A quadratic equation 9x² + 3kx + 4 = 0 has equal roots. Thus, the values of k are -4, and +4.
What is quadratic equation?The equation of the second degree is a quadratic equation. This indicates that it contains a phrase that is squared, at least once. ax² + bx + c = 0, which uses constants or numerical coefficients for the variables a, b, and c, is one of the classic formulae for solving quadratic equations. Unknown variable 'x' is used here.
The given problem can be solved using the concepts of quadratic equations.
1. The given quadratic equation is 9x² + 3kx + 4 = 0.
2. For an equation to have equal roots the value of the discriminant is 0,
=> The discriminant of a quadratic equation ax² + b x + c = 0 is given by the formula,
=> Discriminant ( D ) = [tex]\sqrt{b^2 - 4ac}[/tex]
=> For equal roots D = 0.
3. Substitute the values in the above formula:
⇒ [tex]\sqrt{(3k)^2 - 4*9*4}[/tex] = 0
⇒ [tex]{9k^2 - 144}[/tex] = 0
⇒9k² = 144
⇒ k² = 16
⇒ k = ± 4
Therefore, the values of k are -4, and +4.
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Perimeter = 164. Solve for x and y.
y + 12 cm
y
810
H
x
y - 12 cm
The two sides of the triangle are 76 cm and 88 cm.
What is perimeter?Perimeter is the distance around the outside of a shape or object. It is the total length of the outer boundary of a two-dimensional figure such as a circle, rectangle, triangle, or polygon. Perimeter is calculated by adding together the lengths of all the sides of a figure. It is also used to determine the size of a shape or area.
Let x and y be the two sides of the triangle whose perimeter is 164 cm. Thus,
x + y + 12 = 164
Substituting y = x + 12,
2x + 12 = 164
2x = 152
x = 76
Substituting x = 76 in the equation y = x + 12,
y = 76 + 12
y = 88
Therefore, the two sides of the triangle are 76 cm and 88 cm.
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Which of the following is a possible solution to the inequality below? *
2x > 6
1. 5
2. -5
3. 2
4. -3
Answer: Number 1
Step-by-step explanation:
2 * 5 = 10 > 6 ✓
2 * -5 = -10 > 6 X
2 * 2 = 4 > 6 X
2 * -3 = -6 > 6 X
The correct option for the question is 1.
Inequality is 2x>6
=x>3
hence a number greater than 3 can be the solution to the question.
therefore 1.)5 is the correct option.
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UNIT-6 (QUESTIONS 1-3) HELP. DUE TODAY.
The value of f(-5) for the function f(x) = 3x^2 -2x + 5 is 90.
What is the quadratic function?
A quadratic function is a polynomial of degree 2 and so the equation of quadratic function is of form f(x) = ax^2 + bx + c, where 'a' is a non-zero number; and a, b, and c are real numbers.
To find the value of f(-5), we need to substitute -5 for x in the function f(x) = 3x^2 - 2x + 5.
f(-5) = 3(-5)^2 - 2(-5) + 5
Simplifying the equation:
f(-5) = 3(25) - 2(-5) + 5
f(-5) = 75 - (-10) + 5
f(-5) = 75 + 10 + 5
f(-5) = 90
So the value of f(-5) is 90.
The function f(x) = 3x^2 - 2x + 5 is a quadratic function, which means it has the form ax^2 + bx + c,
where a, b, and c are constants. In this case, a = 3, b = -2, and c = 5. When we substitute -5 for x,
we are finding the value of the function when x is equal to -5.
By plugging in -5 for x, we are able to find the y-coordinate (or the value of the function) when x is -5. In this case, the y-coordinate is 90.
Hence, the value of f(-5) for the function f(x) = 3x^2 -2x + 5 is 90.
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[tex]\it f(-5)=3\cdot(-5)^2-2\cdot(-5)+5=75+10+5=90[/tex]
the manager of a furniture factory finds that it costs $2600 to manufacture 90 chairs in one day and $4800 to produce 290 chairs in one day. (a) express the cost c (in dollars) as a function of the number of chairs x produced, assuming that it is linear.
