The area common to both triangles is [tex]18\sqrt3[/tex] square centimeters.
In a 30-60-90 triangle, the ratio of the side lengths is [tex]1:\sqrt{3} :2[/tex]. Since the hypotenuse is 12 cm, we can determine the lengths of the other sides using this ratio.
The shorter leg (opposite the 30-degree angle) is (1/2) times the hypotenuse, which is (1/2) * 12 cm = 6 cm.
The longer leg (opposite the 60-degree angle) is [tex]\sqrt3[/tex] times the shorter leg, which is 6 * [tex]\sqrt{3[/tex] cm = [tex]6\sqrt3[/tex] cm.
Now, since the two triangles are congruent, the overlapping region forms an isosceles triangle with two sides measuring 6 cm (the shorter leg) and a base measuring [tex]6\sqrt3[/tex] cm (the longer leg).
The base of the isosceles triangle is [tex]6\sqrt3[/tex] cm, and since it's an isosceles triangle, the height is the same as the shorter leg, which is 6 cm.
Common Area = ([tex]6\sqrt3[/tex] cm * 6 cm) / 2 = [tex]36\sqrt3[/tex] cm² / 2 = [tex]18\sqrt3[/tex] cm².
Therefore, the area common to both triangles is [tex]18\sqrt3[/tex] square centimeters.
Read more about congruent triangles,
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The area common to both triangles is 144 square centimeters.
To find the area common to both triangles, we need to determine the overlapping region, which is a rhombus formed by the intersection of the two 30-60-90 triangles.
First, let's consider one of the 30-60-90 triangles. The sides of a 30-60-90 triangle are in the ratio 1:√3:2. In this case, the hypotenuse is 12 cm, so the sides of the triangle are:
Shorter leg (opposite the 30-degree angle) = 12 cm / 2 = 6 cm
Longer leg (opposite the 60-degree angle) = 6 cm * √3
Now, let's look at the overlapping region, which forms a rhombus. The diagonals of a rhombus are perpendicular bisectors of each other, so each diagonal will be twice the length of the shorter leg of the 30-60-90 triangle.
Diagonal of the rhombus = 2 * 6 cm = 12 cm
The area of a rhombus can be calculated using the formula: Area = (diagonal1 * diagonal2) / 2
In this case, both diagonals are equal (12 cm each), so the area of the rhombus (and hence the common area of the triangles) is:
Area = (12 cm * 12 cm) / 2
Area = 144 cm²
So, the area common to both triangles is 144 square centimeters.
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Simpliftly(-8.5)(-5)( -2)
how do i simplify it
Answer:
-85
Step-by-step explanation:
(-8.5)(-5)(-2)
Multiply
(42.5)(-2)
-85
Hope this helps :)
A college bookstore charges $60 for a yearly membership. The first book is free with membership and any book after that costs $7.60 including tax. How much money, m, does a student spend after buying b books and a yearly membership.
Answer:
The equation representing Total money spend being as a member is [tex]m = 60+7.6(b-1)[/tex]
Step-by-step explanation:
Given:
Memberships charges = $60
Cost of 1 book = $7.60
Let number of books be 'b'.
We need to find Total money 'm' spend yearly on buying books after becoming member.
Now we know that 1 book is free for a member.
Total money spend 'm' will be equal to Sum Memberships charges and Cost of 1 book multiplied by number of books bought yearly minus 1.
