Find the equation of the line shown.

Answer:

Step-by-step explanation:

first we can turn these mixed fractions into normal numbers so

1.42<.336 FALSE

.54>1.357 false

.615>.96 false

1.16>1.83 TRUE

The numeric values for the functions are given as follows:

6 - a) f(-2) = -13.

6 - b) g(4) = 11.

To find the numeric value of a function, we replace each instance of the variable by the desired value.

At item 6a, the function is given by:

f(x) = 5x - 3.

The numeric value at x = -2 is:

f(-2) = 5(-2) - 3 = -10 -3 = -13.

Hence f(-2) = -13.

At item 6b, the function is given by:

g(x) = 0.5x² + 3.

The numeric value at x = 4 is:

g(4) = 0.5(4)² + 3 = 8 + 3 = 11.

Hence g(4) = 11.

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The dimensions of the rectangle that has the perimeter 134 inches is, 52 x 15 inches.

Perimeter of the Rectangle:

Perimeter of the rectangle is defined as the total distance covered by its boundaries or the sides.

The formula for the perimeter of a rectangle,

P = 2 (a + b) units

where

“a” is the length of the rectangle

“b” is the breadth of the rectangle

Given,

The length of a rectangle is seven more than triple the width.

Perimeter of the rectangle = 134inches.

Now we need to find the dimensions of the rectangle.

First, let's define the length of the rectangle as l and the width of the rectangle as w.

Next, we can write the relationship between the length and width as:

l = 3w + 7

We also know the formula for the perimeter of a rectangle is:

=> p = 2(l + w)

So, apply the given values on it,

=> 134 = 2 (3w + 7 + w)

=> 134/2 = 4w + 7

=> 67 = 4w + 7

=> 67 -7 = 4w

=> 4w = 60

=> w = 60/4

=> w = 15

So, the length is,

=> l = 3(15) + 7

=> l = 45 +7

=> l = 52.

Therefore, the dimensions of the rectangle is 52 x 15 inches.

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Answer:

174

Step-by-step explanation:

absolute value means the distance from zero.  Distance is always measured with a positive number.  If you asked me how far I lived from my work, I would never say -12 miles away.  If I was going or coming to work, the distance would be the same 12 miles.

134 + 4 + 35 = 174

The width of rectangle is 5 feet.

Let us assume the length of rectangle to be x. So, the width of rectangle will be (x - 3).

Now, as per the known fact, perimeter, length and width of rectangle are related by the formula -

Perimeter = 2 × (length + width)

Keep the values in formula to find the value of width

26 = 2 × (x + x - 3)

Performing addition of variables inside the bracket

26 = 2 × (2x - 3)

Shifting 2 to other side of equation to find the value of x

2x - 3 = [tex]\frac{26}{2}[/tex]

Performing division to find the value of x

2x - 3 = 13

Shifting 3 to other side of equation to find the value of x

2x = 13 + 3

Performing addition to find the value of x

2x = 16

Shifting 2 as denominator to other side of equation to find the value of x

x = [tex]\frac{16}{2}[/tex]

Performing division to find the value of x

x = 8

So, length of rectangle is 8 feet

Width of rectangle = x - 3

Width of rectangle = 8 - 3

Width of rectangle = 5 feet

Hence, the width of rectangle is 5 feet.

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26.27 kgm⁻³

Density is the ratio of  mass to volume

Density = Mass / Volume

Let us assume tree is a cylinder,

d= 1

r = d/2 = 0.5 m

h= 20 m

m= 420kg

Volume = π r²h

              = 22/7 x o.25 x 20

Density = mass / volume

              = 420 / 22/7 x o.25 x 20

              = 26.27 kgm⁻³

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Angle 5 = 180 - 146 = 34

Angle 6 = 146 since vertical angles are congruent

Angle 7 = 34 since vertical angles are congruent, or you could say 180-146 = 34 again. Any pair of adjacent angles add to 180. All four angles add to 360.

