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3 years ago

Pure mathematicsssss

Mathematics

1 answer:

stepan [7]3 years ago

3 0

Answer:

(i) a = 2

b = -1

c = -1

(ii) x= 1

Step-by-step explanation:

Step 1: Factorise

$f(x) = 2(x^{2} -2x+\frac{1}{2})$

Step 2: Use the complete square method.

$f(x)=2(x^{2} -2x+(\frac{-2}{2})^{2} + \frac{1}{2} - (\frac{-2}{2})^{2} )$

Step 3: Have it to $a(x+b)^{2} +c$

$f(x)=2((x-1)^{2} -\frac{1}{2} )\\ = 2(x-1)^{2} -1$

Line of symmetry:

To find line of symmetry, we use -b/2a formula.

Based from $2x^{2} -4x+1$ :

a=2, b=-4

-b/2a = -(-4)/2(2) = 1

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Evaluate the expression -7 1/4x + 3 5/8 for x= -4

Misha Larkins [42]

Answer:

32 5/8 (or 32 and 5/8)

Step-by-step explanation:

Okay, so this problem is asking for us to solve this problem with the substitution of a variable: x = -4. Before we fully solve this problem, we need to replace all of those x variables with -4 so that it is easier to solve.

-7 1/4(-4) + 3 5/8.

To make this problem even easier to solve, let's turn these mixed numbers into improper fractions. To do this, multiply the denominator by the whole number. Then add the numerator to this number. The new number that you just got is now your new numerator for this number.

-29/4(-4) + 3 5/8.

Repeat the last step to turn the other mixed number into an improper fraction.

-29/4(-4) + 29/8.

Now let's multiply that -4 by 29/4. Because a whole number technically has a denominator of 1, we can now set up the next part of our problem. (The symbol * means multiplication since we can't use x since it is already being used as a variable in this equation.)

(-29/4 * -4/1) + 29/8.

29 + 29/8.

Now to solve the rest of this problem, let's convert the whole number of 29 so that it has a denominator of 8. This is that these two numbers are addable.

29 x 8 = 232

1 x 8 = 8

Now these numbers are addable. So:

232/8 + 29/8 = 261/8 = 32 5/8.

I hope that this helps.

4 0

3 years ago

carlas cab ride cost 22$ she wants to leave a 15% tip what is her tip? what is her total cost for the cab ride?

Semenov [28]

Boo you don't know this just do +++++++++++

5 0

3 years ago

Read 2 more answers

Sally has 16 marbles in her collection. John has only 7 marbles. Sally gives John 8 of her marbles. How much marbles does John h

Sati [7]

Answer:

The answer is 15

Step-by-step explanation:

hope this helps

5 0

3 years ago

The probability of event X is 30%. The probability of event Y is 40%. If events X and Y are mutually exclusive, what is the prob

Soloha48 [4]

The probability of event X or Y is P = 0.7, or, in percentage form, the probability is 70%.

<h3>How the get the probability of event X or Y?</h3>

First, two events are mutually exclusive if these events can't happen at the same time.

This means that if happens X, with a 30% of probability, then Y can't happen.

If happens Y, with a 40% of probability, then X can't happen.

Then the probability of X or Y (the probability that one of these two events happens, not both) is just the addition of the two individual probabilities.

Then we have:

P(X or Y) = 0.3 + 0.4 = 0.7

Or, in percent form, we get:

P(X or Y) = 70%

The probability of event X or Y is just 70%.

If you want to learn more about probability:

brainly.com/question/25870256

#SPJ1

7 0

2 years ago

Se quiere construir un muro de 4 m de alto, 12 m de largo y 10 cm de espesor. ¿Cuántos ladrillos de 8 cm de alto, 20 cm de largo

Llana [10]

Answer:

3000

Step-by-step explanation:

Let's start by finding the volume of the wall. The volumen of the wall can be considered as the volume of a rectangular prism. The volume of a rectangular prism is given by:

$V_w=w*l*h\\\\Where:\\\\w=Width=10cm=0.1m\\l=Length=12m\\h=Height=4m$

So the volume of the wall is:

$V_w=0.1*12*4=4.8m^3$

Now, we can find the volume of the brick using the same method since a brick can be considered as a rectangular prism as well:

$V_b=w*l*h\\\\For\hspace{3}the\hspace{3}brick\\\\w=10cm=0.1m\\l=20cm=0.2m\\h=8cm=0.08m$

Hence:

$V_b=(0.1)*(0.2)*(0.08)=0.0016m^3$

In order to know how many bricks are required to build the wall, we just need to fill the wall volume with the number of bricks of this volume. So:

$V_w=nV_b\\\\Where\\\\n=Number\hspace{3}of\hspace{3}bricks$

Solving for n:

$n=\frac{V_w}{V_b} =\frac{4.8}{0.0016} =3000$

Therefore, we need 3000 bricks to build that wall.

Translation:

Comencemos por encontrar el volumen del muro. El volumen del muro puede considerarse como el volumen de un prisma rectangular. El volumen de un prisma rectangular viene dado por:

$V_w=w*l*h\\\\Donde:\\\\w=Espesor=10cm=0.1m\\l=Largo=12m\\h=Alto=4m$

Entonces el volumen del muro es:

$V_w=0.1*12*4=4.8m^3$

Ahora, podemos encontrar el volumen del ladrillo utilizando el mismo método, ya que un ladrillo también puede considerarse como un prisma rectangular:

$V_b=w*l*h\\\\Para\hspace{3}el\hspace{3}ladrillo\\\\w=10cm=0.1m\\l=20cm=0.2m\\h=8cm=0.08m$

Por lo tanto:

$V_b=(0.1)*(0.2)*(0.08)=0.0016m^3$

Para saber cuántos ladrillos se requieren para construir el muro, solo necesitamos llenar el volumen del muro con la cantidad de ladrillos de este volumen. Entonces:

$V_w=nV_b\\\\Donde\\\\n=Numero\hspace{3}de\hspace{3}ladrillos$

Resolviendo para n:

$n=\frac{V_w}{V_b} =\frac{4.8}{0.0016} =3000$

Por lo tanto, necesitamos 3000 ladrillos para construir ese muro.

4 0

4 years ago