Answers
Answer:
21x^2-2x+1
Step-by-step explanation:
The area of shaded region= The area of the floor - area of the identical islands
The area of shaded region=(5x+1)^2-2*(2x)(x+3)=25x^2+1+10x-4x^2-12x=21x^2-2x+1
Related Questions
Point A is located at (2, 6), and point M is located at (−1, 8). If point M is the midpoint of segment AB, find the location of point B.
(5, 4)
(0.5, 7)
(0, 6)
(−4, 10)
Answers
Answer:
(−4, 10)
Step-by-step explanation:
B = (x, y)
(2 + x) ÷ 2 = -1
therefore x is -4
(6 + y) ÷ 2 = 8
therefore y is 10
Feel free to message me if you still have questions :)
The coordinate point of point B (x₁, y₁) will be (−4, 10). Then the correct option is D.
What is coordinate geometry?Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.
Point A is located at (2, 6), and point M is located at (−1, 8). If point M is the midpoint of segment AB.
Then the coordinate of the point B(x₁, y₁) will be
We know that the mid-point formula
[tex]\rm (x,y) \ \ = \left ( \dfrac{x_2+x_1}{2}, \dfrac{y_2+y_1}{2} \right )\\\\(-1, 8) = \left ( \dfrac{2+x_1}{2}, \dfrac{6+y_1}{2} \right )[/tex]
Then the value of x₁ and y₁ will be
[tex]\rm x_1 = -4\\\\y_1 = 10[/tex]
Then the coordinate point of B (x₁, y₁) is (−4, 10).
More about the coordinate geometry link is given below.
https://brainly.com/question/1601567
simplify
(−5abc − 6ac + 7cb) − (10abc + 6ac − 8bc)
Answers
Answer:
-15abc - 12ac + 15bc
General Formulas and Concepts:
Pre-Algebra
Distributive PropertyAlgebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
Identify
(-5abc - 6ac + 7cb) - (10abc + 6ac - 8bc)
Step 2: Simplify
[Distributive Property] Distribute negative: -5abc - 6ac + 7cb - 10abc - 6ac + 8bcCombine like terms: -15abc - 12ac + 15bcFind the 20th term of the following sequence.
-6, -4,-2, O,...
Answers
Step-by-step explanation:
An=-6+(20-1)×2
=-6+19(2)
=-6+38
=32
Marcel invests $2500 for 3 years at a rate of 1.6% per year simple interest. Jacques invests
$2000 for 3 years at a rate of x% per year compound interest.
At the end of the 3 years Marcel and Jacques receive the same amount of interest.
Calculate the value of x correct to 3 significant figures.
Answers
Answer:
x= 1.961
Step-by-step explanation:
Marcel's ,P = 2500 , T = 3, R = 1.6%
SI = PRT/100
=(2500×1.6×3)÷100
Jacques's , P = 2000 , T = 3, R = x%
CI = P( 1 + R/100)^T -P
2000(1 + x/100)^3 -2000
But this is equal to 120
(1 + x/100)^3 = 2120/2000
x= 1.961
I hope this helps !!!!!!!!!!!
A square pyramid has a base with an area of 20 square meters, and its lateral faces have a slant height of x meters. Sydney is constructing a second square pyramid with the same size base, but the lateral faces of her pyramid have a slant height twice as long, 2x. Which statement best describes how the surface area of Sydney’s pyramid compares to the surface area of the original pyramid?
Sydney’s pyramid will have the same surface area because the One-half in the expression for the area of the triangular faces will make up for the slant height being doubled.
Sydney’s pyramid will have the same surface area because the slant height is not used when finding surface area.
Sydney’s pyramid will have a surface area that is exactly double the original pyramid’s because the slant height is used when finding the area of every lateral face.
Sydney’s pyramid will have a surface area that is greater than the original pyramid’s but not double the area because the slant height is not used when finding the area of the base.
