[tex](2x-y)(3x+y)\\\\=2x(3x+y) -y(3x+y)\\\\=6x^2 +2xy - 3xy -y^2\\\\=6x^2 -xy -y^2[/tex]
consider the following :
[tex]f(x) = {x}^{2} - x + 2 \div x - 2 = x + 1 + 4 \div x - 2[/tex]
which polynomials do you think we should call the divisor,dividend,quotient and remainder ?
Step-by-step explanation:
remainder=4
quotient=x+1
divisor=x-2
dividend=x^2 -x +2
Find the equation for the linear function based upon this table. y = mx + b
y -6 -2 2 6 10
x -4 -2 0 2 4
Answer:
y = 2x + 2
Step-by-step explanation:
for each rise of 4 in y
there is a run of 2 in x
m = rise/run
m = 4/2
m = 2
when x = 0, y = 2
therefor the y-intercept, b = 2
y = mx + b
y = 2x + 2
At a store, 4 shirts cost $25 and 6 shirts cost $37.50.
Part A:
Is there a proportional relationship between the shirts and their cost? If so, what is the unit rate for one shirt?
A radio tower is located 425 feet from a building. From a window in the building, a person determines that the angle of elevation to the top of the tower is 30 ∘ ∘ and that the angle of depression to the bottom of the tower is 26 ∘
. How tall is the tower?
The height of the tower is 452.66 ft
The situation will form 2 right angle triangle. One above the line of sight
and one below the line of sight.
Therefore,
Using trigonometric ratio,
tan ∅ = opposite / adjacent side
tan 30° = h(top of the tower) / 425
h(top of the tower) = tan 30 × 425 = 245.373864406
tan 26° = h(bottom of the tower) / 425
h(bottom of the tower) = 425 × tan 26° = 207.28635014
Therefore,
Height of tower = h(top of the tower) + h(bottom of the tower)
Height of tower = 245.37 + 207.29 = 452.66 ft
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Given:In quadrilateral WXYZ , and bisect each other at point A.
Prove: Quadrilateral WXYZ is a parallelogram.
Statement
Reason
1. and bisect each other. given
2. WA = YA
XA = ZA
definition of bisection
3. m∠YAZ = m∠XAW
Vertical Angles Theorem
4.
SAS criterion for congruence
5. ∠ YWX ≅ ∠WYZ
Corresponding angles of congruent triangles are congruent.
6. ||
converse of Alternate Interior Angles Theorem
7. m∠XAY = m∠ZAW
Vertical Angles Theorem
8. ∆XAY ≅ ∆ZAW
SAS criterion for congruence
9. ∠XZW ≅ ∠ZXY
Corresponding angles of congruent triangles are congruent.
10. ||
converse of Alternate Interior Angles Theorem
11. Quadrilateral WXYZ is a
parallelogram.
definition of parallelogram
Answer:
Given:In quadrilateral WXYZ , and bisect each other at point A.
Prove: Quadrilateral WXYZ is a parallelogram.
Statement
Reason
1. and bisect each other. given
2. WA = YA
XA = ZA
definition of bisection
3. m∠YAZ = m∠XAW
Vertical Angles Theorem
4.
SAS criterion for congruence
5. ∠ YWX ≅ ∠WYZ
Corresponding angles of congruent triangles are congruent.
6. ||
converse of Alternate Interior Angles Theorem
7. m∠XAY = m∠ZAW
Vertical Angles Theorem
8. ∆XAY ≅ ∆ZAW
SAS criterion for congruence
9. ∠XZW ≅ ∠ZXY
Corresponding angles of congruent triangles are congruent.
10. ||
converse of Alternate Interior Angles Theorem
11. Quadrilateral WXYZ is a
parallelogram.
definition of parallelogramTriangles can be similar or congruent. Similar triangles will have congruent angles but sides of different lengths. Congruent triangles will have completely matching angles and sides. Their interior angles and sides will be congruent. Testing to see if triangles are congruent involves three postulates, abbreviated SAS, ASA, and SSS.
