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timama [110]
3 years ago
12

Simplify 7(3y-5)+2(4y+3)

Mathematics
2 answers:
Vesna [10]3 years ago
6 0

Answer:

\boxed{ \bold{ \huge{ \boxed{ \sf{29y - 29}}}}}

Step-by-step explanation:

\sf{7(3y - 5) + 2(4y + 3)}

Distribute 7 through the parentheses

Similarly , distribute 2 through the parentheses

\dashrightarrow{ \sf{21y - 35 + 8y + 6}}

Collect like terms

\dashrightarrow{ \sf{21y + 8y - 35 + 6}}

\dashrightarrow{ \sf{29y - 35 + 6}}

Calculate

\dashrightarrow{ \sf{29y - 29}}

Hope I helped!

Best regards! :D

laila [671]3 years ago
4 0

Step-by-step explanation:

7*3y - 7*5 + 2*4y + 12

= 21y - 35 + 8y + 6

= 29y - 29

= 29(y-1)

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a parabola has an x-intercept at 2, its axis of symmetry is the line x=4, and the y-coordinate of its vertex is 6. Determine the
nlexa [21]

Answer:

The standard equation of the parabola is:

y=-\frac{3}{2}x^2+12x-18

Step-by-step explanation:

An x intercept of 2 means that the point (2, 0) is in the graph of the parabola.

We can also write the general expression for the parabola in vertex form, since we can use the information on the coordinates of the vertex: (4, 6) - recall that the axis of symmetry of the parabola goes through the parabola's vertex, so the x-value of the vertex must be x=4.

y-y_{vertex}=a\,(x-x_{vertex})^2\\y-6=a\,(x-4)^2

Now we can find the value of the parameter "a" by using the extra information about the point (2, 0) at which the parabola intercepts the x-axis:

y-6=a\,(x-4)^2\\0-6=a\,(2-4)^2\\-6=a\,4\\a=-\frac{6}{4} =-\frac{3}{2}

Then the equation of the parabola becomes:

y-6=-\frac{3}{2} \,(x-4)^2\\y-6=-\frac{3}{2} (x^2-8x+16)\\y-6=-\frac{3}{2}x^2+12x-24\\y=-\frac{3}{2}x^2+12x-18

7 0
3 years ago
The length of a rectangle is 5959 inches greatergreater than twice the width. if the diagonal is 2 inches more than the​ length,
lorasvet [3.4K]

Length: 2w + 59

width: w

diagonal: (2w + 59) + 2  = 2w + 61

Length² + width² = diagonal²

(2w + 59)² + (w)² = (2w + 61)²

(4w² + 118w + 3481) + w²  = 4w² + 122w + 3721

5w² + 118w + 3481 = 4w² + 122w + 3721

w² + 118w + 3481 = 122w + 3721

w² - 4w + 3481 = 3721

w² - 4w - 240 = 0

a = 1, b = -4, c = -240

w = [-(b) +/- \sqrt{(b)^{2}  - 4(a)(c) }]/2(a)

 = [-(-4) +/- \sqrt{(-4)^{2}  - 4(1)(-240) }]/2(1)

   =  [4 +/- \sqrt{(16  + 960) }]/2        

  = [4 +/- \sqrt{(976) }]/2  

  = [2 +/- 4\sqrt{(61) }]/2  

  = 1 +/- 2\sqrt{(61) }

since width cannot be negative, disregard  1 - 2√61

w = 1 + 2√61  ≈ 16.62

Length: 2w + 59  =  2(1 + 2√61) + 59  = 2 + 4√61 + 59  =  61 + 4√61  ≈ 92.24

Answer: width = 16.62 in, length = 92.24 in

7 0
3 years ago
The product of 5 and a number x is 1414 .
Julli [10]
5x = 1414
x = 1414 / 5
x = 282.80
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3 years ago
What is the radius of a circle whose equation is x2+y2−10x+6y+18=0?
Brums [2.3K]

Answer:

4

Step-by-step explanation:

center | (5, -3)

radius | 4

diameter | 8

area enclosed | 16 π≈50.2655

circumference | 8 π≈25.1327

5 0
3 years ago
Input Years, x: 1, 2, 3 Output, Height of tree in feet: 6, 9, 12. Is this discrete or continous?
BartSMP [9]

Answer:

discrete

Step-by-step explanation:

4 0
3 years ago
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