(4x + 5)(3x + 10) or 12x² + 55x +50
b: The degree of the computed expression is 2 and it is classified as a quadratic expression.c: The polynomial expression written in part a is closed under addition multiplication.Forming the Expression for the Area of Rectangle
The formula for the area of a rectangle is given as,
Area, A = length × breadth
Here, the dimensions of the rectangle are given as,
length = (4x + 5)
breadth = (3x + 10)
∴ The equation for the area of the rectangle is,
A = (4x + 5)(3x + 10)
A = 12x² + 55x +50
Hence, 12x² + 55x +50 is the required expression.
Degree and Classification of the Expression
The highest power of a variable that is present in an expression is known as its degree.
Since the degree of the expression formed in part a is 2, it is classified to be a quadratic expression.
Closure Property For Polynomials
When the output is the same kind of object as the inputs, an expression is said to be closed. The expression obtained for the area of the rectangle is a combination of constants and variables closed under multiplication and addition.
Hence the expression formed in part a indicates at the closure property for polynomials.
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Can someone pls help me with this problem?
For the first blank, since the output increases by 5 for each increase of 1 for the input, the answer is 13+2(5) = 23.For the second blank, since the output increased by 10 compared to 23, the input increased by 2. So, the answer is 5 + 2 = 7.We know the output is of the form 5x+b for some constant b. If we test input of 1 and an output of 3, we get an input of 1 gives 5+b, which is equal to 3, meaning b=-2. So, the answer is 5x-2.
6.
f(a+h)-f(a)
Determine
h
Of(a+h)-f(a)
h
Of(a+h)-f(a)
h
Of(a+h)-f(a)
h
=
for f(x) = x2 + 5x and simplify.
=
2a + h + 5
h
= 2a + 2h+5
2ah + h² - 5a
h
Of(a+h)-f(a) = 2a + h + 5
h
The value of the function operation f(a + h) - f(a) is; h² + 5h + 2ah
How to simplify functions?We are given the function;
f(x) = x² + 5x
We want to find f(a + h) - f(a)
Let us first find f(a + h) to get;
f(a + h) = (a + h)² + 5(a + h)
⇒ a² + 2ah + h² + 5a + 5h
⇒ a² + 5a + h² + 5h + 2ah
Let us now find f(a) to get;
f(a) = a² + 5a
Thus, f(a + h) - f(a) = a² + 5a + h² + 5h + 2ah - a² - 5a
f(a + h) - f(a) = h² + 5h + 2ah
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What polynomial function could be represented by the graph below
(A). F(X)=x^2+x-2
(B). F(X)=2x^2+2x-4
(C). F(X)=x^2-x-2
(D). F(X)=2x^2-2x-4
Answer:
(B). F(X)=2x^2+2x-4
Step-by-step explanation:
-4 means it passes through -4 at the y axis
B and D have -4
graph passes thru x axis at -2 and 1
if you enter x = -2 or 1 in the formula
(B). F(X)=2x^2+2x-4
you get 0
it's not D because when you enter -2 or 1 for x
you don't get 0
you get 8 and -4
Answer: (B). F(x) = 2x² + 2x - 4
Step-by-step explanation:
Let us think about the parent function F(x) = x² to pick our answer.
Options A and C have only shifted 2 units down (showed by the "-2" at the end) and the function graphed is shifted four units down.
Between options B and D, one is shifted 2 units to the right, and one is shifted 2 units to the left. We need the one shifted 2 units to the left. This is shown by the "+2x" in option B meaning it is our answer.
what is the slope of line 2x-3y=19.
Answer:
[tex]\frac{2}{3}[/tex]
Step-by-step explanation:
Given Equation of line: y=mx+c,
where m = slope of line.
So, we will have to make y the subject to find the slope.
[tex]2x-3y=19\\2x-3y-2x=19-2x\\-3y=-2x+19\\y=\frac{-2x+19}{-3} \\y=\frac{2}{3} x-\frac{19}{3}[/tex]
From here, we can see the slope of the line is [tex]\frac{2}{3}[/tex].