Framing in equation form we get;
[tex]m = 60+7.6(b-1)[/tex]
Hence The equation representing Total money spend being as a member is [tex]m = 60+7.6(b-1)[/tex]
Therefore, the final expression for the total cost [tex]\( m \)[/tex] as a function of the number of booksx [tex]\( m \)[/tex] is:
[tex]\[ \boxed{m = \frac{262 + 38b}{5}} \][/tex]
The total cost \( m \) that a student spends after buying \( b \) books and a yearly membership can be calculated using the following formula:
[tex]\[ m = \text{Cost of membership} + (\text{Number of books} - 1) \times \text{Cost per book} \][/tex]
Given that the yearly membership costs $60 and each book after the first free book costs $7.60, we can substitute these values into the formula:
[tex]\[ m = \$60 + (b - 1) \times \$7.60 \][/tex]
Now, let's simplify the expression by converting $7.60 to a fraction to avoid decimals in our calculation:
[tex]\[ m = \$60 + (b - 1) \times \frac{760}{100} \][/tex]
[tex]\[ m = \$60 + (b - 1) \times \frac{38}{5} \][/tex]
[tex]\[ m = \$60 + \frac{38b - 38}{5} \][/tex]
To combine the terms, we need a common denominator, which is 5:
[tex]\[ m = \frac{\$60 \times 5}{5} + \frac{38b - 38}{5} \][/tex]
[tex]\[ m = \frac{300}{5} + \frac{38b - 38}{5} \][/tex]
[tex]\[ m = \frac{300 + 38b - 38}{5} \][/tex]
[tex]\[ m = \frac{262 + 38b}{5} \][/tex]
I need help !!!!!! Please
Answer:
See explanation
Step-by-step explanation:
Statement Reason
1. [tex]\angle M\cong \angle X[/tex] - Given
2. [tex]\angle N\cong \angle Y[/tex] - Given
3. [tex]\overline{YO}\cong \overline{NZ}[/tex] - Given
4. [tex]\overline{OZ}\cong \overline{OZ}[/tex] - Reflexive property
5. [tex]YO=ZN[/tex] - Definition of congruent segments
6. [tex]YZ=YO+OZ[/tex] - Segment addition postulate
7. [tex]ON=ZN+OZ[/tex] - Segment addition postulate
8. [tex]YZ=ZN+OZ[/tex] - Substitution property
9. [tex]YZ=ON[/tex] - Substitution property
10. [tex]\triangle MNO\cong \triangle XYZ[/tex] - AAS postulate
Answer:
What is your gram?
Step-by-step explanation:
the coordinates of endpoint D in CD are at D (5,5).if the midpoint of the segment is at M(1,_1)what are the coordinates of point C?
Answer:
The required points of the given line segment are ( - 3, - 7 ).
Step-by-step explanation:
Given that the line segment CD whose midpoint M is ( 1, - 1 ) and point D is ( 5, 5 ), then we have to find point C of the line segment CD-
As we know that-
If a line segment AB is with endpoints ([tex]x_{1}, y_{1}[/tex] ) and ([tex]x_{2}, y_{2}[/tex] then the mid points C are-
C = ( [tex]\frac{ x_{1} + x_{2} }{2}[/tex] , [tex]\frac{ y_{1} + y_{2} }{2}[/tex] )
Here,
Let C ( x, y ), D ( 5, 5 ) with midpoint M ( 1, -1 )-
then by the midpoint formula-
( 1, -1 ) = ( [tex]\frac{x+ 5}{2}[/tex] , [tex]\frac{y + 5}{2}[/tex]
On comparing x coordinate and y coordinate -
We get,
( [tex]\frac{x+ 5}{2}[/tex] = 1 , [tex]\frac{y + 5}{2}[/tex] = -1 )
( x + 5 = 2, y + 5 = - 2 )
( x = 2 - 5, y = -2 - 5 )
( x = - 3, y = -7 )
Hence the required points C are (- 3, - 7 ).
We can also verify by putting these points into Midpoint formula.
Quaker Oatmeal is a very popular breakfast cereal. If Susan wrapped the entire container without any overlapping paper, what is the minimum amount of paper she will need to wrap the entire container
11cm tall
with a width of 6cm
263.76 cm is the minimum amount of paper she will need to wrap the entire container.
Step-by-step explanation:
As we know that the equation for surface area of a cylinder,
Surface area of cylinder = [tex]2\pi r^{2}+2 \pi r h[/tex]
Where,
r - the radius of the cylinder. Here given diameter (D) as 6. So,
[tex]r=\frac{D}{2}=\frac{6}{2}=3 \mathrm{cm}[/tex]
h - the height of the cylinder (given as 11 cm). The value for pi = 3.14. Now, calculate the surface area of the cylinder as
[tex]A=2(3.14)(3)^{2}+2(3.14)(3)(11)[/tex]
A = 56.52+ 207.24 = 263.76 cm
At a zoo, youth tickets cost $5 and adult tickets cost $9. A group that purchased x youth tickets and y adult tickets spent $90 on tickets.
