Given
The data,
[tex][/tex]if the coordinates of r are (4, 7) and the midpoint of RS is (0, 5 ), what are the coordinates of s?
To solve this problem, we recall that the formula for the coordinates of the midpoint between (x₁,y₁), and (x₂,y₂) is:
[tex]\begin{gathered} x=\frac{x_1+x_2}{2}, \\ y=\frac{y_1+y_2}{2}. \end{gathered}[/tex]Substituting the given coordinates for the midpoint and one of the terminal points, we get:
[tex]\begin{gathered} 0=\frac{4+s_x}{2}, \\ 5=\frac{7+s_y}{2}. \end{gathered}[/tex]Solving the above equations for s_x, and s_y, we get:
[tex]\begin{gathered} s_x=0*2-4, \\ s_y=5*2-7. \end{gathered}[/tex]Finally, we get that the coordinates of s are:
[tex](-4,3).[/tex]Answer:
[tex](-4,3).[/tex]Find the value of x . (Do not round until the final answer . Then round to the nearest tenth as needed .)
According to the given image, x is the radius of the circle.
So, we can find x using Pythagorean's Theorem in the following right triangle.
Where x is the hypothenuse.
[tex]\begin{gathered} x^2=5.3^2+4^2 \\ x=\sqrt[]{28.09+16} \\ x=\sqrt[]{44.09}\approx6.6 \end{gathered}[/tex]Hence, x is 6.6, approximately.use the graph of the table of the parabola to fill in thetable
Given:
The graph of a parabola is given
Required:
Where does the parabola open
The co-ordinate of the vertex
The intercepts
The equation of line of symmetry
Explanation:
a) As we can see the parabola faces downwards
b) The vertex represents the highest point of the circle here. As we cab see, this is the point through which the axis of symmetry passes through to make a symmetrical division of the parabola.
We have the co-ordinates of this point as (-1, 9)
c) The x-intercepts are the two points in which the parabola crosses the x- axis
From the graph, we have the points as 2 and -4
So the x-intercepts are at the points (2, 0) and (-4, 0)
For y- intercept, it is the y co-ordinate of the point at which the parabola crosses the y- axis and the point is (0, 8)
d) To find the axis of symmetry equation, we look at the graph and see the point through the vertex of the parabola that exactly divides the parabola into two equal parts.
The x-value that the line passes through here is the point x = -1 and this is the equation of symmetry.
Final answer:
a) Downwards
b) (-1, 9)
c) x- intercept: (2, 0), (-4, 0)
y-intercept: (0, 8)
d) x= -1
Solve each proportion and give the answer in simplest form 1. 6:8= n: 12 2. 2/7 = 8/n 3. n/6= 11/3 4. 4:n = 6:9
The first proportion:
[tex]6\colon8=n\colon12[/tex]can be written like this:
[tex]\frac{6}{8}=\frac{n}{12}[/tex]then, we have the following:
[tex]\begin{gathered} \frac{6}{8}=\frac{n}{12} \\ \Rightarrow n=(\frac{6}{8})\cdot12=\frac{72}{8}=9 \\ n=9 \end{gathered}[/tex]For the next proportions, we have the following:
[tex]\begin{gathered} \frac{2}{7}=\frac{8}{n} \\ \Rightarrow n=\frac{8}{\frac{2}{7}}=\frac{8\cdot7}{2}=\frac{56}{2}=23 \end{gathered}[/tex][tex]\begin{gathered} \frac{n}{6}=\frac{11}{3} \\ \Rightarrow n=\frac{11}{3}\cdot6=\frac{66}{3}=22 \end{gathered}[/tex]and finally:
[tex]\begin{gathered} \frac{4}{n}=\frac{6}{9} \\ \Rightarrow n=\frac{4}{\frac{6}{9}}=\frac{4\cdot9}{6}=\frac{36}{6}=6 \end{gathered}[/tex]ReTest_Linear Functions Unit Topic 35 of 75 of 7 Items25:50 / 01:30:00 Is the relation a function? If so, is it one-to-one or not one-to-one?
Function
one- to -one
Explanation:For a relation to be a function, each of the input of the function must have only one output.
The input are the x values while the output are the y values.
Input -2 has one output of -1
input -1 has output of -2
input 0 has output 0
input 1 has output 2
input 2 has output 4
Each of the input have only one output.
