Coplanar lines are referred to as parallel lines because they may be extended indefinitely without ever intersecting. || is the sign meaning "parallel to." If two lines are drawn, they don't have to be parallel, and a third line runs across them as seen in the diagram below. We may obtain eight distinct angles by drawing two parallel lines, and then drawing a transverse line through them.
Four pairs of matching angles will be created from all eight angles. One of the pairings is represented by angles F and B in the preceding diagram. If the two lines are parallel, corresponding angles are congruent.
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Use the remainder theorem to find P (3) for P(x) = -x^4+3x^3-2x+3.
Specifically, give the quotient and the remainder for the associated division and the value of P (3).
The most appropriate choice for remainder theorem will be given by-
Quotient = [tex]-x^3-2[/tex]
Remainder = -3
What is remainder theorem?
When f(x) is divided by (x-a), the remainder will be f(a).
If the remainder is zero, (x-a) will become a factor of f(x)
Expression to be divided is called dividend, expression by which dividend is divided is called divisor, expression obtained on division is called Quotient and the other part is the remainder.
There is also a well known formula
Divisor x Quotient + Remainder = Dividend
Here,
P(x) = [tex]-x^4 +3x^3 -2x+3[/tex]
P(3) = [tex]-(3)^4+3(3)^3-2(3)+3[/tex]
= [tex]\\-81+81-6+3[/tex]
= -3
So by Remainder theorem, remainder is P(3)
So, Remainder = -3
Let the quotient be q(x)
divisor = [tex]x - 3[/tex]
We know,
Divisor x Quotient + Remainder = Dividend
[tex](x-3) \times q(x) +(-3) = -x^4 +3x^3 -2x+3\\(x-3) \times q(x) = -x^4 +3x^3 -2x+3 +3\\(x-3) \times q(x) = -x^4 +3x^3 -2x+6\\q(x) = \frac{-x^4 +3x^3 -2x+6}{x -3}\\q(x) =\frac{ -x^3(x-3)-2(x-3)}{x-3}\\q(x) = \frac{(x-3)(-x^3-2)}{x-3}\\q(x) = -x^3-2[/tex]
So, Quotient = [tex]-x^3-2[/tex]
Remainder = -3
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A scale drawing of a field is shown below.8 in.10 in.6 in.The drawing uses a scale of 1 in. = 14 ft. What is the area of the actual field?
We can multiply each side by 14ft yo find the value on feet and late calculate the area
[tex]\begin{gathered} 8\times14=112ft \\ 10\times14=140ft \\ 6\times14=84ft \end{gathered}[/tex]tha area formula is
[tex]A=\frac{b\times h}{2}[/tex]where b=84ft and h=112ft
[tex]\begin{gathered} A=\frac{84\times112}{2} \\ A=4704 \end{gathered}[/tex]the area is 4,704ft2
C = dn or C = 2rn
(What is the radius of a circle with a circumference of 25cm?)
Hello!
Let's take this problem step by-step:
What is the formula for the circumference of a circle:
[tex]\text{Circumference} = 2\pi *\text{radius}[/tex]
Since the circumference is 25 cm
[tex]25 = 2\pi *\text{radius}\\\\\text{radius} = \dfrac{25}{2\pi }[/tex]
Answer: [tex]\text{radius} = \dfrac{25}{2\pi }[/tex]
Hope that helps!
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Fill in the blanks to express the quantities given in ratio language. Ratios must be
expressed in simplest form.
Number of Animals in the Pet Store:
Animal Count
16 cats
8 dogs
For every __ cats in the pet store, there are __dogs.
i need 2 more please help me
Translate this phrase into an algebraic expression. Seven more than the product of 17 and Julie's savings Use the variable j to represent Julie's savings.
17j+7 is the algebraic expression for Seven more than the product of 17 and Julie's savings.
What is Expression?Expression is a combination of variables, operators and numbers.
The given phrase is
"Seven more than the product of 17 and Julie's savings"
and j is variable to represent Julie's savings.
