Answer: [tex]3\sqrt{2}\ m[/tex]
Step-by-step explanation:
The perimeter of a square is:
[tex]P=4s[/tex]
Where "s" is the lenght of a side of the square.
Then, if the perimeter of this square is 12 m, you can solve for "s" and find its value:
[tex]s=\frac{P}{4}\\\\s=\frac{12\ m}{4}\\\\s=3\ m[/tex]
You can calculate the length of the diagonal with this formual:
[tex]d=s\sqrt{2}[/tex]
Where "s" is the lenght of a side of the square.
Substituting the value of "s" into the formula [tex]d=s\sqrt{2}[/tex], you get that the lenght of the diagonal of this square is:
[tex]d=3\sqrt{2}\ m[/tex]
Please help me out please
The purple area is the sum of the circle sector and the triangle:
[tex]A = A_s+A_t[/tex]
Let's compute them one at the time:
The sector is identified by an angle of 260°, because it is the remainder of a 100° angle.
We can build this simple proportion
[tex]\text{total area}\div\text{total angle}=\text{sector area}\div\text{sector angle}[/tex]
The area of the circle is [tex]\pi r^2[/tex], so we have
[tex]\pi 8.35^2\div 360= A_s\div 260[/tex]
Solving for the sector area, we have
[tex]A_s = \dfrac{\pi\cdot8.35^2\cdot260}{360} = \dfrac{8.35^2\cdot 13\pi}{18}[/tex]
The triangle is an isosceles triangle, because two of the sides are radii. This means that the height is also a bisector, so we can cut the triangle in two 90-50-40 triangles.
Using the law of sines, we can deduce that the height is
[tex]8.35\sin(40)[/tex]
And half the base is
[tex]8.35\sin(50)[/tex]
So, the area of the triangle is
[tex]A_t = 8.35^2\sin(40)\sin(50)[/tex]
So, the purple area is
[tex]A = A_s+A_t =\\\dfrac{8.35^2\cdot 13\pi}{18}+8.35^2\sin(40)\sin(50) = 8.35^2\left(\dfrac{13}{18}\pi+\sin(40)\sin(50)\right)\approx 192.5[/tex]
What is the measure of
Answer:
91
Step-by-step explanation:
The lines that are parallel are parallel and because of that 89+91=180 for two angles of the square on the same side.
The histograms below show the ages of dogs at four different shelters. For which set of data is the mean most likely greater than the median?
Answer: the answer is a
Answer:
a
Step-by-step explanation:
HELP! AND PLS EXPLAIN!
Name the point. Write the result in the form a + bi.
Answer:
-7+6i
Step-by-step explanation:
On the Cartesian x-y plane, a point is located by giving the ordered pair of its coordinates. A point in this position on the x-y plane would have coordinates (-7, 6). That is, it is located 7 units to the left of the vertical axis, and 6 units above the horizontal axis.
The complex plane is similar in many ways, but each point represents a single number (not a pair of numbers). That single number has two parts: a real part and an imaginary part. The real part is measured by the real axis, a horizontal axis that looks very much like the x-axis of a Cartesian plane. The imaginary part is measured against the imaginary axis, a vertical axis that looks very much like the y-axis of a Cartesian plane.
Just as an ordered pair locates a point on the Cartesian plane, a complex number with a real part and an imaginary part locates a point on the complex plane. The imaginary part is identified by the "i" multiplier. (In some fields of study, notably Electrical Engineering, "j" is used instead of "i", because "i" has a different meaning.)
Here, your point is 7 units left of the imaginary axis, so has a real part of -7. It is 6 units above the real axis, so has an imaginary part of 6. When both parts are written together, the number is written -7+6i.
Comparing this form to a+bi, we find a=-7, b=6.
what is the period of the parent cosine function, y = cos(x)
Answer:
2π
Step-by-step explanation:
This is a little something you have to memorize, but you could derive it from the equation pb = 2π. In the parent function, the b value is 1, so the period, p, is equal to 2π/1 or just 2π.
What is the period of the parent cosine function, y = cos(x)?
360 degrees
What is the period of the cosine function shown in the graph?
1080 degrees
Which type of transformation of the parent function is shown by the graph?
horizontal stretch
given any triangle ABC labeled as shown, the law of sines states that:
Answer:
A. The ratios of the sine of the angle to the opposite side are the same.
Step-by-step explanation:
The law of sines is ...
sin(A)/a = sin(B)/b = sin(C)/c
Answer:
Option A is correct that is the ratio of the sine of an angle to the length of the opposite side is the same for all part of the triangle.
Step-by-step explanation:
Given:
Three angles of the triangles = ∠A , ∠B and ∠C
Three Sides of the triangle = a , b , c
We need to find statement which states the Law of Sines.
We know that Law of Sines is given by,
[tex]\frac{a}{sin\,A}=\frac{b}{sin\,B}=\frac{c}{sin\,C}[/tex]
or
[tex]\frac{sin\,A}{a}=\frac{sin\,B}{b}=\frac{sin\,C}{c}[/tex]
Therefore, Option A is correct that is the ratio of the sine of an angle to the length of the opposite side is the same for all part of the triangle.
(Please dont ignore, need help) ❗️
Answer:
[tex]5.x=5x\\x^{2} =4, x=2\\x=2[/tex]
Step-by-step explanation:
hope its right
How many solutions does the system of equations have? 2x + 3y = 6 y=-2/3x-1A. 0 B. 1 C. 2 D. infinite
Answer:
0
Because -2/3x-1=2-2/3x
-2/3x+2/3x=2+1
0=3
and that's wrong, so there is no solution.
ANSWER
A. 0
EXPLANATION
The first equation is
2x + 3y = 6
The second equation is
y=-2/3x-1
Let us rewrite the first equation in slope-intercept form.
3y =-2x+ 6
[tex]y = - \frac{2}{3} x + 2[/tex]
We can see that both equations has the same slope,
[tex] m = - \frac{2}{3} [/tex]
but different y-intercepts.
This implies that the two lines do not intersect because they are parallel.
Therefore the system has no solution.
Factor completely. y2 - 12y + 32 A. (y + 4)(y + 8) B. (y - 4)(y - 8) C. (y + 18)(y + 2) D. (y - 18)(y - 2)
Ask: Which two numbers add up to -12 and multiply to 32?
-8 and -4
Rewrite the expression using the above
= (y - 4)(y - 8)
Answer:
The correct answer is option B.
Step-by-step explanation:
Given quadratic equation : [tex]y^2-12y+32[/tex]
Using middle term splitting theorem:
=[tex]y^2-12y+32[/tex]
=[tex]y^2-8y-4y+32[/tex]
=[tex]y(y-8)-4(y-8)[/tex]
=[tex](y-8)(y-4)[/tex]
y = 8, 4
The factors of given quadratic equation is (y-8)(y-4).
What is the value of pi to 10 decimal places
Answer:
3. 415926535
Step-by-step explanation:
I know it's a long question but the reward is great!
Please answer if you truly know how to help!! Thank you!!
After a dreary day of rain, the sun peeks through the clouds and a rainbow forms. You notice the rainbow is the shape of a parabola.
The equation for this parabola is y = -x2 + 36.
In the distance, an airplane is taking off. As it ascends during take-off, it makes a slanted line that cuts through the rainbow at two points. Create a table of at least four values for the function that includes two points of intersection between the airplane and the rainbow.
What is the domain and range of the rainbow? Explain what the domain and range represent. Do all of the values make sense in this situation? Why or why not?
What are the x- and y-intercepts of the rainbow? Explain what each intercept represents.
Is the linear function you created with your table positive or negative? Explain.
What are the solutions or solution to the system of equations created? Explain what it or they represent.
Again thank you if you can help me with this!!
Answer:
Step-by-step explanation:
Here y = -x^2 + 36.
We can choose x values pretty much at random and then calculate the associated y values:
x y = -x^2 + 36
---- --------------------
0 36
2 -2^2 + 36 = 32
-2 -4 + 36 = 32
3 -9 + 36 = 27
You did not share the equation of the slanted line. Let's assume that the equation of this line is y = mx + b. The first two points in the table above are (0, 36) and (2, 32). We could find the equation of this line as follows:
Slope: as we move from (0, 36) to (2, 32), x increases by 2 and y decreases by 4. Thus, the slope is m = rise / run = -4/2, or -2. Using info from the point (0, 36), we find the y-intercept of this straight line:
y = mx + b becomes 36 = m(0) + b, so b = 36, and the line is y = -2x + 36.
