The answer is: D)quadratic trinomial
The solution is Option D.
The quadratic trinomial is given by A = 4x² + 3x + 5
What is Quadratic Equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
The roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
where ( b² - 4ac ) is the discriminant
when ( b² - 4ac ) is positive, we get two real solutions
when discriminant is zero we get just one real solution (both answers are the same)
when discriminant is negative we get a pair of complex solutions
Given data ,
Let the equation be represented as A
Now , the value of A is
A = 4x² + 3x + 5 be equation (1)
On simplifying the equation , we get
There are 3 terms on the equations , so it is a trinomial
And , since the variable is x² , it is a quadratic equation
Therefore , the equation A is quadratic trinomial
Hence , the equation is quadratic trinomial
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Who worthy the book “I love fractions”
A teacher reaches into a bag of game pieces containing 5 black pieces, 3 purple pieces, 1 orange piece, and 6 green pieces. He draws 2 pieces, setting aside the first piece before drawing the second. What is the probability that at least one of the drawn pieces is purple
Answer:
13/35
Step-by-step explanation:
gradpoint
Seven more than half of the cost , c
Mick paid $2.94 in sales tax on an item that cost $42.00 before tax. At that rate, how much would he paying sales tax before an item that cost $58 before tax
Is the expression 2f + 4f + 2 – 3 equivalent to 6f – 1? 6f – 1 evaluated at f = 9 is 53. 2f + 4f + 2 – 3 evaluated at f = 9 is also 53. 6f – 1 evaluated at f = 3 is 17. what is 2f + 4f + 2 – 3 evaluated at f = 3?
Answer: 17
Step-by-step explanation:
If a triangle is an obtuse triangle then it can not be an isosceles triangle.
a. True
b. False
Find two consecutive even integers such that the smaller added to threetimes the larger gives a sum of 30.
The two consecutive even integers that satisfy the given condition are 6 and 8. When the smaller one (6) is added to three times the larger one (8), the sum is 30.
The student has asked for help in finding two consecutive even integers such that the smaller added to three times the larger gives a sum of 30. To solve this, let's designate the smaller even integer as x. Since the numbers are consecutive even integers, the next integer will be x + 2.
The equation based on the problem statement will look like this:
x + 3(x + 2) = 30
Expanding the equation gives:
x + 3x + 6 = 30
Combining like terms:
4x + 6 = 30
Subtracting 6 from both sides:
4x = 24
And dividing by 4:
x = 6
Now, the two consecutive even integers can be determined:
The smaller integer is 6, and the larger integer is 6 + 2, which equals 8. Therefore, the two integers are 6 and 8, and if we check:
6 + 3(8) = 6 + 24 = 30, which matches the required sum.
Which of the following inequalities is best represented by this graph?
5x + y ≤ 2
5x + y ≥ 2
5x − y ≤ 2
5x − y ≥ 2
Answer:the answer is d
Step-by-step explanation:
5x - y ≥ 2
What is the product of -9(5-2x)
The product of -9(5-2x) is found by multiplying -9 by each term inside the parentheses resulting in -45 + 18x.
Explanation:The product of -9(5-2x) is found by distributing the -9 to both terms inside the parentheses. Following the rules of multiplication, when a negative number multiplies a positive number, the result is negative, and when a negative number multiplies a negative number, the result is positive. Hence:
-9 x 5 = -45
and
-9 x -2x = 18x.
Combining these results, we get the final expression:
-45 + 18x
Keep in mind that when simplifying expressions or performing multiplication, we need to adhere to the rules for multiplication of numbers with different signs, as described earlier.
Final answer:
The product of -9(5-2x) is calculated by using the distributive property to multiply -9 by each term inside the parentheses, yielding 18x - 45.
Explanation:
The product of -9(5-2x) can be found by applying the distributive property of multiplication over subtraction. This property states that you multiply the term outside the parentheses by each term inside the parentheses. Here are the steps:
Multiply -9 by the first term inside the parentheses (5), which is -45.
Multiply -9 by the second term inside the parentheses (-2x), which gives us +18x (note that a negative multiplied by a negative gives a positive).
Combine these two products to get the final result, -45 + 18x, or 18x - 45.
