Final answer:
The functions y=x and y=x+5 have the same slope but different y-intercepts. Their graphs are straight lines.
Explanation:
The functions y=x and y=x+5 are related in that they have the same slope of 1. This means that for every increase of 1 in the value of x, the value of y will also increase by 1. However, they have different y-intercepts. The function y=x has a y-intercept of 0, while the function y=x+5 has a y-intercept of 5.
Their graphs are related in that they are both straight lines. The graph of y=x is a line passing through the origin (0,0), while the graph of y=x+5 is a line shifted upward by 5 units compared to the graph of y=x.
In a plane, if a line is perpendicular to one of two blank lines, then it is also perpendicular to the other
What is the slope of a line that is perpendicular to the line y=1
Triangle ABC has vertices at (2,2), (4,3), and (6,1).
Using triangle ABC as the pre-image and origin as the center of dilation, what are the coordinates of a dilation of these vertices that uses a scale factor of 0.5?
A. (10,10)(20,15)(30,5)
B. (-1,-1)(-2,-15)(-3,-0.5)
C. (1,1)(1.5,2)(0.5,3)
D. (1,1)(2,1.5)(3,0.5)
Answer:
The correct answer is D.
Step-by-step explanation:
Recall that when we make a dilation with center at the origin, the only needed operation is to multiply the coordinates of each point by the factor of dilation. In this particular case the dilation factor is 0.5 so we must do the following operations:
0.5*(2,2) = (0.5*2,0.5*2) = (1,1)0.5*(4,3) = (0.5*4,0.5*3) = (2,1.5)0.5*(6,1) = (0.5*6, 0.5*1) = (3,0.5)So, the vertices of the triangle after the dilation are those who appear in D.
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Which piecewise relation defines a function?
The 3rd Image defines a piecewise function because for it to be a function, every input must match to exactly one and only one output. In Images 1, 2, and 4, there are certain inputs that have two outputs or stated otherwise, have two y-values for the same x-value. Only the 3rd Image matches 1 x-value to every 1 y-value. So, that's your answer.
Answer: C! The 3rd graph
Step-by-step explanation: Why does your equations have f(x)= and g(x)= ? Mine is only y= for every graph shown. All same numbers though.
*Will give medal!* Which is the direct linear variation equation for the relationship?
y varies directly with x and y = 10 when x = 2.
A. y = x – 8
B. y = x + 8
C. y = 5x
D. y = 2x + 6
Select the correct product.
(2x + 9)(x + 1)
2x2 + 11x + 9
3x2 + 11x + 9
2x2 - 7x + 9
2x2 + 11x + 10
Perform the indicated operation. (r 4 - r 2 + 4) ÷ (r 2 - r + 2)
r² + r - 2 R -4r+8 just got this wrong on quiz so i know this is the right answer now
The simplified expression of (r⁴ - r² + 4) ÷ (r² - r + 2) is r³ -r+ 4/r ÷ r - 1 + 2/r
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is (r⁴ - r² + 4) ÷ (r² - r + 2)
r power four minus r square plus four divided by r square minus r plus two.
The expression can not be simplified further as the denominator (r^2 - r + 2) cannot be factored into linear factors
The expression is a rational function and can only be simplified by partial fraction decomposition which involves writing it as a sum of simpler fractional terms.
