Answer:
The distance between 2 points is √97 or 9.84
Step-by-step explanation:
The distance between two points can be found using distance formula:
[tex]d(x_{1},x_{2})=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}[/tex]
x₁ = -4, y₁ = -2 x₂ =5 and y₂ = 2
Putting values:
[tex]d(x_{1},x_{2})=\sqrt{(5-(-4))^2+(2-(-2))^2}\\d(x_{1},x_{2})=\sqrt{(5+4)^2+(2+2)^2}\\d(x_{1},x_{2})=\sqrt{(9)^2+(4)^2} \\d(x_{1},x_{2})=\sqrt{81+16}\\d(x_{1},x_{2})=\sqrt{97}[/tex]
So, the distance between 2 points is √97 or 9.84
Answer:
=sqrt(97)
Step-by-step explanation:
The distance between the two points is found by
d = sqrt(( x2-x1)^2 + (y2-y1)^2)
= sqrt( ( 5--4)^2 + (2--2)^2)
= sqrt( ( 5+4)^2 + (2+2)^2)
= sqrt( ( 9)^2 + (4)^2)
= sqrt( 81 + 16)
=sqrt(97)
Help me find the answer to this piecewise problem!! 20 Points !!!!
Answer:
So we have x+3 if -3<=x<=-1
and 5 if -1<=x<=1
Step-by-step explanation:
The one piece from -1 to 1 is horizontal so the line is in the form of y=a number. It goes through 5 on the y-axis so the equation there is y=5.
From -3 to -1, that is a line with positive slope (since that part is increasing).
Slope=rise/run
We see from the filled in dot to the unfilled in dot that the rise is 2 and the run is 2 so the slope is 2/2=1.
So if we did extend this line where we go at on the y-axis? It would go through 3 because starting from the unfilled dot and rising 1 and running 1 will get us to the 3 on the y-axis.
The equation of a line in slope-intercept form is y=mx+b.
We have m=1 and b=3 so the equation is y=1x+3 or just y=x+3.
So we have x+3 if -3<=x<=-1
and 5 if -1<=x<=1
Answer:
[tex]\large\boxed{f(x)=\left\{\begin{array}{ccc}x+3&,\ \text{if}\ -3\leq x<-1\\5&,\ \text{if}\ -1\leq x\leq1\end{array}\right}[/tex]
Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
Read coordinates of the two points on the first piece:
(-3, 0) and (-2, 1).
Calculate the slope:
[tex]m=\dfrac{1-0}{-2-(-3)}=\dfrac{1}{1}=1[/tex]
Put it and coordinates of the point (-3, 0) to the equation of a line:
[tex]0=1(-3)+b[/tex]
[tex]0=-3+b[/tex] add 3 to both sides
[tex]3=b\to b=3[/tex]
[tex]\boxed{y=x+3}[/tex]
Read coordinates of the two points on the second piece:
(-1, 5) and (1, 5) - second coordinates are the same.
It's a horizontal segment. Therefore the equation is [tex]y=5[/tex]
Options for 1st Question: increasing, decreasing, constant
Options for 2nd Question: -3 < x < 0, -7 < x < -3, -9 < x < -7
Options for 3rd Question: (-5,8) , (-5, -8) , (5,-8)
1. constant
2. -7 < x < -3
3. (-5,8)
Initially, there were only 86 weeds in the garden. The weeds grew at a rate of 29% each week. The following function represents the weekly weed growth: f(x) = 86(1.29). Rewrite the function to show how quickly the weeds grow each day.
A.f(x) = 86(1.04)*; grows approximately at a rate of 0.4% daily
B.f(x) = 86(1.04)7%, grows approximately at a rate of 4% daily
C.f(x) = 86(1.29)7%; grows approximately at a rate of 20% daily
D.f(x) = 86(1.297); grows approximately at a rate of 2% daily
Answer:
Option A. [tex]f(x)=86[1.04]^{x}[/tex] ; grows approximately at a rate of 0.4% daily
Step-by-step explanation:
we have
[tex]f(x)=86(1.29)^{x}[/tex]
where
f(x) the number of weeds in the garden
x ----> the number of weeks
Calculate how quickly the weeds grow each day
Remember that a week is equal to seven days
so
[tex]f(x)=86(1.29)^{\frac{x}{7}}[/tex]
Using the law of exponents
b^(x/a) = b^(x*(1/a)) = (b^(1/a))^x
so
[tex]f(x)=86[(1.29)^{\frac{1}{7}}]^{x}[/tex]
[tex]f(x)=86[1.04]^{x}[/tex]
therefore
The rate is approximately
1.04=1+r
r=1.04-1=0.04=4% daily
not sorry, but guy above is w.r.o.n.g
0.4 ain't right
yw for saving you an attempt
A circle has a radius of 20 inches. Find the length of the arc intercepted by a central angle of 45°. Leave answers in terms of π.
