When it comes to right triangles, there's one extremely important equation that you'll have to use almost every single time you come across one: the Pythagorean Theorem.
[tex]a^{2} + b^{2} = c^{2}[/tex]... Does that equation ring any bells? This equation is utilized to solve for any of the sides of a right triangle, given that you know the values of two of the sides. in a right triangle, there are three sides - one of which is known as a hypotenuse (the longest side of a right triangle). Variables a and b represent the lengths of the non-hypotenuse sides (basically, the two smaller sides, the ones that form a right angle). There's no special rule to which side is designated a and which is designated b, so don't worry about trying to figure out which side should be labeled which. Variable c represents the length of the hypotenuse.
Now, how can we apply the Pythagorean Theorem to this question? We are given the values of the two legs of the triangle, 1 m and [tex]\sqrt{15}[/tex] m. Since we are prompted to solve for the length of the hypotenuse, we will use the Pythagorean Theorem and solve for c, the variable for the length of the hypotenuse.
[tex]c^{2} = a^{2} + b^{2}[/tex]
c = [tex]\sqrt{a^{2} + b^{2} }[/tex]
(We square root both sides in order to isolate c. Now, let's plug in the values we were given. As we learned earlier, it doesn't matter which leg is a or b)
c = [tex]\sqrt{1^{2} + \sqrt{15}^{2} }[/tex]
c = [tex]\sqrt{1 + 15}[/tex]
c = [tex]\sqrt{16}[/tex]
c = 4 (m)
The length of the hypotenuse is 4 meters.
And we're done! Though I wrote a lot, the equation is fairly simple and will come extremely handy any time you're faced with questions like these. If you have any questions about anything I wrote here or you need clarification on anything, let me know!
- breezy ツ
A 15 ft long cable is connected from a hook to the top of a pole that has an unknown height. The distance from the hook to the base of the pole is 3 ft shorter than the height of the pole.
a. What can you use to find the height of the pole?
b. Write and solve a quadratic equation to find the height of the pole.
c. How far is the hook from the base of the pole?
Answer:
a) Pythagoras' Theorem: a² + b² = c²
(where a and b are the legs, and c is the hypotenuse, of a right triangle)
b) Given:
a = (x - 3)b = xc = 15Substituting these values into the equation and rearranging:
⇒ (x - 3)² + x² = 15²
⇒ x² - 6x + 9 + x² = 225
⇒ 2x² - 6x - 216 = 0
c) Solve 2x² - 6x - 216 = 0 by factorizing:
2x² - 6x - 216 = 0
⇒ x² - 3x - 108 = 0
⇒ x² - 12x + 9x - 108 = 0
⇒ x(x - 12) + 9(x - 12) = 0
⇒ (x - 12)(x + 9) = 0
⇒ x - 12 = 0 ⇒ x = 12
⇒ x + 9 = 0 ⇒ x = -9
As distance is positive, x = 12 only.
Therefore, the height of the pole is 12 ft.
So the distance from the hook to the base = 12 - 3 = 9 ft
We need x
Apply Pythagorean theorem
[tex]\\ \rm\Rrightarrow 15^2-x^2=(x-3)^2[/tex]
[tex]\\ \rm\Rrightarrow 225-x^2=x^2-6x+9[/tex]
[tex]\\ \rm\Rrightarrow 2x^2-6x-216=0[/tex]
[tex]\\ \rm\Rrightarrow x^2-3x-108=0[/tex]
[tex]\\ \rm\Rrightarrow (x+9)(x-12)=0[/tex]
[tex]\\ \rm\Rrightarrow x=-9,12[/tex]
Distance must be positive so x=12Make a number line and mark the points that represent the following values of x. X ≤ 1 2/3 and x <- 3/4
Answer:
can't you do Russian math homework on your own
Step-by-step explanation:
In the data set (0,-1);(-2,4);(-4,-8);(-1,5);(2,1);(-1,2)},which point is a possible outlier?
que dijiste buenas noches
Samantha gathered the following information on a given day at the dog park.
• There are 3232 dogs playing at the dog park.
• 1515 of the dogs are puppies.
• 1111 of the dogs are not puppies and have long hair.
• There are 66 more dogs that have long hair than dogs that do not have long hair.
Fill in the table completely to represent Samantha's data.
The number of dogs that are not puppies is 17, the number of adult dogs without long hair is 6, the number of puppy dogs with long hair is 8 and the number of puppy dogs without long hair is 7.
