The three inside angles (A, B, C) of a right angled triangle are [tex]\rm \angle A = 35^\circ[/tex] which is the smallest angle, [tex]\rm \angle B = 90^\circ[/tex] which is the right angle and [tex]\rm \angle C = 55^\circ[/tex] which is the third angle of the triangle.
Given :
[tex]\rm \angle A :\angle B:\angle C = 7:18:11[/tex]Smallest angle = [tex]35^\circ[/tex]To solve this kind of problems first let x be in degree. So, angle A, angle B and angle C beecomes:
[tex]\rm \angle A = 7x[/tex] ----- (1)
[tex]\rm \angle B = 18x[/tex] ----- (2)
[tex]\rm \angle C = 11x[/tex] ----- (3)
From the properties of triangle, the sum of interior angles of a triangle is [tex]180^\circ[/tex].
[tex]\rm \angle A +\angle B+\angle C = 180^\circ[/tex] --- (4)
Now, put the values of [tex]\rm \angle A,\;\angle B,\;and \; \angle C[/tex] in equation (4).
[tex]7x+18x+11x=180^\circ[/tex]
[tex]36x = 180^\circ[/tex]
[tex]x = 5[/tex]
Now, put the value of x in equation (1), (2) and (3).
[tex]\rm \angle A = 7\times 5 = 35^\circ[/tex]
[tex]\rm \angle B = 18\times5 = 90^\circ[/tex]
[tex]\rm \angle C = 11\times5=55^\circ[/tex]
The three inside angles (A, B, C) of a right angled triangle are [tex]\rm \angle A = 35^\circ[/tex] which is the smallest angle, [tex]\rm \angle B = 90^\circ[/tex] which is the right angle and [tex]\rm \angle C = 55^\circ[/tex] which is the third angle of the triangle.
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A line is to be graphed through the point (–3, 0). which points can be used to create a line with an undefined slope through (–3, 0)? check all that apply. (–5, –3) (–3, –6) (–3, 2) (–1, 0) (0, –3) (3, 0)
Answer:
[tex](-3,-6)[/tex]
and
[tex](-3,2)[/tex].
Step-by-step explanation:
The given point is [tex](-3,0)[/tex].
If we want to use a point to create a line with an undefined slope through [tex](-3,0)[/tex], then that point must have the same x-coordinates as the given point.
Since the given point, [tex](-3,0)[/tex] has an x-coordinate of [tex]-3[/tex], we check all the points that have an x-coordinate of -3.
The correct answers are;
[tex](-3,-6)[/tex]
and
[tex](-3,2)[/tex].
These point will make the slope undefined, because it will result in division by zero.
Write an equation of the line that passes through the points (-3,4) and (-5,1)
A metallurgist needs to make 12.4 lb. of an 10) alloy containing 50% gold. He is going to melt and combine one metal that is 60% gold with another metal that is 40% gold.How much of each should he use?
A ballroom has a square dance floor. The area of the floor is 400 square feet. If the length of each side of the square increased by one foot, would its area be a rational number? explain
Answer:
The area is a rational number.
Step-by-step explanation:
Consider the provided information.
A ballroom has a square dance floor. The area of the floor is 400 square feet.
Area of square = (side)²
Substitute the respective value in above formula.
400 = (side)²
√400 = side
20 feet = side
Ignore the negative value as side cannot be a negative number.
Now it is given that the length of each side of the square increased by one foot,
Thus, the new side is 20 + 1 = 21 feet
Now find the area of new square = (side)²
A = 21²
A = 21×21
A = 441 square feet
The number 441 is a rational number.
Hence, the area is a rational number.
We have that If the length of each side of the square increased by one foot,
Yes, Area will be a rational number
From the question we are told that
. The area of the floor is 400 square feet
the length of each side of the square increased by one foot,
Generally the equation for the Area of a square is mathematically given as
a=LxB
a=400
Rational Numbers
This simply means expressible as a ratio of whole numbers.
Therefore
If the length of each side of the square increased by one foot then the value will still be expressible as a ratio of whole numbers.
Hence
Yes, Area will be a rational number
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What are the next 2 terms of 0.3, -0.09, 0.0027
The next two terms of the sequence 0.3, -0.09, and 0.0027 are -0.00027 and 0.000027, achieved by continuously multiplying each term by -1/10.