central angle/360 = arc length/2pi•r
Let π = pi
Let A = length of intercepted arc
45/360 = A/2(20)π
1/8 = A/40π
8A = 40π
A = 40π/8
A = 5π
Did you follow?
Answer:
The length of the arc is 5π inches
Step-by-step explanation:
* Lets explain the relation between the central angle and its
intercepted arc
- If the vertex of an angle is the center of the circle and the two sides
of the angle are radii in the circle, then this angle is called a
central angle
- Each central angle subtended by the opposite arc, the name of the
arc is the starting point and the ending point of the angle
- There is a relation between the central angle and its subtended arc
the measure of the central angle equals half the measure of its
subtended arc
- The length of the subtended arc depends on the measure of its
central angle and the length of the radius and the measure of the arc
- The measure of the circle is 360°
- The length of the circle is 2πr
- The length of the arc = central angle/360 × 2πr
* Now lets solve the problem
∵ The radius of the circle r = 20 inches
∵ The measure of the central angle is 45°
∵ The length of the arc = central angle/360 × 2πr
∴ The length of the arc = 45°/360° × 2 × π × 20 = 5π
* The length of the arc is 5π inches
Simplify
8(x + 6) - 10.
Answer:
8 x + 38 higher it is not available
Sarah needs 10 feet of fabric for a project she is working on, but the store only sells the fabric in meters. One meter of fabric costs $1.50. How much will the fabric
cost?
[1 ft = 0.305 m]
A.$49.18
B.$2.03
C.$21.86
D.$4.58
The answer is:
The fabric will cost $4.58
D.$4.58
Why?Since it's a conversion exercise, we need to pay special attention to the conversion procedure.
From the statement we know that:
[tex]1ft=0.305m[/tex]
So, if she needs 10 feet of fabric, we need to convert it to meters, and then, calculate its cost.
We have that:
[tex]10*1ft=10*0.305m\\\\10ft=3.05m[/tex]
Now, we have that each meter of fabric cost $1.50, so, 3.05m of fabric will cost:
[tex]\frac{1m}{1.50(dollars)}=\frac{3.05m}{cost}\\\\cost=\frac{3.05m*1.50(dollars)}{1m}=4.575(dollars)=4.58(dollars)[/tex]
Hence, we have that the cost of the fabric will be $4.58.
The correct option is: D.$4.58
Have a nice day!
Answer:
Sarah will need $4.58 for the fabric. therefor, your answer will be...
D: $4.58
The graph of the equation below is a circle. What is the length of the radius of
the circle?
(x + 5)2 + (y + 7)2 = 212
O A. 441
O B. 42
O C. 10.5
O D. 21
Answer:
D. 21.
Step-by-step explanation:
The general form of the equation of a circle is:
(x - a)^2 + (y - b)^2 = r^2 where r is the radius.
Comparing:
(x + 5)^2 + (y + 7)^2 = 21^2
So r^2 = 21^2
making r = √21^2
= 21.
The length of the radius of the circle is 21.
What is Circle?Circle is a two dimensional figure which consist of set of all the points which are at equal distance from a point which is fixed called the center of the circle.
Standard form of a circle is given by the equation,
(x - h)² + (y - k)² = r²
where, (h, k) is the center of the circle and r is the radius of the circle.
Here, given equation is,
(x + 5)² + (y + 7)² = 21²
Comparing this with the standard form,
(-5, -7) is the center and 21 is the radius.
Hence the correct option is D. 21.
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Find the slope of the line
6. PATTERNS Complete the pattern: 5, 7,
10, 14,
Answer:
19 is the next number
Step-by-step explanation:
5+2=7
7+3=10
10+4=14
14+5=19
The next number in the pattern is 19.
