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3 years ago

Given the equation 4x+5y=20

Mathematics

1 answer:

tester [92]3 years ago

4 0

I hope this helps you

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A line passes through point A (14,21). A second point on the line has an x-value that is 125% of the x-value of point A and a y-

seropon [69]

Answer:

The equation of the line in point-slope form is $y-21 = - \frac{3}{2}\cdot (x-14)$ .

Step-by-step explanation:

According to the statement, let $A(x,y) = (14,21)$ and $B(x,y) = (1.25\cdot x_{A},0.75\cdot y_{A})$ . The equation of the line in point-slope form is defined by the following formula:

$y-y_{A} = m\cdot (x-x_{A})$ (1)

Where:

$x_{A}$ , $y_{A}$ - Coordinates of the point A, dimensionless.

$m$ - Slope, dimensionless.

$x$ - Independent variable, dimensionless.

$y$ - Dependent variable, dimensionless.

In addition, the slope of the line is defined by:

$m = \frac{y_{B}-y_{A}}{x_{B}-x_{A}}$ (2)

If we know that $x_{A} = 14$ and $y_{A} = 21$ , then the equation of the line in point-slope form is:

$x_{B} = 1.25\cdot (14)$

$x_{B} = 17.5$

$y_{B} = 0.75\cdot (21)$

$y_{B} = 15.75$

From (2):

$m = \frac{15.75-21}{17.5-14}$

$m = -\frac{3}{2}$

By (1):

$y-21 = - \frac{3}{2}\cdot (x-14)$

The equation of the line in point-slope form is $y-21 = - \frac{3}{2}\cdot (x-14)$ .

5 0

3 years ago

Which number is real and rational?

kirill [66]

It is D, that is because A - C are not terminating decimals therefore only leaving D

3 0

2 years ago

Given uv = su tu sv prove vt = st

Lady bird [3.3K]

Answer: see proof below

<u>Step-by-step explanation:</u>

$\begin{array}{cl|cl}&\underline{\text{Statement}}&&\underline{\text{Reason}}\\1.&TU\perp SV&1.&\text{Given}\\2.&\angle TUV = 90^o&2.&\text{De finition of Perpendicular angles}\\&\angle TUS = 90^o&&\\3.&\angle TUV=\angle TUS&3.&\text{Transitive Property}\\4.&UV=US&4.&\text{Given}\\5.&TU=TU &5.&\text{Reflexive Property}\\6.&\triangle TUV = \triangle TUS&6.&\text{SAS Congruency Theorem}\\7.&VT=ST&7.&CPCTC\end{array}$