⇒Vertical angles are equal .
This means that ∠1=∠2
⇒The trick is to first find the value of the unknown variable x then substitute it in the expression of ∠1 to get the exact magnitude of the angle.
[tex]5x+12=6x-11\\5x-6x=-11-12\\-x=-23\\\frac{-x}{-1} =\frac{-23}{-1} \\x=23[/tex]
x=23°
To get the exact value of ∠1 Plug in 23° in the place of x in the expression of ∠1:
[tex]< 1=5x+12\\=5(23)+12\\=127[/tex]
∠1=127°
if the numerator of a fraction is multiplied by 4 and the denominator is reduced by 2, the result is 2. If the numerator of the fraction is increased by 15 and 2 is subtracted from the double of the denominator, the result is 9/7. Find the fraction.
Using the given information, the fraction is 3/8
Determining fractionsFrom the question, we are to determine the fraction
Let the numerator of the fraction be x and the denominator be y
From the given information,
"if the numerator of a fraction is multiplied by 4 and the denominator is reduced by 2, the result is 2"
That is,
4x/(y -2) = 2
and
" If the numerator of the fraction is increased by 15 and 2 is subtracted from the double of the denominator, the result is 9/7"
That is,
(x + 15)/(2y - 2) = 9/7
From the first equation,
4x/(y -2) = 2
4x = 2(y-2)
4x = 2y - 4
4x + 4 = 2y
y = 2x + 2 ----------- (3)
From the second equation,
(x + 15)/(2y - 2) = 9/7
7(x + 15) = 9(2y - 2)
7x + 105 = 18y - 18
Substitute equation (3)
7x + 105 = 18(2x + 2) - 18
7x + 105 = 36x + 36 - 18
105 - 36 + 18 = 36x - 7x
87 = 29x
x = 87/29
x = 3
Substitute the value of x into equation (3)
y = 2x + 2
y = 2(3) + 2
y = 6 + 2
y = 8
Thus, the number is 3/8
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A hiker walked 15 miles from 8:00 a.m. to noon. He walked an additional 18 miles from 1:00 p.m. to 7:00 p.m.
What is his average rate for the entire walk, in miles per hour?
The average rate for the entire walk of hiker is 3.75 miles per hour by the concept of average speed.
What is average speed?The instantaneous speed is the upper limit of the average speed as the duration of the time interval approaches zero. An object's average speed during a certain period of time is equal to its distance traveled over that period divided by its duration. Speed and velocity are distinct concepts.
The whole distance traveled divided by the total time results in the average rate for the entire walk, expressed in miles per hour.
Given that:
Distance A = 12.8 miles
Distance B = 17.2 miles
Total distance = Distance A + Distance B
Total distance= 12.8 + 17.2
Total distance= 30 miles
Time A = 9:00 a.m. to noon = 3 hours
Time B = 1:00 p.m. to 6:00 p.m. = 5 hours
Total time = Time A + Time B
Total time= 3 + 5
Total time= 8 hours
Average rate = Total distance/Total time
Average rate= 30 miles/8 hours
Average rate= 3.75 miles per hour
Therefore, the average rate for the entire walk of hiker is 3.75 miles per hour.
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4. You take a $4,500 loan to pay for trip
to the Amazon rainforest to photograph
wild animals. If the loan's interest rate is
8% for 1 year, what is the interest for the
first payment?
A $12.58
C $30.00
B $26.00
D $80.99
The interest for the first payment is $30.00
How to find interest?Interest is how much is paid for the use of money.
Therefore, you take a $4,500 loan to pay for trip to the Amazon rainforest to photograph wild animals.
The loan's interest rate is 8% for 1 year.
Therefore, the interest for the first payment can be calculated as follows:
Interest for the first payment = 8% of 4500 × 1 / 12
Interest for the first payment = 8 / 100 × 4500 × 1 / 12
Interest for the first payment = 8 × 45 × 1 / 12
Interest for the first payment = 360 / 12
Interest for the first payment = $30
Therefore,
interest = $30
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Circle the two subtraction problems that have a difference of 10.2.
