Answers
sin(H) = GF/HF
sin(H) = 5/13
arcsin(sin(H)) = arcsin(5/13)
H = 22.61986 ... which is approximate
H = 23 degrees ... round to the nearest whole number
Answer is choice A
Related Questions
What is the sum of the first eight terms of a geometric series whose first term is 3 and whose common ratio is 1/2?
Answers
[tex]\bf S_8=3\left( \cfrac{1-\left( \frac{1}{2} \right)^8}{1-\frac{1}{2}} \right)\implies S_8=3\left( \cfrac{1-\frac{1^8}{2^8}}{1-\frac{1}{2}} \right) \\\\\\ S_8=3\left( \cfrac{1-\frac{1}{256}}{\frac{1}{2}} \right)\implies S_8=3\left( \cfrac{\frac{255}{256}}{\frac{1}{2}} \right)\implies S_8=3\left( \cfrac{255}{256}\cdot \cfrac{2}{1} \right) \\\\\\ S_8=3\left( \cfrac{255}{128} \right)\implies S_8=\cfrac{765}{128}[/tex]
The sum of the first eight terms of a geometric series whose first term is 3 and whose common ratio is 1/2 is 5.9765625
Sum of geometric seriesSeries are the sum of sequences. The sum of geometric series is expressed as:
Sn = a(1-r^n)/1-r
Given the following
n = 8
a = 3
r = 1/2
Substitute
S8 = 3(1-(1/2)^8)/0.5
S8 = 3(1-1/256)/0.5
S8 = 3(255/256)/0.5
S8 = 5.9765625
Hence the sum of the first eight terms of a geometric series whose first term is 3 and whose common ratio is 1/2 is 5.9765625
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Solve the inequality. Graph the solution set. 26+6b (>=) 2(3b+4 A. All real numbers b. b> or less than 1/2 c. no solutions
Answers
Mr. Chavez spent $199.99 for a new smart phone, 3
Answers
Mr. Chavez spent $299.97 altogether. The estimated total matches approximately with the calculated total, confirming the accuracy of our answer.
To find the total amount Mr. Chavez spent, we need to add the costs of the smartphone, carrying case, and accessories.
Total amount = |-199.99| + |-39.99| + |-59.99|
Now, let's evaluate each absolute value:
|-199.99| = 199.99
|-39.99| = 39.99
|-59.99| = 59.99
Now, let's add them together:
Total amount = 199.99 + 39.99 + 59.99
Total amount = 299.97
So, Mr. Chavez spent $299.97 altogether.
Now, let's check the answer using estimation:
Round each amount to the nearest ten:
- $199.99 is approximately $200.00
- $39.99 is approximately $40.00
- $59.99 is approximately $60.00
Now, let's add them together:
Total estimation = $200.00 + $40.00 + $60.00
Total estimation = $300.00
The estimated total matches closely with the calculated total, confirming the accuracy of our answer.
The complete question is:
Mr. Chavez spent $199.99 for a new smart phone,$39 .99 on a carrying case, and $59.99 on accessories. The expression |-199.99|+|-39.99|+|-59.99| represents the total amount that Mr. Chavez spent. How much did Mr. Chavez spend altogether? Check your answer using estimation.
Please Help!! Find the measure of angle 2. Image Attached
Answers
opposite angles have to equal 180
so 180-111 = 69
angle 2 is 69 degrees
Look at the figure. What is the next step in this construction of a line parallel to AC passing through point B.
A. use a protractor to measure ∠BAC
B. Draw a line through point B that intersects arc 2.
C. Measure the distance between AB and AC along arc 1 with a ruler.
D. Measure the distance between AB and AC along arc 1 with a compass.
Answers
Answer:
Option A is correct
Step-by-step explanation:
In the given figure to draw the parallel line to AC passing through B we have to tell the next step.
As lines AC and AB given and we know if lines are parallel then alternate angles are equal.
Hence, if line through B parallel to AC drawn then alternate angles ∠BAC and ∠ABD equal.
∴ To draw parallel lines our next step is to use a protractor to measure ∠BAC so that the same angle through B is drawn results in equal alternate interior angles.
Hence, Option A is correct.
PLEASE HELP ME FIGURE THIS OUT if i have 6 questions on a test, how many would i get wrong to get a score of 48%
Answers
now, how much is 52% of 6?
whatever% of anything is just (whatever/100) * anything.
thus 52% of 6 is just (52/100) * 6, that many.
Need help on 4.9.2 project: performance task: the subway stop
Answers
The subject of this question is Mathematics.
Explanation:The subject of this question is Mathematics.
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For what values of x is the rational expression below undefined?
Check all that apply.
x-4/3x^2-75
A. -3
B. -4
C. 3
D. -5
E. 4
F. 5
Answers
In order for the rational expression to be undefined, the denominator must be equal to 0.
Thus, set 3(x+5)9(x-5)=0
x=5 and -5
the perimeter of a trapezoid is 39a-7. Three sides have the following lengths: 9a, 5a-1, and 17a-6. What is the length of the fourth side
Answers
how would the expression x^3-3√(3) be rewritten using difference of cubes
Answers
(x^3/2 + 3^3/4)(x^3/2 - 3 ^3/4) or ((√x)³ + (⁴√3)³)((√x)³ - (⁴√3)³)
Answer:
[tex]x^{3}-(\sqrt{x} )^3[/tex]
Step-by-step explanation:
The given expression is x³ - 3√3
We have to rewrite the expression in the forem of difference of cubes.
x³ - 3√3 = x³ - √(3)³
= [tex]x^3-(3)^{\frac{3}{2}}[/tex]
= [tex]x^{3}-(\sqrt{x} )^3[/tex]
Therefore, we can rewrite the expression as
[tex]x^{3}-(\sqrt{x} )^3[/tex]
Joe and Mary each pay the same price for a T-shirt. Before they buy it, Mary has $\$ 2$ more than Joe. To buy the T-shirt, Joe spends $ \$1 $ less than $\frac{2}{5}$ of his money, and Mary spends $\frac{1}{3}$ of her money. What was the total amount of money Joe and Mary originally had altogether?
Answers
i) "Before they buy it, Mary has 2$ more than Joe":
means M=J+2
ii)
"To buy the T-shirt, Joe spends 1 $ less than \frac{2}{5} of his money"
so [tex]T= \frac{2}{5}J-1 [/tex]
iii)
"Mary spends \frac{1}{3} of her money"
means [tex]T= \frac{1}{3}M [/tex]
equalize equations ii) and iii):
[tex]\frac{2}{5}J-1= \frac{1}{3}M[/tex] (they are both equal to T)
substitute M=J+2 from equation i:
[tex]\frac{2}{5}J-1= \frac{1}{3}(J+2)[/tex]
[tex]\frac{2J-5}{5}= \frac{J+2}{3}[/tex]
[tex]3(2J-5)=5(J+2)[/tex]
6J-15=5J+10
J=25
so M=25+2=27 (dollars)
Together Mary and Joe had 27+25=52 (dollars)
Answer: 52 $
Answer:
52
Step-by-step explanation:
Suppose Joe had $J$ dollars to start with. Then Mary had $J + 2$ dollars. Since they both spent the same amount on their shirts, $\frac{2}{5} J - 1 = \frac{1}{3} (J + 2)$. Distributing, we get $\frac{2}{5} J - 1 = \frac{1}{3}J + \frac{2}{3}$. Isolating $J$ on the left side, $\frac{1}{15}J = \frac{5}{3}$. Therefore, $J = 25$. Thus, their original total amount of money was $J + (J + 2) = \boxed{52}$ dollars.
Thomas buys a cardboard sheet that is 8 by 12 inches. Let x be the side length of each cutout. Create an equation for the volume of the box, find the zeroes, and sketch the graph of the function.
Answers
Side of each cutout = x
Length of the base = 12 - x - x = 12 - 2x
width of the base = 8 - x - x = 8 - 2x
area of the base = (12 - 2x) (8 - 2x) = 12*8 - 12*2x - 8*2x + 4x^2 = 96 - 40x + 4x^2
height = x
Volume = (96 - 40x + 4x^2) x = 96x - 40x^2 + 4x^3
Equation of the volume of the box = 96x - 40x^2 + 4x^3
Zeros of the function: use the factored form:
x (12 - 2x) (8 -2x) = 0
=> x = 0, x = 6 and x = 4
Sketch of the graph:
The graph comes growing from (- infinity, -infinity), crosses the origin (0,0), grows until a local maximum before 2, starts to decrease, intercepts the x axis at x = 4, continues decreasing until a local minium before 6, starts to increase again, crosses the x axis at x = 6, and continues increasing toward infinity. If you are using derivatives, you can find the local minimum and maximum.
Answer:
Step-by-step explanation:
Any equation that is equivalent to V = x(12 - 2x)(8 - 2x) is accepted. Any graph that is similar to the graph of the function is accepted.
Sample Student Response:
The box is a cube, so the volume is the length × width × height. The height is the side length of the cardboard, which is x.
The length is the original length minus two side lengths of the cutout, so the length is 12 - 2x.
Similarly, the width is the original width minus two side lengths of the cutout, so the width is 8 - 2x.
Give the number of significant figures in this number 34.20
Answers
1. All nonzero numbers are significant.
2. All zeros between nonzero numbers are significant.
3. All zeros after the decimal point are significant.
Following the rules, I think all of the numbers in 34.20 are significant. Thus, there are a total of 4 significant figures.
Use the drop-down menus to complete each statement to show why √21 is between 4 and 5.
Answers
Answer:
To show: [tex]\sqrt{21}[/tex] is between 4 and 5
We know:
21 is lies between two consecutive integer i.e, 16 and 25
We can write this as:
[tex]16 < 21 < 25[/tex]
or
[tex]\sqrt{16} <\sqrt{21}<\sqrt{25}[/tex]
Simplify:
[tex]4 < \sqrt{21} < 5[/tex]
⇒[tex]\sqrt{21}[/tex] lies between 4 and 5.
Therefore, [tex]\sqrt{21}[/tex] is between [tex]\sqrt{16}[/tex] and [tex]\sqrt{25}[/tex] this means [tex]\sqrt{21}[/tex] lies between 4 and 5.
Answer:
We know that
[tex]16<21<25[/tex]
Because, 16 is less than 21 and 25 is more than 21.
Now, if we apply a square root to each part, we would have
[tex]\sqrt{16} < \sqrt{21}<\sqrt{25}[/tex]
Then, we solve each square root, except the square root of 21, because it doesn't have an exact result
[tex]4<\sqrt{21}<5[/tex], because [tex]\sqrt{16}=4[/tex] and [tex]\sqrt{25}=5[/tex]
So, basically, the reason why [tex]\sqrt{21}[/tex] is between 4 and 5 is beacuse 21 is between 16 and 25. Then, when you apply square roots to each part, you would find that the square root of 21 is between 4 and 5. That's the reason, the position.
For her phone service, Kala pays a monthly fee of $13 , and she pays an additional $0.05 per minute of use. The least she has been charged in a month is $63.15 . What are the possible numbers of minutes she has used her phone in a month? Use m for the number of minutes, and solve your inequality for m .
Answers
0.05m >= 50.15
m >= 1003 minutes
Therefore at least 1003 minutes were consumed to be billed $63.15 or more.
Hope this helps.
Amal had 12 stuffed animals and gave 3 over 4 of them to charity. Maria had 6 stuffed animals and gave 1 third to charity Who had the most stuffed animals left?
Answers
So, 12-9=3
&
1/3 of 6 = 2
So, 6-2=4
3<4
Maria has the most stuffed animals left
Amal gave away 3/4, meaning that he had 1/4 left.
Maria gave away 1/3, meaning she had 2/3 left.
Amal: (12)(1/4)=3 stuffed animals left
Maria: (6)(2/3)=4 stuffed animals left
Answer: Maria had the most stuffed animals left.
Write the standard equation for the circle center (10,-6), r=6
Answers
Therefore, since the center is (10,-6), h=10 and k=-6. The radius is 6 which means r=6.
Substitute these values into the standard form equation.
(x-(10))²+(y-(-6))²=(6)²
(x-10)²+(y+6)²=36
Therefore, the standard equation for the circle centered at (10,-6) where r=6 is (x-10)²+(y+6)²=36.
Does anyone know how to make these statements false with a counterexample? 1) The reciprocal of each natural number is a natural number. 2) The opposite of each whole number is a whole number. 3) There is no integer that has a reciprocal that is an integer.
Answers
Answer the word problem:
Taylor and Blair are driving away from each other in opposite directions. If Blairs speed is 70mph and Taylors speed is 80mph, how many hours will it be before the two are 225 miles apart?
Answers
It will take 1.5 hours (or 1 hour and 30 minutes) before Taylor and Blair are 225 miles apart.
To find out how many hours it will be before Taylor and Blair are 225 miles apart, we can set up an equation based on the distance they travel.
Since they are driving away from each other in opposite directions, their distances add up to the total distance they will be apart.
Let t be the number of hours it takes for them to be 225 miles apart.
Distance traveled by Blair = Blair's speed * time (d = r * t)
Distance traveled by Taylor = Taylor's speed * time (d = r * t)
The total distance they will be apart is 225 miles:
Blair's distance + Taylor's distance = 225 miles
(70 mph * t) + (80 mph * t) = 225 miles
Now, solve for t:
70t + 80t = 225
150t = 225
t = 225 / 150
t = 1.5
So, it will take 1.5 hours (or 1 hour and 30 minutes) before Taylor and Blair are 225 miles apart.
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If the average price of four pairs of shoes is $50, and three of those pairs of shoes are priced at $35, $40 and $55, what is the price of the fourth pair of shoes?
Answers
average price= price1+price2+...priceN/N
In our case , we have four pairs of shoes.So, N=4.
We also know the average price. average price=$50
We also know the price of the first pair of shoes (price1), of the second (price2) and the third (price3). We need to find out Price4:
$50=$35+$40+$55+Price4/4
50*4=$35+$40+$55+Price4
$200=$130+Price4
Price4=200-130
Price4=$70
WILL GIVE A BRAINLIEST IF YOURE RIGHT PLEASE HELP ASAP!!
Find the greatest possible error for each measurement.
18.9 m
a.
0.01 m
b.
0.5 m
c.
9.45 m
d.
0.05 m
Answers
the greatest possible error for meters is 1/2 the increments
since 18.9 is to the tenths place
1/2 x 1/10 = 0.05
so greatest possible error for 18.9 is 0.05m
A blue billiard ball with mass m crashes into a red billiard ball with the same mass that is at rest. The collision results in the blue billiard ball traveling with a velocity of v and the red billiard ball travelling with a velocity of 3v. In terms of v and m, determine the blue billiard ball’s velocity before the collision...
Answers
Each ball has mass = m.
The initial velocity of the blue ball = u.
The initial velocity of the red ball = 0.
Initial total momentum is
P1 = m*u + m*0 = mu
Final momentum is
P2 = mv + 3mv = 4mv
Because momentum is conserved,
mu = 4mv
u = 4v
Answer:
The velocity of the blue ball before the collision is 4v.
This chart shows the total average monthly cost of medical insurance benefits for employees working in the private sector in march 2006. for single coverage, the cost is $322.77, and for family coverage, it is $889.26. if an employee makes $10 per hour (after withholdings) and has to pay the full cost of single coverage medical insurance, about how many hours will he or she have to work each month simply to pay for the cost of the medical insurance
Answers
Final answer:
the employee would need to work approximately 32.3 hours per month to pay for their health insurance.
Explanation:
The student has inquired about the number of hours they would need to work each month to pay for the cost of single coverage medical insurance.
Given that the insurance costs $322.77 per month and the employee earns $10 per hour, we can find the number of hours required by dividing the total cost of the insurance by the hourly wage.
To calculate:
Hours required = Total cost of insurance ÷ Hourly wage
Hours required = $322.77 ÷ $10 = 32.277
Therefore, the employee would need to work approximately 32.3 hours per month (rounding to the nearest tenth of an hour) to pay for their health insurance.
Jones is the chairman of a committee. in how many ways can a committee of 5 be chosen from 10 people given that jones must be one of them?
Answers
So your equation is
1(Jones) • 9( possibilities left) •8( possibilities left)• 7( possibilities left)• 6( possibilities left)
Or
1 • 9 • 8 • 7 • 6
=
3,024 possible ways in which a committee of 5 can be chosen from 20 people given that Jones must be one of them.
Final answer:
A committee of 5 can be chosen in 126 different ways from 10 people if Jones must be one of them, by using the combination formula C(9, 4) to choose the remaining four committee members from the other nine people.
Explanation:
To determine in how many ways a committee of 5 can be chosen from 10 people given that Jones must be one of them, we need to apply the concept of combinations in probability and combinatorics. Since Jones must be on the committee, we are actually choosing the remaining 4 members from the remaining 9 people.
The number of ways to choose 4 people out of 9 is calculated using the combination formula, which is:
C(n, k) = n! / (k!(n - k)!), where n is the total number of items, k is the number of items to choose, and '!' denotes factorial.
Applying this to our scenario:
C(9, 4) = 9! / (4! * (9 - 4)!) = 126
Therefore, there are 126 different ways to form the committee if Jones is already chosen as one member.
A principal of $2600 is invested at 7.5% interest, compounded annually. How much will the investment be worth after 8 years?
Answers
HELP! What is the volume of the regular pyramid below????
Answers
hope this helped!
Justin is evaluating the expression 12.5 + 3.8x, when x is 7.9
Answers
Answer:
Justin should have Multiplied 3.8 and 7.9 first
Step-by-step explanation:
Because all these people that have the wrong answer got me mad
Justin should have multiplied 3.8 and 7.9 first. Therefore, option C is the correct answer.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
The given expression is 12.5 + 3.8x.
When x=7.9 in the given expression, we get
12.5+3.8(7.9)
= 12.5+30.02
= 42.52
Justin should have multiplied 3.8 and 7.9 first. Therefore, option C is the correct answer.
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"Your question is incomplete, probably the complete question/missing part is:"
Justin is evaluating the expression 12.5 + 3.8x, when x is 7.9.
12.5+3.8(7.9)
16.3(7.9)
128.77
What was Justin's error?
1) Justin should have multiplied 12.5 and 7.9 first.
2) Justin should have added 12.5 and 7.9 first.
3) Justin should have multiplied 3.8 and 7.9 first.
4) Justin should have added 3.8 and 7.9 first.
Give an example of a compound inequality that has no solution
Answers
There is no value of c that is greater than -3 AND less that -8
An example of a compound inequality that has no solution:
x >5 and x < -4.
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
What is Number Line?In math, a number line can be defined as a straight line with numbers arranged at equal segments or intervals throughout. A number line is typically shown horizontally and can be extended indefinitely in any direction.
|____|____|____|____|____|____|____|____|____|____|
-5 -4 -3 -2 -1 0 1 2 3 4 5
Here is an example of a compound inequality that has no solution:
x >5 and x < -4.
x may be both higher than 5 and less than -4.
Here it is not possible that x can be both lower than -4 and larger than 5.
Hence, these inequalities have no solution.
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In triangle KLM LM = 7 and angle k equals 45 Find KL.
Answers
In this problem, the student can use the properties of a 45°-45°-90° triangle to determine that the hypotenuse KL is 7 * √2 which is approximately equal to 9.9.
Explanation:In a triangle where you know one angle (45°) and one side (7 units) across from the right angle, it is a typical example of a situation where trigonometry can be used. In this case, you're dealing with a 45°-45°-90° triangle, also known as an isosceles right triangle. In such a triangle, the sides are in a specific ratio. The sides opposite the 45° angles are the same length (let's call it 'a'), and the hypotenuse is a√2.
Given that LM = 7 and angle K is 45°, triangle KLM is therefore an isosceles right triangle and KL (the hypotenuse) is equal to LM multiplied by √2. So, KL = 7 * √2 which approximately equals to 9.9.
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what is the length of the side of a square if the apothem is 7
Answers
[tex]tan45= \frac{7}{x} [/tex]
[tex]x*tan45=7[/tex]
[tex]x= \frac{7}{tan45} [/tex]
and x=7. Now remember that that is only half the base of the whole triangle so the base is 7*2 which is 14. 14 is the length of one side of the square. Well, actually 14 is the length of every side of the square right?