Part (a)
BC = opposite side (furthest leg from the reference angle)
AB = adjacent side (closest leg from the reference angle)
AC = hypotenuse (always opposite the 90 degree angle)
=============================================
Part (b)
i. False. Angle B is 90 degrees as shown by the square angle marker.
ii. False. Side AB is opposite angle C. Note how "C" is part of "BC", so that means we cannot have BC be opposite C.
iii. True. Leg AB is the closer leg to angle A. We have "A" in "AB" to see this without having to draw the diagram. Refer to part (a) above.
iv. False. The longest side of any right triangle is always the hypotenuse. The longest side of any triangle is always opposite the largest angle.
==============================================
Part (c)
cos(theta) = adjacent/hypotenuse = AB/AC
tan(theta) = opposite/adjacent = BC/AB
Refer back to part (a) to determine the opposite,adjacent and hypotenuse side lengths.
==============================================
Part (d)
The reference angle has changed, so the opposite and adjacent sides swap. The hypotenuse remains the same regardless of what reference angle you pick.
sin(C) = opposite/hypotenuse = AB/AC
cos(C) = adjacent/hypotenuse = BC/AC
tan(C) = opposite/adjacent = AB/BC
Note the tangent ratio is the reciprocal of what we found back in part (c).
Answer & Step-by-step explanation:
(a)
The hypotenuse is on line CA (the hypotenuse is always opposite the 90° angle (marked by a little square))
The adjacent is on the line BA (adjacent is next to the given angle, but NOT the hypotenuse)
The opposite is on the line CB (this is opposite the given angle)
(b)
i. false (b is a right angle)
ii. false (the side opposite C is BA)
iii. true
iv. false (the side opposite B is the hypotenuse, and the hypotenuse is always the longest side in a triangle)
(c)
cosine ratio: [tex]cos=\frac{adjacent}{hypotenuse}[/tex]
tangent ratio: [tex]tan=\frac{opposite}{adjacent}[/tex]
The cosine and tangent ratios of the given angle:
[tex]cos0=\frac{AB}{CA} \\\\tan0=\frac{CB}{AB}[/tex]
(d)
Remember SOH-CAH-TOA:
Sine=Opposite/Hypotenuse
Cosine=Adjacent/Hypotenuse
Tangent=Opposite/Adjacent
Using the angle C, plug in the appropriate sides:
[tex]sinC=\frac{BA}{CA}\\\\ cosC=\frac{CB}{CA}\\\\ tanC=\frac{BA}{CB}[/tex]
:Done
what is the expression of 28 19/100
Answer:
the mixed form is 28 [tex]19/100[/tex]
the improper form is ( 28 x 100) = 19 / 100
2819 / 00
Enter an inequality that represents the graph in the box.
Answer:
stop cheating
Step-by-step explanation:
get smart
What is the solution to the system of equations graphed below?
Answer:
A
Step-by-step explanation:
The solution to a system of equations is the point of intersection of the 2 lines.
The lines intersect at (6, 9 ) ← solution
Answer:
A(6, 9)
Step-by-step explanation:
The intersecting points of the two lines gives the solution of the equation.
The length of a rectangular field is 6 metres longer than its width. If the area of the field is 72 square metres, What are the width and the length of the field?
Answer:
Let's call the length of the field "l", and the width of the field "w".
If the area of the field is 72 square meters, then we have:
l x w = 72
And if the length is 6 meters longer than the width, we have:
l = w+6
So looking at the first equation (l x w = 72), we can substitute the l for a w+6.
And we obtain:
(w+6) x (w) = 72
Which simplifies to w^2 + 6w = 72.
This quadratic equation is pretty easy to solve, you just need to factor it.
w^2 + 6w - 72 = 0
(w-6)(w+12)
This leaves the roots of the quadratic equation to be 6 and -12, but in this case, a width of -12 wouldn't make sense.
So, the width of the rectangular field is 6, and the length of the field is 12.
Let me know if this helps!
