The correct answer is:
A=4
B=5
hopes this helps you and future people!
Answer:
a = 4 and b = 5
Step-by-step explanation:
The simplest form of square root of eighty can be written as:
[tex]\sqrt{80}=\sqrt{2\times2\times2\times2\times5}[/tex]
Now as it is a square root function, we will pair up the four 2's in two pairs.
And will take out [tex]2\times2[/tex] outside the square root.
Making the answer = [tex]2\times2\sqrt{5}[/tex]
or [tex]4\sqrt{5}[/tex]
So, a = 4
and b = 5
Who worthy the book “I love fractions”
Answer for number 5?
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.
The band is selling wrapping paper for a fundraiser. Customers can buy rolls of plain wrapping paper and rolls of shiny wrapping paper. The band sold a total of 55 rolls and made $950. If a roll of plain wrapping paper cost $14 and a roll of shiny cost $20, how many rolls of each did they sell ?
The roll of plain wrapping paper sold is 25.
The roll of shiny wrapping paper sold is 30.
What are the linear equations that represent the question?a + b = 55 equation 1
14a + 20b = 950 equation 2
Where:
a = roll of plain wrapping paper sold
b = roll of shiny wrapping paper sold
What is the roll of shiny wrapping paper sold?Multiply equation 1 by 14
14a + 14b = 770 equation 3
Subtreact equation 3 from equation 2
6b = 180
Divide both sides by 6
b = 30
What is the roll of plain wrapping paper sold?
Subtract 30 from 55
55 - 33 = 25
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Using radicals , write an equivalent expression for the expression 2 1/3
I'm assuming that the 1/3 is an exponent.
If so, then
Which is the cube root of 2. Raising any value to the 1/3 power is the same as taking the cube root.
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:
If a triangle is an obtuse triangle then it can not be an isosceles triangle.
a. True
b. False
If three tangents to a circle form an equilateral triangle, prove that the tangent points form an equilateral triangle inscribed in the circle
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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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
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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An initial investment of $200 is now valued at $350. The annual interest rate is 8% compounded continuously. The equation mc022-1.jpg represents the situation, where t is the number of years the money has been invested. About how long has the money been invested? Use a calculator and round your answer to the nearest whole number.
Answer:
7 years
Step-by-step explanation:
An initial investment of $200 is now valued at $350.
The annual interest rate is 8% compounded continuously.
Formula:
[tex]A=Pe^{rt}[/tex]
Where,
A is amount, A=350
P is principle, P=200
R is rate of interest, r=0.08
t is time, t=?
Substitute the value into formula
[tex]350=200e^{0.08\cdot t}[/tex]
[tex]e^{0.8t}=1.75[/tex]
Taking ln both sides
[tex]0.08t = ln(1.75)[/tex]
[tex]t=6.99\approx 7[/tex]
Hence, 7 years ago money was invested.
Answer:
Its 7 years
Step-by-step explanation:
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.
Seven more than half of the cost , c
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
Consider the diagram. What is the length of segment AB?
we know that
A median of a triangle is a line segment joining a vertex to the midpoint of the opposing side, bisecting it.
In this problem the line DB is a median of triangle ADC
The line DB is also the altitude of a triangle ADC, because is perpendicular to the side AC
so
AB=BC
we have that
[tex]BC=9\ units[/tex]
therefore
[tex]AB=9\ units[/tex]
the answer is the option
[tex]9[/tex]
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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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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Rene has a coupon for $3.25 off a package of name brand cookies that normally costs $7.89. The store brand cookies coats $5.58. How much will Rene save if she uses her coupon and buys the name brand cookies instead of the store brand cookies? HELP
Rene will save $0.94 if she uses her coupon and buys the name brand cookies instead of the store brand cookies.
Explanation:To find out how much Rene will save if she uses her coupon and buys the name brand cookies instead of the store brand cookies, we have to first determine how much the name brand cookies will cost after applying the coupon. We subtract the value of the coupon i.e. $3.25 from the original cost of name brand cookies which is $7.89. The result comes out to be $4.64.
To calculate the savings, we now have to subtract the cost of name brand cookies after coupon ($4.64) from the original cost of the store brand cookies ($5.58). Hence, the savings amount to $5.58 - $4.64 which equals $0.94
So, if Rene uses her coupon and buys the name brand cookies instead of the store brand cookies, she will save $0.94.
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Solve the system of equations using the linear combination method.
{9x+5y=35
{2x+5y=0
Enter your answers in the boxes.
x =_
y =_
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.
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.
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
The perimeter of an equilateral triangle with a side of 6 inches is
12 in.
18 in.
36 in.
negative 1 over 2x + 2 = −x + 7
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.
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°.
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:
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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How do I solve and graph this?