To complete the number pattern 5, 7, 10, 14, we observe that the differences between the numbers increase by 1. Continuing this pattern, we add 5 to the last number, which results in 19. Thus, the next number in the pattern is 19
To complete the given number pattern: 5, 7, 10, 14, we need to find the rule that governs the pattern. Let's look at the differences between the numbers:
7 - 5 = 210 - 7 = 314 - 10 = 4We can see that the differences are increasing by 1 each time. If this pattern continues, the next difference should be 5. So we add 5 to the last number in the pattern:
14 + 5 = 19
Therefore, the next number in the pattern is 19.
Which one of the numbers does not belong in the following series: 100-50-52-26-28-12-16-8-10
Answer:
The 12 ( after 28) should be 14.
This 12 does not belong to the series.
Step-by-step explanation:
After every 2 numbers, 2 is added to the last number, so we have 100-50 + 2 = 52 - 26, and the second of the paired numbers is 1/2 of the first.
So after 28 the numbers should be 14 - 16 - 8 - 10. The 12 does not belong.
The variable z is inversely proportional to x. When x is 4, z has the value 3.25. What is the value of z when x= 11? Round to at least the thousandths place if needed.
Answer:
1.182
Step-by-step explanation:
z is inversely proportional to x:
z = k / x
When x is 4, z is 3.25:
3.25 = k / 4
k = 13
When x = 11:
z = 13 / 11
z ≈ 1.182
Comparing decimals 0.49 to 0.94 is that equal ? or 0.94 more..?
the simple fact that 94 is 49 backwards means nothing, anymore than say 001 and 100 are equal quantities or related other than in the digits.
so, 0.49 or 49/100 and 0.94 or 94/100, are two values, both are at the one hundredth level, so to see who is larger, we can nevermind the 100 and look at the numerator, 94 is clearly much larger than 49.
Help please I don’t understand at all
Answer:
6% ( to nearest percent )
Step-by-step explanation:
The percentage change is calculated as
[tex]\frac{change}{original}[/tex] × 100%
Change = 90 - 85 = 5, hence
percent change = [tex]\frac{5}{85}[/tex] × 100% = [tex]\frac{5(100)}{85}[/tex] = 6%
Answer:
Here, you have to calculate the percentage(%) of change.
To calculate this, you have to use this formula-:
[tex] { \bold{\mathfrak{\frac{change}{new} \times 100}}}[/tex]
Step-by-step explanation:
[tex] = \frac{5}{90} \times 100[/tex]
[tex] = \frac{50}{9 }[/tex]
[tex] = 5.55555[/tex]
Now, you have to round of this percentage to the nearest....
And that will be => 6%.
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Roopesh has $24 dollars to spend on a birthday gift. The store where he is shopping has a sale offering $5 off the regular price, r, of any item. Write an inequality that can be used to determine the regular price of an item in the store that Roopesh can afford. (Assume there is no tax.)
What is the unknown?
Which expression can represent the sale price?
Which comparison could be used?
Which inequality represents the situation?
Answer:
r ≤ 29, r-5, The sale price can be compared with the regular price, r-5 ≤ 24
Step-by-step explanation:
Amount to spend = $24Regular price = rSale = $5Sale Price = r-5The regular price will be at most $5 more than the amount Roopesh has to spend.
The sale price will be $24 or less than that for Roopesh to afford.
Inequality for regular price :
r-5 ≤ 24
r ≤ 29
Therefore, the product Roopesh can afford is $29 or less than that.
What is the unknown? r ≤ 29Which expression can represent the sale price? Sale price = r-5 (mentioned above)Which comparison could be used? The sale price can be compared with the regular priceWhich inequality represents the situation? r-5 ≤ 24!!
MATHS HELP PLEASE!!!!
Can anyone help me with question 1????
Answer: For part A, Yakob has 9 friends that like Maths best, 6 friends that like History the best, & 15 friends that prefer either English or Science the best.
Part B: There's a graph I made below.
Step-by-step explanation:
You have to use proportions to answer this question. The bar graph is 10 cm total, therefore it is proportional to the 30 friends that Yakob has in total. After that, you can make proportions out of the data in the chart. For example, History is 2 cm out of the 10 cm total. Think proportions! You had to multiply 3 to 10 to get 30, so you have to apply the same thing to the numerator. In this case, multiply 3 to 2 and you'll get 6. 2/10=6/30! I repeated that for the rest and put it into a graph. The prompt wanted you to combine English and Science, so I did that after separately making their proportions. Hope this helps!
A store owner wants to develop a new snack mix by mixing chocolate and trail mix. How many pounds of chocolate costing $18.90 per pound should be mixed with 22 pounds of trail mix costing $3.30 per pound to create a mixture worth $8.50 per pound.
The owner needs to mix _________ pounds of chocolate (round to the nearest whole pound - NO COMMAS).
Answer:
The owner needs to mix 11 pounds of chocolate
Step-by-step explanation:
Let
x ----> the number of pounds of chocolate needed
we know that
The linear equation that represent this problem is equal to
[tex]18.90x+3.30(22)=8.50(x+22)[/tex]
solve for x
[tex]18.90x+72.6=8.50x+187[/tex]
[tex]18.90x-8.50x=187-72.6[/tex]
[tex]10.4x=114.4[/tex]
[tex]x=114.4/10.4[/tex]
[tex]x=11\ pounds[/tex]
What is the length of line segment AD?
8 units
14 units
22 units
36 units
Answer:
22
Step-by-step explanation:
With a kite, the top 2 segments are always equal, and the bottom 2 segments are always equal. Also, if you look at the little red lines on the sides, you can see that AD and CD have 2, that means they are the same length
(Also can you please rate this answer as brainliest? I need it to level up.)
Answer:
22 units
Step-by-step explanation:
AD = CD because the two little line marks means they are equal to each other
AD = 22
For f (c)=2x+1 and g(x)=x^2 - 7 find (f-g)(x)
Answer:
[tex]\large\boxed{D.\ -x^2+2x+8}[/tex]
Step-by-step explanation:
[tex](f-g)(x)=f(x)-g(x)\\\\f(x)=2x+1,\ g(x)=x^2-7\\\\\text{substitute:}\\\\(f-g)(x)=(2x+1)-(x^2-7)=2x+1-x^2-(-7)=2x+1-x^2+7\\\\=-x^2+2x+(1+7)=-x^2+2x+8[/tex]
The stairway shown is made out of solid concrete. The height of each step is four inches and the width is 10 inches. The length is 6 inches. What is the volume, in cubic inches, of the concrete used to create this stairway?
Answer:
The volume of the stairway is
720 cubic inches
Step-by-step explanation:
we know that
The volume of the stairway is equal to the volume of two rectangular prism
The volume of the rectangular prism is equal to
[tex]V=LWH[/tex]
Find the volume of the larger rectangular prism
we have
[tex]L=6\ in[/tex]
[tex]W=10\ in[/tex]
[tex]H=4+4=8\ in[/tex]
substitute
[tex]V=(6)(10)(8)=480\ in^{3}[/tex]
Find the volume of the smaller rectangular prism
we have
[tex]L=6\ in[/tex]
[tex]W=10\ in[/tex]
[tex]H=4\ in[/tex]
substitute
[tex]V=(6)(10)(4)=240\ in^{3}[/tex]
Find the volume of the stairway
Adds the two volumes
[tex]V=480+240=720\ in^{3}[/tex]
Answer:
Option B
Step-by-step explanation:
We have to calculate the volume of concrete used to create the stairway given in the picture.
Volume of the stairway = volume of small stairway + volume of larger stairway
Dimensions of Large stairway = 10 in × 6 in × (4+4)in
= 10 in × 6 in × 8 in.
Therefore, volume of large stairway = 480 in³
Dimensions of small stairway = 10 in × 6 in × 4 in
= 240 in³
Total volume = 480 + 240
= 720 in³
Option B is the answer.
what is the radius of a circle with an area of 64 sq feet
For this case we have that by definition, the area of a circle is given by:
[tex]A = \pi * r ^ 2[/tex]
Where:
r: It is the radius of the circle
How do we have to:
[tex]A = 64 \ ft ^ 2[/tex]
So:
[tex]64 = \pi * r ^ 2[/tex]
We take[tex]\pi = 3.14[/tex]
[tex]r ^ 2 = \frac {64} {3.14}[/tex]
We apply square root:
[tex]r = \pm \sqrt {\frac {64} {3.14}}[/tex]
We choose the positive value:
[tex]r = 4,515[/tex]
If we round we have that the radius is 4.5 feet.