Answer:

Step-by-step explanation:

We can start by solving for t using the fact that  [tex]cos(t) = \frac{2}{9}[/tex].

[tex]t = cos^{-1}(\frac{2}{9}) = 77.16\\[/tex]

then using that value of t solve for sin(t)

sin(t) = 0.975

As cos(t) is given and t is in the first quadrant then sin(t) will be equal to 8.77/9.

If a mathematical operation includes at least two words that are connected by an operator and either comprise numbers, variables, or both, it is referred to as an expression.

The operations with reflection coefficients include adding, subtracting, multiplying, and dividing. In order to include terms in an expression, a mathematical operation like reduction, addition, multiplication, or division is used.

As per the information in the question,

cos(t) = 2/9

As we know that cos θ = B/H

B = 2 and H = 9

Now, use Pythagoras's theorem,

H² = P² + B²

P² = 9² - 2²

P = √77

P = 8.77

We also know that sin θ = P/H

So, sin(t) = 8.77/9

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Answer:

Step-by-step explanation:

Answer:

The surface area is the sum of all the faces (or surfaces) of a 3D shape. Composite figures are 2 figures put together. (There is an example of a composite figure below) You find an area of both shapes and then add them together, to find the area of the full figure.

Step-by-step explanation:

The value of the quantity d is 0.0462 m^2/s.

Here,

The quantities a=3.7m, b=3.7s, c=80m/s.

We have to find the value of d = a^3/cb^2

What is quantity?

A quantity is an amount, number, or measurement that answers the question 'how much?' Quantities can be expressed in numbers or non-standard units.

Now,

The quantities a=3.7m, b=3.7s, c=80m/s.

The value of d;

[tex]d = \frac{a^{3} }{cb^{2} }[/tex]

[tex]d = \frac{3.7*3.7*3.7 }{80 * 3.7^{2} }[/tex]

[tex]d = \frac{3.7}{80}[/tex]

[tex]d = 0.0462[/tex]

Hence, The value of the quantity d is 0.0462 m^2/s.

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Answer:

not sure what you were asking, but its 15 cups of purple paint

Speed is the constant of proportionality for the relationship between distance and time.

Relationship between these two values is distance is directly proportional to time .

As given,

Distance =400 kilometers

Time=8 hours

Let s, d, and t represents speed, distance and time.

Speed = d / t

           = 400/8

           = 50 km/ hour

           = constant

Hence ,

d = 50t

⇒ d ∝ t

Therefore, speed is the constant of proportionality for the relationship between distance and time.

Relationship between these two values is distance is directly proportional to time .

The complete question is:

An albatross is a large bird that can fly 400 kilometers in 8 hours at a constant speed. using for distance in kilometers and for number of hours, an equation that represents this situation d=50t.

What are two constants of proportionality for the relationship between distance in kilometers and number of hours? What is the relationship between these two values?

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Answer:

x + 2x - 3 = 26

Step-by-step explanation:

Define the variables:

If Maya's car is 3 inches less than 2 times the length of Nate's car, then:

⇒ y = 2x - 3

If the sum of the lengths of both cars is 26 inches, then:

⇒ x + y = 26

Substitute the found expression for y into the equation:

⇒ x + y = 26

⇒ x + (2x - 3) = 26

⇒ x + 2x - 3 = 26

Therefore, the equation to determine the lengths of Nate'a and Maya's cars is:

[tex]\boxed{x + 2x - 3 = 26}[/tex]

Solving the equation for x

⇒ x + 2x - 3 = 26

⇒ 3x - 3 = 26

⇒ 3x - 3 + 3 = 26 + 3

⇒ 3x = 29

⇒ 3x ÷ 3 = 29 ÷ 3

⇒ x = 9.7 in (nearest tenth)

Therefore, Nate's car is 9.7 in (nearest tenth).

To find the length of Maya's car, subtract the length of Nate's car from 26:

⇒ 26 - 9.7 = 16.3 in (nearest tenth).

