Inequality involving the sum of the angles of a triangle i.e,
[tex]\alpha +\beta +y > \pi[/tex]
The area of a spherical triangle ABC with angles a, B, Y are
AABC = ([tex]\alpha[/tex] + [tex]\beta[/tex]+ Y- [tex]\pi[/tex] ) [tex]R^{2}[/tex]
The AA'B'C' = AABC (by sss) as we discuss move.
We just need to demonstrate that IACI = IAC' and C'L IBCI = 1BC '1 will proceed similarly.
since AC & ATC resulted in the same.
the middle.
We now have external proof that the surface and their mon- are real. As of (ABCA) and LA'B'C) cover. A overlapping sphere with appropriate angles for each letter of the alphabet Las offered my first figure of $ segments that are completely separate from one another, so we may write -
( AABC A ) + ( A A'B'C' )A + ( An -x ) + ( Ax-B ) + ( An-V ) = [tex]4\pi R^{2}[/tex]
2 ( A ABC A ) =[tex]4\pi R^{2}[/tex] - 2 ( [tex]\pi -\alpha[/tex] ) [tex]R^{2}[/tex]- 2 ( [tex]\pi -\beta[/tex])[tex]R^{2}[/tex]-2([tex]\pi -Y[/tex])[tex]R^{2}[/tex]
AABCA = [tex](\alpha +\beta +Y-\pi )R^{2}[/tex]
To learn more about triangle click here :
brainly.com/question/2773823
#SPJ4
a. cos x b. tan x c. sec x d. cot x Simplify the expression
First, multiply by 1:
cos x * 1 + cos x tan^2 x
Factor cos x out of cos x tan^2 x
cos x * 1 + cos x (tan ^2 x)
Factor again
cos x (1+ tan^2 x)
Rearrange:
cos x (tan^2 x +1 )
Apply Pythagorean identity:
cos x * sec ^2 x
Rewrite Sec x in terms of sin and cos
cos x * (1 / cos x )^2
Apply product rule:
cos x * 1^2 / cos^2 x
cos x * (1/ cos^2 x )
Cancel common factor cos x
1 / cos x
1/cosx = sec x
Answer : sec x (option c)
You invest $8,000 in 3 investment accounts. The accounts are: paper, metal and glass. Paper returns 2% income, metal returns 4% income, and glass returns 5% income. The amount invested in the glass account was double the amount invested in the metal account. The yield was a total of $280 at the end of one year. How much was invested in each account?
The following investments were done:
Metal account: $ 1,500Glass account: $ 3,000Paper account: $ 3,500How much money has a person invested in three accounts?
In this problem we must determine how much money from a $ 8,000 investment has been deposited in each account based on overall yield after a period of one year. In accordance with the statement, the person deposited the following quantities in each account:
Metal: x
Glass: 2 · x
Paper: 8,000 - 3 · x
And the yield function is equal to:
280 = x · (4 / 100) + 2 · x · (5 / 100) + (8,000 - 3 · x) · (2 / 100)
280 = 0.04 · x + 0.1 · x + 160 - 0.06 · x
120 = 0.08 · x
x = 1500
The person made an investment of $ 1,500 in the metal account, $ 3,000 in the glass account and $ 3,500 in the paper account.
To learn more on investments: https://brainly.com/question/16781185
#SPJ1
The sum of two consecutive integers is 97. What is the smaller integer?
Answer: 48 is the smaller integer
Step-by-step explanation: 48+49=97 48 and 49 are the two integers, 48 is smaller than 49.
Find the value of each variable
Astronomers use a light year to measure distance. a light year is the distance light travels in one year. The speed is approximately 300,00km/sec. how long will it take a rocket traveling 63,000km/hr to reach Alpha Centauri (the ⭐ closest to Earth other than the ). Note: Alpha Centauri is approximately 4.34 light years from Earth. which is 4.11 x 10^13 km away (when using scientific notation). one light year is 9.46 x 10^12 km.
