We add [tex]-3x^3 + 5x^2 +1[/tex] in the polynomial [tex]3x^3 - 2x^2 + 3[/tex] to get the polynomial [tex]3x^2 +4[/tex]. So the option 4 is correct.
In the given question we have to find which polynomial should be added to [tex]3x^3 - 2x^2 + 3[/tex] to get the polynomial [tex]3x^2 +4[/tex].
A polynomial is a mathematical equation made up of variables, constants, and exponents that are mixed using addition, subtraction, multiplication, and division operations.
Let we add the polynomial P to get the polynomial [tex]3x^2 +4[/tex].
[tex]3x^3 - 2x^2 + 3[/tex] + P = [tex]3x^2 +4[/tex]
Subtract the equation [tex]3x^3 - 2x^2 + 3[/tex] on both side, we get
P = [tex]3x^2 +4[/tex] - ([tex]3x^3 - 2x^2 + 3[/tex])
P = [tex]3x^2 +4-3x^3 + 2x^2 - 3[/tex]
Now simplifying the expression
P = [tex]-3x^3 + 5x^2 +1[/tex]
So we add [tex]-3x^3 + 5x^2 +1[/tex] in the polynomial [tex]3x^3 - 2x^2 + 3[/tex] to get the polynomial [tex]3x^2 +4[/tex]. So the option 4 is correct.
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Help w number 1 please super confused
An equilateral triangle is one that has all three of its sides be in line with one another.A slash mark is used to indicate the congruent sides.Congruent angles are ∠L and ∠X, ∠G and ∠Y, and ∠F and ∠T.
How do you identify congruent angles?An equilateral triangle is one that has all three of its sides be in line with one another.A slash mark is used to indicate the congruent sides.An equilateral triangle always has angles that are 60° in length.
It is referred to as an isosceles triangle when a triangle's two sides are identical. When the corresponding sides and angles of two angles match, the angles are said to be congruent.
When stacked, two angles are also congruent if they match.
If they line up with each other after turning or moving it, then.
Also creating equivalent vertex angles are a parallelogram's diagonals.
Congruent sides - L and X, G and Y, and F and T.
Congruent angles - ∠L and ∠X, ∠G and ∠Y, and ∠F and ∠T.
ΔLGF ≅ ΔXYT
Congruent angles are ∠L and ∠X, ∠G and ∠Y, and ∠F and ∠T.
Congruent sides are L and X, G and Y, and F and T.
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A region satisfies the inequalities 1 ≤ x ≤ 5 and 2 ≤ y ≤ a. What value of a would give the region an area of 24 square units?
Answer: 8
Step-by-step explanation:
We can interpret this as a rectangle with dimensions [tex]5-1=4[/tex] by [tex]a-2[/tex].
[tex]4(a-2)=24\\\\a-2=6\\ \\ a=8[/tex]
at a cookie shop, four different kinds of cookies are sold: chocolate chip, macaroon, peanut butter, and white chocolate. in how many different ways can a person choose eight cookies?
The number of different ways can a person choose eight cookies will be 1,680.
What are permutation and combination?A permutation is an act of correctly arranging things or pieces. Combinations are a method of taking stuff or pieces from an assortment of items or sets in which the order of the items is irrelevant.
At a cookie shop, four different kinds of cookies are sold: chocolate chip, macaroon, peanut butter, and white chocolate.
Then the number of different ways can a person choose eight cookies will be given as,
⁸P₄ = 8! / (8 - 4)!
⁸P₄ = 8 x 7 x 6 x 5 x 4! / 4!
⁸P₄ = 1,680
The number of different ways can a person choose eight cookies will be 1,680.
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In the diagram, if PW = 12 and PT = 9, find PX.
The length of segment PX in this problem is given as follows:
PX = 9.
How to obtain the length of segment PX?The theorem used to solve this problem is given as follows:
A line parallel to one side of a triangle divides the other two proportionately.
