Answer:
Let us take 'a' in the place of 'y' so the equation becomes
(y+x) (ax+b)
Step-by-step explanation:
Step 1:
(a + x) (ax + b)
Step 2: Proof
Checking polynomial identity.
(ax+b )(x+a) = FOIL
(ax+b)(x+a)
ax^2+a^2x is the First Term in the FOIL
ax^2 + a^2x + bx + ab
(ax+b)(x+a)+bx+ab is the Second Term in the FOIL
Add both expressions together from First and Second Term
= ax^2 + a^2x + bx + ab
Step 3: Proof
(ax+b)(x+a) = ax^2 + a^2x + bx + ab
Identity is Found .
Trying with numbers now
(ax+b)(x+a) = ax^2 + a^2x + bx + ab
((2*5)+8)(5+2) =(2*5^2)+(2^2*5)+(8*5)+(2*8)
((10)+8)(7) =(2*25)+(4*5)+(40)+(16)
(18)(7) =(50)+(20)+(56)
126 =126
A student reads 56 pages in 4 hours. How many pages will the student read in 7 hours? Find the constant of variation.
The constant of variation here is the reading speed, which is 14 pages per hour.
The student reads 56 pages in 4 hours. To find out how many pages the student will read in 7 hours, we first calculate the constant of variation, which is the student's reading speed per hour. We divide 56 pages by 4 hours to get a reading speed of 14 pages per hour. To find the total number of pages read in 7 hours, we multiply the hourly reading speed by 7 hours.
Calculate hourly reading speed: 56 pages 4 hours = 14 pages/hour.
Multiply the hourly reading speed by the number of hours: 14 pages/hour 7 hours.
The student is expected to read 98 pages in 7 hours (14 pages/hour 7 hours = 98 pages).
hence, the student's constant of variation is their reading speed, which is 14 pages per hour. By multiplying this constant by 7 hours, we find that the student will read 98 pages in 7 hours.
Donald bought a box of golf balls for $9.27. There were 18 golf balls in the box.
About how much did each golf ball cost? Rename the decimal dividend as a whole number that is
compatible with the divisor to estimate the quotient.
Each golf ball costs about
Answer:
Each golf ball costs about $2.
Step-by-step explanation:
Given:
Donald bought a box of golf balls for $9.27. There were 18 golf balls in the box.
Rename the decimal dividend as a whole number that is compatible with the divisor to estimate the quotient.
Now, to find the cost of each golf ball.
As given:
Rename the decimal dividend as a whole number that is compatible with the divisor to estimate the quotient.
As, the cost of golf ball box = $9.27.
So, 9.27 nearest to whole number is 9.
Thus to get the cost of each ball:
18 golf balls cost = $9.
So, 1 golf ball cost = [tex]18\div 9=2.[/tex]
Therefore, each golf ball costs about $2.
PLZ HELP ME THIS IS URGENT HELP!!!!!!!
Answer:
Value is 3.The volume of the rectangular prism is 105 [tex]ft^{3}[/tex]The value will be 186.1Step-by-step explanation:
The value of the expression is [tex]\frac{75}{5} - [(9 - 7) \times 3]\times 2 = 15 - 6\times2 = 15 - 12 = 3[/tex]
The formula to get the volume is [tex]length \times width \times height = 3\times 5\times 7 = 105[/tex]
[tex]\frac{8375}{45} = \frac{1675}{9} = 186.1[/tex]
Answer:
it is explained below..
Step-by-step explanation:
1. by using BODMAS rule: [ brackets of division multiplication addition subtraction] we have to do operations in this order only i.e, from brackets to subtractions.
given expression : 75[tex]\div[/tex]5-[(9-7)*3]*2
first solve brackets part:75[tex]\div[/tex]5-[(2)*3]*2
[as, 9-7=2]
75[tex]\div[/tex]5-[6]*2
[as, 2*3=6]
division part: 15-6*2multiplication part: 15-12 = 32. volume of rectangular prism: length*breadth*height
=7*3*5
=105
3. 8375[tex]\div[/tex]45
use conventional division method as 8375 isn't divisible by 45 directly.
after solving, answer: 186.11...
A circle with radius of 1 cm sits inside a 3 cm x 4 cm rectangle.
What is the area of the shaded region?
Round your final answer to the nearest hundredth.