r (r³ -r+ 4/r) ÷ r(r - 1 + 2/r)
r³ -r+ 4/r ÷ r - 1 + 2/r
Hence, the simplified expression of (r⁴ - r² + 4) ÷ (r² - r + 2) is r³ -r+ 4/r ÷ r - 1 + 2/r
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How to rewrite the function 2x^2-7x+5 by completing the square
To rewrite[tex]\(2x^2 - 7x + 5\) by completing the square, first factor out the coefficient of \(x^2\), then add and subtract \(\frac{49}{16}\) inside the parentheses, rewrite as a perfect square trinomial, and simplify. The result is \(2\left(x - \frac{7}{4}\right)^2 - \frac{9}{8}\).[/tex]
To rewrite the quadratic function[tex]\(2x^2 - 7x + 5\)[/tex]by completing the square, follow these steps:
1. Factor out the coefficient of[tex]\(x^2\):\[2x^2 - 7x + 5 = 2(x^2 - \frac{7}{2}x) + 5\][/tex]
2. Take half of the coefficient of [tex]\(x\)[/tex]and square it:
[tex]\[\left(\frac{-7}{2} \div 2\right)^2 = \left(\frac{-7}{4}\right)^2 = \frac{49}{16}\][/tex]
3. Add and subtract this value inside the parentheses:
[tex]\[2\left(x^2 - \frac{7}{2}x + \frac{49}{16} - \frac{49}{16}\right) + 5\][/tex]
4. Rewrite the expression inside the parentheses as a perfect square trinomial:
[tex]\[2\left[\left(x - \frac{7}{4}\right)^2 - \frac{49}{16}\right] + 5\][/tex]
5. Distribute and simplify:
[tex]\[2\left(x - \frac{7}{4}\right)^2 - 2 \times \frac{49}{16} + 5\]\[= 2\left(x - \frac{7}{4}\right)^2 - \frac{49}{8} + 5\]\[= 2\left(x - \frac{7}{4}\right)^2 - \frac{49}{8} + \frac{40}{8}\]\[= 2\left(x - \frac{7}{4}\right)^2 - \frac{9}{8}\]So, the quadratic function \(2x^2 - 7x + 5\) rewritten by completing the square is \(\boxed{2\left(x - \frac{7}{4}\right)^2 - \frac{9}{8}}\).[/tex]
A chord divides a circle into two segments true or false?
Daria walked 1 2/5 miles this morning and 2 3/10 miles this afternoon. How many miles did Daria walk in all?
Find the x value for point C such that AC and BC form a 2:3 ratio.
A) 6
B) −0.6
C) 4
D) −2.4
The x value for point C is not one of the given options.
Explanation:To find the x value for point C such that AC and BC form a 2:3 ratio, we first need to find the coordinates of point C. The given components are Cx = -2/3, Cy = -4/3, and C₂ = 7/3. Substituting these values into Equation 2.21, we get:
C = sqrt((-2/3)² + (-4/3)² + (7/3)²) = sqrt(23/3)
Therefore, the x value for point C is not one of the options given. None of the options (A) 6, (B) -0.6, (C) 4, or (D) -2.4 are correct.
Final answer:
To find the x value for point C such that AC and BC form a 2:3 ratio, substitute the coordinates of point C into the equation and solve for C.
Explanation:
To find the x value for point C such that AC and BC form a 2:3 ratio, we can use the coordinates of points A, B, and C. We have Cx = -2/3, Cy = -4/3, and C₂ = 7/3. Substituting these values into Equation 2.21 gives:
C = √((-2/3)² + (-4/3)² + (7/3)²) = √(4/9 + 16/9 + 49/9) = √(69/9).
So the x value for point C is √(69/9).
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The percent of the discount in the problem above is 15%. What percent of the original bill is Chumani's bill? How could you solve the problem using this percent?
Chumani's bill represents 85% of the original bill after a 15% discount is applied. The discounted amount can be found by multiplying the original bill by 0.85.
If the discount on an item is 15%, and Chumani is paying after this discount has been applied, we want to find out what percent of the original bill Chumani's bill is. To do this, we subtract the discount rate from 100%. So, 100% - 15% = 85%. Thus, Chumani's bill is 85% of the original bill.
To calculate the discounted bill, you multiply the original bill amount by 0.85 (which represents 85%). If the original bill was, for example, $100, the calculation would be $100 x 0.85 = $85. So, Chumani would pay $85, which is 85% of the original bill amount.
Amare wants to ride a Ferris wheel that sits four meters above the ground and has a diameter of 50 meters. It takes six minutes to do three revolutions on the Ferris wheel. Complete the function, h(t), which models Amare's height above the ground, in meters, as a function of time, t, in minutes. Assume he enters the ride at the low point when t = 0.
The complete function that models Amare's height above the ground, h(t), as a function of time, t, in minutes is:
h(t) = 25 · sin((π / 3) t) + 4
To model Amare's height above the ground, use the equation of a sinusoidal function.
In this case, since the Ferris wheel has a diameter of 50 meters, the amplitude of the function is half of the diameter, which is 25 meters. The Ferris wheel completes three revolutions in six minutes, so the period of the function is 6 minutes.