In this problem, all the horizontal lines are parallel, hence the side is divided proportionality, as the resulting triangles in the context of this problem are all similar.
PX is three-fourths of the length of the segment PW = 12, hence it's length is given as follows:
PX = 3 x 12/4
PX = 3 x 3
PX = 9 units.
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A torch and a battery cost 2. 50 altogether. The torch costs 1. 50 more than the battery. What fraction of the total price is the torch?Give your answer in its simplest form
The fraction of the total price that the torch is is 4/5.
Let x be the cost of the battery.
We know that the torch cost is 1.50 more than the battery cost. So, the cost of the torch is
x + 1.50
The total cost is the sum of the cost of the battery and the torch, so:
x + (x + 1.50) = 2.50
2x + 1.50 = 2.50
Solving this equation we get,
x = 0.50
Therefore the cost of the battery is 0.50 and the cost of the torch is 2.00.
To find the fraction of the total price that the torch is, we divide the cost of the torch by the total cost:
= (2.00) / (2.50)
= 4/5
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If h(x) = -x(1 - x), find h(-3).
Answer:
12
Step-by-step explanation:
h(-3)= -(-3)(1-(-3))=
3(4)=12
Please help
Найти max u min f(x) y=x²-8x+19;xє [-1;5]
Answer:
54 nhcuioogffhuivkoov89
Ishi walked a total of 2 miles on a treadmill. He walked at a constant rate of 4 miles per hour. Which expression shows how long, in minutes, Ishi walked on the treadmill? 2.5 miles : 4 moles/hour x 60 minutes/1 hour 2.5 miles : 4 mmoles/hour x 60 minutes/1 hour 2.5 miles : 4 mom/10 mg x 60 minutes/1 hour 2.5 miles : 4 milem/hour x 60 minutes/1 hour
Ishi walked on the treadmill time for 37.5 minutes, which is equivalent to 2.5 miles at a rate of 4 miles/hour. To find the time Ishi walked on the treadmill, we need to use the equation, Distance (miles) / Rate (miles/hour) x Time (hours) = Time (minutes).
Answer: 2.5 miles : 4 milem/hour x 60 minutes/1 hour
Ishi walked on the treadmill time for 37.5 minutes, which is equivalent to 2.5 miles at a rate of 4 miles/hour.
To find the time Ishi walked on the treadmill, we need to use the equation, Distance (miles) / Rate (miles/hour) x Time (hours) = Time (minutes).
Therefore, 2.5 miles / 4 miles/hour x 1 hour = 0.625 hour or 37.5 minutes.
Ishi walked on the treadmill for time 37.5 minutes, which is equivalent to 2.5 miles at a rate of 4 miles/hour.
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A school has a square courtyard and wants to create diagonal walkways. the length of
each side of the courtyard is 25 meters. approximately how long is each walkway?
The length of each side of the courtyard is 25 meters. Then 35.36 meters long is each walkway.
In the given question, a school has a square courtyard and wants to create diagonal walkways.
The length of each side of the courtyard is 25 meters.
We have to find how long is each walkway.
By dividing the square in half to form a right triangle, you can find the solution. The Pythagorean theorem can then be used to find the hypotenuse.
According the Pythagorean Theorem
[tex]a^2+b^2 = c^2[/tex]
[tex](25)^2+(25)^2=c^2[/tex]
Now solving,
625 + 625 = [tex]c^2[/tex]
[tex]c^2[/tex] = 1250
Taking square root on both side, we get
c = 35.36 meters.
Hence, 35.36 meters long is each walkway.
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Area under the curve
f(x) = x 2 + 2x
g(x) = x + 2
Answer: The area under the curve refers to the area between the curve of a function and the x-axis. To find the area under the curve of a function, you would typically integrate the function with respect to x and then evaluate the definite integral between a set of limits.