What do you call raising a base to the exponent 2
Answer:
Squaring
Step-by-step explanation:
How do I determine z ∈ C:
[tex](\frac{3-2i}{1+i} - \frac{5+3i}{1+2i} )z = \frac{1}{2} - \frac{2}{5}i[/tex]
Simplify the coefficient of z on the left side. We do this by rationalizing the denominators and multiplying them by their complex conjugates:
[tex]\dfrac{3-2i}{1+i} - \dfrac{5+3i}{1+2i} = \dfrac{3-2i}{1+i}\cdot\dfrac{1-i}{1-i} - \dfrac{5+3i}{1+2i}\cdot\dfrac{1-2i}{1-2i}[/tex]
[tex]\dfrac{3-2i}{1+i} - \dfrac{5+3i}{1+2i} = \dfrac{(3-2i)(1-i)}{1-i^2} - \dfrac{(5+3i)(1-2i)}{1-(2i)^2}[/tex]
[tex]\dfrac{3-2i}{1+i} - \dfrac{5+3i}{1+2i} = \dfrac{3 - 2i - 3i + 2i^2}{1-(-1)} - \dfrac{5 + 3i - 10i - 6i^2}{1-4(-1)}[/tex]
[tex]\dfrac{3-2i}{1+i} - \dfrac{5+3i}{1+2i} = \dfrac{3 - 5i + 2(-1)}2 - \dfrac{5 - 7i - 6(-1)}5[/tex]
[tex]\dfrac{3-2i}{1+i} - \dfrac{5+3i}{1+2i} = \dfrac{1 - 5i}2 - \dfrac{11 - 7i}5[/tex]
[tex]\dfrac{3-2i}{1+i} - \dfrac{5+3i}{1+2i} = \dfrac{1 - 5i}2\cdot\dfrac55 - \dfrac{11 - 7i}5\cdot\dfrac22[/tex]
[tex]\dfrac{3-2i}{1+i} - \dfrac{5+3i}{1+2i} = \dfrac{5 - 25i - 22 + 14i}{10}[/tex]
[tex]\dfrac{3-2i}{1+i} - \dfrac{5+3i}{1+2i} = -\dfrac{17 + 11i}{10}[/tex]
So, the equation is simplified to
[tex]-\dfrac{17+11i}{10} z = \dfrac12 - \dfrac{2i}5[/tex]
Let's combine the fractions on the right side:
[tex]\dfrac12 - \dfrac{2i}5 = \dfrac12\cdot\dfrac55 - \dfrac{2i}5\cdot\dfrac22[/tex]
[tex]\dfrac12 - \dfrac{2i}5 = \dfrac{5-4i}{10}[/tex]
Then
[tex]-\dfrac{17+11i}{10} z = \dfrac{5-4i}{10}[/tex]
reduces to
[tex]-(17+11i) z = 5-4i[/tex]
Multiply both sides by -1/(17 + 11i) :
[tex]\dfrac{-(17+11i)}{-(17+11i)} z = \dfrac{5-4i}{-(17+11i)}[/tex]
[tex]z = -\dfrac{5-4i}{17+11i}[/tex]
Finally, simplify the right side:
[tex]-\dfrac{5-4i}{17+11i} = -\dfrac{5-4i}{17+11i} \cdot \dfrac{17-11i}{17-11i}[/tex]
[tex]-\dfrac{5-4i}{17+11i} = -\dfrac{(5-4i)(17-11i)}{17^2-(11i)^2}[/tex]
[tex]-\dfrac{5-4i}{17+11i} = -\dfrac{85 - 68i - 55i + 44i^2}{289-121(-1)}[/tex]
[tex]-\dfrac{5-4i}{17+11i} = -\dfrac{85 - 68i - 55i + 44(-1)}{410}[/tex]
[tex]-\dfrac{5-4i}{17+11i} = -\dfrac{41 - 123i}{410}[/tex]
[tex]-\dfrac{5-4i}{17+11i} = -\dfrac{41 - 41\cdot3i}{410}[/tex]
[tex]-\dfrac{5-4i}{17+11i} = -\dfrac{1 - 3i}{10}[/tex]
So, the solution to the equation is
[tex]z = -\dfrac{1-3i}{10} = \boxed{-\dfrac1{10} + \dfrac3{10}i}[/tex]
a small square garden has an area of 25 square yards. how long is each side of the garden?