What is the domain of the relationship?
A.
x ≤ 5
B.
0 ≤ x ≤ 5
C.
0 ≤ x ≤ 18
D.
x ≤ 18
Answer:
Each person buys there own so there are elderly costs.
Step-by-step explanation:
A.
x ≤ 5
B.
0 ≤ x ≤ 5
C.
0 ≤ x ≤ 18
D.
x ≤ 18
Answer:
The answer is option C.
0 <= x <= 18
Step-by-step explanation:
To find the domain of the relationship in respect to x, we need to find the value of x.
Since;
youth tickets = $5 and
Adult tickets = $9.
Purchased x youth tickets and y adult tickets cost $90
Purchased x youth tickets and y adult tickets = 5x + 9y = 90
5x = 90 - 9y
to find x we divide both side by 5
x = (90-9y)/5
x = 90/5 - 9y/5
x = 18 - 9y/5
Note that in this equation x and y can only be positive value because that are representing number of legible item (ticket)
Therefore:
X can only fall between 0 and 18.
0 <= x <= 18
A drawing is 12 inches long by 9 inches wide. If the new drawing is 8 inches long, how wide will it be?
What is the General form of the parabola of (y-3)^2=6(x+8)
Answer:
x = 1.5[tex]t^{2}[/tex] , y = 3 + 2at.
Step-by-step explanation:
For the parabola [tex]Y^{2}[/tex] = 4aX ,
General form will be
(X = a[tex]t^{2}[/tex] , Y = 2at) ,
Thus , for the parabola [tex](y-3)^{2}[/tex] = 6(x +8)
Here , a = 1.5 and Y from the above equation should be substituted by y - 3 and X must be substituted by x + 8. After substitution of the same we can use the general equation formula for this parabola also.
Thus , general equation comes out to be :-
x + 8 = 1.5[tex]t^{2}[/tex] , y - 3 = 2at
x = 1.5[tex]t^{2}[/tex] , y = 3 + 2at.
Each end of a glass prism is a triangle with a height that is 1 inch shorter than twice the base. If the area of the triangle is 60 square inches, how long are the base and height?
Answer:
Step-by-step explanation:
Let the base = x inches
So, h = 2x - 1
Area of triangle = 60 square inches
(1/2) * base *height = 60
(1/2) * x * (2x-1) = 60
x *(2x-1) = 60*2
2x² - x = 120
2x² - x - 120 = 0
2x² - 16x + 15x - 15*8 = 0
2x ( x - 8) + 15 (x -8) = 0
(x-8) (2x + 15 ) = 0
x- 8 = 0 {ignore 2x +1 as it will give negative value}
x = 8
Base = 8 inches
Height = 2*8 - 1 16 - 1 = 15 inches
15 points!! Please help! please explain how you got you answers
We observe that a line will pass through 3 points, but to find a slope we only need two.
We see that it passes through points (assuming the scale of graph is 1 : 1) [tex]P_1(x_1,y_1)=P_1(0,1)[/tex] and [tex]P_2(x_2,y_2)=P_2(2,-1)[/tex].
We can use slope formula that applies for any line and produce the same slope for any two different points on the line
[tex]m=\dfrac{\Delta{y}}{\Delta{x}}=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-1-1}{2-0}=-1[/tex]
So the slope is -1 also it intersects y-axis at [tex]n=1[/tex] so the general form of the linear function is
[tex]f(x)=mx+n[/tex]
That is in your case
[tex]\boxed{f(x)=-x+1}[/tex]
Hope this helps.
Find the value of x.
30
3. 4. 6. 8
Answer:
x=8
Step-by-step explanation:
BE=1/2(CD) (it's a theorem that you can find in Google)
So you get:
3x=24
x=8
The question lacks sufficient information to solve for x. An equation or context for x is needed to determine its value.
Explanation:The question seems to lack sufficient information to provide an accurate solution. When asked to find the value of x, usually an equation or expression involving x is given. This question doesn't provide such an equation or a context for solving for x. It is possible that the information got cut off or may have been miss-transcribed. Please specify the given equation or problem involving x and I will be glad to help.
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Which of the following shows the expression in factored form x2 + 2x - 8
A) (x-2)(x+4)
B) (x+2)(x+4)
C) (x-2)(x+8)
D) (x+1)(x-8)
Answer:
A) (x-2)(x+4)
Step-by-step explanation:
what is two hundred and eighteen divided by thurty one
Hi there! In this problem, two hundred and eighteen divided by thirty one would be 7.032258064516129. Like this:
281 / 31 = 7.032258064516129
Hope this answers your question!
(P.S. I could really use Brainliest.....)
Answer:
200+18÷31=200.58062452
200÷31=6.451612903
18÷31=0.5806451613
Sam saves 76 tickets every time he goes to the arcade. He needs a total of 4712 tickets to receive a stuffed bear for his girlfriend. So far, he has earned 456 tickets. How many more times will Sam have to go to the arcade to earn the additional points he needs?
Answer:
Sam has to 56 times more to the arcade to earn additional points he need.
Step-by-step explanation:
Given:
Number of tickets already earned = 456
Number of tickets saved each time visit at arcade = 76
Total Number of tickets required to buy Stuffed bear = 4712
We need to find number of times he need to go to arcade to earn the additional points.
Solution:
Let Number of times he need to visit arcade be 'x'.
Now we know;
Number of tickets already earned plus Number of tickets saved each time visit at arcade multiplied by Number of times he need to visit arcade equals to Total Number of tickets required.
Framing in equation form we get;
[tex]456+76x = 4712[/tex]
Now Solving the equation we get;
Subtracting both side by 456 we get;
[tex]456+76x=4712-456\\\\76x= 4256[/tex]
Now Dividing both side by 76 we get;
[tex]\frac{76x}{76} = \frac{4256}{76} \\\\x=56[/tex]
Hence, Sam has to 56 times more to the arcade to earn additional points he need.
What conclusion can you make based on the data/results you collect
To draw a conclusion from collected data, examine the hypothesis compared with the results observed. A careful analysis should lead to generalizations backed by evidence. Presenting and summarizing information thoroughly is vital for conclusions and future inquiries.
Explanation:To draw a conclusion based on the data collected, one must first analyze the data carefully. For example, in an experiment assessing the number of deformed frogs in a non-polluted pond, the data should be compared to the initial hypothesis. If the data shows a significant number of deformed frogs in pristine conditions, this could imply other factors contributing to deformities besides pollution.
In language use among students, if the evidence suggests particular trends or patterns, you can make generalizations about these observations. If your findings are different from the initial answer in the 'Collect the Data' section, it might be due to various reasons such as experimental error or an incomplete hypothesis. When presenting your findings, it is critical to incorporate all the collected information which solidifies your conclusion.
Lastly, when summarizing information about a person's experience, it's necessary to incorporate all relevant data before settling on a conclusion. Afterward, forming a question for further research can open new avenues for exploration.
Amy has $1,000 in a savings account at the beginning of the fall. She wants to have at least $500 in the account by the end of the fall. She withdraws $100 a week for living expenses. Write an inequality for the number of weeks Amy can withdraw money, and solve.
A) 1000 - 100w ≤ 500; w ≥ 6
B) 1000 + 100w ≤ 500; w ≤ 5
C) 1000 + 100w ≥ 500; w ≥ 6
D) 1000 - 100w ≥ 500; w ≤ 5
Answer:
D. [tex]1000 - 100w \geq 500; w \leq 5[/tex]
Step-by-step explanation:
Given:
Initial amount in the bank = $1000
Money withdrawn each week = $100
Final amount should be at least $500.
Now, let the number of weeks the money is withdrawn be 'w'.
Therefore,
Money withdrawn in 'w' weeks = [tex]\textrm{Money withdrawn each week}\times w[/tex]
Total Money withdrawn in 'w' weeks = [tex]100w[/tex]
Now, final amount after 'w' weeks is equal to the difference between initial amount and total withdrawal amount. Therefore,
Final amount = Initial amount - Total withdrawal amount
Final amount = [tex]1000 - 100w[/tex]
Now, final amount must be greater than or equal to $500. So,
[tex]\textrm{Final amount}\geq500\\\\1000-100w\geq500[/tex]
Therefore, the inequality that represents the inequality for the number of weeks Amy can withdraw money is:
[tex]1000-100w\geq500[/tex]
Now, let us solve for 'w'.
Adding -500 and 100w both sides, we get:
[tex]1000-500-100w+100w\geq500-500+100w\\\\500\geq100w\\\\\textrm{The above inequality is reversed when taking 100w on the left side}\\\\100w\leq500\\\\w\leq\frac{500}{100}\\\\\therefore w\leq5[/tex]
Therefore, the correct option is (D).
what is y=-4/3x+2 in point slope form?
Answer:
[tex]y-2=-\frac{4}{3}(x-0)[/tex]
Step-by-step explanation:
we know that
The equation of the line in point slope form is equal to
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]y=-\frac{4}{3}x+2[/tex] ---> equation in slope intercept form
so
Convert to point slope form
subtract 2 both sides
[tex]y-2=-\frac{4}{3}x[/tex]
Rewrite as
[tex]y-2=-\frac{4}{3}(x-0)[/tex]
the slope is [tex]m=-\frac{4}{3}[/tex]
the point is [tex](0,2)[/tex]
Which statement is correct? The range of the graph is all real numbers less than or equal to 0. The domain of the graph is all real numbers less than or equal to 0. The domain and range of the graph are the same. The range of the graph is all real numbers.
Answer:
Option B on edge 2020 guys
Step-by-step explanation:
:)
Which is the same as 73?
CLEAR CHECK
A 7÷13
B 3÷7
C 17 of 3
D 7 divided by 3
Answer: Neither of them.
Step-by-step explanation: 7 divided by 3 is 2.3. So that's not right.
3 divided by 7 is 0.42. Also incorrect. 17 of 3? What does that mean? 17 percent of 3? I'm not sure but that's not the answer either be cause 17% or 3 is not 73. None of these choices are correct nor do they make sense.
Answer:
D) 7 divided by 3
Step-by-step explanation:
Use the net to find the surface area of the square pyramid.
A) 95 ft2
B) 130 ft2
C) 205 ft2
D) 333 ft2
Answer: D
Step-by-step explanation:
9x9=81 (base)
(14x9) divided by 2= 63 (one triangular face)
63x4=252 (all triangular faces)
81+252= 333ft2
Answer:
the answer is D, i know i am right.
Step-by-step explanation:
crackers contain 12 calories each and cookies contain 52 calories each. if you eat 5 crackers and 2 cookies how many calories have u consumed in all?
Answer:
You have consumed 164 calories in total
Step-by-step explanation:
12 calories × 5 crackers = 60 calories
52 calories × 2 cookies = 104 calories
104 + 60 = 164 calories in total
16. Afla numărul necunoscut:
x + 7 = 36
X-9 = 83
X + (13- 8) = 74
a - (14 - 6) = 67
34 - X= 8
82 - x = 9
114
Answer:
9
Step-by-step explanation:
4*7=28
zyz hope that helps
Plz help: You have asked your parents if you can have some money to decorate your bedroom for Christmas. You want to put up a little Christmas tree and some ornaments and some lights. They give you $10. You go to the store and find an incredible deal. You buy a tiny fake tree, some lights and a box of ornaments. You pay with the 10$ your parents gave you and the cashier gives you back three bills of the same denomination and two coins in change. (you receive no dollar coins and no half-dollars). How much did you spend? There are 10 possible answers
1. amount spent:____________ Change given (bills/coins):_________
Answer: ALL THE AMOUNT SPEND ARE 3 1$ bills
1. Amount spent: 6.98
Change: 2- penny
2. Amount Spent: 6.94
Change: Penny Nickel
3. Amount Spent: 6.9
Change: 2 Nickels
4. Amount Spent: 6.89
Change: Penny, Dime
5. Amount Spent: 6.85
Change: Nickel Dime
6. Amount Spent: 6.74
Change: Penny Quarter
7. Amount Spent: 6.50
Change: 2 Quarters
8. Amount Spent: 6.80
Change: Nickel Nickel
9. Amount Spent: 6.70
Change: Quarter Dime
10. Amount Spent: 6.65
Change: Quarter Nickel
Step-by-step explanation:
Pweeeese gimme brainliest answer
To find out how much you spent, subtract the change given from the amount your parents gave you.
Explanation:To find out how much you spent, you need to subtract the change given from the amount your parents gave you. Since the cashier gave you three bills and two coins as change, the total value of the change given is equal to the amount you spent. Since you received no dollar coins and no half-dollars, the change given consists of only bills and coins of smaller denominations. Therefore, the amount you spent is equal to the value of the change given.
(i wont ask anymore after this)
How many solutions does each equation have? a) 7(2+5v)=3v+14 b) -3 (3-6b)=6b+5 c) 2 (a-2)=2a-4
Answer:
a) v = 0
b) b = 7 / 6
c) a = any number
Step-by-step explanation:
a) 7(2+5v)=3v+14
7 x 2 + 7 x 5v = 3v + 14 .... distributive
14 + 35v = 3v + 14
35v - 3v = 14 - 14
32v = 0
v = 0 ...... only v value can fit
b) -3 (3-6b)=6b+5
-9 + 18b = 6b + 5
18b - 6b = 5 + 9
12b = 14
b = 14 / 12 = 7 / 6
c) 2 (a-2)=2a-4
2a - 4 = 2a - 4
2a -4 + 4 = 2a -4 + 4
2a = 2a
a = a ........ a cab be any number
3a²b ÷ 2ab what is the result ?
Answer:3/2a
Step-by-step explanation:
Answer:
3 a /2
Step-by-step explanation:
3 a² b ÷ 2 a b
3 a / 2
please help 10 point + brainlyiest = one big thank u
which of these is the algebraic expression for "five more than the product of ten and some number?
10 + 5x
5 + 10 + x
10x + 5
5 + 10 ÷ x
Two angle measures in a triangle are 47° and 43°. What type of triangle is it?
acute
obtuse
right
isosceles
Answer:
It is a right angled triangle
Step-by-step explanation:
Since we know that the angles in a triangle always add up to 180°, we take 180°-47°-43° = 90°, a right angle is 90°, thus we know it is a right angled triangle.
Answer:
it is a right triangle
Step-by-step explanation:
Multiplying (-9)(-6)(2)=
Answer:
108
Step-by-step explanation:
A class is made up of 12 boys and 13 girls. What fraction of the class is boys?
Answer:
12/25 of the class are boys.
Step-by-step explanation:
12+13=25
12/25
Answer:
12/25, I hope this helped!
The function A(b) relates the area of a trapezoid with a given height of 12 and
one base length of 9 with the length of its other base.
It takes as input the other base value, and returns as output the area of the
trapezoid.
A(b) = 12.579
Which equation below represents the inverse function B(a), which takes the
trapezoid's area as input and returns as output the length of the othef base?
Answer:
[tex]B(a)=\frac{a}{6}-9[/tex]
Step-by-step explanation:
see the attached figure , to better understand the problem
we have
[tex]A(b)=12(\frac{b+9}{2})[/tex]
where
A(b) ---> is the trapezoid's area
b ---> is the other base value
Solve the equation for b
That means ----> isolate the variable b
Divide 12 by 2 right side
[tex]A=6(b+9)[/tex]
Divide by 6 both sides
[tex]\frac{A}{6}=b+9[/tex]
subtract 9 both sides
[tex]\frac{A}{6}-9=b[/tex]
Rewrite
[tex]b=\frac{A}{6}-9[/tex]
Convert to function notation
[tex]B(a)=\frac{a}{6}-9[/tex]
Final answer:
The inverse function for the area of a trapezoid with one base of 9 and height of 12 is B(a) = a/6 - 9, which gives the length of the other base when provided with the area of the trapezoid.
Explanation:
The question revolves around finding the inverse function for the function that represents the area of a trapezoid. Given the area function A(b) = 12.579 for a trapezoid with a height of 12 and one base of length 9, we seek the function B(a) which provides the length of the other base when given the trapezoid's area. To derive this, recall that the area of a trapezoid with bases b and c and height h is given by A = (1/2)(b+c)h. Here, b is 9 and h is 12. Hence, A(b) = (1/2)(9+b)(12) = (9+b)(6).
To find B(a), we express b in terms of A: (9+b)(6) = A → b = A/6 - 9. The inverse function is B(a) = a/6 - 9.