For isosceles trapezoid PQRS the coordinates for point R are;; (a - b, c).
What are the coordinates of the trapezoid?We are told that the following figure is an isosceles trapezoid. This tells us that the two non - parallel sides of the given trapezoid are equal.
A parallel side of the trapezoid lies on the x-axis, which tells us that the opposite side is a horizontal line parallel to the x-axis and that the y-coordinate remains the same for all point lie on that side.
Since the opposite side has vertex (b, c), therefore the y-coordinate for point R is c.
The non-vertical sides are equal. Since the horizontal distance between (0,0) and (b, c) is b, then it means that the horizontal distance between point R and (a, 0) is b. So, the x-coordinate of R is (a - b).
Therefore we conclude that the coordinates for point R are (a - b, c).
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14. What is the ordered pair for point 7
A-045)
B.(4.50)
C. 5,0
D. 0,5
in a recent year, 34.1% of all registered doctors were female. If there were 56,600 female registered doctors that year, what was the total number of registered doctors?
Round your answer to the nearest whole number.
324309
doctors were registered that year.
Explanation:
The questions says, "18.1% of all registered doctors are females"
(Consider, total number of registered doctors as
x
)
that's,
18.1
%
of
x
are female.
and
18.1
%
of
x
is
58
,
700
.
Mathematically,
18.1
100
⋅
x
=
58700
x
=
58700
⋅
100
18.1
x
=
324309
doctors were registered that year.
i need to find da slope
Answer:
Slope is -1
Step-by-step explanation:
-5/5= -1
I am not sure if you want an explanation or just the answer, but I am willing to explain it if needed.
There are 121 males and 104 females participating in a marathon. To the nearest percent, what percent of the participants are female?
Answer:
54% are females
Step-by-step explanation:
In total there would be 225 participants -
104 + 121 = 225
Next, Divide 121 and 225. After, multiply by 100.
225/121(100)=53.78
53.78 rounded to the nearest percent is 54.
I hope this helped your question!
In ADEF, FDFE. Name two congruent angles.
E
D
F
D-0
Step-by-step explanation:
It is not possible to determine the congruent angles in the given statement, as it is incomplete and does not provide enough information. In order to determine congruent angles, we need to know the shape and the specific angles being compared. For example, if the statement was "In a triangle ABC, angles A and C are congruent," then we would know that angles A and C are congruent.
a person runs at a speed of 4.5 kilometres per hour. She runs 10 laps on the outside track and 10 laps on the inside track, the inside track has a diameter of 44m. The outside track is 3m thicker than the inside track, how much more minutes did it take her to run the outside lap?
Answer:
Below
Step-by-step explanation:
Assuming a circular track
Outside track is 3 m 'thicker ' so the diameter is (44 + 3 + 3) = 50 m
Outside track circumference = pi * d = pi * 50 = 50 pi m
Inside track circumference = 44 pi
Outside 10 laps = .500 pi KM time = .5 pi km / 4.5 km/hr = .3490658 hr
Inside 10 laps = .444 pi KM time = .444 pi km / 4.5 km/hr = .309974
Difference = .039095 hr =2.35 minutes
Find the equation of a line that passes through (-7,2) and is parallel to the line 7x+2y=0
Answer:
write the given equation in a standard form of y = mx + c
7x + 2y = 0
2y = -7x
y = -7/2x
parallel lines have equal gradient
m = -7/2
y - y1 = m(x - x1)
y - 2 = -7/2(x - (-7) )
y - 2 = -7/2( x + 7 )
y - 2 = -7/2x - 49/2
y = -7/2x - 49/2 + 2
y = -7/2 - 45/2
Please. Help quickly
Answer: it is a
Step-by-step explanation:
28+16x^4 i need it factored completely
Answer:
[tex]4(x^4+7)[/tex]
Step-by-step explanation:
Taking out the greatest common factor,[tex]16x^4+28=4(x^4+7)[/tex].
