The square of a number 60 greater than half of the number. Form a
quadratic equation and solve to determine the possible values of the
number.

Answers

Answer 1

Answer:

The number could be [tex]-7.5[/tex] or [tex]8[/tex].

Step-by-step explanation:

I'm going to assume this means "The square of a number is 60 greater than half of the number." Let the number be [tex]x[/tex]. The square of [tex]x[/tex] will be [tex]x^{2}[/tex]. "is" denotes that we use the "[tex]=[/tex]" sign, so our equation so far is [tex]x^{2} =[/tex] . Half of [tex]x[/tex] is [tex]\frac{1}{2}x[/tex], and "greater than" implies addition, so [tex]60[/tex] greater than [tex]\frac{1}{2}x[/tex] is [tex]\frac{1}{2}x+60[/tex]. Therefore, the equation is [tex]x^{2} =\frac{1}{2}x+60[/tex].

Solving for [tex]x[/tex], we get:

[tex]x^{2} =\frac{1}{2}x+60[/tex]

[tex]2x^{2} =x+120[/tex] (Multiply both sides of the equation by [tex]2[/tex] to get rid of the fraction)

[tex]2x^{2} -x-120=0[/tex] (Subtract [tex]x+120[/tex] from both sides of the equation to make it easier to solve)

[tex]2x^{2} +15x-16x-120=0[/tex] (Split [tex]-x[/tex] into [tex]15x-16x[/tex] to make the LHS easier to factor)

[tex]x(2x+15)-8(2x+15)=0[/tex] (Take a common factor out of the first two terms and the last two terms)

[tex](2x+15)(x-8)=0[/tex] (Take another common factor out)

[tex]2x+15=0,x-8=0[/tex] (Zero Product Property)

[tex]x=-7.5,8[/tex] (Solve)

Hope this helps!


Related Questions

A chord of a circle is l cm long. The distance of the chord to the center of the circle is h cm and the radius of the circle is r cm. express r in terms of l and h​

Answers

Answer:

r square = half of l square + h square

Step-by-step explanation:

I used phythogoras theorem to express r in terms of l and h

what is the answer to 6−2(3x−5)=−8

Answers

Answer:

x = 4

Step-by-step explanation:

6-2(3x-5)=-8
So first we distribute:
6-6x+10=-8
Combine like terms:
16-6x=-8
Now subtract 16 to -8:
-6x=-24
Divide -6 to both sides:
x=4

What two expressions represent 3/12​?

Answers

Answer:

A and C

3x1/12= 3/12

3x1/2= 3/12

Ron is x years old. His brother, Ray, is y years older than him. How old was Ray when Ron was first born?

Answers

Answer:

Ray was y years old when Ron was born

Step-by-step explanation:

Hey there!

The correct answer is y years old.

If he is y years older, that means that when Ron was 0, or when he was just born, Ray was y years older.

Have a terrificly amazing day! :D

–3y9 number of terms

Answers

Answer and Step-by-step explanation:

[tex]-3y^{9}[/tex]

This value above is ONE term. Even though it is made up of more values and stuff, it is all one term BECAUSE they are all connect, so the -3 is with the y by multiplication, and the 9 is with -3y as an exponent of y.

#teamtrees #PAW (Plant And Water)

simplify ..... 12x^2 / 9x^2y show work please

Answers

Answer:

4/3y

Step-by-step explanation:

Given the expression 12x^2 / 9x^2y

12x^2 / 9x^2y

= (3*4)* x * x/(3*3)*x*x*y

= 4x^2/3x^2y

= 4/3y

hence  the simplified form is 4/3y

ITS AN ANGLE QUESTION PLS HELP

Answers

Answer:

The values of [tex]f[/tex] and [tex]g[/tex] are, respectively:

[tex]f = 6\,cm[/tex], [tex]g = 8\,cm[/tex]

Step-by-step explanation:

The area of the triangle ADE is:

[tex]A_{ADE} = 60\,cm^{2}-48\,cm^{2}[/tex]

[tex]A_{ADE} = 12\,cm^{2}[/tex]

The area of the triangle is defined by the following formula:

[tex]A_{ADE} = \frac{1}{2}\cdot AD\cdot DE[/tex] (1)

If we know that [tex]A_{ADE} = 12\,cm^{2}[/tex] and [tex]DE = 4\,cm[/tex], then the length of the line segment [tex]AD[/tex] is:

[tex]AD = \frac{2\cdot A_{ADE}}{DE}[/tex]

[tex]AD = 6\,cm[/tex]

And the area of the rectangle is:

