Sally paints a room in 4 hours, so in 1 hour she paints 1/4 of a room.
Steve paints a room in 8 hours, so in 1 hour she paints 1/8 of a room.
So,
1 hour -----> 1/4 + 1/8 of a room
x hour -----> 1 of a room
If a line has slope a, what is the slope of its reflection across the line y=x?Question content area bottomPart 1The slope of its reflection across the line y=x will be
By definition, let m be the slope a line, then m can be calculated by the following equation:
[tex]m=\frac{y_2-y_1}{x_2-x_1}^{}[/tex]Given that (x1, y1) and (x2, y2) are known points of the line. By reflecting all the points of the line across the line y = x
which of these answers are in standard for of the linear equation?
hello
the standard linear equation can be written as
[tex]\begin{gathered} x+y=z \\ \text{where z = any variable} \end{gathered}[/tex]in the question here, the options that corresponds to the answer here are
[tex]\begin{gathered} 3x+y=8 \\ x+4y=12 \\ 5x+24y=544 \end{gathered}[/tex]2х +8y = 16 -3х +6y = 30determine the number of solutions
Given: The system of equation below
[tex]\begin{gathered} 2x+8y=16 \\ -3x+6y=30 \end{gathered}[/tex]To Determine: The number of solutions
Solution
Combine the two equations and solve
[tex]\begin{gathered} equation1:2x+8y=16 \\ equation2:-3x+6y=30 \end{gathered}[/tex]Multiply equation by 3 and equation 2 by 2
[tex]\begin{gathered} 3(2x+8y=16)=6x+24y=48==equation3 \\ 2(-3x+6y=30)=-6x+12y=60==equation4 \end{gathered}[/tex]Add equation 3 and 4
[tex]\begin{gathered} 6x-6x+24y+12y=48+60 \\ 36y=108 \\ y=\frac{108}{36} \\ y=3 \end{gathered}[/tex]Substitute y in equation 1
[tex]\begin{gathered} 2x+8y=16 \\ 2x+8(3)=16 \\ 2x+24=16 \\ 2x=16-24 \\ 2x=-8 \\ x=-\frac{8}{2} \\ x=-4 \end{gathered}[/tex]Hence, x = -4, y = 3
Identify the graphs that represent a linear function. Check all that apply.On a coordinate plane, a line has a positive slope.On a coordinate plane, a curve opens down.On a coordinate plane, a graph decreases, increases, and then decreases again.On a coordinate plane, a line has a negative slope.
A linear function is represented by a straight line, that means the right answers are those graph with straight lines.
Therefore, the right graphs are the first and the last one.• The first graph represents a linear function with a positive slope.
,• The last graph represents a linear function with a negative slope.
First and last one.
uhh yeah its right i jus tried it
I need help with this questions please. This is non graded.
Given that we have to write the quadratic equation and then we have to solve it and represent it graphically.
Then,
let the equation be
[tex]x^2+10x-24=0[/tex]To find the roots we will do the factorization then we have
[tex]\begin{gathered} x^2+10x-24=0 \\ x^2+12x-2x-24=0 \\ x(x+12)-2(x+12)=0 \\ (x+12)(x-2)=0 \\ x+12=0\text{ and x-2=0} \\ x=-12\text{ and x = 2} \end{gathered}[/tex]So the roots are -12 and 2.
In the sketch below, A ABC is similar to AXY Z. Find the length of side x
From geometry, we know that if two triangles are similar, then their corresponding sides are in proportion.
From the statement, we know that ΔABC is similar to ΔXYZ.
From the diagram, we see that:
• AB = 15 is the corresponding side to XY = 10,
,• BC = 9 is the corresponding side to YZ = x.
