A fence on a hill uses vertical posts L and M to hold parallel rails N and P. If m∠1 = 6x and m∠12 = 4x, then what is the measure of ∠5?
Answers
Answer;
D: 108 degrees
Answer:
Measure of ∠5 is 108°
Step-by-step explanation:
Given m∠1 = 6x and m∠12 = 4x, we have to find the measure of ∠5.
As ∠1 and ∠5 are alternate exterior angle hence equal i.e ∠1=∠5
Also, ∠5 and ∠12 are co-interior angles ∴these are supplementary
⇒ m∠5+m∠12=180°
⇒ 6x+4x=180°
⇒ 10x = 180° ⇒ x=18
∴ m∠5 = 6x = 6(18) = 108°
Hence, measure of ∠5 is 108°
Related Questions
) a quiz consists of 10 true or false questions. to pass the quiz a student must answer at least 7 questions correctly. if the student makes a random selection on each question, what is the probability that the student will pass the quiz? [ you may use distr key. show the command that was typed in to your calculator.]
Answers
Solve the following equation. Show all your work.
Start Fraction x over x minus 2 End Fraction plus Start Fraction x minus 1 over x plus 1 End Fraction equals negative 1
someone...please..god..
Answers
[tex] (x - 2)(x + 1) \times \dfrac{x}{x - 2} + (x - 2)(x + 1) \times \dfrac{x - 1}{x + 1} = -1(x - 2)(x + 1) [/tex]
[tex] (x + 1)x + (x - 2)(x - 1) = -1(x - 2)(x + 1) [/tex]
[tex] x^2 + x + x^2 - 3x + 2 = -x^2 + x + 2 [/tex]
[tex] 3x^2 - 3x = 0 [/tex]
[tex] 3x(x - 1) = 0 [/tex]
[tex] x = 0~~~or~~~x - 1 = 0 [/tex]
[tex] x = 0 ~~~ or ~~~ x = 1 [/tex]
Since neither 0 nor 1 cause a zero in a denominator in the original equation, 0 and 1 are acceptable as solutions.
Answer: x = 0 or x = 1
Brody is purchasing some tools for his workshop. He has a budget of $120 and needs to buy at least 14 tools. Each hammer costs $10, and each wrench costs $6. If the solution region represents the number of hammers and wrenches that Brody can buy given his budget, determine which graph represents the solution set to the system of inequalities representing this situation.
Answers
x: number of hammers
y: number of wrenches
We write the system of inequations:
10x + 6y <= 120
x + y> = 14
We graph the system of inequations.
The solution set is given by the shaded region of the graph.
Answer:
see attached image.
Answer:
The graph in the attached figure
Step-by-step explanation:
Let
x------> the number of hammers
y------> the number of of wrenches
we know that
[tex]10x+6y\leq 120[/tex] -----> inequality A
[tex]x+y\geq 14[/tex] -----> inequality B
using a graphing tool
The solution of the system of inequalities is the shaded area
see the attached figure
How would you solve the area
Answers
so the composite is just 2 triangles, one rectangle and one parallelogram.
we know the height and base of the triangles and length and width of the rectangle.
now, the parallelogram, we can simply split in in two triangles and a rectangle, like you see the split in the middle, and that gives us two more triangles and one rectangle.
so, we can simply get the area of each of those figures and sum them up, and that's the area of the composite.
[tex]\bf \stackrel{\textit{left triangle}}{\cfrac{1}{2}(11)(8)}~~+~~\stackrel{\textit{left rectangle}}{11\cdot 9}~~+~~\stackrel{\textit{upper middle triangle}}{\cfrac{1}{2}(11)(2)} \\\\\\ +~~\stackrel{\textit{middle rectangle}}{7\cdot 11}~~+~~\stackrel{\textit{lower middle triangle}}{\cfrac{1}{2}(11)(2)}~~+~~\stackrel{\textit{right triangle}}{\cfrac{1}{2}(8)(9)}\\\\ -------------------------------\\\\ 44+99+11+77+11+36\implies 278[/tex]
Plz Help
A survey asked males and females to watch two commercials and select the one they liked best. The results of the survey are shown in the two-way frequency table.
