In the figure, ∆ABD ≅ ∆CBD by Angle-Side-Angle (ASA). Which segments are congruent by CPCTC? BC ≅ AD CB ≅ AB AB ≅ CD DB ≅ DC
Answers
By CPCTC this is the only valid answer:
CB ≅ AB
Another statement should be AD≅ CD
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Find the indicated function given f(x)=2x^2+1 and g(x)=3x-5. When typing your answer if you have an exponent then use the carrot key ^ by pressing SHIFT and 6. Type your simplified answers in descending powers of x an do not include any spaces between your characters.f(g(2))=Answerf(g(x))=Answerg(f(x))=Answer (g \circ g)(x) =Answer (f \circ f)(-2) =Answer
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Given the functions
[tex]\begin{gathered} f(x)=2x^2+1 \\ g(x)=3x-5 \end{gathered}[/tex]1) To find f(g(2))
[tex]\begin{gathered} f(g(x))=2(3x-5)^2+1 \\ f(g(x))=2(9x^2-15x-15x+25)+1=2(9x^2-30x+25)+1 \\ f(g(x))=18x^2-60x+50+1=18x^2-60x+51 \\ f(g(2))=18(2)^2-60(2)+51=18(4)-120+51 \\ f(g(2))=72-120+51=3 \\ f(g(2))=3 \end{gathered}[/tex]Hence, f(g(2)) = 3
2) To find f(g(x))
[tex]\begin{gathered} f(g(x))=2(3x-5)^2+1 \\ f(g(x))=2(9x^2-15x-15x+25)+1=2(9x^2-30x+25)+1 \\ f(g(x))=18x^2-60x+50+1=18x^2-60x+51 \\ f(g(x))=18x^2-60x+51 \end{gathered}[/tex]Hence, f(g(x)) = 18x²-60x+51
3) To find g(f(x))
[tex]\begin{gathered} g(f(x))=3(2x^2+1)-5 \\ g(f(x))=6x^2+3-5=6x^2-2 \\ g(f(x))=6x^2-2 \end{gathered}[/tex]Hence, g(f(x)) = 6x²-2
4) To find (gog)(x)
[tex]\begin{gathered} (g\circ g)(x)=3(3x-5)-5=9x-15-5=9x-20 \\ (g\circ g)(x)=9x-20 \end{gathered}[/tex]solve the following system of inequalities graphically on the set of axes below?witch of the coordinates points would be in the solution set
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An ordinary (Pair) die is a cube with the numbers 1 through 6 on the sides (represented by painted spots). Imagine that such a die is rolled twice in successionand that the face values of the two rolls are added together. This sum is recorded as the outcome of a single trial of andereCompute the probability of each of the following svents.Event A: The sum is greater than 7.Event B: The sum is divisible by 3 or 6 (or both).Write your answers as fractions
Answers
1) We are going to tackle this question starting with the total outcomes of dice rolled twice in succession.
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)
So we can see that there are 36 possibilities.
2) Let's examine the events.
a) P (>7)
Let's bold the combinations of outcomes whose sum is greater than 7
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)
So, we can see that there are 15 favorable outcomes.
Now, we can find the Probability of rolling the dice twice and get a sum greater than 7:
[tex]P(A)=\frac{15}{36}=\frac{5}{12}[/tex]b) Now, for the other event: The sum is divisible by 3 or 6, or both:
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)
Hence, the favorable outcomes are: 12
So now, let's find the probability of getting a sum that way:
[tex]P(B)=\frac{12}{36}=\frac{1}{3}[/tex]What is the radius of a hemispherewith a volume of 281,250 cm??
Answers
Given:
The volume of the hemisphere = 281,250
Find-:
Radius of hemisphere
Explanation-:
The volume of the hemisphere is:
[tex]V=\frac{2}{3}\pi r^3[/tex]Given volume is 281250
[tex]\begin{gathered} V=\frac{2}{3}\pi r^3 \\ \\ 281250=\frac{2}{3}\pi r^3 \\ \\ r^3=\frac{281250\times3}{2\times\pi} \\ \\ r^3=134286.9832 \\ \\ r=51.209 \end{gathered}[/tex]So, the radius is 51.209 cm
Hello, may I please have some help with this question. Thank you.
