What must be true for lines a and b to be parallel lines? Select two options.
Lines a and b are crossed by transversals c and d. The angles formed by lines a, c, and d, clockwise from top left, are (3 x minus 1) degrees, 2, blank, blank, blank, 1. The angles formed by lines b and c are blank, (4 x minus 10) degrees, blank, blank. The angles formed by lines b and d are 58 degrees, blank, blank, blank.
mAngle1 = (4 x minus 10) degrees
mAngle2 = 58Degrees
x = 20
(3 x minus 1) degrees equals = (4 x minus 10) degrees
Angle1 = 58
The expression that must be true for a to be parallel to b are mAngle2 = 58Degrees and <1 = 4x - 10
Lines and anglesA line is the shortest distance between two points and the point where two lines meet is known as an angle
From the figure shown
m<2 = 58 degrees (alternate exterior angle)
Since the sum of angles on a straight line is 180 degrees, hence;
3x-1+<2 + 4x - 10= 180
3x-1 + 58 + 4x - 10 =180
7x + 47 = 180
7x = 180- 47
7x = 133
x = 19
Hence the expression that must be true for a to be parallel to b are mAngle2 = 58Degrees and <1 = 4x - 10
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Answer:
angle 2=58 degrees
angle 1=4x-10 degrees
Step-by-step explanation:
bob baked 60 cookies and brownies. the number of cookies he baked was 4 less than 3 times the number of brownies he baked. how many cookies did bob bake
Answer:
Cookies = 44
Step-by-step explanation:
universal U=60
let the number of cookies be C,
n(C)=(3*b)-4
and the number of brownies be b,
n(b)=?
n(buc)=60
b+c=60
then, c=60-b
substitute for c=60-b.
60-b=3b-4
60+4=3b+b
64=4b
b=16
c=60-b
c= 60-16
c=44
Solve the inequality. Enter the answer as an inequality that shows the value of the variable; for example f > 7, or 6 < w. Where necessary, use <= to write and use >= to write . 15 > y + 10
pls help
The solution to the given inequality is y < 5
Solving inequality expressionsInequality are equations not separated by an equal sign. Given the following parameters
15 > y + 10
Subtract 10 from both sides
15 - 10 > y + 10 - 10
5 > y
Swap
y < 5
Hence the solution to the given inequality is y < 5
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Consider the series one-fourth, startfraction 1 over 16 endfraction startfraction 1 over 64 endfraction startfraction 1 over 256 endfraction ellipsis which expression defines sn? limit of (one-fourth) superscript n baseline as n approaches infinity limit of (1 minus (one-fourth) superscript n baseline) as n approaches infinity limit of one-third (1 minus (one-fourth) superscript n baseline) as n approaches infinity limit of one-third (one-fourth) superscript n baseline as n approaches infinity
The sum of the series is: (c) lim n⇒∝ 1/3(1 - (1/4)^n)
How to evaluate the sum of the series?The complete question is added as an attachment
The given series is a geometric series. So, we first calculate the common ratio (r) using:
r = T2/T1
From the series, we have:
T1 = 1/4 and T2 = 1/16
Substitute the known values in the above equation
r = (1/16)/(1/4)
So, the equation becomes
T = 1/16 / 1/4
Rewrite as product
T = 1/16 * 4
Evaluate the product
r = 1/4
The formula to calculate the sum of a geometric series of is:
Sn = a(1 - r^n)/(1 - r)
Where
a = 1/4 -- the first term
r = 1/4 --- the common ratio
Substitute the known values in the above equation
Sn = 1/4 * (1 - (1/4)^n)/(1 - 1/4)
Simplify the denominator
Sn = 1/4 * (1 - (1/4)^n)/(3/4)
Divide 1/4 by 3/4
Sn = 1/3 * (1 - (1/4)^n)
Take the limit to infinity of the series
Sn = lim n⇒∝ 1/3(1 - (1/4)^n)
We can conclude that, the sum of the series is: (c) lim n⇒∝ 1/3(1 - (1/4)^n)
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Answer:
Step-by-step explanation:
B
When reuben had 3 years left in college, he took out a student loan for $16,902. the loan has an annual interest rate of 4.5%. reuben graduated 3 years after acquiring the loan and began repaying the loan immediately upon graduation.
