Answer:
[tex]x = 5.65m [/tex][tex]\theta = cos^{-1}\bigg(\dfrac{1}{3}\bigg)[/tex]Step-by-step explanation:
Here it's given that a 6m ladder is leaned against a house, and the base of ladder is 2m away from the foot of the house. Here I am assuming x to be the height of the house.
Diagram :-
[tex] \begin{picture}(3,3)\setlength{\unitlength}{1cm} \linethickness{.6mm}\put(0,0){\line(1,0){4}}\put(0.01,0){\line(4,3){4}}\put(4,0){\line(0,1){3}}\put(4.3,1){$\bf x $} \put(2,-0.5){$\bf 2m$}\put(1,1.5){$\bf 6m$}\put(.9,0.2){$\bf\theta $}\put(2,4){$\boxed{\sf - RISH4BH }$}\end{picture} [/tex]
Using, Pythagoras theorem ,
[tex]\longrightarrow h^2=p^2+b^2 [/tex]
Substitute,
[tex]\longrightarrow (6m)^2=x^2+(2m)^2[/tex]
Simplify,
[tex]\longrightarrow 36m^2= x^2+4m^2 [/tex]
Subtracting 4m² on both sides,
[tex]\longrightarrow x^2 = 36m^2 -4m^2=32m^2 [/tex]
Put square root on both sides,
[tex]\longrightarrow x =\sqrt{32m^2}[/tex]
Simplify,
[tex]\longrightarrow \underline{\underline{ x = 5.65\ m}}[/tex]
Again in order to find out the angle of elevation,
[tex]\longrightarrow cos\theta =\dfrac{b}{h} [/tex]
Substitute,
[tex]\longrightarrow cos\theta =\dfrac{2m}{6m}[/tex]
Simplify,
[tex]\longrightarrow cos\theta =\dfrac{1}{3} [/tex]
Take cos inverse both sides,
[tex]\longrightarrow \underline{\underline{\theta =cos^{-1}\bigg(\dfrac{1}{3}\bigg)}}[/tex]
The length of the wall is 5.66m and the angle of elevation is 70.56°
Data;
Length of Ladder (Hypothenuse) = x = 6mDistance from the wall to the foot of the ladder (adjacent)= y = 2mThe length of the side of the house (opposite) = zPythagorean TheoremTo calculate the length of the wall or side of the house, we have to use Pythagorean theorem which is given as
[tex]x^2 = y^2 + z^2[/tex]
Let's substitute the values and solve for the length of the wall
[tex]x^2 = y^2 + z^2 \\6^2 = 2^2 + z^2 \\36 = 4 - z^2\\z^2 = 36 - 4\\z^2 = 32\\z = \sqrt{32} \\z = 5.66m[/tex]
The length of the wall is 5.66m.
Angle of ElevationTo calculate the angle of elevation, we can use trigonometric ratio SOHCAHTOA
since we have the value of all the sides, we can decide to use any of the ratios.
I will use sine angle to solve for the angle of elevation.
[tex]sin \theta = \frac{opposite}{hypothenuse} \\sin \theta = \frac{5.66}{6} \\sin \theta = 0.943\\\theta = sin^-^1 (0.943)\\\theta = 70.56^0[/tex]
The angle of elevation is 70.56°
Learn more on Pythagorean theorem and trigonometric ratio here;
https://brainly.com/question/6241673
Evaluate the following expression, when n=-3 and r=-8
−5 + 3(−2r + 4n)
Pease answer ASAP
Answer:
-8
Step-by-step explanation:
Given that,
n = -3
r = -8
Now we have to find the value of the given expression.
For that, you have to replace n and r with ( -3 ) and ( -8 ) respectively.
Let us solve now.
−5 + 3 ( −2r + 4n )
-5 + 3 ( -2 × -8 + 4 × -3 )
-2 ( 16 - 12 )
-2 × 4
-8
Let me know if you've any other questions. :-)
- Hi1315
help me with this composite figure
Answer: 142 sq. ft
Step-by-step explanation: decompose the figure into two figures. Then, find the length and the width of each figure and find their separate areas. Lastly, add the two areas together to get the total area.
