The value of angle θ will be 16 degrees. Then the correct option is D.
What is the solution of the equation?The solution of the equation means the value of the unknown or variable.
The equation is given below.
24² + 25² – 2(24)(25) cos θ = 7²
Then the value of angle θ will be
24² + 25² – 2(24)(25) cos θ = 7²
576 + 625 – 1200 cos θ = 49
1200 cos θ = 1152
cos θ = 1152 / 1200
θ = cos⁻¹ (1152 / 1200)
θ = 16°
Then the correct option is D.
More about the solution of the equation link is given below.
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write an equation for the nth term of the geometric sequence 5, 10, 20, 40
Final answer:
The nth term of the geometric sequence 5, 10, 20, 40 is given by the formula T_n = 5 × 2ⁿ⁻¹.
Explanation:
To write an equation for the nth term of the geometric sequence 5, 10, 20, 40, we need to determine the first term (a) and the common ratio (r). In this sequence, the first term a=5 and the common ratio r can be found by dividing the second term by the first term (r=10/5=2).
The formula for the nth term (Tn) of a geometric sequence is given by Tn = a × rⁿ⁻¹.
So, for the given sequence, the nth term can be expressed as:
Tn = 5 × 2ⁿ⁻¹.
What is the missing numerator?
2/7 = n/21
A. 3
B. 5
C. 6
D. 8
Answer:
C. 6
Step-by-step explanation:
2 n
-------- = -------------
7 21
We can use cross products to solve this.
2 * 21 = 7 * n
42 = 7n
Divide each side by 7
42/7 = 7n/7
6 =n
The original sale price of an item at markdowns is $110.95. You have an additional 20% off coupon for markdowns for purchases totaling $90.00 or more. Using the coupon, how much more do save when compared to the original sale price?
Answer:
$22.19
Step-by-step explanation:
20% off the original price = $110.95 - (20% x $110.95)
20% x $110.95 = $22.19
$110.95 - $22.19 = $88.76
difference = $110.95 - $88.76 = $22.19
Answer:
You will save $22.19 when compared to the original sale price.
Step-by-step explanation:
The original sale price of an item at markdowns is $110.95.
You have an additional 20% off coupon for markdowns for purchases totaling $90.00 or more.
So, this becomes:
[tex]0.20\times110.95=22.19[/tex] dollars
Hence, you will save $22.19 when compared to the original sale price.
a vehicle with power steering makes a hissing or whirring sound when the wheel is turned all the way to the stops. Technician A says that this is a normal condition. Technician B says a loud squealing noise during sharp turns may be caused by worn ball joints. who is correct?
Answer:
Technician B only
Step-by-step explanation:
Clunking Noises From the Front Suspension. One of the most common symptoms of a problem with suspension ball joints is clunking noises coming from the vehicle's front suspension. ... Usually, the clunking will get continuously louder as the ball joints wear out, or until they eventually completely fail and break.
Final answer:
Technician B is correct. A loud squealing noise during sharp turns may be caused by worn ball joints and indicates a potential issue with the suspension system.
Explanation:
Technician B is correct. A loud squealing noise during sharp turns can indeed be caused by worn ball joints. This indicates a potential issue with the suspension system which includes components like ball joints. On the other hand, a hissing or whirring sound when the wheel is turned all the way to the stops in a vehicle with power steering is not typically considered a normal condition.
can anyone help me graph these problems??? thank you so much :)
please tell me the points to put on the graphs
f(x) = -0.5x + 3
f(x) = -1/2x - 5
f(x) = 3/4x + 2
Answer:
1 = - 1/5
2= - 1/7
3= 3/6
Step-by-step explanation:
the step by step instructions are on the pic. but simply...
go the the full number then count from there. for example:
#2 - you go down 5 then since it says negative u go over 1 to the left then 2 down.
Jackson is buying a good chain that had an original price of $795 but is advertised as 65% off. Sales tax of 8.50% is applied tot he discounted price. How much will Jackson pay for the chain ?
To find out how much Jackson will pay for the gold chain, you calculate the discount price by subtracting 65% of the original price from the original price, then apply an 8.50% sales tax to the discounted price, and add it to the discounted price to get the total cost. Jackson will pay a total of $301.90 for the gold chain.
Jackson is planning to buy a gold chain with an original price of $795 which is advertised at a 65% discount. The formula to calculate the discount price is:
Discount Price = Original Price - (Discount percentage x Original Price)First, we convert 65% to a decimal, which is 0.65:
Discount Price = $795 - ($795 x 0.65)Then, calculate the discount:
Discount Price = $795 - ($516.75)So after the discount, the price becomes:
Discount Price = $278.25On this discounted price, a sales tax of 8.50% is applied. Converting that to decimal will be 0.085 and now we multiply it with the discounted price:
Sales Tax Amount = 0.085 x $278.25Now, find the amount of sales tax:
Sales Tax Amount = $23.65125Round the sales tax to the nearest cent:
Sales Tax Amount = $23.65Finally, add the original discount price and the sales tax:
Total Price = Discount Price + Sales Tax AmountTotal Price:
Total Price = $278.25 + $23.65 = $301.90Jackson will pay $301.90 in total for the gold chain after applying the discount and sales tax.
is the following a function?
Answer:
No
Step-by-step explanation:
For this to be a function there must be only 1 value of y ( range) for any given value of x in the domain.
This is not the case here as
x = - 1 → y = - 2 and x = 6 → y = - 2
Therefore the relation is not a function
What is the square root of -15
Answer:
you cannot do a square root of a negative number so there is no answer.
Step-by-step explanation:
Morgan scored 42 points in 3 games. How many points did she make per game?
Answer:
14 points per game
Step-by-step explanation:
We want to know the number of point per game, so we will take the number of points and divide by the number of games
42 points/ 3 games
14 points per game
A graph of a trapezoid can have diagonals with slopes that are negative reciprocals and two pairs of adjacent sides that are congruent. True or False Explain your reasoning.
Answer: False
Explanation: What this statement describes is not a trapezoid, but rather a kite. A kite is a quadrilateral with two sides that are next to each other (ie adjacent) that are congruent. This is the result of combining two congruent triangles together. The diagonals of any kite are perpendicular, which is another way of saying "the diagonals have slope that are negative reciprocals".
If you had adjacent sides congruent, and a pair of parallel opposite sides, then the other two opposite sides must be parallel as well, but this would make the figure a parallelogram and not a trapezoid. This is another way to see why the answer is false.
Check out the attached image for an example.
3 equivalent ratios for 5/7
Answer:
10/14, 15/21, and 20,28
Step-by-step explanation:
You just need to multiply a number on the numerator and the denominator. Remember, whatever you do to the numerator you have to do on your denominator.
Valerie sold 42 tickets to the school play and mark sold 24 tickets. what is the ratio of the number of tickets Valerie sold to the number of tickets mark sold?
The ratio of tickets sold by Valerie to those sold by Mark is 7:4, after simplifying the original ratio of 42:24 by dividing both numbers by 6.
To find the ratio of tickets sold by Valerie to those sold by Mark, we simply compare the two quantities. Valerie sold 42 tickets, and Mark sold 24 tickets. Therefore, the ratio can be expressed as 42:24. This ratio can be simplified by dividing both numbers by their greatest common divisor, which is 6 in this case. Thus, after simplification, the ratio of tickets sold by Valerie to Mark is 7:4. This process illustrates the method of comparing quantities and simplifying ratios, providing a clear and concise representation of the relative ticket sales between Valerie and Mark.
How much will you save per lb, by buying the least expensive? Round to the nearest cent. 2.5 lbs for $8.75 or 3 pounds for $9.75. A.$0.40 B.$0.35 C.$0.30 D.$0.25.
Answer: The answer is $0.25.
Step-by-step explanation:
divide the amounts of money by the pounds to get dollars for each pound then subtract the numbers
and the answer is $0.25.
Answer:
you're answer is D.) 0.25
Step-by-step explanation:
I took the test and scored pretty good
To which subsets of the real numbers does the number 2.37 belong?
Out of the subsets of real numbers, 2.37 belongs in the rational number subset.
I believe it is A but I am not sure.
Answer: The answer is A
Step-by-step explanation: You use substitution because it says that 4-t is equal to r.
Write an equation for the line that passes through the given point and is parallel to the graph of the given equation
Step-by-step explanation:
To find the equation of a line given a point and a parallel line we must use point-slope form.
y - y1 = m(x - x1)
When we plug into this, we use the point in for (x1, y1) and the slope of the parallel line as m.
plz answer this im desperate and uhm...marking brainliest.......plz help i will do anything u want help me!!!
The elevation we call sea level is actually the average level of the sea. This means that at average sea level, the elevation is zero. In reality, the level of the sea rises and falls in what are called tides. Low tide is the point of lowest sea level in a tidal period. High tide is the point of highest sea level in a tidal period. The height above or below average sea level is called elevation. An elevation below sea level is considered a negative value, while an elevation above sea level is positive.
Winston lives near the ocean. He regularly brings an altimeter to the beach to measure the elevation of the ocean’s surface. You will use the data Winston gathered to complete tasks about the rising and falling of the ocean’s surface. When necessary, sketch a diagram of the situation on a separate sheet of paper to assist you.
On Monday at 1 p.m., when the ocean’s surface was at an elevation of 2.2 feet, Winston went to a surf shop that was 8.2 feet above the ocean’s surface. At 7 p.m. when the ocean’s surface was at an elevation of -2.4 feet, Winston ate dinner at a restaurant whose deck was 10 feet above the ocean’s surface.
uhm answer this.....plzzzzzz i will be ur friend (meaning imma add u, and answer ur stuff
(What was the net change in the elevation of the ocean’s surface from 1 p.m. to 7 p.m.?)
Answer:
-4.6 ft
Step-by-step explanation:
We need to learn to extract only the necessary information to answer question. The surf shop and the restaurant is extra information.
Monday 1 pm 2.2 ft
Monday 7 pm - 2.4 ft
Net change
-2.4 ft - 2.2 ft = -4.6 ft
The ocean went down 4.6 ft from 1 pm to 7 pm on Monday
Answer:
-4.6ft
Step-by-step explanation:
Find the midpoint of the segment with the following endpoints.
(
−
10
,
−
7
)
and
(
−
3
,
−
10
)
(−10,−7) and (−3,−10)
Answer:
M = (-13/2, -17/2)
Step-by-step explanation:
The midpoint of two points is half-way between the x-values and the y-values.
The formula is
M = ((x₁ +x₂)/2, (y₁ + y₂)/2)
For the points (−10,−7) and (−3,−10),
M = ((-3 + (-10))/2), (-10 + (-7))/2))
M = ((-3 - 10)/2), (-10 - 7)/2))
M = (-13/2, -17/2)
The graph below shows your two points at (−10,−7) and (−3,−10) and the mid-point at (-13/2, -17/2).
a farmer bought a number of pigs for $180. However, 3 of them died before he could sell the rest at a profit of 8 per pig. His total profit was $109. how many pigs did he originally buy?
The farmer originally bought 41 pigs.
Let x be the number of pigs the farmer originally bought.The total cost of the pigs is $180.After 3 died, he was left with x - 3 pigs.He sold these pigs at a profit of $8 per pig,Resulting in a total profit of 8(x - 3).We know his total profit was $109. So, we can set up an equation:Profit = Selling price - Cost price8(x - 3) = 109 (his total profit) + 180 (cost price)
Combining like terms:8x - 24 = 289
Adding 24 to both sides:8x = 313
Dividing both sides by 8:x = 39.125
Since the farmer can't buy parts of pigs, we round x up to the nearest whole number, which is 40.However, there's a slight discrepancy because the profit wouldn't be exactly $109 if he had 40 pigs. This is because the profit is calculated per pig, and a fraction of a pig wouldn't generate a proportional profit.Therefore, let's try with x = 41:Profit = 8(41 - 3)= 8 * 38
= $304
Total earnings = Profit + Cost price= $304 + $180 = $484
Since the cost price is $180 and the total earnings are $484,The profit would be $484 - $180 = $304, This matches the calculation with 8 pigs sold at a profit of $8 each.Therefore, the farmer originally bought 41 pigs.
A zoo has 19 monkeys and 10 chimpanzees
Answer: It has 29 animals from this info.
The ratio comparing the number of monkeys to the number of chimpanzees in the zoo is[tex]\(19\) to \(10\), \(19:10\), or \(19/10\). This indicates that for every \(19\) monkeys, there are \(10\)[/tex]chimpanzees in the zoo.
The ratio comparing the number of monkeys to the number of chimpanzees in the zoo is expressed as [tex]\(19\) to \(10\), \(19:10\), or \(19/10\). This indicates that for every \(19\) monkeys, there are \(10\) chimpanzees in the zoo. Additionally, it can be written as \(10\) to \(19\), \(10:19\), or \(10/19\), showing the reverse comparison where for every \(10\) chimpanzees, there are \(19\) monkeys. Lastly, it can be represented as \(1.9:1\) or \(1.9/1\), highlighting that for every \(1.9\) monkeys, there is \(1\)[/tex]chimpanzee. These different representations offer flexibility in conveying the proportional relationship between the two quantities, allowing for a clearer understanding of the relative abundance of monkeys and chimpanzees in the zoo.
complete question
Write a ratio for the situation in three ways, comparing the first quantity to the second quantity. (1 point) A zoo has 19 monkeys and 10 chimpanzees. 19 to 10, 19:10, [tex]19/10 10 to 29, 10:29, 10/19 19 to 29, 19 : 29, 19/29 10 to 19, , 10:19 10/19[/tex]
Last month Rudy’s Tacos sold 22 dinner specials. The next month they released a new commercial and sold 250% of last monrh’s dinners. How many dinner specials did they sell this month?
Answer:
100
Step-by-step explanation:
250/100×22= 5500/100
=55
The United States Air Force has 19 women for every 81 men in enlisted if a squadron has 750 members how many women are there
A:143
B:175
C:607
D:165
I need help nowww it’s a quiz last one ???
Answer:
Step-by-step explanation:
im gonna go out on a limb and say (B)
Use the graph of the function y = (x + 3)(x − 2) to find the solutions of the quadratic equation 0 = (x + 3)(x − 2). The solutions of the quadratic equation 0 = (x + 3)(x − 2) are –6 and 0. –4 and 3. –3 and 2. –2 and 1.
Answer:
option 3 is correct that is (-3,2) is the solution.
Step-by-step explanation:
We have been given the quadratic equation:
y=(x+3)(x-2)
You can look at the attachment to see the graph of the given quadratic equation.
The solution to the given quadratic equation is: -3 and 2
The solution is (-3,0) and (2,0).
Therefore, option 3 is correct.
Solution through graph is the point where line intersects the graph.
Answer:
the answer is c on edg
Step-by-step explanation:
Which value are solution of the inequality? 3r<4r-6
Answer: r > 6
Step-by-step explanation:
3r < 4r - 6
-4r -4r
-r < -6
÷-1 ↓ ÷-1
r > 6
A geometric sequence is shown below: 66 a0, -11, 22, 56 a1, 88, -176. A) What is the common ratio for this geometric sequence? 69 a2 B) What are the missing terms in the geometric sequence shown above?
Answer:
Step-by-step explanation:
Given a geometric sequence as
66 a0, -11, 22, 56 a1, 88, -176
We have to find the common ratio and also the missing numbers.
A geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.
Hence by comparing two consecutive numbers let us find common ratio.
Consider 88 and -176. -176 = 88(-2) Hence common ratio is -2
a0 = -11/-2 = 5.5
a1 = 88/-2 = -44
Missing terms are -132 and 5.5
common ratio = -2
The picture shows a sandwich box:
A sandwich box is shown with a right triangle side. The right triangle has hypotenuse 14 cm and base 12 cm.
What is the approximate minimum height of a shelf in which this box can fit in the position shown in the picture?
5.6 centimeters
6.8 centimeters
7.2 centimeters
18.4 centimeters
Using the Pythagorean theorem we can find the height of the triangle:
height = √(14^2 - 12^2)
height = √(196 - 144)
height = √52
height = 7.2
The answer would be 7.2 centimeters.
C. 7.2 centimeters
How do you calculate the Pythagorean theorem?a 2 + b 2 = c 2. This is known as Pythagorean equation, named after the ancient Greek thinker Pythagoras. This relationship is useful because if 2 sides of the right triangle are known, the Pythagorean theorem could be used to determine the length of the 3rd side. Referencing the above diagram, if. a = 3 and b = 4
Using the Pythagorean theorem we can find the height of the triangle:
height = √(14^2 - 12^2)
height = √(196 - 144)
height = √52
height = 7.2
The answer would be 7.2 centimeters.
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Division in ratio: A company has a policy that the ratio between its full time employees and its part time employees should be fixed. (a) There are 25 full time employees and 10 part time employees. What is the ratio? (b) The company takes on more staff. There are now 30 full time employees. How many part time employees are there? (c) A year later, the firm is successful. There are now 16 part time employees. How many full time employees are there?
Answer:
a) 2.5
b) 12
c) 40
Step-by-step explanation:
a) The ratio would be the relation between fixed and part time employees: for this would be 25/10= 2.5 Fixed per part time employee
b) Previous we got the ratio. So we have to divvide the 30 fixed by 2.5 to meet units
c) b) Previous we got the ratio. So we have to multiply the 16 for 2.5 to meet units
turn 6/5 into mixed mumber
Answer:
[tex]1\frac{1}{5}[/tex]
Answer:
1 1/5
Step-by-step explanation:
There is one whole(5/5) and then 1 extra 5th(1/5), so the answer is 1 1/5.
A string of a kite is 100 meters long and it makes an angle of 60° with horizontal. Find the height of the kite and then find the ground distance from the kite to the person flying the kite,assuming that there is no slack in the string.
1. Draw a figure for the information given in the problems.
2. Using the correct trig function, write out the mathematical problem.
3. Solve the problem to find the missing sides.
Answer:
Height of the kite is [tex]=50 \sqrt{3}[/tex] meters.
Ground distance from the kite to the person flying the kite is 50 meters.
Step-by-step explanation:
Given that a string of a kite is 100 meters long and it makes an angle of 60° with horizontal.
Which mans we are getting a shape of right angle triangle as shown in picture. Where "y" is the height of the kite and "x" is the ground distance from the kite to the person flying the kite. Now we can use trigonometric ratios to find the values of x and y.
[tex]\sin\left(60^o\right)=\frac{\left[opposite\right]}{\left[hypotenuse\right]}=\frac{y}{100}[/tex]
[tex]\sin\left(60^o\right)=\frac{y}{100}[/tex]
[tex]\frac{\sqrt{3}}{2}=\frac{y}{100}[/tex]
[tex]\frac{\sqrt{3}}{2}*100=y[/tex]
[tex]50 \sqrt{3}=y[/tex]
Hence height of the kite is [tex]=50 \sqrt{3}[/tex] meters.
similarly:
[tex]\cos\left(60^o\right)=\frac{\left[adjcent\right]}{\left[hypotenuse\right]}=\frac{x}{100}[/tex]
[tex]\cos\left(60^o\right)=\frac{x}{100}[/tex]
[tex]\frac{1}{2}=\frac{x}{100}[/tex]
[tex]\frac{1}{2}*100=x[/tex]
[tex]50=x[/tex]
Hence ground distance from the kite to the person flying the kite is 50 meters.
The height of the kite and the distance from kite to person are 86.6 meters and 50 meters respectively.
Using Trigonometry concept ;
The height of the kite , y can be obtained thus ;
Sine = opposite / HypotenusSin(60°) = y / 100
y = sin(60°) × 100
y = 86.6 meters
B.)
The distance from the kite to the person would be ;
Tangent = opposite / AdjacentTan(60) = 86.6667 / x
d = 86.6667 / Tan(60)
d = 50 meters
Therefore, the height of the kite and the distance from kite to person are 86.6 meters and 50 meters respectively.
Use Distributive property to rewrite each algebraic expression problem: 4(x+2
Answer:4x+8
Step-by-step explanation:
4x+8, 4*x+4*2 for the distributive property