Answer:
The answer is 48.
Step-by-step explanation:
The formula for discriminant, D = b² - 4ac. Then you have to substitute the following values into the formula :
[tex]D = {b}^{2} - 4ac[/tex]
[tex]let \: a = 2 \\ let \: b = \sqrt{32} \\ let \: c = - 2[/tex]
[tex]D = {( \sqrt{32} )}^{2} - 4(2)( - 2)[/tex]
[tex]D = 32 + 16[/tex]
[tex]D = 48[/tex]
Jessica decides to mix grades of gasoline in her truck. She puts in 8 gallons of regular and 8 gallons of premium for a total cost of $41.04. If premium gasoline costs $0.21 more per gallon than regular, what was the price of each grade of gasoline?
Answer:
The price of the regular gasoline is $2.46, while the premium is $2.67.
Step-by-step explanation:
Let the price of regular gasoline be "x", while the price for the premium be "y", The sum of the amount of each type of gas multiplied by its cost should be equal to the total paid, therefore:
[tex]8*x + 8*y = 41.04[/tex]
We also know that the premium gas costs 0.21 more than the regular one, therefore:
[tex]y = x + 0.21[/tex]
We can apply the second expression on the first, in order to solve for "x".
[tex]8*x + 8*(x + 0.21) = 41.04\\8*x + 8*x + 1.68 = 41.04\\16*x = 41.04 - 1.68\\16*x = 39.36\\x = \frac{39.36}{16} = 2.46[/tex]
[tex]y = 2.46 + 0.21 = 2.67[/tex]
The price of the regular gasoline is $2.46, while the premium is $2.67.
What is the greatest decimal place value?
Answer:
the digit farthest to the left
Answer:
The digit farthest to the left.
Step-by-step explanation:
I hope this helps
What’s 4x^2+28x+24 factored?
Answer:
[tex](4x + 4)(x + 6) \\ [/tex]
Step-by-step explanation:
[tex]4 {x}^{2} + 28x + 24 \\ 4 {x}^{2} + 24x + 4x + 24 \\ 4x(x + 6) + 4(x + 6) \\ (4x + 4)(x + 6)[/tex]
hope this helps you.
brainliest appreciated
good luck!
have a nice day!
YEAR 9 MATHS PLEASE QUICKLY HELP THIS WONT TAKE LONG
Here are six shapes made from centimetre squares.
Write down the letter of a shape with rotational symmetry of order 2.
(1 mark)
Answer:
letter of a shape with rotational symmetry of order 2 is B,D and F
Answer:
Step-by-step explanation:
i strongly believe it is rotational symmetry of order 2 is B,D and F .
hope it helps
-Delilah
HELP PLEASE WITH THE IMAGE BELOW it would mean a lot if someone helped me answer this question and maybe even explain how you got it.
Answer:
65/97 = 0.67
Step-by-step explanation:
using trigonometric ratios
Cosine of angle = [tex]\frac{adj}{hyp}[/tex]
Ian has 20 football cards, and Jason has 44 baseball cards. They agree to trade such that jason
gives Ian 2 baseball cards for every card Ian gives to Jason. After how many such trades will Ian
and Jason each have an equal number of cards?
Answer:
12 trades
Step-by-step explanation:
Let's call 'x' the number of trades they will do.
After each trade, the number of cards Ian has increase by 1 (he gives 1 but receives 2), and the number of cards Jason has decrease by 1 (he receives 1 but gives 2), so after x trades, the number of cards Ian has is 20 + x, and Jason has 44 - x.
To find the number of trades when they will have the same amount of cards, we have that:
20 + x = 44 - x
2x = 24
x = 12 trades
The number of trades will Ian and Jason each have an equal number of cards is 12 trades
The calculation is as follows;
Let's us assume the x' be the number of trades they will do.
