Stimultaneous elimination equations


4x + 2y = 10

X+ 2y = 7

Given the information, the triangle congruence prove is explained below.

If the corresponding sides or measure of angles of two or more triangles have common properties, then the triangles are said to be congruent. Such that on comparing their sides and internal angles, some have equal values.

With the given information in the question, the prove is explained below:

               STATEMENTS                         REASONS

1. AB ≅ CD                                             Given

2. <ABD ≅<CDB                                    Given

3. AD ≅ BC                                            Equal sides of a parallelogram

4. <ADB ≅ <CBD                                   Alternate angle theorem

5. <A ≅ <C                                             Opposite property of a parallelogram

Therefore, it can be deduced that;

ΔABD ≅ ΔCDB

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The graph that passes through the points (4,16) and (6,12) , the equation of trend line is K = -2J + 24 .

A linear relationship is depicted by a trend line. Y = mx + b, where x is the independent variable, y is the dependent variable, m is the slope of the line, and b is the y-intercept, is the equation for a linear relationship.

a graph line indicating the general path that a collection of points appears to take.

When plotting predictions, trendlines, also referred to as lines of best fit or regression lines, are frequently used to graphically represent trends in data series. Typically, a trendline is a line or curve that crosses or links two or more points in a series to indicate a trend.

From the graph that passes through the points (4,16) and (6,12) , the equation of trend line is K = -2J + 24.

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The value of X are 5/6,1/5

A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

Given;

x ÷ 5/6 = 1....1

x ÷ 2 = 1/10....2

Equation.1

(x/5)*6=1

6x/5=1

x=5/6

Equation.2

x/2=1/10

x=2/10

x=1/5

Therefore, the value of x in equations will be 5/6 and 1/5

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The simplest form of the expression is given as 12 + 6√3.

We know that when we are asked to simplify in mathematics, they are asking us to write the expression in the simplest form that the expression can be in. In this case, we are to simplify 6/2 - √3.

Then we would now have to multiply the numerator and the denominator by the conjugate of the denominator such that we have;

6/2 - √3 * 2 + √3/2 + √3

12 + 6√3/4 +2√3 - 2√3 - 3

12 + 6√3/1

12 + 6√3

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the sum is 1) 5/3, 2) 5/6 , 3) 7/10 and the difference is 1) 1/6 , 2)2/15, 3) 1/30. When adding or subtracting fractions with unlike denominators, the first step is to convert the fractions so that they have a common denominator.

1. 1/3+2/3 = 5/3

2. 1/2 + 1/3 = 5/6

3. 2/5+1/2 = 7/10

1. 1/2-1/3 = 1/6

2. 4/5-2/3 = 2/15

3. 4/15-1/10 = 1/30

When adding or subtracting fractions with unlike denominators, the first step is to convert the fractions so that they have a common denominator. To do this, you can use the lowest common denominator, which is the least common multiple of the denominators. For example, in the first problem, the least common multiple of 3 and 2 is 6, so you can convert the fractions to 2/6 and 4/6, or 1/3 and 2/3. Then, you can add or subtract the fractions as normal. For example, 1/3+2/3 would equal 3/3 or 1.

For subtracting fractions with unlike denominators, the same process is used. For example, in the second problem, the least common multiple of 5 and 3 is 15, so you can convert the fractions to 4/15 and 2/15. Then, you can subtract the fractions as normal. For example, 4/15-2/15 would equal 2/15.

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Answer:

0.25 cup of rice; 13 cup of water

Step-by-step explanation:

2 cup of water: 1 cup of rice = 2:1 ratio

Answer:

Step-by-step explanation:

6. XZY

7. YX

a) The exponential function that gives the percent P is: P = (0.85)^x.

b) The percentage of light that will pass through a cloth that is 2.75mm thick is given as follows: 63.96%.

A decaying exponential function is defined as follows:

y = a(1 - r)^x.

In which the parameters are given as follows:

The parameter values for this problem are given as follows:

a = 1, r = 0.15.

Hence the function is:

y = (0.85)^x.

The percentage passing through a cloth that is 2.75 mm thick is given as follows:

y = (0.85)^2.75

y = 0.6396.

