Answer:
22
Step-by-step explanation:
mean = sum of all data/n.o of data
= 24+31+12+38+12+15/6
= 22
Evaluate the following
[tex]tan15 \times \frac{cos15}{sin15} [/tex]
Answer: 1
Step-by-step explanation:
tan(15) * cos(15)/sin(15)
Use tan(x) = sin(x)/cos(x) to transform the expression:
= sin(15)/cos(15) * cos(15)/sin(15)
Cancel opposite terms on both sides:
= 1
How many groups of 2 are in 7 explain your answer
We have: 7 = 2 × 3 + 1
Answer: 3
Ok done. Thank to me :>
help help
what’s the value of x
measure of c
Answer:
x = 29
Angle C = 93°
Step-by-step explanation:
Since all of the interior angles of a triangle add up to 180° and we are given the values of angle A and angle B, we can find angle C by subtracting A and B from 180.
35 + 52 = 87
180 - 87 = 93
Thus, the measure of angle C is 93°.
Now that we know the measure of angle C, we can determine the value of x.
Set up an equation:
3(x + 2) = 93
3x + 6 = 93
3x = 87
x = 29
Answer:
(a) x = 29
(b) m∠C = 93°
Step-by-step explanation:
(a) The sum of the interior angles of a triangle = 180°
⇒ m∠A + m∠B + m∠C = 180
⇒ 35 + 52 + 3(x + 2) = 180
⇒ 87 + 3x + 6 = 180
⇒ 93 + 3x = 180
⇒ 3x = 87
⇒ x = 29
(b) As x = 29
⇒ m∠C = 3(29 + 2)
⇒ m∠C = 3 x 31
⇒ m∠C = 93°
An angel whose measure is less than 90 is called an acute angel
Answer:
Yes, the statement is true
Btw, it's an angle not angel
Please mark as brainliest
Answer:
that is True.
A6 m ladder leans against the side of a house. The bottom of the ladder is 2 m away from the side of the house. Find X, the angle of elevation of the ladder.
Round your answer to the nearest tenth of a degree.
PLEASE HELP
Answer:
[tex]x = 5.65m [/tex][tex]\theta = cos^{-1}\bigg(\dfrac{1}{3}\bigg)[/tex]Step-by-step explanation:
Here it's given that a 6m ladder is leaned against a house, and the base of ladder is 2m away from the foot of the house. Here I am assuming x to be the height of the house.
Diagram :-
[tex] \begin{picture}(3,3)\setlength{\unitlength}{1cm} \linethickness{.6mm}\put(0,0){\line(1,0){4}}\put(0.01,0){\line(4,3){4}}\put(4,0){\line(0,1){3}}\put(4.3,1){$\bf x $} \put(2,-0.5){$\bf 2m$}\put(1,1.5){$\bf 6m$}\put(.9,0.2){$\bf\theta $}\put(2,4){$\boxed{\sf - RISH4BH }$}\end{picture} [/tex]
Using, Pythagoras theorem ,
[tex]\longrightarrow h^2=p^2+b^2 [/tex]
Substitute,
[tex]\longrightarrow (6m)^2=x^2+(2m)^2[/tex]
Simplify,
[tex]\longrightarrow 36m^2= x^2+4m^2 [/tex]
Subtracting 4m² on both sides,
[tex]\longrightarrow x^2 = 36m^2 -4m^2=32m^2 [/tex]
Put square root on both sides,
[tex]\longrightarrow x =\sqrt{32m^2}[/tex]
Simplify,
[tex]\longrightarrow \underline{\underline{ x = 5.65\ m}}[/tex]
Again in order to find out the angle of elevation,
[tex]\longrightarrow cos\theta =\dfrac{b}{h} [/tex]
Substitute,
[tex]\longrightarrow cos\theta =\dfrac{2m}{6m}[/tex]
Simplify,
[tex]\longrightarrow cos\theta =\dfrac{1}{3} [/tex]
Take cos inverse both sides,
[tex]\longrightarrow \underline{\underline{\theta =cos^{-1}\bigg(\dfrac{1}{3}\bigg)}}[/tex]
The length of the wall is 5.66m and the angle of elevation is 70.56°
Data;
Length of Ladder (Hypothenuse) = x = 6mDistance from the wall to the foot of the ladder (adjacent)= y = 2mThe length of the side of the house (opposite) = zPythagorean TheoremTo calculate the length of the wall or side of the house, we have to use Pythagorean theorem which is given as
[tex]x^2 = y^2 + z^2[/tex]
Let's substitute the values and solve for the length of the wall
[tex]x^2 = y^2 + z^2 \\6^2 = 2^2 + z^2 \\36 = 4 - z^2\\z^2 = 36 - 4\\z^2 = 32\\z = \sqrt{32} \\z = 5.66m[/tex]
The length of the wall is 5.66m.
