[tex] \: \: \: \: \: \: \: \: \: \: \: \large\underline{\bf{ANSWER}}[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: [/tex]
[tex] \tt↠(y^2+6)(−2y^2+7)[/tex]
[tex]\tt↠(-2y^2+7)y^2+6(-2y^2+7)[/tex]
[tex]\tt↠-2y^4+7y^2+6(−2y^2+7)[/tex]
[tex]\tt↠-2y^4+7y^2-12y^2+42[/tex]
[tex]\tt↠-2y^4-5y²+42[/tex]
Answer:
-2y⁴ - 5y² + 42
Step-by-step explanation:
[tex](y^2 + 6)(-2y^2 + 7)[/tex]
[tex]\mathrm{Apply\:FOIL\:method}:\quad \left(a+b\right)\left(c+d\right)=ac+ad+bc+bd[/tex]
Here First terms are
[tex]y^2 \textrm{ and } -2y^2\\(y^2)(-2y^2) = -2y^4[/tex]
Outer terms are y² and 7 ==> (y²)(7) = 7y²
Inner terms are 6 and -2y² ==> 6(-2y²) = -12y²
Last terms are 6 and 7 ==> 6.7 = 42
So result is obtained by adding all these terms
-2y⁴ + 7y² - 12² + 42 ==> -2y⁴ - 5y² + 42
Find the volume of the prism.
Answer:
V = 343
Step-by-step explanation:
V = lwh
= 7(7)(7)
= 49(7)
= 343
Is this graph a function ?
Please help
Answer:
Yes
Step-by-step explanation:
To find out whether or not a graph is a function, we can do the vertical line test. If the vertical line only touches one point, then the graph is a function. This is because in a function, an input can only have one output.
1. If f={(-1,6), (0,3), (2,9), (6,10)} and g={(0,2), (3,7), (12,3)}, what is (fog)(0)?
(a) 9
(b) 3
(c) 2
(d) 7
Answer: 9
Step-by-step explanation:
[tex](f \circ g)(0)=f(g(0))\\\\g(0)=2\\\\\implies f(g(0))=f(2)=\boxed{9}[/tex]
What values of a and b make this equation true?
Answer:
a = -4
b=-29
Step-by-step explanation:
Complex number:First write the radicals in simplest form.
i² = -1
[tex]\sf (4 + \sqrt{-49}) -2\left(\sqrt{(-4)^2}+\sqrt{-324}\right)=4 + \sqrt{49i^2} - 2\left(\\\sqrt{16}+\sqrt{324i^2}\right)[/tex]
[tex]\sf =4 + \sqrt{7*7*i*i}-2\left(\sqrt{4*4}+\sqrt{18*18*i*i}\right)\\\\= 4 + 7i - 2(4 + 18i)\\\\= 4 + 7i - 2*4 - 2*18i\\\\= 4 + 7i -8-36i\\\\= 4 - 8 +7i - 36i\\\\= -4 - 29i[/tex]
[tex]\sf \boxed{a = -4 }\\\\\boxed{b=-29}[/tex]
Which of the lines is the graph of x=1−y?
Answer:
y = -x + 1
(Image of what graph looks like is attached)
Step-by-step explanation:
x = 1 - y can be rewritten into y = mx + b format.
x = 1 - y (subtract 1 from both sides)
x - 1 = -y (multiply by -1 to both sides)
y = -x + 1
Brainliest, please :)
Hamza buys a car for £900 and sells it for £1,280. Write the sale price as a percentage of the original price. Give your answer to the nearest whole percent and include the % symbol.
The sale price of the car as a percentage of the original price is 142%
PercentageCost of buying = £900Cost of selling = £1,280Sale price as a percentage of the original price = sale price / buying price
= 1280/900 × 100
= 1.42222222222222 × 100
= 142.22%
Approximately,
142%
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Tim Hortons is hiring and offers $200 every week plus $5 per hour. McDonalds offers $300 every week plus $2 per hour. State the conditions under which Tim Hortons is the better employer.
Answer: After working for 33 [tex]\frac{1}{3}[/tex] hours a week
Step-by-step explanation:
Let us write equations to represent these two places. Let x be hours worked and y be money earned.
Tim Hortons:
$200 + $5x = y
McDonalds:
$300 + $2x = y
Now, to find the conditions of which Tim Hortons is the better employer (on the basis of money earned) we must find the interval that Tim Hortons pays more. This can be found by setting up another equation, or by graphing. I have shown both. See attached for the graph.
$200 + $5x > $300 + $2x
$5x > $100 + $2x
$3x > $100
x > [tex]\frac{100}{3}[/tex]
x > 33.3334
Tim Hortons is the better employer after an employee has worked for 33 [tex]\frac{1}{3}[/tex] hours a week.