Speed of light = 300,000 km/sec
Rocket's speed = 63,000 km/hr or 6.3 x 10⁴ km/hr
Alpha Centauri distance from Earth = 4.11 x 10¹³ km
One light year (distance) = 9.46 x 10¹² km
To solve for the time it takes it travel, we can manipulate the speed formula.
[tex]\begin{gathered} \text{speed}=\frac{dis\tan ce}{\text{time}} \\ \text{time}=\frac{dis\tan ce\text{ }}{\text{speed}} \end{gathered}[/tex]We already have the distance of Alpha Centauri from Earth written above. We also have the speed of the rocket written above too. We will substitute those values to the formula.
[tex]\begin{gathered} \text{time}=\frac{4.11\times10^{13}\operatorname{km}}{6.3\times10^4\operatorname{km}\text{ /hr}} \\ \text{time}=0.6523809524\times10^9 \\ \text{time}=6.52\times10^8\text{ hr} \end{gathered}[/tex]7/12 x 4x3 =? I need help
Cyphon, this is the solution:
We have to multiply the following fractions:
7/12 * 4/3
7 * 4 / 12 * 3
28/36
Simplifying, we have:
7/9 (Dividing by 4 numerator and denominator)
We have to add the following fractions:
- 1/2 + 4/9
Let's find the lowest common denominator between 2 and 9, as follows:
2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22
9, 18, 27, 36
The lowest common denominator is 18
Parallel lines investigation
From the given figure the value of x is 6 and the measure of angle 3 is 57°.
From the given figure, m∠4=(20x+3)° and m∠6=(9x+3)°.
What are angles of parallel lines?Angles in parallel lines are angles that are created when two parallel lines are intersected by another line called a transversal.
22). From the given figure
m∠4+m∠6=180° (Coointerior angles sum is equal to 180°)
(20x+3)°+(9x+3)°=180°
⇒ 29x+6=180
⇒ 29x=174
⇒ x=6
m∠4=(20x+3)°=123°
m∠3+m∠4=180° (Adjacent angles sum is equal to 180°)
m∠3+123=180
m∠3=57°
23). From the given figure
m∠3=m∠6 (Alternate interior angles are congruent)
x+10 = 4x-20
⇒ 3x=30
⇒ x=10
Now, m∠6=4x-20
=20
m∠6+m∠8=180° (Adjacent angles sum is equal to 180°)
20+m∠8=180°
⇒ m∠8=160
Therefore, from the given figure the value of x is 6 and the measure of angle 3 is 57°.
To learn more about the alternate interior angles visit:
https://brainly.com/question/28380652.
#SPJ1
what does x = to in the equation 4x +4<9x +8?
The given inequality is expressed as
[tex]4x\text{ + 4 }\leq\text{ 9x + 8}[/tex]The first step is to collect like terms. Thus, we have
[tex]\begin{gathered} 4x\text{ - 9x }\leq\text{ 8 - 4} \\ -\text{ 5x }\leq\text{ 4} \\ \end{gathered}[/tex]We would find x by dividing both sides of the inequality by - 5. Since - 5 is negative, the inequality symbol would be reversed. Thus, we have
[tex]\begin{gathered} \frac{-\text{ 5x}}{-\text{ 5}}\ge\frac{4}{-\text{ 5}} \\ x\text{ }\ge\text{ }\frac{-\text{ 4}}{5} \end{gathered}[/tex]please help me fill in the boxes its due tomorrow
Answer:
1- 80 miles
2- 3 hours
3- 35 mph
4- 180 miles
5- 5 hours
6- 15 mph
Step-by-step explanation:
if you travel at 40 miles every hour, then in 2 hours you'll travel 80 miles.
Which one of these expressions doesn’t have a value less than 1 please help thank you if u do
The fourth option [tex](3^{5)^{2} }[/tex]/[tex](3)^{4}[/tex] does not have value less than 1.