Angle of ElevationTo calculate the angle of elevation, we can use trigonometric ratio SOHCAHTOA
since we have the value of all the sides, we can decide to use any of the ratios.
I will use sine angle to solve for the angle of elevation.
[tex]sin \theta = \frac{opposite}{hypothenuse} \\sin \theta = \frac{5.66}{6} \\sin \theta = 0.943\\\theta = sin^-^1 (0.943)\\\theta = 70.56^0[/tex]
The angle of elevation is 70.56°
Learn more on Pythagorean theorem and trigonometric ratio here;
https://brainly.com/question/6241673
6. Given that ABCD is a quadrilateral with A(-2,-2), B(1, 1),
C(1,6), and D(-2, 3), determine if it is a parallelogram.
Answer:
it is a parallelogram
Step-by-step explanation:
so first plot out points and then you find the slope for each of the corresponding lines.
First lets find the slope for AB. you must subtract them and make it -2-1/-2-1. it ends up having a slope of 1.
Then find the slope of the corresponding side(CD). this we will subtract -2-1/3-6. this will have a slope of 1 and will be parallel to AB.
Next you find the slopes of the other two sides starting with AC. we will subtract -2-(-2)/-2-3. this will be a vertical line which means it has a slope of 0.
finally the last step is you see if BD has an equal slope to AC. you then subtract 1-1/1-6. this is also a vertical line so the slope is 0 just like AC so they are both parallel.
in conclusion there are two sets of parallel lines so you have a parallelogram
Evaluate the expression. 0.2+0.3–0.6÷6 Write your answer as an integer or a decimal. Do not round.
Answer:
0.4
Step-by-step explanation:
(0.2+0.3) - (0.6/6)
0.5 - 0.1
Hey there!
0.2 + 0.3 - 0.6 ÷ 6
0.2 + 0.3 = 0.50 = 0.5
= 0.5 - 0.6 ÷ 6
0.6 ÷ 6 = 0.10 = 0.1
= 0.5 - 0.1
= 0.40
= 0.4
Thus, your answer is: 0.4
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
How many times greater is the product
of 5x20 compared to 10x20?
Answer:
2 time greater
Step-by-step explanation:
5x20=100
10x20=200
100x2=200
so its 2 times greater
9. V = 300(1.02)* models exponential
growth, where t represents the number
of years.
a) What is the annual rate of growth?
b) Calculate the monthly rate of growth
to the nearest hundredth of a percent.
Answer:
a) 2%
b) 0.17%
Step-by-step explanation:
Exponential growth is modeled by the equation ...
y = a·b^x
where 'a' is the initial value, and 'b' is the growth factor.
When x is has units of time, the growth factor 'b' applies over 1 unit of x. The applicable growth factor for different units of time can be found using the rules of exponents applied to the equation written with x expressed in the different units.
The growth rate is related to the growth factor by ...
b = 1 +r . . . . where r is the growth rate
r = b -1 . . . . solved for r
__
a)Your equation is ...
