Answer:
[tex]radius = \sqrt{13}[/tex] or [tex]radius = 3.61[/tex]
Step-by-step explanation:
Given
Points:
A(-3,2) and B(-2,3)
Required
Determine the radius of the circle
First, we have to determine the center of the circle;
Since the circle has its center on the x axis; the coordinates of the center is;
[tex]Center = (x,0)[/tex]
Next is to determine the value of x through the formula of radius;
[tex]radius = \sqrt{(x_1 - x)^2 + (y_1 - y)^2} = \sqrt{(x_2 - x)^2 + (y_2 - y)^2}[/tex]
Considering the given points
[tex]A(x_1,y_1) = A(-3,2)[/tex]
[tex]B(x_2,y_2) = B(-2,3)[/tex]
[tex]Center(x,y) =Center (x,0)[/tex]
Substitute values for [tex]x,y,x_1,y_1,x_2,y_2[/tex] in the above formula
We have:
[tex]\sqrt{(-3 - x)^2 + (2 - 0)^2} = \sqrt{(-2 - x)^2 + (3 - 0)^2}[/tex]
Evaluate the brackets
[tex]\sqrt{(-(3 + x))^2 + 2^2} = \sqrt{(-(2 + x))^2 + 3 ^2}[/tex]
[tex]\sqrt{(-(3 + x))^2 + 4} = \sqrt{(-(2 + x))^2 + 9}[/tex]
Eva;uate all squares
[tex]\sqrt{(-(3 + x))(-(3 + x)) + 4} = \sqrt{(-(2 + x))(-(2 + x)) + 9}[/tex]
[tex]\sqrt{(3 + x)(3 + x) + 4} = \sqrt{(2 + x)(2 + x) + 9}[/tex]
Take square of both sides
[tex](3 + x)(3 + x) + 4 = (2 + x)(2 + x) + 9[/tex]
Evaluate the brackets
[tex]3(3 + x) +x(3 + x) + 4 = 2(2 + x) +x(2 + x) + 9[/tex]
[tex]9 + 3x +3x + x^2 + 4 = 4 + 2x +2x + x^2 + 9[/tex]
[tex]9 + 6x + x^2 + 4 = 4 + 4x + x^2 + 9[/tex]
Collect Like Terms
[tex]6x -4x + x^2 -x^2 = 4 -4 + 9 - 9[/tex]
[tex]2x = 0[/tex]
Divide both sides by 2
[tex]x = 0[/tex]
This implies the the center of the circle is
[tex]Center = (x,0)[/tex]
Substitute 0 for x
[tex]Center = (0,0)[/tex]
Substitute 0 for x and y in any of the radius formula
[tex]radius = \sqrt{(x_1 - 0)^2 + (y_1 - 0)^2}[/tex]
[tex]radius = \sqrt{(x_1)^2 + (y_1)^2}[/tex]
Considering that we used x1 and y1;
In this case we have that; [tex]A(x_1,y_1) = A(-3,2)[/tex]
Substitute -3 for x1 and 2 for y1
[tex]radius = \sqrt{(-3)^2 + (2)^2}[/tex]
[tex]radius = \sqrt{13}[/tex]
[tex]radius = 3.61[/tex] ---Approximated
PLZ HELP!!!! ASAP !!!!
Answer:
(A)
Sin á = a/c
Cos ∅ = a/c
Tan á = a/b
(B)
Sin á = a/c
Cos á = b/c
Tan á = a/b
Therefore á=
(inverse sin) a/c
Or
(Inverse cos) b/c
Or
(Inverse tan) a/b
(C)
If b = 12 and c = 13
then a =√(c²-b²)
= 5
Hence 5/13 = a/c
Therefore sin á = cos ∅ = a/c = 5/13
Factorise using suitable identities (0.1x-0.2y)^2 plzzz help!!!!!
Answer:
0.1 exponent2 ( x − 2 y ) exponent 2
Step-by-step explanation:
Find the exact value of cos A in simplest radical form.
