Answer:
Approximately 54°
Step-by-step explanation:
So we know Angle A, the side opposite to Angle A, and the side opposite to Angle B (the angle we want to find). Given these circumstances, we can use the Law of Sines.
The Law of Sines states that:
[tex]\frac{\sin(A)}{a} =\frac{\sin(B)}{b} =\frac{\sin(C)}{c}[/tex]
The variables do not really matter. Instead, it's more important that the angle corresponding to the side lines up with each other.
Anyways, since we know Side A, Angle A, and Side B, let's use the first and second ratios:
[tex]\frac{\sin(A)}{a} =\frac{\sin(B)}{b}[/tex]
Plug in 80° for A, 11 for a, and 9 for b:
[tex]\frac{\sin(80)}{11} =\frac{\sin(B)}{9}[/tex]
Cross multiply to solve for B:
[tex]9\sin(80)=11\sin(B)[/tex]
Divide both sides by 11:
[tex]\sin(B)=\frac{9\sin(80)}{11}[/tex]
Use the inverse sine function. And finally, use a calculator to solve:
[tex]\angle B =\sin^{-1}(\frac{9\sin(80)}{11} )\\\angle B\approx53.6829\textdegree\approx54\textdegree[/tex]
Solve the equation below for y.
6x – 3y = 36
A. y = 2x - 12
B. y = 12 - 2x
c. y- 5x+6
D. y-6-5 X
Answer:
it's A
Step-by-step explanation:
[tex]6x-3y=36\\\\-3y=36-6x\\\\y=\frac{36-6x}{-3} \\\\y=\frac{36}{-3}-\frac{6x}{-3}\\\\ y=-12 +2x \\ OR\\y=2x-12[/tex]
If $1205 is borrowed for 11 years at an annual simple interest rate of 11.3%, what is the total
amount that must be repaid rounded to the nearest cent
Answer:
$2,702.82
Step-by-step explanation:
The formula for simple interest is
I = Prt
where
I = interest amount
P = amount invested (the principal)
r = annual rate of interest
t = time in years
11.3% = 0.113 as a decimal
Now we use the formula to find the amount of interest earned.
I = $1,205 * 0.113 * 11
I = $1,497.82
The interest amount is $1,497.82.
Now we add the earned interest to the principal amount.
$1,205 + $1,497.82 = $2,702.82
Plzzzzz help will give brain and points!!! Explain why a quadratic equation with a positive discriminant has two real solutions, And why a quadratic equation with a negative discriminant has no real solution, And a quadratic equation with a discriminant of zero has one real solution.
Answer:
The given equation is -2x^2 = -8x + 8
This can be rewritten as 2x^2 - 8x + 8 = 0
Here the value of a =2, b = -8 and c = 8
Discriminant = b^2 - 4ac
Now plug in the above values in the discriminant, we get
= (-8)^2 - 4*2*8
= 64 - 64
= 0
Here the discriminant is 0, so we will get one real root.
The discriminant is equal to 0, which means the equation has one real number solution.
Hope this will helpful.
Thank you.
Write an equation fo nth term of the given arithmetic sequence 7,13,19,25,...
Answer:
The nth term for the given sequence can be written as:
[tex]a_n=6\,n+1[/tex]
Step-by-step explanation:
Notice that this arithmetic sequence is created by adding to each term a common difference of 6 units:
7 + 6 = 13
13 + 6 = 19
19 + 6 = 25
Then, using the general expression for the nth term of an arithmetic sequence of first term "[tex]a_1[/tex]" and common difference "d" we can write the nth term as:
[tex]a_n=a_1+(n-1)\,d[/tex]
which in this case translates as:
[tex]a_n=a_1+(n-1)\,d= 7\,+(n-1)\,6=7+6\,n-6=6\,n+1[/tex]
Answer:
Step-by-step explanation:
7, 13, 19, 25, .......
Arithmetic sequence.
First term = a = 7
Common difference = d = second term - first term
d = 13 - 7 = 6
nth term [tex]a_{n}=a+(n-1)d\\[/tex]
[tex]a_{n} = 7 +(n-1)*6\\\\\\a_{n}=7 + 6n - 6\\\\\\a_{n} = 1 + 6n[/tex]
6х + Зу = 12
solve for y
Answer:
3.
Step-by-step explanation:
Rearrange to make it easier: 6*x+3*y-(12)=0
Find like factors and eliminate them: 6x + 3y - 12 = 3 x (2x + y - 4)
So then you get 3 = 0. So y would be 3.