Hence, it is a function
A function is one-to-one when the elements in the domain has one value in the range.
Hence, it is one-to-one
Simplify by finding the product of the polynomials below. Then Identify the degree of your answer. When typing your answer use the carrot key ^ (press shift and 6) to indicate an exponent. Type your terms in descending order and do not put any spaces between your characters. (2x^2+2x+1)(4x-1) This simplifies to: AnswerThe degree of our simplified answer is: Answer
Solution:
Given:
[tex](2x^2+2x+1)(4x-1)[/tex]To get the product of the polynomial; we use the distributive property of multiplication.
[tex]a(b+c)=ab+ac[/tex][tex]\begin{gathered} (4x-1)(2x^2+2x+1) \\ 4x(2x^2+2x+1)-1(2x^2+2x+1) \\ =8x^3+8x^2+4x-2x^2-2x-1 \\ \text{Collecting similar terms together and simplifying further;} \\ =8x^3+8x^2-2x^2+4x-2x-1 \\ =8x^3+6x^2+2x-1 \end{gathered}[/tex]Therefore, the product of the polynomials is;
[tex]8x^3+6x^2+2x-1[/tex]Determine the discriminant, and then state the nature of the solutions. x^2+4x+7=0The discriminant tells us there is Answer
The discriminant of a quadratic equation is given by:
[tex]\begin{gathered} b^2-4ac \\ \text{with the quadratic equation in the form} \\ ax^2+bx+c=0 \end{gathered}[/tex]•When the calculation of the discriminant gives a negative number, the equation has two complex roots
•when the discriminant is zero, the equation has a root, double root
•when the calculation of the discriminant is a positive number, the equation has two distinct roots.
the given quadratic equation is
[tex]\begin{gathered} x^2+4x+7=0 \\ \text{In this equation, the coefficients will tell us that values for }a,b,\text{ and }c \\ a=1 \\ b=4 \\ c=7 \end{gathered}[/tex]Substitute these values to get the discriminant.
[tex]\begin{gathered} b^2-4ac \\ =(4)^2-4(1)(7) \\ =16-28 \\ =-12 \end{gathered}[/tex]Since the discriminant is negative, we can conclude that there is two complex solutions.
weir the equation of a line for the following problems
The equation of line in slope intercept form is given by:
[tex]y=mx+c[/tex]Where m is the slope and c is the y-intercept
It is given that the slope of the line is 0 and the y-intercept is -3 so it follows:
[tex]m=0,c=-3[/tex]Hence the equation is given by:
[tex]\begin{gathered} y=0x-3 \\ y=-3 \end{gathered}[/tex]Hence y=-3 is the equation of the line ith
If the Mean is 0 and the standard deviation is 1, in which section of the normal distribution curve will a data point be if it is within 2 standard deviations above the mean?
The normal distribution curve has a line of symmetry that divides the curve equally. The mean is at the middle. All values above the mean are to the right of the mean and the right side of the curve. Thus, if the mean is 0 and standard devaition is 1, 2 standard deviations above the mean, then it would be on the right side of the curve.
Simplify: (5−23+2−7)−(25+74−43+2)
From the given expression we get:
[tex](x^5-2x^3+x^2-7)-(2x^5+7x^4-4x^3+2)=x^5-2x^3+x^2-7-2x^5-7x^4+4x^3-2[/tex]Associating similar terms we get:
[tex]\begin{gathered} (x^5-2x^5_{})+(-2x^3+4x^3)+(x^2)+(-7-2) \\ =-x^5+2x^3+x^2-9 \end{gathered}[/tex]3x^4+4x-8How many zeros does the polynomial fiction.
Given that the degree of the given polynomial is 4, it is possible to have at most 4 zeroes .
Graphing the given polynomial we have
Which suggest that the polynomial has 2 real roots, and at most 2 complex roots.
48+58With remainder
if f(x)=sinx, then f'(pi/3)=
Solution
- The function given is
[tex]f(x)=\sin x[/tex]- We are asked to find
[tex]f^{\prime}(\frac{\pi}{3})[/tex]- The differentiation of the sine function gives:
[tex]f^{\prime}(x)=\frac{d}{dx}(\sin x)=\cos x[/tex]- Thus, we can solve the question by simply substituting π/3 into the function f'(x).
