The domain of the function will be; [0 ∞) and the domain is continuous.
What are the domain and range of the function?The domain of the function includes all possible x values of a function, and the range includes all possible y values of the function.
The number c of calories consumed is a function of the number b bars
eaten is represented by the linear function b = 130c
The domain of the linear function would be [0 ∞).
A whole number or a decimal number may be c.
Any data which can be expressed as a decimal is continuous data.
Therefore, the domain of the function will be; [0 ∞) and the domain is continuous.
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Question 3 of 5
A Galapagos penguin can walk mile in an hour. How many hours would it
take the penguin to walk mile?
O A. x = hour
OB. +=
hours
O c.
hour
OD. + hours
-
Answer:
1 hour
Step-by-step explanation:
Since the penguin supposedly walks a 1 mile per hour, it would take one hour to achieve 1 mile
A bag contains 4 blue and 6 white tokens. Two tokens are drawn from the bag one after another, without replacement. Find the probability that: the first is blue and the second is white.
Concept; Probability
Step1: The total number of tokens is
[tex]6\text{white +4 Blue}=\text{ 10 tokens}[/tex]let the probability of blue be P(B) and the probability of red be P(R)
The probability that the first is Blue is
[tex]\begin{gathered} P(B)=\frac{number\text{ of blue }}{total\text{ number of tokens}}=\frac{4}{10}=\frac{2}{5} \\ \end{gathered}[/tex]The probability the second is white without replacement is
[tex]P(R)=\frac{number\text{ of white}}{total\text{ token}}=\frac{6}{9}=\frac{2}{3}[/tex]Hence the combined probability of Blue and Red is
[tex]P(BR)=\frac{2}{5}\times\frac{2}{3}=\frac{4}{15}[/tex]Therefore the probability that the first is blue and the second is white is 4/15
What is (9 x 10^4) (6 x 10^-7)?
Answer:0.0008994
Step-by-step explanation:
What’s the answer plss
The length of XY=19.894 cm when the angle XYZ=90° and angle YZX=61° and the length of hypotenuse=17.4 cm. Using the property of trigonometry, a=b.sinα/sinβ.
What is trigonometry?Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six common trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and abbreviations (csc).
What is Hypotenuse?The longest side of a right-angled triangle, or the side opposite the right angle, is known as the hypotenuse in geometry. The Pythagorean theorem, which states that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides, can be used to determine the length of the hypotenuse.
Here,
a=b.sinα/sinβ
=17.4·sin(90°)/sin(61°)
=19.89436 cm
≈19.9 cm
When the hypotenuse is 17.4 cm long and the angles XYZ and YZX are 90° and 61°, respectively, the length of XY is 19.894 cm. Using the trigonometric formula a=b.sinα/sinβ.
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The graphs below have the same shape. What is the equation of the blue graph? G(x) = _ A. G(x) = x2 + 5 B. G(x) = (x + 5)2 C. G(x) = x2 - 5 D. G(x) = (x - 5)2
The blue graph is represented by the equation g(x) = (x - 5)²
How to determine the equation represented by the blue graph?The possible graph that completes the question is added as an attachment
From the attached graph, we have the following parameters
Red graph = f(x)Blue graph = g(x)Also from the graph, we have the equation of the function f(x) to be
f(x) = x²
Solving further, we can see that:
The function g(x) is on the same level as the function f(x) Also, the function has the same size as .f(x)The only difference is that, f(x) is shifted to the right by 5 units
This means that
g(x) = f(x - 5)
So, we have
g(x) = (x - 5)²
Hence, the blue graph equation is g(x) = (x - 5)²
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Choose the number and type of roots of each quadratic function.
Function
f(x)=x²-9x + 21
f(x) = x² + 16x - 64
f(x) = -4x²-4x²10x +84
f(x) = 3x² + 24
The number and type of roots of each quadratic function are:
f(x) = x² - 9·x + 21, Has complex rootsf(x) = x² + 16·x - 64 has two real and distinct rootsf(x) = -4·x² + 10·x + 84 has two real and distinct rootsf(x) = 3·x² + 24 has complex rootsWhat determines the type of root that a quadratic function has?The type of roots of a quadratic function is given by the value of the discriminant, which is the value under the square root of the quadratic formula.
The types of roots of a quadratic equation are;
Two real and distinct rootsTwo real and equal rootsComplex rootsThe roots or solution to the quadratic equation, a·x² + b·x + c = 0, are given by the quadratic formula, [tex]x = \dfrac{-b\pm \sqrt{b^2 - 4\cdot a \cdot c} }{2\cdot a}[/tex]
Where:
b² - 4·a·c is known as the discriminant of the quadratic equation.