For example, to find the area under the curve of f(x) = x^2 + 2x from x=0 to x=a, we would integrate the function with respect to x,
∫[0,a] (x^2 + 2x) dx = (1/3)x^3 + x^2 evaluated from x=0 to x=a,
Similarly, to find the area under the curve of g(x) = x + 2 from x=0 to x=a, we would integrate the function with respect to x,
∫[0,a] (x + 2) dx = (1/2)x^2 + 2x evaluated from x=0 to x=a
It's important to note that the definite integral is only defined if the function is continuous and has no vertical asymptotes on the interval.
Step-by-step explanation:
By what factor would you need to change the radius of a sphere, such that its volume increased by a factor of 7? Please include step by step calculations!
The factor by which radius of the sphere be changed is 1.91, which is calculated by applying the concepts of surface area and volume on the assigned problem.
What do you mean by volume?
Volume is defined as the 3D measurement that deals with the amount of space required by an object. It is always calculated in cubic units. Its basic unit is cubic metre.
Calculation of the change in radius of sphere when its volume is increased by 7Let the radius and volume of sphere be r and v respectively
Volume of sphere, v = 3.16 × ( r )3 —- 1
Now, changed radius, R = xr
Where x is the factor, we need to calculate
Changed volume, V = 7v = 3.16 × ( R )3 -— 2
From equations 1 and 2, we get,
7v / v = ( R )3 / ( r )3
7 = ( xr )3 / ( r )3
7 = (x)3 × 1
Taking cube root both sides,
x = 1.913
Hence, the factor by which radius of the sphere be changed is 1.91.
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What is the 4 in front of the formula called?
The 4 in front of the formula is called a coefficient.A coefficient is a number that is multiplied by a variable or a constant in an algebraic expression.
In this case, the 4 is being multiplied by the formula, which makes it a coefficient.
A coefficient is a numerical value that is used in an algebraic expression or equation. It is placed in front of a variable or a constant, and it is multiplied by that particular element. The coefficient is used to adjust the value of the expression or equation, and it can be any number, including fractions, negative numbers, and decimals. For example, if a formula were written as 4x + 2 = 10, then the 4 in front of the x is the coefficient. This number is used to adjust the value of the expression, and it can be changed to any other number in order to alter the equation. Coefficients are very useful in mathematics, and they can be used to solve many types of equations and problems.
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If you were going to place a streetlight so it was equidistant from three sidewalks, would you use the incenter or circumcenter to find the best location?
We can use the incenter to find the best location, because the point that is equidistant to all sides of a triangle is called the incenter.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Now, We know that;
The incenter is equidistant from the sides of the triangle and the point that is equidistant to all sides of a triangle.
Hence, We can use the incenter to find the best location, to place a streetlight so it was equidistant from three sidewalks.
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If a square is 12 cm 8 cm and 10 cm what is the volume 
Answer: 960cm^2
Step-by-step explanation: 12 x 8 = 96 x 10 = 960
Answer:
a) 1728 [tex]cm^{3}[/tex]
b) 512 [tex]cm^{3}[/tex]
c) 1000 [tex]cm^{3}[/tex]
Step-by-step explanation:
(I think your question is ...a little mixed up as a square has same length for all of its respective sides. So I will attempt to do them a little differently as I believe the question must have had three different sub questions)
a) [tex]V = s^{3}[/tex]
"s" here represents the respective length for the sides.
The answer for if a side was 12 centimeters, then the volume would be
[tex]V = 12^{3}[/tex]
Which would give us a volume of 1728 [tex]cm^{3}[/tex]
b)[tex]V = s^{3}[/tex]
"s" here represents the respective length for the sides.
The answer for if a side was 8 centimeters, then the volume would be
[tex]V = 8^{3}[/tex]
Which would give us a volume of 512 [tex]cm^{3}[/tex]
c)[tex]V = s^{3}[/tex]
"s" here represents the respective length for the sides.
