The value of y is 15 and angle is 68°
What is a triangle?A triangle is a polygon with three edges and three vertices.
Given that, a triangle KLM
We have, KL = MK
We know that, In a triangle, sides opposite to equal angles are equal, therefore,
∠ M ≅ ∠ L
5y-19 = 56
5y = 75
y = 15
We know, Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.
∠ M + ∠ L + ∠ K = 180°
56° + 56° + ∠ K = 180°
∠ K = 180° - 112°
∠ K = 68°
Hence, the answers are; ∠ K = 68° and y = 15
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The population for Rainbow City is 36,000. The growth rate is 3%. About how many people will it have after 5 years
Answer:
41,500 people
Step-by-step explanation:
First you find 3% of 36,000= 1,080
Then you do 1080 x 5= 4,500
Then finally do 36,000 + 4,500= 41,500
Please help me.
Fiona wants to rope off a triangular region in her yard for a vegetable garden. She has 90 feet of rope to use, she wants the distance between each stake to be an integer, and the distance between two of the stakes must be 36 feet.
A. What is the greatest possible distance between any of the stakes?
B. If she wants to create a right triangular region and use all of the 90 feet of rope, what would be the lengths of the sides of the region?
Answer:
A.) The greatest possible distance between any of the stakes is 53 feet.
B.) A triangle with sides 15, 36, and 39 is a right triangle and has perimeter 90 feet.
Step-by-step explanation:
Given - Fiona wants to rope off a triangular region in her yard for a vegetable garden. She has 90 feet of rope to use, she wants the distance between each stake to be an integer, and the distance between two of the stakes must be 36 feet.
To find - A. What is the greatest possible distance between any of the stakes?
B. If she wants to create a right triangular region and use all of the 90 feet of rope, what would be the lengths of the sides of the region?
Solution -
A.)
Let us assume that,
Length of side 1 = x
Length of side 2 = y
Length of side 3 = z
Now,
Given that,
She has 90 feet of rope to use
⇒x + y + z = 90
And
The distance between two of the stakes must be 36 feet.
So, Let z = 36.
∴ we get
x + y + 36 = 90
⇒x + y = 90 - 36
⇒x + y = 54
Now,
Let x be as large as possible.
i.e. To make x to be large, y has to be as small as possible.
It happens when y = 1.
( We can not take y = 0, or else a triangle won't form)
∴ we get
y = 1
⇒x + 1 = 54
⇒x = 54 - 1
⇒x = 53
∴ we get
The greatest possible distance between any of the stakes is 53 feet.
B.)
We know that,
(5,12,13) is a Pythagorean triple.
Because 5² + 12² = 13²
So,
As, we have a Pythagorean triple,
This means a triangle with sides 5, 12, 13 is a right triangle.
Now,
If a triangle has sides 5, 12, 13,
⇒ The perimeter becomes 5 + 12 + 13 = 30.
By Triple each side we get,
Length of sides 15, 36, 39.
The perimeter i= 15 + 36 + 39 = 90
Also,
We can see that,
15² + 36² = 39².
This means we have a right triangle and (15, 36, 39) is another Pythagorean triple.
Because any scaled version of a Pythagorean triple, is also a Pythagorean triple.
∴ we get
A triangle with sides 15, 36, and 39 is a right triangle and has perimeter 90 feet.
isabella is setting up a cheese board for a neighborhood Super Bowl viewing party. the top of the cheese board is shaped like a triangle. the base of the triangle is 24 inches long, and its heigh is 20 inches. what is the area of the top of the cheese board
To find the area of a triangle, you can use the formula:
area = (base * height) / 2
In this case, the base of the triangle is 24 inches and the height is 20 inches, so plugging these values into the formula gives:
area = (24 * 20) / 2
area = 240 / 2
area = 120 square inches
So the area of the top of the cheese board is 120 square inches.
2) Ms. Van is going to build a small rectangular garden in a part of her yard. The
garden's length will be four meters longer than three times the width of the garden.
Write a polynomial expression to represent the area of the garden.
