1. Simon drives 32 miles in 15 minutes. What is his speed in miles per hour?
2. Triangle BIG is similar to triangle CAT. If BG is 6 units and CT is 15 units, then what is the length of IG if At is 20 units?
3. Quadrilateral SMAK is similar to quadrilateral DOWN. Assuming the length of SM is 34u and the length of DO is 17u, what is the ratio of AK to WN in simplest form?
1) the speed of Simon per hour is 128 miles/Hr
2) The length of IG is 20 Units.
3) The ratio of SM is 2:1
What is the explanation of the above answer?1) For 1, to obtain the speed of Simon per hour, all you need to do is multiply 32 x 4.
This is because in every hour, 15 minutes occurs four times. That is:
1 hour = 60 minutes
Hence, if 32 miles is done in 15 minutes, then 60 minutes =
32 x 4
= 128 miles
Hence the speed of Simon per hour is 128 Miles/ Hour
2) Given that the two triangles are identical, it means that on the basis on RHS theorem we have been given all the sides. Note that BG is 6 Units (we are assuming that this is the base) , then AT from the other triangle (see attached) is 20.
We assume this is the Hypotenuse. CT is also given. We assume this is the height. If we have CT and AT, and both triangles are the same, then IG is 20 units.
3) For the quadrilateral, recall that in quadrilaterals opposite sides are equal. If one side is 34u on one, and the other side is 17u on the other quadrilateral, then we already have the measure of the sides for both quadrilaterals.
So the Ratio of AK to WN
34u: 17u - Simplified by dividing by 17u we have
Ratio 2:1
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Find the equation of the parabola with the given x-intercepts and point on the graph. Use y = a(x-p)(x-q).
3. x-int: (-4,0) , (7,0)
P (3,8)
Answer:
y = -2/7(x + 4)(x - 7)=============================
Givenx- intercepts (-4, 0) and (7, 0),Point P (3, 8).SolutionThe given translates as:
p = -4, q = 7, x = 3, y = 8Use given x - intercepts to get the equation:
y = a(x + 4)(x - 7)Use the coordinates of P to find the value of a:
8 = a(3 + 4)(3 - 7)8 = a*7*(-4)8 = - 28aa = 8 / - 28a = - 2/7The equation of this parabola is:
y = - 2/7(x + 4)(x - 7)Answer:
[tex]\textsf{Intercept form}: \quad y=-\dfrac{2}{7}(x+4)(x-7)[/tex]
[tex]\textsf{Standard form}: \quad y=-\dfrac{2}{7}x^2+\dfrac{6}{7}x+8[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6 cm}\underline{Intercept form of a quadratic equation}\\\\$y=a(x-p)(x-q)$\\\\where:\\ \phantom{ww}$\bullet$ $p$ and $q$ are the $x$-intercepts. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}[/tex]
If the x-intercepts are (-4, 0) and (7, 0) then:
p = -4q = 7Substitute the values of p and q into the formula:
[tex]\implies y=a(x-(-4))(x-7)[/tex]
[tex]\implies y=a(x+4)(x-7)[/tex]
To find a, substitute the given point on the curve P (3, 8) into the equation:
[tex]\implies 8=a(3+4)(3-7)[/tex]
[tex]\implies 8=a(7)(-4)[/tex]
[tex]\implies 8=-28x[/tex]
[tex]\implies a=\dfrac{8}{-28}[/tex]
[tex]\implies a=-\dfrac{2}{7}[/tex]
Substitute the found value of a into the equation:
[tex]\implies y=-\dfrac{2}{7}(x+4)(x-7)[/tex]
Expand to write the equation in standard form:
[tex]\implies y=-\dfrac{2}{7}(x^2-3x-28)[/tex]
[tex]\implies y=-\dfrac{2}{7}x^2+\dfrac{6}{7}x+8[/tex]
a car travels a distance of 60 miles at an average speed of 30 mph. how fast would the car have to travel for the same 60 mile distance home to average 60 mph over the entire trip?
It is impossible to travel for the same 60-mile distance home to average 60mph over the entire trip.
car travels a distance of 60 miles long and averages 30 miles per hour. As a result,
time = distance/speed = 60/30 = 2
the car traveled for 2 hours.
The car would have to travel for exactly 2 hours (120/60) to average 60 mph over 120 miles.