The answer for if a side was 10 centimeters, then the volume would be
[tex]V = 10^{3}[/tex]
Which would give us a volume of 1000 [tex]cm^{3}[/tex]
3 times what equals 5?
Answer: its 1.6667.
Answer:
Step-by-step explanation
3*X=5
X=5/3
X=1.67
Wyatt has $780 to spend at a bicycle store for some new gear and biking outfits. assume all prices listed include tax.
he buys a new bicycle for $398.35.
he buys 2 bicycle reflectors for $19.41 each and a pair of bike gloves for $35.27.
he plans to spend some or all of the money he has left to buy new biking outfits for $46.60 each.
write and solve an inequality which can be used to determine oo, the number of outfits wyatt can purchase while staying within his budget.
The inequality which can be used to determine too, the number of outfits Wyatt can purchase while staying within his budget is:
780 ≥ 472.44 + 46.60x
Inequality:
In mathematics, equations are not always balanced on both sides using equal signs. It can also be about "not equal" relationships, such as one being greater than the other or less than the other. In mathematics, an inequality refers to a relationship in which two numbers or other mathematical expressions do not compare equally. These formulas belong to algebra and are called inequalities.
An inequality means that two things are not the same. One of them may be less than, greater than, less than or equal to, greater than or equal to the other.
p ≠ q means p is not equal to qp < q means p is less than qp > q means p is greater than qp ≤ q means p is less than or equal to qp ≥ q means p is greater than or equal to qAccording to the question:
As based on the information,
he can't spent more than $780.
Four cycle reflector cost = 2 × $19.41
= $38.82
Let maximum number of outfit = x
and Cost = 46.60x
and the the pair of glove is for $35.27.
Therefore,
New bicycle + Bicycle reflectors + Biker gloves + Biking Outfit ≤ 780
⇒ $398.35 + $ 38.82 + $ 35.27 + $46.60 x ≤ 780
⇒ 472.44 + $ 46.60x ≤ 780
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The citizens of a certain community were asked to choose their favorite pet. The pie chart below shows the distribution of the citizens' answers. If there are 130,000citizens in the community, how many chose Cats, Dogs, or Birds
On solving the provided question, we can say that be equation the value we obtain Number of citizens × total percentage = 140,000 x (23%+11%) = 47,600
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
number of citizens who chose cat or fish is 47,600
Number of citizens × total percentage
140,000 x (23%+11%)
140,000 x 34%
= 47,600
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Dr. Coleman is a zoologist who studies giant pandas. Giant pandas are very tiny when they are born but grow to be quite large. The function f(x) gives the weight, in pounds, of a particular female panda when she was x years old. What does f(4)=f(30) tell you?
The information shows that f(4)=f(30) tells us that the weight of a particular female panda at 4 years old is the same as her weight at 30 years old.
What is the function?It is a mathematical expression, rule, or law that establishes the relationship between an independent variable and a dependent variable (the dependent variable).
In this case, Dr. Coleman is a zoologist who studies giant pandas. Giant pandas are very tiny when they are born but grow to be quite large. The function f(x) gives the weight, in pounds, of a particular female panda when she was x years old.
The function illustrated shows that the weights are the same.
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A rocket is set to blast from the surface of Earth. What speed will it need to achieve in order to stay in orbit around the Earth at an altitude of 300 km? Note distance here to the center of the Earth is 6.7*10^6 km and the mass of Earth is 6*10^24.
Answer:
For example, a spacecraft leaving the surface of Earth needs to be going 7 miles per second, or nearly 25,000 miles per hour to leave without falling back to the surface or falling into orbit.
In ΔKLM, k= 1.2 cm, � m∠L=93° and � m∠M=6°. Find the length of I, to the nearest 10th of a centimeter
Using the law of sines, the length of l is: 12.1 cm.
What is the Law of Sines?The Law of Sines is a theorem in triangle geometry that relates the lengths of the sides of a triangle to the sine of its angles. It states that for any triangle, the ratio of the length of a side to the sine of the angle opposite that side is the same for all three sides.
