Solve the simultaneous equations.
Show all your working.
3x + 4y = 14
5x+2y=21

The linear equation of line passing through the (-14,-5) and (4,5) is given by -5x + 9y = 25

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( -14 , -5 )

Let the second point be Q ( 4 , 5 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( -5 - 5 ) / ( -14 - 4 )

Slope m = -10 / -18

Slope m = 5/9

Now , the equation of line is y - y₁ = m ( x - x₁ )

y - 5 = ( 5/9 ) ( x - 4 )

Multiply by 9 on both sides , we get

9y - 45 = 5x - 20

Adding 45 on both sides , we get

9y = 5x + 25

Subtracting 5x on both sides , we get

-5x + 9y = 25

Hence , the equation of line is -5x + 9y = 25

To learn more about equation of line click :

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Answer:

Yes the samples can be drawn from a population with the same mean and standard deviation 10 hours

Step-by-step explanation:

We are given;

Sample mean for male employees; x1¯ = 63

Sample mean for female employees; x2¯ = 66

Sample size = 50

Standard deviation; σ = 10

First,let's define the hypotheses of the question;

Null hypothesis; H0: μ1 = μ2

Alternative hypothesis; Ha: μ1 ≠ μ2

Now, let's find the test statistic from the formula;

z = (x1¯ - x2¯)/(σ√(2/n))

Thus;

z = (63 - 66)/(10√(2/50))

z = -3/2 = - 1.5

Now, we are not given the significance value but usually when it is not given, we can adopt α = 0.05.

Thus, from online p-value from z-score calculator using; z = -1.5; α = 0.05; two tailed test; we have;

p-value = 0.13364

The p-value is greater than the significance value and thus we will fial to reject the null hypothesis and conclude that these samples can be drawn from a population with the same mean and standard deviation

Answer:

60º

Step-by-step explanation:

The two triangles on the left are equilateral as the sides are all conguent.

The angles of an equilateral triangle are all 60º

Therefor the two angles to the left of angle 1 are both 60º for a combined value of 120º

Angle 1 must be 180 - 120 = 60º

To find angle 1, you have to add all adjacent angles, which equal 180°

Step-by-step explanation:

let the expression of the equation be :

x+y=0

x²+y²= 5

hope it is helpful to you

Answer:

∅ = 83.9º

Step-by-step explanation:

tan = opp/adj

opp = 15 - 1 = 14

tan∅ = 14/1.5

∅ = arctan 14/1.5

use calculator

∅ = 83.884496433714593º

Rounded

∅ = 83.9º

Answer:

90 kilometers

Step-by-step explanation:

https://www.bing.com/search?q=kilometers+are+there+in+9000000cm

Answer:

The bulding is 381,623 meters high.

Step-by-step explanation:

To dertermine the height of the bulding I would use tanα = rectangulair side / closest rectangulair side.

19,08 = the height/ 20m.

<=> 19,08.20m= the height = 381,623 m

Answer:

The slope 7/5 and the y intercept is -3

Step-by-step explanation:

Y=7/5x-3

This equation is written in slope intercept form

y = mx+b where m is the slope and b is the y intercept

The slope 7/5 and the y intercept is -3

please edit your question man

Answer:

12 cm

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Trigonometry

[Right Triangles Only] Pythagorean Theorem: a² + b² = c²

Step-by-step explanation:

Step 1: Define

Identify variables

a = 12 cm

c = 17 cm

Step 2: Solve for b

Answer:

it could only accomplish it's goal on Friday

Step-by-step explanation:

all you had to do was multiply 8 with the number of people and 2 with the number of tickets on each day and add them together to see if it was more than 1650. it was only more on Friday

Answer:

9notebooks

Step-by-step explanation:

5×y≤45( where y is number of notebooks)

$5=1notebook

$45=$45/$5x1

=9

therefore, you'll be able to buy nine notebooks with$45

Answer:

$5n = $45

n = 9

Step-by-step explanation:

Let n represent the amount of notebooks

$5n = $45

Divide each side by 5

$5n/5 = $45/5

n = 9

so the maximum number of notebooks you can buy is 9

Answer:

4%

Step-by-step explanation:

264 interest/3 years=88 interest/year

principal x interest rate =interest/year

2200 x interest rate =88

interest rate =88/2200

interest rate =.04 or 4%

Answer:

Is the question original or you simply made it.

