After the conversion, we get T² = 1/3 A
It is given that
T = [tex]A^{\frac{3}{2} }[/tex]
We have to convert the equation without rational exponents
T³ = A²
1/2 T = A³
T² = A³
T² = 1/3A
Therefore we get T² = 1/3 A without using the exponents.
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Just 16 and 17 please!
Answer:
1(7-6)1/6
Step-by-step explanation:
Convert the polar equation to rectangular form and identify the graph. Support your answer by sketching the graph. Show and explain your work.
The polar equation r = - 4 · cos θ is equivalent to the equation of the circle (x + 2)² + y² = 2², whose radius is 2 and center is (h, k) = (- 2, 0).
How to transform a polar expression into its rectangular formPolar and rectangular forms are related by this relation: (x, y) → (r · cos θ, r · sin θ), where r is the radial distance with respect to the origin and θ is the angle in standard position. We can use this fact to change the given expression into its rectangular form:
r = - 4 · (x / r)
r² = - 4 · x
x² + y² = - 4 · x
y² = - (x² + 4 · x)
y² - 4 = - (x² + 4 · x + 4)
y² - 4 = - (x + 2)²
(x + 2)² + y² = 4
(x + 2)² + y² = 2²
In a nutshell, the polar equation r = - 4 · cos θ is equivalent to the equation of the circle (x + 2)² + y² = 2², whose radius is 2 and center is (h, k) = (- 2, 0).
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Divide using synthetic division. (4x² + 3x³ + 9x− -20) + (x + 2)
The synthetic division solution of (4x² + 3x³ + 9x− -20) / (x + 2) is mathematically given as
3x^2-2x+13-(6/x+2)
This is further explained below.
What is synthetic division?Generally, Synthetic division is a technique that may be used to manually conduct Euclidean division of polynomials.
Compared to long division, the synthetic division requires less writing and fewer calculations to complete. The approach is most often taught for dividing by linear monic polynomials; however, it may be extended to divide by any polynomial.
In conclusion, The synthetic division solution is mathematically given as
3x^2-2x+13-(6/x+2)
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PLEASE ANSWER
Simplify the expression -4 1/6 - -6 1/3 Explain your solution using the additive inverse property.
The Additive Inverse is -32/6
Additive Inverse of Real Numbers:
The given number can be whole number, a natural number, an integer, a fraction, a decimal, or any real number. The additive inverse of real numbers is just the negative of the given number.
What is Additive Inverse?
Additive Inverse simply means changing the sign of the number and adding it to original number to get an answer is equal to 0.
Now, Come to the question:
Expression is : [tex]-4\frac{1}{6} -(-6)\frac{1}{3}[/tex]
Solve it : [tex]\frac{-25}{6}-\frac{(-19)}{3}[/tex]
Taking the L.C.M
=[tex]\frac{-25+57}{6}[/tex]
=32/6
Additive inverse of 32/6 is -32/6
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Need help with this asap
Answer: x=21, y=8
Step-by-step explanation:
18y+5=10x-61 ==> 18y+5 and 10x-61 are congruent angle, so they're equal
x+10+10x-61=180 ==> x+10 and 10x-61 are supplementary angles since they're on a straight line(a straight line measures 180 degrees and is called a straight angle), so they add up to 180 degrees.
x+10x+10-61=180
11x-51=180
11x=231
x=21
18y+5=10(21)-61
18y+5=210-61
18y+5=149
18y=144
y=8
(Please someone help me!)
The ordered pair we are looking for is the values of the variables [tex]x[/tex] and [tex]y[/tex], or [tex](x, y).[/tex] We are given that [tex]x=2[/tex], and that the formula to evaluate [tex]y[/tex] is [tex]y = 5^x[/tex]. Note we are given [tex]x[/tex] so we can evaluate [tex]y[/tex] as [tex]y = 5^2 = 25[/tex]. Now, we have both the values of [tex]x[/tex] and [tex]y[/tex], so our ordered pair is thus [tex](x,y) = (2,25).[/tex]
Determine whether the relation is a function. Explain. x y 4 –5 –1 –10 0 –9 1 –7 9 1 Multiple choice question. cross out A) Yes; for each element of the domain, there is only one element of the range. cross out B) Yes; for each element of the range, there is only one element of the domain. cross out C) No; the element 1 is in both the domain and the range. cross out D) No; for each element of the domain, there is not only one element of the range.
It is not a function because: C) the element 1 is in both the domain and the range.
What makes a Relation a Function?A relation can be defined as a function if each of the domain values each has exactly one corresponding range value. This means that an element of the domain must not have two different elements from the range that it is related or corresponded to.
In the given function, 1 as an element of the domain is related to two different range elements, 10 and 7. This doesn't satisfy a function property.
Therefore, we can state that: it is not a function because: C) the element 1 is in both the domain and the range.
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On a map , 1 inch represents 50 miles. You measure the distance on the map between two towns as 3 1 2 inches. How many miles apart are the towns?
The towns are 15600 miles apart.
WHAT IS MAP SCALE ?The term "map scale" refers to the proportion between a distance on a map and its corresponding distance on the ground. Lets see an example like, On a map with a scale of 1:100,000, one kilometer on the ground is equivalent to one centimeter. The scale of a map refers to the proportion between a distance on a map and its actual distance on the ground. This simple concept is complicated by the fact that scale must vary across a map due to the curvature of the Earth's surface. The concept of size is now important in two different ways as a result of this development.
The size of the producing globe is compared to the size of the Earth in the first technique. a theoretical globe known as the generating globe, upon which the map is projected and the Earth is compressed. The ratio of the size of the Earth to that of the generating globe is known as the nominal scale, also known as the major scale or representative fraction.
CALCULATION∵ 1 inch = 50 miles on the map
∴ 312 inches = 312 * 50 = 15600 miles .
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The real solutions to the equation 3x5 + 25x4 + 26x3 – 82x2 + 76x = 48 are shown on the graph. What are the nonreal solutions? StartFraction 1 + i StartRoot 5 EndRoot Over 3 EndFraction, StartFraction 1 minus i StartRoot 5 EndRoot Over 3 EndFraction. StartFraction negative 1 + i StartRoot 5 EndRoot Over 3 EndFraction, StartFraction negative 1 minus i StartRoot 5 EndRoot Over 3 EndFraction. StartFraction negative 1 + StartRoot 5 EndRoot Over 3 EndFraction, StartFraction negative 1 minus StartRoot 5 EndRoot Over 3 EndFraction. StartFraction 1 + StartRoot 5 EndRoot Over 3 EndFraction, StartFraction 1 minus StartRoot 5 EndRoot Over 3 EndFraction.
Using the Factor Theorem, the non-real solutions are given as follows:
[tex]\frac{1 + \sqrt{5}i}{3}, \frac{1 - \sqrt{5}i}{3}[/tex]
What is the Factor Theorem?The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
In which a is the leading coefficient.
For this problem, the function is:
f(x) = 3x^5 + 25x^4 + 26x³ - 82x² + 76x - 48.
The function can be written as:
f(x) = g(x)h(x).
In which:
g(x) is the polynomial with the real solutions.h(x) is the polynomial with the non-real solutions.Using a calculator, as the graph is not given, the real solutions are given as follows:
[tex]x_1 = -6, x_2 = -4, x_3 = 1[/tex]
Hence:
g(x) = (x + 6)(x + 4)(x - 1)
g(x) = (x² + 10x + 24)(x - 1)
g(x) = x³ + 9x² + 14x - 24.
f(x) is of degree 5, g(x) of degree 3, hence h(x) is of degree 2 and:
f(x) = g(x)h(x)
3x^5 + 25x^4 + 26x³ - 82x² + 76x - 48 = (x³ + 9x² + 14x - 24)(ax² + bx + c)
Hence:
ax^5 = 3^5 -> a = 3.-24c = -48 -> c = 2.-24bx + 14cx = 76x
-24b + 28 = 76
-24b = 48
b = -2.
Then the equation with the non-real solutions is:
h(x) = 3x² - 2x + 2.
Which is a quadratic equation with coefficients a = 3, b = -2 and c = 2, thus:
[tex]\Delta = b^2 - 4ac = (-2)^2 - 4(3)(2) = -20[/tex][tex]x_1 = \frac{2 + \sqrt{-20}}{6} = \frac{2 + 2\sqrt{5}i}{6} = \frac{1 + \sqrt{5}i}{3}[/tex][tex]x_2 = \frac{2 - \sqrt{-20}}{6} = \frac{2 - 2\sqrt{5}i}{6} = \frac{1 - \sqrt{5}i}{3}[/tex]Hence the non-real solutions are:
[tex]\frac{1 + \sqrt{5}i}{3}, \frac{1 - \sqrt{5}i}{3}[/tex]
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solve for y -2(x + 3y) = 18
Answer:
[tex] \sf\large \: y = \frac{ - 1}{3} x - 3[/tex]
Step-by-step explanation:
Let's solve for y.
−2(x+3y)=18
Step 1: Add 2x to both sides.
−2x−6y+2x=18+2x
−6y=2x+18
Step 2: Divide both sides by -6.