The problems with a difference of 10.2 are:
16.29 - 6.09 = 10.236.1 - 25.9 = 10.2We are given some subtraction problems for which we need to find the ones with a difference of 10.2.
The problems are:
12.05 - 2.03
16.29 - 6.09
36.1 - 25.9
22.09 - 21.07
10.82 - 9.8
We find the difference for each of them one-by-one after subtraction.
12.05 - 2.03 = 10.0216.29 - 6.09 = 10.236.1 - 25.9 = 10.222.09 - 21.07 = 1.0210.82 - 9.8 = 1.02The question is incomplete. Find the complete question below:
Circle the two subtraction problems that have a difference of 10.2.
12.05 - 2.03
16.29 - 6.09
36.1 - 25.9
22.09 - 21.07
10.82 - 9.8
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Part B If m=18, what must be the value of n for the equation to have infinitely many solutions? Explain your answer
The equation have infinitely many solution when n is equal to -15.41.
What is linear equation?A linear equation in one variable is an equation which has a maximum of one variable of order 1. It is of the form ax + b = 0, where x is the variable. This equation has only one solution.
Given equation is;
24( mx + n ) = 3x + 17
where; m and n are real numbers.
Part 1. If m = 14 and n = 13 then
Putting the value of m and n in the equation we get;
= 24( 14.x + 13 ) = 3x + 17
= 336x + 312 = 3x + 17
= 336x - 3x = 17- 312
= 333x = -295
x = 0.886
Hence, x = 0.886 the equation having one solution .
part 2. if m = 18 then to find n .
put m = 18 in the given equation;
= 24(18.(0.886) + n ) = 3(0.886) + 17
= 24(15.94) + 24n = 2.658 + 17
= 382.56 + 24n = 19.658
= 24n = 19.658 - 382.56
n = -15.41
Hence, The equation have infinitely many solution when n is equal to -15.41.
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The complete question is;
PART A: Rosie writes the equation 24(mx+n)=3x+17, where m and n are real numbers.
If m=14 and n=13, does the equation have one solution, infinitely many solutions, or no solutions? Explain your answer.
Write an equivalent expression for -3(7+5g)
Answer:
-3(12g)
Step-by-step explanation:
Because if we simplify the 7+5g to 12g because 7+5=12.
Therefore,
-3(7+5g)= -3(12g)
Multiply. Write your answer as a fraction in simplest form.
What is the minimum additional information would you need in order to be able to state that the triangles are congruent by AAS?
The minimum additional information needed in order to be able to state that the triangles are congruent by AAS is . Option A
[tex]\angle A B C=\angle A D C[/tex]
This is further explained below.
What is the congruent angle?Generally, The triangles are said to be congruent if they satisfy the AAS (Angle-Angle-Side) condition, which states that if two angles and a non-included side in one triangle are congruent to two angles and the equivalent non-included side in another triangle, then the triangles are congruent.
In conclusion, The following pieces of knowledge are the bare minimum that is required in order to be able to make the assertion that the triangles are congruent according to AAS:
[tex]\angle A B C=\angle A D C[/tex]
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GET A CROWN 20 POINTS
Suppose a certain die has six sides, numbered from 1 to 6, but that the die is peculiar, in that it has the following properties: On any roll, the probability of rolling either a 1, a 4, or a 5 is 1/2, just as it is with an ordinary fair die. Moreover, the probability of rolling either a 5, a 3, or a 2 is again 1/2. However, the probability of rolling a 5 is 7/16, not 1/6 as one would expect of an ordinary fair die.
what is the probability of rolling a 6, a 3, or a 2 on a 6 sided fair die?
What is the probability of rolling anything but a 6?
A. P( 2∪3∪6 ) = 1/2
B. P( 1∪2∪3∪4∪5 ) = 9/16
The probability of an occurrence e can be written as P (e), and its equation is as follows:
P (e) = Number of favorable outcomes / Total number of outcomes
This can only be used with a straightforward event.
