Find the length of side x in simplest radical form with a rational denominator.
30°
60°
√12
D
The value of x is 10√3 .
The missing figure is attached with the answer
What is a Triangle ?A triangle is a polygon with three sides , three angles and three vertices.
A right angle is a triangle in which one of the sides of a triangle is equal to 90 degree.
As it is a right angled triangle therefore the trigonometric ratios are applicable
From the given figure sin 60 needs to be determine to find the value of x
sin x = Perpendicular / Hypotenuse
sin 60 = 5 / x
[tex]\rm \dfrac{\sqrt{3}}{2} = \dfrac{5}{x}[/tex]
x = 10√3
Therefore the value of x is 10√3
To know more about Triangle
https://brainly.com/question/2773823
#SPJ1
At Pine Time Summer Camp, 12 campers sign up to go swimming. Of the 12 campers, 2/3 of them are advanced swimmers. How many of these campers are advanced swimmers?
(not highschool)
find the eslope of the line pasing throungh the points A(5,-9) and B (-5,7).
Step-by-step explanation:
(7+9)/(-5-5)= 16/-10= -8/5
y + 9 = -8/5(x - 5)
y + 9 = -8/5x + 8
y = -8/5x - 1
PLSS HELP ME PLSSS
a) Write 2 expressions for the area of the shaded region. (2 marks)
b) Find the length of the shaded region if the perimeter is 48cm. (2 marks)
c) Find the area of the shaded region if perimeter is 48cm. (1 mark)
Answer:
(1) 85×9=765 (2) 127×3=381
help please asap and thank you
Step-by-step explanation:
I am not sure I can see the room limitations.
what I see is that the kitchen is one large rectangle from
(-8, 8) to (0, 0).
the rec room is Amado one large rectangle from
(5, 6) to (8, -7).
I am basing the rest in this.
for the area calculations, please consider that the area of a rectangle is length × width, and the area of a triangle is half of the rectangle it splits in half with its baseline (as diagonal).
A)
area 1 =
rectangle (-8, 8) to (-5, 3)
plus
half of the rectangle (-5, 8) to (-3, 3)
3×5 + 1/2 × 2×5 = 3×5 + 1×5 = 15 + 5 = 20 yd²
area 2 =
half of the rectangle (-5, 8) to (-3, 3)
plus
rectangle (-3, 8) to (0, 3)
1/2 × 2×5 + 3×5 = 20 yd²
area 3 = area 4 =
half of the rectangle (-8, 3) to (0, 0)
1/2 × 8×3 = 4×3 = 12 yd²
B)
the total area of the kitchen is the sum of all 4 areas
20 + 20 + 12 + 12 = 64 yd²
we can also calculate this in general, seeing that the general dimensions of the kitchen are 8×8 : from (-8, 8) to (0, 0).
8×8 = 64 yd²
i need the missing numbers
Answer:
Step-by-step explanation:
1) y = [tex]\frac{1}{3}[/tex]
2) x = [tex]\frac{1}{3}[/tex]
3) y = -3
4) x = [tex]\frac{-1}{-12}[/tex]
Answer:
11,3,3,12
Step-by-step explanation:
1st y= 11 because -2/3(-6)=4 4+7=11
1st x= 3 because -2/3(3)=-2 and -2+7 is 5
2nd y=-3 because -2/3(15)=-10 -10 +7=-3
2nd x=-12 because -2/3(-12)=8 8+7=15
factorise the following expressions:
a) 14w + 21
b) 27x+18
Step-by-step explanation:
a) 14w + 21
- Factor out 7 from the expression
7 (2w + 3)
b) 27x + 18
- Factor out 9 from the expression
9 (3x + 2)
Hi!
___________________________________________________________
[tex]\rightsquigarrow\circ\boldsymbol{Answer}\circ\leftharpoonup[/tex]
#1 7(2w+3)
#2 9(3x+2)
[tex]\rightsquigarrow\circ\boldsymbol{Explanation}\circ\leftharpoonup[/tex]
We need to factor these two expressions.
[tex]\twoheadrightarrow\sf 14w+21[/tex] and [tex]\twoheadrightarrow\sf 27x+18[/tex]
For now let's focus on the first expression.
Note that both terms, 14w and 21, have something in common.
In fact, they have 7 in common. So we factor it out by dividing 14w and 21 by 7.