Answer:
4.5 feet
Find the volume of the cone. Round your answer to the nearest hundredth.
A.
32.05 cubic feet
B.
38.39 cubic feet
C.
56.54 cubic feet
D.
100.69 cubic feet
Answer:
V=100.63 cubic feet
Step-by-step explanation:
The formula for the volume of the cube is given as
[tex]V=\frac{1}{3}\pi r^{2}h[/tex]
Where r=4.3 ft
And h is height = 5.2 ft
Now we put the value of h and r in the formula for volume
[tex]V=\frac{1}{3}\times \pi \times 4.3^{2} \times 5.2[/tex]
[tex]V=\frac{1}{3}\times \pi \times 96.148[/tex]
[tex]V=\frac{1}{3}\times 3.14 \times 96.148[/tex]
[tex]V=\frac{1}{3}\times 301.904[/tex]
V=100.63 cubic feet
To compute the volume of a cone, one needs to use the formula 1/3πr²h, where 'r' represents the radius of the base and 'h' represents the height of the cone. The specific dimensions of the cone are needed to provide a concrete answer. The given options can't be validated without these details.
Explanation:Without specific parameters such as the radius and height of the cone, we cannot directly calculate the volume of the cone. However, the general formula for finding the volume of a cone is 1/3πr²h, where r represents the radius of the base and h represents the height of the cone. This formula is derived from the geometric principles of a cone's structure. Once the values of r and h are known, they can be substituted into this formula to compute the volume. The answer would then be rounded to the nearest hundredth if necessary. Unfortunately, the choices provided A.32.05 cubic feet, B.38.39 cubic feet, C.56.54 cubic feet, D.100.69 cubic feet aren't helpful without knowledge of the specific cone dimensions.
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Create a mapping diagram of the relation. Define the domain and range. Tell whether the relation is a function. For both.
ANSWER
For the first relation the ordered pairs are:(-2,-5),(-2,3),(1,-1),(2,3),(6,2)The domain refers to set of x-values of the relation.Domain: {-2,1,2,6}Range {-5,-1,2,3}Range refers to the set of all y-values of the relation.This relation is not a function because -2 alone has two different y-coordinates which are -5 and 3.For the second relation, the ordered pairs are: (-5,-4), (-3,-2), (-2,1),(0,2),(2,1),(3,0)Domain: {-5,-3,-2,1,0,2,3}Range:{-4,-2,0,1,2}This relation is a function because no x-value maps on to more than one y-value.For a mapping diagram, the set of all the x-coordinates form the domain and the corresponding y-coordinates are in the RangeSee attachment for the mapping diagram s.Find the diagonal of the rectangular solid with the given measures. (Part of the answer is provided for you.) l = 18, w = 10, h = 2
Answer:
Step-by-step explanation:
first find one side:
18^2+10^2=c^2, so c=20.59
we need to find the length of one of the sides of the remaining triangle:
20.59^2+2^2=c^2
c=20.68 = the diagonal.
Answer:
2 square root 107
Step-by-step explanation:
Find the value of x if A, B, and C are collinear points and B is between A and C.
AB=5x−1,BC=14,AC=25−x
Answer:
x = 2
Step-by-step explanation:
Collinear means that the points A, B and C all lie in a straight line, hence
AB + BC = AC, substitute values
5x - 1 + 14 = 25 - x
5x + 13 = 25 - x ( add x to both sides )
6x + 13 = 25 ( subtract 13 from both sides )
6x = 12 ( divide both sides by 6 )
x = 2
The value of x is:
[tex]x=2[/tex]
Step-by-step explanation:Three points are said to be collinear if they lie along a straight line.
Also, it is given that:
Here A, B, and C are collinear points and B is between A and C.
This means that:
[tex]AB+BC=AC-----------(1)[/tex]
Also we are given:
[tex]AB=5x-1,\ BC=14,\ AC=25-x[/tex]
Using property (1) we have:
[tex]5x-1+14=25-x\\\\i.e.\\\\5x+13=25-x[/tex]
Now on adding x on both the side of the equation we have:
[tex]5x+13+x=25\\\\i.e.\\\\5x+x+13=25\\\\i.e.\\\\6x+13=25[/tex]
Now on subtracting 13 on both the sides of the equation we have:
[tex]6x=25-13\\\\i.e.\\\\6x=12\\\\i.e.\\\\x=\dfrac{12}{6}\\\\i.e.\\\\x=2[/tex]
- 7.5x - 1.2y = -2.7
- 1.5x + 1.2y = -3.3
Answer:
x = 2/3 , y = -23/12
Step-by-step explanation:
Solve the following system:
{-7.5 x - 1.2 y = -2.7
{1.2 y - 1.5 x = -3.3
In the first equation, look to solve for x:
{-7.5 x - 1.2 y = -2.7
{1.2 y - 1.5 x = -3.3
-7.5 x - 1.2 y = -(15 x)/2 - (6 y)/5 and -2.7 = -27/10:
{-(15 x)/2 - (6 y)/5 = -27/10
Add (6 y)/5 to both sides:
{-(15 x)/2 = 3/10 (4 y - 9)
{1.2 y - 1.5 x = -3.3
Multiply both sides by -2/15:
{x = 1/25 (9 - 4 y)
{1.2 y - 1.5 x = -3.3
Substitute x = 1/25 (9 - 4 y) into the second equation:
{x = 1/25 (9 - 4 y)
{1.2 y - 0.06 (9 - 4 y) = -3.3
1.2 y - 0.06 (9 - 4 y) = 1.2 y + (0.24 y - 0.54) = 1.44 y - 0.54:
{x = 1/25 (9 - 4 y)
{1.44 y - 0.54 = -3.3
In the second equation, look to solve for y:
{x = 1/25 (9 - 4 y)
{1.44 y - 0.54 = -3.3
1.44 y - 0.54 = (36 y)/25 - 27/50 and -3.3 = -33/10:
(36 y)/25 - 27/50 = -33/10
Add 27/50 to both sides:
{x = 1/25 (9 - 4 y)
{(36 y)/25 = -69/25
Multiply both sides by 25/36:
{x = 1/25 (9 - 4 y)
{y = -23/12
Substitute y = -23/12 into the first equation:
Answer: x = 2/3 , y = -23/12
Answer:
x = 2/3 y = -23/12
Step-by-step explanation:
- 7.5x - 1.2y = -2.7
- 1.5x + 1.2y = -3.3
Add the equations together
- 7.5x - 1.2y = -2.7
- 1.5x + 1.2y = -3.3
---------------------------
-9x = -6
Divide each side by -9
-9x/-9 =-6/-9
x =2/3
Now we need to find y
-1.5 (2/3) +1.2y = -3.3
-1 +1.2y = -3.3
Add 1 to each side
-1+1 +1.2y = -3.3+1
1.2y = -2.3
Divide by 1.2
1.2y/1.2 = -2.3/1.2
y =-23/12
Perform the following operations and prove closure. Show your work.
(x/x+3) + (x+2/x+5)
Answer:
[tex]\frac{2(x^{2} + 5x + 3)}{(x+3)(x+5)}[/tex]
Step-by-step explanation:
We need to sum the following two expressions:
[tex]\frac{x}{x+3} + \frac{x+2}{x+5}[/tex]
[tex]\frac{x(x+5) + (x+2)(x+3)}{(x+3)(x+5)}[/tex]
expanding the polynomial in the numerator:
[tex]\frac{2x^{2} + 10x + 6}{(x+3)(x+5)}[/tex]
[tex]\frac{2(x^{2} + 5x + 3)}{(x+3)(x+5)}[/tex]
This is the most simplified form we can get:
[tex]\frac{2(x^{2} + 5x + 3)}{(x+3)(x+5)}[/tex]
Answer:
[tex]\frac{2(x^{2}+5x+3)}{(x+3)(x+5)}[/tex]
Step-by-step explanation:
The given expression is [tex]\frac{x}{x+3}+\frac{x+2}{x+5}[/tex]
We have to simplify the given expression
[tex]\frac{x}{x+3}+\frac{x+2}{x+5}[/tex]
= [tex]\frac{x(x+5)+(x+2)(x+3)}{(x+3)(x+5)}[/tex] [Distributive law]
= [tex]\frac{x^{2}+5x+x^{2}+3x+2x+6}{(x+3)(x+5)}[/tex]
= [tex]\frac{2x^{2}+10x+6}{(x+3)(x+5)}[/tex]
= [tex]\frac{2(x^{2}+5x+3)}{(x+3)(x+5)}[/tex]
Finally the simplified form of the given expression is [tex]\frac{2(x^{2}+5x+3)}{(x+3)(x+5)}[/tex]
(x²-2xy+y²)+(x²+2xy+y²)=?
(x²-2xy+y²)-(x²+2xy+y²)=?
Answer:
See below in bold.
Step-by-step explanation:
(x²-2xy+y²)+(x²+2xy+y²)
= x²-2xy+y²+ x²+2xy+y²
= 2x² + 4xy + 2y².
(x²-2xy+y²)-(x²+2xy+y²)
= x²- 2xy + y²- x² - 2xy - y²
= -4xy.
Answer:
2
Step-by-step explanation:
If the constant of proportionality is k then,
y=kx
What number do we multiply by x to get y?
The constant of proportionality is 2.
Select the statement that correctly describes the expression below.
(x - 5)(x + 3)
OA. the product of the difference of x and 5 and the sum of x and 3
OB. the difference of x and the product of 5 and the sum of x and 3
OC. the sum of 3 and the product of x and the difference of x and 5
OD.
the product of the difference of x and 3 and the sum of x and 5
A. the product of the difference of x and 5 and the sum of x and 3.
Not really sure how I should explain this because the answer is just the expression in word form.
The expression (x - 5)(x + 3) correctly corresponds to 'the product of the difference of x and 5 and the sum of x and 3', matching option OA.
The expression (x - 5)(x + 3) is the product of two binomials: the first binomial is the difference of x and 5, and the second binomial is the sum of x and 3. Therefore, the correct description of the expression is 'the product of the difference of x and 5 and the sum of x and 3', which corresponds to option OA. This understanding illuminates how binomials are multiplied and underscores the significance of recognizing the individual terms within the expression to comprehend its meaning and structure effectively.
If ax7yb is a term from the expansion of (x + y)12, describe how to determine its coefficient a and missing exponent b without writing the entire expansion.
ANSWER
a) Use the homogeneous property of the binomial expansion to find the missing exponent
b) Use the binomial theorem to find the coefficient
EXPLANATION
The given binomial expansion is:
[tex](x+y)^{12} [/tex]
When we compare this to
[tex](a + b) ^{n} [/tex]
We have
[tex]n = 12[/tex]
Therefore the of each term in the expansion must be 12.
[tex] \implies \: 7 + b = 12[/tex]
[tex]b = 12 - 7[/tex]
[tex]b = 5[/tex]
Since the coefficient of x and y are unity, we use the formula
[tex]^{n} C_r = \frac{n!}{(n - r)!r!} [/tex]
to find the coefficient.
Where n=12 and r=5(the exponent of the y-term).
Therefore the coefficient is
[tex]^{12} C_5= \frac{12!}{(12- 5)!5!} [/tex]
[tex]^{12} C_5= \frac{12!}{7!5!} [/tex]
[tex]^{12} C_5= \frac{12 \times 11 \times 10 \times 9 \times 8 \times 7!}{7! \times 5 \times 4 \times 3 \times 2 \times 1} [/tex]
When we simplify further we get:
[tex]^{12} C_5= 11 \times 9 \times 8 = 792[/tex]
A tank holds 17 3/5 gallons after losing 36 2/3 gallons, 4 5/6 gallons,and 27 1/12 gallons in 3
Consecutive days. If at the beginning the tank was 20 3/4 gallons short of capacity. What is the capacity of the tank? NEED HELP PLSSS ASAP
Answer:Maybe if you studded you would have the answer young man
Step-by-step explanation:
Answer:
Step-by-step explanation:
Given that A tank holds 17 3/5 gallons after losing 36 2/3 gallons, 4 5/6 gallons,and 27 1/12 gallons in 3
Consecutive days. If at the beginning the tank was 20 3/4 gallons short of capacity.
Tank full capacity = loss for 3 days + holding of tank after losing + shortage of capacity
To add these first let us convert these into improper fractions, then take lcd to add
Full capacity = [tex]\frac{88}{5} +\frac{110}{3} +\frac{29}{6} +\frac{325}{12} \\=\frac{88}{5} +\frac{440+58+325}{12} \\=\frac{1056+4115}{60} =[/tex][tex]=86.183[/tex] gallons