The probability will also be influenced by other factors, whether they are imposed or a result of the event's inherent characteristics.
Using a six-sided die,
A) First, in order to gather as much information as possible from the question, we concentrate on the probabilities provided P(1∪4∪5)=1/2 and P(2∪3∪5)=1/2 and we need to use P(5)=7/16.
It's crucial to remember that while using a dice, receiving two values on the same roll is impossible. Due to this and the likelihood of certain circumstances:
P(1∪4∪5) = P(1) + P(4) + P(5) - P(1∩4)(= 0) - P(4∩5)(= 0) - P(1∩5)(= 0) + P(1∩4∩5)(= 0)
P(1∪4∪5)=P(1) + P(4) + P(5)
1/2 = P(1) + P(4) + 7/16
P(1)+P(4)=1/16
If we do the same with P(2∪3∪5), we get:
P(2) + P(3) = 1/16
Now that we have this new knowledge, we can determine P(6):
P(6) = 1 - P(1∪2∪3∪4∪5)
P(6) = 1 - [P(1) + P(2) + P(3) + P(4) + P(5)] -- (There is no chance that two of these will occur simultaneously.)
P(6) = 1 - (1/16 + 1/16 + 7/16)
P(6) = 1 - 9/16
P(6) = 7/16
And with it, we can find P(2∪3∪6):
P(2∪3∪6) = P(2) + P(3) + P(6)
P(2∪3∪6) = 1/16 + 7/16
P(2∪3∪6) = 8/16 = 1/2
B) Keep in mind that the probability you need to know if you wish to roll anything other than a 6 is P(1∪2∪3∪4∪5)" but we found that in part A
P(1∪2∪3∪4∪5) = 9/16
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PLease help it’s due tomorrow morning
Explain the step that is used to solve the equation
-x = -16
Answer:x=16
Step-by-step explanation:
just divide both sides by negative 1
Solve the given system of equations.S =t =-6s+ 3t = - 45-s-5t= -2
1. Solve s in the second equation:
[tex]\begin{gathered} -s-5t=-2 \\ -s=-2+5t \\ s=-(-2+5t) \\ s=2-5t \end{gathered}[/tex]2. Substitute the s in the first equation by the value you get in the previous step:
[tex]-6(2-5t)+3t=-45[/tex]3. Solve t:
[tex]\begin{gathered} -12+30t+3t=-45 \\ -12+33t=-45 \\ 33t=-45+12 \\ 33t=-33 \\ t=\frac{-33}{33} \\ \\ t=-1 \end{gathered}[/tex]4. Use the value of t to solve s:
[tex]\begin{gathered} s=2-5t \\ s=2-5(-1) \\ s=2+5 \\ s=7 \end{gathered}[/tex]Then, the solution of the given system of equations is s=7t= -1PLEASE HELP SOON!!
Q.1 What is the expression written in simplified radical form? 6 sqrt 27 + 11 sqrt 75
Q.2 53√5 x (-103√50)
Q.3 Which expressions simplify to a rational answer?
Select each correct answer.
1/4 + 1/2
sqrt3 + 4
sqrt4 + 7
2 x sqrt9
7 x sqrt6
4x2sqrt3
3. 7 x (1/3)
7 x sqrt81
Step-by-step explanation:
Q.1
6×sqrt(27) + 11×sqrt(75) =
= 6×sqrt(3×9) + 11×sqrt(3×25) =
= 3×6×sqrt(3) + 5×11×sqrt(3) =
= 18×sqrt(3) + 55×sqrt(3) = 73×sqrt(3)
Q.2
53×sqrt(5) × (-103×sqrt(50)) =
= 53×-103 × sqrt(5)×sqrt(50) =
= -5459 × sqrt(5×50) = -5459 × sqrt(250) =
= -5459 × sqrt(10×25) = -5459 × 5×sqrt(10) =
= -27,295 × sqrt(10)
Q.3
1/4 + 1/2 rational (as both terms are rational)
sqrt3 + 4 irrational (as sqrt(3) is not rational)
sqrt4 + 7 rational (sqrt(4) = 2, 2+7 = 9)
2 x sqrt9 rational (sqrt(9) = 3, 2×3 = 6)
7 x sqrt6 irrational (sqrt(6) is not rational)
4x2sqrt3 irrational (sqrt(3) is not rational)
3. 7 x (1/3) rational (all terms are rational)
7 x sqrt81 rational (sqrt(81) = 9, 7×9 = 63)
I will Award Brainlist !! Help its a Math Question! Algebra 2 (basic)
At time 1.75 seconds the ball is in the 51 feet high.
