The two x intercept of the equation [tex]y=\frac{1}{2}(x+2)^2-4[/tex] is -2(√2+1) and 2(√2-1).
In the given question we have to find the two x intercept of the equation.
The give equation is [tex]y=\frac{1}{2}(x+2)^2-4[/tex].
We can find the x intercept by putting y=0. Then solving the equation for x.
Now putting y=0 in the given equation.
0= [tex]\frac{1}{2}(x+2)^2-4[/tex]
Add 4 on both side, we get
[tex]\frac{1}{2}(x+2)^2[/tex] = 4
Multiply by 2 on both side, we get
[tex](x+2)^2[/tex] = 8
Taking square root on both side, we get
x+2 = √8
x+2 = ±2√2
Subtract 2 on both side we get
x=±2√2-2
Taking 2 common
x=2(±√2-1)
Now the values of x
x={2(-√2-1), 2(√2-1)}
x={-2(√2+1), 2(√2-1)}
Hence, the two x intercept of the equation [tex]y=\frac{1}{2}(x+2)^2-4[/tex] is -2(√2+1) and 2(√2-1).
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Identify which sequence of transformations could map pentagon ABCDE onto pentagon A”B”C”D”E”
For the given sequence of transformation mapping of pentagon ABCDE onto pentagon A"B"C"D"E" is given by Line reflection followed by a translation.
As given in the question,
Given sequence of transformation mapping of pentagon ABCDE onto pentagon A"B"C"D"E" is given by :
a. dilation followed by a rotation :
Here dilation means enlarge or reduced the original shape which is not true for the given pentagon ABCDE.
b. translation followed by a rotation :
Translation means moves around a fixed point by certain degrees that is horizontal or vertical shift.
Not true.
c. Line reflection followed by a translation:
In this case preimage is flipped across the line or get reflected.
True.
d. Line reflection followed by a line reflection:
Here fixed line is or a line is used as mirror . You get a image of the original.
Not true.
Therefore, for the given sequence of transformation mapping of pentagon ABCDE onto pentagon A"B"C"D"E" is given by Line reflection followed by a translation.
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The sum of two numbers is 15. One less than three times the smaller is equal to the larger. Find the numbers.
Answer:
The numbers are:
4 and 11
Step-by-step explanation:
a + b = 15 Eq. 1
3a - 1 = b Eq. 2
Replacing Eq. 2 in Eq, 1
a + (3a - 1) = 15
a + 3a = 15 + 1
4a = 16
a = 16/4
a = 4
From Eq. 1:
a + b = 15
4 + b = 15
b = 15 - 4
b = 11
Check:
From Eq. 2:
3a - 1 = b
3*4 - 1 = 11
12 - 1 = 11
The table how the height and weight of a few tudent in a cla. Height (inche) Weight (pound) height weight
58 122
59 128
60 126
62 133
63 145
64 136
66 144
68 150
70 152
Complete the following entence baed on your obervation. The data eem to have a correlation coefficient cloe to _____. Thi indicate that the weight of a tudent ______ a the height of the tudent increae
Correlation coefficient = 0.945 ( approx) and weight of a student increases as the height of the student increases.
What is correlation coefficient?
A statistical indicator of the strength of a linear link between two variables is the correlation coefficient. Its values may be between -1 and 1.
Main Body:
Here, value of x are =58, 59, 60, 62, 63, 64, 66, 68, 70
Value of y are, = 122, 128, 126, 133, 145, 136, 144, 150, 151.
∑x = 570, ∑y= 1236, ∑ = 36234, ∑ = 170694
∑xy=78617
Thus the correlation coefficient r =
formula is in the image,
Where n is the number of the term.
here n = 9
thus, correlation coefficient
r= [tex]\frac{9*78617- 570*1236}\sqrt{{9*36234- (570^{2} )}\sqrt{9*170794- (1235)^{2} }[/tex]
Thus, r= 0.94452987512
Which is closed to 0.95 and less than 1.