Helppppppppp please !!!
Answer:
Hey there!
Rhianna has 1/2 of a box of pencils left after using some at school.
The bottom two boxes would be 3÷3=1.
Let me know if this helps :)
Answer:
2Step-by-step explanation:
There are 6 spaces and three are shaded
= [tex]6\div 3 = 2\\[/tex]
The Article states:
Jim LeBrecht is a former Jened camper. He uses a wheelchair because he has
spina bifida. In a documentary about the camp, LeBrecht described the frustration
he felt as a teen: "I wanted to be part of the world, but I didn't see anyone like me in
it."
Which is the closest antonym for the word former?
A traditional
B
skillful
с
patient
D
current
"Former" means "past", more or less. So he used to be a camper.
Antonym means the opposite.
I would say "future" is more opposite than "past", but "current" works as well too.
Gary used candle molds, as shown below, to make candles that were perfect cylinders and spheres: What is the approximate difference in the amount of wax needed to make a candle from each of these molds? Use π = 3.14. A.) 16.75 cubic inches B.) 20.93 cubic inches C.) 24.25 cubic inches D.) 33.49 cubic inches
Answer:
A.) 16.75
Step-by-step explanation:
First, find the volume of each mold:
[tex]Cylinder_{volume}[/tex] = πr²h
Where,
π = 3.14
r = 2 in
h = 4 in
[tex]Cylinder_{volume} = 3.14*2^2*4 = 50.24 in^3[/tex]
[tex]Sphere_{volume}[/tex] = ⁴/3πr³
Where,
π = 3.14
r = 2 in
[tex]Sphere_{volume} = \frac{4}{3}*3.14*2^3 = 33.49 in^2[/tex]
Approximate difference in the amount of wax needed = 50.24 - 33.49 = 16.75 in^3
Answer:
A
Step-by-step explanation:
Use the number line below, where RS = 7y + 2, ST = 2y +6, and RT = 13y - 12
a. What is the value of y?
b. Find RS, ST, and RT.
R
What is the value of y?
Answer: a. y=5
b. RS = 37 , ST =16 and RT = 53 .
Step-by-step explanation:
Given: On number line we have,
RS = 7y + 2, ST = 2y +6, and RT = 13y - 12.
a. Since its on number line so we have
RT = RS+ ST
i.e. 13y - 12 = (7y + 2) + ( 2y +6)
⇒ 13y - 12 = 7y + 2 + 2y +6
⇒ 13y-12 = 9y+8
⇒ 13y-9y = 8+ 12 [Subtract 9y from both sides and add 12 in both sides]
⇒ 4y = 20
⇒ y= 5 [Divide both sides by 4 ]
b. Now , RS = 7(5) + 2 = 35+2= 37,
ST = 2y +6 = 2 (5)+6 = 10+6 =16,
and RT = 13y - 12 = 13 (5)-12 = 65-12 = 53.
Hence, RS = 37 , ST =16 and RT = 53 .
in the figure on the right, the lenght of the segment A must be x + 3, the length of segment B must be x +2, and the length of segment C must be x + 1. the perimeter of the triangle is 30cm. equate the sum of the lengths of the segments to 30 and solve for x
Answer:
x=8
Step-by-step explanation:
A= x+3
B= x+2
C= x+1
A+B+C=30
[tex]x+3+x+2+x+1=30\\3x+6=30\\3x=30-6\\3x=24\\x=\frac{24}{3}\\x=8[/tex]
ANS: X=8
Plz help ASAP!!!!!! Will mark brainliest
Answer:
D. 180cubic cm
Step-by-step explanation:
volume=h*w*L
V=6*5*6
v=180
the sum of squares of two consecutive odd numbers is 514 find the numbers
Correct Question : The sum of squares of two consecutive positive odd numbers is 514. Find the numbers.
[tex]\rule{130}1[/tex]
Solution :
Let the two consecutive positive odd numbers be x and (x + 2)
[tex]\rule{130}1[/tex]
☯ [tex]\underline{\boldsymbol{According\: to \:the\: Question\:now :}}[/tex]
[tex]:\implies\sf x^2 + (x + 2)^{2} = 514 \\\\\\:\implies\sf x^2 + x^2 + 4x + 4 = 514\\\\\\:\implies\sf 2x^2 + 4x + 4 = 514 \\\\\\:\implies\sf 2x^2 + 4x = 514 - 4\\\\\\:\implies\sf 2x^2 + 4x = 510 \\\\\\:\implies\sf 2x^2 + 4x - 510 = 0\\\\\\:\implies\sf x^2 + 2x - 255 = 0 \:\:\:\:\:\Bigg\lgroup \bf{Dividing\:by\:2}\Bigg\rgroup\\\\\\:\implies\sf x^2 + 17x - 15x - 255 = 0\\\\\\:\implies\sf x(x + 17) - 15(x + 17) = 0\\\\\\:\implies\sf (x + 17) (x - 15)\\\\\\:\implies\sf x = - 17\:or\:x = 15\\\\\\:\implies\underline{\boxed {\sf x = 15}}\:\:\:\:\:\Bigg\lgroup \bf{Positive\:odd\: number}\Bigg\rgroup[/tex]
When,
[tex]\bullet\: \textsf {x = } \textbf {15} [/tex]
[tex]\bullet\: \sf x + 2 = 15 + 2 =\textbf{ 17} [/tex]
[tex]\therefore\:\underline{\textsf{The required positive integer is \textbf{15 and 17}}}.[/tex]
cual es la raíz cuadrada de cuatro
Answer:
2
Step-by-step explanation:
√4 = 2
X+5x -9 + XY - 2 -3X +2XY - 4 -3XY
Answer:
3x-15
Step-by-step explanation:
> First start off by rewriting with each term that has the same variable beside each other
5x+ x -3x+xy+2xy-3xy-4-2-9
> Start to combine like terms
3x + 0xy - 15
> Rewrite
3x-15
I NEED HELP FASTT PLEASE
Answer:
x'5/3.y1/3 is the correct answer
What is the length of segment RS? On a coordinate plane, line R S has points (negative 4, negative 3) and (1, 9). StartRoot 65 EndRoot 12 13 StartRoot 153 EndRoot
Answer: Length of RS = 13
Step-by-step explanation: Segment is a line connecting two points.
Length or Distance of a segment is the distance between these two points and is calculated as:
[tex]d=\sqrt{(x_{1}-x_{2})^{2}+(y_{1}-y_{2})^{2}}[/tex]
For the line RS:
[tex]d=\sqrt{[1-(-4)]^{2}+[9-(-3)]^{2}}[/tex]
[tex]d=\sqrt{(1+4)^{2}+(9+3)^{2}}[/tex]
[tex]d=\sqrt{(5)^{2}+(12)^{2}}[/tex]
[tex]d=\sqrt{25+144}[/tex]
[tex]d=\sqrt{169}[/tex]
d = 13
The length of segment RS is 13 units.
Answer:
^ Answer is C
Step-by-step explanation:
Write an exponential function in the form y=ab^x that goes through points (0,14) and (3,3024).
Answer:
y = 14 [tex](6)^{x}[/tex]
Step-by-step explanation:
For an exponential function of the form y = a[tex]b^{x}[/tex]
Use the given points to find a and b
Using (0, 14 ), then
14 = a[tex]b^{0}[/tex] ( [tex]b^{0}[/tex] = 1 ) , thus
a = 14
y = 14[tex]b^{x}[/tex]
Using (3, 3024 ) , then
3024 = 14 b³ ( divide both sides by 14 )
216 = b³ ( take the cube root of both sides )
b = [tex]\sqrt[3]{216}[/tex] = 6 , thus
y = 14 × [tex]6^{x}[/tex] ← exponential function
Is √3600 rational or irrational? choose all statements are true
Answer:
Rational
Step-by-step explanation:
A surd is an irrational number. An irrational number refers to any number that can not be written in the form a/b where a and b are integers.
Given √3600, which can be written as √36 × √100 = 6 ×10 = 60.
Hence √3600 is a rational number.
PLEASE HELP TO BE MARKED THE BRAINLIEST
The school ski club went on a ski trip. The ski changed the group $1120 for 32 lift tickets. How much was each ticket?
Answer:
$35 per ticket
Step-by-step explanation:
1120 divided by 32 is 35, I used a calculator. If you divide the cost by the quantity you will get the cost for one quantity
POSS
If points D and E are on a number line at D = -2 and E = 3, what is the distance between them?
2
Answer:
It would be 5.
Step-by-step explanation:
3 - 5 is -2, because it goes like this:
-5 -4 -3 -2 -1 0 1 2 3 4 5 (just count down)
Which of the following graphs represent functions Circle your answers. If it is a function, state the domain
and range. If the graph is not included, make a table and graph the function by hand.
Answer:
Step-by-step explanation:
A). y = |2x - 3| + 1
Domain of function is defined by the x-values (Input values) and Range by the y-values(Output values).
From the graph,
Domain : (-∞, ∞)
Range : [1, ∞)
B). Table of the input-output values of the function,
y = x² - 2x + 1
x -2 -1 0 1 2
y 9 4 1 0 1
By graphing the function as attached,
Domain of the function : (-∞, ∞)
Range of the function : [0, ∞)
C). x² + y² = 3²
Domain of the function : [-3, 3]
Range of the function : [-3, 3]
D). x = 5
Domain of the line : [5, 5]
Range of the line : (-∞, ∞)
12. Rice is sold in 75 gram packs and 120 gram packs.
The masses of both packs are given correct to the nearest gram.
Calculate the lower bound for the difference in mass between the two packs.
Answer:
44g
Step-by-step explanation:
Rice is sold in 75-gram packs and 120-gram packs.
74.5 to 75.5 119.5 to 120.5
lowest possible difference = 119.5 - 75.5 = 120-75-1 = 44g
Find the distance between the points (3,4) and (5,9). Leave in simplest radical form.
Answer:
√29
Step-by-step explanation:
The distance between points (x1, y1) and (x2, y2) is:d = √(x2-x1)² + (y2-y1)²We have points (3,4) and (5,9), so the distance:
d = √(5-3)² + (9-4)² = √4 + 25 = √29evaluate 3+11t -9uwhen t = 9 and u =11
Answer:
3
Step-by-step explanation:
[tex]3+11t-9u\\\\\rightarrow\boxed{t = 9; u = 11}\\\\3+11(9)-9(11)\\\\3+99-99\\\\102-99\\\\\boxed{3}[/tex]
Hope this helps.
PLZ HELP HURRY PLZ Below are the data collected from two random samples of 100 members of a large travel club regarding the type of vacation they prefer: Which of the following inferences can be made based on the data? Most members prefer a beach vacation. Most members prefer a adventure vacation. More members prefer an adventure vacation and a ski vacation than a cruise vacation. More members prefer a beach vacation and ski vacation than an adventure vacation.
More members prefer a beach vacation and ski vacation than an adventure vacation.
======================================================
Explanation:
Let's go through the four answer choices to see which one is true.
Choice A is false because most members prefer a cruise, as 70+72 = 142 is the largest column sum. Choice B is false for the same reasoning as choice A.Choice C is false. We have 6+1 = 7 people who prefer adventure and 19+21 = 40 who prefer to ski, giving 7+40 = 47 people who prefer either. But this is nowhere near 142 we found back in choice A above. So more people prefer a cruise than the combined amount for adventure and ski.Choice D is true. Adding the column totals for "beach" and "ski" gives (5+6)+(19+21) = 11+40 = 51, and this exceeds the column total of "adventure (6+1 = 7).Solve the equation
(please show work if possible)
Answer:
-10
Step-by-step explanation:
imma be honest all i do is put in different numbers until it is right. But the way to do it is subract 2 by puting it under the negative 3 and you get -5. then multiply the 2 by putting it under the -5. you get -10. and the answer will read r = -10. Therefore r is -10
Answer:
I’m sorry I thought I saw a positive 3, The correct answer would be -10.
A cylindrical storage vessel is 7cm in diameter and 6m long. Find its volumes.
211 cu. Cm
231 cu. Cm
251 cu. Cm
271 cu. Cm
Calculate the volume of a cylindrical container, whose diameter is 24cm and height is 14cm.
6336 cu. cm
6326 cu. cm
6226 cu. cm
6126 cu. cm
Calculate the total surface area of a cone of height 7cm and base radius 7cm.
306 sq. cm
307 sq. cm
308 sq. cm
309 sq, cm
Answer accurately.
1)Option B is the correct option.
231
2)Option A is the correct option.
6336
3)Option B is the correct option.
307 (not sure)
if the compound interest on Rs 16000 in 3 years is Rs 2522 find the rate of interest
Answer:
Step-by-step explanation:
present value | $741.37 (US dollars)
how many teacher are there in your class-7 including your class supervisor? how many are Male teachers and female teachers?express Male and female teachers in percent.
soln
total teachers = 11
male teachers = 5
female teachers =6
now,
Answer:
45% male teachers
55% female teachers
Step-by-step explanation:
multiply the number of teachers with 100 and divide it by the total number of teachers