The expression of the total cost as a function of the number of chairs produced (x) is: C(x) = 1,610 + 11 x
The production cost comprises two components: fixed cost and variable cost.
Let:
F = fixed cost
p = variable cost per unit chair
x = number of chairs produced.
C(x) = total cost
Hence,
C(x) = F + p . x
2600 = F + 90 p .... (equation 1)
4800 = F + 290 p .... (equation 2)
Subtract those questions:
4800 = F + 290 p
2600 = F + 90 p _
2200 = 200 p
p = 11
Substitute p = 1 into equation 1:
2600 = F + 90 x 11
F = 2600 - 990 = 1,610
Thus, the expression for the total cost is:
C(x) = 1,610 + 11 x
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Raisa is in her office. From her office, she took the elevator down eight floors to the parking garage. Which number represents the distance AND direction from her office to the parking garage?
–2
2
-8
8
The number that represents the distance and direction from her office to the parking garage is; -8
How to solve absolute value problems?The absolute value of a number is defined as the distance of that specific number from zero.
Now, when we talk about an elevator, an upward motion indicates a positive sign while a downward motion indicates a negative sign. Now, we are told that from Raisa's office, she took the elevator down eight floors to the parking garage.
Since it is a downward motion, the distance will be negative and since it is 8 floors downward, we conclude that the distance and direction is given by -8
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when researchers observe a correlation between two variables, such as between the amount of time spent studying and test scores, they know that:
When researchers observe a correlation between two variables, they know that there is a relationship between these variables but they do not know if one variable is causing the other.
Correlation is a statistical measure that indicates the strength and direction of a linear relationship between two variables. It ranges from -1 to 1, with -1 indicating a perfect negative correlation, 0 indicating no correlation, and 1 indicating a perfect positive correlation.
A correlation between two variables, such as time spent studying and test scores, suggests that there is a relationship between these variables, but it does not indicate causality.
There could be other variables that influence both of these variables, or the relationship between them could be spurious.
Therefore, researchers must conduct further investigation to determine the cause-and-effect relationship. Researchers might use experimental designs to control for other variables and establish causality.
Additionally, researchers might use other statistical techniques, such as regression analysis, to further explore the relationship between variables.
In conclusion, when researchers observe a correlation between two variables, such as between the amount of time spent studying and test scores, they know that there is a relationship between these variables but they do not know if one variable is causing the other.
To establish causality, researchers must conduct a further investigation using experimental designs and other statistical techniques.
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What is the rule for acute angles?
Answer:
If given angle limits less than a quarter of a full circle, then it is an acute angle. A straight angle is half a full angle. If given angle limits less than a half of a straight angle, then it is an acute angle. If given angle limits close to a half or more than a half of a straight angle, then it is not an acute angle.
Step-by-step explanation:
The population of a city increased to 705600 in 2017 at the rate 5% per annum. (a) find the population in 2015.
(b) find the population in 2019.
a) Population of city in 2015 = 640000
b) Population of city in 2019 = 777924
What is population growth?Population-growth happens when an initial population increases by the same percentage or factor over equal time increments or generations.
Given,
Population of city in 2017 (P) = 705600
Rate per annum r = 5% = 0.05
a) Population of city in 2015 (p) = ?
Time difference 2015 and 2017 = 2 years
Population of city in 2017
P = p(1 + r)ⁿ
705600 = p(1 + 0.05)²
p = 705600/1.05²
p = 705600/1.1025
p = 640000
b) Population of city in 2019 = ?
Time difference 2017 and 2019 n = 2 years
Population of city in 2019
= P(1 + r)ⁿ
= 705600(1+0.05)²
= 705600(1.05)²
= 705600 × 1.1025
= 777924
Hence, 640000 is population of city in 2015.
777924 is population of city in 2019
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Demonstrate at least two different ways how to solve the equation 5(2x-1)=25
Answer:
divided both sides by the numeric factor on the left then solve x = 3
Step-by-step explanation:
helppppppppppp meeeeeeeeee
Answer:
maybe 3/2
Step-by-step explanation:
Answer:
Step-by-step explanation: I think the answer is A
What is the length of JA’?
