The lengths of the sides of the triangles are 13cm, 14cm, and 15cm. Is the triangle a right triangle?

Given:

The equation is

[tex]y=x^2+2x+3[/tex]

To find:

The vertex form of the given equation, i.e., [tex]y=x^2+2x+3[/tex].

Solution:

We have,

[tex]y=x^2+2x+3[/tex]

It can be written as

[tex]y=(x^2+2x)+3[/tex]

Add and subtract square of half of coefficient of x, i.e., [tex]\left(\dfrac{2}{2}\right)^2=1[/tex].

[tex]y=(x^2+2x+1)-1+3[/tex]

[tex]y=(x^2+2(x)(1)+1^2)+2[/tex]

[tex]y=(x+1)^2+2[/tex]                   [tex][\because (a+b)^2=a^2+2ab+b^2][/tex]

Therefore, the required form of given function is [tex]y=(x+1)^2+2[/tex].

Answer:

(5,3)

Step-by-step explanation:

I plotted the point (3,1) on desmos graphing caculator and labeled it as the vertex.

Next I plotted the point (1,3).

Then I counted the spaces between point 1,3 and 3,1 as shown in the picture

Finally I graphed the point and connected the lines to make sure it looked like a parabola.

Answer:

your answer will be the last Option 5

Step-by-step explanation:

hope it helps

Answer:

$53.14

Step-by-step explanation:

$51.00+4.2%

53.14200

round:53.14

Answer and Step-by-step explanation:

The answer should be 54 million.

Plug in 1 for x, which you get 54.5.

Then you plug in 2 for x, which you get 108.5

Now, subtract the subtract the 1st one from the 2nd one.

108.5 - 54.5 = 54 (million)

#TEAMTREES #PAW (PLANT AND WATER)

Answer:

72.5°

Step-by-step explanation:

180° - 35° = 2y°

145° = 2y

145/2 = 50+22+0.5 = 72.5

Answer:

20.306≈ 20.3

Step-by-step explanation:

Answer:

angles J and N

Step-by-step explanation:

vertical angles are congruent angles that are vertically across from each other

angle j and angle n are both right angles and they are both vertically across from each other therefore A is your answer

Answer:

8 out of 40 trials- 8/40

simplify that and it becomes 1/5

1/5 of 10 is 2

so, I'd estimate there are 2 purple marbles.

Answer:

otf grandson c or b or a

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer:

7 mm

Step-by-step explanation:

A square has 4 equal sides, so the piece of confetti will have 4 sides of the exact same length.

Find the length of each side by dividing the perimeter by 4

28/4

= 7

So, each side of the confetti piece is 7 mm

Answer:

96 cm

53 cm

4,5 Cm

1,5 Cm

1.7dm

0,5m

Step-by-step explanation:

Dm to Cm ×10

mm to cm ÷10

Answer:

Step-by-step explanation:

9x5=45

45=area

9+9+5+5=28

28=Per

#2

π x 8^2

=16

A=16π

2 x π x 8

P=16π

#3

hxb/2

=10x24/2

=120

A=120

P=60

Answer:

n = 3

Step-by-step explanation:

plug in 3 for n in the equation:

Numerator: n + 1 = 3 + 1 = 4

Denominator: 2^n = 2^3 = 2 * 2 * 2 = 4 * 2 = 8

Simplify the fraction. Divide common factors from both the numerator and denominator:

(4/8)/(4/4) = 1/2

1/2 = 1/2 ∴ n = 3

~

Answer:

[tex](a)[/tex] [tex]V = -H^3+ 5H^2 + 36H[/tex]

[tex](b)[/tex] [tex]Length = 5in; Width = 9in; Height = 5in[/tex] or [tex]Length = 3in; Width = 10in; Height = 6in[/tex]

Step-by-step explanation:

Let:

[tex]W=Width; L = Length; H = Height[/tex]

Given

[tex]W = 4 + H[/tex]

[tex]L = 9 - H[/tex]

Solving (a): The polynomial for the volume in terms of height

Volume (V) is calculated using:

[tex]V = L * W * H[/tex]

[tex]V = (9 - H) * (4 + H) * H[/tex]

Expand

[tex]V = (9 - H) * (4H + H^2)[/tex]

Open brackets

[tex]V = 36H + 9H^2 - 4H^2 - H^3[/tex]

[tex]V = 36H + 5H^2 - H^3[/tex]

Rewrite as:

[tex]V = -H^3+ 5H^2 + 36H[/tex]

Solving (b): The dimensions when Volume = 180

Substitute 180 for V in: [tex]V = -H^3+ 5H^2 + 36H[/tex]

[tex]180 = -H^3+ 5H^2 + 36H[/tex]

Rewrite as:

[tex]H^3 - 5H^2 - 36H + 180 = 0[/tex]

Factorize:

[tex]H^2(H - 5) - 36(H - 5) = 0[/tex]

[tex](H^2 - 36)(H - 5) = 0[/tex]

Express [tex]H^2 - 36[/tex] as difference of two squares

[tex](H - 6)(H + 6)(H - 5) =0[/tex]

This gives:

[tex]H - 6 =0==> H = 6[/tex]

[tex]H + 6 =0==> H = -6[/tex]

[tex]H - 5 =0==> H = 5[/tex]

Since the height can not be negative, then H = 5 or H = 6

Recall that:

[tex]W = 4 + H[/tex]

[tex]L = 9 - H[/tex]

When H = 5

[tex]W = 4 + 5 = 9[/tex]

[tex]L = 9 - 5 = 4[/tex]

When H = 6

[tex]W = 4 + 6 = 10[/tex]

[tex]L = 9 - 6 = 3[/tex]

Hence, the dimensions of the box are:

[tex]Length = 5in; Width = 9in; Height = 5in[/tex]

or

[tex]Length = 3in; Width = 10in; Height = 6in[/tex]

The volume of the box is given by -h³ + 5h² + 36h

Volume is the amount of space occupied by a three dimensional object. The volume (V) of a box is given by:

V = length * width * height

Let h represent the the height, hence width = h + 4, length = (9 - h)

V = h(h + 4)(9 - h) = h(5h -h² + 36) = -h³ + 5h² + 36h

For a volume of 180 in³:

180 = -h³ + 5h² + 36h

h = 5 or 6.

The volume of the box is given by -h³ + 5h² + 36h

Find out more on Volume at: https://brainly.com/question/1972490

Answer:

The is coming this:-

500,000,500,000

Did you get this in vedantu

Answer:

(-2, -4)

Step-by-step explanation:

[y = 2x, y = -x -6]

Solve by substitution:

-x - 6 = 2x

simplify

3x = -6

divide

x = -2

Plug back in one equation to solve for y coordinate:

y = 2(-2)

y = -4

(-2, -4)

Answer:

Original price = $60

Step-by-step explanation:

Given:

Sales price of shoes = $45

Discount rate = 25%

Find:

Original price

Computation:

Original price = Sales price of shoes[1/(1-Discount rate)]

Original price = 45[1/(1-25%)]

Original price = 45[1/(1-0.25)]

Original price = 45[1/(0.75)]

Original price = $60

Answer:

Step-by-step explanation:

$60

Answer:

325

Step-by-step explanation:

65% of 500 is 325

Answer:

No, you would graph the y-intercept, you do not graph the m-value (slope). The slope value is the rate that the y-value increases per unit of x. This is how you graph your line from the y-intercept

Answer:

No you are incorrect. The correct answer is (y - intercept) b = -4

Step-by-step explanation:

You need to plot the y - intercept first so that you can create the line using the slope starting from the y - intercept. You can't plot the line unless you first plot a point on the line which would be the y - intercept or -4 THEN from there you use the slope to create the line.

Answer:

41°

Step-by-step explanation:

the sum of the interior angles is 180 degree

so,

38 + x + 101 = 180

139 +x = 180

x = 180 - 139

x= 41°

Answer:

53.2 ft

Step-by-step explanation:

A wire makes a 70 degrees angle with the ground and is attached to the top of a 50 ft. antenna. How long is the wire?

We solve the above question using the Trigonometric function of Sine

sin theta = Opposite/Hypotenuse

Theta = 70°

Hypotenuse = x = Length of the wire

Opposite = 50ft antenna

Hence,

sin 70 = 50/x

Cross Multiply

50 = sin 70 × x

x = 50/sin 70

x = 53.208888624 ft

Approximately x = 53.2 ft

The length of the wire is 53.2 ft

Answer:

thisis answer okkkkkkk

Answer:

x=108 degrees

Step-by-step explanation:

Since ST is a straight line, it measures 180 degrees. This means that x+(2/3)x=180. The simplified version is 5x/3=180. Now, we multiply both sides by 3. The equation becomes 5x=540; which is ultimately x=108.

Answer: x=108 degrees

Step-by-step explanation:

Since ST is a straight line, it measures 180 degrees.

This means that:

x+(2/3)x=180

The simplified version is 5x/3=180. Now, we multiply both sides by 3. The equation becomes 5x=540; which is ultimately x=108.

Answer:

C

Step-by-step explanation:

Answer:

B is the correct choice:

(10 x 10 x 30) + (10 x 10 x 12)

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer:

2. 10 + 5 x 2                    $20

3. 10 + 5 x 3                    $25

4. 10 + 5 x 4                    $30

Hope that helps!

Step-by-step explanation:

Answer:

2) 10+5x2= 20

3) 10+5x3= 25

4) 10+5x4= 30

Step-by-step explanation:

just add 5 every time