The sum of two numbers is 5. Three times the first is thirteen more than ten times the second. Find the numbers

Answer:

- 26

Step-by-step explanation:

(3−√7)(3−√7)

9 - 3√7 -3√7 + √7√7

9 - 6√49 + √49

9 - 6*7 + 7

9 - 42 + 7

= -26

To answer this question we first draw the triangle to help us:

As a note on the problem: This is not necessarily the triangle we have, we drew just to helps us solve it.

Now, to find the angle J we can use the law of cosines:

Plugging the values we have and solving for J we have:

Therefore the angle J is 60°.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

The value of n in the equation 672,342 = 6.72342 x 10n is 10,000

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x = 9 is an equation.

6x+ 2 = 9 is ana equation.

We have,

672,342 = 6.72342 x 10n

Divide both sides by 6.72342

672,342 / 6.72342 = 10n

We get,

100000 = 10n

Divide both sides by 10.

100000 / 10 = n

n = 10,000

Thus,

The value of n in the equation 672,342 = 6.72342 x 10n is 10,000

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3/10 +1/4 + 4/5 =  27/20

The first step to solving the equation is to; C. add x to both sides

The second step  to solving the equation is to; C. cube both sides

Solving the equation for x initially yields; C. two possible values

Checking the solutions shows that; D. none are valid solutions

We are given the linear equation;

4x[tex]^{1/3}[/tex] - x = 0

From the linear equation above, seeing that we have an x that is raised to the power of one-third, and we have a single x variable, the first step would be to add x to both sides to get;

4x[tex]^{1/3}[/tex] - x + x = 0 + x

4x[tex]^{1/3}[/tex] = x

Now, to remove the fraction root, what we will now do as the second step is to cube both sides to get;

(4x[tex]^{1/3}[/tex])³ = x³

4³x = x³

64x = x³

Divide both sides by x to get;

x² = 64

Take square root of both sides to get;

x = ±√64

x = ±8

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Table A represents a function.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.

Functions are crucial instruments in the creation of mathematical models because we continually develop beliefs about connections between variables in nature and society. Typically, functions in school mathematics contain numerical inputs and outputs and are frequently specified by algebraic expressions.

Given,

Table A represents a function,

A visual table with columns and rows that shows the function in relation to the input and output is called a function table. Function tables are frequently referred to as function machines by younger students. Each function has a rule that governs how the input and output are related to one another.

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Answer:

Add 55.5 and 35, then subtract 36.9.

Step-by-step explanation:

x+36.9=55.5+35

x+36.9=90.5

Subtraction Equality

x + 36.9 + (-36.9)= 90.5 (-36.9)

x = 53.6

Answer:you could do

You would need to rile a two and a one together though

Step-by-step explanation:

-3(1+6r) = -3-18r =14-r

17r = -17 Therefore, r = -1

Answer:

y = -3x - 11

Step-by-step explanation:

Slope = -3

so...

-3x

y = -3x + (b)

given : (-5, 4) x=-5 y=4

4 = -3(-5) + b

4 = 15 + b

b = -11

so...

y = -3x - 11

Sin 73° has a value of 0.9563. (approximately).

Trigonometric ratios are based on the value of the ratio of sides of a right-angled triangle and contain the values of all trigonometric functions. The trigonometric ratios of a given acute angle are the ratios of the sides of a right-angled triangle with respect to that angle. If you know the lengths of two of the triangle's sides, you can use trigonometric ratios to get the measurements of one (or both) of the acute angles.

Given Data

Trigonometric ratio of

sin73°

The sine trigonometric function for an angle of 73 degrees has a value of sin 73 degrees.

Sin 73° has a value of 0.9563. (approximately).

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Answer:

Ryan had 10.20 dollars and Jeffery had 11.40 dollars.

Step-by-step explanation:

Let Ryan have x dollars originally, then Jeffrey has x + 1.20 dollars.

From the given info:

After getting 7.50 from Ryan, Jeffrey has:

x + 1.2 + 7.5 dollars and Ryan has x - 7.50 dollars.

Jeffreys money is now is 7 times as much as Ryan's, so:

x + 8.7 = 7(x - 7.5)

x + 8.7 = 7x - 52.5

8.7 + 52.5 = 7x - x

6x = 61.2

x = 10.20 dollars.

The most appropriate choice for acceleration will be given by

Acceleration of the body = 7.59 [tex]m/s^2[/tex]

What is acceleration of a body?

At first it is important to know about velocity of a body.

The rate of change of displacement of a body is called velocity of a body. Velocity is a vector quantity.