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The total distance that Kim walked in 3 days is 6 2/3 miles. We would convert this distance to mixed numbers. To do this, we would multiply 6 by 3 and add 2. The denominator would still be 3. It becomes
20/3 miles
If she walked 20/3 miles in 3 days, the number of miles that she walked per day would be
total distance/number of days
It becomes
(20/3) / 3
If we change the division sign to multiplication, it means that we would flip 3 such that it becomes 1/3. Thus, we have
20/3 * 1/3 = 20/9
= By converting to mixed numbers, we would find how many 9's are in 20. It is 2. The remainder is 20 - 18 = 2
Thus, the answer is
2 2/9 miles per day
Tony is a hiring director at a large tech company in Chicago, and he gets hundreds of resumes each week. How long does Tony MOST likely spend looking over each resume?30 seconds50 seconds3 minutes30 minutes
Answers
The time needed to look over the resumes depends on how many papers is the resume
But it is convenient to have a speed looking on each one
so, the answe will be 50 seconds
From the given proportional relationship, which of the following points lie on the same line?
Answers
As per given by the question,
There are given that a graph of line.
Now,
h
The graph of polynomial f is shown. Select all the true statements about the polynomial.aThe degree of the polynomial is even.bThe degree of the polynomial is odd.cThe leading coefficient is positive.dThe leading coefficient is negative.eThe constant term of the polynomial is positive.fThe constant term of the polynomial is negative.
Answers
Explanation:
From the graph,
we can see that the graph is symmetric about the y axis
Hence,
We can say that the Polynomial is even
Also, Because th opwning of the function is downwards,
Hence the leading coefficient is negative
Also we can see that the y-intercept is positive
That is when x=0, y=3
Hence,
The constant term of the polynomial is positive.
Therefore,
The final answers are OPTION A,OPTION D,OPTION E
A small radio transmitter broadcasts in a 60 mile radius. If you drive along a straight line from a city 75 miles north of the transmitter to a second city 76 miles east of the transmitter, during how much of the drive will you pick up a signal from the transmitter?
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Answer:
Explanation:
We start by having a diagrammatic representation as follows:
Determine whether the equation represents an exponential growth function, anexponential decay function, and give the percent growth or decay.17. y = 18(1.3)^t
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A exponential growth or decay function has the next general form:
[tex]y=a(1\pm r)^t[/tex]If it is :
(1+r) , (>1) the function growth
(1-r) , (<1) the function decay
------
The given equation:
[tex]y=18(1.3)^t[/tex]As the (1+r) is equal to 1.3 (> 1) then it is a exponential growth function.In (1+r) the r is the percent of growth, then for the given equation you have:
[tex]\begin{gathered} 1+r=1.3 \\ r=1.3-1 \\ \\ r=0.3 \end{gathered}[/tex]The percent of decay is 0.3 or 30%Suppose elephant poaching reduces an initial animal population of 25,000 animals by 15% each year. 1. Find the rate of change.2. How many animals will be left in 10 years?
Answers
Answer
Initial animal population, P₀ = 25,000
1. Rate of change = 15% = 0.15
2. Animal left in 10 years?
To calculate the animals left in 10 years, we use the formula:
P(t) = P₀ (1 - r)^t in t years
t = 10, P₀ = 25,000, r = 15% = 0.15)
P₍₁₀₎ = 25000 (1 - 0.15)¹⁰
P₍₁₀₎ = 25000 (0.85)¹⁰
P₍₁₀₎ = 25000 (0.1969)
P₍₁₀₎ = 4922.50
Therefore, 4922.50 animals will be left in 10 years.
As cashier, you need to record all over times you worked in hours. If you worked 330 mnts of over time how many hours will you record ?
