Use the Pythagorean theorem to find the length of the line

An equation that represents the relationship between x and y shown in the table is y = 1.5x.

In order to write an equation that represents the relationship between x and y shown in the table, we would have to find the slope from the table and then write the required equation based on the data points by using the point-slope form.

Mathematically, the point-slope form of a line is given by this mathematical equation:

y - y₁ = m(x - x₁)

Where:

By substituting the given parameters into the point-slope formula, an equation for the data points contained in this table is given by;

y - y₁ = m(x - x₁)

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 21 = (96 - 21)/(64 - 14)(x - 14)

y - 21 = 75/50(x - 14)

y - 21 = 1.5(x - 14)

y = 1.5x - 21 + 21

y = 1.5x

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Answer:

x - intercept = (15, 0)

y - intercept = (0, 6)

Step-by-step explanation:

x-int. is when y = 0

y-int. is when x=0

Plug in y = 0 and x = 0 to get intercepts.

FOR X-INT.:

12x + 30(0) = 180

12x = 180

x = 15

x-int. is (15, 0)

FOR Y-INT. :

12(0) + 30y = 180

30y = 180

y = 6

y-int. is (0, 6)

90° is the angle between the lines  2x = 3y = -z and 6x = -y = -2z and explained with directions of ratios as below

Direction ratios of line 2x = 3y = -z  which can be mentioned as [tex]\frac{x}{1/2} = \frac{y}{1/3} = \frac{z}{-1}[/tex] hence  [tex](\frac{1}{2} , \frac{1}{3} ,-1 )[/tex]

Direction ratios of line  6x = -y = -2z  which can be mentioned as

[tex]\frac{x}{1/6} = \frac{y}{-1} =\frac{z}{-1/4}[/tex] hence   [tex](\frac{1}{6} , -1 , \frac{-1}{4} )[/tex]

hence the dot product of the direction ratio of two line is

[tex]\frac{1}{2} .\frac{1}{6} + \frac{1}{3} . (-1) + (-1) . \frac{-1}{4}[/tex]  

= [tex]\frac{1}{12} -\frac{1}{3} + \frac{1}{4}[/tex]  

= 0

hence this shows that angle between the given equations is 90°

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Answer:

Translate(1.3, -1)

Scale Factor: 2/3

Step-by-step explanation:

First, perform a dilation about the origin. This will make the original shape smaller.

From the given diagram, we can see that R'S' is 10 units long. RS is 15 units long. Using this information, we can create this ratio.

[tex]\frac{10}{15}[/tex]

This means that Triangle R'S'T' is 2/3 of Triangle RST. Construct lines from the origin (the center of dilation) to each point on the original triangle. Then, find two thirds of that line. The new point will be the new y-coordinate.

The new coordinates will (approx.) be:

R = (-2, 4.7)

S = (-2, -5.3)

Only two coordinates are necessary to perform this translation. As per the graph, this triangle must shift approximately 1.3 units up and 1 unit to the left. Thus, the final translation is:

Translate(1.3, -1)

Scale Factor: 2/3

Answer:

Rate = 7.0% per year

Step-by-step explanation:

Formula: rate = In(A/P)/t

I = interest

n = compound, in this case continuous

A = Total amount ($133,000)

P = Principal ($33,000)

t = time (20 years)

Plug in the values and solve:

rate = In(133000/33000)/20

rate = 0.06969

Convert to percentage:

rate = 6.969%

Round to the nearest tenth of a percent:

rate = 7.0%

Answer: d

cause it says its the same

Step-by-step explanation:

neither it is just 4

Step-by-step explanation:

unless this is a joke. 2x11=22.

Answer:

Hold up, wait a minute...

Ummmm A? 22

Step-by-step explanation:

Logic:

2 + 2 (Combined)

= 22

So, the answer is 22.

Answer:

I can’t seem to see it properly

Step-by-step explanation:

When the treasurer is solving a problem using the expression shown. -23.50 ÷ 5, the problem that the treasurer is lost likely solving is D. A total of -$23.50 in dues is owed to the club. There are 5 club members who each owe the same amount in dues. What is the balance,in dollars, of each members account?