Answer:
Reuben will have to pay $19,183.77 when he starts to pay the loan off after 3 years.
Step-by-step explanation:
There are 3 important parts to this equation:
1) 16,902
2) 4.5%
3) 3 years
First, let's find the interest rate in decimal form. This is easy enough to do.
take the interest rate (4.5%) and divide by 100. You can do this in your head by moving the decimal point but I will just write it out for the example:
4.5/100 = 0.045
Now that we have that number. we want to get the dollar amount for the interest. this is done by taking the loan amount and multiplying it by the decimal form of the percentage:
16,902 * 0.045 = 760.59
Since the interest rate is NOT compounding the rest is simple.
760.59 * 3 = 2,281.77
2,281.77 + 16902 = 19,183.77
Hope this helps.
In AON networks, a(n) __________ is a point where one or more lines (arrows) begin or terminate, commonly used for depicting an event or activity.
In AON networks, "node" is a point where one or more lines (arrows) begin or terminate, commonly used for depicting an event or activity.
What is Activity-on-Node (AON) diagram?Scheduling logic diagrams of the most fundamental kind. Any activity on the schedule that has no float; Total Float = 0; is considered a critical activity.
Between the project's start and finish, there are vital activity(s) that must be completed continuously. This is known as the critical path.
The importance of AON diagram are-
Because it helps identify the essential path, the arrow diagram is crucial for the project timeline. The critical route is used to determine the most effective schedule while still achieving the objectives required for a project to be successful. The critical path indicates the longest time of every dependent task.It is possible to organize tasks and determine not only when they must be finished but also which ones must be performed and which ones can be skipped while still reaching the project's goals and objectives by creating a schedule. An arrow diagram is essential because of this. It results in the project's ideal schedule.To know more about the AOA and AON networks, here
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im being timed so please be quick thank you !!
Answer:
#3
Step-by-step explanation:
The y-intercept (the point where the line intersects with the y-axis) is -2, and the slope is 2/3 (two units up every three units to the right).
Answer:
C.
Step-by-step explanation:
First, look for the graph that shows a line with a y-intercept of -2. There is only one graph that shows a line with a y-intercept of -2. The graph will be the third graph. Please see attachment for the equation in a graphing calculator.
Hope this helps!
18 *2^5t = 261 what is the solution of the equation
Answer:
0.772
Step-by-step explanation:
Original equation:
[tex]18 * 2^{5t}=261[/tex]
Divide both sides by 18
[tex]2^{5t} = 14.5[/tex]
Rewrite in logarithmic form ([tex]b^x=c \implies log_bc=x[/tex])
[tex]log_214.5 = 5t[/tex]
Divide both sides by 5
[tex]\frac{log_214.5}{5}=t[/tex]
Rewrite the equation so that base is 10 using change of base formula: [tex]log_ba = \frac{log_na}{log_nb}[/tex]
[tex]\frac{(\frac{log14.5}{log2})}{5}=y[/tex]
Keep, change, flip
[tex]\frac{log14.5}{log2}*\frac{1}{5} = \frac{log14.5}{5 * log2}[/tex]
Use a calculator to approximate log14.5 and log2
[tex]\frac{1.161368}{5 * 0.301029996} = t[/tex]
Multiply in denominator
[tex]\frac{1.161368}{1.505149978} = t[/tex]
Divide two values
[tex]t\approx 0.771596[/tex]
Round to nearest thousandth
[tex]t\approx 0.772[/tex]
Mr. smith has 5 courses he teaches at the community college. his course a has 102 students with an average tardiness of 3 students each day. another course has an average tardiness of 5 students each day with 85 enrolled. the average of these two courses receive a b+. what percent of students are tardy in course a? do not include % in answer and round to nearest hundredth. example, if answer is 19.567%, put 19.57.
