The statue of liberty casts a 122 foot shadow at the same time ryan casts a 2 foot shadow. If the statue of liberty is 305 feet tall how tall is ryan?
Step-by-step explanation:
2 objects and their shadows create 2 similar right-angled triangles.
that means all angles are the same, and the side lengths of one triangle correlate to the corresponding side lengths of the other triangle via the same factor.
so,
122 × f = 2
f = 2/122 = 1/61
therefore, Ryan is
305 × f = 305 × 1/61 = 5 ft
tall.
If the Statue of Liberty is 305 feet tall, Ryan is 5 feet tall.
What is proportion?A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio.
Given that,
The length of shadow of Statue of Liberty = 122 foot.
The length of shadow of Ryan = 2 foot.
Also, the height of Statue of Liberty = 305 feet.
Let the height of Ryan = x
To find the value of x,
Use ratio and proportion method,
122 / 305 = 2 / x
x = 2 x 305 / 122
x = 305 / 61
x = 5
The height of Ryan is 5 feet.
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I need help with this problem
Solve the following system of equations using elimination by multiplication.
If the given equations are indeed
[tex]\begin{cases}x-\frac4{5y} = 9\frac45 \\ -14x - 4y = -46\end{cases}[/tex]
we can solve by substitution. Solve the second equation for x :
[tex]-14x - 4y = -46[/tex]
[tex]\implies 7x + 2y = 23[/tex]
[tex]\implies7x = 23 - 2y[/tex]
[tex]\implies x = (23 - 2y)/7[/tex]
Substitute this into the first equation and solve for y :
[tex]\dfrac{23-2y}7 - \dfrac4{5y} = 9\dfrac45[/tex]
On the right side, write the mixed number as an improper fraction:
[tex]9 + \dfrac45 = \dfrac{45}5 + \dfrac45 = \dfrac{45+4}5 = \dfrac{49}5[/tex]
[tex]\implies \dfrac{23-2y}7 - \dfrac4{5y} = \dfrac{49}5[/tex]
Multiply both sides of this equation by 35y (the LCM of the denominator of all three fractions)
[tex]35y \times \dfrac{23-2y}7 - 35y \times \dfrac4{5y} = 35y \times \dfrac{49}5[/tex]
[tex]5y\times(23-2y) - 7\times4 = 7y \times 49[/tex]
[tex]115y - 10y^2 - 28 = 343y[/tex]
[tex]10y^2 + 228y + 28 = 0[/tex]
[tex]5y^2 + 114y + 14 = 0[/tex]
To solve the quadratic, I'll complete the square :
[tex]5\left(y^2 + \dfrac{114}5y\right) + 14 = 0[/tex]
[tex]5\left(\left(y + \dfrac{57}5\right)^2 - \left(\dfrac{57}5\right)^2 \right) + 14 = 0[/tex]
[tex]5\left(y + \dfrac{57}5\right)^2 - \dfrac{57^2}5 + 14 = 0[/tex]
[tex]5\left(y + \dfrac{57}5\right)^2 = -\dfrac{3179}5[/tex]
This system has no real solutions since the square of any real number must be positive.
If we allow complex numbers, we can continue solving to end up with two complex solutions for y,
[tex]\left(y + \dfrac{57}5\right)^2 = -\dfrac{3179}{25}[/tex]
[tex]y + \dfrac{57}5 = \pm i \sqrt{\dfrac{3179}{25}}[/tex]
[tex]y = -\dfrac{57}5 \pm i\dfrac{17\sqrt{11}}5[/tex]
and we can go on to solve for x.
Hence my comment; I suspect you meant to write the system
[tex]\begin{cases}x-\frac45 y = 9\frac45 \\ -14x - 4y = -46\end{cases}[/tex]
because its solution is far simpler. Multiplying through the first equation by 5 gives
[tex]5\times x - 5 \times \dfrac45 y = 5 \times 9\dfrac45[/tex]
[tex]\implies 5x - 4y = 49[/tex]
(since we know 9 + 4/5 = 49/5)
Meanwhile, multiplying through the second equation by -1 gives
[tex]-1 \times (-14x) + (-1) \times (-4y) = -1 \times (-46)[/tex]
[tex]\implies 14x + 4y = 46[/tex]
So if we combine the two equations, we can eliminate y and solve for x :
[tex](5x - 4y) + (14x + 4y) = 49 + 46[/tex]
[tex]\implies 19x = 95[/tex]
[tex]\implies \boxed{x = 5}[/tex]
and solving for y gives
[tex]14x + 4y = 46[/tex]
[tex]\implies 70 + 4y = 46[/tex]
[tex]\implies 4y = -24[/tex]
[tex]\implies \boxed{y = -6}[/tex]
SOLVE FOR ASA
-GEOMETRY
Step-by-step explanation:
Hope It Helps You
Here You Answer
Each student bus goes on a field trip holds 36 students and four adults there are six found buses on the field trip how many people are going on a field trip
Answer:
240
Step-by-step explanation:
36+4=40
40x6=240
Determine the intercepts of the line.