What are the zeros of this function?
A. x = 0 and x = -6
B. X = 2 and x = -6
C. X = 0 and x = 5
D. x = 0 and x = -5
Answer:
c
Step-by-step explanation:
the parabola crosses the x axis at (0,0) and (4,0)
Multiply. Write your answer in simplest form. 4 1/6 x6
NEED ANSER A SAP 20 POINTS
Answer:
41
Step-by-step explanation:
41/6*6
41*6=246
246/6=41
Answer:
[tex]4 \frac{1}{6} \times 6 \\ \\ \frac{25}{6} \times 6 = 25[/tex]
solve the equation for theta (0°≤theta<360°)
2 sin theta = 1
Answer:
30 degrees
Step-by-step explanation:
To figure out theta is using a bit of simple trigonometry.
2sin(theta) = 1
= sin(theta) = 0.5
Using arcsin (sin^-1) we can isolate x
x = arcsin(0.5)
x = 30
What is 1/4 divided by -1/2?
Answer:
1/2
Step-by-step explanation:
KEEP 1/4 CHANGE the sign to multiplication FLIP 1/2 to 2/1
new equation: 1/4 x 2/1
now we can solve
we do: 1 x 2= 2
so 2 is our nominator
then we do: 4 x 1= 4
so 4 is our denominator
combine the nominator and denominator and we get
1/2 which in decimal form is 0.5
Alex’s SUV gets an average of only 15 miles per gallon. Gas costs $2.19 per gallon. Write a rule that gives the cost of a trip C when you know the number of miles d that Alex travels.
Answer:
(d miles)/(15 miles/gallon)*($2.19/gallon)
Step-by-step explanation:
Fuel efficiency = 15 miles/gallon.
Gas is $2.19/gallon.
Total cost is y.
miles is d
The equation that provides the total fuel for a trip in Alex's SUV would be:
Fuel for d miles (gallons) = (d miles)/(15 miles/gallon)
This is the total fuel required for a trip of d miles. Multiply this times the cost per gallon to find the total ciost of the trip:
(d miles)/(15 miles/gallon)*($2.19/gallon) = Total cost for a trip of d miles.
What is 5.8×10^6 seconds in minutes?
Answer:
9.66 x 10⁴ minutes
Step-by-step explanation:
To convert seconds into minutes, simply divide by 60.
=> 5.8 x 10⁶ / 60
=> 580 x 10⁴ / 60
=> 29 x 10⁴ / 3
=> 9.66 x 10⁴ minutes
Answer:
9.6×10^4
Step-by-step explanation:
1 min=60sec
5.8＊10^6 / 60= 9.6×10^4
Solve the equation to find the measures of the unknown angle
Answer:
41 degrees
Step-by-step explanation:
A supplementary angle pair is 180 degrees.
139+x=180
180-139=41
x=41
6) Write a function that can be used to represent
the total cost of apples purchased if one pound
Answer:453.59237
Step-by-step explanation: we know that each apple weighs 120 grams so we can add them up to get 453.59237 it would take about 3 apples to get 453.59237 so 453.59237 is our awnser
melissa is making punch for her party. The recipe calls for 2/5 cups of orange juice for every 1/4 cup of cranberry juice. If melissa uses 1 1/5 cups of orange juice, How many cups of cranberry juice should she use
Answer:
3/4 cups of cranberry juice
if a submarine is 3750 feet below sea level what is the integer
Answer:
-3750
Step-by-step explanation:
+3750
The opposite of + is -
So it would be -3750
A jar contains 125 marbles. Given 2% of the marbles are green, 54% of the marbles are blue, and the rest are red, how many red marbles are in the jar?
there are 55 red marbles in the jar
Answer:
There are 55 red marbles in the jar.