Explanation:To find the next terms of the sequence 0.3, -0.09, and 0.0027, you need to understand the pattern in the sequence. Here, each term is multiplied by -1/10 (or -0.1) to get the next term. So, to find the next term, we multiply the last given term (0.0027) by -1/10, which gives -0.00027. Therefore, the fourth term of the sequence is -0.00027. For the fifth term, we do the same process and multiply -0.00027 by -1/10, to get 0.000027. So, the next two terms in the sequence are -0.00027 and 0.000027.
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What is the greatest common factor of 20a^2, 12a^2 and 8a
WILL MARK BRAINLIEST!
A sample was taken of dogs at a local dog park on two random days. The counts are displayed in the table below. If there are estimated to be 50 dogs at the park at any given time, which proportion could be used to find the average number of shepherd mixes at the park at any given time?
Answer:
⇒[tex]\frac{8}{21} =\frac{x}{50}[/tex]
Step-by-step explanation:
Let average no. of shepherds be x
there are estimated to be 50 dogs
Thus average no. of dogs / estimated no. of dogs =x/50
Since in sample 1 there are 7 shepherd mix
In sample 2 there are 9 shepherd mix
So total shepherd mix = 9+7=16
Total dogs according to table = 4+7+3+1+2+5+9+5+2+4=42
Thus total shepherd / total dogs = 16/42
A.T.Q
[tex]\frac{16}{42} =\frac{x}{50}[/tex]
⇒[tex]\frac{8}{21} =\frac{x}{50}[/tex]
This proportion could be used to find the average number of shepherd mixes at the park at any given time
Thus option A is correct
The average number of shepherd mixes at the park at any given time is equal to [tex]\frac{8}{21} =\frac{x}{50}[/tex].
Let the average number of shepherd mixes be x.Given the following data:
Estimated population = 50 dogs.To determine the average number of shepherd mixes at the park at any given time:
How to calculate the shepherd mixes.First of all, we would determine the total number of shepherd mixes in sample 1 and sample 2.
Total shepherd mixes = [tex]7 + 9[/tex] = 16 dogs.
For the total dogs:
Total dogs = [tex]4+1+7+3+2+5+9+5+2+4[/tex] = 42 dogs.
The average number of shepherd mixes is given by this mathematical expression:
[tex]\frac{16}{42} =\frac{x}{50}[/tex]
Simplifying further, we have:
[tex]\frac{8}{21} =\frac{x}{50}[/tex]
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The rectangular piece of property measures 10 mi by 4 mi. find an equation for the ellipse if the path is to touch the center of the property line on all 4 sides.
Why is it preferable to measure a penny in millimeters?
Millimeters are preferred for measuring a penny because they offer greater precision and accuracy, enabling us to measure the dimensions of small objects like a penny with closer to exact measurements.
It is preferable to measure a penny in millimeters because millimeters provide a more precise and accurate measurement due to their smaller size compared to centimeters. The standard width of a penny is 1.9 cm, which is equivalent to 19 mm. Since scientists have established the convention of using the degree of precision dependent on the measuring device, millimeters are more appropriate for small objects like a penny to get an accurate measurement. A millimeter allows us to report the size of the penny to the nearest millimeter, facilitating a precise estimation.
When choosing a unit of measurement, one must consider the object's size and the necessary precision. For very small objects like a paper clip or a penny, millimeters would give the most accurate measurement, compared to centimeters, which are 10 times bigger and could provide a less accurate measurement. Therefore, for tasks requiring precise measurements of small dimensions, millimeters are preferred.
Find the equation (in terms of xx and yy) of the tangent line to the curve r=3sin2θr=3sin2θ at θ=π/6θ=π/6
Why do have to ignore the absolute value sign while solving differential equation?
Rita earned $20 each day. lauren earned $2 the first day, $3 the second day, $4 the third day, and so on. richard earned $25 a day. lisa earned $1 the first day, $2 the second day, $4 the third day, and $8 the fourth day, and so on. who earned the most money in 10 days?
Lisa earned $385 in 10 days, which is highest among others.
What is Simplification?Simplification in mathematical terms is a process to convert a long mathematical expression in simple and easy form.
Given that,
Money earned by Rita in one day = $20,
Therefore, money earned by Rita in 10 days = 10 x 20 = $200
Money earned by Lauren on first day = $2
Second day = $3,
Third day = $4, and so on....
Total money earned in 10 day by Lauren = 2 + 3 + 4 + .....11 = $65
Money earned by Richard in one day = $25,
Therefore, money earned by Richard in 10 days = 25 x 10 = $250
Lisa earned $1 for first day, $2 for 2nd day, $4 for 3rd day and $8 for 4th day and so on..
Total money earned by Lisa in 10 days = 1 + 2 + 4 + 8 + ........
= 10 x (10+1) x (20+1) / 6 = 385
Maximum amount is earned by Lisa, which is $385.
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Michael pays $30 to enter a state fair, plus $4 for each ride. Which of the following equations represents his total cost? A. y=34x. B. y=4x+30 C. y=30x+4. D. y=4x+34
The correct mathematical equation representing Michael's total cost at the state fair, considering his base fee and cost per ride, is y=4x+30.
Explanation:The question centers around linear equations, a subject in mathematics. In this context, Michael's total cost of his trip to the state fair is calculated by his base fee, 30 dollars, plus the number of rides he goes on multiplied by the cost per ride, 4 dollars. The correct equation representing this situation would be y=4x+30, where y is the total cost, x is the number of rides he goes on, and 30 is the flat entry fee.
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What is the truth value for the following conditional statement?
p: true
q: true
p → q
T T → F
F T → T
T T → T
T F → T
Answer:
T T → T
Step-by-step explanation:
Boolean table,
p q p → q
T T T
T F F
F T T
F F T
Given, the conditional statement:
p : True
q : True,
Then by using above table,
p → q is true,
Hence, the correct answer is,
T T → T
⇒ Third option is correct.
What value is added to both sides of the equation x2 − 8x = −10 in order to solve by completing the square?−816−44?
Answer:
The correct option is 2. 16 is added to both sides of the equation.
Step-by-step explanation:
The given equation is
[tex]x^2-8x=-10[/tex]
If an expression is defined as [tex]x^2+bx[/tex], then we need to add [tex](\frac{b}{2})^2[/tex] in the expression to make it perfect square.
In the given equation b=-8.
[tex](\frac{b}{2})^2=(\frac{-8}{2})^2=(-4)^2=16[/tex]
We need to add 16 on both the sides to solve by completing the square.
Therefore the correct option is 2. 16 is added to both sides of the equation.
ABC has coordinates of A (-8, -8), B(4, -2) and C (2, 2). Find the coordinates of its image after a dilation centered at the origin with a scale factor of 1.5
1. A(-12, -8), B(6, -2), C(3, 2)
2. A(-12,-12), B(6, -3), C(3, 3)
3. A(-8, -8), B(4, -2) C(2, 2)
4. A(-5.33, -5.33), B 2.67, -1.33), C(1.33, 1.33)
The coordinates of the image after dilation with a scale factor of 1.5 are A(-12, -12), B(6, -3), and C(3, 3).
Explanation:To find the coordinates of the image after a dilation, we need to multiply the coordinates of each point by the scale factor. The scale factor is 1.5, so multiplying the x-coordinate and y-coordinate of each point by 1.5 will give us the new coordinates.
For point A (-8, -8), the new x-coordinate is -8 * 1.5 = -12 and the new y-coordinate is -8 * 1.5 = -12. So the image of A is (-12, -12).
Using the same process, we can find the new coordinates for points B and C as well. The correct answer is option 2: A(-12, -12), B(6, -3), C(3, 3).
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In 4 hours, a car travels 200 miles. What is the speed of the car
Answer:
50 miles per hour
Step-by-step explanation:
200 ÷ 4 = 50
200 = miles in 4 hours
50 = miles in 1 hour
Final answer:
The speed of the car is calculated by dividing the distance traveled (200 miles) by the time taken (4 hours), resulting in a speed of 50 miles per hour.
Explanation:
To determine the speed of the car, we use the formula for speed, which is distance traveled divided by the time taken. In this case, the car travels 200 miles in 4 hours. Plugging in numbers, we calculate the speed as follows:
Divide the distance by the time:Therefore, the speed of the car is 50 miles per hour (mph).
