Find the missing side. Be sure to show all of your work. Round to the nearest tenth
if necessary
Answers
Answer:
x=3.9 approximately
Step-by-step explanation:
Using Pythagorean theorem:
[tex]x^{2} + (5x)^{2} = 20^{2}[/tex]
[tex]x^{2} + 25x^{2} = 400[/tex]
26x^2 =400
x^2 = 15.3846
x=3.9
Equality Properties
Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of EqualityGeometry[Right Triangles Only] Pythagorean Theorem: a² + b² = c²
a is a legb is another legc is the hypotenuseApplicationStep 1: DefineLet's define what the problem gives us:
We are given a right triangle, indicated by the square box inside the triangle, with side lengths 5x and x and a hypotenuse of 20.We can set these measurements equal to our variables defined above in our Pythagorean Theorem equation:
a = 5xb = xc = 20Step 2: WorkNow, we can substitute our variables and solve for x, which will help us find the side lengths as well:
[Pythagorean Theorem] Substitute in variables:[tex]\displaystyle\begin{aligned}a^2 + b^2 & = c^2 \\(5x)^2 + x^2 & = 20^2 \\\end{aligned}[/tex][Order of Operations] Simplify:
[tex]\displaystyle\begin{aligned}a^2 + b^2 & = c^2 \\(5x)^2 + x^2 & = 20^2 \\25x^2 + x^2 & = 400 \\\end{aligned}[/tex][Simplify] Combine like terms:
[tex]\displaystyle\begin{aligned}a^2 + b^2 & = c^2 \\(5x)^2 + x^2 & = 20^2 \\25x^2 + x^2 & = 400 \\26x^2 & = 400 \\\end{aligned}[/tex][Equality Properties] Divide both sides by 26:
[tex]\displaystyle\begin{aligned}a^2 + b^2 & = c^2 \\(5x)^2 + x^2 & = 20^2 \\25x^2 + x^2 & = 400 \\26x^2 & = 400 \\x^2 & = \frac{200}{13} \\\end{aligned}[/tex][Equality Properties] Square root both sides:
[tex]\displaystyle\begin{aligned}a^2 + b^2 & = c^2 \\(5x)^2 + x^2 & = 20^2 \\25x^2 + x^2 & = 400 \\26x^2 & = 400 \\x^2 & = \frac{200}{13} \\x & = \sqrt{\frac{200}{13}} \\\end{aligned}[/tex][Simplify] Evaluate:
[tex]\displaystyle\begin{aligned}a^2 + b^2 & = c^2 \\(5x)^2 + x^2 & = 20^2 \\25x^2 + x^2 & = 400 \\26x^2 & = 400 \\x^2 & = \frac{200}{13} \\x & = \sqrt{\frac{200}{13}} \\& = \frac{10 \sqrt{26}}{13}\end{aligned}[/tex][Evaluate] Approximate:
[tex]\displaystyle\begin{aligned}a^2 + b^2 & = c^2 \\(5x)^2 + x^2 & = 20^2 \\25x^2 + x^2 & = 400 \\26x^2 & = 400 \\x^2 & = \frac{200}{13} \\x & = \sqrt{\frac{200}{13}} \\& = \frac{10 \sqrt{26}}{13} \\& \approx \boxed{3.9} \\\end{aligned}[/tex]
∴ our x approximately equals 3.9.
Now we can use our value of x to solve for the missing triangle lengths:
Length of 5x:
Substitute in x:[tex]\displaystyle\begin{aligned}\text{Side Length} & = 5x \\& = 5(3.9) \\\end{aligned}[/tex]Evaluate:
[tex]\displaystyle\begin{aligned}\text{Side Length} & = 5x \\& = 5(3.9) \\& = \boxed{19.5}\end{aligned}[/tex]
∴ this particular side length has a length of 19.5.
Length of x:
Substitute in x:[tex]\displaystyle\begin{aligned}\text{Side Length} & = x \\& = \boxed{3.9}\end{aligned}[/tex]
∴ this particular side length has a length of 3.9.
Answer∴ the side lengths of this particular triangle are 19.5 and 3.9, respective to their variables 5x and x.
___
Learn more about Triangles: https://brainly.com/question/20094559
Learn more about Geometry: https://brainly.com/question/16909531
___
Topic: Geometry
Unit: Triangles
Related Questions
Simplify (or FOIL) the following binomial expression (x−2)(x−2)
Answers
Answer:
x^2-4x+4
Step-by-step explanation:
x^2-2x-2x+4
=x^2-4x+4
3/11 x 3 1/4 Answer this question
Answers
Answer: 39/44
Step-by-step explanation:
3 1/4 = 13/4
13/4 times 3/100 = 13 times 3/4 times 11 which equals 39/44
The value of multiplication improper fraction 3/11 and mixed number 3 1/4 is 39/44.
