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Sphinxa [80]
3 years ago
5

Jim and Tony are in opposing teams in a soccer match their running after the same ball Jim's path is the line Y equals 3X Tony's

path is the line Y equals negative 2X +100 find the cornets of the ball
Mathematics
1 answer:
Gekata [30.6K]3 years ago
5 0
y=3x

y=2x+100

y=y

3x=2x+100

x=100

y=3(100)

y=300

Answer: (100,300)
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Need the answer asapp with the working out please thanks :)
patriot [66]
Hi,

The two numbers should be 12 and 30. 12=2x2x3 while 30=2x3x5.

Their HCF is 2x3=6 and their LCM is 2x3x2x5. Because of their HFC, we know that they are both multiple of 6. Also, the question says they both are GREATER than 6, so they can’t be 6 but are 6 times “something”. Thanks to the LCM, we know that “something” is equal to 2 for the first number and to 5 for the second one, the numbers hence being 12 and 30.

I hope this helps. If I was not clear enough or if you’d like further explanation please let me know. Also, English is not my first language, so I’m sorry for any mistakes.
7 0
3 years ago
If a,b,c and d are positive real numbers such that logab=8/9, logbc=-3/4, logcd=2, find the value of logd(abc)
Eva8 [605]

We can expand the logarithm of a product as a sum of logarithms:

\log_dabc=\log_da+\log_db+\log_dc

Then using the change of base formula, we can derive the relationship

\log_xy=\dfrac{\ln y}{\ln x}=\dfrac1{\frac{\ln x}{\ln y}}=\dfrac1{\log_yx}

This immediately tells us that

\log_dc=\dfrac1{\log_cd}=\dfrac12

Notice that none of a,b,c,d can be equal to 1. This is because

\log_1x=y\implies1^{\log_1x}=1^y\implies x=1

for any choice of y. This means we can safely do the following without worrying about division by 0.

\log_db=\dfrac{\ln b}{\ln d}=\dfrac{\frac{\ln b}{\ln c}}{\frac{\ln d}{\ln c}}=\dfrac{\log_cb}{\log_cd}=\dfrac1{\log_bc\log_cd}

so that

\log_db=\dfrac1{-\frac34\cdot2}=-\dfrac23

Similarly,

\log_da=\dfrac{\ln a}{\ln d}=\dfrac{\frac{\ln a}{\ln b}}{\frac{\ln d}{\ln b}}=\dfrac{\log_ba}{\log_bd}=\dfrac{\log_db}{\log_ab}

so that

\log_da=\dfrac{-\frac23}{\frac89}=-\dfrac34

So we end up with

\log_dabc=-\dfrac34-\dfrac23+\dfrac12=-\dfrac{11}{12}

###

Another way to do this:

\log_ab=\dfrac89\implies a^{8/9}=b\implies a=b^{9/8}

\log_bc=-\dfrac34\implies b^{-3/4}=c\implies b=c^{-4/3}

\log_cd=2\implies c^2=d\implies\log_dc^2=1\implies\log_dc=\dfrac12

Then

abc=(c^{-4/3})^{9/8}c^{-4/3}c=c^{-11/6}

So we have

\log_dabc=\log_dc^{-11/6}=-\dfrac{11}6\log_dc=-\dfrac{11}6\cdot\dfrac12=-\dfrac{11}{12}

4 0
3 years ago
Samuel used 1/5 of an ounce of butter to make 1/25 of pound of jelly how many ounces of butter is there per pound of jelly
Svetach [21]
1 ounce --> ?
1/5 -->  1/25
i chaged the freactions to decimal this is what i got,
1ounce --> ?
0.2 ounce--> 0.04 ounces
divide 0.2 ounces by 0.04 ounces and you'll get the answer
0.2 is the answer per pound of jelly you will use o.2 ounces
4 0
3 years ago
Please help. Question is in the picture
kumpel [21]
Number 4: line XZ; number 5: theory of congruent triangles.
4 0
3 years ago
What is the constant of proportionality for the graph?
Lelechka [254]

Answer:

k = 5

Step-by-step explanation:

y = kx

10 = 2k

k = 5

3 0
3 years ago
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