V = 300(1.02^t)
where t is expressed in years. Then the corresponding annual growth rate is ...
b = 1.02
r = b -1
r = 1.02 -1 = 0.02 = 2% . . . annual rate of growth
__
b)When the equation is written so that t is expressed in months, it becomes ...
V = 300(1.02)^(t/12)
V = 300(1.02^(1/12))^t
Now, the growth factor (per month) is
b = 1.02^(1/12)
and the monthly growth rate is ...
r = 1.02^(1/12) -1 ≈ 1.00165158 -1 = 0.00165158
r ≈ 0.17% . . . . monthly rate of growth
1) Ben has been 30 minutes late to work on each of the last 7 days. The number of hours that he has been late will be deducted from his usual 40 hour work week. How many hours will be deducted?
A) 2 hours
B) 3 hours
3.5 hours
D) 4.5 hours
E) 5 hours
Answer:
C) 3.5 hours
Step-by-step explanation:
30 minutes is a half of an hour.
So that would be seven halves of an hour.
If we multiply the amount of halves by the amount of day late we get our answer.
0.5 x 7 = 3.5
Or we could simply add 0.5 seven times.
PLSSSSSSSSSSSS HELP MEEEEE
Answer:
Step-by-step explanation:
1/2 * 8 * 15 * x=3360 c^3
x = 56 units
the population of town increases by5℅ every year. In the last year, the population was 80,000. 1) find the present population 2) find the population of the town in the next two years.
explain step by step please
Answer:
last year it was 80k
Step-by-step explanation:
Population increases by 5% every year
Last year it was 80,000
PRESENT POPULATION
Present population = 80,000 + 5% off 80,000
= 80,000 + 5/100 × 80,000
= 80,000 + 5 × 800
= 80,000 + 4,000
= 84,000
AFTER ONE YEAR
After this , the population again increases by 5%
Population = 84,000 + 5% off 84,000
= 84,000 + 5/100 × 84,000
= 84,000 + 5 × 840
= 84,000 + 4,200
= 88,200
ANSWERS
The population of present year is 84,000
After one year , the population becomes 88,200
Hope it helps :-)
Answer:
1. The Present population is 84,000
2. The next years population 88,200 and the year after that would be 92,610
Step-by-step explanation:
If you take the previous year and multiply it by 1.05 you you get the current population. After that you take the current population and multiply it again by 1.05 since the population increases by 5% so continue multiplying by 1.05 to get the later years and so forth
For a ride on a rental scooter, Ahmad paid an $8 fee to start the scooter plus 6 cents per minute of the ride. The total bill for Ahmad's ride was $14.96. For how many minutes did Ahmad ride the scooter?
Order -4, -8.2, 6, -9, and 1 3/4 from least to greatest.
Answer:
-9, -8.2, -4, 6, 1 3/4
Step-by-step explanation:
The larger the number is if it's a negative, the lower it is (if that makes sense). For example, -9 is lower than -7.
1 3/4 = 1.75
What is the slope of the line that passes through the points ( − 1 , − 7 ) (−1,−7) and ( 1 , − 13 ) (1,−13)? Write your answer in simplest form.
Answer:
[tex]y = -3x -10[/tex]
Step-by-step explanation:
Slope-intercept formula: [tex]\frac{y_2-y_2}{x_2-x_1}[/tex]
Find slope of (−1, −7) and (1, -13)
[tex]\frac{y_2-y_2}{x_2-x_1}\\\\\\frac{-13-(-7)}{1-(-1)}\\\\\\frac{-6}{2}\\\\\-3[/tex]
[tex]y = mx + b[/tex]
[tex]y = -3x +b[/tex]
[tex]y = -3x +b\\-7 = -3(-1) + b\\-7 = 3 +b\\-3 -3\\-10 = b[/tex]
[tex]y = -3x -10[/tex]
Hope this helps!
Two similar triangles have a corresponding sides of length 7cm and 4cm respectively. Find the ratio of their areas.
