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riadik2000 [5.3K]
3 years ago
9

Find the solution to the following equations below

Mathematics
1 answer:
zvonat [6]3 years ago
8 0

Answer: A. infinite solutions

B. no solution

C. one solution

Step-by-step explanation:

A. firstly we distribute: -2x-6=-2x-6

since they are the same it is infinite solutions.

B. firstly we distribute: 4x-4=1/2x-4

                                   =2x=0

x=0

C. 3x-7=10+4x

x=17

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At a school dance, the ratio of girls to boys is 8:3. If there are 528 students at the dance, how many are boys and how many are
weqwewe [10]

Answer:

144 boys and 384 girls

Step-by-step explanation:

8 girls to every 3 boys. You can make an equation to solve this: 8x + 3x = 528. 528 = 11x. Then divide 528 by 11 to get 48. x=48. 8(48) = 384 girls. 3(48) = 144 boys.

6 0
3 years ago
onsider the following problem: A box with an open top is to be constructed from a square piece of cardboard, 3 ft wide, by cutti
Sholpan [36]

Answer:

V (max)  = 2 ft³

and x side of the base is  x  =  0,5 feet

Step-by-step explanation:  See annex ( two different cubes)

We have a square piece of cardboard of  3 inches wide

Let  x be lenght of side to cut in each corner

Then the base of the (future cube) is    3  -  2x,  and the area is  

( 3 - 2x )²

And  the height   is x  Then volume of the cube as a function of x is:

V(x)  =  ( 3 - 2x )² *x   or       V(x)  =    ( 9 + 4x² - 12x )*x

V(x)  =  4x³  -  12x²  + 9x

Taking derivatives on both sides of the equation

V´(x)  =  12x² - 24x  + 9

V´(x)  =  0       12x² - 24x  + 9  =  0   simplifying   4x² - 8x  + 3  =  0

Second degree equation solving for x

x₁,₂ =  [ 24 ± √( 576) - 432  /24

x₁,₂ =  [24 ±√144 ]/24

x₁,₂ = ( 24 ± 12) /24         x₁  =  1.5 feet        x₂  = 0,5 feet

Of these two values we have to dismiss x₁  because if  x = 1.5 we don´t have a cube ( 0 height )

Then we take x  = 0,5  feet

And

V (max)  =  (2)²*0,5   =  4*0,5

V (max)  = 2 ft³

5 0
3 years ago
Solve x + 3y = 9<br> 3x – 3y = -13 (1 point)
Mariana [72]

Answer:

The values of x and y to the given equations are x=-1 and y=\frac{10}{3}

The solution is (-1,\frac{10}{3})

Step-by-step explanation:

Given equations are x+3y=9\hfill (1)

and 3x-3y=-13\hfill (2)

to solve the given equations by elimination method :

Adding the given two equations (1) and (2) we get

x+3y=9

3x-3y=-13

_______________

4x=-4

x=-\frac{4}{4}

Therefore x=-1

Now substitute the value x=-1 in equation(1) we get

(-1)+3y=9

3y=9+1

y=\frac{10}{3}

Therefore the values of x and y to the given equations are x=-1 and y=\frac{10}{3}

The solution is (-1,\frac{10}{3})

8 0
3 years ago
Help me plz thank you
DIA [1.3K]

Answer:C

Step-by-step explanation: 100 x 23/100=23

8 0
3 years ago
The measure of ∠P is five less than four times the measure of ∠Q. If ∠P and ∠Q are supplementary angles, find m∠P
Murljashka [212]

Answer:

m∠P = 143°

Step-by-step explanation:

We know that supplementary angles add up to 180, and with the knowledge that angle P is 5 times than 4 less (5x-4) the measure of angle Q (x), we can set up the equation (4x-5)+(x)=180. We can then solve and get x = 37, and then we can plug X back into 5x-4 to get the angle of 143 degrees.

8 0
3 years ago
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