Answer:
we assume one side is x and other side must be x+6 and when we multiple it together we can find x²+6x =72
Step-by-step explanation:
one side is 6 and. other is 12 so the lenght= 12 the width=6
Question 6(Multiple Choice Worth 1 points) (06.01 LC) Choose the correct classification of 5x + 2x2 − 8 by number of terms and by degree. A.Third degree polynomial B.Fourth degree trinomial C.Second degree trinomial D.Sixth degree polynomial
Question 7: Choose the correct simplification of the expression (3x − 6)(2x2 − 4x − 5)
Answer:
C) 6x³ - 24x² + 9x + 30
Step-by-step explanation:
(3x - 6)(2x² - 4x - 5)
3x • 2x² = 6x³
3x • -4x = -12x²
3x • -5 = -15x
-6 • 2x² = -12x²
-6 • -4x = 24x
-6 • -5 = 30
Combine terms.
6x³ - 12x² - 15x - 12x² + 24x + 30
Combine like terms.
6x³ - 24x² + 9x + 30
Learn with another example:
https://brainly.com/question/28001380
What is the solution to 7 × p = -56? A. -49 B. -8 C. 8 D. 49
Answer:
-8
Step-by-step explanation:
Hello!
What we do to one side of the equation we do to the other side
7 * p = -56
Divide both sides by 7
p = -8
The answer is -8
Hope this helps!
Which of the following is an example of how a scientist might use a model?
A wrench is used to tighten a nut onto a piece of wood.
A microscope is used to magnify a group of cells on a slide.
The end of a slinky is moved vertically up and down to simulate a wave.
A stopwatch is used to time the rate of a chemical reaction.
Answer:
C
Step-by-step explanation:
The end of a slinky is moved vertically up and down to simulate a wave.
Find the coordinates of point X that lies along the directed line segment from Y(-8, 8) to T(-15, -13) and partitions the segment in the ratio of 5:2. A. (-5, -15) B. (-23, -5) C. (-13, -7) D. (-11.5, -2.5)
Answer:
C. (-13, -7)
Step-by-step explanation:
The location of a point O(x, y) that divides a line AB with location A[tex](x_1,y_1)[/tex] and B[tex](x_2,y_2)[/tex] in the ratio m:n is given by:
[tex]x=\frac{m}{m+n} (x_2-x_1)+x_1\\\\y=\frac{m}{m+n} (y_2-y_1)+y_1[/tex]
Therefore the coordinates of point X That divides line segment from Y(-8, 8) to T(-15, -13) in the ratio 5:2 is:
[tex]x=\frac{5}{5+2} (-15-(-8))+(-8)\\\\x=\frac{5}{7} (-15+8)-8=\frac{5}{7}(-7)-8=-5-8=-13 \\\\\\y=\frac{5}{5+2} (-13-8)+8\\\\y=\frac{5}{7} (-21)+8=5(-3)+8=-15+8=-7[/tex]
Therefore the coordinates of point X is at (-13, -7)
The family size bottle of sunscreen holds 12121212 fluid ounces (fl oz)(\text{fl oz})(fl oz)(, start text, f, l, space, o, z, end text, )of sunscreen. The regular bottle holds 75%75\%75%75, percent less.How many fewer fluid ounces does the regular bottle of sunscreen hold?
Answer:
The regular bottle holds 9 fl oz less
Step-by-step explanation:
Given
Family Size = 12 fl oz
Required
Determine the size held less by the regular bottle
From the question, we have that the regular bottle holds 75% less;
[tex]Regular\ Size = 75\% * Family\ Size[/tex]
Substitute 12 fl oz for Family Size
[tex]Regular\ Size =75\% * 12\ fl\ oz[/tex]
Convert percentage to fraction
[tex]Regular\ Size = \frac{75}{100} * 12\ fl \oz[/tex]
[tex]Regular\ Size = \frac{75 * 12\ fl\ oz}{100}[/tex]
[tex]Regular\ Size = \frac{900\ fl\ oz}{100}[/tex]
[tex]Regular\ Size = 9\ fl\ oz[/tex]
Hence, the regular bottle holds 9 fl oz less
A pizza parlor offers 4 different pizza toppings. How many different kinds of 2-topping pizzas are available?