Answer: 2/3
Step-by-step explanation:
2x-3y=19
minus 2x from both sides
-3y=-2x+19
divide both sides by -3
y=2/3x-19/3
slope is 2/3
rewrite the expression so that everything is under the same root sign and simplified
please please help :) GIVING BRAINLIEST
Step-by-step explanation:
[tex] \frac{2 {}^{4} }{3 \sqrt{xy} } [/tex]
[tex] \frac{2 { }^{4} }{ \sqrt{9xy} } [/tex]
[tex] \frac{1}{2 {}^{ - 4} \sqrt{9xy} } [/tex]
[tex] \frac{1}{ \frac{ \sqrt{9xy} }{16} } [/tex]
[tex] \frac{1}{ \frac{ \sqrt{9xy} }{ \sqrt{256} } } [/tex]
[tex] \frac{1}{ \sqrt{ \frac{9xy}{256} } } [/tex]
[tex]( \sqrt{ \frac{9xy}{256} } ) {}^{ - 1} [/tex]
What is the answer to thisss?
The value of x is 14
How to solve for x?From the question, the lines from the center of the circle to the chords have equal measures of 9 units
This line divides a chord into equal segments, where each segment is 7 units
So, we have:
x = 7 + 7
Evaluate
x = 14
Hence, the value of x is 14
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Each side of a square is increasing at a rate of 6 cm/s. At what rate (in cm2/s) is the area of the square increasing when the area of the square is 9 cm2
36 cm²s⁻¹ is the rate at which the area of the square is increasing.
Given each side of the square is increasing at a rate of 6cm/s
Area, A = s², s is the side length
=> [tex]\frac{dA}{dt} =\frac{dA}{ds}* \frac{ds}{dt} =2s*(\frac{ds}{dt} )[/tex] {chain rule of differentiation}
[tex]\frac{ds}{dt}[/tex] = 6 cm/s
When A = 9 cm² => 9 = s²
=> s = √(9) => s = 3 cm
Hence, [tex]\frac{dA}{dt}[/tex] = 2 × 3 × 6 = 36 cm²s⁻¹
Hence, 36 cm²s⁻¹ is the rate at which the area of the square increases
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Assuming the world population growth rate is 1% and the current population is about 7 billion, next year the population will be:
Assuming the world population growth rate is 1% and the current population is about 7 billion, next year the population will be 7.01 billion.
To calculate the percentage increase rate, use the fundamental increase charge formulation: subtract the original from the brand new cost and divide the results by way of the original cost. to show that right into a percent boom, multiply the results by 100.
The population of a given area is described as the range of humans generally residing in that vicinity, measured on 1 January in a given 12 months. The supply can be the most latest population census.
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Accordding to this function
What is:-
limf(x)
x approches 2⁺
Answer:
Limit does not exist
Step-by-step explanation:
This is a piece-wise function, since we are finding the limit of f(x) when x is approaching 2 from the right, we know that x must be more than 2. However, based on the piece-wise function, there is no function that satisfy this condition, therefore the limit does not exist for this piece-wise function
Gisela would owe $15,500 in taxes each year if she were not eligible for any tax deductions.
This year, Gisela is eligible for tax deductions that reduce the amount of taxes she owes by
$2,325.00. If these tax deductions reduce the taxes Gisela owes this year by d%, what is the
value of d?
Answer:
15%
Step-by-step explanation:
$2325/$15500
Answer: 15
Step-by-step explanation: It’s given that the deductions reduce the original amount of taxes owed by $2,325.00. Since the deductions reduce the original amount of taxes owed by d%, the equation 2,32515,500=d100 can be used to find this percent decrease , d . Multiplying both sides of this equation by 100 yields 232,50015,500=d, or 15 = d. Thus, the tax deductions reduce the original amount of taxes owed by 15%.
b) In the last year, the average rainfall in Pokhara valley during the first 6 months was 150 mm and the average rainfall of the remaining months was 60 mm. Find the average rainfall of the whole year. The average selling of the first 4 days of a shop in the last week was c) Rs 425 and the average selling of the remaining days was Rs 250. Find the average selling of the shop in the whole week. a) Shashwat obtained an average marks of 15 in 3 subjects. When the marks obtained in another subject is also included, the average marks is increased by 1. Find the marks obtained in the fourth subject. b) The average marks of English, Nepali, Science and Social Studies obtained by Sunayana is 70. If the marks obtained in Mathematics is also included, the average marks is increased by 5. Find her marks in Mathematics. eative Section - B The a . b ) In the last year , the average rainfall in Pokhara valley during the first 6 months was 150 mm and the average rainfall of the remaining months was 60 mm . Find the average rainfall of the whole year . The average selling of the first 4 days of a shop in the last week was c ) Rs 425 and the average selling of the remaining days was Rs 250. Find the average selling of the shop in the whole week . a ) Shashwat obtained an average marks of 15 in 3 subjects . When the marks obtained in another subject is also included , the average marks is increased by 1. Find the marks obtained in the fourth subject . b ) The average marks of English , Nepali , Science and Social Studies obtained by Sunayana is 70. If the marks obtained in Mathematics is also included , the average marks is increased by 5. Find her marks in Mathematics .