Answers
First, we need the next equivalence
1 hour = 60 min
we have 330 min in order to know the number of hours we need to divide the 330 min between 60
[tex]\frac{330}{60}=5.5[/tex]He will record 5.5 hours
It takes 14 electricians 18 days to wire a new housing subdivision. How many days would it take 24 electricians to do the same job?
Answers
Answer: 31 electricians
Step-by-step explanation:
We could set up a ratio for this problem. It takes 14 electricians 18 days to wire a new housing subdivision, so it would take 24 electricians x days to do the same job. 14/18 = 24/x. We can then cross multiply to find x.
X = 30.8 or approximately 31.
The picture shows a system of linear and quadratic equations.
Drag each label to show whether it is a solution of the system or is not a solution of the system, or if it cannot be determined.
Answers
By identifying the intercepts in the given image, we conclude that the solutions of the system of equations are points B and F.
Does the system have solutions?When we have a system of 2 equations:
y = f(x)
y = g(x)
To solve it graphically, we have to graph both functions in the same coordinate axis and see in which points the graphs intercept (if they do). Each of these interceptions in the form (x, y) will be a solution for the equation f(x) = g(x) = y
In this case, we can see a line and a parabola (each of these is a different equation from the system), and we can see that the graphs intercept at points F and B (i think, the image is really small). Then the two solutions of the system of equations graphed are the points F and B
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Answer:
solution: F and B
NOT solution: the rest of the letters
Step-by-step explanation:
I did the work on imagine math
Which angles are adjacent to <2? Select all that apply.
Answers
review the rental and purchase property information to answer the question: calculate the difference in total move-in cost between the two properties. $31,497.35 $35,842.95$39,285.45$4,976.55
Answers
Let us calculate the move-in costs of both properties.
Rental Property
The monthly rent is $1,350.
The move-in costs are:
First month = $1,350
Last month = $1,350
Security deposit = 55% of one month's rent
[tex]\Rightarrow\frac{55}{100}\times1350=742.5[/tex]Therefore, the move-in cost is:
[tex]\Rightarrow1350+1350+742.5=3442.5[/tex]Purchase Property
The purchase price is $195,450.
The move-in costs are:
Down payment of 18% of purchase price:
[tex]\Rightarrow\frac{18}{100}\times195450=35181[/tex]Closing costs of 2.1% of purchase price:
[tex]\Rightarrow\frac{2.1}{100}\times195450=4104.45[/tex]Therefore, the move-in cost is:
[tex]\Rightarrow35181+4104.45=39285.45[/tex]Difference in Total Move-In Cost
This is calculated to be:
[tex]\Rightarrow39285.45-3442.5=35842.95[/tex]ANSWER
The difference in total move-in cost is $35,842.95
Determine (Freshman) Small Cafeteria). Interpret this answer in the context of the situation.
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Step 1:
[tex]\text{Probability = }\frac{N\text{umber of required outcomes}}{N\text{umber of total possible outcome}}[/tex]Step 2:
a)
Total possible outcome = 2640
Total number of freshman = 625
[tex]\begin{gathered} P(\text{Freshman) = }\frac{625}{2640} \\ \text{= }\frac{125}{528} \\ \text{= 0.237} \end{gathered}[/tex]Step 3:
b)
Total number of senior and large cafeteria = 350
[tex]\begin{gathered} P(\text{senior and large cafeteria) = }\frac{350}{2640} \\ =\text{ }\frac{70}{528} \\ =\text{ }\frac{35}{264} \\ =\text{ 0.132} \end{gathered}[/tex]Step 4:
c)
Number of Sophomore or student center = 650 + 595 - 125 = 1120
[tex]\begin{gathered} P(\text{Sophomore or student center) = }\frac{1120}{2640} \\ =\text{ }\frac{112}{264} \\ =\text{ 0}.424 \end{gathered}[/tex]Step 5:
d)
[tex]\begin{gathered} p(\text{freshman}|\text{small cafeteria) = }\frac{n(freahman\text{ and small cafeteria)}}{n(small\text{cafeteria)}} \\ =\frac{435}{860}\text{ } \\ =\text{ }\frac{87}{172} \\ =\text{ 0.506} \end{gathered}[/tex]one motorcycle travels 80 miles per hour and the second motor ctcle travels 60 miles per hour if the faster motorcycle travels 1 hour longer than the slower motorcycle and it also travels twice the distance of the slower motorcylce what distace does each of the motorcyle travel
Answers
The faster motorcycle travelled 240 miles and the slower motorcycle travelled 120 miles .