Therefore, weight of a student increases as the height of the student increases.
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james can go 144 miles with 12 gallons of gas in his truck.how far can he go on 17 gallons?
Answer: 204 miles
Step-by-step explanation:
The rectangular floor of a classroom is 24 feet in length and 30 feet in width. A scale drawing of the floor has a length of 4 inches. What is the area, in square inches, of the floor in the scale drawing?.
The area of the floor in the scale drawing is 20 square inches.
Firstly calculating the width of scale drawing. For this we will equate the two fractions.
Length/width (rectangle) = length/width (scale drawing)
Let the width of scale drawing be x
24/30 = 4/x
x = 4×30/24
Performing multiplication on Right Hand Side of the equation
x = 120/24
Performing division on Right Hand Side of the equation
x = 5
So, the area of scale drawing = length × breadth
Area of scale drawing = 4 × 5
Performing multiplication on Right Hand Side of the equation
Area of scale drawing = 20 square inches
Hence, the area is 20 square inches.
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I need help with this please
Answer:
No they are not
Step-by-step explanation:
6.23x10^2=623
62,300/10^3=62.3
623>62.3
-Hope this helped
May someone please help me!!!!!!!!!!
Answer:
below
Step-by-step explanation:
The angle dimensions given for each triangle sum to 180 °
so
(x+10) + y+15 + 70 = 180 Simplifies to
x +y = 85
and
x + 20 + 50 + 60 = 180 ° simplifies to
x = 50° use this value in the underlined equation to find y = 35°
Kelly is knitting a scarf for her brother. It took her 13 hour to knit 38 foot of the scarf. How fast is Kelly's knitting speed, in feet per hour?
Kelly's knitting speed is 2.92 feet per hour
How to determine how fast is Kelly's knitting speedFrom the question, the given parameters are:
Length of knot = 38 foot
Time to cover this length = 13 hours
The speed of the knitting the scarf is calculated as
Speed = Length of knot /Time to cover this length
Substitute the known values in the above equation
So, we have the following equation
Speed = 38/13
Evaluating the quotient in the above equation, we have
Speed = 2.92
Hence, the speed of knotting the scarf is 2.92 feet per hour
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v- 15
------- = 2
2
What is the answerrr :D
Answer:
Can you tell me what i'm supposed to be finding
Step-by-step explanation:
question is on image
The equation of the line that passes through the point (-6, 6) and (-3, 7) is y = 1 / 3 x + 8
How to find equation of a line in slope intercept form?The equation of a line in slope intercept form can be represented as follows:
y = mx + c
where
m = slope of the linec = y-interceptHence, the line passes through the point (-6, 6) and (-3, 7)
m = slope = 7 - 6 / -3 + 6
m = 1 / 3
Therefore, the y-intercept of the line can be found using (-6, 6)
y = 1 /3 x + b
6 = 1 / 3 (-6) + b
6 = -2 + b
b = 6 + 2
b = 8
Therefore, the equation of the line is y = 1 / 3 x + 8
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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.
x > 5 represents a line with an open circle at 5 and going indefinitely toward infinity.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Given inequality is - 3(2x - 5) < 5(2 - x).
- 6x + 15 < 10 - 5x.
- x < - 5.
x > 5 (think of moving x to make it positive).
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2.3.PS-17 Julio says, "If you subtract 14 from my number and multiply the difference by -4, the result is -48." What is Julio's number?
Answer:
12
Step-by-step explanation:
y it equal to 12 is
-48÷-4=12
A fish 12 m below the surface of the ocean swims down 3 m. Then it swims
up 9m. What is the fish's new position? Show your work.
selecting a counter displays information about that counter's collected data as a chart type. which chart type displays the current value of each performance counter in decimal format? group of answer choices line histogram bar report stacked area
The Bar graph, Line graph and Report displays the counter in decimal format.
Selecting a counter displays information about that counter's collected data as a chart type. The bar graph, line graph and report displays the current value of each performance counter in decimal format.
Line graph: - Line graph, also known as a line chart or line plot, is commonly drawn to show how something changes over a period of time. scientists and engineers use these graphs to understand and derive meaning from large chunks of data.
Bar graph: - This are the pictorial representation of data, in the form of vertical or horizontal rectangular bars, where the length of bars are proportional to the measure of data. They are mostly used in business and finance, but they can also be found in other contexts. This can be used to show the distribution of different heights of students in a class.
Report: - A report is a document that presents information in an organized format for a specific audience and purpose. All the skills and the knowledge of the professionals are communicated through reports. Reports help the top line in decision making. A rule and balanced report also helps in problem solving.
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differentiate 2x-3/2x+1
Differentiation of [tex]\frac{2x-3}{2x+1}[/tex] is [tex]\frac{8}{4x^{2}+4x+1}[/tex] .
Differentiation formula for [tex]\frac{d}{dx}(\frac{u}{v}) = \frac{v\frac{d}{dx} - v\frac{d}{dx}}{v^{2} }[/tex]
Here, u = 2x - 3
v = 2x + 1
[tex]\frac{d}{dx}u[/tex] = 2
[tex]\frac{d}{dx}v[/tex] = 2
[tex]v^{2} = (2x+1)^{2}[/tex]
[tex]= 4x^{2}+4x+1[/tex]
Putting the values,
[tex]\frac{d}{dx}(\frac{2x-3}{2x+1}) = \frac{(2x+1)(2)-(2x-3)(2)}{4x^{2}+4x+1}[/tex]
[tex]=\frac{4x+2-(4x-6)}{4x^{2}+4x+1}[/tex]
[tex]=\frac{4x+2-4x+6}{4x^{2}+4x+1}[/tex]
[tex]=\frac{8}{4x^{2}+4x+1}[/tex]
Hence, Differentiation of [tex]\frac{2x-3}{2x+1}[/tex] is [tex]\frac{8}{4x^{2}+4x+1}[/tex] .
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edith tutors after school for which she gets paid at a rate of $20 an hour. she has also accepted a iob as a library assistant that pays $15 an hour. she will work both jobs, but she is able to work no more than a total of ll hours a week, due to school commitments. edith wants to earn ar reasr$185 a week working a combination of both jobs. which inequality can be used to represent the situation?
Inequality can be used to represent the situation is s + l <= 2 and 20s + 15l >= 185.
Given:
Edith tutors after school for which she gets paid at a rate of $20 an hour. she has also accepted a job as a library assistant that pays $15 an hour. she will work both jobs, but she is able to work no more than a total of ll hours a week, due to school commitments.
Edith wants to earn at least $185 a week working a combination of both jobs.
Let s and l be the hours of school and library.
s + l <= 2
20s + 15l >= 185.
Therefore Inequality can be used to represent the situation is s + l <= 2 and 20s + 15l >= 185.
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how do I put 8x=26+14y in standard form
The standard form of the equation of the given straight line is 4x + (-7)y = 13.
We are given an equation. The equation is linear in nature. The equation represents a straight line. The equation is given below.
8x = 26 + 14y
We need to convert this equation to standard form. The standard form of an equation for a straight line is given below.
Ax + By = C
We need to rearrange the given equation so that it matches the correct format. The equation is written below.
8x - 14y = 26
We can simplify the equation further by dividing the whole equation by two.
4x + (-7)y = 13
Hence, the standard form of the equation is 4x + (-7)y = 13.
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find the quadratic function
For the quadratic function y = ax² + bx + c , for which graph passes through the points (2, 31), (3 , 45) , (1, 19) is given by y = x² + 9x + 9.
As given in the question,
Standard form of quadratic function,
y = ax² + bx + c
Graph of the quadratic function passes through the points (2, 31),
(3 , 45) , (1, 19) .
When passes through (2, 31)
31 = 4a + 2b + c __(1)
Passes through (3,45)
45 = 9a + 3b + c __(2)
Passes through (1, 19)
19 = a + b + c __(3)
Multiply 9 to (3) and subtract (2) from it,
9a + 9b + 9c =171
9a +3b + c = 45
6b + 8c = 126 ____(4)
Now, Multiply 4 to (3) and subtract (1) from it,
4a + 4b + 4c =76
4a +2b + c = 31
2b + 3c = 45____(5)
Multiply 3 to (5) and subtract (4) from it,
6b + 9c = 135
6b + 8c =126
c = 9
Substitute c= 9 in (5) we get,
2b + 3(9) = 45
⇒ b = 9
Now , substitute b = 9, c = 9 in (3) we get,
a + 9 + 9 = 19
⇒ a = 1
Required quadratic function is :
y = x² + 9x + 9
Therefore, for the quadratic function y = ax² + bx + c , for which graph passes through the points (2, 31), (3 , 45) ,(1, 19) is given by y =x² + 9x + 9.
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A student on the cross-country team runs 30 minutes a day as a part of her training.
Write an equation to describe the relationship between the distance she runs in
miles, , and her running speed, in miles per hour, when she runs:
The equation that describes the proportional relationship between the distance she runs in miles, and her running speed, in miles per hour, when she runs, is:
d = 0.5v.
What is a proportional relationship?A proportional relationship is a special case of a linear function, with intercept zero, in which the output variable is given by the multiplication of the input variable and the constant of proportionality, given as follows:
y = kx
The distance as a function of the velocity and of the time in hours, is given as follows:
d = vt.
30 minutes is half an hour, hence the constant of the proportional relationship is given as follows:
v = 0.5.
Then the equation is:
d = 0.5v.
In which:
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1. Which equation below is n = 2 a solution for?
3n = 6
n-1=2
9+n=12
3+n=8
The equation 3n = 6 has a solution n = 2.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
We have to find that which equation below is n = 2 a solution.
Then substitute n = 2;
3n = 6
3(2) = 6
This equation has a solution n = 2.
2. n-1=2
Then substitute n = 2;
2 - 1 = 1
The solution of the equation is not n = 2
3. 9+n=12
Then substitute n = 2;
9 + 2 = 11
The solution of the equation is not n = 2
4. 3+n=8
Then substitute n = 2;
3 + 2 = 5
The solution of the equation is not n = 2
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marko has 45 comic books in his collection and tamara has 61 comic books marko buys 4 new comic books each month and tamara buys 2 comic books each month after how many months will marko and tamara have the same number of comic books
Answer: 8 months
Step-by-step explanation:
view picture please!!!
Answer:
70/3
Step-by-step explanation:
[tex]f(0)=\frac{140}{1+5e^{-2(0)}} \\ \\ =\frac{140}{1+5(1)} \\ \\ =\frac{140}{6} \\ \\ =\frac{70}{3}[/tex]
the cost of using a parcel service is r dollars for the first 3 pounds and s dollars for each additional pound. which of the following expressions represents the cost, in dollars, of sending a parcel that weighs 9 pounds?
a) r+3s
b) r+6s
c) 3r+6s
d) 3r+9s
e) 9r+9s
Answer:
The correct answer is: c) 3r + 6s
Step-by-step explanation:
the first 3 pounds are always going to be r dollars, then every additional pound will be s dollars.
Since we have a package that weighs 9 pounds; 3 pounds will cost r dollars and 6 pounds wills cost s dollars.
example:
lets say that r = 10 and s = 5
the first 3 pounds will cost 10 dollars and then every pound after would be 5 dollars
so:
3(10) + 6(5)
This is just an example, since we don't know the actual values of r and s, we just use those variables.
Use the relationship among the three angles of any triangle to solve.
Two angles of a triangle have the same measure and the third angle is 66° greater than the measure of the other two.
Find the measure of each angle.
1. Measure of the top angle is (?)
2. Measure of the bottom left angle is (?)
3. Measure of the bottom right angle is (?)
Answer:
1. 104
2. 38
3. 38
Step-by-step explanation:
3x + 66 = 180
3x = 114
x = 38
Simplify 4√20- 3√45. Show your work.