Commercial A Commercial B
Males 0.28 0.14
Females 0.33 0.25
What percent of the respondents were female?
Answers
Answer: There is 58% of female respondents.
Step-by-step explanation:
Commercial A Commercial B Total
Males 0.28 0.14 0.42
Females 0.33 0.25 0.58
Total 0.61 0.39 1.00
So, Percentage of the respondents were females is given by
[tex]\dfrac{0.58}{1}\times 100\\\\=58\%[/tex]
Hence, there is 58% of female respondents.
What are the zeros of f(x) = x(x – 8)?
A. x = 0 and x = 8
B. x = 0 and x = –8
C. x = 0 only
D. x = 8 only
Answers
if x = 0 then 0 * (x - 8) = 0 because anything multiplied by 0 is zero.
if x = 8 then 8 * (8 - 8) = 8 * 0 = 0
A <<<<<< Answer
The zeros of the function f(x) = x(x – 8) are x = 0 and x = 8, which correspond to each factor of the equation being set equal to zero. Therefore, the correct answer is option A.
To identify the zeros of the function f(x) = x(x – 8), we should solve for x when f(x) is set to zero. Setting the function equal to zero gives us the equation 0 = x(x – 8).
We can find the zeros by looking for the values of x that make each factor in the equation equal to zero. The first factor is x, and it is equal to zero when x = 0. The second factor is (x – 8), which is equal to zero when x = 8.
Therefore, the zeros of the function f(x) are x = 0 and x = 8.
Selection A is the correct answer: The zeros of the function x(x – 8) are x = 0 and x = 8.
What is the quotient (x3 – 3x2 + 3x – 2) ÷ (x2 – x + 1)?
Answers
_______________
x^2-x+1 | x^3 - 3x^2 + 3x - 2 x^3 - x^2 + x --------------
-2x^2 + 2x -2 -2x^2 + 2x - 2 ------------------ 0
Quotient = x - 2
The quotient when [tex](x^3-3x^2+3x-2)\div(x^2-x+1)[/tex] is [tex](x-2)[/tex].
Given :
Equation -
[tex]\dfrac{x^3-3x^2+3x-2}{x^2-x+1}[/tex]
Solution :
[tex]\dfrac{x^3-3x^2+3x-2}{x^2-x+1} = \dfrac{x^3-2x^2-x^2+2x+x-2}{x^2-x+1}[/tex]
[tex]= \dfrac{(x^2(x-2)-x(x-2)+1(x-2))}{x^2-x+1}[/tex] ------ (1)
Now taking (x - 2) common from numerator in equation (1) we get,
[tex]= \dfrac{(x-2)(x^2-x+1)}{x^2-x+1}[/tex]
[tex]=(x-2)[/tex]
Therefore the quotient when [tex](x^3-3x^2+3x-2)\div(x^2-x+1)[/tex] is [tex](x-2)[/tex].
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a newspaper carrier earns a fixed amount for each newspaper he delivers, and yesterday his average hourly wage was 7.50 an hour. If he worked 4 hours yesterday and delivered 120 newspapers, how much does he earn for each newspaper delivered?
Answers
The larger square garden at Volterra Hall has sides twice as long as the smaller square garden. Together the gardens cover 18,000 square feet. Find the dimensions of each garden.
Answers
The gardens are square. There are two of them. The total is 18000 square feet. There is a relationship between smallest and largest square.
Development of the Equation.
Formula for a square = s*s
The first garden has a side of s
The larger garden has a side of 2s
The area of the first garden = s^2
The area of the 2nd garden = (2s)^2
The two areas together are
s^2 + (2s)^2 = 18000
Solve
s^2 + 4s^2 = 18000 Add the like terms on the left.
5s^2 = 18000 Divide by 5
s^2 = 18000/5
s^2 = 3600 Take the square root of both sides.
sqrt(s^2) = sqrt(3600)
s = 60 For the small garden
2s = 2*s = 2*60 = 120 for the large garden.
Answers
Small garden = 60 by 60
Large garden = 120 by 120
Check
Area of the small garden = 60 * 60 = 3600
Area of the large garden = 120*120 = 14400
Total Area = 18000 and it checks.
HELP WHOEVER ANSWERS CORRECTLY WILL BE BRAINLIEST!!!!
Answers
7.25 x 9.5 x 2 = 137.75 gets the surface area of the two rectangle sides.
To get the bottom rectangle, do 8 x 9.5 = 76
To find the two triangles, do 6 x 8 x 0.5 x 2 = 48
Now add them all together: 137.75+76+48=261.75
So, the answer is 261.75 square feet of material.
PLEASE ANSWER ASAP!!! GIVING BRAINLIEST
explain how you would create and use a spinner to simulate the probability of an event
Answers
To simulate the probability in a spinner divide the spinner into colors depending on the probability each color represents.
What does the word "probability" mean?This word refers to the likelihood for an event to occur. Moreover, it is often expressed either as a fraction, a percentage, or a number.
In this case, each of the colors represents a probability:
Green 20%
Blue 1/4 or 25%
Yellow 2/5 or 40%
Orange 15%
Now, Due to this, the best is to divide the spinner by colors and considering the percentages of each color.
Hence, For example 40% of the spinner should be red, while 15% should be orange.
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complete question;Explain how you would create and use a spinner to simulate the probability of an event with the following probabilities:
Percent chance: 20% green, ¼ blue, ⅖ yellow, and 15% orange
which undefined geometric term is described as a two dimensional set of points that has no beginning or end
Answers
It is a series of 2 points that has no beginning or an end and is two-dimensional.
Gary number has 6 in thousands and a7 in hundred and a 5 in ones. when rounded to the nearest ten, the number is 6760. what is gary's number
Answers
If a number is 5 or more, round up.
If a number is 4 or less, round down.
I hope this helps!
A cone with radius 5 units is shown below. Its volume is 105 cubic units. Find the height of the cone.
Answers
Answer:
height of the cone = 4.01273885 units
Step-by-step explanation:
Volume of a cone(V) is given by:
[tex]V = \frac{1}{3} \pi r^2h[/tex] ....[1]
where,
r is the radius and h is the height of the cone.
As per the statement:
A cone with radius 5 units and ts volume is 105 cubic units
⇒r = 5 units and V = 105 cubic units
Substitute these given values and use [tex]\pi = 3.14[/tex] in [1] we have;
[tex]105 = \frac{1}{3} \cdot 3.14 \cdot 5^2 \cdot h[/tex]
Multiply both sides by 3 we have;
⇒[tex]315 = 78.5 \cdot h[/tex]
Divide both sides by 78.5 we have;
[tex]4.01273885 = h[/tex]
or
h = 4.01273885 units
Therefore, the height of the cone is, 4.01273885 units
The height of the cone is 4 units.
What is the volume of a cone?The volume of the cone is equal to;
[tex]\rm Volume \ of \ cone=\dfrac{1}{3} \times b \times h[/tex]
Where; B is the area of the circular base of the cone, and h is the height of the cone.
The base of the cone is given by;
[tex]\rm Base=\pi r^2[/tex]
Substitute all the values in the equation
[tex]\rm Volume \ of \ cone=\dfrac{1}{3} \times b \times h\\\\Volume \ of \ cone=\dfrac{1}{3} \times \pi r^2\times h \\\\ 105=\dfrac{1}{3} \times 3.14 \times 5^2\times h\\\\h = \dfrac{105\times 3}{25 \times 3.14}\\\\h=64[/tex]
Hence, the height of the cone is 4 units.
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Find the surface area of a triangular prism that has a height of 11 meters and the following triangular base. All dimensions are in meters.
Answers
Perimeter of the base = 4 + 4 + 4 = 12 m
Surface area = 7 + 7 + 12 x 11 = 146 m²
Answer: 146 m²
Answer:
146
Step-by-step explanation:
given that A=43 degrees , B=82 degrees and c=28, solve triangle ABC. Round to the nearest hundredth. A) C= 93 degrees , b= 33.8 , a= 23.3 B) C= 55 degrees , b= 33.8 , a= 23.3 C) C= 55 degrees , b= 23.3 , a= 33.8 D) C= 93 degrees , b= 23.3 , a= 33.8
Answers
B=82°
c=28
1) A+B+C=180°
Replacing A=43° and B=82° in the equation above:
43°+82°+C=180°
125°+C=180°
Solving for C. Subtracting 125° both sides of the equation:
125°+C-125°=180°-125°
C=55° (option B or C)
2) Law of sines
a/sin A=b/sin B=c/sin C
Replacing A=43°, B=82°, C=55°, and c=28 in the equation above:
a/sin 43°=b/sin 82°=28/sin 55°
2.1) a/sin 43°=28/sin 55°
Solving for a. Multiplying both sides of the equation by sin 43°:
sin 43°(a/sin 43°)=sin 43°(28/sin 55°)
a=28 sin 43° / sin 55°
Using the calculator: sin 43°=0.681998360, sin 55°=0.819152044
a=28(0.681998360)/0.819152044
a=23.31185549
Rounded to one decimal place
a=23.3
2.2) b/sin 82°=28/sin 55°
Solving for a. Multiplying both sides of the equation by sin 82°:
sin 82°(b/sin 82°)=sin 82°(28/sin 55°)
b=28 sin 82° / sin 55°
Using the calculator: sin 82°=0.990268069, sin 55°=0.819152044
b=28(0.990268069)/0.819152044
b=33.84903466
Rounded to one decimal place
b=33.8
Answer: Option B) C=55°, b=33.8, a=23.3
NEED HELP ASAP!!!
find the equation that goes through points (18,3) and (21,1) find slope and y-intercept
Answers
Dylan opened a credit card account with $675.00 of available credit. Now that he has made some purchases, Dylan's account only has $384.75 of available credit. What is the percentage decrease of the amount of available credit in Dylan's account?
Answers
675-384.75=290.25
290.25/675=.43*100%=43%
My answer for this question is Graph D, but it looks like Graph B could also be a candidate. B and D both show decreasing graphs, and I've chosen D simply because it "looks" like it is decreasing faster. At x = 0, the slope of Graph D is less than that of Graph B. I am guessing that Graph B shows a parabola whereas Graph D shows something exponential (i.e. with an increasing rate)?
Answers
Choice B starts off with a slow pace of decreasing and then speeds up in terms of how much is decreasing. In other words, it is accelerating in how fast it is decreasing. How can we tell? Because of the slope of the tangent line. The slope of the tangent line at x = -1 is much less steep compared to the slope of the tangent at x = 5. The more steep the line, the faster the amount of decrease.
Choice D is the opposite of choice B in a sense. It starts off with fast decrease and that decreasing pace slows down. So if it asked "decreasing at a decreasing rate", then choice D would be the answer.
Answer: Choice B
Edit: one example graph B could model is the amount of water left in a large container. If we had a small hole at the bottom, then the water would leak out slowly at first. If the hole progressively gets bigger (say the water eats at the hole), then the water would leak faster and faster, which makes the curve steeper and steeper.
if a crate contains 25,500 oz of rice , about how many kg does it contains ? 1 pound equals 16 oz & 1 pound equals 0.454 kg
351 kg
724 kg
25500 kg
185000 kg
Answers
Your problem statement tells you that both 0.454 kg and 16 oz are equal to a pound, so they are also equal to each other. Their ratio (with kg on top and oz on the bottom) is a suitable conversion factor.
[tex]25,500\,oz \times \dfrac{0.454\,kg}{16\,oz}=723.5625\,kg[/tex]
The best choice is ...
724 kg
To find the mass of 25,500 ounces of rice in kilograms, one needs to convert ounces to pounds, then pounds to kilograms. After the conversions, the crate contains approximately 724 kg of rice.
Explanation:To calculate the mass of 25,500 ounces of rice in kilograms, we first convert ounces to pounds and then pounds to kilograms using the conversion rates provided.