3 cm
The area of shaded-region is 8.86 cm^2
Step-by-step explanation:
We can see that there is a circle and a triangle in the given figure
In order too find the area of shaded region, we have to find the area of rectangle and circle first. The area of the shaded region will be obtained by subtracting the area of circle from the area of rectangle.
So,
Area of circle:
Radius = r = 1 cm
So,
[tex]A_c = \pi r^2\\= 3.14 * (1)^2\\= 3.14*1\\= 3.14\ cm^2[/tex]
Area of rectangle:
Length of rectangle = l = 4 cm
Width of rectangle = w = 3 cm
So,
[tex]A_r = l*w\\= 4 *3\\=12 cm^2[/tex]
Now,
[tex]Area\ of\ shaded-region = A_r - A_c\\= 12 - 3.14\\=8.86\ cm^2[/tex]
The area of shaded-region is 8.86 cm^2
Keywords: Area, shaded regions
Learn more about area at:
brainly.com/question/10435836brainly.com/question/10541435#LearnwithBrainly
17. The length of a rectangle is 12 in, and the perimeter is 56 in. Find the width of the rectangle.
Oo oo
O A. 16 in.
O B. 32 in.
O c. 22 in.
O D. 21 in.
Answer:
Step-by-step explanation:
P = 2(L + W)
P = 56
L = 12
now sub...we are looking for w
56 = 2(12 + W)
56 = 24 + 2W
56 - 24 = 2W
32 = 2W
32/2 = W
16 = W <==== the width is 16 inches
check...
P = 2(L + W)
56 = 2(12 + 16)
56 = 2(28)
56 = 56 (correct)
Find the point, M, that divides segment AB into a ratio of 2:3 if A is at (0.15) and B is at (20.0)
Answer:
M = (8,9)
Step-by-step explanation:
Notice that the points (0,15), and (20,0) form with the origin of coordinates (0,0), a right angle triangle (please see attached image). This triangle has twon perpendicular sides of length 15 and 20 respectively. Therefore, we can find the length of the segment that joins points A (0,15) and B (20,0) by finding the length of the hypotenuse in a right angle triangle (with the Pythagorean Theorem):
[tex]AB=\sqrt{15^2+20^2} =\sqrt{625} =25[/tex]
Now, to get a 2:3 proportion on Segment AB which is of length 25, we need to divide it in five equal parts (see the picture on the right of the attached image), and place point M at two of these divisions from point A (0,15) and along segment AB.
In order to find the appropriate location in (x,y) coordinates, we consider a smaller triangle (pictured in orange in the image) that is similar to the first larger triangle (pictured in blue). Notice that if the length of AB is 25, each of its five equal divisions would be of length "5", and therefore two of them will render a length of "10" (which is the hypotenuse of this smaller right angle triangle.
Now, in order to find the sides of this smaller triangle (which can give us the clues on the horizontal and vertical coordinates of point M), we can use proportions.
To find the length "x" of the horizontal side , we do:
[tex]\frac{x}{10} =\frac{20}{25} \\x=\frac{10*20}{25} \\x=8[/tex]
To find the length "y" of the vertical side , we do:
[tex]\frac{y}{10} =\frac{15}{25} \\y=\frac{10*15}{25} \\y=6[/tex]
Then, the coordinate "x" of point M will be "8", while we can calculate the y position of point M subtracting "6" from 15 (the length of the vertical side in the original triangle). This gives us the coordinates (8,9) for point M as marked in orange in the picture.
are the two equations -6 + y = 2x and 2y - 4x = 12 dependent?
Yes they are linearly dependent, essentially the same equation.
Start from one of them:
-6 + y = 2x
Move things around:
y - 2x = 6
Multiply both sides by 2,
2y - 4x = 12
That's the second equation, which we've shown is equivalent to the first, so they're linearly dependent.
Can someone help me with 1c? I don’t understand how to find an equation for an asymptote.
Answer:
y = 0
Step-by-step explanation:
1 c.
If we have an exponential function of the form [tex]f(x)=a^x[/tex], where "a" is any positive integer, say, then that function will take the general shape of the function shown in the picture.
It will always approach the x-axis but never meet (touch). Any line that a function (graph) approaches but never touches, is known as an asymptote to the graph.
Since the function [tex]f(x)=4^x[/tex] follows the path of the general form shown above, this also approaches the x-axis, but never touches. So, the x-axis is the asymptote of the function.