Answer:
Step-by-step explanation:
A square has an area of base times height which is identical to base.
If x is the length of a side, A = x•x = x²
x² = 25
x = √25
x = 5 yards
can i have some help pls
Answer:
the first recipe
Step-by-step explanation:
We can answer by finding the ratio of nuts to cereal. The one that has the higher ratio of nuts to cereal is the nuttier one.
Recipe 1: 2 1/2 cups of nut per 5 cups of cereal.
nuts to cereal ratio = 2 1/2 : 5 = 1 : 2
Recipe 2: 1 cups of nuts per 3 cups of cereal.
nuts to cereal ratio = 1 : 3
1 : 2 is a higher ratio than 1 : 3
Answer: the first recipe
A die is weighted in such a way that each of 2, 4, and 6 is twice as likely to come up as each of 1, 3, and 5. Find the probability
distribution?
Considering that each of 2, 4, and 6 is twice as likely to come up as each of 1, 3, and 5, the probability distribution is given by:
[tex]P(X = 1) = 0.1111[/tex]
[tex]P(X = 2) = 0.2222[/tex]
[tex]P(X = 3) = 0.1111[/tex]
[tex]P(X = 4) = 0.2222[/tex]
[tex]P(X = 5) = 0.1111[/tex]
[tex]P(X = 6) = 0.2222[/tex]
The symbolic distribution is:
[tex]P(X = 1) = y[/tex]
[tex]P(X = 2) = x[/tex]
[tex]P(X = 3) = y[/tex]
[tex]P(X = 4) = x[/tex]
[tex]P(X = 5) = y[/tex]
[tex]P(X = 6) = x[/tex]
The sum of all probabilities is 1, hence:
[tex]3x + 3y = 1[/tex]
Simplifying by 3:
[tex]x + y = 0.3333[/tex]
[tex]y = 0.3333 - x[/tex]
2, 4, and 6 is twice as likely to come up as each of 1, 3, and 5, hence:
[tex]x = 2y[/tex]
[tex]x = 2(0.3333 - x)[/tex]
[tex]3x = 0.6667[/tex]
[tex]x = \frac{0.6667}{3}[/tex]
[tex]x = 0.2222[/tex]
Then:
[tex]y = 0.3333 - x = 0.3333 - 0.2222 = 0.1111[/tex]
Hence, the distribution is:
[tex]P(X = 1) = 0.1111[/tex]
[tex]P(X = 2) = 0.2222[/tex]
[tex]P(X = 3) = 0.1111[/tex]
[tex]P(X = 4) = 0.2222[/tex]
[tex]P(X = 5) = 0.1111[/tex]
[tex]P(X = 6) = 0.2222[/tex]
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You invest AED 5000 in a saving account that earns 4% interest each year. If you do not use the account for a year, how much money will you have in your account after a year?
Answer:
5200 AED or 1404 USD
Step-by-step explanation:
You have 5000 in your account. If your money grows 4% each year, it's basically like multiplying by 1.04.
5000 * 1.04 = 5200
If the question is asking in USD, the conversion rate from AED to USD is
AED * 0.27 = USD
We can substitute
5200 AED* 0.27 = 1404 USD.
what is 282.74 in terms of pi
Answer:
90π
Step-by-step explanation:
282.74 / π
282.74 / 3.14159 = 90
282.74 = 90π
grahm's birthday Is on 26th May which day of the week Is his birthday?
Answer:
Wednesday, 2021,Thursday, 2022
Make g the subject of the formula r = 4g +7
Answer:
4 better explanation inbox
Step-by-step explanation:
How many solutions are there to the equation shown below?
4(2x−3)−2x=6x+8
pls answer ASAP I will give brainliest to the first
Answer:
0 = 20
Step-by-step explanation:
4(2x−3)−2x=6x+8
8−12−2=6+8
combine like terms.
8x−12−2x=6x+8
6−12=6+8
Add 12 to both sides of the equation
6x−12=6x+8
6−12+12=6+8+12.