First, we need to find out how many pounds are equivalent to 25,500 ounces. We use the proportion 1 pound = 16 ounces.Divide the total number of ounces by 16 to find the number of pounds:Now, we'll convert pounds to kilograms: 1 pound = 0.454 kg.Multiply the number of pounds by the kilogram equivalent:When we round this number to the nearest whole number, we get 724 kg, which is the approximate mass of the rice in the crate.
Juan makes 8 dollars for each hour of work. Write an equation to represent his total pay p after working h hours
Answers
h hours = $8h
Answer: p = $8h
Juan's total pay p after working h hours is calculated using the equation p = 8h. This represents a direct relationship between hours worked and total earnings.
To represent Juan's total pay p after working h hours at a rate of 8 dollars per hour, we use the equation p = 8h. This equation shows that the total pay (p) is equal to the rate of pay per hour (8 dollars) multiplied by the number of hours worked (h).
For example, if Juan works for 8 hours a day, his total pay would be calculated as p = 8 * 8, which equals $64. If we consider a full day of work to be 8 hours producing a value of $160, we can see that Juan is being paid for only half the hours at that rate, since 8 hours' labor would have a value of $80 at his rate of pay.
Savings account A has 1500 and pays 3.5% interest yearly. Savings account B has 1400 and pays 4% interest yearly. the savings account that earned the most interest after one year is savings account.
Answers
Savings Account B earned the most interest after one year.
Explanation:To determine which savings account earned the most interest after one year, we can calculate the interest earned by each account using the formula:
Interest = Principal x Rate
For Account A: Interest = 1500 x 0.035 = $52.50
For Account B: Interest = 1400 x 0.04 = $56.00
Therefore, Account B earned more interest after one year, with a total of $56.00.
Which regular polygon would have each of its interior angles measure 120°? hexagon heptagon octagon nonagon?
Answers
____________
A box without a top is to be made from a 30 cm by 30 cm rectangular piece of cardboard by cutting out square corners with a side length of x and then folding up and taping the sides.
What is the maximum possible volume of the box?
What value of x maximizes the volume of the box?
Answers
V = x(30 -2x)²
A graphing calculator can show the local maximum of this function.
a) The maximum possible volume is 2000 cm³.
b) The value of x that maximizes the volume of the box is 5 cm.
Please Help! Will give Brainliest!! 1. ______________ is process that you can do over and over, where each result does not affect the next. Ex. Flipping a coin, rolling dice, choosing a card, etc. 2. ________________ are the possible results of an experiment. Example: Heads, tails; 1, 2, 3…; Ace, King, Queen…; etc. 3. ______________is the measure of how likely an event is. 4. An ________________ event has a 0% chance of occurring Example : Rolling a 7 on a 6 sided die. 5. A ________________ event has a 100% chance of occurring. Example: Picking a red ball from a bag of only red balls. 6._______________ probability is what you expect to happen. 7.________________ probability is what actually happened. 8.The ___________ is the average value of all data in a set.
Answers
In probability, an experiment is any procedure that can be infinitely repeated and has a well-defined set of possible outcomes. Thus, an experiment is a process that you can do over and over, where each result does not affect the next. For example: Flipping a coin, rolling dice, choosing a card, etc. are all experiments.
Part 2.
Outcomes are the possible results of an experiment. For example: When a coin is tossed, you either get a Heads or a Tails. Thus, Head, Tail are the outcomes of tossing a coin The set of possible outcomes from an experiment is called the sample space of the experiment.
Part 3.
Probability is the measure of how likely an event is to occur. Probability takes values between 0 and 1, where, 0 indicates impossibility and 1 indicates certainty. The higher the probability of an event, the more likely it is that the event will occur.
Part 4.
An impossible event has a 0% chance of occurring. Like stated in part 3 above, probability takes values between 0 and 1, where, 0 indicates impossibility and 1 indicates certainty. A probability of 0 implies that the occurrence of the event is impossible. For example: It is impossible to roll a 7 on a 6 sided die.
Part 5.
A certain event has a 100% chance of occurring. Like stated in part 3 above, probability takes values between 0 and 1, where, 0 indicates impossibility and 1 indicates certainty. A probability of 1 implies that the occurrence of the event is certain. For example: It is certain that a ball picked from a bag containing only red balls will be red.
