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3 years ago

Find the system of x.

Mathematics

2 answers:

marissa [1.9K]3 years ago

6 0

Answer:

61 degrees

Step-by-step explanation:

A right angle equals 90 degrees.

90-29= 61

Svetlanka [38]3 years ago

5 0

Answer:

Step-by-step explanation:

X + 29 = 90, so X must be 61.

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X² + y² = 8

ohaa [14]

Answer:

$(2,2)~ \text{and}~ (-2,-2)$

Step by step explanation:

$x^2 +y^2 =8~~~~~~...(i)\\\\x-y=0~~~~~~~~~...(ii)\\\\\text{From (ii):}\\\\x-y = 0 \implies x = y\\\\\text{Substitute x = y in eq (i):}\\\\~~~~~~y^2 +y^2 =8\\\\\implies 2y^2 = 8\\ \\\implies y^2 = \dfrac 82\\\\\implies y^2 = 4\\\\\implies y = \pm\sqrt 4\\\\\implies y = \pm 2\\\\\text{Substitute y = x in equation (i):}\\ \\~~~~~~x^2 +x^2 = 8\\ \\\implies 2x^2 = 8\\\\\implies x^2 = \dfrac 82\\\\\implies x^2 = 4\\\\\implies x = \pm\sqrt 4\\\\\implies x = \pm2\\\\$

$\text{Hence,}~ (x,y) = (\pm2, \pm 2)$

3 0

2 years ago

(Hehe...Please ignore the markings)

inysia [295]

Answer:

See below:

Step-by-step explanation:

Problem 1:

Multiply Equation 1 by 4, keep Equation 2 the same.

x+y=8, multiply each term by 4:

4*x=4x, 4*y=4y, 8*4=32

so, the equivalent system is: 4x+4y=32 and x-y=2

Solve the system of equations:

x-y=2 becomes x=y+2

plug into 4x+4y=32 to solve for y

4(y+2)+4y=32---> 4y+8+4y=32--->8y=24---> y=3

Plug into x-y=2---> x-3=2---> x=5

Problem 1 Answer:

Equivalent system: 4x+4y=32, x-y=2; solution: x=5, y=3

Problem 2:

Keep Equation 1 the same. Add 1 and 2.

To add an equation, add the left sides together, and then the rights.

so: x+y=8 + x-y=2 gives us: 2x=10

solve for x ---> 2x/2=10/2--->x=5

plug x into x+y=8--->5+y=8--->y=3

Problem 2 answer:

Equivalent system: x+y=8, 2x=10; solution:x=5, y=3

Problem 3:

Subtract Equation 2 from 1, and keep 2 the same.

To subtract an equation, subtract the left sides, then the rights. We are subtracting 1<em> from </em>2, so its 2-1.

x-y=2 - x+y=8 gives us: -2y=-6

Solve for y by dividing by -2-->-2y/-2=-6/-2---> y=3

Plug into x-y=2---> x-3=2---> x=5

Problem 3 answer:

Equivalent system: -2y=-6, x-y=2; solution: x=5, y=3

Problem 4:

Multiply the sum of Equation 1 and 2 by a factor of 3. Keep equation 2 the same.

First we add 1 and 2: (we did this earlier) ---> 2x=10 ---> now we multiply it all by 3---> 2x*(3)=10*(3)---> this gives us: 6x=30---> now divide by 6 to solve for x: 6x/6=30/6 gives us: x=5

Now, solve for y by plugging x into equation 2: x-y=2---> 5-y=2--->y=3

Problem 4 answer:

Equivalent system: 6x=30, x-y=2; solution: x=5, y=3

______

Quick Tip: One thing inherent of Equivalent systems is that they have the same set of solutions. Thus, we know the systems are equivalent when they have the same set of solutions for x and y. Moreover, you don't need to solve every time after you attempt to find an equivalent system, instead, just plug in the values found in problem 1 to each new set of equations to test if they are equivalent.

If we find x=5 and y=3 for x+y=8 and x-y=2, then all we have to do is plug them in to 6x=30 and -2y=-6 to see if they are equivalent.

6(5)=30 ---> true

-2(3)=-6 ---> true

3 0

3 years ago

What is an expression to represent One minus the quotient of one and a number x.

Advocard [28]

Quotient is the result of a division.

1 - 1/x

8 0

3 years ago

Roberto has a sample of an unknown liquid. The label in the bottle of the sample indicates that the liquid has a mass of 117 gra

Tomtit [17]

Answer:

It is Milk

Step-by-step explanation:

The liquid in the bottle has mass given in grams and the mass of that substance is 117 grams.

The volume of the substance is 15 cubic centimeters.

Now, using the formula of density we can estimate which substance could it be.

$d=\frac{m}{v}$ , where 'd', is the density, 'm' is the mass, and 'v' is the volume of the substance.

Plugging the value of mass and volume we get:

$d=\frac{117}{15} =7.8g/cm^3$

So the density of the substance is 7.8 grams per cubic centimeter.

It cannot be water since the density of water is 1 grams per cubic centimeter.

It cannot be gasoline because its density is 0.77 grams per cubic centimeter.

It cannot be mercury because the density of mercury is 13.56 grams per cubic centimeter.

Since, the density in this case matches the density of thick milk and hence,therefore, the liquid in the bottle is milk.

7 0

3 years ago

Frank, who lives in Texas, and his sister Lilly, who lives in Japan, correspond regularly. From what he can tell from the postma

Hoochie [10]

Question:

The available options are:

(A) There is convincing evidence that there is no difference in the mean delivery times.

(B) There is convincing evidence that there is a difference in the mean delivery times.

(C) There is convincing evidence that the mean delivery time from Japan to Texas is greater than the mean delivery time from Texas to Japan.

(D) There is not convincing evidence that the mean delivery time from Japan to Texas is greater than the mean delivery time from Texas to Japan. (E) The t-test cannot be used for sample sizes that are this small.

Answer:

The correct option is;

(A) There is convincing evidence that there is no difference in the mean delivery times.

Step-by-step explanation:

Here we have the formula for the two-sample t-test given s;

$t =\frac{\overbar\overline{\rm x}_1 - \overbar\overline{\rm x}_2 }{\sqrt{\frac{\sigma ^2_1}{n_1} } +\frac{\sigma ^2_2}{n_2} }}$

To Texas N₁ = 12, $\overline{\rm x}_1$ =8.74 σ₁ = 2.92 SE Mean₁ = 0.84

To Japan N₂ = 9 $\overline{\rm x}_2$ = 6.75 σ₂ = 2.56 SE Mean₁ = 0.85

t = 1.667

Where the null hypothesis is

mu To Texas = mu To Japan and the alternative is

mu To Texas > mu To Japan

Here since the observed P value of P = 0.058 is greater than the significance level of 0.05 we fail to reject the null hypothesis and we will therefore, not accept the alternative hypothesis.

Hence, there is convincing evidence that there is no difference in the mean delivery times.

3 0

3 years ago

Find the system of x.​

Find the system of x.