We need to find the points of intersection of y = -2x + 36 and y = -x^2 + 36. We can equate these equations to eliminate y: -2x + 36 = -x^2 + 36, or
-2x = -x^2. Equivalently, 2x - x^2 = 0, or (x)(2 - x) = 0. Then x = 0 and x = 2.
This says that the line and the parabola intersect in at least two places:
(0, 36) and (2, 32).
Charlene's swimming pool is rectangular. It has an area of 120 ft2. Charlene drew a scale drawing of the pool using the scale LaTeX: 1\frac{1}{2} 1 1 2 centimeters = 2 feet. What was the area of the scale drawing?
Answer:
The area of the scale drawing is [tex]67.5\ cm^{2}[/tex]
Step-by-step explanation:
The scale drawing is
[tex](1\frac{1}{2})/2\ \frac{cm}{ft}[/tex]
Convert to an improper fraction
[tex](1\frac{1}{2})=3/2[/tex]
substitute
[tex](1\frac{1}{2})/2=(3/4)=0.75\ \frac{cm}{ft}[/tex]
The area is equal to
[tex]120\ ft^{2}[/tex]
substitute
[tex]120*(0.75)^{2}=67.5\ cm^{2}[/tex]
The area of the scale drawing of Charlene's swimming pool is [tex]\( 67.5} \)[/tex] square feet.
To find the area of the scale drawing of Charlene's swimming pool, we need to understand the scale given and how it applies to the dimensions and area.
Given:
Actual area of the swimming pool: [tex]\( 120 \) ft\(^2\)[/tex]
Scale of the drawing: [tex]\( 1 \frac{1}{2} \) centimeters = 2 feet[/tex]
First, convert the scale to centimeters:
[tex]\[ 1 \frac{1}{2} \text{ centimeters} = 1.5 \text{ centimeters} \][/tex]
Now, determine the scale factor for the dimensions:
[tex]\[ \text{Scale factor} = \frac{1.5 \text{ cm}}{2 \text{ ft}} \][/tex]
To find the area of the scale drawing, we need to square the scale factor, because area is two-dimensional:
[tex]\[ \text{Area scale factor} = \left(\frac{1.5}{2}\right)^2 \][/tex]
[tex]\[ \text{Area scale factor} = \left(0.75\right)^2 \][/tex]
[tex]\[ \text{Area scale factor} = 0.5625 \][/tex]
Now, calculate the area of the scale drawing:
[tex]\[ \text{Area of scale drawing} = 0.5625 \times 120 \text{ ft}^2 \][/tex]
[tex]\[ \text{Area of scale drawing} = 67.5 \text{ ft}^2 \][/tex]
Zack has two strings of equal length. One string is red the other is yellow. After cutting 2.5 meters of the red string and 3.8 M of the yellow string, the length of the red string is 1.5 times that of the yellow strain. Find the original length of the yellow string.
Answer:
6.4 m
Step-by-step explanation:
We have 2 expressions here. The first one is the fact that r = y. That's one of 2 equations. The second one involves whats' left after cutting off certain lengths of each color string. We cut 2.5 m from red, we cut 3.8 m from yellow. We know that what's left of red is 1.5 times the length of what's left of yellow. What's left of red is r - 2.5; what's left of yellow is y - 3.8. We know that r = 1.5y, so filling that in with our corresponding expressions gives us
r - 2.5 = 1.5(y - 3.8)
Distribute to get
r - 25 = 1.5y - 3.2
Now from the first expression, r = y, so fill in y for r to get an equation in one variable:
y - 2.5 = 1.5y - 3.2
Combine like terms:
-.5y = -3.2 and divide to get
y = 6.4
Check it to make sure it works. What's left of red should be 1.5 times the length of what's left of yellow and y = 6.4:
What's left of red: 6.4 - 2.5 = 3.9
What's left of yellow: 6.4 - 3.8 = 2.6
1.5 x 2.6 = 3.9, just like it should!
How many of those 100 customers would likely want the store to stay open late.
Answer:
Step-by-step explanation:
find the percentage of the people who want the store open longer. of the 40 customers that were surveyed, 12 would want that. 12 divided by 40 is .30, so 30 percent of the customers want it open.
100 more customers are surveyed, so you take 30 percent of 100, which is 30. your answer is "B"
How many milliliters are equal to 4 liters
Answer:
[tex]4,000 ml = 4 liters[/tex]
Hope this helps!
Find the value of x, rounded to the nearest tenth.