To calculate the product of 3/11 and 3 1/4, we need to convert the mixed number 3 1/4 into an improper fraction.
To convert the mixed number 3 1/4 to an improper fraction, we multiply the whole number (3) by the denominator (4) and add the numerator (1). The result becomes the new numerator, and the denominator remains the same.
3 1/4
= (3 x 4 + 1) / 4
= 13/4
Now we can multiply 3/11 by 13/4:
(3/11) x (13/4)
= (3 x 13) / (11 x 4)
= 39/44
Therefore, the product of 3/11 and 3 1/4 is 39/44.
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∠A and ∠B are complementary. Find m∠A and m∠B.
m∠ A (15x + 3)*
m∠ B (5x - 13)*
Answers
[tex]m < a =78 \\ m < b =12\\ solution \\ 15x + 3 + 5x - 13 = 90(sum \: of \: complementary \: angles) \\ or \: 15x + 5x + 3 - 13 = 90 \\ or \: 20x - 10 = 90 \\ or \: 20x = 90 + 10 \\ or \: 20x = 100 \\ or \: x = \frac{100}{20} \\ x = 5 \\ m < a = 15x + 3 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 15 \times 5+ 3 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 78\\ m < b = 5x - 13 \\ \: \: \: \: \: \: \: \: \: \: = 5 \times 50- 13 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 20 - 13 \\ \: \: \: \: \: \: \: \: \: \: \: \: = 12\\ hope \: it \: helps[/tex]
Answer:
m∠ A=78°
m∠ B=12°
Step-by-step explanation:
∠A+∠B=90°
15x+3+5x-13=90
20x-10=90
20x=100
x=5
∠A=(15×5+3)°=(75+3)°=78°
∠B=(5×5-13)°=(25-13)°=12°
You design a tree house using a coordinate plane in which the coordinates are measured in feet. The vertices of the floor are (-2,-3),
(-2,4), (5,4) and (5,-3). Find the perimeter in yards and the area in square yards of the floor.
Answers
Answer:
Perimeter = 28 yards
Area = 49 square yards.
Step-by-step explanation:
Distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Let as consider the vertices of the floor are A(-2,-3), B(-2,4), C(5,4) and D(5,-3).
Using distance formula, we get
[tex]AB=\sqrt{(-2-(-2))^2+(4-(-3))^2}=\sqrt{(-2+2)^2+(4+3)^2}=\sqrt{0+7}^2=7[/tex]
Similarly,
[tex]BC=\sqrt{(5-(-2))^2+(4-4)^2}=7[/tex]
[tex]CD=\sqrt{(5-5)^2+(4-(-3))^2}=7[/tex]
[tex]AD=\sqrt{(5-(-2))^2+(-3-(-3))^2}=7[/tex]
It is conclude that, [tex]AB=BC=CD=AD[/tex].
From the given points it is clear that all sides lie on either vertical or horizontal lines.
Since all sides are equal, and adjacent sides are perpendicular, therefore, the base is a square with edge 7 yards.
Perimeter of square floor is
[tex]P=4a=4(7)=28\text{ yards}[/tex]
Area of square floor is
[tex]A=a^2=7^2=49\text{ sq. yards}[/tex]
Therefore, the perimeter is 28 yards and the area is 49 square yards.
There are 6 brooms and 4 mops in a janitor's closet. What is the ratio of the
number of brooms to the number of mops?
O A.
MIN
0110
OC.
O D.
nim
SURA
Answers
Answer:
i believe it is A because 6/2=3, 4/2=2, which gives the ratio 3/2.
Step-by-step explanation:
The ratio of the number of brooms to the number of mops is 3:2.
What is Ratio?In mathematics, a ratio is a phrase used to compare two or more numbers. It is used to express how large or tiny an amount is in comparison to another. A ratio compares two quantities by dividing them. The dividend is referred to as the "antecedent," while the divisor is referred to as the "consequent."
We have,
Number of brooms= 6
Number of mops= 4
So, the ratio of the number of brooms to the number of mops
= 6/4
=3/2
Thus, the required ratio is 3:2.
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Solve the formula A= 8/2 for r.
Answers
Answer:
The steps are :
[tex]A = \pi {r}^{2} [/tex]
[tex] \frac{A}{\pi} = {r}^{2} [/tex]
[tex]r = \sqrt{ \frac{A}{\pi} } [/tex]
Therefore, the answer is B.