Step-by-step explanation:
The x-intercept is the value of x when y is 0
So you need to substitute:
0 = 4x + 7
-7 = 4x
-7/4 = x
(-7/4,0)
Similarly, the y-intercept is the value of y when x is 0
So:
y = 4x + 7
y = 4(0) + 7
y = 7
(0,7)
A camp charges $75 per day to use the camp plus $15 per day for food and supplies for each student. The cost for one day can be modelled using the equation C= 15s + 75.
a) What do the variables C and s represent?
b) A school raised $375 for a one-day trip. How many students can go?
((see pic for textbook question))
b:375:75=5 or 370:100=3.75 but it doesn't make sence B=5
g^2+(-4g^4)+5g+9+(-3g^3)+3g^2+(-6)
The least common multiple of two whole numbers is 28 the ratio of the greater number to the lesser number is 7:2 what are the two numbers
Answer:
14, 4
Step-by-step explanation:
First things first, we can name out pairs with the ratio of 7:2.
7, 2
14, 4
21, 6
We can then test these pairs out with the first condition and find the answer.
The least common multiple has to be 28:
LCM(7, 2) = 14
LCM(14, 4) = 28
Ah, ha! We can see that the least common multiple of 14 and 4 is 28.
helllp meeeeeeeeeeeeeeee
Daniel went to Target and bought a magazine for $5.99, a book for $15.99, and a DVD for $20.99. What was his total bill including 6% sales tax?
Erin bought 4 jars of jelly and 6 jars of peanut butter for $19.32. Adam bought 3 jars of jelly and 5 jars of peanut butter for $15.67. Find the cost of a jar of peanut butter?
Answer:
the jar of peanut butter is $2.36
Step-by-step explanation:
Answer: $2.36
Step-by-step explanation:
2x − 4y = -4 , 3x + 2y = 22 solve the system by elimination.
Answer: 5, 7/2
Step-by-step explanation:
2x − 4y = -4
3x + 2y = 22
divide both sides of the equation by 2
x − 2y = -2
3x + 2y = 22
Eliminate one variable by adding the equation; sum the equations vertically to eliminate at least one variable
4x=20
Divides both sides by 4
x=5
Substitute the given value of x into the equation 2x-4y = -4
2*5-4y =-4
solve the equation for y
y=7/2
34x+24x^2=35+57y
Solve for x
1) Move all terms to one side.
[tex]34x+24x^{2} -35-57y=0[/tex]
2) Use Quadratic Formula.
[tex]x=\frac{-34+2\sqrt{1368y+1129} }{48} ,\frac{-34-2\sqrt{1368y+1129} }{48}[/tex]
3) Simplify solutions.
[tex]x=-\frac{17-\sqrt{1368y+1129} }{24} ,-\frac{17+\sqrt{1368y+1129} }{24}[/tex]
Four students, Adrian, Claire, Jackson, and Wyatt, line up one behind the other. How many different ways can they stand in line?
Answer:
8
Step-by-step explanation:
4*3*2*1 i had the same problem
The number of different ways the students can stand in line is A = 24 ways
What are Permutations?A permutation is an ordered arrangement.
The number of ordered arrangements of r objects taken from n unlike objects is:
Permutation ⁿPr = n! / ( n - r )!
Given data ,
Let the number of different ways the students can stand in line be A
Now , There are 4 students to choose from for the first position in the line, then 3 remaining students for the second position, 2 remaining students for the third position, and only 1 student left for the last position.
Therefore, there are
4 × 3 × 2 × 1 = 24 different ways for the students to stand in line
Therefore , the value of A = 24 ways
Hence , the students have 24 ways to stand in line
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Slope formula: trying to make sure I’m doing this right
Answer:
Yup ur Right ;D
Step-by-step explanation:
Hii I would love if anyone would be able to give me the answer to this <3
Answer:
×=40
Step-by-step explanation:
The total value of all the angles on any line is 180
so x+(4x-20)=180
40+(4×40-20)=180
Answer:
40°
Step-by-step explanation:
The sum of angles x and (4x - 20) is 180°
x + (4x - 20) = 180
5x = 200
x = 40°
$800 at 9% per year for 1 year
Answer:
The answer should be 72.
Step-by-step explanation:
You're finding the interest earned. I = Prt, I for simple interest, P for principal, r for rate, and t for time.
Substitute p for $800, r for 9%, and t for is 1 year.
You would multiply these three numbers together.
$800(0.09)(1) should give you 72.
(Will give 1,000 points!) Look at the two 3s in this number:
89.033
Which of these statements is true? Choose all that apply.
A
The blue 3 on the left is 300 times the value of the orange 3 on the right.
B
The blue 3 on the left is 100 times the value of the orange 3 on the right.
C
The blue 3 on the left is 10 times the value of the orange 3 on the right.
D
The blue 3 on the left is equivalent to the orange 3 on the right.
E
The orange 3 on the right is 1/10 of the value of the blue 3 on the left.
(And yes there are multiple answers!)
The only true statement is "the orange 3 on the right is 1/10 of the value of the blue 3 on the left"
This question bothers on place values.
Given the decimal value 89.033, the place value of the blue 3 on the left is the hundredth place (1/100) while the place value of the orange 3 is in the thousandth place(1/1000).
We need to check which of the statement is correct.
For the first option, the blue 3 on the left is 300 times the value of the orange 3 on the right;
1/100 = 300(1/1000)1/100 = 3/10Since 0.01≠0.3, hence the first option is wrong
For the second option, the blue 3 on the left is 100 times the value of the orange 3 on the right;
1/100 = 100(1/1000)1/100 = 1/100.01≠0.1, hence the second option is wrong.
The blue 3 on the left is equivalent to the orange 3 on the right is also wrong since they are positioned in a different place
The orange 3 on the right is 1/10 of the value of the blue 3 on the left, is expressed as;
1/1000 = 1/10(1/100)0.001 = 0.001Hence the only true statement is "the orange 3 on the right is 1/10 of the value of the blue 3 on the left"
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Need help!!!!!!!!!!!!!!!!!!!!!!!!
[tex]\mathfrak{( \frac { 6 x } { y } ) ( \frac { y } { 3 x - 3 } ) } [/tex]
[tex]\mathfrak{ \frac{6xy}{y\left(3x-3\right)} } [/tex]
[tex]\mathfrak{ \frac{6x}{3x-3} } [/tex][tex]\mathfrak{ \frac{6x}{3\left(x-1\right)} } [/tex]
[tex]=\boxed{\mathfrak{\frac{2x}{x-1} } }[/tex]
☆ Option 3 is correct.
[tex]\mathbb{MIREU} [/tex]
How do I factor this problem?
Answer:
[tex]7x(4x-1)[/tex]
Step-by-step explanation:
First, find the largest integer that divides evenly into both numbers. In this case, 28 and 7 are both divisible by 7.
Next, find the highest degree of the variable that divides evenly into both. Here, that's just x. I'll show another example of that below.
Multiply those together, and you get 7x. That is what we need to factor out. Divide by that factor while multiplying by that factor at the same time to keep the value of the expression equal:
[tex]28x^2-7x\\\\7x(\frac{28x^2}{7x}-\frac{7x}{7x})\\\\7x(4x-1)[/tex]
Another example of what I said above would be this:
Take 4x + 2. The largest integer that divides these is 2, and the highest degree of x that divides them is 0. That is an x⁰, and that is equal to 1. Multiply those, and you just get 2.
[tex]4x+2\\\\2(\frac{4x}{2}+\frac{2}{2})\\\\2(2x+1)[/tex]
Can someone please help me with number 49? :D ty!
Answer:
The answer is 4.5 cups I hope this helps :D
what should I put?????
huang 3 shirts that each cost the same amount, a pair of pants that cost $12, and he pays with a $100 bill. Which
expression represents the amount of change Huang should receive? Select three options.
100-(3)
100--12)
(100-12) - 3
(100-12)*x*)
100-x) - 12
Answer:
(100-12) - 3
Step-by-step explanation:
we dont know what the cost of the shirts are so that one should be it.
Find the value of x
3x = 9²
[tex]\huge\boxed{Hi\:there!}[/tex]
[tex]\huge\sf{3x=9^2}[/tex]
[tex]\huge\sf{3x=81}[/tex]
[tex]\huge\sf{Divide\:both\:sides\:by\:3\:to\:isolate\:x:}[/tex]
[tex]\huge\sf{x=27}[/tex]
[tex]\huge\boxed{Hence,\:x=27.}[/tex]
[tex]\huge\sf\underline{Hope\:it\:helps}[/tex]
[tex]\boxed{CheerfulGirlie\:here\:to\:help}[/tex]
Find the value of x
3x = 9²
Answer:-x = 27
Explanation:-=> 3x = 9²
=> 3x = 81 [9² = 9×9 = 81]
=> x = 81/3
=> x = 27
PLEASE HELP QUESTION IN PICTURE
Answer:
Perimeter= 40
Area= 120.71
Step-by-step explanation:
NO LINKS!!!!! Plz
Round 0.864595 to the ten-thousandths place.
Answer:
0.8646
Step-by-step explanation:
The digit in the hundred-thousandths place is 9, so is greater than 4. That means the digit in the ten-thousandths place is increased by 1 when the number is rounded.
0.864595 rounds to 0.8646
Write your own formula. List the first 4 terms and solve for the 10th term using the formula.
Answer:
Below
Step-by-step explanation:
Formula for an arithmetic sequence is an = 4n - 5
First 4 terms are
-1, 3, 7, 11.
10th term = 4(10) - 5
= 35.
What is the circumference of a circle whose radius is 20 feet? Leave answer in terms of it. ) A) 107 feet B) 20 feet 407 feet D) 1007 feet
Help me plz plz plz plz plz plz plz plz plz plz plz
Help please
Pleasssssse
Answer:
a) Draw a line horizontally on 4 on the y axis
b)x=2,y=3