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2 years ago

Multiply: (x+4)(x^2+2x+3) Simplify and write your answer in Standard Form.

Mathematics

1 answer:

Oxana [17]2 years ago

6 0

Answer:

x^3+6x^2+11x+12

Step-by-step explanation:

(x+4)(x^2+2x+3)

=x(x^2+2x+3)+4(x^2+2x+3) [by multiplying with bith sides]

=x^3+2x^2+3x+4x^2+8x+12

=x^3+2x^2+4x^2+3x+8x+12

=x^3+6x^2+11x+12

(please mark me brainliest)

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Jude has 30 coins of quarters and nickels. The total amount he has is $5.10. How many of each coin does Jude have? Write the sys

Lyrx [107]

Answer: Required system

x+y= 30

0.25x+0.05y=5.10

Jude has 18 quarters and 12 nickels.

Step-by-step explanation:

Let x= Number of quarters

y= Number of nickels

As per given,

x+y= 30 (i)

0.25x+0.05y=5.10 (ii) [1 quarter = $0.25 , 1 nickel = $0.05]

Multiply 0.25 on both sides of equation (i)

0.25x+0.25y= 7.5 (iii)

Eliminate (ii) from (iii) , we get

0.20y=2.4

⇒ y = 12 [divide both sides by 0.20]

Put value of y in (i\), we get

x+12=30

⇒ x= 30-12= 18

Hence, Jude has 18 quarters and 12 nickels.

8 0

3 years ago

Please help with this problem

Andre45 [30]

Answer:

The length of the short side is 14.5 units, the length of the other short side is 18.5 units, and the length of the longest side is 23.5 units.

Step-by-step explanation:

The Pythagorean Theorem

If a and b are the lengths of the legs of a right triangle and c is the length of the hypotenuse, then the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.

This relationship is represented by the formula:

$a^2+b^2=c^2$

Applying the Pythagorean Theorem to find the lengths of the three sides we get:

$(x)^2+(x+4)^2=(x+9)^2\\\\2x^2+8x+16=x^2+18x+81\\\\2x^2+8x-65=x^2+18x\\\\2x^2-10x-65=x^2\\\\x^2-10x-65=0$

Solve with the quadratic formula

$\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}$

$x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$\mathrm{For\:}\quad a=1,\:b=-10,\:c=-65:\quad x_{1,\:2}=\frac{-\left(-10\right)\pm \sqrt{\left(-10\right)^2-4\cdot \:1\left(-65\right)}}{2\cdot \:1}\\\\x_{1}=\frac{-\left(-10\right)+ \sqrt{\left(-10\right)^2-4\cdot \:1\left(-65\right)}}{2\cdot \:1}=5+3\sqrt{10}\\\\x_{2}=\frac{-\left(-10\right)- \sqrt{\left(-10\right)^2-4\cdot \:1\left(-65\right)}}{2\cdot \:1}=5-3\sqrt{10}$

Because a length can only be positive, the only solution is

$x=5+3\sqrt{10}\approx 14.5$

The length of the short side is 14.5, the length of the other short side is $14.5+4=18.5$ , and the length of the longest side is $14.5+9=23.5$ .

3 0

3 years ago

Pls help 3.60 km 2.80 km 3.20 km 3.24 km

trapecia [35]

Answer:

3.24 km

Step-by-step explanation:

Because the two triangles are similar, we can set the sides of as a proportion:

$\frac{TR}{QR} = \frac{ST}{PQ}$

Now, let's plug in the side lengths:

$\frac{1.25}{2.25} = \frac{1.80}{PQ}$

Lastly, Solve for PQ.

$\frac{1.25}{2.25} = \frac{1.80}{PQ}\\\\1.80*2.25 = 1.25*PQ\\\\4.05 = 1.25*PQ\\\\\frac{4.05}{1.25} = PQ\\\\3.24 = PQ$

8 0

3 years ago

5x^{2} -60 = 20 Solve by using the quadratic formula PLZ help

almond37 [142]

Answer: x=4,-4 Solve the equation for x by finding a, b, and c of the quadratic then applying the quadratic formula

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3 years ago

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Hoochie [10]

Using the property of inverse, $f^{-1}(f(x))=x$ , we can extend the given table
x f(x) f^(-1)(f(x))
-1 1 -1
2 3 2 $f^(-1)(3)=f^{-1}(f(2))=2$
3 6 3
5 7 5
7 8 7 $f^(-1)(8)=f^{-1}(f(7))=7$

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3 years ago