So we must have the equality:
[tex]\begin{gathered} \frac{AB}{XY}=\frac{BC}{YZ}, \\ \frac{15}{10}=\frac{9}{x}, \\ 1.5=\frac{9}{x}. \end{gathered}[/tex]Solving for x, we get:
[tex]\begin{gathered} 1.5x=9, \\ x=\frac{9}{1.5}=6. \end{gathered}[/tex]Answerx = 6
In what they call “Year Zero," a group of 26 people started a settlement. Every yearthe population changes as babies are born, people move in, and people move out.Generally, the population increases by an average of 2.6 people a year.At the same time, a nearby established community discovered that their populationcould be described by the following function, where f(x) is the population, inpeople, and x is the time, in years, from "year zero."f(x) = -5.3x + 256Part AUsing your knowledge of functions, explain specifically why both communities' waysof expressing their populations represent functions. Provide evidence to supportyour answerPart BAnalyze the functions and compare the populations for the two communities overtime by describing in detail under what conditions one community's population isgreater than the other's population. Provide evidence to support your answer.
Solution
In the first paragraph,
It is given that a group of 26 people started a settlement and the population increased by an average of 2.6 people a year.
We can represent the population function as ;
g(x) = 26 + 2.6 x
Where x denotes the number of years and g(x) is the population after some certain years.
At a nearby community, it was discovered that the population can be written as;
f(x) = -5.3x + 256
Part A.
The population can be expressed as a function because the population at a particular time depends on the number of years x.
Specifically, it can be represented as a linear function because the rate at which the population increases per year is constant.
Part B.
Equating the functions
-5.3x + 256 = 26 + 2.6x
=> 5.3x + 2.6x = 256 - 26
=> 7.9x = 230
=> x = 29
Therefore, if the number of years is less than 29
The population of the first community will be less than the population of the second community
If the number of years is greater than 29
The population of the first community will be greater than the population of the second community
determine if the following sequence is Arithmetic if so what is the common difference 77 44 16 -12
Answer:
The sequence is not an arithmetic sequence.
Explanation:
Given the sequence:
[tex]77,44,16,-12,\ldots[/tex]Calculate the difference between the terms below:
[tex]\begin{gathered} 44-77=-33 \\ 16-44=-28 \\ -12-16=-28 \end{gathered}[/tex]Observe that the differences between the terms are not the same all through.
Thus, there is no common difference which implies that the sequence is not an arithmetic sequence.
Find the upper quartile of the first ten natural numbers.
Answer:
8
Explanation:
The first ten natural numbers are:
[tex]1,2,3,4,5,6,7,8,9,10[/tex]To find the upper quartile, separate the numbers into two halves:
• Lower Half: 1,2,3,4,5
,• Upper Half: 6,7,8,9,10
The upper quartile is the number in the middle of the upper half.
The number in the middle of the upper half = 8
Therefore, the upper quartile of the first ten natural numbers is 8.
what line is perpendicular to the line y = 2x+4 ? what line is parallel to the line y+2xt4? Options1) y=2x+12) y=1/2x+63) y=-1/2x+104) y=-2x+3
Given the line
[tex]y=2x+4[/tex]The line is expressed in slope-intercept form:
[tex]y=mx+b[/tex]Where
m is the slope
b is the y-intercept
1) Any line that has the same slope as this line will be parallel to it.
The slope of the line is m=2
From the given options, the only one that has the same slope as the given line is the first one
[tex]y=2x+1[/tex]2) For perpendicular lines, the slope of a line perpendicular to another is the inverse negative of the slope of the line.
So let
[tex]y=nx+c[/tex]Represent the equation of the line perpendicular to the given one. The relationship between their slopes can be expressed as:
[tex]n=-\frac{1}{m}[/tex]The slope of the line is m=2 so the slope of the perpendicular line is
[tex]n=-\frac{1}{2}[/tex]A line with slope -1/2 will be perpedicular to the given one. Looking at the options, the line that can be perpendicular to this one is
[tex]y=-\frac{1}{2}x+10[/tex]The correct option is the third one.
George is a salesperson in a jewelry store and earns $100 per week, plus 10% of his weekly sales. If George makes $425 in one week , what are his sales for that week? $5,250$4,250$4,000$3,250
Since George earns $100 per week plus 10% of his weekly sales
Assume that his weekly sales are $x
Then he earns 100 + 10% of x
Since he makes $425 in a week, then
[tex]\begin{gathered} 100+\frac{10}{100}\times x=425 \\ 100+0.1x=425 \end{gathered}[/tex]Subtract 100 from both sides
[tex]\begin{gathered} 100-100+0.1x=425-100 \\ 0.1x=325 \end{gathered}[/tex]Divide both sides by 0.1
[tex]\begin{gathered} \frac{0.1x}{0.1}=\frac{325}{0.1} \\ x=3250 \end{gathered}[/tex]His sales for that week are $3250
The answer is D
What is the mean? 8 3 9 8 6 8
The mean of 8 3 9 8 6 8 is
[tex]\frac{8+3+9+8+6+8}{6}=\text{ 7}[/tex]The mean is 7
The set of all nunbers, including all rational and irrational number?
Rational numbers are type of real numbers that can be represented as a simple fraction. Rational numbers can be formed by dividing 2 integers, Rational number can be represented in this form x/y. Where y is not equal to zero.
Example of rational numbers are as follows
[tex]r=1.5,5,\frac{3}{4}[/tex]Use the diagram and problem below to find the missing anglemeasure.
Given:
BAC = 33 degrees
BDC = 35 degrees
Solution:
From the properties of an isosceles triangle:
The base angles of an isosceles triangle are equal. Hence from triangle BDC, we have:
[tex]\angle\text{BDC = }\angle\text{BCD = 35}^0[/tex]We can obtain angle DBC using the theorem that the sum of angles in a triangle is 180 degrees:
[tex]\begin{gathered} \angle DBC=180^0-35^0-35^0 \\ =110^0 \end{gathered}[/tex]To find angle ABD, we use the theorem of congruency. i.e
[tex]\Delta\text{ ABD }\cong\text{ }\Delta\text{ ABC}[/tex]Hence,
[tex]\angle\text{ ABD = }\angle\text{ ABC}[/tex]Since the angles ABD, ABC and DBC lie at a point, we have:
[tex]\begin{gathered} Let\text{ }\angle\text{ ABD = x} \\ x+x+110^0=360^0 \\ 2x=250^0 \\ x=125^0 \end{gathered}[/tex]Answer : angle ABD = 125 degrees
Which of the following graphs to the probability that z-score is between 0 and 1?
The z-score of a measure is given by the following formula
[tex]z=\frac{x-\mu}{\sigma}[/tex]where x represents the measure, mu represents the mean of the distribution, and sigma represents the standard deviation.
If we have a z-score equal to zero, our measure will be
[tex]\begin{gathered} 0=\frac{x-\mu}{\sigma} \\ 0=x-\mu \\ x=\mu \end{gathered}[/tex]a z-score equal to zero represents the mean of the distribution.
For a z-score equal to 1, we have
[tex]\begin{gathered} 1=\frac{x-\mu}{\sigma} \\ \sigma=x-\mu \\ x=\mu+\sigma \end{gathered}[/tex]Then, the interval between z = 0 and z = 1 is the interval between the mean and one positive standard deviation.
[tex](\mu,\mu+\sigma)[/tex]The graph that represents this interval is the first graph.
If ƒ (7) = 22, thenf-¹(f(7)) = [?]
Remember the following property of invertible functions:
[tex]f(x)=y\qquad\Leftrightarrow\quad f^{-1}(y)=x[/tex]Then:
[tex]f^{-1}(f(x))=x\qquad\forall x[/tex]Then:
[tex]f^{-1}(f(7))=7[/tex]Therefore, the answer is: 7.
a dodecagon is a polygon with 12 sides. what's the sum of the interior angles of a dodecagon
Answer:
1800 degrees
Explanation:
The sum of the interior angles of a dodecagon can be calculated using the following equation:
Sum of the interior angles = ( n - 2 ) x 180
Where n is the number of sides of the polygon.
So, if we replace n by 12, we get:
Sum of the interior angles = ( 12 - 2 ) x 180
Sum of the interior angles = 10 x 180
Sum of the interior angles = 1800
Therefore, the sum of the interior angles of a dodecagon is 1800 degrees.
Write the coordinates of the vertices after a translation 2 units left and 1 unit up. 10 D E F -10 0 10 -10 D(-6, 4) → E(0,4) → Ell F(-4, 2) + FIC D
We need to subtract 2 from our x-coordinate and add 1 to our y-coodrinate. Doing this gives us
[tex]D(-6,4)\rightarrow D(-8,5)[/tex][tex]E(0,4)\rightarrow E(-2,5)[/tex][tex]F(-4,2)\rightarrow F(-6,3)[/tex]And hence, we have correctly given the coordinates of our translated points.
How many times smaller is 2 x 10^-12 than 4 x 10^-10?
the ratio is,
[tex]=\frac{4\times10^{-10}}{2\times10^{-12}}[/tex][tex]\begin{gathered} =2\times10^{12-10} \\ =2\times10^2 \\ =200 \end{gathered}[/tex]so 2 x 10 ^-12 is 200 times smaller than 4 x 10 ^-10
The enrollment at a local college increased 3% over last year's enrollment of 500. Find the current enrollment.
Given:
Last year's enrollment is 500.
Enrollment increased percentage is 3%
[tex]\begin{gathered} \text{Increased enrollment=500}\times\frac{3}{100} \\ \text{Increased enrollment=}5\times3 \\ \text{Increased enrollment=}15 \end{gathered}[/tex][tex]\begin{gathered} \text{Current enrollment=500+15} \\ \text{Current enrollment=}515 \end{gathered}[/tex]Eleanor had an average daily balance of $250.82 in her chargeaccount. She paid 1.7% interest on that amount. Compute her financecharge.a. $254.58b. $.13c. $37.63d. $4.26
For an daily balance of P in her charge account and an interest paid at a rate of r, her finance charge is given by the expression:
F = r*P
For r = 1.7% and P = $250.82, we have:
F = 0.017*250.82
F = $4.26
Answer: d
a hot air balloon ascended to a height of 35 meters 2 minutes after launch after some time the ballons altitude began to change by -3¼ meters every 9 minutes to avoid a tree the hot air ballon flew up by 5½ meters what is the new altitude of the hot air balloon
Our objective for this case is find the final altitude for this problem
The first distance is x1=35 m after 2 min =120 sec
The second distance is :
[tex]x_2=-\frac{13}{4}\frac{m}{mi}\cdot9\min =-\frac{117}{4}m[/tex]Then flight up:
[tex]x_3=5\frac{1}{2}m=\frac{11}{2}m[/tex]Then the final altitude would be:
[tex]x_1+x_2+x_3[/tex]And replacing we got:
[tex]35m-\frac{117}{4}m+\frac{11}{2}m[/tex]And after we operate we got:
[tex]\frac{45}{4}m=11.25m[/tex]134TIME REMAINING22:39Which statements about the diagram are true? Selectthree optionsDE+EF > DFD A DEF is an isosceles triangle5
Statements that are true:
DE + EF > DF
DEF is an scalene triangle
5 < DF < 13
Consider the circle Which instructions can be used to find the circle correctly
Answer:
Explanation:
Given a circle, we want to identify its center
A way to do this is to draw two chords at any part of the circle
A chord is a line inside the circle that joins two points on the circumference
The next thing to do here is to draw a perpendicular bisector through each of these chords
Now, the point at which these perpendicular bisectors intersect is the center of the circle
This mean option B is the correct answer choice
b. What is the sample space if you spin the spinner TWO TIMES?RedYellowBlueRedYellowBluec. One spin, P(red)(fraction)d. Two spins, Pared then blue)(decimal to 2 places)e. Two spins, P(yellow or red)=% (percent to 1 decimal place)
Hanna, this is the solution:
As you can see there are three equal sectors colored yellow, blue, red, therefore, the sample space for spinning the spinner two time is:
{yellow-yellow, blue-yellow, red-yellow, red-blue, red-red, blue-blue}
Spin the spinner one time:
• Red = 1/3 or 0.33
,• Blue = 1/3 or 0.33
,• Yellow = 1/3 or 0.33
Spin the spinner a second time:
• Red - Red = 1/3 * 1/3 = 1/9 or 0.11
,• Red - Blue = 1/3 * 1/3 = 1/9 or 0.11
,• Red - Yellow = 1/3 * 1/3 = 1/9 or 0.11
,• Blue - Blue = 1/3 * 1/3 = 1/9 or 0.11
,• Blue - Red = 1/3 * 1/3 = 1/9 or 0.11
,• Blue - Yellow =1/3 * 1/3 = 1/9 or 0.11
,• Yellow - Yellow = 1/3 * 1/3 = 1/9 or 0.11
,• Yellow - Red = 1/3 * 1/3 = 1/9 or 0.11
,• Yellow - Blue = 1/3 * 1/3 = 1/9 or 0.11
,•
I need some help, this one is hard
Arithmetic progression: -25, -37, -49
d = - 12
General formula
An = -25 + (n -1)*(-12)
A85 = - 25 + 84*(-12) = -1033
Which polynomial function is graphed below?-10A. (x) = (x – 3yº (x + 2)B. f(x) = (x - 2y(x +3)C. (*) - (x - 2)(x+3)D. *(x) = (x-3)(x + 2y4
Every polynomial can be written in the form:
[tex]f(x)=(x-a_1)(x-a_2)\ldots_{}[/tex]The a_1, a_2.... are the roots of the polynomial, meaning that f(a_1) = f(a_2) = ... = 0. This happens wen the graph of the polynomial intersects or tangency the x-axis. Whe it only tangecy the x-axis, it means that you have two of the root.
In this case, we have the polynomial tangency the x-axis in x = -2 and intersect the x-axis in x = 3. This means that the polynomial has roots -2, -2 (again) and 3. So:
[tex]\begin{gathered} f(x)=(x-(-2))(x-(-2))(x-3) \\ f(x)=(x+2)(x+2)(x-2) \\ f(x)=(x+2)^2(x-3) \end{gathered}[/tex]Since the order doesn't metter, we can right in this way:
[tex]f(x)=(x-3)(x+2)^2[/tex]Which corresponds to alternative D.
Find the two positive consecutive odd integers whose product is 63.3 and 217 and 89 and 117 and 9
Given: Two positive consecutive odd integers.
Required: To find two positive consecutive odd integers whose product is 63.
Explanation: Let x be a positive odd integer. Then (x+2) is the consecutive positive odd integer. Now according to the question
[tex]x(x+2)=63[/tex]Or
[tex]x^2+2x-63=0[/tex]which can be factorized as follows
[tex](x+9)(x-7)=0[/tex]Which gives
[tex]\begin{gathered} x=7\text{ or } \\ x=-9 \end{gathered}[/tex]Since x is a positive odd integer,
[tex]x\ne-9\text{ }[/tex]Hence the two required integers are
[tex]\begin{gathered} x=7\text{ and } \\ x+2=9 \end{gathered}[/tex]We can also verify our result as the product of 7 and 9 is 63.
Final Answer: Option D is correct.
Find the slope of the line passing through the points (-3, 5) and (-6, 4).13-13-3131
Step 1
Given; Find the slope of the line passing through the points (-3, 5) and (-6, 4).
Step 2
Slope is given as;
[tex]\begin{gathered} y_2=4 \\ y_1=5 \\ x_2=-6 \\ x_1=-3 \end{gathered}[/tex][tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{4-5}{-6-(-3)} \\ m=\frac{-1}{-3}=\frac{1}{3} \end{gathered}[/tex]Answer;
[tex]slope=\frac{1}{3}[/tex]In a mini pharagh, how would I explain wether the rectangles are similar and explain how I know?
If they are similar then the ratio between RS and RQ has to be tha same to the ratio between WV and WX:
RS/RQ = WV/WX
8/5 = 24/15 = 3(8)/3(5) = 8/5
8/5 = 8/5
Answer:
Therefore both rectangles are similar because the ratio of their lenght to their widht is the same (8/5)