Answer:
Area = 3x^2 + 4x
Step-by-step explanation:
Givens
W = x
L = 3x + 4
Formula
Area = L * W
Solution
Area = x(3x + 4)
Area = 3x^2 + 4x
Pls help pls help pls I’m begging
Answer:
side=8 unit
Area=777 unit^2
SEE IMAGE FOR SOLUTION
Hope it helps
Have a great day
The scale on a map of Florida is 2 inches = 50 miles. What is the distance in miles
represented by a length on the map of 7 inches?
The distance in miles represented by a length on the map of 7 inches is 0.28
What is scale factor?The ratio between comparable measurements of an item and a representation of that thing is known as a scale factor in arithmetic.
Given;
The scale of a map says that 2 inches represents 50 miles.
2 inches = 50 miles
1 Mile = 2/50 inches
Hence, 7 Mile = 7 * 2/50 inches
7 Mile = 14/50 inches
7 Mile = 0.28 inches
Therefore, the scale factor of 7miles in the map will be 0.28inches
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How do you find the ratios for sin A and cos A?
In given right triangle ACB, the ratios for sin A and cos A :
sin(A) = 48/50
cos(A) = 14/50
Consider the following diagram.
In a right triangle ACB, the angle ACB = 90 degrees.
We know that in right triangle for an angle θ, the trigonmetric ratios are:
sin(θ) = opposite side of θ/ hypotenuse
cos(θ) = adjacent side of θ / hypotenuse
Here, side AC = 14 units, side CB = 48 units and the hypotenuse AB = 50 units
We need to find the ratios for sin A and cos A
In right triangle ACB for angle A,
sin(A) = opposite side of angle A/ hypotenuse
sin(A) = CB/AB
sin(A) = 48/50
And cos(A) = adjacent side of A / hypotenuse
cos(A) = AC/AB
cos(A) = 14/50
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Study the example showing a function. Then solve
problems 1-6.
Example
The table and graph show the
relationship between the length
of the sides of a square, in feet, and
the perimeter of the square in feet.
Side Length (input) 1 2 3 4 S
Perimeter (output) 4
812 16 20
The relationship is a function because
there is only one output value for
each input value.
Perimeter (output)
20
18
16
14
12
10
8
6
4
2
Perimeters of Squares
0 1 2 3 4 5 6 7 8 9
Side Length (input)
1 Describe the relationship between the input and output
values in the example.
2 Can you represent the function in the example with an
equation? If so, what equation can you write? If not,
why not?
Vocabulary
function a rule that
The relationship between the input and output is that the perimeter of a square is always equal to four times the length of one of its sides.
What is the perimeter of square?The perimeter of a square is the total distance around the outside of the square. It is the sum of the lengths of all four sides. To find the perimeter of a square, you simply multiply the length of one side by four, since all sides of a square are equal in length. The formula is P=4S
1.The relationship established between (side length of the square) and output (perimeter of the square) represent that A square's perimeter is always equal to 4 times one of its sides.
2.Yes, the function can be represented with an equation. The equation would be:
Perimeter = 4 × Side Length.
Side Length (input) 1 2 3 4 5
Perimeter (output) 4 8 12 16 20
This equation states that the perimeter of a square is equal to four times the length of one of its sides.
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Given the following system of equations, solve for 'X', 'y' and 'z.
2x - 32= -18
-4y + 2z = 4
3x + 10y= 1
x=7, y=-2, and z=-2
just trust me on it
Where is quadrant 4?
The fourth quadrant, often known as Quadrant IV, is the bottom right quadrant. The x-axis in this quadrant is positive, whereas the y-axis is negative.
Two-dimensional Cartesian axes separate the plane into four infinite areas known as quadrants, each of which is bordered by two half-axes. These are frequently numbered 1 through 4.
90° arc; one-fourth of a circle. the region enclosed by such an arc and two sketched radii, one at each extreme. a component of a machine that has a quarter-circle form.
The x- and y-coordinates are both positive in quadrant I.
The x-coordinate is negative and the y-coordinate is positive in quadrant II.