Answer:
x= 36.2
Step-by-step explanation:
Because that's a right triangle and the reference angle and adjacent side measures are given to us, we can use the trig ratio for cosine. Cosine relates the side adjacent to (next to...NOT ever the hypotenuse!) the angle to the hypotenuse. Therefore, our equation will look like this:
[tex]cos(28)=\frac{32}{x}[/tex]
Solving for x we have
[tex]x=\frac{32}{cos(28)}[/tex]
Perform that operation on your calculator in degree mode and you'll get that the length of the hypotenuse is 36.2. If for some reason, your math gave you the length of the hypotenuse and it was shorter than one of the other sides, you did something wrong. The hypotenuse will ALWAYS be the longest side in a right triangle.
What are the domain and range of f(x) = (1/6)x + 2? domain: ; range: {y | y > 0} domain: ; range: {y | y > 2} domain: {x | x is a real number}; range: {y | y > 2} domain: {x | x is a real number}; range: {y | y > –2}
Final answer:
The domain of f(x) = (1/6)x + 2 is all real numbers and the range is y > 2.
Explanation:
The domain of the function f(x) = (1/6)x + 2 is {x | x is a real number} because there are no restrictions on the input values. The range of the function is {y | y > 2} because any value of x will give a y-value greater than 2. To find the range, you can consider that the slope of the function is positive, meaning that as x increases, y will also increase, but it will never go below 2.
PLEASE CAN SOMEONE HELP ME ON THIS , IM NOT SURE WHATS SUPPOSE TO BE DONE OR WHAT TO DO. PLEASE HELP PLS
Answer:
[tex]x^{2/3}[/tex]
Step-by-step explanation:
When you have a power then a root like that, you have to divide the power by the root.
So, in this case, you have q square (x²) and a cubic root (³√).
So, you take your square (2) and divide it by the cube (3), to get a new power of 2/3.
Let's verify it with x = 2
[tex]\sqrt[3]{2^{2} } = \sqrt[3]{4} = 1.59\\\\\\2^{2/3} = 1.59[/tex]
So, both expressions equal the same thing, it means they're equivalent.
Find the measure of Angle A. Type the correct answer rounded to one decimal place.
Answer:
22.6°
Step-by-step explanation:
Since all three sides of the right triangle are given, you can use any of the trig ratios to find the angle. I choose to use the tangent.
tan(A) = BC/AC = 5/12
Then the inverse trig function tells you ...
A = arctan(5/12) = 22.6°
Check the picture below.
make sure your calculator is in Degree mode.
A plane flying against the wind flew 270 miles in 3 hours. Flying with the wind, the plane traveled 260 miles in 2 hours. Find the rate of the plane in calm air and the rate of the wind. I want to know the answer for this pleasee
Answer:
The plane would have been going the amount as it supposed to g.
Step-by-step explanation:
The plane flying against the wind is going 90 mph and the plane flying with the wind is traveling at 130 mph. Your welcome
Find the 18th term of the sequence 5, 8, 11, 14, 17...
Answer:
The answer would be 56.
Answer:
56 will be your answer
Step-by-step explanation:
20 23 26 29 32 35 38 41 44 47 50 53 56
Please mark Brainiest.
A bowl contains 24 marbles consisting of 6 white marbles, 8 blue marbles, 7 black marbles, 3 red marbles. What is the probability of drawing a black marble?
6/24
5/24
17/24
7/24
Answer:
D 7/24
Step-by-step explanation:
Because on the first choice, there is a total of 24 marbles
if theres 7 black marbles the chance of pulling a black marble is 7/24
Find the value in degrees 2x+6. X 96
Answer:
x = -0.04166666667
Step-by-step explanation:
2x + 8 * 96 = 0
2x * 96 = -8
x/2 * 96 = -8/2
x * 96 = -4
x = -4/96
x = -0.04166666667
Answer:
198
Explanation:
The way to solve this equation is by using the "X=96" from moving it to the x in the equation witch makes it "2(96) + 6" When the variable is after the letter like 2x it always means multiplying. So when you multiply 2(96) together you get 192, then you would add 6+192 which would equal 198. I hope I helped! :D
Please help me with this
Answer:
first name the triangles
triangle 1=triangleABC
triangle2=trianglePQR
therefore,SSS:sideAB of ABC=sidePQ of PQR
Which expressions are perfect cubes? –1,000,27r21,343p, g3h30 , 1
Answer:
Step-by-step explanation:
1000 = 10³ is a perfect cube.