Answer:
49 : 16
Step-by-step explanation:
ratio of their sides = 7 : 4
ratio of their areas = 7^2 : 4^2 = 49 : 16
what is 3.31 + 1 kilometer
Answer:
4.31 kilometer
..........................................
Find the distance between each pair of parallel lines with the guven equation y=2x+7 y=2x-3
Answer:
10
Step-by-step explanation:
The y-intercept for each line is...
y=2x+7 (0, 7)
y=2x-3 (0, -3)
Note this is because...
y=mx+b
b represents the y-intercept
Using the distance formula...
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2[/tex]
[tex]d=\sqrt{(0-0)^2+(7-(-3))^2[/tex]
[tex]d=\sqrt{0+(10)^2[/tex]
[tex]d=\sqrt{0+100}[/tex]
[tex]d=\sqrt{100}[/tex]
[tex]d=10[/tex]
how would I write 5 more than 1/2 of a number as a expression?
Answer:
[tex]\frac{n}{2}[/tex] + 5
Step-by-step explanation:
-> An expression does not have an equal sign
-> Let n be "a number"
-> What I underline becomes apart of our mathematical expression in the next line;
5 more than 1/2 of a number
5 more than [tex]\frac{n}{2}[/tex]
[tex]\frac{n}{2}[/tex] + 5
The graph shows the distance, y, in miles, of a moving motorboat from an island for a certain amount of time, x, in hours:
A graph titled Distance Vs Time is shown, with Time in hours labeled on the x-axis and Distance from Island in miles labeled on the y-axis. The scale on the x-axis shows the numbers 1, 2, 3, 4, 5, 6, 7, and the scale on the y axis shows the numbers 0, 22, 44, 66, 88, 110, 132, 154, 176, 198. The graph shows a straight line joining the ordered pairs 0, 22, and 1, 66, and 2, 110, and 3, 154, and 4, 198.
What is the speed of the motorboat?
198 miles per hour
22 miles per hour
44 miles per hour
66 miles per hour
Answer:
44 mph
Step-by-step explanation:
[tex]\implies \mathsf{speed=\dfrac{change \ in \ y}{change \ in \ x}}[/tex]
[tex]\implies \mathsf{speed=\dfrac{198-22}{4-0}=44 \ mph}[/tex]
Using the following diagram, solve for x. Show work
Answer:
x = 7.5
Step-by-step explanation:
A line parallel to a side of a triangle and intersecting the other 2 sides, divides those sides proportionally, that is
[tex]\frac{8}{10}[/tex] = [tex]\frac{6}{x}[/tex] ( cross- multiply )
8x = 60 ( divide both sides by 8 )
x = [tex]\frac{60}{8}[/tex] = 7.5
hi guys can you guys pls help me with this question
Answer:
A.600
B.980
C.350
D.210
Step-by-step explanation:
just see what the arrow
Kaylee is a high school basketball player. In a particular game, she made some two point shots and some three point shots. Kaylee scored a total of 24 points and made 3 more three point shots than two point shots. Graphically solve a system of equations in order to determine the number of two point shots made, x,x, and the number of three point shots made, yy.
how would you graph this?
Answer:
Step-by-step explanation:
Let Kayla made number of 2 points shots = x
and the number of 3 points shots = y
Since she made total nine shots so the equation will be
x + y = 9 --------(1)
She scores a total of 22 points so the equation will be
2x + 3y = 22 --------(2)
Now we multiply equation (1) by 2 and subtract it from equation (2)
(2x + 3y) - 2(x + y) = 22 - 18
2x + 3y - 2x - 2y = 4
y = 4
from equation (1)
x + 4 = 9
x = 5
Therefore, number of 2 shots are 5 and number of 3 shots are 4.
A scout group is having a cake sale to raise $90 for camping supplies. The troop spent $18 on ingredients for cakes. Cake slices will sell for $1 each. The equation below can be used to find the number of slices of cake the troop needs to sell to raise $90. n−18=90 How many slices of cake does the troop need to sell to raise $90?