In the phrase we have Seven more than, it means we are adding 7 to something.
According to problem we are adding 7 to "product of 17 and Julie's savings"
Product means multiplying a number with another factor. Here the factor is julies saving j.
17j+7 is the translated algebraic expression.
Hence 17j+7 is the translation of Seven more than the product of 17 and Julie's savings.
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Solve the equation for x. −0.24x − 16.4 = 1.48 x = −62.2 x = 62.2 x = −74.5 x = 74.5
hurry pls
The solution of the given linear equation is x = -9.53
How to solve the equation for x?Here we have the linear equation:
-0.24*x - 16.4 = 1.48*x
To solve this, first we need to move all the terms with x to the left and the terms without x to the right.
-0.24*x - 1.48*x = 16.4
(-0.24 - 1.48)*x = 16.4
-1.72*x = 16.4
Now we can divide both sides by -1.72 to get:
x = 16.4/-1.72 = -9.53
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Answer: c) (is it c?)
Step-by-step explanation: c) x= - 74.5
0.24x+16.4=-1.48 step 1- subtract: -1.48- 16.4
0.24x= -17.88 (divide)
x= −74.5
there
i hope this helps!!
Amy got a prepaid debit card with $20 on it. For her first purchase with the card, she bought some bulk ribbon at a craft store. The price of the ribbon was 19 cents per yard. If after that purchase there was $16.77 left on the card, how many yards of ribbon did Amy buy? pls answer this!
Answer:
price for one ribbon =19 cents
she got $20
20- 16.77 the rest from the money = 3.23
so she spends 3.23 from buying the ribbon
how much ribbon does she buy
3.23 ÷ 0.19= 17 ribbons
The graph of f(x) is shown.
For what values of x does f(x) = 0?
A) −1, 1, 2
B) −2, −1, 1
C) −3, −1, 1
D) −1, 1, 3
Answer:
C
Step-by-step explanation:
f(x) =0
when the curve intersects the x axis
goodluck :)
A pedestrian is walking at a speed of 3 km/hr. Express the distance in kilometers, d, as a function of time in hours, t.
The question format : d(t) =
This is because
distance = rate*time
Rate is another term for speed.
Thu has the same amount of money automatically deposited into a new savings account each week. After 2 weeks, she has $14. After 5 weeks, she has $35. The unit rate is measured in dollars per week. What is the constant of proportionality?
For the given data of saving account, unit rate is measured in dollars per week then constant of proportionality is equal to $7.
As given in the question,
For the saving account,
Amount deposited is directly proportional to the number of weeks
Let y be the amount deposited and x be the number of weeks
y ∝ x
y = kx
'k' is the constant of proportionality
As per data unit rate is measured in dollars per week
For y = $14 then x = 2 weeks
14 = 2k
⇒ k = $7
For y = $35 then x = 5weeks
35 =5k
⇒ k = $7
Therefore, for the given data of saving account, unit rate is measured in dollars per week then constant of proportionality is equal to $7.
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What are the The values of X and why that satisfy this equation (x+yi)+(4+9i)=9-4i
The values of x and y that satisfy the equation (x+yi)+(4+9i)=9-4i is x = 5 and y = -13 .
In the question ,
the equation is given as
(x+yi)+(4+9i)=9-4i
to find the value of x and y , we solve LHS and RHS of the equation separately
So LHS =
(x+yi)+(4+9i)
x+yi+4+9i
Adding the real and imaginary terms , we get
(x+4)+(y+9)i which is equal to RHS that is 9-4i
So , on comparing , we get
x+4 = 9 and y+9 = -4
x= 9-4 and y = -4-9
x = 5 and y = -13
Therefore , the values of x and y that satisfy the equation (x+yi)+(4+9i)=9-4i is x = 5 and y = -13 .
The given question is incomplete , the complete question is
What are the The values of X and Y that satisfy this equation (x+yi)+(4+9i)=9-4i ?
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Find the value of x.
