You are given the height of the building and the length of the shadow the building gives, so you can set that up as a proportion of Height of building over the length of the shadow so 31/28.
Now you can set the same proportion for Julian, using X for her height, so you would have x/6.
To solve for her height, set the two proportions equal and solve for x:
31/28 = x/6
Cross multiply:
31 * 6 = 28 *x
186 = 28x
Divide both sides by 28:
x = 186 / 28
x = 6.64 feet tall
To find Julian's height using the proportion between the building's height and shadow length and Julian's shadow length, we set up a proportion as follows: 31 feet (building height) / 28 feet (building's shadow) = Julian's height / 6 feet (Julian's shadow). Solving for Julian's height, we determine it is approximately 6.64 feet.
The question pertains to similar triangles and proportionality in shadows cast by objects. Using the concept of similar triangles, we can set up a proportion to find Julian's height. The shadows and the objects (Julian and the building) form two sets of similar triangles because the angles of the sunshine are the same for both objects, and thus their corresponding sides are proportional.
To set up the proportion, we use the building's shadow and height relation and compare it to Julian's shadow and unknown height. So, we write:
Building's height / Building's shadow length = Julian's height / Julian's shadow length
31 feet / 28 feet = Julian's height / 6 feet
To generate an accurate answer, we solve for Julian's height as follows:
Julian's height = (31 feet / 28 feet) \ 6 feet = (31 / 28) \ 6
Julian's height = 6.64 feet (approximately)
This proportional relationship can be used to find unknown heights or lengths of shadows when a reference object is used, provided the angle of light is the same.
solve for x
kx + c = 9
kx + c = 9
Subtract C from both sides:
kx = 9-c
Divide both sides by k:
x = (9-c)/k
A pair of jeans was in a 15% off sale but, when Bill came to buy them a month later, the sale was over and he had to pay the regular price of $70. How much money did Bill lose?
Answer:
10.5
Step-by-step explanation: if he got the pants on sale the price would be 59.5 becuase 70*15%=10.5 and u would subtract 70-10.5=59.5
70-59.5=10.5
Answer:
$10.5
Step-by-step explanation:
I need help with this right away. Please.
A baseball team loses twice as many games as it wins.The baseball season is 162 games long.How many games will the team loses?
Answer:
11
Step-by-step explanation:
I guessed
Determine between which consecutive integers the real zeros of f(x)=2x^2-5x+1 are located a. between 0&1 and 1&2 c. between 0&1 and 2&3 b. between -1&0 and 2&3 d. between 1&2 and 2&3
Answer:
c. between 0&1 and 2&3
Step-by-step explanation:
The roots of the given quadratic functions lie between 0&1 and 2&3 thus option (C) is correct.
What is a quadratic equation?An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax2 + bx + c = 0, where x is the variable, and a must not be zero.
As per the given quadratic equation,
f(x) = 2x² - 5x + 1
The value of x will be as,
x = [-(-5) ± √((-5)² - 4 ×2 × 1)]/(2 × 2)
x = (5 ± √17)/4
x = 0.219 and x = 2.28
So, 0 < 0.219 < 1 and 2 < 2.28 < 3.
Hence "The roots of the given quadratic functions lie between 0&1 and 2&3".
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Brad puts an equal amount of money in his savings account once a month. He started with $27. The next month, he had $44 in his account. Two months after that, he had $78 in his account. How much money will Brad have in his account after 6 months?
Brad deposits $17 per month. Hence, after 6 months, Brad will have $115 in his account.
Explanation:The subject of the question is a simple arithmetic problem involving Brad's savings account. The first month, he started with $27. The next month, he had $44 in his savings account, so he adds ($44-$27) = $17 to his account each month. In the third and fourth months, he added the same amount twice, so he had $78 ($44 + $17*2). Hence, after 6 months, he will have $115 in his savings account because for the fifth and sixth months he will add ($17*2 = $34) to his account of $78 from the fourth month.
In simpler terms, we can break down these steps into the following:
Determine the monthly deposit amount ($44-$27)= $17.Add the monthly deposit to the current amount for each subsequent month.Calculate for the 6th month: $27 + $17 * 5 = $115.Learn more about Arithmetic progression here:
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Given the fact that Brad saves an equal amount of $17 each month, after 6 months, his total saved amount will be $129.