This demonstrates the rules of multiplication where multiplying two numbers with opposite signs results in a negative product, and multiplying two numbers with the same sign results in a positive product.
negative 1 over 2x + 2 = −x + 7
Point P is the center of the circle that is circumscribed around the triangle. What does point P represent with regard to the triangle
Answer: d) the point of concurrency of the perpendicular bisectors
Step-by-step explanation:
How do I solve and graph this?
Answer for number 5?
Of the 8760 hours in a year, one television was on for2628hours. what percent is this?
An equiangular triangle can never be scalene. true or false?
The given statement "An equiangular triangle can never be scalene." is true.
What is an equiangular triangle?An equiangular triangle is a triangle that has three equal angles.
What is a scalene triangle?A scalene triangle is a triangle that has three unequal sides.
Therefore, a scalene triangle has three different angles.
Therefore, an equiangular triangle and scalene triangle are two completely different triangles.
Hence, an equiangular triangle can never be a scalene triangle.
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Bonnie wants to make a picture frame for a 5 x 8-inch photo. What is the area of the frame if the frame is 1 inch thick? square inches
The area of the frame if the frame is 1 inch thick will be 30 inch².The area of the frame is found as the product of the length and breadth of the frame.
What is the area?The space filled by a flat form or the surface of an item is known as the area.
If the frame is 1 inch thick then the total area is found as;
The area of the rectangular picture is;
[tex]\rm A = 5 \times 8 \\\\\rm A =40 \ inch^2 \\\\[/tex]
The total area of the frame is found as;
Area of frame = Total area - area of the picture
Area of frame =70 -40
Area of frame = 30 inch²
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What is the true solution to 3 in 2 + in 8 = 2 in(4x)
a. x=1
b. x=2
c. x=4
d. x=8
The true solution to [tex]3 log 2+log8 =2log(4x)[/tex] is [tex]x=2[/tex]. The correct option is b. [tex]x=2[/tex].
Given expression is[tex]3 \log 2+\log8 =2\log(4x)[/tex].
We have to calculate the value of [tex]x.[/tex]
Properties of logarithm:We know that,
[tex]n \log m= \log(m)^n[/tex]
and
[tex]\log m + \log n = \log(mn)[/tex]
Solving the equation:
[tex]3 \log 2+\log8 =2\log(4x)[/tex][tex]\log(2)^3+\log8 =\log(4x)^2[/tex]
{using [tex]n \log m= \log (m)^n[/tex]}
[tex]\log8+\log 8= \log 16x^2[/tex]
[tex]\log (8 \times8)=\log16x^2[/tex] {using [tex]log m + log n = log(mn)[/tex]}
Since log is on both sides so it is eliminated from both sides,
[tex]8 \times8=16x^2\\64=16x^2\\[/tex]
[tex]x^{2} =\frac{64}{16}\\x^{2}=4\\x=2[/tex]
Hence the true solution to [tex]3 log 2+log8 =2log(4x)[/tex] is [tex]x=2[/tex].
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A test is worth 140 points. Ten percent of those points are from one short-answer question. How many points is the short-answer question worth?
The short-answer question worth of 14 points.
What is unitary Method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given:
Total points of test =140
and 10 % of those points are from one short-answer question.
So, the points for short-answer question are
=10 % of 140
=10/100 x 140
=1400/100
=14
Hence, short-answer question worth of 14 points.
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Michelle and Andrea are walking laps for charity. The amount of money, y, that each girl raises for a certain number of laps, x, is shown in the tables below. Michelle mc020-1.jpg Andrea mc020-2.jpg Which statement explains who will raise $100 with the fewest number of laps? Michelle will, because the slope of the line described by the data in her table is the greatest. Andrea will, because the slope of the line described by the data in her table is the greatest. Michelle will, because her number of laps are increasing at a faster rate. Andrea will, because her number of laps are increasing at a slower rate
Answer:
The answer would be a im sure
Step-by-step explanation:
Eric plans to rent a car for a day from Easy Car Rental. He has a coupon for 25% off the daily base rate of $40. He will also have to pay an additional $0.15 for each mile he drives. Which expression represents the situation? (m represents the number of miles)
Answer:
30 + 0.15m
Step-by-step explanation:
base rate = 40(1 − 0.25) = 40(0.75) = 30
per mile = 0.15m
thus,
30 + 0.15m
The correct expression represents the situation is,
⇒ 30 + 0.15m
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Eric plans to rent a car for a day from Easy Car Rental.