Part 6.
Theoretical probability is what you expect to happen. In theoretical probability, we do not conduct an experiment, rather we use our knowledge about a situation, some logical reasoning, and/or known formula to calculate the probability of an event happening. Theoretical probability is given by the number of favorable outcomes divided by the total number of possible outcomes.
Part 7.
Experimental probability is what actually happened. Experimental probability is when the probability of an event happening is calculated by conducting an experiment. Experimental probability is given by the numberof event occurrences divided by the number of trials.
Part 8.
The arithmetic mean is the average value of all data in a set. The arithmetic mean is a measure of central tendency calculated by adding all the data values in the data set and dividing the sum by the total number of observations.
algebra mid-unit review quiz Unit 3 lesson 5
1. simplify the rational expression; 2m^2 - 72/ m - 6.
A. 2 ( m+6)
B. 2
C. 2 ( m-6)
D. m + 12
2. simplify the rational expression; -8z^2/ z^4 - z^2.
A. -8z
B. -8
C. -8/ z^2
D. -8/ z^2 - 1
3. simplify the rational expression; 6x-54/ 7x-63.
A. - 6/7
B. 6/7
C. 6(x-9)/ 7
D. 6/ 7 (x-9)
Answers
1 is A 2 is D3 is B
Good luck.
The solutions to the problems in the mid-unit review quiz for Algebra Unit 3 Lesson 5 are A(2(m+6)), D(-8/(z^2-1)), and B(6/7). These are found by factoring out common factors and simplifying the expressions.
Explanation:Let's solve the algebra mid-unit review quiz Unit 3 lesson 5 one by one.
To simplify the rational expression 2m^2 - 72/ m - 6, first factor out a 2 from the numerator to obtain 2(m^2 - 36). This can be further broken down as 2(m - 6)(m + 6). Given the denominator is (m - 6), we cancel out (m - 6) from both the numerator and denominator to get the answer as 2(m+6) hence option A is correct.To simplify the rational expression -8z^2/ z^4 - z^2, first take out -8z^2 from the numerator to get -8*z^2/z^2*(z^2 - 1). On simplifying, we are left with -8/(z^2-1), i.e. option D is correct. To simplify the rational expression 6x-54/ 7x-63, we factor out a 6 from the numerator and a 7 from the denominator. This gives us 6(x - 9)/7(x - 9). By cancelling out the common factor, (x - 9), we get 6/7, i.e., option B is correct.Learn more about Algebra simplification here:
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HELPPPPPPPPP and explain why
Answers
=================================================
x^2 = x*x
5x = 5*x
Both x^2 and 5x have a factor of x in common
x^2 + 5x = x*x + 5*x
x^2 + 5x = x*x + x*5
x^2 + 5x = x*(x+5) .... use the distributive property in reverse
x^2 + 5x factors to x*(x+5)
As a way to check, you can distribute the x back in
x*(x+5) = x*x + x*5
x*(x+5) = x^2 + 5x
and we get the original expression again
[tex] {x}^{2} + 5x \\ x(x + 5)[/tex]
notice there's no whole number in front of the x^2, so no number can factor out both terms, but both have at least one x, so one x factors out of both
Find f(-7) if f(x) = 2x + 8.
Answers
A circle has the equation (x-2)^2+y^2=5. Whay are the coordinates of the circles center?
Answers
(x-2)^2 + (y-0)^2 = (rt(5))^2
-h = -2
h = 2
k=0
Center(2, 0)
Answer:
(2,0)
Step-by-step explanation:
Following the circle formula: [tex](x-h)^2 + (y-k)=r^2[/tex], we can deduce the values of Point(h,k).
The point is (2,0).
What values of x makes the inequality true? 2(x−4)−9x≤-4x+13
Answers
Answer : x >= -7
On simplifying,
2x - 8 - 9x <= -4x + 13
-7x - 8 <= -4x + 13
-3x - 8 < = 13
-3x <= 21
x >= -7