Answer:
you need to be more specific.
Step-by-step explanation:
Find from the first principle the derivative of 4x² -2with respect to x. Brailiest will be given please hurry
Answer:
8x
Step-by-step explanation:
Using differentiation from first principles
f'(x) = [tex]lim_{h>0}[/tex] [tex]\frac{f(x+h)-f(x)}{h}[/tex]
= [tex]lim_{h>0}[/tex] [tex]\frac{4(x+h)^2-2-(4x^2-2)}{h}[/tex]
= [tex]lim_{h>0}[/tex] [tex]\frac{4x^2+8hx+4h^2-4x^2+2}{h}[/tex]
= [tex]lim_{h>0}[/tex] [tex]\frac{8hx+4h^2}{h}[/tex]
= [tex]lim_{h>0}[/tex] [tex]\frac{4h(2x+h)}{h}[/tex] ← cancel the h on numerator/denominator
= 4(2x)
= 8x
Answer:
8x
Step-by-step explanation:
Pls I hope this helps
What are the roots of the equation x2 + 6x - 4 = 0?
A6+2V13
B.-6+2V13
C.3V13
D.-3V13
Answer:
The answer is D
Step-by-step explanation:
use the quadratic formula, plug and chug, and voila!
A can do a piece of work in 15 days. B can do the same work in 12 days and C can
finish the same piece of work in 20 days. They started the work together for 2 days
and then B and C leaves. In how many days will A finish the remaining work?
Answer:
[tex]9\ days[/tex]
Step-by-step explanation:
[tex]We\ are\ given:\\No.\ of\ days\ A\ takes\ to\ complete\ some\ amount\ of\ work=15\ days\\No.\ of\ days\ B\ takes\ to\ complete\ the\ same\ amount\ of\ work=12\ days\\No.\ of\ days\ C\ takes\ to\ complete\ the\ same\ amount\ of\ work\ as\ A\ and\ B\ =20\ days\\[/tex]
[tex]Now,\\We\ can\ say\ that\ an\ object\ has\ to\ complete\ \frac{1}{n}th\ of\ the\\ work\ daily,\ to\ complete\ the\ work\ in\ n\ number\ of\ days.\ This\ is\ however\\ only\ true\ if\ the\ object\ covers\ equal\ amounts\ of\ work\ each\ day.[/tex]
[tex]Here,\\In\ 1\ day,\\A\ would\ cover\ \frac{1}{15}th\ of\ the\ work.\\B\ would\ cover\ \frac{1}{12}th\ of\ the\ work.\\C\ would\ cover\ \frac{1}{20}th\ of\ the\ work.[/tex]
[tex]Now,\\We\ are\ also\ given\ that:\\They\ work\ together\ for\ 2\ days\ on\ the\ same\ work.\\Hence,\\Total\ work\ done\ in\ 1\ day\ by\ A,B\ and\ C=\frac{1}{15}+\frac{1}{12}+\frac{1}{20}=\frac{4+5+3}{60}=\frac{12}{60}=\frac{1}{5}\\Hence, Total\ work\ done\ in\ 2\ days\ by\ A,B\ and\ C=2*\frac{1}{5}=\frac{2}{5}[/tex]
[tex]Hence,\\The\ portion\ of\ the\ total\ work\ left=1-\frac{2}{5}=\frac{5-2}{5}=\frac{3}{5}\\So,\\Since\ A\ has\ to\ complete\ \frac{3}{5}th\ of\ the\ work,\ lets\ compute\ the\ no.\ of\ days\ it\ takes\ to\ do\ so.\\Hence,\\No.\ of\ days\ A\ takes\ to\ complete\ the\ entire\ work=15\ days\\Hence,\\No.\ of\ days\ A\ takes\ to\ complete\ \frac{3}{5}th\ of\ the\ entire\ work=15*\frac{3}{5}=9\ days[/tex]
Answer:
9 days
Step-by-step explanation:
A does in 15days, so A in 1day does 1/15part
B does in 12days, so B in 1day does 1/12part
C does in 20days, so C in 1day does 1/20part
So. A+B+C in 1 day-- 1/15+1/12+1/20=(4+5+3)/60= 12/60=1/5 and in 2days 2/5 part..hence remaining work=1/1–2/5=(5–2) =3/5part.
