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Dimas [21]
3 years ago
12

100) 4030 What’s the greatest common factor

Mathematics
1 answer:
Dima020 [189]3 years ago
5 0

Answer: 10

Step-by-step explanation:

100/10=10

4030/10=403

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Write the equation of the parabola that has the vertex at point (2,7) and passes through the point (−1,3).
mariarad [96]
Step One
Use the vertex to determine the basic equation for the parabola.

y = a(x - 2)^2 + 7 Notice the sign change for x. I have provided a graph to show how this would look with a = 1 (in red.)

What it means is the  2 has to be minus in order that the vertex will shift 2 units in the x direction.

Step Two
Use the point to solve for a.
y = a(x - 2)^2 + 7
When x = - 1
Then y = 3

3 = a(-1 - 2)^2 + 7                combine -1 with - 2
3 = a (-3)^2 + 7
3 = 9a + 7                            Subtract 7 from both sides
3 - 7 = 9a
-4 = 9a                                 Divide by 9.
a = -4/9 
or                                
a = - 0.4444

y = -0.4444(x + 2)^2 + 7 <<<<< answer
y = - 4/9 (x + 2)^2 + 7

Note: if you have choices, list them please.

Note: The red graph is y = (x - 2)^2 + 7 ; a = 1
The blue graph is y = - 4/9(x - 2)^2 + 7 ; a = - 0.44444

You should notice that the a does 3 things to the graph. Before you read the answer, what are those three things? The answer is in the comments.

8 0
3 years ago
After a hike, a group of students equally share 5 boxes of granola bars. Each box has 8 granola bars. Which algebraic expression
SIZIF [17.4K]

Answer: B.

First, we have to have a question for this problem to create a solution. So, the example sentence is how many granola bars does each student get.

Second, an algebraic expression has a variable in it. So since we are trying to find the number of students, the variable is s.

From looking at C and D, we can already eliminate them. This question has mostly multiplication and division words in it, so it can't be addition and multiplication.

Now, we only have A and B left. A tip on  how to figure this out is reading the word problem out thoroughly. I will use B as an example. 5 boxes of granola bars were multiplied by the number of granola bars each student got. From reading this, it makes more sense. But it does change the example sentence, though.

I hope this helped and this is the right answer!

8 0
3 years ago
Last time Martha made fruit punch, she used x cups of pineapple juice and y cups of cranberry juice. What expression represents
snow_tiger [21]

Answer:

x + y  

Step-by-step explanation:

Cups of pineapple juice = x

+Cups of cranberry juice = <u>y       </u>  

                       Total cups = x + y

4 0
3 years ago
X^2 + Y^2 +ax + 2y + 3 = 0<br><br> What number is this equation the equation of a circle?
Sav [38]

Answer:

Eq: (x+a/2)²+(y+1)²=(a²-8)/4

Center: O(-a/2, -1)

Radius: r=0.5×sqrt(a²-8)

Mandatory: a>2×sqrt(2)

Step-by-step explanation:

The circle with center in O(xo,yo) and radius r has the equation:

(x-xo)²+(y-yo)²=r²

We have:

x²+y²+ax+2y+3=0

But: x²+ax=x²+2(a/2)x+a²/4-a²/4= (x+a/2)²-a²/4

And

y²+2y+3=y²+2y+1+2=(y+1)²+2

Replacing, we get:

(x+a/2)²-a²/4+(y+1)²+2=0

(x+a/2)²+(y+1)²=a²/4-2=(a²-8)/4

By visual inspection we note that:

- center of circle: O(-a/2, -1)

- radius: r=sqrt((a²-8)/4)=0.5×sqrt(a²-8). This means a²>8 or a>2×sqrt(2)

6 0
3 years ago
|x-1|+2&lt;4 solving for x
Ganezh [65]

Answer:

x < 3 and x > -1

Step-by-step explanation:

Step 1: Subtract 2 from both sides.

  • |x-1| + 2 - 2 < 4 - 2
  • |x-1|

Step 2: Solve absolute value.

  • We know x - 1 < 2 and x - 1 > -2.

Condition 1:

  • x - 1 < 2
  • x - 1 + 1 < 2 + 1 (Add 1 to both sides)
  • x < 3

Condition 2:

  • x - 1 > -2
  • x - 1 + 1 > -2 + 1 (Add 1 to both sides)
  • x>-1

Therefore, the answer is x < 3 and x > -1.

8 0
2 years ago
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