Here, He has a coupon for 25% off the daily base rate of $40.
And, He will also have to pay an additional $0.15 for each mile he drives.
Let m represents the number of miles.
Hence, We can formulate;
⇒ 40 (1 - 0.25) + 0.15m
⇒ 40 × 0.75 + 0.15m
⇒ 30 + 0.15m
Thus, The correct expression represents the situation is,
⇒ 30 + 0.15m
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Find the area of the shaded portion in the square (assuming the center point of each arc is the corresponding central point of the line and the arcs intersect at the center point of the circle)
Answer:
The answer is 2. hope it helps!
Step-by-step explanation:
Answer: The area of the shaded portion is [tex](\pi-2)~\textup{sq. units}.[/tex]
Correct option is 2.
Step-by-step explanation: We are given to find the area of the shaded portion in the figure.
Since, the centre point of each arc is the corresponding central point of the line and the arcs intersect at the centre point of the circle,
so let us divide the figure into four equal parts, one of them is square ABCD as shown in the attached figure.
The area of the square ABCD will be
[tex]A_{ABCD}=\left(\dfrac{1}{2}\times 2\right)^2\\\\\\\Rightarrow A_{ABCD}=1~\textup{sq. units}.[/tex]
Now, area of the shaded portion inside the square ABCD will be
[tex]A_s=2\times \textup{area of the quarter circle with radius 1 unit}}-\textup{area of square ABCD}\\\\\Rightarrow A_s=2\times \left(\pi\times \left(\dfrac{1}{2}\right)^2\right)-A_{ABCD}\\\\\\\Rightarrow A_s=2\times\left(\dfrac{\pi}{4}\right)-1\\\\\\\Rightarrow A_s=\left(\dfrac{\pi}{2}-1\right)~\textup{sq. units}.[/tex]
Since all the four squares are identical in the attached figure, so the required area of the total shaded portion in the figure is
[tex]A=2\times\left(\dfrac{\pi}{2}\right)\\\\\\\Rightarrow A=(\pi-2)~\textup{sq. units}.[/tex]
Thus, the area of the shaded portion is [tex](\pi-2)~\textup{sq. units}.[/tex]
The correct option is 2.
Find the first six terms of the sequence.
a1 = -4, an = an-1 + 7
-4, 3, 10, 17, 24, 31
-4, 7, 14, 21, 28, 35
3, 10, 17, 24, 31, 38
0, 7, 14, 21, 28, 35
Answer: A) -4, 3, 10, 17, 24, 31
Step-by-step explanation: To solve the given problem we need to calculate the first six terms of the sequence (starting with a1):
a1=-4
a2=a1+7
a2=-4+7
a2=3
a3=a2+7
a3=3+7
a3=10
a4=a3+7
a4=10+7
a4=17
a5=a4+7
a5=17+7
a5=24
a6=a5+7
a6=24+7
a6=31.
The half-life of iodine-123 is about 13 hours. You begin with 52 grams of iodine-123. (a) Write an equation that gives the amount of iodine-123, I , remaining after t hours. Write your answer in the form I ( t ) = a ⋅ b t . Round your answer for b to three decimal places.
Final answer:
The amount of iodine-123 remaining after t hours can be expressed as I(t) = 52 · 0.945^t, where the constant 0.945 is calculated using the half-life of 13 hours.
Explanation:
The half-life of a radioactive isotope is the time it takes for half of the radioactive atoms to decay. For iodine-123, which has a half-life of approximately 13 hours, we can use an exponential decay model to express the amount of iodine-123 remaining after t hours.
The decay formula is generally given by I(t) = I0e-kt, where I0 is the initial amount, k is the decay constant, and t is time. However, the question asks us to express the equation in the form of I(t) = a · bt, which is another common representation for exponential decay.
To find the value of b, we know that after one half-life, b13 = 1/2. Thus, b = (1/2)1/13.
Let's calculate b: b = (0.5)1/13 ≈ 0.945 (rounded to three decimal places).