(5x − 17)°
13
132
12
48
Answer:
its 12
Step-by-step explanation:
Question 4(Multiple Choice Worth 1 points)
(03.01 MC)
Simplify square root of three times square root of twenty one.
square root of twenty four
square root of sixty three
three square root of seven
nine square root of seven
The Simplification of square root of three times square root of twenty one is; C: three square root of seven
How to use law of Exponents?The Laws of Exponents are;
When multiplying like bases, ensure that the base is kept the same while we add the exponents. When raising a base with a particular power to another specific power, ensure that the base is kept the same and multiply the exponents. When dividing like bases, ensure that the base is kept the same and subtract the denominator exponent from the numerator exponent.We have the expression;
√3 * √21
= √3 * √3 * √7
= (√3 * √3) * √7
= 3√7
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Evaluate g(18), when g(x)=−8x+14
Answer:
-130
Step-by-step explanation:
g(18)= -8(18)+14
=-144+14
=-130
Determine the range of the following graph:
Answer:
The range is the allowed values of y.
Set notation: { y | -9 [tex]\leq[/tex] y [tex]\leq[/tex] 0, y ∈ R}
Interval notation: [-9,0]
Hope that helps
Which of the following shows the values of −0.5, −2.8, 1.9, 0.9, and −1.7 plotted on a number line?
A number line starting at negative 3.3 with tick marks every one tenth unit up to 2.1. The values for negative 2.9, negative 2, negative 0.6, 0.9, and 1.7 are plotted.
A number line starting at negative 3.3 with tick marks every one tenth unit up to 2.1. The values for negative 2.8, negative 1.7, negative 0.5, 0.9, and 1.9 are plotted.
A number line starting at negative 3.3 with tick marks every one tenth unit up to 2.1. The values for negative 3, negative 1.9, negative 0.7, 0.8, and 1.9 are plotted.
A number line starting at negative 3.3 with tick marks every one tenth unit up to 2.1. The values for negative 2.9, negative 2, negative 0.6, 0.9, and 1.9 are plotted.
The statement that shows the values of -0.5,-2.8,1.9,0.9 and -1.7 plotted on a number line is " A number line starting at negative 3.3 with tick marks every one tenth unit up to 2.1. The values for negative 2.8, negative 1.7,negative 0.5,0.9 and 1.9 are plotted."
Here the values are
-0.5,-2.8,1.9,0.9 and -1.7
The number line a graphical representation that a line on which numbers are marked at intervals, used to represents the simple numerical operations.
Here there are three negative numbers -0.5,-2.8 and -1.7
The positive numbers are 1.9 and 0.9
The statement "A number line starting at negative 3.3 with tick marks every one tenth unit up to 2.1. The values for negative 2.8, negative 1.7, negative 0.5,0.9 and 1.9 are plotted" is suited of all the given conditions
Hence, The statement that shows the values of -0.5,-2.8,1.9,0.9 and -1.7 plotted on a number line is " A number line starting at negative 3.3 with tick marks every one tenth unit up to 2.1. The values for negative 2.8, negative 1.7, negative 0.5, 0.9, and 1.9 are plotted."
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Write an equation is point slope form of a line given that the slope is 2/3 and that the line goes through the point (5,-2)
Answer:
[tex](y+2)=\frac{2}{3} (x-5)[/tex]
Step-by-step explanation:
Point slope form is shown below:
[tex](y-y_1)=m(x-x_1)[/tex]
We are given the slope m = 2/3 and the point x1 = 5, y1 = -2
Simply plug in these numbers into the above equation.
[tex](y--2)=\frac{2}{3} (x-5)[/tex]
Simplify:
[tex](y+2)=\frac{2}{3} (x-5)[/tex]
help meeeeeeeeeeee pleaseeeeeeeeeeeeee!!
Answer:
Yes, is a function
Step-by-step explanation:
it does not repeat x's
Water is drained at constant rate of 2 gallons per minute from a fish tank containing 28 gallons of water which equation represent the number of gallons of water remaining in the tank y based on the number of minutes t since water started draining from the fish tank where 0<_t_<14?
The equation represent the number of gallons of water remaining in the tank is y = 28 - 2t
What is an equation?A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
The water remaining is illustrated as y.
The time taken is t.
The appropriate equation will be:
y = 28 - (2 × t)
y = 28 - 2t
This illustrates the water remaining in the tank.
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A local builder estimated that each year 57 homes are built in the surrounding area. In 2002 there was 43,800 homes. Find the number of homes in 2011.
The number of homes in 2011 is 44,313
Explanation:Given that 57 homes are built each year, in 2002, there were 43,800 homes, then the next years have the number of homes as follows:
2003: 43,800 + 57
2004: 43,800 + 57 + 57
2005: 43,800 + 57 + 57 + 57
This goes on until 43,800 + 57n
where n is the number of years after 2002.
2011 is 9 years after 2002, so the number of homes will be:
43,800 + 57(9)
= 43,800 + 513
= 44,313
I need help with this
Answer:
113.85
Step-by-step explanation:
230*55% because 100%-45%=55% is 126.5
Then 126.5*90% because 100%-10%=90% which is 113.85
the long division method to find the result when 12x^{3}+5x^{2}-27x+1312x
3
+5x
2
−27x+13 is divided by 3x-13x−1. If there is a remainder, express the result in the form q(x)+\frac{r(x)}{b(x)}q(x)+
b(x)
r(x)
(hope it makes sense)
The solution of the polynomial division 12x³ + 5x² - 27x + 13 is divided by 3x - 1 is; 4x² + 3x - 8 + (5/(3x - 1))
How to carry out Polynomial Long Division?
We want to use long division method to solve the polynomial division when 12x³ + 5x² - 27x + 13 is divided by 3x - 1.
4x² + 3x - 8
-------------------------
3x - 1 | 12x³ + 5x² - 27x + 13
- 12x³ - 4x²
-----------------------------
9x² - 27x
- 9x² - 3x
-----------------------------
-24x + 13
- -2x + 8
-----------------------------
5
-----------------------------
Expressing the solution of the polynomial division in the given quotient and remainder form gives us; 4x² + 3x - 8 + (5/(3x - 1))
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Two polynomials P and D are given. Use either synthetic or long division to divide P(x) by D(x), and express P in the form P(x) = D(x) Q(x) + R(x).
P(x) = 3x³-4x²-3x, D(x) = 3x - 4
P(x) =
The value of Q(x) = x² - 1
R(x) = 4
What is Long Division?
Long division is a common division procedure in mathematics that may be easily performed manually and is appropriate for dividing multi-digit Hindu-Arabic numbers. It simplifies a division problem into several shorter stages.
By long Division method:
x² - 1
_______________________________
(3x - 4) | 3x³ - 4x² - 3x
3x³ - 4x²
_________________
0 - 0 - 3x
- 3x + 4
___________________
0 + 4
Q(x) = x² - 1
R(x) = 4
Hence, (3x³-4x²-3x) = (3x - 4)(x² - 1 ) + 4
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Simplify the expression,
Assume all variables are positive.
Answer:
x²[tex]\sqrt{5}[/tex]
Step-by-step explanation:
using the rule of radicals
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]
given
5[tex]\sqrt{20x^4}[/tex] - 3[tex]\sqrt{45x^4}[/tex]
simplify the 20 and 45 inside the radicals
[tex]\sqrt{20}[/tex] = [tex]\sqrt{4(5)}[/tex] = [tex]\sqrt{4}[/tex] × [tex]\sqrt{5}[/tex] = 2[tex]\sqrt{5}[/tex]
[tex]\sqrt{45}[/tex] = [tex]\sqrt{9(5)}[/tex] = [tex]\sqrt{9}[/tex] × [tex]\sqrt{5}[/tex] = 3[tex]\sqrt{5}[/tex]
Then
= 5(2[tex]\sqrt{5}[/tex] x² ) - 3(3[tex]\sqrt{5}[/tex] x² )
= 10[tex]\sqrt{5}[/tex] x² - 9[tex]\sqrt{5}[/tex] x²
= x²[tex]\sqrt{5}[/tex]
Determine the rule for translating ABC to A'B'C'
Correct answer is A, the rule for translating ABC to A'B'C' is left 2, up 9.
