A function that gives the length of the hypotenuse of an isosceles right triangle with side length s is given by h(s)=s√2 and the length of the side of the triangle is approximately 4.24 inches.
The hypotenuse of a right angled triangle is defined as the longest side of the triangle. The hypotenuse is also located opposite the right angle.
From the Pythagorean Theorem we know that for a right angled triangle, the sum of the square of the legs of the triangle is equal to the square of the hypotenuse.
Given legs of the right triangle is s. Let us consider a function h(s) for the hypotenuse.
Therefore we can define the function h(s) as
h(s)=s√2
The inverse of the function can be written as
y=s√2
or, s=y²/2
Hence the inverse function is:
h⁻¹(s)=s²/2
Now for hypotenuse = 6 inches.
Each side can be calculated using the inverse function h⁻¹(s)=s²/2.
s=6÷√2
or, s=4.242...
Hence the length of the side of the triangle is approximately 4.24 inches.
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Find the inverse of each function. Is the inverse a function? f(x)=√x+3-4
The inverse of the function is x²+8x+13
In mathematics, an inverse function is a arithmetic operator that "reverses" another function: if the function f applied to an input x gives a result of y, then applying its inverse function g to y provides the result x, and contrariwise, i.e., f(x) = y if and only if g = x.
To get the inverse of any function f(x) [ just make sure that it passes the horizontal line test] follow the steps:- Solve for x, i.e separate x in one side and the other terms in the other side, included f(x).-
Swap x and f(x).-
The result is the inverse of the original function .
y=√x+3-4
y+4=√x+3
on squaring with sides we get
y²+16+8y=x+3
y²+8y+13=x
swapping x And y we get y=x²+8x+13
f inverse x =x²+8x+13
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17. For what values of x and y is quadrilateral ABCD a
parallelogram?
a.
b.
C.
d.
D
4y+20
9x-40
x = 12, y = 3
x = 6, y = 12
x = 6, y = 3
x = 74, y = 105
C
8x-34
6x-4
The values of x and y that makes quadrilateral ABCD a parallelogram are x = 9 and y = 3
How to determine the values of x and y?The figure that completes the question is added as an attachment
The opposite sides of a parallelogram are congruent
This means that
5x - 20 = 7x - 38
4y + 11 = 6x - 31
So, we have
5x - 20 = 7x - 38
Collect the like terms
7x - 5x = 38 - 20
Evaluate the like terms
2x = 18
Divide through by 2
x = 9
Substitute x = 9 in 4y + 11 = 6x - 31
So, we have
4y + 11 = 6 x 9 - 31
Evaluate the product
So, we have
4y + 11 = 23
This gives
4y = 12
So, we have
y = 3
Hence, the values of x and y that makes quadrilateral ABCD a parallelogram are x = 9 and y = 3
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If you want to bisect a line segment, what would be the order of the following steps?
If you are aware of the line's length or have access to a ruler, bisecting (or cutting in half) a line is not difficult. However, you can still cut the line in half with a straightedge and compass even if you don't know how long it is.
Draw the section of the line you need to divide. You must use a straightedge to create the line segment if it is not already present. Put the compass needle on either terminal to accomplish this. Approximately half of the length should be covered by the compass when it is opened.
Using the compass, aim to keep the needle on the endpoint and refrain from changing the compass's setting. To do this, position your straightedge on the intersection of the arcs above the line and line them up with the intersection below the line. The line is bisected at a 90-degree angle by the line you draw connecting the two arc intersections.
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What is each expression written as a single natural logarithm?
(b) 3 ln x-2 ln 2 x
Expression written as a single natural logarithm 3 ln x-2 ln 2 x is [tex]ln(x^{} )[/tex] .
What is natural logarithm?3 ln x-2 ln 2 x is
= [tex]ln x^{3} - lnx^{2}[/tex]
= [tex]ln(x^{3} /x^{2} )[/tex]
=[tex]ln(x^{} )[/tex]
The inverse of an exponential function, the natural log is the logarithm to the base of the number e. Natural logarithms are unique varieties of logarithms that are employed in the treatment of time and growth-related issues.