Answer:
[tex] \cos(A) = \frac{2 \sqrt{6} }{7} [/tex]Step-by-step explanation:
Since we are finding cos A we have
[tex] \cos(A) = \frac{AC}{AB} [/tex]From the question
AC = √96
AB = 14
Substitute the values into the above formula
That's
[tex] \cos(A) = \frac{ \sqrt{96} }{14} [/tex]We have the final answer as
[tex] \cos(A) = \frac{2 \sqrt{6} }{7} [/tex]Hope this helps you
what is 40-32divited by8=5x-2
How would you write The product of 2 and the difference of a number and 9
Answer:
[tex]\large \boxed{2(x-9)}[/tex]
Step-by-step explanation:
Let the number be x.
The product of 2 and the difference of x and 9.
“product” is multiplication.
“difference” is subtraction.
[tex]2 \times (x-9)[/tex]
The mathematical expression is 2(n - 9) if the product of 2 and the difference of a number and 9.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
It is given that:
The product of 2 and the difference of a number and 9.
Let the number is n; n is the real number.
The difference of a number and 9 = n - 9
The linear expression can be defined as the relation between two variables, if we plot the graph of the linear expression we will get a straight line.
If in the linear expression, one variable is present, then the expression is known as the linear expression in one variable.
The product of 2 and (n - 9)
= 2(n - 9)
Thus, the mathematical expression is 2(n - 9) if the product of 2 and the difference of a number and 9.
Learn more about the expression here:
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#SPJ2
4 Points
is
For the function y = 3x + 5
what is the output of the
function if the input is 10?
Answer:
[tex]35[/tex]
Step-by-step explanation:
One is given the following function ([tex]y=3x+5[/tex]). The given problem asks one to find the output of the function when the input is (10). Keep in mind, a general rule for dealing with functions is that, when present, the variable (x) represents the input. Whereas the variable (y) represents the output. Thus, if one were to substitute (10) in place of (x), and simplify: the result one would get is the output. Apply this idea to the given scenario:
[tex]y=3x+5[/tex]
[tex]y=3(10)+5[/tex]
[tex]y=30+5[/tex]
[tex]y=35[/tex]
Given two consecutive integers whose sum is 92, find the larger of the two integers.
please help, i really dont understand this. will give brainliest.
There are 6 dogs and 5 cats.
Answer:
13) 11C5 or 11C6 = 462
14) it appears to be only 1
DCDCDCDCDCD
15) 9 choose 6 or 9 choose 3 = 84
Step-by-step explanation:
What is the value of r?
Answer:
r = 11
Step-by-step explanation:
Hi there!
This scenario represents a linear relation, given the equation [tex]m=rp+k[/tex].
Linear equations are typically written in the form [tex]y=mx+b[/tex], where m is the slope and b is the y-intercept. As you can see, [tex]y=mx+b[/tex] and the given equation [tex]m=rp+k[/tex] share the same form.
This makes r the slope. This is also stated in the question, as r is the amount of money ($) paid per page.
The ordered pairs in the table represents points on a graph, if we were to graph this. For example, (9, 308) and (12, 341) both fall on the graph of this relation.
To solve for r, we must solve for the slope using the slope equation:
[tex]r=\displaystyle \frac{y_2-y_1}{x_2-x_1}[/tex] where two points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex].
We can use any two points from the table in this equation. For example, (9, 308) and (12, 341):
[tex]r=\displaystyle \frac{341-308}{12-9}\\\\r=\displaystyle \frac{33}{3}\\\\r=11[/tex]
Therefore, the value of r is 11.
I hope this helps!
Answer ASAP, will give brainliest
Answer:
Step-by-step explanation:
1) Diagonal bisect the angles of Rhombus
∠CAB = ∠CAD
∠CAB = 71
2) ∠DAB = ∠CAB + ∠CAD
∠DAB = 71 + 71 = 142
In Rhombus, adjacent angles are supplementary
∠DAB + ∠ABC = 180
142 + ∠ABC = 180
∠ABC = 180 - 142
∠ABC = 38
3) In rhombus, opposite angles are congruent
∠ADC = ∠ABC
∠ABC = 38
In rhombus, diagonal bisect angles
∠BDC = (1/2)*∠ADC
∠BDC= 38/2
∠BDC = 19
4) Diagonals bisect each other at 90
∠DEC = 90
5) Diagonals bisect each other
BE = DE
BE + DE = DB
7x -2 +7x -2 =24 {add like terms}
14x - 4 =24
14x = 24+4
14x = 28
x = 28/14
x = 2 m
6) AB = 13m
BE = 7x - 2 = 7*2 -2 = 14 -2 = 12 m
In right angle ΔAEB, {use Pythagorean theorem}
AE² + BE² = AB²
AE² + 12² = 13²
AE² + 144 = 169
AE² = 169 - 144
AE² = 25
AE = √25
AE = 5 m
Diagonals bisect each other
AE = EC
AC = 2*5
AC = 10 m
7)Side = 13 m
Perimeter = 4*side
= 4*13
Perimeter = 52 m
8) d1 = AC = 10 m
d2 = DB = 24 m
Area = [tex]\frac{d_{1}*d_{2}}{2}[/tex]
[tex]=\frac{10*24}{2}\\[/tex]
= 10 *12
= 120 m²
Part 1: You work 4 hours and earn $36. What is your earning rate (dollars per hour)?
Answer:
9 dollars per hour
Step-by-step explanation:
36/4=9
Answer:
9
Step-by-step explanation:
4 hours : $36
1 hour : $ x
we need to find x so,
4 hours ÷ 4 = 1 hour
1 : $
since we have divided 4 by 4,
we need to do that to 36 aswell
36 ÷ 4 = 9
1 hour : $9
1. A rectangular pyramid is intersected by a plane to create the frustum shown. If the height of the original pyramid is 14 m, what is the volume of the frustum?
10 m
4 m
8 m
6 m
12m
The volume of the frustum that is shown in the diagram is: C. 256 m³.
What is the Volume of Frustum?The volume of frustum = Volume of the bigger rectangular pyramid - Volume of smaller rectangular pyramid.
Find the volume of the original (bigger) rectangular pyramid:
Volume of rectangular pyramid = 1/3(lwh) = 1/3(12 × 6 × 14)
Volume of rectangular pyramid = 336 m³
Find the volume of the smaller (the top that was removed) rectangular pyramid:
Volume of rectangular pyramid = 1/3(lwh) = 1/3(10 × 4 × 6)
Volume of rectangular pyramid = 80 m³
The volume of frustum = Volume of the bigger rectangular pyramid - Volume of smaller rectangular pyramid = 336 - 80 = 256 m³.
Thus, the volume of the frustum that is shown in the diagram is: C. 256 m³.
Learn more about volume of frustum on:
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22. Find the area of circle with radius 7cm ( π)
Answer:
Sol:Here
Radius (R) =7cm
Area of circle (A) =pie*r^2
=22/7*7^2
=3.14*7^2
=3.14*49
=153.86
Answer:
A=49πcm²Step-by-step explanation:
A=πr²
Given r=7,A=π(7²)=49πcm²
solve the equation 2x+1=x-3
How to solve your problem
Topics: Algebra, Quadratic Equation
2
+
1
=
−
3
2x+1=x-3
2x+1=x−3
Solve
1
Subtract
1
1
1
from both sides of the equation
2
+
1
=
−
3
2x+1=x-3
2x+1=x−3
2
+
1
−
1
=
−
3
−
1
2x+1{\color{#c92786}{-1}}=x-3{\color{#c92786}{-1}}
2x+1−1=x−3−1
2
Simplify
Subtract the numbers
Subtract the numbers
2
=
−
4
2x=x-4
2x=x−4
3
Subtract
x
x
from both sides of the equation
2
=
−
4
2x=x-4
2x=x−4
2
−
=
−
4
−
2x{\color{#c92786}{-x}}=x-4{\color{#c92786}{-x}}
2x−x=x−4−x
4
Simplify
Combine like terms
Multiply by 1
Combine like terms
=
−
4
x=-4
x=−4
Solution
=
−
4
What are three collinear points on line l?
points A, B, and F
points A, F, and G
points B, C, and D
points B, F, and G
Answer:
Points A, F, and G are three collinear points on line l.
Step-by-step explanation:
Answer:
Points A, F and G
Step-by-step explanation:
If no grouping symbols or exponents are in an expression, then do _____ first.
15=3y+7.y= please help me with my assignment i havelike 57 more questions to answer and 10% im trying by myself to solve the rest are kinda difficult
Answer:
8/3 or 2.67 to nearest hundredth.
Step-by-step explanation:
15 = 3y + 7
15 - 7 = 3y
3y = 8
y = 8/3
I need help ASAP!! Finding the angle Please help me
Answer:
Does the answer help you?
[tex]\\ \sf\longmapsto Sin\Theta=\dfrac{P}{H}[/tex]
[tex]\\ \sf\longmapsto sin\Theta=\dfrac{49}{52}[/tex]
2decimal places:-[tex]\\ \sf\longmapsto sin\Theta=0.94[/tex]
[tex]\\ \sf\longmapsto sin\Theta=sin71°[/tex]
[tex]\\ \sf\longmapsto \Theta=71°[/tex]
Or
[tex]\\ \sf\longmapsto cos19°[/tex]
1decimal place:-[tex]\\ \sf\longmapsto sin\Theta=0.9[/tex]
[tex]\\ \sf\longmapsto sin\Theta=sin70[/tex]
[tex]\\ \sf\longmapsto \Theta=70°[/tex]
Or[tex]\\ \sf\longmapsto cos20°[/tex]
(2 + i)(3 - i)(1 + 2i)(1 - i)(3 + i)
Answer:
50+50iStep-by-step explanation:
Given the expression (2 + i)(3 - i)(1 + 2i)(1 - i)(3 + i), we are to take the product of all the complex values. We must note that i² = -1.
Rearranging the expression [(3 - i)(3 + i)] [(2 + i)(1 - i)](1 + 2i)
On expansion
(3 - i)(3 + i)
= 9+3i-3i-i²
= 9-(-1)
= 9+1
(3 - i)(3 + i) = 10
For the expression (2 + i)(1 - i), we have;
(2 + i)(1 - i)
= 2-2i+i-i²
= 2-i+1
= 3-i
Multiplying 3-i with the last expression (1 + 2i)
(2 + i)(1 - i)(1 + 2i)
= (3-i)(1+2i)
= 3+6i-i-2i²
= 3+5i-2(-1)
= 3+5i+2
= 5+5i
Finally, [(3 - i)(3 + i)] [(2 + i)(1 - i)(1 + 2i)]
= 10(5+5i)
= 50+50i
Hence, (3 - i)(3 + i)(2 + i)(1 - i)(1 + 2i) is equivalent to 50+50i
Solve for x: 3(x + 1) = -2(x - 1) + 6. (1 point)
Answer:
Isolate the variable by dividing each side by factors that don't contain the variable.
x = 1
First: distribute 3(x+1)= -2(x-1)+6
3x+3=2(x-1)+6
Then you have too distribute again
3x+3=2(x-1)+6
3x+3= -2x+2+6
Third: add the numbers
3x+3= -2x+2+6
3x+3= -2x+8
Fourth: add the same term to both sides of the equation
3x+3= -2x+8
3x+3-3= -2x+8-3
Fifth: Simplify 3x= -2x+5
Sixth: add same term to both sides of the equation
3x= -2x+5
3x+2x= -2x+5+2x
Seventh: simplify again
5x =5
Eigth: divide both sides of the equation by the same term
5x=5
5x/5 =5/5
Last: Simplify
X=1
1. Escribe las razones de los siguientes enunciados: a. En una clase de un colegio cada pelota es utilizada por cada equipo de cinco niños, o sea que tenemos cinco alumnos por cada pelota de fútbol. b. En un estacionamiento hay coches de fábricas asiáticas y de fábricas americanas. En total hay 3060 coches, de los cuales, 1740 son de fabricación asiática y el resto, 1320, son de fabricación americana. (es urgentee.. Es para una tarea)
Answer:
a. 5 n/p o 1 p/ 5n
b. 1720 autos asia/3060 autos, o 1320 autos USA/3060 autos
Step-by-step explanation:
Se entiende como razón a la fracción que compara dos elementos entre sí.
Por ejemplo en una clase de 24 alumnos donde 15 son mujeres y 9 son varones, podemos decir que:
- Por cada 15 mujeres hay 9 varones 9/15
- Por cada 9 varones hay 15 mujeres, 15/9
Para el ejercicio a. nos cuentan que 1 pelota es utilizada cada 5 niños, por lo que la razón la podemos escribir como 1/5, 1 pelota cada 5 o directamente 5, ya que por cada 5 alumnos, tenemos 1 pelota.
El ejercicio b es más fácil: ya tenemos el total de autos, 3060. Entonces:
- Cada 3060 autos, 1720 son asiáticos
- Cada 3060 autos, 1320, son americanos
Which is the graph of y = [x]-2?
Please please helped timed 20points
Answer:
3rd graph
Step-by-step explanation:
answer to question 3 please ?
Answer:
Step-by-step explanation:
Equation for the height of a plant is,
h = 0.5d + 4
Function representing he height 'f(x)' of a plant with respect to time 'x' (in days) will be,
f(x) = 0.5x + 4
[By substituting the input values of x we get the output values of 'y' from the given equation]
Table to plot the points on the graph will be,
x 0 1 2 3 4 5 6
f(x) 4 4.5 5 5.5 6 6.5 7
Now plot these points on graph as given in the attachment.
Emília ganhou 350 reais de sua avó. Com esse dinheiro, ela comprou um sapato, e uma roupa que custou o dobro do preço do sapato. Os 200 reais que sobraram foram depositados por Emília em sua conta poupança.
Qual é a equação eu permite determinar o preço x, em reais, que Emília pagou por esse sapato?
A) x + 2× = 350
B) x + 2× 200 = 350
C) x + (x + 2) + 200 = 350
D) x + ײ + 200 = 350
Parabolic microphones are used for field audio during sports events. The microphones are manufactured such that the equation of their cross section is x=1/34y^2, in inches. The feedhorn part of the microphone is located at the focus
a. How far is the feedhorn from the edge of the parabolic surface of the microphone?
b. What is the diameter of the microphone? Explain your reasoning
c. If the diameter is increased by 5 inches, what is the new equation of the cross section of the microphone?
Answer:
a. 8.5 in.
b. 34 in
c. x = 1/39 x^2.
Step-by-step explanation:
Part a.
x = 1/34 y^2
y^2 = 34x
Comparing with y^2 = 4px where p is the focus:
4p = 34
p = 8.5 in.
Part b.
The diameter = 4p = 34 in.
Part c.
Diameter = 4p = 34 + 5 = 39 in
The new equation is x = 1/39 x^2.
36. Given that y varies directly with x,
what is the equation of direct variation
if y is 3 when x is 7?
Answer:
A. y = 3/7x
Step-by-step explanation:
Direct variation: y = kx
3 = 7k
k = 3/7
y = 3/7x
pls help me due tomorrow
Answer:
Step-by-step explanation:
f(x) = 2x - 4
g(x) = 1/2x - 4
6)
f(4) means that wherever you see an x on the right, you put a 4.
f(4) = 2x - 4
f(4) = 2*4 - 4
f(4) = 8 - 4
f(4) = 4
7)
g(x) = 1/2x - 4
g(2) = 1/2(2) - 4
g(2) = 1 - 4
g(2) = - 3
8)
f(-5) = 2*-5 - 4
f(-5) = -10 - 4
f(-5) = -14
9)
g(-6) = 1/2 ( - 6) - 4
g(-6) = -3 - 4
g(-6) = - 7
Due to employee safety negligence at a nuclear waste facility, 2000 tons of a radioactive element is spilled into the nearby pond. The half-life of the radioactive element is 36 days. In order to be declared safe for swimming, based on its size and the amount of water, there must be less than 100 tons of the material found in the pond. How long, to the nearest day, until it is safe to swim again?
How long, to the nearest day, until it is safe to swim again will be 156 days
Let x represent number of day until it is safe to swim again
First step
=2000 *1/2^x
100=2000 *0.5^x
0.05=0.5^x
Second step
Log 0.05=xLog 0.5
Log 0.05/L0g 0.5=x
x=36 days* Log 0.05/L0g 0.5
x=36 days*43.22
x=156 days
Inconclusion How long, to the nearest day, until it is safe to swim again will be 156 days
Learn more about radioactive element here:
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Please help! I have an answer but idk if it's right so please check and tell me if I made any mistakes! Thank you!
Answer:
p(1)=2-a+4-4
or,10=2-a
so,a=-8
Step-by-step explanation:
hope it helps you
HAI HELP ME ASAP PLEASE
Answer:
Y/X = 2/3 x^2 + 16/3
Y= 2/3 x^3 + 16/3 x
Just replace y with y/X and X with x^2