What is Power or Exponent?Power of a number is defined as how many times to use the number in a multiplication. We also call Powers as Exponents or Indices. For example, [tex]8^{2}[/tex] could be called “8 to the power 2” or “8 to the second power”, or simply “8 squared”.
Step-by-step explanation:
In first option, [tex]4^{11}[/tex]/[tex]4^{14[/tex], if we solve this, the answer comes out to be 1/[tex]4^{3}[/tex] which will be 1/64 which is 0.015 that is lesser than 1.
In second option, [tex](5^{4)^{2} }[/tex]×[tex]5^{-11}[/tex],if we solve this, the answer comes out to be 1/[tex]5^{3}[/tex] which will be 1/125 which is 0.008 that is lesser than 1
In third option,[tex](2^{3)^{-2} }[/tex],if we solve this, the answer comes out to be 1/[tex]2^{6}[/tex] which will be 1/64 which is 0.015 that is lesser than 1
in Fourth option ,[tex](3^{5)^{2} }[/tex]/[tex]3^{4}[/tex] , if solve this, the answer comes out to be [tex]3^{6}[/tex] which will be 729 that is larger than 1
∴fourth option will be the answer.
To know more about Exponent, Visit:
https://brainly.com/question/219134
#SPJ13
a candy manufacturer produces bags of jelly beans. the weight of a bag of jelly beans is normally distributed with a mean of 12 ounces and a standard deviation of 0.4 ounces. if a random sample of 4 bags of jelly beans is selected what is the probability that the sample average will be greater than 11.6?
Answer:
2%
Step-by-step explanation:
Use slope to determine if lines AB and CD are parallel, perpendicular, or neither 10. A(3, 1), B(3,-4), C(-4,1), D (-4,5)m(AB) m(CD) Types of lines
Neither parallel nor perpendicular
Explanations:The points are:
A(3, 1), B(3,-4), C(-4,1), D (-4,5)
The slope of a line is given as:
[tex]m\text{ = }\frac{y_2-y_1}{x_2-x_1}[/tex]The slope of the line AB, m(AB), with gthe points A(3, 1), B(3,-4) is given as:
[tex]\begin{gathered} m(AB)\text{ = }\frac{-4-1}{3-3} \\ m(AB)\text{ = }\frac{-5}{0} \\ m(AB)\text{ =- }\infty \end{gathered}[/tex]The slope of the line CD, m(CD), with the points C(-4,1), D (-4,5) is given as:
[tex]\begin{gathered} m(CD)\text{ = }\frac{5-1}{-4-(-4)} \\ m(CD)\text{ = }\frac{4}{-4+4} \\ m(CD)\text{ = }\frac{4}{0} \\ m(CD)\text{ = }\infty \end{gathered}[/tex]A line that has an infinite slope is a vertical line
For the two lines to be parallel, m(AB) should be equal to m(CD)
For the two lines to be perpendicular, m(AB) = -1 / m(CD)
None of the conditions for paralleleism and perpendicularity is met, the lines AB and CD are neither parallel nor perpendicular
how can I covert this 0.688= to a fraction
You have to convert the following number into a fraction:
[tex]0.6\bar{8}\bar{8}[/tex]This is a periodic decimal number, which explicitely is 0.68888888....
In order to convert this number to a fraction you proceed as follow:
[tex]0.6\bar{8}=\frac{68-0}{99}=\frac{68}{99}[/tex]You put 0.68 and not 0.688 because to do the convertion you need only the first periodic number (that is, only the first 8). The key is to put in the numerator the complete number as whole number, that is, 68. To this number you subtract the whole part of the decimal number, this whole part is 0 because of the 0.688. Then, in the numerator you have 68 - 0. In the denominator you write a number composed only by 9's. The number of 9 numbers is determined by the number of digits of the first number in the numerator. That is two 9 numbers
Need help on this asap
Answer:
K=0 N=3 and I=-2
it's
3+-20= -17
write an equation in slope-intercept form for the line with slope 4/3 and y-intercept -5
Remember the slope-intercept of a line is
[tex]y=mx+b[/tex]where:
• m ,is the slope of the line
,• b, is the y-intercept of the line
Now, let's substitute the data we're given. Thereby, the equation would be
[tex]y=\frac{4}{3}x-5[/tex]Please help me with 24For the following exercises, write the equation for the hyperbola in standard form if it is not already, and identify the vertices and foci, and write equations of asymptotes.