Answer:
For b), the answer is 105mm
Step-by-step explanation:
(150+60)/2
Triangle PQR is transformed to similar triangle P’Q’R’
What is the scale factor of dilation?
1/2
1/3
1/4
1/5
Scale factor = (image)/(preimage)
[tex]QR=3\\\\Q'R'=1[/tex]
So, the scale factor is 1/3
PLEASE HELP ME I WILL MARK CORRECT ANSWER BRAINLIEST
Answer:
36 units
Step-by-step explanation:
to do this you must first find the lengths of all the sides with pythagorean theorem
for a to b you use
3^2 + 4^2 = c^2
9 + 16 = c^2
25 = c^2
c = 5
5 is one of the lengths
b to c uses the same equation
so
5 is another one of the lengths
for d to c your equation is
5^2 + 12^2 = c^2
25 + 144 = c^2
169 = c^2
13 is another of the lengths
d to a has the same length as c to d so there is another 13 unit length
so
5 + 5 + 13 + 13 is your equation to find the perimeter
5 + 5 + 13 + 13 = 36
that is your answer
help me i dont understand this
The supplement of a 162 degree angle is an angle that measures
Answer:
18 degrees
Step-by-step explanation:
Supplementary angles are angles that when added together equal 180 degrees.
A + 162 = 180
- 162 -162
A = 18
Answer:
18
Step-by-step explanation:
When your are asked the supplement you minus 162 from 180. When you join SU from supplement and add a 1 behind SU you'll get 180. [1SU TO 180]
180-162
18
what is the equation of the given line in the point -slope form
Answer:
E
Step-by-step explanation:
the equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b ) a point on the line
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 1) and (x₂, y₂ ) = (3, 4) ← 2 points on the line
m = [tex]\frac{4-1}{3-0}[/tex] = [tex]\frac{3}{3}[/tex] = 1
using (a, b ) = (3, 4 ) , then
y - 4 = 1 (x - 3) → E
Complete the number pattern
Answer:
1, 4, 9, 16, 25, 36, 49, (....)
may someone help me please :)
Answer:
Answer is Similar-AA :D
Reason:
We're given these two angle congruences:
[tex]\angle P \cong \angle S\\\\\angle Q \cong \angle T[/tex]
These are the blue and red angles marked in the diagram below. Since we have two pairs of congruent angles, we can use the AA similarity theorem to prove the triangles are similar.
Similar triangles have the same shape, but are likely different sizes. Triangles with the same shape indicates the corresponding angles are congruent.
The info that PR = 12 and SU = 3 isn't used or needed. Your teacher may have put that in there as a distraction or filler.
If your player is Erik, write an inequality that shows all of the ways that Erik will win
if Nita chooses 7. If your player is Nita, write an inequality that shows all of the ways
that Nita will win if Erik chooses 17.
An inequality that shows all of the ways that Nita will win if Erik chooses 17 is
Eric will win if Nita chooses 7 and he chooses and number that is less than 17 (ex. n<17).Nita will win if Eric chooses 17 and she chooses a number less than 8 (ex. n<8).What is an Inequality?This refers to the relation in mathematics that makes an unequal comparison between two numbers or expressions.
Therefore, according to the rules of the game, they would have to make random selections from 0 to 20 and if the difference between their two numbers is less than 10, then Erik wins, the inequality that would show all of the ways that Nita will win if Erik chooses 17 are listed above.
Hence, we can see that the complete question goes thus:
"Erik and Nita are playing a game with numbers. In the game, they each think of a random number from zero to 20. If the difference between their two numbers is less than 10, then Erik wins. If the difference between their two numbers is greater than 10, then Nita wins.
Use what you know about inequalities and absolute values to better understand the game."
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Donna sells pencils for $2 and pens $3. She sold 11 items and made $30. How many pens did she sell ?
