find the equation of a line with slope 2 and 6 unit away from the origin​

The measure of indicated angle in the given triangle is 71.035°.

The sides and angles of a right-angled triangle are dealt with in Trigonometry. The ratios of acute angles are called trigonometric ratios of angles. The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

In the given right angled triangle, hypotenuse side is 74 units and the two legs of triangle are 70 units and 24 units.

Let the unknown angle be x.

We know that, tanθ =Perpendicular/Base

Now, tan x= 70/24

tan x= 2.91

x =71.035°

So, one of the angle in the triangle is 71.035°.

Therefore, the measure of unknown angle is 71.035° in the given triangle.

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One knief costs 5.52 dollars

Let the cost of knief be x dollars and the cost of spoon be y dollars.

A knife costs 3 times the cost of a spoon.

So, we get an equation,

x = 3y                       ..............(1)

9 spoons and 12 knives cost $82.80

So, we get an equation,

12x + 9y = 82.80        .........(2)

Substitute above value of x in equation (2),

12(3y) + 9y = 82.80

45y = 82.8

y = 1.84

Subatitute above value of y in equation (1),

x = 5.52

Therefore, the cost of knief is 5.52 dollars

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Answer:

36 ounces or if over 150 lbs drink more water than 36 ounces

Step-by-step explanation:

For every pound of sweat you lose you need to drink 16 ounces of water!

Mr. Ramli's investment in the small entrepreneurship will be doubled in 8 year.

For the stated equation-

rate of increase is given as-

dy/dx = 2(x + 121) < - rate of the change

dy = 2(x + 121)dx

Integrating;

∫dy = ∫2(x + 121)dx

y = x² + 242x + C

At x = 0, y(0) = 0 Thus,

(0)² + 242(0) + C = 2000

C = 2000

Now, y = x² + 242x + 2000

Calculate 't' to get the y(t) = 40,000 (double the amount)

4000 = x² + 242x + 2000

x² + 242x - 2000 = 0

Find the factor;

x = 8 and x = -250

As, x is time in year. So, x = 8 years.

Therefore, it takes eight years for his investment capital to double from what he initially put up.

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Answer:

time is gold ............

Answer:

q1: it arrived at 11:45

q2: 8 hours and 45 minutes

q3: a: 6:59 AM b: 498 minutes

Step-by-step explanation:

q1: 10:30 + 1:15 = 11:45

q2: 0:30 +7:30 +0:45 +8 hours and 45 minutes

q3: a(8:18 + 10:41 PM = 6:59 AM) b(8x60= 480 +18= 489)

The value of ordered pair of   (x,y) is (-2, -3)

x - 5y = 13

4x - 3y = 1

Solve the equation for x

x - 5y = 13

Move '5y' to R.H.S and change it's sign

x=13+5y

Substitute the given value of X into the equation

4x - 3y = 1

4(13+5y)-3y = 1

Solve the equation for y

distribute 4 through the parentheses

52+20y -3y =1

Collect like terms

52+17y = 1

Move constant to R.H.S and change it's sign

17y = 1 - 52

Calculate

17y =  - 51

Divide both sides of the equation by 17

17y/17 = -51/17

Calculate

y = -3

Now, substitute the given value of y into the equation

x = 13 + 5y

x= =13+5x(-3)

Solve the equation for x

Multiply the numbers

= 13 - 15

Calculate the difference

= -2

The possible solution of the system is the ordered pair

( x , y )

( x , y ) = ( - 2 , - 3 )

-----------------------------------------------------------------------

Check if the given ordered pair is the solution of the system of equation

-2-5×(-3)=15

4×(-2)-3×(-3)=1

Simplify the equalities

13 = 13

1=1

Since all of the equalities are true, the ordered pair is the solution of the system

( x , y ) = ( - 2 , - 3 )

Therefore the value of ordered pair of   (x,y) is (-2, -3)

The complete question is : Solve the system by substitution. x−5y=13 4x−3y=1 Enter your answer as an ordered pair (x,y).

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Answer:

Zachary pays $150 per month for his computer

Step-by-step explanation:

after 2 months:

2x + 1100y = 1400..... equation 1

after 4 months:

4x + 800y = 1400...... equation 2

we can either multiply equation 1 by 2 or we can divide equation 2 by 2, the purpose is simply to get the x values equal so it can be eliminated from the equation.

dividing equation 2 by 2:

2x + 400y = 700 ...... equation 3

Now equation 1 minus equation 3:

0x + 700y = 700

700y = 700

y = 700/700

y = 1

substituting y=1 into equation 3

2x + 400(1) = 700

2x = 700 - 400

2x = 300

x = 300/2

x= 150

Therefore it is concluded that Zachary has a payment plan where he pays $150 each month for the computer

Answer:

see attached

Step-by-step explanation:

The value of the 35x + 10y is 330.

What is the linear equation?

A linear equation is an equation of a straight line, written in the form y = mx + b. In this equation, m is the slope of the line and b is the y-intercept. Linear equations are used to describe relationships between variables, and they can also be used to solve problems with multiple unknowns. For example, if you know the slope of a line and the y-intercept, you can use a linear equation to calculate the x-intercept. Linear equations can also be used to model real-world situations, such as calculating the cost of a product or the amount of money saved over a period of time.

We have given:

the value of 35x + 10y, When x=8 and y=5.

Using substitution, substitute the given values of x and y.

35x + 10y

35(8) + 10(5)

280 + 50 = 330

Hence, the value of the 35x + 10y is 330.

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Complete Question:

Find the value of 35x+10y, When x=8 and y=5

Answer:

56x-32

Step-by-step explanation:

7x-4 Times 8x+8

7xtimes8x

56x-4times8

56x-32

Step-by-step explanation:

[tex] {x}^{2} - 12x + 36 = - 36[/tex]

[tex](x - 6) {}^{2} = - 36[/tex]

[tex](x - 6) {}^{} = 6i[/tex]

[tex]x = 6 + 6i[/tex]

[tex]x = 6 - 6i[/tex]

Answer:

Step-by-step explanation:

Answer:

  1800

Step-by-step explanation:

You want the least common multiple (LCM) of 72 and 150 given their prime factorizations:

The LCM is found as follows:

  LCM(72, 150) = 2³ × 3² × 5² = 1800

Answer: [tex]x^{2} -5x+3\\[/tex]

Step-by-step explanation:

Answer:

Volume= 62.8 cubic inch

Step-by-step explanation:

V=B×h

B=

[tex]\pi {r}^{2} [/tex]

= 3.14×2^2=12.56

V=12.56×5= 62.8 cubic inch

The price that that club members pay for the computer is $465.92.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. The percentage therefore refers to a component per hundred.

Since the selling price was first at 728, but then the store advertised a 20% markdown on the system and members of the store's loyalty club get an additional 20% off their computer purchases.

The cost will be calculated thus:

582.40 - (20% × $582.40)

= $582.40 - $116.48

= $465.92

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Using cosine law of triangle and using the provided value for the sides, the value of angle C is [tex]118^{o}[/tex] .

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes.

It is especially helpful for filling in the gaps in a triangle's information. The cosine rule, for instance, enables one to determine any of the angle measurements when all three sides of a triangle are known. Similar to this, using the cosine rule, one can determine the length of the third side given two sides and the angle between them are known.

a=80

b=51

c=113

[tex]cos(C) = \frac {a^{2}+b^{2} - c^{2}}{2ab}[/tex]

cos(c)= -0.4617

C= [tex]118^{o}[/tex]

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Answer:

X = 33.19

Step-by-step explanation:

You're welcome.

The mean and standard deviation of T, the mean and standard deviation of R, and the mean and standard deviation of Q.

a. The mean and standard deviation of 7-G is

7-1=6 and 0.12, respectively.

b. Let X be the weight of a single grapefruit, so the mean and standard deviation of X are 1 and 0.12, respectively.

The mean and standard deviation of R=G+G+G are

3*1=3

and

√(3)*0.12=0.2, respectively.

c. The mean and standard deviation of

Q=T-R are 7-3=4

√0.2((0.12^2)+(0.2^2))=0.2236 respectively.

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The solution of the given system of equations is (-1, 2).

What is system of equations?

A group of equations involving one or more variables is known as a system of equations. The variable mappings that satisfy each component equation, or the points where all of these equations intersect, are the solutions to systems of equations.

Consider, the given system of equations.

x^2 - x + 3y - 8 = 0           ..(1)

x - y + 3 = 0                       ..(2)

From equation (2),

x = y - 3            ..(3)

Plug the value of x in equation (1).

⇒ (y - 3)^2 - (y - 3)  + 3y - 8 = 0

y^2 - 6y + 9 - y + 3 +3y - 8 = 0

y^2 - 4y + 4 = 0

y^2 - 2y - 2y + 4 = 0

y(y - 2) - 2(y - 2) = 0

(y - 2)(y - 2) = 0

(y - 2)^2 = 0

y = 2

Now plug y = 2 in equation (3)

x = 2 - 3

x = -1

hence, the solution of the given system of equations is (-1, 2).

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Considering the information, the minimum and maximum size of the concrete walkway is is -900 and -450 units respectively

Minimum and maximum values of the area of the square garden is the area the square garden can occupy.

The given parameters are

A=S²

S= a side of the square= A(x) = (15+2x)

Now, hence A=S²

This implies that

(15+2x)(15+2x)

Expand the brackets to get

225+60x+4x=0

Solving the equation using the quadratic formula

x=± (√b²-4ac)÷2a

This implies that  

x= -60±(√60²-4*4*225)÷2*4

Simplifying the equation we have

(-60±0)÷8

x=-30

Now if x= -3

Therefore (15+2*-30) = -45 and (15*x)

= 15*-30=-450 units

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Answer:  55.7 inches and 60.3 inches

Step-by-step explanation:

I saw this question before in math class, so I know the answer! Hope you find this helpful!

Answer: It is perpendicular because it makes a 90-degree angles

Step-by-step explanation: A perpendicular is when it makes a 90-degree angle or has the same length!

The resulting triangle is 9/5 the original triangle.

The focuses in the direction planes are A(0, 2), B(2, 1), C(- 2, - 2). In the event that the scale factor is 2, each direction point of the first triangle is duplicated by the scale factor 2. Subsequently, the expanded triangle will be A'B'C' and the direction focuses got are A'(0, 4), B'(4, 2), C'(- 4, - 4).

Let we have a triangle ABC,If this triangle undergoes a dilation with a scale factor of 9/5,

Then changed triangle is  A'B'C'

So, relation between them is A'B'C' = 9/5(ABC)

Thus, the resulting triangle is 9/5 multiple of triangle ABC.

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Answer:

C)117

Step-by-step explanation:

50%=1/2

If you want to figure out how much is left of a half all you do is have to divide the total number of whatever it is, in this case, its roses, by 2.

So now that we know that, let's get started.

234/2=117

Which we know is correct because it's one of your answer choices.

So 117 roses are not red. The other half was.

I hope this helps!!!

The inequality does not belong with the other three is  - 1 ≤ x/1.25.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Given,

1.  4x ≥ 12 ⇒ x ≥ 3.

2.  - 1 ≤ x/5 ⇒ - 5 ≤ x.

3.  12 > x/1.25 ⇒ x < 15.

4.  2.5x > - 6.4 ⇒ x > - 2.56.

x ≥ 3 and  x < 15 is,    3 ≤  x < 15.

- 5 ≤ x and x > - 2.56 here one common region is x > - 2.56 so - 5 ≤ x does not fit.

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Answer:

(0,2)

Step-by-step explanation:

im not too educated with this topic but i believe we multiple x and y by 1/2

0x1/2=0

4x1/2=2

(0,2) is the answer

:)

Fraction form  12.5%  question did Paul get wrong .

What do math fractions mean?

An element of a whole is a fraction. In mathematics, the number is represented as a quotient, where the numerator and denominator are divided.

                                           Both are integers in a simple fraction. In the numerator or denominator of a complex fraction is a fraction. A proper fraction has a numerator that is lower than its denominator.

Fraction of incorrect question = 1/8

Present of incorrect question

Computation:

Present of incorrect question = (Fraction of incorrect question)(100)

Present of incorrect question = (1/8)(100)

Present of incorrect question = 12.5%

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