Find the unknown side length, x. Write your answer in simplest radical form.
Answers
Answer: The required value of x is 32.
Step-by-step explanation: We are given to find the length of the unknown side.
That is, x = ?
From the figure, we see a right-angled triangle with
length of the hypotenuse, h = 68 units,
length of the other two sides, a = 60 units and b = x.
Using Pythagoras theorem in the given right-angled triangle, we have
[tex]h^2=a^2+b^2\\\\\Rightarrow 68^2=60^2+x^2\\\\\Rightarrow x^2=68^2-60^2\\\\\Rightarrow x^2=4624-3600\\\\\Rightarrow x^2=1024\\\\\Rightarrow x=\pm32.[/tex]
Since x is the length of a side of the triangle, so it cannot be negative.
Therefore, x = 32 units.
Thus, the required value of x is 32.
Related Questions
Which expressions are polynomials?
Select each correct answer.
6x² + 5x
−7x^2+5/3x
−x^2 +5x
x^2+5x ^1/5
Answers
Answer:
[tex]6x^2+ 5x[/tex]
[tex]-x^2 +5x[/tex]
Step-by-step explanation:
Expression is a polynomial when it contains variables, numbers and operators. Expression that contains fractional exponent is not a polynomial. Expression with variable in the denominator is not a polynomial.
[tex]6x^2+ 5x[/tex]
It is a polynomial
[tex]-7x^2+ \frac{5}{3x}[/tex]
It is not a polynomial because x is in the denominator
[tex]-x^2 +5x[/tex]
It is a polynomial
[tex]x^2+5x ^ \frac{1}{5}[/tex]
It is not a polynomial because it has fractional exponent
The expressions that are polynomials include 6x² + 5x, −7x²+5/3x, and −x² +5x, because they have non-negative integer exponents and a finite number of terms. The expression x²+5x[tex]^{(1/5 )}[/tex]is not, due to the non-integer exponent.
The expressions that are polynomials must have non-negative integer exponents and a finite number of terms. Given the options:
6x² + 5x is a polynomial because the exponents are integers and it has a finite number of terms.
−7x²+5/3x is also a polynomial with non-negative integer exponents and finite terms.
−x² +5x is a polynomial as well, following the same reasoning.
x²+5x[tex]^{(1/5)}[/tex] is not a polynomial because the exponent 1/5 is not an integer.
Therefore, the expressions that are polynomials are 6x² + 5x, −7x²+5/3x, and −x²+5x.
Galileo wanted to release a wooden ball and an iron ball from a height of 100100100 meters and measure the duration of their fall. He found a plane with an incline of 12^\circ12 ∘ 12, degree that he could climb until he could get to an altitude of 100\text{ m}100 m100, space, m. How far should Galileo walk up the inclined plane?
Answers
The Galileo walk 480.97 or 481 meters up the inclined plane if the Galileo wanted to release a wooden ball and an iron ball from a height of 100 meters and measure the duration of their fall.
What is the trigonometric ratio?The trigonometric ratio is defined as the ratio of the pair of a right-angled triangle.
We have:
Galileo wanted to release a wooden ball and an iron ball from a height of 100 meters.
The plane with an inclined an 12°
Let's suppose the Galileo walk x meters up the inclined plane.
As per right angle triangle, The ratio of Sin
[tex]\rm Sin12\° = \frac{100}{x}[/tex]
[tex]\rm x = \frac{100}{Sin12\°}[/tex]
Sin12° = 0.20791
x = 100/0.20791
x = 480.97 meters or
x = 481 meters
Thus, the Galileo walk 480.97 or 481 meters up the inclined plane if the Galileo wanted to release a wooden ball and an iron ball from a height of 100 meters and measure the duration of their fall.
Know more about trigonometry here:
brainly.com/question/26719838
#SPJ3
Nelson finds a video game for $38.50. The game is on sale for $31.57. What is the percent of discount on the game?
Answers
31.57 = ?
Multiply: 31.57 x 100 = 3,157
Divide: 3,157 ÷ 38.50 = 82%
100-82= 18% discount
Please help number 1
Answers
x = 50/tan(12°) ≈ 235 . . . . ft
helpppppppppppppppppppppppppppppppp
Answers
Second choice is the correct one
Explanation:
Let's check the choices:
Choice 1:
-2^-3 = -1/(2)^3 = -1/8 ........> wrong choice
Choice 2:
(-1/2)^-3 = (-2)^3 = -8 ......> correct choice
Choice 3:
(1/2)^-3 = (2)^3 = 8 ........> wrong choice
Choice 4:
2^-3 = (1/2)^3 = 1/8 ..........> wrong choice
Hope this helps :)
Phil received a prize of x dollars from a poker tournament. The tournament cost him 100 dollars to enter. What were Phil's net winnings from the tournament? Write your answer as an expression.