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The distance between PQ : 7

    Given  points  P: (1,6)

                            Q : (7,2)

   distance between two points formula is : √(x2-x1)^2 + (y2-y1)^2

    (x1,y1)= (1,6)

    (x2,y2) = (7,2)

    therefore

                  =  √(7-1)^2 +(2-6)^2

                  = √36+16

                  = √52

                  = 7.211

Answer: t = 10.50c

Step-by-step explanation: The relationship between the number of climbs, c, and the total cost, t, is proportional. This means that the ratio of t to c is constant. One way to represent this relationship is through an equation of the form:

t = kc

where k is a constant of proportionality. In this case, we know that 5 climbs cost $52.50, so we can use this information to find the value of k:

52.50 = k(5)

k = 52.50/5 = 10.50

So the equation that represents the total cost, t, of c climbs is:

t = 10.50c

Where t is the total cost, c is the number of climbs and 10.50 is the constant of proportionality.

Answer: x = -8

Step-by-step explanation:

12 ( x + 10 ) = 24

First we divide the two sides of the exercise by 12.

[tex]\boldsymbol{\sf{x+10=\dfrac{24}{12} }}[/tex]

We divide 24 by 12..

x + 10 = 2

Subtract 10 from both sides.

x = 2 - 10

Subtract 10 from 2 to get. Since the number 10 is greater than 2, the result will be negative.

x = -8

Answer:

[tex] \sf \: x = - 8[/tex]

Step-by-step explanation:

Given equation,

→ 12(x + 10) = 24

Now the value of x will be,

→ 12(x + 10) = 24

→ 12(x) + 12(10) = 24

→ 12x + 120 = 24

→ 12x = 24 - 120

→ 12x = -96

→ x = -96 ÷ 12

→ [ x = -8 ]

Hence, the value of x is -8.

Answer:

Start at 1 on y-intercept and go down 2 units and right 1 unit

Step-by-step explanation:

First you have to graph your y-intercept (1) *which is the red dot in the graph I made for you*

Then you must use your slope (-2) to graph the rest

Since your slope is negative you have to go down from your y-intercept. In your case you are going down 2 units from your intercept. And since your slope is a whole number instead of a fraction you just go to the right 1 unit to make the coordinate (1,-1).

That is how you graph your equation.

I hope this helped!

The solution for linear equations given will be x=-1 and y=2 using substitution method.

What is a linear equation ?

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form

Ax + B = 0

e.g. x-10=0. Here, x is a variable, A is a coefficient and B is constant.

The standard form of a linear equation in two variables is of the form

Ax + By = C

e.g. 2x-4y=10. Here, x and y are variables, A and B are coefficients and C is a constant.

Now

Given 4x+3y=2 -->1

x-2y=-5 --->2

Using substitution method, In this method, first, solve the equation for one variable, and substitute the value of the variable in the other equation.

From 2,  x=2y-5

Put x=2y-5 in 1

4(2y-5)+3y=2

11y-20=2

y=22/11

y=2

Hence,

           x=2*2-5

             x= -1

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Mary's Tuesday distance is 1/8 times her Monday distance

On Monday Mary ran 1 3/5 miles

= 8/5

On Tuesday Mary ran 1/5 miles

Therefore the number of times her Tuesday distance was her Monday distance can be calculated as follows

1/5 ÷ 8/5

= 1/5 ×5/8

= 1/8

Hence her Tuesday distance was 1/8 times her Monday distance

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We randomly take a card, if it is not a, then the probability that it is b, is 1/4.

We have to find the the probability that it is a card of b, if it is not a.

We have total number of cards = 20

The cards of a = 10

The cards of b = 5

The cards of c = 5

We don't select the card a, then;

The probability of choosing card b = The total number of card b/total number of cards

The probability of choosing card b = 5/20

The probability of choosing card b = 1/4

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To go from slope intercept form of line to standard form Ax + By + C = 0, collect all terms on the left side of the equation and multiply by the denominator B.

We know that the standard form of equation of line is Ax + By + C = 0. And the slope intercept form of line is y = mx +b, where m is the slope of the line, and b is the y-intercept i.e., the value of y when x = 0.

