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3 years ago

Solve 2(x + 1) = 2x + 5.

Mathematics

2 answers:

jarptica [38.1K]3 years ago

6 0

Answer:

No solution

Step-by-step explanation:

Use the distributive property on the first side of the equation by multiplying 2 to all the terms in the parentheses

2x + 2 = 2x + 5

Subtract 2x from both sides

2 = 5

2 ≠ 5

This is not a true statement so there are no solutions

BlackZzzverrR [31]3 years ago

4 0

Answer:

No solutions

Step-by-step explanation:

2(x+1)=2x+5

Expand the parentheses:

2x+2=2x+5

Subtract 2x from both sides:

2=5

Since this is not true, this equation has no solutions. Hope this helps!

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A park district has 45 pine trees and 30 oak trees to be planted. They are separating the trees for different areas. They want e

Lady_Fox [76]

Answer:

greatest number of areas that can be created=5

Step-by-step explanation:

given data

Number of pine trees = 45

Number of oak trees = 30

solution

we want area have same number of both trees

so we get here greatest number of area

we find here greatest common factor of 45 and 30

so Prime factorization of 45 and 30 are

45 = 3 × 3 × 5

30 = 2 × 3 × 5

as here GCF = 5

so here greatest number of areas that can be created=5

6 0

3 years ago

What is the product?

Bas_tet [7]

For the a factor in a 1 and then do the problem once you find the product plug your a back in

4 0

3 years ago

The volume of a sphere whose diameter is 18 centimeters is _ cubic centimeters. If it’s diameter we’re reduced by half, it’s vol

kaheart [24]

<h2>Answer:</h2>

<u>First Part</u>

Given that

$Volume = \frac{4}{3} \pi r^{3}$

We have that

$Volume = \frac{4}{3} \pi r^{3} = \frac{4}{3} \pi (\frac{Diameter}{2})^{3} = \frac{4}{3} \pi 9^{3} = 972\pi cm^{3} \approx 3053.63 cm^{3}$

<u>Second Part</u>

Given that

$Volume = \frac{4}{3} \pi r^{3}$

If the Diameter were reduced by half we have that

$Volume = \frac{4}{3} \pi r^{3} = \frac{4}{3} \pi (\frac{r}{2}) ^{3} = \frac{\frac{4}{3} \pi r^{3}}{8}$

This shows that the volume would be $\frac{1}{8}$ of its original volume

<h2>Step-by-step explanation:</h2>

<u>First Part</u>

Gather Information

$Diameter = 18cm$

$Volume = \frac{4}{3} \pi r^{3}$

Calculate Radius from Diameter

$Radius = \frac{Diameter}{2} = \frac{18}{2} = 9$

Use the Radius on the Volume formula

$Volume = \frac{4}{3} \pi r^{3} = \frac{4}{3} \pi 9^{3}$

Before starting any calculation, we try to simplify everything we can by expanding the exponent and then factoring one of the 9s

$Volume = \frac{4}{3} \pi 9^{3} = \frac{4}{3} \pi 9 * 9 * 9 = \frac{4}{3} \pi 9 * 9 * 3 * 3$

We can see now that one of the 3s can be already divided by the 3 in the denominator

$Volume = \frac{4}{3} \pi 9 * 9 * 3 * 3 = 4 \pi 9 * 9 * 3$

Finally, since we can't simplify anymore we just calculate it's volume

$Volume = 4 \pi 9 * 9 * 3 = 12 \pi * 9 * 9 = 12 * 81 \pi = 972 \pi cm^{3}$

$Volume \approx 3053.63 cm^{3}$

<u>Second Part</u>

Understanding how the Diameter reduced by half would change the Radius

$Radius =\frac{Diameter}{2}\\\\If \\\\Diameter = \frac{Diameter}{2}\\\\Then\\\\Radius = \frac{\frac{Diameter}{2} }{2} = \frac{\frac{Diameter}{2}}{\frac{2}{1}} = \frac{Diameter}{2} * \frac{1}{2} = \frac{Diameter}{4}$

Understanding how the Radius now changes the Volume

$Volume = \frac{4}{3}\pi r^{3}$

With the original Diameter, we have that

$Volume = \frac{4}{3}\pi (\frac{Diameter}{2}) ^{3} = \frac{4}{3}\pi \frac{Diameter^{3}}{2^{3}}\\\\ = \frac{4}{3}\pi \frac{Diameter^{3}}{2 * 2 * 2} = \frac{4}{3}\pi \frac{Diameter^{3}}{8}\\\\$

If the Diameter were reduced by half, we have that

$Volume = \frac{4}{3}\pi (\frac{Diameter}{4}) ^{3} = \frac{4}{3}\pi \frac{Diameter^{3}}{4^{3}}\\\\ = \frac{4}{3}\pi \frac{Diameter^{3}}{4 * 4 * 4} = \frac{4}{3}\pi \frac{Diameter^{3}}{4 * 2 * 2 * 4} = \frac{4}{3}\pi \frac{Diameter^{3}}{8 * 8} = \frac{\frac{4}{3}\pi\frac{Diameter^{3}}{8}}{8}$

But we can see that the numerator is exactly the original Volume!

This shows us that the Volume would be $\frac{1}{8}$ of the original Volume if the Diameter were reduced by half.

3 0

2 years ago

Una empresa comercial vende automóviles cuyo precio es de S/. 60 000, con una cuota inicial del 20%, para cancelar el saldo en 3

Inessa05 [86]

Responder:

2560

Explicación paso a paso:

Dado lo siguiente:

Precio del automóvil = 60000

Cuota inicial = 20% del precio = (0.2 * 60000 = 12,000

Saldo = (60000 - 12000) = 48000

La empresa cobra un interés simple del 12% cada 6 meses

Periodo de pago = 30 meses / 6 = 5 periodos

Interés simple: p * r * t

= 48000 * 0,12 * 5 = 28800

Por lo tanto, monto total a reembolsar, incluidos los intereses:

Balance + 28800; 48000 + 28800 = 76800

El reembolso mensual es fijo;

Por lo tanto,

76800/30 = 2560

4 0

3 years ago

Can someone help me, I don't need to see how u did it just make sure it is correct.

ladessa [460]

Y = - 4x^2 - 3x + 3 This thing is complex with fractions. I have to work it out.
y = -4(x^2 + 3/4 x) + 3
y = -4(x^2 + 3/4 x + (3/8)^2 ) + 3
y = -4(x + 3/8)^2 +3 + 4*(9/64)
y = -4(x + 3/8)^2 + 3 + 9/16
y = -4(x + 3/8)^2 + 3 9/16 Equation in Vertex form. <<<<< answer
y = -4(x + 0.385) + 3.5625 Equation in Vertex form. <<<< answer
One is in decimal form. One in fraction form.

the vertex (-3/8, 3 9/16) or alternately
the vertex (-0.375,3.5625)

You might want the graph to confirm my answer.

4 0

3 years ago