Which expressions are equivalent to -3 -(7.5+4)

Using a graphing utility, find the exact solutions of the system. Round to the nearest hundredth and choose a solution to the sy

Margaret [11]

Answer:

Part 1) The exact solutions are

$(\frac{-1+\sqrt{21}} {2},4+\sqrt{21})$ and $(\frac{-1-\sqrt{21}} {2},4-\sqrt{21})$

Part 2) (1.79, 8.58)

Step-by-step explanation:

we have

$y=x^{2} +3x$ ----> equation A

$y=2x+5$ ----> equation B

we know that

When solving the system of equations by graphing, the solution of the system is the intersection points both graphs

Find the exact solutions of the system

equate equation A and equation B

$x^{2} +3x=2x+5\\x^{2} +3x-2x-5=0\\x^{2} +x-5=0$

The formula to solve a quadratic equation of the form

$ax^{2} +bx+c=0$

is equal to

$x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$x^{2} +x-5=0$

so

$a=1\\b=1\\c=-5$

substitute in the formula

$x=\frac{-1\pm\sqrt{1^{2}-4(1)(-5)}} {2(1)}$

$x=\frac{-1\pm\sqrt{21}} {2}$

so

The solutions are

$x_1=\frac{-1+\sqrt{21}} {2}$

$x_2=\frac{-1-\sqrt{21}} {2}$

Find the values of y

First solution

For $x_1=\frac{-1+\sqrt{21}} {2}$

$y=2(\frac{-1+\sqrt{21}} {2})+5$

$y=-1+\sqrt{21}+5\\\\y=4+\sqrt{21}$

The first solution is the point $(\frac{-1+\sqrt{21}} {2},4+\sqrt{21})$

Second solution

For $x_2=\frac{-1-\sqrt{21}} {2}$

$y=2(\frac{-1-\sqrt{21}} {2})+5$

$y=-1-\sqrt{21}+5\\\\y=4-\sqrt{21}$

The second solution is the point $(\frac{-1-\sqrt{21}} {2},4-\sqrt{21})$

Round to the nearest hundredth

First solution

$(\frac{-1+\sqrt{21}} {2},4+\sqrt{21})$ -----> $(1.79,8.58)$

$(\frac{-1-\sqrt{21}} {2},4-\sqrt{21})$ -----> $(-2.79,-0.58)$

see the attached figure to better understand the problem

6 0

3 years ago

Help 50 PTS

Leno4ka [110]

Answer:

It tells you 2 different things

Step-by-step explanation:

1. It could tell you that Tyler's book is much more expensive than Felix's.

2. It could tell you that they're the same price but Tyler sold more.

3 0

3 years ago

A metalworker has a metal alloy that is 15% copper and another alloy that is 60% copper. How many kilograms of each alloy shou

coldgirl [10]

18 kg of 15% copper and 72 kg of 60% copper should be combined by the metalworker to create 90 kg of 51% copper alloy.

Step-by-step explanation:

Let x = kg of 15% copper alloy

Let y = kg of 60% copper alloy

Since we need to create 90 kg of alloy we know:

x + y = 90

51% of 90 kg = 45.9 kg of copper

So we're interested in creating 45.9 kg of copper

We need some amount of 15% copper and some amount of 60% copper to create 45.9 kg of copper:

0.15x + 0.60y = 45.9

but

x + y = 90

x= 90 - y

substituting that value in for x

0.15(90 - y) + 0.60y = 45.9

13.5 - 0.15y + 0.60y = 45.9

0.45y = 32.4

y = 72

Substituting this y value to solve for x gives:

x + y = 90

x= 90-72

x=18

Therefore, in order to create 90kg of 51% alloy, we'd need 18 kg of 15% copper and 72 kg of 60% copper.

6 0

3 years ago

If x=0. Find the value of 8x-2(6-x)

Harrizon [31]

Answer:

-12

Step-by-step explanation:

8x - 2(6 - x)

Substitute 0 for each x

8*0 - 2(6 - 0)

Solve.

0 - 2*6

0 - 12

-12

7 0

3 years ago

Read 2 more answers

en una fiesta hay 16 personas de las cuales el 25% son mujeres, luego llegan mas mujeres a la fiesta, de tal manera que ahora lo

coldgirl [10]

Answer:

English (Ingles):
10 Women come to the party.

Spanish (Espanol):

10 Las mujeres vienen a la fiesta.

Step-by-step explanation:

English (Ingles):

We know that there are 16 people there at the start. 25% of those people are women. We can work out by subtracting 100 by 25 that 75% of the p-eople there are men. We need to do 25% of 16 so we can work out how many men and women there are there.

So we find 10% of 16 which is 1.6 then we take off 5% of 1.6 which is 0.08. We then double 1.6 to get 20% which gives us 3.2. We now add on the 5% to make it 25% which gives us 4.

This means 25% of 16 is 4.

This tells us that there are 4 women at the party and 12 men as 16 - 4 = 12.

It now says that more women arrive which makes the percentage for men go down to 60%. We now need to add 5% on to the 25% of women there are which will tell us how many more women there are now and it will let us work out how many women and men there are in total now.

As we can't do this without it giving us 4.8, we know that 25% of people is 4 women which means 50% of people would be 8 women and we make an estimate of how many women have joined which gives us 6 people which means the total amount of women at the party is 10.

Spanish (Espanol):

Sabemos que hay 16 personas allí al principio. El 25% de esas personas son mujeres. Podemos calcular restando 100 por 25 que el 75% de las personas son hombres. Necesitamos hacer el 25% de 16 para poder calcular cuántos hombres y mujeres hay allí.

Así que encontramos el 10 % de 16, que es 1,6, luego quitamos el 5 % de 1,6, que es 0,08. Luego duplicamos 1,6 para obtener el 20%, lo que nos da 3,2. Ahora sumamos el 5% para convertirlo en 25%, lo que nos da 4.

Esto significa que el 25% de 16 es 4.

Esto nos dice que hay 4 mujeres en la fiesta y 12 hombres como 16 - 4 = 12.

Ahora dice que llegan más mujeres lo que hace que el porcentaje de hombres baje al 60%. Ahora necesitamos agregar un 5% al 25% de mujeres que hay, lo que nos dirá cuántas mujeres más hay ahora y nos permitirá calcular cuántas mujeres y hombres hay en total ahora.

Como no podemos hacer esto sin que nos dé 4.8, sabemos que el 25% de las personas son 4 mujeres, lo que significa que el 50% de las personas serían 8 mujeres y hacemos una estimación de cuántas mujeres se han unido, lo que nos da 6 personas que significa que la cantidad total de mujeres en la fiesta es 10.

4 0

1 year ago