Given the following:
k = 1.2 cm
m<L = 93°
m<M = 6°
m<K = 180 - 93 - 6 = 81°
Using the law of sines, sin K/k = sin L/l:
sin 81/1.2 = sin 93/l
Find l:
(sin 81)(l) = (sin 93)(12)
l = (sin 93)(12)/(sin 81)
l = 12.1 cm
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Can anyone help me answer this question?
In a geometric progression, the first term is 7, the last term 448 and the sum 889. Find
the common ratio.
Answer:
Step-by-step explanation:
Given : In a GP the first term is 7
the last term is 448
and the sum 889
To find : Common ratio ? The number of terms is 7.
The common ratio is 2
Answer:
common ratio (r) = 2
Step-by-step explanation:
solution in picture
Please Help me out!!
The solution to f(g(h(x))) = [tex]x^{2} - 12x^{3/2} + 54x -108\sqrt{x} + 87[/tex]
f(x) = [tex]x^{4} + 6[/tex]
g(x) = [tex]x-3[/tex]
h(x) = [tex]\sqrt{x}[/tex]
Therefore to find f(g(h(x))),
fogoh(x) = f(g(h(x)))
We first substitute the value of h(x) as above,
f(g([tex]\sqrt{x}[/tex] )) ....... as h(x) = [tex]\sqrt{x}[/tex]
Now, we substitute the value of g(x) where x is [tex]\sqrt{x}[/tex]
f([tex]\sqrt{x} -3[/tex]) ....... as g(x) = [tex]x-3[/tex]
Then we substitute the value of x in f(x) with [tex]\sqrt{x} -3[/tex]
[tex](\sqrt{x} -3)^{4} + 6[/tex]
Now we further solve to find a simpler form of the equation,
[tex](\sqrt{x} -3)^{4} + 6[/tex]
= [tex](x^{2} -12x^{3/2} +54x- 108\sqrt{x} +81) + 6[/tex]
= [tex]x^{2} - 12x^{3/2} + 54x -108\sqrt{x} + 87[/tex]
Therefore, fogoh(x) = f(g(h(x))= [tex]x^{2} - 12x^{3/2} + 54x -108\sqrt{x} + 87[/tex]
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here are the number of hours that 9 students spend on the computer on a typical day: 1 6 7 6 8 11 6 12 15 the data from the above 9 students form what type of distribution?
The data from the 9 students represents the number of hours that they spend on the computer on a typical day. It forms a distribution known as a frequency distribution.
A frequency distribution is a tabular representation of data that shows how often each value or set of values of a variable occurs in a data set. The data set is typically divided into a number of classes or bins, and the frequency of each class is recorded.
In this case, the data represents the number of hours that 9 students spend on the computer on a typical day. Each student is represented by one data point, and the frequency of each value (the number of hours) is recorded.
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What is the lateral surface area of this figure in cm2? Round to the nearest 10th. Hint: you will need Pythagorean Theorem to solve.
The surface area of the prism in this problem is given as follows:
46 cm².
What is a surface area?A surface area is given by the sum of all the areas that compose the figure.
The prism in this problem is composed as follows:
One square of side length s = 2 cm.Two right triangles of dimensions 2 cm and 7 cm.Two rectangles of dimensions 2 cm and 7 cm.The area of the square is given by the side squared, hence:
As = 2² = 4 cm².
The area of a right triangle is given by half the multiplication of the side lengths, hence:
At = 2 x 0.5 x 2 x 7 = 14 cm².
The area of a rectangle is given by the multiplication of the dimensions, hence:
Ar = 2 x 2 x 7 = 28 cm².
Hence the surface area of the prism is then obtained as follows:
S = As + At + Ar
S = 4 + 14 + 28
S = 46 cm².
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. This semester there are 67 students performing in the middle school's
production of "Beauty and the Beastly." Of these students, 49 are 7th and 8th
graders. Write a proportion and solve for s, the percent of 6th grade students
that are in the play. Round your answer to the nearest tenth of a percent.