−6y/−6 = 2x+18/−6
y= −1/3x−3
One number is six less than three times another number. If the sum of the numbers is 38, find the numbers
Answer:
consider the two number as x and y
first given condition
x-6 = 3y
i.e. x= 3y + 6 eqn 1
second given condition
x+ y = 38
i.e. x= 38-y eqn 2
solving eqn 1 and 2
3y + 6 = 38-y
3y + y = 38-6
4y = 32
y = 8
substituting the value of y in eqn 2
x = 38 - y
x= 38-8
x= 30
hence the required numbers are 8 and 30
A recipe for oatmeal cookies calls for 5 cups of flour for every 8 cups of oatmeal. How much flour is needed for a big batch of cookies that used 16 cups of oatmeal?
Answer:
10 cups
Step-by-step explanation:
Since 16 cups is twice 8 cups, it needs twice 5 cups of flour which is 10 cups.
We can also use a proportion.
5/8 = x/16
8x = 5 × 16
x = 5 × 2
x = 10
Answer: 10 cups
The width of a rectangle measures (10p - 9p) centimeters, and it’s length measures (7p + 8p) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?
Answer:
c
Step-by-step explanation:
write the function whose graph is the graph of y=x^2 but is translated 9 units to thre left
Answer:
y= (x+9)^2
Step-by-step explanation:
If h<0 ( negative) then it shifts to the right, if it is is h>0 ( positive number) then it shift to the left!
y = x2
Shift 2 units left: y = (x+2)2
Then, shift up 9 units: y = (x+2)2 + 9
Then, reflect in the x-axis: y = -(x+2)2 - 9
someone help me please its for a practice
Answer:
5a,3a
Step-by-step explanation:
Given 4x=12x+22 prove x=-4
the required simplified value of given expression 4x = 12x + 32 is x = -4 (hence proved).
Given that,
An expression is given 4x = 12x + 32,
We have to prove x = -4 as of simplified solution.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
4x = 12x + 32
Taking 12x to the left side of the equal sign and it becomes -12x
4x - 12x = 32
Applying subtraction property between 4x and 12
- 8x = 32
Dividing both sides by -6
x = -4
Thus, the required simplified value of the given expression is x = -4 (hence proved).
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can anyone write out step-by-step directions and end up with the solution for this equation
2(3b - 2) = 2(2b + 12)
One way to solve is to follow these steps
2(3b - 2) = 2(2b + 12)
2*3b - 2*2 = 2*2b + 2*12
6b - 4 = 4b + 24
6b-4b = 24+4
2b = 28
b = 28/2
b = 14
Final answer: b = 14Select all the correct answers.
If a figure is a square, its diagonals divide it into isosceles triangles.
p: A figure is a square.
q: A figure's diagonals divide into isosceles triangles.
Which represents the converse of this statement? Is the converse true?
0
0
0
The converse of the statement is sometimes true and sometimes false.
q+p
The converse of the statement is false.
The converse of the statement is true.
9-P
P-9
O ~p~9
Answer:
q arrow p, and p arrow q
Step-by-step explanation:
edmentum
please help i have a timer
Answer: 56.25 of 70% and 93.75pints of 90%
Step-by-step explanation: First find the ratios. One juice is 70% and the other is 95%. Your goal is 85%. This is 15% from 70 and 10% from 95. This means you need (15)/(15+10) of 95, which is 3/5 of all the juice to be 95. This means you will need more of the 95% juice, which makes sense because 85 is closer to 95. So 3:5 and total 150=56.25 of 70% and 93.75pints of 90%
Create a formula for a function f (x) that has f (9 )= 10. Do not give a simple constant function (like f (x) = 10 ) as your answer.
f(x)=x+1 is a formula for a function f(x) that has f(9)=10
What is a simple definition for function?
A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input
a constant function is a function whose (output) value is the same for every input value. For example, the function y(x) = 10 is a constant function because the value of y(x) is 10 regardless of the input value x
if we take f(x)= x+1
then put x=9 we get f(9)= 10
Hence , f(x)=x+1 is a formula for a function f(x) that has f(9)=10
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The Taj Mahal is an enormous ivory-white marble monument in India that is known for
its architecture. More than 2 x 104 workers were involved in building the Taj Mahal.
Which number shows another way to express 2 x 10¹?
Answer:the iconic Indian building named Taj Mahal
Step-by-step explanation:
Pie/Circle Graph: As a wildlife biologist, one of your duties is to catch, tag, and
release different species of mammals found in Oak Mountain, Alabama. Use
the data provided below to determine the percentage of each mammal
species caught and then label the different sections found in the pie graph
provided. During a 24 hour period, six cotton mice were caught, nine Norway
rats, 17 pine voles, and two eastern chipmunks.
Six cotton mice has 64%, nine Norway rats has 95%, 17 pine voles has 180%, and two eastern chipmunks has 21% were taken in a 24-hour period from the pie chart.
Given that,
In the figure there is a chart pie chart with 4 parts and 4 colors.
Six cotton mice, nine Norway rats, 17 pine voles, and two eastern chipmunks were taken in a 24-hour period.