Therefore, Maya's car is 16.3 in (nearest tenth).

Answer:

d) x + 2x - 3 = 26

Step-by-step explanation:

Given that,

→ Maya's car is 3 inches less than 2 times the length of Nate's car.

→ The sum of the lengths of both cars is 26 inches.

Now the equation will be,

→ x - 3 + 2x = 26

→ x + 2x - 3 = 26

→ 3x = 29

Hence, option (d) is correct answer.

Step-by-step explanation:

You want to demonstrate the identity ...

  (1-tan⁴(A))·cos⁴(A) = 1 -2·sin²(A)

Working with the left side, we have ...

  [tex](1-\tan^4(A))\cos^4(A)=1-2\sin^2(A)\\\\(1-\dfrac{\sin^4(A)}{\cos^4(A)})\cos^4(A)=1-2\sin^2(A)\qquad\text{use tangent identity}\\\\\cos^4(A)-\sin^4(A)=1-2\sin^2(A)\qquad\text{multiply it out}\\\\(\cos^2(A) +\sin^2(A))(\cos^2(A)-\sin^2(A))=1-2\sin^2(A)\qquad\text{factor}\\\\1((1-\sin^2(A))-\sin^2(A)) = 1-2\sin^2(A)\qquad\text{use $\cos^2$ identity}\\\\1-2\sin^2(A)=1-2\sin^2(A)\qquad\text{Q.E.D.}[/tex]

__

Additional comment

The referenced identities are ...

  tan = sin/cos

  cos² = 1 -sin²

and the factorization of the difference of squares:

  a² -b² = (a +b)(a -b).

Answer:

It's the graph with two dots and no area marked, first image (for me).

Step-by-step explanation:

|x| = 1 means "the distance from x to the 0 point on the axis is exactly 1". There's only 2 numbers x that satisfy that condition: -1 and 1

The second and third image both show an area marked, so it cannot be the right answer, while the first image shows precisely two numbers: -1 and 1

Answer: 51.33

Step-by-step explanation:

7+8.75+12.5+15.33+7.75 = 51.33

For the following equation of the line: y = (1/5)x + 1, y = (1/5)x + 5, y = 5x + 1, and y = 5x + 5, the line that is perpendicular to it and has the same y - intercept is: y = -5x + 1, y = -5x + 5, y = (-1/5)x + 1, and y = (-1/5)x + 5, respectively.

If two equations of the line are perpendicular with each other, then their slopes are negative reciprocal of one another.

To generate the equation of the line perpendicular to the given lines, with the same y-intercept,

1. Get the slope of each line and determine its y-intercept

2. Take the negative reciprocal of the slope and use it and the same y-intercept to get the equation.

y = (1/5)x + 1

slope = 1/5

y-intercept = 1

perpendicular line :

slope = -5

y-intercept = 1

equation : y = -5x + 1

y = (1/5)x + 5

slope = 1/5

y-intercept = 5

perpendicular line :

slope = -5

y-intercept = 5

equation : y = -5x + 5

y = 5x + 1

slope = 5

y-intercept = 1

perpendicular line :

slope = -1/5

y-intercept = 1

equation : y = (-1/5)x + 1

y = 5x + 5

slope = 5

y-intercept = 5

perpendicular line :

slope = -1/5

y-intercept = 5

equation : y = (-1/5)x + 5

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Answer:

C     y = 5x + 1

Step-by-step explanation:

Took the test on edu

The slope of the line is -10/9 and the value of y-intercept of the line is 50/3.

Slope of the line:

A slope of a line is the change in y coordinate with respect to the change in x coordinate.

Given,

The point (9,10) that cuts off the least area from the first quadrant

Here we need to find the slope and y intercept of the line.

A line is passing through a point (9,10) cuts off least area in first quadrant.