The distinction between log and ln is that log is expressed in terms of base 10, while ln is expressed in terms of base e. As an illustration, log of base 2 is denoted by log2 and log of base e by loge = ln (natural log).
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Please help now ASAP pleaseee
pls help w this pretty urgent
Answer:
[tex]\begin{aligned} \textsf{a)} \quad & \textsf{Position function}: \quad s(t) = -16t^2+1362 \\ & \textsf{Velocity function}: \quad v(t) = -32t\end{aligned}[/tex]
[tex]\textsf{b)} \quad \overline{v}=-48\:\: \sf ft/s[/tex]
[tex]\begin{aligned}\textsf{c)} \quad v(1) & = -32\:\: \sf ft/s\\ v(2) & = -64\:\: \sf ft/s\end{aligned}[/tex]
[tex]\textsf{d)} \quad t = 9.226\:\: \sf s \:\: (3\: d.p.)[/tex]
[tex]\textsf{e)} \quad v = -292.242\:\: \sf ft/s \:\: (3\: d.p.)[/tex]
Step-by-step explanation:
Given:
[tex]s(t)=-16t^2+v_0t+s_0[/tex]
Part (a)If v₀ is the initial velocity, and s₀ is the initial position:
[tex]\implies v_0=0[/tex]
[tex]\implies s_0=1362[/tex]
Therefore:
[tex]\begin{aligned}\textsf{Position function}: \quad s(t) & =-16t^2+0+1362\\ \implies s(t) & = -16t^2+1362 \end{aligned}[/tex]
[tex]\begin{aligned}\textsf{Velocity function}: \quad v(t)&=s\:'(t)\\ \implies v(t) &=-32t\end{aligned}[/tex]
Part (b)Average velocity is the change in displacement divided by the change in time:
[tex]\overline{v}=\dfrac{s(t_2)-s(t_1)}{t_2-t_1}[/tex]
Given interval: 1 ≤ t ≤ 2
[tex]\implies t_1=1[/tex]
[tex]\implies t_2=2[/tex]
Find the values of s(t) at t = 1 and t = 2:
[tex]\implies s(1)=-16(1)^2+1362=1346[/tex]
[tex]\implies s(2)=-16(2)^2+1362=1298[/tex]
Substitute the values into the formula:
[tex]\overline{v}=\dfrac{s(2)-s(1)}{2-1}=\dfrac{1298-1346}{2-1}=-48\:\: \sf ft/s[/tex]
Part (c)To find the velocity at t = 1 and t = 2, substitute these values into the velocity function found in part (a):
[tex]\implies v(1)=-32(1)=-32\:\: \sf ft/s[/tex]
[tex]\implies v(2)=-32(2)=-64\:\: \sf ft/s[/tex]
Part (d)The time required for the coin to reach ground level is when s(t) = 0:
[tex]\begin{aligned}s(t) & = 0\\-16t^2+1362 & = 0\\16t^2 & = 1362\\t^2 & = 85.125\\t & = \sqrt{85.125}\\t & = 9.226\: \sf s\:\:(3\:d.p.)\end{aligned}[/tex]
Part (e)To find the velocity of the coin at impact with the ground, substitute the found value of t from part (d) into the equation for velocity found in part (a):
[tex]\begin{aligned}v(t) & = -32t\\\implies v(\sqrt{85.125}) & = -32(\sqrt{85.125})\\ v & =-295.242\:\: \sf ft/s\:\:(3\:d.p.)\end{aligned}[/tex]
Note: I have used the non-rounded value of t from part (d) for accuracy.
Help I shall need to thou problem.
Answer: I got 48
Step-by-step explanation: to find the length of the larger square, 4+2+2=8, 8x10=80, plus the smaller squares on each side equal to (4x2)x2=16, and 80+16=96. 1/2 of 96 is 48
I hope this helps you! (☞ﾟヮﾟ)☞
Answer:
The correct answer is 48.