Answers
1. Consider the pyramid ABCDE in the figure 1 attached:
Each side of the square base equals (units)
Area of 1 lateral side of pyramid ABCDE is
so the total lateral area is (units squared)
and the total surface area is (units squared)
2. Now consider the second figure KLMNP, Sydney's pyramid:
The lateral area is
so the total area of the second pyramid is
So 2 things can be said about the areas:
i) the lateral area of Sydney's pyramid is times larger than the lateral area of the original pyramid.
ii) The total area of Sydney's pyramid is units squared larger than the total area of the original pyramid.
Which equation can be used to find the number of students needed to make 1,500 in profit ?
Answers
Answer:
we can use simple equation
hich math expression means "the product of 16 and 26"?
O 16 - 26
26-16
16 - 26
0 16 +26
Answers
Answer:
infjfkflflfmdbfufifldndndhfififkfnf
I need help and fast I was supposed to turn this in last week
Answers
Answer:
The answer is below
Step-by-step explanation:
If two lines intersected by a transversal form congruent corresponding angles, then the lines are parallel.
If two angles are supplementary to the same angle, then the two angles are congruent.
Statement Reason
1) line p is parallel to line q Given
2) angle 1 and angle 4 are Given
supplementary i.e. ∠1 + ∠4
= 180° (definition of supplementary)
3) angle 3 and angle 4 are consecutive interior angles
supplementary
4) angle 1 congruent to angle 3 congruent supplements theorem
supplementary
5) line r parallel to line s corresponding angle converse
Write the equivalent fraction, the reduced fraction, and the decimal equivalent for 45%. Jenny solved this problem and her work is shown below. What mistake did she make? 45% = StartFraction 45 Over 100 EndFraction = StartFraction 9 Over 20 EndFraction = 4.5
Answers
Answer: See explanation
Step-by-step explanation:
The equivalent fraction of 45% is solved as follows:
First, we'll change the percentage to fraction which will be:
45% = 45/100
Then, we'll reduce to lowest term which will be:
45/100 = 9/20
Now, we'll convert the fraction to decimal which will be:
9/20 = 0.45
The mistake that Jenny made was that she divided 90 by 20. This will give 4.5.
Answer: The decimal equivalent is not correct. The decimal point is in the wrong position. The decimal point should be to the left of the 4, so the correct answer is 0.45.y-step explanation:
A batch of peanut butter cookies requires \dfrac34 4 3 start fraction, 3, divided by, 4, end fraction of a jar of peanut butter. You want to make 333 batches. How many jars of peanut butter do you need?
Answers
Answer: 3 Jars
Step-by-step explanation:
Given
A batch of peanut butter cookies requires [tex]\frac{3}{4}[/tex] of a jar
For 3 batches of Cookies, No of Jars required
[tex]\Rightarrow 3\times \dfrac{3}{4}=\dfrac{9}{4}\\\\\Rightarrow \dfrac{9}{4}=2+\dfrac{1}{4}[/tex]
That is 2 complete Jar and one-fourth of third. In totality, it would be 3
jars.
