Answer:
1/2a (4a+7)
Step-by-step explanation:
First You Divide:7/2a+ 2a^2
Rearrange Terms: 2a^2+ 7/2a
Find the Common Factor: 1/2(4a^2+7a)
Rewrite in the Fraction Form: 1/2a (4a+7)
I know this is the right answer because I learned this in 5th grade.
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What is the probability of rolling a number less than or equal to 3 on a standard six-sided die
Answer:
P(les than/equal to 3): ½
Salina and Nessa combined like terms using the same expression. Salina’s answer differs from Nessa’s. The table shows both of their solutions.
Salina
Nessa
6 x squared y minus 3 + x squared y + 2 x y squared + 2 x y minus 6 = 7 x squared y minus 9 + x squared y + 2 x y squared + 2 x y
6 x squared y minus 3 + x squared y + 2 x y squared + 2 x y minus 6 = 7 x squared y minus 9 + 2 x y squared + 2 x y
Which statement is correct regarding their solutions?
Salina combined the x squared y terms correctly but then left the Plus x squared y term in her answer.
Salina did not add the constant terms correctly.
Nessa combined the constants correctly but then left the Plus 2 x y squared term in her answer
Nessa did not combine the x squared y terms correctly.
The statement that is correct regarding their solutions is A. Salina combined the x squared y terms correctly but then left the Plus x squared y term in her answer.
How to illustrate the expression?From the information, Salina and Nessa combined like terms using the same expression.
The expression given is illustrated as.
6x²y - 3 + x²y + 2xy² + 2xy - 6
It should be noted that the like terms are:
6x²y and x²y as well as -3 and -6.
Combine the like terms
6x²y + x²y = 7x²y
Also, -3 + (-6) = -9
Therefore, the value will be 7x²y + 2xy² + 2xy - 9
The correct option is A as it illustrated the mistake Salina made.
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Answer:
A is the answer
Step-by-step explanation:
Use polar coordinates to find the volume of the given solid: Inside the sphere x^2 + y^2 + z^2 = 16 and outside the cylinder x^2 + y^2 = 4.
Using polar coordinates, volume of the given solid is, 32√3π.
What is volume of solid?
An object's space requirement is expressed in terms of its volume. The amount of unit cubes required to completely fill the solid is how much it weighs. We have a total of 30 unit cubes in the solid, so the volume is as follows: 2 units 3 units 1 unit Equals 30 cubic units
We have to find the volume of the solid Inside the sphere x^2 + y^2 + z^2 = 16 and outside the cylinder x^2 + y^2 = 4 using polar coordinates.
So, the volume is
[tex]2\int\limits\int\limits_D {\sqrt{16-x^2-y^2} } \, dA[/tex]
[tex]2\int\limits^2^\pi _0 {\int\limits^4_2 {\sqrt{16-r^2} } rdrdtheta[/tex]
[tex]2\int\limits^2^\pi _0 {(-\frac{1}{3})(16-r^2)_2^4 } \, dtheta[/tex]
[tex]2\int\limits^2^\pi _0 {(-\frac{1}{3})(-2\sqrt{3}) } \, dtheta[/tex]
[tex]\int\limits^2^\pi _0 {16\sqrt{3} } \, dtheta[/tex]
[tex]32\sqrt{3}\pi[/tex]
Hence, the volume of the given solid using polar coordinates is, [tex]32\sqrt{3}\pi[/tex].
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help fast plsss bout to turn it in
Answer:
Box A: -2x
Box B: 2/9
Step-by-step explanation:
Multiply 1/3 by each of the expressions above the rectangle.
Box A: 1/3 × (-6x) = -2x
Box B: 1/3 × 2/3 = 2/9
Sara volunteered to get hot dogs for her softball team. Of the 16 players on the team, 12 wanted ketchup, 7 wanted mustard, and 4 wanted both. How many players wanted: H. only ketchup? O. only mustard? W. neither ketchup nor mustard?
Answer:
H) 8, O) 3, W) 1------------------------------
GivenTotal players = 16,Wanted ketchup = 12,Wanted mustard = 7,Wanted ketchup and mustard = 4.Find the numbers of players who ...Wanted only ketchup = 12 - 4 = 8,Wanted only mustard = 7 - 4 = 3,Wanted neither ketchup nor mustard = 16 - (8 + 4 + 3) = 1Here's a brain teaser.
(I already know the answer)
1=5
2=10
3=15
4=20
5=?
Answer:
5 = 1
or
5 = 25
Step-by-step explanation:
I've seen two answers to this.
1. Since we are told 1 = 5, then 5 = 1.
One answer is 1 = 5
2. Since each number on the right is 5 times the number on the left, then 25 corresponds to 5, and 5 = 25.
Answer: 5=1 (The correct answer) 5=25 (The answer that makes sense but is not correct).
Step-by-step explanation:
Explanation for answer 1: It say's that 1 = 5.
Explanation for answer 2: If we follow the pattern of adding 5 each time we go up a number then 5 would equal 25.
This is the kinetic energy of a 64 kg object travelling at 12 m/s.
11.2kj
4.6kj
960j
Kinetic energy of a 64 kg object travelling at 12 m/s is 4.6kj.
Kinetic energy = KE = [tex]\frac{1}{2}mv^{2}[/tex]
Mass = m = 64 kg
Velocity = v = 12 m/s
KE = [tex]\frac{1}{2}*64*(12)^{2}[/tex]
= 4608 J
1000 j = 1 kj
1 j = 1/1000 kj
4608 j = 4608/1000 kj
= 4.608 kj
Hence, kinetic energy is 4.6 kj.
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Replace the _ with the symbol that makes a true sentence 2/15_0.83
Answer:
See below
Step-by-step explanation:
2 /1 5 = .1333
so 2/15 < .83
Use your calculator to find the angle, to the nearest hundredth of a degree, whose tangent value is
O 0.35
O 18.43
O 0.32
O 71.57
Answer:18.43
Step-by-step explanation:
HELP PLEASE!! Dominique is selling merchandise for a school fundraiser. She is selling calendars for $8 each and coffee mugs for $12 each. She must sell at least $800 of merchandise, including at least 60 calendars, to meet her goals.
If x represents the number of calendars and y represents the number of mugs, which system of inequalities represents this scenario?
8x + 12y ≥ 800 and x ≥ 60
8x + 12y ≥ 800 and y ≥ 60
8x + 12y > 800 and y > 60
8x + 12y > 800 and x > 60
The inequality that represents the given situation is option A 8x + 12y ≥ 800 and x ≥ 60.
Given,
The cost for one calendar = $8
The cost for one coffee mug = $12
Dominique must sell at least $800 of merchandise and it should include at least 60 coffee mugs.
Here,
x be the number of calendars and y be the number of coffee mugs;
We have to find an inequality which represents the given situation;
So,
The inequality be;
8x + 12y ≥ 800 and x ≥ 60
That is,
The inequality that represents the given situation is option A 8x + 12y ≥ 800 and x ≥ 60.
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The velocity function of a car is given by v(t) = -3t2 + 18t + 9 m/s. Find the acceleration of the car three seconds before it comes to a stop.
A.
a = -6.46 m/s²
B.
a = -2.76 m/s²
C.
a = -0.46 m/s²
D.
a = 2.76 m/s²
Answer: In photo below
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The acceleration of the car three seconds before it comes to a stop is -2.76 m/s² (Letter B).
Derivative
Derivative indicates the rate of change of a function with respect to a variable. Thus, when you derivate the position function, you find the velocity function. And, when you derivate the velocity function, you find the acceleration function.
In other words, the velocity function represents the first derivative of the position, meanwhile, the acceleration function represents the second derivative of the position.
For derivating an equation, you should apply the rule: [tex](\frac{d}{dx} ) (x^n ) = nx^{n-1}[/tex]. Example: x²= 2x
The car stops when the velocity is equal to zero. Thus, v(t) = -3t² + 18t + 9 =0. Therefore, you should solve this quadratic function:
Δ=b²-4ac=[tex]18^2-4\left(-3\right)\cdot \:9=324+12*9=324+108=432[/tex]
[tex]t_{1,\:2}=\frac{-18\pm \sqrt{432}}{2\left(-3\right)}\\ \\ t_{1,\:2}=\frac{-18\pm \sqrt{432}}{-6}[/tex]
[tex]t_1=\frac{-18+12\sqrt{3}}{-6}=3-2\sqrt{3}[/tex]
[tex]t_2=\frac{-18-12\sqrt{3}}{-6}=3+2\sqrt{3}[/tex]
Like t is a positive number, you should use [tex]t_2[/tex]. Thus, the value of t that you should apply to find the acceleration of the car three seconds before it comes to a stop is [tex]2\sqrt{3}[/tex].
The acceleration can be found from the derivative of the velocity function. See below.
a(t)= -6t+18 , for t=[tex]2\sqrt{3}[/tex]
a(t)= -6*[tex]2\sqrt{3}[/tex]t+18
a(t)= [tex]-12\sqrt{3}[/tex]t+18
a(t)=-2.76
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Which triangle congruence postulate would be used to prove the following triangles congruent?
1. AAS
2. SSS
3. SAS
4. HL
There are 8 kites in the sky, and 5 of those kites are striped. What fraction of
the kites are striped?
A. 6/8
B.5/8
C.5/13
D.4/8
Solve the equation for all values of x.
2x(x + 7)(x²+49) = 0
Answer:
Step-by-step explanation:
2x(x + 7)(x²+49) = 0
(apply the zero product)
x=0 or x+7 =0 or x² + 49 = 0
x+7 =0
x=-7
x² + 49 = 0
no real solution for this i think
Answer = x=0 or x=-7
Dave's science class is competing to see who can build the tallest tower. Each group of students gets 10 newspapers and 2 yards of tape. Dave's group decides to roll up each of their newspapers. Then, they tape each roll with 4 inches of tape. How many inches of tape do they have left?
32 inches more of tape students need.
Given that,
Students in Dave's science class are trying to build the tallest structure. Ten newspapers and two yards of tape are given to each group of kids. The decision is made by Dave's group to roll up each newspaper. Then, they use 4 inches of tape to seal each roll.
We have to find how many more inches of tape are there.
We know that,
1 yard is 36 inches.
So,
2 yards is 2 times 36 is 72 inches.
The inches of the tape they need is 10 times 4 is 40.
So,
72-40 is 32 inches
Therefore, 32 inches more of tape students need.
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Work out the perimeter of this quarter circle.
Take to be 3.142 and write down all the digits given by your calculator.
4 cm
Step-by-step explanation:
Where's the calculator
How many solutions does the equation a+b+c+d=15 have?
The equation a+b+c+d=15 has infinite many solutions
How to determine the number of solutions?From the question, the equation is given as
a+b+c+d = 15
From the above representation of the equation, we can see that:
The equation is a linear equationAlso, the equation has 4 variablesWhen a linear equation that has more than one variable is given, the number of solutions cannot be quantified i.e. infinite number of solutions
Hence, the equation has infinite number of solutions
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Evaluate if xy + 2x if x = 7 and y = 5
Answer:
49
Step-by-step explanation:
35+14=49
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What is 8370dividedby62
one number is 10 more than another. their product is -25
Answer: resource - trust me bro
Step-by-step explanation: Let x = the smaller numberLet 2x + 10 = the larger numberx(2x + 10) = 1002x^2 + 10x - 100 = 0Divide both sides of the equation by 2.x^2 + 5x - 50 = 0(x - 5)(x + 10) = 0x - 5 = 0 or x + 10 = 0x = 5 or x = -10, not a positive number2x + 10 = 2(5) + 10 = 20
Solve the system of equations by the substitution method.
x+y=8
y=-3x
Using the substitution method, the solution to the system of equations is: x = -4 and y = 12.
How to Solve a System of Equations by Substitution?To solve a system of equations using the substitution method, find the value of one of the variables in one equation, then substitute it in the second equation and solve to find the value of the second variable.
Given the equations:
x + y = 8 --> eqn. 1
y = -3x --> eqn. 2
Substitute -3x for y into equation 1:
x + (-3x) = 8
x - 3x = 8
-2x = 8
-2x/-2 = 8/-2
x = -4
Substitute x = -4 into equation 2:
y = -3(-4)
y = 12
The solution is, x = -4 and y = 12.
