What is the square root of 325 rounded to two decimal places?
If BY = 4, YC = 7, XC = 10. Which of the following proportions could be used to solve for AC?
4/7 = 10/AC
7/4 = 10/AC
4/11 = 10/AC
7/11 = 10/AC
Answer:
The correct option is 4.
Step-by-step explanation:
In triangle ABC and XYC,
[tex]\angle BAC=\angle YXC=60^{\circ}[/tex] (Given)
[tex]\angle BCA=\angle YCX[/tex] (Reflexive Property)
By AA rule of similarity,
[tex]\triangle ABC\sim \triangle XYC[/tex]
The corresponding sides of similar triangles are proportional.
Since triangle ABC and XYC, therefore
[tex]\frac{XC}{AC}=\frac{YC}{BC}[/tex]
[tex]\frac{XC}{AC}=\frac{YC}{BY+YC}[/tex]
[tex]\frac{10}{AC}=\frac{7}{4+7}[/tex]
[tex]\frac{10}{AC}=\frac{7}{11}[/tex]
Therefore option 4 is correct.
If sin x =1/2 what
is cos x
Suppose two fair six-sided dice are rolled. what is the probability that they will both come up with the same number?
How to find all values of x where the tangent line is horizontal?
To find x-values where a function's tangent line is horizontal, find the derivative, set it to zero, and solve for x considering any function's restriction.
Explanation:To find all the values of x where the tangent line is horizontal, we need to understand that these are the points where the derivative of the function is zero. This is because the derivative of a function at a point gives us the slope of the tangent line at that point. And, for a line to be horizontal, its slope needs to be zero.
So, to find these values:
Find the derivative of the given function. Set this derivative equal to zero.Solve the equation for x.The solutions will give you the x-values where the tangent line is horizontal. Do note that you need to be aware of the domain and any restrictions of the original function to have valid solutions.
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Help please? what is the length of side x?
Triangle AAS use sine rule
Help me please.
Luke Skywalker's height is 68 inches. The mean height for all Jedi is 66.5 inches and the standard deviation of the Jedi heights is 2.4 inches. What is the z score for Luke Skywalker's height?
Round to the nearest thousandth
The z-score for Luke Skywalker's height is 0.625, indicating that his height is 0.625 standard deviations above the mean.
Z-score Formula: The z-score for Luke Skywalker's height can be calculated using the formula: z = (x - μ) / σ, where x is the individual's height, μ is the mean height, and σ is the standard deviation.
Plugging in the values, we get z = (68 - 66.5) / 2.4 = 0.625 (rounded to the nearest thousandth).
Solve the inequality. Graph the solution set.
2r−9≤−6
There is an expression some people use that says, “What you put into it is what you get out of it.” People might use this expression to describe your skills at a sport or activity and how that relates to the amount of time and effort you spend practicing that activity. Does this expression apply to functions? How? Give an example to support your answer.
The phrase 'What you put into it is what you get out of it' applies to functions in mathematics, where given an value x (input) into a function, you get an output y. It also applies to real life examples, like sports practice, where your input of time and effort has a corresponding output of skill level.
Explanation:Yes, the expression “What you put into it is what you get out of it” can be applied in mathematics, particularly to functions. In mathematical context, this statement represents the fundamental concept of a function, where an input (what you put into it) mapped to an output (what you get out of it). For example, consider a linear function y = 2x + 3. The value of y (output) depends on the value chosen for x (input). Thus, if x = 2 (input), y = 7 (output). The output here is a result of the input 'fed' into the function.
The same idea can be extrapolated to functions in everyday life, such as practicing a sport. The input to the 'function' is the time and effort you put in, and the output is the proficiency you achieve. As with mathematical functions, each 'input' in life tends to have a corresponding 'output', reinforcing the idea of causes having effects.
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The expression 'What you put into it is what you get out of it' applies to functions such that what you put into the function (input) directly influences what you get out of the function (output).
Explanation:Yes, the expression 'What you put into it is what you get out of it' can indeed be applied to the concept of functions in mathematics. A function is a special relation from a set of inputs to a set of possible outputs where each input is related to exactly one output. The input you 'put into' a function is the independent variable and the output or 'what you get out of' the function is the dependent variable.
