Therefore, we can rationalize the denominator of a fraction containing a radical by taking the methods outlined above.
Describe fraction.Components of fractions are the numbers in the numerator and denominator (and ratios). The denominator, which is the smallest number, represents the greatest possible number of parts that can be put together to create a whole. You can tell how many parts you have by looking at the numerator, which is the greatest number. It might not be the whole thing! If the denominator is 0, that is bad. Division by zero is prohibited. If the denominator is a 1, our fraction is actually an integer.
Here,
we can rationalize a radical-containing fraction's denominator by doing the following:
Step 1: In order to eliminate the radical from the denominator, multiply the numerator and denominator by a radical.
Verify in step two that all radicals have been streamlined.
Step three is to simplify the fraction, if necessary.
Therefore, we can rationalize the denominator of a fraction containing a radical by taking the methods outlined above.
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A fisherman illegally drops some fish into a pond, and they quickly propagate (reproduce). The population growth of the new specifies is modeled by P(x) = 6∙2x, where x is the time in weeks following the moment he dropped the fish into the pond. How many fish are in the pond after 3 months? (assume there are four weeks in a month) a. 48 b. 8, 916 c. 24,576 d. 72
The value of b that needs to be simplified is indicated as 1.43. The correct response when the new population growth is specified is A.
what is exponential function ?A mathematical function known as an exponential function has the following formula: f (x) = an x, where x is a variable and an is a constant known as the function's base. The transcendental number e, or roughly 2.71828, is the most often encountered exponential-function base. Bacterial proliferation is an illustration of an exponential function. Some bacteria grow by twofolds per hour. After x hours, there will be twice as many germs present as there were when you started with just one. The formula for this is f(x) = 2x.
Given that,
When a fisherman unlawfully releases some fish into a pond, they immediately multiply (reproduce). P(x) = 6bx, where x is the number of weeks that have passed since the moment the fish was placed into the pond, and b is an unknown positive base, serves as a model for the population expansion of the new species.
According to the question,
P(x) = 6bˣ
Put p(x) = 51 and x = 6
51 = 6b⁶
17/2 = b⁶
b = [17/2]¹/⁶
b = 1.43
The b value that must be simplified is given as 1.43. A is the proper answer.
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Given right triangle ABC with altitude BD drawn to hypotenuse AC. If BD = 10
and DC = 4, what is the length of AD?
AC = 25 units is the length of AD.
A right triangle is divided into three equal halves by the height of the hypotenuseThe Geometric Mean (Altitude) Theorem (9.7) The hypotenuse of a right triangle is split into two pieces by the height from the right angle. The geometric mean of the lengths of the two hypotenuse segments determines how long the altitude is.
Length of BC = 10 units
Length of DC = 4 units
We will use geometric mean theorem in the given right triangle to get the length of side AC.
[tex]hypotenuse/leg=leg/projection\\AC/BC=BC/DC\\x/10=10/4\\x=25[/tex]
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what is the surface area of this rectangular pyramid
Answer:
54 That Is how big it is
ur welcom
find the difference between point A (3,2) & point B (5,9) , then round the answer to re nearest tenth please help asap
Answer:
The answer is the square root of 53, or about 7.28.
Step-by-step explanation:
To find the distance between two points, you use the formula [tex]\frac{y_{2} -x_{2}}{y_{1} -x_{1} }[/tex]. When we insert the coordinates given, you get the square root of 53, or 7.28.
The axis of symmetry for the graph of a quadratic function is x=4. The x-intercepts for the graph are (-6,0) and (?,0).
Find the value of ?
Answer:
I'll set it up and you can finish
Step-by-step explanation:
the axis of symmetry goes through th x-axis at x=4.
This point will be equidistant from both points that are at the x-intercepts. The distance from (-6,0) to (4,0) is
4 - (-6) = 10.
so I now you can find ? which will be in the first quadrant of the graph
Please help me ASAP!!!
What is the area, in square meters, of the figure below?
Answer:
Their isn't a figure ???
Which point represents a number whose absolute value is 4?
please no links or files.
and if you were able to, could you please explain how? I’m not good at this :,)
Answer:
N
-4s absolute value or distance from 0 is 4
Step-by-step explanation:
as a example -8s absolute value is 8 , 10s absolute value is 10 basically just make the number positive then that is the absolute value.