Answer:

bacteria 1

Step-by-step explanation:

i got it right

Answer: I don't know but i have the formula.

Step by Step: [tex]A=\frac{1}{2}b h[/tex]

Answer:

x=12

hope it will helpful to you

9514 1404 393

Answer:

  B. both a relation and a function

Step-by-step explanation:

Every linear equation with defined slope is both a relation and a function.

__

Only a vertical line of the form x=constant is linear equation that is a relation, but not a function.

Answer:

B = 25 because 180-25-130 = 25 and all angles within triangle add to 180 degrees

a = 6  because the triangle is isosceles and we can see symmetry and draw this to prove on two opposite lines, therefore we can now find height easier.

c = 10. 876  because 130/2 = 65 degree and with new central height we can find Right Angle and using 6 x sin (65) = 5. 438 then we multiply by 2 to find c  

Then all you have to do is re-write and round to the nearest 10th and check the units and write degree sign where required.

Step-by-step explanation:

Answer:

d=67257

c=93

Step-by-step explanation:

Given:

The table and the relative frequency histogram show the distribution of the number of tails and three coins are tossed.

To find:

The probability [tex]P(T=3)[/tex].

Solution:

In the given table T represents the number of tails.

From the given table it is clear that the value of probability is [tex]\dfrac{1}{8}[/tex] and [tex]T=3[/tex]. So,

[tex]P(T=3)=\dfrac{1}{8}[/tex]

Therefore, the probability [tex]P(T=3)[/tex] is equal to [tex]\dfrac{1}{8}[/tex].

Answer:

128cm

Step-by-step explanation:

Your Welcome :)

Answer:

D

Step-by-step explanation:

The radius of a circle refers to a segment connecting the center of the circle to the circumference of the circle. This can be seen in selection D), as a segment connects the center of the circle (O) to the circumference or outer edge of the circle.

Answer: 9/7

Step-by-step explanation:

Answer:

B. Identity

Step-by-step explanation:

Answer:

The null (H[tex]_{0}[/tex]) and alternative (H[tex]_{1}[/tex]) hypotheses can be stated as follows:

H[tex]_{0}[/tex]:  μ[tex]_{1}[/tex] = μ[tex]_{2}[/tex].

H[tex]_{1}[/tex]: μ[tex]_{1}[/tex] > μ[tex]_{2}[/tex].

Step-by-step explanation:

In the question, the given assertion is that carpeted rooms have more bacteria than uncarpeted rooms, i.e. μ[tex]_{1}[/tex] > μ[tex]_{2}[/tex].

The assertion made in the question can either be the null hypothesis (H[tex]_{0}[/tex]) or the alternate hypothesis (H[tex]_{1}[/tex]). An equality must be present in the null hypothesis. The alternative hypothesis expresses the exact opposite of the null hypothesis if the claim is the null hypothesis.

Therefore, the null (H[tex]_{0}[/tex]) and alternative (H[tex]_{1}[/tex]) hypotheses can be stated as follows:

H[tex]_{0}[/tex]:  μ[tex]_{1}[/tex] = μ[tex]_{2}[/tex].

H[tex]_{1}[/tex]: μ[tex]_{1}[/tex] > μ[tex]_{2}[/tex].

Answer:

if it cost 410 dollars to make 6 chairs we can divide 410 by 6 which is 68.3333333333 or 68 1/3

now for the other set of chairs we can divide 570 by 22 which is

25.9090909091 or 25.9

and for the rest it doesn't make any sense to me sorry