The rate of change of velocity of a body is called acceleration.

Acceleration is also a vector quantity as the direction is taken into account

Here,

Initial velocity of an object = 23m /s

Final velocity of an object = 85 m/s

Time  = 8.3 s

Acceleration of the object =

                                              [tex]\frac{85 - 23}{8.3}\\\\\frac{63}{8.3}\\\\[/tex]

                                              7.59 [tex]m/s^2[/tex]

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The line shown in the graph have slope of line as 13/27 with rise 13 and run 27.

What is slope of line?
The definition of slope in mathematics is pretty close to how we normally define it. Slope is a mathematical term used to indicate a line's steepness and direction. A line's slope can be inferred from its graph alone, especially in comparison to other lines shown on the same coordinate plane.

The formula to calculate the slope of any line is given by:

[tex]slope = \frac{rise}{run}[/tex]

We know that, '

rise = y₂ - y₁

run = x₂ - x₁

As we can see in the graph

x₂ = 10, y₂ = 3

x₁ = -7,  y₁ = -10

putting the values in above formula

rise = y₂ - y₁ = 3 -(-10) = 13

run = x₂ - x₁ = 10 -(17) = 27

so, slope = 13/27

Hence the slope of the line shown in graph is 13/27.

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Answer:

Step-by-step explanation:

Systems of equations may be solved in one of two manners:  substitution and graphing.  This requaests they be solved by substitution, but I'll add the graphing solution, also.

Substitution:

We want to eliminate one of the two variables to result in an expression that only has one of the two remaining.  We can do that by manipluating one of the equations such that, when it is combined with the other, results in the elimination of one of the variables.

Given:

-2x-y=-9

5x-2y=18

we can multiply or divide one of the equations so that one of the terms has equal, but opposite, values.  We could multiply the first equation by 2.5 so that it becomes -5x -2.5y = 9*(2.5).  Then it could be added to the second to eliminate the x term.

My preference is to find a way to avoid fracticious fractions, so I will multiply the first equation by -2 so that we can eliminate y:

-2*(-2x-y =-9)

4x+2y = 18

No add this to the second equation:

  4x+2y = 18

  5x-2y = 18

   9x = 36

     x = 4

Since x = 4:

-2x-y=-9

-2*(4)-y=-9

-8 - y = -9

y = 1

The solution is (4,1).  It is the point the satisfies both equations.

-2x-y=-9

-2(4)-(1)=-9  

-8-1=-9   YES

----

5x-2y=18

5(4)-2(1)=18

20 - 2 = 18  YES

Graphing:

The solution to these equations is the point at which the lines intersect.  See the attached graph.  The lines intersect at (4,1).

Answer:

-6

Step-by-step explanation:

Replace the variable x with 1 in the expression.

f(1)=−4−2

Then simplify -4 and -2 (subtract 2 from -4)

= -6

Given the expression:

The GCF of p^4 and p^3 = p^3

And the greatest common factor of 16 and 4 = 4

so,

So, the factors of the given expression will be:

Answer: parrallelograms have 4 sides

Step-by-step explanation:

In geometry, a square is a flat shape with four equal sides and four right angles (90°). A square is an unique sort of parallelogram as well as an equilateral rectangle (an equilateral and equiangular one).

The formula for a2 + b2 + c2 is written as a square plus b square plus c square. A2 + b2 + c2 = (a + b + c)2 - 2(ab + bc + ca) is how it is expanded.

Give an example to explain what square is?

A square has four equal sides, four vertices, and is a closed, two-dimensional object. It has parallel sides on either side. A square is also equivalent to a rectangle with equal length and width. Many objects can be found in your surroundings that have a square shape.

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Answer:

g(x) = 4x - 23

Step-by-step explanation:

We will assume a linear function for g(x)

This will be of the form g(x) = ax + b where a and b are constants

Given the info,

g(3) = a(3) + b = -11

g(7) = a(7) + b = 5

Thus we have two equations in a and b
3a + b = -11  [1]
7a + b = 5    [2]

Subtract [1] from [2]:
7a + b - (3a + b) = 5 - (-11)
7a + b - 3a - b = 5 + 11

4a = 16

a = 4

Substitute for a in equation [2]:

4(7) + b = 5
28 + b = 5

b = 5-28 = -23

So equation of g(x) is
g(x) = 4x - 23

The value of angle a, b and c in the triangle are 60, 90 and 30 degrees respectively and the summation of these angles is equal to 180 degree.

The total sum of angles in a triangle is equal to 180 degrees.

To solve this problem, we have to write out equations to represent the unknown values.

Let;

Mathematically,

[tex]a + b + c = 180^0[/tex]

Let's represent each of the statement mathematically;

[tex]y = 3z...eq(i)\\x = 2z ...eq(ii)\\[/tex]

Let's substitute the values and find the value of angle C

[tex]a + b + c = 180\\2z + 3z + z = 180\\6z = 180\\z = 30\\c = 30^0\\b = 90^0\\a = 60^0[/tex]

From the calculations above, the value of a, b and c are 60 degrees, 90 degrees and 30 degrees respectively.

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40 = 5X

X = 10 dollars

Now divide 40/5 = 8

On average, each girl spends $8 dollars

Now write an inequality ,for this situation

5X ≤ 40

(a + b + c + d + e)/5 = 40

Answer:

1.1l +0.4+0.3+0.5

answer = 2litres 3milimetres

The years when the spending be more than $66 billion is in 4 years time.

A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

The equation is given as y=12.7x+15.2 and the amount is $66 billion. Therefore, the value of x will be:

y=12.7x+15.2

66 = 12.7x + 15.2

Collect like terms

12.7x = 66 - 15.2

12.7x = 50.8

Divide

x = 50.8 / 12.7

x = 4

The number of years is 4.

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Each gallon of water weighs by itself is 8.4 pounds, option (C) 8.4 pounds is correct.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that is +, -, ×, and ÷.

From the data given:

When the Amount of Water in Can (gallons) = 0

Weight of Cans (pounds) = 2

It means the weight of the can = 2 pounds

For the 0.5 gallons, the weight of the can = 6.2 pounds

For the 0.5 gallons, the weight of the water = 6.2 - 2 = 4.2 pounds

For the 1 gallon, the weight of the water = 2x4.2 pounds

= 8.4 pounds

Thus, each gallon of water weighs by itself is 8.4 pounds, option (C) 8.4 pounds is correct.

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Answer:

4

Step-by-step explanation

(a)

In the given diagram,

∠α and ∠β can be determined using trigonometric functions,

tan α = Opposite side/Adjacent side

⇒ tan α = 4/6

⇒ tan α = 2/3

⇒ α = tan^-1 (2/3)

⇒ α = 33.7°

Similarly,

tan (α + β) = 4+4/6

⇒ tan (α + β) = 8/6

⇒ tan (α + β) = 4/3

⇒ (α + β) = tan^-1 (4/3) = 53.1°

⇒ 33.7 + β = 53.1°

⇒ β = 19.4°

(b)

For the cables adjacent to the perpendicular height, i.e., adjacent to ∠α, on both the sides

Cable length^2 = 4^2 + 6^2 .............................. (Pythagoras theorem)

⇒ Cable length^2 = 16 + 36

⇒ Cable length^2 = 52

⇒ Cable length = 7.21 m

For the cables far from the perpendicular, on both the sides,

Cable length^2 = 6^2 + 8^2 .............................. (Pythagoras theorem)

⇒ Cable length^2 = 36 + 64

⇒ Cable length^2 = 100

⇒ Cable length = 10 m

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(a) The expression to represent the length of the rectangle is

h = (x-16/x)/(x/4+1).

(b) The length of the rectangular prism is L = ((7/x)-(3/5x))/(2/x)(4/x).

A rectangle is a quadrilateral with all four interior angles measures of 90°.

(a) Given that, the area of the rectangle is x-16/x and its width is x/4 +1.

Let the length of the rectangle be h, then it follows:

h×(x/4 + 1) = x - 16/x

h = (x-16/x)/(x/4+1)

Hence, the expression to represent the length of the rectangle is

h = (x-16/x)/(x/4+1).

(b) Given that, the volume of the rectangular prism is (7/x)-(3/5x), the width is 2/x, and the height is 4/x.

Let the length of the rectangular prism be L, then it follows:

L× (2/x) ×(4/x) = (7/x)-(3/5x)

L = ((7/x)-(3/5x))/(2/x)(4/x)

Hence, the length of the rectangular prism is L = ((7/x)-(3/5x))/(2/x)(4/x).

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Answer: 150.72 in^3

Step-by-step explanation:

the radius (r) is 2 because the diameter of the cylinder is 4.

the height (h) is 12 (obviously because that's provided in the picture.)

the formula to find the volume of the cylinder is:

[tex]3.14(2^2)\times 12[/tex]

therefore, it is 150.72 in^3

i hope this helps :)

Answer:

[tex]2x + 6y = 36[/tex]

[tex]x + 3y = 18[/tex]