Since we start with 52 grams of iodine-123, our initial amount (a) is 52. Therefore, the equation for the amount of iodine-123 remaining after t hours is:
I(t) = 52 · 0.945t
The equation to calculate the amount of iodine-123 remaining after t hours is I(t) = a * b^t, where a is the initial amount of iodine-123, b is the decay constant, and t is the time in hours. The decay constant can be calculated using the formula b = 0.693 / t1/2, where t1/2 is the half-life of iodine-123. In this case, the half-life is 13 hours.
Explanation:The equation that gives the amount of iodine-123 remaining after t hours can be written as:
I(t) = a * b^t
Where:
I(t) is the amount of iodine-123 remaining after t hoursa is the initial amount of iodine-123b is the decay constant, which can be calculated using the half-life formulat is the time in hoursTo calculate the decay constant b, we can use the formula:
b = 0.693 / t1/2
where t1/2 is the half-life of iodine-123. In this case, the half-life is 13 hours, so:
b = 0.693 / 13 = 0.053
Therefore, the equation becomes:
I(t) = a * 0.053^t
Round the value of b to three decimal places, so b = 0.053.
What is the volume of a right circular cylinder with a diameter of 19.6 yd and a height of 23.52 yd?
Enter your answer in the box. Use 3.14 for pi and round only your final answer to the nearest hundredth.
yd³
Answer:
7092.82
Step-by-step explanation:
i took the quiz
Given: What type of angles are ∠2 and ∠3 are adjacent angles.
Which of the following options describes the adjacent angles in terms of their sum? complementary angles, 90° complementary angles, 180° supplementary angles, 90° supplementary angles, 180°
Final answer:
Adjacent angles can be either complementary or supplementary depending on their sum. Complementary angles add up to 90°, while supplementary angles sum to 180°. The term for adjacent angles in terms of their sum is 'supplementary angles', adding up to 180°.
Explanation:
Adjacent angles are two angles that have a common side and vertex, and don't overlap. In terms of their sum, if adjacent angles add up to 90 degrees, they are called complementary angles. If they add up to 180 degrees, they are called supplementary angles. Since the question involves angles ∠2 and ∠3 as adjacent angles but does not provide their specific measures, it's not possible to definitively classify them as complementary or supplementary without additional information. However, the question asks which term describes adjacent angles in terms of their sum. The correct answer is supplementary angles, which have a sum of 180°.
Kathleen has been tracking how fast she walks over the last month and determined that she walks 1 1/4 miles in 2/5 of an hour. Lynn has been tracking how fast she walks over the last few weeks and determined that it takes her 19 minutes and 12 seconds to walk 1 mile. Part A: Write both Kathleen's and Lynn's walking rate in the same format, either miles per hour, miles per minute, minutes per mile, or hours per mile and compare their rates to each other. Part B: Give a logical argument on why that format was chosen over the other three.
Select all that have a value of 0.
Answer:
It's 1,3, and 5.
The functions that have a value of 0 are : [tex]cos(\frac{\pi}{2} ),~sin(0),~tan(\pi)[/tex]
What is function?"It defines a relation between input and output values.""In function for each input there is exactly one output."For given question,
We have been given some trigonometric functions.
We need to find the functions that have a value zero.
[tex]i)~cos(\frac{\pi}{2} )=0\\\\ii)~cos(0)=1\\\\iii)~sin(0)=0\\\\iv)sin(\frac{3\pi}{2} )=-1\\\\v)tan(\pi)=0[/tex]
From above, we can observe that functions [tex]cos(\frac{\pi}{2} ),sin(0)[/tex] and [tex]tan(\pi)[/tex] have a value of zero.
Therefore, the functions that have a value of 0 are : [tex]cos(\frac{\pi}{2} ),~sin(0),~tan(\pi)[/tex]
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Suppose ÐABC = 60o. If ÐABC is bisected, each of the new angles would be __________.
Solve the system of equations using the linear combination method.
{9x+5y=35
{2x+5y=0
Enter your answers in the boxes.
x =_
y =_
Which three lengths CANNOT be the lengths of the sides of a triangle?
Question 2 options:
A. 21 m, 6 m, 10 m
B. 11 m, 11 m, 12 m
C. 23 m, 17 m, 14 m
D. 5 m, 7 m, 8 m