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The length and width of a rectangle are consecutive integers. The perimeter of the rectangle is 30 meters. Find the length and width of the rectangle.
The length of the rectangle is 8m and width of the rectangle is 7m
The perimeter of a rectangle is the total length around the outside of rectangle. The total boundary of the rectangle is its perimeter If length of the rectangle is l and breadth of the rectangle is b, then perimeter ofvthe rectangle is given by P = 2 (l+b)Given that the length and width of a rectangle are consecutive integers
Let the length of the rectangle be x+1 meter
Let the breadth of the rectangle be x meter
Also given that perimeter of the rectangle is 30 meters
To find length and breadth of the rectangle
We know that perimeter of the rectangle is P = 2 (l+b)
30 = 2 (x+x+1)
15 = 2x + 1
2x = 14
x = 7
x+1 = 8
Hence, the length of the rectangle is 8m and width of the rectangle is 7m
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the ratio equivalent to tan P and tan Q
Answer:
Tan p is 20/21
Tan q is 21/20
Step-by-step explanation:
Tan is short for tangeant.
tangeant means opposite/adjacent
the opposite of vertices p is 20.
the adjacent of vertices p is 21.
so tan p= 20/21
The opposite of vertices q is 21
the adjacent of vertices q is 20
so tan q is 21/20
Mel wants to buy a pair of shoes that costs $120. She has saved $45 and has a job that pays her $10 per hour. The number of hours she has to work to have enough to buy the shoes is given by the inequality 10x + 45 > 120, where x is the number of hours she works.
The fewest number of hours she has to work to buy the shoes is
Step-by-step explanation:
[tex]10x+45 > 120\\10x+45-45 > 120-45\\10x > 75\\\frac{10x}{10} > \frac{75}{10} \\x > 7.5[/tex]
Therefore, Mel has to work at least 7.5 hours or 8 total hours.
George has opened a new store and he is monitoring its success closely. He has found that this store's revenue each month can be modeled by r(x) = x² + 5x + 14 where x represents the number of months since the store opens the doors and r(x) is measured in hundreds of dollars. He has also found that his expenses each month can be modeled by c(x) = x² - 4x + 5 where x represents the number of months the store has been open and c(x) is measured in hundreds of dollars. What does (r-c) (5) mean about George's new store?
A. the new store will sell 5400 items in its fifth month in business
B. The new store will have a profit of $5400 after its fifth month in business
C. The new store will have a profit of $900 after its fifth month in business
D. The new store will sell 900 items In its fifth month in business
Answer:
The new store will have a profit of $5400 after its fifth month.
(R-C)(x) = (x²+5x+14)-(x²-4x+5) = x²-x²+5x--4x+14-5 = 5x+4x+14-5=9x+9
(Use 5 for x)
(R-C)(5) = 9(5) + 9 = 45+9 = 54
Find the first four terms of the sequence given by the following. an=6 x (-4)^n-1, n= 1, 2, 3...
The first four terms of the sequence are 6, -24, 96 and -384
How to determine the first four terms?
The sequence is given as:
an=6(-4)^n-1
When n = 1, we have:
a(1)=6(-4)^(1-1)
This gives
a(1) = 6
When n = 2, we have:
a(2)=6(-4)^(2-1)
This gives
a(2) = -24
When n = 3, we have:
a(3)=6(-4)^(3-1)
This gives
a(3)=96
When n = 4, we have:
a(4)=6(-4)^(4-1)
This gives
a(4)=-384
Hence, the first four terms of the sequence are 6, -24, 96 and -384
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Which graph represents the function f (x) = StartFraction 3 x minus 2 Over x minus 2 EndFraction?
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 2, and the horizontal asymptote is at y = 0.
On a coordinate plane, a hyperbola is shown. One curve opens up and to the left in quadrant 2, and the other curve opens down and to the left in quadrant 4. A vertical asymptote is at x = 1, and the horizontal asymptote is at y = 1.
On a coordinate plane, a hyperbola is shown. One curve opens up and to the left in quadrant 2, and the other curve opens down and to the left in quadrant 4. A vertical asymptote is at x = negative 2, and the horizontal asymptote is at y = 4.
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 2, and the horizontal asymptote is at y = 3.
The graph which represents the rational function is; On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 2, and the horizontal asymptote is at y = 3.
Which graph represents the rational function?It follows from the task content that the rational function given is; f(x) = 3x-2/x-2.
Hence, since the numerator and denominator polynomials are of the same order, it follows that the horizontal asymptote is the quotient; 3/1 = 3.
Additionally, the vertical asymptote of the function is the value of x which renders the denominator equal to 0 and consequently, the function undefined.
Hence, x -2 = 0 and x= 2.
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Answer: THE PERSON ABOVE IS CORRECT!!
The answer is D.) On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 2, and the horizontal asymptote is at y = 3.
Is it possible to have a polygon whose sum of the interior angles is 850 degrees
Answer: No
Step-by-step explanation:
The sum of the interior angles of a polygon with n sides is given by [tex]180(n-2)[/tex]. Setting this equal to 850 degrees,
[tex]180(n-2)=850\\\\n-2=\frac{85}{18}\\\\n=\frac{121}{18}[/tex]
Since this gives n to be a non-integer value, this is an impossible situation since a polygon must have an integer number of side lengths.
You withdraw $140 from your savings account. then you withdraw $49 more. using an integer, which number represents your balance?
The integer represent the balance in your account is Z = + Y. The representation of integer is positive because withdrawal is always less then or equal to the amount present in the bank account.
Total rupees withdraw from saving account is $149
Let total amount in account before withdrawing is X= $500
Amount left after withdraw the money is calculated by a
AMOUNT LEFT = TOTAL AMOUNT - WITHDRAW AMOUNT
So, put the values then
Y= X($500) - $149
Y= $500 - $149
Y= $351
If we represent the balance of saving account in the integer form then it become the Z = + Y. The representation of integer is positive because withdrawal is always less then or equal to the amount present in the bank account.
So, The integer represent the balance in your account is Z = + Y. The representation of integer is positive because withdrawal is always less then or equal to the amount present in the bank account.
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A tape diagram. 0 dollars is 0 percent. Question mark dollars is 23 percent. 52 dollars is 100 percent.
Jared has earned 23% of the $52 he needs to buy a new jacket. Find 23% of $52.
Answer:Jared has earned 23% of the $52 he needs to buy a new jacket. Find 23% of $52.Which expression can you use to find 23% of 52? ✔ 0.23 × 5223% of $52 is $✔ 11.96.An easy way to check your answer is to use the friendly ✔ 25%and divide 52 by ✔ 4to get ✔ 13
Step-by-step explanation:
What are the solutions to the equation x-7/x=6
Answer:
x=7 and x = 1
Step-by-step explanation:
This is pretty much a quadratic in disguise.
If we multiply both sides by x, we get:
x^2-7=6x
move 6x to the left
x^2-6x-7 = 0
We can either use the quadratic formula, or we can use factoring.
with factoring*, we get:
(x-7)(x+1) = 0 , and so the solution to the equation is x=7, and x=-1
*in a equation: x^2+ax+b = (x+c)(x+d), c+d equals a, and c*d equals b
On to the quadratic formula, a=1, b=-6, and c=-7, so:
(6±sqrt(36+4*7))/2 = x
=(6±8)/2
=3±4
x=7 and x = 1
Please help me with this questions. I am stuck on them. Whoever help I will mark brainlest.
The graph has been shifted to the left and moved up and stretched as scaling is done ,
What is Transformation ?Reflecting , Rotating , Dilating a function to form a new function is called Transformation.
The graph of the function f(x) = 1/ x is given
and a transformed function is given
The graph has been shifted to the left and moved up and stretched as scaling is done ,
Therefore three types of transformation are done on the parents function.
The transformation can be seen through the graph attached.
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20 POINTS
A circle has a diameter of 24cm. What is its circumference?
Use 3.14 for π, and do not round your answer. Be sure to include the correct unit in your answer
Answer:
c = 75.36 cm
Step-by-step explanation:
The equation of the circumference is:
[tex]c=\pi d[/tex] In which "d" represents the measurement of the diameter
in this case d= 24cm, π = 3.14
Calculate the circumference:
[tex]c=\pi d=(3.14)(24)=75.36cm[/tex]
Hope this helps
A circle has a diameter of 24cm. The circumference of the circle is c = 75.36 cm.
What is the circumference of the circle?The circumference of the circle that has a radius of r is defined as the product of diameter to the pie value.
The circumference of the circle = 2πr
Given information;
A circle has a diameter of 24cm.
"d" represents the measurement of the diameter, so
d= 24cm, π = 3.14
Radius = d/ 2 = 12
Calculate the circumference:
The circumference of the circle = 2πr
= 2 ( 3.14 ) ( 12)
= 75.36
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Use the law of sines to find the length of side c
Answer:
B. 44.93
Step-by-step explanation:
The law of sines states
[tex]\frac{a}{sinA} = \frac{b}{sinB} = \frac{c}{sinC}[/tex]
where a, b and c are the 3 sides of the triangle and A is the angle opposite side a, B the angle opposite side b and C the angle opposite side c
In this particular problem we have
side a = 44, angle A = 46.7
side c = ? , angle C = 48
So 44/sin(46.7) = c/sin(48) or by multiplying both sides by sin(48)
c = sin(48) * 44/sin(46.7) = 44.92937 which is 44.93 rounded to 2 decimal places
Jake packed 12 jars of paint in a wooden tool box. Each jar and its contents weigh 10 ounces. The empty box weighs 1 pound 14 ounces. What is the total weight of the packed box
The total weight of the packed box is 9 lb 6 oz
According to question:
The weight of 12 jars is 12 times the weight of one jar
The weight of jars and box together is the sum of those weights.