Answer: the answer is B.
Find the vertex of the parabola.
f(x) = 5x2 - 30x +49
a. (3,0)
b. (3,4)
C. (4,0)
d. (4,3)
Answers
Answer:
B.
Step-by-step explanation:
because the vertex of parabola is f(x)
Find the area of the figure in the picture please!!!
Answers
Answer:
365cm^2
Step-by-step explanation:
Answer:
365cm ^2
I think
Katie sewed costumes for the high school's annual play. She spent the following number of hours on each dress. What is the mean number of hours spent on each dress? 5 1/4 4 1/2 3 3/4 4
Answers
Answer:
round down to 2.9 if to 1dp
Step-by-step explanation:
write an equation for the graph. help :)
Answers
Answer:
Since the y-intercept is 400 and the y value fourths for every increase of 2 in x, the equation is y = 400 * (0.5)^x.
50 POINTS! SOMEONE PLEASE HELP ME! :(
Answers
Answer:
a dot in an equation means multiplication
3 1/4 x 1 1/3 Please help!!! ~Kweenie~
Answers
how much is a mass in kilograms ?
Answers
Answer:
1,000 grams, we have 1 kilogram
Step-by-step explanation:
Step-by-step explanation:
1000 grams in 1 kilograms
Which ordered pair would form a proportional relationship with the point graphed below?
Answers
Answer:
B
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
Option B falls inside of the line, keeping it proportional
find the product of -8 (-12)
Answers
-8 ( -12 ) = 96
Negative times negative equals positive
Answer:
-8(-12) = 96
Step-by-step explanation:
The word product, in mathematical terms, is the answer you get after multiplying something. So, to find the product of -8(-12), you have to multiply. A negative times a negative is equal to a positive, so -8 times -12 is equal to positive 96.
Oil prices are projected to increase by 125% by next August. A quart of oil currently costs $1.25. What is the projected cost of a gallon of oil next August? Round your answer to the nearest hundredth.
Answers
Answer:
$2.81
Step-by-step explanation:
1.25 is 100% of the price
125% + 100% = 225%
x = price by august
x = 225% (1.25)
225% = 2.25
2.25(1.25) = 2.8125 ≈ $2.81
Another way to see it:
[tex]\frac{1.25}{x}[/tex] = [tex]\frac{100}{225}[/tex]
225(1.25) / 100 = 2.8125
Answer:
11.25
Step-by-step explanation:
if my final exam is worth 60 points, and i get an 80%, how many questions did i get right?
Answers
Answer:
48
Step-by-step explanation:
Total points = 60
% = 80%
Therefore no. of points right = 80/100×60 = 48
Mr. Karas needs to find the perimeter of
the patio shown at the right. What is the
perimeter of the patio? How can Mr. Karas find
the perimeter?
Answers
Answer: 54 yds
Step-by-step explanation: add all of the sides to get the perimeter
14+9+14+10+7=54
P= 54yd
What is a salesperson's commission on a $1000 sale if the commission rate is 20%?
Answers
Simplify. x+5/x^2+6x+5
1/x+1; where x ≠ -1
1/x+1; where x ≠ -1,-5
1/x-5; where x ≠ 5
X-5
Answers
Answer:
7x3 + 5x2 + 5
x2
= 0
Step-by-step explanation:
Answer:
Step-by-step explanation:
Sum =6
Product =5
Factors = 5 , 1
x² + 6x + 5 = x² + x + 5x + 5*1
= x(x + 1) + 5(x+1)
= (x+1) (x +5)
[tex]\frac{x+5}{x^{2}+6x+5}=\frac{x+5}{(x + 1)(x+5)}\\\\=\frac{1}{x+1}[/tex]
A cylindrical tin of height 15 cm and radius 4 cm is filled with sand from a rectangular box. How many times can the tin be filled if the dimensions of the box are 50 cm by 40 cm by 20 cm?
Answers
Answer:
Volume of Box / volume of tin = number of tins required
Volume of box =50*40*20= 40000 cu.cm
Volume of Tin = pi*r^2*h=pi*4^2*15 = 754 cu.cm
4000/754= 53 tins (rounded off)
Step-by-step explanation: i'm sorry if this is a bit complicated but i hope it answers your question. Take care.
Find the lateral area of a right circular cone whose radius is 6 feet and height is 8 feet.
48π ft2
60π ft2
96π ft2
Answers
Answer:
60π ft2
Step-by-step explanation:
The formula for the lateral surface area of a cone is: πr [tex]\sqrt{h^{2} + r^{2} }[/tex]. You substitute the h for the height and r for the radius and tada! 60π ft2!