The length of JA' after dilated with a scale factor of 1/4 is 4 mm.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Segment JA = 16 mm
Dilated with a scale factor r = 1/4.
This means,
Segment JA'
= 1/4 x 16 mm
= 4 mm
Thus,
The length of JA' is 4 mm.
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How do you find the inverse of a log function on a calculator?
An inverse log is defined as the anti-log of a log function raised to a negative value.
Enter a number and a base into the calculator.
The calculator will display the inverse log of the number and base entered.
The base of the natural log is equal to e=2.71828. The standard base for the log is base 10.
The following formula is used to calculate the inverse log of a number and base.
㏒[tex]b^{-1}[/tex](y) = [tex]b^{y}[/tex]
Where x is the value you are calculating
b is the base
and y is the number to take the log of
To calculate an inverse log, raise the base value to the power of the number being taken in the log.
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What are the main features of production possibility curve?
The main features of the production possibility curve are it slopes downward from left to right and the curve is concave to the origin.
In business, a production possibility curve (PPC) is made to estimate the performance of a manufacturing system when two commodities are manufactured together. The management uses this graph to plan the perfect proportion of goods to produce in order to reduce wastage and costs while maximising profits.
The two basic properties of the production possibility curve are:
It slopes downward from left to right- The production possibility curve slopes downward because both the variables involved in the equation are inversely related as one increases then another decreases and vice versa.
The curve is concave to the origin- Since resources are used specifically, therefore every time when one more unit of a commodity is produced more units of the other commodity are sacrificed which results in increasing marginal opportunity cost which leads to the concave shape of the production possibility curve.
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What value of x satisfies the equation
-3(4x-5) = 2(1 - 5x) ?
F. 2
G. -끎
22
용품
H. -1
J.
K.
3
17
13
2
A
Answer:
K. [tex]\frac{13}{2}[/tex]
Step-by-step explanation:
[tex]-3(4x-5)=2(1-5x) \\ \\ -12x+15=2-10x \\ \\ 15=2+2x \\ \\ 2x=13 \\ \\ x=\frac{13}{2}[/tex]
HELP ASAP!!!!! What is the value of the following expression?
[6 • 4 + 50 ÷ (12 + 13) + 2] • 3
The value of the given expression [6 • 4 + 50 ÷ (12 + 13) + 2] • 3 is 84.
Explanation:
To evaluate the given expression, we follow the order of operations (PEMDAS). Let's break it down step by step:
Inside the square brackets, we have 6 • 4 + 50 ÷ (12 + 13) + 2.Next, we evaluate the expression inside the parentheses: 12 + 13 = 25.Now, we substitute the result back into the expression: 6 • 4 + 50 ÷ 25 + 2.Next, we perform the multiplication: 6 • 4 = 24.Then, we perform the division: 50 ÷ 25 = 2.Now, we substitute the results back into the expression: 24 + 2 + 2.Finally, we perform the addition: 24 + 2 + 2 = 28.Now, we multiply the result by 3: 28 • 3 = 84.Therefore, the value of the given expression is 84.
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What is the quotient of −213 and 3?
−639
−71
71
639
Answer: -71
Step-by-step explanation:
-213/3 = -71
-71 is the quotient.
-213 : 3= - 71
____________________
In parallelogram JKLM, JK=5x–1, KL=11x+3, and LM=3x+7.
The perimeter of the parallelogram JKLM is 132 units
What is a parallelogram?A parallelogram is a quadrilateral (has four sides and four angles) in which opposite sides are equal and parallel.
From the diagram:
JK = LM
5x - 1 = 3x + 7
5x - 3x = 7 + 1
2x = 8
x = 4
JK = LM = 5(4) - 1 = 19
KL = 11x + 3 = 11(4) + 3 = 47
Perimeter of JKLM = 2(JK + KL) = 2(19 + 47) = 132 units
The perimeter of JKLM is 132 units
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the bloch sphere geometric representation of a quantum state is parameterized by two angles and such that . what are the values of the angles and for the state
The range of values for θ and φ is such that they must not repeat in order to cover the entire sphere θ∈[0,π) and φ∈[0,2π).