You are ordering shirts for the math club at your school. Short-sleeved shirts cost $8 each. Long-sleeved shirts cost $16 each. You have a budget of $300 for the shirts. The equation $8x+16y=160$ models the total cost, where $x$ is the number of short-sleeved shirts and $y$ is the number of long-sleeved shirts. a. Graph the equation. Interpret the intercepts
The graph equation has been plotted on the graph which crosses the points (0, 10) and (20, 0) on the y and x axis.
What is a graph equation?Write the equation in the form y = MX + b to determine the slope m and the y-intercept.
This will allow you to graph the equation using the slope and y-intercept (0, b).
The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.
So, we have the equation:
8x+16y=160
Where:
x represents the short sleeves.
y represents the long sleeves.
Now, we need to plot the equation as follows:
(Refer to the graph attached below)
So, the equation crosses the points (0, 10) and (20, 0) on the y and x axis.
Therefore, the graph equation has been plotted on the graph which crosses the points (0, 10) and (20, 0) on the y and x axis.
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A rectangular vegetable garden will have a width that is feet 2 less than the length, and an area of 48 square feet. If x represents the length, then the length can be found by solving the equation: x(x-2)=48
What is the length, x, of the garden?
The length is blank feet. I ended up getting x=8 and x=-6
Answer:
Welcome to Brainly! I saw that this was your very first question. I will gladly assist you with your problem. (see explanation)
Step-by-step explanation:
We must create equations from the provided data and relationships in order to determine the length of the rectangular flower garden. The area and the relationship between the width and length are the measurements that are provided. We create the necessary equations from these. What we do is:
Area = Length x Width
where length = x ft
width = x - 3 ft
area = [tex]54 ft^2[/tex]
[tex]54 ft^2 = x ft (x -3) ft\\\54 ft^2 = x^2 - 3x ft^2[/tex]
When we solve for x, we will get two answers, one of which is x = -6 ft (NOTE: This number cannot be the solution because the length cannot have a negative value).
Which means the correct answer is:
length(x)=9ft
(Hope this helped you
can someone help me with this
The composition function for the given situation is (c·r·b)(x) or (r·c·b)(x). Therefore, options B and F are the correct answers.
The given functions are c(x)=2x, b(x)=x+5 and r(x)=0.75x.
What is the composite function?When the result of one function is used as the input for another, this is known as a composite function.
The most common kind of critical hit simply deals additional damage, most commonly dealing double the normal damage that would have been dealt, but many other formulas exist as well (such as ignoring defense of the target or always awarding the maximum possible damage).
A critical hit has the base damage x multiplied, next the damage reduction is applied to the critical hit. Bonus damage is not subject to damage reduction or critical hits, so this is applied last.
Here, Critical hit × Bonus × Damage reduction
That is, (c·r·b)(x) or (r·c·b)(x)
The composition function for the given situation is (c·r·b)(x) or (r·c·b)(x). Therefore, options B and F are the correct answers.
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The diameters of ball bearings are distributed normally . The mean diameter is 81 millimeters and the variance is 16. Find the probability that the diameter of a selected bearing is greater than 85 millimeters . Round your answer to four decimal places .
The required probability is approximately 0.0228 that the diameter is greater than 85 millimeters.
The probability that the diameter of a selected bearing is greater than 85 millimeters can be found by calculating the z-score for 85 millimeters and then using the standard normal table to find the corresponding probability.
First, we need to standardize the value 85 millimeters by subtracting the mean diameter and dividing by the standard deviation:
z = (85 - 81) / (4 / sqrt(16)) = 4 / 2 = 2
Next, we can use the standard normal table to find the probability that a randomly selected bearing has a diameter greater than 85 millimeters.
Since the distribution is symmetric, we can find the probability that the diameter is less than 85 millimeters and then subtract this probability from 1 to find the probability that the diameter is greater than 85 millimeters. Looking up the z-score 2 in the standard normal table, we find that the probability that the diameter is less than 85 millimeters is approximately 0.9772.
