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2 years ago

Solve the following system of equations by substitution 3 x + 0.5 y = 11 x + 2 y = 0

Mathematics

1 answer:

SVEN [57.7K]2 years ago

6 0

The solution to the system of equations using substitution is given by:

x = 4 and y = 2.

<h3>What is a system of equations?</h3>

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

For this problem, the equations are given by:

3x + 0.5y = 11.

x + 2y = 0.

From the second equation, we have that:

x = -2y.

Replacing in the first equation, we have that:

3(-2y) + 0.5y = 11

-5.5y = 11.

5.5y = -11

y = -11/5.5

y = -2.

Then the solution for x is:

x = -2y = -2(-2) = 4.

The solution to the system of equations using substitution is given by:

x = 4 and y = 2.

More can be learned about a system of equations at brainly.com/question/24342899

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Express 17.5m in dm,cm,dam,mm,hm,km

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Answer:

17.5 metres

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Step-by-step explanation:

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3 years ago

Read 2 more answers

The volume of a cylinder is 176 π cm and its height is 11 π cm.

Liula [17]

Answer:

r = sqrt(16/pi)

Step-by-step explanation:

Cylinder formula = r^2 x pi x height

176 pi/11pi = 16

16 = r^2 x pi

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2 years ago

Determine the cross product b*a a=2i+2j-5k b=6i-j+2k

Misha Larkins [42]

Recall the definition of the cross product:

i x i = j x j = k x k = 0

i x j = k

j x k = i

k x i = j

The cross product is antisymmetric, or anticommutative, meaning that for any vectors u and v, we have u x v = - (v x u).

It's also distributive, so for any vectors u, v, and w, we have (u + v) x w = (u x w) + (v x w).

Taking all of these properties together, we get

b x a = (6i - j + 2k) x (2i + 2j - 5k)

b x a = 12 (i x i) - 2 (j x i) + 4 (k x i)

............. + 12 (i x j) - 2 (j x j) + 4 (k x j)

............. - 30 (i x k) + 5 (j x k) - 10 (k x k)

b x a = 1 (j x k) + 34 (k x i) + 14 (i x j)

b x a = i + 34j + 14k

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3 years ago

Find two positive consecutive odd integers such that square of the smaller integer is 10 more than the larger integer

Otrada [13]

Let $2n+1$ be the smaller integer. The larger integer is then $2n+3$ , and we have

$(2n+1)^2=10+(2n+3)\implies4n^2+4n+1=2n+13$

$\implies4n^2+2n-12=0$

$\implies2n^2+n-6=0$

$\implies(2n-3)(n+2)=0$

$\implies 2n-3=0\text{ or }n+2=0$

$\implies n=\dfrac32\text{ or }n=-2$

We omit $n=-2$ , since $2(-2)+1=-3$ is negative.

Then for $n=\dfrac32$ we find $2\left(\dfrac32\right)+1=4$ , but this is not odd.

There are no consecutive odd integers that satisfy the given condition!

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3 years ago

Vector v has a direction of (5,3) find the direction angle for v to the nearest degree

Vesnalui [34]

Answer:

$31^{\circ}$

Step-by-step explanation:

We have been given that vector v has a direction of (5,3). We are asked to find direction angle for v to nearest degree.

We know that direction of vector with components $(a,b)$ can be determined by $\theta=\text{tan}^{-1}(\frac{b}{a})$ .

Upon substituting the components of given vector in above formula, we will get:

$\theta=\text{tan}^{-1}(\frac{3}{5})$

$\theta=30.9637565^{\circ}$

Upon rounding to nearest degree, we will get:

$\theta\approx 31^{\circ}$

Therefore, the direction angle for vector v is 31 degrees.

3 0

3 years ago