Answer:
We know that there are 67 students performing in the middle school's production of "Beauty and the Beastly." and 49 of them are 7th and 8th graders.
We can write a proportion to find the percent of 6th grade students in the play:
6th grade students / Total students = s / 100
We know that 49 of the students are 7th and 8th graders, so the number of 6th grade students is 67 - 49 = 18.
Now we can substitute the values in the proportion and solve for s:
18 / 67 = s / 100
To find s, we can cross-multiply and divide:
18 * 100 = 67 * s
1800 = 67 * s
s = 1800 / 67
s = 26.87
Rounding to the nearest tenth of a percent: 26.9 %
So, the percent of 6th grade students that are in the play is 26.9%.
refer to exercise 75. how surprising would it be for more than 4 elk in the sample to survive to adulthood? calculate an appropriate probability to support your answer.
According to the given possibility the event of more than 4 elk surviving to adulthood is not surprising and the appropriate probability is 0.1402.
Here we have given that it be for more than 4 elk in the sample to survive to adulthood.
Then the probability is calculated by using the binomial probability,
And here we have to use the addition rule for mutually exclusive event, then we get,
=> P(AUB) = P(A or B) = P(A) + P(B)
At the possibility of k = 5 we have the binomial probability to be evaluated as follows:
=> P(X = 5) = 21 (0.44)⁵ (0.56)² ≈ 0.1086
At the possibility k = 6 then the binomial probability to be calculated as,
=> P(X = 6) = 7(0.44)⁶ (0.56)¹ ≈ 0.0284
Finally at the value of k = 7 then the binomial probability to be evaluated as,
=> P(X = 7) = 1 (0.44)⁷(0.56)° ≈ 0.0032
Therefore the two different numbers of successes are impossible on same simulation is by applying the addition rule for mutually exclusive events is calculated as,
=> P(X > 4) = P(X = 5) + P(X = 6) + P(X = 7)
=> 0.1086 +0.0284 + 0.0032
=> 0.1402
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Determine the values of the following quantities. (Round your answers to three decimal places.) A. t0.10,14 B. t0.05,14C. t0.05,27D. t0.05,60E. t0.005,60
The values of such following quantities are (A), 1.345, (B), 1.761, (C), 1.706, (D), 1.676, and (E), 2.678 according to the stated statement.
What types of amounts are there?Any logical combining of a number, changeable, or other quantity is referred to as a quantity in a mathematical equation. For example, the equation x + 6 = Fifteen denotes four different numbers: 6, 15, x, and the sum of x plus 6, or x + 6. The concept is that just being exposed to something increases our likelihood of like it more. We are far more likely to enjoy someone or something the more often we interact with them.
The following table lists the quantities of the quantities:
(A). Here,
[tex]$\alpha=0.10, d f=14$$t_{0.10,14}=1.345$[/tex]
(B). Here,
[tex]$\alpha=0.05, d f=14$$t_{0.05,14}=1.761$[/tex]
(C). Here,
[tex]$\alpha=0.05, d f=26$$$t_{0.05,26}=1.706$$[/tex]
(D). Here,
[tex]$\alpha=0.05, d f=50$$$t_{0.05,50}=1.676$$[/tex]
(E). Here,
[tex]$\alpha=0.005, d f=50$$$t_{0.005,50}=2.678$$[/tex]
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Find the Wronskian of the following vector functions: u(t) = [3t - 1 -2t], v(t) = [-2t + 1 3t] a). 12 t^2 b). -12 t^2 - t c). -13 t^2 - t d). -5 t^2 + 2t e). 5t^2 - t f). None of the above.
The Wronskian of the given vector functions is [tex]5t^2-t[/tex]. So the option e is correct.