As an example, consider an equation of a function like y = 2x. Here, 'x' represents the inputs and 'y' the outputs. If you 'put into' this function x = 3 (input), you 'get out of' the function y = 6 (output). Thus, what you 'put into' the function (input) directly influences what you 'get out of' the function (output), demonstrating the principle of 'What you put into it is what you get out of it'
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Find the dot product, a • b. a = 6i + 5j, b = -5i + 4j
Answer:
-10
Step-by-step explanation:
took the test
Zekia divides of 6 cups of fruit juice equally among 8 friends two of her friends don't drink the juice how much juice is leftover
Final answer:
Since Zekia has 6 cups of fruit juice to divide among 8 friends, with 2 not drinking, there will be no juice leftover because each of the 6 drinking friends will receive 1 cup each.
Explanation:
Zekia has 6 cups of fruit juice that she wants to divide equally among her 8 friends, but 2 friends don't drink any. Initially, we would divide 6 cups by 8 to find out how much each friend gets. However, since 2 friends aren't drinking, only 6 friends will be actually consuming the juice.
First, let's calculate the amount of juice each of the 6 friends would receive:
Total juice = 6 cups
Number of friends drinking = 8 - 2 = 6
Juice per friend = Total juice ÷ Number of friends drinking = 6 cups ÷ 6 = 1 cup
So, each of the 6 friends will get 1 cup of juice. Since all 6 cups of juice are consumed, there is no juice leftover.
a garden patio is covered with grey slabs and yellow slabs. 1/5 is grey. 1/4 is yellow. there’s 55 slabs in total. what is the number of yellow slabs
Answer:
44
Step-by-step explanation:
1:4
4+1=5
55/5=11
11*4=44
the answer is 44
PLZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Find the value of x and y.
jen is thinking of a number. the product of this number and 3.4 is 176.8. find jens number.
(need help!) A dart is thrown at the board shown. It hits the board at a random point. Find the probability that it will land in the unshaded region. Round to the nearest percent.
20%
33%
17%
25%
[tex] |\Omega|=360\\
|A|=120\\\\
P(A)=\dfrac{120}{360}=\dfrac{1}{3}\approx33\% [/tex]
3 problems, 50 points
Find the area of the rectangle below (3x-2) (4x-7)
The measure of an angle is two times the measure of a supplementary angle. what is the measure of each angle
Answer:
60 and 120 have a good day!
Step-by-step explanation:
Find the price per ounce rounded to the nearest cent: 1 lb 10 oz for $10.98.
A.) 0.5
B.) 1.98
C.) 0.42
D.) 0.9
The dot product of u with itself is 12. what is the magnitude of u?
Answer: The magnitude of the vector u is √12 units.
Step-by-step explanation: Given that the dot product of a vector u with itself is 12.
We are to find the magnitude of the vector u.
Let <a, b> represents the vector u.
That is, u = <a, b>
Then, according to the given information, we have
[tex]u.u=12\\\\\Rightarrow <a, b>.<a, b>=12\\\\\Rightarrow a^2+b^2=12\\\\\Rightarrow \sqrt{a^2+b^2}=\sqrt{12}\\\\\Rightarrow |u|=\sqrt{12}.[/tex]
Thus, the magnitude of the vector u is √12 units.
Which expression is equivalent to 3(4m − 5)?
The equivalent expression for the given expression is 12m-15.
What is an equivalent expression?Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.
The given expression is 3(4m-5).
Using distributive property A(B+C)=AB+AC, we get
3×4m-3×5
= 12m-15
Therefore, the equivalent expression for the given expression is 12m-15.
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What is the slope-intercept form equation of the line that passes through (3, 4) and (5, 16)?
What is the equation of this circle in general form? x² + y² + 2x + 6y + 4 = 0 x2+y2−2x−6y−26=0 x2+y2−2x−6y+4=0 x2+y2+2x+6y−26=0 a circle on a coordinate plane centered at begin ordered pair 1 comma 3 end ordered pair. the horizontal x-axis ranges from negative 10 to 10 increments of 1. the vertical y-axis ranges from negative 10 to 10 in increments of 1. the circle passes through begin ordered pair negative 5 comma 3 end ordered pair, begin ordered pair 1 comma 9 end ordered pair, begin ordered pair 7 comma 3 end ordered pair, and begin ordered pair 1 comma negative 3 end ordered pair?