[tex]\twoheadrightarrow\sf14w\div7=2x\\\twoheadrightarrow\sf21\div7=3[/tex]
[tex]\bullet[/tex] Put the terms together, with a plus sign in between since they are positive
[tex]\twoheadrightarrow\sf 2w+3[/tex]
[tex]\bullet[/tex] Put parentheses around 2w+3
[tex]\twoheadrightarrow\sf (2w+3)[/tex]
[tex]\bullet[/tex] Put7 outside the parentheses
[tex]\twoheadrightarrow\sf7(2w+3)[/tex]
[tex]\bullet[/tex] Great job! We factored the expression
__________________________________________________________
This problem can be solved the same way!
This time, both terms have a 9 in common.
[tex]\twoheadrightarrow\sf 27x+18[/tex]
So we divide both terms by 9.
[tex]\twoheadrightarrow\sf 27x\div9=3x\\\twoheadrightarrow\sf18\div9=2[/tex]
[tex]\bullet[/tex] Put the terms together, with a plus sign in between since they're positive
[tex]\twoheadrightarrow\sf 3x+2[/tex]
[tex]\bullet[/tex] Next, put parentheses around 3x+2 and put 9 outside the parentheses
[tex]\twoheadrightarrow\sf 9(3x+2)[/tex]
[tex]\bullet[/tex] Great job! We factored both expressions
--
Hope that this helped! Best wishes.
[tex]\textsl{Reach far. Aim high. Dream big.}\\\boldsymbol{-Greetings!-}[/tex]
--
what is the area of aregular hexagon with side length of 10units square?
Answer:
h ≈ 259.81
Step-by-step explanation:
i used the hexagon calculator
Answer:
150 sqrt 3 = 259.8076 units^2
Step-by-step explanation:
Interior angles of hexagon = 120 degrees ....now look at the Right 1/2 of the hexagon... see illustration....this is a trapezoid...
One base is 10 units
the other labelled 'base' is
10 cos 60 + 10 cos 60 + 10 = 20 units
the height of this trapezoid is 10 sin 60 = 10 * sqrt(3)/2 = 5 sqrt(3)
the area of this trapezoid is then 1/2 ( 10+ 20) * 5 sqrt (3) = 75 sqrt 3
there are TWO of these trapezoids in the hexagon so total area is then
2 * 75 sqrt 3
150 sqrt 3
A tree height when planted was 5ft. 8inches. It has grown 14ft. 10 inches how much did it grown
Answer:
Subtraction will happen in this case.
14ft-5ft= 9ft
10 inches-8 inches= 2 inches
So, it grew 9ft. and 2 inches.
Find the indicated conditional probability
using the following two-way table:
Grade
Sophomore
Junior
Senior
Drive to school Take the bus
2
13
25
25
20
5
Walk
3
2
5
P(Drive to school | Sophomore ) = [? ]
Round to the nearest hundredth.
Answer:
[tex]0.07[/tex]
Step-by-step explanation:
FORMULA :
[tex]p\left( A|B\right) =\frac{p\left( A\cap B\right) }{p\left( B\right) }[/tex]
……………………………
then
[tex]p\left( \text{drive to school} |sophomore\right) =\frac{p\left( \text{drive to school} \cap \text{sophomore} \right) }{p\left( \text{sophomore} \right) }[/tex]
[tex]= \frac{2}{2+25+3}[/tex]
[tex]=\frac{2}{30}[/tex]
[tex]=\frac{1}{15}[/tex]
[tex]=0.066666666667[/tex]
You are drawing an angle in standard position and you swing the terminal side until an angle of 281 is made. how many more degrees can you continue swinging so that the terminal side is at the same position as the initial side
Answer:
79°
Step-by-step explanation:
An angle in standard position has it "initial" side glued on to the positive x-axis. The other ray that makes the angle swings around the origin, (0,0) like a hand of a analog clock (but moving backwards) straight up is 90°, straight to the left is 180° straight down is 270°. And all the way back to the start is 360°.
If the angle is 281° it can go 79° more degrees before getting back to the start.
360° - 281° = 79°
4. How are the zeros of a polynomial function used to create a graph?
The steps that are used for creation of the graph of a polynomial function are listed below.