Now A in 1/15 part takes 1day
So, in 3/5 part 15×3/5 = 9 days.
Can someone help me on these ones. PLEASE HELP ME !!
[tex]\huge\blue{ANSWER}:—[/tex]
Plz mark me as brainliest as I have solve all the questions for you
Answer:1 : x is 95/3
4 x is -32/10
7 b is 6
10 x is 20/7
13 x is 9/2
Step-by-step explanation:
Please answer answer question
Answer:
c=13.42
Step-by-step explanation:
[tex]A^2+B^2=C^2\\6^2+14^2=C^2\\C^2=144+36\\C^2=180\\\sqrt{c^2}=\sqrt{180} \\c=13.42[/tex]
Brad invests $3700 in an account paying 3% compounded monthly. How much is in the account after 8 months?
Answer:
Amount after 8 month (A) = $3775 (Approx)
Step-by-step explanation:
Given:
Amount invested (P) = $3,700
Rate of interest (r) = 3% = 0.03 / 12 = 0.0025 monthly
Number of month (n) = 8 month
Find:
Amount after 8 month (A)
Computation:
[tex]A=P(1+r)^n\\\\ A=3700(1+0.0025)^8\\\\A=3700(1.02017588)\\\\ A = 3774.650676[/tex]
Amount after 8 month (A) = $3775 (Approx)
Simplify (3 1/2+7)divided by (4 1/3-3)
Answer:
63/8
Step-by-step explanation:
3 1/2 = 7/2
4 1/3 = 13/3
[tex] \frac{ \frac{7}{2} + 7 }{ \frac{13}{3} - 3} [/tex]
[tex] = \frac{ \frac{21}{7} }{ \frac{4}{3} } [/tex]
[tex] = \frac{63}{8} [/tex]
58°
X Х
jsut give a quick
Answer:
32
Step-by-step explanation:
The sum of the angles of a triangle is 180
58+90+x = 180
148+x = 180
x = 180-148
x=32
The angle sum property of a triangle:
The total measure of the three angles of a triangle is 180°
Solution[tex]\large\bf \longrightarrow \: {\underline{\red{x \: + \: 58 \degree \: + \: 90 \degree \: = \: 180 \degree}}}[/tex]
[tex]\large\bf \longrightarrow \: {\underline{\red{x \: + \: 148 \: = \: 180 \degree}}}[/tex]
[tex]\large\bf \longrightarrow \: {\underline{\red{x \: = \: 180 \degree \: - \: 148 \degree}}}[/tex]
[tex]\large\bf \longrightarrow \: {\underline{\red{x \: = \: 32 \degree}}}[/tex]
A, B are the points (-4, -3) and (2, 5). If the interval AB is now divided into 4
equal parts, find the coordinates of these three points.
Answer:
D(-2,5;1); C(-1,1); E(0.5,3).
Step-by-step explanation:
Imagine that there is a line AB, it is divided into 4 equal parts. If there are 4 parts, There are 4+1=5 points. That's obvious that if parts are equal , the third point is on the middle of the line AB, suppose it is the point C
xc= (xa+xb)/2
xc=( -4+2)/2= -1
yc= (-3+5)/2=1
(-1,1)
There are to unknown points D (between A and C), and E (between C and B). D is on the middle of AC .