What is the information missing?To complete the chart it is necessary to determine:
Number of dogs that are not puppies.Number of puppies with and without long hairNumber of adult dogs without long hairNumber of dogs that are not puppies:
32 (total dogs) - 15 (puppies) = 17 dogsAdult dogs without long hair:
17 (total adult dogs) - 11 (adult dogs with long hair) = 6 dogsPuppy dogs with and without long hair
Total of puppy dogs = 15, this number can be obtained by adding 9+6 or 7+8. From these combinations, the only one that meets the rule "There are 6 more dogs that have long hair than dogs that do not have long hair" is 8 puppies with long hair and 7 puppies without long hair.
Note: This question is not written correctly; here is the correct and complete question.
Samantha gathered the following information on a given day at the dog park.
There are 32 dogs playing at the dog park.
15 of the dogs are puppies.
11 of the dogs are not puppies and have long hair.
There are 6 more dogs that have long hair than dogs that do not have long hair.
Fill in the table completely to represent Samantha’s data.
Learn more about dogs in: https://brainly.com/question/8565422
PLS HELP!! NO LINKS!! WILL MARK YOU BRAINLIEST!!
Answer:
(d) -11
Step-by-step explanation:
The sum of the acute angles of a right triangle is 90°. (That makes the sum of all angles be 180°, as it is for any triangle.)
65° +(36 +x)° = 90°
x = 90 -101 . . . . . . . . divide by °, subtract 101
x = -11
How many times greater than 6 x 10^6 is 2.4 x 10^8 ? Show ur work
Answer:
you think about it. if you dont do the work yourself u wont ever learn.
Step-by-step explanation:
6x10^6=6,000,000
2.4x10^8=240,000,000
The sides of a triangular plot are in the ratio 3 : 5 : 7 and its perimeter is 300 m. find its area
Given :
The sides of a triangular plot are in the ratio 3 : 5 : 7 .Its perimeter is 300 m.⠀
To Find :
Its area.⠀
Solution :
Let us assume the sides in metres be 3x, 5x and 7x .⠀
Then, We know,
[tex] \qquad \sf \dashrightarrow \: 3x + 5x + 7x = 300 \: \: \: \: \: \: \: Perimeter_{(Triangle)}[/tex]
[tex]\qquad \sf \dashrightarrow \: 15x = 300 [/tex]
[tex]\qquad \sf \dashrightarrow \: x = \dfrac{300}{15} [/tex]
[tex]\qquad \bf\dashrightarrow \: x = 20 [/tex]
⠀
So, The sides of the triangle are :
[tex]\qquad \sf \dashrightarrow \: 3 \times 20 \: m = \bf60 \: m [/tex]
[tex]\qquad \sf \dashrightarrow \: 5 \times 20 \: m = \bf 100 \: m [/tex]
[tex]\qquad \sf \dashrightarrow \: 7 \times 20 \: m = \bf140 \: m [/tex]
⠀
Now, Using Heron's formula :
We have,
[tex]\qquad \sf \dashrightarrow \: s = ( {60 + 100 + 140}) \: m = 300 \: m [/tex]
[tex]\qquad \sf \dashrightarrow \: s = \dfrac {60 + 100 + 140}2 \: m = 150 \: m [/tex]
⠀
And the Area will be :
[tex]\qquad \sf \dashrightarrow \: \sqrt{150(150 - 60)(150 - 100)(150 - 140)} \: {m}^{2} [/tex]
[tex]\qquad \sf \dashrightarrow \: \sqrt{150 \times 90 \times 50 \times 10} \: \: {m}^{2} [/tex]
[tex] \qquad \sf \dashrightarrow \: 1500 \sqrt{3} \: {m}^{2} [/tex]
Answer:
2598m²
Step-by-step explanation:
Figure :
[tex]\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\thicklines\qbezier(1, 0)(1,0)(3,3)\qbezier(5,0)(5,0)(3,3)\qbezier(5,0)(1,0)(1,0)\put(2.85,3.2){$\bf A$}\put(0.5,-0.3){$\bf C$}\put(5.2,-0.3){$\bf B$}\put(5,1){$\bf 3x $}\put(2.5, - .5){$\bf 7x $}\put(.5,1){$\bf 5x $}\put(4.5,4){$\bf not \: to \: scale \: $}\end{picture} [/tex]
Here we are given that the ratio of sides of a triangular plot is 3:5:7 and its perimeter is 300m . We are interested in finding the area of the rectangle . Firstly , let us take the given ratio's HCF be x , then we may write the ratio as ,
[tex]\longrightarrow 3x : 5x : 7x [/tex]
According to the question ,
[tex]\longrightarrow 3x + 5x + 7x = 300m \\ [/tex]
[tex]\longrightarrow 15x = 300m\\ [/tex]
[tex]\longrightarrow x =\dfrac{300m}{15}\\ [/tex]
[tex]\longrightarrow x = 20m [/tex]
Therefore , the sides will be ,
[tex]\longrightarrow 3x = 3(20m) = \red{60m}\\ [/tex]
[tex]\longrightarrow 5x =5(20m)= \red{100m}\\ [/tex]
[tex]\longrightarrow 7x =7(20m)=\red{140m}[/tex]
Now we may use Heron's Formula to find out the area of triangle as ,
Heron's Formula :-
If three sides of a ∆ is a , b , c then the area is given by [tex]\sqrt{ s(s-a)(s-b)(s-c)}[/tex] , where s is the semi perimeter .Here ,
[tex]\longrightarrow s =\dfrac{300m}{2}=150m [/tex]
Therefore ,
[tex]\longrightarrow Area =\sqrt{ 150(150-60)(150-100)(150-140)}m^2\\ [/tex]
[tex]\longrightarrow Area =\sqrt{ 150 \times 90 \times 50 \times 10}m^2\\ [/tex]
[tex]\longrightarrow Area = \sqrt{ 50^2 \times 30^2\times 3}m^2\\[/tex]
[tex]\longrightarrow Area = 50\times 30 \times 1.732 m^2\\[/tex]
[tex]\longrightarrow\underline{\underline{ Area = 2598m^2}} [/tex]
And we are done !
