The points of tangency are:

How much of 30% HCI and 45% HCI would be needed to mix and produce 50 liters of 35% HCI

VladimirAG [237]

Answer:

33 1/3 liters of 30%
16 2/3 liters of 45%

Step-by-step explanation:

Let x represent the liters of 45% solution needed. Then the amount of HCl in the mix is ...

0.45x +0.30(50 -x) = 0.35(50)

0.15x = 0.05(50) . . . . . simplify, subtract 0.30(50)

x = (0.05/0.15)(50) = 50/3 = 16 2/3 . . . liters of 45% HCl

33 1/3 liters of 30% and 16 2/3 liters of 45% HCl are needed.

_____

Comment on the solution

You may notice that the general solution to a mixture problem of this sort is that the fraction of the mix that is the highest contributor is ...

(mix % - low %) / (high % - low %) = (.35 -.30) / (.45 -.30) = .05/.15 = 1/3

5 0

3 years ago

I need help can anyone help me with this pls

Cerrena [4.2K]

It might be 2.5 but I could be wrong

3 0

3 years ago

Part

goldfiish [28.3K]

When a shape is rotated, it must be rotated around a point.

To determine the location of the new triangle, Sonja must subtract (5,-1) from the coordinates of the original triangle, before rotating by $90^o$ .

From the question, we have:

$C = (5,-1)$ --- the center of rotation

Let the vertices of the triangle be (x,y).

First, she must subtract the coordinates of the center of rotation from the vertices of the triangle.

This gives:

$(x,y) \to (x - 5, y + 1)$

Then the vertices are rotated by $90^o$

The rule of $90^o$ rotation is:

$(x,y) \to (-y,x)$

So, we have:

$(x - 5,y + 1) \to (-y - 1,x - 5)$

From the attachment, the coordinates of the triangle are: (0,2), (0,5) and (4,2)

After rotation, the coordinates are calculated as follows:

$(0,2) \to (-2-1,0-5) \to (-3,-5)$

$(0,5) \to (-5-1,0-5) \to (-6,-5)$

$(4,2) \to (-2-1,4-5) \to (-3,-1)$

Hence, the coordinates are: (-3,-5), (-6,-5) and (-3,-1)

Read more about rotations at:

brainly.com/question/1571997

3 0

3 years ago

1. Una escalera de 4 m de longitud se apoya sobre una pared vertical. Si la distancia entre la base de la escalera a la pared es

enot [183]

Answer:

puedes resolver de dos maneras si diste teorema de Pitágoras lo aplicas

hipotenusa al cuadrado = cateto 2 +cateto 2 ( el 2 significa al cuadrado)

sustituyes

hipotenusa= 4m

cateto= 2,5

hay que hallar el otro cateto que nos daría la altura a la que está la escalera

despejamos y tenemos

cateto 2= hip2 -cat2

cat2=(4)2-(2,5)2=

= 16-6,25=9,75

luego hallamos la raíz cuadrada de 9,75= 3,12

la altura a la que se encuentra es 3,12m

-si aun no diste Pitágoras podes representarlo en una hoja utilizando cm en lugar de metros( a escala). trazas el triángulo rectángulo la base te la da la distancia a la cual se encuentra la escalera de la pared es decir 2,5cm trazas la hipotenusa de 4cm de manera que coincida con el cateto opuesto , y mides el valor de este ,será de 3,12cm no olvides que la respuesta la debes dar en metros ya que es la unidad de medida que te da.

4 0

2 years ago

Solve the inequality 4t^2 ≤ 9t-2 please show steps and interval notation. thank you!

Misha Larkins [42]

Answer:

[0.25, 2]

Step-by-step explanation:

We have

4t² ≤ 9t-2

subtract 9t-2 from both sides to make this a quadratic

4t²-9t+2 ≤ 0

To solve this, we can solve for 4t²-9t+2=0 and do some guess and check to find which values result in the function being less than 0.

4t²-9t+2=0

We can see that -8 and -1 add up to -9, the coefficient of t, and 4 (the coefficient of t²) and 2 multiply to 8, which is also equal to -8 * -1. Therefore, we can write this as

4t²-8t-t+2=0

4t(t-2)-1(t-2)=0

(4t-1)(t-2)=0

Our zeros are thus t=2 and t = 1/4. Using these zeros, we can set up three zones: t < 1/4, 1/4<t<2, and t>2. We can take one random value from each of these zones and see if it fits the criteria of

4t²-9t+2 ≤ 0

For t<1/4, we can plug in 0. 4(0)²-9(0) + 2 = 2 >0 , so this is not correct

For 1/4<t<2, we can plug 1 in. 4(1)²-9(1) +2 = -3 <0, so this is correct

For t > 2, we can plug 5 in. 4(5)²-9(5) + 2 = 57 > 0, so this is not correct.

Therefore, for 4t^2 ≤ 9t-2 , which can also be written as 4t²-9t+2 ≤ 0, when t is between 1/4 and 2, the inequality is correct. Furthermore, as the sides are equal when t= 1/4 and t=2, this can be written as [0.25, 2]

8 0

3 years ago