A circle on a coordinate plane is centered at the beginning ordered (1, 3). The equation of the circle is x²+y²-2x-6y-26=0
What is the equation of the circle with radius r units, centered at (x,y)?If a circle O has radius of r units length and that it has got its center positioned at (h, k) point of the coordinate plane, then, its equation is given as:
[tex](x-h)^2 + (y-k)^2 = r^2[/tex]
A circle on a coordinate plane is centered at the beginning ordered (1, 3).
The horizontal x-axis ranges from negative 10 to 10 increments of 1. and the vertical y-axis ranges from negative 10 to 10 in increments of 1.
The equation of the circle is
[tex]x^2+y^2-2x-6y-26=0[/tex]
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A pet store is selling a new dog collar for $12.00. If there is a sales tax of 10 percent, what is the actual cost of the collar
The endpoints of one diagonal of a rhombus are (-5,2) and (1,6). If the coordinates of the 3rd vertexare (-6,10), what arethe coordinates of the 4th vertex?
A.(2,-2)
B.(-8,0)
C.(4,8)
D.(-9,8)
Answer:
A. (2,-2)
Step-by-step explanation:
That is the right answer. Hope this helps!!!
Which sequence is modeled by the graph below? Coordinates are 1,1 2,2 3,4 4,8
An item that originally cost $100 is decreased by 8%. The reduced price is then increased by 8%.
The resulting price is _____.
Answer:
The resulting price is $99.36.
Step-by-step explanation:
Original cost of the item = $100
The decrease percentage is 8% or 0.08
So, the reduced price becomes :
[tex]100-(0.08\times100)=92[/tex] dollars
Now again the reduced price is increased by 8%.
So, multiplying the reduced price by 8% and adding it again we get;
[tex]92+(0.08\times92)[/tex] =$99.36
So, the resulting price is $99.36.
Techechtium-99m has a half-life of 6 hours. If 1000mg is in use, in how many hours will 62.5mg remain?
Techechtium-99m has a half-life of 6 hours. It will take 96 hours for 62.5 mg of Techechtium-99m to remain from an initial amount of 1000mg.
Explanation:To determine how many hours it will take for 62.5 mg of Techechtium-99m to remain from an initial amount of 1000mg, we can use the concept of half-life.
Techechtium-99m has a half-life of 6 hours, which means that after every 6 hours, half of the initial amount will decay.
So, to find the number of half-lives required to reach 62.5 mg, we can divide the initial amount by the remaining amount:
1000mg / 62.5mg = 16.
Since each half-life is 6 hours, we can multiply the number of half-lives by 6 to find the total number of hours:
16 x 6 = 96.
Therefore, it will take 96 hours for 62.5 mg of Techechtium-99m to remain from an initial amount of 1000mg.
Which ordered pairs are in the solution set of the system of linear inequalities? y > -1/2x y <1/2 x + 1
Look at the picture.
[tex]y=-\dfrac{1}{2}x\\\\for\ x=0\to y=-\dfrac{1}{2}\cdot0=0\to(0;\ 0)\\\\for\ x=2\to y=-\dfrac{1}{2}\cdot2=-1\to(2;\ -1)\\\\\\y=\dfrac{1}{2}x+1\\\\for\ x=-2\to y=\dfrac{1}{2}\cdot(-2)+1=-1+1=0\to(-2;\ 0)\\\\for\ x=0\to y=\dfrac{1}{2}\cdot0+1=1\to(0;\ 1)[/tex]
Answer: Every points on orange area.
Answer: is c on edge (5,-2) , (3,1) ,(4,2)
Haley measured the distances between her house and two of her friends' houses. ellen's house is 1.41 miles away from haley's, and dirk's house is 6,547 feet away from haley's. whose house is farther away from haley's, and how many feet farther away is it, to the nearest whole foot?
Answer: Ellen's house is farther away by 898 feet.
Step-by-step explanation:
Given: The distance between Haley's house and Ellen's house = 1.41 miles
We know that 1 mile = 5,280 feet
Then, [tex]1.41\text{ miles}=1.41\times5,280\text{ feet}=7,444.8\text{ feet}[/tex]
The distance between Haley's house and Dirk's house = 6,547 feet
Clearly, 6,547<7,444.8
And [tex]7444.8-6547= 897.8\approx898[/tex]
Therefore, Ellen's house is farther away by 898 feet.