In the question ,
let the time travelled by the slower motorcycle be "t" .
given , the faster one travelled 1 hour longer ,
So , the time travelled by faster motorcycle = "t+1" hour .
the speed of slower motorcycle = 60 miles per hour .
the speed of faster motorcycle = 80 miles per hour .
So , the distance covered by slower motorcycle = speed * time
= 60*(t)
the distance covered by the faster motorcycle = 80*(t+1) .
given that faster motorcycle travels twice the distance of the slower motorcycle
So According to the question
80*(t+1) = 2*60*(t)
simplifying further , we get
80t + 80 = 120t
120t - 80t = 80
40t = 80
t = 2 hours
distance covered by slower motorcycle = 60(2) = 120 miles
distance covered by faster motorcycle = 80(2+1) = 80*3 = 240 miles .
Therefore , The faster motorcycle travelled 240 miles and the slower motorcycle travelled 120 miles .
The given question is incomplete , the complete question is
One motorcycle travels 80 miles per hour and the second motorcycle travels 60 miles per hour, if the faster motorcycle travels 1 hour longer than the slower motorcycle and it also travels twice the distance of the slower motorcycle . What distance does each of the motorcycle travel ?
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Will you ever completely remove the drug from your system? Explain your reasoning.
Answers
Answer
The drug cannot be completely eliminated from one's system.
This is because the kidney removes 25% of the drug, leaving 75% at any time; the 75% of any number will give a smaller number, but never zero.
So, the amount of the drug in the body system can become extremely low, but it can never be 0.
The mathematical proof is shown under explanation.
Explanation
We are told that the kidney filters off 25% of the drug out of the system every 4 hours.
This means that 75% of the dosage of the drug remains in the person's system every 4 hours.
If one starts with A₀ of the drug and classify every 4 hour time period as n
At n = 1,
A₁ = 0.75 (A₀)
A₂ = 0.75 (A₁) = 0.75² (A₀)
Aₙ = 0.75ⁿ (A₀)
For this question, we start wit 1000 mg
A₀ = 1000 mg
We are then asked to calculate if Aₙ, the amount of drug in the system after n time periods, can ever be 0
Aₙ = 0.75ⁿ (A₀)
0 = 0.75ⁿ (1000)
To solve for n, if there's an n for when the value of Aₙ = 0, we first divide both sides by 1000
0 = 0.75ⁿ (1000)
0 = 0.75ⁿ
We then take the natural logarithms of both sides
In 0 = In (0.75ⁿ)
In (0.75ⁿ) = In 0
n (In 0.75) = In 0
But, since In 0 does not exist, it shows that there is no value of n that can make the value of Aₙ go to 0.
Hope this Helps!!!
A brownie recipe asks for two and two thirds times as much sugar as chocolate chips. If four and one third cups of sugar is used, what quantity of chocolatechips would then be needed, according to the recipe?0308X5?
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Let's call C to the cups of chocolate chips and S to the cups of sugar. We are told that the cups of sugar are 2 2/3 times the cups of chocolate, then we can formulate the following equation:
[tex]S=2\frac{2}{3}C[/tex]In the case 4 1/3 of sugar is added, we can replace 4 1/3 for S to get:
[tex]4\frac{1}{3}=2\frac{2}{3}C[/tex]By dividing both sides by 2 2/3 we get:
[tex]\begin{gathered} 4\frac{1}{3}\div2\frac{2}{3}=2\frac{2}{3}C\div2\frac{2}{3} \\ 4\frac{1}{3}\div2\frac{2}{3}=C \end{gathered}[/tex]We can rewrite the mixed fractions to get:
[tex]\begin{gathered} \frac{4\times3+1}{3}\div\frac{2\times3+2}{3}=C \\ \frac{12+1}{3}\div\frac{6+2}{3}=C \\ \frac{13}{3}\div\frac{8}{3}=C \end{gathered}[/tex]By changing the division symbol to a multiplication symbol and flipping the 8/3, we get:
[tex]\begin{gathered} \frac{13}{3}\times\frac{3}{8}=C \\ \frac{13}{8}=C \\ \frac{8+5}{8}=C \\ \frac{8}{8}+\frac{5}{8}=C \\ 1+\frac{5}{8}=C \\ 1\frac{5}{8}=C \\ C=1\frac{5}{8} \end{gathered}[/tex]Then, 1 5/8 cups of chocolate chips are needed
help meeeeeeeeee pleaseee !!!!!
Answers
The values of the functions are:
a. (f + g)(x) = 9x + 1
b. (f - g)(x) = -7x - 17
c. (f * g)(x) = 8x² - 55x - 72
d. (f/g)(x) = (x - 8)/(8x + 9)
How to Evaluate Functions?To evaluate a function for a given value of input, substitute the value of the input, x, into the function equation, evaluate and simplify.
Given the following:
f(x) = x - 8
g(x) = 8x + 9
a. (f + g)(x) = (x - 8) + (8x + 9)
Combine like terms
(f + g)(x) = 9x + 1
b. (f - g)(x) = (x - 8) - (8x + 9)
(f - g)(x) = x - 8 - 8x - 9
Combine like terms
(f - g)(x) = -7x - 17
c. (f * g)(x) = (x - 8)(8x + 9)
Expand
(f * g)(x) = x(8x + 9) -8(8x + 9)
(f * g)(x) = 8x² - 55x - 72
d. (f/g)(x) = (x - 8)/(8x + 9)
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What is the slope of the line passing through the points (−1, 7) and (4, −1)? −5/62−8/5−2
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Given the points:
(−1, 7) and (4, −1)
The slope of the line passing through the points is given by:
[tex]slope=\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}=\frac{-1-7}{4-(-1)}=\frac{-8}{5}[/tex]So, the answer will be Slope = -8/5
solve the equation by completing the square. Show all solutions8x^2 + 16x = 42
Answers
8x² + 16x = 42
x² + 16/8x = 42/8 dividing by 8 at both sides
x² + 2x = 5.25
x² + 2x - 5.25 = 0
If we compute (x + 1)², we get:
(x + 1)² = x² + 2*x*1 + 1² = x² + 2x + 1
Then,
x² + 2x - 5.25 + 1 - 1 = 0
(x² + 2x + 1) + (-5.25 - 1) = 0
(x + 1)² - 6.25 = 0
(x + 1)² = 6.25
x + 1 = √6.25
This has 2 solutions,
x + 1 = 2.5 or x + 1 = -2.5
x = 2.5 - 1 x = -2.5 - 1
x = 1.5 x = -3.5
Use slope to determine if lines AB and CD are parallel, perpendicular, or neither 6. A(-3, 8), B(3, 2), C(7,1), D(5,-1)m(AB) m(CD) Types of Lines
Answers
Bob wants to build an ice skating rink in his backyard, but his wife says he can only use the part beyond the wood chipped path running through their yard. What wouldbe the area of his rink if it is triangular-shaped with sides of length 18 feet, 20 feet, and 22 feet? Round to the nearest square foot.
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In order to calculate the area of the triangle, given the length of its three sides, we can use Heron's formula:
[tex]A=\sqrt{p\left(p-a\right)\left(p-b\right)\left(p-c\right)}[/tex]Where p is the semi-perimeter.