Therefore, the probability that the diameter is greater than 85 millimeters is approximately 1 - 0.9772 = 0.0228.
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Which expression is equivalent to sin
12
COS
os (72) - cos (1) sin (72)?
12
Answer:
Step-by-step explanation:
13. Identify the table that does not represent a function.
The four tables available in choices, table option D is not a function. This is because there is the same x value, x = 2 i.e : ( 2, 3 ) , ( 2, 5 ) , ( 2, 7 ).
What is Function?
Function is a relation which each member of the domain is mapped onto exactly one member of the codomain.
There are many types of functions in mathematics such as :
Linear Function → f(x) = ax + b
Quadratic Function → f(x) = ax² + bx + c
Trigonometric Function → f(x) = sin x or f(x) = cos x or f(x) = tan x
Logarithmic function → f(x) = ln x
Polynomial function → f(x) = axⁿ + bxⁿ⁻¹ + ...
If function f : x → y , then inverse function f⁻¹ : y → x
Let us now tackle the problem!
According to the definition above, it can be concluded that a function cannot have the same x value.
Of the four tables available in choices, table option D is not a function. This is because there is the same x value, x = 2 i.e :
( 2, 3 ) , ( 2, 5 ) , ( 2, 7 ).
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Help pls any one pls fast
Answer:
p=106
Step-by-step explanation:
p and 106 are corresponding so they are =
Write a polynomial to this
The polynomial of degree 3 in factored form is calculated and of the form: y = x(x + 3)(x - 10) + 210
How to write the polynomialInformation given in the question include
degree 3
leading coefficient 1
x intercept (10, 0) and (-3, 0)
y intercept (0, -210)
The polynomial is written starting from the x intercept
x = 10, (x - 10)
x = -3, (x + 3)
(x + 10)(x - 10)
y = (x + 3)(x - 10)
for a polynomial of degree three and leading coefficient 1
y = x(x + 3)(x - 10)
for a y intercept (0, -210)
y = x(x + 3)(x - 10)
- 210 = 0
y = x(x + 3)(x - 10) + 210
The factored form of the polynomial is y = x(x + 3)(x - 10) + 210
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Helppp me reallll fast
Answer:
Reflection over the line y=x
the function f(x) = x(x+2)^3 has the first derivative f'(x) = (4x+2)(x+2)^2 and second derivative f"(x) = 12(x+1)(x+2).
A) Find the intervals where f(x) is increasing or decreasing.
B) Find the values of x where f(x) has local maximum and local minimum values (if there are any).
C) Find the intervals of concavity and the (x,y) coordinates of inflection points (if there are any).
D) Use the info from parts a - c to sketch the graph.
Answer:
A) Increasing: (-0.5, ∞)
Decreasing: (-∞, -2) ∪ (-2, -0.5)
B) x = -¹/₂
C) Concave up: (-∞, -2) ∪ (-1, ∞)
Concave down: (-2, -1)
Points of inflection: (-2, 0) and (-1, -1)
D) See attachments.
Step-by-step explanation:
Given function and derivatives:
[tex]f(x) = x(x+2)^3[/tex]
[tex]f'(x) = (4x+2)(x+2)^2[/tex]
[tex]f''(x) = 12(x+1)(x+2)[/tex]
Part A[tex]\textsf{A function is \textbf{increasing} when the \underline{gradient is positive}}\implies f'(x) > 0[/tex]
[tex]\textsf{A function is \textbf{decreasing} when the \underline{gradient is negative}} \implies f'(x) < 0[/tex]
Increasing function
[tex]\begin{aligned}f'(x) & > 0\\(4x+2)(x+2)^2 & > 0\\2(2x+1)(x+2)^2 & > 0\\(2x+1)(x+2)^2 & > 0\end{aligned}[/tex]
Therefore, the function is increasing on the Interval:
[tex]\left(-\dfrac{1}{2}, \infty \right)[/tex]
Decreasing function
[tex]\begin{aligned}f'(x) & < 0\\(4x+2)(x+2)^2 & < 0\\2(2x+1)(x+2)^2 & < 0\\(2x+1)(x+2)^2 & < 0\end{aligned}[/tex]
Therefore, the function is decreasing on the Interval:
[tex](- \infty, -2) \cup \left(-2,-\dfrac{1}{2} \right)[/tex]
Part BLocal minimum/maximum points occur when f'(x) = 0.
[tex]\begin{aligned}f'(x) &= 0\\(4x+2)(x+2)^2 & = 0\\2(2x+1)(x+2)^2 & = 0\\(2x+1)(x+2)^2 &= 0\\\\2x+1&=0 \implies x=-\dfrac{1}{2}\\(x+2)^2&=0 \implies x=-2\end{aligned}[/tex]
[tex]f''\left(-\dfrac{1}{2}\right) = 12\left(-\dfrac{1}{2}+1 \right)\left(-\dfrac{1}{2}+2 \right)=9 > 0\implies \textsf{minimum}[/tex]
[tex]f''\left(-2\right) = 12\left(-2+1 \right)\left(-2+2 \right)=0\implies \textsf{point of inflection}[/tex]
Therefore, the value of x where f(x) has a local minimum is x = -¹/₂.
Part CAt a point of inflection, f''(x) = 0.
[tex]\begin{aligned}f''(x) &=0\\12(x+1)(x+2)&=0\\(x+1)(x+2)&=0\\\\x+1&=0 \implies x=-1\\x+2&=0 \implies x=-2\end{aligned}[/tex]
Substitute the found values of x into the original function to the find the y-coordinates of the points of inflection:
[tex]\implies f(-1) = -1(-1+2)^3=-1[/tex]
[tex]\implies f(-2) = -2(-2+2)^3=0[/tex]
Therefore, the inflection points are:
(-2, 0) and (-1, -1)A curve y = f(x) is concave up if f''(x) > 0 for all values of x.
A curve y = f(x) is concave down if f''(x) < 0 for all values of x.
Concave up
[tex]\implies f''(x) > 0[/tex]
[tex]\implies 12(x+1)(x+2) > 0[/tex]
[tex]\implies (x+1)(x+2) > 0[/tex]
Therefore, the function is concave up at:
[tex]\left(-\infty,-2\right) \cup \left(-1,\infty \right)[/tex]
Concave down
[tex]\implies f''(x) < 0[/tex]
[tex]\implies 12(x+1)(x+2) < 0[/tex]
[tex]\implies (x+1)(x+2) < 0[/tex]
Therefore, the function is concave down at:
[tex](-2,-1)[/tex]
Part DSee attachment 1 for how to sketch the graph using the information from parts A-C.
See attachment 2 for the final sketch of the graph.
What is the equation of a hyperbola with a = 7 and c = 9? Assume that the transverse axis is horizontal.
The equation of a hyperbola with a=7 and c=9 is (x-0)²/a²-(y-0)²/b²=1, x²/49-y²/32=1.
Define Hyperbola.A hyperbola is a kind of smooth curve that appears to lie in a plane. It is made up of two connected components or branches that are mirror reflections of one another and look like two infinite bows. A hyperbola is a collection of points whose difference in distance between two foci is a fixed amount. This discrepancy is calculated by subtracting the distance from the farther focus from the distance from the closest focus.
As we know the standard equation of the hyperbola with a horizontal transverse axis is:
(x-h)²/a²-(y-k)²/b²
Now, put the given values a=7 and c=9 in the Pythagorean theorem to get the value of b.
c²=a²+b²
(9)²=(7)²+b²
81=49+b²
81-49=b²
32=b²
Now square root both sides:√
32=√b²
√32=b
Assuming that the center of a hyperbola is (0,0):
(x-0)²/a²-(y-0)²/b²=1
x²/a²-y²/b²=1
x²/(7)²-y²/(√32)²=1
x²/49-y²/32 = 1
Therefore, the equation of a hyperbola with a=7 and c=9 (x-0)²/a²-(y-0)²/b²=1, x²/49-y²/32=1.
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Sydney is designing a new board game, and is trying to figure out all the possible
outcomes. How many different possible outcomes are there if she spins a spinner
with four equal-sized sections labeled Red, Green, Blue, Orange and flips a coin?
Please help
Answer:
8
Step-by-step explanation:
For each different outcome of the spinner, there are 2 different outcomes of the coin flip.
4 × 2 = 8
Answer: 8
Use the drawing tool(5) to form the correct answer on the provided number line.
Draw a line segment with a length of 1.5 and a midpoint of -0.5
A line segment with a length of 1.5 and a midpoint of -0.5 is given below:
In the given question, we have to use the drawing tool to form the correct answer on the provided number line.
We have to draw a line segment with a length of 1.5 and a midpoint of -0.5.
As we know that;
Line section on a number line is referred to as a number line segment. A line segment varies from the a lines because a line continues infinitely in both directions, while a line segment is limited by end points. The shortest distance between any two points is a section of a line.
So a line segment with a length of 1.5 and a midpoint of -0.5 is given below:
A line segment a length of 1.5 and a midpoint of -0.5 is notify in the color of red in the graph below.
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Jesus and Isabella spent $3043.51 to buy a new computer together. Jesus spent $438.47 more than Isabella. How much did Jesus spend and how much did Kara spend?
Answer:
Isabella spent $1302.52 and Jesus spent $1740.99.
Step-by-step explanation:
In order to figure out how much each individual person spent, we need to write a mathematical equation to express this situation. An equation in math is a statement that relates two expressions that are equal in value, and can be used to solve for variables. A linear equation with one variable is often presented in is standard form, [tex]ax+b=0[/tex].
In this case, we can represent the amount that Isabella spent with the variable x. Since Jesus spent $438.47 more than Isabella, this amount can be represented with x + 438.47. We can set up our equation as follows:
[tex]x+(438.47+x)=3043.51[/tex]
*Note that the use of parentheses is not necessary but may be useful in making your work clearer!
To solve for x, we should combine like terms and then move the variables to one side and constants to the other. The variable can be isolated by subtracting 438.47 from 3043.51:
[tex]2x+438.47=3043.51[/tex][tex]2x=2605.04[/tex]Now that we have the variable by itself, we can divide by 2 on both sides to solve for x.
[tex]x=1302.52[/tex]As we defined, x equals the amount of money that Isabella spent, which is $1302.52. We can plug that number into x + 438.47 to get the amount that Jesus spent, which we calculate to be $1740.99.
Thus, Isabella spent $1302.52 and Jesus spent $1740.99.
To check our work, we can simply add up the two amounts to see if it totals to $3043.51:
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I don't need help but I am giving the answer to everyone :) hope it helps
The number of cannonballs in illustration is 506.
What is illustration?Math Illustrations enables you to produce more useful geometry figures for your students in less time by fusing the constraint-based design of Geometry Expressions with simple-to-use sketching and graphing features.
The number of cannonballs in the first layer = 1² = 1
Number of cannonballs in the second layer = 2² = 4
Number of cannonballs in the third layer = 3² = 9
So, the generalized formula to count the balls is given as
= n(n + 1) (2n + 1)/ 6
Here, n= the total number of layers
Put n =11
11(11 + 1)(2(11) + 1) / 6
= 11(12)(23)/6
= 3036/6
= 506
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y=-2x+4y=−2x+4y, equals, minus, 2, x, plus, 4 Complete the missing value in the solution to the equation. ((left parenthesis ,-2),−2)
After solving the equation for x, the resultant answer is (3, -2).
What are equations?The definition of an equation in algebra is a mathematical statement that shows the equivalence of two mathematical expressions.
For example, the equation 3x + 5 = 14 comprises the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
So, we have the equation:
y = -2x +4
Now, get value of x for y = -2 as follows:
Fill in the equation with the value of y and find x:
-2 = -2x +4 . . . . use -2 for y
-6 = -2x . . . . . . . subtract 4
3 = x . . . . . . . . . .divide by -2
Therefore, after solving the equation for x, the resultant answer is (3, -2).
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Complete question:
y=−2x+4y, equals, minus, 2, x, plus, 4
Complete the missing value in the solution to the equation.
Given NEB NE is 7.5cm and TAN of B is 4 Fill in the rest of the triangle.
Answer:
Hope the picture will help you........
What do the following equations represent in R3?
Match the two sets of letters:
a. a vertical plane
b. a horizontal plane
c. a plane which is neither vertical nor horizontal
A. −5x+3y=−5
B. x=3
C. y=−9
D. z=−10
A. −5x+3y=−5=a vertical plane
B. x=3=a =a vertical plane
C. y=−9=a=a vertical plane
D. z=−10=b=a horizontal plane
What is a vertical plane?A plane that crosses a vertical line: a perspective plane that is parallel to both the ground plane and the image and passes through the point of sight.
What is a horizontal plane?The body is divided into superior and inferior halves by an anatomical plane called the transverse plane, also referred to as the horizontal plane, axial plane, and transaxial plane. Its angle with the coronal and sagittal planes is perpendicular.
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please help (question above)
The solution of the line is, (3, 2), (-1, 1), (1, 3/2), and the equation of the line is y = 1 / 4 x + 5 / 4, so options A, B, C, E, and F are correct.
What is a line?A line is a shape with an infinite length but no width, depth, or curvature. Lines are one-dimensional objects even though they can exist in two, three, or higher-dimensional contexts.
Given:
The graph of linear equation,
As you can see from the graph the line has coordinates of (3, 2), (-1, 1), (1, 3/2).
Calculate the equation of the line by using the coordinates as shown below,
[tex]y - y_1 = [y_2 - y_1 / x_2 - x_1] (x- x_1)[/tex]
y - 1 = [1 - 2 / -1 - 3] [x-(-1)]
y - 1 = -1 / (-4) (x + 1)
4y - 4 = x + 1
y = 1 / 4 x + 5 / 4
And line can have many solutions, as it can have more than two values.
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Helppppp!!!!!!! Please
Then translons the resulting image units to the right is y=0 5 units.
What is line?
A line segment in geometry is a section of a straight line that is enclosed by two clearly defined end points and contains all of the points on the line that are inside those endpoints. The Euclidean distance between two ends of a line segment determines its length.
Reflect [tex]$\triangle P Q R$[/tex] across the line [tex]$y=0$[/tex]. we can get [tex]$\Delta P^{\prime} Q^{\prime} R^{\prime}$[/tex]. then translate [tex]$\Delta P^{\prime} Q^{\prime} R^{\prime}$[/tex] 5 units to the right. we can get s STU. So the answer is A. y=0 5 units.
A line has length but no breadth, making it a one-dimensional figure. A line is made up of a collection of points that may be stretched indefinitely in opposing directions. Two points in a two-dimensional plane determine it. Collinear points are two points that are located on the same line.
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Shayla’s family room measures 20 ft by 17 ft. There is an area rug centered in the room, 3 ft away from each wall. Shayla wants to pay a company to steam clean just the area outside the rug.
If they charge $10 per square foot, how much will Shayla have to pay?
Shyla pay $2380 to clean the area outside the rug.
What is steam clean?
To use a device that generates hot steam to clean (something).
Given:
Shayla’s family room measures 20 ft by 17 ft.
There is an area rug centered in the room, 3 ft away from each wall.
So, the remaining area of the room will be 17 ft by 14 ft.
Shayla wants to pay a company to steam clean just the area outside the rug.
The total area of the room outside the rug is
17 ft x 14 ft = 238 square feet.
The charge for one square foot is $10.
So, the charge for 238 square foot will be
238 x $10 = $2380.
Hence, Shyla pay $2380 to clean the area outside the rug.
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