Slope (m) = 12/6

Slope (m) = 2.

Therefore, the equation in slope-intercept form is given by:

y = mx + c

y = 2x + 3

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105 watts

The middle wattage is found by taking the average of the highest and lowest wattages. To find the average, you add the two numbers together and then divide by 2. In this case, the lowest wattage is 60 and the highest is 150, so when we add these two numbers together, we get 210. Then, when we divide 210 by 2, we get 105. So the middle wattage is 105 watts.

Answer: 30 cars left

Step-by-step explanation:

if from 33 cars we subtract 3, we get 30 cars left.

33 - 3 = 30 ...answer

hope that helps...

Answer:  x = 7

Step-by-step explanation:

    [tex]\frac{2x}{7} =\frac{6}{3}[/tex]

we cross multiply, we get

2x(3) = 6(7)

   6x = 42

     x = 7

The required volume of the given right rectangular prism is 2x³ - 4x² cubic units.

Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.

here,
From the figure,
Volume = length × width × height
            = [2x - 4] × x × x
            = [2x³ - 4x²]

Thus, the required volume of the given right rectangular prism is 2x³ - 4x² cubic units.

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The total surface area painted black is 50.2 square feet.

Let's call the radius of the base of the cone r. We can find it using the formula for the circumference of a circle:

C = 2πr

8π = 2πr

r = 4

Next, let's find the slant height of the cone, which is the distance from the tip of the cone to the base along a straight line that passes through the center of the base. We can use the Pythagorean theorem:

s^2 = r^2 + h^2

s^2 = 4^2 + 12^2

s^2 = 16 + 144

s^2 = 160

s = sqrt(160) = 12.8

Next, let's find the surface area of one cone. The surface area of a cone is equal to π times the radius of the base times the slant height, plus π times the radius of the base squared:

A = πr * s + πr^2

A = π * 4 * 12.8 + π * 4^2

A = 50.24 + 16π

A = 50.24 + 50.24

A = 100.48

Since the base and 50% of the lateral surface of each cone is painted red, that means 50% of the surface area is painted black:

black_area = 0.5 * 100.48

black_area = 50.24

Rounding to the nearest tenth, the total surface area painted black is 50.2 square feet.

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Answer:

The shelf should be 0 degrees relative to the floor.

Step-by-step explanation:

When an object is parallel to the floor, it means that it is aligned with the floor at the same angle and does not slope up or down.

In other words, the angle between the shelf and the floor is 0 degrees.

So, to attach the shelf so that it is parallel to the floor, Dana should ensure that the angle between the shelf and the floor is 0 degrees.

The answer is 506 not to sure since I haven't done this in a while

Answer:

506

Step-by-step explanation:

According to the order of operations(or PEMDAS), you would first evaluate the exponent in the problem: [tex]8^3[/tex]. [tex]8^3[/tex] is equivalent to [tex]8*8*8[/tex], which is just 512. Therefore, the equation would now be 512 - 9 * 2 ÷ 3

Next step would be to do out the multiplication and division left to right. First is 9 * 2 which is 18. Then that is divided by three to get 6. The equation would now be 512 - 6.

512 - 6 is just 506.

The scatterplot of the residuals should display random scatter if a linear model is suitable, and the histogram should appear about normal.

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As per the natural tendency of cooling with temperature the rate of decrese in temperature is also decresing so the cooling of a soup cannot be described by a linear model.

A relationship that has one output for each input value (x-value) is called a function (y-value). All functions are hence relations. However, not all relationships are functions since not every relationship will satisfy the condition that every distinct input generates just one output.

Check to see if there is a horizontal asymptote or an oblique asymptote by comparing the degrees of the numerator and denominator to the function's end behavior. Plot the asymptotes that are horizontal or oblique.

As per the natural tendency of cooling with temperature the rate of decrese in temperature is also decresing so the cooling of a soup cannot be described by a linear model.

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Answer:

60.48

Step-by-step explanation:

Answer:51.52

Step-by-step explanation:

Answer:

7. √149 ft or 12.2 ft

8. 5√2 m or 7.07 m

9. √36.75 in. or 6.06 in.

Step-by-step explanation:

7.

a² + b² = c²

7² + 10² = x²

49 + 100 = x²

x² = 149

x = √149

x ≈ 12.2

Answer: √149 ft or 12.2 ft

8.

perimeter = 20 m

side = perimeter/4 = 5 m

a² + b² = c²

5² + 5² = x²

25 + 25 = x²

x² = 50

x = 5√2

Answer: 5√2 m or 7.07 m

9.

a² + b² = c²

3.5² + x² = 7²

12.25 + x² = 49

x² = 49 - 12.25

x² = 36.75

x = √36.75 = 6.06

Answer: √36.75 in. or 6.06 in.

Answer:

  7.  12.2 ft

  8.  7.07 m

  9.  6.06 in

Step-by-step explanation:

You want the hypotenuse of at right triangle with legs 7 and 10 ft, the diagonal of a square with perimeter 20 m, and the altitude of an equilateral triangle with side length 7 inches.

These problems all make use of the Pythagorean theorem, which tells yo the relation between sides a, b and hypotenuse c of a right triangle is ...

  a² +b² = c²

The length of the leash (c) is ...

  c² = (7 ft)² +(10 ft)² = 149 ft²

  c = √149 ft ≈ 12.2 ft

The leash is about 12.2 feet long.

Each side of the square is 1/4 of the perimeter, so is 5 m. The diagonal is the hypotenuse of a right triangle with legs that length. Its measure is ...

  c = √(5² +5²) = 5√2 ≈ 7.07 . . . . meters

The length of the diagonal is about 7.07 meters.

The altitude of an equilateral triangle is a perpendicular bisector of one side. Its length is ...

  b = √(c² -a²)

  b = √(7² -3.5²) = √36.75 ≈ 6.06 . . . . inches

The altitude of the triangle is about 6.06 inches.

__

Additional comment

The triangles of problems 8 and 9 are known as the two "special" right triangles.

The side lengths of an isosceles right triangle (angles 45°-45°-90°) have the ratios 1 : 1 : √2.

The side lengths of a triangle with angles 30°-60°-90° have the ratios 1 : √3 : 2.

That is, the diagonal of the square is √2 times its side length, and the altitude of the equilateral triangle is (√3)/2 times is side length.

It can be useful to remember these triangles and their side ratios.

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Answer:

2x+3 i think

a)

C = 23.8°C

b)

F = 113°F

c)

F = -4°F

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

a) 75°F

b) 45°C

c) -20°C

Conversion formulas:

C = (F - 32) / 1.8

F = 1.8C + 32

Now,

75°F

C = (F - 32) / 1.8

C = (75 - 32) / 1.8

C = 23.8°C

45°C

F = 1.8C + 32

F = 1.8 x 45 + 32

F = 113°F

-20°C

F = 1.8C + 32

F = 1.8 x (-20) + 32

F = -4°F

Thus,

The temperature conversion is given above.

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