Answer:
N=108
Step-by-step explanation:
You just have to add the $90 they need to raise plus the ingredients price to get $108.
-(-4)(-6)-3/5(10+15)/1/3
Answer:
[tex]-29[/tex]
solving steps:
[tex]\sf \hookrightarrow -\left(-4\right)\left(-6\right)-3/5\left(10+15\right)/1/3[/tex]
[tex]\sf \hookrightarrow -\left(-4\right)\left(-6\right)-3/5\cdot \:25/1/3[/tex]
[tex]\sf \hookrightarrow -24-3/5\cdot \:25/1/3[/tex]
[tex]\sf \hookrightarrow -24-5[/tex]
[tex]\sf \hookrightarrow -29[/tex]
Answer:
the answer is 29.
Step-by-step explanation:
use the order of operations to solve
PEMDAS
PLEASE HELP ASAP!!!!!!
Answer:
[tex]\frac{1}{axy}[/tex]
Step-by-step explanation:
[tex]\frac{xy}{a^2+a^3}[/tex] × [tex]\frac{a+a^2}{x^2y^2}[/tex] ( factorise denominator and numerator of 2 fractions )
= [tex]\frac{xy}{a^2(1+a)}[/tex] × [tex]\frac{a(1+a)}{x^2y^2}[/tex]
Cancel (1 + a) from both fractions
= [tex]\frac{xy}{a^2}[/tex] × [tex]\frac{a}{x^2y^2}[/tex]
Cancel a and xy from both fractions
= [tex]\frac{1}{a}[/tex] × [tex]\frac{1}{xy}[/tex]
= [tex]\frac{1}{axy}[/tex]
a ≠ 0 , x ≠ 0 , y ≠ 0
as this would would make the function undefined
Answer:
Step-by-step explanation:
[tex]\dfrac{xy}{a^2+a^3}\times \dfrac{a+a^2}{x^2y^2}[/tex]
Apply the fraction rule [tex]\dfrac{a}{b}\times \dfrac{c}{d}=\dfrac{a \times c}{b \times d}[/tex] :
[tex]\implies \dfrac{xy(a+a^2)}{x^2y^2(a^2+a^3)}[/tex]
Cancel the common factor [tex]xy[/tex] :
[tex]\implies \dfrac{(a+a^2)}{xy(a^2+a^3)}[/tex]
Factor [tex](a+a^2)=a(1+a) \ \ \textsf{and} \ \ a^2+a^3=a^2(1+a)[/tex] :
[tex]\implies \dfrac{a(1+a)}{xy \cdot a^2(1+a)}[/tex]
Cancel the common factor [tex]a(1+a)[/tex] :
[tex]\implies \dfrac{1}{axy}[/tex]
I think the "if" part is a, x and y cannot equal zero, as otherwise the expression will be undefined.
So I would put: [tex]x\neq 0; y\neq 0, a\neq 0[/tex]
i frl hate khan academy help
Answer:
52%
Step-by-step explanation:
There are 25 filled in squares in the first image, and 13 filled in squares in the second image.
To find the percentage we can divide the part of the base (a) by the base (b).
a = 13
b = 25
13/25 = 0.52
Move the decimal two places over to the right.
ASAP PLEASE HELP
5 of 10
Solve for
52 - 2 > 6
Give your answer as an improper fraction in its simplest form,
Answer:
True, 52-2 equals 50, 50 is greater than 6.
Step-by-step explanation:
3. The area of quadrilateral ABCD is 12 sq. units. Find X.
x is 9
Okay bye bye
:9 :O)
Rearrange each of the following formula so the pronumeral in the bracket becomes the subject of the equation
3x+y=5 (Y)
Answer:
y = 5 - 3x
Step-by-step explanation:
3x + y = 5 ( subtract 3x from both sides )
y = 5 - 3x
Answer:
y = 5 - 3x
making y the subject:
3x + y = 5y = 5 - 3xchanging sides, changes positive (+) sign to negative (-)
changing sides, changes negative (-) sign to positive (+)
