To find the value of x, we can use the fact that the sum of the lengths of the line segments in a triangle is equal to the total length of the triangle.
In this case, we have:
AC = 8x - 9
AB = 3x + 1
BC = 4x - 5
The sum of the lengths of the line segments AB, BC, and AC should be equal to the total length of the triangle ABC. Therefore, we can set up the equation:
AB + BC + AC = total length of triangle ABC
(3x + 1) + (4x - 5) + (8x - 9) = total length of triangle ABC
Simplifying the equation, we get:
15x - 13 = total length of triangle ABC
Since we don't have any additional information about the triangle, we can't determine the exact length of the total triangle. Therefore, we cannot find the exact value of x using the given figure.
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Find x,
1. cos^2x = sin^2x + 1/2
2. 2cos( π/2 - x) * sin (π/2 + x) - 1 = 0
3. 8sin x/2 * cos x/3 * cosx * cos2x = 1
4. 1 + cosx = cos x/2
1)
Given:
cos^2x = sin^2x + 1/2
Now,
Further simplify the trigonometric equation to get the value of x .
cos²x - sin²x = 1/2
∴cos² - sin²x = cos2x
cos2x = 1/2
2x = cos^-1(1/2)
2x = 60
x = 30° .
Hence the value of x is 30° .
2)
Given:
2cos( π/2 - x) * sin (π/2 + x) - 1 = 0
∴cos(90-x) = sinx
∴sin(90 +x) = cosx
2sinxcosx = 1
sin2x = 1
2x = sin^-1(1)
2x = 90
x = 45° .
Hence the value of x is 45° .
3)
Given:
1 + cosx = cos x/2
Further simplifying,
1 = cosx/2 - cosx
Put x = 180
1 = cos90 - cos180
1 = 0 - (-1)
1 =1
Hence LHS = RHS and x = 180°
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Trevor earns $12 per hour and Brian earns $10 per hour. Which of the following situations can be modeled by the inequality below?
The situation that can be modelled with the inequality is if Trevor and Brain works x hour, Trevor's earnings is at least $30 more than Brian. (second option)
Which situation is modelled?The first step is to determine inequality signs and what they mean.
> means greater than
< means less than
≥ means greater than or equal to
≤ less than or equal to
The given inequality is:
$12x - $30 ≥ $10
If the inequality is rearranged, it becomes:
$12x ≥ $10x + $30
This can be interpreted as if both of them work x hours, Trevor's income is at least $30 more than Brian's.
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PLEAse ILL DO ANYTHING HELP 18 in.
21 in.
23 in.
What is the volume of this figure?
16 in.
Total volume of figure is,
V = 10,488 inches³
We have to given that,
The figure shown in image is made with cuboid and triangular prism.
Since, WE know that,
Volume of cuboid is,
V = b × h × l
And, Volume of triangular prism is,
V = 1/2 × b × h × l
Substitute all the values, we get;
Volume of cuboid is,
V = b × h × l
V = 18 x 23 x 16
V = 6624 inches³
And, Volume of triangular prism is,
V = 1/2 × b × h × l
V = 1/2 x 21 x 23 x 16
V = 3864 inches³
Thus, Total volume of figure is,
V = 6624 inches³ + 3864 inches³
V = 10,488 inches³
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1,2,5,10,17,26,37,50 ??
Answer: 65,82,101,122
Step-by-step explanation:
Its adding odd numbers because first it was +1 then +3, +5 +7, +9 +11, +13 and so on :)))
The speed that a tsunami can travel is modeled by the equation s=365
The speed that a tsunami can travel is modeled by the equation s = 356 StartRoot d EndRoot , where S is the speed in kilometers per hour and d is the average depth of the water in kilometers.
This is written mathematically as:
S = 356√d
S = 200km/hr
Hence:
200km/hr = 356√d
Divide both sides by 356
200/356 = 356√d/356
√d = 200/356
Square both sides
(√d)² = (200/356)²
d =(0.5617977528)²
d = 0.3156167151km
Approximately = 0.32km
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Rewriting 3x^2=6x and solving with rewritten
Answer:
x = 0 , x = 2
Step-by-step explanation:
3x² = 6x ( subtract 6x from both sides )
3x² - 6x = 0 ← factor out 3x from each term
3x(x - 2) = 0
equate each factor to zero and solve for x
3x = 0 ⇒ x = 0
x - 2 = 0 ( add 2 to both sides )
x = 2
solutions are x = 0 , x = 2
Mr Jones had invested $2000 and his friend Me Williams had invested $1450 in a company. After 1 year they made a profit of $690. How much profit each will get if they share the profit in terms of their investment?
