The substitution which should be made to rewrite given equation 4x⁴ + 21x² + 20 = 0 as a quadratic equation is U = x² .
The Quadratic Equations are the type of polynomial equations which has the highest degree of 2 ,
The quadratic equations are algebraic equation of the second degree in the variable x .
given equation is ⇒ 4x⁴ + 21x² + 20 = 0 ;
we have to make this equation as a quadratic equation ,
So , we substitute , U as x² in given equation ,
we get ;
⇒ 4(x²)² + 21x² + 20 = 0 ;
⇒ 4(U)² + 21U + 20 = 0 ;
the equation becomes as ⇒ 4U² + 21U + 20 = 0 , which is a quadratic .
Therefore , the substitution of U = x² , should be used .
The given question is incomplete , the complete question is
What substitution should be used to rewrite 4x⁴ + 21x² + 20 = 0 as a quadratic equation ?
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The theater sells two types of tickets: adult tickets for $11 and child tickets for $3.
Last night, the theater sold a total of 464 tickets for a total of $3520. How many adult tickets did the theater sell last night?
The adult tickets sold were 409.
What number of total adult ticket were sold?11a + 3c = 3520
Where "a" is the number of adult tickets sold and "c" is the number of child tickets sold.
We also know that the theater sold a total of 464 tickets, so we can add the following equation:
a + c = 464
We can now use the first equation to solve for one of the variables, and then substitute it into the second equation:
11a + 3c = 3520
3c = 3520 - 11a
c = (3520 - 11a)/3
We know that:
a + c = 464
We can substitute the value of c into this equation:
a + (3520 - 11a)/3 = 464
a + (3520 - 11a) = 464*3
a + 3520 - 11a = 1392
12a = 4912
a = 4912/12
a = 409
So, the theater sold 409 adult tickets last night
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There are eight different sizes of puzzles. Each person takes a turn selecting and keeps it. What is the probability that the first puzzle chosen is a 100-peice and the second is a 1000-piece puzzle
Answer:
Step-by-step explanation:
the answer to the first puzzle being choose will be 100 pieces is 8 out of 100
For the following set of data, find the percentage of data within 2 population standard deviations of the mean, to the nearest 10th of a percent. 90, 40, 63, 62, 65, 67, 63, 68 90, 40, 63, 62, 65, 67, 63, 68
The percentage of data within 2 standard deviations of the mean is given as follows:
100%.
What are the mean and the standard deviation of a data-set?The mean of a data-set is given by the sum of all values in the data-set, divided by the number of values.The standard deviation of a data-set is given by the square root of the sum of the differences squared between each observation and the mean, divided by the number of values.Using a calculator, the measures for this problem are given as follows:
Mean: 64.75.Standard deviation: 12.65.The bounds within two standard deviations of the mean are given as follows:
64.75 - 2 x 12.65 = 39.45.64.75 + 2 x 12.65 = 90.05.All the measures in this problem are within these bounds, hence the percentage is of 100%.
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How does the sum rule work?.
The formula for the sum rule is: P(A or B) = P(A) + P(B) - P(A and B)
The sum rule, also known as the addition rule of probability, states that the probability of any two events occurring together is the sum of the probability of each event occurring individually, minus the probability of them both occurring at the same time. The formula for the sum rule is:
P(A or B) = P(A) + P(B) - P(A and B)
where A and B are two events and P(A) and P(B) are the probabilities of each event occurring individually, and P(A and B) is the probability of both events occurring at the same time.
The sum rule is used when the two events are mutually exclusive, meaning that they cannot happen at the same time. In this case, P(A and B) = 0, so the formula becomes:
P(A or B) = P(A) + P(B)
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what is the following product? Assume x>0 3root x^2 times 4 root x ^3
the product of the given expressions will be x([tex]x^{5/12}[/tex])
What is a fraction?
If the numerator is bigger, it is referred to as an improper fraction and can also be expressed as a mixed number, which is a whole-number quotient with a proper-fraction remainder.
Any fraction can be expressed in decimal form by dividing it by its denominator. One or more digits may continue to repeat indefinitely or the result may come to a stop at some point.