The x- and y-coordinates are positive in quadrant III.
Quadrant IV: The x-coordinate is positive and the y-coordinate is negative.
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Beth and Amy's tennis coach is picking 2 athletes from the 10 on the tennis team to speak at an assembly. What is the probability the coach will pick Beth and Amy?
Answer:
Is it beth AND amy or Beth OR Amy?
... due tomorrow... help pls
Can some kind person help me on this assignment pls
Answer:
D, B
Step-by-step explanation:
Question 8.
The shaded area should be on or below the line [tex]y=\frac{5}{2}x-2[/tex] AND below but not on the line [tex]y=\frac{1}{2}x+2[/tex]
Question 9.
See the attached image.
Shade on or under the line [tex]y=\frac{1}{2}x-1[/tex] AND above but not on the line [tex]y=\frac{3}{2}x+1[/tex].
The surveyor walked 120 ft away from one of the sensors so that her walking path made a 90 degree angle with the width of the lake when she stop she measured the lake when she stopped she measured the angle between her lines of sight to both sensors and it was 70 degrees
Therefore ,the answer to the above trigonometry issue is therefore that the river is 70 feet wide.
What is trigonometry?The study of the connections between the angles and sides of triangles is known as trigonometry. Due to the fact that each straight-sided figure may be reduced to a collection of triangles, trigonometry is commonly utilized in geometry. There are a mind-boggling number of connections between trigonometry and other branches of mathematics, especially algebra, real or complex, integrals, logarithms, and infinite series.
Here,
Figure depicts a right triangle which, in relation to angle, its next side has length d or its wrong side is equal to the river's width, y. As a result,
tanθ= d/ y
=> y=dtanθ
=> y = (100m)tan(35.00)=70ft
The river measures 70 feet in width.
As a result, the trigonometry problem's answer indicates that the river's width is 70 feet.
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4 Select the correct answer. Annabelle wanted to find out how many people in her neighborhood were going to the rock concert over the weekend. She asked a couple of her immediate neighbors. On the basis of the answers she got, she drew her conclusion. What kind of statistical investigation did Annabelle perform
Annabelle collected data from a sample of people that were convenient for her to access, such as her immediate neighbors, and used this to draw her conclusion.
Annabelle performed a convenience sample investigation, which is a type of statistical investigation. This involves collecting data from a sample of people that are convenient for the researcher to access. In this case, Annabelle asked a couple of her immediate neighbors to find out how many people in her neighborhood were going to the rock concert..
Convenience sampling is useful when time or resources are limited, however the results may not be representative of the larger population. Therefore, it is important to consider the limitations of the sample when drawing conclusions. For example, Annabelle may not have considered that the neighbors she asked may not be representative of the whole neighborhood.
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Ellis put 57 equal size bags of potatoes onto the shelf at the grocery store. The total weight was 60.42 pounds. What is the weight of each bag of potatoes
Answer: 1.06 pounds per bag of potatoes
Step-by-step explanation:
Total weight = 60.42
# of bags of potatoes = 57
60.42/57 = 1.06 pounds per bag
Use the distributive property to fill in the blanks below. Pls help me :| This is for a grade and today for me is the last day of school :|
Answer:8 in each box
Step-by-step explanation:
U are multiplying 2 and 7 each by 8
plz help lol i’m stuck
Answer:
the length of arc=
[tex]2\pi \times 6 \times \frac{60}{360} \\ 2\pi[/tex]km
Write the equation of the line that passes through the points (6, 1) and
(6, -8). Put your answer in fully simplified point-slope form, unless it
is a vertical or horizontal line.
something noteworthy is that the x-coordinate is the same for each point, so Check the picture below.
PLEASEEE ANSWERRR ASAP
If point A(-3, 9) is dilated by a scale factor of 6 with the origin as the center of
dilation, what would be the coordinates of the new image at point A'?