The type of root of a quadratic equation is given by the discriminant, b² - 4·a·c, as follows:
If the discriminant, b² - 4·a·c is less than 0, then the quadratic equation has no roots or no real rootsIf b² - 4·a·c = 0, then the quadratic equation has two real and equal roots (or one real root)If the discriminant, b² - 4·a·c > 0, then the quadratic equation has two real and distinct roots.The given functions are:
f(x) = x² - 9·x + 21Comparing the above equation to the, general form of a quadratic equation, f(x) = a·x² + b·x + c, we have;
a = 1, b = -9, and c = 21
The discriminant is therefore, (-9)² - 4 × 1 × 21 = -3 < 0
The quadratic equation therefore, has complex roots.
f(x) = x² + 16·x - 64The quadratic equation, f(x) = x² + 16·x - 64 has a discriminant given as follows;
The discriminant is: 16² - 4 × 1 × (-64) = 512 > 0, therefore, the quadratic equation two real roots, given by the equation;
[tex]x = \dfrac{-16\pm \sqrt{16^2 - 4\times 1 \times 64} }{2\times 1}= \dfrac{-16\pm \sqrt{512} }{2}= \dfrac{-16\pm 16\cdot \sqrt{2} }{2}[/tex]
x = -8 + 8·√2 or x = -8 - 8·√2
f(x) = -4x² + 10·x + 84The value of the discriminant is 10² - 4 × (-4) × 84 = 1444 > 0, therefore, the equation has two real and distinct roots, given by the equation;[tex]x = \dfrac{-10\pm \sqrt{1444} }{2\times (-4)}= \dfrac{-10\pm 38 }{-8}[/tex]
[tex]x = \dfrac{28 }{-8}= -3.5[/tex] and [tex]x = \dfrac{-48 }{-8}= 6[/tex]
f(x) = 3·x² + 24The discriminant of the above quadratic equation is; 0² - 4 × 3 ×24 = -288 < 0
Therefore, the quadratic equation, f(x) = 3·x² + 24, has no real roots or complex roots
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Find the values of Y and X
Find the radius of a cylinder whose height is 10 cm and the total surface area is 352 cm².
Answer: the radius of a cylinder is 4 cm
Step-by-step explanation:
[tex]S_{ts}=352\ cm\ \ \ \ H=10\ cm\ \ \ \ \ r=?[/tex]
The total surface area:
[tex]\displaystyle\\ S_{ts}= 2\pi r^2+2\pi rH\\\\S_{ts}=2\pi (r^2+rH)\\\\352=2\pi (r^2+10r)\\\\[/tex]
Divide both parts of the equation by 2π:
[tex]\displaystyle\\56=r^2+10r\\\\56-56=r^2+10r-56\\\\0=r^2+10r-56\\\\Thus,\\\\ r^2+10r-56=0\\\\D=(-10)^2-4(1)(-56)\\\\D=100+224\\\\D=324\\\\\sqrt{D}=\sqrt{324} \\\\\sqrt{D}=18\\\\ r=\frac{-10б18}{2(1)} \\\\r=-14\notin\ (r > 0)\\\\r=4\ cm[/tex]
Answer:
r ≈ 4 cm
Step-by-step explanation:
Total Surface Area of a cylinder
A = Base Area x 2 + Lateral Surface Area
A = 2(πr²) + 2πrh
where r = radius of base and h = height of cylinder
Solving for r we get
[tex]\displaystyle r = \dfrac{1}{2} \sqrt{h^2 + 2 \dfrac{A}{\pi} }-\dfrac{h}{2}\\\\[/tex]
Given h = 10 cm and A = 325 we get
[tex]\displaystyle r = \dfrac{1}{2} \sqrt{10^2 + 2 \dfrac{352}{\pi} }-\dfrac{10}{2}\\\\\\[/tex]
[tex]\sqrt{10^2 + 2 \dfrac{352}{\pi} } =\sqrt{100+\dfrac{704}{\pi }}\\\\= \sqrt{100 + 224.09}\\\\\\[/tex]
= [tex]\sqrt{324.09}[/tex]
= 18.0025
1/2 x 18.0025 ≈ 9
So r ≈ 9 - 10/2 = 9 -5 = 4
r ≈ 4 cm
When and where does the story The circuit take place?