20 + x = 44 - x
2x = 24
x = 12 trades
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solve the following equation 2x-7/4=x+3/3
Answer:
x=11/4
Step-by-step explanation:
2x-7/4=x+3/3
2x-7/4=x+1
-x -x
x-7/4=1
+7/4 +7/4
x=11/4
There are 130 people in a sport centre.
76 people use the gym.
60 people use the swimming pool.
32 people use the track.
23 people use the gym and the pool.
8 people use the pool and the track.
20 people use the gym and the track.
6 people use all three facilities.
A person is selected at random.
What is the probability that this person doesn't use any facility?
Answer:
7/130Step-by-step explanation:
Using set notation to answer the question. let:
n(U) be the total people in a sport centre =130
n(G) be number of people that use the gym. = 76
n(P) be number of people that use the swimming pool. = 60
n(T) be number of people that use the track = 32
n(G∩P) be number of people that uses the gym and the pool = 23
n(P∩T) be number of people that uses the pool and the track = 8
n(G∩T) be number of people that uses the gym and the track = 320
n(G∩P∩T) be number of people that uses all three facilities = 6
Using the relationship below;
n(U)= n(GUPUT)+n(GUPUT)'
where n(GUPUT)' is the number of people that doesn't use any facility.
Before we can get that, we need to know n(GUPUT) using the formula;
n(GUPUT) = n(G) + n(P)+n(T)-n(G∩P)-n(P∩T)-n(G∩T)+n(G∩P∩T)
n(GUPUT) = 76+60+32-23-8-20+6
n(GUPUT) = 123
n(GUPUT)' = n(U)- n(GUPUT)
n(GUPUT)' = 130 - 123
n(GUPUT)' = 7
This means that 7 person doesn't use any facility.
Probability that a person selected at random doesn't use any facility = n(GUPUT)' /n(U) = 7/130
I need help please it’sGeometry
Answer:
Congruent triangles have the same perimeter so the answer is 13.
Jon is playing a game with his friend Mike. Mike rolls two dice three times. Each time Mike rolls the dice, Jon squares both numbers and subtracts the smaller square from the larger square. After all three rolls, Jon adds the three numbers he obtained from the three rolls. If Mike rolls a 4 and a 3 on the first roll, a 6 and a 2 on the second roll, and a 3 and a 1 on the third roll, what is the sum that Jon obtains?
Answer:47
Step-by-step explanation:
On first roll Mike gets 4 and 3
So number he gets after subtraction of square is
[tex]\Rightarrow 4^2-3^2=7[/tex]
On second roll Mike gets 6 and 2
So number he gets after subtraction of square is
[tex]\Rightarrow 6^2-2^2=32[/tex]
On Third roll Mike gets 3 and 1
So number he gets after subtraction of square is
[tex]\Rightarrow 3^2-1^2=8[/tex]
Sum of numbers[tex]=7+32+8=47[/tex]
John obtains [tex]47[/tex] as sum
Two friends can paddle a canoe at a rate of 6 km/h in still water. It takes them 1 h in total to paddle 2 km up a river and another 2 km back. Find the speed of the current, rounded to the nearest tenth.
Answer: The speed of the current is 3.5 km/h.
Step-by-step explanation:
When they move in the river, the speed of the canoe is:
Sc is the speed of the canoe and Sr is the speed of the current.
Sc + Sr (when they move in the same direction as the current)
Sc - Sr (when they move in the opposite direction as the current)
So we have that in one hour, they moved 2km and then they returned other 2km.
Now, using the relation:
Velocity*time = distance
we can write 1hour = T1 + T2 such that:
(Sc + Sr)*T1 = 2km
(Sc - Sr)*T2 = 2km
T1 + T2 = 1hour -------> T2 = 1h - T1
Sc = 6km/h.
So we can write this as two equations:
(6km/h + Sr)*T1 = 2km
(6km/h - Sr)*(1h - T1) = 2km.
Now, the first step will be isolate one of the variables in one equation, we can get:
T1 = 2km/(6km/h + Sr)
and replace it in the second equation:
(6km/h - Sr)*(1h -2km/(6km/h + Sr)) = 2km.