Step-by-step explanation:
Hope this helped!Dont forget to hit that Brainliest button!
What is the rational expression in simplest form? State any restrictions on the variables.
b. x² + 2 x-8 / x²-5 x+6
The required simplification of rational expression is (4 + x) / (x - 3).
What is a rational number?
Any real number that can be represented in the form of p/q, where q is not equal to 0 is called a rational number. The decimal expansion of rational numbers is terminating and repeating.
Simplifying the rational expression: x² + 2x - 8 / x² - 5x + 6
Given a rational expression,
x² + 2x - 8 / x² - 5x + 6
On simplifying, we get,
For numerator, x² + 2x - 8: (x - 2)(x + 4)
For denominator, x² - 5x + 6: (x - 2)(x - 3)
Now, x² + 2x - 8 / x² - 5x + 6 = (x - 2)(4 + x) / (x - 2)(x - 3)
= (4 + x) / (x - 3)
Restriction is that the denominator, x - 3 should not be 0.
Hence, the required simplification of rational expression is (4 + x) / (x - 3)
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HELP PLS IM CONFUSED
Use long division to convert 3 4/5 to a decimal.
Answer:3.8
Step-by-step explanation:
3.8
A rectangular classroom is 9 feet wide. It is five times as long as it is wide. What is the perimeter of the classroom?
The perimeter of rectangular classroom with its length five times its width is 108 ft.
What is a Rectangle?Rectangle is two - dimensional shape with four sides such that the pair of two opposite sides are equal and parallel to each other.
Given is the width of rectangular classroom which is 9 ft wide. Its length is five times its width. From this, we can write -
Width [W] = 9 ft
Length [L] = 5W = 5 x 9 = 45 ft
The perimeter of rectangle is the sum of the length of its sides. Therefore, the perimeter [P] of the rectangle will be -
[P] = 2(L + W) = 2(9 + 45) = 2 x 54 = 108 ft
Therefore, the perimeter of rectangle with its length five times its width is 108 ft.
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What is 0.34 times 0.02
Answer:
0.0068
Step-by-step explanation:
i had this question
Melinda is at tennis practice. She hits 32 tennis balls a minute. She hit 45 tennis balls before practice. If Melinda hit a total of 1,645 tennis balls, how long was she at practice?
If Melinda hit a total of 1,645 tennis balls and she hits 32 balls per minute, it means she has been in the tennis practice for 50 minutes
How many of the hits of 1645 are attributable to only practice?
Out of the 1645 tennis balls so far hit by Melinda only 1,600 are attributable to the tennis practice because she has already hit 45 tennis balls before the tennis practice commenced
number of tennis balls in tennis practice=1645-45
number of tennis balls in tennis practice=1600
number of minutest at practice=1600/32
number of minutest at practice=50 minutes
In essence, Melinda has been at the practice for 50 minutes
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Lin knows that there are 4 quarts in a gallon. She wants to convert 6 quarts to gallons, but she can’t decide if she should multiply 6 by 4 or divide 6 by 4 to find her answer. What should she do? Explain your reasoning.
Lin knows that there are 4 quarts in a gallon. To figure out how many gallons are in six quarts, she should divide six by four.
This is further explained below.
What should she do?Generally, The unitary method is an approach to problem-solving that involves first determining the value of a single unit and then determining the component values by multiplying the value of the single unit by itself.
6 qs=0.25* 6gallons
6=1.5gallons
In conclusion, in order to calculate how many gallons are in six quarts, she needs to divide six by four.
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The perimeter P of a triangle is equal to the sum of the lengths of sides AB and C
Answer:
P = a + b + c
Step-by-step explanation:
A triangle has 3 sides. Perimeter is the measurement of the length around a shape. If you add sides A, B, and C, you will get the perimeter. You can also find a missing side by subtracting two known sides of the triangle if you know the perimeter.