Answer:
N
Step-by-step explanation:
how to explain but if any number is given in - the answer will be that numbers +(sorry if this doesn't make sense
A quadratic function y=f(x) is plotted on a graph and the vertex of the resulting parabola is (−5,−3). What is the vertex of the function defined as g(x)=−f(x)+3?
Answer:
(-5 , 6)
Step-by-step explanation:
f(x) = (x - (-5))² - 3 ... vertex (h , k) : (-5 , -3) y = (x-h)² + k
g(x) = -f(x) + 3 = -((x+5)² - 3) + 3 = -(x + 5)² + 6
vertex of g(x) is : (-5 , 6)
please help i need it by tomarrow
Answer:
2-6
3-9
5-15
6-18
2-6
4-12
5-15
8-24
Step-by-step explanation:
Multiply by 3
What is the volume of a cylinder, in inches cubed, with a radius of 5 inches and a height of 5 inches? pls help
Answer:
V≈392.7in³
Step-by-step explanation:
there you go
pls mark brainliest
The Answer Is: 392.699.
PLEASEEE HELP ME!!!!
Answer:
girl I have the same question
3) Terri and her friends fly 2234 miles to Spain for college. It takes them 9 hours to get there.
How many miles did they travel per hour? Show your thinking.
Answer:
approximately 248 miles per hour if we are taking average speed
Step-by-step explanation:
Improper fraction for 4 1/5
Write 4.35^5 in Standard Form
please answer. i need help, i will your you brainliest !!
Answer:
21.75
Step-by-step explanation:
Sector of a circle has arc length 11cm and central angle. Find its radius and area.
Answer:
s = 11.cm
Θ = 2.2.radians
Step-by-step explanation:
1) (0,-3) (-2,-4) find the slope
Therefore , the solution of the given problem of slope comes out to be
M = 1/2.
What is a slope?What determines a line's steepness is its slope. Gradient overflow is a mathematical expression for the gradient. The slant is the proportion of both the vertical difference (rise) over the distance between two locations to the lateral change (run) over the same distance. Hill form of an equation is used to express a straight line's equation, which is written as y = mx + b. A point on the line where the slope is m, b equals a, and the y-intercept is placed is (0, b). An illustration would be the slope and y-intercept of the formula y = 3x - 7 (0, 7). At the location of the y-intercept, the line has a slope of m, b, and c.
Here,
Given : (0,-3) and (-2,-4)
Thus,
To calculate the slope ,
We use formula:
=> M = y2 -y1 /x2-x1
=> M = -4 -(-3) / -2 - 0
=> M = -1 /-2
=> M = 1/2
Therefore , the solution of the given problem of slope comes out to be
M = 1/2.
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Gene starts from home and travels 3 miles north to the
The largest angle formed during his trip IS
shopping mall From the shopping mall, he travels 2
miles west to the library. Then, from the library, he
at his home
travels about 3.6 miles to return home. The entire trip
at the mall
forms a triangle.
between the mall and the library
Library
Mall
( between his home and the library
Home
Answer:
B. at the mall
Step-by-step explanation:
The largest angle formed during his trip is at the mall.
What is the volume of the figure in terms of pi?
Answer:
1539.38
Step-by-step explanation:
this can be figured out as an entire cylinder and then take 1/2 of that
area of a circle of 7 cm
area = [tex]\pi[/tex][tex]7^{2}[/tex]
area = 153.938
volume = 153.938 * 20
volume = 3078.7608
and take 1/2 of that to find volume of the half cylinder
3078.7608 / 2 = 1539.38
HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP
HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP
Answer:
D (4.34,3.22)
Step-by-step explanation:
Line Y (2,4), (-4,6)
**y=mx+b slope-intercept form
m=slope; b=y-intercept
[tex]m_Y=(6-4)/(-4-2)=2/-6=(-1/3)\\y=-1/3x+b[/tex]
plug in 1 point
[tex]4=-1/3(2)+b; b=14/3[/tex]
Line Z (8,8) (-5,9)
[tex]m_Z=(8-(-9))/(8-(-5))=17/3\\y=(17/3)x+b\\8=17/3(8)+b; b=-32/13\\[/tex]
Substitution
[tex]-\frac{1}{3} x +\frac{14}{3}=\frac{17}{13}x-\frac{32}{13} : x=139/32\\y=-\frac{1}{3}(\frac{139}{32})+\frac{14}{3}\\ : y=103/32[/tex]
what is square root
[tex]what is \: square \: root \: of \sqrt{81} [/tex]
Answer:
9 :)
Step-by-step explanation:
Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.