Explanation:The question is about calculating the amount of money Brad will have saved in 6 months, given that he saves an equal amount each month. From the information provided, we can determine that Brad saves $17 each month ($44 - $27 = $17). After two months, we can see that $78 - $44 = $34, which confirms that Brad is indeed saving $17 each month, since $34 / 2 = $17. Now, to find how much Brad will have saved after 6 months, we need to multiply the monthly saving amount by 6 and add that to the initial amount. This gives us: $27 + ($17 * 6) = $27 + $102 = $129.
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Flo told her coach that she swam 5.4 kilometers in the pool. The chart shows the length of a standard-sized pool and the distance around a standard-sized running track.
Venue
Kilometers
Pool
0.05
Running Track
0.4
Which is the best method to find the number of laps Flo swam?
divide 5.4 by 0.05
multiply 5.4 by 0.05
divide 5.4 by 0.4
multiply 5.4 by 0.4
Answer:
Divide 5.4 by 0.5
Step-by-step explanation:
It's says to find the number of laps she swam. It doesn't ask us to figure out how many laps she could have run with the amount of laps she did.
To find the number of laps Flo swam, divide the total distance Flo swam (5.4 km) by the length of one lap in the pool (0.05 km). This results in 108 laps.
Explanation:To find out the number of laps Flo swam, we must take the total distance she swam and divide it by the length of one lap in the pool. According to the chart, the length of one lap in a standard-sized pool is 0.05 kilometers. Therefore, the best method would be to divide 5.4 (the total distance Flo swam in kilometers) by 0.05 (the length of one lap in kilometers).
So, we take 5.4/0.05 = 108. This means that Flo swam 108 laps in the pool. Remember, when you want to find how many times a certain distance fits into another, you should utilize division.
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What are the zeroes of the polynomial function f(x)=x^3+2x^2-x-2
[tex]f(x)=x^3+2x^2-x-2\\\\f(x)=0\iff x^3+2x^2-x-2=0\\\\x^2(x+2)-1(x+2)=0\\\\(x+2)(x^2-1)=0\iff x+2=0\ \vee\ x^2-1=0\\\\x+2=0\qquad\text{subtract 2 from both sides}\\\\\boxed{x=-2}\\\\x^2-1=0\qquad\text{add 1 to both sides}\\\\x^2=1\to x=\pm\sqrt1\\\\\boxed{x=-1\ \vee\ x=1}\\\\Answer:\ -2,\ -1,\ 1[/tex]
Answer: -2, -1, 1
Step-by-step explanation:
f(x) = x³ + 2x² - x - 2
0 = x³ + 2x² - x - 2
= x²(x + 2) -1(x + 2)
= (x² - 1) (x + 2)
= (x - 1) (x + 1) (x + 2)
0 = x - 1 0 = x + 1 0 = x + 2
1 = x -1 = x -2 = x
Geometry help! Will give brainliest!! The slope of line b is -1/6. What is the slope of the line parallel to line b?
1/6
-1/6
-6
6
Answer:
-1/6
Step-by-step explanation:
Parallel lines are lines which have the exact same slope but different y-intercepts. This means any line which is parallel and does not cross will have the exact same slope of -1/6.
lim
x->infinity (1+1/n)
Answer:
Can not be determined.
Step-by-step explanation:
We can easily notice that the limit is x tends to infinity, whereas x is not present in the given function, we are given (1 + 1/n). So we can not evaluate the given limit for x as parameter, we must have some function of x to solve this problem.
Hence, option C is correct i.e. the limit can not be determined.
Statewide, there are 20 full-time employees to every 3 part-time employees. If there are 250,000 full-time employees, how many part-time employees are there statewide?
Divide total full time employees by 20 to find how many groups of 20 there are, then multiply that number by 3 to find total part time employees:
250,000 / 20 = 12,500
12,500 x 3 = 37,500 part time employees.
Which of these figures represents a line segment?
Nathan has just bought a new car. He models the value, V, in dollars, of the car after t years as V(t) = 21,000(0.861)t. Based on this model, by what percent does the value of Nathan's car decrease each year?
