Answer:
[tex]x = 10\\y = 5[/tex]
Step-by-step explanation:
1. Approach
The easiest method to solve this problem is to use the side ratios in a special right triangle. One should start by proving that the triangle is a (30 - 60 - 90) triangle. Since the problem gives on the information that one of the sides has a measure of ([tex]5\sqrt{3}[/tex]), one can use this combination with the ratio of the sides in a special right triangle, to find the unknown side lengths.
2. Prove this triangle is a (30 - 60 - 90) triangle
One is given a right triangle. This means the triangle has a (90) degree or right angle in it. This is indicated by a box around one of the angles. One is given that the other angle in this triangle has an angle measure of (30) degrees. The problem asks for one to find the third angle measure. A property of any triangle is that the sum of angle measures in the triangle is (180) degrees. One can use this to their advantage by stating the following:
[tex](90) + (30) + (unknown) = 180\\[/tex]
Simplify,
[tex](90) + (30) + (unknown) = 180[/tex]
[tex]120 + unknown = 180\\[/tex]
Inverse operations,
[tex]120 + unknown = 180\\[/tex]
[tex]unknown = 60[/tex]
Thus, this triangle is a (30 - 60 - 90) triangle, as its angles have the measures of (30 - 60 - 90).
3. Solve for (y)
The sides ratio in a (30 - 60 - 90) triangle is the following:
[tex]n - n\sqrt{3} - 2n[/tex]
Where (n) is the side opposite the (30) degree angle, ([tex]n\sqrt{3}[/tex]) is the side opposite the (60) degree angle and finally (2n) is the side opposite the (90) degree angle. The side (y) is opposite the (30) degree angle. This means that it is equal to the side opposite the (60) degree angle divided by ([tex]\sqrt{3}[/tex]). Therefore, one can state the following:
[tex]\frac{5\sqrt{3}}{\sqrt{3}}=y\\5=y[/tex]
4. Solve for (x)
Using the same thought process one used to solve for side (y), one can solve for side (x). The side (x) is opposite the (90) degree angle, hence, one can conclude that it is twice the length of the side with the length of (y). Therefore, one can state the following:
[tex]x = 2y\\x = 2(5)\\x = 10[/tex]
In a right triangle, two sides are 12 and 13. Find the measure of the third side. Consider all cases
Answer:
Case 1
12 and 13 are legs, then find the hypotenuse.
c = [tex]\sqrt{12^2+13^2} = \sqrt{313}[/tex] ≈ 17.69Case 2
13 is hypotenuse, 12 is a leg, find the missing leg.
b = [tex]\sqrt{13^2-12^2} = \sqrt{25} = 5[/tex]Answer:
Solution given:
Case 1:
if base=12
hypotenuse=13
perpendicular=??
By using Pythagoras law
hypotenuse²=perpendicular²+base²
13²=perpendicular ²+12²
perpendicular ²=13²-12²
perpendicular=[tex]\sqrt{13²-12²}=\sqrt{25}=5[/tex]units
Case:2:
Case 1:
if base=12
hypotenuse=13
perpendicular=??
By using Pythagoras law
hypotenuse²=perpendicular²+base²
13²=perpendicular ²+12²
perpendicular ²=13²-12²
perpendicular=[tex]\sqrt{13²-12²}=\sqrt{25}=\bold{\large{5}}[/tex]units
Case:2:
if base=12
hypotenuse=??
perpendicular=13
By using Pythagoras law
hypotenuse²=perpendicular²+base²
hypotenuse²=13 ²+12²
hypotenuse² ²=13²+12²
hypotenuse²=[tex]\sqrt{13²+12²}=\sqrt{313}=\bold{\large{17.7}}[/tex]units
Find the number in which 8 is in tenths place.
8945.4534
456.89732
9738.45621
6875.1234
the number in which 8 is in tenth place is
6875.1234
plese mark me as braniliest
NOW ASAP NEED FAST ANSWERRRRRRRRRRRRRRRRRRR
Answer:
C.
Step-by-step explanation:
Dis means apart and junc means join so disjunction means the "state of being disconnected".
toán lớp 8
giải bất phương trình: 2x + 2 > 4
Answer:
x>1
Step-by-step explanation:
Answer:
x>1
I hope it will help you
please find the answer
there are options given below
plz give answer asap
Answer
33.3
Step-by-step explanation:
if u multiply the 2, and then find the ratio of them in comparison to the number under, you will find the rate decreases by 10 percent every time, the first situation it is 4/8 = 5/10, second situation is it 32/80= 4/10, and htis situation is most like 3/10, right ? so the answer would be 33.3 :)
I need help please! Will mark brainliest! (both are seprate questions!
Step-by-step explanation:
if you want to find volume of cone you must you this formula: hπr² so 10*π(3)*r²(4)= 120ft² and
if you want to find volume of cylinder you should use this formule: πr²*h/3 =π(3)*r²(4)*h(3)/3= 12 the figure has 132 volume in totally.