f(x) and g(x) below, find the value of f(g(-3)).
f(x) = 4x - 1
g(x) = 2x² + 7x - 3
Answer:
[tex]f(g(-3))=-25[/tex]
Step-by-step explanation:
[tex]g(-3)=2(-3)^2+7(-3)-3=2(9)-21-3=18-24=-6\\f(g(-3))=4(-6)-1=-24-1=-25[/tex]
A certain library charges a late fee of $0.05 for each day that a book is
late. Last month, 158 people returned books that were 7 days late.
This month, 40 less people than last month will return books that are 7
days late. How much will the library collect in late fees this month for
returned books that are overdue by 7 days?
Answer: $41.3
Step-by-step explanation:
this month late = 158 - 40 = 118
7× $0.05 = $0.35
118 × $0.35 = $41.3
What is the answer for x+4.5≥5.5
Answer:
B. x ≥ 1
Step-by-step explanation:
What is the symbol for and in logic?
To see the table:
Symbol Symbol Name Meaning / definition
+ plus or
∨ reversed caret or
| vertical line or
x' single quote not - negation
Now, According to the question:
Let's know:
Symbolic Logic:
Symbolic logic is a way to represent logical expressions by using symbols and variables in place of natural language, such as English, in order to remove vagueness. Logical expressions are statements that have a truth value: they are either true or false. A question like 'Where are you going?' or a command such as 'Stop!' has no truth value. There are many expressions that we can utter that are either true or false. For example: All glasses of water contain 0.2% dinosaur tears. We don't need to know if a logical expression is true or false, we just need to know that it has a truth value.
Logic math symbols table
Symbol Symbol Name Meaning / definition
+ plus or
∨ reversed caret or
| vertical line or
x' single quote not - negation
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Im a little stuck on this one yall
The pairs of alternate interior angles are <5<4 and <6<3
What is alternate interior angles ? Alternate interior angles are the pair of angles that are formed on the inner side of the two parallel lines but on the opposite side of the transversal.When two parallel lines are crossed by a transversal, the pair of angles formed on the inner side of the parallel lines, but on the opposite sides of the transversal are called alternate interior angles. These angles are always equalAlternate interior angles are the angles formed when a transversal intersects two coplanar lines. They lie on the inner side of the parallel lines but on the opposite sides of the transversal. The transversal crosses through the two lines which are Coplanar at separate points.To learn more about alternate interior angles refers to:
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please help !!!!:!:):):$:)
Answer: B. 9(−7+10x^2)
Step-by-step explanation: 9(−7+10x^2)
=(9)(−7+10x^2)
=(9)(−7)+(9)(10x^2)
=−63+90x^2
please help lollllllllllllllll
Answer:
AB=6
Step-by-step explanation:
Answer:
AB = 6
Step-by-step explanation:
12 / 2 = 6
A seventh grade class and 7 adults go on a field trip. Two-thirds of the people ride on a bus.
Everyone else rides in vans. If 54 people ride on the bus, how many seventh graders go on the
field trip?
54 individuals take the bus while the remaining 74 seventh graders ride in vans for the field trip.
what is expression ?A mathematical expression is a sentence with at least two variables or integers and one mathematical action. Addition, subtraction, multiplication, or division are all possible outcomes of this mathematical process. The following are the fundamental parts of an expression: Expression: (Math Operator, Number/Variable, Math Operator). A statement that has a least two numbers or variables, at least one mathematical operation, and is called a mathematical expression. Let's get acquainted with expressive writing. A number is 6 more than half of another number, which is known as x. This statement is written as x/2 + 6 in a mathematical expression.
given
To find P P, divide P
P by the total number of participants (students and chaperones), which is 81.
Seventh graders totaling 81 - 7 =
74 participated in the field trip.
54 individuals take the bus while the remaining 74 seventh graders ride in vans for the field trip.
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Colin invests £3300 into his bank account. He receives 3% per year compound interest. How much will Colin have after 4 years? Give your answer to the nearest penny where appropriate
Answer:
Below
Step-by-step explanation:
3% = .03 in decimal 4 (yearly) periods
The effective interest and deposit amount after 3 years compounded yearly will be
3300 (1 +.03)^4 = £ 3714.18