We know
x-axis has equation y = 0, and
y-axis has equation x = 0
Here, the x-axis is the asymptote, so the equation is:
y = 0
The number -2.34 can be found between which two integers?
(Full question above)
Answer:
last option
Step-by-step explanation:
imagine a number line
________________________________________________
-3 -2 -1 0 1 2 3
|
-2.34 would be found somewhere over there
Match each number on the left with the correct description of the number on the right.
Answer options on the right may be used more than once.
(Full question above)
Step-by-step explanation:
An integer is a number that can be written without a fractional component.
A rational number is a number that can be represented as a fraction with a non-zero denominator, and its decimal expansion is finite or infinite and repeat.
An irrational number is a real number which is not a rational number.
[tex]\bold{integer:}\\-2,\ 150\\\\\bold{rational\ but\ not\ an\ integer:}\\\\-\dfrac{1}{2},\ 6.\overline{6}\\\\\bold{irrational:}\\\\-\sqrt3[/tex]
What is 8,427 divided by 6??????
Answer:
1404.5 is your answer when you divide 8,427 by 6
Answer:
1404.5
Step-by-step explanation:
8427 divided by 6 in decimal = 1404.5
8427 divided by 6 in fraction = 8427/6
8427 divided by 6 in percentage = 140450%
The shortest and longest sides of a right triangle have lengths of 11.1 inches and 18.5 inches, respectively. What is the length of the third side of the triangle?
Answer: 14.8
Step-by-step explanation:
11.1^2 + x^2 = 18.5^2
X is 14.8
HELP U WILL MARK YOU AS A BRAINLIEST!!(I’m dumb sorry)
Which pairs of numbers have a greatest
common factor of 10?
Select all that apply.
A. 2 and 5
B. 5 and 10
C. 10 and 20
D. 30 and 50
E. 40 and 60
Answer:
C. 10 and 20
Step-by-step explanation:
A common factor is just a value that both numbers can be divided by to give you an integer. (an integer is a number without a decimal point btw or anything that is not a fraction)
Answer A and B are too small so there's no way they can be divided by 10.
D and E are too big, so they can be divided by a number bigger than 10. (the question did ask for the biggest dividing number to be 10)
The only answer left is C.
O que significa a letra E depois de números grandes?
E é usado para significar "10 à potência de". Por exemplo, 1.314E + 1 significa 1.314 * 101, que é 13.14.
What is the approximate length of arc s on the circle below? Use 3.14 for pi. Round your answer to the nearest tenth
14.1in
22.5in
42.3in
56.5in
Answer: 14. 1 in
Step-by-step explanation:
The formula for calculating the length of an arc is given as :
L = Ф/360 x 2πr
where Ф is the angle subtended by the arc
r = radius
substituting the given values
L = 135/360 x 2 x 3.14 x 6
L = 5086.8/360
L = 14.13
L ≈ 14.1 in to the nearest tenth
Answer:
The answer is A
Step-by-step explanation:
edge 2021
What is the value of X
4(x - 3) = -8
Solving for x...
4(x-3)=-8
Divide by 4.
x-3=-2
Add 3.
x=1
Answer: x = +1
Step-by-step explanation: To solve for x in this equation, our first step is to simplify the left side by distributing the 4 through both terms inside the parentheses.
When we do that, we get 4 times x which is 4x and 4 times -3 which is -12. So we have 4x - 12 = -8. Our next step is to isolate the x-term by adding 12 to both sides of the equation. On the left, -12 + 12 cancels and we are left with 4x. On the right, -8 + 12 simplifies to 4.
Now we have the equation 4x = 4.
To get x by itself, we divide both sides by 4 and x = +1.
the table shows amounts of money that carol deposited and withdrew from her bank account. what is the overall amount of deposit or withdrawl
deposit: $400
deposit: $125
rent: -$300
Deposit: $50
Bill: -$74
What is the sum of 4 radical 12 and 2 radical 27 in simplest form
Answer:
14√3
Step-by-step explanation:
4√12 + 2√27
First, simplify both terms:
4√3√4 + 2√9√3
4 * 2√3 + 2 * 3√3
8√3 + 6√3
Now, combine the terms:
14√3
To find the sum of 4 radical 12 and 2 radical 27 in simplest form, we simplify each radical expression individually and then add the simplified expressions together, resulting in 5 times the square root of 3.