If 7 sandwich rolls cost $1.54, how much will 30 rolls cost?
If 5 ib of pasta salad serves 14 people how much pasta salad should you bring to a picnic with 49 people
Final answer:
To determine how much pasta salad is needed for 49 people when 5 pounds serves 14 people, calculate the proportion based on ounces, resulting in 17.5 pounds needed for 49 people.
Explanation:
If 5 pounds of pasta salad serves 14 people, the amount needed for 49 people can be calculated by setting up a proportion because the number of people and the amount of pasta salad are directly proportional. First, we convert 5 pounds of pasta salad to ounces, since the standard conversion is 1 pound = 16 ounces, so 5 pounds equals 80 ounces.
Next, we set up the proportion as follows:
14 people → 80 ounces of pasta salad
49 people → x ounces of pasta salad
To solve for x, you cross-multiply and divide:
14x = 80 * 49
x = (80 * 49) / 14
x = 280 ounces
Thus, you will need 280 ounces of pasta salad, which is equivalent to 17.5 pounds (since 280 ounces divided by 16 ounces per pound equals 17.5 pounds). Therefore, for a picnic with 49 people, you should bring 17.5 pounds of pasta salad.
Shirt cost $20 each and ties cost $12 each. Write an expression for the cost of s shirts and t ties
Answer:
The cost of "s" shirts and "t" ties = $20s + $12t
Step-by-step explanation:
Given:
Shirt cost = $20 each
Ties cost = $12 each.
The number of shirts represented by "s" and the number of ties represented by "t"
Cost = $20*the number of shirts + $12*the number of ties
so, the cost of "s" shirts and "t" ties = 20s + 12t
Example:
If we want to find the cost 2 shirts and 3 ties, we need to plug s = 2 and t= 2 in the above expression.
The cost of 2 shirts and 3 ties = 20*2 + 12*3
= 40 + 36
= $76
The cost of 2 shirts and 3 ties is $76.
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Analyze the function f(x) = - 2 cot 3x. Include:
- Domain and range
- Period
- Two Vertical Asymptotes
Penny uses 3/4 yard fabric for each pillow she makes. How many pillows can she make using 6 yards of fabric. Please show your work
Satellites KA-1212 and SAL-11 have spotted a UFO. Scientists want to determine its distance from KA-1212 so they can later determine its size. The distance between the satellites is 900 km. If KA-1212's camera is focused on SAL-11 , it must rotate 60° to see the UFO. If SAL-11's camera is focused on KA-1212, it must rotate 75° to see the UFO. How far is the UFO from KA-1212? Round your answer to the nearest kilometer.
Answer:
The distance of UFO from KA-1212 is 1229.7 km.
Step-by-step explanation:
We are given that,
Distance between the satellites = 900 km
Angle made by the satellite KA-1212 = 60°
Angle made by the satellite SAL-11 = 75°
So, from the figure below,
The third angle is given by = 180° - (60°+75°) = 180° - 135° = 45°
Then, using the law of sines, we have,
[tex]\dfrac{x}{\sin 75}=\dfrac{900}{\sin 45}\\\\x=\dfrac{900\times \sin 75}{\sin 45}\\\\x=\dfrac{900\times 0.966}{0.707}\\\\x=\dfrac{869.4}{0.707}\\\\x=1229.7[/tex]
Thus, the distance of UFO from KA-1212 is 1229.7 km.Satellites KA-1212 and SAL-11 have spotted a UFO. Scientists want to determine its distance from KA-1212 So, it is 1229.7 km.
What is a law of sine?Law of sines is a formula relating the length of the sides of a triangle to the angles of the triangle.
It is given that
Distance between the satellites KA-1212 and SAL-11 = 900 km
Angle made by the satellite KA-1212 = 60°
Angle made by the satellite SAL-11 = 75°
So, the third angle is given by
= 180° - (60°+75°)
= 180° - 135°
= 45°
Using the law of sines, we get
x/sin75° = 900/sin 45°
x = 900 × sin75°/ sin 45°
x = 900 × 0.966/ 0.707
x = 1229.7
Thus, the distance of a UFO from KA-1212 is 1229.7 km.
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Which statement about the equation is true? 3y – 1 = 13 – 4y The equation has one solution. The equation has no solution. The equation has a few solutions. The equation has many solutions.
Answer:
The equation has one solution
Step-by-step explanation:
Add 4y +1 and divide by 7.
3y -1 = 13 -4y
7y = 14
y = 2
There is one solution.
Answer:
equal to 2
Step-by-step explanation:
Can someone help me please? (Math)
subtract 6a squared plus 3a minus 4a squared plus 2a
Select a rule for the following pattern. 44; 440; 4,400; 44,000 . . .
The rule for the following pattern is to multiply 10 with a constant number 44 everyu sequence.
What is mathematical sequence ?Explanation;
44; 440; 4,400; 44,000.
44
44*10 = 440
440*10 = 4400
4400*10 =44000 and so on
A series is an ordered listing of numbers or other factors like geometric items, that often comply with a specific pattern or characteristic. Sequences can be both finite and limitless. A series is a listing of numbers in a sure order. each number in a series is known as a term . every time period in a series has a role.
Sequences are useful in a number of mathematical disciplines ... specially, sequences are the idea for series, which might be crucial in differential equations and evaluation. Sequences are also of hobby of their own proper and can be studied as styles or puzzles, including in the look at of prime numbers.
A number series is a fixed of numbers that observe a selected pattern or rule to get from time period to time period. There are foremost kinds of exclusive sequences, they are mathematics sequences, geometric sequences, quadratic sequences and special sequences. It assists with comprehension, specially for narrative texts. series structures assist college students of various abilities organize information and ideas successfully.
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What is the angle of rotation of this regular octagon? what is the measure of an interior angle?
Final answer:
The angle of rotation of a regular octagon is 45°, and the measure of an interior angle of a regular octagon is 135°.
Explanation:
The angle of rotation for a regular octagon can be found by dividing the full circle of 360 degrees by the number of sides, which is 8 for an octagon. Therefore, the angle of rotation is 360° / 8 = 45°.
The measure of an interior angle of a regular octagon is determined by the formula (n-2) × 180° / n, where 'n' is the number of sides. Substituting 8 for 'n', the measure of an interior angle is (8-2) × 180° / 8 = 6 × 180° / 8 = 135°.
YZ has endpoints Y(0,5) and Z (12,3). Find the length of YZ to the nearest tenth.
Answer: The answer is 2√37 units.
Step-by-step explanation: Given that the line segment YZ has endpoints Y(0, 5) and Z(12, 3). We are to find the length of the line segment YZ.
The length of YZ will be the distance between the endpoints Y and Z.
The distance between Y and Z will be given by
[tex]YZ=\sqrt{(0-12)^{2}+(5-3)^2}=\sqrt{144+4}=\sqrt{148}=2\sqrt{37}=12.16\sim 12.1.[/tex]
Thus, the length of YZ is 12.1 units.
The solution to an inequality is given in set builder notation as {x l x > }. What is another way to represent this solution set?
(–∞ , ]
(–∞ , )
(, ∞)
[, ∞)
A set-builder notation is a mathematical notation for describing a set by enumerating its elements or stating the properties that its members must satisfy. In your case, the set builder notation {x l x > } means that the set consists of all elements that are greater than.
Consider number line. Plot the point as unfilled circle that goes after > sigh and shade the ray that goes from this point to the right. Then another way to represent this solution is
( ,∞).
Answer: correct choice is C
Final answer:
The correct alternative representation of the set builder notation { x | x > A } in interval notation is ( A, ∞ ), which includes any number greater than A up to positive infinity, but does not include A itself.
Explanation:
The solution to an inequality given in set builder notation as { x | x > A } can be represented in interval notation in several ways, depending on the specifics of the inequality. If the set includes all numbers greater than A, but does not include the number A itself, the interval notation is ( A, ∞ ). This means that the solution set includes any number greater than A, extending to positive infinity, but it does not include A because of the use of the parenthesis.
Interval notation such as [ A, ∞ ) would mean that the set includes the number A and extends to positive infinity. However, this is not the correct representation if the initial set builder notation specifies that x is greater than A, not greater than or equal to A. Similarly, intervals ( -∞ , A ] and ( -∞ , A ) represent sets that include numbers less than or equal to A, and less than A, respectively, which again isn't the case here.
Therefore, the correct answer is 2nd option