Answer:
Mr Jones: $399.69
Mr Williams: $290.31
Step-by-step explanation:
Calculate the total investment: $2000 + $1450 = $3450.
Calculate Mr Jones' share: ($2000 / $3450) * $690 ≈ $399.69.
Calculate Mr Williams' share: ($1450 / $3450) * $690 ≈ $290.31.
Hence, Mr Jones will receive approximately $399.69 in profit, while Mr Williams will receive approximately $290.31 in profit.
Vijay surveyed 2 passengers on a city bus. Is this sample of the inhabitants of the city likely to be representative? A. Yes B. No
B. No
Step-by-step explanation:
tho im not 100% sure i think this is the answer because there is enough data to be able to calculate the average of the data to represent the city.
h9pe that helps
VI. In a class of 40 students, the marks obtained in Mathematics (out of 50) are as under: 44,50,44,49,42,47,45,42,44,48,49,48,47 49,47,41,45,48,41,48,41,42,47,49,49,48, 50.47.49.48.46.44.45.45.46.44.42.47.48.45 ow answer the following questions: a) b) c) d) e) Find the number of students getting more than 45 marks. Find the number of students getting less than 45 marks. Find the maximum number of students getting the same marks. Find the average marks obtained by the students in the class. Find the number of students getting more than average marks.
a) To find the number of students getting more than 45 marks, we count the students whose marks are greater than 45 in the given list.
In the given list, the students with marks greater than 45 are: 50, 49, 47, 48, 49, 48, 47, 49, 48, 50, 47, 49, 48, 46, 47, 48, 47.
Counting these numbers, we find that there are 17 students who obtained more than 45 marks.
b) To find the number of students getting less than 45 marks, we count the students whose marks are less than 45 in the given list.
In the given list, the students with marks less than 45 are: 44, 44, 42, 41, 41, 42, 41, 44, 44, 42, 45, 45, 45, 44, 45.
Counting these numbers, we find that there are 15 students who obtained less than 45 marks.
c) To find the maximum number of students getting the same marks, we look for the mark that appears most frequently in the given list.
In the given list, the marks obtained by the students are: 44, 50, 44, 49, 42, 47, 45, 42, 44, 48, 49, 48, 47, 49, 47, 41, 45, 48, 41, 48, 41, 42, 47, 49, 49, 48, 50, 47, 49, 48, 46, 44, 45, 45, 46, 44, 42, 47, 48, 45.
Counting the frequency of each mark, we find that the marks 47 and 48 appear most frequently, with a count of 6 each. Therefore, the maximum number of students getting the same marks is 6.
d) To find the average marks obtained by the students in the class, we sum up all the marks and divide by the total number of students.
Total marks = 44 + 50 + 44 + 49 + 42 + 47 + 45 + 42 + 44 + 48 + 49 + 48 + 47 + 49 + 47 + 41 + 45 + 48 + 41 + 48 + 41 + 42 + 47 + 49 + 49 + 48 + 50 + 47 + 49 + 48 + 46 + 44 + 45 + 45 + 46 + 44 + 42 + 47 + 48 + 45
= 1912
Total number of students = 40
Average marks = Total marks / Total number of students
= 1912 / 40
= 47.8
Therefore, the average marks obtained by the students in the class is 47.8.
e) To find the number of students getting more than the average marks, we count the students whose marks are greater than 47.8.
In the given list, the students with marks greater than 47.8 are: 50, 50, 49, 48, 49, 48, 49, 48, 50, 49, 49, 48, 48, 50, 49, 49, 48, 48, 47, 49, 49, 48, 50, 47,
49, 49, 48, 50, 47, 49, 49, 48, 48, 49, 48, 47, 48, 49, 49, 48, 50, 49.
Counting these numbers, we find that there are 40 students who obtained more than the average marks.
Ken owns 500 shares of LaceNBrace, which makes hockey equipment. He receives a notice stating the company will be paying $0.15 dividend per share. What is the total dividend payment he receives for that quarter? O $750 O $8.50 O $7.55 O $75
Ken will receive a total dividend payment of $75 for that quarter.
We have to given that,
Ken owns 500 shares of LaceNBrace, which makes hockey equipment.
And, He receives a notice stating the company will be paying $0.15 dividend per share.
Now, For the total dividend payment Ken receives for that quarter, we can multiply the dividend per share by the total number of shares he owns:
= $0.15 per share x 500 shares
= $75
Therefore, Ken will receive a total dividend payment of $75 for that quarter.