Explanation:To find the sum of 4 radical 12 and 2 radical 27 in simplest form, we first need to simplify each radical expression individually. The square root of 12 can be simplified as the square root of 4 times the square root of 3, which is 2 times the square root of 3. Similarly, the square root of 27 can be simplified as 3 times the square root of 3.
Now, we can add these simplified radical expressions. 4 radical 12 plus 2 radical 27 equals (2 times the square root of 3) plus (3 times the square root of 3). This can be simplified as 5 times the square root of 3.
Learn more about Simplifying radical expressions here:https://brainly.com/question/31873903
#SPJ2
82nd term of the arithmetic sequence -8, 9, 26, ...−8,9,26
The 82nd term of the arithmetic sequence -8, 9, 26 can be solved using the arithmetic sequence formula, which results in the 82nd term being 1369.
Explanation:The subject of this question is related to finding the 82nd term of the arithmetic sequence -8, 9, 26. Arithmetic sequences follow a pattern of adding a consistent value, this consistent value is called the common difference. From the given sequence, the common difference (d) can be calculated by subtracting the first term from the second term, or the second from the third, and so on. So d = 9 - (-8) = 17 or 26 - 9 = 17.
The formula for finding the nth term of an arithmetic sequence is a_n = a_1 + (n - 1) * d. Here, a_1 is the first term of the sequence and n is the term number we're interested in.
Thus, the 82nd term of the sequence can be found by substituting the values into the formula: a_82 = -8 + (82 - 1) * 17 = 1369. So, the 82nd term of the given arithmetic sequence is 1369.
Learn more about Arithmetic Sequence here:https://brainly.com/question/35880655
#SPJ12
The [tex]82^{nd}[/tex] term of the arithmetic sequence -8, 9, 26, ..., is 1369.
An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. This difference is known as the common difference (d).
To find the [tex]82^{nd}[/tex] term of the given arithmetic sequence, we can use the formula for the nth term:⇒ aₙ = a₁ + (n - 1) × d
where a₁ is the first term, n is the term number, and d is the common difference.
Given the arithmetic sequence: -8, 9, 26, ...Identify the first term (a₁):⇒ a₁ = -8.
Find the common difference (d):⇒ d = 9 - (-8) = 17.
Use the nth term formula:⇒ n = 82
⇒ a₈₂ = -8 + (82 - 1) × 17
Calculate:⇒ a₈₂ = -8 + 81 × 17
⇒ a₈₂ = -8 + 1377
⇒ a₈₂ = 1369
Therefore, the [tex]82^{nd}[/tex] term of the sequence is 1369.
Complete question:
Find [tex]82^{nd}[/tex] term of the arithmetic sequence -8, 9, 26, ....
Determine the length across the river, x to the nearest hundred
Answer:
[tex]x=20.67\ ft[/tex]
Step-by-step explanation:
we know that
The Midpoint Theorem says that the line segment joining the midpoints of any two sides of a triangle is parallel to the third side and equal to half of the third side
so
in this problem
Applying the midpoint theorem
[tex]x=\frac{124}{3}:2=\frac{124}{6}=\frac{62}{3}=20.67\ ft[/tex]
What’s the best answer to 7h+3=
Answer:
Step-by-step explanation:
Incomplete question. 7h+3 is just an algebraic expression.
Find an expression for the number of squares in the nth pattern of the sequence. I noticed that the number of squares you add in each pattern it depends on the pattern number (see image) but I don't know how to get the expression.
The answer is T(n)=5(n-1)+n+1
because = T(4)=5(4-1)+4+1
=T4=5(3)+5
=T4=15+5
=T4=20
this took me half an hour
help please!!!!!!!!!!!!!
Answer:
3
Step-by-step explanation:
What Do You Mean Graphy But I Just Think It Is 3
Jackson drove 1,080 miles
in 20 hours. What was his
speed in miles per hour?
Answer:
54mph
Step-by-step explanation:
To find the speed in "miles per hour" or miles/hour, divide the number of miles by number of hours.
1080 miles/20 hours
= 54miles/hour
His speed is 54 miles per hour.
Translate this sentence into an equation.
Five less than two times Mary's age is 13.
Use the variable m for Mary's age.
Which expression has the same value as 2n + n
Answer:
3nStep-by-step explanation:
2n + n combine like terms
= 2n + 1n = (2 + 1)n = 3n
Answer:
3n
Step-by-step explanation:
2n + n Combine like terms
= 2n + 1n = (2+1)n= 3n
If and CX = 5 units, what is DZ?
