Two sides of a square are divided into fourths and another side of the square is trisected, as shown. A triangle is formed by connecting three of these points, as shown. What is the ratio of the area of the shaded triangle to the area of the square? Express your answer as a fraction.
Answers
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Explanation:
Let's say this is a 1 by 1 square. The area is 1*1 = 1 square unit. Whatever the area of the triangle is, we divide it over 1 and it will yield the same value as the area of the triangle. In other words, the area of the triangle will be the answer.
Along the top we have 3 ticks to indicate the top segment has been cut into 3+1 = 4 equal parts. The horizontal distance from the the vertical side of the triangle to the peak of the triangle is 3/4 units. This is because we travel 3 ticks out of 4 total. So this is the height when we consider the vertical segment of the triangle to be the base.
The base is 1 unit as it spans the original square's side length
base = 1
height = 3/4
area of triangle = (1/2)*(base*height)
area of triangle = (1/2)*(1*3/4)
area of triangle = 3/8
ratio of triangle area to square area = (triangle area)/(square area)
ratio of triangle area to square area = (3/8)/1
ratio of triangle area to square area = 3/8Answer:
3/8
Step-by-step explanation:
let side of square=x
Area of a square =x^2
height of a triangle= 3x/4 ( 4/4=1/4) since height is only 3x/4 from the square)
( base =x same side as a square)
Area of a triangle=1/2 bh=1/2(x*3x/4)= 3x^2/8
the ratio of shaded triangle to the area= (3x^2/8)/x^2=3x^2/8x^2=3/8
Related Questions
Find an equation of the line that passes through the point (2, 1) and
is perpendicular to the line x + 2y=-2
Answers
Answer:
2x - y = 3
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Given
x + 2y = - 2 ( subtract x from both sides )
2y = - x - 2 ( divide all terms by 2 )
y = - [tex]\frac{1}{2}[/tex] x - 1 ← in slope- intercept form
with slope m = - [tex]\frac{1}{2}[/tex]
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{1}{2} }[/tex] = 2 , thus
y = 2x + c ← is the partial equation
To find c substitute (2, 1) into the partial equation
1 = 4 + c ⇒ c = 1 - 4 = - 3
y = 2x - 3 ← equation in slope- intercept form
add 3 to both sides
y + 3 = 2x ( subtract y from both sides )
3 = 2x - y, thus
2x - y = 3 ← equation in standard form
]
can u solve these asap pls
Answers
Step-by-step explanation:
1We will use the Thales theorem since ED and CB are parallel and A,D and B are in the same lign wich is the same for C,E and A
[tex]\frac{x}{12}[/tex] = [tex]\frac{2}{2+4}[/tex] [tex]\frac{x}{12}[/tex] = [tex]\frac{2}{6}[/tex] [tex]\frac{x}{12}[/tex] = [tex]\frac{1}{3}[/tex] x= [tex]\frac{12*1}{3}[/tex] x= 4 2since we have two similar sides and one similar angle between them it will be SAS similarity
How many solutions does this system have? x minus y = negative 4. 3 x + y = 8. one two an infinite number no solution
Answers
Answer:
One solution
Step-by-step explanation:
Answer:
The correct answer is A.) one
Step-by-step explanation:
I just did the test on edge 2021 and got it right!
Which of the following best describes the slope of the line below?
Answers
Answer:
I think positive
Step-by-step explanation:
Answer:
zero, D
Step-by-step explanation:
a horizontal line (left to right) would be zero
a verticle line (up and down) would be undifined
Which of the following is the product of the rational expressions shown
below?
Answers
Answer:
The answer is b
Step-by-step explanation:
since 2*9=18 and (x)(2x+3)=2x^2+3x
Answer: B
Step-by-step explanation:
A tunnel must be made through a hill. As a result, a surveyor and an engineer create a sketch of the area. The sketch, displayed below, includes information they have either researched or measured. They need to build a tunnel from the point E to the point H on the sketch. Calculate the distance from E to H. When similar triangles are used, explain how you know they represent similar triangles before performing the calculation.
Answers
Answer:
498 m
Step-by-step explanation:
The AAA theorem states that triangles are similar if all three corresponding angles are equal.
1. Compare triangles FHS and ILS
(a) Reason for similarity
∠F = ∠I = 90°
∠S is common.
∴ ∠H = ∠L
(b) Calculate SL
[tex]\begin{array}{rcl}\dfrac{SF}{SH} & = & \dfrac{SI}{SL}\\\\\dfrac{225}{380} & = & \dfrac{225 + 475}{SL}\\\\225SL & = & 380 \times 700\\& = & 266000\\SL & = & \textbf{1182 m}\\\end{array}[/tex]
2. Compare triangles ILS and GLE
(a) Reason for similarity
∠I = ∠G = 90°
∠L is common.
∴ ∠S = ∠E
(b) Calculate LE
[tex]\begin{array}{rcl}\dfrac{IS}{GE} & = & \dfrac{LS}{LE}\\\\\dfrac{700}{180} & = & \dfrac{1182}{LE}\\\\700LE & = & 180 \times 1182\\& = & 212800\\LE & = & \textbf{304.0 m}\\\end{array}[/tex]
3. Calculate EH
LE + EH + HS = LS
304.0 m + EH + 380 m = 1182 m
EH + 684 m = 1182 m
EH = 498 m
The distance from E to H is 498 m.
PLEASE ANSWER THIS ASPA Which of the following choices is equivalent to -6x > -42? x > 7 x -7 x < -7
Answers
Answer:
x < 7
Step-by-step explanation:
-6x > -42
Divide each side by -6, remembering to flip the inequality
-6x/-6 < -42/-6
x < 7
Answer:
[tex]\boxed{x<7}[/tex]
Step-by-step explanation:
[tex]-6x > -42[/tex]
Divide both sides by -6 (flip sign).
[tex]\displaystyle \frac{-6x}{-6} < \frac{-42}{-6}[/tex]
[tex]x<7[/tex]
There are 4 pieces of paper, numbered 10 to 13, in a hat. After another numbered piece of paper is added, the probability of picking a number between 10 and 13 inclusive is 4/5. Which of the following numbers could
Answers
Answer: The fifth piece of paper could have any number 9 and less or 14 and greater.
Step-by-step explanation: The list of choices is not given in the question, but it makes sense that the new number would not be a duplicate of any of the numbers 10, 11, 12, 13. Otherwise that would change the probability to 5/5.
So any other number could be a possibility.
Please answer this in two minutes
Answers
Answer:
15
Step-by-step explanation:
Use the Pythagorean Thereom:
[tex]r^{2}[/tex] = [tex]9^{2}[/tex]+[tex]12^{2}[/tex]
[tex]r^{2}[/tex] = 81+144
[tex]r^{2}[/tex] = 225
[tex]r[/tex]= 15
Please mark me as Brainliest!
I need this answered in ONE minute
Place the indicated product in the proper location on the grid. Write your answer in descending powers of x. (x^ 2 + 3x + 1)(x^2 + x + 2)
Answers
Answer:
[tex]x^4 + 4x^3 + 6x^2 + 7x + 2[/tex]
Step-by-step explanation:
We are asked to multiply the given polynomials.
[tex](x^ 2 + 3x + 1) \times (x^2 + x + 2)[/tex]
Multiply each term of the first polynomial to each term of the second polynomial.
[tex]x^ 2 \times (x^2 + x + 2) = x^4 + x^3 + 2x^2[/tex]
[tex]3x \times (x^2 + x + 2) = 3x^3 + 3x^2 + 6x[/tex]
[tex]1 \times (x^2 + x + 2) = x^2 + x + 2[/tex]
Add the results
[tex](x^4 + x^3 + 2x^2) + (3x^3 + 3x^2 + 6x) + ( x^2 + x + 2)[/tex]
Combine the like terms
[tex]x^4 + 4x^3 + 6x^2 + 7x + 2[/tex]
The answer is written in descending powers of x.
Angle EFB is 108º a)Find the size of angle x. b) which one of these justifies your answer? A-corresponding angles B- Alternate angles C- vertically opposite angles
Answers
Answer:
a) x° = 108°
b) vertically opposite angles (C) justifies my answer.
Answer:
The answer is option c.
Its an vertically opposite angle because when two lines intersect eachother then theangles formed opposite to it is called v.o.a (vertically opposite angle)
Hope it helps...
Please help ASAP! If correct will mark brainliest
Answers
Answer:
95
Step-by-step explanation:
a=3,b=2
3^2+3(2)-2^2
a=11,b=13
11^2+11(13)-13^2
= 95
Answer:
95
Step-by-step explanation:
If a ∆ b = a² + ab - b²,
Then (3 ∆ 2) ∆ 13:
a = 3
b = 2
3 ∆ 2 = 3² + 3 × 2 - 2² = 11
a = 11
b = 13
11 ∆ 13 = 11² + 11 × 13 - 13² = 95
The answer is 95.
Please answer it now in two minutes
Answers
Answer:
Remember to round!
(x+1)(x-2)=0
Solve the quadratic equation using factoring
Answers
Answer:
x= -1 or x= 2
Step-by-step explanation:
(x+1)(x-2) = 0x+1 = 0 or x-2=0 x = -1 or x = 2Un avión volaba a 14.800 metros de altura. Primero bajó 23.000 decímetros y luego bajó 54 Hectómetros más ¿ A qué altura, en Kilómetros, vuela ahora? AYUDA
Answers
Answer:
7.1 km
Step-by-step explanation:
Bien, este es un problema de conversión de unidades.
Procedemos de la siguiente manera;
Convirtamos todas las alturas que tenemos a metros.
Comenzamos con 23,000 decímetros a metros Matemáticamente, 1 metro = 10 decímetros Entonces 23,000 decímetros = 23,000 / 10 = 2,300 metros
En segundo lugar, convertimos 54 hectómetros a metros.
Matemáticamente; 1 hectómetro = 100 metros Entonces 54 hectómetros = 54 * 100 = 5400 metros Por lo tanto, su nueva altura sería; 14,800-2300-5400 = 7,100 metros Ahora, procedemos a convertir 7.100 metros a kilómetros.
Matemáticamente 1000 m = 1 km Entonces 7,100 m serán = 7100/1000 = 7.1 km
Responder:
7,1 kilómetrosExplicación paso a paso:
Altura inicial del avión = 14.800 m.
Como se redujo en 23,000 decímetros y luego en 54 hectómetros, la caída total de altura se obtiene al agregar 23,000 decímetros y 54 hectómetros
Antes de agregarlos, necesitamos convertir ambos valores a metros
1 decímetro = 0.1m
23,000 decímetros = x
x = 23,000 * 0.1
x = 2,300 metros
Además, si 1 hectómetro = 100 m
54 hectómetros = y
y = 54 * 100
y = 5400 metros.
Sumando ambas alturas;
x + y = 2300m + 5400m = 7700 metros
Esto significa que el avión cae por una altura total de 7700 metros
Para calcular la altura a la que volará el avión después de la caída, tomaremos la diferencia entre la altura inicial y la altura total caída.
La altura que el avión está volando ahora será 14,800 - 7,700 = 7,100 metros
Convirtiendo la respuesta final a kilómetros.
1000m = 1km
7.100m = z
z = 7100/1000
z = 7.1 km
Esto significa que el avión está volando a una altura de 7.1 kilómetros después de la caída.
How to do this question plz answer me step by step plzz plz
Answers
Answer:
x=10 cm
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean theorem
a^2 + b^2 = c^2
x^2 + ( sqrt(200) )^2 = (sqrt(300))^2
x^2 +200 = 300
Subtract 200 from each side
x^2 +200-200 = 300-200
x^2 = 100
Take the square root of each side
sqrt(x^2) = sqrt(100)
x = 10
An infinite geometric series converges if the common ratio is
Answers
Answer:
a proper fraction
what is the value of x if e^3+6+8
Answers
Answer:
A
Step-by-step explanation:
What the correct answer do not want the wrong answer please
Answers
Answer:
388.5yd²
Step-by-step explanation:
We have Triangle TUV
In the question, we are given already
Angle U = 32°
Angle T = 38°
Angle V = ???
Side t = 31yd
Side u = ?
Side v = ?
Area of the triangle= ?
Step 1
We find the third angle = Angle V
Sum of angles in a triangle = 180°
Third angle = Angle V = 180° - (32 + 38)°
= 180° - 70°
Angle V = 110°
Step 2
Find the sides u and v
We find these sides using the sine rule
Sine rule or Rule of Sines =
a/ sin A = b/ Sin B
Hence for triangle TUV
t/ sin T = u/ sin U = v/ sin V
We have the following values
Angle T = 38°
Angle U = 32°
Angle V = 110°
We are given side t = 31y
Finding side u
u/ sin U= t/ sin T
u/sin 32 = 31/sin 38
Cross Multiply
sin 32 × 31 = u × sin 38
u = sin 32 × 31/sin 38
u = 26.68268yd
u = 26.68yd
Finding side x
v / sin V= t/ sin T
v/ sin 110 = 31/sin 38
Cross Multiply
sin 110 × 31 = v × sin 38
v = sin 110 × 31/sin 38
v = 47.31573yd
v = 47.32yd
To find the area of triangle TUV
We use heron formula
= √s(s - t) (s - u) (s - v)
Where S = t + u + v/ 2
s = (31 + 26.68 + 47.32)/2
s = 52.5
Area of the triangle = √52.5× (52.5 - 31) × (52.5 - 26.68 ) × (52.5 - 47.32)
Area of the triangle = √150967.6032
Area of the triangle = 388.5454973359yd²
Approximately to the nearest tenth =388.5yd²
PLEASE HELP ME! I will not accept nonsense answers, but will give BRAINLIEST if you get it correct with solutions:)
Answers
Answer: B. He loses 1/5 of his points in the next crash
Plug in x = 0 to get y = 100(4/5)^0 = 100. He starts with 100 points
After x = 1 crash happens, he has y = 100(4/5)^1 = 80 points left. He lost 20/100 = 1/5 of his points after one crash.
WILL GIVE BRAINLEST ANSWER IF ANSWERED IN 24 HOURS Determine whether a triangle can be formed with the given side lengths. If so, use Heron's formula to find the area of the triangle. a = 240 b = 132 c = 330
Answers
By using Heron’s formula
S=a+b+c/2
S=240+132+330/2=351
Area = root of s(s-a)(s-b)(s-c)
By substituting the values
We get that 13385.874....
Please answer this question now
Answers
Since HJ is tangent to circle G, it forms a right angle with the radius that intersects it.
This means HG and HG are perpendicular and we have a right angle.
We have a (right) triangle with angle measurements 43 and 90, and we want to find the value of the last angle.
All the angles in a triangle must add up to 180, thus we can create the following equation to find the measurement of the last angle:
[tex]180-90-43[/tex]
[tex]=47[/tex]
The measure of angle G is 47 degrees. Let me know if you need any clarifications, thanks!
Answer:
<G = 47 degrees
Step-by-step explanation:
For this problem, we need to understand two things. This tangent on the circle, with a line drawn to the center, forms a right angle at H. Additionally, the sum of the angles of a triangle is 180. Now with these two things, let's solve.
<G = 180 - (43 + 90)
<G = 180 - 133
<G = 47 degrees
Hope this helps.
Cheers.
NEED HELP ON THIS ASAP WEE WOO WEE WOO
Answers
Answer:
50
Step-by-step explanation:
The length of the room is 2½ times the breadth. The perimeter of the room is 70 m. What are the length and breadth of the room?
Answers
Answer:
length=25m
breadth=10m
Step-by-step explanation:
2.5units+2.5units+1unit+1unit=7units
70/7=10
length=10x2.5=25
breadth=10
(sorryy im not really sure but i hope it helps :D)
Answer:
Length = 25 cm
Breadth = 10 cm
Step-by-step explanation:
Let breadth of the room be 'x'
Let length of the room be ''
Perimeter ( P ) = 70 cm
Now, let's find the breadth of the room 'x '
Perimeter of rectangle = 2(l+b)
plug the values
70=2(2.5x+x)
Collect the like terms
70=2x3.5x
Calculate the product
70=7x
Swap the sides of the equation
7x=70
Divide both sides of the equation by 7
7x / 7= 70/7
Calculate
x=10cm
Breadth = 10 cm
Now, Let's find the length of the room ' 2.5x '
Length of the room = 2.5x
Plug the value of X
2.5x10
Calculate the product
25cm
Thus , The length and breadth of the room is 25 cm and 10 cm respectively.
Hope this helps..
Best regards!!
Un estanque tiene 13/2 litros de leche y se le agregan 87/10. ¿Cuánta leche quedó en el estanque? ¿Sí en el estanque caben 65/4 litros, cuántos litros más se pueden agregar?
Answers
Find the coordinates for the equation.
{y=-x^2+5
{-x+y=3
Answers
Answer:
I hope you will get help from these...
A square has diagonals of length 10 cm. Find the sides of the square
Answers
Answer:
5[tex]\sqrt{2}[/tex]
Step-by-step explanation:
The diagonal divides the square into 2 right triangles.
let s be the side of the square with the diagonal being the hypotenuse.
Applying Pythagoras' identity to one right triangle, gives
s² + s² = 10² , that is
2s² = 100 ( divide both sides by 2 )
s² = 50 ( take the square root of both sides )
s = [tex]\sqrt{50}[/tex] = [tex]\sqrt{25(2)}[/tex] = [tex]\sqrt{25}[/tex] × [tex]\sqrt{2}[/tex] = 5[tex]\sqrt{2}[/tex]
A staining solution bottle in a medical laboratory contains 30 ounces (oz). A blood staining test requires 3/4 oz of solution. A tissue staining test requires 1/2 oz of solution. If four blood tests and five tissue tests are performed, how many oz of solution are left in the bottle
Answers
Answer:
24.5 oz
Step-by-step explanation:
First lets calculate the blood tests, 3/4 oz of solution.
3/4 multiplied by four tests= 3. (.75*4=3)
So 3 oz of Blood Tests were performed, now lets calculate the amount of tissue staining tests for performed.
1/2 multiplied by five tests= 5/2 or 2.5 oz of tests. (.5*5=2.5)
3oz+2.5=5.5oz
Now let's subtract that amount by 30.
30-5.5=24.5
Find the surface area of the regular pyramid shown in the accompanying diagram. If necessary, express your answer in simplest radical form.
Answers
Answer:
84 squared units.
Step-by-step explanation:
In order to find the surface area of the pyramid, you use the following formula:
[tex]S=b^2+\frac{1}{2}ps[/tex] (1)
b: base of the pyramid = 6
p: perimeter of the base = 6*4 = 24
s: slant height
Then, you first calculate the slant height, by using the Pythagoras' theorem:
[tex]s=\sqrt{(5)^2-(\frac{6}{2})^2}=4[/tex]
Thus, you replace the values of b, p and s in the equation (1):
[tex]S=(6)^2+\frac{1}{2}(24)(4)=84[/tex]
The surface area of the pyramid is 84 squared units.
Answer:
Step-by-step explanation:
wrong
what is the equation of the following line (10 -2) (0 0) a. y= -5x b. -x c. y= 5x d. -1/5x e. y= x f. y= 1/5x
Answers
Answer:
Step-by-step explanation:
(0+2)/(0-10)= 2/-10 = -1/5
y - 0 = -1/5(x - 0)
y = -1/5x
solution is D