PLEASE OF YOU CAN SHOW THE WORK:
The accompanying diagram shows a flagpole that stands on level ground. Two cables, r and s, are attached to a pole at a point 20 feet above the ground. The combine length of the two cables is 70 feet. If cable r is attached to the ground 8 feet from the base of the pole, what is the measure of the angle, x, to the nearest degree, that cable s makes with the ground? N = 20 ft S 8 t
Answers
Answer:
[tex]x\approx24^\circ[/tex]
Step-by-step explanation:
We know that r and s have a combined length of 70. Therefore:
[tex]r+s=70[/tex]
Notice that we can determine r by using the Pythagorean Theorem. In this case, r is the hypotenuse, and 20 and 8 are the legs. Therefore:
[tex]a^2+b^2=c^2[/tex]
Substituting 20 and 8 for a and b and r for c yields:
[tex]20^2+8^2=r^2[/tex]
Compute:
[tex]464=r^2[/tex]
Therefore:
[tex]r=\sqrt{464}=\sqrt{16\cdot 29}=4\sqrt{29}[/tex]
Now, we can determine s. We know that:
[tex]s+r=70[/tex]
So, by substitution:
[tex]s+4\sqrt{29}=70[/tex]
Therefore:
[tex]s=70-4\sqrt{29}[/tex]
Now, notice that, with respect to x, 20 is the opposite side and s is the hypotenuse.
Therefore, we can use the sine ratio. The sine ratio is the ratio between a right triangles opposite side to its hypotenuse.
In this case, the opposite to x is 20, and the hypotenuse is s, or 70-4√29. Therefore:
[tex]\displaystyle \sin(x^\circ)=\frac{20}{s}[/tex]
By substitution:
[tex]\displaystyle \sin(x^\circ)=\frac{20}{70-4\sqrt{29}}[/tex]
Take the inverse sine of both sides:
[tex]\displaystyle x^\circ=\sin^{-1}\Big(\frac{20}{70-4 \sqrt{29}} \Big)[/tex]
Use a calculator. Therefore:
[tex]x\approx24.37^\circ\approx24^\circ[/tex]
Related Questions
Please answer correctly !!!!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!!!!
Answers
p = √24
Step-by-step explanation:
5² = 1² + p²
25 - 1 = p²
p² = 24
p = √24
The following rectangle has an area of 3x^2-5x-12. What are the possible side lengths, in terms of x? Explain your answer and justify how you know that the sides you found are possible lengths
Answers
Answer:
the possible side lengths:
3x+4 and x-3
Step-by-step explanation:
factorize the the expression and you will get two expressions in terms of x. those expressions are the lengths of the rectangle
[tex]3 {x}^{2} - 5x - 12[/tex]
1) write -5x as a difference
[tex]3 {x}^{2} + 4x - 9x - 12[/tex]
2) factor out x from the expression 3x²+4x
[tex]x(3x + 4) - 9x - 12[/tex]
3) factor out -3 from the expression -9x-12
[tex]x(3x + 4) - 3(3x + 4)[/tex]
4) factor out 3x+4 from the expression
[tex](3x + 4)( x - 3)[/tex]
the possible lengths are 3x+4 and x-3
to check whether the answer is correct, you can just multiply the both lengths using the area of rectangle formulae
area of rectangle formulae
[tex]length \times height[/tex]
(3x+4)(x-3)
= 3x²-9x+4x-12
= 3x²-5x-12 ( proven )
which graph represents the equation (x-3)^2 + y^2 =16
Answers
Answer:
C
Step-by-step explanation:
Got it right
Answer:
Graph C
Step-by-step explanation:
Edge
What value of x is in the solution set of 9(2x + 1)< 9x-18?
O4.
O-3
) -2
)-1
Answers
Answer:
x < -3
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Step-by-step explanation:
Step 1: Define
9(2x + 1) < 9x - 18
Step 2: Solve for x
Distribute 9: 18x + 9 < 9x - 18Isolate x terms: 9x + 9 < -18Isolate x term: 9x < -27Isolate x: x < -3Here we see any value x smaller than -3 would work as a solution to the inequality.
