All categories

2 years ago

Select the correct answers.

Mathematics

1 answer:

Annette [7]2 years ago

5 0

Answer:

1and3

Step-by-step explanation:

You might be interested in

A graphics company charges $50 per hour to create a logo plus $250 for the ownership rights of the logo. A private contractor ch

slavikrds [6]

Answer: $50x+250=75x+100$

Step-by-step explanation:

Given: A graphics company charges $50 per hour to create a logo plus $250 for the ownership rights of the logo.

Let x be the number of hours , then the total cost to create the logo plus is given by :-

$C(x)=250+50x$

A private contractor charges $75 per hour to develop a logo plus a $100 supply fee.

The total cost to develop logo plus is given by :-

$c(x)=100+75x$

The equation to represent the costs would be the same is given by :_

$C(x)=c(x)\\\Rightarrow50x+250=75x+100$

4 0

2 years ago

Read 2 more answers

Multiplying StartFraction 3 Over StartRoot 17 EndRoot minus StartRoot 2 EndRoot EndFraction by which fraction will produce an eq

ziro4ka [17]

The fraction which produce an equivalent fraction with a rational denominator is $\left(\frac{\sqrt{17}+\sqrt{2}}{\sqrt{17}+\sqrt{2}}\right)$

Explanation:

The equation is $\frac{3}{\sqrt{17}-\sqrt{2}}$

To find the rational denominator, let us take conjugate of the denominator and multiply the conjugate with both numerator and denominator.

Rewriting the equation, we have,

$\frac{3}{\sqrt{17}-\sqrt{2}}\left(\frac{\sqrt{17}+\sqrt{2}}{\sqrt{17}+\sqrt{2}}\right)$

Multiplying, we get,

$\frac{3(\sqrt{17}+\sqrt{2})}{(\sqrt{17})^{2}-(\sqrt{2})^{2}}$

Simplifying the denominator, we get,

$\frac{3(\sqrt{17}+\sqrt{2})}{17-2}$

Subtracting, the values of denominator,

$\frac{3(\sqrt{17}+\sqrt{2})}{15}$

Dividing the numerator and denominator,

$\frac{\sqrt{17}+\sqrt{2}}{5}$

Hence, the denominator has become a rational denominator.

Thus, the fraction which produce an equivalent fraction with a rational denominator is $\left(\frac{\sqrt{17}+\sqrt{2}}{\sqrt{17}+\sqrt{2}}\right)$

6 0

1 year ago

Read 2 more answers

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

2 years ago

On babylonian tablet ybc 4652, a problem is given that translates to this equation: x (x/7) (1/11) (x (x/7)) = 60 what is the so

Yanka [14]

Thanks for posting your question here. The answer to the above problem is x = 48.125. Below is the solution:

x+x/7+1/11(x+x/7)=60
x = x/1 = x • 7/7
x • 7 + x/ 7 = 8x/7 - 60 = 0
x + x/7 + 1/11 • 8x/7 - 60 = 0
8x • 11 + 8x/ 77 = 96x/ 77
96x - 4620 = 12 • (8x-385)
8x - 385 = 0
x = 48.125

5 0

2 years ago

Read 2 more answers

Sometimes a dilation is an enlargement, and sometimes it is a reduction. Explain what types of numbers for scale factors causes

vovikov84 [41]

If your scale factor has absolute value greater than 1, the dilation is an enlargement.
If your scale factor has abs value less than 1, the dilation is a reduction. 
If the scale factor is equal to 1, the image is congruent to the preimage.

3 0

2 years ago

Read 2 more answers