So, calculating the value of p and then the area of the triangle, we have:
[tex]\begin{gathered} p=\frac{a+b+c}{2}=\frac{18+20+22}{2}=\frac{60}{2}=30 \\ A=\sqrt{30\left(12\right)\left(10\right)\left(8\right)} \\ A=\sqrt{28800} \\ A=169.7\text{ ft^^b2} \end{gathered}[/tex]Rounding to the nearest square foot, the area is 170 ft².
In a class of 10 boys and 12 girls, a committee of 4 members is to be formed. What is the probability to form a committee consisting of 2 boys and 2 girls?0.30400.40600.50600.2060
Answers
Consider all the different possible combinations of 4 members of the committee (b,b,b,b), (b,b,b,g),...(g,g,g,g). We need to use the binomial distribution given below
[tex]P(k)=(nbinomialk)p^k(1-p)^{n-k}[/tex]In our case
[tex]k=2,n=4,p=\frac{10}{10+12}=\frac{10}{22}=\frac{5}{11}[/tex]Then,
[tex]\begin{gathered} P(2)=(\frac{4!}{2!(4-2)!})(\frac{5}{11})^2(\frac{6}{11})^2 \\ \Rightarrow P(2)=6\cdot\frac{900}{14641} \\ \Rightarrow P(2)=0. \end{gathered}[/tex]Please help I need by today only questions 5 and 6 need to show work
Answers
Part a: Pot the points X, Y and Z are obtained on graph.
Part b: Distances; XY = 3, YZ = 5 and XZ = √34 units.
Part c: Measure of angles; X = 59.04 degrees and Z = 30.96 degrees.
What is termed as the Pythagorean theorem?The Pythagorean theorem states that the sum of a squares just on legs of a right triangle equals the square just on hypotenuse.For the given question, Triangle XYZ with the vertexes are given.
Part a: Pot the points.
X = (6, 6)
Y = (6, 3)
Z = (1, 3)
The points on the graph are plotted.
Part b: Distances;
XY = 6 - 3 = 3 units
YZ = 6 - 1 = 5 units
XZ , use Pythagorean theorem.
XZ² = XY² + YZ²
Put the values.
XZ² = 3² + 5²
XZ² = 9 + 25
XZ² = 34
XZ = √34 units.
Part c: Measure of angles.
In right triangle XYZ
cos X = XY/XZ
cos X = 3/ √34
X = 59.04 degrees.
cos Z = ZY/XZ
cos Z = 5/ √34
Z = 30.96 degrees.
Thus, the value of the triangle are obtained.
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There are 16 appetizers available at a restaurant. From these, Pablo is to choose 12 for his party. How many groups of 12 appetizers are possible?
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EXPLANATION
This is a combinatory, as there are 12 groups, the combinatory will be as follows:
16C12 = 16!/[12!*(16-12)!] = 1820
In conclusion, there will be 1820 possible groups of 12 appetizers.
A teacher gets snacks for the class for $50 and also purchases 6 boxes of pencils. The teacher spent a total of $62. Write an equation that models the situation with x, the cost of one box of pencils.
Answers
Answer:
50 + 6x = 62
Explanation:
If x represents the cost of one box of pencils and the teacher got snacks for $50, purchased 6 boxes of pencils, and spent a total of $62, we can write the equation that models the above situation as shown below;
[tex]50+6x=62[/tex]two parallel lines are intersected by a transversal one angle is 100 degrees, more info on the picture
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Obtuse angles (90°–180°) are those that fall within this range. Right angles are those that have a 90 degree angle ( = 90°). Straight angles are those that have a 180 degree ( = 180°) angle.
Explain about the obtuse angle?Any angle more than 90 degrees is deemed obtuse: A straight angle is one with a 180° measurement. A zero angle is one with a measurement of 0°: Angles with measures that add up to 90 degrees are said to be complementary angles: Angles with measures that add up to 180° are referred to as supplementary angles.
We now understand that an obtuse angle is one that is greater than 90 degrees but less than 180 degrees. Obtuse angle examples include 110°, 135°, 150°, 179°, 91°, and more. As a result, all angles between 90° and 180° are obtuse angles.
Hence obtuse angle is one of the angle which is not correct 100 degree angle
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