number of solutions of quadratic equations

Answer:

[tex]\boxed{4x^{2} - 48x + 144}[/tex]

Step-by-step explanation:

Given expression:

To simplify the expression, we will use the formula (a - b)² = a² - 2ab + b².

[Where "a and b" are the first and second term in (a - b)²]

[tex]\rightarrowtail (2x - 12)^{2}[/tex]

In this case, the first term of (2x - 12)² is "2x" and the second term is "12".

[tex]\rightarrowtail (2x)^{2} - 2(2x)(12) + (12)^{2} \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\small\text{First term = a = 2x; Second term = b = 12]}[/tex]

Now, simplify the expression.

[tex]\rightarrowtail (2x)^{2} - 2(2x)(12) + (12)^{2}[/tex]

[tex]\rightarrowtail (2x)(2x) - (4x)(12) + (12)(12)[/tex]

[tex]\rightarrowtail \boxed{4x^{2} - 48x + 144}[/tex]

Answer: 76 meters

Step-by-step explanation:

top side left blank = 18 because it is congruent to the bottom

left side blank is 4 + 4 + 4 (right side lengths added)

left side blank is 12

add all side lengths together for perimeter

12 + 18 + 4 + 8 + 4 + 8 + 4 + 18 = 76

76 meters

Answer:

30.4

Step-by-step explanation:

17+28+32+35+59+20+19+33+30+31=304

304/10=30.4

Answer:

A.

Step-by-step explanation:

I would advise finding the difference between 300 and 200 and 450 and 300:

[tex]300-200=100\\450-300=150[/tex]

We can eliminate C and D since she saves 100 the first month and 150 the second month.

The next step would be to find the increase every month:

[tex]\frac{Final value}{initial value}=x\\\\\frac{300}{200}=1.5 \\\\\frac{450}{300} = 1.5[/tex]

If we would write the increase as a function, we would get:

[tex]y= 1.5x[/tex]

we can check this by substituting values:

[tex]y=1.5*200\\y=300\\\\\\y=1.5*300\\y=450[/tex]

An exponential function looks like this:

[tex]y= a^x[/tex]

A linear function looks like this:

[tex]y=mx+b[/tex]

Our m is 1.5, a linear increase by 150% and our b is 0, which can be written like:

[tex]y=1.5x+0\\y=1.5x[/tex]

Therefore our function resembles a linear function more than an exponential function, eliminating answer B.

Let's first try to figure out the whole. Looking at the number line, we can see that the shaded portion of the box goes up to 2 1/3. So, this is our first number.

Then, we need to figure out what 2 1/3 was divided by. This is pretty obvious from the groupings on the box. 2 1/3 was divided by 2/3.

2 1/3 divided by 2/3 = ?

Once again using the box and the groupings, we can see that 2/3 goes into 2 1/3 evenly 3 times, leaving 1/3 left over.

2 1/3 divided by 2/3 = 3 1/2

Correct Answer: A

Hope this helps!

Answer:

What is the question? Also, your answer looks a bit wrong  1 think t should be 1 oz

Step-by-step explanation:

For every 15 oz potatoes, Garry uses 0.5 oz less cheese than Heather. So Heather's cheesy potatoes have more cheese.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

For Gary's recipe of cheesy potatoes has 15oz of potatoes and 4oz of cheese.

Ratio of potatoes to cheese in Gary's recipe = 15/4

Heather's recipe of cheesy potatoes has 10 oz of potatoes and 3 oz of cheese.

Ratio of potatoes to cheese in Heather's recipe = 10/3

Multiplying with 1.5 in numerator and denominator

Ratio of potatoes to cheese in Heather's recipe = 15/4.5

Thus, for every 15 oz potatoes heather uses 4.5 oz of cheese.

Hence, In Heather's recipe amount of cheese is 0.5 oz more than Garry's recipe per 15 oz. of potatoes.

Learn more about ratio here:

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#SPJ2

Answer:

They do not pay the same amount. Manuel's family pays more than Amelia's.

Step-by-step explanation:

General:

Child: c

Adult: 4 + c

Senior: 3 + c

Amelia's Family:

Total cost = 3(c) + 2(4 + c)

= 3c + 8 + 2c

= 5c + 8

Manuel's Family:

Total cost: 2(c) + 4 + c + 2(3 + c)

= 2c + 4 + c + 6 + 2c

= 5c + 10

The comparison of the number of stuffed animals in both years is an illustration of inequalities

The statement that compares the number of stuffed animals is 189909 < 198909

The given parameters are:

By comparing the number of stuffed animals in both years, we have:

198909 > 189909 or 189909 < 198909

Hence, the statement that compares the number of stuffed animals is 189909 < 198909

Read more about inequalities at:

https://brainly.com/question/11234618

Answer:

a) organized-

3,4,5,6,6,7,9,28

median is 6

68/8=8.5

the mean is 8.5

b) the median, because there is an outlier

Answer:

2

5

YES

trinomial

Step-by-step explanation:

Given expression:  [tex]5x^2+3x+6[/tex]

The degree of the polynomial is the highest exponent = 2

The leading coefficient, is the coefficient (value) before the [tex]x^2[/tex] = 5

The constant in the polynomial is the value without a variable, i.e. 6 = YES

This expression can be called a trinomial expression since it is a polynomial with exactly three terms.

Expression given:-

So

Answer: 144 degrees, 136 degrees

Question 1:

The first x should be 144 because a straight line should equal 180, so you just subtract the (left angle or 36 degrees) with 180 to get the opposite angle.

Question 2:

For the second x, add the 2 interior angles and subtract it by 180 or the total sum of the interior angles.

49 + 87 = 136

180 - 136 = 44

Then follow the same steps in the first question.