Answer:
Answer:
- [tex]\sqrt{5}[/tex]
Step-by-step explanation:
using the rule of radicals
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]
simplifying radicals
[tex]\sqrt{20}[/tex]
= [tex]\sqrt{4(5)}[/tex]
= [tex]\sqrt{4}[/tex] × [tex]\sqrt{5}[/tex]
= 2[tex]\sqrt{5}[/tex]
and
[tex]\sqrt{45}[/tex]
= [tex]\sqrt{9(5)}[/tex]
= [tex]\sqrt{9}[/tex] × [tex]\sqrt{5}[/tex]
= 3[tex]\sqrt{5}[/tex]
Then
4[tex]\sqrt{20}[/tex] - 3[tex]\sqrt{45}[/tex]
= 4(2[tex]\sqrt{5}[/tex] ) - 3(3[tex]\sqrt{5}[/tex] )
= 8[tex]\sqrt{5}[/tex] - 9[tex]\sqrt{5}[/tex]
= - [tex]\sqrt{5}[/tex]
Finding Angle Measures When Parallel Lines Are Cut By a Transversal
Answer:
Below
Step-by-step explanation:
3 6 and 7 = 82 °
1 4 5 8 = 180 - 82 = 98 °
Point n is located at (3, 5). If point n is translated 3 units right and 2 units down, the new coordinates will be.
The revised coordinates for the indicated site are (6, 3).
Given information;
Location of Point n (3, 5). The new coordinates will be if point n is moved 2 units down and 3 units right.
To get new coordinates we have to transform given points;
Transformation of the coordinate system:
Defining new coordinate systems on the plane frequently involves coordinate transformations. The transformation's u- curves are representations of vertical lines with the form u- constant, while the v- curves are representations of horizontal lines with the form v- constant.
∴ (3, 5) ⇒ (3 + 3, 5 - 2)
⇒ (6, 3)
Hence, (6, 3) are the new coordinates of the given point.
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In a town, 100 people need 600 liters of water to drink everyday. At a festival time how many liters of water do they need to drink with their 50 guests?
The amount of water needed to drink with their 50 guests is 900 liters.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
In a town, 100 people need 600 liters of water to drink every day.
This can be written as,
100 people = 600 liters of water
50 guests are added.
The number of people = 100 + 50 = 150 people.
Now,
100 people = 600 liters of water
Multiply 150/100 on both sides.
150 people = 150/100 x 600 litres of water
150 people = 900 liters of water
Thus,
The amount of water needed to drink with their 50 guests is 900 liters.
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6
If 12 grams of coffee costs x dollars and each
gram makes y cups of coffee, what is the cost
of one cup of coffee in terms of x and y?
A)
B)
C)
D)
12y
12x
12x
y
12y
The cost of one cup of coffee in terms of x and y is x/12y.
Given in question,
Cost of 12 grams coffee = x dollars
Cost of 1 gram coffee = x/12 dollars
1 gram coffee make cups = y
Cost of 1 cup = (x/12)/y
= x/12y
Hence, the cost of one cup of coffee in terms of x and y is x/12y.
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HElp if your good whit money
According to the concept of card payment, the true statement is "If you purchase an item using debit card, the money will deducted from your bank account".
Card payment:
Card payment refers any transaction whereby the Card is used to settle bills or to pay for certain goods and/or services at a Post Office branch.
Given,
Here we need to find the true statement according to the purchase.
While we looking into the given options,
The first option is incorrect because it says there is no interest for credit card purchase. This one is wrong because we have to pay interest for credit card purchase.
The second option is wrong because it tells that the money will be deducted from your account. If anyone can purchase using the credit card the money will only be deducted at the end of the month with some interest on it.
The third option is incorrect because debit card transaction are truly based on the amount within you account so it is not a borrowed one.
Therefore, the final statement is the correct one.
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