Julie is 6 feet tall. If she stands 15 feet from the flagpole and holds a cardboard square, the edges of the square line up with the top and bottom of the flagpole. Approximate the height of the flagpole
Answers
Answer:
43.5 ft
Step-by-step explanation:
Given: Julie is 6 feet tall
She stands 15 feet from the flagpole.
The edges of the square line up with the top and bottom of the flagpole.
Picture drawn to show side and angle formed by Julie and flagpole.
Lets assume the height of flagpole be "h".
As given, the edges of the square line up with the top and bottom of the flagpole.
∴ Angle and base of triangle are same then ratio of corresponding sides are also equal.
Now, finding the height of flagpole by using tangent rule.
we know, [tex]tan\theta= \frac{Opposite}{adjacent}[/tex]
Remember, both the angle are equal.
∴ Ratio of opposite and adjacent leg for both right angle triangle= [tex]\frac{6}{15} : \frac{h-6}{15}[/tex]
We can put it; [tex]\frac{6}{15} = \frac{15}{h-6}[/tex]
Solving the equation now
⇒ [tex]\frac{6}{15} = \frac{15}{h-6}[/tex]
Multiplying both side by 15
⇒[tex]6 = \frac{15\times 15}{h-6}[/tex]
Multiplying both side by (h-6)
⇒ [tex]6\times (h-6) = 15\times 15[/tex]
Distributive property of multiplication
⇒ [tex]6h-36= 225[/tex]
Adding both side by 36
⇒[tex]6h= 225+36[/tex]
Dividing both side by 6
⇒[tex]h= \frac{261}{6}[/tex]
∴ [tex]h= 43.5\ feet[/tex]
Hence, the height of flagpole is 43.5 feet.
The height of the flagpole is given by the length of the hypotenuse side
formed by the right triangle Julie forms with the cardboard.
Response:
Height of the flagpole is 17.4 feetWhich method is used to calculate the height of the flagpole?The triangle formed by the edges of square lined up with the top and
bottom of the flagpole is a right triangle.
The altitude of the right triangle formed with the height of the flagpole as the base = 15 feet
Length of a leg of the right triangle = √(15² + 6²) = 3·√(29)
The other angle formed by the right triangle = (90° - arctan(15/6))
h × sin(arctan(15/6)) = 3·√29
[tex]h = \mathbf{\dfrac{3 \cdot \sqrt{29} }{sin(arctan(15/6))} } = 17.4[/tex]
Height of the flagpole, h = 17.4 feet
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Related Questions
7 is underlined 0.673 is the place value for 7
Answers
On Tuesday James bought seven CDs. On Wednesday half of all the CDs that he had were destroyed. On Thursday he had 12 left. How many did he have on Monday?
Answers
Answer:
He have 17 CDs on Monday.
Step-by-step explanation:
Given:
On Tuesday James bought seven CDs. On Wednesday half of all the CDs that he had were destroyed. On Thursday he had 12 left.
Now, to find the CDs he have on Monday.
Let the CDs he have on Monday be [tex]x.[/tex]
So, on Tuesday as James bought 7 CDs:
[tex]x+7.[/tex]
Now, on Wednesday half of all the CDs that he had were destroyed:
[tex]\frac{x+7}{2}[/tex]
As, given on Thursday he had left CDs = 12.
According to question:
[tex]\frac{x+7}{2}[/tex] [tex]=12[/tex]
Multiplying both sides by 2 we get:
[tex]x+7=24[/tex]
Subtracting both sides by 7 we get:
[tex]x=17.[/tex]
Therefore, he have 17 CDs on Monday.
Sheila mixed 3 ounces of blue paint with
2 ounces of yellow paint. She decided to
create 20 ounces of the same mixture. How
many ounces of yellow paint does Sheila
need for the new mixture?
Answers
Answer:
she needs 6 ouonces of yellow paint
Step-by-step explanation:
she has 5oz, 3 blue: 2 red, she needs 20oz. which means she needs 15oz more. 15/5=3. 3*2=6
Write an equation in slope-intercept form with a slope of 1 and a y-intercept of (0, -7).
Answers
Answer:
y = x - 7
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = 1 and c = - 7, thus
y = x - 7 ← equation of line
PLZ HELP WILL GIVE 10 PTS + BRAINLIEST THX SO SO SO SO SO SO MUCH!!!!