Step-by-step explanation:
Green marbles = 125 x 2/100 = 2.5
Blue marbles = 125 x 54/100 = 67.5
Red marbles = 125 - 67.5 - 2.5 = 55
How many times larger is 90,000 than 900
Answer:
100 times larger
Step-by-step explanation:
All you do is 90,000 divided by 900
90000/900 is 100
This scale drawing shows a reduction in a figure.
What is the value of x?
Enter your answer as a decimal in the box.
x =
Two trapzoids of different sizes. The first trapezoid has a side labeled 8 and the smaller base labeled 3. The second trapezoid has the corresponding side labeled 6 and the corresponding base labeled x.
Answer:
2.25
Step-by-step explanation:
took the quiz, got it wrong, saw the right answer ;)
Which number is an irrational number?
A. 100 squared
B. 1/8
C. -2.2675
D. 3/16
Answer
the answer is D square root of 16 expression 3
Each year the Student Council conducts a food drive. At the end of the drive, the members report on the items collected.
A. Describe two different ways that the students can sort the items that were collected.
B.Write two expressions to represent the number and type of items collected.
C. Share your expression with classmates. How are the expressions similar? How are they different? Why are they different?
Enter your answer.
Answer:
A) Canned and Packet
Grain, Meat and Vegetables
B) Let C = canned goods, let P = packet goods
20C + 7P
Let G = grain, let M = meat, let V = vegetables
7G + 3M + 17V
C) The number of grain and packet goods are the same in each expression, as this food group has been packaged in the same way.
The other variables in both expression are different. The meat and vegetable food groups have been separated in the second expression, whereas they are part of the same group in the first expression.
1.2.2 If aunt Abby needs 625ml of flour, determine how many wedding cakes she can bake with a 2 kg flour.
What are the values of the three trigonometric ratios for angle L, in simplest form?.
The value of the three trigonometric ratios for angle L are 4/5, 3/5, and 4/3.
What are the trigonometric ratios?
The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.
Given
The opposite side of the triangle is 20, the adjacent side is 15, and the hypotenuse is 25.
The three trigonometric ratios are given by;
[tex]\rm Sin \theta=\dfrac{Opposite}{Hypotenuse}\\\\Sin\theta=\dfrac{20}{25}\\\\Sin\theta=\dfrac{4}{5}\\\\\rm Cos\theta=\dfrac{Adjacent}{Hypotenuse}\\\\ \rm \rm Cos\theta=\dfrac{15}{25}}\\\\ \rm Cos \theta =\dfrac{3}{5}\\\\\rm Tan\theta =\dfrac{Opposite }{Adjacent}\\\\\rm Tan \theta =\dfrac{20}{15}\\\\Tan \theta=\dfrac{4}{3}[/tex]
Hence, the value of the three trigonometric ratios for angle L are 4/5, 3/5, and 4/3.
To know more about trigonometric ratios click the link given below.
https://brainly.com/question/8308608
One weekend Ella sells a total of 52 prints for a total of $2,975.Small prints cost $50 and large prints cost $75. How many of each size print did Ella sell?
Answer:
ella sold 37 small prints and 15 large prints.
Step-by-step explanation:
37×50=1850
15×75=1125
1850+1125=2975
16. Find mZW.
X
15
W
Y
25°
22
Z
Answer:
a 14 can be close so that we can get are our answer
Answer:48.7
Step-by-step explanation: its right
Please help me fill the graph!!!
I am writing an essay. I want to write about Italian Greyhounds, but don't have one. Does anybody here have one who can tell me some stories?
answer:
reddit has a lot of stories on various topics i recommend checking out
the app or website. i have an american pitbull terrier, so i have stories about them not greyhounds. although, you can also search ‘raising a Italian-greyhound blog post’ so that you can have access to multiple stories from different perspectives that way.
best of luck!
Round 6,824 to the nearest ten.
Answer:
It would be 6.8
Answer:
6,820
Step-by-step explanation:
round from the tens place digit.
