The value of m and n that shows that point p(m,5-n) when reflected on line y=0 is m = 3, n = 3.
What is a transformation?Transformation is the movement of a point from its initial point to a new location. Types of transformation are reflection, rotation, translation and dilation.
The rule for the reflection over the line y = 0 (x axis) is (x, y) ⇒ (x, -y)
If the point p(m,5-n) is reflected on line y=0, this would give (m, -(5 - n)) = p'(2m-3,2n-8). Hence:
2m - 3 = m
m = 3
Also:
-(5 - n) = 2n - 8
-5 + n = 2n - 8
n = 3
The value of m and n that shows that point p(m,5-n) when reflected on line y=0 is m = 3, n = 3.
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Line l contains points (2,4) and (5,1). Point P has coordinates (1,1). Find the distance from P to l.
The least distance from point P to line l is approximately equal to 3.536 units.
How to find the least distance between a line and a point outside the line
There are several ways to calculate the least distance, in this case we decided to use the approach based on vectors and projections. First, we generate two auxiliary vectors:
Vector parallel to the line l
[tex]\overrightarrow {AB} = (5, 1) - (2, 4)[/tex]
[tex]\overrightarrow{AB} = (3, - 3)[/tex]
A vector from one point on the line l to the point P
[tex]\overrightarrow{AP} = (1, 1) - (2, 4)[/tex]
[tex]\overrightarrow {AP} = (- 1, - 3)[/tex]
Now we proceed to find the vector distance by using the following vectorial formula:
[tex]\vec d = \frac{\overrightarrow{AP} \,\bullet\, \overrightarrow {AB}}{\overrightarrow {AB} \,\bullet \,\overrightarrow {AB}} \cdot \overrightarrow{AB} - \overrightarrow {AP}[/tex]
[tex]\vec d = \frac{(-1)\cdot (3) + (- 3) \cdot (- 3)}{3^{2}+ (-3)^{2}} \cdot (3, - 3) - (-1, - 3)[/tex]
[tex]\vec d = - \frac{1}{6}\cdot (3, - 3) - (- 1, - 3)[/tex]
[tex]\vec d = \left(-\frac{1}{2}, \frac{1}{2} \right) + (1, 3)[/tex]
[tex]\vec d = \left(\frac{1}{2}, \frac{7}{2} \right)[/tex]
The magnitude of the vector distance is determined by Pythagorean theorem:
[tex]d = \sqrt{\left(\frac{1}{2} \right)^{2}+\left(\frac{7}{2} \right)^{2}}[/tex]
d ≈ 3.536
The least distance from point P to line l is approximately equal to 3.536 units.
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3)If the interior angle of a regular polygon is 35" how many sida does it have?A)5. B) 8 C)6 D) 7
The number of sides the regular polygon has is: B. 8.
How to Find the Interior Angle of a Regular Polygon?A polygon with an n-side have a sum of interior angles which can be determined using the formula: (n - 2)180, where n is the number of sides of the regular polygon.
Thus, to find the measure of each interior angle of the polygon, we have: interior angle of a polygon = sum of interior angles ÷ number of sides.
Given the following information about the regular polygon:
Interior angle of the regular polygon = 135 degrees.
Plug this into the given formula for finding the interior angle of a polygon:
135 = (n - 2)180/n
Multiply n by both sides of the equation
135 × n = (n - 2)180/n × n
135n = (n - 2)180
Open the bracket
135n = 180n - 360
Subtract both sides by 180n
135n - 180n = 180n - 360 - 180n
-45n = -360
Divide both sides by -45
-45n/-45 = -360/-45
n = 8
Thus, the number of sides that the regular polygon has is: B. 8 sides.
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pls help The surface area of a cone is given by the formula
S= al +712. Solve the formula for 2.
Answer:
l = (S/pi)-r^2
Step-by-step explanation:
Just rearrange the equation.
S = pi*l + pi * r^2
S-pi*r^2 = pi*l
l = (S-pi*r^2)/pi
l = (S/pi)-r^2
(3.5x0.71) ÷ √8.2-7.5
24.85
Step-by-step explanation:
First find the square root of 8.2 and subtract from the square root of 7.5. Multiply 3.5 by 0.71, the answer you get divide it by the answer you get after finding the square root.
