The steps that Patel could he use to solve the quadratic equation include:
8(x² + 2x) = –3
8(x² + 2x + 1) = –3 + 8
x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot
How to illustrate tye information?It is preferred to solve quadratic equations without the use of the known quadratic formula solver. This can be completing squares and solving for x.
The equation given is:
8x² + 16x + 3 = 0
8(x² + 2x) = -3
Completing squares in the brackets and balancing the equation:
8(x² + 2x + 1) = -3 + 8
Factoring the perfect square will give 8(x + 1)² = 5.
This is illustrated in the options picked for the step.
Learn more about equations on:
https://brainly.com/question/14201243
#SPJ1
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].
To know more about the volume of solid, click on the link
https://brainly.com/question/16717260
#SPJ1
3f + -4 = 0 solve for f
Answer:
f = 4/3
f = 1.3
f = 1 1/3
Step-by-step explanation:
Move all terms that don't contain f to the right side and solve.
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.
Learn more about system of equations on:
https://brainly.com/question/13729904
#SPJ1
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
An ice cream factory has 4 machines that make the same type of ice cream. The rate of production for each machine is shown in the table. Based on the date given, which machine works atthe fastest rate?
Using division operations and based on the rates of production, given, Machine D works the fastest.
How is the rate of production determined?The rate of production can be computed using the division operation, which divides the dividend by the divisor, to obtain the quotient (rate).
The rate of production is the number of goods that can be produced during a given period of time.
The rate of production or production rate also refers to the time consumed in the production of a unit of goods or services.
There are, therefore, two ways of determining production rate. Firstly, we can divide the total production by the hours consumed.
Secondly, the production rate can be computed by dividing the total production time by the number of goods produced.
Units Production Rate of
Produced Hours Production
Machine A 10,000 15 667 cups per hour
Machine B 25,000 20 1,250 cups per hour
Machine C 30,000 30 1,000 cups per hour
Machine D 15,000 10 1,500 cups per hour
Thus, using division operation, Machine D produces at the fastest rate than the other three machines.
Learn more about division operations at https://brainly.com/question/4721701
#SPJ1
Question Completion:Units Production
Produced Hours
Machine A 10,000 15
Machine B 25,000 20
Machine C 30,000 30
Machine D 15,000 10
HALPPPPPPPPPPPPPPPP NED QUESTIEON ANSERWDDDDD 1 MILLION POINTS
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
Read more about equations at
https://brainly.com/question/19543653
#SPJ1
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
Learn more about linear equations:
https://brainly.com/question/1884491
#SPJ1
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
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:
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.
Learn more about expressions on:
brainly.com/question/10004139
#SPJ1
Answer:
A is the answer
Step-by-step explanation:
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) = 1help 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
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
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
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.
To learn more about Kinetic energy here:
https://brainly.com/question/12669551
#SPJ1
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
Which triangle congruence postulate would be used to prove the following triangles congruent?
1. AAS
2. SSS
3. SAS
4. HL
Using front-end estimation, find a reasonable estimate of: 719x26=?
The estimation of 719 x 26 is 14,000
What is rounding off?Making a number simpler so that its value stays near to its original state is known as rounding. Although less exact, the outcome of rounding off a number is simpler to utilise.
Although the term "rounding" is a general one, we typically use the terms "round up" or "round down" to indicate whether the number has gone up or down after being rounded. The supplied number is said to be rounded up when the rounded number is increased, and it is said to be rounded down when the rounded number is dropped.
Given:
Estimation of 719 x 26
Now, Round off nearest hundred for 719 which is 700
i.e., Round 719 = 700
Now, Round off nearest hundred for 26 which is 20
i.e., Round 26 = 20
Hence, the estimation is 700 x 20 = 14,000.
Learn more about rounding off here:
https://brainly.com/question/13391706
#SPJ1
A Starbucks gift card has a balance of $75. Assume that the person who owns the gift card only uses it to purchase Frappuccino drinks that cost $4.65 apiece.
Write the prime factorization of 48
The prime factorization of 48 is 2⁴ × 3.
What are prime numbers?Those greater than one are known as prime numbers. They simply have two variables: the number itself and factor 1. This indicates that these numbers cannot be divided without leaving a remainder by any number other than 1 and the number itself.
Given:
The number is 48,
Factorize 48 we get 2 × 2 × 2 × 2 × 3
= 2⁴ × 3
Therefore, the prime factorization of 48 is 2⁴ × 3.
To know more about prime numbers:
https://brainly.com/question/18845305
#SPJ1
Here'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.
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
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
Evaluate if xy + 2x if x = 7 and y = 5
Answer:
49
Step-by-step explanation:
35+14=49
mark me on brainliest please follow me to
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.
To learn more about inches visit: https://brainly.com/question/16311877
#SPJ1
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.
Learn more about inequality here;
https://brainly.com/question/28823603
#SPJ1
What is 8370dividedby62
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:
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
You're Welcome :)
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
Read more about the derivative here:
https://brainly.com/question/29257155
#SPJ1