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Question 4
Simplify the expression: (7x + 2)²
A 49x² + 4
B 49x² + 28x + 4
C 49x² - 4
D 25x² + 9
Answer:
B
Step-by-step explanation:
(7x+2)(7x+2)
7x×7x=49
7x×2+2×7x=28x
2x2=4
HALPPPPPPPPPPPPPPPP NED QUESTIEON ANSERWDDDDD 1 MILLION POINTS
4. Which expression represents 7 more than the quotient of 12 and 4?
A. (12+4) + 7
B.7 x (12+4)
C.7+(12-4)
D. (7+12) + 4
Answer:
C
Step-by-step explanation:
Even though quotient means divide I instead used the minus symbol since they both mean something negative or taking away. Then, the 7 goes before everything adding onto what was left from the second part.
Critical thinking questions:
Write a system of equations with the solution (4, -3).
Answer: (4,-3)
Step-by-step explanation:
4x+5y=1 (1)
3x-2y=18 (2)
Multiply both parts of equation (1) by 2 and both parts of equation (2) by 5:
8x+10y=2
15x-10y=90
Sum these equations:
23x=92
Divide both parts of the equation by 23:
x=4
Substitute the value of x=4 into equation (1):
4(4)+5y=1
16+5y=1
16+5y-16=1-16
5y=-15
Divide both parts of the equation by 5:
y=-3
Thus, (4,-3)
This season, the probability that the Yankees will win a game is 0.45 and the probability that the Yankees will score 5 or more runs in a game is 0.6. The probability that the Yankees win and score 5 or more runs is 0.34. What is the probability that the Yankees will win when they score fewer than 5 runs? Round your answer to the nearest thousandth.
The probability that the Yankees will win when they score fewer than 5 runs is; 0.567
How to solve conditional probability?We are given;
Event A which is when Yankees win has a probability of; P(A) = -.45
Thus, Event that the Yankees don't win which is when they lose is;
P(A') = 1 - 0.45 = 0.55
Event B which is the event that the Yankees score 5 or more runs has a probability of; P(B) = 0.6
Event that the Yankees score 4 or less run is given by the probability;
P(B') = 1 - 0.6 = 0.4
The probability that the Yankees win and score 5 or more runs is;
P(A' ∩ B') = 0.34
Thus, the probability that the Yankees will win when they score fewer than 5 runs wanted is given by the chain rule in conditional probability of the formula;
P(A' | B') = P(A' ∩ B')/P(B') = 0.34/0.6
P(A' | B') = 0.567
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The graph of a linear function passes through the points ; negative one; negative 1 over 4. and ; one, negative 3 over 4.. Y; X. Which equation represents the function? A Y equals negative one over 2 X. minus one over four. B Y equals 1 over 2 X. plus 1 over 4. C Y equals negative 1 over 4 X. minus 1 over 2. D Y equals 1 over 4 X. plus 1 over 2.
The linear equation that passes through the two given points is:
y = (-1/4)*x - 2/4
Which is the equation of the line?A general linear equation is written as:
y = m*x + b
Where m is the slope and b is the y-intercept.
If the line passes through two points (x₁, y₁) and (x₂, y₂), then the slope of the line is:
m = (y₂ - y₁)/(x₂ - x₁)
Here we know that the line passes through (-1, -1/4) and (1, -3/4)
Then the slope is:
m = (-3/4 + 1/4)/(1 + 1)
m = (-2/4)/2 = -2/8 = -1/4
the line is:
y = (-1/4)*x + b
To find the value of v we can replace the point (1, -3/4) so we get:
-3/4 = (-1/4)*1 + b
-3/4 + 1/4 = b
-2/4 = b
The linear equation is:
y = (-1/4)*x - 2/4
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The slide at the playground has a height of 9 feet. The base of the slide measured onthe ground is 12 feet. What is the length of the slide?
O 15 feet
O 45 feet
21 feet
36 feet
Step-by-step explanation:
this creates a right-angled triangle, with the length of the slide being the Hypotenuse (the side opposite of the 90° angle), and height and base are the legs.
so, we can use Pythagoras
c² = a² + b²
with c being the Hypotenuse, a and b being the legs.
length² = 9² + 12² = 81 + 144 = 225
length = sqrt(225) = 15 ft
How many hour is 4:30 until 6:00
Answer: 1 hour and 30 minutes or 1.5 hours
Answer:
1 hour and 30 minutes
Step-by-step explanation:
Evaluate 4x ÷ y if y = 2 and x = 4
Answer:
18
Step-by-step explanation:
x = 4
4x
= 4 * 4
= 16
y = 2
4x + y
= 16 + 2
= 18