Jason bought 10 of the 30 raffle tickets for a drawing. assuming that he chooses the winning ticket each time, what is the probability that jason will win all 3 of the prizes if once a raffle ticket wins a prize it is thrown away?
Answer: 2.96% rounded
Step-by-step explanation: 10/30) x (9/29) x (8/28) = 720 / 24,360 = 6/203 = 2.96%
John ate a whole pizza which has 2,368 Cal. If he burns 125 Cal by walking for 30 minutes, how long would it take to burn off the entire pizza by walking
The time taken to burn off the entire pizza by walking is 568.32 minutes.
Time taken to burn caloriesTotal calories in pizza = 2,368Total calories burnt per 30 minutes walk = 125Number of 30 minutes walk to burn all calories = w2,368 = 125 × w
2,368 = 125w
w = 2,368 / 125
w = 18.944
Total time needed to burn all calories = 30 minutes × 18.944
= 568.32 minutes
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Is this a function or not because there’s a vertical line but the plots also go above each other .
Answer:
not a function because it doesn't pass the vertical line test
Step-by-step explanation:
even though they have different y coordinates they still don't pass the test
how do u write 99.09 - 98.29 in a long subtraction line by line and where do u put the answer?
The computation of the subtraction implies that 99.09 minus 98.29 will be 0.80.
How to calculate the value?It should be noted that the subtraction line is simply used to subtract numbers.
In this case, the computation of the subtraction implies that 99.09 minus 98.29 will be 0.80.
When subtracting the numbers on the number line, we will move towards the left hand side of the number line.
An illustration of the number line is given.
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Find the missing side length of the triangle
Answer:
b = 24 meter
Step-by-step explanation:
Using Pythagoras theorem:
a² + b² = c²
Here given: a = 10 m, b = ?, c = 26 m
Insert values
10² + b² = 26²
b² = 26² - 10²
b² = 676 - 100
b² = 576
b = √576
b = 24
Answer:24
Step-by-step explanation: i found the answer using the pythogaras theorem,the formula used is, h squared=b squared +p squared,formula used to find missing legnths of triangles such as hypotaneous and height.in this question you have to find the height,as you can see to the opposite of hypotaneous its height/perpendicular.
so according to formula,h squared=b squared+p squared
so,26 squared=10 squared+p squared.
in order to find p
p squared=26 squared -10 squared
which gives us 576
and p squared =576
the square on the p will go on the other side and become an underroot.
take the underoot of 576
which gives us p=24.
so the legnth is 24, found using pythogares theorem.by rearranging the formula and making p the subject in the formula
tengo 2/3 de lo que cuesta una computadora ¿Cuanto vale la computadora si me faltan solo 318 dolares para comprarla?
A toilet is leaking at the rate of 1 fluid ounces per minute. How many gallons is
the toilet leaking per hour?
O 0.47 gal/hr
O 0.94 gal/hr
O 28.13 gal/hr
O 2.13 gal/hr
1 gallon (gal) = 128 fluid ounce (fl oz)
1 hour (hr) = 60 minutes (min)
Convert 1 fl oz/min to gal/hr.
[tex]\dfrac{1\,\rm fl.oz}{1\,\rm min} \times \dfrac{1\,\rm gal}{128\,\rm fl.oz} \times \dfrac{60\,\rm min}{1\,\rm hr} = \dfrac{60}{128} \dfrac{\rm gal}{\rm hr} \approx \boxed{0.47 \dfrac{\rm gal}{\rm hr}}[/tex]
Which equations are true for x = –2 and x = 2? Select two options
x2 – 4 = 0
x2 = –4
3x2 + 12 = 0
4x2 = 16
2(x – 2)2 = 0
The equations that are true for x = -2 and x = 2 are (a) x^2 - 4 = 0 and (d) 4x^2 = 16
How to determine the true equations?We have:
x = -2 and x = 2
Rewrite as:
x + 2 = 0 and x - 2 = 0
Multiply both equations
(x + 2)(x - 2) = 0
This gives
x^2 - 4 = 0 --- option (a)
Add 4 to both sides
x^2 = 4
Multiply by 4
4x^2 = 16 --- option (d)
Hence, the equations that are true for x = -2 and x = 2 are (a) x^2 - 4 = 0 and (d) 4x^2 = 16
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Please answer with everything needed i appreciate everyones help:0
A scenario that would best model the graph on Holly, her home, and school is:
Holly was trying to get to school from home but fell ill when 4 miles from home. Holly waited to catch her breath and gain some strength. Holly reached school and reported her condition. The school allowed her to go home.What happened Holly's journey to school?As Holly was heading to school, she felt uneasy and had to wait for 10 mins to catch her breath.