Convert 20 mi/hour to feet per second (5280 feet = 1 mile)
Answer:
d'accord est-ce moi ou pas la même chose que j'ai fait
Answer:
29.33333... feet per second
Step-by-step explanation:
20×5280=105600 Because 1 mi=5280ft, you multiply 20 by 5280
105600÷60=1760 You divide 105600 by 60 because there are 60 minutes in an hour
1760 ÷ 60 You divide it by 60 again because there are 60 seconds in a minute
Your answer is 29.33333...
Part H
PLEASE HELP !!
Complete the table to find the rule for the dilation, the coordinates of trapezoid P′Q′R′S′, and the coordinates of the dilated image, trapezoid P″Q″R″S″
given coordinates dilated coordinates
p' ( 4, 6 ) p'' ( 4, -6 )
Q' ( 2, 2 ) Q'' ( 2, -2 )
R' ( 6, 2 ) R'' ( 6, -2 )
S' ( 6, 6 ) S'' ( 6, -6 )
Given data
p' ( 4, 6 )
Q' ( 2, 2 )
R' ( 6, 2 )
S' ( 6, 6 )
How to find the coordinates of the dilated image trapezoid P″Q″R″S″ using the rule in the tableThe given coordinates is gotten by ( x, y ) and the coordinates is gotten to be ( x, -y ). Applying the rule is solve as follows:
given coordinates dilated coordinates
( x, y ) ( x, -y )
p' ( 4, 6 ) p'' ( 4, -6 )
Q' ( 2, 2 ) Q'' ( 2, -2 )
R' ( 6, 2 ) R'' ( 6, -2 )
S' ( 6, 6 ) S'' ( 6, -6 )
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!!!!Please help!!! I am dying!!
Answer:
Therefore (x,y)=(3,7)
Step-by-step explanation:
put the second equation into the first
x+4=3x-2
x-3x=-2-4
-2x=-6
x=3
plug x=3 into the second equation
y=3+4=7
What is the solution? √x+11=4
1800 people attended a football game. If 5% of the people who attended were
teenagers, how many teenagers attended the game?
Answer:
90
Step-by-step explanation:
Espero que te ayude :)
Answer:
90
Step-by-step explanation:
1800 x 0.05 = 90
Hope this helps :)
PLEASE HELP GEOMETRY HIGH SCHOOL
Select all the statements about the diagram that you cannot conclude.
The statements about the diagram that can be concluded, includes;
[tex] \overleftrightarrow{AB}[/tex] intersects [tex] \overleftrightarrow{CD}[/tex][tex] \overleftrightarrow{HC} \perp \overleftrightarrow{ CD}[/tex][tex] \overleftrightarrow{FA} \perp \overleftrightarrow{ CD}[/tex]How can the statements that cannot be concluded be found?The first statement that cannot be concluded is the option;
[tex] \overleftrightarrow{AB}[/tex]
intersects [tex]\overleftrightarrow{CD}[/tex]
[tex] \overleftrightarrow{AB}[/tex] is on plane T, [tex]\overleftrightarrow{CD}[/tex] is on plane S
[tex]\overleftrightarrow{AB}[/tex] is offset from [tex]\overleftrightarrow{CD}[/tex] by [tex] \overline{BC}[/tex]
Therefore;
[tex]\overleftrightarrow{AB}[/tex] cannot intersect [tex]\overleftrightarrow{CD}[/tex]
The second statement that cannot be concluded is the option;
[tex] \overleftrightarrow{HC} \perp \overleftrightarrow{ CD}[/tex]
The angle [tex] \angle {DCH} [/tex] appears more to be obtuse than 90° such that [tex] \overleftrightarrow{HC} [/tex] cannot be [tex] \perp [/tex] to [tex]\overleftrightarrow{ CD}[/tex]
The third statement that cannot be concluded is the option;
[tex] \overleftrightarrow{FA} \perp \overleftrightarrow{ CD}[/tex]
The reason the above statement cannot be concluded is that [tex] \overleftrightarrow{FA} [/tex] and [tex] \overleftrightarrow{ CD}[/tex] are lines that do not intersect.
