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skad [1K]
3 years ago
14

Convert y = x^2 + 2x - 5 into the form y-k = a( x- h)^2

Mathematics
1 answer:
leva [86]3 years ago
7 0

Answer:

y+6=(x+1)^{2}

Step-by-step explanation:

we have

y=x^{2}+2x-5

This is the equation of a vertical parabola open upward (because the leading coefficient is positive)

The vertex is a minimum

The equation of a vertical parabola into vertex form is

y-k=a(x-h)^2

where

(h,k) is the vertex of the parabola

Convert the equation into vertex form

Move the constant term to the left side

y+5=x^{2}+2x

Complete the square

y+5+1=x^{2}+2x+1

y+6=x^{2}+2x+1

Rewrite as perfect squares

y+6=(x+1)^{2}

therefore

a=1\\h=-1\\k=-6

The vertex is the point (-1,-6)

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What are the answers for 7 and 8??? please help
wolverine [178]

Answer:

7.)

Therefore FT is 33 unit.

8.)

Therefore SU is 98 unit.

Step-by-step explanation:

7.)

Given:

ΔFUT ~ ΔFHG

FU = 39

FH = 130

FG = 110

To Find:

FT = ?

Solution:

ΔFUT ~ ΔFHG  ............Given

If two triangles are similar then their sides are in proportion.  

\dfrac{FU}{FH} =\dfrac{FT}{FG} \textrm{corresponding sides of similar triangles are in proportion}\\

Substituting the values we get

\dfrac{39}{130} =\dfrac{FT}{110}\\\\FT=\dfrac{110\times 39}{130}=33\\FT=33\ unit  

Therefore FT is 33 unit.

8.)

Given:

ΔSTU ~ ΔFED

ST= 63

FE = 9

FD = 14

To Find:

SU = ?

Solution:

ΔSTU ~ ΔFED  ............Given

If two triangles are similar then their sides are in proportion.  

\dfrac{ST}{FE} =\dfrac{SU}{FD} \textrm{corresponding sides of similar triangles are in proportion}\\

Substituting the values we get

\dfrac{63}{9} =\dfrac{SU}{14}\\\\SU=\dfrac{882}{9}=98\\\\SU=98\ unit

Therefore SU is 98 unit.

5 0
3 years ago
What’s the degree 2xy5
frutty [35]

Answer:

  6

Step-by-step explanation:

The degree of the term

  2xy^5

is the sum of the exponents of the variables, so is 1+5 = 6.

The degree of the term is 6.

6 0
3 years ago
The figure shows a construction completed by hand.
Tresset [83]

Based on the construction, we can logically deduce that: A. yes; the compass was kept at the same width to create the arcs for points C and D.

<h3>What is a line segment?</h3>

A line segment can be defined as the part of a line in a geometric figure such as a triangle, circle, quadrilateral, etc., that is bounded by two (2) distinct points and it typically has a fixed length.

In Geometry, a line segment can be measured by using the following measuring instruments:

  • A scale (ruler)
  • A divider
  • A compass

<h3>What is an arc?</h3>

In Geometry, an arc can be defined as a trajectory that is generally formed when the distance from a given point has a fixed numerical value.

Based on the construction with arcs created above and below the line segment from points A, we can infer and logically deduce that it is true that the compass was kept at the same width to create the arcs for points C and D.

In conclusion, yes, the construction demonstrated how to bisect a line segment correctly by hand.

Read more on arcs here: brainly.com/question/11126174

#SPJ1

Complete Question:

The construction has a given segment AB. Arcs have been created above and below the segment from points A that are equidistant from point A. The compass was kept at the same distance, placed on point B, and two additional arcs were created above and below the segment that intersect with the first arcs created. The intersection of the arcs above the segment created point C. The intersection of the arcs below the segment created point D. A line was drawn from point C to D through the segment.

Does the construction demonstrate how to bisect a segment correctly by hand?

A. Yes; the compass was kept at the same width to create the arcs for points C and D.

B. Yes; a straightedge was used to create segment CD.

C. No; the compass was not kept at the same width to create the arcs for points C and D.

D. No; a straightedge was used to create segment CD.

7 0
2 years ago
What is the ratio 44/12 in simplest form
mylen [45]

Answer:

11/3

<em>Alternative Form: </em>3 2/3, 3.6

Step-by-step explanation:

44/12

Dive the numerator and denominator by 4

44/4 / 12/4

11/ 12/4

11/3

3 0
3 years ago
Read 2 more answers
-2+9=-2(x+3)+8<br> Is this Infinitely Many Solutions<br> No solutions<br> Or One solutions
Margarita [4]

Answer:

i think it is many but i am not sure

Step-by-step explanation:

3 0
3 years ago
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