[tex]x^{2/3}[/tex] * [tex]x^{3/4}[/tex]
= [tex]x^{2/3+3/4}[/tex]
=[tex]x^{17/12}[/tex]
=x([tex]x^{5/12}[/tex])
Hence the product of the given expressions will be x([tex]x^{5/12}[/tex])
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A flu epidemic has hit a local day care facility.
The population of sick children is represented
in the equation below where P is the number
of sick children, and t is the number of days
since the first child was diagnosed. How
many days will it take for 50 children to catch
the flu?
P =
110
1+7e-0.22t
It will take 8 days for 50 children to catch the flu
How to determine the number of days?
The given equation states as follows:
P = 110/(1+7e⁻⁰²²ⁿ (Where n stands for t)
P = 110/(1+7e⁻⁰²²ⁿ = 2.2
7.e⁻⁰²²ⁿ = 2.2 - 1
7.e⁻⁰²²ⁿ = 1.2/7
0.22n = In (12/7)
n= 8.02
Recall that n=t
Therefore t = .02
Therefore time = 8 days
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Solve for x...............
[tex]\bf 4x+6=14[/tex]
Is 0 infinite or no solution?.
No, 0 is neither an infinite solution nor no solution.
The solution x = 0 implies that the value 0 satisfies the equation, so there is a solution. “No solution” implies that there is no value, not even 0, which would satisfy the given equation.
Let us take an example for a more reasonable interpretation,
An example is the equations
² + 1 = 0 and
− 3 = 2 − 3
Suppose that is real.
The first equation has no solution, while the second equation has a solution = 0.
Hence, 0 can be a solution to a system of equations.
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What is the axis of symmetry and vertex for the function /( x 3 x 2 2 4?.
The axis of symmetry is the y-axis and the vertex for the function
f(x) = 3(x - 2)²+ 4 is (2,4).
Given f(x) = 3(x - 2)² + 4
The graph will be symmetrical to the y-axis and since a> 0, the parabola opens up.
The axis of symmetry is the line that divides a parabola into two symmetrical parts. The vertex is the point where the axis of symmetry intersects the parabola.
The axis of the symmetry is x=2
The vertex form of a parabola is y = a (x - h)²+ k
The vertex is given by (h,k) coordinates.
In order to find the vertex, we need to compare the given equation to the vertex form of the parabola.
f(x) = 3(x - 2)²+ 4=0
a = 3, h = 2 and k = 4
Thus the vertex of the function is (2,4).
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For each sequence below: (a) use a difference table to find a formula, then check your formula for a few values of n (b) use your formula to calculate the next three terms in the sequence. 3 14, 32, 60, 98, ...
helpp please
The subsequent three words in the list. 3 14, 32, 60, 98, ... is 276 . In this case, the order is 3, 14, 32, 60, 98, and 276.
How do you find the nth term formula?(a)An arithmetic sequence's nth term is determined by a = a + (n - 1)d in step 1. As a result, enter the given values for a and d into the formula to determine the nth term. Step 2: Now, change the nth term in the equation to n = 5 to determine the fifth term. Consecutive integers in an arithematic sequence often differ from one another. Simply subtract the first term from the second term to discover it, or the second term from the third, and so forth. Our shared difference is thus eight.(b)the subsequent three words in the list. 3 14, 32, 60, 98, ... is 276 . In this case, the order is 3, 14, 32, 60, 98, and 276.To learn more about Sequence refer to :
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The next three terms in the sequence are 79, 90, and 101.
What is sequence?An ordered group of numbers or items is referred to as a sequence.Since each element in a series has a particular place in the sequence, the order of the elements is crucial.Sequences can either have a finite or infinite number of words, meaning they can either end or continue eternally.A formula that can be used to determine any term in a series given its location can be used to characterize sequences.a) To find a formula for the sequence, we can use a difference table.
First, let's write out the first few terms of the sequence:
3, 14, 32, 60, 98, ...
Next, we'll create a difference table:
n | Term | Difference
1 | 3 |
2 | 14 | 11
3 | 32 | 18
4 | 60 | 28
5 | 98 | 38
We see that the difference is increasing by 10 each time, so our formula can be written as:
Term = 11n + 3
To check the formula, we can plug in a few values of n and see if it matches the terms in the sequence:
n = 1, Term = 11(1) + 3 = 14
n = 2, Term = 11(2) + 3 = 32
n = 3, Term = 11(3) + 3 = 60
The formula matches the terms in the sequence, so it is correct.
b) To find the next three terms in the sequence, we can use our formula:
n = 6, Term = 11(6) + 3 = 79
n = 7, Term = 11(7) + 3 = 90
n = 8, Term = 11(8) + 3 = 101
So the next three terms in the sequence are 79, 90, and 101.
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A scale on a blueprint drawing of a house shows that 10 centimeters represents 2 meters. what number of actual meters are represented by 18 centimeters on the blueprint?
The required number of actual meters represented by 18 centimeters on the blueprint is 3.6 meters.
What is the scale factor?The scale factor is defined as the ratio of the modified change in length to the original length.
Here,
A scale on a blueprint drawing of a house shows that 10 centimeters represent 2 meters.
Scale factor,
10 centimeter: 2 meters = 1 centimeters : 0.2 meters
So,
18 centimeters = 18 × 0.2 meters = 3.6 meters.
Thus, the required number of actual meters represented by 18 centimeters on the blueprint is 3.6 meters.
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Can someone tell me what number on the number line is greater than -9 for an inequality?
Draw a circle over the number to begin plotting an inequality, such as x>9, on a number line (e.g., 9). If the sign also says equal to (or), then complete the circle.
What is inequality in math example?An inequality compares two values and indicates whether one is lower, higher, or just not equal to the other. It is implied by the expression a b that a and b are not equal. If a b, then a must be smaller than b. When a > b, an is greater than b.A relationship between two expressions or values that is not equal to each other is known as inequality in mathematics. So inequality emerges from an imbalance.When resolving an inequality, you can either add or subtract the same amount from each side, or multiply or divide each side by the same positive amount. The inequality sign appears if each side is multiplied or divided by a negative number.To learn more about inequality refer to:
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i need answer by today
The total cost of the fence will be £841. The solution is obtained using the concept of perimeter of triangle.
What is perimeter of triangle?
Any two-dimensional figure's perimeter is determined by the space surrounding it. By summing the lengths of the sides, we can determine the perimeter of any closed shape.
We are given a right-angled triangle with one angle 59° and the adjacent side as 145 meters.
We know that tan θ = Opposite side/Adjacent side
⇒ tan 59° = Opposite side/145
⇒ 1.66 = Opposite side/145
⇒ 241 meters(approx) = Opposite side
Now, using pythagoras theorem,
⇒Hypotenuse^2 = Base^2 + Perpendicular^2
⇒Hypotenuse^2 = 241^2 + 145^2
⇒Hypotenuse^2 = 58,081 + 21,025
⇒Hypotenuse^2 = 79,106
⇒Hypotenuse = 281 meters(approx)
Perimeter of triangle = Sum of three sides
⇒ Perimeter = 145 + 241 + 281
⇒ Perimeter = 667 meters
The fence costs £ 1.26 per meter
Total cost of fence = 1.26 * 667 = £840.42 = £841
Hence, the total cost of the fence will be £841.
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What is the distance between − 2 − 3 and − 4 − 5 )?.
The distance between points (2, 3) and (-4, 5) is 6.3 units.
As we know according to the distance formula the distance between points (x₁, y₁) and (x₂, y₂) is given by,
[tex]d = \sqrt{[(x_2 - x_1)^2 + (y_2 - y_1)^2]}[/tex]
Here we have been given points (2,3) and (-4,5)
Let us assume that (x₁, y₁) = (2, 3)
and (x₂, y₂) = (-4, 5)
Let d represents the distance between points (2,3) and (−4,5)
Using above distance formula the distance d between given points would be,
[tex]\Rightarrow d = \sqrt{[(x_2 - x_1)^2 + (y_2 - y_1)^2]}\\\\\Rightarrow d = \sqrt{[(-4 - 2)^2 + (5 - 3)^2]}\\\\\Rightarrow d = \sqrt{[(-6)^2 + (2)^2]}\\\\\Rightarrow d = \sqrt{36+4}\\\\\Rightarrow d = \sqrt{40}\\\\\Rightarrow d = 6.3~units[/tex]
Therefore, the distance is 6.3 units.