Answer:
A' = (-18, 54)
Step-by-step explanation:
You buy clothing at a sale. You buy sneakers at 2 3 of their original price of $60, a sweater at 7 10 of its original price of $35, and a jacket at 5 6 of its original price of $45. Answer each question and show all your work. How much money did you spend
We spent a total of 40.2 + 24.5+ 37.8 = $102.50
Explain about the fractions?A fraction is a metric unit for describing a piece or component of a whole. It represents the appropriate parts of the totality. A fraction is made up of two parts: the numerator and the denominator. The number at the top is the numerator, and the number at the bottom is the denominator.
Fractions are used to represent the parts of an entity or collection of entities. The components of a fraction are two. The figure at the top of the line is the numerator. It provides information on how many equal sections from the total or collection were taken. The number that appears below the line is the denominator.
We multiply the initial price by the fractions' decimal conversions to determine how much we spent. The quantities are then combined.
You purchased sneakers for $60 and paid 2/3 of that amount, or $0.6666, for a total of $40.20, saving $19.80.
Sweater costs $35 and you paid $7.50 for it, saving you $10.50. 35(0.7)=$24.50.
You paid $45 for a jacket, and since 5/6=0.8333, 45(0.84)=$37.80, you made a $7.20 profit.
We spent a total of 40.2 + 24.5+ 37.8 = $102.50
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Did I divided the polinoms in a correct way?
If I didn't please explain how
Answer:
siesta bien
Step-by-step explanation:
HELP ME PLS ILL GIVE YOU BRAINLIST
Determine the slope, x-intercept and y-intercept of the line given by the equation 2x+3y=6
What is the midpoint formula of quadratic equation?
The midpoint formula of a quadratic equation is given by: x = -b/(2a), where a, b and c are the coefficients of the quadratic equation ax2 + bx + c = 0.
This formula is used to determine the midpoint of the roots of a quadratic equation. It works by taking the coefficients of the equation and plugging them into the formula. The result of the formula will be the x-coordinate of the midpoint of the two roots.
This formula is useful when solving quadratic equations, because it allows us to quickly find the midpoint of the two roots without having to solve for both roots first. It is also useful for graphing the quadratic equation, as it reveals the location of the vertex of the parabola. Knowing the midpoint of the two roots also makes it easier to determine the nature of the roots, whether they are real or imaginary.
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Is algebra.
PLEASE HELP NO LINKS OR FILES.
I don't want links.
I don't want links.
I don't want links.
I don't want links.
Answer:
for question 3 - b
for question 4- b
Step-by-step explanation:
7x -2y =-10 slope interceept form
Answer:
y = 7/2x + 5
Step-by-step explanation:
The slope intercept form is: y = mx + b
Our equation is
7x -2y = -10
We subtract 7x both sides
-2y = -7x - 10
Divided by -2, both sides
y = 7/2x + 5
So, the answer is y = 7/2x + 5
An object has a mass of 440 kg and a volume of 11 m3.
Find the density of the object in kg/m3.
Answer:
40 kg/m³
Step-by-step explanation:
To find the density divide the mass by the volume
440kg / 11 m³ = 40 kg/m³
Answer:
40 Kg/m cube
Step-by-step explanation:
What is the value of S3= infinity sigma n-1 5(1/3)^n-1
If 1 and -2 are zeroes of x^2+ax+b=0. Find a and b. First and correct answer will be marked brainliest.
Answer:
a = 1, b = -2
Step-by-step explanation:
You are given values of x are 1 and 2 when the equation is 0
To solve the problem substitute the values of x into the equation
For x =1
1^2 + a(1) + b = 0
1 + a + b = 0
a+b = -1(call this equation i)
For x = -2
-2^2 + a(-2) + b = 0
4 - 2a + b = 0
-2a + b = -4 (call this equation ii)
Now solve equation i and ii simultaneously to get values of a and b.
a+b = -1
-2a+b = -4
By elimination method (also you can solve by substitution method) subtract equation ii from equation i, we get
3a = 3
Divide 3 both sides, you get
a = 1
Take the value of a above substitute it into either equation i or ii to get the value of b
Here i considered equation i
a + b = -1
1 + b = - 1
b = - 1 - 1
b = -2
Therefore a = 1, b = -2