From the information, the club treasurer is solving a problem using the expression shown. -23.50 ÷ 5. An expression show the relationship between the variables.

In this case, a total of $23.50 in dues is owed to the club. There are 5 club members who each owe the same amount in dues.

The correct option is D.

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Answer:

y = 2x + 10

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

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

with (x₁, y₁ ) = (- 5, 0) and (x₂, y₂ ) = (0, 10) ← 2 points on the line

m = [tex]\frac{10-0}{0-(-5)}[/tex] = [tex]\frac{10}{0+5}[/tex] = [tex]\frac{10}{5}[/tex] = 2

the line crosses the y- axis at (0, 10 ) ⇒ c = 10

y = 2x + 10 ← equation of line

Answer:

-6 +12

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let the costs of 1 t - shirt and 1 pair of pants be 'x' and 'y' respectively then:

Case 1 --> 8x + 5y = 220 ----------(1)

Case 2 --> 5x + y = 112 ----------(2)

Multiplying equation (2) by 5:

8x + 5y = 220

25x + 5y = 560 ------(3)

Subtracting equation (1) from equation (3) we get :

17x = 340

x = 20

Putting x in (2):

5 x 20 + y = 112

y = 12

therefore, cost of each t-shirt is 20 rupees and the cost of each pair of pants is 12 rupees

If Zoe already has $80 and can save an additional $6 per week using money from her after school job then the total amount of money that Zoe saved after 6 week of saving is $116  and

the expression that represent amount of money Zoe would have saved in w weeks is [tex]80+6w[/tex]  .

The amount that Zoe already saved = $80 ;

the amount that she can additionally save is = $6 per week ,

the amount of money that can be saved after 6 weeks can be written as :

[tex]Amount = \$80+(Amount Saved Per Week)\times(Number Of Weeks)[/tex]

Amount = [tex]80+6\times6[/tex]

= [tex]80+36[/tex]

= $116

and the expression for w weeks will be = [tex]80+6\times w[/tex]

The expression is ⇒ [tex]Amount = 80+6w[/tex].

The given question is incomplete , the complete question is

Zoe is saving up to buy a new bicycle. She already has $80 and can save an additional $6 per week using money from her after school job. How much total money would Zoe have after 6 week of saving ?

Also, write an expression that represent the amount of money Zoe would have saved in w weeks ?

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Answer:

Area: 2,088 Perimeter: 202

Step-by-step explanation:

Since it's a rectangle, both small sides are going to be the same, and both long sides are going to be the same. So for perimeter add up 29+72+29+72 to equal 202. For area you just multiply 29 times 72:)

The polynomial in intercept form so that P(x)=0 has the given roots is, x^2 - √3x - 2x + 2√3 = 0.

What is polynomial?

A polynomial is an expression in mathematics that only uses the operations of addition, subtraction, multiplication, and powers of positive-integer variables. It consists of indeterminates and coefficients. The polynomial x^2 4x + 7 is an illustration of one with a single indeterminate x.

We have to find the polynomial in intercept form so that P(x)=0 has the roots 2 and √3.

Let 2 and √3 are the roots of the polynomial so,

x = 2,  x = √3

⇒ x - 2 = 0,  x - √3 = 0

⇒ (x - 2)(x - √3) = 0

x^2 - √3x - 2x + 2√3 = 0

Hence, the polynomial in intercept form so that P(x)=0 has the given roots is, x^2 - √3x - 2x + 2√3 = 0.

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Answer: There are 12 mountain bikes in the shop

Step-by-step explanation:

Total number of bikes in the bike shop =120

Percentage of mountain bikes =10%

Number of mountain bikes in the shop  =10% of 120

=10% x 120

==0.1 x 120=12

Answer:

y= -1/5x

Step-by-step explanation:

hope this helps :)

Answer:

Step-by-step explanation:

x² = 17² - 8²

x² = 289 - 64

x² = 225

x = √225

x = 15in

8 + 15 + 8 + 15 =

46in

Answer:

x = 10

Step-by-step explanation:

the legs of an isosceles triangle are congruent.

the perimeter is the sum of the 3 sides of the triangle

sum the 3 sides and equate to 106

x + 5x - 2 + 5x - 2 = 106

11x - 4 = 106 ( add 4 to both sides )

11x = 110 ( divide both sides by 11 )

x = 10

The standard form of the polynomial -n²(n² + 5n + 6) is  -n⁴ - 5n³ - 6n².

Polynomials are algebraic expressions that consist of variables and coefficients.

The standard form of a polynomial is expressed by writing the highest degree of terms first then the next degree and so on.

Hence, let's represent the polynomial in standard form as follows:

-n²(n² + 5n + 6)

Open the brackets

-n²(n² + 5n + 6) = -n⁴ - 5n³ - 6n²

Hence,

-n²(n² + 5n + 6) = -n⁴ - 5n³ - 6n²

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Answer:

b

Step-by-step explanation:

I think number B is the answer. because the square becomes root when it crosses the = . So, the answer is B

Answer:

  b.  ±√60

Step-by-step explanation:

You want to know the solution to x² = 60.

In general, the process of solving for a variable's value requires you to "undo" what is done to the variable. This generally means you use inverse operations. The inverse of the squaring operation is the square root operation.

Taking the square root of both sides, we get ...

  √(x²) = √60

  |x| = √60 . . . . . . simplify the left side

  x = ±√60 . . . . . . . write the equivalent without the absolute value bars

__

Additional comment

As with any operation performed on an equation, it must be done to both sides of the equal sign.

You will get a ±(radical) result whenever you take an even-index root: square root, fourth root, sixth root, and so on. Odd-index roots will have the same sign as the value under the radical.

  √64 = ±8

  ∛64 = 4; ∛-64 = -4

Answer:

0.545 your welcome :D

Step-by-step explanation:

109÷200

Answer: 0.545

I just searched it up...... ya welcome homie

Step-by-step explanation:

search it "109 divided by 200" you'll get ur answer

Answer: the answer is A

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Answer:

5907.2 grams

Step-by-step explanation:

16 x 28.4 x 13 = 5907.2grams

Answer:

surface area ---> i

volume ---> b

radius ---> d

Step-by-step explanation:

surface area= 4πr² =4x3.14x14²=2461.76cm²

volume= (4÷3)πr³= (4÷3)x3.14x14³=11488.21cm³

radius = half the diameter = 14cm

Answer:

To draw an isosceles acute triangle, the first step is to draw a line segment horizontally which will be the base of the triangle.

Step-by-step explanation:

Now, draw two angles of equal measurements (each should be less than 90 degrees) on both the ends of the line segment. Join the arms of the angles. In this way, we will get an acute isosceles triangle.

Answer:

37/56

Step-by-step explanation:

Answer: 3/5 = 0.6

Step-by-step explanation:

1. 2 2/5 x 1/4 = 12/20

2. 2 times 5 over 5 + 2/5 = 10 + 2 over 5 = 12/5

3. 12/5 times 1/4 = 12/20

4. 12/20=3/5

6.022× [tex]10^2^3.[/tex]particles are in one mole.

The correct option is 6.022× [tex]10^2^3.[/tex]

Now, According to the question:

Avogadro's number

Avogadro's number, number of units in one mole of any substance (defined as its molecular weight in grams), equal to 6.02214076 × [tex]10^2^3.[/tex] The units may be electrons, atoms, ions, or molecules, depending on the nature of the substance and the character of the reaction.

Now, According to Avogadro's law, one mole of any substance contains a fixed number of particles i.e.,6.022× [tex]10^2^3.[/tex]particles (atoms, molecules or ions) which is also known by the name Avogadro's number.

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Answer:

x) = 1 + 2(0.94)*

The y-intercept = (0, [?])

For x ≥ 0, the horizontal as

Answer:

Papyrus

Step-by-step explanation:

the one that's not right is the 3rd one