Answers
Phil's net winnings from the poker tournament are represented by the expression 'x - 100', where x is the prize amount he won. To calculate his actual profit, we subtract the cost of entry (100 dollars) from his prize money.
Explanation:The student has asked what Phil's net winnings are from a poker tournament after he received a prize of x dollars and the entry to the tournament cost him 100 dollars. To answer this, we will create an expression to represent Phil's net winnings.
Net winnings are calculated by subtracting the cost of entering the tournament from the prize amount. Since Phil won x dollars and spent 100 dollars to enter, we subtract 100 from x.
Phil's net winnings = Prize amount - Entry cost
Phil's net winnings = x - 100 dollars
This expression shows the actual profit Phil made from participating in the tournament, after the cost of entry has been accounted for.
Final answer:
Phil's net winnings from the poker tournament can be expressed as x - 100, where x represents the prize money.
Explanation:
To find Phil's net winnings from the poker tournament, we need to calculate the difference between the prize money and the entry fee. Given that Phil received a prize of x dollars and the tournament cost him 100 dollars to enter, his net winnings can be expressed as:
x - 100
For example, if Phil won $500, his net winnings would be $500 - $100 = $400.
It will take 4 people a total of 63 hours to build a deck. How many people are needed to build the same type of deck in 36 hours?
Answers
63/4 = 15.75
15.75
567
63 divided by 4 equals 15.75
So, each person holds 15.75 hours.
15.75 * 2 people = 31.5 hours, so that would not work.
15.75 * 3 people = 47.25, which is the closest you're going to get.
Correct answer: 3 people
Divide using synthetic division, and write a summary statement in fraction form. Two x cubed minus three x squared minus five x plus four divided by quantity x minus two.
2x2 + 7x + 9 + Twenty-two divided by quantity x minus two.
2x2 + x - 3 + Negative two divided by quantity x minus two.
2x2 - 7x + 11 + Eighteen divided by quantity x minus two.
2x2 + x + 3 + Ten divided by quantity x minus two.
Answers
Answer B: 2x²+x-3+(-2)/(x-2)
[tex] \begin{array}{cccccc}&|&x^3&x^2&x&1\\\\&|&2&-3&-5&4\\&|&&4&2&-6\\\\x=2&|&2&1&-3&-2\end{array}[/tex]
The base of a ladder is 25 meters due west of a burning building. If the angle of elevation of the ladder is 51°, how long is the ladder (round to the nearest meter)? A)33 meters B) 34 meters C) 39 metersD) 40 meters
Answers
x ThenCos 51 degree = 25/x0.6293
= 25/xx = 25/0.6293 = 39.72 meters≈40 meters from the above deduction, so the correct answer is D, because it is the closest, and that it is correct.
The ladder is approximately 40 meters long to the nearest tenth.
The information will form a right angle triangle.
The base of the ladder 25 meters due west of the burning building is the base(adjacent side) of the triangle formed.
How long is the ladder describe the hypotenuse of the triangle formed.
Therefore, using trigonometric ratio we can find the length of the ladder as follows:
cos 51 = adjacent / hypotenuse
cos 51 = 25 / hypotenuse
hypotenuse = 25 / cos 51°
hypotenuse = 25 / 0.62932039105
hypotenuse = 39.7253932266 meters
hypotenuse ≈ 40 meters
Therefore, the ladder is approximately 40 meters long to the nearest tenth
read more: https://brainly.com/question/3525533?referrer=searchResults
Can someone please help me
I really would appreciate it.
Answers
b = 9
h = 5
Area = 1/2 5 * 9
Area = 1/2 45
Area = 22.5 cm^2
A = HB/2
H is the Height and B is the Base of the triangle. Plug in the information to the formula to get:
A = 5 × 9 / 2
A = 45 / 2
A = 22.5
The area of the triangle would be 22.5 (I hope this helps)
A road crew can repave 1/56 miles of road each hour. They must repave a road that is 7/8 miles long. How long will it take the crew to repave the road?
Answers
1/56 miles = 1 hour
[7/8 = 49/56]
49/56 miles = 1 x 49 hours
49/56 miles = 49 hours
7/8 miles = 49 hours
Answer: 49 hours
Step-by-step explanation:
Given : A road crew can repave [tex]\dfrac{1}{56}[/tex] miles of road each hour.
i.e. the rate of of repave = [tex]\dfrac{1}{56}[/tex] miles per hour.