The equation of the line passing through point (9,10) and has slope m can be expressed as,

=> y - 10 = m (x - 9)

=> y = m(x - 9) + 10

=> y - mx = - 9m + 10

Divide the terms by - 9m + 10, then we get,

=> (y/- 9m+10) - (mx/ - 9m+10) = 1

=> (mx/9m+10) - (y/9m+10) = 1

It can be rewritten as,

[tex]\implies\frac{x}{\frac{9m-10}{m}} -\frac{y}{10-9m}[/tex]

We know that,

The equation of straight line in intercept form is

=> x/a + y/b = 1

So, the intercept made by the line on x-axis i.e. a and on y-axis i.e. b are:

a = 9m-10/m

b =  10 - 9m

The area of the triangle made by the line in first quadrant can be expressed as,

=> A = 1/2 x (9m-10/m) x (10 - 9m)

=> A = -1/2 (9m-10)²/m-----------------------(1)

Differentiate the equation (1) with respect to m.

[tex]\frac{dA}{dm}=-\frac{1}{2}[\frac{2m(9m-10).9-(9m-10)^2}{m^2}][/tex]

[tex]\frac{dA}{dm}=-\frac{9m-10}{2m^2}[2m.9-(9m-10)][/tex]

[tex]\frac{dA}{dm}=-\frac{9m-10}{2m^2}[18m-9m-10)][/tex]

when we simplify it,

=> dA/dm = -(9m-10)/2m² [9m-10]

Let dA/dm = 0, then

=> 0 = -1/2m² (9m-10)(9m-10)

=> 0 = 1/m² (10-9m)(9m-10)

=> 0 = (10 - 9m) (9m -10)

Therefore, the value of m is,

=> 10 - 9m = 0

=> -9m = -10

=> m = 10/9

And

=> 9m - 10 =0

=> 9m = 10

=> m = 10/9

The line will be in first quadrant and forms a triangle with axes if the slope is negative.

Substitute m = -10/9

Then, b = 10-9m

Then,

=> y = 10 - 6(-10/9)

=> y = 10 + 20/3

=> y = 50/3

So, the slope of the line is -10/9 and the value of y-intercept of the line is 50/3.

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Answer:

Step-by-step explanation:

x = -3 to 3

means that they are asking for the graph from -3 to 3 on the x-axis

gradient is (-1/2) which means rise is -1 when run is 2

y-intercept is 3.

go to 3 on the y axis which means the coordinate (0,3) go downwards by 1 and to the right by 2. This will lead you to coordinate (2,-1). Now connect both points by a straight line.

Answer:

70.42 kilometers.

Step-by-step explanation:

43 minutes/60 minutes (1 hour is 60 minutes) = 0.71 hours.

Now we set up a problem here.

50 kilometers/0.71 hours = x kilometers/1 hour

We multiply out 1 hour and cancel out from both sides.

50/0.71 kilometers = 70.42 kilometers.

Therefore, the train was traveling at 70.42 kilometers per hour.

Light is about 874052.5 times faster than sound

From the question, we are to determine the magnitude by which light is faster than sound

From the given information,

The speed of light is about 2.998 x 10⁸ meters per second.

and

The speed of sound is about 343 meters per second.

To determine how many rimes faster the speed of light is than the speed of sound, we will divide the speed of light by the speed of sound

That,

The magnitude by which light is faster than sound = (2.998 x 10⁸) / 343

The magnitude by which light is faster than sound = 874052.5

Hence, light is about 874052.5 times faster than sound

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Given x is Complimentary angle

Also, line1 is parallel to line2

Thus,
x [tex]+[/tex]  139° [tex]=[/tex] 132° [Alternate angle]

x [tex]=[/tex] 132°[tex]_[/tex][tex]_[/tex]- 139°

x[tex]=[/tex] -7°

What is Complimentary angle?

When two angles are added together, complementary angles are defined. When the total of the two angles is 90 degrees, we get a pair of complimentary angles. In other terms, two angles are said to be complimentary if they combine to make a right angle. In this case, we say that the two angles work well together.