Because the car has already traveled for two hours, it is impossible for it to average 60 mph for the duration of the journey.
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HELP ASAP PLEASE
What is the equation of p(x) in vertex form? p(x) = 2(x − 1)2 − 2 p(x) = 2(x + 1)2 − 2 p(x) = 3(x − 1)2 − 2 p(x) = 3(x + 1)2 − 2
Answer:
p(x)=-2*p*x+4*x+-4=1*-2*p*x+4*x+4=1*-2*p*x+6*x+-6=6*x+4*1*1
Step-by-step explanation:
Identity the domain and the range of each function
a) The domain of the function is {2,3,4,5,6},
The range of the function is {0,1,2,3,4}
b) The domain of the function is {-3,-1,1,3,4}
The range of the function is {1,3,-2,2,6}
Given,
Domain and Range;-
The domain of a function is the set of values that we are allowed to enter into our function. This collection represents the x values in a function like f. (x). A function's range is the set of possible values that it can accept. This collection contains the values that the function returns when we enter an x value.
Here,
a) Domain is the set of x values:
x={2,3,4,5,6}
The range is the set of y values:
y={0,1,2,3,4}
b) Domain is the set of x values:
x={-3,-1,1,3,4}
The range is the set of y values:
y={1,3,-2,2,6}
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for the function g(x)=-1/5 x^2 + 4x+1, find the range of g(x)
Plotting the graph of the quadratic function g(x)=-1/5x^2 + 4x + 1 the range is
y ≥ -19How to determine the range of the quadratic functionThe range of the quadratic function is seen at the vertex were the maximum or minimum y value is seen
The graph of the function g(x)=-1/5x^2 + 4x + 1 is plotted and attached
From the graph the vertex coordinates is v(-10, -16). The y coordinates of the vertex is -19 and this is the minimum values for y
Therefore the range is y ≥ -19
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September 2022 1 Thursday Twelve large bottles of water cost $9 . What is the cost per bottles of water
Answer:
75 cents
Step-by-step explanation:
If 12 bottles cost $9, in order to find the cost of one bottle we must divide the cost by the number of bottles.
[tex] \frac{9}{12} = 0.75[/tex]
therefore the cost of one bottle is 75 cents
23. Triangle ABC with vertices A(-7, 1), B(-5, 6), and C(-1, 2): k = 2
The coordinates after scaling of triangle ABC will become -
A'(- 14, 2)
B'(-10, 12)
C'(-2, 4)
What is triangle?A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically -
∠x + ∠y + ∠z = 180°
The sum of two sides of a triangle is greater then the third side. Mathematically -
a + b > c
There are different types of triangles such as -
equilateral triangle , scalene triangle , isosceles triangle etc.
Given is a triangle ABC with vertices A(-7, 1), B(-5, 6), and C(-1, 2) and
K = 2
After scaling, the coordinates will become -
A(x, y) ⇒ A'(Kx, Ky)
The coordinates after scaling of triangle ABC will become -
A'(- 14, 2)
B'(-10, 12)
C'(-2, 4)
Therefore, the coordinates after scaling of triangle ABC will become -
A'(- 14, 2)
B'(-10, 12)
C'(-2, 4)
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a rectangular garden has a length that is six feet more than twice its width. it takes 120 feet of fencing to completely enclose the garden's area. write an equation that could be used to find the width of the garden. clearly define your variable.
Length (L) = 42
Width (W) = 18
and the equation which helps to find the width of the garden is
L = 6 + 2W
Now, we have to find the length and width of the garden area.
It is given that,
we know that the Length is 6 feet more than twice the width, this in other words, it means that:
L = 6 + 2W -------------------------(1)
So, let's denote W as X
The perimeter of the garden is 120 and the expression to calculate is:
P = 2W + 2L ------------------------(2)
Replacing all the values in the above expression we have the following:
120 = 2x + 2(6 + 2x) ---------------------(3)
Solving for x from the above equation (3), we have:
⇒120 = 2x + 12 + 4x
⇒120 - 12 = 6x
⇒108 = 6x
⇒x = 108/6
⇒ x = 18
So the Width is 18, therefore the Length from equation (1):
L = 6 + 2(18)
⇒L = 6 + 36
⇒L = 42
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What is the answer to this question
Answer:141
Step-by-step explanation:
angles 4+2= 78
360-78 = 282
282/2 = 141
4,2 equal 6,8
1,3 equal 5,7
Answer:
m7= 141 degrees ; m5 = 141 degrees
Step-by-step explanation:
m3 + m4 = 180
m3 + 39 = 180
m3 = 180 - 39
m3 = 141 degrees
m3 = m5 = 141 degrees
m4 = m8 = 39 degrees
m3 = m7 = 141 degrees
1.
Which set of ordered pairs does not represent
a function?
B
A) (4, 1), (6, 2), (7, 5), (9, 2)
(0, 5), (1, 7), (2, 9), (3, 11)
(-2, 5), (0, 2), (9,-6), (8, 7)
D (5, 5), (6, 10), (10, 15), (5, 20)
D set of ordered pairs does not represent a function.
In the given question we have to check which set of ordered pairs does not represent a function.
The given set of ordered pair
(A) (4, 1), (6, 2), (7, 5), (9, 2)
(B) (0, 5), (1, 7), (2, 9), (3, 11)
(C) (-2, 5), (0, 2), (9,-6), (8, 7)
(D) (5, 5), (6, 10), (10, 15), (5, 20)
As we know that in the function a x value always have only one corresponding y value which means for a value of x have only a y value.
But when we see in the ordered pair D. In this pair have pair (5, 5) and (5, 20). This shows different value of y in same value of x.
So, D set of ordered pairs does not represent a function.
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Use the arithmetic sequence 12,15,18,21...
what is the equation of the nth term of the sequence
Answer:
The equation of the nth term of the sequence is 3n+9.
Step-by-step explanation:
- Describe all transformations from the parent
function
given the function below.
f(x)=(x-3)² +7
A rival company offers you an annual salary of $36,000. Except for the pay, everything is identical between the companies. Do you accept or reject the rival company's offer, and why?
I will have to reject the offer of the rival company since it's lesser than $40560.
How to calculate the amountFrom the information, the person works a basic week of 40 hours and the basic rate is $19.50 per hour. It should be noted that there are 52 weeks in a year. The total amount will be:
= 40 × 19.50 × 52
= $40560
The rival company offers you an annual salary is $36000.
I'll reject the rival company's offer since it's lower.
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Complete question
You work a basic week of 40 hours and your basic rate is $19.50 per hour. A rival company offers you an annual salary is $36.000. Except for the pay, everything is identical between the conpanies. Do you accept or reject the rival company's offer, and why?
The graph to the right is the uniform probability density function for a friend who is x minutes late
(a) Find the probability that the friend is between 25 and 30 minutes late.
(b) It is 10 A.M. There is a 10% probability the friend will arrive within how many minutes?
(a)The probability that the friend is between 25 and 30 minutes late is 1/2.
(b) It is 10 A.M. There is a 10% probability the friend will arrive within 1 minute.
What is probability?
Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.Uniform distribution
a = 0
b = 10
a) P(friend is between 25 and 30 minutes late) = (30 - 25)/(b - a)
= 5/(10-0)
= 1/2
b) Let the time for arrival be A minutes
(A - 0)/(b-a) = 0.10
A = 0.10 x (10 - 0)
A = 1 minute
Hence, The probability that the friend is between 25 and 30 minutes late is 1/2 and It is 10 A.M. There is a 10% probability the friend will arrive within 1 minute.
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Andrew has picked out some party favors. He calculates that they will cost $7 per guest.
Write an equation that shows how the total cost of the party favors, y, depends on the number of guests, x
Do not include dollar signs in the equation. what does y equal?
Answer:
Step-by-step explanation:
y=7x is the equation that shows how the total cost of the party favors, y, depends on the number of guests, x
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
Andrew has picked out some party favors.
He calculates that they will cost $7 per guest.
We need to find the equation that shows how the total cost of the party favors, y, depends on the number of guests, x
So y=7x where y is the total cost and x is the number of guests and 7 is the cost per guest.
If there are 2 guests then the total cost will be 14.
Hence y=7x is the equation that shows how the total cost of the party favors, y, depends on the number of guests, x
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the lifetime of a certain type of battery is normally dis- tributed with mean value 10 hours and standard deviation 1 hour. there are four batteries in a package. what life- time value is such that the total lifetime of all batteries in a package exceeds that value for only 5% of all packages?
The total lifetime of all batteries in a package exceeds that value for only 5% of all packs will be 43.29.
