All categories

2 years ago

Melissa bought 42 pine seedlings and 30 juniper seedlings

Mathematics

1 answer:

hram777 [196]2 years ago

8 0

Answer:

See below

Step-by-step explanation:

GCF (greatest common factor ) of 42 and 30 is 6

each row will have 6 seedlings

there will be ( 42+30) / 6 = 12 rows

7 pine rows 5 juniper rows

You might be interested in

Find the length of the diameter of circle 0

r-ruslan [8.4K]

Answer:

Diameter = 19.33

Step-by-step explanation:

Imaging a radius line from O to the endpoints of the 7. call this line R.

Label the part of the vertical line from O to the 90 degree intersection y.

Now you have a right triangle.

Using the Pythagorean theorem:

R² = 7² + y²

also

y = R - 3

substitute for y:

R² = 49 + (R-3)²

R² = 49 + R² - 6R + 9

simplify:

0 = 58 - 6R

6R = 58

R = 9.6667

Diameter = 2(9.6667) = 19.33

5 0

1 year 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

Can someone help me please, ASAP!! Thank you!

forsale [732]

Use a proportional that will give you x=4

4 0

2 years ago

The perimeter of the square

Rama09 [41]

Answer:

x = 20/49 units; P = 8 48/49 units

Step-by-step explanation:

All sides of a square are congruent.

That means that the two given side lengths are equal.

We set the two lengths equal and solve the equation for x.

5.5x = (1/5)(3x + 10)

Multiply both sides by 5.

27.5x = 3x + 10

Subtract 3x from both sides.

24.5x = 10

x = 10/24.5

x = 20/49

The perimeter of a square is 4s, where s is the length of a side.

P = 4s

= 4(5.5x)

= 4 * 5.5 * 20/49

= 22 * 20/49

= 440/49

= 8 48/49

Answer: x = 20/49 units; P = 8 48/49 units

4 0

3 years ago

Identify the x- and y- intercepts of this equation. 5 − 4 = 20

Alinara [238K]

T he x and y intercepts of the equation: $5x-4y=20$ are : y-intercept is (0,-5) and x-intercept is (4,0)

So, Option D is correct.

Step-by-step explanation:

we need to identify the x and y intercepts of the equation: $5x-4y=20$

Finding x-intercept

For finding x-intercept put y=0

We are given the equation:

$5x-4y=20$

Solving:

$5x-4y=20\\5x-4(0)=20\\5x=20\\x=\frac{20}{5}\\x=4$

So, x-intercept is (4,0)

Finding y-intercept

For finding y-intercept put x=0

We are given the equation:

$5x-4y=20$

Solving:

$5x-4y=20\\5(0)-4y=20\\-4y=20\\y=\frac{20}{-4}\\y=-5$

So, y-intercept is (0,-5)

the x and y intercepts of the equation: $5x-4y=20$ are :y-intercept is (0,-5) and x-intercept is (4,0)

So, Option D is correct.

Keywords: x and y intercepts

Learn more about x and y intercepts at:

#learnwithBrainly

6 0

3 years ago