What is substitution method?
Find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.
Given that;
The height of the football could be describe by the model,
h = - 16t² + 56t + 2 ..... (i)
Where, h describes the height of the ball in feet.
and t is the time in seconds after the ball was kicked.
Now,
At height 51 feet, the time is calculated as;
Substitute h = 51 in equation (i), we get;
h = - 16t² + 56t + 2
51 = - 16t² + 56t + 2
16t² - 56t - 2 + 51 = 0
16t² - 56t + 49 = 0
Solve for t by using quadratic formula;
t = - (-56) ± √(-56)² - 4 × 16 × 49 / 2 × 16
t = 56 ± √3,136 - 3,136 / 32
t = 56 ± 0 / 32
t = 56 / 32
t = 1.75 seconds
Thus, At time 1.75 seconds the ball is in the 51 feet high.
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What is a hour and how manyyyy
Answer:
An hour is a unit of time.
Step-by-step explanation:
An hour is a period of 60 minutes.
1 hour = 60 minutes.
Answer:
an hour is the si unit of time
1 hour = 60 minutes
1 minutes = 60 seconds
pls mark as brainliest
Step-by-step explanation:
don’t know what to do
A power function has the formula f(x) = kxⁿ,
A power function is a function that has a single term that is the product of a real number, a coefficient, and a variable raised to a fixed real value. (A coefficient is a value that increases an exponent by a variable.)
A power function has the formula f(x) = kxⁿ, where k and n are both real numbers. You can change the appearance of a power function's graph by changing the values of k and n. As a result, in this graph, n is greater than zero.The Power function produces an integer that has been raised to a particular power. Power is an alternative for the exponent operator in a mathematical equation (^). The Power function only takes two arguments: number and power. Number must be a numeric value that is either a hardcoded constant or a cell reference.Monomial functions:
Linear: y=3x+5
Quadratic: y = x²
Constant: y = 6
Cubic: y = x³+5
Quartic : y = x⁴
Quantic : y = x⁵
Therefore the function with a power function is given by y = k xⁿ
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Vă rog mult de tot
√ ( 2√2-3 ) ² + |2√2 + 5|-|-2,5 |
Answer: 4√2-0.5
Step-by-step explanation:
[tex]\sqrt{(2\sqrt{2}-3)^2 } +|2\sqrt{2}+5|-|-2.5|=\\\\|2\sqrt{2}-3|+(2\sqrt{2}+5)-(2.5 )=\\\\2\sqrt{2}-3+2\sqrt{2}+5-2.5 =\\\\4\sqrt{2} -0.5[/tex]
76,300,000 in scientific notation
Answer:
7.63 x 10⁷
Step-by-step explanation:
To convert to scientific notation you have to move the decimal place to where there is only one number in front of it. In this cause the number in front is 7. You have to maintain the same number of significant figures which in this case was 3 then multiply by 10 to the exponent of how many times you moved the decimal place.
Answer:
=76.3×10⁶
Step-by-step explanation:
=76,300,000÷1,000,000
=76.3×10⁶
Which expression can be used to find the total number of squares below?
6 × 7
7 × 5
6 × 1
7 + 5
6 + 1
An expression which can be used to find the total number of squares below (see attachment) is: B. 7 × 5
What is an expression?An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.
In this exercise, you're required to determine the total number of squares that are shown in the image attached below. By critically observing the image, we can reasonably and logically deduce that there are five (5) categories of squares and each of them comprises seven (7) squares.