Converting from slope intercept form to standard form:

⇒ y = mx + b

⇒ y - mx = (mx - mx) + b           .........(subtract mx from each side)

⇒ y - mx = b

⇒ y - mx - b = b -b                    .........(subtract b from each side)

⇒ y - mx - b = 0

⇒ - mx + y - b = 0

Above equation is of the form Ax + By + C = 0

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The difference between their heights in feet and inches is 6'6.3"

From the question, we have the following parameters that can be used in our computation:

Robert Wadlow was 8’11” tall.

Pingping was 2’4.7" tall

The difference in their heights can be calculated by subtracting the smaller height from the larger

So, we have

Difference = 8’11” - 2’4.7"

Evaluate the difference

Difference = 6'6.3"

Hence, the difference is 6'6.3"

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The coordinates of vertices after dilation by scale factor of 1.5 with center of dilation is D'(3,-3), E'(6,-3) and  F'(1.5,-6).

A dilation is just a transformation which enlarges or contracts the size of a figure. This means that the preimage and image are similar and are scaled up or down using a factor.

The vertices of the triangle are D(2,-2), E(4,-2), F(1,-4).

The origin-centered dilation with a scale factor of k is defined as,

(x,y) → (kx,ky)

As a result, dilation with a scale factor of 1.5 centered at the origin is defined as,

(x,y) → (1.5x,1.5y)

The image's vertices are

D(2,-2) → D'(3,-3)

E(4,-2) → E'(6,-3)

F(1,-4) → F'(1.5,-6)

Therefore the coordinates of vertices after the dilation by the given scale factor 1.5 is D'(3,-3), E'(6,-3) and  F'(1.5,-6).

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Answer:

C. gaining confidence

The cor() returns the correlation between two variables.

Correlation shows us how strong the relationship is between two variables.

Hence, option (c) is the correct choice.

Correlation quantifies the intensity of a link between two variables and is symmetrical, meaning that the correlation between A and B is the same as the correlation between B and A.

Correlation is a statistical term that describes the degree to which two variables are linearly connected (meaning they change together at a constant rate). It's a common way of explaining simple interactions without stating a cause and effect relationship.

In R, the cor() function is used to calculate the correlation coefficient between two vectors. Correlations may be generated using the cor() function, while covariances can be generated using the cov() function. The type of correlation is specified.

There are three options: Pearson, Spearman, and Kendall.

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The complete questions should be like:

A data analyst is using statistical measures to get a better understanding of their data. What function can they use to determine how strongly related are two of the variables?

A sd()

B mean()

C cor()

D bias()

Answer:

60

Step-by-step explanation:

You're not slow.

So given was the formula for perimeter

12x + 1/2 - 4x - 8.5 + 2x + 8

They want you to find perimeter is x = 6, so this is a matter of plug and play. so everywhere you see an x, you'll replace it with the number 6

And we will start simplifying what we can

P = 12(6) + 1/2 - 4(6) - 8.5 + 2(6) + 8

P = 72 + 0.5 - 24 - 8.5 + 12 + 8

P = 72 - 24 - 8 + 12 + 8

P = 72 - 12

P = 60

Answer:

[tex]\dfrac{-8y}{y-3}[/tex]

Step-by-step explanation:

[tex]\sf \dfrac{49 - y^2}{6y^2 +42y}=\dfrac{7^2-y^3}{6y^2 +6*7y}\\\\[/tex]

                 [tex]\sf =\dfrac{(7+y)(7-y)}{6y(y + 7)}=\dfrac{(7+y)(7-y)}{6y(7+y)}\\\\\\=\dfrac{7-y}{6y}[/tex]

y² - 10y + 21

sum = -10

Product = 21

Factors = (-7) , (-3)   {(-7)*(-3) = 21  & (-7)+ (-3) = -10}

y² - 10y + 21 = y² - 7y - 3y + 21

                    = y(y - 7) - 3(y - 7)

                   = (y - 7) ( y - 3)

[tex]\sf \dfrac{49 -y^2}{6y^2 + 42y}*\dfrac{48y^3}{y^2 - 10y + 21}=\dfrac{7-y}{6y}*\dfrac{48y^3}{(y-7)(y-3)}\\\\\\[/tex]

                                         [tex]\sf = \dfrac{(-1)(y-7)}{6y}*\dfrac{48y^3}{(y-7)(y-3)}\\\\\\=\dfrac{(-1)*8y^2}{y-3}\\\\\\=\dfrac{-8y^}{y-3}[/tex]

The volume of the cuboid is 16 cubic yards.

A cuboid is a solid in three dimensions with six rectangular faces, eight vertices, and twelve edges. Three dimensions, including length, breadth, and height, define a cuboid. A cuboid with integer edges is referred described as being perfect.

Given:

A cuboid with height 2 yards, length 2 yards and width 4 yards.

The volume of the cuboid,

= length x width x height

= 4 x 2 x 2

= 16 cubic yards.

Therefore, the volume is  16 cubic yards.

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Step-by-step explanation:

I am not sure what you mean. you don't round the intermediate numbers and results. only the final result.

you keep the irrational terms (like square root) like variable terms as they are and apply operations on them without actually expressing them as numbers.

only at the very last moment (when the final result is calculated) would you express them as actual number. and then you round the final result.

so, this is solved via Pythagoras :

c² = a² + b²

c being the Hypotenuse (the side opposite of the 90° angle), a and b are the legs.

in our case we have

BP² = BN² + NP² = 7² + sqrt(95)² = 49 + 95 = 144

you see ?

no need ever to bring the actual result of sqrt(95) into the picture. just keep it at sqrt(95) and do with it, what you would do with any actual number.

BP² = 144

BP = sqrt(144) = 12

so, we never had to deal with the actual irrational number.

we know how it is created, so we keep using that term to represent it.

After n years Alex will earn salary which can be expressed as $(1 + 0.03)^n * 35,000.

The total amount Alex has earned in his first year of his career is $35,000.

In the second year of his career, he gets a 3% raise, which is an increase of 3/100 * $35,000 = $1,050.

So his salary for the second year is $35,000 + $1,050 = $36,050.

In the third year of his career, he again gets a 3% raise, which is 3/100 * $36,050 = $1,081.50

So his salary for the third year is $36,050 + $1,081.50 = $37,131.50

We can see that for each year, his salary is increasing by a fixed percentage of the previous year's salary.

This pattern can be represented by the expression:

(1 + 0.03)^n * 35,000

Where n is the number of years since the start of his career. This expression gives the total amount Alex has earned in his first n years of his career.

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Amanda's explanation is not correct. The growth factor of an exponential function is the constant value that the function is multiplied by for each expansion in the information variable.  

It is not determined by dividing one value in the table by the previous value.

To find the growth factor of an exponential function, one ought to take the proportion of any two consecutive f(x) values and distinguish the normal proportion. The growth factor is equivalent to this normal proportion.

For instance, assuming the function is [tex]f(x) = 2^x[/tex], and the table of values is:

x f(x)

0 1

1 2

2 4

3 8

The growth factor can be tracked down by taking the proportion of f(x) values for consecutive x:

f(1)/f(0) = 2/1 = 2

f(2)/f(1) = 4/2 = 2

f(3)/f(2) = 8/4 = 2

For this situation, the growth factor is 2, meaning that the function is multiplied by 2 for each increase in x.

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keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{9}{8}}x-9\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ \cfrac{9}{8}} ~\hfill \stackrel{reciprocal}{\cfrac{8}{9}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{8}{9} }}[/tex]

so we're really looking for the equation of a line whose slope is -8/9 and it passes through (-2 , 2)

[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{2})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{8}{9} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{- \cfrac{8}{9}}(x-\stackrel{x_1}{(-2)}) \implies y -2= -\cfrac{8}{9} (x +2) \\\\\\ y-2=-\cfrac{8}{9}x-\cfrac{16}{9}\implies y=-\cfrac{8}{9}x-\cfrac{16}{9}+2\implies {\Large \begin{array}{llll} y=-\cfrac{8}{9}x+\cfrac{2}{9} \end{array}}[/tex]

The final cost of the laptop be if jamal buys it on saturday is $695.79

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

Thus, that thing in number is

[tex]\dfrac{a}{100} \times b[/tex]

Given;

The new laptop is currently priced at $859

On saturday the store is giving a 25% discount off all laptops

Sales tax on final purchase=8.5%

Now, the final value on saturday be x

x*100/859=25

x=25*859/100

x=214.75

The value will be 859-214.75=644.25

8% of 644.25

x*100/644.25=8

x=8*644.25/100

x=51.54

Final cost= 644.25+51.54

=695.79

Therefore, the final cost after 8 percent sales tax will be $695.79

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