The question is missing the figure. So, it is attached below.
Answer:
DZ = 4 units
Step-by-step explanation:
Given:
CD || XZ
YC = 25 units, CX = 5 units, YD = 20 units.
We know that,
If CD is parallel to XZ , then the line CD divides the sides XY and YZ of the triangle XYZ proportionally. This is true by triangle proportionality theorem.
Therefore, the lengths YC, CX, YD and DZ are in proportion. This gives,
[tex]\frac{YC}{CX}=\frac{YD}{DZ}[/tex]
Rewrite in terms of DZ. This gives,
[tex]DZ=\frac{YD\times CX}{YC}[/tex]
Plug in [tex]YC=25,CX=5,YD=20[/tex]. Solve for DZ.
[tex]DZ=\frac{20\times 5}{25}\\\\DZ=\frac{100}{25}=4[/tex]
Therefore, the length of DZ is 4 units.
Answer:
4
Step-by-step explanation:
What is the rule for 4,7,13,25,49,97
Answer:
The rule is x2 -1 (times two minus one)
4 - 1 = 3
4 + 3 = 7
7 - 1 = 6
7 + 6 = 13
13 - 1 = 12
13 + 12 = 25
25 - 1 = 24
25 + 24 = 49
49 - 1 = 48
49 + 48 = 97
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match the systems of equations with their solution sets.
y + 12 = x2 + x
x + y = 3
y - 15 = x2 + 4x
x - y = 1
y + 5 = x2 - 3x
2x + y = 1
y- 6 = x2 – 3x
x + 2y = 2
y-17 = x2 - 9x
-x + y = 1
y - 15 = -x2 + 4x
x + y = 1
Solution Set
Linear-Quadratic System of Equations
{(-2,3), (7,-6)
{(-5, 8). (3,0)
{(-2,5),(3,-5)
{(2, 3), (8,9)
Answer:
{(-2,3), (7,-6) } -----> y - 15 = -[tex]x^{2}[/tex] + 4x
x + y = 1
{(-5, 8). (3,0) } ----> y + 12 = [tex]x^{2}[/tex] + x
x + y = 3
{(-2,5),(3,-5) } -----> y + 5 = [tex]x^{2}[/tex] - 3x
2x + y = 1
{(2, 3), (8,9)} -----> y-17 = [tex]x^{2}[/tex] - 9x
-x + y = 1
Step-by-step explanation:
The simplest way to find the answer is by solving all the equations and finding the value of x and y for each of them.
Solving the equations ->
y + 12 = [tex]x^{2}[/tex] + x
x + y = 3
Substitute y = 3-x from second equation to first and solving the quadratic equation obtained i.e solving [tex]x^{2}[/tex] + 2x -15 = 0 , we get values of x = -5 , 3 and the corresponding values of y by substituting values of x in second equation , y = 8, 0 respectively. So, solution matched = {(-5, 8). (3,0) }.
Similarly solving other equations using exactly the same method as above we get the following solutions,
For,
y - 15 = [tex]x^{2}[/tex] + 4x
x - y = 1
we don't get any integer solution for this hence it has no match.
For,
y + 5 = [tex]x^{2}[/tex] - 3x
2x + y = 1
we get x = 3,-2 and corresponding y = -5,5
So, solution is {(-2,5),(3,-5) }
For,
y- 6 = [tex]x^{2}[/tex] – 3x
x + 2y = 2
we again don't get any integer solution for x and y so this has no match.
For,
y-17 = [tex]x^{2}[/tex] - 9x
-x + y = 1
we get x = 2,8 and corresponding y = 3,9
So, {(2, 3), (8,9)} is the solution match.
Lastly for,
y - 15 = -[tex]x^{2}[/tex] + 4x
x + y = 1
we get x = -2,7 and corresponding y = 3,6
So, {(-2,3), (7,-6)} is the solution match.
Does (2,1 ) make the equation true? 2x+7y>=10
Answer:
2x+7y>=10
Replace x and y with 2 and 1
2*2+7*1>=10
2*2=4
7*1=7
4+7>=10
7+4=11
2x+7y>=10 is a true statement
Because 11 is greater than 10 and it doesnt have to be equal to 10 as long as its greater.
Answer:
No. it does not
Step-by-step explanation:
(i assumed you meant 2x+7y=10)
1.) 2(2)+7y=10
2.)2(2)+7(1)=10
3.)4+7=10
4.)11=10