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3 years ago

If x2 = 30, what is the value of x?

Mathematics

2 answers:

nataly862011 [7]3 years ago

6 0

Subtract 30, then factor the equation.

... x² = 30

... x² - 30 = 0

... (x -√30)(x +√30) = 0

By the zero product rule, the solutions are values of x that make a factor be zero.

... x - √30 = 0 . . . . the first factor is zero

... x = √30

... x + √30 = 0 . . . . the second factor is zero

... x = -√30

The solutions are . . .

... x = ±√30 . . . . . matches your 3rd choice

klasskru [66]3 years ago

4 0

Answer: C

Step-by-step explanation: hope it helps :)

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A grain of sand has a mass of 2.6 × 10–3 gram. A grain of salt has a mass of 6.5 × 10–2 gram. How many times greater is the mass

myrzilka [38]

Answer:

Step-by-step explanation:

2.6 x10^-3= .0026

6.5 x10^-2=.065

.065/.0026=25

5 0

3 years ago

Identify the expicit function for the sequence in the table.

marysya [2.9K]

It is B. Because the formula for sequences in in the form of a+(n-1)d where a is the first number in the sequence, n is the nth term(position) and d is the difference between terms. So if a=9 and d=5 the answer is 9 + (n-1)*5

4 0

2 years ago

Evaluate the triple integral ∭ExydV where E is the solid tetrahedon with vertices (0,0,0),(5,0,0),(0,9,0),(0,0,4).

Elan Coil [88]

Answer: $\int\limits^a_E {\int\limits^a_E {\int\limits^a_E {xy} } \, dV$ = 1087.5

Step-by-step explanation: To evaluate the triple integral, first an equation of a plane is needed, since the tetrahedon is a geometric form that occupies a 3 dimensional plane. The region of the integral is in the attachment.

An equation of a plane is found with a point and a normal vector. Normal vector is a perpendicular vector on the plane.

Given the points, determine the vectors:

P = (5,0,0); Q = (0,9,0); R = (0,0,4)

vector PQ = (5,0,0) - (0,9,0) = (5,-9,0)

vector QR = (0,9,0) - (0,0,4) = (0,9,-4)

Knowing that cross product of two vectors will be perpendicular to these vectors, you can use the cross product as normal vector:

n = PQ × QR = $\left[\begin{array}{ccc}i&j&k\\5&-9&0\\0&9&-4\end{array}\right]$ $\left[\begin{array}{ccc}i&j\\5&-9\\0&9\end{array}\right]$

n = 36i + 0j + 45k - (0k + 0i - 20j)

n = 36i + 20j + 45k

Equation of a plane is generally given by:

$a(x-x_{0}) + b(y-y_{0}) + c(z-z_{0}) = 0$

Then, replacing with point P and normal vector n:

$36(x-5) + 20(y-0) + 45(z-0) = 0$

The equation is: 36x + 20y + 45z - 180 = 0

Second, in evaluating the triple integral, set limits:

In terms of z:

$z = \frac{180-36x-20y}{45}$

When z = 0:

$y = 9 + \frac{-9x}{5}$

When z=0 and y=0:

x = 5

Then, triple integral is:

$\int\limits^5_0 {\int\limits {\int\ {xy} \, dz } \, dy } \, dx$

Calculating:

$\int\limits^5_0 {\int\limits {\int\ {xyz} \, dy } \, dx$

$\int\limits^5_0 {\int\limits {\int\ {xy(\frac{180-36x-20y}{45} - 0 )} \, dy } \, dx$

$\frac{1}{45} \int\limits^5_0 {\int\ {180xy-36x^{2}y-20xy^{2}} \, dy } \, dx$

$\frac{1}{45} \int\limits^5_0 {90xy^{2}-18x^{2}y^{2}-\frac{20}{3} xy^{3} } \, dx$

$\frac{1}{45} \int\limits^5_0 {2430x-1458x^{2}+\frac{94770}{125} x^{3}-\frac{23490}{375}x^{4} } \, dx$

$\frac{1}{45} [30375-60750+118462.5-39150]$

$\int\limits^5_0 {\int\limits {\int\ {xyz} \, dy } \, dx$ = 1087.5

The volume of the tetrahedon is 1087.5 cubic units.

3 0

3 years ago

Which shows the image of quadrilateral ABCD after the transformation R0 90?

Arisa [49]

Answer:

second picture

Step-by-step explanation:

The rule to rotate a point counterclockwise about the origin is:

Or in words, we switch the coordinates of the point and change the sign of the y-coordinate.

We know from the first picture that the coordinates of our quadrilateral ABCD are A = (-1, 0), B = (0, -1), C = (-2, -3), and D = (-3 , -2), so let's apply the rotation rule to each one of those points:

Now we know that the coordinates of the quadrilateral after a rotation of 90° are A' = (0, 1), B' = (1, 0), C' = (3, -2), and D' = (2, -3), which corresponds to the second picture

7 0

3 years ago

Solve this equation by the substitution method f(x)={2x+3y=25, {x-y=5

Kipish [7]

The second equation is perfect. We can add y to both sides to make the equation equal x.
X=5+y; let's plug that in for x in the first equation.
2(5+y)+3y=25
10+2y+3y=25
5y+10=25
Let's subtract 10 from both sides.
5y=15
Now divide both sides by 5.
Y=3
So y is 3. We can plug 3 in for y in the second equation.
X-3=5
X=8
So, X=8 and Y=3.

8 0

3 years ago

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