We have to find by use the information below to calculate the percentage of each species of captured mammal, and then use that information to name the various pie-shaped sections.
Each value must be converted into a circle's angle for the pie chart.
Total=6+9+17+2=34
Cotton mice=(6/34)×360°=64°
Norway rats=(9/34)×360°=95°
Pine voles=(17/34)×360°=180°
Eastern chipmunks=(2/34)×360°=21°
Therefore, Six cotton mice has 64%, nine Norway rats has 95%, 17 pine voles has 180%, and two eastern chipmunks has 21%.
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Given the equation x(x - 1)²(x + 5)³, the degree is
07
0 3
05
6
Answer:
Dear Friend
the answer is 6
Step-by-step explanation:
Just see the highest possible degree x in each term being multiplied and add the degree
that is
x has a degree 1
(x-1)² has a highest possible x degree as 2
for (x+5)³ it is 3
1+2+3=6
What must be subtracted from x² + 2x - 3 to get 2x² - 4
The term (- x² + 2x + 1 ) must be subtracted from (x² + 2x - 3) to get
(2x² - 4).
Here,
We have to find the number which must be subtracted from x² + 2x - 3 to get 2x² - 4.
What is Number system?
A system of writing to express the number is called number system.
Now,
Let 'a' must be subtracted from x² + 2x - 3 to get 2x² - 4.
It can be written as;
(x² + 2x - 3) - a = 2x² - 4
a = (x² + 2x - 3) - (2x² - 4)
a = x² + 2x - 3 - 2x² + 4
a = - x² + 2x + 1
Therefore, The term (- x² + 2x + 1 ) must be subtracted from x² + 2x - 3 to get 2x² - 4.
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Round 67536 to the nearest hundred
Answer:
67,500
Step-by-step explanation:
i think this is the answer.
Answer: 67500
This is because 536 is closer to 500 than it is to 600
find the median 2.5,2.3,2.3,1.8,2.3,1.5
Answer:2.1
Step-by-step explanation:
i added them then divided by 7
[(10-9+8)-7] + [6-((5+4] ÷ 3)] ² - 1
Answer:
10
Step-by-step explanation:
1 Simplify 10-910−9 to 11.
1+8-7+{(6-(5+4)\div 3)}^{2}-1
1+8−7+(6−(5+4)÷3)
2
−1
2 Simplify 5+45+4 to 99.
1+8-7+{(6-9\div 3)}^{2}-1
1+8−7+(6−9÷3)
2
−1
3 Simplify 9\div 39÷3 to 33.
1+8-7+{(6-3)}^{2}-1
1+8−7+(6−3)
2
−1
4 Simplify 6-36−3 to 33.
1+8-7+{3}^{2}-1
1+8−7+3
2
−1
5 Simplify {3}^{2}3
2
to 99.
1+8-7+9-1
1+8−7+9−1
6 Simplify 1+81+8 to 99.
9-7+9-1
9−7+9−1
7 Simplify 9-79−7 to 22.
2+9-1
2+9−1
8 Simplify 2+92+9 to 1111.
11-1
11−1
9 Simplify.
10
K
Monica's car will go 455 miles on 17.5 gallons of gasoline in highway driving.
a) How many gallons will it take to drive 2629 miles from her house to a friend's house?
b) How far can the car be driven on 139 gallons of gasoline?
***
Which graph is a parabola?
Step-by-step explanation:
THE THIRD GRAPH IS THE PARABOLA!
HOPE THIS HELPS!
Use the graph to determine a. the function's domain; b. the function's range; c. the x-intercepts, if any; d. the y-intercept, if any; and e. the missing function values, indicated by question marks, below.
f(-2) = ? f(2) = ?
The domain is ___. (use interval notation)
From the graph of the function, we have that:
a) The domain is all real values.
b) The range is y ≤ 4.
c) The x-intercepts are x = -4 and x = 1.
d) The y-intercept is y = 3.
e) f(-2) = 3, f(2) = -5.
What are the domain and the range of a function?The domain of a function is the set that contains all the values of the input. In a graph, the domain is composed by the values of x.The range of a function is the set that contains all the values of the output. In a graph, the domain is composed by the values of y.Hence, for this problem:
a) The domain is all real values.
b) The range is y ≤ 4.
What are the intercepts of a function?The x-intercepts of a function are the values of x when f(x) = 0, that is, the values of x for which the function crosses the x-axis.The y-intercept of a function is the values of f(x) when x = 0, that is, the value of y for which the function crosses the y-axis.Hence:
c) The x-intercepts are x = -4 and x = 1.
d) The y-intercept is y = 3.
What are the numeric values?For the graph, when x = -2 y = 3 and when x = 2 y = -5, hence:
f(-2) = 3, f(2) = -5.
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