Answer:
13.9%
Step-by-step explanation:
The value of car is modeled as:
[tex]V(t)=21,000(0.861)t[/tex]
Here we can see that, each year Nathan has considered 0.861 of the previous year value or we can say that Nathan has considered 86.1% of the previous year value. So,
[tex]100-86.1=13.9[/tex]
We subtract the percentage value considered from 100 to find out the percentage decrease in the value of the car.
The value of new car is decreasing by 13.9% each year.
Final answer:
Nathan's car decreases in value by 13.9% each year according to the depreciation model [tex]V(t) = 21,000(0.861)^t.[/tex]
Explanation:
The value of Nathan's car decreases by a certain percentage each year, which can be determined from the depreciation model [tex]V(t) = 21,000(0.861)^t.[/tex]The model shows that each year, the value is multiplied by 0.861. To find the percent decrease, we subtract this number from 1 and then convert the result into a percentage:
1 - 0.861 = 0.139
0.139 imes 100% = 13.9%
Therefore, the value of Nathan's car decreases by 13.9% each year based on this model.
Find the value of x to the nearest tenth.I will mark the brainlest
Answer:
The value of x nearest to tenth is, 1.5 units
Step-by-step explanation:
In right angle triangle as shown in figure
by definition of tangent ratio i,e [tex]\tan \theta = \frac{opposite side}{Adjacent side}[/tex]
[tex]\tan 37^{\circ} = \frac{x}{2.1}[/tex]
[tex]0.7535540501= \frac{x}{2.1}[/tex]
or
[tex]x = 0.7535540501 \times 2.1 = 1.58246351[/tex] units
Therefore, the value of x nearest to tenth is, 1.5 units
In first gear, or low gear, an automobile's engine runs about three times as fast as the drive shaft. In second gear, the engine does not have to run as fast; usually it runs about 1.6 times faster than the drive shaft. Finally, in third, or high gear, the engine runs at the same speed as the drive shaft. Engine speed = 4,100 r.p.m. Transmission in first gear Drive-shaft speed (to nearest r.p.m.) =
a) 1367
b) 12,300
c) 6560
Answer:
A 1367
Step-by-step explanation:
Solve this system of linear equations. Separate the x- and y- values with a coma. 3x=36-15y. 11x =-78+15y
Answer:
(-3,3)
Step-by-step explanation:
3x=36-15y and 11x =-78+15y
We move all x and y terms to the left hand side of the equation , so that we can apply elimination method
3x=36-15y , Add 15 y on both sides , 3x + 15y = 36
11x =-78+15y, subtract 15y on both sides, 11x -15y = -78
Now we add both equations
3x + 15y = 36
11x -15y = -78
------------------------
14x = -42
divide both sides by 14
x= -3
Now Plug in -3 for x in any one of the given equation
3x=36-15y
3(-3) = 36 - 15y
-9 = 36 - 15y
Subtract 36 on both sides
-45 = -15y
Divide both sides by -15
So y= 3
Answer is (-3,3)
Hailey ran a few laps. D(n) models the duration (in seconds) of the time it took for Hailey to run her n lap. When did her lap duration increase
Answer:
2 hours
Step-by-step explanation:
Answer:
during the 7th and the 9th lap
Step-by-step explanation:
I just did it
PLEASE HELP!!!!!
WILL MARK BRAINLIEST!!!!
Answer:
D
Step-by-step explanation:
Rational functions are functions whose main operation on the variable is a ratio or fraction. This means we find x or the input value in the denominator of the function. Since fractions involve division and division has special circumstances, this reflects on the graph. Because when we divide we cannot divide by 0, any x value which makes the denominator 0 is an asymptote. On the graph, asymptotes are represented by dashed lines where the function doesn't follow.
To find the asymptotes, we set the factors in the denominator to 0 and solve for x. Let's do the each for each options:
a. (x+5)=0 so x=-5 and (x-2)=0 so x=2. This matches our graph.
b. x=0 and x+5=0 so x=-5. This does not match the graph.
c. x=0. This does not match the graph.
d. (x+5)=0 so x=-5 and (x-2)=0 so x=2. This matches our graph.
This means only a and d are options. We will substitute a value to see the behavior of the graph. We pick x=-2. In D, this would give us a positive y. This matches the graph. In A, this would give us a negative y which does not match the graph.
help!! at least take a look
What is the recursive rule for this geometric sequence?
27, 9, 3, 1, ...