The percentage of tardiness among the 102 pupils is 2.94.
Calculation of the percentageAccording to the query,
Course A: Total number of students = 102
Number of tardy students = 3
Percent of students tardy in course A = (number of tardy students/total
number of students) * 100
=(3/102)*100
= 2.941
≈2.94
In case of course B: Total number of students = 85 & tardy student = 5
So, the percent of tardy student = (5/85)*100 = 5.88 %
Therefore, it is concluded that the percentage of student tardiness in course A is 2.94.
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how do u solve this? what’s the answer?
The functions that have the properties are (d) I and II only
How to determine the functions?The function property is given as:
[tex]a(x) = a^{-1}(x)[/tex]
The above implies that the inverse function and the original function are equal.
From the list of options, we have:
(a) y = x
Make x the subject
x = y --- the same as the original function
(b) y = 1/x
Make x the subject
x = 1/y --- the same as the original function
Hence, the functions that have the properties are (d) I and II only
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Which one of the following would most likely have a negative linear correlation coefficient? A. distance driven in a car compared to the hours spent driving B. length of a driveway compared to number of cars owned C. temperature of a refrigerator compared to the number of items inside of it D. amount of money spent on baby food as a child ages
The statement that would most likely have a negative linear correlation coefficient is amount of money spent on baby food as a child ages
What is correlation?Correlation coefficient is the value that relates two variables in question. Correlation can be positive, negative or no correlation
Note that the correlation coefficients are only values from 0 and 1. The statement that would most likely have a negative linear correlation coefficient is amount of money spent on baby food as a child ages
The amount of money spent on a baby is never a function of its age. The baby will age regardless.
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What is the domain and range of each function?
FIRST PERSON TO ANSWER GETS BRAINLIEST OR 5 STARS :D
A) f(x) = −2x
Domain:
Range:
g(x) = ½x2 + 5
Domain:
Range:
For f(x) we have:
domain: set of all real numbers.range: set of all real numbers.And for g(x):
domain: set of all real numbersrange: set of all real numbers such that y ≥ 5.How to get the domain and range of each function?
The domain of a function is the set of inputs that we can use on the function, and the range is the set of outputs.
a) f(x) = -2x
This is just a linear equation, as you can see, for no value of x we have a problem, then the domain is the set of all real numbers.
Similar for the range, it covers the set of all real numbers, then:
domain: set of all real numbers.range: set of all real numbers.b) g(x) = 0.5*x² + 5
This is a quadratic function, so the domain is the set of all real numbers again.
Now the range will have a minimum, which is at the vertex of the parabola.
For the parabola the vertex is at x = 0:
g(0) = 0.5*0² + 5 = 5
Then the range is the set of all real numbers equal to or larger than 5.
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Don't get this question
Answer:
17 and 18
Step-by-step explanation:
Writing every 2 digit number gives us :
10-99 including 10 and 99
For the first one we are looking for numbers where the number 3 appears only once so 33 would be invalid.
13,23,30,31,32,34,35,36,37,38,39,43,53,63,73,83,93
There are 17 2-digit numbers that have 3 exactly once
For the second one we are looking for number where the number 3 appears a minimum of once so 33 would be valid :
13,23,30,31,32,33,34,35,36,37,38,39,43,53,63,73,83,93
There are 18 2-digit numbers that have 3 at least once
Hope this helped and have a good day
Which of the following could be appropriate values for an equation to be in Standard Form (Ax + By = C)?
A=-6, B = 8 and C = 3
A=4, B = 0 and C = 9
A=1/6, B = 2/9 and C=0
A=4, B = 1/4 and C=0
Answer:
(2) A=4, B=0, C=9 . . . (4x = 9)
Step-by-step explanation:
A linear equation in standard form has mutually prime integer coefficients with a positive leading coefficient.
Choices:The leading coefficient is negative. Not appropriateCoefficients meet the criteria. Appropriate valuesCoefficients are not integers. Not appropriateCoefficients are not integers. Not appropriateThe values that would be the appropriate values for an equation to be in standard form (Ax + By = C) is A = 4, B = 0 and C = 9.
