The height of a woman whose femur (f) measures 49 centimeters is equal to 173.15 centimeters.
What is a function?A function can be defined as a mathematical expression that defines and represents the relationship that exists between two or more variable of a data set.
In order to determine the height of a woman whose femur (f) measures 49 centimeters, we would substitute this numerical value into the first function as follows:
G(f) = 2.57f + 47.22
G(49) = 2.57(49) + 47.22
G(49) = 125.93 + 47.22
G(49) = 173.15 centimeters.
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please help i dont know
The table gives information about the height of some trees draw a histogram for the information of some trees
2.3+2.2y uneed to pus the 2 on the 3 and answer is uten
If an emitter current is changed by 4 mA, the collector current changes by 3.5 mA. The value of beta will be :
change in emitter current, ∆l(E) = 4 mA
change in collector current,∆I(C) = 3.5 mA
To find -:value of B
Solution :-∆I(E) = ∆I(C) + ∆l(B), here ∆l(B) is the change in base current.
4 = 3.5 + ∆l(B)
∆I(B) = 0.5 mA
Now, B = ∆l (C) ÷ ∆l (B)B = 3.5 ÷ 0.5
B = 7.0
so, the value of A = 7.0In function notation, f(x)is used instead of the letter ___ to represent the __________ variable.
In function notation, f(x) is used instead of the letter y to represent the output variable.
How to complete the blanks?A function is represented as:
f(x)
The above means that:
The function of x
As a general rule, the function can be rewritten using the letter y (i.e. the output variable)
Hence, the words that complete the blanks are y and output
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let a and b be roots of x² - 4x + 2 = 0. find the value of a/b² +b/a²
Answer:
[tex]\dfrac a{b^2} + \dfrac b{a^2} = 10[/tex]
Step-by-step explanation:
[tex]\text{Given that, the roots are a,b and } ~ x^2 -4x+2 = 0\\\\\text{So,}\\\\a+b = -\dfrac{-4}1 = 4\\\\ab = \dfrac 21 = 2\\\\\text{Now,}\\\\~~~~~\dfrac a{b^2} + \dfrac b{a^2}\\\\\\=\dfrac{a^3 +b^3}{a^2b^2}\\\\\\=\dfrac{(a+b)^3 -3ab(a+b)}{(ab)^2}\\\\\\=\dfrac{4^3 -3(2)(4)}{2^2}\\\\\\=\dfrac{64-24}{4}\\\\\\=\dfrac{40}{4}\\\\\\=10[/tex]
Answer:
[tex]\dfrac{a}{b^2}+\dfrac{b}{a^2}=10[/tex]
Step-by-step explanation:
Given equation: [tex]x^2-4x+2=0[/tex]
The roots of the given quadratic equation are the values of x when [tex]y=0[/tex].
To find the roots, use the quadratic formula:
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]
Therefore:
[tex]a=1, \quad b=-4, \quad c=2[/tex]
[tex]\begin{aligned}\implies x & =\dfrac{-(-4) \pm \sqrt{(-4)^2-4(1)(2)}}{2(1)}\\& =\dfrac{4 \pm \sqrt{8}}{2}\\& =\dfrac{4 \pm 2\sqrt{2}}{2}\\& =2 \pm \sqrt{2}\end{aligned}[/tex]
[tex]\textsf{Let }a=2+\sqrt{2}[/tex]
[tex]\textsf{Let }b=2-\sqrt{2}[/tex]
Therefore:
[tex]\begin{aligned}\implies \dfrac{a}{b^2}+\dfrac{b}{a^2} & = \dfrac{2+\sqrt{2}}{(2-\sqrt{2})^2}+\dfrac{2-\sqrt{2}}{(2+\sqrt{2})^2}\\\\& = \dfrac{2+\sqrt{2}}{6-4\sqrt{2}}+\dfrac{2-\sqrt{2}}{6+4\sqrt{2}}\\\\& = \dfrac{(2+\sqrt{2})(6+4\sqrt{2})+(2-\sqrt{2})(6-4\sqrt{2})}{(6-4\sqrt{2})(6+4\sqrt{2})}\\\\& = \dfrac{12+8\sqrt{2}+6\sqrt{2}+8+12-8\sqrt{2}-6\sqrt{2}+8}{36+24\sqrt{2}-24\sqrt{2}-32}\\\\& = \dfrac{40}{4}\\\\& = 10\end{aligned}[/tex]
What is the output of this program?
numA = 2
numB = 3
if numA == 2 or numB == 2:
print("yes")
elif numA == 2 and numB == 3:
print("no")
Output:
PLEASE HELP ME PLEASE
Which quadrilateral is not a parallelogram?
Rhombus
O Rectangle
Kite
Square
Answer:
Kite is not a parallelogram
Step-by-step explanation:
The sides aren't evenly lined up properly to be a parallelogram
ANSWER:
kite
STEP BY STEP EXPLANATION
A kite isnerally not a parallogram because it is a quadrilateral whose four sided can be grouped into two pairs of sideame length that arch other
The point −20, 21 is on the terminal arm of an angle = in standard position. Find sin = and cos =.
The point −20, 21 is on the terminal arm of an angle = in standard position. Hence, sinФ = 21/29 and cos Ф = -20/29
What are trigonometric identities?Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.
Given Data
A (-20 , 21)
We have to find sin = ? and cos = ?
The point is in the fourth quadrant
We have the Opposite side and the Adjacent side
Calculate the hypotenuse
c² = (-20)² + (21)²
c² = 400 + 441
c² = 841
c = 29
Hence,
sinФ = 21/29
cos Ф = -20/29
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HELP NEEDED ASAP
answer this question for me, image below
Answer: Heyaa! ~
Your Answer Is... 13
Step-by-step explanation:
385 divided by 28 = 13. 75Reduce the expression, if possible, by cancelling the common factors.Hopefully this helps you! ~
Consider the linear system:
[tex]\overrightarrow y'=\begin{bmatrix}-6 & -4 \\12 & 8\end{bmatrix}\overrightarrow y[/tex]
a. Find the eigenvalues and eigenvectors for the coefficient matrix.
b. For each eigenpair in the previous part, form a solution of [tex]\overrightarrow y' = A\overrightarrow y[/tex]. Use [tex]t[/tex] as the independent variable in your answers.
c. Does the set of solutions you found form a fundamental set (i.e., linearly independent set) of solutions?
a. If A is the coefficient matrix, solve det(A - λI) = 0 for the eigenvalues λ :
[tex]\det\begin{bmatrix}-6-\lambda & -4 \\ 12 & 8-\lambda\end{bmatrix} = (-6-\lambda)(8-\lambda)+48 = 0 \implies \lambda(\lambda-2)=0[/tex]
[tex]\implies \lambda = 0, \lambda = 2[/tex]
Let v = [v₁, v₂]ᵀ be the eigenvector corresponding to λ. Solve Av = λv for v :
[tex]\lambda=0 \implies \begin{bmatrix}-6&-4\\12&8\end{bmatrix}\begin{bmatrix}v_1\\v_2\end{bmatrix} = \begin{bmatrix}0\\0\end{bmatrix} \implies 3v_1 + 2v_2 = 0[/tex]
If we pick v₂ = -3, then v₁ = 2, so [2, -3]ᵀ is the eigenvector for λ = 0.
[tex]\lambda = 2 \implies \begin{bmatrix}-8&-4\\12&6\end{bmatrix}\begin{bmatrix}v_1\\v_2\end{bmatrix} = \begin{bmatrix}0\\0\end{bmatrix} \implies 2v_1 + v_2 = 0[/tex]
Let v₁ = 1, so v₂ = -2.
b. λ = 0 and v = [2, -3]ᵀ contributes a constant solution,
[tex]\vec y_1 = e^{\lambda t} v = \begin{bmatrix}2\\-3\end{bmatrix}[/tex]
while λ = 2 and v = [1, -2]ᵀ contribute a solution of the form
[tex]\vec y_2 = e^{\lambda t} v = e^{2t} \begin{bmatrix}1\\-2\end{bmatrix}[/tex]
c. Yes; compute the Wronskian of the two fundamental solutions:
[tex]W(1, e^{2t}) = \det\begin{bmatrix}1 & e^{2t} \\ 0 & 2e^{2t}\end{bmatrix} = 2e^{2t} \neq 0[/tex]
The Wronskian is non-zero, so the solutions are independent.
with full explanation from the internet like before
1/(x-5)+3/(x+2)=4
Solution :
[tex]x = \frac{4 + \sqrt{43} }{2} .x = 4 + \frac{4 - \sqrt{43} }{2} [/tex]
Step-by-step explanation:[tex] \frac{1}{(x - 5)} + \frac{3}{(x - 2)} - 4[/tex]
1. Multiply by LCM[tex]x = 2 + 3( x - 5) = 4 - (x - 5)(x + 2)[/tex]
2. Solve[tex]x = 2 + 3(x - 5) = 4 (x - 5)(x + 2)[/tex][tex]x = \frac{4 + \sqrt{43} }{2} .x = 4 + \frac{4 - \sqrt{43} }{2} [/tex]3.Verify SolutionsFind undefined (singularity) points : x=5,x=–2[tex]x = \frac{4 + \sqrt{43} }{2} .x = 4 + \frac{4 - \sqrt{43} }{2} [/tex]
[tex]\\ \rm\Rrightarrow \dfrac{1}{x-5}+\dfrac{3}{x+2}=4[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{x+2+3x-15}{(x-5)(x+2)}=4[/tex]
[tex]\\ \rm\Rrightarrow 4x-13=4(x-5)(x+2)[/tex]
[tex]\\ \rm\Rrightarrow 4x-13=4(x(x+2)-5(x+2))[/tex]
[tex]\\ \rm\Rrightarrow 4x-13=4(x^2+2x-5x-10)[/tex]
[tex]\\ \rm\Rrightarrow 4x-13=4(x^2-3x-10)[/tex]
[tex]\\ \rm\Rrightarrow 4x-13=4x^2-12x-40[/tex]
[tex]\\ \rm\Rrightarrow 4x^2-16x-53=0[/tex]
On solving we get
[tex]\\ \rm\Rrightarrow x=2\pm\dfrac{69}{2}[/tex]
Find the quartiles for these data values:
5,7,7,8,10,11,12,15,17
A. Q1=7, Q2=11, Q3=15
B. Q1=7, Q2=10, Q3=13.5
C. Q1=6, Q2=9, Q3=12
D. Q1=7.5, Q2=10.5, Q3=13.5
Q1 = 7, Q2 = 10, Q3 = 13.5
=============================================================
Explanation:
Start with {5,7,7,8,10,11,12,15,17}
Notice how this data set is already sorted for us from smallest to largest.
Cross off the first and last items to get {7,7,8,10,11,12,15}
Repeat the last step to get this smaller set {7,8,10,11,12}
Repeat again: {8,10,11}
Repeat one more time: {10}
The 10 is at the very center, so it is the median aka the value of Q2.
-------------
An alternative way to get the median is to follow these steps:
There are n = 9 numbers in the original set before we crossed off any items. The middle number is in slot 5 because n/2 = 9/2 = 4.5 rounds up to 5. The value in the fifth slot is 10, so 10 is the median.
There are 4 items below the median and 4 items above it, giving n = 4+1+4 = 9 items total.
-------------
Next, break the data set into two smaller groups
L = lower set = every value below the median
L = {5, 7, 7, 8}
U = upper set = every value above the median
U = {11, 12, 15, 17}
The median itself is in neither set L nor set U.
The median of set L is (7+7)/2 = 7, so this is the value of Q1
The median of set U is (12+15)/2 = 13.5 which is the value of Q3
-------------
Summary:
Q1 = 7
Q2 = 10 (aka the median of the original set)
Q3 = 13.5
Answer:
B. Q1=7, Q2=10, Q3=13.5
Step-by-step explanation:
First Solution:
The first quartile of the data set is 7.
The first quartile (or lower quartile or 25th percentile) is the median of the bottom half of the numbers. So, to find the first quartile, we need to place the numbers in value order and find the bottom half.
5 7 7 8 10 11 12 15 17
So, the bottom half is
5 7 7 8
The median of these numbers is 7.
Second Solution:
The median of the data set is 10.
Quartile 2, also known as the median, is the middle number in a sorted list of numbers. So, to find the median, we need to place the numbers in value order and find the middle number.
Ordering the data from least to greatest, we get:
5 7 7 8 10 11 12 15 17
So, the median is 10 .
Third Solution:
The third quartile of the data set is 13.5.
The third quartile (or upper quartile or 75th percentile) is the median of the upper half of the numbers. So, to find the third quartile, we need to place the numbers in value order and find the upper half.
5 7 7 8 10 11 12 15 17
So, the upper half is
11 12 15 17
The median of these numbers is 13.5.
a man is carrying load attached at the end of a stick load placed over his shoulder . show that the pressure at his shoulder is directly proportional to the distance between the shoulder and the load?
According to the above information, it can be stated that the pressure on the man's shoulders is directly proportional to the distance between the shoulder and the load, since the greater the distance he will feel the more weight due to instability.
What is a directly proportional relationship?A directly proportional relationship is a term that refers to the relationship between two variables in which if one of the variables increases, the other also increases.
How is the directly proportional relationship demonstrated in the situation presented?According to the information, it can be inferred that the man will feel more weight on his shoulders if the load is more distant because this causes greater instability on his shoulders, so he will have to make a greater effort to move the load.
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If f(x) = 2x + 3, what is f(–2)?
Substitute -2 for x
[tex]f( - 2) = 2( - 2) + 3 \\ y = - 4 + 3 \\ y = - 1[/tex]
Hope it helps
Please give brainliest
Answer:
-1
Step-by-step explanation:
Hi student! Let me help you out on this question.
_____________________
To find the value of f(-2), we need to stick in -2 for x.
[tex]\mathsf{f(-2)=2\cdot(-2)+3}[/tex]. Multiply first.
[tex]\mathrm{f(-2)=-4+3}[/tex]. Now simplify completely.
[tex]\mathsf{f(-2)=-1}[/tex]. Which is our final answer.
Hope that this helped you out! have a good day ahead.
Best Wishes!
[tex]\star\bigstar\underline{\underline{\overline{\overline{\textsf{Reach far. Aim high. Dream big.}}}}}\bigstar\star[/tex]
◆◈-Greetings!-◆◈
__________________
answer the problem please
Answer: Point C is (-2, -2), which is the third option.
Step-by-step explanation:
The midpoint formula is [tex]m=(\frac{x_{1}+x_{2} }{2},\frac{y_{1}+y_{2} }{2})[/tex]
All we have to do is plug in the numbers and solve the fractions from there.
[tex]m=(\frac{-10+6}{2},\frac{-6+2}{2} )[/tex]
[tex](\frac{-4}{2},\frac{-4}{2} )[/tex]
[tex]m=(-2, -2)[/tex]
I hope this helps!!
Click on the pic there will be the question (very easy I’m just lazy lol)
Answer: ......... 14.85
Step-by-step explanation:
4.95 × 3
...
14.85
bros lazy lol
Findthe domain of the function f(x) = √19-x
Answer:
(-∞,19)
Definition: The domain of a function is the set of input or argument values for which the function is real and defined
Answer:
(-∞, 19]
Step-by-step explanation:
The domain of this function is only true for all real values of f(x).
That means the lower limit of the function is -∞ as the values are positive, and the upper limit is 19, because that is the greatest value it can become before becoming negative.
The domain is : (-∞, 19]
solve for y :
[tex]\longrightarrow \: \bold{3 + y = 18}[/tex]
ty! ~
Answer:
y = 15
Step-by-step explanation:
Given :
3 + y = 18
This a simple algebraic equation.
Subtract 3 from both sides :
⇒ 3 + y - 3 = 18 - 3
⇒ y = 15
Answer:
y = 15
Step-by-step explanation:
Given equation:
3+y=18To Find:
Value of ySolution:
We can rewrite this equation as:
y+3 = 8[This'll ain't change the answer]
Now we could solve on a easy way.
STEPS:
Transpose +3 to the RHS, make sure to change it's sign from “+” to “-”.
=> y = 18-3
Subtract the integers which's on the RHS:
=> y = 15
Hence,the value of y will be 15.
[tex] \rule{225pt}{2pt}[/tex]
The sum of the three interior angles of a triangle is 180°. Suppose one angle is 68° and the remaining two angles are the same measure. Reason numerically to find the measures of the remaining angles.
Answer:
56°Step-by-step explanation:
Let ∠A and ∠B and ∠C.
be the three interior angles of the triangle.
∠A + ∠B + ∠C = 180
If ∠A = 68 and ∠B = ∠C .
Then
∠B + ∠C = 180 - 68 = 112
Then
2∠B = 112
Then
∠B = 112 ÷ 2 = 56°
6 children were jumping rope.
5 children joined them.
2 children left because the line was too long.
How many children were jumping rope then
Answer:
9 children were jumping then.
Step-by-step explanation:
6+5 equals to 11 - 2 of the children left would equal 9 children left.
Solve 24x ⋅ 321-x = 8x+2
Answer:
[tex]x=2/7695[/tex]
≡ Small number, yes, but the steps explain why x is equal to this.
Step-by-step explanation:
simplify
[tex]24x\cdot 321-x=8x+2\\\left(24\cdot 321\right)x-x=8x+2\\7703x=8x+2[/tex]
group
[tex]7703x=8x+2\\7703x-8x=8~x+2-8x\\7695x=8x+2-8x\\7695x=8x-8x+2\\7695x=2[/tex]
isolate
[tex]7695x=2\\\frac{7695x}{7695}=\frac{2}{7695}\\x=\frac{2}{7695}[/tex]
The fraction is in its simplest form, so that is the final answer.
[tex]\frac{1}{2} (5x - 9 ) = 2 (\frac{1}{3} + 6 )[/tex]
Answer: 103/15
Step-by-step explanation:
We can simplify the right-hand side to be [tex]2 \left(\frac{1}{3}+6 \right)=2 \left(\frac{19}{3} \right)=\frac{38}{3}[/tex].
This means we need to solve:
[tex]\frac{1}{2}(5x-9)=\frac{38}{3}\\5x-9=\frac{76}{3}\\5x=\frac{103}{3}\\x=\boxed{\frac{103}{15}}[/tex]
The linear equation y = 25x describes how far from home Gary is as he drives from Montreal to Miami. Let x represent the number of hours and y represent the number of miles. How far from home is Gary in 12 hours? Graph the equation and tell whether it is linear.The linear equation y = 25x describes how far from home Gary is as he drives from Montreal to Miami. Let × represent the number of hours and y represent the number of miles. How far from home is Gary in 12 hours? Graph the equation and tell whether it is linear.
The distance that Greg is from home after 12 hours is given as follows:
300 miles.
How to calculate the numeric value of a function or of an expression?To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.
The function for this problem is given as follows:
y = 25x.
Hence the distance after 12 hours is given as follows:
y = 25 x 12
y = 300 miles.
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Determinar cuales de las siguientes frases son proposiciones
a) 3+2 = 0 c) ¡Hola!
b) x + 1 = 4 d) Yo estudio
The exercise is designed to test the students knowledge of prepositions. The correct answer thus is (Option D) Yo estudio (which translates) "I study".
What is the explanation for the answer above?To understand the answer, you need to know what a preposition is. A preposition, in simple terms, is a word or group of words that comes before a noun.
The function of a preposition (much like an adjective) is to give clarity to the noun that it precedes.
Let us complete the Preposition phrase to give meaning to it:
"I study Mathematics". Where;
"Mathematics" is the noun;
"I Study" is the prepositional phrase. Hence the correction answer to the question above is Option D.
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FGH and HGJ form a linear pair. Find the measurement of the anglesif FGH=11x and HGJ+(6x-7)
The angles are 121 and 59 degrees, respectively
How to determine the angles?The given parameters are:
FGH = 11x
HGJ = 6x - 7
Linear pair angles add up to 180.
So, we have:
11x + 6x - 7 = 180
Evaluate the like terms
17x = 187
Divide both sides by 17
x = 11
Substitute x = 11 in FGH = 11x and HGJ = 6x - 7
FGH = 11 * 11=121
HGJ = 6 * 11 - 7 = 59
Hence, the angles are 121 and 59 degrees, respectively
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How is the product of 3 and –2 shown using integer tiles?
3 positive tiles and 2 negative tiles.
3 negative tiles and 2 positive tiles.
3 sets of 2 negative tiles.
3 sets of 2 positive tiles.
x²-12x+36
A. (x-6)(x+6)
B. (x+9)(x-4)
C. (x+6)(x+6)
D. (x-6)(x-6)
SUBMIT
Answer:
x²-12x+36
x²-6x-6x+36
x(x-6)-6(x-6)
(x-6)(x-6)
=(x-6)²
I don’t quite understand this problem could someone help me please
Answer:
[tex]\frac{7\sqrt{65}}{65}[/tex]
Step-by-step explanation:
Cosine is the ratio of the side adjacent to the angle and the right triangle hypotenuse.
[tex]cos[/tex] B = [tex]\frac{7}{\sqrt{65}}[/tex] = [tex]\frac{7\sqrt{65}}{65}[/tex]
√324 + 6 √64
what is the answer to this question.
Answer:
66
Step-by-step explanation:
[tex]\sqrt{324} + 6 \sqrt{64}\\\\=\sqrt{18^2} +6 \sqrt{8^2}\\\\=18+6(8)\\\\=18+48\\\\=66[/tex]
Answer:
hmm
Step-by-step explanation:
not enough words to know u steal my points I steal yours kid
Which choice shows 19 + 32 + 11 rewritten correctly using the commutative property and then simplified correctly?
19+43 = 62
19+11+32= 30+32 = 62
11+9+10+32 20+32 = 52
19+11+32 = 30 +43 = 73
The choice shows 19 + 32 + 11 rewritten correctly using the commutative property and then simplified correctly is option B; 19+11+32= 30+32 = 62.
What is the commutative property of addition?The commutative property of addition says that it doesn't matter how we add two numbers, the result of the addition would be same.
For two numbers x and y, we have:
x + y = y + x
WE have given
19 + 32 + 11
The sum would be 62.
We know that by commutative property of addition,
For two numbers x and y,
x + y = y + x
Thus, if we take 3 numbers as a,b and c, then:
c + a + b = c + b + a
Similarly,
19 + 32 + 11 = 19+11+32
= 30+32
= 62
Therefore, the option B is the correct answer.
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