If (6^2)^p = 6^10, what is the value of p?
a. 2
b. 3
c. 4
d. 5
ty! :D
Answers
Answer:
d. 5
Step-by-step explanation:
Which pair of expressions below is equivalent?
A. 9x+2y and 11xy
B. 4x-5y and 5y-4x
C. 5(2x-3y) and 10x-3y
D. X+y+x+y and 2(x+y)
Answers
because you can’t add or subtract unlike terms for A and B meaning the equations wouldn’t change
for C it would be 10x-15y not -3y
D) x+y+x+y=2x+2y
2(x+y)= 2x+2y
Natasha has a red and a white sweater. She can wear with a blue skirt, yellow skirt and a black skirt. How many different combinations can she make
Answers
Natasha can make 6 different combinations by pairing 2 sweaters with 3 skirts. She can pair each of her red and white sweaters with each of her blue, yellow, and black skirts.
Explanation:Natasha has a red sweater and a white sweater that she wants to pair with a blue skirt, yellow skirt, and a black skirt. To determine the number of different combinations she can make, we use basic combinatorics. Each sweater can be paired with any of the skirts, so we multiply the number of sweaters by the number of skirts.
Here is the calculation:
Number of sweaters: 2 (red and white)Number of skirts: 3 (blue, yellow, and black)Thus, Natasha can make 2 sweaters imes 3 skirts = 6 combinations.
These combinations are:
Red sweater with blue skirtRed sweater with yellow skirtRed sweater with black skirtWhite sweater with blue skirtWhite sweater with yellow skirtWhite sweater with black skirtIf y = 2x - 1 and (3, 5) and (4.7) are part of the pattern then what is the y coordinate of (5, _ )?
Answers
Answer:
y = 9
Step-by-step explanation:
Substitute the x- coordinate of the point into the equation and solve for y, that is
y = 2(5) - 1 = 10 - 1 = 9
Thus point is (5, 9 )
What is ×7 9/27 reduced to lowest term
Answers
Answer:
[tex]2 \frac{1}{3} [/tex]
Step-by-step explanation:
Assuming the question is
[tex]7 \times \frac{9}{27} [/tex]
reduced to the lowest term.
We proceed as follows:
[tex]7 \times \frac{9}{3 \times 9} [/tex]
We cancel the common factors to get:
[tex]7 \times \frac{1}{3} [/tex]
This simplifies to
[tex] \frac{7}{3} = 2 \frac{1}{3} [/tex]
Please answerrrr I need it desperately please EXPLAIN. I WILL PUT YOU AS A BRANLIEST ANSWER IF YOU EXPLAIN AND TRY YOUR BEST!!!!! Good luck and remember to EXPALIN.
Answers
Answer:
Option B
see the attached figure
Step-by-step explanation:
we know that
Opposite number or additive inverse of any number (n) is a number which, if added to n, results in 0
so
In this problem
The opposite of -1/2 is 1/2
so
point M is 1/2 ----> point M is located in the interval (0,1)
The opposite of 5/2 is -5/2
so
point N is -5/2 ----> point M is located in the interval (-3,-2)
therefore
The correct answer is the option B
what is 1.498 divived by 30. plz show your work.
Answers
Answer:
[tex]0.0749[/tex]
Step-by-step explanation:
[tex]1.498/30[/tex]
To divide the form directly in fraction divide the numerator and denominator by a common number to simplify the values.
Simplifying the value
Removing the decimal in the numerator makes 1000 in denominator
[tex]\frac{1498}{30}*\frac{1}{1000}[/tex]
dividing by a common value i.e 2
[tex]\frac{749}{10}*\frac{1}{1000}[/tex]
Now, removing the decimals from denominator puts the decimal in the numerator gives [tex]0.0749[/tex]
Answer:
1.498 divided by 30 equals 749/15000 OR 0.04993
Step-by-step explanation:
Simply divide as you would a whole number, but place the decimal point above in your answer. So, your first step would be to calculate how many times 30 goes into 149. Your answer will go two places AFTER your decimal point. Then you continue to solve, as you would a whole number!
math help
simplify. your awnser should contain only positive exponents with no fractional exponents in the denominator
Answers
The solution using laws of exponents is: [tex]y^{\frac{7}{12} } * z^{\frac{1}{2} }[/tex]
How to use laws of exponents?