Linear equation in standard form:The linear equation is the equation which has the coefficient as the mutual prime numbers and the coefficient must be the positive leading coefficient.
From the choices,
A = -6, B = 8 and C = 3. In this case, the coefficient of x (A = -6) is negative, which doesn't leads to positive leading coefficient.A = 4, B = 0 and C = 9. In this case, the coefficient also leads to positive leading coefficient and also lead to mutual prime.A = 1/6, B = 2/9 and C = 0. In this case, the coefficient of x and y which are A = 1/6 and B = 2/9 are integers, which doesn't leads to mutual prime.A = 4, B = 1/4 and C = 0. In this case, the coefficient of y which is B = 1/4 is integers, which doesn't leads to mutual prime.Therefore, the values that would be the appropriate values for an equation to be in standard form as it lead to positive leading coefficient and mutual prime is A = 4, B = 0 and C = 9.
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question-
jack jogs and rides his bike for a total of 75 minutes every day. he rides his bike 15 minutes more than he jogs.
part a: write a pair of linear equations to show the relationship between the number of minutes jack jogs (x) and the number of minutes he rides his bike (y) every day.
part b: how much time does jack spend jogging every day?
part c: is it possible for jack to have spent 60 minutes riding his bike every day? explain your reasoning.
The answers have been shown below.
To find the answers:Questions regarding the time spent by Jack jogging and bike riding are needed to be answered.
(A) The equations are [tex]x+y=75, y=15+x[/tex]
Time spent jogging is 30 minutes
The total time would be [tex]45+60=105[/tex] minutes which is not equal to 75 minutes.
(B) Let [tex]x[/tex] be the time spent jogging.
[tex]y[/tex] be the time spent bike riding.
[tex]x+y=75\\y=15+x\\x+15+x=75\\2x+15=75\\x=\frac{75-15}{2} =30[/tex]
Time spent jogging is 30 minutes.
[tex]y=60\\x+y=75[/tex]
(C) If he rides his bike 15 minutes longer than he jogs then he would have to jog [tex]60-15 = 45[/tex] minutes.
Therefore, the total time would be [tex]45+60=105[/tex] minutes which is not equal to 75 minutes.
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I can find the perimeter and area of the rectangle
Answer:
A = 72, P = 38
Step-by-step explanation:
Area can be found by getting the area of the overall figure, and then subtracting the blank space in the corner
12 * 7 = 84
3 * 4 = 12(invisible rectangle in top right)
84 - 12 = 72
Perimeter can be found by adding all of the sides
12 + 7 + (12-4) + 3 + 4 + (7-4)
The numbers in brackets are the unlabeled sides on the top and left.
Answer:
[tex]P=38\\ A=72[/tex]
Step-by-step explanation:
To find the perimeter (P), add up all of the side lengths of the figure:
(numbers in parenthesis are the unlabeled values in the figure).
[tex]12+7+(8)+3+4+(4)=38[/tex]
To find the area of the figure (A), multiply the length and width of the original rectangle [tex](12*7=84)[/tex]. Then, subtract this amount (84) minus the area of the missing rectangle in the top left corner [tex](4*3=12)[/tex].
Subtract the required values: [tex]84-12=72[/tex].
Therefore, the perimeter of the figure is 38 units, and the area of the figure is 72 units.
In fig. 6.39, side QP and RQ of ΔPQR are produced to points S and T respectively, if ∠SPR = 135° and ∠PQT = 110°, find ∠PRQ.
Answer:
PRQ = 65 degrees
Step-by-step explanation:
Angles SPR and QPR and angles TQP and RQP form linear pairs, so they are supplementary (angle measures add up to 180 degrees).
SPR + QPR = 180
135 + QPR = 180
QPR = 45
TQP + RQP = 180
110 + RQP = 180
RQP = 70
Since interior angles of a triangle add up to 180 ...
QPR + RQP + PRQ = 180
45 + 70 + PRQ = 180
PRQ = 65
The error in the measurement of the radius of a sphere is 1%, then the error in the measurement of its volume is:
The error in the measurement of its volume is 3%.
What is the radius?The radius of a circle is the distance measured from its center to its edge.The radius of your cushion's corners can be determined by placing a framing square along the edges of your corners (see illustration) and measuring from the point where the curve begins to the corner of the square.The error in the measurement of its volume is:
Volume[tex]=\frac{4\pi r^{3} }{3}[/tex]
Δv/v*100=3 ΔR/R*100
[tex]3*\frac{1}{100} *100[/tex]
=3
The error in the measurement of its volume is 3%.
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Harmony earns a $42,000 salary in the first year of her career. Each year, she gets a 4%, percent raise.
Which expression gives the total amount Harmony has earned in her first n years of her career?
Answer:
42000*1.04^(n-1)
Step-by-step explanation:
4% is equal to 0.04, a raise is 1+0.04=1.04
1.04 is now the number we are multiplying by to get a new yearly salary for Harmony.
42000*1.04^(n-1) since n is how many years after she has the job you have to raise it to the power and subtract one.
Quick algebra 1 question for some points!
Only answer if you know the answer, quick shout-out to Subtomex0, tysm for the help!
[tex] \frac{y}{x} = \frac{4}{ - 3} = \frac{8}{ - 6} = \frac{12}{ - 9} \\ this \: relation \: holds \: so \: y \: varies \\ directly \: with \: x[/tex]
[tex] \frac{ 4}{3} m = \frac{8}{ - 6} \\ m = \frac{ \frac{ - 8}{6} }{ \frac{3}{ - 4} } = \frac{8 \times 4}{6 \times 3} = \frac{32}{18} = 2 \\ multipling \: by \: 2[/tex]
2)[tex] \frac{y}{x} = \frac{ - 40}{ - 0.5} = \frac{8}{2.5} = \frac{5}{4} \\ \frac{y}{x} = 80 = 3.2 = 1.25 \\ this \: is \: untrue \: so \: y \: is \: not \\ varying \: directly \: with \: x[/tex]
[tex]no \: constant \: of \: variation[/tex]
4)[tex] \frac{y}{x} = \frac{21}{3} = \frac{31.5}{4.5} = \frac{38.5}{5.5 \\ } \\ \frac{y}{x} = 7 = 7 = 7 \\ y \: varies \: directl y\: with \: x \\ consant \: of \: var = \frac{y}{x} = 7[/tex]5)[tex] \frac{y}{x} = \frac{30}{6} = \frac{35}{7} = \frac{96}{8} \\ \frac{y}{x} = 5 = 5 = 12 \\ y \: does \: not \: vary \: directly \: with \: x[/tex]
A soccer game lasts 90 minutes without running into overtime. The coach
plans to switch players out every 12 1/2 minutes. Approximately how many
switches will the coach make in one game?
Answer: 7 Switches will be made.
Step-by-step explanation:
[tex]\frac{90}{12.5}=[/tex] number of switches
[tex]7.2=[/tex] number of switches
however you cannot have a fraction of a switch so you must round it to a whole number, which in this case is 7.Write the equation of the line through the points (1,3) & (-2,5)in slope-intercept form
Answer:
y = -⅔x + 11/3
Step-by-step explanation:
The slope is
[tex] \frac{5 - 3}{ - 2 - 1} = - \frac{2}{3} [/tex]
Substituting into point-slope form,
y - 3 = -⅔(x - 1)
y - 3 = -⅔x + ⅔
y = -⅔x + 11/3
Will Make BRAINLIEST!!!
In the figure below, parallel lines I and m are intersected by the transversal t. Based on the information given in the figure, what is the measure, in degrees, of x?
Answer:
there should have been names of every line and joining parts
PLEASE HELP AND SHOW ALL STEPS
Combining the like terms, the simplified polynomials are given as follows:
a) 4x² - 14x + 17
b) -5x² - 20x + 8
How are polynomials simplified?Polynomials are simplified combining the like terms, that is, adding these numbers with the same variable.