Xd= (-4-1)/2=-2.5
yd= (-3+1)/2=-1
(-2,5;1)
E is on the middle of CB
xe= (-1+2)/2= 0.5
ye=(1+5)/2=3
(0.5, 3)
Which of the following equations have exactly one solution? Choose all answers that apply: Choose all answers that apply: (Choice A) A 2x-31=2x-31 (Choice B) B 2x-31=-2x-31 (Choice C) C 2x+31=2x-31 (Choice D) D 2x-2=2x-31
Answer:
B 2x - 31 = -2x - 31 have exactly one solution
Step-by-step explanation:
Which of the following equations have exactly one solution?
Choose all answers that apply:
A 2x - 31 = 2x - 31
B 2x - 31 = -2x - 31
C 2x + 31 = 2x - 31
D 2x - 2 = 2x - 31
A. 2x - 31 = 2x - 31
2x-31=2x-31
Collect like terms
2x-2x= -31+31
0=0
Infinite number of solutions
B 2x - 31 = -2x - 31
2x - 31 = -2x - 31
Collect like terms
2x+2x=-31+31
4x=0
x=0
One solution
C 2x + 31 = 2x - 31
2x + 31 = 2x - 31
Collect like terms
2x-2x= -31-31
0= -62
No solution
D 2x - 2 = 2x - 31
2x - 2 = 2x - 31
Collect like terms
2x-2x= -31+2
0= -29
No solution
Determine the value of x is
Answer:
x = 5
Step-by-step explanation:
The measure of an arc equals the measure of the central angle that intercepts it.
The measure of an arc intercepted by a diameter is 180 deg.
m(arc)EH = 180
m(arc)EF + m(arc)FG + m(arc)GH = m(arc)EH
10x + 8 + 67 + 11x = 180
21x + 75 = 180
21x = 105
x = 5
For the mathematics projects, a teacher divides 27 students into 2 groups. One group has more students than twice the number of students in the other group by 3. Find the number of students in both groups.
Write as a equation.
Answer:
8, 19
Step-by-step explanation:
let group 1 have x students and group 2 have y students
x + y = 27
but group 2 has 2x + 3 students
the sum of students from both groups is 27
x + 2x + 3 = 27
3x + 3 = 27
3x = 24
x = 8
y = 2x + 3
y = 19
Select the two values of x that are roots of this equatio 2x - 5 = - 3x ^ 2
alright I can help!
so to find the two values of x that are roots of the equation we need to put the variables all on one side so that we can set up the quadratic formula.
3x^2+2x-5=0 (the -3x^2 becomes positive when moved across the equal sign)
now we can set up the quadratic formula. the equation is x= (-b+-(sqrt of b^2 -4ac))/ 2a
so now we just plug in our variables.
x= (-2+-(sqrt of 2^2 -4×3×-5))/ 2×3
x= (-2+-8)/6
now we just seperate the equations so that we have the two roots. and then just solve!
x= (-2-8)/6 -> x= -5/3
x= (-2+8)/6 -> x=1
hope this helps! best wishes and best of luck!!
Mr. Ellington has a total of 32 students in his class , The ratio of girls to boys is 3:5, how many girls are in Mr . Ellington's class ?
Add the ratio: 3 + 5 = 8
Divide total students by that:
32/8 = 4
The ratio for girls is 3, multiply the 4 by 3:
4 x 3 = 12
There are 12 girls
Answer:
12
Step-by-step explanation:
If the ratio of girls to boys is 3:5, that means that for every 8 total students, 3 would be girls and 5 would be boys. Therefore 3/8 of the students are girls and 5/8 are boys. If 3/8 are girls, then:
[tex]\frac{3}{8}[/tex] of 32
= [tex]\frac{3}{8} * 32[/tex]
[tex]=\frac{3 * 32}{8} \\= \frac{96}{8} \\= 12[/tex]
There are 12 girls.
arrange0.2,¼,30%,10%in ascending and descending order
Answer:
Ascending- 10%, 0.2, 1/4, 30%
Descending- 30%, 1/4, 0.2, 10%
Step-by-step explanation:
0.2 = 2/10 = 4/20
1/4 = 5/20
30% = 30/100 = 6/20
10% = 10/100 = 2/20
Ascending
-2/20, 4/20, 5/20, 6/20
- 10%, 0.2, 1/4, 30%
Descending
- 6/20, 5/20, 4/20, 2/20
- 30%, 1/4, 0.2, 10%
WILL GIVE BRAINLIEST!!!
Answer:
2 x^2 sqrt(13)
Step-by-step explanation:
sqrt( 52x^4)
sqrt( 4*13 * x^2 * x^2)
We know that sqrt(ab) = sqrt(a) sqrt(b)
sqrt( 4)*sqrt(13) *sqrt( x^2) *sqrt( x^2)
2 sqrt(13) x*x
2 x^2 sqrt(13)
52|2
26|2
13|13
1
[tex]\sqrt{52x^4}=\sqrt{2^2\cdot13\cdot(x^2)^2}=2x^2\sqrt{13}[/tex]
There are 9 classes of 25 students each, 4 teachers, and two times as many chaperones as teachers.
Each bus holds a total of 45 people.
What is the least number of buses needed for the field trip?
5 buses is the answer pls mark me brainliest
Least number of bus require for trip = 5 buses
What is Unitary method?It is a method where we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit.
Steps to Use Unitary Method
First, let us make a note of the information we have. There are 5 ice-creams. 5 ice-creams cost $125.
Step 1: Let’s find the cost of 1 ice cream. In order to do that, divide the total cost of ice-creams by the total number of ice-creams. The cost of 1 ice-cream = Total cost of ice-creams/Total number of ice-creams = 125/5 = 25. Therefore, the cost of 1 ice cream is $25.
Step 2: To find the cost of 3 ice-creams, multiply the cost of 1 ice cream by the number of ice-creams. The cost of 3 ice-creams is cost of 1 ice-cream × number of ice-creams = 25 × 3 = $75. Finally, we have the cost of 3 ice-creams i.e. $75.
Given:
Total number of classes = 9
Number of student in each class = 25
Number of teacher = 4
Number of chaperones = Double of teacher
Bus hold = 45 people
Now,
Total number of student = 9 × 25
= 225
Number of chaperones = 4 × 2
= 8
Total people = 225 + 8 + 4
= 237
Least number of bus require for trip = Total people / Bus hold
= 237 / 45
= 5.266
Learn more about unitary method here:
https://brainly.com/question/22056199
#SPJ2
Find the value of X. 40,x
Answer:
x = 70°
Step-by-step explanation:
x = one of the congruent angles in the triangle
Given angle measure: 40°
x = ? + ? = 180 - 40 = 140
x = 70
Answer:
x = 70°
Step-by-step explanation:
x = one of the congruent angles in the triangle
Given angle measure: 40°
x = ? + ? = 180 - 40 = 140
x = 70
i'm doing domain and range, and I'm kinda having a hard time with this... can someone help?
Answer:
Domain : any real number
Range : y ≥0
Step-by-step explanation:
The domain is the values that x can be
X can be any real number
The range is the values the y can be
Y can be zero or any positive value since y = x^2
Domain : any real number
Range : y ≥0
Answer:
[tex]\boxed{\sf Option \ A}[/tex]
Step-by-step explanation:
[tex]y=x^2[/tex]
[tex]\sf The \ domain \ of \ a \ function \ is \ all \ possible \ values \ for \ x.[/tex]
[tex]\sf There \ are \ no \ restrictions \ on \ the \ value \ of \ x.[/tex]
[tex]\sf The \ domain \ is \ all \ real \ numbers.[/tex]
[tex]\sf The \ range \ of \ a \ function \ is \ all \ possible \ values \ for \ y.[/tex]
[tex]\sf When \ a \ number \ is \ squared \ the \ result \ is \ always \ greater \ than \ or \ equal \ to \ 0.[/tex]
[tex]\sf The \ range \ is \ \{y:y\geq 0\}[/tex]
enter the repeating digit
[tex] \frac{9}{11} [/tex]
Answer:
Step-by-step explanation:
[tex]\frac{9}{11}=0 .818181....[/tex]
__
= 0.81