Donna sold 3 pencils and 8 pens solved using simultaneous equation
What is a simultaneous equation?
Simultaneous equation refers to related equations that are solved at the same to derive answers to the unknown variables
Let assume that X pencils were sold and Y pens were sold
The total revenue is the sum of the prices multiplied by the quantities sold.
2X+3Y=30 (equation 1)
The sum of X and Y sold is 11
X+Y=11 (equation 2)
multiply the second equation by 2
2*(X+Y=11)
2X+2Y=22 (equation 3)
subtract equation 3 from 1
(2X+3Y=30)-(2X+2Y=22)
Y=8
Substitute for Y in equation 2
X+8=11
X=11-8
X=3
Which means he sold 3 pencils and 8 pens.
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Answer:
8
Step-by-step explanation:
If f = 36 when a = 9, find f when a = 8
Answer:
2=A
Step-by-step explanation:
We know that F is directly proportional to A then the equation relating them is
F = kA ← k is the constant of proportion
To find k use the condition F = 36 when A = 9, then
36 = 9k ( divide both sides by 9 )
4 = k
F = 4A ← equation of proportion
When F = 8, then
8 = 8A ( divide both sides by 4 )
2 = A
Points u, m, and d are collinear with m between u and d. given um=5x+30 md=3x+80 ud=10x+20
The lengths um, md and ud are 255 units, 215 units and 470 units respectively, when given that points u, m, and d are collinear with m between u and d and um=5x+30, md=3x+80, ud=10x+20. This can be obtained by adding um and md which is equal to ud. An equation is obtained and solve for x.
What is the required lengths ?Given that, um=5x+30
md=3x+80
ud=10x+20
We know that m is the midpoint of ud
Thus, um + md = ud
5x+30 + 3x+80 = 10x+20
5x+3x + 30+80 = 10x+20
8x + 110 = 10x+20 (taking terms with x to one side of equation)
10x - 8x = 110 - 20
2x = 90
⇒ x = 45
Therefore the lengths,
um=5x+30 = 5(45)+30 = 225 + 30 = 255
md=3x+80 = 3(45)+80 = 135 + 80 = 215
ud=10x+20 = 10(45)+20 = 450 + 20 = 470
Hence the lengths um, md and ud are 255 units, 215 units and 470 units respectively, when given that points u, m, and d are collinear with m between u and d and um=5x+30, md=3x+80, ud=10x+20.
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The graph could be divided up into three different periods of relatively consistent ticket price change: The years 1980 – 1988, 1989 – 1993 and 1994 – 2011. Can you find a typical rate of change in the price of a ticket for each of these time periods? In other words, on average, by how much did the price of a ticket increase by each year during each of these time periods?
In time period of 1980-1988 the rate of ticket price is $0.2 per year
Between time period 1989-1993 there is constant rate.
Between year 1994-2011 the increase in rate is same $0.2 per year
The graph could be divided up into three different periods of relatively consistent ticket price change: The years 1980 – 1988, 1989 – 1993 and 1994 – 2011.
The statistic is the study of mathematics which deal with relations between comprehensive data.
The graph is not available, in the question, so the graph could be as attached
For period 1980-1988
rate of change = 4.2-2.8/ 8 = 0.2
In time period of 1980-1988 the rate of ticket price is $0.2 per year
for period 1989-92 there is a straight line so,
Between time period 1989-1993 there at constant rate.
For period, 1994-2011
rate of change = 4.4-8/17 = 0.2
Between year 1994-2011 the increase in rate is same $0.2 per year
Thus, for the 3 Time period we have rate of change in ticket price is $0.2 per year, no change in ticket price, $0.2 per year respectively.
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Need help with this!
Answer:
488
Step-by-step explanation:
Calculate 20% of their take-home pay
3600 * 0.20 = 720
They already pay 122 and 110 per month
720 - (122 + 110)
720 - 232
488
So the largest monthly car payment they can afford is 488
Suppose y varies inversely with x, and y = 25 when x = -15. What inverse variation equation relates x and y ?
a) y=5/x
b) y=-5/x
x) y=-5x
d) y=5x
The inverse variation equation is y = -5/x
What is equation?Equation is the defined as mathematical statements that have a minimum of two terms containing variables or numbers is equal
y varies inversely as x
Let variation constant = k
y = k/x, y = 25 and x = -15
25 = k/(-15), k = -375 divded by 75 ,So k = -5
The inverse variation equation is y = -5/x
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can you help me i dont understand U_U
Answer:
$7.76
Step-by-step explanation:
So you can express the price in the slope-intercept form: y=mx+b where m is the slope, but in this context it's the price per km, and b is the y-intercept, but in this context it's the base price (how much it costs even if the length is 0 km)
So it gives you the slope of $0.22 per km. so you now have the equation
y = 0.22x + b
To find the base amount or y-intercept, you can take some of the given points, the price will be y, and the length will be x.