What is the standard deviation?It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.
[tex]\rm \sigma = \sqrt{\dfrac{ \sum (x_i-X)}{n}[/tex]
σ is the standard deviation
xi is each value from the data set
X is the mean of the data set
n is the number of observations in the data set.
It is given that,
mean,μ=10 hr
standard deviation,σ=1hr
n=4
The lifespan of four batteries combined is,
=4μ
=4×10
=40 hr
z = (x-μ)/σ
1.645=(x-40)/2
x-40=3.29
x=43.29
Thus, the total lifetime of all batteries in a package exceeds that value for only 5% of all packs will be 43.29.
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Help fast pleaseee thank u
The relative frequency of all students surveyed who go to Cook Middle School and prefer Energy flow is 57%.
What is relative frequency?This refers to how many times a particular type of occasion takes place within the total number of observations. This type of frequency uses percentages, fractions, and proportions.
Formula for calculating Relative Frequency:
Relative Frequency = Count of event
Total number of Observation
From the question:
No of students that like Gym Juice in Elim School =5
No of students that like Energy Flow in Elim School =10
Total Number of students in Elim School =15
No of students that like Gym Juice in Cook Middle School =15
No of students that like Energy Flow in Cook Middle School =20
Total Number of students in Cook Middle School =35
Calculating The relative frequency of all students surveyed who go to Cook Middle School and prefer Energy flow:
Relative Frequency = Count of event
Total number of Observation
Relative Frequency = 20
35
=0.57 or 57%
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An old-fashioned gardener measures the height of a plant as 6 3/8 inches. A week later the height is measured as 8 3/5 inches. How much did the plant grow during the week?
The plant grew by 2 9/40 inches during the week.
What is mixed fraction?A fraction represented with its quotient and remainder is a mixed fraction. For example, 2 1/3 is a mixed fraction, where 2 is the quotient, 1 is the remainder. So, a mixed fraction is a combination of a whole number and a proper fraction.
Initial height of plant = 6 3/8 inches
Final height = 8 3/5 inches
Difference in height = 8 3/5 inches - 6 3/8 inches
converting the mixed fraction to improper fraction
8 3/5 = 43/5
6 3/8 = 51/8
43/5 - 51/8
multiply 43/5 by 8/8 and 51/8 by 5/5 so that both fractions have common denominator, it becomes
344/40 - 255/40
Collect only the numerator we have,
344- 255 = 89 which is no 89/40
divided by 40, we have 2 9/40 inches
In conclusion, the plant grew by 2 9/40 inches
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61.92x5.50 what is it??????????brguquwdw
Answer:
Step-by-step explanation:
340.56
Answer:
61.92 x 5.50 = 340.56
Evaluate Expressions
Nov 12, 10:01:46 AM
Watch help video
What is the value of the expression below when y = 8?
Answer:
2y - 3
Submit Answ
Answer:
13
Step-by-step explanation:
2y - 3;
y = 8;
---> 2*8 - 3 =
16 - 3 = 13
I really need help! Can anyone please answer this!!
The function f has domain : [-4, 5], range : [0, 9], zero : (3, 0), the function is increasing in intervals at [-4, 0] U [3, 5], decreasing in intervals at (0, 3], the relative minimum values of f : (3, 0), and relative maximum values of f : (5, 9).
What are the domain and range of the function?The domain of the function includes all possible x values of a function, and the range includes all possible y values of the function.
The function f is given in the graph.
According to the given function, the required solution would be as:
The domain and range of f will be :
domain : [-4, 5]
range : [0, 9]
The zero of f will be :
(x, y) = (3, 0)
The function is increasing in intervals at [-4, 0] U [3, 5]
The function is decreasing in intervals at (0, 3]
The relative minimum values of f : (3, 0)
The relative maximum values of f : (5, 9)
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if you can buy three loaves of bread for 5 dollars, how many loaves can you buy with 12 dollars?
Answer: 20 loaves
Step-by-step explanation:
3/5 = .6
12/.6 = 20
I’m not 100% sure but this is what I believe is the answer
20 Loaves
Graph y=x+4 on a graph
Answer:
Take a look at the attachment...
Hope this helps! :)
y = x + 4
Simplify:1/6x+42+2/5x-8/3x-19
Answer:
C; -21/10X + 23
Step-by-step explanation:
Combine like terms and simplify
Find the length of YZ when Y is the midpoint of XZ
X
20+2a
Y
8 +6a
Z
XZ=
The length of the line YZ is 26 units
The Y is the mid point of the line XZ
The length of the line XY = 20 + 2a
The length of the line YZ = 8 + 6a
When Y is the mid point of the line XZ, then the length of the line XY is equal to the length of the line YZ
The length of the line XY = The length of the line YZ
Substitute the values in the equation and find the value of a
20 + 2a = 8 +6a
Rearrange and group the like term
6a - 2a = 20 - 8
4a = 12
a = 12 / 4
a = 3
The length of the YZ = 8 +6a
= 8 + 6×3
= 8 + 18
= 26 units
Hence, the length of the line YZ is 26 units
The complete question is:
Find the length of YZ when Y is the midpoint of XZ, if XY = 20+2a and YZ = 8+6a.
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What is the solution of the system?
10x + 3y = 50
- 5x - y = -20
(2, 4. 4)
(4. 4, 2)
(2,10)
(10, 2)
The linear equation two variables can be solved by various methods one of the methods to solve the linear equations is the substitution method. The solution of the given equation is x=2 and y=10.
What is linear equation in two variables ?
A specific point on the graph represents the solution of a linear equation in two variables, ax+by = c, where the total of these two values will equal c when the x-coordinate is multiplied by a and the y-coordinate by b.
Main body:
The given equations are :
10x+3y=50 .... (1)
-5x-y=-20 ....(2)
Multiply equation (2) by 3 and then add the equation (1) to eliminate the variable y.
10x+3y+3(-5x-y)=50+3*-20
-5x=-10
x=2
Now putting the value of x in equation (1), and solve it further.
10*2+3y=50
3y=30
y=10
Hence, the value of x is 2 and the value of y is 10.
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In a farm houe, there are 80 cow and 30 buffaloe. What i the rate of the cow
and the buffaloe
If there are 80 cow and 30 buffaloe , the ratio of the cow and the buffaloe is 8:3 .
In the question,
it is given that ,
the number of cows in the farm house = 80
the number of buffaloe in the farm house = 30
we need to find the ratio of cow and the buffaloe .
the ratio can be calculated using the formula .
ratio = (number of cows)/(number of buffaloe)
Substituting the vales , we get
= 80/30
cancelling out the common factor 10 , from both numerator and denominator , we get
= 8/3
So , the ratio is 8:3 .
Therefore , If there are 80 cow and 30 buffaloe , the ratio of the cow and the buffaloe is 8:3 .
The given question is incomplete , the complete question is
In a farm house, there are 80 cows and 30 buffaloes . What is the ratio of the cow and the buffaloe ?
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Two sevenths divided by 1 half
Answer:
4/7
Step-by-step explanation:
2/7 ÷ 1/2 = 2/7 × 2/1 = 4/7
Answer:
Step-by-step explanation:
1. Write Words into math
2/7/1/2
2. Solve
2/7/1/2=
2/7*2/1=
4/7
Answer: 4/7
A group entering a zoo purchased 32 admission tickets for a total of $148. Adult tickets cost $7. 50, and tickets for children cost $3. 50. How many of each type of ticket were purchased?.
23 tickets are purchased for children and 9 tickets are purchased for adults.
Given,
In the question:
A group entering a zoo purchased 32 admission tickets for a total of $148. Adult tickets cost $7. 50, and tickets for children cost $3. 50.
To find the how many of each type of ticket were purchased?
Now, According to the question:
It is given in the question that 32 tickets are purchased by group which cost total $148.
Let the number of children of the group who are entering the zoo be x. Then the number of adults will be 32- x
Now cost of one ticket for adult = $7.50
Total amount spent on adult tickets = 7.50 × (32-x)
Similarly, cost of one ticket for child= $3.50
Total amount spent on children tickets = 3.50 × x =3.5x
Total amount spent by group on tickets = $148
⇒ 7.5 × (32-x) + 3.5x = 148
⇒ 240 - 7.5x + 3.5x = 148
⇒ 7.5x - 3.5x = 240 - 148
⇒ 4x = 92
⇒ x = 23
Children = 23
Adults = 32-x = 32-23 = 9
Hence, 23 tickets are purchased for children and 9 tickets are purchased for adults.
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