The ratio of boys and girls riding the bus is 4:3 if there are a total of 56 students on the bus,how many girls are on the bus

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:

17/24 pizza

7/8 of questions

7/10 of   the newspapers

dylan 1 1/4 miles sonia 1 1/10 miles

answer b

Step-by-step explanation:

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:

[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

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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:

(-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:

72.5°

Step-by-step explanation:

180° - 35° = 2y°

145° = 2y

145/2 = 50+22+0.5 = 72.5

Answer:

i don't know the answer today I say tomorrow

Answer:

325

Step-by-step explanation:

65% of 500 is 325

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

Answer is in the file below

tinyurl.com/wtjfavyw

Answer:

x + 5 + x + 5

5 + 5 + x + x

Step-by-step explanation:

Answer:

:

Step-by-step explanation:

2x+10

2x+5+5

............

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

The volume of the cone is [tex]\frac{\pi}{4}[/tex] the volume of the pyramid

The ratio of the area is given as:

[tex]R= \frac{\pi r^2}{4r^2}[/tex]

or

[tex]R= \frac{\pi}{4}[/tex]

The volume of a cone is:

[tex]V_1 = \frac 13 \pi r^2 h[/tex]

For a pyramid, the volume is:

[tex]V_2 = \frac 43 r^2h[/tex]

Rewrite as:

[tex]V_2 = 4 * \frac 13 r^2h[/tex]

Divide by 4

[tex]\frac{V_2}{4} = \frac 13 r^2h[/tex]

Substitute [tex]\frac{V_2}{4} = \frac 13 r^2h[/tex] in [tex]V_1 = \frac 13 \pi r^2 h[/tex]

So, we have:

[tex]V_1 = \frac{V_2}{4} * \pi[/tex]

This gives

[tex]V_1 = \frac{\pi}{4} V_2[/tex]

Hence, the volume of the cone is [tex]\frac{\pi}{4}[/tex] the volume of the pyramid

Read more about volumes at:

https://brainly.com/question/9554871

Answer:

[tex]c=\frac{5}{\cos35^{\circ}}[/tex]

Step-by-step explanation:

Using basic trig for right tringles ([tex]\cos\theta =\frac{\text{adj}}{\text{hyp}}[/tex]), we have the following equation:

[tex]\cos 35^{\circ}=\frac{5}{c},\\c=\boxed{\frac{5}{\cos 35^{\circ}}}[/tex].

The value of c in the right triangle ABC is 5 / cos 35°

Right triangle has one of its sides as 90 degrees. The sides of a right triangle can be found using trigonometric ratios as follows;

cos 35 = adjacent  / hypotenuse

where

adjacent side = 5 inches

c = hypotenuse

Therefore,

cos 35° = 5 / c

cross multiply

c cos 35° = 5

divide both sides by cos 35°

c = 5 / cos 35°

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Answer:

otf grandson c or b or a

Step-by-step explanation:

Answer:

C

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:

C

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

is this answer

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:

The is coming this:-

500,000,500,000

Did you get this in vedantu

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:

using above inequality equation, we can find the total hours in which the clown can be at the party

The correct inequality for the Dan's spending in terms of h, the number of hours that the clown can be at the party will be;

⇒ $180 + $35h < $400

What is Inequality?

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

Dan is planning an event for which the total cost cannot exceed $400.

And, Dan plans to spend $180 on food and to hire a clown at the rate of $35 per hour.

Now,

Let number of hours = h

So, We can formulate;

Total spend money = $180 + $35h

Hence, The correct inequality for the Dan's spending in terms of h, the number of hours that the clown can be at the party will be;

⇒ $180 + $35h < $400

Thus, The correct inequality for the Dan's spending in terms of h, the number of hours that the clown can be at the party will be;

⇒ $180 + $35h < $400

Learn more about the inequality visit:

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#SPJ5

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:20 and 15 gallons

Step-by-step explanation:

Given

The first car gets 25 miles per gallon

The second car gets 15 miles per gallon

Two cars consumed 35 Gallons

they went for 725 miles in total

suppose the first car consumes x gallons

so, the second car consumes 35-x gallons of gas

We can write

[tex]\Rightarrow 25x+15(35-x)=725\\\Rightarrow 25x-10x=725-525\\\Rightarrow 10x=200\\\Rightarrow x=20[/tex]

First consumed 20 gallons and second consumed 15 gallons

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:

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