2. Which of the following represents a function? 5 points A. {(9, 15), (0, 0), (4, 0), (9, 2)} B. {(2, 5), (-2, 0), (1, -8), (2, 2)} C. {(3, 7), (4, 7), (5, 7), (6, 7)} D. {(3, 3), (-1, 4), (3, -2), (5, 4)
Answer:
C
Step-by-step explanation:
Each input value can have only one output value for it to be a function. In other words, there should only be one y value for each x value. The only option that satisfies this is C.
if p= 6-2y, work out p when y=-5
Answer:
the answer is so you need takes Away -5
A box of crisps contains 48 packets. How many packets will there be in 263 boxes
Answer:
12624 packets
Step-by-step explanation:
To solve this let the unknown number of packets be x.
1 box ⇒ 48 packets
263 boxes ⇒ x
Now let us use cross multiplication to find the value of x.
1 × x = 48 × 263
1x = 12624
Divide both sides by 1.
x = 12624
What type of solid is shown?
Answer:
x^2-x^2=BC4
oh yeaa u know im right
Please help me I’m lost
We are given with an equation and need to find it's solution set also we are given with a condition that m ≠ {0, 1} . So , let's start ;
So we are given with :
[tex]{:\implies \quad \sf \dfrac{6}{m}+2=\dfrac{m+3}{m-1}}[/tex]
First , we will simplify the given Equation and then we will solve it . So , now taking LCM in LHS ;
[tex]{:\implies \quad \sf \dfrac{6+2m}{m}=\dfrac{m+3}{m-1}}[/tex]
Now , Cross Multiplying ;
[tex]{:\implies \quad \sf (m-1)(6+2m)=m(m+3)}[/tex]
[tex]{:\implies \quad \sf m(6+2m)-1(6+2m)=m^{2}+3m}[/tex]
[tex]{:\implies \quad \sf 6m+2m^{2}-6-2m=m^{2}+3m}[/tex]
Now , transposing whole RHS to LHS and collecting like terms ;
[tex]{:\implies \quad \sf (2m^{2}-m^{2})+(6m-2m-3m)-6=0}[/tex]
[tex]{:\implies \quad \sf m^{2}+m-6=0}[/tex]
Now , we will solve this by splitting the Middle term ;
[tex]{:\implies \quad \sf m^{2}+3m-2m-6=0}[/tex]
[tex]{:\implies \quad \sf m(m+3)-2(m+3)=0}[/tex]
[tex]{:\implies \quad \sf (m+3)(m-2)=0}[/tex]
So , now either , m+3 = 0 or m-2 = 0 . On simplification we will get , m = 2 , -3. So m = {-3, 2}
Hence Option 1) {-3, 2} is correct
Which value for x will result in the greatest relative frequency given discrete random variable X, when X∼B(4,110)? x=5 x=1 x=0 x=3
The greatest relative frequency is the relative frequency that gives the highest probability
The greatest relative frequency given discrete random variable X, when X∼B(4,110) is x=3
How to determine the greatest relative frequencyFor a discrete random variable, the smaller the value of the variable, the higher its relative frequency.
This means that:
A variable x = 0 would have a greater relative frequency than a variable x = n, where n > 0
This means that, the greatest relative frequency given discrete random variable X, when X∼B(4,110) is x=3
Read more about relative frequency at:
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Please help and give an explanation. I have a test on this soon.
Answer:
(a) = 26.4 or (132/5); 0
(b) = 26.4 or (132/5); -220
(c) = 0; -220
(d) = 0
Step-by-step explanation:
-5k²- 22k + 15
(a)
-5( -3/5 )² - 22( -3/5 ) + 15
-1.8 + 13.2 + 15 = 26.4 or
(-9/5) + (66/5) + 15 = (132/5)
I don't know if you do decimal points or fractions so I did both.
-5( -5 )² - 22( -5 ) + 15
-125 + 110 + 15 = 0
(b) -5 ( -3/5 )²- 22( -3/5 ) + 15
-1.8 + 13.2 + 15 = 26.4 or
(-9/5) + (66/5) + 15 = (132/5)
-5 ( 5 )²- 22( 5 ) + 15
-125 - 110 + 15 = -220
(c)
-5 ( 3/5 )²- 22( 3/5 ) + 15
-1.8 - 13.2 + 15 = 0 or
(-9/5) - (66/5) + 15 = 0
-5 ( 5 )²- 22( 5 ) + 15
-125 - 110 + 15 = -220
(d)
-5 ( 3/5 )²- 22( 3/5 ) + 15
-1.8 - 13.2 + 15 = 0 or
(-9/5) - (66/5) + 15 = 0
-5( -5 )² - 22( -5 ) + 15
-125 + 110 + 15 = 0
I hope this helps!
Express the area of the following figure as a monomial.
It's a rectangle
Length=x^5Breadth=x^2Area:-
Length×Breadthx^5(x^2)x^5+2x^7125 people work at a hotel, 12% work in the kitchen. How many
people work in the kitchen?
Step-by-step explanation:
12% of 125
or is ×
12% × 125
12% as a decimal
do you know what 12% is as a decimal comment below
Answer:
15
Step-by-step explanation:
12% of 125 is 15
On a coordinate plane, a line X Y has points (negative 2, 4) and (3, negative 2).
Which points can be used in the diagram as the third vertex to create a right triangle with hypotenuse XY? Select all that apply.
(–4, –2)
(–2, 1)
(–2, –2)
(2, 4)
(3, 4)
=====================================================
Explanation:
The x coordinate of (-2,4) is -2
The y coordinate of (3,-2) is -2
Joining those two up gets us (-2,-2) as one of the answers
--------------
The x coordinate of (3,-2) is 3
The y coordinate of (-2,4) is 4
This leads to the other answer (3,4)
Check out the diagram below.
The answer points are marked in red.
Answer:
C. (–2, –2) and E. (3, 4)
Step-by-step explanation:
What is 2. 4% written as a decimal?0. 240. 240. 242. 4
Answer: 0.024
Step-by-step explanation:
percents are out of 100 so 2.4% divided by 100 = the decimal. 2.4/100 = 0.024
Helena has taken out a $9,300 unsubsidized stafford loan to pay for her college education. she plans to graduate in four years. the loan has a duration of ten years and an interest rate of 6.4%, compounded monthly. by the time helena graduates, how much greater will the amount of interest capitalized be than the minimum amount that she could pay to prevent interest capitalization? round all dollar values to the nearest cent. a. $238.46 b. $496.00 c. $595.20 d. $324.33
Answer:
$324.33
Step-by-step explanation:
the answer is $324.33
The amount of interest capitalized is greater than the minimum amount that she could pay to prevent interest capitalization by; D: $324.33
What is the minimum Principal?We will use the formula: A = P(1 + r/n)^(nt)
Where:
A = final amount
P = initial principal ($9300)
r = interest rate (6.4% or 0.064)
n = number of times interest applied per time period
t = number of time period elapsed.
Thus;
9300(1 + 0.064/12)^(12*4) - 9300 = $2705.13
Also;
9300(0.064/12) * 4 * 12 = $2380.8
Answer = $2705.13 - $2380.8
Answer = $324.33
Read more about Principal amount at; https://brainly.com/question/25545513
1, 6, 13, 22, 33, 46, 61 what comes next???????
Answer:
76
its going by 15's so you add 15
>> Question
1, 6, 13, 22, 33, 46, 61 what comes next??
>> Answer :
1, 6, 13, 22, 33, 46, 61, 78, 97, 118, 141, 166
= +5 , +7, +9 , +11, +13, +15, +17, +19, +21, +23, +25
Step-by-step explanation:
I Hope This Helps
1 and 2 are complementary angles. The measure of 1 is 83 . The measure of 2 is 7x-1 . Find the value of x.