Given the equation,
[tex]-9x^2+72x+16y^2+16y+4=0[/tex]Complete squares as shown below,
[tex]\begin{gathered} -9x^2+72x-a^2=-(9x^2-72x+a^2)=-9(x^2-8x+b^2) \\ \end{gathered}[/tex]Thus,
[tex]\begin{gathered} \Rightarrow-9x^2+72x-a^2=-9(x^{}-4)^2 \\ \Rightarrow a^2=16\cdot9=144\Rightarrow a=12 \\ \Rightarrow-9x^2+72x-144=-9(x^{}-4)^2 \end{gathered}[/tex]Similarly,
[tex]\begin{gathered} 16y^2+16y=16(y^2+y) \\ \Rightarrow16(y+\frac{1}{2})^2=16(y^2+y+\frac{1}{4}) \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} -9x^2+72x+16y^2+16y+4=0 \\ \Rightarrow-9(x-4)^2+16(y+\frac{1}{2})^2+4=-144+4 \\ \Rightarrow-9(x-4)^2+16(y+\frac{1}{2})^2=-144 \end{gathered}[/tex]Finally, the standard form is.
[tex]\begin{gathered} \Rightarrow-\frac{(x-4)^2}{16}+\frac{(y+\frac{1}{2})^2}{9}=-1 \\ \Rightarrow\frac{(x-4)^2}{16}-\frac{(y+\frac{1}{2})^2}{9}=1 \end{gathered}[/tex]As for the vertices, foci, and asymptotes,
[tex]\begin{gathered} c=\pm\sqrt[]{16+9}=\pm5 \\ \text{center:}(4,-\frac{1}{2}) \\ \Rightarrow\text{foci:}(4-5,-\frac{1}{2})_{},(4+5,-\frac{1}{2})_{} \\ \Rightarrow\text{foci:}(-1,-\frac{1}{2}),(9,-\frac{1}{2}) \end{gathered}[/tex]Foci: (-1,-1/2), (9,-1/2)
Vertices
[tex]\begin{gathered} \text{center:}(4,-\frac{1}{2}),\text{vertices:}(4\pm a,-\frac{1}{2}) \\ \text{vertices:}(4+4,-\frac{1}{2}),(4-4,-\frac{1}{2}) \\ \text{vertices:}(8,-\frac{1}{2}),(0,-\frac{1}{2}) \end{gathered}[/tex]Vertices: (8,-1/2), (0,-1/2)
Asymptotes:
[tex]\begin{gathered} y=\pm\frac{3}{4}(x-4)-\frac{1}{2} \\ \Rightarrow y=\frac{3}{4}x-\frac{7}{2} \\ \text{and} \\ y=-\frac{3}{4}x+\frac{5}{2} \end{gathered}[/tex]Asymptotes: y=3x/4-7/2 and y=-3x/4+5/2
hi I need help with this question anyone got answers??? please its due tmrrrr!!!!!
5 1/4 ÷ 2/4
NOBODY IS ANSWERING!! I WILL GIVE BRAINLIEST!! PLS HELP!!
Find the area of thisirregular figure.9 ft8 ft15 ft26 ft
The area of the irregular figure will be equal to the sum of area of triangle and the area of the rectangle.
