Which is the best estimate for the mass of a rose

Find the solution to the system of equations, x + 3y = 7 and 2x + 4y = 8.

kobusy [5.1K]

Answer: Hello there!

here we have two equations:

1) x + 3y = 7

2) 2x + 4y = 8

a) first we want to isolate x in the first equation:

x + 3y = 7

x = 7 -3y

done!

b) now we want to replace it in the second equation, and in this way get a equation that depends only on the variable y.

2x + 4y = 8

2(7 - 3y) + 4y = 8

c) now we sole this equation and obtain the value of y.

14 - 6y + 4y = 8

14 - 2y = 8

-2y = 8 - 14 = -6

y = 6/2 = 3

d) now we have the value of y, and we can substitute it on the equation that we got in the part a)

x = 7 - 3y

x = 7 - 3*3 = 7 - 9 = -2

e) now we knowt that x = -2 and y = 3, then the pair (x,y) can be written as:

(-2,3).

8 0

3 years ago

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Match the graph with the correct equation

devlian [24]

(2,2)
hoped I helped
Sorry if its wrong

6 0

4 years ago

The height of one solid limestone square pyramid is 21 m. A similar solid limestone square pyramid has a height of 30 m. The vol

Elina [12.6K]

Answer:

Part a) The scale factor of the smaller pyramid to the larger pyramid in simplest form is $\frac{7}{10}$

Part b) The ratio of the volume of the smaller pyramid to the larger pyramid is $\frac{343}{1,000}$

Part c) The volume of the smaller pyramid is $4,116\ m^{3}$

Step-by-step explanation:

Part a) The scale factor of the smaller pyramid to the larger pyramid in simplest form

we know that

If two figures are similar, then the ratio of its corresponding sides is equal and this ratio is called the scale factor

so

Let

z----> the scale factor

x----> the height of the smaller pyramid

y----> the height of the larger pyramid

$z=\frac{x}{y}$

substitute the values

$z=\frac{21}{30}$

Simplify

$z=\frac{7}{10}$ -----> scale factor in simplest form

Part b) Ratio of the volume of the smaller pyramid to the larger pyramid

we know that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

so

Let

z----> the scale factor

x----> the volume of the smaller pyramid

y----> the volume of the larger pyramid

$z^{3}=\frac{x}{y}$

we have

$z=\frac{7}{10}$

substitute

$\frac{7}{10}^{3}=\frac{x}{y}$

Rewrite

$\frac{x}{y}=\frac{343}{1,000}$ -----> ratio of the volume of the smaller pyramid to the larger pyramid

Part c) The volume of the smaller pyramid

we know that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

so

Let

z----> the scale factor

x----> the volume of the smaller pyramid

y----> the volume of the larger pyramid

$z^{3}=\frac{x}{y}$

we have

$z=\frac{7}{10}$

$y=12,000\ m^{3}$

substitute the values and solve for x

$(\frac{7}{10})^{3}=\frac{x}{12,000}$

$x=\frac{343}{1,000}(12,000)=4,116\ m^{3}$

8 0

3 years ago

Help please? 15 points here

MakcuM [25]

Answer:

64°

Step-by-step explanation:

In circle with center P, AD is diameter.

$\therefore m\angle DPE + m\angle APE = 180\degree \\\therefore (33k-9)\degree + 90\degree = 180\degree \\\therefore (33k-9)\degree = 180\degree -90\degree \\\therefore (33k-9)\degree = 90\degree \\\therefore 33k-9 = 90\\\therefore 33k= 90+9\\\therefore 33k= 99\\\therefore k= \frac{99}{33}\\\therefore k=3\\ m\angle CPD = (20k +4)\degree \\\therefore m\angle CPD = (20\times 3 +4)\degree \\\therefore m\angle CPD =(60+4)\degree \\\therefore m\angle CPD =64\degree \\m\overset {\frown}{CD} = m\angle CPD\\\therefore m\overset {\frown}{CD} = 64\degree$

4 0

3 years ago

Simplify.<br><br><img src="https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%5C%5C%7D" id="TexFormula1" title="\frac{1}{2\\}" alt="\fra

topjm [15]

1/2d*12d
1*d*12d/2
12d^2/2
6d^2

4 0

2 years ago

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