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3 years ago

What is the solution to the system of equations? Use the substitution method. {y=2x+43x−6y=3

1 answer:

5 0

We have that
y=2x+4--------> equation 1
3x−6y=3-------> equation 2

step 1
I substitute the value of y in equation 1 for the value of y in equation 2
so
3x−6*[2x+4]=3-------> 3x-12x-24=3
-9x=3+24
-9x=27------> 9x=-27
x=-27/9
x=-3

step 2
I substitute the value of x in equation 1 to get the value of y
y=2x+4--------> y=2*(-3)+4--------> y=-6+4
y=-2

the answer is
the solution is the point (-3,-2)
x=-3
y=-2

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1 5/6 −(x− 7/12 )+2 1/12 =0.9

iren [92.7K]

The answer is x=3.6 or 3 3/5.

First we convert the decimal answer to a fraction; 0.9 is read as "nine tenths," so the corresponding fraction is 9/10:

1 5/6 - (x - 7/12) + 2 1/12 = 9/10

Now we find a common denominator. The first thing that 6, 12 and 10 will all divide into is 60:

1 50/60 - (x - 35/60) + 2 5/60 = 54/60

Distributing the negative, we have:
1 50/60 - x + 35/60 + 2 5/60 = 54/60

Combining like terms, we have:
-x + 4 30/60 = 54/60

Subtracting 4 30/60 from each side, we have:
-x + 4 30/60 - 4 30/60 = 54/60 - 4 30/60
-x = -3 36/60

Divide both sides by -1:
-x/-1 = (-3 36/60)/-1
x = 3 36/60 = 3 3/5 = 3.6

5 0

3 years ago

The radius of the base of the cylinder is 2x cm and the height of the cylinder is h cm.

valentina_108 [34]

Answer:

h = 9x

Step-by-step explanation:

Given: i. for the cylinder, base radius = 2x cm, height = h cm

ii. for the sphere, radius = 3x cm

iii. volume of the cylinder = volume of the sphere

volume of a cylinder is given as;

volume = $\frac{1}{3}$ $\pi$ $r^{2}$ h

where: r is its base radius and h the height

volume of the given cylinder = $\frac{1}{3}$ $\pi$ x $(2x)^{2}$ x h

= $\frac{1}{3}$ $\pi$ x 4 $x^{2}$ x h

= $\frac{4}{3}$ $\pi$ $x^{2}$ h

volume of a sphere = $\frac{4}{3}$ $\pi$ $r^{3}$

where r is the radius.

volume of the given sphere = $\frac{4}{3}$ $\pi$ x $(3x)^{3}$

= $\frac{4}{3}$ $\pi$ x 9 $x^{3}$

= 12 $\pi$ $x^{3}$

Since,

volume of the cylinder = volume of the sphere

Then we have;

$\frac{4}{3}$ $\pi$ $x^{2}$ h = 12 $\pi$ $x^{3}$

4 $\pi$ $x^{2}$ h = 36 $\pi$ $x^{3}$

subtract $x^{2}$ from both sides

4 $\pi$ h = 36 $\pi$ x

divide both sides by 4 $\pi$

h = $\frac{36\pi x}{4\pi }$

= 9x

h = 9x

5 0

3 years ago

Three values on a number line are labeled F, G, and H . Which number line correctly shows the values of F, G, and H?

oksian1 [2.3K]

Answer:

Step-by-step explanation:

F must be on -4

H must be on 4 (because it is -f=-(-4)=-1•-4=4)

6 0

3 years ago

Given: AB ≈ DC ; AC ≈ DB

Anit [1.1K]

Answer:

Step-by-step explanation:

Given:

AB ≅ DC and AC ≅ DB

To Prove:

ΔABC ≅ ΔDCB

Statements Reasons

1). AB ≅ DC and AC ≅ DB 1). Given

2). BC ≅ CB 2). Reflexive property

3). ΔABC ≅ ΔDCB 3). SSS property of congruence

8 0

3 years ago

One leg of a right triangular piece of land has a length of 24 yards. They hypotenuse has a length of 74 yards. The other leg ha

anastassius [24]

Solutions

To solve this problem we have to use the Pythagorean theorem. You can only use the Pythagorean theorem in Right Triangles. The longest side of the triangle is called the "hypotenuse". C² is the longest side so it is the hypotenuse . To calculate c² we have to do α² + β² = c².

Given

One leg of a right triangular piece of land has a length of 24 yards. They hypotenuse has a length of 74 yards. The other leg has a length of 10x yards.

First leg (24 yards) would be α

Second leg would be β

Hypotenuse (74 yards) would be c

Now we have points α β c.

a² (24) + β² ( x ) = c² (74)

Calculations

c² = α² + β²

74² = 24²+ β²

5476 = 576 + β²

5476 - 576 = β²
 
4900 = β²

→√4900
 
β = 70 yards

70 = 10x

x = 70÷10 = 7 yards

The second leg = 7 yards

3 0

3 years ago