Answer:
Mexico to the United States in 1947
Step-by-step explanation:
8b^2 + 56b + 48 = 0
Solve for X
Answer:
b= -1, -6
Step-by-step explanation:
divide by common factor
then use x=- b+- sqrt b^2-4ac/2a
separate the equations and solve them
The length of a rectangle is 3 inches greater than the width. (Hint: draw a pictureand label itA. Write a polynomial that represents the area of the rectangle.B. Find the area of the rectangle when the width is 4 inches..
We are given that the length of a rectangle is 3 inches greater than the width.
Let us draw a rectangle and label the width and length.
Part A:
Let the width of the rectangle is x inches.
Then the length of the rectangle is (x + 3) inches.
Now recall that the area of a rectangle is given by
[tex]A=L\cdot W[/tex]Where L is the length and W is the width of the rectangle.
[tex]\begin{gathered} A=(x+3)\cdot x \\ A=x^2+3x \end{gathered}[/tex]Therefore, the above polynomial represents the area of the rectangle.
Part B:
We are given that the width is 4 inches.
Substitute the width (x = 4) into the equation of the area that we found in part A.
[tex]\begin{gathered} A=x^2+3x \\ A=(4)^2+3(4) \\ A=16+12 \\ A=28in^2 \end{gathered}[/tex]Therefore, the area of the rectangle is 28 square inches.
an industrial manufacturing company uses an inverted conical (cone-shaped) tank to dispense liquid into containers. the tank measure 24 inches with a base radius of 48 inches. if the liquid flows out of the tank at a rate of 40 cubic inches per minute, at what rate is the height of the liquid falling when the height of the liquid is 10 inches deep?
If the liquid flows out of the tank at a rate of 40 cubic inches per minute, the height of the liquid will decrease at rate 0.0318 in./minute
Referring to the attached picture, the two triangles in a cone are similar. Hence,
r/h = 48/24
or
r = 2h.
The volume of the liquid is given by:
V = 1/3 . πr²h
Substitute r = 2h,
V = 1/3 . π(2h)²h = 4/3 . πh³
Take the derivative with respect to t
dV/dt = 4/3 . 3πh² . dh/dt
dV/dt = 4 . πh² . dh/dt
Substitute dV/dt = -40 and h = 10
-40 = 4 . π(10)² . dh/dt
dh/dt = - 0.0318 in./minute
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Find the measure of each angle in the diagram
A bacterial colony starts with 120 cells and quadruples in size each day. Write an equation that relates the population of cells in this colony (P) at the start of each day and the number of days (d). Find the population on day 8.
Answer:
P = 120*([tex]2^{2d-2}[/tex])P(8) = 1, 966, 080Step-by-step explanation:
Since the population quadruples each day, the population for the subsequent day would be 4*(population of the previous day).
Thus, the evolution of the population value takes the form of a geometric progression, with a common ratio, r = 4
The n-th term of a geometric progression is given by:
[tex]a_{n}[/tex] = [tex]ar^{n-1}[/tex] (1)
Where a is the 1st term of the progression.
From (1), our population would generally take the form:
[tex]P_{d}[/tex] = [tex]P_0r^{d-1}[/tex] (2)
In this case, the initial value (1st term) [tex]P_{0}[/tex] = 120.
So putting r and [tex]P_{0}[/tex] into (2):
P(d) = 120*([tex]4^{d-1}[/tex])
Noting that 4 = 2²:
P(d) = 120*([tex]2^{2(d-1)}[/tex])
P(d) = 120*([tex]2^{2d-2}[/tex])FOR d = 8:
P(d) = 120*([tex]2^{2d-2}[/tex])
becomes:
P(8) = 120*([tex]2^{2(8)-2}[/tex])
P(8) = 120*([tex]2^{16-2}[/tex])
P(8) = 120*([tex]2^{14}[/tex])
P(8) = 120*(16,384)
P(8) = 1, 966, 080PLEASE HELP NOW DUE AT 11 PM. Are the linear expressions equivalent? Drag the choices to the boxes to correctly complete the table. .
In these linear expressions one is equivalent which is 3- 2( - 2.6x + 2.1) = 5.2x - 1.2 and one is not .
What are linear expressions?An algebraic expression known as a linear expression has terms that are either constants or variables raised to the first power.
Alternatively pluging; we will see that none of the exponents can be greater than 1.
2x - 3(1.3x - 2.5) = 5.9x + 7.5
2x -3.9x + 7.5 = 5.9 + 7.5
-1.9x + 7.5 ≠ 5.9 + 7.5
thus linear expression is not equivalent.