Distance required to cover = [tex]\dfrac{7}{8}[/tex] miles.
The formula used here is :-
[tex]\text{Time}=\dfrac{\text{Distance}}{\text{rate of repave}}[/tex]
i.e. [tex]\text{Time}=\dfrac{\dfrac{7}{8}}{\dfrac{1}{56}}[/tex]
i.e. [tex]\text{Time}=\dfrac{7}{8}\times56=7\times7=49[/tex]
Hence, it will take 49 hours to repave the road.
1. What is the sum of the series?
2. What is the sum of the series?
Answers
3(1^2)+3(2^2)+3(3^2)+3(4^2)=90
Same for the next one, except this is for all values of k between 3 and 6:
(-5(3)+20)+(-5(4)+20)+(-5(5)+20)+(-5(6)+20)=-10
Answer:
1).90
2).-10
Step-by-step explanation:
1).
(3(1)^2)+(3(2)^2)+(3(3)^2)+(3(4)^2)
3 + 12 + 27 + 48
=90
2). (-5(3)+20)+(-5(4)+20)+(-5(5)+20)+(-5(6)+20)
(-15+20) + (-20+20) + (-25+20) + (-30+20)
5 + 0 + -5 + -10
=-10
PLEASE HELP
8.03a
1. Find the vertices and foci of the hyperbola with equation x squared over nine minus y squared over sixteen = 1.
A) Vertices: (± 5, 0); Foci: (± 3, 0)
B) Vertices: (± 3, 0); Foci: (± 5, 0)
C) Vertices: (0, ± 3); Foci: (0, ±5)
D) Vertices: (0, ± 5); Foci: (0, ± 3)
2. Find the vertices and foci of the hyperbola with equation quantity x minus three squared divided by sixteen minus the quantity of y plus four squared divided by nine = 1.
A) Vertices: (7, -4), (-1, -4); Foci: (-2, -4), (8, -4)
B) Vertices: (-4, 7), (-4, -1); Foci: (-4, -2), (-4, 8)
C) Vertices: (6, -4), (0, -4); Foci: (0, -4), (6, -4)
D) Vertices: (-4, 6), (-4, 0); Foci: (-4, 0), (-4, 6)
3. Graph the hyperbola with equation A horizontal hyperbola is shown on the coordinate plane centered at, negative one, four, with vertices at, negative four, negative four and two, negative four. = 1.
A) A vertical hyperbola is shown on the coordinate plane centered at the origin with vertices at, zero, two and zero, negative two.
B) A horizontal hyperbola is shown on the coordinate plane centered at, negative three, three, with vertices at, negative five, three and negative 1, three.
C) A vertical hyperbola is shown on the coordinate plane centered at, three, negative three, with vertices at, three, negative one and three, negative five.
D) A horizontal hyperbola is shown on the coordinate plane centered at the origin with vertices at, negative two, zero and two, zero.
4. Find an equation in standard form for the hyperbola with vertices at (0, ±2) and foci at (0, ±7).
A) y squared over forty nine minus x squared over four = 1
B) y squared over forty five minus x squared over four = 1
C) y squared over four minus x squared over forty nine = 1
D) y squared over four minus x squared over forty five = 1
5. Find an equation in standard form for the hyperbola with vertices at (0, ±6) and asymptotes at y = ± three divided by four times x..
Answers
Please, see the attached files.
Thanks.
PLEASE HELP ME PLEASE PLEASE
Answers
48 - 3x > 10
The second row makes the bottles grow. I wish this were true, but it is not.
After x gets to 13, she has dropped down below where she does not need to shop for more bottles.
48 - 3x > 10 Add 3x to both sides.
48 > 10 + 3x Subtract 10
38 > 3x Divide by 3
12 . 66666 So she can finish the 13th bottle but when she does, she has to go out and get more.
The graph shows the quadratic function f(x) . What is the average rate of change for the quadratic function from x = 6 to x = 8? Enter your answer in the box.
Answers
Answer:
The average rate of change for the quadratic function from x = 6 to x = 8 is -1.
Step-by-step explanation:
The average rate of change for the quadratic function from x₁ to x₂ is defined as
[tex]m=\frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]
From the given graph it is clear that the value of function is 6 at x=6 and the value of function is 4 at x=8.
The average rate of change for the quadratic function from x = 6 to x = 8.
[tex]m=\frac{f(8)-f(6)}{8-6}[/tex]
[tex]m=\frac{4-6}{2}[/tex]
[tex]m=\frac{-2}{2}[/tex]
[tex]m=-1[/tex]
Therefore the average rate of change for the quadratic function from x = 6 to x = 8 is -1.
5 ×
1
2
= ?
A)
More than 5 because you are multiplying by a whole number
B)
5
10
because you multiply the numerator and denominator by 5
C)
Less than 5 because you are multiplying by a number that is more than 1
D)
Less than 5 because you are multiplying by a number that is less than 1
16)
Robert is running on a track that is 3
3
4
miles long. He has run 1
2
5
of a mile.
How many more miles are there until Robert reaches the end of the track?
A)
2
7
20
miles
B)
2
5
9
miles
C) 7 2/0
miles
D) 3 5/9
miles
Answers
3 3/4 - 1 2/5 = 47/20 or 2.35 or 2 7/20 So the answer would also be A.
I hope this helps!!!!!!!!!!!
Find the lateral area of the prism. 27 sq. ft. 36 sq. ft. 54 sq. ft. Find the total area of the prism. T.A.= Find the volume.
Answers
It is 54 because that is the ansewr to this question bra
Which shows two triangles that are congruent by ASA?
Answers
The second one, as shown in the attached picture.
Further explanationThe ASA (Angle-Side-Angle) postulate for the congruent triangles: two angles and the included side of one triangle are congruent to two angles and the included side of another triangle; the included side properly represents the side between the vertices of the two angles. The SAS (Side-Angle-Side) postulate for the congruent triangles: two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle; the included angle properly represents the angle formed by two sides.The SSS (Side-Side-Side) postulate for the congruent triangles: all three sides in one triangle are congruent to the corresponding sides within the other.The AAS (Angle-Angle-Side) postulate for the congruent triangles: two pairs of corresponding angles and a pair of opposite sides are equal in both triangles.- - - - - - - - - -
Notes
The angle-side-side postulate for the congruent triangles doesn't exist because an angle and two sides don't guarantee that two triangles are congruent. If two triangles have two congruent sides and a congruent non-included angle, then triangles don't seem to be necessarily congruent. This can be why there's no side-side-angle (SSA) and there's no angle-side- side postulate.The AAA (angle-angle-angle) postulate for congruent triangles does not work because having three corresponding angles of equal size is not enough to prove congruence. This principle is usually used for the similarity of two triangles.Learn moreAbout the lengths of the legs of the triangle https://brainly.com/question/13027296 About vertical and supplementary angles https://brainly.com/question/13096411 Calculate the measures of the two angles in a right triangle https://brainly.com/question/4302397Martha rolls a number cube with sides 1, 2, 3, 4, 5, and 6. What is the probability of NOT rolling a 3?
Answers
Lets see... When rolling a 6 sided dice, their are 6 potential outcomes
1,2,3,4,5,6
Of these 6 outcomes, 5 of them are NOT 3. So 5 of the 6 outcome will give you a number other than three.
P(not 3)=5/6
Factor the trinomial below.
5x2 + 29x - 6
Which of the following binomials is a factor of the trinomial?
A. x - 6
B. x + 3
C. x - 3
D. x + 6
Answers
The trinomial 5x^2 + 29x - 6 factors into (5x - 1)(x + 6)
To factor the trinomial 5x2 + 29x - 6, we need to find two numbers that multiply to (5)(-6) = -30 and add to 29. These two numbers are 30 and -1, as 30 - 1 = 29. Thus, we can rewrite the trinomial as 5x2 + 30x - x - 6 and factor by grouping:
(5x2 + 30x) - (x + 6)
5x(x + 6) - 1(x + 6)
The trinomial factors into (5x - 1)(x + 6), which means the correct binomial factor is option D: x + 6.
Is it possible for triangle JKL to be similar to triangle XYZ Explain.
Answers
J corresponds to X and they are both 71
K corresponds to Y and they are both 52 because 180-(71+57)= 52
L corresponds to Z and they are both 57 because 180-(71+52) = 57
Hope this helped :)
Answer: Yes it is possible for triangle JKL to be similar to triangle XYZ.
Step-by-step explanation:
Given: In ΔJKL
m∠J=71° , m∠K=52°
In ΔXYZ
m∠X=71° , m∠Z=57°
Using Angle sum property of triangle in ΔJKL, we have
m∠J+m∠K+m∠L=180°
⇒71°+52°+m∠L=180°
⇒m∠L=180°-123°
⇒m∠L=57 °
Now in ΔJKL and ΔXYZ , we have
m∠J=m∠X=71°
and m∠L= m∠Z=57°
Therefore , By AA-similarity criteria , we have
ΔJKL≈ΔXYZ
Hence, Yes it is possible for triangle JKL to be similar to triangle XYZ.
How do you work out 5 2/3 - 2 3/4 ???
Answers
i worked out the problem and I attached the picture
helppppppppppppppppppppppppppppppp
Answers
Third choice is the correct one
Explanation:
No fraction can have a denominator = 0 because this would make it undefined.
Therefore, the solution would be all the real values except for those that make the denominator = 0
Let's check the terms in the denominator:
i. c-3 = 0 at c = 3
ii. c = 0
iii. c(c-3) = 0 at c = 0 or c = 3
Therefore 0 and 3 are the values that would make the denominator zero.
Based on the above, the solution is all real numbers except 0 and 3
Hope this helps :)
Mark Y inside regular pentagon PQRST so that PQY is equilateral Is RYT straight? explain
Answers
By the same logic, ∠Q in our pentagon is 108°. Since ΔPYQ is equilateral, ∠PQY = 60°. That means that ∠YQR = 108-60 = 48°. Since QR = QY, ΔQYR is isosceles, which means the base angles are congruent. We take 180-48 = 132 and divide that by 2 to get each base angle, ∠QYR and ∠QRY, is 66°. Looking at the 3 angles around point Y: If ∠RYT is a straight angle, these 3 along this path should add up to 180°. We have ∠PYT=66° + ∠PYQ=60° + ∠QYR=66° for a total of 192°. Therefore ∠RYT is not a straight angle.
Only boxes less than 3 1/2 feet wide will fit through a doorway. Which measurements show the widths of three boxes that will fit through a doorway? Please help!! Choices:
A. 36 in., 42 in., 40 in.
B. 42 in., 43 in., 38 in.
C. 40 in., 37 in., 41 in.
D. 38 in., 40in., 42 in.
Answers
Dan invests £2200 into a savings account. The bank gives 5% compound interest for the first 3 years and 4% thereafter. How much will Dan have after 7 years to the nearest pound?
Answers
interest rates =5% for 3 years, and 4% afterwards
no. of periods = 7
Future value=2200*(1.05)^3(1.04)^(7-3)
=£2979.367 (please round to appropriate number of decimals)
The correct answer, to the nearest pound, is:
2979
Explanation:
Compound interest can be written as an equation of the form
[tex]y=a(1+r)^t[/tex],
where a is the initial deposit, r is the interest rate as a decimal number, and t is the number of years.
For the first 3 years, we have a = 2200, r = 5% = 5/100 = 0.05; and t = 3:
[tex]y=2200(1+0.05)^3
\\
\\=2200(1.05)^3=2546.775[/tex]
This will be the "initial deposit" in the account with 4% interest. This gives us that
a = 2546.775; r = 4% = 4/100 = 0.04; and t = 7-3 = 4:
[tex]y=2546.775(1+0.04)^4
\\
\\=2546.775(1.04)^4=2979.367 \approx 2979[/tex]
One brand of cereal sells for $2.89 for 9 ounces. What is the unit
price per pound?
a. $.32
b. $4.29
c. $2.15
d. $5.14
ANSWER IS NOT A
Answers
Over what interval is the growth rate of the function decreasing?
Answers
Use the substitution method to solve the system of equations. Choose the correct ordered pair. x + 2y = 12 –x = –y – 6
A. (9, 3)
B. (7, 1)
C. (6, 0)
D. (8, 2)
Answers
Answer: D
Step-by-step explanation:
The ordered pair of the system of equations is (8, 2).
Option D is the correct answer.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 = 9 is an equation.
We have,
x + 2y = 12 _____(1)
x = 12 - 2y _____(2)
-x = -y - 6 _______(3)
Putting (2) in (3) we get,
-(12 - 2y) = -y - 6
-12 + 2y = -y - 6
-12 + 6 = -y - 2y
-6 = -3y
y = 2
Now,
y = 2 in (2)
x = 12 - 2 x 2
x = 12 - 4
x = 8
Thus,
The ordered pair is (8, 2).
Learn more about equations here:
https://brainly.com/question/17194269
#SPJ2
How to simplify equation with 2 parenthesees multiplication?
Answers
Answer:
Distributive Property
Step-by-step explanation:
Use the distributive property to multiply each term in each parenthesis.
Example:
To simplify the expression (x-3)(x^2-4x-7), apply the distributive property. The distributive property states to multiply each term in each parenthesis.
x*x^2=x^3
x*-4x=-4x^2
x*-7=-7x
-3*x^2=-3x^2
-3*-4x=12x
-3*-7=21
This gives the expression x^3-4x^2-7x-3x^2+12x+21. Combine like terms and get x^3-7x^2+5x+21.