Enter your answers in the boxes.
an= ⋅an−1
a1=
A recursive rule for a geometric sequence:
[tex]a_1\\\\a_n=r\cdot a_{n-1}[/tex]
---------------------------------------------------
[tex]a_1=27;\ a_2=9;\ a_3=3;\ a_4=1;\ ...\\\\r=\dfrac{a_{n+1}}{a_n}\to r=\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=\dfrac{a_4}{a_3}=...\\\\r=\dfrac{9}{27}=\dfrac{1}{3}\\\\\boxed{a_1=27;\qquad a_n=\dfrac{1}{3}\cdot a_{n-1}}[/tex]
(a+b+c)(d+e+f)(a+b+c)(d+e+f). The expression consists of 3 factors, and each factor contains 2 terms.
Answer:
Not true
Step-by-step explanation:
It is in fact an expression with 4 factors, each with 3 terms.
Factors are things you multiply, terms are things you add.
Angel Grant takes out a $150,000 mortgage this is a 30 year at $725 per month what is the total amount of interest that angel will pay on this mortgage
Todd is saving for a vacation. The cost of his vacation is 1,089. Todd has a year to save the money. About how much does he need to save each month to reach his goal
Answer:
He needs to save $90.75 each month to reach his goal.
Step-by-step explanation:
We have the cost of his vacation that is $1089.
We know that Todd has a year to save the money.
We know that a year in terms of time is twelve months (12 months).
If we want to calculate how much does he need to save each month we need to divide the total cost of his vacation by the amount of months in a year ⇒
[tex]\frac{1089}{12}=90.75[/tex]
We find that Todd needs to save $90.75 per month to reach his goal.
Suppose logbx = logcx, where b ≠ c. Then the value of x can be
A) 0 only
B) 1 only
C) b^c or c^b only
D) any positive real number
Not A: We can't have [tex]x=0[/tex] because [tex]\log0[/tex] is undefined for a logarithm of any base.
B is true: [tex]\log1=0[/tex] for any base.
Not C: If [tex]x=b^c[/tex], then [tex]\log_bb^c=c[/tex], but [tex]\log_cb^c=c\log_bc[/tex] which only reduces to [tex]c[/tex] if [tex]\log_bc=1[/tex]. This can only happen if [tex]b=c[/tex], however, but we've assumed otherwise.
Not D: The reasoning for C not being correct is enough to rule out this possibility.
Dentify the constant of proportionality in the equation. 4y = 48x A) 1 B) 4 C) 12 D) 48
The constant of proportionality in the equation 4y = 48x is 12 (option C) after dividing both sides of the equation by 4 to get the equation into the form y = kx, with k representing the constant of proportionality.
Explanation:The question is asking for the constant of proportionality in the equation 4y = 48x. In an equation of the form "y = kx", "k" is the constant of proportionality. Here, to make this equation look like "y = kx", we need to divide both sides of the equation by 4. Doing this gives us:
y = 12x
So, the constant of proportionality in this equation is 12 which corresponds to option C.
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Who knows please help me I legit love you guys ASAP NEED ANSWERS
Answer:
I think the answer would be B because volume is length times width times height. Therefore, if you multiply the base which is length time width and the height you will get your answer. Let me know if this helps, if not I can further explain it to you.
Step-by-step explanation:
Sharma is building a shed and wants to determine the measurements for the roof. The span of the roof will be 10 feet and she plans to use a 5:12 roof pitch. This means that the roof will rise 5 inches for every 12 horizontal inches. Complete her diagram by determining the unknown angle measures, to the nearest degree, and side lengths, to the nearest tenth of a foot.
Answer:
In the figure below :
d = 2.08, e = 5, c = 5.42 , a = 22.78°, b = 67.22°
Step-by-step explanation:
Side lengths :
[tex]2\cdot e=10\\ \Rightarrow e=5 feet\\\frac{d}{e}=\frac{5}{12}\\\Rightarrow d=\frac{25}{12}\approx 2.08 feet[/tex]
By pythagoras theorem,
[tex]c^2=d^2+e^2\\c^2=29.33\\c\approx 5.42 feet[/tex]
Now to find angles,
[tex]a+b+90^{\circ}=180^{\circ}\\\Rightarrow a+b=90^{\circ}\\\tan a=\frac{d}{e}\\\Rightarrow \tan a =0.42\\\Rightarrow a=22.78^{\circ}\\\Rightarrow b=67.22^{\circ}[/tex]
The unknown side lengths of the shed's roof are:
Angle measure at the top of the roof: 22.62 degrees
Vertical length of the roof (rise): 4.17 feet
Horizontal length of the roof (run): 5 feet
To determine the unknown angle measures and side lengths of the shed's roof, we can use the given information about the roof pitch and span.
