Answer:
-7, 14
Step-by-step explanation:
We start by writing this in the form $x^2 + bx + c = 0$, so we subtract 98 from both sides of the equation.
This gives us $x^2 - 7x - 98 = 0$. We proceed by factoring $x^2 - 7x - 98$, so we seek numbers that multiply to $-98$ and add to $-7$. We find that $7$ and $-14$ work.
Thus, our equation becomes $(x + 7)(x - 14) = 0$. We can now apply the fact that if the product of two real numbers is zero, then at least one of the real numbers must be 0.
Solving $x + 7 = 0$ and $x - 14 = 0$, we find that the solutions are $\boxed{x =-7~\text{and}~x = 14}$.
The value of the equation is given by x = 14 or x = -7
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
x² - 7x = 98 be equation (1)
Subtracting 98 on both sides of the equation , we get
x² - 7x - 98 = 0
Now , on simplifying the equation , we get
x² - 14x + 7x - 98 = 0
Taking x as the common factor of the equation , we get
x ( x - 14 ) + 7 ( x - 14 ) = 0
On further simplification , we get
( x + 7 ) ( x - 14 ) = 0
Now , the two solutions to the equation is
( x + 7 ) = 0
Subtracting 7 on both sides of the equation , we get
x = -7
( x - 14 ) = 0
Adding 14 on both sides of the equation , we get
x = 14
Therefore , the value of A is 14 or - 7
Hence , the equation x² - 7x - 98 = 0 has the solutions of 14 and -7
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A bag of coins contains only quarters and dimes.
• The number of dimes in the bag can be represented by x.
• The number of quarters is 6 more than twice the number of dimes.
• There are a total of 276 coins in the bag.
What is x, the number of dimes in the bag?
helpp pls
Answer:
Number of dimes in the bag = 90
Number of quarters in the bag = 186
Step-by-step explanation:
Let
x = Number of dimes in the bag
y = Number of quarters in the bag
= 2x + 6
Total = 276
276 = x + 2x + 6
276 = 3x + 6
276 - 6 = 3x
270 = 3x
x = 270/3
= 90
x = 90
Number of dimes in the bag = 90
Number of quarters in the bag = 2x + 6
= 2(90) + 6
=180 + 6
= 186
Total = Number of dimes in the bag + Number of quarters
= 90 + 186
= 276
A shoe store is having a clearance sale on their summer shoes. All summer shoes are marked 55% off. A sign states you can take an additional 10% off the clearance sale prices. Kelly is deciding between two pairs of sandals shown in the table.
Shoes Original Price
Blue Sandals $75
Tan Sandals $68
If she buys the blue sandals, what is the final price Kelly will pay? Round to the nearest cent.
Answer:
$30.38
Step-by-step explanation:
Final Price = Original Price - Discount
Final Price = 75 - 41.25
Final Price = $33.75
Then its the additional 10%
So now you make your original cost $33.75 to make it easier so
Final Price = Original Price - Discount
Final Price = 33.75 - 3.375
Final Price = $30.38
Final Answer: $30.38
The final price Kelly will pay round to the nearest cent is $30 38¢
What is percent?In mathematics, a percent is a number or ratio expressed as a fraction of 100. It is often denoted using percentage sign "%".
Now it is given that,
Discount = 55%
Additional discount = 10%
Original Price of Blue Sandals = $75
Original Price of Tan Sandals = $68
Since Kelly bought blue sandels,
So, discount on Blue Sandals = 55% of $75
⇒ discount on Blue Sandals = 0.55 * $75 = $41.25
So, Cost of Blue Sandals = $75 - $41.25
⇒ Cost of Blue Sandals = $33.75
Now there is additional discount of 10%
Additional discount = 10% of $33.75
⇒ Additional discount = 0.10% * $33.75
⇒ Additional discount = $3.375
Thus, Final Cost of Blue Sandals = $33.75 - $3.375
⇒ Final Cost of Blue Sandals = $30.375
Round to the nearest cent final cost of Blue Sandals = $30 38¢
Thus, the final price Kelly will pay round to the nearest cent is $30 38¢
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Plz Help The function shown models the total number of insects in a colony x months after a small number of the insects are brought into a region.
What was the total number of insects in the colony when they were first brought into the region ? Enter your answer in the box
Answer:
I think it's 25? If I can edit I'll come back with answer..(if it's not 25.)
Step-by-step explanation:
There are 12 teams in the Jayhook Hockey League. Each team plays every other team twice per season, once at home and once away from home. Last season 34 of the matches played resulted in a tie. Of the others, 18 more were won by the home team than by the away team. 1: How many games did any one particular team play?
Answer:
Each team played 22 games.
Step-by-step explanation:
There are 12 teams in the league, so each team has 11 rival teams. Since each team will play against a rival team twice, that means that each team will need to play 11 x 2 = 22 games per season. Of these 22 games, 11 games will be played at home while 11 games will be played away from home.
We can calculate this by using the following formula:
Total number of games played by each team = (n - 1) x 2, where n is the total number of teams in a league.
In this question, all lengths are in centimetres.
Given
AB: AC = 1:2
AB= 3x-4
AC= 2x + 12
show that
AC: BC = 2:3
BС= 7X-2
Answer:
Step-by-step explanation:
AB/AC =1/2
(3x-4)/(2x+12)=1/2
2(3x-4) = 1(2x+12)
6x-8=2x+12
4x=20
X=5
AC/BC =3x-4/7x-2=22/33=2/3
AB/AC=3x-4/7x-2=22/33=2/3
AB/AC=3x-4/2x+12
6x-8=2x+12
You would get 4/5 still trying to work out the last mark
Step-by-step explanation:
First find x:
AB:AC=1:2
2(3x-4)=2x+12
6x-8=2x+12
4x-8=12
4x=20
x=5
Substitute:
AC=2x+12
=(2x5)+12
=10+12
=22
BC=7x-2
=(7x5)-2
=35-2
=33
22/33=2/3
Therefore AC:BC = 2:3
I(t) = 27, 992 * (1.017) ^ t covert to log
Answer:
By 2034 Texas per capita income would reach at least $50,000
Step-by-step explanation:
Given;
[tex]I(t) = 27,992(1.017)^t[/tex]
Converting the given function to log;
[tex]I(t) = 27,992(1.017)^t \\\\\frac{I(t)}{27,992} = (1.017)^t\\\\Log_{1.017} ( \frac{I(t)}{27,992} )= t \\\\(Based \ on \ log \ rule; if \ a = b^y , in \ log \ it \ will \ be \ written \ as, Log_b \ a = y)[/tex]
(B) When I(t) = $50,000, the time "t" will become;
[tex]Log_{1.017} ( \frac{I(t)}{27,992} )= t\\\\Log_{1.017} ( \frac{50,000}{27,992} ) = t\\\\Log_{1.017} (1.7862) = t\\\\34.4 \ years = t[/tex]
Thus, by 2034 Texas per capita income would reach at least $50,000
Find the measurements of angles a, b and c. PLZ HELP
Need help ASAP!!!!!!!!!!!
Answer:
Step-by-step explanation:
5/6 + 1/8 + 3/4 = 1 17/24
Option A is the correct answer
Find the slope of the line that passes through (8,6) and (4,15)
PLZ HELP The function shown models the total number of insects in a colony x months after a small number of the insects are brought into a region. What was the total number of insects in the colony when they were first brought into the region ? Enter your answer in the box
Answer:
I think it 25?
Step-by-step explanation:
Skittles come in many different colors in my bag of 40 Skittles I had 12 green ones what percent of the bag was Green?
Answer:
4.8
Step-by-step explanation:
Why do scientists use models?
A)
Models are unreliable.
B)
Models waste natural resources.
Models predict not just describe events.
Models are based on scientific laws and principals so they are more
reliable than the real thing.
D)
plz help me asap i need help plz i will mark you as brainlist
Answer:
the third one
8. It takes Juan 40 minutes to walk 2.5 miles to the park. At this rate, how many minutes
should it take him to walk 4 miles? HELPP PLZ!!!
Answer:
64 minutes
Step-by-step explanation:
40 divided by 2.5 = 16
4 times 16 = 64 minutes
It will take 64 minutes to walk 4 miles.
What is a Ratio?A ratio indicates the number of times one number contains another.
Given that, Juan walks 2.5 miles in 40 minutes.
2.5 miles = 40 minutes
1 mile = 40/2.5 minutes
4 miles= (40/2.5)4 minutes
4 miles = 64 minutes.
Hence, It will take 64 minutes to walk 4 miles.
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help me: [tex]\int\limits^\pi _0 sin({x}) \, dx[/tex]
Answer:
[tex]\int^{\pi}_{0}sin(x)dx = 2[/tex]
Step-by-step explanation:
To solve for the value of [tex]\int^{\pi}_{0}sin(x)dx[/tex], we need to first find the antiderivative of [tex]sin(x)[/tex].
Since the derivative of [tex]cos(x)[/tex] is [tex]-sin(x)[/tex], therefore the derivative of [tex]-cos(x)[/tex] is [tex]sin(x)[/tex]. With this:
[tex]\int^{\pi}_{0}sin(x)dx = -cos(\pi)-(-cos(0))[/tex]
[tex]=-cos(\pi)+cos(0)[/tex]
[tex]=-(-1)+1[/tex]
[tex]=2[/tex]
∴ [tex]\int^{\pi}_{0}sin(x)dx = 2[/tex]
Hope this helps :)
y + 12.5 = 21.7, y =
Answer:
y = 9.2
Step-by-step explanation:
21.7 - 12.5 = 9.2
Answer:
y = 9.2
Step-by-step explanation:
Neeeeeed help?!?!!!!!!!
Step-by-step explanation:
number of minutes I guess
PLEASE HELO ME I NEED HDLP PLEASE
Answer:
what's that 120 which angle is that
Step-by-step explanation:
Triangle AGB has Angle AGB = 120° and AG = GB. (given)
Since it is isosceles, x = (180° - 120°)/2 = 30°.
What is the solution for the system below?
у
4
-2
0
2
4
4
(2,0)
(0-2)
0 (1-1)
Answer:
the solution is (1,-1)
Step-by-step explanation:
the lines meet at (1,-1)
can someone please help me out its due very soon,
Answer:
yes it is ok
Step-by-step explanation:
40 ok equate
1 Which expression is equivalent to 1/3y?
A 1/3(y+12)-12
B 1/6y+1/3(y+3)
C 1/6y+1/6(y+12)-2
D 1/3y+1/3(6-y)
Answer:
D is your answer HOPE THIS HELPS THANK ME PLEASE
Step-by-step explanation:
HELP WILL MARK BRAINLIEST
Answer:
The answer is D: y = -2x + 6
Step-by-step explanation:
the y-intercept is 6, and the slope goes down 2 and right 1. -2/1 is the same as -2.
I hope this helped and if it did I would appreciate it if you marked me Brainliest. Thank you and have a nice day!
Can someone help me please? I will give brainly
Answer:106 I think
Step-by-step explanation: If its 2z+7w and z and w means 8 it makes 2z 28 and makes 7w 78 and then u add 28+78= 106
Urgent! Please help!
Solve the given equation:
3(x-2)^4/3 =243
Answer:
x is equal to 29.
Step-by-step explanation:
[tex]3(x - 2)^{\frac{4}{3}} = 243\\(x - 2)^{\frac{4}{3}} = 243 / 3\\(x - 2)^{\frac{4}{3}} = 243 / 3\\(x - 2) =( 243 / 3)^{\frac{3}{4}}\\x - 2 = 81^{\frac{3}{4}}\\x = 3^3 + 2\\x = 27 + 2\\x = 29[/tex]
Lulu tells her little brother, Jack, that she is holding 20 coins, all of which are either dimes or quarters. They have a value of $4.10. She says she will give him the coins if he can tell her how many of each she is holding. Solve this problem for Jack." How many dimes and quarters in Lulu holding? Enter your final answer in the space below. Please make sure you write your interpretation in a complete sentence
Given :
Lulu tells her little brother, Jack, that she is holding 20 coins, all of which are either dimes or quarters.
They have a value of $4.10. She says she will give him the coins if he can tell her how many of each she is holding.
To Find :
How many dimes and quarters in Lulu holding?
Solution :
4.10 dollar = 410 cents
Let, number of dimes and quarter are x and y.
So, x + y = 20 ...1)
Also, 10x + 25y = 410 ...2)
Putting value of 1) in equation 2), we get :
10x + 25( 20 - x ) = 410
10x + 500 - 25x = 410
15x = 90
x = 6
y = 14
Therefore, number of dimes and quarters are 6 and 14 respectively.
Hence, this is the required solution.
If 4 raffle tickets is 6 dollars how much is 1 raffle ticket
help pls lol ✋
i literally do not get this at all and i’m typing this cause apparently i need 20 words which is dumb but yeah okay bye
Please answer! solve for x
Answer:
it 180 degree try to add them all the subtract with 180 and that equals x
Step-by-step explanation:
Answer:
x = -10
Step-by-step explanation:
The angles of a triangle always add up to 180°. This means that (x+46) + 52 + 92 = 180.
First, subtract 92 from both sides of the equation to get (x+46) +52 = 88. Then, subtract 52 from both sides of the equation to get x + 46 = 36. Finally, subtract 46 from both sides of the equation to get x = -10
3w-5>2w+-7 and 6(c+3) 2+-3
Answer:
w>−2 and 12c+33
Step-by-step explanation:
Answer:
&&&&
Step-by-step explanation:
Sorry, Don't know buddy
okay I need an answer to this from scale through 1 to 10 how much naughtier can my cat be like I need some good answers
Answer:
Wow your cat is so naughty but cute. On a scale from one to 10 I say 10
Step-by-step explanation:
This is why I dont have pets