180 - 44 = 136

Answer:

(x-1)^2 + (y-1)^2 = 16

Step-by-step explanation:

center, (h,k) = (1,1)     radius = 4

put in standard form for a circle

(x-h)^2 + ( y-k)^2 = r^2  

Answer:

0 or 6x+4=6x+4  (Technically no slope at all!!)

Step-by-step explanation:

You need to do distributive property and then solve for x!!

meaning the 2(3x+2) has to get distributive property process.

6x+4=6x+4

That shall be equal together!!! (You could stop here!!)

If continue:

6x-6x=4-4

0=0

Answer:

1. Where you shop at

2. The tax in the state you live in.

Hope this helps!

Answer:

1. Where you shop at2. The tax in the state you live in.

Step-by-step explanation:

Answer: Center: (13, -11)

              Radius: 19

Step-by-step explanation: yeah

Answer:

check the attachment and explanation below

Step-by-step explanation:

Explanation for statement 3 :

Suppose The number of shoppers on Saturday is 100 and the number of shoppers on Sunday is 200

Total number of shoppers = 300

On Saturday :

Q₃ = 70 then 25% of shoppers spent more then $70

then 25 shopper spent more then $70

On Sunday:

M’ = 70 then 50% of shoppers spent more then $70

then 100 shopper spent more then $70

On both days:

(100+ 25) shopper spent more then $70

Then 125 shopper spent more then $70

But 125 is not 75% of 100+200=300

Answer:

12 years old

Step-by-step explanation:

3x+5=41

3 times a number and 5 more

'more' usually means adding

41-5 =36

36/3 =12

Answer:

Equation: 41 = 3x + 5

x = 12

Step-by-step explanation:

Hello!

Betty is 5 more than 3 times Jadyn's age. Since Jadyn's age is unknown, we'll call that unknown variable x.

Betty is 5 more than 3 times x. Betty is also 41 years old.

Equation: 41 = 3x + 5

Now we have to solve for x

Solve for x:

Jadyn is 12 years old.

Answer:

8

Step-by-step explanation:

[tex]a^2+b^2=c^2\\a^2+6^2=10^2\\a^2+36=100\\[/tex]

subtract 36 from each side

[tex]a^2=64\\\sqrt{a^2=64}\\a=8[/tex]

or you could recognize the 3-4-5 Pytagorean triple, as the ratio is doubled.

Surface area

Answer:

n = 6 and n = 11

Step-by-step explanation:

Answer:

.858 cm^2

Step-by-step explanation:

Area of square - area of circle = grey corner areas

(2 * 2)  - ( pi * 1^2 ) =

4 - pi = .858 cm^2

Answer:

See below.

Step-by-step explanation:

I have already answered #6 in a previous post. Kindly find the link to the solution below :

#7) Maximum Height

#8) Time taken to land on the ground

Answer: 1,950,000

Step-by-step explanation: Divide by 2 beginning with the first digit which is 3 up to the last zero

The equation for the subtraction of length of AB is -3-(-14)

The distance between two points is the measure of the distance covered by an object.

From the given diagram, we are to find the distance between the point A and B. Since the x-coordinate are equal, hence:

AB = y2 - y1
AB= -3 - (-14)

AB = 11 units

Hence the equation for the subtraction of length of AB is -3-(-14)

Learn more on distance here: https://brainly.com/question/24775607

Answer:

It took 4/5 of an hour or 48 minutes

Step-by-step explanation:

When both Ali and his sister have eaten, the fraction of the pizza that is left will be 5/12.

From the complete information, Ali eats 1/3 and his sister eats 1/4 of the pizza. Therefore, the number eaten by Ali will be:

= 1/3 × 6 = 2

The number eaten by the sister will be:

= 1/4 × 6 = 1.5

The remaining fraction will be:

=1 - (2 + 1.5)/6

= 1 - (3.5/6)

= 2.5/6

= 5/12

Learn more about fractions on:

https://brainly.com/question/78672

Answer: c. Step-by-step explanation:

Answer:

2.3 inches

Step-by-step explanation:

v = lwh (volume equals length times width times height)

5.52 = 2.4 x 1 x d
multiply l and w, which is 2.4 x 1

5.52 = 2.4 x d
divide 5.52 by 2.4

2.3 = d

Answer: 2.12

Step-by-step explanation: Okay, you first add 2.4+1, which is obviously 3.4.

Then you subtract 5.52 by 3.4.

You should get 2.12.

I hope I helped. <3

Answer:

90 degrees

Step-by-step explanation:

a triangles angles add up to 180

this means that you can add all the angles together and get 180

you can first add 30 and 60 and then subtract the sum from 180

30 + 60 = 90

180 - 90 = 90

the last angle is 90 degrees

Hey ! there

Answer:

Step-by-step explanation:

In the question we are given with two angles of the triangles that are 30° and 60° . And we are asked to find the third angle of triangle .

For solving this question we must have knowledge of angle sum property which says that the sum of all the angles which are present inside the triangle ( interior angles ) is equal to 180°.

Solution : -

As we know that ,

So ,

[tex] \longmapsto \qquad \: 30° + 60° + x° = 180°[/tex]

Step 1 : Adding 30° and 60° :

[tex] \longmapsto \qquad \:90° + x° = 180° [/tex]

Step 2 : Subtracting 90° from both sides :

[tex] \longmapsto \qquad \: \cancel{90°} - \cancel{90 ° } + x° = 180° - 90° \: [/tex]

On further calculations , We get :

[tex] \longmapsto \qquad \: \blue{\underline{\boxed{\frak{x° = 90°}}}}[/tex]

Verifying : -

Now we are verifying our answer by adding all the angles of triangle and equating them with 180° because of angle sum property. So ,

Therefore, our solution is correct .