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The complete question is:
What is the distance between points (2,3) and (−4,5) ?
What is the multiplicative inverse of − 3 − 8?.
The multiplicative inverse of 'a' is indicated by a-1 or 1/a. In other words, the multiplicative inverse of a number is explained as 1 divided by the number.
The multiplication inverse of 3 is 1/3.
The multiplication inverse of 8 is. 1/8.
The multiplicative inverse is defined as the reciprocal of a given number. It is used to clarify mathematical expressions.
The word 'inverse' infers something opposite/contrary in effect, position, order, or direction. A number when multiplied by its multiplicative inverse results in 1.
The multiplicative inverse formula is called that the product of a number and its reciprocal is 1.
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question= 3 x + 2 / x + 7
solved, 3x+2/x+7 = 3x²+21x+2/x+7
solution:
3x+2/x+7
To add or subtract expressions, expand them to make their denominators the same. Multiply 3x times x+7/x+7
we get,
3x(x+7)/x+7 + 2/x+7
since 3x(x+7)/x+7 and 2/x+7 have the same denominator, add them by adding their numerators.
we get,
3x (x+7) +2/x+7
Do the multiplications in 3x(x+7)+2.
we get, 3x²+21x+2/x+7
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What’s 14x+14x
x= 1/2
Answer in simplest form please and thank you!
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{14x + 14x}\\\\\mathsf{= 14(\dfrac{1}{2}) + 14(\dfrac{1}{2})}\\\\\mathsf{= \dfrac{14}{1}\times \dfrac{1}{2} + \dfrac{14}{1} \times \dfrac{1}{2}}\\\\\mathsf{= \dfrac{14\times1}{1\times2} + \dfrac{14\times1}{1\times2}}\\\\\mathsf{= \dfrac{14}{2} + \dfrac{14}{2}}\\\\\mathsf{= 7 + 7}\\\\\mathsf{= 14}\\\\\\\huge\text{Therefore, your answer should be:}\\\huge\boxed{\mathsf{14}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
Answer:
14x + 14x = 14
Step-by-step explanation:
Given expression,
→ 14x + 14x
Now we have to use,
→ x = 1/2
Let's simplify the expression,
→ 14x + 14x
→ 14(1/2) + 14(1/2)
→ (14/2) + (14/2)
→ 7 + 7
→ 14 => {final value}
Hence, required answer is 14.
Jan 19, 4:48:05 PM
What is the surface area of the cylinder with height 3 m and radius 6 m?
Round your answer to the nearest thousandth.
The surface area of a cylinder is given by the formula 2πr (r + h) where r is the radius and h is the height.
Plugging in the given values, we get: 2π(6) (6 + 3) = 2π(6)(9) = 108π.
Rounded to the nearest thousandth, this is approximately 342.8.
What is surface area?The surface area of an object is the total area that the object's surface occupies. It is a measure of the total area of all the exposed surfaces of an object. It is typically measured in square units, such as square meters or square inches. The surface area of an object can be calculated using various formulas, depending on the shape of the object. For example, the surface area of a cube is the area of all six faces of the cube, while the surface area of a sphere is the area of the spherical surface. The surface area is an important property of an object in fields such as engineering, physics, chemistry, and architecture.
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Which pair of related inequalities can be graphed to find the solution set to 4*-7 <1?
O y<4*-7 and y < 1
Oy> 4*-7 and y < 1
O y<4*-7 and y> 1
O y> 4*-7 and y> 1
Answer:
The second one :( y> 4x - 7) and y<1
What is the value of k such that the following pair of equations have infinitely many solutions?.
For the value of k is equal to 6, the system of equations,
kx + 3y - (k – 3) = 0 and 12x + ky - k = 0 have infinitely many solutions
Here we have equations
kx + 3y - (k – 3) = 0
12x + ky - k = 0
For a system of 2 linear equations,
a₁x + a₂y + a₃ = 0
b₁x + b₂y + b₃ = 0
They will have infinitely many solutions if
a₁/b₁ = a₂/b₂ = a₃/b₃
here,
k = a₁, 3 = a₂ - (k – 3) = a₃
12 = b₁ k = b₂ - k = b₃
Hence
k/12 = 3/k = (3 - k)/(-k)
Taking up
3/k = (3 - k)/(-k)
we get
3 = k - 3
or, k = 6
hence for k = 6, the equations will have infinite solutions.
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Complete Question
What is the value of k such that the following pair of equations has infinitely many solutions?
kx + 3y - (k – 3) = 0
12x + ky - k = 0
5. City B has constructed their own subway system. The Green Line and the Orange Line run parallel to each other and the purple line runs perpendicularly to the Green Line and the Orange Line. The Silver Line intersects with the purple line and the green line at the same station. Angles 1 and 6 have the same measure. What is the measure of angle 9?
Answer:
135°
Step-by-step explanation:
Angles 1 and 6 have the same measure and sum to a 90 degree angle
so they are each 45°
Angles 1 and 4 are equal as well 45°
then angle 5 = 90 + 45 = 135 °
Angles 5 2 9 and 7 are all equal angle 9 = 135 °
Andrew and Michael went for a hike in the Great Smoky
Mountains. They drank 500 fluid ounces of water during
their hike. What possible combinations of water could
Andrew and Michael have each drank while they were
hiking?
Here are some suggestions to assist you make sure you are consuming enough liquids to keep your hydration levels at good levels.
How much water should you drink while walking?By multiplying the hourly sweat rate by 4, you may calculate how much to drink every 15 minutes. This becomes the recommended amount of fluid consumption every 15 minutes of walking or running.Every hour of hiking for adults typically requires 2 cups of water. For every hour of hiking, kids typically need 1-2 cups. However, depending on whether you can filter water along the journey, the weather, and your own level of thirst, you might require more or less than this.An excellent general advice is one half-liter of water for every hour of moderate activity in temperatures between 50 and 60 degrees. If the temperature and level of exercise increase, you might need to drink more.To learn more about hydration refer to:
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There are an infinite number of combinations of water that Andrew and Michael could have each drank as long as the sum is 500.
How to solve the equation?Since Andrew and Michael drank a total of 500 fluid ounces of water, any combination of water that they drank must add up to 500 fluid ounces.
Let's call the amount of water Andrew drank as "a" and the amount of water Michael drank as "m". Then, we can write the equation: a + m = 500.
There are an infinite number of combinations of water that Andrew and Michael could have each drank as long as the sum is 500. Here are a few examples:
Andrew drank 250 fluid ounces and Michael drank 250 fluid ounces.
Andrew drank 200 fluid ounces and Michael drank 300 fluid ounces.
Andrew drank 100 fluid ounces and Michael drank 400 fluid ounces.
and so on.
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What is the product of 64?.
The product of 64 are 1, 2, 4, 8, 16, 32, 64 and its factors in pairs are (1, 64), (2, 32), (4, 16), and (8, 8).
A factor is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product because the product is divisible by them.
The set of integers that can be divided evenly by 64 is called the factorization of 64. Overall, there are 7 components that make up 64: 1, 2, 4, 8, 16, 32, and 64, with 64 being the largest. The prime factors for the number 64 are 1, 2, 4, 8, 16, 32, and 64. Its factors in pairs are 1, 64, 2, 32, 4, and 16. (8, 8).
Factors of 64: 1, 2, 4, 8, 16, 32 and 64Negative Factors of 64: -1, -2, -4, -8, -16, -32 and -64Prime Factors of 64: 2Prime Factorization of 64: 2 × 2 × 2 × 2 × 2 × 2 = 26Sum of Factors of 64: 127Learn more about Factors:
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A fair die is rolled 5 times. What is the probability of having no 1 and no 2 among the rolls
Answer:
40%
Step-by-step explanation:
There are 5 options to roll: 1, 2, 3, 4, and 5.
This means you have a 1 out of 5 chance of rolling each number.
This question is asking for 1 AND 2, not just one number. So, we have a 2 out of 5 chance of rolling that, because 2 options are acceptable instead of just one number.
I'm not sure which form you are looking for, but 2 out of 5 is the same as saying 2/5. Most probability solutions are wanted as a percentage. To find that just solve 2/5, which is 0.4. Move the decimal to the right twice, and that is a 40% chance.