27r^21 can be re-written as (3r^7)³ and is a perfect cube.
343p can be rewritten as (7)³·∛p. (7)³ is a perfect cube, but ∛p is not.
g³h^30 can be rewritten as (g·h^10)³ and is a perfect cube.
1 is a perfect cube: 1³ = 1
Answer:
A, B, D, E
Step-by-step explanation:
A = 1,000
B = [tex]27r^{21}[/tex]
D= [tex]g^{3}h^{30}[/tex]
E = 1
(just took it on edge)
Consider the two equations, y=5(x-2)^2-6 and (y+2)^2=9
How many solutions are there to this system? Without solving, give a convincing argument explain why there are that many solutions to the system.
Answer:
One solution. A system of linear equations has one solution when the graphs intersect at a point.
1\small{1}
1
2\small{2}
2
3\small{3}
3
-1\small{\llap{-}1}
-
1
1\small{1}
1
2\small{2}
2
3\small{3}
3
-1\small{\llap{-}1}
-
1
yy
y
xx
x
No solution. A system of linear equations has no solution when the graphs are parallel.
1\small{1}
1
2\small{2}
2
3\small{3}
3
-1\small{\llap{-}1}
-
1
1\small{1}
1
2\small{2}
2
3\small{3}
3
-1\small{\llap{-}1}
-
1
yy
y
xx
x
Infinite solutions. A system of linear equations has infinite solutions when the graphs are the exact same line.
Step-by-step explanation:
What is the rectangular form of r=6/costheta
Answer:
The line x=6.
Step-by-step explanation:
The usual translations between polar and rectangular coordinates are ...
x = r·cos(θ)y = r·sin(θ)If we multiply the given equation by cos(θ), we get ...
r·cos(θ) = 6
Using the above translation, this becomes ...
x = 6
Determine which of the mapping diagrams represents a relation that is not a function.
I really need help with this, thank you
A function is a relation where each input is related to exactly one output. In mapping diagrams, if an 'x' value is associated with multiple 'y' values, the relation is not a function. Make sure to check the mapping to determine this.
Explanation:In mathematics, specifically in the area of functions and relations, a function is a type of relation where each input (or 'x' value) is related to exactly one output (or 'y' value). If a relation has an 'x' value that is associated with more than one 'y' value, we say that this relation is not a function. When examining mapping diagrams, you can tell if it's a function or not by checking this rule.
For example, if you have a mapping diagram where the number 1 (the 'x' value) is mapped to both 2 and 3 (the 'y' values), this would not be a function because one input is associated with more than one output. On the other hand, if you have a mapping where every 'x' value is mapped to one 'y' value, such as 1 to 2, 2 to 3 and 3 to 4, this is a function.
Learn more about Functions and Relations here:https://brainly.com/question/2253924
#SPJ12
An engineer measured the slopes of the four straight sections of a roller coaster track listed in the table below. The steepness of each slope is equal to the absolute value of the slope.
I believe it is section 3 because it is the closest to 0.
someone help please?
Two students are using estimation to determine reasonable solutions to the expression 89.1 x 9.3 Katie uses the 99 x 10. Amaya uses the expression 89 x 9.
A.Which is the best comparison of the estimates and the actual product?
B.Both estimates will be less than the original product.
C. Both estimates will be greater than the original product.
Katie’s estimate will be less than the actual product, and Amaya’s estimate will be greater than the actual product.
D. Katie’s estimate will be greater than the actual product, and Amaya’s estimate will be less than the actual product.
Choice D), since Katie went way over the decimals, and Amaya went slightly under to the closest number
Answer:
Amaya's estimate is the closer one.
D. Katie’s estimate will be greater than the actual product, and Amaya’s estimate will be less than the actual product
Step-by-step explanation:
The original expression is 89.1 x 9.3. Katie changed the 89.1 to 99 (difference of 9.9) and the 9.3 to 10 (difference of 0.7). On the other hand, Amaya changed the 89.1 to 89 (0.1 difference) and the 9.3 to 9 (0.3 difference).
Therefore the best comparison would be Amaya's estimate since her numbers are closer to the original expression.
Katie's estimate will be greater than the actual product because she rounded up the numbers and Amaya's estimate will be less than the actual product because she rounded down the numbers.