If two angles sum to 90 degrees, they are said to be complimentary angles. In other terms, a right angle is created when two complimentary angles are combined (90 degrees). If the sum of angles 1 and 2 equals 90 degrees (i.e., angle 1 plus angle 2 = 90°), then the angles are complementary and are referred to as one another's complements.

60° + 30° in the illustration below equals 90°. These two angles are therefore complimentary according to the "Definition of Complementary Angles." The term "complement" refers to each angle that is one of the complimentary angles. Here,

The opposite of 30° is 60°.

The opposite of 60° is 30°.

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Domain

[tex]-\infty \: < x < \infty[/tex]

Range

[tex]f\left(x\right)\ge \:-7\:[/tex]

A distribution of scores in which almost the entire class scored very high, but a few students scored fairly low would be representing a negatively skewed distribution.

A real-valued random variable's probability distribution's asymmetry can be quantified by looking at how skew it is around its known as skewness.

There are three types of probabilities of a value can be:

Positively skewed

negatively skewed

unskewed

From the given question, the distribution of scores in which almost the entire class scored very high, but a few students scored fairly low would be representing a negatively skewed distribution.

Therefore the correct answer would be an option (D)

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Your question is incomplete, probably the missing part is:

A distribution of scores in which almost the entire class scored very low, but a few students scored fairly high would be ______.

a. normally distributed

b. positively skewed

c. unskewed

d. negatively skewed

The wire that Marlee had left is 20.8 inches.

From the information given, it was stated that Marlee is making jewelry for a class craft show and that she began with 115 inches of wire.

Amount used for rings = 25.75 inches..

Amount given to her by the teacher = 30 1/4 inches.

Amount used for bracelets = 38 1/2

inches.

Amount used for necklace = 60.2 inches

It should be noted to know the wire left, we have to subtract the values that were used and then add the value that her teacher gave her from the original value. This will be calculated thus:

This will be:

= 115 - 25.75 + 30.25 - 38.5 - 60.2

= 20.8 inches

Therefore, in conclusion, the wire that Marlee had will be 20.8 inches left.

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Answer:

130.94

Step-by-step explanation:

'Combine' I assume is to add so here's the answer!

23.8+40+38.94+28.2= 130.94

Definition of Relation:

Let A and B be sets. A relation R from A to B is a subset of Ax B

Definition of Function:

A function f from a set A (domain) to a set B (codomain) is a relation that satisfies the following properties:

1) Every element in A there is an element y in B such that (x,y) F

2) For all elements z in A there exist a unique element y in B.

The cartesian product of the sets A (a, b) and B (r,y) is

A x B {(a,z) (a,y).(b,),(b,s)}

Step 2

1. T ((a,x), (a,y))

Since T-((a,z), (a,y)) is a subset of (a, b) x (x,y).

so T is a relation from (a,b) to (x,y).

But for the element a in domain, there exist two different images x and y in co-domain.

This violates the definition of function.

Therefore, T_{1} = \{(a, x), (a, y)\} is a relation but not a function.

Step 3

2. T_{2} = \{(b, x), (b, y)\}

Since T_{2} - \{(b, x), (b, y)\} is a subset of \{a, b\}\{x, y\} .

so T_{1} is a relation from \{a, b\} to \{x, y\}

But for the element b in domain, there exist two different images x and y in co-domain

This violates the definition of function

Therefore, T_{2} = \{(b, x), (b, y)\} is a relation but not a function.

Step 4

,T 1 =\ (a,z)\

Since 7-((a,z)) is a subset of \{a, b\}\{x, y\}

so Ty is a relation from \{a, b\} * to (x,y\

But the element & in domain does not map with any element in co-domain

This violates the definition of function

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Answer:

-4

Step-by-step explanation:

x is a variable, so to do g(2) you have to write g(x), but substitute 2 in place of x:

g(2) = 4*2² + 2*2 - 24 = 16 + 4 - 24 = -4