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Xelga [282]
2 years ago
5

for each x-y table given,copy the table, find the pattern and fill in the missing entries. Then write the rule for the pattern i

n words.​

Mathematics
1 answer:
mash [69]2 years ago
8 0

Answer:

  see the attached for the table and rules

Step-by-step explanation:

a) A graph of the given points shows they lie on the same line, one with a slope of 3 and a y-intercept of 2. Thus the rule is ...

  y = 3x +2

see the attachment for table values

__

b) The ratios of given points are all the same: y/x = 5/2, so that is the constant of proportionality:

  y = (5/2)x

see the attachment for table values

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Elliot collects miniature toy cars. He wants to fill 4 display cases.each display case holds 15 cars. He has 28 cars now, and he
baherus [9]

Answer:

Elliot has to wait 11 months before he has enough cars

Step-by-step explanation:

Elliot has 4 display cases with each case being able to hold 15 cars. Thus we know

total # of cars Elliot can place in his display case = 4 * 15 = 60 cars

From this, we can figure out how many more cars Elliot needs by subtracting the amount of cars he already has

# of cars Elliot needs = 60 - 28 = 32 cars

Now to find the number of months Elliot needs, we divide by how many he can buy each month

# of months Elliot needs to save up for = 32 / 3 = 10 2/3

Assuming Elliot does not get his allowance until the end of the month, we will have to round the number of months up to the nearest integer, 11

7 0
2 years ago
Jessica is 5 years older than her sister Jenna. Jenna tells her sister that in 5 years, she will be as old as Jessica was 5 year
emmasim [6.3K]
                          Jenna's age                   Jessica's age

today                         x                               x + 5


in 5 years                 x+5 

5 years ago                                                   x + 5 - 5


Equality                  x + 5 = x + 5 - 5

=> x + 5 = x


The equation is x + 5 = x


That equation has not any solution, because it reduces to 5 = 0, which is an absurd.


So, the conclusion is that information given by Jenna is wrong.


It is logical: if the difference of the ages is 5, in five years Jenna will have 10 years more than what her sister had 5 years ago, no 5 as she told Jessica.
5 0
2 years ago
Read 2 more answers
EXAMPLE 5 If F(x, y, z) = 4y2i + (8xy + 4e4z)j + 16ye4zk, find a function f such that ∇f = F. SOLUTION If there is such a functi
Valentin [98]

If there is such a scalar function <em>f</em>, then

\dfrac{\partial f}{\partial x}=4y^2

\dfrac{\partial f}{\partial y}=8xy+4e^{4z}

\dfrac{\partial f}{\partial z}=16ye^{4z}

Integrate both sides of the first equation with respect to <em>x</em> :

f(x,y,z)=4xy^2+g(y,z)

Differentiate both sides with respect to <em>y</em> :

\dfrac{\partial f}{\partial y}=8xy+4e^{4z}=8xy+\dfrac{\partial g}{\partial y}

\implies\dfrac{\partial g}{\partial y}=4e^{4z}

Integrate both sides with respect to <em>y</em> :

g(y,z)=4ye^{4z}+h(z)

Plug this into the equation above with <em>f</em> , then differentiate both sides with respect to <em>z</em> :

f(x,y,z)=4xy^2+4ye^{4z}+h(z)

\dfrac{\partial f}{\partial z}=16ye^{4z}=16ye^{4z}+\dfrac{\mathrm dh}{\mathrm dz}

\implies\dfrac{\mathrm dh}{\mathrm dz}=0

Integrate both sides with respect to <em>z</em> :

h(z)=C

So we end up with

\boxed{f(x,y,z)=4xy^2+4ye^{4z}+C}

7 0
2 years ago
Agent Hunt is transferring classified files from the CIA mainframe to his flash drive. The variable S models the size of the fil
amid [387]

Answer:

<h2>50MB</h2>

Step-by-step explanation:

\bold{METHOD\ 1:}\\\\\text{Calculate the value of }S\ \text{in}\ 10s,\ 20s,\ 30s,\ ... \text{and difference if them}\\\\for\ t=10:\\\\S=5(10)+45=50+45=95\\\\for\ t=20:\\\\S=5(20)+45=100+45=145\\\\for\ t=30:\\\\S=5(30)+45=150+45=195\\\\195-145=50\\145-95=50\\\\\boxed{50\ MB\ per\ 10s}

\bold{METHOD\ 2:}\\\\S_1=5t+45\to \text{in t second}\\\\S_2=5(t+10)+45\to \text{10 second leter}\\\\\text{Difference}\\\\S_2-S_1=5(t+10)+45-(5t+45)=5t+50+45-5t-45=50\\\\\boxed{50MB\ per\ 10s}

6 0
2 years ago
Read 2 more answers
Given: △PTC
Natalka [10]
Given the the two angles find the missing angle of P which is 30 degrees.

Since angle P and C are identical their sides are congruent.

The hypotenuse, the largest side is PC because it corresponds to angle T

Using Pythagorean Theorem
a^2 + b^2 = c^2

(PT)^2 + (CT)^2 = (PC)^2
Given that PT is 4 and knowing PT and CT are congruent we can rewrite this
(4)^2 + (4)^2 = (PC)^2
PC = rad(32)

Someone fact check plz
6 0
2 years ago
Read 2 more answers
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