find the inverse of the following function
Answers
f-¹(x)=[tex]\frac{2-7x}{x+2}[/tex]
Answer:
Solution given:
f(x)=[tex]\frac{-2x+2}{x+7}[/tex]
Let f(x)=y
y=[tex]\frac{-2x+2}{x+7}[/tex]
Interchanging role of x and y
x=[tex]\frac{-2y+2}{y+7}[/tex]
doing crisscrossed multiplication
x(y+7)=-2y+2
now solve it:
xy+7x=-2y+2
keep like terms in one side
xy+2y=2-7x
take common
y(x+2)=2-7x
make a value of y
y=[tex]\frac{2-7x}{x+2}[/tex]
So,
f-¹(x)=[tex]\frac{2-7x}{x+2}[/tex]
Answer:
ƒ^-1 (x) = [tex]\frac{2-7x}{2+x}[/tex]
Step-by-step explanation:
Substitute y for f (x)
[tex]y = \frac{-2x+2}{x+7}[/tex]
Interchange x and y
[tex]x=\frac{-2y+2}{y+7}[/tex]
Swap the sides of the equation
[tex]\frac{-2y+2}{y+7} = x[/tex]
Multiply both sides of the equation by y + 7
-2y + 2 = (y + 7)x
Distribute x through the parentheses
-2y + 2 = xy + 7x
Move the expression/constant to the left-hand side and change its sign
-2y - xy + 7x - 2
Factor out from the expression
(-2 - x)y = 7x - 2
Divide both sides of the equation by -2 - x
[tex]y = \frac{7x-2}{-2-x}[/tex]
Simplify the expression
[tex]y = \frac{2-7x}{2+x}[/tex]
Substitute ƒ ^-1 (x) for y
[tex]f^{-1} (x) = \frac{2-7x}{2+x}[/tex]
Anyone knows the answer?
Answers
Answer:
a) yes
b) y = -x
c) yes it goes thru the origin (0,0)
Step-by-step explanation:
a) x**2 + y**2 = 17
(-4)**2 + (-1)**2 = 17
16 + 1 = 17 YES
b) the slope of DE is
(y1 - y2)/(x1 - x2)
(-1 -4)/(-4 -1) = -5/-5 = 1, so a perpendicular segment will have a
slope of - 1/current slope or -1.
The midpoint of DE is
x = (x1 + x2)/2 = (-4 +1)/2 = -3/2
y = (y1 + y2)/2 = (-1 +4)/2 = 3/2 so
y = mx + b
y = -x + b plug in the point (-3/2,3/2)
3/2 = -(-3/2) + b
b = 0 SO y = -x
c) The circle equation dictates that it has no offset so centers around the origin (0,0) and the equation of the bisector y = -x indeed fits (0,0).
A salesman sold twice as much pears in the afternoon than in the morning. If he sold 360 kilograms of pears that day, how many kilograms did he sell in the morning and how many in the afternoon?
Answers
Answer:
120 kg in morning and 240 kg in afternoon
Step-by-step explanation:
x+2x=360 kg
Work:
x + 2x = 360 kg
3x = 360 kg
3x/3 = 360 kg/3
x = 120
2x=2(120 kg) =240 kg
Final Answer:
So, 120 kg in morning and 240 kg in the afternoon.
Hope this helps!
Please help me solve this!
Please help quickly!
Answers
==========================================================
Explanation:
Focus on triangle TUS. The inner angles here are:
T = yU = xS = 180-2xNote how the angle measure for S is the supplement of 2x, which is adjacent to the angle S we have.
Add up those three angles and set the sum equal to 180
T+U+S = 180
y+x+180-2x = 180
y-x = 180-180
y-x = 0
y = x
We'll use this later.
-----------------
The diagram shows that angle VTU = y+y = 2y.
Focus your attention on triangle TUV.
Since TU = UV, this means the base angles T and V (which are opposite the congruent sides) are congruent angles. We found that angle T was 2y earlier. This means angle V is also 2y.
-----------------
Now shift your focus to triangle TSV.
This triangle has the inner angles
S = 2xT = yV = 2yRecall earlier that we found y = x at the conclusion of the first section. Using that and the fact that the angles of triangle TSV add to 180, we get...
T+S+V = 180
2x+y+2y = 180
2x+3y = 180
2x+3x = 180 .... replace y with x, since y = x
5x = 180
x = 180/5
x = 36
This is the value of y as well.
What is the best approximate for the input value when f(x)=g(x)?
Answers
Answer:
(1.5 ,1)
Step-by-step explanation:
f(x) = g(x) where the two graphs intersect
x=1.5 and y = 1
(1.5 ,1)
Combine and simplify the following radical expression
Answers
Answer:
[tex]2 \sqrt[3]{3} [/tex]Step-by-step explanation:
[tex] \sqrt[3]{6} . \sqrt[3]{4} [/tex]
[tex] = \sqrt[3]{6 \times 4} [/tex]
[tex] = \sqrt[3]{3 \times 2 \times 2 \times 2} [/tex]
[tex] = 2 \sqrt[3]{3} (ans)[/tex]
25 x square - 4y Square = 36 equation 1
5 x - 2 y=2equation 2
Answers
It is hard to find out question cn u pls take a pic and upload so it will more easier to find out the question
for what is values of x does 4(3x-2) = 12x - 5? select all that apply.
A.12
B.-8
C.3
D.-3
E.none of these
Answers
Answer:
‼️A) 12‼️
Step-by-step explanation:
Key skills needed: Interior Angle Measure Theorem, Equation Creation
Step 1) First, we need to classify this shape. It has 7 sides, which means that we can use the Interior angle Theorem to find out the sum of all the interior angle measures
The theorem is: S = (n - 2)180S=(n−2)180
S is the sum of all interior angle measures
n is the number of sides of the polygon
Step 2) With this, we can plug in 7 for "n" (Since the figure has 7 sides) and get:
---> S = (7-2)180S=(7−2)180
---> (7-2) is 5 since 7 - 2 = 5 so --> S = 5(180)S=5(180)
---> 5(180) is the same as 5 x 180 which is 900 so --> S = 900S=900
This means that the sum of all interior angles is 900 degrees.
Step 3) Now, we have to find out the sum of all the angles that they gave us so:
---> 10x + 10x + 9 + 133 + 9x + 14 + 12x - 9 + 10x + 5 + 136 = 90010x+10x+9+133+9x+14+12x−9+10x+5+136=900
The left side is the sum of all interior angles in the shape, and the right side is what the sum should be when expressed as a number.
Step 4) We have to combine all like terms on the left side:
---> 10x + 10x + 9x + 12x + 10x = 51x10x+10x+9x+12x+10x=51x
---> 9 + 133 + 14 -9+5+136 = 2889+133+14−9+5+136=288
Step 5) This means that ---> 51x + 288 = 90051x+288=900
Subtract 288 from both sides and get:
---> 51x = 61251x=612 (900-288 = 612)
Then divide by 51 from both sides and get:
---> x = 12x=12 (612 ÷ 51 = 12)
Therefore A) 12 is your answer.
I think it should be none of these.
The term on the left has to be even no matter what value of x and the right has to be odd no matter what value of x. Therefore, there shouldn't be an integer value of x that satisfies the equation, let alone the answer choices A-D.
Which is the graph of the linear inequality {x-2y> -6?
Answers
Answer:
7
Step-by-step explanation:
Answer:
I think it is d
Step-by-step explanation:
Passing through point (4, 9) and perpendicular to the line y= -1/5x -3
Answers
Answer:
y = 5x-11
Step-by-step explanation:
The slope intercept form of a line is y =mx+b where m is the slope
y = -1/5 x-3
The slope is -1/5
Lines that are perpendicular have negative reciprocal slopes
-1 /(-1/5)
-1 * -5/1
5
The slope of the line that is perpendicular is 5
y=5x+b
Using the point (4,9)
9 = 5(4)+b
9 = 20+b
9-20 =b
-11
y = 5x-11
Solve for the product (6x−−√)(15x3−−−−√)without a perfect square factor in the radicand. Group of answer choices 90x4−−−−√ 3x210−−√ 310x4−−−−√ 3x410−−√
Answers
Answer:
[tex]3x^{2} \sqrt10[/tex]
Step-by-step explanation:
There are nine different marbles in a bag. Supposed you reach in and draw one at a time. And do this three times. How many ways can you draw the three marbles if you do not replace the marble each time
Answers
Answer: 504 ways
Step-by-step explanation:
Given
There are nine different marbles in a bag
For the first time, there are 9 possible ways to draw a marble
After removal of first marble, there are 8 possible ways to draw a marble
for the third time, there are 7 possible ways
so, total ways to draw three marble are
[tex]\Rightarrow 9\times 8\times 7=504\ \text{ways}[/tex]
Now that you know the vertex, find the y-values that pair with a few x-values that are less than 2 and a few that are greater than 2.
Plsssss help!!!!!!!
Answers
y when x=1: 2
y when x=3: 2
y when x=4: 3
Write the words that represent s + 21.
Answers
Answer:
A number s plus 21
Step-by-step explanation:
s+21
A number s plus 21
David's goldfish ate 20 grams of food in 4 weeks. At this rate, how long would it take the fish to eat the food
in a 100-gram container?
Answers
Please help:)))))))))))
Answers
Answer:
good evening good evening good evening good evening
congruent figure help please :)
Answers
Answer:
x = 29
Step-by-step explanation:
ΔABC ≅ ΔDEC,
So, ∠BAC ≅∠CDE {Corresponding parts of congruent triangles}
∠BAC = 74°
InΔABC,
∠ABC + ∠BAC + ∠BCA = 180
2x + 74 + 48 = 180
2x + 122 = 180
Subtract 122 from both sides
2x = 180 - 122
2x = 58
Divide both sides by 2
x = 58/2
x = 29
please help with this too
Answers
Answer:
The area of the sector in circle G formed by segments [tex]\overline{AG}[/tex], and [tex]\overline {GB}[/tex] is approximately 125.66 square units
Step-by-step explanation:
The given parameters are;
The radius of the circle with center G, r = 15
The measure of the given angle, m∠AGB = 64°
The area of a sector is given as follows;
Area of a sector of a circle = (θ/360°) × π × r²
Therefore;
The area of the sector in circle G formed by segments [tex]\overline{AG}[/tex], and [tex]\overline {GB}[/tex] is given as follows;
The area of the sector in circle G = (64°/360°) × π × 15² ≈ 125.66 square units
Do someone mind helping me pls :)
Answers
=========================================================
Explanation:
The uppercase E represents "ten to the"
So saying E8 means "ten to the 8th power"
In other words, 9.837 E 8 = 9.837 * 10^8
The exponent positive 8 tells us to move the decimal point over to the right 8 spots.
So that's how we go from 9.837 * 10^8 to 983,700,000
There are 5 zeros in that value after the "9837" portion.
When we move from 9.837 to 9837.0, that's exactly 3 spots so far. Then the decimal point has to move another 5 spots to go from 9837.0 to 983,700,000 which is therefore 3+5 = 8 total shifts to the right.
The number 983,700,000 is slightly over 983 million. If anything, it's more closer to 984 million.
Answer: Standard Form = 983, 700, 000
Step-by-step explanation:
Concept:
The term "E" is usually used in calculators or on-screen which stands for exponents. It has been used to display numbers in scientific notations.
Scientific notation is a form of presenting very large numbers or very small numbers in a simpler form. Usually in the form of [ a × 10ᵇ ] where a is a number 0<a<10 and b are integer exponents.
"E" in simpler words is basically the base "10" in scientific notation, while the number after "E" would be the exponents on "10"
Solve:
Given = 9.837 E 8
"E" = 10
"8" = ⁸
E 8 = 10⁸
10⁸ basically means that there are 8 zeros after 1.
Therefore, to find the standard form of 9.837E8, we have 3 zeros to get 9.837 to become an integer, then add the remaining 5 zeros at the end to get the final answer.
9.837 × 10⁸ = 983,700,000Hope this helps!! :)
Please let me know if you have any question
simplify (4^3)^5 someone help
Answers
Answer:
Exact Form:
235235
Decimal Form:
4.64.6
Mixed Number Form:
4 3/5
Answer:
5649
Step-by-step explanation:
4^3=64
64^5=5649