75% students out of 80 are present in a test , the students absent are :
Answer:
20 students are absent
Step-by-step explanation:
75/100 × 80 = 60
If 60 were present out of the 80
80 - 60 = 20
Have a great day :)
Find the value of x for which (4/5)-4 x (4/5)-7 =(4/5)2x-1 Can some1 say this ans fast plz
Answer:
Fraction form: x = -21/4
Decimal Form: x = -5.25
Step-by-step explanation:
See the picture for steps :)
write the equation of the graph below
Answer:
Step-by-step explanation:
This is a parabola with a vertex at h = 4 and k = 5; the graph goes through the coordinate x = 6 and y = 6. We will use those 4 values to fill in the equation:
[tex]y=a(x-h)^2+k[/tex] and this will allow us to solve for the value of a:
[tex]6=a(6-4)^2+5[/tex] and
[tex]6=a(2)^2+5[/tex] and
6 = 4a + 5 and
1 = 4a so
[tex]a=\frac{1}{4}[/tex] and the equation is
[tex]y=\frac{1}{4}(x-4)^2+5[/tex]
Find the domain of h(x) = 2x - 9 given a range of (-7,5,11)
Answer:
D = 1,7,10
Step-by-step explanation:
-7 = 2x - 9
x = 1
5 = 2x - 9
x = 7
11 = 2x - 9
x = 10
the domain of (1,7,10)
Find the measure of KM. PLEASE PLEASE PLEASE HELP ASAP!!!!!!!!!!!!!!!
A. 7
B. 17
C. 12
D. 14
Answer:
C
Step-by-step explanation:
Given 2 secants from an external point to the circle, then
The product of the external part and the whole of one secant is equal to the product of the external part and the whole of the other secant , that is
ML × KM = MN × MR, substitute values
7 × KM = 6(6 + 8)
7 KM = 6 × 14 = 84 ( divide both sides by 7 )
KM = 12 → C
Answer:
C.) 12
Step-by-step explanation:
I got it correct on founders edtell
Determine what type of model best fits the given situation: the temperature of a cup of coffee decreases by 5 F every 20 minutes.
A. liner
B. exponential
C. quadratic
D. none of these
Answer: T = -t / 4 + T0 where t is the temperature in minutes elapsed, T is the final temperature, and T0 is the initial temperature
Explanation: This is a linear equation in T and t
(-1 / 4 represents -5 deg / 20 min = - 1 deg / 4min
If two lines represent the same line, then what is the nature of its solution?
Step-by-step explanation:
If a consistent system has exactly one solution, it is independent . If a consistent system has an infinite number of solutions, it is dependent . When you graph the equations, both equations represent the same line. If a system has no solution, it is said to be inconsistent .
Answer:
Infinite
Step-by-step explanation:
Solution between 2 lines is considered the point of their intersection. Now, since two lines are same (not only parallel but same), it tends to have infinite solutions.
Name the property shown by the statement 2a = a2
Distributive property
screenshot if you need more words. seems to be a well illustrated and compact explanation right there
Find the missing length indicated
Answer:
x = 240
Step-by-step explanation:
Using the Altitude- on- Hypotenuse theorem
(leg of large triangle)² = ( part of hypotenuse below it) × (whole hypotenuse)
x² = 144 × 400 = 57600 ( take the square root of both sides )
x = [tex]\sqrt{57600}[/tex] = 240
x = 240
Using Pythagoras' theorem on the 3 triangles of sides (as shown in the graphic - the 2 smaller inner triangles and the large main triangle) it can be shown that the height is the square root of the product of both segments of the baseline.
let's call the 2 segments p and q.
p+q = 400
p = 144
q = 400 - 144 = 256
so, as said before, height = sqrt(p×q) = sqrt(144×256) = 192
now the main Pythagoras with the smallest triangle to get x
x² = 192² + 144² = 36864 + 20736 = 57600
x = 240
now, FYI, why is that formula true ?
as we said, we called the segments of the long baseline p and q.
then we can the sides of the main triangle x and y.
and the height is simply h.
so, then we have for the main rectangular triangle
(p+q)² = x² + y²
and for the 2 smaller triangles
x² = p² + h²
y² = q² + h²
=>
p² +2pq + q² = p² + h² + q² + h²
2pq = 2h²
h² = pq
h = sqrt(pq)
and there you have it. just as simple as that.
The radius of a circle is 14cm. Find the radius of the circle whose area is double of the area of circle.
Answer:
14√2 cmStep-by-step explanation:
Area of circle equation:
A = πr²Let the radius of bigger circle is x.
We have:
π(14²)*2 = πx²Solve for x:
x² = 2(14²)x = √2(14²)x = 14√2 cm19.8cm
Step-by-step explanation:
First find area of small circle:
A = πr2
A = 22/7 x 14 x 14
A = 22 x 2 x 14
A = 616cm2
Area of bigger circle is double that of the small circle:
= 616 x 2
= 1,232 cm2
πR2 = A
22/7 x r2 = 1,232
r2 = (1,232 x 7) ÷ 22
r2 = 8624 ÷ 22
[tex] \sqrt{r ^{2} } = \sqrt{392} [/tex]
radius of bigger circle = 19.8cm
I NEED HELP JANSJEHEHSHSBSBSBSH
Answer:
The answer is a translation
Step-by-step explanation:
In Math, translation is the displacement of a shape or object from one place to another.
Since the picture shows that the shape moved from one place to the next while remaining the same size, it is translation.
Need help we will be posting questions no leaks max points
Answer:
6
Step-by-step explanation:
To find the mean you need to add up all the number & then divide it by the total number of numbers.
7+6+7+6+6+7+6+4+5= 54/9 = 6
Answer from Gauthmath
Answer:
6
Step-by-step explanation:
To get the mean, you must add all numbers and divide it by how many digits you have. So 54 (Sum of all numbers) divide by 9 (9 digits) is 6
True or False:
4x and 4x2 are like terms
Actually its false
In algebra 4x and 4x² are two different terms and are not like terms.
Must click thanks and mark brainliest
Solid #1
SA= 539 cm?
V = 2058 cm
Solid #2
SA = 704 cm?
V?
Answer:
2688 cm³
Step-by-step explanation:
2058×704/539 = 2688 cm³
One of the lengths of a leg on a right angled triangle is 15 ft the length of the hypotenuse is 17 ft find the length of the other leg
what is the degree of the polynomial below
Answer:
d
Step-by-step explanation:
trust me gang
Answer:
the degree is the value of the highest exponent... 4x^3 the exponent is a three
answer "D"
Step-by-step explanation:
what’s the answer for the first question? pls help i don’t have much time…
Answer and Step-by-step explanation:
1.
Since we known how much money Jane and Mark have in total, we can subtract the amount Jane has to find the amount Mark has.
750 - 175 = $575
Mark has $575.
2.
We know how many cards Jamal sold, so if we add it to the amount he still has left, we can find the original amount of cards Jamal had.
17 + 83 = 100
Jamal had 100 cards.
#teamtrees #PAW (Plant And Water)
Answer:
Mark will have $575.
Step-by-step explanation:
Take the total amount ($750) and subtract Jane's contribution ($175) to get Mark's contribution($575).
$750-$175=$575
Write an example of an equation for an exponential growth function
Answer:
f(x) = 2^x
Step-by-step explanation:
Please help me if you can...
The roof of another Green House contains clear glass panels Isosceles Trapezium in shape, all the same size and one glass panel, REGULAR HEXAGON in shape, in the middle surrounded by the Trapezium. Its walls are squares in shape.
Q1. Illustrate the above situation with the diagram (cross section of the Green house).
Q2. The 2 angles of the Isosceles Trapezium are 1050 and 750, find the other 2 angles.
Q3. How much tape does Jane require to join the roof and the walls, if the walls are in the shape of squares of side 10m.
Answer:
Q2.the 2 angles of the isoceles trapezium are 1050 and 750,find the other 2 angles.
Can sone One help me please, Thanks a lot
Answer:m
Step-by-step explanation:m
Mar-Vell Studios' blockbuster movie Gray Widow: It's About Time She Got a Movie premiered last weekend simultaneously in theaters and on streaming video. On opening weekend, the total revenue from the movie was $127,265,468, with the movie making 75% more revenue in theaters than it did via streaming video. How much money did Gray Widow make in theaters on opening weekend
Answer:
Gray Widow made $111,357,284.5 in theaters on opening weekend.
Step-by-step explanation:
75% more revenue in theaters than it did via streaming video.
The sum of the revenues is 100%.
So the theaters were responsible for the following percentage:
[tex]P = 50 + \frac{75}{2} = 50 + 37.5 = 87.5[/tex]
How much money did Gray Widow make in theaters on opening weekend?
87.5% of the total revenue, that is, 0.875 out of $127,265,468.
0.875*127,265,468 = $111,357,284.5
Gray Widow made $111,357,284.5 in theaters on opening weekend.
A 10-foot tall tree casts a 4-foot shadow. How tall is the building next to the tree if the building’s shadow is 38 feet long?
Step-by-step explanation:
It Jun glt tm my tb my tu meri of ft me rh my
Someone help me out please
Answer:
142.5
Step-by-step explanation:
π×11²×135/360
= 363π/8
= 142.5 (rounded to the nearest tenth)
Answered by GAUTHMATH
The domain for f(x) and g(x) is the set of all real numbers.
Let f(x) = 3x + 5 and g(x) = x2.
Find (f − g)(x).
3x3 − 5x2
−x2 + 3x + 5
x2 − 3x − 5
−3x3 − 5x2
Answer:
below
Step-by-step explanation:
that's is the solution above