Answer: 8/7
Step-by-step explanation:
Please help me out I've been struggling for 3 days now.
A contractor estimates he will need 18 sheets of drywall and 65 square feet of tile to remodel a bathroom. He actually uses 14 sheets of drywall and 42 square feet of tile. To the nearest percent, what is the difference in the percent errors of the estimates? Show your work.
Question 12. Is the one I need help on
Four Answers:
Choice AChoice CChoice DChoice J====================================================
Explanation:
A rational number is any fraction of two whole numbers.
Examples: 7/9 and -8/12
This can be extended to some numbers like [tex]\sqrt{49}[/tex] because
[tex]\sqrt{49} = \sqrt{7^2} = 7 = \frac{7}{1}[/tex]
As you can see, any whole number is also rational but not the other way around.
So far, these examples help show that choices A, C, D, and J are rational numbers. Choice D might need a bit of rewriting like so:
[tex]\frac{0.5}{8} = 0.5 \div 8\\\\ = \frac{1}{2} \div \frac{1}{8} \\\\= \frac{1}{2} \times \frac{8}{1}\\\\ = \frac{8}{2}\\\\ = 4[/tex]
In short, the expression for choice D simplifies to 4 = 4/1 showing that is rational. Or you can use the shortcut that rational/rational = rational.
------------------
A number like [tex]\sqrt{13}[/tex] is NOT rational because the 13 is not a perfect square. There's no way to rewrite that square root as a ratio or fraction of integers. This allows us to rule out choice B. Choices E, F, and G are eliminated for similar reasoning.
Choice H is ruled out because circle areas involve pi = 3.14159... which is famously an irrational number. The proof of which is very lengthy to go over, but the short version is the decimal digits go on forever without a pattern. This is an informal way to check if we have an irrational number.
Choice I is only eliminated if and only if the side lengths of the square are rational, and also when the side lengths are whole numbers. Its not clear what your teacher's intentions here are, but I'll assume this is the case.
------------------
To summarize, we eliminated B, E, F, G, H, I
We're left with A, C, D, J as the final answers. They either can be written as fractions of integers, or already are fractions of integers.
What is the slope of the line perpendicular to x= 3?
A) 0
B) Undefined
C) 3
D) -1/3
Answer:
A) 0
Step-by-step explanation:
x = 3 is a vertical line.
A line perpendicular to x = 3 is a horizontal line.
A horizontal line has slope = 0.
The number of blocks in a two-dimensional pyramid is a sequence that follows a recursive formula. What is a recursive definition for the sequence?
Answer:
A recursive sequence is a sequence in which terms are defined using one or more previous terms which are given. If you know the nth term of an arithmetic sequence and you know the common difference , d , you can find the (n+1)th term using the recursive formula an+1=an+d .
2+3×=2×+3 ---> ×=1
Help please
Answer It's gonna have to be i think mabey also 12
Please this is URGENT!!!!!! need it in the next 5 mins!!!!!!!
Please be my life saver and help me out!
Angelica uses a coordinate plane to make a map of her neighborhood. The point at (4, 3) represents the location of her house, and the point at (10, 8) to represent the location of the gas station. She wants to drive to the gas station using the straight line shown below. Use what you know about right triangles to find out how far she will drive. Each unit on the graph represents 1 mile.
In this answer, give the length of the straight line shown on the graph, and explain how you calculated it.
Answer:
distance: 7.81 miles
Explanation:
simply use distance formula: [tex]\sf \sqrt{(y_2 -y_1)^2 + (x_2-x_1)^2}[/tex]
coordinates: (4, 3), (10, 8)using the equation:
[tex]\hookrightarrow \sf \sqrt{(8-3)^2+(10-4)^2}[/tex]
[tex]\hookrightarrow \sf \sqrt{(5)^2+(6)^2}[/tex]
[tex]\hookrightarrow \sf \sqrt{25+36}[/tex]
[tex]\hookrightarrow \sf \sqrt{61}[/tex]
[tex]\hookrightarrow \sf 7.81 \ miles[/tex]
What is the area of a rectangle with width =7 inches and diagonal =25 inches
Answer:
The area of any rectangular place is or surface is its length multiplied by its width. For example, a garden shaped as a rectangle with a length of 10 yards and width of 3 yards has an area of 10 x 3 = 30 square yards. A rectangular bedroom with one wall being 15 feet long and the other being 12 feet long is simply 12 x 15 = 180 square feet.
Step-by-step explanation:
Round 4,276 to the nearest hundred.
Find the measure of each marked angle.
What is top left and what is bottom right equivalent to!?
And brainliest shall be given.