{16
x+y = 4.25
16.90x + 4y = 36.35
1. What does the solution to the system represent?
Answers
Answer:
See below.
Step-by-step explanation:
It represents the coordinates of the point of intersection of the lines represented by the 2 equations.
Do you want them solved?
Simplify: (5x2 - 9x + 3) + (4x2 + 4x - 12)
(1) 9x2 + 5x - 9
2) 9x2 - 5x + 15
3) 9x² - 5x-9
4) 9x2 - 13x - 9
Answers
Answer:
3) 9x² - 5x - 9
Step-by-step explanation:
Combine like terms
5x² - 9x + 3 + 4x² + 4x - 12 = 5x² + 4x² - 9x + 4x + 3 - 12
= 9x² - 5x - 9
NEED HELP ASSP!! please help!!??
Answers
Answer:
Step-by-step explanation:
this is a 30 60 90 triangle.. b/c 2 of the angles are given and you know the total is 180 around a triangle so the last angle is 30
also you know the hypotenuse of this triangle is 10 so use cos and sin to figure out the other sides
Use SOH CAH TOA to remember how the sin and cos functions fit on the triangle
CAH = Cos(Ф) = Adj/ Hyp we are given the Ф angle and we know the hypotenuse so solve for the Adj side
Hyp*Cos(Ф)= Adj
10 * Cos(60) = Adj
5 = Adj = y
Use Sin for the other side and the mnemonic to remember how it fits on the triangle and solve for the Opposite , since we don't know that .. yet
Sin(Ф) = Opp/ Hyp
Hyp * Sin (Ф) = Opp
10 * Sin(60) = Opp
10 *[tex]\sqrt{3}[/tex]/2 = Opp
5*[tex]\sqrt{3}[/tex] = Opp = x
:) I know Sin(60) = [tex]\sqrt{3}[/tex]/2 from a table and also my memory .. know that one from memory
Write an equation that will satisfy the x and y values in the table below.
Answers
Answer:
The equation that will satisfy x and y values in the table is y = 2x + 3
Step-by-step explanation:
The form of the linear equation is y = m x + b, where
m is the slope of the line that represents the equation b is the y-intercept, value y at x = 0The rule of the slope of the line is m = [tex]\frac{y2-y1}{x2-x1}[/tex] , where
(x1, y1) and (x2, y2) are two points on the lineFrom the given table
∵ x = 0 and y = 3, x = 1 and y = 5
∴ x1 = 0 and x2 = 1
∴ y1 = 3 and y2 = 5
→ Substitute them in the rule of the slope above
∵ m = [tex]\frac{5-3}{1-0}[/tex] = [tex]\frac{2}{1}[/tex]
∴ m = 2
∵ b is the value of y at x = 0
∵ y = 3 at x = 0
∴ b = 3
→ Substitute the values of m, b in the form of the equation above
∴ y = 2x + 3
∴ The equation that will satisfy x and y values in the table is y = 2x + 3
Why do 25 ÷ 10 and 250 ÷ 100 give the same answer?
Answers
Answer:
One zero can be cancel out from both the numerator and denominator of [tex]250[/tex] ÷ [tex]100[/tex]
Step-by-step explanation:
[tex]25[/tex] ÷ [tex]10[/tex] [tex]=\frac{25}{10}=\frac{5}{2}[/tex]
[tex]250[/tex] ÷ [tex]100[/tex] [tex]=\frac{250}{100}=\frac{5}{2}[/tex]
Therefore,
[tex]25[/tex] ÷ [tex]10[/tex] [tex]=[/tex] [tex]250[/tex] ÷ [tex]100[/tex]
Here, 25 ÷ 10 and 250 ÷ 100 give the same answer.
Here, one zero can be cancel out from both the numerator and denominator of [tex]250[/tex] ÷ [tex]100[/tex]
Can someone please help
Answers
Answer:
-3/4 is correct answer
What is electrical energy converted to inside a toaster?
A. thermal energy and light
B. nuclear energy
C. chemical energy
D. kinetic energy
Answers
could somebody help me on the 2 question please
Answers
Answer:
on question 2 the one which you need to write is -20 degrees bcz it's colder than -10 degreesStep-by-step explanation:
where is the question 1
+this sentence :" is -20 degrees bcz it's colder than -10 degrees "is a 2answer sentence
hope this helps
Multiple Choice!!!!!!What congruence theorem can you use to show that the two skateboard ramps have the same height?