Can it be true that a 10 year old child weighs 30%
more than a 6 year old child?
Answer:Kids grow at their own pace. Big, small, tall, short — there is a wide range of healthy shapes and sizes among children. Genetics, gender, nutrition, physical activity, health problems, environment, and hormones all play a role in a child's height and weight. And many of these things can vary widely from family to family.
Step-by-step explanation:
The side length of the square is 11 cm. The diameter of the circle is 14 cm. Find the area of the shaded region. Use . A 153.86153.86153.86 cm2 B 94.98594.98594.985 cm2 C 32.8632.8632.86 cm2 D 615.44615.44615.44 cm2
Answer:
32.9 cm^2
Step-by-step explanation:
In the absence of a diagram, lets use the one shown in the attached worksheet. The assumption is that the "blue areas" are the four sections of the circle that extend beyond the square boundaries. The approach is to calculate areas for both the circle and the square.
Square = (11 cm)^2 = 121 cm^2
Circle = (3.14)*(14/2 cm)^2 = 153,9 cm^2
Subtract the square from the circle. That removes all the circle area, except for the four sections outside the square. The result is 32.9 cm^2
What type of function is Y =- 2x 3?.
The type of the function y = -2x + 3 is a linear function.
Function in math is known as a rule that gives value of a dependent variable that corresponds to specified values of one or more independent variables.
Here we have given that the function y = -2x +3 and here we need to identify the type of the function.
As we all know that the type of function called linear function is defined as a function that has either one or two variables without exponents.
While we consider the definition we have identified that the given function is is the linear function because in the given function there is no exponents in it so it can fall under the category of the function called exponents.
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What is the solution to the system of equations y 2x 3. 5 and x 2y =- 14?.
The point (7, 10.5) is on the graph of both equations and satisfies the system of equations.
To find the solution to a system of equations, we need to find the values of x and y that satisfy both equations simultaneously.
The system of equations is:
y = 2x - 3.5
x - 2y = -14
We can begin by solving one of the equations for one of the variables, for example, we can solve the first equation for y:
y = 2x - 3.5
Next, we can substitute this expression for y into the second equation:
x - 2(2x - 3.5) = -14
This gives us:
x - 4x + 7 = -14
-3x = -21
x=7
Now we can substitute this value of x back into the first equation to find the corresponding value of y:
y = 2(7) - 3.5
y = 10.5
So the solution to the system of equations is x = 7, y = 10.5.
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HELP PLEASE THIS IS DUE IN 1 MINUTE!!!!!!!!
A sixth grade class is going on a field trip. The school is providing one sack lunch for each student. Each lunch has either a ham, turkey, or bologna sandwich along with either carrots or celery.
Identify which list below shows all the possible outcomes of sack lunches, and select the outcomes from that list that represent picking a ham or turkey sandwich with carrots if there are an equal number of each type of sack lunch and students are randomly selecting their lunch. Use this information to mark the probability on the number line.
The required probability has been shown on the number as illustrated in the figure.
What is probability?Probability can be defined as the ratio of favorable outcomes to the total number of events.
Here,
There are two veggies (carrots, and celery) and three types of meat (ham, turkey, and bologna),
This results in 3*2 = 6 distinct combinations of meat and a vegetable. Here, we are limited to choosing just one of each kind. List 2 shows the 6 different combinations. List 1 is inaccurate because you can only take one vegetable at a time and not both.
List 2 alternatives that state "ham, carrots" and "turkey, carrots" should be circled. Two things have been circled. This is one of a total of six.
Probability is given as,
= 2/ 6
= 1/3
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Solve using substitution.
x = –3
x + 7y = 18
(, )
The value of y in the expression x + 7y = 18 when x = - 3 is 3.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
We know Substitution in mathematics is when we replace some specific numerical values with variables according to our wants or given in the problem.
Given, x = - 3 and x + 7y = 18.
Replacing x with - 3 in x + 7y = 18.
- 3 + 7y = 18.
7y = 18 + 3.
7y = 21.
y = 21/7.
y = 3
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https://brainly.com/question/29199574
#SPJ1
