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3 years ago

The sum of two numbers is 47. one of the numbers is 2 more than twice the other number. find the value of the smaller number.

1 answer:

4 0

X + y = 47
x = 2y + 2

2y + 2 + y = 47
3y + 2 = 47
3y = 47 - 2
3y = 45
y = 45/3
y = 15

x = 2y + 2
x = 2(15) + 2
x = 30 + 2
x = 32

ur numbers are 15 and 32

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2 years ago

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Solve 4 by 216 raise to minus 2 by 3 + 1 by 256 raise to 3 by 4 + 2 by 243 raise to 1 by 5

olchik [2.2K]

Answer:

214....

Step-by-step explanation:

If the question is : solve 4 by 216 raise to minus 2 by 3 + 1 by 256 raise to minus 3 by 4 + 2 by 243 raise to minus 1 by 5

The given expression can be written as:

4/(216)-2/3+1/(256)-3/4+2/(243)-1/5

This expression has three terms.

Notice that the exponents are negative:

We will change the division into multiplication so that the exponents will become positive;

4*(216)^2/3+ 1*(256)^3/4+ 2*(243)^1/5

If we multiply 6 three times it will give us 6^3=6*6*6=216

If we multiply 4 four times it will give us 4^4=4*4*4*4=256

If we multiply 3 five times it will give us 3^5=3*3*3*3*3=243

So we will write it as:

=4*(6^3)^2/3+ 1(4^4)3/4 +2(3^5)^1/5

=4(6)^2+(4)^3+2(3)

=4*36+64+6

=144+64+6

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The answer is 214....

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2 years ago

If Dominik completes a project by himself, it will take him 8 hours. Working with Katarina, it will take them 5 hours. If they w

Marysya12 [62]

The main formula we use here is Work=Rate*Time,

1. The rate (speed of working) of Dominik is

$r_D=1project/8hours= \frac{1}{8}(prj/h)$

2. Let the the rate of Katarina be $r_K=x(prj/h)$

Together they have a rate of $r_D_K$ equal to $\frac{1}{8}+x$ (project per hour)

so $(\frac{1}{8}+x) ( \frac{proj}{hr})*5(hr)=1(proj)$

simplify the units:

$(\frac{1}{8}+x) *5=1$

$\frac{1}{8}+x = \frac{1}{5}$

$x= \frac{1}{5}- \frac{1}{8}= \frac{8-5}{40}= \frac{3}{40}$

so the rate of Katarina is 3/40 (proj per hour)

Now, the rate of Dominik was 1/8 (pr/hr)=5/40 (pr/hr)

In 5 hours Dominik complets 5*5/40=25/40 of the project

Katarina completes 5*3/40=15/40 of the project.

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2 years ago

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12. Let yo = O. Write parametric equations to represent the path of the ballsthrown by Sami and T'Aisha given the following cond

ira [324]

SOLUTION:

We want to write the x and y parametric equation for Sami and T'Aisha given their following data.

$\begin{gathered} Sami:v_0=15\frac{ft}{s},\theta=35^o,y_0=5.4ft \\ T^{\prime}Aisha:v_0=19\frac{ft}{s},\theta=50^o,y_o=5.8ft \\ x_0=0 \end{gathered}$

The parametric equations for x and y are given by;

$\begin{gathered} x(t)=x_0+(v_0cos\theta)t \\ y(t)=y_0+(v_0sin\theta)t+0.5gt^2 \end{gathered}$

Inserting, the values, we have; For Sami;

$\begin{gathered} Sami: \\ x\left(t\right)=15cos35t, \\ y\left(t\right)=5.4+15sin35t-16t^2 \end{gathered}$

For T'Aisha;

$\begin{gathered} T^{\prime}Aisha: \\ x\left(t\right)=19cos50t, \\ y\left(t\right)=5.8+19sin50t-16t^2 \end{gathered}$

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11 months ago

Which is the slope of the line that passes through the points

padilas [110]

Answer:

The slope is -5/7

Step-by-step explanation:

Slope is rise / run. In other words, the change in y / change in x:

$m= \frac{\Delta y}{\Delta x}\\m= \frac{y_2-y_1}{x_2-x_1}\\m= \frac{4-(-1)}{-2-5}\\m= \frac{5}{-7}$

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2 years ago