Item a:
4(x - 2)(x + 1) - 5(2x - 5)
Applying the distributive property:
4(x² - x - 2) - 10x + 25
4x² - 4x - 8 - 10x + 25
Combining the like terms:
4x² - 4x - 10x - 8 + 25
4x² - 14x + 17
Item b:
-5(x + 2)² + 28
-5(x² + 4x + 4) + 28
-5x² - 20x - 20 + 28
-5x² - 20x + 8
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Choose the function that shows the correct transformation of the quadratic function shifted eight units to the left and one unit down.
ƒ( x) = ( x + 8) 2 + 1
ƒ( x) = ( x - 8) 2 + 1
ƒ( x) = ( x + 8) 2 - 1
ƒ( x) = ( x - 8) 2 - 1
we conclude that the correct option or the translated function is the last one.
f(x) = (x - 8)² - 1
Which is the correct equation for the transformed function?The parent quadratic function is:
y = g(x) = x²
If we translate this function 8 units to the left, then we will have the new function:
f(x) = g(x - 8)
And if now we translate this function one unit downwards, we will get:
f(x) = g(x - 8) - 1
Now we can replace g(x) by the parent quadratic function we willl get:
f(x) = (x - 8)² - 1
From this, we conclude that the correct option is the last one.
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For questions 4-5, determine which function is graphed.
Rational functions v and w both have a point of discontinuity at x = 7. which equation could represent function w?
The correct option is C.
The formula that could be used to represent a function w is
= w(x)=v(x-7)+7
What is Rational function?A polynomial divided by another polynomial can be used to represent a rational function. Since polynomials are defined everywhere, the set of all numbers excluding the zeros in the denominator constitutes the domain of a rational function.
Example 1. x = f(x) (x - 3). The denominator, x = 3, only contains one zero. When the denominator is zero, rational functions are no longer defined.
According to the given Information:
Rational functions whose point of discontinuity is at x=7.
When a point of discontinuity exists for a rational function,
It occurs when:
q(x) = r(x-a), x=a
In this instance, we are required to notice the following relationship, which is a union of a parent rational function and a vertical translation:[tex]w(x)=v(x-a)+k\\ \forall k \in \mathbb{R}[/tex], (2)
If we are aware of a=7 and k=7 .
The equation that could be used to represent a function w is. w(x)=v(x-7)+7
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I understand that the question you are looking for is:
Rational functions v and w both have a point of discontinuity at x = 7. Which equation could represent function w?
A. w(x)=v(x-7)
B. w(x)=v(x+7)
C. w(x)=v(x-7)+7
D. w(x)=v(x)+7
A classroom fish tank contains x goldfish the tank contains four times as many cups as goldfish enter an equation that represents the total number of guppies y in the fishtank
Function n models a cubic function in function n represents a cubic function that passes through the points (-1,0) (0,2) brainly
The y-intercept of m is smaller than n of y-intercept.
function's y-interceptThe points where a line crosses an axis are known as the x-intercept and the y-intercept, respectively.
A function's y-intercept is the value of y when
x= 0
The cubic function represented by function n traverses the points (-1,0) and (0,2).
When, x=0 ,y=2 and y = 2 is the y-intercept.
Operation m:
When, x=0,y = -6 the y-intercept is y = -6, which is less than 2, meaning that the y-intercept of m is smaller than the y-intercept of n, and option A provides the correct response.So the y-intercept of m is smaller than n of y-intercept.
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Check all the true statements.
We can conclude that the true statement from the given expressions are DE || AC and 2DE = AC
Similar trianglesTriangles are similar if the measure of the similar sides are all equal to a constant.
From the given diagram, you can see that the measure of BA is congruent to BC. This shows that the line DE is parallel to AC that is DE || AC.
Also twice the measure of the sides DE will be equivalent to AC that is 2DE = AC.
Hence we can conclude that the true statement from the given expressions are DE || AC and 2DE = AC
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