What does translating a triangle mean?An example of a transformation is a translation, which moves every point in a figure uniformly and in one direction. are frequently called slides. You can use notation or words to express a translation, such as "moved up 3 and over 5 to the left."
A translation in geometry is a type of transformation that shifts a geometric figure in a certain direction without altering its size or orientation. The figures are congruent before and after the transformation since it is a type of stiff transformation.
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If what is the length of DF?
Answer:
DF = 13
Step-by-step explanation:
Congruent triangles:
In ΔABC & ΔDEF,
∠A = ∠D
∠C = ∠F
CB = FE
ΔABC ≅ ΔDEF {Angle Angle Side congruency}
DF = AC = 13
The midpoint of GH is M(3, 6). One endpoint is H(6, 5). Find the coordinates of the other endpoint G.
The coordinates of the endpoint G is (0, 7).
The midpoint of the coordinate is the centre point which can be calculated by finding the average. So, the relation representing the endpoints and midpoint is as follows -
Midpoint (x, y) = ([tex] x_{1}[/tex] + [tex] x_{2}[/tex]/2), ([tex] y_{1}[/tex] + [tex] y_{2}[/tex]/2)
Keep the value in mentioned formula to find the endpoint G, represented as [tex] x_{1}[/tex] and [tex] y_{1}[/tex].
(3, 6) = ([tex] x_{1}[/tex] + 6/2) ([tex] y_{1}[/tex] + 5/2)
Relating the x and y values -
x value :
3 = [tex] x_{1}[/tex] + 6/2
[tex] x_{1}[/tex] + 6 = 3×2
[tex] x_{1}[/tex] + 6 = 6
[tex] x_{1}[/tex] = 6 - 6
[tex] x_{1}[/tex] = 0
y value :
6 = [tex] y_{1}[/tex] + 5/2
[tex] y_{1}[/tex] + 5 = 6×2
[tex] y_{1}[/tex] + 5 = 12
[tex] y_{1}[/tex] = 12 - 5
[tex] y_{1}[/tex] = 7
Thus, the coordinates of point G from the line GH is (0, 7).
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X - 11 = -44 solve one step equation.
Answer: x = -33
Explanation:
Given the following question:
x - 11 = -44
Step 1: collect the like terms
x = -44 + 11
x = -33
Therefore, x = -33
Select the pair that could be a reasonable approximation for the diameter and
circumference of a circle.
5 meters and 22 meters
19 inches and 60 inches
33 centimeters and 80 centimeters
Explain your reasoning.
Your answer
We know that pair (B) (19 inches and 60 inches) can be a fair estimation of a circle's diameter and circumference.
What is a circle?All points in a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant. Simply put, a circle is a rounded shape without any edges or line segments. It has the geometric shape of a closed curve.So, let 'D' be the diameter and 'C' be the circumference.
Calculate C as:
C = πD (π = 3.14)(A) D = 5 m and C = 22 m
C = πD C = 3.14 × 5C = 15.7 mSo, C = 15.7 m does not approximate 22 m.
(B) D = 19 in and C = 60 in
C = πD C = 3.14 × 19C = 59.66 inSo, C = 59.66 approximates 60 in.
(C) D = 33 cm and D = 80 cm
C = πD C = 3.14 × 33C = 103.62cmSo, C = 103.62cm does not approximate 80cm.
Therefore, we know that pair (B) (19 inches and 60 inches) can be a fair estimation of a circle's diameter and circumference.
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The correct question is given below:
Select all the pairs that could be reasonable approximations for the diameter and circumference of a circle. * 1 point A. 5 meters and 22 meters. B. 19 inches and 60 inches. C. 33 centimeters and 80 centimeters.