In the given question, we have to find the Wronskian of the following vector functions:
[tex]u(t) = \left [ \begin{matrix}3t - 1\\ -2t\end{matrix} \right ][/tex] and [tex]u(t) = \left [ \begin{matrix}-2t + 1\\ 3t\end{matrix} \right ][/tex]
Thomas Muir gave the Wronskian determinant its name after Józef Hoene-Wroski introduced it in 1812. It is applied to the study of differential equations, and in some cases, it can reveal linear independence among a group of solutions.
Wronskian vector functions = [tex]\left | \begin{matrix}3t - 1 & -2t\\ -2t + 1 & 3t\end{matrix} \right |[/tex]
Now solving the vector
Wronskian vector functions = (3t-1)3t - (-2t)(-2t+1)
Wronskian vector functions = [tex]9t^2-3t + 2t(-2t+1)[/tex]
Wronskian vector functions = [tex]9t^2-3t -4t^2+2t[/tex]
Wronskian vector functions = [tex]5t^2-t[/tex]
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Hi I need some help through this problem: Find the equation of a line parallel to 2x+4y-12=0 that passes through the point (-2,5).
equation in slope-intercept form.
Answer:
y = - [tex]\frac{1}{2}[/tex] x + 4
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
2x + 4y - 12 = 0 ( subtract 2x - 12 from both sides )
4y = - 2x + 12 ( divide through by 4 )
y = - [tex]\frac{2}{4}[/tex] x + [tex]\frac{12}{4}[/tex]
y = - [tex]\frac{1}{2}[/tex] x + 3 ← in slope- intercept form
with slope m = - [tex]\frac{1}{2}[/tex]
• Parallel lines have equal slopes , then
y = - [tex]\frac{1}{2}[/tex] x + c ← is the partial equation of the parallel line
to find c substitute (- 2, 5 ) into the partial equation
5 = - [tex]\frac{1}{2}[/tex] (- 2) + c = 1 + c ( subtract 1 from both sides )
4 = c
y = - [tex]\frac{1}{2}[/tex] x + 4 ← equation of parallel line
Answer:
y = -(1/2)x + 4
Step-by-step explanation:
Lets look for an equation of the form y=mx+b, where m is the slope and b is the y-intercept (the value of y when x = zero). Lets rewrite the given equation to conform to this format:
2x+4y-12=0
4y = -2x+12
y = -(2/4)x +(12/4)
y = -(1/2)x +3
This line has a slope of -(1/2). Parallel lines have the same slope as the reference line. So the new line will also have a slope of -(1/2) and we can write the new line equation as:
y = -(1/2)x + b
Any line with a slope of -(1/2) will be parallel. Any value of b is acceptable. But we want this line to intersect the point (-2,5), so we need to pick a value of b that forces the line through this point. To find the value of b to make that happen, enter the point (-2,5) in the parallel line equation from above:
y = -(1/2)x + b
5 = -(1/2)*(-2) + b for point (-2,5)
5 = 1+b
b = 4
The parallel line that intersects (-2,5) is
y = -(1/2)x + 4
See the attached graph.
A city planner make a cale drawing of a propoed playground. The length of the actual playground i 78 feet, and the width i 42 feet. Suppoe a cale of 0. 5 inch = 6 feet i ued. Which dimenion repreent the playground on the cale drawing?
The dimensions size on the scale drawing is 6.5 inches by 3.5 inches.
Dimensions in mathematics are the measure of the size or distance of an object or region or space in one direction. In simpler terms, it is the measurement of the length, width, and height of anything.
In Geometry we can have different dimensions, The number of dimensions is how many values are needed to locate points on a shape.
Multiplying the actual dimensions by the scale gives the scale dimensions:
(0.5 in)/(6 ft) × {78 ft, 42 ft}
= {39/6 in, 21/6 in}
= {6.5 in, 3.5 in}
Therefore, the dimensions size on the scale drawing is 6.5 inches by 3.5 inches.
To learn more about dimensions visit : brainly.com/question/29835748
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