The required area can be determined as,
[tex]\begin{gathered} A=A_t+A_r \\ =(\frac{1}{2}\times8\text{ ft}\times9\text{ ft)+(15 ft}\times26\text{ ft)} \\ =36ft^2+390ft^2 \\ =426ft^2 \end{gathered}[/tex]Thus, the required area of the irregular figure is 426 square feet.
Can someone pls answer thiss!! rlly need help asap
The inverse of f(x) will be a relation if the original function's graph contains any location where a horizontal line would cross itself twice, but the inverse of that function won't be a function in and of itself.
Does a function's inverse always represent a relationship?
Essentially, obtaining an inverse is only a matter of changing the x and y coordinates. Although it might not always be a function, this newly generated inverse will be a relation. Sometimes a function's inverse isn't actually a function!
The inverse will also be a function if all horizontal lines only ever intersect one place on the original graph.
To learn more about function's inverse refer to:
https://brainly.com/question/11735394
#SPJ13
if 5 people can finish 3 cups of rice,
how many cups of rice will 35 people
eat at the same rate
Answer:
21 cups
Step-by-step explanation:
This question tests on the the concept of Unit Conversion.
Unit ConversionUnit Conversions involving converting values into per unit values.
Example: 15 apples in 3 days = (15 ÷ 3) apples per day = 5 apples per day
ApplicationFor this Question, we are given:
5 people per 3 cups of rice.
We are asked to find the number of cups of rice that 35 people can finish.
5 people = 3 cups
(5 ÷ 5) people = (3 ÷ 5) cups
1 person = 0.6 cups
(1 × 35) people = (0.6 × 35) cups
35 people = 21 cups
A farm is being divided so that each section of land has equal access
to the canal running through the property for watering crops. If the road on the
opposite side of the property runs parallel to the canal, explain how this can be
done.
The best way to divide the land having canal and road parallel, is divide land with the line perpendicular to the road and canal.
What is parallel and perpendicular?
In simple geometry, two geometric objects cross at a right angle (90 degrees or /2 radians) if they are perpendicular to one another. The perpendicular symbol,⟂, can be used to graphically depict the condition of perpendicularity. It can be defined between two planes, between two lines (or line segments), and between two lines.
In geometry, parallel lines are coplanar, straight lines that never intersect. Any parallel planes in the same three-dimensional space are those that never intersect. Parallel curves are those that have a predetermined minimum separation between them and do not touch or intersect.
We need to give equal access of canal to each section of land so, the best way to divide land is divide land perpendicularly to canal and the road.
To know more about parallel and perpendicular, go to link
https://brainly.com/question/25429151
#SPJ13
11. FINANCIAL LITERACY The surf shop has a weekly overhead of $2300. b. How many skimboards and longboards must the shop sell each week to make a profit a. Write an inequality to represent the number of skimboards and longboards the shop sells each week to make a profit.
Skimboard costs 115 longboard costs 685
A glacier is moving at a rate of 0.3 inches every hour. The table below represents this relationship.
Glacial Movement
Distance Moved (inches)
Time
(hours)
0.3
1
0.6
2
0.9
3
x
4
What value of x completes the table?
1.2
1.5
3.6
13.3
Answer:
1.2
Step-by-step explanation:
solve the equation, and enter the solutions from least to greatest. If there is only one solution, enter “n.a” for the second solution. (picture of equation listed below)
Answer
x = 1 or x = n.a.
Step-by-step explanation
[tex]\frac{1}{x}+\frac{1}{x-10}=\frac{x-9}{x-10}[/tex]Multiplying by (x - 10) at both sides of the equation:
[tex]\begin{gathered} (x-10)(\frac{1}{x}+\frac{1}{x-10})=\frac{x-9}{x-10}(x-10) \\ \text{ Distributing and simplifying:} \\ \frac{x-10}{x}+\frac{x-10}{x-10}=x-9 \\ \frac{x-10}{x}+1=x-9 \end{gathered}[/tex]Multiplying by x at both sides of the equation:
[tex]\begin{gathered} x(\frac{x-10}{x}+1)=x(x-9) \\ \text{ Distributing and simplifying:} \\ \frac{x(x-10)}{x}+x=x^2-9x \\ x-10+x=x^2-9x \\ 2x-10=x^2-9x \end{gathered}[/tex]Subtracting 2x and adding 10 at both sides of the equation:
[tex]\begin{gathered} 2x-10-2x+10=x^2-9x-2x+10 \\ 0=x^2-11x+10 \end{gathered}[/tex]We can solve this equation with the help of the quadratic formula with the coefficients a = 1, b = -11, and c = 10, as follows:
[tex]\begin{gathered} x_{1,2}=\frac{-b\pm{}\sqrt{b^2-4ac}}{2a} \\ x_{1,2}=\frac{11\pm\sqrt{(-11)^2-4\cdot1\operatorname{\cdot}10}}{2\operatorname{\cdot}1} \\ x_{1,2}=\frac{11\pm\sqrt{81}}{2} \\ x_1=\frac{11+9}{2}=10 \\ x_2=\frac{11-9}{2}=1 \end{gathered}[/tex]The solution x = 10 is not possible because it makes zero the denominator in 2 of the rational expressions of the original equation. In consequence, it must be discarded.
Berti is the Shape Factory's top employee. She has received awards every month for having the top sales
figures so far for the year. If she stays on top, she will receive a $5000 bonus for excellence. She currently has
sold 16, 250 shapes and continues to sell 340 per month.
EMPL
Since there are eight months left in the sales year, Sarita is working hard to catch up. While she has only sold
8,830 shapes, she is working overtime and on weekends so that she can sell 1, 082 per month. Will Sarita
catch up with Berti before the end of the sales year? If so, when?
No, Sarita will not be able to catch up with Berti before the end of the sales year.
Berti currently has sold 16, 250 shapes
She continues to sell 340 per month.
In eight months she will be able to sell
16250 + 8 x 340
= 16250 + 2720
= 18970
Sharita has only sold 8,830 shapes
Working overtime and on weekends so that she can sell 1, 082 per month
In eight months she will be able to sell
8830 + 8 x 1082
8830 + 8656
17486
No, Sarita will not be able to catch up with Berti before the end of the sales year.
To learn more about word problem refer here
https://brainly.com/question/13818690
#SPJ1
Y-4x is equal to or less than -6
Answer:
don't forget to give me brainest
star, like.
this is the correct solution.
Maths problem in indices. Pls help
Answer:
x = 9
Step-by-step explanation:
using the rule of indices
[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex] , then
[tex]5^{x}[/tex] = [tex]\frac{5^{8} }{5^{-1} }[/tex] = [tex]5^{(8-(-1))}[/tex] = [tex]5^{(8+1)}[/tex] = [tex]5^{9}[/tex]
since bases on both sides are equal, both 5 , then equate indices
x = 9
if square one is the largest of the three squares in the model,which statement is true?
_______________
I'm reading your question
___________________
According to the Pythagorean theorem
Hypotenuse ^2 = Side 1 ^2 + Side 2 ^2
The hypotenuse is the case (Square 1 )
area of the sqaure= side of the square^2
________________________
That means the area of 1 is = area of square 2 + area fo square3 (J is false)
_______________________________
We are not sure about the relation between square 2 and 3 just the addition is the square 1 (F and H we have no certainty)
______________________________
G is true
______________________________
Answer
G
What is the linear equation for the line graphed below?
Answer:
y = -3x + 7
Step-by-step explanation:
Hello!
Slope-Intercept Form: y = mx + b
m = slopeb = y-interceptThe y-intercept of the graph, or the point where the graph intersects the y-axis, is 7.
We can find the slope by finding the Rise/Run.
The graph rises negatively by 3 units as it runs positively by 1 unit, so the slope is -3/1 or -3.
Given the slope and y-intercept, the equation of the line is y = -3x + 7.
