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const2013 [10]
3 years ago
11

Write a word phrase for 1/5 (3x+4).

Mathematics
1 answer:
IrinaVladis [17]3 years ago
3 0
One fifth times the sum of three times a number plus four.
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a. Find symmetric equations for the line that passes through the point (4, −4, 8) and is parallel to the vector −1, 4, −3b. Find
daser333 [38]

The line has equation

\vec r(t)=(4,-4,8)+(-1,4,-3)t

where t is any real number. (-1,4,-3)t is the line containing all scalar multiples of the vector (-1, 4, -3); we add (4, -4, 8) to shift the line so that it passes through this point while remaining parallel to the the line.

To get the symmetric form, we have

\begin{cases}x(t)=4-t\\y(t)=-4+4t\\z(t)=8-3t\end{cases}

Solving for t in each equation gives the symmetric form,

t=\boxed{4-x=\dfrac{y+4}4=\dfrac{8-z}3}

The line has intercepts in the coordinate planes wherever either the x, y, or z coordinate is 0.

xy-plane:

z=0\implies\begin{cases}4-x=\frac83\\\frac{y+4}4=\frac83\end{cases}\implies\left(\dfrac43,\dfrac{20}3,0\right)

yz-plane:

x=0\implies\begin{cases}\frac{y+4}4=4\\\frac{8-z}3=4\end{cases}\implies\left(0,12,-4\right)

xz-plane:

y=0\implies\begin{cases}4-x=1\\\frac{8-z}3=1\end{cases}\implies\left(3,0,5\right)

7 0
3 years ago
Define the variables and write a system of equations to represent the given situation do not solve
Kaylis [27]

Answer:  28x  + 15y = 131   and x + y =  7   where x is the number of Dress shirt and y is the number of T-shirt.

Step-by-step explanation:

We will represent the number of Dress shirt he bought by x and we will represent the number of T-shirt he bought by y.

We know that he spent 131 so the cost of each dress shirt plus the cost of each T-shirt has to equal  131.  Also, he bought 7 total shirts so x plus y has to equal 7.

28x  + 15y = 131  

x + y =  7

Note: it says don't solve so I didn't solve but if you want to solve use these equations.

4 0
3 years ago
The ponce de leon lighthouse in St.Augustine, Florida, is the second tallest brick tower in the United States.It was built in 18
vovikov84 [41]
Using a right triangle formed by boat with base and top of lighthouse.Note: 15 minutes = 0.25 degreesLet d be distance the boat is from shore.tan(90−13.25)=d/175
d=175∗tan(76.75)=743.2
6 0
3 years ago
Read 2 more answers
Two or more complete sentences, explain how to use ordered pairs of points in f(x) and g(x) to determine if f(x) and g(x) are in
kati45 [8]
If f(x) is an inverse of g(x),

when
f(x)=y
g(y)=x

aka
f(g(x))=x
g(f(x))=x


basically, the values should be swiched

example
f(x)=
(1,2)
(2,3)
(4,5)
then g(x)=
(2,1)
(3,2)
(5,4)
6 0
3 years ago
What is 10/n = 15/45 solved?
Lina20 [59]
The answer would be 3.33333. I think because 10*15= 150. Then you would divide it by 45 and you would get 3.333. If you get it wrong im sorry.
8 0
3 years ago
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