[tex]A_{ABCD} = AD\cdot CD[/tex] (2)

If we know that [tex]A_{ABCD} = 48\,cm^{2}[/tex] and [tex]AD = 6\,cm[/tex], then the length of the line segment [tex]CD[/tex] is:

[tex]CD = \frac{A_{ABCD}}{AD}[/tex]

[tex]CD = 8\,cm[/tex]

Hence, the values of [tex]f[/tex] and [tex]g[/tex] are, respectively:

[tex]f = 6\,cm[/tex], [tex]g = 8\,cm[/tex]

In a triangle with vertices A,B and C, if C =64° and the lengths AC= 40mm and BC= 70mm find the length AB using cosine rule

Answers

Answer:

63.6mm

Step-by-step explanation:

According to cosine rule;

AB² = BC²+AC²-2(BC)(AC)cos m<C

Substitute the given values

AB² = 70²+40²-2(70)(40)cos 64

AB² = 4900+1600-5600cos64

AB² = 6500-5600(0.4384)

AB² = 6500-2,454.87

AB² = 4,045.12

AB = √4,045.12

AB = 63.6mm

Hence the length of AB is 63.6mm

I want to switch from online school to in-person school next school year and my mom wants to know why and I just think it would be fun but I can't tell her that so what do I say???? Please Help!

Answers

Answer:

just tell her that you want to see your friends again or say that you think it will have a better effect on your grades. you could say that it would be eaiser to pay attention in class and that CV cases are droping so it would be still be safe to go.

Step-by-step explanation:

Hope this helps!

Answer:

I have already switched from online to in-person, and I would say it was a pretty great decision. Some points you could bring up are ;

o It'll help your grades. (Personally, I was really struggling with my grades while doing online but, as soon as I switched my grades raised quick!)

o You miss your friends, or just seeing humans lol. (It's been almost an entire year we've been on lockdown! No one can see friends, or people in general. If you look it up, its this has taken a big toll on people's mental health.)

o Just to be able to get out of the house for a few hours. (We've been stuck inside with nothing to do besides, sit and do school and spend all of our time looking at our screens. Just tell her it's to much and you need a break.)

Hope this helps !!

Which property is demonstrated below?

(a+b)+c=(b+a)+c

A. Commutative property of addition

B.Associative property of addiction

C.Identity property of addition

D.Distributive property

Answers

Answer:

Associative property of addition

Answer:

B.Associative property of addiction

Step-by-step explanation:

What is the product of a,b, and c?

Answers

Answer:

[tex] abc = - \frac{16}{3} [/tex]

Step-by-step explanation:

[tex] {x}^{ - 2} {y}^{3} \sqrt[3]{ 64{x}^{5} {y}^{3} } = a {x}^{b} {y}^{c} \\ \\ {x}^{ - 2} {y}^{3} \times 4 \times {x}^{ \frac{5}{3} } \times y= a {x}^{b} {y}^{c} \\ \\ 4 {x}^{ \frac{5}{3} - 2 } {y}^{3 + 1} = a {x}^{b} {y}^{c} \\ \\ 4 {x}^{ \frac{5 - 6}{3} } {y}^{4} = a {x}^{b} {y}^{c} \\ \\ 4 {x}^{ \frac{ - 1}{3} } {y}^{4} = a {x}^{b} {y}^{c} \\ \\ equating \: like \: terms \: on \: both \: sides \\ \\ a = 4 \\ \\ b = - \frac{1}{3} \\ \\ c = 4 \\ \\ abc = 4 \times ( - \frac{1}{3} ) \times 4 \\ \\ = 16 \times ( - \frac{1}{3} ) \\ \\ abc = - \frac{16}{3} [/tex]

Solve this equation 53y - 55 = 42y

Answers

53y-42y=55
11y=55
Y=55/11 =5

Work out the area of this semi circle Take pi to be 3.142 and write down all the digits given by your calculator

Answers

Answer:

628.4cm²

Step-by-step explanation:

Find the diagram attached

Area of the semi circle = πr²/2

r is the radius = 10cm

Area of the semi circle = π(10)²/2

Area of the semi circle = 3.142(100)/2

Area of the semi circle = 314.2×2cm²

Area of the semi circle =628.4cm²

Hence the area of the semicircle is 628.4cm²

Sara collected $135 in donations for the hospital. This represents 5% of the total amount collected by her class. How much did the class collect in all?

A.$6.75
B.$130
C.$140
D.$2700

Answers

Answer:

Step-by-step explanation:

A(5/100)=135

A=100(135)/5

A=$2700

Answer:

D

Step-by-step explanation:

5/100 = 135/x

Cross multiply

5 × x = 100 × 135

5x = 13500

Divide both sides by 5 to isolate the variable

x = 2700

$2700

Check work by plugging the x value into the equation

5/100 = 135/2700

Convert 5/100 so that it has the same denominator as the other fraction

5 × 27/100 × 27

135/2700

135/2700 = 135/2700

Do they equal?

Yes, so our answer is correct

Solve graphically.
5x+7y=1 and x+4y=-5​

Answers

Answer:

{x,y} = {3,-2}

Step-by-step explanation:

Then the intersection point is (3, -2). Then the solution of the equations will be (3, -2).

What is a linear equation?

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

x/a + y/b = 1

Where 'a' is the x-intercept of the line and ‘b’ is the y-intercept of the line.

The equations are given below.

5x + 7y = 1

x + 4y = -5​

Convert the equation into an intercept form. Then we have

From equation 1, then we have

5x + 7y = 1

x / (1/5) + y / (1/7) = 1

From equation 2, then we have

x + 4y = -5​

x / (-5) + y / (-5/4) = 1

The lines are drawn below.

Then the intersection point is (3, -2). Then the solution of the equations will be (3, -2).

More about the linear equation link is given below.

https://brainly.com/question/11897796

#SPJ2

In a card game, one of the players wants to draw two DIAMONDS in a row from a newly shuffled deck. (Recall a deck of cards has 52 total cards
and 13 of each symbol, including 13 diamonds.)
Create a tree diagram.
What is the probability ONE of the two cards is a diamond?
What is the probability the second card is a diamond, GIVEN the first card drawn was a diamond?
(CLICK YOUR ANSWER FROM THE OPTIONS BELOW. DON'T TYPE YOUR ANSWER IN.)
Word Bank:
382.59.235.254.191 25.559 231
Blank 1:
Blank 2:

Answers

Part A

The probability of getting diamonds on the first draw is 13/52 since we have 13 diamonds out of 52 total.

The probability of getting a non-diamond card on the second selection is 39/51 since we have 39 non-diamond cards out of 52-1 = 51 cards left over. Whatever card that was selected first is not put back. In this scenario, we are picking exactly one diamond card.

The probability of both events occurring is (13/52)*(39/51) = 13/68. I skipped a few steps but hopefully you can see how I arrived at that fraction.

The same probability shows up if we had a non-diamond card drawn first followed by a diamond card. This is because we compute (39/52)*(13/51) = 13/68.

So overall, the answer as a fraction is 13/68 + 13/68 = 26/68 = 13/34

The answer in decimal form is roughly 13/34 = 0.3824 which converts to 38.24%

---------------

Answer in fraction form = 13/34Answer in decimal form = 0.3824  (approximate)Answer in percent form = 38.24%  (approximate)

============================================================

Part B

We're told that "given the first card drawn was a diamond" so we only need to worry about the second card.

We have 13-1 = 12 diamonds left out of 52-1 = 51 total.

The probability of picking another diamond is 12/51 = 0.2353 approximately. This converts to 23.53%

-----------------

Answer in fraction form = 12/51Answer in decimal form = 0.2353 (approximate)Answer in percent form = 23.53% (approximate)

Which of the following choices shows the equation solved for y
7x + 2y = 10

1. y = -7/2x + 5
2. y = 7/2x +10
3. y = 7/2x + 5
4. y = -7x + 10​

Answers

Answer:

#1; [tex]y = -\frac{7}{2}x+5[/tex]

Step-by-step explanation:

[tex]7x+2y=10[/tex]

[tex]2y = -7x + 10[/tex]

[tex]\frac{2y}{2} = -\frac{7x}{2} + \frac{10}{2}[/tex]

[tex]y = -\frac{7}{2}x + 5[/tex]

Here is a right square pyramid. Round answers on this problem to the nearest tenth if necessary. what is the height of the pyramid? what is the volume of the pyramid?​

Answers

Answer:

height = 6

volume = 60 in³

Hope this helps!

Answer:

Height = 4

Volume = 48 units ^3

Step-by-step explanation:

y = (-3/2)x + 9 2x + 4y = 17 solve the system of equations
step by step​

Answers

Answer:

x = 19/4 and y = 15/8

Step-by-step explanation:

Given:

y = (-3/2)x + 9

2x + 4y = 17

Move y to one side:

2x + 4y = 17

y = 17/4 - x/2

Solve for x:

(-3/2)x + 9 = 17/4 - x/2

x = 19/4

Substitute x to solve for y:

y = (-3/2)(19/4) + 9

y = 15/8

2(19/4) + 4y = 17

y = 15/8

n is an integer with -5 < 2n <6
write down all the values of n?

Answers

Answer:

The values of n are less than 3 and more than (-5/2)

Step-by-step explanation:

The given inequality is :

-5 < 2n <6

We need to write the values of n.

Dividing both sides of the inequality by 2. So,

[tex]\dfrac{ -5}{2} < \dfrac{2n}{2} <\dfrac{6}{2}\\\\=\dfrac{ -5}{2}<n<3[/tex]

So, the values of n are less than 3 and more than (-5/2).

*EXTRA POINTS* find the volume please :))

Answers

Answer:

904.32 ft^3

Step-by-step explanation:

Sphere Volume Formula: [tex]\frac{4}{3}[/tex][tex]\pi r^{3}[/tex]

Plug in the numbers:

[tex]\frac{4}{3}\pi 6^{3}[/tex]≅904.78

???????......????...??..??…??..?.?.?..​

Answers

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

A store manager earns $ 24.00 per hour. If the manager works 8 hours one day and donates 1 10 of the day's earnings to charity, how much of the earnings are left?

Answers

If u meant $1.10 donated then it would be $190.9

But if u donated 110 then it would be $82

PLEASE HELP FAST I WILL GIVE BRAINLIST AND EXTRA POINTS FOR YOU TO DRAW THE GRAPH

Answers

Answer:

literally straight on the x axis

Can someone please answer this for me

Answers

Answer:

3.5

Explanation:

Take any two points of the line and simply use the formula slop = y2-y1/x2-x1

Two points that I consider

(x1, y1) = (5,0)

(x2,y2) = (7,7)

Now using the above mentioned formula,

y2-y1/x2-x1 = 7-0/7-5 = 7/2= 3.5

Hence slop of line is 3.5

Thanks for joining brainly community!

In a computer catalog, a computer monitor is listed as being 25 inches. If the height of the screen is 15 inches, what is the area of the screen to the nearest inch?

Answers

Answer: 20inch

Step-by-step explanation:

Using the Pythagoras theorem:-

25^2 = 15^2 + x^2    where x = the width of the screen.

625 = 225 + x^2

x = √(625 - 225) = √400

= =  20 ins

what is the surface area of the figure?

Answers

Answer:

96

Step-by-step explanation:

first off you know that it is a square pyramid, so you can assume that all base lengths are 6.

i am going to find the base first. it is 36 because 6*6-36 save this in your mental memory

next, we have to find the 4 triangles

we know that they are 5 by 6 but you have to divide them by 2

so 30/2=15 and there are 4 of them

15*4=60

now add together 60 and 36 and you get 96

hope this helps!

EMERGENCY! NEED QUICK
if

Answers

Answer:

100 degrees

Step-by-step explanation:

hi again,

By the linear pair theorem, Angle B + Angle E will equal 180 degrees

Angle B + 128 = 180

Angle B = 52

By the triangle Sum Theorem, Angle A + Angle B + Angle C = 180

48 + 52 + Angle C = 180

100 + Angle C = 180

Angle C = 80

Like I said, by the linear pair theorem, Angle C + Angle F will equal 180 degrees

80 + Angle F = 180

Angle F = 100

Xander goes to the movies with his family. Each family member buys a ticket and two boxes of popcorn. There are five members of his family. Let t represent the cost of a ticket and p represent the cost of a box of popcorn. Explain how each expression describes the situation in a different way.

Answers

Answer:

t + 2p = cost of 1 family member

Step-by-step explanation:

Because there are 5 family members who buy 1 ticket and 2 boxes of popcorn, we must multiply the cost of one family member by five .

5(t + 2p) = total cost of the whole family.

We can distribute 5 and the above equation will become.

5t + 2(5)p ⇒ 5t + 10p = total cost of the whole family.

Hope that helps! :)

Answer:

Step-by-step explanation:

t + 2p = cost of 1 family member

since there are 5 family members who bought one ticket and 2 popcorn, we simply multiply the cost of 1 family member by 5.

5(t + 2p) = total cost of the whole family.

We can distribute 5 and the above equation will become.

5t + 2(5)p ⇒ 5t + 10p = total cost of the whole family.

what is the common ratio? {250, 50, 10, 2...}

Answers

Answer:

5

Step-by-step explanation:

The common ration can be found by dividing the 2nd number from the 1st number:

250 / 50

which equals 5

250 / 50 = 5

         you can do this by any number, for example:

         50 / 10 =5

         10 / 2 = 5

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