Therefore, the total number of squares can be calculated by using this expression:
Total number of squares = 7 × 5
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If 2x² + 7x + 10 = p(x+q)² +r for all values of x, find the values of p and q
If the coordinates of the vertex of a parabola are known [tex]V(p,k)[/tex], the equation for that parabola can be written by the following formula;7
[tex]y=a.(x-p)^2+k[/tex]Now let's find the vertex of the given equation.
[tex]V(p)=\frac{-b}{2a}=\frac{-7}{4} =p[/tex][tex]V(k)=f(p)=2(\frac{-7}{4} )^2+7(\frac{-7}{4} )+10=\frac{31}{8} =k[/tex]We've found our vertex.
[tex]V(p,k)=(\frac{-7}{4} ,\frac{31}{8} )[/tex]Let's substitute the unknowns in the formula I've given.
[tex]p(x+q)^2+r=p(x+\frac{7}{4} )^2+\frac{31}{8}[/tex]Let's expand the expression and find the coefficient p.
[tex]px^2+\frac{7px}{2}+\frac{49p}{16}+\frac{31}{8} =2x^2+7x+10[/tex][tex]p=2[/tex]Finally;
[tex]q=\frac{7}{4}[/tex]
[tex]p=2[/tex]
Solve the equation for C
R-C=P
PLEASE HELP!!!! 40 POINTS
solve for y. 49-y=6y
Answer:
y = 7
eight grade math comes back to haunt me
The value of y varies directly with x. If y = 8, when x = 4, what is y when x = 48?
Answer:
96
Step-by-step explanation:
If Y is directly proportional (or in this case varies directly) then whatever you do to one value you do to the other.
So in this case, when Y = 8 and X = 4 that means that Y is double of X (cause 8 is double 4).
So when X = 48 all you need to do is double X which will give you 96.
15. what are the coordinates of point u, point v, and point w
Answer:
is there a picture because this can't be solved without a picture
6- 1/3x=-1 what is x
Answer:
x=21
Step-by-step explanation:
6-1/3x=-1
-6 -6
-1/3x=-7
__ __
-1/3 -1/3
x=21
Hello!
Let's solve:
[tex]\text{Copy down the equation}\\6-\dfrac{x}{3}=-1 \\\\\text{Move 'x/3' to the right side and '-1 to the other side}\\6+1=\dfrac{x}{3}\\ 7=\dfrac{x}{3} \\\\\text{Multiply 3 to both sides}\\7*3=3*\frac{x}{3} \\x = 21[/tex]
Answer: x = 21
Hope that helps!
identify the y-intercept: 6 - 2y = -6
We know that the equation of a line is given by
y = mx + b, where m and b are numbers:
m is the slope of the line and b is the y intercept.
In this case we have the equation:
6 - 2y = - 6
We clear y so we can identify m and b
6 - 2y = -6
6 = -6 + 2y
6 + 6 = 2y
12 = 2y
12/2 = y
6 = y
In this case
y = 6
Then m=0 and b = 6
Then, the y-intercept is b =6Wilson viaja 53.7 millas en 1.6 horas. ¿Cuál es su velocidad promedio a la décima de milla por hora
más cercana?
Uniform line movement.
The uniform rectilinear movement is the movement that maintains a variation of the distance with respect to time always constant, since the acceleration is zero.
If we know that Wilson travels 53.7 miles in 1.6 hours, we determine the average speed from the following equation:
Speed = distance / time
Speed = 53.7 miles / 1.6 hours
Speed = 33.5625 miles/hour
V = 33.6 miles/hour
The average speed that Wilson travels is: V = 33.6 miles/hour.
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Dale has $100 in a saving account that earns 5% annually, the interest earned is a simple interest. How much will he earn in 3 years? pleasee help asap tyty
The earned amount by Dale in 3 years is: 15 dollars.
How to calculate the amount?
To calculate the annually amount based on the principal money is by using simple interest method. This interest was given by the bank. And it is calculated by multiplying the principal amount, rate and time and divided by 100.
According to the question, the given amount parameters for the simple interest calculation is as follows:
Principal amount: $100
Rate of interest: 5%
Time(years): 3 years
Using standard simple interest formula, we get:
S.I. = (P x R x T)/100
S.I. = (100 x 5 x 3)/100 = 15 dollars
Hence, the earned amount by Dale in 3 years is: 15 dollars
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Julia owns a food truck that sells tacos and burritos. She only has enough supplies to make 67 tacos or burritos. She sells each taco for $3.75 and each burrito for $6. Julia must sell no less than $330 worth of tacos and burritos each day. If 42 burritos were sold, determine all possible values for the number of tacos that Julia must sell in order to meet the requirements. Your answer should be a comma separated list of values. If there are no possible solutions, submit an empty answer.
Julia must sell 21 tacos to meet the requirement .
Given: Price of each taco = $ 3.75
Price of each burrito = $ 6
Total amount of money she needs to earn = $ 330
Also the number of burritos sold= 42.
So the total amount earned on selling these burritos= 42× 6 = $ 252
And as it is given that total money she needs to earn is $ 330 .
so required money= $ 330- $ 252
=$ 78
Thus the total number of tacos she needs to sell = 78/ price of 1 taco
= 78/ 3.75
= 20.8 ≈ 21
Thus Julia must sell 21 tacos to meet the requirement .
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Given P(A) = 0.6, P(B) = 0.42 and P(B|A) = 0.63, find the value ofP(An B), rounding to the nearest thousandth, if necessary
Here, we are given;
P(A)=0.6
P(B)=0.42
P(B/A)=0.63
We have to find;
[tex]P(A\cap B)[/tex]Now,
[tex]P(\frac{B}{A})=\frac{P(A\cap B)}{P(A)}[/tex]This is the formula for finding conditional probability.
From here,we can see that we have values of P(B/A) and P(A) and we can easily find P(Aand B) from here.
Since P(A)>0 so we can use this formula.
Therefore,
[tex]\begin{gathered} P(A\cap B)=P(A)\times P(\frac{B}{A}) \\ P(A\cap B)=0.6\times0.63 \\ P(A\cap B)=0.378 \end{gathered}[/tex]which situation is best modeled by an exponential distribution? tafadzwa runs between 10 and 16 laps every day. his times get slower as he gets tired, but his daily average is 48.2 s per lap. what is the probability that his mean lap time tomorrow will be less than 45 s? suppose that meteors large enough to cause mass extinction strike the earth at regular, although exceedingly large, intervals. what is the probability that a large meteor strike will cause a mass extinction event within the next 1000 years? on a dark desert highway, drivers fall asleep and run off the road randomly. what is the probability that a driver will run off the road in one particular 10-mile stretch of this highway? suppose that people call in sick randomly and independently of one another at a business called acme anvil supply. on average, one person calls in sick per week. what is the probability that no one will call in sick next week? suppose that 0.76% of tires are defective, and defective tires occur independently of one another. what is the probability that no more than three of the next 100 tires are defective?
The situation that is best represented by an exponential distribution is given by the following option:
Tafadzwa runs between 10 and 16 laps every day. his times get slower as he gets tired, but his daily average is 48.2 s per lap. what is the probability that his mean lap time tomorrow will be less than 45 s?.
Exponential distributionThe exponential probability distribution, with mean m, is described by the following mass function:
[tex]f(x) = \mu e^{-\mu x}[/tex]
In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.
From this, we get that the exponential distribution is used when we want to study the time between events in a distribution, and only the first option in this problem gives it.
As for the other options, the distributions are as follows:
Meteor: Poisson distribution or binomial distribution, mean in a given time, we want to find the probability of a number.Drivers asleep in the highway: Poisson or binomial, also number of events in an interval.People calling in sick: Binomial distribution.Defective tires: Binomial distribution.More can be learned about the exponential distribution at https://brainly.com/question/16371214
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