The equation for the height function is given by:
h(t) = A · sin((2π / T) t + φ) + h0
Where:
A is the amplitude (25 meters)
T is the period (6 minutes)
φ is the phase shift (0 radians, since Amare enters at the low point)
h0 is the vertical shift (4 meters, since the Ferris wheel sits four meters above the ground)
Substitute the given values into the equation
h(t) = 25 · sin((2π / 6) t + 0) + 4
Simplifying further:
h(t) = 25 · sin((π / 3) t) + 4
Therefore, the complete function that models Amare's height above the ground, h(t), as a function of time, t, in minutes is:
h(t) = 25 · sin((π / 3) t) + 4
Complete question
Amare wants to ride a Ferris wheel that sits four meters above the ground and has a diameter of 50 meters. It takes six minutes to do three revolutions on the Ferris wheel. Complete the function, h(t), which models Amare's height above the ground, in meters, as a function of time, t, in minutes. Assume he enters the ride at the low point when t = 0.
h(t)=--- ·sin---- πt+---- π )+ ----
Sara has 20 sweets.
12 liquorice, 5 mint, 3 humbug.
Sara is going to take at random two sweets.
work out the probability that the two sweets will not be the same type. Give your answer as a fraction
Answer:
111/190
Step-by-step explanation:i know you dont want to see explanation so yeah...
Probabilities are used to determine the chances of an event.
The probability that the two selected sweet will not be of the same type is [tex]\frac{111}{190}[/tex]
The given parameters are:
[tex]n = 20[/tex] --- number of sweet
[tex]L = 12[/tex]
[tex]M = 5[/tex]
[tex]H = 3[/tex]
First, we calculate the probability that the two selected sweet will be of the same type.
This is calculated as:
[tex]P(Same) =P(L\ and\ L) + P(M\ and\ M) + P(H\ and\ H)[/tex]
Because the selection is without replacement, the equation becomes
[tex]P(Same) = \frac{12 \times 11}{20 \times 19} +\frac{5 \times 4}{20 \times 19} + \frac{3 \times 2}{20 \times 19}[/tex]
[tex]P(Same) = \frac{132}{380} +\frac{20}{380} + \frac{6}{380}[/tex]
Add fractions
[tex]P(Same) = \frac{132+20+6}{380}[/tex]
[tex]P(Same) = \frac{158}{380}[/tex]
Using the complement rule, the probability that the two selected sweet will not be of the same type is:
[tex]P(Not\ same) = 1 - P(Same)[/tex]
This gives
[tex]P(Not\ same) = 1 - \frac{158}{380}[/tex]
Take LCM
[tex]P(Not\ same) = \frac{380 - 158}{380}[/tex]
[tex]P(Not\ same) = \frac{222}{380}[/tex]
Simplify
[tex]P(Not\ same) = \frac{111}{190}[/tex]
Hence, the required probability is: [tex]\frac{111}{190}[/tex]
Read more about probabilities at:
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The sum of three consecutive numbers is greater than 40. The inequality that represents this is x + x + 1 + x + 2 > 40. Which values of x hold true for the inequality?
choices are 8,10,12,13,9,15,7
Answer:
15
Step-by-step explanation:
An angle is 14° more than the measure of its complement. find the number of degrees in each angle. the angles measure
Which term can be combined in the expression below? check all that apply. 5/6a - 2b - 16.3 + b/12 + c - 0.9b
Answer:
Option 2nd , 4th and 6th correct
[tex]-2b[/tex], [tex]\frac{b}{12}[/tex] and [tex]-0.9b[/tex]
Step-by-step explanation:
Like terms are those terms which have same variable to the same power.
Given the expression:
[tex]\frac{5}{6}a-2b-16.3+\frac{b}{12}+c-0.9b[/tex]
Combine like terms;
[tex]\frac{5}{6}a+b(-2+\frac{1}{12}-0.9}-16.3+c[/tex]
Simplify:
[tex]\frac{5}{6}a-2.81666667b-16.3+c[/tex]
Therefore, the term can be combined in the given expression is,
[tex]-2b[/tex], [tex]\frac{b}{12}[/tex] and [tex]-0.9b[/tex]
Part A) Julio makes a scale drawing of the kitchen floor to determine how many square feet of flooring he needs to buy . The scale of his drawing is 1 inch:4 feet. (The length is 4 1/2 and the width is 3 3/8)
What is the actual are of Julio's kitchen floor?
Part B) Julio makes a scale drawing of part of the kitchen wall to design a tile pattern. He will use gray tiles and white tiles to form the pattern shown. The length of each square in the drawing represents 1/2 foot on the actual kitchen wall. (There are 14 gray tiles and 10 white tiles)
If Julio uses 2-inch by 2-inch tiles, how many tiles of each color will he need?
Answer:
Sample response: Julio divided 6 whole parts into groups of 2 instead of dividing them into groups of
1
2
which would make the quotient 12, not 3.
Step-by-step explanation:
For a school play the teacher asked the class to set up chairs in 20 rows with 25 chairs in each row after setting up all the chairs they were five chairs short how many tears did the class setup
A regular pyramid has a _____ base and a vertex over the center of the base.
Regular Polygon~~~~ APEX
Factor the expression.
24−18y
Enter your answers in the boxes to complete the factored expression.
____(___ − 3y)
Answer:
6(4 - 3y)
Step-by-step explanation:
Factor the expression 24−18y
The first thing to check is the common factor to be able to factorize the expression. Take for instance where we have
xa - xb = x ( a - b)
The common factor is x which is outside the bracket
24−18y
The greatest common factor between 24 and 18 is 6.
Therefore,
24−18y = 6(4 - 3y)
24−18y = 6(4) - 6(3y)
Blueberry bushes are planted in a field in the year 2009. The blueberry bushes start to grow and cover the field in such a way that the area covered by the bushes doubles every year. If they continue to grow in this way, the field will be entirely covered with blueberry bushes by the year 2016.
When will the field be covered 25% of the way
Tourists were on a hiking trip for three days. On the first day, they hiked 1/8 of the trail. On the second day they hiked 4/7 of the remaining trail. On the third day they hiked 1/3 of the remaining trail and the last 8 km. How many km is the whole trail?
The total distance of the trail is 100/7 km, which simplifies to approximately 14.29 km.
To find the total distance of the trail, let's break down the information provided step by step.
First day: They hiked 1/8 of the trail.
Second day: They hiked 4/7 of the remaining trail after the first day. So, on the second day, they covered (1 - 1/8) × (4/7) of the total trail.
Third day: They hiked 1/3 of the remaining trail after the second day, plus the last 8 km.
Now, we can set up an equation to solve for the total distance:
1/8 + (1 - 1/8)× (4/7) + (1 - 1/8 - (1 - 1/8)× (4/7)) × (1/3) + 8 = Total Distance.
Let's calculate each part:
First day: 1/8 of the total trail.
Second day: (1 - 1/8)× (4/7) = 28/56 - 7/56 = 21/56 of the total trail.
Third day: (1 - 1/8 - 21/56)× (1/3) = (56/56 - 7/56 - 21/56) × (1/3) = 28/56× (1/3) = 28/168 = 1/6 of the total trail.
Now, let's add all these parts together:
1/8 + 21/56 + 1/6 + 8 = Total Distance.
To simplify, let's find a common denominator:
1/8 + 3/8 + 14/56 + 8/8 = Total Distance.
Now, add the fractions:
16/56 + 14/56 + 14/56 + 56/56 = Total Distance.
Combine:
100/56 = Total Distance.
Now, simplify:
Total Distance = 100/56×8/8 = 800/56 km.
Divide both numerator and denominator by the greatest common divisor, which is 8:
Total Distance = 100/7 km.
So, the whole trail is approximately 14.29 km.
Which equation is equivalent to
What is the solution of the system? Use the elimination method. {4x+3y=62x+2y=5 The only solution is (−32, 4) .
The only solution is (0, 2) .
There are an infinite number of solutions.
There is no solution.
David drops a ball from a bridge at an initial height of 100 meters.
(a) What is the height of the ball to the nearest tenth of a meter exactly 3 seconds after he releases the ball?
(b) How many seconds after the ball is released will it hit the ground?
John has a blueprint for a square-shaped office. He decides to change the layout and so draws a new blueprint such that the width of his office increased by 15 feet. The area of his office according to the new blueprint is given by the expression below, where x is the side length, in feet, of the original square-shaped office.
x^2+15x
Which statement best describes the term 15x?
the area of the office according to the old blueprint
the width of the office according to the new blueprint
the area added to the office according to the new blueprint
the area of the office according to the new blueprint
Answer:
The area added to the office according to the new blueprint
Step-by-step explanation:
you're welcome
The result of rounding the whole number 2,746,052 to the nearest hundred thousands place is:
Answer:
maybe 2,800,000