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Sofia is a tutor who charges 25 dollars per hour. she would like to earn 440dollars to buy a new gaming console .write am equation to show how much money m sofia makes after working h hours
Answer: 440-25h = m
Step-by-step explanation:
She makes 25 dollars per hour (25h=m)
If u subtract the amount that the console costs the equation becomes
440-25=m
Im assuming u are in 7th grade math which is what i was in last year so i hope this helps! :)
Can some help me please
The function d(t) = 186,000t gives the distance d(t), in miles, that light travels in t seconds.
How far does light travel in 30 seconds?
why would we use m^3 instead of cm^3 to describe the volume of a room?
Answer:
29
Step-by-step explanation:
firat 4 78374748383838
Let f(x)=7 x+5 and g(x)=x² . Perform each function operation and then find the domain of the result.
(f+g)(x)
Function operations are the rules we use to solve functions. There is a specific way to deal with function addition, multiplication, and division.
x² + 7x + 5 is the domain of all real numbers.
What is meant by function operation?Function operations are the rules we use to solve functions. There is a specific way to deal with function addition, multiplication, and division.
Let the two functions be f and g then f(x) = 7x + 5 and g(x) = x².
we have to calculate (f + g)(x)
Which is equivalent to:
(f + g)(x) = f(x) + g(x)
Taking the two functions and substituting them into this expression, we get,
f(x) + g(x) = (7x + 5) + (x²)
simplifying the above function, we get
f(x) + g(x) = x² + 7x + 5
Therefore, (f + g)(x) = x² + 7x + 5.
We must also determine the domain of the new function. However, because this is a second-order function with no denominators, logarithms, or roots, there are no restrictions on the value of x; thus, the domain is all real numbers.
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Divide and simplify -1/6 divided by 2/6
Answer:
-1/2
Step-by-step explanation:
[tex]-\frac{1}{6}[/tex] ÷ [tex]\frac{2}{6}= -\frac{1}{6}[/tex] x [tex]\frac{6}{2} \\[/tex] = [tex]\frac{-6}{-12} =- \frac{1}{2}[/tex]
In the given figure, ABCD is a square of side 14 cm. Find the area of the shaded region. Take π = 2²/2)
Answer:
Step-by-step explanation:
Area of shaded region = Area of Square ABCD− Area of 4 quadrants of circle
Side of square =14cm
Area of Square =(side)
2=(14) 2=196cm 2Radius of circle = half of the side of square = 214=7cmArea of quadrant of circle = 41πr 2
Area of 4 quadrants of circle =4( 41 πr 2)= 722×7×7=154cm 2 Area of shaded region =196−154=42cm 2
Judah worked at the bakery for 14 hours last week. He spent $15 of his earnings on a cake for his father's birthday. If he was left with $156.92 after buying
the cake, what is Judah's hourly wage?
per hour
Answer:
Judah's hourly wage is $7/hr.
Step-by-step explanation:
x=(86+12)/14
x=98/14
x=7
What is the value of each logarithm?
a. log₅125
The answer for the given logarithmic function is 3
Logarithm is a mathematical tool used to make high value calculations simple.
It is the exponent to the power of which a number must be raised to give a certain result.
Some of the important formulas in logarithm are:
loga[tex]b^{n}[/tex] where a is considered as base of the logarithm and b is the argument
is given as nlogab
when base and the argument is same , log is given as 1
logabc where a is the base is given as logab+logc
loga b/c where a is the base is given as logab-logac
Now it is given to us to find the value of log₅125
where 5 is the base and 125 is the argument
125 = 5x5x5 which is [tex]5^{3}[/tex]
hence 125 can be written as 5^3
Thus the logarithmic function becomes
log₅125=log₅[tex]5^{3}[/tex]
thus it can be written as3log₅5
Now we know that log₅5 can also be written as log5/log5
And hence log5/log5 becomes 1
Thus 3log₅5 = 3*1 =3
Hence the answer to the given logarithm is 3
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The teacher kept track of what students drank at a school picnic. For 3 grades, the ratios of the amount of water consumed to the amount of fruit juice consumed were equivalent. Complete the table
Answer:
8 and 12
Step-by-step explanation: