Quadrilateral FGHI is similar to quadrilateral JKLM. Find the measure of side JK. Round your answer to nearest tenth if necessary,
Answers
Answer:
JK ≈ 12.3
Step-by-step explanation:
Since the figures are similar then the ratios of corresponding sides are equal, that is
[tex]\frac{FI}{JM}[/tex] = [tex]\frac{FG}{JK}[/tex] , substitute values
[tex]\frac{59}{26}[/tex] = [tex]\frac{28}{JK}[/tex] ( cross- multiply )
59 JK = 728 ( divide both sides by 59 )
JK ≈ 12.3 ( to the nearest tenth )
Related Questions
Find the Value of x
Answers
Answer:
42
Step-by-step explanation:
(adjacent straight angles sum up to 180)
3x+54=180
x=42
Caroline is going to invest in an account paying an interest rate of 5.2% compounded continuously. How much would Caroline need to invest, to the nearest dollar, for the value of the account to reach $940 in 6 years?
Answers
Answer:
688
Step-by-step explanation:
For delta math
Right angle Trigonometry, please help me solve and explain!
Answers
Answer:
theta = arctan 8/5 = 58 degrees
Step-by-step explanation:
The tangent function relates the angle theta to the two side lengths 5 and 8:
tan theta = 8/5 We need to find the angle, theta.
Using a calculator with the inverse tangent funtion built-in, we find that the angle theta is
theta = arctan 8/5 = 58 degrees.
The sound pressure P for a given sound is given by:
P= 10 log W/ Wo
Its units are decibels (dB). W is the size of a variable energy source (called the sound power), measured in Watts. Wo is the lowest threshold of sound that humans can typically hear. It is a constant given by:
Wo=10^-12 W/m2
a) Find the rate of change of the sound pressure P with respect to time if W=7.2 and dW/dt = 0.5 at some given time t.
b) If the variable sound power W is given by W = t2 +t +1, find the rate of change of the sound pressure P, at time t = 3s.
c) If W = cos 0.2t, find the rate of change of the sound pressure P, at time t = 15 (calculators in radians)
Answers
Answer:
a. 0.302 dB/s
b. 2.34 dB/s
c. 1.24 dB/s
Step-by-step explanation:
a) Find the rate of change of the sound pressure P with respect to time if W=7.2 and dW/dt = 0.5 at some given time t.
Since P = 10log(W/W₀), its rate of change with respect to time is
dP/dt = dP/dW × dW/dt
dP/dW = d[10logW - 10logW₀]/dt
dP/dW = d[10lnW/2.303 - 10logW₀]/dt
= 10/2.303W - 0
= 10/(2.303W)
dP/dt = dP/dW × dW/dt
dP/dt = 10/(2.303W) × dW/dt
Since dW/dt = 0.5 when W = 7.2, then
dP/dt = 10/(2.303 × 7.2) × 0.5
dP/dt = 10/16.5816 × 0.5
dP/dt = 0.603 × 0.5
dP/dt = 0.302 dB/s
b) If the variable sound power W is given by W = t² + t + 1, find the rate of change of the sound pressure P, at time t = 3s.
Since P = 10log(W/W₀), its rate of change with respect to time is
dP/dt = dP/dW × dW/dt
dP/dW = d[10logW - 10logW₀]/dt
dP/dW = d[10lnW/2.303 - 10logW₀]/dt
= 10/2.303W - 0
= 10/(2.303W)
and dW/dt = d(t² + t + 1)/dt = 2t + 1
So, dP/dt = dP/dW × dW/dt
dP/dt = 10/(2.303W) × (2t + 1)
dP/dt = 10(2t + 1)/(2.303W)
dP/dt = 10(2t + 1)/[2.303(t² + t + 1)]
we then substitute t = 3 into the equation
dP/dt = 10(2t + 1)/[2.303(t² + t + 1)]
dP/dt = 10(2(3) + 1)/[2.303((3)² + 3 + 1)]
dP/dt = 10(6 + 1)/[2.303(9 + 3 + 1)]
dP/dt = 10(7)/[2.303(13)]
dP/dt = 70/29.939
dP/dt = 2.34 dB/s
c) If W = cos 0.2t, find the rate of change of the sound pressure P, at time t = 15 (calculators in radians)
Since dP/dt = dP/dW × dW/dt and dP/dW = 10/(2.303W) and W = cos(0.2t), dW/dt = -0.2sin(0.2t)
So, dP/dt = dP/dW × dW/dt
dP/dt = 10/(2.303W) × -0.2sin(0.2t)
dP/dt = -20sin(0.2t)/(2.303W)
dP/dt = -20sin(0.2t)/(2.303cos(0.2t))
dP/dt = -20tan(0.2t)/2.303
when t = 15, we have
dP/dt = -20tan(0.2 × 15)/2.303
dP/dt = -20tan3/2.303
dP/dt = -20 × -0.1425/2.303
dP/dt = 2.8509/2.303
dP/dt = 1.238
dP/dt ≅ 1.24 dB/s
A rectangle has vertices (−5, 6), (−1, 6), (−1, 3), and (−5, 3). It is first dilated by the rule (x, y)→(7x, 7y) and then translated 10 units down. What are the coordinates of the image?
A(−35, 32), (−7, 32), (−7, 11), (−35, 11)
B(−45, 42), (−17, 42), (−17, 21), (−45, 21)
C(−105, 42), (−77, 42), (−77, 21), (−105, 21)
D(−35,−28), (−7,−28), (−7,−49), (−35,−49)
Answers
Passion wants to rent a car to take a trip and has a budget of $75. There is a fixed rental fee of $25 and a daily fee of $10. Write ab inequality that would be used to solve for the maximum number of days for which passion can rent the car on her budget
Answers
Answer:
5 days
Step-by-step explanation:
75 = 10d +25
-25 -25
50 = 10d
/ /
10 10
5 = d
plz answer this very important
Answers
Answer:
16
Step-by-step explanation:
From the question given above, the following data were obtained:
1 = 1
2 = 4
3 = 9
4 =?
Observing the data, we can see that the numbers on the right side are simple the squares of the numbers on the left side. This is illustrated below:
1 = 1² = 1
2 = 2² = 4
3 = 3² = 9
Thus, we shall use the same logic to obtain that of 4. This is illustrated below:
4 = 4² = 16
Thus the answer to the question is 16.
For the matrices below. Find all (real) eigenvalues.
A= [7 9]
[0 9]
Answers
Answer:
The answer is "9 and 7".
Step-by-step explanation:
Given:
[tex]A=\left[\begin{array}{cc}7&9\\0&9\end{array}\right][/tex]
Using formula:
[tex]|A-\lambda \cdot I|= 0\\\\[/tex]
[tex]\to |\left[\begin{array}{cc}7&9\\0&9\end{array}\right]-\lambda \left[\begin{array}{cc}1&0\\0&1\end{array}\right] |=0\\\\\\ \to |\left[\begin{array}{cc}7&9\\0&9\end{array}\right]- \left[\begin{array}{cc}\lambda&0\\0&\lambda\end{array}\right] |=0\\\\\\\to|\left[\begin{array}{cc}7-\lambda &9\\0&9-\lambda\end{array}\right]|=0\\\\\\\to|(7-\lambda)(9-\lambda)|=0\\\\\to (7-\lambda)(9-\lambda)=0\\\\\to 7-\lambda=0 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 9-\lambda=0\\\\[/tex]
[tex]\to \lambda=7 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \lambda=9\\\\[/tex]
What is the expected price of a calculator in the year 2000 if it costs $13 in 2015
Answers
Answer:
$10.90
Step-by-step explanation:
I don't know why but it wants me to talk when I dont need to
I’ve been stuck on this problem I can’t seem to get 7 9/4 into the ABC form
Answers
Answer:
7 square root 9^4
Step-by-step explanation:
Dina invests $600 for 5 years at a rate of 2% per year compound interest.
Calculate the value of this investment at the end of the 5 years.
Answers
Answer:
The value of this investment at the end of the 5 years is of $662.5.
Step-by-step explanation:
Compound interest:
The compound interest formula is given by:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.
Dina invests $600 for 5 years at a rate of 2% per year compound interest.
This means that [tex]P = 600, t = 5, r = 0.02, n = 1[/tex]. Thus
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]A(t) = 600(1 + \frac{0.02}{1})^{t}[/tex]
[tex]A(t) = 600(1.02)^t[/tex]
Calculate the value of this investment at the end of the 5 years.
This is A(5). So
[tex]A(5) = 600(1.02)^5 = 662.5[/tex]
The value of this investment at the end of the 5 years is of $662.5.
Use the following figure to answer the questions
<5 and <7 are what angles
Answers
Answer:
<5 and <7 are corresponding angles.
Step-by-step explanation:
<5 and <7 are corresponding angles. They are on the same side of the transversal and on the same position on each of the parallel lines
Need Help Quick !!!!!!!!
Answers
Given:
The graph of a function.
As [tex]x\to -5^-, f(x)\to \_\_\_[/tex].
As [tex]x\to -5^+, f(x)\to \_\_\_[/tex]
To find:
The correct values for the given blanks.
Solution:
From the given graph it is clear that the function approaches to infinity as x approaches to -5 from the left side. So,
As [tex]x\to -5^-, f(x)\to \infty[/tex].
From the given graph it is clear that the function approaches to negative infinity as x approaches to -5 from the right side. So,
As [tex]x\to -5^+, f(x)\to -\infty[/tex].
Therefore, the correct option (d).
From 22 potential women jurors and 25 potential men jurors, a jury of 12 is chosen at random. Let X be the number of women selected. Find the probability mass function of X.
Answers
Answer:
The probability mass function is:
[tex]P(X = x) = h(x,47,12,22) = \frac{C_{22,x}*C_{25,12-x}}{C_{47,12}}[/tex]
Step-by-step explanation:
The people are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability mass of the hypergeometric probability distribution is given by:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
In this question:
22 + 25 = 47 jurors, so [tex]N = 47[/tex]
22 are women, which means that [tex]k = 22[/tex]
Jury of 12, which means that [tex]n = 12[/tex].
Thus
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = x) = h(x,47,12,22) = \frac{C_{22,x}*C_{25,12-x}}{C_{47,12}}[/tex]
Which is the probability mass function.
Find the equation (in terms of x ) of the line through the points (-2,5) and (3,4)
y=
Answers
Answer:
y = (-1/5)x + 23/5
Step-by-step explanation:
Given:
Two points;
(-2,5) and (3,4)
Find:
Equation of slope
Computation:
y = mx + b
5 = m(-2) + b
5 = -2m + b .......... Eq1
4 = m(3) + b
4 = 3m + b .......... Eq2
Eq2 - Eq1
-1 = 5m
m = -1/5
5 = -2m + b
5 = -2(-1/5) + b
5 = 2/5 + b
b = 23/5
y = mx + b
y = (-1/5)x + 23/5
Pls help I really need help beg you you
Answers
Answer:0,5
Step-by-step explanation:
Write an equation of the line that has a slope of -3 and y-intercept 7 in slope-intercept form.
Answers
Answer:
Step-by-step explanation:
No. 1 “The printing of more
currency notes will increase inflation.”
NEED ASAP
What is the product?
а-3
11
5
15а а-3
о
о
Cul —
за
о за
O3
Answers
Answer:
1/3a
Step-by-step explanation:
[tex] \frac{(a - 3)}{15a} \times \frac{5}{(a - 3)} = \frac{5}{15a} = \frac{1}{3a} [/tex]
Any help? Algebra I
Answers
9514 1404 393
Answer:
2p +3d = 18.25; 4p +2d = 27.50popcorn: $5.75; drink: $2.25Step-by-step explanation:
a) Let p and d represent the prices of a bag of popcorn and a drink, respectively.
Mohamed's purchase is ...
2p +3d = 18.25
Miguel's purchase is ...
4p +2d = 27.50
__
b) We can subtract half the second equation from the first to get an equation for the cost of a drink.
(2p +3d) -1/2(4p +2d) = (18.25) -1/2(27.50)
2d = 4.50 . . . . . . simplify
d = 2.25 . . . . . . divide by 2
4p +2(2.25) = 27.50 . . . . substitute for d in the second equation
4p = 23.00 . . . . . . . . . subtract 4.50
p = 5.75 . . . . . . . . . divide by 4
The cost of a bag of popcorn is $5.75; the cost of a drink is $2.25.
what is the value of x?
Answers
Answer:
46
ayo how r u doin siahsvsgshsgsgsgsg
What is the slope of the line?
I will mark the brainliest!
Answers
Answer:
1
Step-by-step explanation:
Slope = change in y over change in x
If you look at the graph as y goes up 1 x goes up 1
So slope = 1/1 or just 1
Answer:
m=1
Step-by-step explanation:
Hi there!
We're given the graph of a line and we need to find the slope of the line
There are many ways to do this, but the easiest is to calculate it from two points
The formula for the slope (m) calculated from 2 points is [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex], where ([tex]x_{1}[/tex],[tex]y_{1}[/tex]) and ([tex]x_{2}[/tex],[tex]y_{2}[/tex]) are points
So we can take 2 points from the graph of the line to find the slope
For example, let's take (-1,0) and (0,1)
Let's label their values to avoid any confusion before we substitute their values into the formula
[tex]x_{1}[/tex]=-1
[tex]y_{1}[/tex]=0
[tex]x_{2}[/tex]=0
[tex]y_{2}[/tex]=1
now substitute into the formula *remember: we have SUBTRACTION in the slope formula
m=[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
substitute
m=[tex]\frac{1-0}{0--1}[/tex]
simplify
m[tex]\frac{1}{0+1}[/tex]
simplify again
m=[tex]\frac{1}{1}[/tex]
divide
m=1
Therefore the slope of the line is 1
Hope this helps! :)
help please show work
Answers
1/2 • 4.7 x 8 = 18.8
8.) 40.96 square miles
6.4^2 = 40.96
9.) 7 square meters
1/2 • 4 • 3.5 = 7
10.) 36.4 square centimeters
(2.6 + 7.8) ÷ 2 x 7
11.) 22.8 square yards
6 • 3.8 = 22.8
12.) 30.6 square centimeters
5.1 • 6 = 30.6
Explanation:
FORMULAS FOR AREAS OF:
Triangle: 1/2 • base • height
Square: side^2
Parallelogram: base • height
Rectangle: Length • width
Trapezoid: (a + b) ÷ 2 x height
(a & b are the two bases)
hope this helps!
the picture
says it
all
Answers
Answer:
B. L BAT = L CAT
Step-by-step explanation:
__________
please help i need the explanation to go look back at for similar questions in the future. last word is Bold.
Answers
Answer:
50
Step-by-step explanation:
The given angles in the triangle are vertically opposite angles. Hence;
9x - 4 = 8 + 7x
Collect the like terms
9x - 7x = 8 + 4
2x = 12
x = 12/2
x = 6
Get the bolded angle
Bolded angle= 8 + 7x
Blded angle = 8 + 7(6)
Bolded angle = 8 + 42
Bolded angle = 50
Which expression is equivalent to (6x2 + 4)(x + 5) ?
A 6x2 + 20
B 6x2 + 16x + 20
C 603 + 30x2 + 4x + 20
D) 6x3 + 11x2 + 3x + 20
Answers
Answer: [tex]6x^3 +30x^2 +4x+20[/tex]
Step-by-step explanation:
[tex](6x^2 +4)(x+5)\\\\ =6x^3 +30x^2 +4x+20[/tex]
Express in simplest radical form.
V9
Answers
Answer:
3
Step-by-step explanation:
[tex]\sqrt{9}=\sqrt{3*3} = 3[/tex]
A gas pump measures volume of gas to the nearest 0.01 gallon. Which measurement shows an appropriate level of precision for the pump?
Answers
Answer:
12.3 Gallons
Step-by-step explanation:
Options of the question:-
Option A. 12.33 gallons
Option B. 10 gallons
Option C. 12 gallons
Option D. 12.3 gallons
Option D is the answer :-
As the least count or zero error is 0.1 so it can measure only upto one decimal place so answer will be 12.3
The measures of the angles of the triangle are 32°, 53º,
950. Based on the side lengths, what are the measures
of each angle?
m2A = 95°, mZB = 53º, mZC = 32°
MZA= 32º, mzB = 53º, mZC = 95°
MZA= 43º, mZB = 32°, m2C = 95°
OmZA= 53º, m B = 95°, m2C = 32°
Answers
Answer:
m∠A = 32°
Step-by-step explanation:
8^2 = 12^2 + 15^2 - 2*12*15*cosA
Answer:
B
Step-by-step explanation:
did it on edge
What is the sum of additive inverse and multiplicative inverse of 2?
answer fast
Answers
Answer:
-3/2
Step-by-step explanation:
Additive inverse of 2 = -2
Multiplicative inverse of 2 = ½
→ Sum = -2 + ½
→ Sum = (-4 + 1)/2
→ Sum = -3/2
Which of the following represents the factorization of the trinomial below?
X2 - 2x - 48
ANSWER ASAP
Answers
Answer:
(X+6)(x-8)
Step-by-step explanation:
Answer:
(x-8)(x+6)
Step-by-step explanation:
Factor the trinomial using the AC method.
x * x = x^2
-8 + 6 = -2
-8 * 6 = -48