I'll use the point (6, 4.68)
Plugging these values into the equation you get:
4.68 = 0.22(6) + b
multiply
[tex]4.68 = 1.32 + b[/tex]
subtract 1.32 from both sides
[tex]3.36 = b[/tex]
So now we have the full equation:
y = 0.22x + 3.36
Now to find the price if the length is 20km, simply plug in 20 as x
y = 0.22(20) + 3.36
Multiply
y = 4.4 + 3.36
Add
y=7.76
Solve this simultaneous equation.
[tex]x + y = 5 \\ \frac{1}{x} + \frac{1}{y} = \frac{9}{14} \\ [/tex]
Answer: x∈∅ (there is no decision).
Step-by-step explanation:
[tex]\left \{ {{x+y=5} \atop {\frac{1}{x} +\frac{1}{y}=\frac{9}{14} }} \right.\ \ \ \ \ \left \{ {{x+y=5} \atop {\frac{y+x}{x*y}=\frac{9}{14} \ |*14*x*y\ (x\neq 0;\ y\neq 0) }} \right. \ \ \ \ \left \{ {{x+y=5} \atop {14*(x+y)=9*x*y}} \right. \ \ \ \ \left \{ {{x+y=5} \atop {14*5=9*x*y}} \right.\ \ \ \ \left \{ {{x+y=5} \atop {9*x*y=70}} \right. \\[/tex]
[tex]\left \{ {{y=5-x} \atop {9*x*y=70\ |:9}} \right. \ \ \ \ \left \{ {{y=5-x} \atop {x*(5-x)=\frac{70}{9} }} \right.\ \ \ \ \left \{ {{y=5-x} \atop {5x-x^2=\frac{70}{9} }} \right. \ \ \ \ \left \{ {{y=5-x} \atop {x^2-5x+\frac{70}{9} =0\ |*9}} \right.\ \ \ \ \left \{ {{y=5-x} \atop {9x^2-45x+70=0}} \right.[/tex]
[tex]\left \{ {{y=5-x} \atop {D=-495}} \right. \ \ \ \ \Rightarrow\ \ \ \ x\in\varnothing.[/tex]
Can you help me please
Answer: Option D
[tex]\displaystyle d=\frac{C}{\pi}[/tex]
Step-by-step explanation:
To solve the formula for d, we will isolate the d variable.
Given:
C = πd
Divide both sides of the equation by π:
[tex]\displaystyle\frac{C}{\pi}=\frac{\pi d}{\pi}[/tex], [tex]\displaystyle\frac{C}{\pi}=d[/tex]
Reflexive property
[tex]\displaystyle d=\frac{C}{\pi}[/tex]
8-2|4-5y|=4
| | stands for absolute value
Answer:
y = (2/5) OR y = (6/5)
Step-by-step explanation:
The first step is isolating the expression within the absolute value bars. The first thing we can do is subtract both sides by 8. If we do that, we get -2|4-5y| = -4. Now, to completely isolate the absolute value, we would have to divide by -2. This yields |4 - 5y| = 2. Finally, we can remove the absolute value bars. However, to do this, we need to first understand what an absolute value bar does to an equation. Lets say that |x| = 2. Absolute value describes the DISTANCE of some quantity from 0 (on the number line). Therefore, x (which is inside the absolute value bars) can be either positive or negative 2 (they are BOTH two units away from 0). Similarly, in this case, (4 - 5y) can either be 2 or -2 (because the absolute value of both is 2). Now we have two possible solutions to solve for:
4 - 5y = 2 OR 4 - 5y = -2
5y = 2 OR 5y = 6
y = (2/5) OR y = (6/5)
If we plug both of these answers back into the equation we can see that they both check out.
Find the area of the sector. Use π = 3.14.
120°
11 mi
Answer:
Step-by-step explanation: