If [tex]x=p+2[/tex] and [tex]y=p-3[/tex], then
[tex]x+y = (p+2) + (p-3) = 2p - 1 \implies x+y+1=2p[/tex]
and
[tex]x-y = (p+2)-(p-3) = 5 \implies x-y-5=0[/tex]
as required.
My square patio is tiled with square tiles, all the same size. All the tiles are gray, except the tiles along the two diagonals, which are all yellow. (The corners are yellow, the center is yellow, and all the tiles along the diagonal in between are yellow.) If there are $89$ yellow tiles, how many gray tiles are there
Answer:
1936
Step-by-step explanation:
We can start by removing the center tile, because all four diagonals over lap on that tile. We'll add it back later. 88/4=22. which means there are 22 tiles per half, 44+1(the center tile) total tiles per side, which means there are a total of 1936 tiles.
AOPS ANSWER:
Suppose that we have a square with dimensions [tex]$e \times e$[/tex]. The diagonals each have [tex]$e$\\[/tex] tiles. If [tex]$e$\\[/tex] is even, the number of yellow tiles is [tex]$2e$[/tex], because the [tex]2[/tex] diagonals don't intersect. If [tex]$e$[/tex] is odd, then the number of yellow tiles is [tex]$e+e-1=2e-1$[/tex]. (We have to subtract [tex]1[/tex] because the center tile is counted [tex]2[/tex] times). We know that there are [tex]89[/tex] yellow tiles, which is an odd number, so [tex]$89=2e-1$[/tex]. This implies that [tex]$e = 45$[/tex]. So the dimensions of the floor are [tex]$45 \times 45$[/tex], or [tex]2025\\[/tex] square units. Since all of the other tiles are gray, there are [tex]$2025-89=\boxed{1936}$[/tex] gray tiles.
Jacob is calculating the amount of time it takes a rocket to get to the moon. the moon is around 239,000 miles from earth. how many hours would it take a rocket that can travel at 250 miles per minute to travel to the moon? round to the nearest hour.
Answer:
16hr
Step-by-step explanation:
distance= time x speed
250mi/min=250x60mi/hr =15000mi/hr
239000/15000≈15.9333hr
Round up to 16hr
please help me with this
The range of possible heights is given by the inequality:
d ≥ 300.125 m
How to find the possible heights of the building?
We know that the time that it takes for an object to fall from a distance d is:
[tex]t = \frac{\sqrt{2d} }{4.9}[/tex]
In this case, we know that t ≥ 5s.
Then we can solve for the minimum distance, which is given when t = 5s.
[tex]5 = \frac{\sqrt{2d} }{4.9}\\\\(5*4.9)^2/2 = d = 300.125[/tex]
So the minimum height of the building is 300.125 meters, then the range of possible heights is:
d ≥ 300.125 m
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Golf balls cost $0.90 each at Jerzy’s Club, which has an annual $25 membership fee. At Rick and Tom’s sporting-goods store, the price is $1.35 per ball for the same brand. Where you buy your golf balls depends on how many you wish to buy. Explain, and illustrate your reasoning with a graph.
Answer:
See attached graph.
Step-by-step explanation:
Each situation can be expressed as an equation:
Jerzy: Total Cost (y1) is the $25 membership fee plus $0.80/golf ball (x):
y1 = $25 + $0.90x
Rick and Tom's: Total Cost (y2) is $1.25 per golf ball, x.
y2 = $1.25x
See the attached graphs of these two equations. Jerzy's cost less after 56 balls are purchased.
What type of association does the following scatterplot represent?
Answer:
Positive Linear Association
Step-by-step explanation:
A positive/negative association can be determined by seeing if the slope of the line of best fit is positive or negative. A positive slope indicates a positive relationship and a negative slope indicates a negative relationship.
If y increases as x increases => positive
If y decreases as x increases => negative
In the graph, the line of best fit clearly has a positive slope. I.e. as x increases, y also increases. Therefore, the association is positive.
Next determine if the relationship is linear or nonlinear. A linear relationship can be modeled strongly with a straight line. Anything else is nonlinear. In the graph, a straight line can be draw through the points with a strong correlation, therefore the association is linear.
Therefore, the best answer is Positive Linear Assosciation
The vertex of the parabola below is at the point (2, 4), and the point (3,6) is
on the parabola. What is the equation of the parabola?
10
(3,6)
(2,4)
-10
10
-10
O A. y=2(x-2)² +4
OB. x= 4(y-3)² +1
O C. y= 6(x-2)2 +4
OD. y=3(x-4)2 +2
← PREVIOUS
The equation of the parabola is y = 2(x - 2)^2 + 4
How to determine the parabola equation?The given parameters are:
Vertex, (h,k) = (2,4)Point (x,y) = (3,6)A parabola is represented as:
y = a(x - h)^2 + k
Substitute (h,k) = (2,4)
y = a(x - 2)^2 + 4
Substitute (x,y) = (3,6)
6 = a(3 - 2)^2 + 4
Evaluate the difference
6 = a(1)^2 + 4
This gives
6 = a + 4
Subtract 4 from both sides
a = 2
Substitute a = 2 in y = a(x - 2)^2 + 4
y = 2(x - 2)^2 + 4
Hence, the equation of the parabola is y = 2(x - 2)^2 + 4
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Prism M and pyramid N have the same base area and the same height. Cylinder P and prism Q have the same height and the same base perimeter. Cone Z has the same base area as cylinder Y, but its height is three times the height of cylinder Y.
The figures
and
have the same volume.
The figures Сone Z and Cylinder Y have the same volume.
How to calculate the volume of a cone?Mathematically, the volume of a cone can be calculated by using this formula:
V = 1/3 × πr²h
Where:
h is the height.r is the radius.Similarly, the volume of a cylinder can be calculated by using this formula:
V = πr²h
In this context, we can infer and logically deduce that Сone Z and Cylinder Y have the same volume because they both have the same base area, while the cone's height is three (3) times the height of Cylinder Y.
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The line contains the point (5,0) and is parallel to the line defined by "-3x=4y"
Answer:
Step-by-step explanation:
Solve the equation
This is a question from a mock exam I could not answer
Area of a sector
Find the perimeter of this sector.
Give your answer rounded to 3 SF.
Pls help
The perimeter of the sector is 96.34 m if the radius of the circle is 48 m and the measure of the central angle is 115 degrees.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)
We have given a part of the circle.
As we know:
s = rθ
s is the arc length
r is the radius of the circle
θ is the central angle in radians
The central angle is 115 degrees which is in radians:
θ = 2.00713
s = 48×(2.00713)
s = 96.34 m
The perimeter of the sector = s = 96.34 m
Thus, the perimeter of the sector is 96.34 m if the radius of the circle is 48 m and the measure of the central angle is 115 degrees.
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Which of the following is correct for determining the length of x to the nearest tenth of a metre?
cos 42 = x/6
tan 48 = x/5
sin 48 = x/5
tan 42 =x/6
Today an electronics store took
5% off the price of a computer,
and for the next two days, it will
take 5% off the previous day's
price. if the price of the
computer yesterday was
$2000.00, what will be the price
of the computer two days from
now?
Answer:
$ 1805
Step-by-step explanation:
2000 × 95%
= 1900
1900 × 95%
= 1805
Question 11 of 25
What is an equation of the line that is perpendicular to y + 1 = -3(x-5) and
passes through the point (4, -6)?
Ay-6--(x+4)
OB. y-6=3(x+4)
C. y+6=(x-4)
D. y+6=-3(x-4)
SUBMIT
Answer: y+6 = 1/3(x-4
The equation of line perpendicular to the given line and passes through the point P ( 4 , -6 ) is y + 6 = ( 1/3 ) ( x - 4 )
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
y + 1 = -3 ( x - 5 )
So , the slope of the line is m = -3
Now , the lines are perpendicular , so the slope of the line m₂ is
m₂ = 1/3
Let the first point be P ( 4 , -6 )
And , the equation of line is y - y₁ = m ( x - x₁ )
On simplifying , we get
y - ( -6 ) = ( 1/3 ) ( x - 4 )
y + 6 = ( 1/3 ) ( x - 4 )
Hence , the equation of line is y + 6 = ( 1/3 ) ( x - 4 )
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387 kilograms = x grams
Answer:
a. 387,000g
b. 38,700g
c. 387g
d. 3.87g
Answer:
a
Step-by-step explanation:
I kilogram is 1000 grams
What is the median of the data?
Answer:
The median is 3.
Step-by-step explanation:
Since, most of the values presented are 0-8 and median is the middle of any data set. It has to be 3.
Step 4: Make a prediction with your data.
a) Using your equation from step 2d, ( y=0.14x+0.75 ) estimate the GPA of a student who studies for 15 hours a
week. Justify your answer.
Answer:
estimated gpa: 2.85
Step-by-step explanation:
Evaluate y=0.14x+0.75 at x = 15 (hours):
y = 0.14(15 hours) + 0.75
= 2.1 + 0.75
y = 2.85 = estimated gpa corresponding to 15 houirs of study
If side b measures 5√3, what is the length of side c?
Answer:
10
Step-by-step explanation:
cos(30) = b / c
c = b / cos(30)
c = 5xsqrt(3) / 0.866
c = 10
Which inequality defines the shaded region graphed below?
Answer:
Every ordered pair within this region will satisfy the inequality y ≥ x. Incorrect. The boundary line here is y = x, and the correct region is shaded, but remember that a dotted line is used for < and >. The inequality you are graphing is y ≥ x, so the boundary line should be solid.
The coordinate grid shows points A through K. What point is a solution to the system of inequalities? y < −2x + 10 y < 1 over 2x − 2 coordinate grid with plotted ordered pairs, point A at negative 5, 4 point B at 4, 7 point C at negative 2, 7 point D at negative 7, 1 point E at 4, negative 2 point F at 1, negative 6 point G at negative 3, negative 10 point H at negative 4, negative 4 point I at 9, 3 point J at 7, negative 4 and point K at 2, 3 I B A F Question 8(Multiple Choice Worth 1 points) (04.06 MC) In the graph, the area below f(x) is shaded and labeled A, the area below g(x) is shaded and labeled B, and the area where f(x) and g(x) have shading in common is labeled AB. Graph of two intersecting lines. One line g of x is solid and goes through the points negative 3, 0, negative 4, negative 1 and is shaded in below the line. The other line f of x is solid, and goes through the points 1, 1, 2, negative 1 and is shaded in below the line. The graph represents which system of inequalities? y ≤ −2x + 3 y ≤ x + 3 y ≥ −2x + 3 y ≥ x + 3 y ≤ −3x + 2 y ≤ −x + 2 y > −2x + 3 y > x + 3 Question 9(Multiple Choice Worth 1 points) (04.06 LC) Choose the graph that represents the following system of inequalities: y ≤ −3x + 1 y ≤ 1 over 2x + 3 In each graph, the area for f(x) is shaded and labeled A, the area for g(x) is shaded and labeled B, and the area where they have shading in common is labeled AB. Graph of two intersecting lines. Both lines are solid. One line f of x passes through points negative 2, 2 and 0, 3 and is shaded above the line. The other line g of x passes through points 0, 1 and 1, negative 2 and is shaded above the line. Graph of two lines intersecting lines. Both lines are solid. One line g of x passes through points negative 2, 2 and 0, 3 and is shaded below the line. The other line f of x passes through points 0, 1 and 1, negative 2 and is shaded above the line. Graph of two intersecting lines. Both lines are solid. One line passes g of x through points negative 2, 2 and 0, 3 and i
The graph that represents the system of inequalities will be y ≤ −2x + 3; y ≤ x + 3
How to depict the graph?The equation of the line will be:
y = mx + b
In this case, we can observe that both lines have the same y intercept and that the lines are solid.
Hence, graph that represents the system of inequalities will be y ≤ −2x + 3; y ≤ x + 3. The graph is attached.
When the coordinate grid shows points A through, the point that is a solution to the system of inequalities is negative 6 point G at negative 3, negative 10 point H at negative 4.
Finally, the graph that represents the following system of inequalities: y ≤ −3x + 1 y ≤ 1 over 2x + 3 is the graph of two intersecting lines where both lines are solid.
One line of x passes through points negative 2, 2 and 0, 3 and is shaded above the line. The other line g of x passes through points 0, 1 and 1, negative 2 and is shaded above the line.
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Which two points on the number line represent numbers that can be combined to make zero?
B and D
A and B
C and D
A and C
Solve for x..........
[tex]5x - x - 8 = 15 + 3x[/tex]
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:x = 23 [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: 5x - x - 8 = 15 + 3x[/tex]
[tex]\qquad \tt \rightarrow \: 4x - 8 = 15 + 3x[/tex]
[tex]\qquad \tt \rightarrow \: 4x - 3x = 15 + 8[/tex]
[tex]\qquad \tt \rightarrow \: x = 23[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Answer:
x = 23
Explanation:
⇒ 5x - x - 8 = 15 + 3x
collect like terms
⇒ 5x - x - 3x = 15 + 8
add or subtract like terms
⇒ x = 23
Checking:
5(23) - 23 - 8 = 15 + 3(23)
115 - 23 - 8 = 15 + 69
84 = 84
please help this is so confusing
Answer:
f(x)=f(6)= 6^2 - 2*6=36-12= 24
Step-by-step explanation:
This is a function, so we replace x with 6. When we do this, we use it to replace x in the above equation, so instead of having x^2-2x, we have 6^2 -2x. Then we just solve the equation, leaving us with the final solution of 24.
Jithu is curating Christmas hampers for his neighbours.
A minimum of 6 cupcakes are to be included in a hamper box.
If he wants to pack 665 cupcakes evenly into hamper boxes, what could be the smallest number of cupcakes that can be included in one hamper box?
1 hamper box, curated by Jithu can be contained 5 cupcakes.
Calculation:The total amount of cupcakes =665 nos.
Jithu wants to create a gift box, each of which contains 6 cupcakes.
We have to see first, whether 665 could be equally distributed or not.
Hence, 665/6= 110.84 unit
It is seen that the number is in a fraction.so, It can be said that 665 cakes cannot be equally distributed to each gift pack carrying 6 cakes.
Hence, 110*6=660 cupcakes.
∴665-660= 5 cupcakes in one box
So, it is concluded that Jithu could be prepared 110 gift boxes containing 6 cakes each & 1 box containing 5 cupcakes.
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50 people were asked if they speak French or German or Spanish. Of these people, 31 speak French 2 speak French, German and Spanish 4 speak French and Spanish but not German 7 speak German and Spanish 8 do not speak any of the languages all 10 people who speak German speak at least one other language How many people only speak Spanish?
The number of people that speak only spanish = 6
How to Interpret Venn Diagrams?We are given;
Total number of people surveyed = 50
31 speak French 2 speak French, German and Spanish.
4 speak French and Spanish but not German.
7 speak German and Spanish.
8 do not speak any of the languages.
All 10 people who speak German speak at least one other language.
Thus;
From the Venn diagram;
Number of people that speak only French and German = 10 - 5 - 2 - 0 = 3
Number that speak only spanish = 50 - 22 - 3 - 2 - 4 - 5 = 6
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Which of the following equations demonstrate the multiplication property of equality for the equation x = 2? Check all
that apply.
✔x(3) = 2(4)
x(5) = 10
x(1.5) = 2(2)
x(0.5) = 2(0.5)
x(12) = 12
Intro
Done
3 of 12
Answer: x(5) = 10 has the multiplication property.
Step-by-step explanation:
To verify the multiplication property of equality , We need to put the value of x= 2
1. x(5) = 10
Solution = 2(5) = 10 ✔
2. x(1.5) = 2(2)
Solution = 2 (1.5) = 3 X
3. x(0.5) = 2(0.5)
Solution = 2 (0.5) = 1 X
4. x(12) = 12
Solution = 2 (12) = 24 X
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Answer:
Step-by-step explanation:
answer B and D
I got it right and didnt spell the entire constitution
The distance on a map between a student’s house and her job is 6 cm. On the same map, the distance between her house and her school 8 cm. The actual distance from her house to school is 12 km. If d represents the approximate distance in km between her house and her job, what is d? A. 4 km B. 9 km C. 48 km D. 16 k
The approximate distance in km between her house and her job is 9 km.
What is the approximate distance?The map is a scale drawing of the places mentioned. A scale drawing is a smaller image of a larger place or diagram.
The scale of the map = 8cm : 12km
Distance between the house and the job = (12 x 6) / 8 = 9m
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Please help asap
What is the domain and range of T
Answer:
Domain = {-3, -2}Range = {-4, -3, 4}Step-by-step explanation:
The domain is the set of x-values, and the range is the set of y-values.
What is m2?
What is m<1?
Answer:
∠ 2 = 75° , ∠ 1 = 105°
Step-by-step explanation:
∠ 2 and 75° are alternate angles and are congruent , then
∠ 2 = 75°
∠ 1 and ∠ 2 are a linear pair and sum to 180° , that is
∠ 1 + ∠ 2 = 180°
∠ 1 + 75° = 180° ( subtract 75° from both sides )
∠ 1 = 105°
A sequence is defined by the recursive function f(n + 1) = one-half(n). If f(3) = 9 , what is f(1) ?
The value of f(1) is 81
What is Recursive function?Recursive Function is a function that repeats or uses its own previous term to calculate subsequent terms and thus forms a sequence of terms
Given:
f(n + 1) = 1/3* f(n)
f(3) = 9
let n=0
f(0+1) = 1/3 * f(0)
f(1) = 1/3 * f(0)
Let n=1
f(1+1) = 1/3 * 1/3*f(0)
f(2) = 1/9 * f(0)
let n=2
f(2+1) = 1/3 * 1/9* f(0)
f(3) = 1/27 * f(0)
Also, f(3) =9
So,
9 = 1/27 * f(0)
f(0) = 27 * 9
f(0) = 243
Now,
f(1) = 1/3 * f(0)
f(1) = 1/3/ 243
f(1) = 81
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the average height of 10 pupils is 140cm if a new pupil joined the group the average height of 11 pupils become 148
cm find the height of new pupils
Answer:
228 cm
Step-by-step explanation:
the average is calculated as
average = [tex]\frac{sum}{count}[/tex] , then
[tex]\frac{sum}{10}[/tex] = 140 ( multiply both sides by 10 to clear the fraction )
sum = 1400
let the height of new pupil be x , then
[tex]\frac{sum+x}{11}[/tex] = 148 ( multiply both sides by 11 )
sum + x = 1628 , that is
1400 + x = 1628 ( subtract 1400 from both sides )
x = 228
height of new pupil is 228 cm