Rod has to read a book which has p pages. He plans to read r pages each day for d days.
Write an equation for the number of pages left, b, in the book, after d days.
Answers
Answer:
Look at the attachment
The equation is an illustration of a linear function.
The equation for the number of pages left in the book is [tex]b =p- rd[/tex]
The total number of pages is:
[tex]Total = p[/tex]
The daily rate is:
[tex]Rate = r[/tex]
So, the number of pages read in d days is:
[tex]Pages = Rate \times Days[/tex]
This gives
[tex]Pages = r \times d[/tex]
Multiply
[tex]Pages = rd[/tex]
The number of pages left (b) is then calculated as:
[tex]b =Total - Pages[/tex]
So, we have:
[tex]b =p- rd[/tex]
Hence, the equation for the number of pages left in the book is [tex]b =p- rd[/tex]
Read more about linear equations at:
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Which equations are true?
Choose all answers that apply:
Ⓐ 0 = 0+1-2
Ⓑ 0=(-2)-(-2) +0
Ⓒ None of the above
Answers
Answer:
B
Step-by-step explanation:
A is false. 0 + 1 - 2 = -1, not 0.
B is true.
(-2)-(-2) +0
= -2 + 2 + 0
= 0
C is false, since B is true.
Equation B 0=(-2)-(-2) +0 is true, which is simplified by subtraction.
What is the equation?The equation is defined as a mathematical statement that has a minimum of two terms containing variables or numbers that are equal.
For equation A:
0 = 0+1-2
We can simplify the right-hand side of the equation by combining like terms:
0 = -1
This is not true, so we might be tempted to say that equation A is false.
For equation B:
0 = (-2)-(-2) + 0
We can simplify the right-hand side of the equation by performing the subtraction:
0 = 0 + 0 + 0
This simplifies to:
0 = 0
This equation is true.
Therefore, equation B is true.
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The graph shows the numbers of miles two cars travel.
Car B travels ___ more miles than Car A each hour.
Answers
Answer:
b goes 5 miles more than a, in 1 hour
Answer: 5 miles more than car A each hour
Step-by-step explanation: We have to look at each line carefully and the steepness as well as the numbers and we could clearly see that Car B thus travels 5 more miles than car A each hour!
Hope this helps <3
-Carrie
P.S. Please be sure to mark brainliest
STAY SAFE
PLEASE HELP! WILL MARK BRAINLIEST!!
A bag has 4 red marbles, 12 blue marbles and 6 yellow marbles. What is the probability of picking a yellow marble, replacing it, and then picking a blue marble?
1/18
18/121
55/22
22/131
In a bag of marbles, you have 4 green, 3 yellow, 5 blue, and 8 red marbles. What is the probability of picking a blue marble from the bag?
3/20
1/5
1/10
1/4
Answers
Answer:
18/121
1/4
(not 100% sure)
please help, will give brainliest
Answers
Answer:
4/7
Step-by-step explanation:
4/7 is squared and then square rooted, changing nothing.
Help me on this maths please
Answers
Answer: √300.89 or 17.3
Step-by-step explanation:
a^2 + b^2 = c^2
6.7^2 + b^2 = 16^2
b^2 = 16^2 - 6.7^2
= 256 - 44.89
b = √211.11 = 14.5
here to this question we have to use Pythagoras theorem that is
[tex] {a}^{2} + {b}^{2} = {hypotnuse}^{2} [/tex]
here,
a=6.7
b=x (cuz' we don't know it's value)
c= hypotenuse =16
now, substitute these values in the above formula then we get,
[tex] {6.7}^{2} + {x}^{2} = {16}^{2} \\ = 14.529[/tex]
as the answer should be given to 1 decimal place we get 14.529
The concentration determined for an unknown sample of hydrochloric acid by a student is 0.1354 M.According to the instructor’s information, the true molarity (M) of this solution is 0.1364 M. What is the percent error in this experiment? Round your answer to the nearest tenth.
Answers
Answer:
≈ 0.7% error
Step-by-step explanation:
To solve for percent error, first you have to do 0.1354-0.1364 and take the absolute value, which is 0.001.
Then, divide 0.001 by 0.1364, and then multiply by 100, and the answer is 0.007331378299.
The percent error is approximately 0.7%
Need help solving this plzz
Answers
Answer:
[tex]25[/tex]
Step-by-step explanation:
[tex]125^2 \div 125^{4/3}\\[/tex]
[tex]125^{2-4/3}[/tex]
[tex]125^{2/3}[/tex]
[tex]\sqrt[3]{125} ^2[/tex]
[tex]5^2[/tex]
[tex]=25[/tex]