Some of the laws of exponents are:
- When multiplying by like bases, keep the same bases and add exponents.
- When raising a base to a power of another, keep the same base and multiply by the exponent.
- If dividing by equal bases, keep the same base and subtract the denominator exponent from the numerator exponent.
The expression we want to solve is given as:
[tex]\frac{(x^{-\frac{3}{2} } y^{\frac{5}{3} } z^{-1})^{-1} }{zx^{\frac{3}{2} } y^{-\frac{1}{4} } * y^{-2} z^{\frac{1}{2} } }[/tex]
Using laws of exponents, we have:
[tex]x^{0} * y^{\frac{7}{12} } * z^{\frac{1}{2} }[/tex]
=[tex]y^{\frac{7}{12} } * z^{\frac{1}{2} }[/tex]
Which situation described relates to the graph?
A)A small pizza cost $2, and each topping costs an additional $6.
B)A small pizza cost $4, and each topping costs an additional $2.
C)A small pizza cost $6, and each topping costs an additional $2.
D)A small pizza cost $6 and each topping costs an additional $4.
Answers
Answer:
C) A small pizza cost $4, and each topping costs and additional $2.
Step-by-step explanation:
Answer:
A small pizza cost $6, and each topping costs an additional $2.
-4h - 3 < 9
h < 12
h > -3
h < -3
h > -12
Answers
The solution of the inequality is h > -3 ⇒ 2nd answer
Step-by-step explanation:
Let us revise very important notes about solving inequalities
You can add and subtract both sides of inequality by a number without change the sign of inequalityYou can multiply or divide both sides of inequality by a positive number without change the sign of inequalityYou can multiply or divide both sides of inequality by a negative number with change the sign of inequality (-2x < 4 ⇒ ÷ (-2) makes it x > -2)∵ -4 h - 3 < 9
- Start with adding both sides by 3 to separate the variable
in one side and the numerical term in the other side of the
inequality sign
∴ -4 h - 3 + 3 < 9 + 3
∴ -4 h < 12
- Now divide both sides by -4 and use the last note above
∵ -4 ÷ -4 = 1
∵ 12 ÷ -4 = -3
∵ < must change to > (because we divide both sides by (-) number
∴ h > -3
The solution of the inequality is h > -3
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Answer:
h> -3
Step-by-step explanation:
Why does 5x2/3 =10x1/3
Answers
Explanation of how to simplify expressions with exponents by subtracting exponents. The answer shows the equivalence of 5×2/3 and 10×1/3.
The expression [tex]( \frac{5 \times 2}{3} )[/tex] equals [tex]( \frac{10}{3} )[/tex]. Let's break it down:
[tex]\( \frac{5 \times 2}{3} \)[/tex] means you multiply 5 and 2 first, which gives you 10, then you divide by 3, resulting in [tex]\( \frac{10}{3} \)[/tex].
However, if you're asking why [tex]\( \frac{5 \times 2}{3} \)[/tex] and [tex]\( 10 \times \frac{1}{3} \)[/tex] are equal, it's because multiplication is distributive over division.
In other words, [tex]\( a \times \frac{b}{c} = \frac{a \times b}{c} \)[/tex].
So, [tex]\( 10 \times \frac{1}{3} \)[/tex] can be written as [tex]\( \frac{10 \times 1}{3} \)[/tex], which simplifies to [tex]\( \frac{10}{3} \)[/tex], the same as [tex]\( \frac{5 \times 2}{3} \)[/tex].
The difference of 5 and n cubed
Answers
Answer:
6n
Step-by-step explanation:
Final answer:
The difference of 5 and n cubed is calculated by subtracting n cubed from 5. This involves simple algebraic manipulation.
Explanation:
The difference of 5 and n cubed can be represented as 5 - n³. This means subtracting the cube of the variable n from 5.
To illustrate, if n=2, the calculation would be 5 - 2³ = 5 - 8 = -3.
Therefore, the result of the difference between 5 and n cubed is 5 - n³.
x=9y
5x+3y= -48
What does x equal?
What does y equal?