The steps to create the graph of a polynomial function.In Mathematics, the steps that are used for creation of the graph of a polynomial function are:
Predict the end behavior of the polynomial function.Determine the real zeros of the polynomial function. Also, you should check if the function can be rewritten in factored form to find the zeros. Else, you should use Descartes' rule of signs in identifying the possible number of real zeros.Make a table of values to solve for several points.Plot these points and draw a smooth-continuous curve to connect the points.Read more on polynomials here: https://brainly.com/question/19571593
#SPJ1
Type the correct answer in the box
Answer:
[tex]log\boxed{7}[/tex]
Step-by-step explanation:
[tex]log\frac{14}{3}+log\frac{11}{5}-log\frac{22}{15}[/tex][tex]=log\bigg(\frac{14}{3}*\frac{11}{5}\bigg)-log\frac{22}{15}[/tex][tex]=log\bigg(\frac{14*11}{3*5}\bigg)-log\frac{22}{15}[/tex][tex]=log\bigg(\frac{154}{15}\bigg)-log\frac{22}{15}[/tex][tex]=log\bigg(\frac{154}{15}\div\frac{22}{15}\bigg)[/tex][tex]=log\bigg(\frac{154}{15}\times\frac{15}{22}\bigg)[/tex][tex]=log\bigg(\frac{154}{22}\bigg)[/tex][tex]=log\boxed{7}[/tex]Triangle BDC is isosceles.
Circle A is shown. Line segments A B, A C, and A D are radii. Lines connect each of the points on the circle to the other points to form a triangle. Sides C B and B D are congruent.
Which angle is congruent to ?
As per the question, the answer is ∠CAB is congruent to ∠BAD.
The isosceles triangle :An isosceles triangle named BDC is positioned within a circle. The segments of the circle they pass through are congruent because the faces of the triangles BC and BD are congruent, or identical.
Due to the triangle's faces BC and BD being identical and congruent
BC=BD
Additionally, the segments of the circle it goes across are congruent.
In the case of ΔBAC & ΔBAD
AC=AD= the radius of the circle
AB=BA
Thus, BAC is consistent with BAD according to SSS guidelines.
As a result, the central angles of the sections are also congruent; hence, BAD and CAB are congruent.
As a result, ∠BAD is equivalent to ∠BAC OR ∠CAB.
Learn more about SSS guidelines:
https://brainly.com/question/535562?referrer=searchResults
#SPJ10
Answer:
B on edge
Step-by-step explanation:
CAD
Mila is preheating her oven before using it to bake. The initial temperature of the oven is 75° and the temperature will increase at a rate of 10° per minute after being turned on. What is the temperature of the oven 15 minutes after being turned on? What is the temperature of the oven t minutes after being turned on?
Temp after 15 minutes:
Temp after t minutes
need answer quickly
Vertical lines m and n are intersected by lines k and j. At the intersection of lines m and k, the bottom right angle is (x minus 30) degrees. At the intersection of m and j, the uppercase right angle is y. At the intersection of lines k and n, the bottom left angle is (x + 50) degrees.
Find the values of x and y that make k || j and
m || n.
x =? °
y = ?°
Using the same-side interior angles theorem, the values of x and y are:
x = 80
y = 130
What is the Same-side Interior Angles Theorem?The same-side interior angles theorem states that two interior angles on same side of a transversal are supplementary.
(x - 30) and (x + 50) are same-side interior angles, therefore:
(x - 30) + (x + 50) = 180
Solve for x
x - 30 + x + 50 = 180
2x + 20 = 180
2x = 180 - 20
2x = 160
x = 160/2
x = 80
(x - 30) + y = 180
Plug in the value of x
(80 - 30) + y = 180
50 + y = 180
y = 180 - 50
y = 130
Learn more about the same-side interior angles theorem on:
https://brainly.com/question/13867198
#SPJ1
Answer:
X= 80
Y= 130
Step-by-step explanation:
do you trust me???
Use the given graph to determine the limit, if it exists.
The limit in the given graph [tex]\lim_{x \to \ 2^{-} } f(x)[/tex] is 3 and [tex]\lim_{x \to \ 2^{+} } f(x)[/tex] is -2
Given graph of a function and we have to determine the limits when x tends to 2 minus and when x tends to 2 plus.
When we see the graph we can find that the graph is not of the linear function because it is not straight line.
From x=2 and onwards it gives values values of only -2 because it is parallel to x-axis at y=-2.From x=2 and leftwards it gives values values of only 3 because it is parallel to x-axis at y=3.
Hence the limit of the function whose graph is shown is 3 and -2.
Learn more about limits at https://brainly.com/question/27517662
#SPJ10
Which expression has a value of 16 when n = 5?
StartFraction 25 Over n EndFraction + 7
30 minus 3 n
7 + StartFraction 45 Over n EndFraction
n cubed minus 114
The expression that has a value of 16 when n = 5 is [tex]\rm 7+ \dfrac{45}{n}[/tex] , Option C is the correct answer.
What is an Expression ?An expression is mathematical statement consisting of variables , constant and mathematical operators.
The expression given in the question is
[tex]\rm \dfrac{ 25}{n} + 7 \\\\30-3n\\\\7+\dfrac{45}{n}\\\\n^3 -114[/tex]
On solving it can be seen that
The value of 16 when n= 5 is given by
7 +45/5 = 7+9 = 16
Therefore Option C is the right answer.
To know more about Expression
https://brainly.com/question/14083225
#SPJ1
A с Which diagram shows all the lines of symmetry of the regular hexagon? B D A с Which diagram shows all the lines of symmetry of the regular hexagon ? B D please help
The diagram that shows all the lines of symmetry is diagram B.
Which diagram shows all the lines of symmetry of the regular hexagon?
We define a line of symmetry as a line such that if we perform a reflection over that line, the image coincides with the preimage (so the reflection does not change the figure).
With that in mind, any line that cuts the hexagon in exactly two halves is a line of symmetry.
So the image that shows all the lines of symmetry of the regular is B, where it shows all the lines that cut the hexagon in two equal halves.
If you want to learn more about lines of symmetry:
https://brainly.com/question/547436
#SPJ1
Solve for y.
Enter your answer in the box.
Answer:
y=10
Step-by-step explanation:
Since this triangle has equal length sides, it is equilateral and also has equal measured angles. This means that each angle is 180/3=60 degrees.
To solve for y, we can do 5y+10=60. Simplifying, we get
5y=50
y=10.
Answer:
4
Step-by-step explanation:
So all the angles will have the same value. In a triangle all the angles will add up to 180, so each angle would have to be 60 degrees. So to know Y we need 6x+6=5y+10. So subtract 10 from each side, then subtract 6x from each side to get 4=x
What value of x is in the solution set of 3(x – 4) ≥ 5x 2? –10–5510
3(x-4) ≥ 5x +2
3*x - 3*4 ≥ 5x +2
3x - 12≥ 5x - 2
-12 + 2 ≥ 5x- 3x
-10 ≥ 2x
2x ≤ -10
x ≤ -5
what is the result of applying the square root property to the equality of the equation X plus B over two a squared equals -4 AC plus B2 over 4a two squared
After doing simplification, the result that we got is the quadratic formula
x = [-b ±√(b² - 4ac)] / 2a.
The given statement can be explained with the following equation:
[x + (b/2a)]² = (b² - 4ac) / 4a²
Now, we will take the root on both the sides:
x + (b/2a) = ±√[(b² - 4ac) / 4a²]
x = -(b/2a) ± √[(b² - 4ac) / 4a²]
x = [-b ±√(b² - 4ac)] / 2a
The final equation resembles the quadratic formula.
So, the result of applying the square root property to this equation is that we get the quadratic formula after simplification.
For more explanation about quadratic equations, refer to the following link:
https://brainly.com/question/1214333
#SPJ10
The cost of 5kg of rice is Rs.425. find the cost of 1kg of rice
Answer:
Rs 85
Step-by-step explanation:
Cost of 5kgs of rice = Rs 425
Cost of 1 kg of rice = 425/5
= Rs 85
So, the cost of a kg of rice is Rs 85
How many solutions are there for the system of equations of shown on the graph?
O No solution
O One solution
O Two solutions
O Infinitely many solutions
Answer:
one solution
(second option listed)
Step-by-step explanation:
We can that these two lines, each representing one equation/function, only meet at one specific value.
In a system of equations, we are essentially looking for a solution that works for both equations.
So, if both lines share a point/value (meaning they intersect), that point is a solution to the system of equations.
Because these lines only overlap at one point, this system of equations has one solution.
Answer:
1 solution (C)
Explanation:
They have one point of intersection.
Janelle is painting a spherical model of a human cell for a science fair. She uses 615.44 square inches of paint to
evenly cover the outside of the cell with one coat of paint. What is the diameter of the cell model? (Use 3.14 for the
value of n.)
7 in.
8 in.
14in
16in
The diameter of the cell model according to the taks content is; 14in.
Diameter of the cell modelVolume of paint = 615.44 square inches
π = 3.14
Volume of a sphere = 4πr²
615.44 = 4 × 3.14 × r²
615.44 = 12.56/r²
r² = 615.44 ÷ 12.56
r² = 49
r = 7
Hence, the diameter of the cell is; 2 × r = 2 × 7 = 14in.
Learn more about volume of sphere:
https://brainly.com/question/10171109
#SPJ1
Mikaela and Viktoria both competed in a curling match on opposing teams. Mikaela
said to Viktoria, "2 more than twice my team's score is the
same as three times your team's score reduced by 3." If
Viktoria's team's score was 7, what was Mikaela's team's
score?
Mikaela's team's score is 8.33
what is Algebra?Algebra is the part of mathematics that helps represent problems or situations in the form of mathematical expressions.
Viktoria's team's score = 7
According to question,
= 2+ 7*2 = 16
so, Mikaela team score= 16/3+3= 8.33
Learn more about algebra here:
https://brainly.com/question/953809
#SPJ1
Classify the following polynomials. Combine any like terms first.
2x-x²+4x+x²
x^3-5x^2 + 3-2
x^3-x^3+x²-x²+3
7x-x^2+x³+4x²
-6x-x^3 +6x-4x
Answer:
A resposta certa é:
[tex]6x \\x^3 - 5x^2 + 1 \\3 \\x^3 + 3x^2 + 7x \\-x^3 - 4x[/tex]
Step-by-step explanation:
1° equação:
Como há um x² positivo e um negativo, ambos irão se anular, sobrando apenas as incógnitas de potência 1 (ou, 6x)
2° equação:
Esta resulta em uma equação de 3° grau incompleta, já que há uma incógnita de potência 3, uma de potência 2, não há uma incógnita de potência 1 mas há as constantes, que as unindo forma a constante 1.
3° equação:
As incógnitas presentes há uma negativa e uma positiva de mesma potência, anulando-as e sobrando apenas a constante 3.
4° equação:
Considerando que há um 4x² e um -x² na equação, unindo-os forma o 3x², após isso é só repetir a equação.
5° equação:
Há -10x (-6x -4x = -10x) e 6x, resultando em um -4x, e então é só repetir a equação
Nota: I'm Brazilian, so I found it more practical to write the entire explanation in Portuguese, so if you can't understand, I ask you to use the translator, thanks for understanding :)
Help me pleas. You might have to zoom in on the picture to see better.
Answer:
1/2, -1/8, 1/32
Step-by-step explanation:
[tex] - 2( - \frac{1}{4} ) = \frac{1}{2} [/tex]
[tex] \frac{1}{2} ( - \frac{1}{4} ) = - \frac{1}{8} [/tex]
[tex] - \frac{1}{8} ( - \frac{1}{4}) = \frac{1}{32} [/tex]
Expand . ( 3x –2 ) 2 please help me with this.
Answer:
6x-4
Step-by-step explanation:
3x•2= 6x
-2•2=-4
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{9x}^2\textsf{ - 12x + 4}[/tex]
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{(3x - 2)}^2[/tex]
Find: [tex]\textsf{Simplify the expression}[/tex]
Solution: It looks like 2 is at the end of the parenthesis where the power would be instead of distributing the number. If so the following steps would be followed.
Expand
[tex]\textsf{(3x - 2)}^2[/tex][tex]\textsf{(3x - 2)(3x - 2)}[/tex][tex]\textsf{(3x * 3x) + (3x * (-2)) + (3x * (-2)) + (-2 * (-2))}[/tex]Simplify
[tex]\textsf{9x}^2\textsf{ - 6x - 6x + 4}[/tex][tex]\textsf{9x}^2\textsf{ - 12x + 4}[/tex]Therefore, after following the provided information we are able to determine that the expanded form would be 9x^2 - 12x + 4.
The ratio of Michaels's points on an English test to Paloma's points on the same test is 12:11. The ratio of Michaels's points on the English test on the same test was 4:3. the 3 students score a total of 224 points on the same test. What is the difference between Palomas and Antons' points on the English test? Try to explain fully, if possible. Thank you SO MUCH!
The difference between Palomas and Antons' points on the English test is of 14 points.
What is Ratio ?When two numbers can be written in the form as p:q , they are said to be in Ratio.
It is given that
The ratio of Michaels point to Paloma point is 12 :11
The ratio of Michaels point to Anton's Point is 4:3
Let Paloma's point be x
then Michaels point will be 12x/11
and Anton's points will be
(12x/11 ) / Anton's points = 4 /3
Anton's points = 9x/11
It is given that the sum of the points of the three students is 224
so
x + (12x/11)+ (9x/11) = 224
32x /11 = 224
x = 77
Paloma's points = 77
Anton's Points = 9x/11 = 63
The difference between Palomas and Antons' points on the English test
=77 -63
= 14 points.
To know more about Ratio
https://brainly.com/question/13419413
#SPJ1