3- 2( - 2.6x + 2.1) = 5.2x - 1.2
3 + 5.2x - 4.2 = 5.2x - 1.2
5.2x - 1.2 = 5.2x - 1.2
thus, linear expression is equivalent.
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A ball is thrown directly upward from a height of 7 ft with an initial velocity of 28 ft/sec. The function s(t)= -16t+28t+7 gives the height of the ball, in feet, t seconds after it has been thrown. Determine the time at which the ball reaches the maximum height and find the maximum height.
Answer:
Brainliest Answer?
( 7 / 8 ) seconds
( 77 / 4 ) feet
Step-by-step explanation:
The question is a bit confusing but I will do it both ways. I will assume that you made a mistake copying over the function because the graph s( t ) is linear. Linear functions have a maximum value of infinity because it is an odd-degree polynomial.
AlgebraAssume that s( t ) = - 16t² + 28t + 7;
The equation forms an upside-down parabola which means it has a maximum value.
Complete the square to get the axis of symmetry and the maximum value of the parabola or use my very cool formula. The variables h and k represent the axis and max respectively.
Formulaax² + bx + c = a( x - h )² + k;
ax² + bx + c = a( x - ( - b / 2a ) )² + c - ( b² / 4a );
Completing the Squareax² + bx + c;
Take a as a factor.
a( x² + ( b / a )x + ( c / a ) );
Add and subtract the square of ( 1 / 2 ) of ( b / a ). This is called completing the square because it forms a perfect square trinomial.
a( x² + ( b / a )x + ( b / 2a )² - ( b / 2a )² + ( c / a ) );
Factorise the trinomial.
a( ( x + ( b / 2a ) )² - ( b / 2a )² + ( c / a ) );
Use the distributive property of multiplication.
a( x + ( b / 2a )² + a( ( c / a ) - ( b / 2a )² );
a( x + ( b / 2a )² + a( ( c / a ) - ( b² / 4a² ) );
Simplify the fractions.
a( x + ( b / 2a )² + c - ( b² / 4a );
SolutionSubstitute the values.
- 16( t - ( - 28 / 2( - 16 ) )² + 7 - ( ( 28 )² / 4( - 16 ) );
Time is the x-axis so we need to solve for the axis of symmetry.
h = ( - 28 / 2( - 16 ) );
h = ( - 28 / - 32 );
Simplify the fraction.
h = ( 7 / 8 );
Maximum height is the parabola's y of the vertex.
k = 7 - ( ( 28 )² / 4( - 16 ) );
k = 7 - ( ( 28 )( 28 ) / - 64 );
k = 7 - ( 784 / - 64 );
k = 7 - ( - 49 / 4 );
k = ( 28 / 4 ) + ( 49 / 4 );
k = 77 / 4;
PLEASE HELP!!!!!!!!! It’s algebra
Answer:
See below
Step-by-step explanation:
From 5 to 10 mugs is 5 mugs
These cost 110 - 67.50 = 42.50
So each mug costs 42.50 / 5 = 8.50 each
With a 'base cost' of 25 dollars
(Base cost might be artwork, design, order processing, shipping or whatever.....but this amount is added to each order)
(As a check 20 mugs would be 25 + 20 (8.50) = 195 <====yep
150 mugs will then be 25 + 150 ( 8.50) = 1300 dollars
Rain fell at a rate of .25 inches per hour. Before the rain began, 6 inches had already fallen that month. At this rate, how much total rain will have fallen after 4 hours?
Answer:
y=.25x+6
Step-by-step explanation:
Given: ZADB = ZCBD ZABDZCDB m ZA= 3x + 15 mZC=8x-20 Find: x and m ZA A4 D B
Answer:
x = 7 , ∠ A = 36°
Step-by-step explanation:
since ∠ ADB ≅ ∠ CBD ( alternate angles )
and ∠ ABD ≅ ∠ CDB ( alternate angles )
then ABCD is a parallelogram
the opposite angles of a parallelogram are congruent , so
∠ C = ∠ A , that is
8x - 20 = 3x + 15 ( subtract 3x from both sides )
5x - 20 = 15 ( add 20 to both sides )
5x = 35 ( divide both sides by 5 )
x = 7
Then
∠ A = 3x + 15 = 3(7) + 15 = 21 + 15 = 36°
Answer: x = 7 and m∠A = 36
Step-by-step explanation:
Here ∠ADB ≅ ∠CBD and ∠ABD ≅ ∠CDB
This configuration is found when a quadrilateral has two parallel sides which have a diagonal as their transversal. Thus the figure is of parallelogram. In a parallelogram, opposite angles are equal. Thus m∠A = m∠C
⇒3x +15 = 8x - 20
⇒3x + 15 - 3x = 8x - 3x -20
⇒5x = 20 + 15
⇒x = 7
Now m∠A = (3X7) +15 = 36
triangle RST had coordinates: R(-2, 1) S(-8, 2) T(-4, 5) Draw the translation of RST 8 units right and 4 units down on your recording sheet. what are 3 coordinates of R'A. R'(-3, 6)B. R'(0, -2) C. R'(6, -3) D. R'(4, 1)
Since the translation is 8 units right and 4 units down, we have to add 8 to the x coordinate and subtract 4 to the y coordinate.
R=(-2,1)
R' = (-2+8,1-4)= (6,-3)
R' = (6,-3)
f(x)= x-6/2
g(x)=√x-4
Express the function gf in the form gf(x) = ...
Give your answer as simply as possible.
The function is given below
What is a function?
The value of a function f at an element x of its domain is indicated by f(x); the numerical value resulting from the function evaluation at a given input value is expressed by substituting x with this value; for example, the value of f at x = 4 is denoted by f(x) (4). When the function is not named and is represented by an expression E, the function's value at, say, x = 4 can be expressed by E|x=4. In science, engineering, and the bulk of the mathematical disciplines, functions are commonly used. Functions are claimed to be "the central objects of research" in most branches of mathematics.
The given function is
f(x) = x - 6/2
The function in gf is
g{f(x)} = √(x - 6/2) - 4
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The value of the required composite function is [tex]g(f(x))=\sqrt{x-\frac{6}{2} } -4[/tex].
What is a composite function?
When the result of one function is utilized as the input for another, a composite function is created.
Given that:
[tex]f(x)=x-\frac{6}{2}[/tex] and [tex]g(x)=\sqrt{x}-4[/tex]
To find the composite function [tex]g(f(x))[/tex], it is required to use the output of the first function as the input of the second function. It means that replace [tex]x[/tex] by [tex]f(x)[/tex] in the second function as:
[tex]g(x)=\sqrt{x}-4\\g(f(x))=\sqrt{f(x)}-4[/tex]
Now, substitute the value of [tex]f(x)[/tex] on the right side of the above equation as:
[tex]g(f(x))=\sqrt{x-\frac{6}{2}}-4[/tex]
Hence, the required answer is:
[tex]g(f(x))=\sqrt{x-\frac{6}{2}}-4[/tex]
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Part of the proceeds from a garage sale was 535$ worth of 5$ and 20$ bills. If there were 2 more 5$ bills than 20$ bills, find the number of each denomination
Using concept of Linear equation in two variables, we got 23 is denomination count of 5$ bills and 21 is denomination count of 20$ bills.
Linear equations are used to solve equation in which two variables are connected with each other via some specific methods.
The linear equations in two variables are the equations in which each one of the two variables are of the highest exponent order of the 1 and have one, none, or may be infinitely many solutions. The standard form of a two-variable linear equation is given by ax + by + c = 0 where x and y are the two variables. The solutions can also be written in form of ordered pairs like (x, y).
It is given that 5$ bills are 2 more than 20$ bills,
so let suppose 20$ bills denomination count is x,
then 5$ bills denomination count=x+2;
It is also given that 535$ worth is summation of 5$ bills and 20$ bills
Therefore,[5×(x+2)+(20×x)]=535
On solving for x, we get x=21
Therfore,20$ bills denomination count is 21,and 5$ bills denomination count is 23.
Hence,5$ bills denomination count is 23 and 20$ bills denomination count is 21
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pulse rates of adult females are normally distributed with a mean of 74.0 beats per minute (bpm) and a standard deviation of 12.5 bpm. what is the percentage of adult females with pulse rates between 49.0 bpm and 86.5 bpm? what percentage of adult females have pulse rates below 90 bpm?
The percentage of adult females with pulse rates between 49.0 bpm and 86.5 bpm - 81.86%
The percentage of adult females have pulse rates below 90 bpm - 89.97%
a)
X ~ N ( µ = 74 , σ = 12.5 )
P ( 49 < X < 86.5 )
Standardizing the value
Z = ( X - µ ) / σ
Z = ( 49 - 74 ) / 12.5
Z = -2
Z = ( 86.5 - 74 ) / 12.5
Z = 1
P ( -2 < Z < 1 )
P ( 49 < X < 86.5 ) = P ( Z < 1 ) - P ( Z < -2 )
P ( 49 < X < 86.5 ) = 0.8413 - 0.0228
P ( 49 < X < 86.5 ) = 0.8186 ≈ 81.86%
b)
X ~ N ( µ = 74 , σ = 12.5 )
P ( X < 90 )
Standardizing the value
Z = ( X - µ ) / σ
Z = ( 90 - 74 ) / 12.5
Z = 1.28
P ( ( X - µ ) / σ ) < ( 90 - 74 ) / 12.5 )
P ( X < 90 ) = P ( Z < 1.28 )
P ( X < 90 ) = 0.8997 ≈ 89.97%
What is pulse rate ?
The pulse rate, or the number of times the heart beats each minute, is gauged by the pulse rate. The arteries enlarge and constrict with the flow of blood as the heart pumps blood through them. An elevated heart rate, or tachycardia, can occur for any reason. Exercise-induced or stress-related heart rate increases are two possible causes (sinus tachycardia). Sinus tachycardia is not seen as an illness but rather a symptom. Another factor contributing to tachycardia is an unsteady heartbeat (arrhythmia).
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Do You Like Guns N' Roses, If So, What Is Your Favorite Song?
Answer:golden hour by JVKE
Step-by-step explanation:
it is decided that this barrel must be painted pink and the barrel's surface area is requested in order to determine the amount of paint needed. what is the surface area of the barrel g
The surface area of the barrel needs to be calculated in order to determine the amount of paint. The surface area of the barrel, including the lid, is 13 m²
Missing data from the problem:
radius of the barrel = 0.4 meters
height of the barrel = 1.2 meters
The shape of a barrel is cylinder. The surface area of the barrel, including the lid) is:
A = 2. πr² + 2. πr.h
Where:
r = radius
h = height
Plug the parameters into the formula:
A = 2. π(0.4)² + 2. π(0.4).(1.2)
A = 13 m²
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3/4+(1/2+1/4) 2⋅2
NEED HELP.
Answer:
15/8 for exact form
1.875 for decimal form
And
1 and 7/8 for mixed number form
hope this helps you!
(also already in the simplest form :)
Either Table A or Table B shows a proportional relationship.
Plot the points from the table that shows a proportional relationship.
Table A shows a proportional relationship
What is proportional relationship?
When the value of independent variable changes the value of dependent variable changes. that means if the value independent variables is increase the value of dependent variable will also be increased.
In the figure we are given 2 tables
We plot both the curve on the graph we get
Table A shows a linear relationship where are Table b Does not shows a proportional relationship
Hence Table A shows a proportional relationship
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Answer:
Step-by-step explanation:
What is the number sentence for "4 and N together make9"?
Given:
The number sentence for 4 and n
Required:
We have to find the given sentence
Explanation:
4 and N, simply means you mixed them up, you sum them up
your result is 9, 4+N=9
Required solution :
4+N=9
In a race, Kara ran eight- eighteenths of a kilometer and cycled sixteen-eighteenths of a kilometer. Estimate how many kilometers the race was in all.
a) 1/2 kilometer
b) 1 kilometer
c) 1 1/2 kilometers
d) 2 kilometers
Number of kilometers the race was in all is [tex]1\frac{1}{3}[/tex] kilometers.
Given that, Kara ran 8/18 of a kilometer and cycled 16/18 of a kilometer.
What is addition of two fractions?To add two fractions, with different denominators, we need to rationalise the denominators by taking out the LCM and make the denominator same. Then add the numerators of the fractions, keeping the denominator common.
Now, total distance in race
8/18 + 16/18
= (8+16)/18
= 24/18
= 4/3
= [tex]1\frac{1}{3}[/tex] kilometers
Therefore, number of kilometers the race was in all is [tex]1\frac{1}{3}[/tex] kilometers.
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150 14 Solve for x. Round to the nearest tenth. 63.5 54.1 3.6 74.9
The given triangle is a right angled triangle having the follwoing sides;
Hypotenuse = x (longest side)
Opposite = 14 (side facing the given acute angle)
Theta = 15 degrees
Using the SOH trigonometry identity;
sin 15 = opposite/hypotenuse
sin15 = 14/x
x = 14/sin15
x = 14/0.2588
x = 54.09
x is approximately equal to 54.1. Option B is coorect