Answers
you can plug the x value (9y) into the second equation
5(9y) + 3y = -48
45y + 3y = -48
48y = -48
y = -1
x = 9(-1)
x = -9
Answer:
x = 9
y = -31
Step-by-step explanation:
5x+3y
y = -31
x = 9
plug it in
Veronica tried to solve an equation step by step. \begin{aligned} 8&=y-4.6\\\\ 8+4.6&=y-4.6+4.6&\green{\text{Step } 1}\\\\ 12.6&=y&\blue{\text{Step } 2} \end{aligned} 8 8+4.6 12.6 =y−4.6 =y−4.6+4.6 =y Step 1 Step 2 Find Veronica's mistake.
Answers
Answer:
she did not make a mistake
Step-by-step explanation:
Answer:
veronica didn't make a mistake.
Step-by-step explanation:
The difference between of two numbers is 9. If the large number is one more than twice the smaller number, find the larger number.
Answers
The larger number is 17
Solution:
Let "x" be the larger number
Let "y" be the smaller number
The difference between of two numbers is 9
Therefore,
larger number - smaller number = 9
x - y = 9 -------- eqn 1
The large number is one more than twice the smaller number
Larger number = 1 + 2(smaller number)
x = 1 + 2y ------ eqn 2
Let us solve eqn 1 and eqn 2
Substitute eqn 2 in eqn 1
1 + 2y - y = 9
1 + y = 9
y = 9 - 1
y = 8
Substitute y = 8 in eqn 1
x - 8 = 9
x = 8 + 9
x = 17
Thus the larger number is 17
Tanya went to Robs diner for lunch and received the bill for her meal even though the receipt was ripped she still knew that the sales tax was 6.5%. how much is the total for her meal after the sales tax is added to the subtotal of $8.50?
Answers
Answer:
Therefore total for her male after the sales tax is added to the subtotal of $8.50 is = $(8.50+0.55) = $9.05
Step-by-step explanation:
Given the sales tax was 6.5%.
The sales tax for Tanya's meal is [tex]=\$ \frac{6.5}{100}\times 8.50[/tex]
= $0.55
Therefore total for her male after the sales tax is added to the subtotal of $8.50 is = $(8.50+0.55) = $9.05
What is the significance of the point of intersection of a pair of simultaneous equations
Answers
Answer:
The point of intersection gives the solution set(s) of the associated system.
Step-by-step explanation:
If we have a pair of simultaneous equations in 2 variables in x and y, then the point of intersection is the ordered pair (x,y).
This could be a unique intersection, only one point or infinitely many intersection.
This gives us the solution of the simultaneous equations.
Therefore the significance of the point of intersection of a pair of simultaneous equations is that, it gives us the solution set(s) of the associated system.
Help pls will mark brainlist !! :)
Answers
Answer:
144 cubic inches
Step-by-step explanation:
a=lxwxh a=6*6*4
Yo sup??
we should know that the volume of a cuboid is l*b*h
from the given figure we can say that
l=6 inches
b=6 inches
h=4 inches
therefore
V=6*6*4
=144 inches^3
therefore the correct answer is option C
Hope this helps.
Briana has been offered a sales job in another city. The offer was for $42,500 plus 8% of her total sales. In order to make it worth the move, Briana needs to have an annual salary of at least $66,500. What would her total sales need to be for her to move?
Answers
Answer:
[tex]Total\ sales\ should\ be=\$ 300000[/tex]
Step-by-step explanation:
[tex]Let\ her\ total\ sale=x[/tex]
Total Earning:
[tex]The\ offer=\$ 42500\\\\Income\ from\ the\ sales=8\%\ of\ total\ sale\\\\Income\ from\ the\ sales=8\%\ of\ x\\\\Income\ from\ the\ sales=\frac{8}{100}\times x\\\\Income\ from\ the\ sales==0.08x\\\\Total\ earning=Offer+Income\ from\ the\ sales\\\\Total\ earning=42500+0.08x[/tex]
Required Earning=$66500
[tex]To\ move\ that\ city\\\\Total\ earning=required\ earning\\\\42500+0.08x=66500\\\\0.08x=66500-42500\\\\0.08x=24000\\\\x=\frac{24500}{0.08}\\\\x=300000\\\\Total\ sales\ should\ be=\$ 300000[/tex]
Her total sales would need to be at least $300,000 for her to move
Step-by-step explanation:
Briana has been offered a sales job in another city
The offer was for $42,500 plus 8% of her total salesBriana needs to have an annual salary of at least $66,500We need to find what would her total sales need to be for her to move
Assume that her total sales is x
∵ The offer was for $42,500 plus 8% of her total sales
∵ Her total sales = x
- To find her annual salary multiply x by 8% and add the
product to $42,500
∴ Her annual salary = 8% × x + 42,500
∵ 8% × x = [tex]\frac{8}{100}[/tex] × x = 0.08 x
∴ Her annual salary = 0.08 x + 42,500
∵ Briana needs to have an annual salary of at least $66,500
- At least means ≥
∴ Her annual salary ≥ 66,500
- Substitute her annual salary by the expression above
∴ 0.08 x + 42,500 ≥ 66,500
- Subtract 42,500 from both sides of inequality
∴ 0.08 x ≥ 24,000
- Divide both sides by 0.08
∴ x ≥ 300,000
∴ Her total sales ≥ $300,000
Her total sales would need to be at least $300,000 for her to move
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Is 40/48 proportional to 56/42
Answers
Answer:
To find if something is proportional you want to reduce them to there simplest form, so we want to reduce each fraction down
40/48= 5/6
56/42= 8/7
Therefore; these two fractions are not proportional because they reduce to different numbers
Hope this helps ;)
Answer:
no
Step-by-step explanation:
Cross multiply:
40 * 42 = 48 * 56
Simplifying
40 * 42 = 48 * 56
Multiply 40 * 42
1680 = 48 * 56
Multiply 48 * 56
1680 = 2688
Solving
1680 = 2688
You found an apartment you really
like. The rent is $625 per month. This is 25% of your
monthly income. How much is your monthly income?
Answers
Answer:
$2500
Step-by-step explanation:
25% is one fourth of the total monthly income.
If $625 is = x/4 then multiply both sides of the equation with 4
4 × 625 = x/4 × 4 ➡ 2500 = x
find the lateral area of the figure
Answers
Answer:
you just have to add or divide
How can fishermen save gas
Answers
A fishermen can save gas by implementing the strategies Plan Efficient Routes, Maintain Proper Boat Speed, Reduce Idle Time, Optimize Load and Equipment and Regular Maintenance
Fishermen can save gas by implementing the following strategies:
Plan Efficient Routes: By planning their fishing trips in advance and mapping out efficient routes, fishermen can minimize the distance traveled and save on gas consumption.
Maintain Proper Boat Speed: Operating the boat at an appropriate speed can significantly impact fuel efficiency.
Reduce Idle Time: Minimizing idle time while on the water can help save gas.
Optimize Load and Equipment: Carrying excessive weight on the boat can increase fuel consumption.
Regular Maintenance: Keeping the boat and engine properly maintained is essential for fuel efficiency.
Utilize Wind and Tides: When feasible, fishermen can take advantage of wind and tidal currents to reduce reliance on the engine.
Share Resources: Collaborating with other fishermen or joining fishing cooperatives can help share resources and reduce individual fuel consumption.
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Which equation can be used to find 40 percent of 25?
Answers
Answer:
a=40% · 25
a=0.40 · 25
0.40 · 25= 10
a=10
Step-by-step explanation:
Answer:
Would be 25/10
Step-by-step explanation:
solve y= 2/3x +7 and 3y= 2x -3
Answers
Answer:
The system has no solution
Step-by-step explanation:
we have
[tex]y=\frac{2}{3}x+7[/tex] ----> equation A
[tex]3y=2x-3[/tex]
Isolate the variable y
Divide by 3 both sides
[tex]y=\frac{2}{3}x-1[/tex] ------> equation B
Compare equation A and equation B
Both lines have the same slope and different y-intercept
so
Line A and Line B are parallel lines
The lines do not intersect
therefore
The system has no solution, because both lines are parallel
see the attached figure to better understand the problem
House prices in a certain area went
up by 150% between 1995 and 2005.
The price of a house in the area was
£180 000 in 2005.
What was its price in 1995?
Answers
Answer:
£60000
Step-by-step explanation: