In an isosceles triangle the length of the legs is 8 cm and the angle between them is 150°. Find the altitude to the legs and the area of the triangle.
Find AH and Aᴬᴮᶜ
Answer:
AH = 4 units
Area of ΔABC = 16 square units
Step-by-step explanation:
Since ΔABC is an isosceles triangle,
AC = BC
∠CAB ≅ ∠ABC [Opposite angles of the equal sides in a triangle are equal]
In ΔABC,
m∠CAB + m∠ABC + m∠ACB = 180°
m∠ABC + m∠ABC + 150° = 180°
2m∠ABC = 30°
m∠ABC = 15°
Now we apply cosine rule in ΔABC,
AB² = AC² + BC² - 2(AB)(BC)cos(m∠ACB)
AB² = 8² + 8² - 2(8)(8)cos(150°)
AB² = 128 + 110.85
AB = [tex]\sqrt{238.85}[/tex]
AB = 15.45
In ΔABH,
sin(m∠ABH) = [tex]\frac{AH}{AB}[/tex]
sin(15°) = [tex]\frac{AH}{15.45}[/tex]
AH = 15.45sin(15°)
AH = 3.998
AH ≈ 4.0 units
HC = [tex]\sqrt{8^{2}-4^2}[/tex]
= [tex]\sqrt{48}[/tex]
= 6.93
Area of the triangle ABC = [tex]\frac{1}{2}(BC)(AH)[/tex]
= [tex]\frac{1}{2}(8)(4)[/tex]
= 16 square units
A waterfall is n times the height of its picture on a postcard.
Which equation represents the height, y, of the waterfall if
the picture is 6 cm tall?
A y = 6+n
y = 6+n
y = 6n
y=n-6
Answer: y=6n
Step-by-step explanation:
Solve: -19x- 1 = -12x + 34
19−1=−12+34
19x-1=-12x+34
19x−1=−12x+34
19−1+1=−12+34+1
Terry is an up and coming florist who specializes in weddings. He uses 5 roses, 3 daises, and 4 bundles of green filler to make one bouquet. If r is the cost of a rose and d is the cost of a daisy, and f is the cost of a bundle of green filler, which expression represents the cost for making 75 bouquets
Answer:
75 (5r + 3d + 4f)
Step-by-step explanation:
Cost of 5 roses: 5rCost of 3 daises: 3dCost of 4 green fillers: 4fAmount of bouquets: 75Put them together: 75 (5r + 3d + 4f)I hope this helps!
Which fraction is equivalent to 20
Answer:
4/16
Step-by-step explanation:
PLS HELP ASAP
Write a word problem that can be represented by the expression 5/6 divided by 1/3.
Answer:
I have 5/6 of a candy bad and I want to give each of my 3 friends some. How much would each friend get?
Step-by-step explanation:
The word problem that can be represented by the expression 5/6 divided by 1/3 is "There are a total of 5/6 chocolates. Divide these chocolates such that each person will get 1/3 part of that".
Given :
The expression 5/6 is divided by 1/3.
The following steps can be used in order to determine the word problem that can be represented by the expression 5/6 divided by 1/3:
Step 1 - The knowledge of arithmetic operations can be used in order to determine the word problem that can be represented by the expression 5/6 divided by 1/3.
Step 2 - There are a total of 5/6 chocolates. Divide these chocolates such that each person will get 1/3 part of that.
Step 3 - Solve the above problem by dividing 5/6 by 1/3.
[tex]= \dfrac{5\times 3}{6\times 1}[/tex]
= 2.5
For more information, refer to the link given below:
https://brainly.com/question/25834626
which verb would make this statement an example of personification?
the cell phone
a. shook
b. rang
c. danced
d. lit up
John has $100 in his bank account, and is spending $3 a day on lunch. How long until he has $55 in his account?
Answer:
15 days
Step-by-step explanation:
We know that John has $100 in his bank account and he is spending $3 a day.
We want to find how many days until he has $55 left.
d=days
55=100-3d
55+3d=100
100-55=3d
3d=45
Solving for d, we divide by 3.
Your answer is 15.
help me pls I don't get this question
Answer:
To multiply mixed numbers:
Step-by-step explanation:
1. convert to improper fractions
2. top * top
3. bottom * bottom
4. convert back into a mixed number
Answer:
Hi!
In these questions you're being asked to multiply mixed numbers. The easiest way to do this is to convert the mixed numbers to improper fractions, and then multiply them in that form.
For the first question:
[tex]1\frac{3}{5} = \frac{8}{5} ; 1\frac{2}{5} =\frac{7}{5} \\[/tex] To convert the mixed numbers to improper fractions, you just multiply the denominator by the whole number, and then add it to the current numerator, forming the new numerator. The denominator stays the same.
[tex]\frac{8}{5} *\frac{7}{5} = \frac{56}{25}[/tex] Next, multiply together the numerators, and then multiply together the denominators.
[tex]\frac{56}{25} = 2\frac{6}{25}[/tex]
Podemos calcular la profundidad d
de la nieve, en centímetros, que se acumula en el jardín de Harper durante las primeras h horas de una tormenta usando la ecuación
d=5h
Cuántas horas tarda en acumularse 1
centímetro de nieve en el jardín de Harper?
Cuántos centímetros de nieve se acumulan por hora?
Answer:
a) Cuántas horas tarda en acumularse 1
centímetro de nieve en el jardín de Harper?
0.508 horas o 30.48 minutos
b) Cuántos centímetros de nieve se acumulan por hora?
5 cm
Step-by-step explanation:
a) ¿Cuántas horas se necesitan para acumular 1 pulgada de nieve en el jardín de Harper?
1 pulgada de nieve = 2.54 cm de nieve
d = 5 × h
2.54 = 5 h
h = 2.54 / 5
h = 0.508 hora
Convertir a minutos = 0.508 horas × 60 minutos
= 30.48 minutos.
Por lo tanto, se necesitarían 0.508 horas o 30.48 minutos para acumular 1 pulgada de nieve en el jardín de Harper.
b) ¿Cuántos centímetros de nieve se acumulan por hora?
d = 5 h
Por hora = 1 hora
d = 5 × 1
d = 5 cm
Por tanto, se acumulan 5 cm de nieve por hora.
Please help me figure this out-
Find the measure of the indicated angle that makes lines U and V parallel.
Answer:
80
Step-by-step explanation:
100°+?=180
?=180-100=80
GEOMETRY Write and solve an equation to find the value of x so that it figures have the same area.
Answer:
C. x=7 and the expression is (5+x)9=x*(15 3/7)
Step-by-step explanation:
The width of the first shape is 5+x and the length is 9
The width of the second shape is x and the length is 15 3/7
You want the same area of the figures, so they are equal. And the formula for the area of a rectangle is l*w. So...
(5+x)9=x*(15 3/7)
45+9x=(108/7)x
315+63x=108x
63x-108x=-315
-45x=-315
x=7
So, your answer is C.
Evaluate `int cosec^(2)(7-5x)dx
Answer:
∫ cosec²(7-5x) dx =[-cot(7-5x)]/-5 +c
=(1/5)cot(7-5x)+c
note: d/dx(cotx)=- cosecx
Independent and Dependent Samples Which of the following involve independent samples?
A) Data Set 14 "Oscar Winner Age" in Appendix B includes pairs of ages of actresses and actors at the times that they won Oscars for Best Actress and Best Actor categories. The pair of ages of the winners is listed for each year, and each pair consists of ages matched according to the year that the Oscars were won.
B) Data Set 15 "Presidents" in Appendix B includes heights of elected presidents along with the heights of their main opponents. The pair of heights is listed for each election.
C) Data Set 26 "Cola Weights and Volumes" in Appendix B includes the volumes of the contents in 36 cans of regular Coke and the volumes of the contents in 36 cans of regular Pepsi.
Answer:
(A) Independent
(B) Independent
(C) Independent
Step-by-step explanation:
Independent samples are those samples are drawn from two different population.
Dependent samples are sample collected from the same population but at different times. They are also known as matched pair samples.
(A)
The data collected is for the pair of ages of actresses and actors at the times that they won Oscars for Best Actress and Best Actor categories.
That is the data is in the form (x, y). Here x represents the age of actresses and y represents the age of actors.
Since the data is collected from two different population of male and female, the sample are independent.
(B)
The data collected is for the heights of elected presidents along with the heights of their main opponents.
Again the data is in the form (x, y). Here x represents the heights of elected presidents and y represents the heights of the main opponents.
The samples collected is independent.
(C)
The data collected is for the volumes of the contents in 36 cans of regular Coke and the volumes of the contents in 36 cans of regular Pepsi.
Again the data is in the form (x, y). Here x represents the volumes in the regular Coke cans and y represents the volumes in the regular Pepsi cans.
The samples collected is independent.
Which of the following equations have no solutions?
Choose all answers that apply:
Choose all answers that apply:
(Choice A)
A
-60x+32=-60x+60−60x+32=−60x+60minus, 60, x, plus, 32, equals, minus, 60, x, plus, 60
(Choice B)
B
-60x+32=32x-60−60x+32=32x−60minus, 60, x, plus, 32, equals, 32, x, minus, 60
(Choice C)
C
-60x+32=-60x-32−60x+32=−60x−32minus, 60, x, plus, 32, equals, minus, 60, x, minus, 32
(Choice D)
D
-60x+32=32x+60−60x+32=32x+60
Answer:
B & D
Step-by-step explanation:
Options B and D have a solution from the given set of equations.
We need to find from the given which equation does not have solutions.
How to determine whether the equation has no solution?Solve the given equation for x. If you get any value then the equation has a solution.
From option (A):
-60x+32=-60x+60
⇒-60x+60x=60-32
By simplifying the above equation we get no x value. So, there are no solutions.
From option (B):
-60x+32=32x-60
⇒-60x-32x=-60-32
⇒-92x=-92
⇒x=1
From option (C):
-60x+32=-60x-32
By simplifying the above equation we get no x value. So, there are no solutions.
From option (D):
-60x+32=32x+60
⇒-92x=28
⇒x=0.304
Therefore, options B and D have a solution.
To learn more about the system of equations visit:
https://brainly.com/question/14506845.
#SPJ5
What is the slope of the line?
Answer:
y = 2x-3.
Step-by-step explanation:
Slope is y =mx+b. If we look at the graph, the line passes by (0,-3) and (1,-1). Taking rise over run, (y/x), we can find out that y goes up 2 and x goes right 1. This means that it is a positive slope and that slope would be 2/1, simplified to just 2.
16) 56 is what percent of 40?
%
140
Step-by-step explanation:
56:40*100 =
(56*100):40 =
5600:40 = 140
The ratio of cows to chickens on Jack's farm is 3:5. Choose ALL correct statements that describe this relationship.
Round the numbers to the nearest thousands.
4 252-
8 683-
50 000-
59 490-
96 156-
Answer:
1. 4,000
2. 9,000
3. 50,000
4. 59,000
5. 100,000
7b-2/5=6b-7/5 nudfghnkdfbvugyteugdyvbbbvybhjedfs
Answer:
b=−1
Step-by-step explanation:
please help me i give brainliest
Answer:
Step-by-step explanation:
1. 120+21=141
2. 21-3=18
3. 7x-21
4. 20+x
5. 45+4x
6. 40+5c
7. 20+22r+26s
It will be nice if you give me brainliest
Good luck!
The value of the x-intercept for the graph of 4x - 5y = 40 is
Answer: The x intercept is 10 or (10,0)
Step-by-step explanation:
4x - 5y = 40 The x-intercept of a line is when its y coordinate is equal to zero. Input zero into the equation for y and solve for x to find the x intercept.
4x-5(0) = 40
4x + 0 = 40
4x = 40
x= 10
The x intercept is 10 or (10,0)
Give the 10th term of the following sequence:
1, 4, 7. 10
Answer:
28
Step-by-step explanation:
Answer:
29
Step-by-step explanation:
please help!!!!!!!!!!!
Answer:
pumpkin: 5
witch: 10
leaf: 50
bat: 20
ghost: 60
Answer:
Bat: 20
Pumpkin: 5
Ghost: 60
Leaf: 50
Witch: 10
Andrew and Connie are both teachers at their local school. There are 15 female teachers at the school and 35 male teachers. What is the ratio of male to female teachers?
Answer:
7:3
Step-by-step explanation:
List all the factor pairs for the
number 48.
List all the factor pairs for the
number 23.
List all the factor pairs for the
number 12.
List the first 5 multiples for the
number 12.
List the first 5 multiples for the
number 8.
DON'T FORGET TO USE THE
MULTIPLE MONSTER.
(repeated addition or Math
Facts)
List the first 5 multiples for the
number 9.
List the first 5 multiples for the
number 4.
List the first 5 multiples for the
number 7.
Answer:
1 x 48, 2 x 24, 3 x 16, 4 x 12, and 6 x 8
Sorry I can do more if needed
Step-by-step explanation:
8 Determine if the product of 32 and 8V 18 is
rational or irrational. Explain your answer.
Answer: It is irrational.
Step-by-step explanation:
√18 is an irational number. Multiplying most rational numbers by an irrational number results in an irrational number.
What is the first step to solve 2 (x - 2)< (1 + 2) + 5
Answer:
The first step would be to distribute the 2 outside of the parenthesis
Then the left side of the equation would look like: 2x-4
Step-by-step explanation:
9514 1404 393
Answer:
add 1+2
Step-by-step explanation:
According to the Order of Operations, the first step is to evaluate expressions in parentheses. Here, there are two expressions in parentheses: (x -2) and (1 +2). The first one cannot be evaluated. So, the first step is to evaluate ...
(1 +2) = 3
Then the inequality becomes ...
2(x -2) < 3 +5
3x + 6 = y
solve for x
Answer:
x=1/3y - 2
Step-by-step explanation:
Determine the type and number of solutions for the follow equation.
x² – 8x=-7