... 12 × (10 oz) + 1 lb + 14 oz = 1 lb + 134 oz
... = 1 lb + 8 × (16 oz) + 6 oz . . . . . . 1 lb = 16 oz
... = 9 lb 6 oz
How to convert Ounces to Pounds?1 ounce (oz) is equal to 0.0625 pounds (lb).
1 oz = (1/16) lb = 0.0625 lb
The mass m in pounds (lb) is equal to the mass m in ounces (oz) divided by 16:
m(lb) = m(oz) / 16
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Can someone help me?
Alex and Bobby are in the woods and are standing 240
yards apart.. Both boys spot a plane with angles of
elevation of 40 degrees and 45 degrees respectively. How
far from the plane is Bobby? Round to the nearest tenth of
a yard. Enter a number answer only.
The distance from Bobby to the plane is 154.7 yards.
How to find the distance of the plane to Bobby using angle of elevation?Sine law can be used to find the distance of the plane to Bobby.
Therefore,
x / sin 40 = 240 / sin 95
cross multiply
Hence,
x sin 95 = 240 sin 40
divide both sides by sin 95
x = 240 sin 40 / sin 95
x = 240 × 0.64278760968 / 0.99619469809
x = 154.08 / 0.9961
x = 154.683264732
x = 154.7 yards
Therefore, the distance from Bobby to the plane is 154.7 yards.
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Write the equation for a parabola with a focus at (9,0) and a directrix at y=-4y
The required equation of parabola is y = (-1/4)(x-9)² +4
What is a Parabola ?
A parabola is a U shaped Curve , whose all point are at same distance from a point called as Focus and a line called as Directrix.
Let (x,y) be any point on the parabola.
the distance between (x,y) and the focus and the distance between (x,y) and directrix is equal.
The focus is at (9,0) and a directrix at y= - 4
[tex]\rm \sqrt {(x-9)^2 + (y -0)^2[/tex] = | y +4|
[tex]\rm {(x-9)^2 + (y -0)^2 = (y-4)^2[/tex]
(x-9)² + y² = y² +16 -4y
On solving this
4y = - (x-9)² +16
y = (-1/4)(x-9)² +4
Therefore this is the required equation of parabola .
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help meeeeeeeeeeeeeeeeee
Let x = number of hours washing cars
Let y = number of hours landscaping
System of equations:
[tex]10x+8y=84\\\\x=2y[/tex]
Select the correct answer. What is one root of this equation? 2x^2-4x+9
Answer:
1±i sqrt(7/2)
Step-by-step explanation:
For this equation you would need to use quadratic formula: x=(-b+-square root b^2-4ac)/2a
Answer:the answer is option E (see pic)
Step-by-step explanation:
One root would be: x =(4-√88)/-4=1+1/2√ 22 = 1.345
help me out plsss I need to turn this in now
Answer:
Complementary angles are:
∠ORS and ∠SRQ
Supplementary angles are:
∠ORP and ∠PRQ
These triangles
are congruent by
the triangle
congruence
postulate [ ? ]
A. SSS
B. SAS
C. Neither, they are not congruent
Answer:
ksb said did bud did did it did did gc victory in suf did did zudbxudng jc fn facing did fjgduf bdyrut during their fyrhfb hi f f7djdufj fhdf. Is A
i need help right now
here u go hope this helps
AD= in
Help me please, stuck on this question. Thankss
Using the cosine ratio, the value of AD in the diagram is: 2√3π in.
How to Apply the Cosine Ratio?If we have the following given in a right triangle like triangle ADC in the diagram:
AC = 4π (hypotenuse)
AD = ? (adjacent side)
The cosine ratio, CAH would be applied, which is:
Cos 30 = adjacent/hypotenuse
Cos 30 = AD/4π
AD = cos 30 × 4π = √3/2 × 4π [cos 30 = √3/2]
AD = 2√3π in.
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three pieces of piping are needed on construction site. The second piece needs to be 2m longer than the first, and the third piece needs to be 7m longer than the first, the combined length of the piping is 72m. Determine the lengths of the three pieces of pipe
Step-by-step explanation:
x + 2x + 7x
72 = 9x
72 - 9 = x
63 = x
63 ÷ 3 = 21
piece 1 = 21
piece 2 =21+2 = 23
piece 3 =21+7 = 28
21+23+28 = 72 This proves the above is correct.