Now we solve this for Sr, i will ignore the units, so it is easier to read the math.
(6 - Sr) - 2*(6 - Sr)/(6 + Sr) = 2
(6 - Sr)*(6 + Sr) - 2*(6 - Sr) = 2*(6 + Sr)
6^2 - Sr^2 - 12 + 2*Sr - 12 - 2*Sr = 0
-Sr^2 + 36 -12 -12 = 0
-Sr^2 + 12 = 0
Sr = √12 = 3.5km/h
(where we take the positive value of the square root)
The speed of the current is 3.5 km/h
Speed is the ratio of distance travelled to time taken. It is given by:
Speed = distance / time
Let a represent the speed of the current and t₁ represent the time spent paddling up and t₂ represent the time spent paddling back. Hence:
(6 - a)(t₁) = 2 km
t₁ = 2 / (6 - a) (1)
(6 + a)(t₂) = 2 km
t₂ = 2 / (6 + a) (2)
t₁ + t₂ = 1 hour
[2 / (6 - a)] + [2 / (6 + a)] = 1
12 + 2a + 12 - 2a = 36 - a²
a² - 12 = 0
a = 3.5 km/h
The speed of the current is 3.5 km/h
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answer this plz to be rater 5 stars
Answer:
Step-by-step explanation:
3 min 20 seconds = 3*60 + 20 = 180 +20 = 200 seconds
2 min 44 seconds = 2*60 + 44 = 120 + 44 = 164 seconds
Improvement = 200 - 164 = 36 seconds
Percentage =(36/200) *100
= 18 %
Solve the equation. y + 6 = –3y + 26
Answer:
y = 5
Step-by-step explanation:
y + 6 = –3y + 26
Add 3y to each side
y+3y + 6 = –3y+3y + 26
4y +6 = 26
Subtract 6 from each side
4y+6-6 = 26-6
4y = 20
Divide by 4
4y/4 = 20/4
y = 5
The solution of y in the equation y + 6 = - 3y + 26 is,
⇒ y = 5
We have to given that;
Expression is,
⇒ y + 6 = - 3y + 26
Now, We can simplify as;
y + 6 = - 3y + 26
Add 3y to each side
y + 3y + 6 = - 3y + 3y + 26
4y + 6 = 26
Subtract 6 from each side
4y + 6 - 6 = 26 - 6
4y = 20
Divide by 4
4y/4 = 20/4
y = 5
Thus, The solution of y in the equation y + 6 = - 3y + 26 is,
⇒ y = 5
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Jim, Dan and David share some sweets in the ratio 3:1:5. Jim gets 21 sweets. How many more sweets does David get over Dan?
Answer:
David gets 28 more than Dan
Step-by-step explanation:
Jim: Dan : David: total
3 : 1 : 5 : 3+1+5 = 9
Jim gets 21
21/3 = 7
Multiply each number by 7
Jim: Dan : David: total
3*7 : 1*7 : 5 *7 : 9*7
21 : 7 : 35 : 63
David has 35 and Dan has 7
35-7 = 28
David gets 28 more than Dan
Which of these is an equation? 8t+4=76 8t+4 8z 8+4
Answer:
8t+4=76
Step-by-step explanation:
An equation needs an equals sign otherwise it is an expression
you have a 5-inch by 7-inch picture that you framed. When you hung the picture, you found that the entire area is 69.56 in. What is the width of the frame?
Answer:
d. 2.4 in
Step-by-step explanation:
So initially w/o frame the area was 5 x 7 = 35 sq in.
Now we have to add the width of the frame to both dimensions.
(5+w)(7+w) = 69.56 sq in
35 + 7w + 5w + w² = 69.56
w² + 12w + 35 = 69.56
w² + 12w - 34.56 = 0
I use the quadratic formula to solve this (x = -b±√b²-4ac / 2a). I cheat by using a quadratic program on the calculator :,)
w = 2.4
w = -14.4
Since we can't have a negative width, the answer must be w = 2.4 inches.
You can also just plug the answer choices one-by-one into the calculator with guess-and-check because this is multiple choice.
Answer: d) 2.4 inches
Step-by-step explanation:
Let x represent the width of the frame
Then the area of the frame is:
(x + 5)(x + 7) = 69.56
Rewrite it in Standard form of a quadratic equation:
x² + 12x + 35 = 69.56
x² + 12x - 34.56 = 0
Use Quadratic Formula to solve for x:
[tex]x=\dfrac{-b+\sqrt{b^2-4ac}}{2a}\\\\\\x=\dfrac{-12+\sqrt{12^2-4(1)(-34.56)}}{2(1)}\\\\\\x=\dfrac{-12+\sqrt{282.24}}{2}\\\\\\x=\dfrac{-12+16.6}{2}\\\\\\x=\dfrac{4.8}{2}\\\\\\x=\large\boxed{2.4}[/tex]
Misha found that the equation –|2x – 10| – 1 = 2 had two possible solutions: x = 3.5 and x = –6.5. Which explains whether or not her solutions are correct? She is correct, because both solutions satisfy the equation. She is not correct, because she made a sign error. She is not correct, because there are no solutions. She is not correct, because there is only one solution: x = 3.5. help plz
Answer:
She is not correct, because there are no solutions
Step-by-step explanation:
–|2x – 10| – 1 = 2
Add 1 to each side
–|2x – 10| = 3
Divide by -1
|2x – 10| = -3
An absolute value is positive and it would have to equal -3
This cannot happen so there is no solution
Answer:
She is not correct, because there are no solutions
Step-by-step explanation: C
If the point (9, 5) is translated 6 units left and 5 units up, then find the
translated coordinates of the point.
Answer:
I think it might be (-3,10). I am not a 100% sure.
Step-by-step explanation:
Please help ASAP! Which ordered pair is a solution of this
equation?
-5x - 9y = -8
Click on the correct answer
A.
(2,-1)
B.
(-1,2)
C.
(-22)
D.
(2,-2)
========================================================
Explanation:
For each possible answer choice, you'll plug in the given coordinates to see which results in a true equation or not.
If we try choice A, then we plug in x = 2 and y = -1 to get
-5x-9y = -8
-5(2)-9(-1) = -8
-10+9 = -8
-1 = -8 which is false
So (x,y) = (2,-1) is not a solution. We can cross choice A off the list.
You'll find a similar situation happens with choices B and D. They don't work either.
-------
Choice C works because...
-5x-9y = -8
-5(-2)-9(2) = -8 .... replaced x with -2, replaced y with 2
10-18 = -8
-8 = -8
We get a true equation. So (-2,2) has been confirmed to be a solution.
Which word describes a triangle with three angles, if each angle measures less than 90°? Please help
Answer:
acute triangle
Step-by-step explanation:
If an angle measures less than 90 degrees it is an acute angle
A triangle with all acute angles is an acute triangle
A total of 70 tickets were sold for a concert and earn the organizers $804. If the cost of each ticket is either $10 or $12, how many tickets of each type were sold?
A. $18 tickets cost $10 AND 52 tickets cost $12
B. 52 tickets cost $10 and 18 tickets cost $12
C. 65 tickets cost $12 and 5 tickets cost $10
D. 5 tickets cost $12 and 65 tickets cost $10
WILL GIVE BRAINLIEST WHEN I CAN!!!!!!
Answer:
52 tickets cost $10 and 18 tickets cost $12
Step-by-step explanation:
10x+12y=804. (1)
x+y=70. (2)
From (2)
x=70-y
Substitute x=70-y into (1)
10x+12y=804
10(70-y)+12y=804
700-10y+12y=804
700+2y=804
2y=804-700
2y=104
y=104/2
y=52
Recall
x+y=70
x+52=70
x=70-52
x=18
52 tickets cost $10 and 18 tickets cost $12
By solving a system of equations we will see that the correct option is A.
How to write and solve a system of equations?
First, let's define the variables:
x = number of $10 tickets sold.y = number of $12 tickets sold.First, we know that 70 tickets were sold, so:
x + y = 70
And we know that they reached $804, then we have:
x*$10 + y*$12 = $804
Then our system is:
x + y = 70
x*$10 + y*$12 = $804
To solve this, we first need to isolate one of the variables in one of the equations, I will isolate x on the first equation:
x = 70 - y
Now we can replace that in the other equation to get:
(70 - y)*$10 + y*$12 = $804
$700 - y*$10 + y*$12 = $804
$700 + y*$2 = $804
y*$2 = $804 - $700 = $104
y = $104/$2 = 52
So, 52 $12 tickets were sold, then the other 18 tickets were $12, so the correct option is A.
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A baseball team won 9 games, which was 60% of the total number of games the team played. How many total games did the team play?
Answer: The team played 15 games total
Step-by-step explanation: 9 is 60 percent of 15.
What is x value?? :D
Answer:
x=6
Step-by-step explanation:
You can reach this answer by doing
4+(x-3) = 2x-5
If you do this equation you will get 6 as your answer.
Hope this helps :)
Isosceles and Equilateral triangles question! 60 POINTS!!
How do I figure out what "a" is equal to? Thanks!
Answer:
a = 43
Step-by-step explanation:
If PQ = PR, then P = R
The sum of the angles of a triangle is 180
P+Q+R = 180
47+2a + 47 = 180
Combine like terms
94 + 2a = 180
Subtract 94 from each side
2a = 180-94
2a = 86
Divide by 2
2a/2 = 86/2
a = 43
Answer:
43
Step-by-step explanation:
PQ = PR, so P = R
P + Q + R = 180
47+2a + 47 = 180
2a = 180 - 47 - 47
2a = 86
= 43
Hope this helps!
Which arcs are congruent? Check all that apply. Arc B C ≅ Arc M P Arc B C ≅ Arc M O Arc C F ≅ Arc K P Arc E G ≅ Arc K L Arc L O ≅ Arc M P
Answer:
Step-by-step explanation:
The arcs that are congruent are:
Arc B C ≅ Arc M P. Arc E G ≅ Arc K L. Arc L O ≅ Arc M P.What congruent angles in math?
Two geometric figures can be described as congruent if on can be superpose on the other.
Conclusively, congruent' is said to be a word that connote 'exactly equal' when looking at the shape and size of the angles. The options chosen above are congruent because they have the sides to be equal.
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Given the following functions, find each: f(x)=x2+5x−14 g(x)=x−2 (f+g)(x)= (f−g)(x)=
Answer:
(f+g)(x) = x²+5x-14 + (x-2)
= x²+5x-14+x-2 = x²+6x-16
(f-g)(x) = x²+5x-14 - (x-2)
= x²+5x-14 - x+2
= x²+5x-14-x+2 = x²+4x-12
Find the surface area.
Find the equation of the circle whose center and radius are given. center ( 5, 6), radius=3
Answer:
(x-5)^2 + (y-6)^2 = 9
Step-by-step explanation:
The equation of a circle is given by
(x-h)^2 + (y-k)^2 = r^2 where ( h,k) is the center and r is the radius
(x-5)^2 + (y-6)^2 = 3^2
(x-5)^2 + (y-6)^2 = 9
What is the value of x in the equation - 3X+9
x+9= 3-37?
What is the decimal multiplier to increase by 39%?
The decimal multiplier to increase by 39% is 1.39
A decimal multiplier is used when determining the percentage of a particular amount.
From the information given:
the decimal multiplier required to increase by 39% can be determined as follows:
[tex]\mathbf{=\dfrac{100}{100} + \dfrac{39}{100}}[/tex]
[tex]\mathbf{=1 +0.39}[/tex]
= 1.39
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