: Two manufacturers supply paper cups to a catering service. Manufacturer A supplied 100 packages and 5 were damaged. Manufacturer B supplied 50 packages and 3 were damaged. If a package is damaged, find the probability that it came from Manufacturer A.1 I.e., Find probability P(Manu
If a package is damaged, the probability that it came from Manufacturer A is 62.5%.
Given that two manufacturers supply paper cups to a catering service, and manufacturer A supplied 100 packages and 5 were damaged, while Manufacturer B supplied 50 packages and 3 were damaged, to determine, if a package is damaged, the probability that it came from Manufacturer A, the following calculation must be performed:
5 + 3 = 100 5 = X 5 x 100/8 = X 62.5 = X
Therefore, if a package is damaged, the probability that it came from Manufacturer A is 62.5%.
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D.Solve the following problems.Show your solution
1.A boy ran a distance of 5.8 kilometers. How many meters did he run?
2. Jose walks 378 meters while Rene walks 0.67 kilometers.What is the difference between the distances which they walked,in centimeters
SHOW YOUR SOLOTION PLSSS
I will ggive u points
sana
no link no bot please right fast but right
Answer:
12 in
Step-by-step explanation:
3in + 3in + 3in + 3in = 12
Which equation has the correct sign on the product?
a. 27(-5)=-135
b. 22 x 4= -88
c. (-4)(-4)= -16
d. (-61)(3)= 183
Answer: a.
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The difference of a number and six is negative four
What is the equation of the line in slop-intercept form?
Enter your answer in the blank spots
y= __x + __
Answer:y=2.5x+5 i thank
Step-by-step explanation:
Round your answer to the Nearest tenth
Answer:
3.3 or [tex]\frac{56}{17}[/tex]
Step-by-step explanation:
v/7 = 8/17
Cross multiply ... v times 17 & 7 times 8
17v = 56
Divide both sides by 17
v = 56/17
Keep your answer as a fraction OR
Convert to a decimal : 3.3
Find the angles of a triangle which are in the ratio 4:3:2.
Answer:
80o, 60o, 40o
Step-by-step explanation:
The sum has to add up to 180 degrees because of the three sides and this is what matches.
Answer:
Let the given angles of the triangle be 4x, 3x and 2x.
We know that the sum of all interior angles of a triangle is 180°.
Therefore,
4x+3x+2x = 1809x = 180x = 180/9x = 20Hence, the angles of the triangle are -
4x = 4×20 = 80°3x = 3×20 = 60°2x = 2×20 = 40°What is the length of CD, given that figure ABCD is a rectangle?
B
13
С
10
A
D
O A. 26
O B. 10
O C. 13
O D. 20
Answer:
It'll be B.10
Step-by-step explanation:
Rectangles always have 2 side lower than the other2 . BC and AD are same length so they are both 13. BA and CB are the same length to It has to be 10.
Hope this helps :)
y=3x+5 what are the missing values
A.) ONLY (2,11)
B.) ONLY (3,13)
C.) BOTH (2,11) and (3,13)
D.) NEITHER
Answer:
A
Step-by-step explanation:
so first substitute 2 into the x so 3*2=6 then and 5+6= 11 then substitute 11 into the y and boom it works. (3,13) doesnt work because if you substitute them in 3*3=9 then 9+5=14 but we needed 13 so only (2,11) works.
1. Write the equation of a horizontal line that passes through the point (–2, 2). x = –2 y = –2 y = 2 x = 2
Answer:
x = 2
Step-by-step explanation:
The given point is (-2, 2). A horizontal line passing through this point is x = 2.
What is the value of y in the following system of equation3x-4y=-20 -x+2y=10
What is 5 times 9 divided 5 add 40 subtract 100
Answer:
-51
Step-by-step explanation:
please help meeeee c:
Answer:
x = - 2
Step-by-step explanation:
Don't let the points disturb you. They are actually meant to confuse you.
plzz help don't understand
Answer:
3b
Step-by-step explanation:
[tex]3\sqrt{b^{2} }[/tex]
= 3b