After doing so, she then continued to school which was 6 miles from her home. When she got there, she went to the nurse's office.
She waited in school for 15 minutes and was then told to go home to rest and recuperate. She then made the journey back home in a car and arrived in 10 minutes.
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TIME REMAINING
53:34
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.
x < 5
–6x – 5 < 10 – x
–6x + 15 < 10 – 5x
A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
Option 3 and 4. The two options that shows the correct representation of the inequality are:
- 6x + 15 < 10 - 5xAn open circle is at 5 and a bold line starts at 5 and is pointing to the right How to solve the inequality–3(2x – 5) < 5(2 – x)
We have to open up the brackets by multiplying the sides
= -6x + 15 < 10 - 5x
Hence the third option is certified to be correct.
Next this inequality has to be shown on a number line.
To do this we have to solve the inequality completely
From -6x + 15 < 10 - 5x
we have to take like terms
-6x+5x < 10 - 15
-x < -5
x<5
The sign of inequality has to be reversed given that the coefficient of x was negative.
Hence x>5. The number line would start from the right and it would move towards the right
From the solution here, we can see that the two correct options are
–6x + 15 < 10 – 5x An open circle is at 5 and a bold line starts at 5 and is pointing to the right.Read more on number lines here:
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Math
The equation 5 + 10x = 20 can be used
to find x, the cost of a ride ticket at
an amusement park. Which statement
explains the best possible first step to find
the cost of a ride ticket?
1
A Add 5 to both sides.
BSubtract 20 from both sides.
CMultiply both sides by 10.
D Subtract 5 from both sides.
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Random note:}[/tex]
[tex]\large\textsf{(We will solve for your given question as well because it}\\\large\textsf{pops up in solving for your question.)}[/tex]
[tex]\huge\textbf{Solving for your original answer:}[/tex]
[tex]\mathbf{5 + 10x = 20}[/tex]
[tex]\mathbf{10x + 5 = 20}[/tex]
[tex]\huge\textbf{SUBTRACT 5 to BOTH SIDES:}[/tex]
[tex]\mathbf{10x + 5 - 5 = 20 - 5}[/tex]
[tex]\huge\textbf{Simplify it!}[/tex]
[tex]\mathbf{10x = 20 - 5}[/tex]
[tex]\mathbf{10x = 15}[/tex]
[tex]\huge\textbf{DIVIDE 10 to BOTH SIDES:}[/tex]
[tex]\mathbf{\dfrac{10x}{10}=\dfrac{15}{10}}[/tex]
[tex]\huge\textbf{Simplify it!}[/tex]
[tex]\mathbf{x = \dfrac{15}{10}}[/tex]
[tex]\mathbf{x = \dfrac{15\div5}{10\div5}}[/tex]
[tex]\mathbf{x = \dfrac{3}{2}}[/tex]
[tex]\mathbf{x = 1 \dfrac{1}{2}}[/tex]
[tex]\mathbf{x = 1.5}[/tex]
[tex]\huge\textbf{Therefore, the overall answer should be:}[/tex]
[tex]\huge\boxed{\star\boxed{\mathsf{\ x= \dfrac{3}{2} \ }}\star}[/tex]
[tex]\huge\textbf{And to answer your question, the very}\\\\\huge\textbf{first step in solving for this equation}\\\\\huge\textbf{[5 + 10x = 20] is:}[/tex]
[tex]\huge\boxed{\textsf{Option D. Subtract 5 to both sides}}\huge\checkmark\\\\\\\\\\\large\text{Look at the explanation above to see how we chose that.}\\\\\large\text{Remember: addition opposite is subtration \& subtraction opposite}\\\large\text{is addition, whereas multiplication is division \& divsion is}\\\large\text{is multiplication.}[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
a senator wishes to estimate the proportion of united states voters who favor new road construction. what size sample should be obtained in order to be 95% confident
The size of the sample should be obtained at 2401 in order to be 95% confident
Given that:
Margi of error, [tex]ME=0.02[/tex]
Population proportion, [tex]p=0.50[/tex]
To Find: The size of the sample that should be obtained in order to be 95% confident
Let the size of the sample be n
Using formula,
[tex]n=(p*(1-p))*(z(0.05/2)/ME)^{2} \\n=(0.5*(1-0.5))*(1.96/0.02)^{2} \\n=0.25*9604\\n=2401[/tex]
Therefore, the size of the sample should be obtained at 2401 in order to be 95% confident
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Jen has collected information about the students in her class and the month they were born.