If a rounded number has a ones place digit of less than 5, round to 0. If a rounded number has a ones place digit of 5, round to the next ten.If a rounded number has a ones place digit of more than 5,round to the next ten.
pls pls pls pls help me ( show your work ).
Answer:
14:250 15:2800
Step-by-step explanation:
14: 32%=80 dividing both sides by 8 we get 4% = 10. multiply both sides by 25 and we get 100%=250
15: same strategy, 2%=56 so 1%=28. multiply by 100 to get 100%=2800
A sandwich shop has 60 stores and 80% of the stores are in California. The rest of the stores are in Nevada.
How many stores are in California and how many are in Nevada?
Paisley and her dad are digging a pond in their yard. They know the diameter will be 50 yards. What will the area of the pond be?
pls help i need soon will give brain liest if right
Answer:
See step-by-step, as it depends which value of pi you use.
Step-by-step explanation:
Equations
Diameter = [tex]2r[/tex]Area of a circle = [tex]\pi r^2[/tex] (where r is the radius)Assuming the pond is circular...
Diameter of pond = 50 yd ⇒ r = 50 ÷ 2 = 25 yd
Substitute r = 25 into the equation for the area of a circle:
[tex]\implies A= \pi \times25^2=625\pi[/tex] yd²
Using [tex]\pi =3.14[/tex], area = 1962.5 yd²
Using [tex]\pi=\dfrac{22}{7}[/tex], area = 1964.3 yd² (nearest tenth)
Using [tex]\pi[/tex], area = 1963.5 yd² (nearest tenth)
Find the lateral surface area of the triangular prism. A) 84 in2 B) 90 in2 C) 96 in2 D) 104 in2.
The lateral surface area of the provided triangular prism is 96 square inches. Option C is the correct option.
What is surface area?Surface area of any solid or the 3 dimensional body is the area of each faces by which the solid body is enclosed.
The lateral surface area of the triangular prism can be calculated with the following formula.
[tex]A_{LS}=h(a+b+c)[/tex]
Here, (a,b,c) are the bases of the rectangular faces and (h) is the common height.
The image of the triangular prism is attached below. In the given triangular prism, the common height is 8 in and bases of the rectangular faces are 5 in, 4 in and 3 in long.
To find the lateral surface area of the given triangular prism, put the values in the above formula.
[tex]A_{LS}=8(5+4+3)\\A_{LS}=8(12)\\A_{LS}=96\rm\; in^2[/tex]
Thus, the lateral surface area of the provided triangular prism is 96 square inches. Option C is the correct option.
Learn more about the surface area here:
https://brainly.com/question/20771646
Question 1
What value of “n” makes the equation true?
Provide evidence.
-n + 8 = 12
Answer: " n = - 4 " .
__________
Step-by-step explanation:
Given:
-n + 8 = 12 ; solve for "n" ;
Subtract "8" from each side of the equation:
-n + 8 - 8 = 12 - 8 ;
to get:
-n = 4 ;
Which is the same as:
-1n = 4 ;
Divide each side of the equation by "-1" ; to isolate "n" on one side of the equation; and to solve for "n" :
-1n / -1 = 4 / -1 ;
to get:
" n = - 4 " ; which is our answer.
_______________
Now, let's check our answer:
_______________
→ by plugging in our value obtained for "n" ; which is " - 4 " ;
_______________
-(-4) + 8 ≟ 12 ?? ;
_______________
From the "left-hand sign" of the equation:
_______________
" - (-4) = ⁺ 4 " ;
_______________
Note: The opposite of negative value; or the negative of a negative value; is equal to that very positive value.
_______________
⇒ " 4 + 8 ≟ 12 ? ;
⇒ " 12 ≟ 12 ? ; Yes!
_______________
The correct answer is: " n = - 4 " .
_______________
Hope this helps! Best wishes!
_______________
A square has a side length of n + 6. A rectangle has length n + 15 and width of
n - 3.
Find the perimeter of each figure. Are the perimeters the same? Explain
your reasoning.
Answer:
I'm pretty sure you have to add everything
