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3 years ago

X(x+7)=4x+10 then needs to get the normal form of the equation x= ?, x=?

Mathematics

1 answer:

Vanyuwa [196]3 years ago

8 0

Answer:

x = - 5, x = 2

Step-by-step explanation:

Given

x(x + 7) = 4x + 10 ← distribute left side

x² + 7x = 4x + 10 ( subtract 4x + 10 from both sides )

x² + 3x - 10 = 0 ← in standard form

(x + 5)(x - 2) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 5 = 0 ⇒ x = - 5

x - 2 = 0 ⇒ x = 2

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What is the name of the tide when the sun, moon, and earth are all aligned, causing the greatest pull for highest and lowest tid

Naily [24]

Answer:

Whenever the earth, moon and sun are aligned, the gravitational pull of the moon is augmented by the gravitational pull of the sun, causing larger than average tidal ranges — meaning especially high high tides and very low low tides. These extreme tides are called “spring tides.”

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

The sum of three consecutive terms in an arithmetic sequence is 27, and their product is 585. find the three terms.

sammy [17]

$\text{the three consecutive terms in an arithmetic sequence}\\a;\ a+d;\ a+2d\\\\\text{system of equals}\\\\ \left\{\begin{array}{ccc}a+a+d+a+2d=27\\a(a+d)(a+2d)=585\end{array}\right\\ \left\{\begin{array}{ccc}3a+3d=27&|:3\\a(a+d)(a+2d)=585\end{array}\right\\ \left\{\begin{array}{ccc}a+d=9&\to d=9-a\\a(a+d)(a+2d)=585\end{array}\right\\$
$\text{substitute to the second equation}\\\\a(a+9-a)(a+2(9-a))=585\\\\a(9)(a+18-2a)=585\\9a(18-a)=585\ \ \ |:9\\a(18-a)=65\\18a-a^2=65\ \ \ |\text{change the signs}\\a^2-18a=-65\\a^2-2a\cdot9=-65\ \ \ |+9^2\\\underbrace{a^2-2a\cdot9+9^2}_{(a-b)^2=a^2-2ab+b^2}=-65+9^2\\(a-9)^2=16\to a-9\pm\sqrt{16}\\a-9=-4\ \vee\ a-9=4\ \ \ |+9\\a=5\ \vee\ a=13\\\\d=9-5=4\ \vee\ d=9-13=-4$
$Answer:\ a=5;\ a+d=9; a+2d=13\ vee\ a=13;\ a+d=9;\ a+2d=5$

5 0

3 years ago

A.(2,1)

Alex17521 [72]

Answer:

D(6, 3)

Step-by-step explanation:

The diagonals of a rectangle bisect each other, so the midpoint of AC is the same as the midpoint of BD. This means ...

(A +C)/2 = (B +D)/2 . . . . the midpoints are the same

A +C = B +D . . . . . . . . . multiply by 2

D = A +C -B = (2+5-2, 1+5-3) . . . . . solve for D, substitute given coordinates

D = (6, 3)

4 0

3 years ago

Given two vectors A=2i+3j+4k,B=i-2j+3k find the magnitude and direction of sum<br>(physics question)

Law Incorporation [45]

Answer:

$Magnitude =\sqrt{59} \\\\Direction \: of \: \overrightarrow{A + B} = \frac{3}{\sqrt {59}} , \:\frac{1}{\sqrt {59}} , \:\frac{7}{\sqrt {59}}$

Step-by-step explanation:

A=2i+3j+4k

B=i-2j+3k

Sum of the vectors:

A + B = 2i+3j+4k + i-2j+3k = 3i + j + 7k

$Magnitude =\sqrt{3^2 + 1^2+ 7^2} \\\\Magnitude =\sqrt{9+1+49} \\\\Magnitude =\sqrt{59}$

Direction of the sum of the vectors:

$\widehat{A + B} =\frac{\overrightarrow{A + B}}{Magnitude\: of \:\overrightarrow{A + B}} \\\\\widehat{A + B} =\frac{3i + j + 7k}{\sqrt {59}} \\\\\widehat{A + B} =\frac{3}{\sqrt {59}} i +\frac{1}{\sqrt {59}} j+\frac{7}{\sqrt {59}} k\\\\Direction \: of \: \overrightarrow{A + B} = \frac{3}{\sqrt {59}} , \:\frac{1}{\sqrt {59}} , \:\frac{7}{\sqrt {59}} \\\\$

3 0

2 years ago

Greensboro gets 12 times as many inches of snow as Redville gets. Altoghter, the two towns gets 65 inches of snow.How many inche

Tomtit [17]

Inches of snow Greensboro gets = g
Inches of snow Redville gets = r

$\left \{ {{g=12r} \atop {g+r=65}} \right. \\ \\ (12r)+r=65 \\ 13r=65 \\ r=5$

Redville gets 5 inches of snow.

6 0

3 years ago