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Which equation matches the graph below?
−2sin(x)
−2cos(x)
2cos(x)
2sin(x)
The equation matches the graph is -2cosx.
The graph of the function y = -2cos(x) represents a cosine function that has been reflected vertically and stretched by a factor of 2.
The cosine function is a periodic function that oscillates between -1 and 1. The negative sign in front of the function (-2cos(x)) reflects the graph across the x-axis. This means that all the positive values of the cosine function become negative, and vice versa.
So, the coefficient of -2 stretches the graph vertically by a factor of 2. This means that the amplitude of the graph doubles, and the oscillations are more spread out vertically.
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james has been subscribed to our bronze address rental package. he pays us £12.87 per quarter in advance he has been using our services for 1 year and has paid for 4 quarters in full. he has told us he wants to cancel his subscription and is requesting a refund for 1 month's subscription
James is eligible for a refund of £47.19 for one month's subscription.
To calculate the refund for James's subscription, we need to determine the cost of one month's subscription and subtract it from the total amount he has paid for four quarters.
James pays £12.87 per quarter, which means he pays £12.87 x 4 = £51.48 for a full year in advance.
To find the cost of one month's subscription, we divide the annual cost by 12 (number of months in a year):
£51.48 / 12 = £4.29
The cost of one month's subscription is £4.29.
To calculate the refund, we subtract the cost of one month's subscription from the total amount James has paid:
£51.48 - £4.29 = £47.19
We must figure out the price of a month's membership and deduct it from the total amount James has paid for four quarters in order to compute the refund for his subscription.
James pays £12.87 every quarter, or £12.87 x 4 = $51.48 for the entire year up front.
We divide the yearly cost by 12 (the number of months in a year) to get the price for a month's subscription:
£51.48 / 12 = £4.29
Therefore, a membership for one month costs £4.29 in total.
We deduct the price of a single month's membership from James' overall payment to determine the refund:
£51.48 - £4.29 = £47.19
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A worker at a local aquarium is instructed to estimate the population of anchovies in the tank. She catches 32 anchovies, marks them with special paint, and returns them to the tank. Then she catches 950 anchovies and finds that 16 of them are marked. To the nearest whole number, what is the best estimate for the anchovy population?
Answer:
1900
Step-by-step explanation:
Use a proportion:
16 is to 950 as 32 is to x.
16/950 = 32/x
32/16 = x/950
x/950 = 2
x = 1900
Answer: 1900
I need 5 sentences this is for 100 points so give a proper answer
The value of x and y from the given triangle are 52.3 feet and 42.84 feet respectively.
Given that, an engineer sketches a right triangle to show that the screen in a movie theater is 30 ft high and that the vertical viewing angle from the from row is 35 degree.
We know that, sinθ = Opposite/Hypotenuse
sin35° = 30/x
0.5736 = 30/x
x = 30/0.5736
x = 52.3 feet
We know that, tanθ = Opposite/Adjacent
tan35°=30/y
0.7002=30/y
y = 30/0.7002
y = 42.84 feet
Therefore, the value of x and y from the given triangle are 52.3 feet and 42.84 feet respectively.
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In a test the average marks for the three classes were 74,58 and 51 if the classes contained were 25,22and 23 students respectively what was the average marks for the three classes altogether
Answer:
Step-by-step explanation:
Simplify (3x^6y^4)(-4x^2y^3)
1: -x^8y^7
2: -12x^12y^12
3: -12x^8y^7
4: -12x^8y^12
Hello!
(3x⁶y⁴)(-4x²y³)
= -12x⁶y⁴x²y³
= -12x⁸y⁷
Carol earns $14050.00 per year and budget at 11% for clothes. estimate her yearly clothes budget.
Write the statements in symbolic form using the symbols ∧,∨ and ¬.
Let h = "John is healthy," w = "John is wealthy," and s = "John is wise."
John is healthy and wealthy but not wise.
John is not wealthy but he is healthy and wise.
John is neither healthy, wealthy, nor wise.
John is neither wealthy nor wise, but he is healthy.
John is wealthy, but he is not both healthy and wise.
These symbolic representations use the symbols ∧ (and) to indicate that all conditions must be true, ∨ (or) to indicate that at least one condition must be true, and ¬ (not) to negate a statement.
Using the given symbols ∧ (and), ∨ (or), and ¬ (not), we can represent the statements as follows:
Let h = "John is healthy," w = "John is wealthy," and s = "John is wise."
John is healthy and wealthy but not wise.
Symbolic form:
h ∧ w ∧ ¬s
John is not wealthy but he is healthy and wise.
Symbolic form:
¬w ∧ h ∧ s
John is neither healthy, wealthy, nor wise.
Symbolic form:
¬h ∧ ¬w ∧ ¬s
John is neither wealthy nor wise, but he is healthy.
Symbolic form:
¬w ∧ ¬s ∧ h
John is wealthy, but he is not both healthy and wise.
Symbolic form:
w ∧ (¬h ∨ ¬s)
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6. Which graph best represents the solution of the inequality y < –x + 3?
The graph of the inequality is on the image at the end.
Which graph best represents the solution of the inequality?Here we want to find the graph of the inequality:
y < -x + 3
To graph this, we need to graph the line:
y = -x + 3
With a dashed line (because the points in the line aren't solutions for the inequality)
And we can see that y is smaller than the line, then we need to shade all the region below that dashed line.
The graph of the inequality is the one you can see in the image at the end.
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what is the circumference of a circle of radius one metre
The circumference of a circle is calculated using the formula:
[tex]\sf\:C = 2 \pi r \\[/tex]
where C represents the circumference and r represents the radius of the circle.
Given that the radius of the circle is one meter (r = 1), we can substitute this value into the formula to find the circumference:
[tex]\sf\:C = 2 \pi (1) \\[/tex]
[tex]\sf\:C = 2 \pi \\[/tex]
Therefore, the circumference of a circle with a radius of one meter is [tex]\sf\:2 \pi \\[/tex] meters.
50 Points! Multiple choice geometry question. Photo attached. Thank you!
5/6 is the probability that the number landed on an odd or is greater than 4
Probability conceptProbability is defined as the likelihood or chance that an event will occur.
If a number cube is rolled, the sample space will be:
(S) = {1, 2, 3, 4, 5, 6}
n(S) = 67
If it lands on a odd number, the number of events will be:
(E) = {1, 3, 5}
n(E) = 3
If it lands on a number greater than 4 the number of events will be:
(E) = {5, 6}
n(E) = 2
Pr(even or greater then 4) = 3/6 + 2/6
Pr(even or greater then 4) = 5/6
The probability that the number landed on an odd or is greater than 4 is 5/6
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Answer: 4/6 or 2/3
Step-by-step explanation:
Even number=3/6 or 1/2 chance
Greater than 4=2/6 chance or 1/3 chance
Union basically means either or
So: 1/2+1/3 or 3/6+2/6 or 5/6
This doesn't always work though, so we use trial and error
1 2 3 4 5 6
1 3 5 are the ones not even
13 are the ones not greater than 4
mesuare crayon and half pencil dreambox
The measurement of a crayon and half a pencil dreambox will depend on the specific dimensions of the dreambox. As there is no information provided about the exact size or shape of the dreambox.
To measure the crayon and half pencil dreambox, you would typically need a measuring tool such as a ruler or tape measure. Here are the steps to measure it:
1. Determine the length measurement: Place the dreambox on a flat surface and measure the length from one end to the other using the measuring tool. Make sure to align the measuring tool properly to get an accurate measurement.
2. Measure the width: Measure the width of the dreambox by placing the measuring tool perpendicular to the length measurement. Again, ensure that the measuring tool is aligned correctly to obtain an accurate width measurement.
3. Measure the height: Measure the height of the dreambox by placing the measuring tool vertically from the bottom to the top of the dreambox. Ensure that the measuring tool is aligned properly for an accurate height measurement.
By following these steps and using a measuring tool, you can obtain the measurements of the crayon and half pencil dreambox accurately.
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What is the common ratio of the geometric sequence below?
–96, 48, –24, 12, –6, ...
[tex] \sqrt[5]{ {2}^{13} \times {3}^{5} } [/tex]
[tex] \sqrt[5]{ {2}^{13} } [/tex]
If a fair die is rolled 5 times, what is the probability, rounded to the nearest
thousandth,
of getting at most 1 five?
Answer:
0.482 is the probability of the fair die of getting at most 1 five.
Step-by-step explanation:
Probability is the Number of favorable outcomes divided by the total number of outcomes.Getting at most 1 five means there can be 1 five or 0 five.
Condition 1:
Getting 0 fives, there are 5 roles, there are five possible outcomes (numbers from 1 to 6 exclude 5).The total number of outcomes for fair die rolling five times is 5 x 5 x 5 x 5 x5 = 3125.Condition 2:
Getting 1 five, there are 5 rolls, and we need exactly 1 of them to result in a five.The total number of outcomes for fair die rolling five times is 5 x 5^4 = 625.We sum up the favorable outcomes ( 0 five and 1 five) and divide it by the total outcomes to find the probability.
P = ( Number of favorable outcomes) / (Total number of outcomes)
p = (3125 +625)/6^5 => 3750 / 7776 => 0.482
p = 0.482
Therefore the probability is 0.482.
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Ronnie made a scale drawing of a shopping center. A bakery in the shopping center is 7 inches wide in the drawing. The actual bakery is 42 feet wide. What is the scale of the drawing?
Answer:
1:72
Step-by-step explanation:
The scale of a drawing is the ratio of the length in the drawing to the real length.
Drawing length: 7 inches
Real length: 42 ft × 12 in. / ft = 504 in.
Scale:
7 in. to 504 in.
Divide both numbers by 7:
1 in. to 72 in.
Scale: 1:72
in a continuous series, if the sum of weights of 50 students is 1,850 kg find their average weights.
The average weight of the 50 students is 37 kilograms.
In mathematics, a continuous series is a sequence of numbers that has no gaps between any of its values. In order to find the average weight of a continuous series of 50 students, we can divide the sum of their weights by the total number of students.
Let us assume that the weight of each student is measured in kilograms. If the sum of the weights of 50 students is 1,850 kilograms, then the average weight can be calculated as follows:
Average weight = Total weight / Number of studentsIn this case, the total weight is 1,850 kilograms and the number of students is 50. Therefore, we can substitute these values into the formula and simplify as follows:
Average weight = 1,850 / 50Average weight = 37 kilograms It is important to note that this calculation assumes that all of the weights are evenly distributed among the students and that there are no outliers or extreme values that would skew the average.
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Need help asap!! For this algebra
It is noticed that the factors then the x-intercepts are the same value as that of factors.
Given that, the quadratic equation represented on the graph in factored form is y=(x-3)(x+2).
From the graph, x-intercepts are x=-2 and x=3.
The vertex of the given quadratic graph is (0.5, -6)
Therefore, it is noticed that the factors then the x-intercepts are the same value as that of factors.
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Jane received a $80 gift card for a coffee store. She used it in buying some coffee that cost $7.56 per pound. After buying the coffee, she had $49.76 left on
her card. How many pounds of coffee did she buy?
Answer:
Jane spent on coffee.
She started with $80 on her gift card and ended with $49.76, so she spent:
80 - 49.76 = $30.24
We know that she bought coffee that cost $7.56 per pound, so we can set up an equation to find how many pounds of coffee she bought:
7.56x = 30.24
where x is the number of pounds of coffee she bought.
Solving for x, we get:
x = 30.24 / 7.56 = 4
So Jane bought 4 pounds of coffee with her gift card.
Lihle is going to bake some vanilla cupcakes that she wants to sell to raise money for charity. Use the recipe below to answer the questions that follow. VANILLA CUPCAKES Ingredients 185g butter 220g castor sugar 3 extra-large eggs 3ml vanilla essence 80ml water 80ml milk 300g cake flour 20ml baking powder Butter Icing 80g butter 115g icing sugar 15ml boiling water 1 tub vermicelli for garnishing MAKES 24 CUPCAKES 1.1.1. Lihle does not have a measuring spoon so she decides to use a teaspoon. How many teaspoons (5ml) of baking powder does Lihle need for one batch of cupcakes? (2)
netry B Unit 5 Test 2023 Unit Test: Unit 5 Test 2023: Geometry Applications The maximum altitude currently allowed by drones is 400 feet, which is approximately 0.12 km. This is to ensure that drones do not interfere with other aircraft or cause safety hazards. If cameras in a drone are set to film toward the horizon, what is the greatest distance that can be filmed, given that the radius of the Earth is approximately 6378 km? Round your answer to the nearest kilometer.
The greatest distance that can be filmed by the drone is 6374.5 km. Rounded to the nearest kilometer, 6375 km.
Now, For the greatest distance that can be filmed by a drone with a maximum altitude of 0.12 km, we can use the Pythagorean theorem.
Let's a right triangle with one leg being the radius of the Earth 6378 km and the other leg being the maximum altitude of the drone 0.12 km.
Hence, The hypotenuse of this triangle represents the line of sight from the drone's camera to the horizon.
Hence, By Using the Pythagorean theorem, we can solve for the length of the hypotenuse:
h² = 6378² + 0.12²
h = √40684000.145
h = 6374.5 km
Therefore, The greatest distance that can be filmed by the drone is 6374.5 km. Rounded to the nearest kilometer, 6375 km.
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