Which of the following statements would be true about this information?
It is both a relation and a function.
It is not a relation, but it is a function.
It is a relation but not a function.
It is neither a relation nor a function.
The true statement about this information is that: A. It is both a relation and a function.
What is a function?A function can be defined as a mathematical expression which can be used to define and represent the relationship that exist between two or more variables in a population.
In this context, we can infer and logically deduce that the true statement about this information collected by Jen is that it's both a relation and a function because it indicates a relationship between two variables.
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Answer:
It is both a relation and a function.
Step-by-step explanation:
peating decimal 0.353535...? 35+ 0.35 +0.0035 + ... 0.0035 + 0.000035 + 0.00000035 + ... 0.35 +0.0035 + 0.000035 + ... OMPLETE he first term of the geometric series is 0.35.- v COMPLETE vity Intro Final COMPLETE The simplified fractional representation of 0.353535... is 35 99 COMPLETE X0.01. 10 of 11 O TU peating decimal 0.353535 ... ? 35+ 0.35 +0.0035 + ... 0.0035 + 0.000035 + 0.00000035 + ... 0.35 +0.0035 + 0.000035 + ... OMPLETE he first term of the geometric series is 0.35.- v COMPLETE vity Intro Final COMPLETE The simplified fractional representation of 0.353535 ... is 35 99 COMPLETE X0.01 . 10 of 11 O TU
The only option that represents the correct repeating decimal is; Option C; 0.35 + 0.0035 + 0.000035
How to Identify a Repeating Decimal?
We want to find the option that is equal to the repeating decimal 0.353535.
Option A; 35 + 0.35 + 0.0035
When we add the above, we arrive at 35.3535 which is not equal to 0.353535. Thus, option A is incorrect.
Option B; 0.0035+ 0.000035 + 0.00000035
When we add the above, we arrive at 0.00353535 which is not equal to 0.353535. Thus, option B is incorrect.
Option C; 0.35 + 0.0035 + 0.000035
When we add the above, we arrive at 0.353535 which is not equal to 0.353535. Thus, option C is correct.
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Answer:
1.) C - 0.35+0.0035+0.000035+...
2.) The first term of the geometric series is 0.35.
3.) The common ratio of the geometric series is 0.01
4.) The simplified fractional representation of 0.353535... is 35 / 99
Step-by-step explanation:
Edge
Robin was just hired at Groceries & More as a cashler. They pay her $12 an hour. She works 20 hours a week and is going to save all her money to buy a new cell phone that costs $950 The amount of deductions from her weekly paycheck is $34. How many weeks will Robin have to save for in order to buy the new computer? Enter your answer rounded to the nearest whole number.
Answer:
5 weeks
Step-by-step explanation:
We know that she works at a rate of $12 an hour, she also works 20 hours a week.
The total amount she makes per week is $240 (12 x 20). However, that is without deductions. We have to subtract $34 from the $240.
$240 - $34 = $206.
$206 is the amount she makes in a week and she wants to save $950. How many weeks does she have to save? Well, let's divide.
$950 / $206 = 4.6 weeks. However, if we have to round up to 5 weeks.
Use your graphing calculator to find the equation of the trend line for the scatterplot below.
The equation of the trend line is y = 3x + 15
How to determine the equation of the trend line?Start by entering the table of values in a graphing calculator.
From the graphing calculator, we have the following summary:
Sum of X = 21Sum of Y = 153Mean X = 3.5Mean Y = 25.5Sum of squares (SSX) = 17.5Sum of products (SP) = 52.5The equation of the trend line is represented as:
y = bx + a
Where
b = SP/SSX = 52.5/17.5 = 3
a = MY - bMX = 25.5 - (3*3.5) = 15
This gives
y = 3x + 15
Hence, the equation of the trend line is y = 3x + 15
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THAT IS THE QUATION OF Y=7X+300
Answer:
Slope=14.000/2.000=7.000
x-intercept = 300/-7 = -42.85714
y-intercept = 300/1 = 300.00000
Step-by-step explanation:
The unit digit of a two digit number is one less than the ten digit number. If the number is increase by 8 and then divided by the unit of the digits, the results is 8. Find the number.
