Answers
QUESTION 1
Recall the mnemonics; SOH
[tex]\sin L =\frac{Opposite}{Hypotenuse}[/tex]
[tex]\sin L =\frac{12}{13}[/tex]
QUESTION 2
Recall the mnemonics; CAH
[tex]\cos L =\frac{Adjacent}{Hypotenuse}[/tex]
[tex]\sin L =\frac{5}{13}[/tex]
QUESTION 3
Recall the mnemonics; TOA
[tex]\tan M =\frac{Opposite}{Adjacent}[/tex]
[tex]\tan M =\frac{5}{12}[/tex]
QUESTION 4
[tex]\sin M =\frac{Opposite}{Hypotenuse}[/tex]
[tex]\sin M =\frac{5}{13}[/tex]
QUESTION 5
a) From the Pythagoras Theorem,
[tex]AC^2+AB^2=BC^2[/tex]
[tex]AC^2+4^2=5^2[/tex]
[tex]AC^2+16=25[/tex]
[tex]AC^2=25-16[/tex]
[tex]AC^2=9[/tex]
[tex]AC=\sqrt{9}[/tex]
[tex]AC=3yd[/tex]
b) Using the cosine ratio,
[tex]\cos (m\angle B)=\frac{4}{5}[/tex]
Take the inverse cosine of both sides;
[tex] m\angle B=\cos ^{-1}(\frac{4}{5})[/tex]
[tex] m\angle B=36.86[/tex]
[tex]\therefore m\angle B=36.9\degree[/tex] to the nearest tenth.
c) [tex]m\angle B +m\angle C=90\degree[/tex]
[tex]\Rightarrow 36.9\degree +m\angle C=90\degree[/tex]
[tex]\Rightarrow m\angle C=90\degree-36.9\degree[/tex]
[tex]\Rightarrow m\angle C=53.1\degree[/tex]
QUESTION 6
a) using the sine ratio,
[tex]\sin(51\degree)=\frac{DE}{18}[/tex]
[tex]DE=18\sin(51\degree)[/tex]
[tex]DE=13.99[/tex]
[tex]\therefore DE=14.0yd[/tex] to the nearest tenth.
b) Using the cosine ratio,
[tex]\cos (51\degree)=\frac{EF}{18}[/tex]
[tex]EF=18\cos (51\degree)[/tex]
[tex]EF=11.3yd[/tex] to the nearest tenth.
c) [tex]m\angle D+ m\angle F=90\degree[/tex]
[tex]\Rightarrow m\angle D + 51\degree=90\degree[/tex]
[tex]\Rightarrow m\angle D=90\degree-51\degree[/tex]
[tex]\Rightarrow m\angle D=39\degree[/tex]
QUESTION 7
a) Using the Pythagoras Theorem;
[tex]lG^2+GH^2=lH^2[/tex]
[tex]l15^2+GH^2=17^2[/tex]
[tex]225+GH^2=289[/tex]
[tex]GH^2=289-225[/tex]
[tex]GH^2=64[/tex]
[tex]GH=\sqrt{64}[/tex]
[tex]GH=8km[/tex]
b) Using the sine ratio,
[tex]\sin(m\angle H)=\frac{15}{17}[/tex]
[tex]m\angle H=\sin^{-1}(\frac{15}{17})[/tex]
[tex]m\angle H=61.9\degree[/tex]
c) [tex]m\angle l + m\angle H=90\degree[/tex]
[tex]m\angle l +61.9\degree=90\degree[/tex]
[tex]m\angle l =90\degree-61.9\degree [/tex]
[tex]m\angle l =28.1\degree [/tex]
QUESTION 8
We plot the points as shown in the diagram.
QUESTION 9
From the diagram, the side lengths XY and YZ can be obtained by counting the boxes. Each box is 1 unit.
This implies that;
XY =3 units
YZ=5 units.
We use Pythagoras Theorem, to obtain XZ.
This implies that;
[tex]XZ^2=XY^2+YZ^2[/tex]
[tex]XZ^2=3^2+5^2[/tex]
[tex]XZ^2=9+25[/tex]
[tex]XZ^2=34[/tex]
[tex]XZ=\sqrt{34}[/tex] units
QUESTION 10.
a) Using the tangent ratio;
[tex]\tan(m\angle X)=\frac{5}{3}[/tex]
[tex]m\angle X=\tan^[-1}(\frac{5}{3})[/tex]
[tex]m\angle X=59.0\degree[/tex]
b) [tex]m\angle Z+m\angle X=90\degree[/tex]
[tex]m\angle Z+59.0\degree=90\degree[/tex]
[tex]m\angle Z=90\degree-59.0\degree[/tex]
[tex]m\angle Z=31.0\degree[/tex]
QUESTION 11
a) Triangle BCD is shown in the attachment.
The length of side DC=|3-2|=1 unit
The length of side DB=|4-3|=1 unit
Using Pythagoras Theorem;
[tex]BC^2=DC^2+DB^2[/tex]
[tex]BC^2=1^2+1^2[/tex]
[tex]BC^2=1+1[/tex]
[tex]BC^2=2[/tex]
[tex]BC=\sqrt{2}[/tex]
b) DB is perpendicular to DC, therefore m<D=90 degrees.
The length of DB is equal the length of DC.
This implies that;
m<C=m<B=45 degrees.
QUESTION 12
[tex]\sin 30\degree=\frac{1}{2}[/tex]
QUESTION 13
[tex]\cos 30\degree=\frac{\sqrt{3} }{2}[/tex]
QUESTION 14
[tex]\tan 30\degree =\frac{\sqrt{3} }{3}[/tex]
QUESTION 15
[tex]\tan 45\degree =1[/tex]
QUESTION 16
[tex]\cos 45\degree =\frac{\sqrt{2} }{2}[/tex]
QUESTION 17
[tex]\tan 45\degree =1[/tex]
Check attachment for the rest
Related Questions
Albert buys a car for $12,000. The value of the car depreciates about 9% per year. After about how many years will the car be worth $7500?
Answers
Answer:
[tex]5\ years[/tex]
Step-by-step explanation:
we know that
The formula to calculate the depreciated value is equal to
[tex]D=P(1-r)^{t}[/tex]
where
D is the depreciated value
P is the original value
r is the rate of depreciation in decimal
t is Number of Time Periods
in this problem we have
[tex]P=\$12,000\\r=9\%=0.09\\D=\$7,500[/tex]
substitute in the formula above and solve for t
[tex]\$7,500=\$12,000(1-0.09)^{t}[/tex]
[tex](7,500/12,000)=(0.91)^{t}[/tex]
Apply log both sides
[tex]log(7,500/12,000)=t*log(0.91)[/tex]
[tex]t=log(7,500/12,000)/log(0.91)=5\ years[/tex]
What is the perimeter of the shape below
Answers
Answer:
20
Step-by-step explanation:
look at picture and you can add all the numbers becuase i counted the sides
6 x 10^-4 in standard form. explain how you did it pleeeeasee
Answers
0.0006=6x10^-4
Since the exponent is negative, the number will get smaller. A negative exponent shows that the decimal point is shifted that number of places to the left. The exponent is -4, so the decimal place will move 4 places to the left.
Answer:
0.0006
Step-by-step explanation:
A number in scientific notation if it has the form a × 10ⁿ.
A negative exponent indicates
A number between 0 and 1. That the decimal point is shifted that number of places to the left.6 × 10⁻⁴ tells you that the decimal number is 6. with the decimal point moved four places to the left.
Thus, 6 × 10⁻⁴ becomes 0.0006
A bowl has 3 plums and 5 pears. A second bowl has 2 plums and 4 pears. You randomly chose one piece of fruit from the first bowl and one piece of fruit from the second bowl. What is the probability that they are both plums?
Answers
3x/5y = 60% 2x/4y=50%
Brew Ha Ha Coffee produces two types of coffee blends: Morning,x,and House,y. The Morning blend has 9oz of a Guatemalan coffee and 7oz of Brazilian coffee. The company makes $2 in profit from each bag of Morning Blend sold and $2.50 in profit from each bag of House Blend sold. The company has 400oz of both the Guatemalan and Brazilian coffees available.
This set of inequalities represent the constraints in this situation.
9x+6y<400
7x+10y<400
X>0
Y>0
The company wants to maximize its profits by using the objective function P = 2x + 2.5y
What is the maximum profit.
88
0
160
106
Answers
Answer:
Fourth option
Step-by-step explanation:
When graphing the given inequalities you will get a region like the one shown in the attached image. This region is delimited by 4 straight
[tex]x = 0\\\\y = 0\\\\9x + 6y = 400\\\\7x + 10y = 400[/tex]
The points indicated at the ends of the region are the maximum possible values of x and y.
We must test these points in the objective function [tex]P = 2x + 2.5y[/tex] and see which point maximizes the value of P.
Remember that the boundaries of the region are not included.
We can prove the point x = 0 and y = 39 because (0,4) is not included in the region.
[tex]P = 2(0) + 2.5(39) = 97.5[/tex]
Now we test the point x = 33 and y = 16
[tex]P = 2(33) + 2.5(16) = 106[/tex]
Now we test the point x = 44 and y = 0
[tex]P = 2(44) + 2.5(0) = 88[/tex]
Finally the optimal value is:
x = 33 oz
y = 16 oz
With a gain of $106
can someone help me find this expression!! i don’t understand it at all, please comment only if you can help !!
Answers
Check the picture below.
Please help! Easy scatter plot multiple choice questions
Answers
The correct answer would be a, because the left side of the graph indicates that the y axis represents how many customers and since it says 7.pm in the question, it would be choice A
What is the product? 2y/y-3 multiplied by 4y-12/2y+6
Answers
The answer is [tex]\frac{4y}{y+3}[/tex]
Step-by-step explanation:See the attached figure
Answer:
[tex] \frac { 4y } { y + 3 } [/tex]
Step-by-step explanation:
We are given the following terms and we are to find their product:
[tex] \frac { 2y } { y - 3 } \times \frac { 4y - 12 } { 2y + 6 } [/tex]
[tex] \frac { 8y^2 - 24y } { 2y^2 - 6y + 6y - 18 } [/tex]
Taking the common terms out and cancelling them to get:
[tex] \frac { 2 (4y^2 - 12y ) } { 2 (y^2 - 9 ) } [/tex]
[tex] \frac { 4y ( y - 3 ) } { ( y + 3 ) ( y - 3 ) } [/tex]
[tex] \frac { 4y } { y + 3 } [/tex]
What is 0.95 rounded off to the nearest whole number
Answers
1.00 would be your answer because 95 rounded up is 100. So, 0.95 is closest to 1.00
You increase the size of a page by 50% then you decrease it by 50% what is the size of the page now
Answers
Answer:
75% of the original paper’s size.
Step-by-step explanation:
Let’s say that the original size was 10 inches.
You then increase it by 50%. It is now 15 inches.
Now, you decrease it by 50%. 50% of 15 is 7.5. So, the paper is now 7.5 inches.
7.5 inches is 75% of the original paper size.
I hope I helped!
Let me know if you need anything else!
~ Zoe
Answer:
Smaller than you started with.
Plz helppppppppppppppp
Answers
Answer:
[tex]\large\boxed{Area:\ 69\ ft^2}\\\\\boxed{Perimeter:\ 58\ ft}[/tex]
Step-by-step explanation:
Look at the picture.
The perimeter:
[tex]P=3+17+12+2+9+15=58\ ft[/tex]
We have two rectangles 12 ft × 2 ft and 15 ft × 3 ft.
Calculate the areas of the rectangles:
[tex]A_1=(12)(2)=24\ ft^2\\\\A_2=(15)(3)=45\ ft^2[/tex]
The area of the figure:
[tex]A=A_1+A_2\\\\A=24+45=69\ ft^2[/tex]
What is the volume of a square pyramids
Answers
Answer:
[tex]\large\boxed{V=75\ in^3}[/tex]
Step-by-step explanation:
The formula ogf a volume of a pyramid:
[tex]V=\dfrac{1}{3}BH[/tex]
B - area of a base
H - height
We have a base length a = 5 in and a height H = 9 in.
In the base we have a square. The formula of an area of a square is:
[tex]B=a^2[/tex]
Substitute:
[tex]B=5^2=25\ in^2[/tex]
Calculate the volume:
[tex]V=\dfrac{1}{3}(25)(9)=(25)(3)=75\ in^3[/tex]
What is the solution to the following system of linear equations? 4y − 36 = −12x 3x + y = −9 Select one: A. (-2, 3) B. (1, 5) C. no solution D. infinitely many solutions
Answers
I think it's c. No solution
The solution for the given system of linear equations is (1, -2), which is not provided in the options given. A possible typo may exist in the options.
Explanation:This question is asking for the solution to a system of linear equations. The equations were given as 4y − 36 = −12x and 3x + y = −9. To solve this system, we can use the method of substitution or elimination. First, let's rewrite the first equation in terms of x. Dividing each side of 4y - 36 = -12x by -12, we get x = -y/3 + 3. We can then substitute (-y/3 + 3) for x into the second equation, yielding 3(-y/3 + 3) + y = -9. Solving Yields y = -2 and substituting y = -2 into x = -y/3 + 3 gives x = 1. So, the solution to this system is x = 1, y = -2. So the correct answer is (1, -2), which was not provided in the options. It seems there might be a typo in the options provided.
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suppose you are in your last semester of college and have a 2.75 GPA after 105 credit hours if you are taking 15 credit hours in your last semester and get a perfect 4.0 GPA what will your overall GPA be is it possible to get your GPA up to 3.0 for the graduation
Answers
Answer:
The overall CGPA would be 2.90 so it is not possible for hum to secure a CGPA of 3 for graduation.
Step-by-step explanation:
Given,
CGPA = 2.75
Credit hours = 105
Last semester GPA = 4
Last semester credit hours = 15
CGPA = [tex]\frac{sum of (Credit hours of each subject * GPA of each subject)}{Total credit hours}[/tex]credit hours * gpa
in our case, it would be:
CGPA = [tex]\frac{(2.75*105)+(4*15}{105+15}[/tex]
=> [tex]\frac{(288.75)+(60)}{120}[/tex]
=> [tex]\frac{348.75}{120}[/tex]
=> 2.90
The overall CGPA would be 2.90 so it is not possible for hum to secure a CGPA of 3 for graduation.
The sum of 18 and twice a number use n to rep
Repesent unknown number
Answers
18+2n. For sure hope it helps
18+2n. Hope this helps!
3(q-7)=27 solve for q
Answers
Answer:
q =16
Step-by-step explanation:
q - 7 = 27/3
q = 9 + 7
q = 16
Best regards
First, divide both sides o the equation by 3.
q - 7 = 27 / 3
q - 7 = 9
Now, add 7 on both sides.
q = 16
What is 4/5 turned into a percent
Answers
Answer:80 %
Step-by-step explanation:
Answer:
80%
Step-by-step explanation:
4 divided by 5 is 0.8. 0.8 is 80%.
how do i answere this
Answers
Answer:
F. m/1.05=0.7/1.4
Step-by-step explanation:
The first expression is not true as the side labelled m in figure I corresponds to the side labelled 1.05 in figure II the side labelled but as for the the other set in the comparison i.e 0.7/1.4 it should start with the side that from figure I in the order in which they appear in the first ratio. The sides in the other ratios in the options correspond to each other and appear int the order in which the first ratio in each set appears
Brahim completed 18 free throws and missed 12.
Using experimental probability, how many free throws is he predicted to complete in the next 100 tries?
A.
6
B.
36
C.
48
D.
60
Answers
Most likely I would pick B
Answer:
The answer is D. 60
Step-by-step explanation:
Step 1: 18 + 12 = 30
18 = 60% of 30, therefor with this knowledge we know that 60% of a hundred, or 60 will be the answer.
(I also have proof, as I have done this quiz before.)
I hope my answer is correct.
[Please give brainliest!]
Have a good day,
-johannelbekian
simplify (3x-8)+(2x+5)-(4x-8)
Answers
Answer:
[tex]\large\boxed{(3x-8)+(2x+5)-(4x-8)=x+5}[/tex]
Step-by-step explanation:
[tex](3x-8)+(2x+5)-(4x-8)\\\\=3x-8+2x+5-4x-(-8)\\\\=3x-8+2x+5-4x+8\qquad\text{combine like terms}\\\\=(3x+2x-4x)+(-8+5+8)\\\\=x+5[/tex]
To simplify the expression (3x-8)+(2x+5)-(4x-8), distribute the negative sign, combine like terms, and simplify to x+5.
Explanation:To simplify the expression (3x-8)+(2x+5)-(4x-8), we need to combine like terms. Start by distributing the negative sign in front of the parentheses that contain (4x-8):
(3x-8)+(2x+5)-4x+8
Now, combine the like terms:
3x+2x-4x-8+5+8
Combine similar terms:
1x+5
So, the simplified expression is x+5.
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Mrs Cambell gave her algebra I students a list of teinomials to factor for homework. which of these can be factored into two binomials
a) x^2+3x+2
b) x^2+4x+5
c) x^2+5x+7
D) x^2+6x+10
Answers
Answer: option a.
Step-by-step explanation:
To factor a polynomial of degree 2, with the form [tex]ax^{2}+bx+c[/tex], you must find two number whose sum is a and whose product is c. Then:
a) [tex]x^2+3x+2\\(x+1)(x+2)[/tex]
(it can be factored into two binomials)
b) [tex]x^2+4x+5[/tex] cannot be factored into two binomials.
c) [tex]x^2+5x+7[/tex] cannot be factored into two binomials.
d) [tex]x^2+6x+10[/tex] cannot be factored into two binomials.
Therefore, the answer is the option a.
Your science teacher recently gave a quiz to 28 students present in class. The class average was an 82.5. Five students that were absent made up the quiz after schoolamd their scores were a 78, 89,92,,99, & 63. Find the new class average with the newscores
Answers
Total students in the class who got the quiz = 28
The average of the class average was = 82.5
Five students that were absent made up the quiz after school and their scores were a 78, 89,92,99, & 63.
The formula for an average= (sum of values) / (count of values)
As the average is given as 82.5 and there were 28 students, so sum of the 28 values will be = [tex]28\times82.5=2310[/tex]
Total students of the class = 28+5(absent) = 33
For 33 students the total score was = 2310 +(78+89+92+99+63)
= 2731
So, average for 33 students will be = [tex]\frac{2731}{33} =82.757[/tex] or 82.76
So, the new class average is 82.76
Will mark brainest! Please look at the image for the question! (:
Answers
what is the sum of the polynomials? (4x^5+3x^3-x-6)+(3x^3-9x-4)
Answers
Answer:
You only can to sum expressions with the same exponent, so:
Step-by-step explanation:
(4x^5+3x^3-x-6)+(3x^3-9x-4)
4x^5 + 6x^3 - 10x - 10Best regards
Answer:
4x^5+6x^3-10x-10
Step-by-step explanation:
you get rid of the parenthesis and combine like terms
a window in the shape of a parrallelogram has a base of 36 inches and a height of 45 inches. what is the area of the window
Answers
I think the answer is 1620 inches.
Because 36 times 45 is 1620
how so i
simplify and factor this expression
-8c - 17 - 2c - 3
Answers
Answer: -10c-20
Step-by-step explanation:
Equation: -8c - 17 - 2c - 3
First, you factor -8c+17+ -2c+ -3
Then, combine like terms: (-8c+ -2c)+(-17+ -3)
Answer: -10c - 20
Match the functions to their x-intercepts.
f(x) = log x – 1
f(x) = -(log x – 2)
f(x) = log(-x – 2)
f(x) = -log -(x – 1)
(0, 0)
arrowBoth
(-3, 0)
arrowBoth
(10, 0)
arrowBoth
(100, 0)
arrowBoth
Answers
Answer:
f(x) = log x – 1 ⇒ x-intercept = (10 , 0)
f(x) = -(log x – 2) ⇒ x-intercept = (100 , 0)
f(x) = log(-x – 2) ⇒ x-intercept = (-3 , 0)
f(x) = -log -(x – 1) ⇒ x-intercept = (0 , 0)
Step-by-step explanation:
* lets talk about the log
- If log a = b, that means the base of the log is 10
- To solve it we will change it to exponential function
∴ [tex]10^{b}=a[/tex]
* Now do that in each one of the problem
* ∵ f(x) = log x - 1
- To find the x-intercept put y = 0
∴ log x - 1 = 0 ⇒ add 1 to both sides
∴ log x = 1 ⇒ change it to exponential function
∴ [tex]10^{1}=x[/tex]
∴ x = 10
* The x-intercept = (10 , 0)
* ∵ f(x) = -(log x - 2)
- To find the x-intercept put y = 0
∴ -(log x - 2) = 0 ⇒ Multiply both sides by -1
∴ log x - 2 = 0 ⇒ add 2 to the both sides
∴ log x = 2 ⇒ change it to exponential function
∴ [tex]10^{2}=(x)[/tex]
∴ x = 100
* The x-intercept = (100 , 0)
* ∵ f(x) = log (-x - 2)
- To find the x-intercept put y = 0
∴ log (-x - 2) = 0 ⇒ change it to exponential function
∴ [tex]10^{0}=(-x-2)[/tex] ⇒ any number to the power of zero = 1 except 0
∴ -x - 2 = 1 ⇒ add 2 to the both sides
∴ -x = 3 ⇒ multiply both sides by -1
∴ x = -3
* The x-intercept = (-3 , 0)
* ∵ f(x) = -log -(x - 1)
- To find the x-intercept put y = 0
∴ -log -(x - 1) = 0 ⇒ multiply both sides by -1
∴ log -(x - 1) = 0 ⇒ change it to exponential function
∴ [tex]10^{0}=-(x-1)[/tex] ⇒ any number to the power of zero = 1 except 0
∴ -(x - 1) = 1 ⇒ multiply both sides by -1
∴ x - 1 = -1 ⇒ add 1 to both sides
∴ x = 0
* The x-intercept = (0 , 0)
Answer:
Please mark as Brainliest :)
Step-by-step explanation:
HELP ASAP! GIVING BRAINLIEST!!
Trapezoid RSTU is reflected over X and then over Z. What is the image of the rotation?
A) Trapezoid NOLM
B) Trapezoid BADC
C) Trapezoid RSTU
Answers
Answer:
A
Step-by-step explanation:
B C were already used in the graph
The answer is A) Trapezium NOLM. If you reflect RSTU over the X axis it produces the trapezium in the top left. Then flipping it over the Z axis is bottom right, NOLM.
What is the opposite of 0?
What is the opposite of opposite of -3?
What is the opposite of -9
Answers
Answer:
0
3
9
Step-by-step explanation:
0 has no opposite
-3 = 3
-9 = 9
3
9
40 POINTS AND BRAINLIEST IF FAST!!!!!!! Anwser the picture!!!!! Pls rn!!!!
Answers
Answer:
Length is your answer
Answer: The answer is COLOR
Step-by-step explanation:
Extensive means covering or affecting a large area and all other options are numerical values expect color. :)