Angle Measures
The roof pitch is 5:12, which means that for every 12 horizontal inches, the roof rises 5 inches. This corresponds to an angle of approximately 22.62 degrees.
Side Lengths
The span of the roof is 10 feet, which represents the horizontal distance from one side of the shed to the other.
Since the roof pitch is 5:12, we can calculate the rise of the roof by dividing the span by 12 and multiplying by 5:
Rise = (10 feet * 12 inches/foot) * (5/12) = 41.667 inches ≈ 4.17 feet
Therefore, the unknown side lengths of the shed's roof are:
Angle measure at the top of the roof: 22.62 degrees
Vertical length of the roof (rise): 4.17 feet
Horizontal length of the roof (run): 5 feet
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A student who didn't study for the upcoming quiz decides to 'wing it' and just guess on the 10 question quiz. Every question is a True/False question. What is the pobability that he will pass the quiz with a grade of at least 70%? Please express your answer as a percent rounded to the hundredths decimal place. Include the '%' symbol.
Answer:
There is around a 40% chance if I have done my calculations correctly
Answer: 17.19%
Step-by-step explanation:
[tex]P=\dfrac{_{10}C_7 + _{10}C_8 + _{10}C_9 + _{10}C_{10}}{2^{10}}[/tex]
[tex]= \dfrac{120+45+10+1}{1024}[/tex]
[tex]= \dfrac{176}{1024}[/tex]
= 0.171875
= 17.1875%
What is the solution to the equation 3c/8 = c+4/4
Answer:
c=8
Step-by-step explanation:
3c/8 = (c+4)/4
We can use cross products to solve
3c c+4
----- = ----------
8 4
3c*4 = 8 *(c+4)
12c = 8c+32
Subtract 8c from each side
12c-8c = 32
4c = 32
Divide by 4
4c/4 = 32/4
c =8
The solution to the equation 3c/8 = c+4/4 is found by first simplifying the equation to 3c = 4c + 16, then isolating 'c' gives -c = 16, and finally multiplying both sides by '-1' gives the solution, c = -16.
Explanation:To solve the equation 3c/8 = c+4/4, firstly we'll simplify it, eliminating fractions by multiplication. The equation becomes 3c = 4c + 16.
Next, we rearrange the equation to isolate 'c', by subtracting '4c' from both sides which results in -c = 16.
Finally, to get the value of 'c', we multiply both sides by '-1'. Hence, the solution to the equation is c = -16.
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Number 19 only! 100 points!
Rewrite each expression in terms of sine and cosine, and simplify as much as possible.
Answer:
The answer is sin^2 (theta) cos (theta) .
Step-by-step explanation:
We need to rewrite tan (theta) as sin (theta) /cos (theta)
tan^2 (theta) = sin^2 (theta)/ cos^2 (theta)
We also need to rewrite sec (theta) as 1/ cos(theta)
sec^3 = 1 / cos^3( theta)
tan^2 (theta) sin^2 (theta)
------------------ = ----------------
sec ^3 (theta) cos ^ 2(theta)
---------------------------
1
-----------
cos ^3 (theta)
Remember when dividing fractions, we can use, copy dot flip
sin^2 (theta) cos^3 (theta)
------------------ * -------------------
cos ^ 2(theta) 1
Canceling a cos^2(theta) from the top and bottom,
sin^2 (theta) cos (theta)
------------------ * -------------------
1 1
we are left with
sin^2 (theta) cos (theta)
The answer is sin^2 (theta) cos (theta) .
The answer is sin^2
Dan Williams took out a simple interest loan at 14.5% interest for 12 months. His previous balance is $119.42. What is the final payment if the loan is paid off with the next payment?
Answer:
$132.90
Step-by-step explanation:
Answer:
$120.86
Step-by-step explanation: