Answer: [tex](-5.5,4.062)\ \text{and}\ (-5.5,-8.062)[/tex]
Step-by-step explanation:
Given
The two vertices of a equilateral triangle are [tex](-9,-2)\ \text{and}\ (-2,-2)[/tex]
Suppose the third vertex is [tex](x,y)[/tex]
Side length in equilateral triangle are equal.
[tex]\Rightarrow \sqrt{\left( -2+9\right)^2+\left( -2+2\right)^2}=\sqrt{\left( x+9\right)^2+\left( y+2\right)^2}\\\text{squaring both sides}\\\\\Rightarrow 7^2=\left( x+9\right)^2+\left( y+2\right)^2\quad \ldots(i)\\\\[/tex]
Similarly,
[tex]\Rightarrow \sqrt{\left( -2+9\right)^2+\left( -2+2\right)^2}=\sqrt{\left( x+2\right)^2+\left( y+2\right)^2}\\\\\Rightarrow 7^2=\left( x+2\right)^2+\left( y+2\right)^2\quad \ldots(ii)[/tex]
Subtract (i) and (ii)
[tex]\Rightarrow \left( x+9\right)^2-\left(x+2\right)^2=7^2-7^2\\\\\Rightarrow (x+9+x+2)(x+9-x-2)=0\\\Rightarrow (2x+11)7=0\\\\\Rightarrow x=-\dfrac{11}{2}[/tex]
Insert the value of [tex]x[/tex] in equation (ii)
[tex]\Rightarrow \left(-5.5+2\right)^2+\left(y+2\right)^2=7^2\\\\\Rightarrow \left(-5.5+2\right)^2+\left(y+2\right)^2-\left(-5.5+2\right)^2=7^2-\left(-5.5+2\right)^2\\\\\Rightarrow \left(y+2\right)^2=36.75\\\\\Rightarrow y=4.06217\dots ,\:y=-8.06217[/tex]
So, two possible vertex are [tex](-5.5,4.062)\ \text{and}\ (-5.5,-8.062)[/tex]
De 1.620 trabajadores de una empresa textil 7/9 trabajan en confeccion y el resto en tareas administrativas. ¿cuantos trabajadores trabajan en confeccion?
Answer:
The number of employees work in clothing is 1260.
Step-by-step explanation:
Out of 1,620 workers in a 7/9 textile company work in clothing and the rest in administrative tasks. How many workers work in clothing?
Total workers = 1620
employees works for clothing = 7/9
So, the number of employees = 7/9 x 1620 = 1260
Usando la informacion dada, veremos que el número de trabajadores que trabajan en confección es 1,260.
Sabemos que hay un total de 1,620 trabajadores en la empesa textil.
7/9 de ellos trabajan en confección.
Queremos ver el número de trabajadores que trabaja en confección, para ello, simplemente debemos multiplicar la fracción del número total que trabaja en confección por el número total, es decir:
N = (7/9)*1,620 = 1,260
1,260 trabajadores trabajan en confección.
sí quieres aprender más, puedes leer:
https://brainly.com/question/12668006
I need help finding the solution
Answer:
170°
Step-by-step explanation:
The total degrees of a circle is 360°. So the math is pretty straight forward.
130 + 60 = 190 (First you find what the known degrees are together)
360 - 190 = 170 (Next you take that added total and subtract it from 360)
x = 170 (And there you go! Your answer!)
I hope this helped :)
(2sin60°)(3tan60°)—(4tan45°)(2cos45°)
Answer:
[tex]9 - 4\sqrt{2}[/tex]
Step-by-step explanation:
sin60° = [tex]\frac{\sqrt{3} }{2}[/tex]
tan60° = [tex]\sqrt{3}[/tex]
tan45° = 1
cos45° = [tex]\frac{1}{\sqrt{2} }[/tex]
(2sin60°)(3tan60°) - (4tan45°)(2cos45°)
now substitute the values of each trigonometrical angles
[tex](2*\frac{\sqrt{3} }{2} )(3*\sqrt{3} ) - (4*1)(2*\frac{1}{\sqrt{2} } )[/tex]
[tex]\sqrt{3} * (3\sqrt{3}) - 4*(\frac{2}{\sqrt{2} } )[/tex]
[tex]3*3 - 4*\frac{2}{\sqrt{2} } *\frac{\sqrt{2} }{\sqrt{2} }[/tex]
[tex]9 - 4 *\frac{2\sqrt{2} }{2}[/tex]
[tex]9 - 4 * \sqrt{2}[/tex]
[tex]9 - 4\sqrt{2}[/tex]
What is the solution set?
O (0-2)
O (2.0)
O (7,0)
O (5,3)
Answer:
D. (5,3)
Step-by-step explanation:
The solution is (x,y). so in this case, you find the point where both arrows meet.
on the x-axis, which is positive right 5, and positive 3 up, on the y-axis
Answer:
(5,3)
Step-by-step explanation:
The solution set is where the two lines cross
The lines cross at x = 5 and y = 3
A laptop computer is purchased for $2050. After each year, the resale value decreases by 30%. What will the resale value be after 4 years?
Use the calculator provided and round your answer to the nearest dollar.
$
Answer:
492.205
$492
Step-by-step explanation:
2050/100 = ?/ 70 <- repeat four times changing 2050 to the new value.
The resale value of the laptop after 4 years will be approximately $492.
How to calculate the resale value?To calculate the resale value "b" of the item after "n" years, we need to apply the annual decrease in value to the original price "a" for each year (n). We can do this using a loop or by using a formula.
b = a x (1 - decrease rate)ⁿ
As per the question, the old value is $2050, the decrease rate is 30%, and the number of years is 4. Plugging these values into the formula gives us:
new value = $2050 x (1 - 0.30)⁴
Simplifying this expression gives us:
new value = $2050 x 0.70⁴
new value = $2050 x 0.2401
Which simplifies to:
new value = $492.205
Rounding this result to the nearest dollar gives us $492.
Therefore, the resale value of the laptop after 4 years will be approximately $492.
To learn about the markup rate click here:
brainly.com/question/11999225
#SPJ2
The mean temperature for the first 7 days in January was 6 °C.
The temperature on the 8th day was 5 °C.
What is the mean temperature for the first 8 days in January?
Hope this help!!!
Have a nice day!!!
64,872 rounded to the nearest hundred is
64,872 rounded to the nearest hundred should be 64,900
Answer:
64900
Step-by-step explanation:
Look at number after hundred's place
if its 5 or higher round up
if its 4 or less round down
How do you find the angle using a protractor
Answer:
Place the midpoint of the protractor on the VERTEX of the angle.
Line up one side of the angle with the zero line of the protractor (where you see the number 0).
Read the degrees where the other side crosses the number scale.
Step-by-step explanation:
Hope this helps!! :))
The newspaper in Haventown had a circulation of 80,000 papers in the year 2000. In 2010, the circulation was 50,000. With x=0 representing the year 2000, the graph below models this scenario.
A coordinate plane showing Newspaper Circulation, Years Since 2000 on the x-axis and Circulation on the y-axis. A line starting at (0, 80,000), passing through a point at (10, 50,000) and ending at (18, 25,000).
What number will complete the point-slope equation that models this scenario?
y−50,000=[_______](x−10)
−3,000
−2,000
2,000
3,000
Answer:
-3,000
Step-by-step explanation:
got it correct on edg
Answer:
-3000
Step-by-step explanation:
Right on edge 2021
Solve the system of equations by substitution. Simplify your answer. Write the
solution as an ordered pair.
y= 3x - 13
3x + 2y = 19
Answer:
x = 5 y = 2
Step-by-step explanation:
3x + 2(3x - 13) = 19
3x + 6x - 26 = 19
9x = 45
x = 5
y = 3(5) - 13
y = 15 - 13
y = 2
Please I need help The original price of a car was reduced by $3000. Its discount price is now 16000
Answer:
$19,000
Step-by-step explanation:
The original or initial price of the car = discount price + amount by which the car was reduced
$16,000 + $3000 = $19,000
The percentage decrease in price = (amount discounted / original price) x 100
( $3000 / $19,000) x 100 = 15.79%
ILL GIVE BRAINLIEST IF ANSWERED GOOD. DUE IN AN HOUR.. Write a quadratic equation that is the same width as y = -2x^2+ x + 1.
Answer:
The answer is:
y=-2x+2+x+1
y=_2x+x+2+1
y=x+3
Hope it helps
can u help me part 3..
The numbers below represent side lengths of various triangles. Which of the triangles are right triangle?
1. 5, 6, 9 A. Right triangle
2. 9, 11, 13 B. Not a right triangle
3. 20, 21, 29
4. 7, 24, 25
5. 9, 40, 41
Answer:
Step-by-step explanation:
Number 5
WRITE AN EQUATION THAT REPRESENTS THE LINE. USE EXACT NUMBERS.
Answer:
[tex]y=\frac{6}{5}x-5[/tex]
Step-by-step explanation:
Hi there!
Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when x is 0)
1) Determine the slope (m)
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Plug in the two given points (0,-5) and (5,1)
[tex]m=\frac{1-(-5)}{5-0}\\m=\frac{1+5}{5-0}\\m=\frac{6}{5}[/tex]
Therefore, the slope of the line is [tex]\frac{6}{5}[/tex]. Plug this into [tex]y=mx+b[/tex]:
[tex]y=\frac{6}{5}x+b[/tex]
2) Determine the y-intercept (b)
[tex]y=\frac{6}{5}x+b[/tex]
On the graph, we can see that when x is 0, y is equal to -5 (we're also given the point (0,-5). Therefore, the y-intercept of the line is -5. Plug this back into the equation:
[tex]y=\frac{6}{5}x-5[/tex]
I hope this helps!
Answer:
y = 6/5x - 5
Step-by-step explanation:
To find the equation of a linear line you need 2 things: the slope and the y-intercept.
The slope can be found by taking two points and dividing the change in y by the change in x. Using the two points highlighted, the slope would be (1 - -5)/(5-0) = 6/5.
The y-intercept is where the line crosses the y-axis, which on this line is at -5. Then plug in this information into point slope form, y = mx + b, where m is the slope.
So you get y = 6/5x - 5.
Here is standard form too if you need this instead: 6x - 5y = 25
What is the value of x?
2
to
64°
X =
Answer:
26
Step-by-step explanation:
64 + x = 90 ( whole part axioms )
x = 90 - 64
x = 26
HELPPP PLEASE!!!!!!!!!!
work out the answer of the given fractions 3/12+1/6=
20. The tens and units digit of the number are the same. When the number is
added to its reverse, the sum is 110. What is the number?
Answer:
55
Step-by-step explanation:
55 has both its tens and units the same and when you reverse it, it is still 55 hence 55+55 is 110
Given : The tens and units digit of the number are the same
Let the given number be : NN
Given : When the number is added to its reverse, the sum is 110
As the tens and units digit of the number are same, the reversed number is also : NN
⇒ NN + NN = 110
⇒ 2NN = 110
⇒ NN = 55
Answer: The Number is 55
Which equation is equivalent to
y-1= 5(x+2) ?
Step-by-step explanation:
We can simply by opening the brackets ,
=> y - 1 = 5( x - 2 )
=> y - 1 = 5x - 10
=> y - 5x = -9
=> 5x - y + 9 = 0
UERGENT!!!!!!
Find the values of x and y
5x - 17 = 48
5x − 17 + 17 = 48 + 17
5x = 65
x = 13
180 - 48 = 132
y = 132
Change the units up above to the correct answer from (a) to (d)
Answer:
Step-by-step explanation:
1 cm = 10 mm
a) 0.1 cm = 1 mm
1 mm = 1000 m
b) 25000mm = 25 m
1 g = 0.001 kg
c) 7g = 0.007 kg
1ml = 0.000001
d) 30000ml = 0.03 kl
A baseball is thrown straight up in the air with an
initial velocity of 128 feet per second from a point
exactly 4 feet off the ground.
Write the function for the height of this object at any
time (t seconds)
Answer:
Step-by-step explanation:
[tex]h(t)=-16t^2+v_0t+h_0[/tex] where
h(t) is the height of the ball after a certain amount of time has gone by,
-16t² is the pull of gravity in ft/s/s,
v₀t is the initial upwards velocity, and
h₀ is the height from which the ball was initially thrown. Our equation is then, filling in the info in the correct places:
[tex]h(t)=-16t^2+128t+4[/tex] where 128 is the given initial velocity and 4 is the number of feet from which the ball was initially launched.
ava,jayden,edwina,lexi,luis, and trina are helping clean up a hiking trail during the summer. The trail is 10 miles long. Edwina, lexi, and luis plant a tree every 1/4 of a mile along the trail. Write and evaluate a division expression to find the number of trees they will plant.
Answer:
120 trees
Step-by-step explanation:
4x10=40
40x3=120
120 trees will be planted
PLS HELP Find the value of x.
A. 30
B. 15
C. 45
D. 6
Answer:
B.
[tex](3x - 15) -(45 - x) = 0 \\ 4x -60 = 0 \\ 4x = 60 \\ x = 15[/tex]
please help with the question above!!
Answer:
5
Step-by-step explanation:
1+2+2+3+3+3+4+5+6+6+7+7
+7+8+9 = 73
73/15 = 4.86667
you add all the numbers and divide by how many numbers there were.
so round it up and it should be 5.
In a two-digit number, the units digit is twice the tens digit. If the number is doubled
it will be 9 more than the number reversed. Find the number.
T=Tens
U=Unit
From the question... The Unit digit is twice the Tens digit
Let the Number be xy
Meaning
y is the unit number
x is the tenth Number
Can be inferred for the question that
y=2x ...........(i)
Also
If the Number is doubled x2(times 2)
"It'll be 9more than the reversed"
Now listen
if you want to express a 2digit Number...
Let's say 45...
It can be expressed as 10x4 + 5 = 45
or
66 can be expressed as 10x6 + 6 = 66
So
It'd be better if we express this our unknown number like that too
So
Let's express "xy" like "10x + y"
Hope you grab?
Now from the second statement of the question..
If The Number is doubled...It'll be 9 more than the reversed
What is the reverse of that Number??
The reverse would be "10y + x"
You can see that x and y switched places.
so
The statement said...
2(10x + y) + 9 = 10y + x (reversed)
20x + 2y + 9 =10y + x ........(ii)
Recall from our first eqn
y=2x
Now substitute y=2x into eqn ii
20x + 2(2x) + 9 = 10(2x) + x
20x + 4x +9 = 20x + x
20x - 20x + 4x - x = -9
3x = -9
x=-3
y=2x
y=2(-3)
y=-6
So The Number is 10x + y
= 10(-3) + (-6)
=-30-6
=-36
This answer obeyed the first part of the question because the unit is twice digit(2x3)
Let's check if it obeyed the second part
2[(10(-3) + (-6)] + 9 = 10(-6) + (-3)
2(-30-6) + 9 = -60-3
-63=-63
The 2nd part is also true.
So
Our Number is -36.
I'm Open to corrections if you spot any.
If 8 subtracted from the product of 3 and a number the result is 10. Find the number
Please help me with this
Answer:
V ≈ 254.5 in³
Step-by-step explanation:
The volume (V) of the cylindrical tube is calculated as
V = πr²h ( r is the radius and h the height ) , then
V = π × 3² × 9 = π × 9 × 9 = 81π ≈ 254.5 in³ ( to 1 dec. place )
La velocidad maxima permitida en una autopista es de 120km/h. Se considera infraccion si se sobrepasa segun al rodar el 12% de esa velocidad. A que velocidad como minimo iba un conductor que cometio una infraccion
Answer:
La velocidad mínima a la que debe ir un conductor que cometa una infracción es de:
134.5 Km/hO si se desea un número entero:
135 Km/hStep-by-step explanation:
Para identificar la velocidad que debe levar un conductor para cometer una infracción, se deben tener en cuenta las pautas dadas en el ejercicio:
Velocidad Máxima Permitida: 120 Km/hCausa de infracción: Sobrepasar el 12% de la velocidad máxima.Ahora debemos calcular el 12% de la velocidad máxima permitida y sumarlo a dicha velocidad, con el fin de calcular la velocidad límite justo antes de cometer la infracción:
Velocidad límite antes de la infracción = 120 Km/h + (120 Km/h * 12%)Velocidad límite antes de la infracción = 120 Km/h + 14.4 Km/hVelocidad límite antes de la infracción = 134.4 Km/hCómo puedes ver, cuando el conductor está manejando a 134.4 Km/h está justo al límite antes de cometer una infracción, ya que recuerda que en el enunciado se menciona que "se considera infracción si se sobrepasa según al rodar el 12% de esa velocidad", por lo tanto, la velocidad que debe tener para cometer esa infracción debe ser mayor a la velocidad límite, la cual puede ser 134.5 Km/h, aumentando solo una décima a la velocidad límite, o 135 Km/h si se requiere que la respuesta sea un número entero.