Answers
Answer:HL
Step-by-step explanation:
Transitive Property of Congruence
If MN = LK and LK = OP, then
Answers
Answer:
If MN=LK and LK=OP, then MN= OP
Answer:
MN = OP
Step-by-step explanation:
How do you use substitution to solve a system of linear equations?
Answers
Answer:
Step 1 : First, solve one linear equation for y in terms of x .
Step 2 : Then substitute that expression for y in the other linear equation. ...
Step 3 : Solve this, and you have the x -coordinate of the intersection.
Step 4 : Then plug in x to either equation to find the corresponding y -coordinate.
(hope this helps :) )
I have a question on Khan Academy and it says super salad dressing is made with 8 mL of oil for every 3 ml of vinegar which of the following mixtures will take the same as super salad dressing
then it says choose 3 answers there's 5 choices a b c and d a is 80 ml of oil with 30 ml of vinegar
B is 3 ml oil with 8 ml of vinegar
C is 56 mL of oil with 21 mL of vinegar
d 40 mL of oil with 25 mL of vinegar
e is 48 mL of oil with 18 mL of vinegar
Answers
Answer:
e
Step-by-step explanation:
8ml x 6= 48ml of oil
3ml x 6= 18ml of vineger
I need help wit this
Answers
Answer:
75
Step-by-step explanation:
\+_+/
Name the property that justifies the following statement: If 2x + 4 = y and y = 3x - 6 then 2x + 4 = 3x - 6.
Answers
9514 1404 393
Answer:
transitive property of equality
Step-by-step explanation:
The transitive property of equality says ...
if a = b and b = c, then a = c.
Here, we can use this form with ...
a = 2x+4
b = y
c = 3x-6
__
We have ...
a = b ⇒ 2x +4 = y
b = c ⇒ y = 3x -6
so, ...
a = c ⇒ 2x +4 = 3x -6 . . . . transitive property of equality.
_____
On the other hand, ...
The substitution property of equality says ...
if a = b, we can use b wherever 'a' is seen.
We can use this with ...
a = y
b = 3x -6
and do the substitution in the equation ...
2x +4 = y
Replacing y with its equal, we get ...
2x +4 = 'a' ⇒ 2x +4 = 'b' ⇒ 2x +4 = 3x -6 . . . . substitution property of equality
_____
Additional comment
These are two different ways to say that anything can be replaced by its equal.
Graph y < x and y ≥ 4x + 2
Answers
Answer:
Image is attached.
Step-by-step explanation:
Remember since the blue line is greater than, instead of being dashed like the red line, it's solid.
Frankie wants to build a path from one corner of his hard to the opposite corner his yard measures 20ft x 32ft what will be the length of his path to the nearest tenth of a foot
Answers
Answer:
37.7 feet
Step-by-step explanation:
Given that:
Measurements of Frankie's yard = 20ft x 32ft
He wants to build a path from one corner to another.
To find:
The length of path = ?
Solution:
Let us consider a rectangle [tex]ABCD[/tex] as shown in the attached image in the answer area.
We are given the two adjacent sides of a rectangle and we have to find diagonal of the rectangle.
To find the diagonal, we can use the Pythagorean Theorem.
We are given the base and perpendicular of the right angled triangle and we have to find the hypotenuse.
According to Pythagorean theorem:
[tex]\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Perpendicular}^{2}[/tex]
[tex]Diagonal = 20^2 + 32^2\\\Rightarrow Diagonal = 400 + 1024\\\Rightarrow Diagonal = \bold{37.7\ ft}[/tex]
a factor of all even numbers other than 1? pls answer quick
Answers
Explanation: 2 is a prime number that is a factor for all even numbers.
if an object has a density of 3.6g/ml and you put it into water, will it sink or float?
Answers
Answer:
Sink
Step-by-step explanation:
We need to find if an object with a certain density will float or sink in water.
The object will sink in water.
The density of the object is 3.6 g/mL
The density of water is generally [tex]1000\ \text{kg/m}^3[/tex]
An object which has a density more than the liquid it is in then the object will sink.
Let us convert the density of the object to [tex]\text{kg/m}^3[/tex]
[tex]1\ \text{g}=10^{-3}\ \text{kg}[/tex]
[tex]1\ \text{mL}=10^{-6}\ \text{m}^3[/tex]
[tex]1\ \text{g/mL}=\dfrac{10^{-3}}{10^{-6}}=10^3\ \text{kg/m}^3[/tex]
[tex]3.6\ \text{g/mL}=3.6\times 10^3=3600\ \text{kg/m}^3[/tex]
The density of the object [tex](3600\ \text{kg/m}^3)[/tex] is greater than that of water [tex](1000\ \text{kg/m}^3)[/tex].
Hence, the object will sink.
Learn more:
https://brainly.com/question/18950364
https://brainly.com/question/2200299
solve for x parallel
Answers
7 years older than 2 times kates age what is the number if kate is 3
Answers
Answer:
13
Step-by-step explanation:
Which point on the graph best represents the location of left parenthesis minus 4.5 comma space minus 7 right parenthesis ?
Answers
Answer:
The answer would be A which is L
Answer:
so its A?
Step-by-step explanation:
P(x) = 2x3 – x2 + 4x + 5 is divided by x + 2. Choose the correct option from each drop-down menu.
When P(x) is divided by x + 2, the remainder is [ ] P(–2) = [ ]. The Remainder Theorem is [verfied/not verified] ]
Answers
The remainder of the division of polynomial, P(x) = 2x3 – x2 + 4x + 5 by (x + 2) is; -23
The remainder of the division of the polynomial, P(x) = 2x3 – x2 + 4x + 5 by (x + 2) can be evaluated by the remainder theorem.
This involves adding evaluating the value of the polynomial at, x = -2.
Since, (x +2) is the Divisor, we evaluate, P(x) at x = -2Therefore, we have;
P(-2) = 2 ×(-2)³ -(-2)² + 4(-2) + 5P(-2) = -16 -4 -8 +5P(-2) = -23.Therefore, the remainder when P(x) = 2x3 – x2 + 4x + 5 is divided by (x + 2) is; -23
Read more:
https://brainly.com/question/11456067
Why is the boxplot incorrect?
The following are the temperatures, in degrees
Fahrenheit, of 20 US cities on April 3rd. The boxplot
represents the data
42, 47, 48, 50, 50, 50, 51, 51, 52, 52, 54, 55, 55, 55, 56,
57, 58, 59, 59, 60
O The minimum temperature is 42°F, but the boxplot
shows 46°F.
O The maximum temperature is 60°F, but the boxplot
shows 66°F.
O The median temperature is 53°F, but the boxplot
shows 52°F.
O The first quartile temperature is 50°F, but the
boxplot shows 53°F.
April 3 Temperatures
46 48 50 52 54 56 58 60
Answers
Step-by-step explanation:
The minimum temperature is 42F, but the boxplot shows 46F
Answer:
A) The minimum temperature is 42°F, but the boxplot
shows 46°F.
Identify the parent function. 5 --5
a absolute
b reciprocal
c cube root
d square root
Answers
Step-by-step explanation:
For an absolute value function, the graph will look like an arrow with a sharp inflection point.
Reciprocal function will tend towards a limit when stretched to infinity.
Cube root and square root functions do not tend towards infinity at x = 0, because it is either 0 or the constant value.
The best answer here is Reciprocal. (B)
Answer:
b reciprocalStep-by-step explanation:
The graphed is the function y = 1/x, it is an odd function and the graph is hyperbola
The function is reciprocal
Correct option is B
Find the rate of change
Pls help thx
Answers
Answer:3
Step-by-step explanation:
Go up from one point to the other and whatever the number comes is the answer.
HURRY PLEASEEE!!!! it’s due soon!!
Answers
Answer:
Cost for 2 hours= $19
Step-by-step explanation:
11+4t
Answer:
2 hours: $19
t hours: 4t+11
Step-by-step explanation:
you pay 4 dollars per hour so it would be 4t and the entry fee is 11, so you add them together.