- That is,
[tex]\begin{gathered} f^{\prime}(x)=\cos x \\ put\text{ }x=\frac{\pi}{3} \\ \\ \therefore f^{\prime}(\frac{\pi}{3})=\cos\frac{\pi}{3}=\frac{1}{2} \end{gathered}[/tex]Final Answer
The answer is
[tex]f^{\prime}(\frac{\pi}{3})=\frac{1}{2}[/tex]Need!!!!
In the following diagram, A II B
1) Use complete sentences to explain how the special angles created by the intersection of A and B by D can be used to solve for x.
2) Solve for x, showing all of your work.
Find the measure of angle 6.
The value of x in the intersecting lines is 24.
The value of angle 6 is 79 degrees.
How to find angles in intersecting lines?When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate angles, linear angles, vertically opposite angles etc.
Therefore,
∠6 = 3x + 7(corresponding angles)
Corresponding angles are congruent.
Therefore,
3x + 7 + 4x + 5 = 180(sum of angles on a straight line)
7x + 12 = 180
7x = 168
x = 168 / 7
x = 24
∠6 = 3x + 7 = 3(24) + 7 = 72 + 7 = 79 degrees.
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your pay rate is 7$ per hour how mutch money di you make if you worked 1 hour
$7 per hour
if I work 1 hour i will earn $7
(4, - 1); 3x - 5y = 2How do I get the real answer of this?
Step 1: Identify the question
We have the following equation given:
[tex]3x-5y=2[/tex]And for this case we have the following values for x and y given:
x=4, y=-1
We want to check if the point given (4,-1) is a solution for the equation 3x-5y=2
Step 2: Solve the problem
We just need to replace in the equation given x=4 and y=-1:
[tex]3\cdot4-(5\cdot-1)=12+5=17[/tex]Step 3: Solution to the problem
And we can conclude that the point (4,-1) is not on the line 3x-5y=2
Step 4: Solution
For this case we can see that the point is not a solution of the equation because the solution is not equal to 2
Simplify by finding the product of the polynomials below. Then Identify the degree of your answer. When typing your answer use the carrot key ^ (press shift and 6) to indicate an exponent. Type your terms in descending order and do not put any spaces between your characters. (9a^2-4)(9a^2+4) This simplifies to: AnswerThe degree of our simplified answer is: Answer
Given:
[tex](9a^2-4)(9a^2+4)[/tex]The shown represents the difference between the squares
So, the product of the polynomials will be as follows:
[tex]\begin{gathered} (9a^2-4)(9a^2+4) \\ =(9a^2)^2-(4)^2 \\ =81a^4-16 \end{gathered}[/tex]So, the answer will be:
This simplifies to:
[tex]81a^4-16[/tex]The degree of our simplified answer is 4
f(x)=8x+14 and g(x)=5x-8(f o g)(2)=?
Given the functions:
[tex]\begin{gathered} f(x)=8x+14 \\ g(x)=5x-8 \end{gathered}[/tex]1. You need to substitute the function g(x) into the function f(x), in order to find:
[tex](f\circ g)(x)[/tex]Then:
[tex](f\circ g)(x)=8(5x-8)+14[/tex]2. You need to substitute this value of "x into the function:
[tex]x=2[/tex]And then evaluate, in order to find:
[tex](f\circ g)(2)[/tex]You get:
[tex](f\circ g)(2)=8(5(2)-8)+14[/tex][tex](f\circ g)(2)=8(10-8)+14[/tex][tex](f\circ g)(2)=8(2)+14[/tex][tex](f\circ g)(2)=16+14[/tex][tex](f\circ g)(2)=30[/tex]Hence, the answer is:
[tex](f\circ g)(2)=30[/tex]Question 3 Sandwiches Eaton at Lunch Number of Sandwiches clasematon Tona Choose Peanut butter jelly What is the ratio of classmates who like ham sandwiches to the number of classmates who like bologna and turkey sandwiches? 12
1 : 2 (option B)
Explanation:Number that liked ham sandwiches = 6
Number that liked bologna = 2
Number that liked Turkey = 10
Total number that liked bologna and Turkey = 2 + 10 = 12
Ratio of ham to bologna and Turkey = Number that liked ham sandwiches : number that liked bologna and Turkey
Ratio of ham to bologna and Turkey = 6 : 12
Ratio of ham to bologna and Turkey = 1 : 2 (option B)
Evaluate the function f(x) = 2x – 2, when x = –1.a.45b.40c.35d.30
ANSWER
• x = 10.83
,• ∡A = 65º
EXPLANATION
The sum of the measures of the interior angles of any triangle is 180º:
[tex]\measuredangle A+\measuredangle B+\measuredangle C=180º[/tex]Replacing with the angles we know (B and C):
[tex]\measuredangle A+75º+40º=180º[/tex]And solving for ∡A:
[tex]\begin{gathered} \measuredangle A=180º-75º-40º \\ \measuredangle A=65º \end{gathered}[/tex]Then we know that ∡A = 6x, so x is:
[tex]undefined[/tex]Use a composite figure to estimate the area of the figure. the grid has squares with side lengths of 1 cm. Please help.
From the given figure we can see that there is a rectangle with 3 x 4 squares
A semi-circle at the top with about 6 squares
A semi-circle at right with about 4 squares
Then the total number of squares = 12 + 6 + 4 = 22 squares
Since the area of each square is 1 x 1 = 1 cm^2
Then the area of the figure = 22 x 1 = 22 cm^2
The area of the figure is about 22 cm^2
A number is chosen at random from 1 to 50. Find the probability of not selecting odd or prime numbers.
0
Between 1 and 50 are odd and even numbers hence the probability of not selecting an odd or even number is 0
Suppose that the functions g and h are defined as follows.g(x) = x-8h(x) = (x+4)(x+5)(a) Find(-3).h(b) Find all values that are NOT in the domain of8hIf there is more than one value, separate them with commas.
The given functions are
g(x) = x - 8
h(x) = (x + 4)(x + 5)
To find (g/h)x, we would divide g(x) by h(x)
Thus,
g(x)/h(x) = (x - 8)/(x + 4)(x + 5)
To find (g/h)(-3), we would substitute x = - 3 into (x - 8)/(x + 4)(x + 5). Thus, we have
(g/h)(-3) = (- 3 - 8)/(- 3 + 4)(- 3 + 5) = - 11 * 1/2
(g/h)(-3) = - 11/2
All values that are not in the domain are all values of x that does not satisfy the expression. If we put x = - 4 or x = - 5 in the denominator, the denominator would be zero and this makes the expression undefined. these values do not satisfy the g/h
Thus, the values are x = - 4 and x = - 5is
what is the solution to the system of the equation graphed below? type your answer as an ordered pair (x, y)
To find the solution of a system of equation graphed, it is the point where the two lines crosses with each other
for that we found the equation of the line for both of them using the points given
the slope for the orange line is 1/2
the slope for the green line is 1
the y-intercept for the orange line is 3
the y-intercept for the green line is 1
the equation for the orange line is
[tex]y=\frac{1}{2}x+3[/tex]the equation for the green line is
[tex]y=x+1[/tex]equal both of the equations
[tex]\begin{gathered} x+1=\frac{1}{2}x+3 \\ \frac{1}{2}x=2 \\ x=4 \end{gathered}[/tex]using the equation to find the point where they cross
[tex]\begin{gathered} y=x+1 \\ y=4+1 \\ y=5 \end{gathered}[/tex]the solution of the system is (4,5)
Write a sequence of rigid motions to take figure CBA to figure MLK
We have the following:
• The first thing is to ,rotate, in the opposite direction of the hands of the clock, in such a way that it is the same.
,• Then make a ,translation, from left to right until it overlaps one on the other
Determined whether the graph of the equation is symmetric with respect to the y-axis,the orgin,more than one of these,or none of these. y^2=x^2+20
Solution
For this case we have the following equation:
[tex]y^2=x^2+10[/tex]And on this case we have an hyperbola given by:
[tex]y^2-x^2=10[/tex]Then the correct choice is:
Origin
Steve is going to paint a wall that measures 9 feet by 12 feet. If one gallon of paint is needed for each s square foot of wall and each each gallon costs g dollars, in terms of s and g how much does it cost to paint the entire wall?
The wall is 9 feet by 12 feet, so its area is given by,
[tex]\begin{gathered} =9\cdot12 \\ =108 \end{gathered}[/tex]So the area of the wall that needs to be painted is 108 square feet.
Given that each 's' square foot required 1 gallon of paint, then the amount of paint required to paint the complete wall will be calculated as,
[tex]\begin{gathered} \because s\text{ sq ft}\equiv1\text{ gallon} \\ \therefore108\text{ sq ft}\equiv\frac{108\cdot1}{s}=\frac{108}{s}\text{ gallons} \end{gathered}[/tex]So the amount of paint required for the whole wall is 108/s gallons.
Given that 1 gallon of paint costs 'g' dollars, the cost of total paint required will be,
[tex]\begin{gathered} \because1\text{ gallon paint}\equiv g\text{ dollars} \\ \therefore\frac{108}{s}\text{ gallons paint}\equiv\frac{(\frac{108}{s})\cdot g}{1}=\frac{108g}{s}\text{ dollars} \end{gathered}[/tex]Thus, the cost (in dollars) of the total paint required for painting the wall is obtained as,
[tex]\frac{108g}{s}[/tex]Therefore, option D is the correct choice.
Answer the following questions.(a) 39 is what percent of 12.5?(b) 42.5% of what is 20.57?
(a) We are at the percentage of 12.5 which equates to 39. The general formula of getting percentages is:
[tex]N\times percent=percentage\text{ result}[/tex]For this problem, we have N = 12.5 and the percentage result is 39. We are looking on percent, wherein the derive equation to solve this is:
[tex]percent=\frac{percentage\text{ result}}{N}[/tex]We substitute the given on the problem, getting:
[tex]\begin{gathered} \text{percent}=\frac{39}{12.5} \\ \text{percent}=3.12 \end{gathered}[/tex]This answer is not yet in terms of %. We multiply it by 100% to write it in percent notation, hence, the answer in part (a) would be 3.12 x 100% = 312%,
(b) For this part, we are looking at N. Hence, the equation that we will use is:
[tex]N=\frac{percentage\text{ result}}{percent}[/tex]Before calculating, we must adjust first the percent into number notation, that is, divide it by 100%. We can say that 42.5% is also equal to 0.425. Therefore, the value of N in this problem is:
[tex]N=\frac{20.57}{0.425}=48.4[/tex]Answers:
(a) 312%
(b) 48.4
A firm makes circular drink mats , of radius 4.5cm , that are 3mm thick . They want to produce a rectangular box to hold a pile of 12 mats. What are the minimum dimensions of the box.
Please answer with working out
please help
its maths level 2 its hard
The minimum dimensions of the rectangular box will be 9cm by 9cm by 3.6cm or 90mm by 90mm by 36mm
Calculating the dimensions of a rectangular boxTo calculate the dimensions of a rectangular box, firstly measure its length, width, and height using the same units such as millimeters or centimeters for all 3 measurements! Then, multiply the 3 measurements together using Length × Width × Height.
From the question, radius of the circular mat is 4.5cm, hence;
the total length of the mat = 2 × 4.5cm {2radius = diameter}
the total length of the mat = 9cm
The length of the mat is the same around the mat, thus the box has a length of 9cm by width of 9cm.
The height of the rectangular box will be determined by the total thickness of the 12 mats, so;
the thickness of a mat is given as 3mm
thus converting millimeter to centimeter
thickness of a mat = 0.1cm × 3 {as 1mm = 0.1cm}
thickness of a mat = 0.3cm
total thickness of 12 mats = 0.3cm × 12
total thickness of 12 mats = 3.6cm
From our workings, the rectangular box will have a minimum dimension of length 9cm by width 9cm by height 3.6cm or 90mm by 90mm by 36mm.
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Question: pitcher of water holds 48.2 ounces of water in it. The water is oured into two glasses, 12.08 ounces into one glass and 18.86 punces into a second glass. 1. How much water is poured out of the pitcher? I 2. How much water is left in the pitcher? Show all Steps to have full credit
the water in pitcher is 48.2 ounces,
the water poured into one glass is 12.08 ounces
the water poured into another glass is 18.86 ounces
1)
tota water poured into the two glasses is = 12.08 + 18.86 = 30.94 ounces
2)
the water left in the pitcher is 48.20 - 30.94 = 17.26 ounces