The equation that can be used to find the measure of angle GFE is given by: Option B: cos−1(11.9/14.5) = θ
What are the six trigonometric ratios?Trigonometric ratios for a right angled triangle are from the perspective of a particular non-right angle.
In a right angled triangle, two such angles are there which are not right angled(not of 90 degrees).
The slant side is called hypotenuse.
From the considered angle, the side opposite to it is called perpendicular, and the remaining side will be called base.
From that angle (suppose its measure is θ),
[tex]\sin(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of Hypotenuse}}\\\cos(\theta) = \dfrac{\text{Length of Base }}{\text{Length of Hypotenuse}}\\\\\tan(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of base}}\\\\\cot(\theta) = \dfrac{\text{Length of base}}{\text{Length of perpendicular}}\\\\\sec(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of base}}\\\\\csc(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of perpendicular}}\\[/tex]
The missing information, not present in this question are:
Length of FG = |FG| = 14.5Length of FE = |FE| = 11.9Angle ∠GFE = θSince for the triangle GFE, if we look from the angle ∠GFE, the sides given are hypotenuse FG and the base FE.
Thus, we can use cosine ratio, and then its inverse to find the value of angle θ.
Thus, we get:
[tex]\cos(\theta) = \dfrac{|FE|}{|FG|} = \dfrac{11.9}{14.5} \\\\\theta = \cos^{-1}\left(\dfrac{11.9}{14.5}\right)\\\\[/tex]
Thus, the equation that can be used to find the measure of angle GFE is given by: Option B: cos−1(11.9/14.5) = θ
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Answer:
option B
Step-by-step explanation:
Charlene has a monthly salary of $3,410. with her present budget, charlene has a net income that is 7% of her monthly salary. charlene is going to reduce her net income by $125 each month and put this money towards paying down her debt. what will charlene’s new net income be? a. $113.70 b. $176.70 c. $229.95 d. $238.70
Charlene has a monthly salary of $3,410. with her present budget, the corrected net income is $113.70
What is income tax?Income tax is a tax applied on individuals or entities concerning income or profit earned by them.
Charlene has a monthly salary = $3,410.
Charlene has a net income that is 7% of her monthly salary.
The computation of the new net income is shown below
= Monthly salary × net income percentage - reduced amount of net income per month
= $3,410 × 7% - $125
= $113.70
Hence, the corrected net income is $113.70
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A group of hikers buys 8 bags of mixed nuts. Each bag contains 3 and 1/2 cups of mixed nuts. the mixed nuts are shared evenly among 12 hikers. How many cups of mixed nuts will each hiker receive? Explain your answer
Answer:
2 1/3 cups for each hiker
Step-by-step explanation:
8bags x 3.5 cups in each bag =28 cups in total
28 cups shared among 12 hikers = 28/12 = 2 1/3 cups for each hiker
Please help me
What evidence does the article provide to support one claim in favor of adding expanded learning time?
A: Andover school are already top performers in state.
B: Funding for longer school days in only guaranteed for one year.
C: Some are convinced that ELT will encourage positive parent involvement.
D: More time is needed for current academic lessons and special projects.
Answer:
D
Step-by-step explanation:
More time is needed for current academic lessons and special projects.
What is the missing angle?
3x + 27 =180
-27
3x = 153
÷3
x = 51
a=142
(vertically opposite angles are equal)
Reflex angles adds up to 360
360 - (142x2) = 76
76/2 = 38
t & c = 38
Hope this helps!
Answer:
Here you go :) if you need anything tell me!
A rectangular prism has a volume of 120 cubic inches. The length of the prism is 5 inches, the width iS (x-2) inches, and the height is (x+3) inches. What are the width and height of the prism?
A
width: 6 in., height: 4 in.
B
width: 8 in., height: 3 in.
width:
in. height: 6 in.
D
width: 3 in., height: 8 in.
d
1+1 =
9+10 =
6+9 =
4+20 =
Apple + Orange =
Trick questions!!!
If you invest $8,600 at a 3.95% simple annual interest rate, approximately how long will it take for you to have a total of $21,000? a. 25.3 years b. 36.5 years c. 45.9 years d. 60.7 years
The time taken to have a total of $21,000 is 36.5 years.
To calculate the time it takes to reach $21,000 with a simple annual interest rate, we can use the formula for simple interest:
Interest = Principal × Rate × Time
Where:
Interest is the additional amount earned on the initial investment (in this case, the difference between $21,000 and $8,600),
Principal is the initial investment ($8,600),
Rate is the annual interest rate (3.95% expressed as 0.0395),
and Time is the unknown variable we want to find.
We can rearrange the formula to solve for Time:
Time = Interest / (Principal × Rate)
Let's plug in the values:
Interest = $21,000 - $8,600 = $12,400
Principal = $8,600
Rate = 0.0395
Time = $12,400 / ($8,600 × 0.0395) ≈ 36.5
So, it will take approximately 36.5 years to have a total of $21,000.
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What is -20sin(theta)-10=0
Answer:
~ 3.473
Step-by-step explanation:
Assuming that theta means the middle angle at the origin, you are simply finding the sine of -10, and then multiplying it by -20. Using a scientific calculator, sin -10 comes out to about -0.174. Multiplying this by -20 gives us about 3.473.
Hope this helps!
Elaine has 14 3/4 cups of flour. She divides the flour into equal portions of 2 7/8 cups. Which is the best estimate for the number of portions she can make?
A) 3
B) 5
C) 7
D) 15
[tex]\huge\fcolorbox{blue}{aqua}{Answer:}[/tex]
════════════════════
Elaine has 14 3/4 cups of flour. She divides the flour into equal portions of 2 7/8 cups. Which is the best estimate for the number of portions she can make?
Answer: [tex]= 5[/tex]
Solution:
[tex]14 \frac { 3 } { 4 } \div 2 \frac { 7 } { 8 } =[/tex]
[tex]\frac{\left(14\times 4+3\right)\times 8}{4\left(2\times 8+7\right)} [/tex]
[tex]\frac{2\left(3+4\times 14\right)}{7+2\times 8} [/tex]
[tex]\frac{2\left(3+56\right)}{7+2\times 8} [/tex]
[tex]\frac{2\times 59}{7+2\times 8} [/tex]
[tex]\frac{118}{7+2\times 8} [/tex]
[tex]\frac{118}{7+16} [/tex]
[tex]\frac{118}{23} [/tex]
=[tex]5 [/tex]
I evaluated it so the answer is= Letter B.[tex]5 [/tex]
════════════════════
Explanation:
#Carry on learning
Dahlia runs a fruit store. She started Monday with 22 cherries in stock. During the day, she sold 19 cherries and got a shipment of fresh cherries. The shipment contained 3 times as many cherries as she started the day with. How many cherries does Dahlia have in stock at the end of the day?
The amount of cherrries that Dahlia has in stock at the end of the day is 69.
How many cherries does Dahlia have in stock at the end of the day?The first step is to determine the number of cherries that were remaining after 19 were sold.
Cherries remaining = 22 - 19 = 3
Number of cherries in the shipment == 22 x 3 = 66
Total number of cherries at the end of the day = 66 + 3 = 69
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Kassie and Luke timed each other during swimming practice. The speed at which swims is represented by the equation d = 1. 22t, where d is the number of meters she swims in t seconds. The speed at which Luke swims is represented in the table.
This means that a graph of Kassie speed given by the function d = 1.22t would have a slope of 1.22 m/s.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let d represent the number of meters she swims in t seconds. Hence:
d = 1.22t
This means that a graph of Kassie speed would have a slope of 1.22 m/s.
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HELP ASAP I REALLY NEED IT MY HEAD HURT BECAUSE OF THIS PLS WOULD GIVE 30pts If Jim spins the spinner 16 times, how many times would you predict the spinner to land on blue based on theoretical probability? Show your work in the box below the image.
Answer:
4
Step-by-step explanation:
Hey there!
To figure this out you need to calculate 4/16
that is 1/4
which is the size of one of the 1/4 circles
1/4 is equal to 4/16 which means the answer is 4
The function f(t) = -16t2 + 64t + 5 models the height of a ball that was hit into the
air, where t is measured in seconds and h is the height in feet.
This table represents the height, g(t), of a second ball that was thrown into the air.
Time,
(in seconds)
0
Height, g(t)
(in feet)
4
1
2
36
36
4
3
Which statement BEST compares the length of time each ball is in the air?
The ball represented by f(t) is in the air for about 4 seconds, and the ball
represented by g(t) is in the air for about 3 seconds.
The ball represented by f(t) is in the air for about 5 seconds, and the ball
represented by g(t) is in the air for about 3 seconds.
The ball represented by f(t) is in the air for about 3 seconds, and the ball
represented by g(t) is in the air for about 5 seconds.
The ball represented by f(t) is in the air for about 3 seconds, and the ball
represented by g(t) is in the air for about 4 seconds.
The best statement that compares the length of time each ball is in the air is seen in the second option.
What is the function of a quadratic equation?A quadratic function follows the condition: f(x) = ax² + bx + c. Here (a, b, and c) are real numbers and a ≠ 0.
From the given information:
The function f(t) = -16t² +64t + 5 models the height of a ballWhere;
time (t) ⇒ secondsheight (h) ⇒ feetThe table given is as follows:
Time (in seconds) height, g(t) in feet
0 4
1 36
2 36
3 4
From the table, when t = 0, the function becomes:
f(t) = -16t² +64t + 5
f(t) = -16(0)² + 64(0) + 5
f(t) = 5
Therefore, we can conclude that the best statement that compares the ball is: f(t) is in the air for about 5 seconds, and the ball represented by g(t) is in the air for about 3 seconds.
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Agrocery store sells steak for $4.85 per pound.
What would be the cost of 23 pounds of steak?
$11.64
0 $7.46
0 $12.61
0 $23.58
Answer:
the answer is 12.61 so that means it's c
1
(2 × 105) + (5 × 104)
4.52+10.82
4
Answer:
a) 5.85
b) 0.0004
Step-by-step explanation:
[tex]a) \: \: \sqrt{ \frac{ {4.5}^{2} + {10.8}^{2} }{4} } \\ \\ = \sqrt{ \frac{ 20.25 + 116.64 }{4} } \\ \\ = \sqrt{ \frac{136.89}{4} } \\ \\ = \sqrt{34.2225} \\ \\ = 5.85 \\ \\ b) \: \: \frac{1}{(2 \times {10}^{5} ) + (5 \times {10}^{4}) } \\ \\ = \frac{1}{(20\times {10}^{4} ) + (5 \times {10}^{4}) } \\ \\ = \frac{1}{(20 + 5) \times {10}^{4} } \\ \\ = \frac{1}{25 \times {10}^{4} } \\ \\ = 0.04 \times {10}^{ - 4} \\ \\ = 0.0004[/tex]
HELP NEEDED RIGHT NOW/ASAP. PLS NO LINKS AND NO JOCKING.
AND PLS SHOW UR WORK (STEP BY STEP)
IMPROPER (LINKS AND JOCKING)/ INAPPROPRIATE ANSWERS WILL BE REPORTED
THANKS 4 THE HELP AND HAVE GREAT WEEKEND
THE ANSWER IS D
By using properties for exponents, we will see that the equivalent expression is:
[tex]2x^{-4}y^6[/tex]
Which is the equivalent expression?Here you need to remember the property:
[tex]a^n/a^m = a^{n - m}[/tex]
We have the expression:
[tex]\frac{-4x^{-3}y^4}{-2xy^{-2}}[/tex]
We can separate the fraction to:
[tex]\frac{-4x^{-3}y^4}{-2xy^{-2}} = \frac{-4}{-2}*\frac{x^{-3}}{x} *\frac{y^4}{y^{-2}}[/tex]
Now we can simplify by using the above relation, we will get:
[tex]\frac{-4x^{-3}y^4}{-2xy^{-2}} = \frac{-4}{-2}*\frac{x^{-3}}{x} *\frac{y^4}{y^{-2}} = 2*x^{-3-1}*y^{4 - (2)} = 2*x^{-4}*y^6[/tex]
So the correct option is the last one.
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[tex]\\ \rm\Rrightarrow (-4x^{-3}y^4)\div(-2xy^{-2})[/tex]
a^m÷a^n=a^m-n[tex]\\ \rm\Rrightarrow 2x^{-3-1}y^{4+2}[/tex]
[tex]\\ \rm\Rrightarrow 2x^{-4}y^6[/tex]
Option D
if x= -1 and y=2 is the solution of the simultaneous equations,
ax-by= 1
ay+bx= - 7
find the value of a and b with the proper steps
Answer:
a = -3, b = 1
Step-by-step explanation:
1. Plug in the given values into the equations:
a(-1) - b(2) = 1
a(2) + b(-1) = -7
2. Isolate a in the first equation:
a(-1) - b(2) = 1 = a · -1 - b · 2 = 1
-a - 2b = 1
-a -2b+2b = 1+2b
-a = 1 + 2b
[tex]\frac{-a}{-1} =\frac{1}{-1} +\frac{2b}{-1}[/tex]
a = -1 - 2b
3. Substitute "a = -1 - 2b" in for a in the second equation:
(-1 - 2b)2 + b(-1) = -7
4. Simplify:
-2 - 4b + b(-1) = -7
-2 - 4b -b = -7
-2 -5b = -7
5. Isolate for b:
-2+2 - 5b = -7+2
-5b = -5
[tex]\frac{-5b}{-5} =\frac{-5}{-5}[/tex]
b = 1
6. Substitute the b value into an equation to solve for a:
a = -1 -2 · 1
a = -3 · 1
a = -3
hope this helps!
25 points
You are shopping and see an item that is normally priced for $950 on sale for 20% off. However, you have a coupon for an additional 30% off. (The cashier will apply your coupon to the sale price, not the normal price.)
What is the final cost of the time (before sales tax) after the sale and coupon discounts?
Answer:
The final cost before sales tax is $475.
Step-by-step explanation:
you add the 30% to the 20% and that equals 50% off. Which is half off so you have to divide $950 by 2. That equals $475. Easy :)
Which property of addition is shown in the equation below? a bi 0 0i = a bi commutative property inverse property identity property associative property
The property of addition that is shown in the equation (a+bi)+(0+0i)=(a+bi) is the identity property of addition.
What is the Identity property of addition?The identity property of addition states that when any number and 0 are added, the result will be the number itself.
The property of addition that is shown in the equation [tex](a+bi)+(0+0i)=(a+bi)[/tex] is the identity property of addition.
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Answer:
C Identity property
Step-by-step explanation:
Edge 2022
I need help with this maths question
Answer:
7,986
Step-by-step explanation:
Picture that shows steps and how to do it with formula!!
Hope this helped!!!
~ Kaitlyn
Point W is located at (-2,3) on a coordinate plane. Point W is reflected over the x-axis to create Point W. Point W is then reflected over the y-axis to create point W. What ordered pair describes the location of point W?
Answer: W is now at (2,-3)
Step-by-step explanation: flip by the x-axis to turn (-2,3) to (-2,-3) then flip it on the y-axis to turn (-2,-3) to (2,-3).
Q17.
Jim wants to buy 10 rolls of wallpaper
He sees these prices.
Wallpaper
Single roll £12. 50
Pack of 3 rolls
£34. 50
Pack of 5 rolls
€58. 75
What is the cheapest price for 10 rolls?
with a length of 24 inches, a width of 12 inches, and a height of 16 inches, what is the volume?
Answer:
The volume is 4,608.
Step-by-step explanation:
To solve for volume, multiply the length (l), width (w), and height (h) values together. So, 24 * 12 * 16 = 4,608. Therefore, the volume is 4,608. Good luck!
What is the value of this expression?
27+4×(8−4)
Answer:
43
Step-by-step explanation:
First, you have to find the value inside the parentheses. That would be 8-4, which is 4.
Now, use the rule of Pedmas, or Bedmas, whatever you prefer. That is Parentheses, exponents, multiplication, addition, subtraction. So, now you have the equation:
27 + 4 x 4.
You would multiply before addition, as shown above, so you would get:
27 + 16
which would equal:
43.
I need helpppppp please
Answer:
7/8
Step-by-step explanation:
7/8 is a larger fraction than 4/5, so the decimal must be larger. You can check this using a calculator, and dividing the numbers.
Answer:
C. 0.625
Step-by-step explanation:
You want to know if the given decimals are correctly written as the given fractions.
Decimal equivalentIt is generally easier to find the decimal equivalent of a fraction, but some calculators can go the other way, as well.
The decimal 0.625 corresponds to the fraction 5/8, not 7/8.
0.625 was converted incorrectly.
__
Additional comment
You can factor out 125 from numerator and denominator of the fraction equivalent of 0.625:
[tex]0.625=\dfrac{625}{1000}=\dfrac{5(125)}{8(125)}=\dfrac{5}{8}[/tex]
<95141404393>
Can someone help me on this answer
10p
hope it really helps...!!!
Answer:
10p
Step-by-step explanation:
3 +7 =10
p+p=p
3p+7p=10p
Help pls ………:.::::::::::…………
On the number line 0/2 1/2 2/2 3/2 4/2 5/2 6/2 7/2 8/2 what fraction on this number line is equal to one
Answer:
2/2
Step-by-step explanation:
all the number are either improper or mixed number etc.
2/2= 1
and u wanted to know which equals one and that is 2/2 because it is 1 whole.
4t- 2=14 what is t
Could you please show your work
Answer:
t=4
Step-by-step explanation:
Let's solve your equation step-by-step.
4t−2=14
Step 1: Add 2 to both sides.
4t−2+2=14+2
4t=16
Step 2: Divide both sides by 4.
4t
4
=
16
4
t=4
Answer:
t=4
Which figure below is a translation of this diagram?