The tens digit is 3; the units digit is 3-1 = 2; and the number itself is 32.
Lets simplify the problem,
Let assume the "tens" digit be x
Then the "units" difference = (x-1), according to the condition.
Hence, the number itself is N = 10x + (x-1).
Then the number N+8 is 10x + (x-1) + 8 = 10x + x + 7 = 11x + 7.
From the last statement of the problem, we have this equation
[tex]N+8 = 8*(x+y),or11x + 7 = 8*(x+(x-1)).[/tex]
Simplify and find "x"
[tex]11x + 7 = 8*(2x-1)11x + 7 = 16x - 87 + 8 = 16x - 11x15 = 5xx = 15/5 = 3[/tex].
Thus the tens digit is 3; the units digit is 3-1 = 2; and the number itself is 32.
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Drag a statement or reason to each box to complete this proof.
If −3(x+8)=−21, then x=−1.
Drag a statement or reason to each box to complete this proof.
If 3x−4=14, then x=6.
Drag a statement or reason to each box to complete the proof.
If 3(x−4)=x+4, then x=8.
The different statements and reasons to prove that −3(x + 8) = −21 are as detailed below.
How to utilize properties of Algebra?Statement 1; −3(x + 8) = −21
Reason 1; Given
Statement 2; −3(x + 8)/-3 = −21/-3
Reason 2; Division property of Equality
Statement 3; x + 8 - 8 = 7 - 8
Reason 3; Subtraction Property of Equality
Statement 4; x = -1
Reason 4; Given
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can someone please help me
Answer:
The answer is C. U=3x and V=2y^3
Step-by-step explanation:
3x*3x=9x^2
2y^3*-2y^3=-4y^6
Other variables cancel each other out
(b) An advertising agency finds that, of its 170 clients, 115 use Television, 110 use Radio and 130 use Magazines. Also 85 use Television and Magazines, 75 use Television and Radio, 95 use Radio and Magazines, 70 use all the three. Draw Venn diagram to represent these data. Also find:
(i) how many use only Radio?
(ii) how many use only Television?
(iii) how many use Television and Magazine but not radio?
Answer:
Here you go with your correct answer
Translate the statement into a mathematical equation.
9 times a number subtracted from 7 times the number is 26.
Answer:
7x - 9x = 26
Step-by-step explanation:
9 times a number = 9x
7 times the number = 7x
=26 because it says so
and 9x subtracted from 7x is 7x - 9x
How many solutions does this system of equations have? x² + y² = 25
x² - 6=0
The system of equation have one solution.
How to solve system of equation?x² + y² = 25
x² - 6 = 0
x² = 6
x = √6
Therefore, let's substitute the value of x in equation (i)
x² + y² = 25
(√6)² + y² = 25
y² = 25 - 6
y² = 19
hence,
y = √19
Therefore, the system of equation have one solution.
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how can i do scientific notifacation please
Use the point and the slope to graph each line. Write the equation of the line :
The line passes through the point (1,-1) and is parallel to a line that has slope 1.
What is the equation of the line
Answer:
Step-by-step explanation:
Since the new line is parallel to the one that has a slope of 1, we can write:
y = 1x + b for the new line
Remember that y=mx+b, where m is the slope and b the y-intercept, the value of y when x=0.
We need to find a value of b that forces the line through point (1,-1). Use (1,-1) in the equation and solve for b:
y = 1x + b
-1 = 1*(1)+b
b = -2
The equation of the line parallel to one with slope of 1 and going through point (1,-1) is:
y = 1x - 2
Find the area of the following shape
Answer:
56.8 m²
Step-by-step explanation:
This shape is clearly a trapezium / trapezoid. So :
Area of a trapezium is given by the formula :
[tex]\frac{a+b}{2} h[/tex]
Substitute values given in diagram :
a = 4.2
b = 10
h = 8
[tex](\frac{4.2+10}{2} )8[/tex]
7.1 × 8 = 56.8
Units will be m² as this is area
Giving us our final answer of 56.8 m²