The Bloch sphere representation, which bears Felix Bloch's name, is the outcome of the foregoing. This illustration is a unit 2-sphere with two mutually placed spheres at the north and south poles. In contrast, quantum bits cover the entire sphere, whereas these are the only conceivable states for the classical bit representation.
(Disclaimer: One could counter that since the classical bit is represented by voltages, the classical bit representation also contains the axis linking the two poles. As a result, the Bloch sphere illustrates that there is substantially more information involved in quantum bits. When the qubit is measured, one of the two poles is what remains. Exactly which pole is determined by the direction the arrow in the Bloch representation points.
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What is the smallest integer greater than the square root of 44
Answer:
7
Step-by-step explanation:
We need [tex]\sqrt{44} < x[/tex], where x is the unknown integer.
To make this easier, we can square both sides:
44 < [tex]x^{2}[/tex]
To aid here, recall values of low integers squared:
[tex]1^{2}[/tex] = 1, [tex]2^{2}[/tex] = 4, ... [tex]6^{2}[/tex] = 36, [tex]7^{2}[/tex] = 49
7 is the first integer where its square is greater than 44.
Therefore 7 is the first integer greater than the square root of 44.
Mrs. Wicklund sets a lawn sprinkler to cover part of a circular region. The central angle and radius for the covered part
are shown.
130⁰
25 ft-
To the nearest 10 square feet, what is the area of the 130° part covered by the sprinkler? Enter your answer in the box.
square feet
Answer:
701.25 feet squared
Step-by-step explanation:
when you calculate the total area of the circle it comes to 1963.5ft
360 degrees divided by 130 degrees is 2.8 which means you need to divide the total area by 2.8 and the final answer comes to 701.25 feet squared
conjecture for the relationship between the volume of a sphere with a radius that equals to y and the volume of a sphere with a radius equal to 2y
7y³ is the relationship between the volume of a sphere with a radius that equals to y and the volume of a sphere with a radius equal to 2y.
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
Volume is defined as the space occupied within the boundaries of an object in three-dimensional space.
Volume of a sphere is 4/3πr³
the volume of a sphere with a radius that equals to y and the volume of a sphere with a radius equal to 2y
4/3πy³=4/3π(2y)³
4/3πy³=4/3π×8y³
y³=8y³
=(1-8)y³
7y³
Hence, 7y³ is the relationship between the volume of a sphere with a radius that equals to y and the volume of a sphere with a radius equal to 2y.
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What is the ln of 0?
The real natural logarithm function ln(x) is defined only for x>0. So the natural logarithm of zero is undefined.
What has a natural log of 0?Undefined log 0 is. Due to the fact that nothing can ever be raised to the power of zero, the number is not real. Zero is an infinitely big and negative number that can never be reached; instead, it can only be approached.Ln(0) is not possible since anything or any number raised to the power of 0 is equal to one, and you cannot have the power of something being 0. As e to the power 0 is 1, ln(1) equals 0. If e to the power of a number is 0, which never happens, then ln(0) would imply that. So, it is not defined. The idea of infinity can also be used to define log of zero. The log of zero is infinite in this situation, thus we can state.To learn more about natural log of 0 refer to;
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9800 workers in Arizona retired in 2010 as compared to 23,430 in 2009. What is the absolute
change in the number of workers that retired?
Some people decide to continue working because they need the money, while others love what they do and can't imagine not doing it anymore or just need to stay busy.
What is absolute change?
Absolute change refers to the simple difference in the indicator over two periods in time, i.e. Relative change expresses the absolute change as a percentage of the value of the indicator in the earlier period, Absolute change refers to the simple difference in the indicator over two periods in time, i.e. Relative change expresses the absolute change as a percentage of the value of the indicator in the earlier period, Absolute change refers to the simple difference in the indicator over two periods in time, i.e. Relative change expresses the absolute change as a percentage of the value of the indicator in the earlier period.To learn more about workers refers to:
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Which of these is a random sampling technique which is frequently chosen by researchers for its simplicity and its periodic quality?
Simple random sampling is a frequently chosen for its simplicity and periodicity.
What is frequently ?
Frequently refers to something that happens or occurs often or many times. It is an adverb that describes the regularity of an action or event, indicating that it happens with a high frequency or on a regular basis.
Simple random sampling is a random sampling technique that is frequently chosen by researchers for its simplicity and its periodic quality. This technique involves randomly selecting a sample from a larger population, with each individual in the population having an equal chance of being selected. Simple random sampling is considered to be an unbiased and efficient method for selecting a representative sample, and it is often used as a benchmark for comparing other sampling methods.
Simple random sampling is a frequently chosen for its simplicity and periodicity.
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what is the LCM of 3,6,and 18
Answer: The Least Common Multiple (LCM) of 3, 6, and 18 is 18
Step-by-step explanation:
Work out the equation of the line shown
below.
Give your answer in the form y = mx + c,
where m and c are integers or fractions in
their simplest forms.
Y
-160-
140-
-120-
-100-
80-
60-
40-
20-
-80 -70 -60 -50 -40 -30 -20 -10 0
-20
--40-
-60
-80-
-100-
120-
-140-
--160-
10 20 30 40 50 60 70 80 x
Answer: y = -3x + 1
Step-by-step explanation: the line crosses the y-axis at (0,1) then c = 1
The points (0,1) and (1,-2) lie on the line then
m = slope = [(-2)-1]÷(1-0) = [-3]÷(1) = -3÷1 = -3
Therefore, the equation of the line is : y = -3x + 1
What are the 5 properties of division?
According to the division property of equality, if both sides of an equation are divided by a common real integer that is not zero, the quotients remain equal.
Commutative property, associative property, distributive property, and identity property are the four number properties. Only the algebraic operations addition, subtraction, multiplication, and division are linked with number characteristics.
The four key terminology used in the division process are dividend, divisor, quotient and remainder. Dividend Divisor = Quotient + Remainder is the formula for dividing two numbers.
Commutative property, associative property, distributive property, and identity property are the four number properties. Only the algebraic operations addition, subtraction, multiplication, and division are linked with number characteristics.
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Convert the measurements. why take here me doy
hug 1 + 9
[tex]589[/tex]
The introduction of the "Metric System" was caused by the new measurement unit. The measurement is equivalent to 31 quarts.
What is conversion to metric?In order to measure any quantity, the units that are available must be converted to the necessary units using the term "metric conversion."
The introduction of the "Metric System" was caused by the new measurement unit.
United States Customary Units (USCU) are the metric units used in the US (USCS).
Metric conversion is the process of changing the given units for any quantity that has to be measured into the required units.
In light of this, 7 gallon, 3 quarts
A gallon, which is equivalent to 4 quarts, 16 cups, or 8 pints, is most frequently used to measure liquid volume.
7 gallon, 3 quarts, please.
= 7×4+3
33 quarts
Consequently, the measurement is equivalent to 31 quarts.
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Misty Gonzalez receives her paycheck weekly. She earns a
straight commission of 4% on sales of $5,000 or less and 5% on sales in
excess of $5,000. One week Misty had a gross pay of $462. What was that
week's total sales amount?
Find the quotient of 4 7 and 3 5 give your answer as a fraction in its simplest form.
The quotient of 4 7 and 3 5 can be expressed as a fraction as 20/35 which is the simplest form of the fraction. This fraction can be created by dividing the numerator 4 by the denominator 7, and dividing the numerator 3 by the denominator 5, and then combining the two fractions by multiplying the numerators and denominators together.
1. 4/7 ÷ 3/5
2. (4/7) × (5/3)
3. (20/21)
4. 20/35 (simplest form)
The quotient of 4 7 and 3 5 can be expressed as a fraction in its simplest form as 20/35. To calculate this fraction, the first step is to divide the numerator 4 by the denominator 7, and divide the numerator 3 by the denominator 5. This gives two fractions, 4/7 and 3/5. The next step is to combine the two fractions by multiplying the numerators and denominators together. This gives the fraction 20/21. The final step is to simplify the fraction, which can be done by dividing the numerator and denominator by the same number to give 20/35, which is the simplest form of the fraction.
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