Write an equation of the line with a slope of 2 that passes through the point (2,0)
Answers
[tex] y = mx + b [/tex]
m is the slope. We are told m = 2.
Now we have
[tex] y = 2x + b [/tex]
We need to find b, the y-intercept. We are given a point, (2, 0). We replace x with 2 and y with 0. Then we solve for b.
[tex] 0 = 2(2) + b [/tex]
[tex] -4 = b [/tex]
Now that we know that b = -4, we replace b with -4.
[tex] y = 2x - 4 [/tex]
Hence, the line with a slope [tex]2[/tex] that passes through the point [tex](2,0)[/tex] is
[tex]y=2x-4[/tex]
What is the line of equation?
The equation of a line is an algebraic form of representing the set of points, which together form a line in a coordinate system.
The numerous points which together form a line in the coordinate axis are represented as a set of variables [tex]x, y[/tex] to form an algebraic equation, which is referred to as an equation of a line.
As we know the line of the slope is
[tex]y=mx+b[/tex]
where [tex]m[/tex] is the slope we have [tex]m = 2.[/tex]
So it would be
[tex]y=2x+b[/tex]
Given the point, [tex](2, 0)[/tex]
Now, we replace [tex]x[/tex] with [tex]2[/tex] and [tex]y[/tex] with [tex]0[/tex].
Now, we solve for [tex]b[/tex].
So,
[tex]0=2(2)+b\\b+4=0\\b=-4[/tex]
Since we get [tex]b = -4[/tex], we replace [tex]b = -4[/tex]
i.e., [tex]2x-4[/tex]
Hence, the line with a slope [tex]2[/tex] that passes through the point [tex](2,0)[/tex] is
[tex]y=2x-4[/tex]
To know more about the line of equation
https://brainly.com/question/24092819
#SPJ2
Related Questions
PLEASE HELP
Is this A, B, or C?
Answers
The sum can be written like this:
[tex]-4\frac{1-\left(\frac{1}{2}\right)^6}{1-\frac{1}{2}}=-8\left(1-\dfrac{1}{2^6}\right)\\ =-8\dfrac{63}{64}\\=-\dfrac{63}{8}[/tex]
The correct answer is the second one.
If a 10. m3 volume of air (acting as an ideal gas) is at a pressure of 760 mm and a temperature of 27 degrees Celsius is taken to a high altitude where the pressure is 400. mm Hg and a temperature of -23 degrees Celsius, what volume will it occupy? (Hint: remember the temperature must be in Kelvin)
Answers
P1V1/T1 = P2V2/T2, Where P1, V1 and T1 are the initial pressure, volume and temperature respectively, while P2,V2 and T1 are the new pressure, volume and temperatures respectively.
Thus; P1= 760 mmHg, V1=10 m^3, T1 = 27 +273 = 300 K
P2= 400 mmHg, V2= ? and T2= -23 +273 = 250K
V2 = (P1V1T2)/T1P2
= (760×10×250)/(300×400)
= 1900000/120000
= 15.83
Therefore, the new volume is 15.83 m³
Answer:
16. m3
Step-by-step explanation:
27 degrees Celsius= 27+273= 300 kelvin
23 degrees Celsius= -23+273=250 kelvin
Combined Gas Law: P1V1/T1 = P2V2/T2
(760mm*10 m3)/300 K=(400mm*x m3)/250 K x= 16. m3
The volume that it will occupy is 16. m3.
(Don't forget the sig fig, 15.83--->16. because the question said 10.)
A rectangle is 2 times as long as it is wide. if the area is 18 square feet, find its perimeter.
Answers
The following is an incomplete paragraph proving that the opposite angles of parallelogram ABCD are congruent: According to the given information, and . Using a straightedge, extend segment AB and place point P above point B. By the same reasoning, extend segment AD and place point T to the left of point A. Angles BCD and PBC are congruent by the Alternate Interior Angles Theorem. Angles PBC and BAD are congruent by the ____________. By the Transitive Property of Equality, angles BCD and BAD are congruent. Angles ABC and BAT are congruent by the _____________. Angles BAT and CDA are congruent by the Corresponding Angles Theorem. By the Transitive Property of Equality, ∠ABC is congruent to ∠CDA. Consequently, opposite angles of parallelogram ABCD are congruent. What theorems accurately complete the proof?
Answers
Given a parallelogram ABCD, refer to the attached image.
To prove: Opposite angles are congruent.
Proof:
According to the given information,
Step 1: Using a straightedge, extend segment AB and place point P above point B.
Step 2: By the same reasoning, extend segment AD and place point T to the left of point A.
Step 3: Angles BCD and PBC are congruent by the Alternate Interior Angles Theorem.
Step 4: Angles PBC and BAD are congruent by the Corresponding Angles Theorem. ( If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. Corresponding angles are the angles which occupy the same relative position at each intersection where a straight line crosses two others.)
Step 5: By the Transitive Property of Equality, angles BCD and BAD are congruent.
Step 6: Angles ABC and BAT are congruent by the Alternate Interior Theorem.(The Alternate Interior Angles theorem states, if two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent. Alternate Interior angles are a pair of angles on the inner side of each of those two lines but on opposite sides of the transversal.)
Step 7: Angles BAT and CDA are congruent by the Corresponding Angles Theorem.
Step 8: By the Transitive Property of Equality, ∠ABC is congruent to ∠CDA. Consequently, opposite angles of parallelogram ABCD are congruent.
The proof requires the use of specific theorems such as the Vertical Angles Theorem and Corresponding Angles Theorem to establish the congruence of angles in a parallelogram.
Theorems that accurately complete the proof:
Angles PBC and BAD are congruent by the Vertical Angles Theorem.
Angles ABC and BAT are congruent by the Corresponding Angles Theorem.
Theorem 12 states that if two angles are congruent, their supplementary angles are also congruent.
Would be glad if you answer my question!
Answers
and it's not that you just have to divide the 'a' from both sides giving the answer as p = (px+c) ÷ a, but you have to write in terms of ' a,x and c'.
so ap = px+c
1)collect all the likes to one side (ap - px = c)
2) Take the common out [ p(a-x) = c ]
3) Divide by '(a-x)' to put equation in terms of "p="
4) therfore, p = c ÷ (a-x)
Hope this answered your question
in a given circuit, the supplied voltage is 1.5 volts, and the resistor value is 3 ohms. use ohm's law to determine the current in the circuit
Answers
Final answer:
The current in a circuit with a supplied voltage of 1.5 volts and a resistance of 3 ohms is calculated using Ohm's Law (I = V/R), resulting in a current of 0.5 amperes.
Explanation:
Using Ohm's Law to Calculate Current
To determine the current in a circuit with a supplied voltage of 1.5 volts and a resistor value of 3 ohms, we can use Ohm's Law, which is stated as I = V/R, where I is the current, V is the voltage, and R is the resistance. Plugging in the values, we have I = 1.5 volts / 3 ohms. Therefore, I = 0.5 amperes or 500 milliamperes. This is the current flowing through the circuit.
Ohm's Law is a fundamental principle in physics used for analyzing simple circuits where the relationship between voltage, current, and resistance is linear. Remember that this law holds true for ohmic materials where the resistance remains constant over a range of voltages and temperatures.
At a furniture manufacturer, worker A can assemble a shelving unit in 5 hours. Worker B can assemble the same shelving unit in 3 hours. Which equation can be used to find t, the time it takes for worker A and worker B to assemble a shelving unit together?
Answers
t = total time it takes to assemble a shelving unit together.
We then have the following equation:
1/5 + 1/3 = 1 / t
Solving the equation we have:
3t + 5t = 15
8t = 15
t = 1,875 hours
Answer:
the time it takes for worker A and worker B to assemble a shelving unit together is:
t = 1,875 hours
The equation 1/t = 1/5 + 1/3 can be used to find the time it takes for worker A and worker B to assemble a shelving unit together.
To find the time t it takes for worker A and worker B to assemble a shelving unit together, we need to add their work rates.
Worker A's work rate is 1 unit per 5 hours (or 1/5 units per hour), and worker B's work rate is 1 unit per 3 hours (or 1/3 units per hour).
The combined work rate is the sum of their individual work rates:
1/5 + 1/3 = (3 + 5) / 15 = 8 / 15 units per hour
If t is the time they take together to complete one shelving unit, then their combined work rate is 1 unit per t hours. Setting this equal to their combined rate, we get:
1/t = 8/15
Solving for t gives:
t = 15/8 hours
Therefore, the equation 1/t = 1/5 + 1/3 can be used to find the time it takes for worker A and worker B to assemble a shelving unit together.
The city of Beijing has a population of more than 10 to the 7th power people. Write 10 to the 7th power without using an exponent
Answers
Answer:
[tex]10\times 10\times 10\times 10\times 10\times 10 \times 10[/tex]
Step-by-step explanation:
Exponentiation is the operation used to write the product of two or more equal factors. This expression can written as follows:
[tex]a^n\\\\Where:\\\\a=Base\\n=Exponent[/tex]
That is, [tex]a^n[/tex] is the product of multiplying n bases:
[tex]a^n=a\times...\times...\times a[/tex]
In this sense:
[tex]10^7=10\times 10\times 10\times 10\times 10\times 10 \times 10[/tex]
The line segment is dilated by a factor of 1/2 with respect to the origin. What is the length of the dilated line segment?
A. 1 unit
B. 2 units
C. 3 units
D. 4 units
Answers
The length of the dilated line segment is 2 units. ( option B)
A scale factor is a ratio that describes the proportional change in size between two similar geometric figures.
Scale factor = Dimension of new length /dimension of original length
The dimension of the original length is 4 units
scale factor = 1/2
let the new length be x
Therefore;
1/2 = x/4
2x = 4
x = 4/2 = 2units
Therefore, the length of the dilated segment is 2units
In a Quadratic Regression problem, a graph is a perfect fit for the data when r = ? a. 1 c. 2 b. 0 d. 100 Please select the best answer from the choices provided A B C D
Answers
Answer:
the answer is A on edge :)
Step-by-step explanation:
The graph that is a perfect fit for the given data in a quadratic regression problem is when r is; A: 1
What is a quadratic regression?Quadratic regression is defined as a statistical technique that is used to find the equation of the parabola that best fits a set of data.
Now, this type of regression is an extension of simple linear regression that is used to find the equation of the straight line that best fits a set of data.
Thus, in this type of regression, we say a graph is a perfect fit when r = 1.
Read more about Quadratic Regression at; https://brainly.com/question/26174369
#SPJ5
in quadrilateral abcd , angle A=57 degrees , angle B=65 degrees and angle c=118 degrees What is the measure of an exterior angle at D
Answers
you are given 57, 65, 118
That is 240
to solve for the last angle
360-240
120
The exterior angle of a D would be the number that you add that will make it 180 degrees.
meaning 180-120 is
The exterior angle of angle D is 60 degrees.
Hope this helps
if the remainder on division of x^3+2x^2+kx+3 by x-3 is 21,find the quotient and the value of k. Hence,find the zeroes of the cubic polynomial x^3+2x^2+kx-18.
Answers
On dividing p(x) by x-3, the remainder is 21. Therefore,
P(3)=21
Substituting x=3 in p(x)
P(3)=3^3 +2*(3)^2+k*3+3
=27+18+3k+3
=48+3k
We know that, p(3)=21.
So, 48+3k=21
3k=21-48
3k=-27
k=-27/3 =-9
now, p(x) =x^3+2x^2-9x-18
-2 is a factor of p(x) on inspection. Therefore, divide p(x) by x+2 to find the
zeroes of the polynomial.
On dividing, we get the factors to be, (x^2-9)(x+2)
(x^2-3^2)(x+2)
Factorizing using the identity a^2-b^2=(a+b)(a-b) we get,
(x+3)(x-3)(x+2)
Therefore, the zeroes of the polynomials are -3,+3 and -2.
The formula used to find the length of a line segment in space.
Answers
length = √((∆x)^2 +(∆y)^2 +(∆z)^2)
.. where ∆x, ∆y, ∆z are the differences between the end-point coordinates in the x-, y-, and z-directions, respectively.
if youre doing the vocab thing -- Distance
Danielle poured 3/4 gallon of water from a 7/8 gallon bucket. How much water is left in the bucket?
Answers
Subtract 3/4 from 7/8 and we get
7/8 - 3/4 = 7/8 - 6/8 = (7-6)/8 = 1/8
There is 1/8 of a gallon left
Which of the following is a logarithmic function? A. Y=0.25X B. Y=x^0.25 c.y=log25^x d.y=(0.25)^x
Answers
Answer:
The correct option is C .
Step-by-step explanation:
A logarithm function is written in the form of [tex]y=log_ax[/tex],
Since, y = 0.25x is the type of function y = mx + c,
Which is the general form of a linear function,
⇒ y = 0.25x is not a logarithm function,
[tex]y=x^{0.25}[/tex] is the type of function [tex]y=kx^a[/tex], where k and a are any real number,
Which is the general form of a power function,
⇒ [tex]y=x^{0.25}[/tex] is not a logarithmic function.
[tex]y=(0.25)^x[/tex] is the type of function [tex]y=ab^x[/tex]
Which is the general form of exponential function,
⇒ [tex]y=(0.25)^x[/tex] is not a logarithmic function,
Hence, only the function in option C has written in the form of [tex]y=log_ax[/tex].
Option C is correct.
Which graph represents the function over the interval [−3, 3]?
Answers
Function floor (or ground), that to each real number assigns the nearest whole number by defect, that is to say, the greater whole number equal or smaller than that real number.
Let's evaluate the extremes of the interval
x = -3
g (-3) = floor (-3) -2 = -5
x = 3
g (3) = floor (3) -2 = 1
Therefore, the graph that best corresponds to the function in the given interval is the attached graph.
Third graphrepresents the function [tex]f\left( x \right) = \left\lfloor x \right\rfloor-2[/tex] over the interval [tex]\left[ { - 3,3} \right].[/tex]
Further explanation:
Given:
The function is [tex]f\left( x \right) = \left\lfloor x \right\rfloor- 2.[/tex]
The function is defined in the interval [tex]\left[ {-3,3}\right].[/tex]
Explanation:
The greatest integer function is represented [tex]y = \left\lfloor x \right\rfloor.[/tex]
The greatest integer can also be known as floor function. The function is integral part of real numbers.
The values of greatest function [tex]f\left( x \right)= \left\lfloorx \right\rfloor- 2[/tex] in interval [tex]\left[{ - 3,3}\right][/tex] can be obtained as follows,
Substitute [tex]-3[/tex] for [tex]x[/tex] in the function [tex]f\left( x \right)= \left\lfloor x \right\rfloor- 2.[/tex]
[tex]\begin{aligned}f\left({- 3} \right)&=\left\lfloor{ - 3} \right\rfloor- 2\\&=- 3- 2\\&=- 5\\\end{aligned}[/tex]
Substitute [tex]3[/tex] for [tex]x[/tex] in the function [tex]f\left( x \right)=\left\lfloor x \right\rfloor- 2.[/tex]
[tex]\begin{aligned}f\left( 3 \right)&= \left\lfloor3\right\rfloor- 2\\&=3- 2\\&=1\\\end{aligned}[/tex]
The minimum value of the function in [tex]\left[ { - 3,3} \right] {\text{is}\: \boxed{ - 5}.[/tex]
The maximum value of the function in [tex]\left[ { - 3,3} \right] {\text{is}\: \boxed{1}.[/tex]
Third graphrepresents the function [tex]f\left( x \right)=\left\lfloor x\right\rfloor- 2[/tex] over the interval [tex]\left[{ - 3,3}\right].[/tex]
Kindly refer to the image attached.
Learn more
1. Learn more about the polynomial https://brainly.com/question/12996944
2. Learn more about logarithm model https://brainly.com/question/13005829
3. Learn more about the product of binomial and trinomial https://brainly.com/question/1394854
Answer details:
Grade: High school
Subject: Mathematics
Chapter: Number system
Keywords: factor, factorization, polynomial, quadratic, cubic, greatest common factor, groups, multiplication, product, identities, common factor, expression, terms, grouping.
Ben and Marge are purchasing a house with a 20-year, 5/1 ARM for $265,000 at 5.25% with a 3/12 cap structure. What will the difference in payments be from year 5 to year 6?
A. $925.81
B. $880.29
C. $369.32
D. $234.39
Answers
The difference in payments from year 5 to year 6 is approximately $369.32 for the 5/1 ARM mortgage.
To calculate the payment difference from year 5 to year 6 for a 5/1 ARM (Adjustable Rate Mortgage) with a 3/12 cap structure, we need to understand how the ARM works and how the caps affect the adjustment.
1. Initial Mortgage Parameters :
- Loan Amount: $265,000
- Interest Rate: 5.25%
- Term: 20 years
2. Adjustment Frequency : The 5/1 ARM adjusts after the initial 5-year fixed period, then annually.
3. Cap Structure :
- Initial Adjustment Cap: 3%
- Subsequent Adjustment Cap: Each year after the initial adjustment, the rate can adjust up to 3% from the previous rate.
4. Calculation Steps :
a. Calculate the initial monthly payment using the loan amount, interest rate, and term.
b. Determine the new interest rate for year 6 based on the cap structure.
c. Calculate the monthly payment for year 6 with the new interest rate.
d. Find the difference between the payments from year 5 to year 6.
Let's start the calculations:
a. Calculate the initial monthly payment using the loan amount, interest rate, and term. We'll use the formula for a fixed-rate mortgage:
[tex]\[ P = \frac{P_r \cdot A}{1 - (1 + r)^{-n}} \][/tex]
Where:
- [tex]\( P \)[/tex] = Monthly Payment
- [tex]\( P_r \)[/tex] = Periodic Interest Rate (annual rate divided by 12)
- [tex]\( A \)[/tex] = Loan Amount
- [tex]\( r \)[/tex] = Periodic Interest Rate
- [tex]\( n \)[/tex] = Total number of payments (loan term in years multiplied by 12)
For the initial fixed period of 5 years:
[tex]\[ P_r = \frac{5.25\%}{12} = 0.004375 \][/tex]
[tex]\[ n = 20 \times 12 = 240 \][/tex]
Plugging these values into the formula:
[tex]\[ P = \frac{0.004375 \cdot 265000}{1 - (1 + 0.004375)^{-240}} \][/tex]
[tex]\[ P \approx 1645.80 \][/tex]
So, the initial monthly payment is approximately $1,645.80.
b. Determine the new interest rate for year 6 :
- The initial rate can adjust up to 3% in year 6.
- So, the new interest rate could be up to \( 5.25\% + 3\% = 8.25\% \).
c. Calculate the monthly payment for year 6 :
- Use the formula for the monthly payment again with the new interest rate:
[tex]\[ P_r = \frac{8.25\%}{12} = 0.006875 \][/tex]
Plugging into the formula:
[tex]\[ P = \frac{0.006875 \cdot 265000}{1 - (1 + 0.006875)^{-240}} \][/tex]
[tex]\[ P \approx 1985.09 \][/tex]
So, the monthly payment for year 6 is approximately $1,985.09.
d. Find the difference in payments from year 5 to year 6:
[tex]\[ Difference = Payment_{Year6} - Payment_{Year5} \][/tex]
[tex]\[ Difference = 1985.09 - 1645.80 \][/tex]
[tex]\[ Difference \approx 339.29 \][/tex]
So, the difference in payments from year 5 to year 6 is approximately $339.29.
Therefore, the closest answer is C. $369.32 .
Maria sets a goal of jogging 17.5miles this week. She plans on running 2.75 miles each day for 7 days . If she follows her plan which is true
Answers
19.25 miles.
She completes her goal of jogging 17.5 miles that week.
Tickets for the school play cost $17 each. Gary wrote the expression n X 17 to find the cost of n tickets to the play. He used the Distributive Property to find the product. Use the Distributive Property to write Gary's expression another way.
Answers
We have then that the expression used by Gary:
n = X * 17
Using the distributive property we have another way to rewrite the expression is:
n = 17 * X
Where,
x: is the sum of all tickets sold.
Answer:
n = 17 * X
A small plane leaves an airport at a speed of 252 miles per hour. A jet leaves the airport 2 hours later traveling at 672 miles per hour. How long will the small plane be flying before the jet catches up to it? What unit will you use for your answer?
Answers
the small plane runs at a rate of 252 mph, the jet runs at 672 mph, but the jet takes off 2 hours later.
if the jet plane say has been traveling for "t" hours by the time they meet, the small plane was already rolling before the jet, actually 2 hours earlier, so if the jet has gone for "t" hours, the small plane has been going for "t+2" hours.
now, by the time they both meet, the distance covered by say the small plane is "d" miles, but the distance covered by the jet is also the same "d" miles, since they're meeting.
[tex]\bf \begin{array}{lccclll} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ &------&------&------\\ \textit{small plane}&d&252&t+2\\ \textit{jet plane}&d&672&t \end{array} \\\\\\ \begin{cases} d=252(t+2)\\ d=672t\\ --------\\ 252(t+2)=672t \end{cases} \\\\\\ 252t+504=672t\implies 504=420t\implies \cfrac{504}{420}=t\implies \cfrac{6}{5}=t \\\\\\ \textit{an hour and 12 minutes}=t[/tex]
No, thanks to you, I got the question wrong it was hours.
Michelle draws a card from a standard deck of 52 cards. She replaces the card and draws a second card. What is the probability that she draws a red card and then a black card
A) 1/16
B)1/26
C)1/4
D)1/52
Answers
Multiply the probabilities.
1/2 * 1/2 = 1/4
The answer is C. 1/4
Can someone help me please!!!
Answers
3x + 2(5x - 1) = 11
3x + 10x - 2 = 11
13x = 13
x = 1
y = 11 - 3x
y = 11 - 3
y = 8
y = 5x -1
Using substitution
3x + 2(5x-1) = 11
3x + 10 x -2 = 11
13x = 13
x = 1
but, y= 5x -1
y = 5 (1)- 1
= 4
Therefore, y =4 and x = 1
Question 2
Using linear combination method
2x -3y = 13
x+2y = -4 multiplying the second equation by 2 to eliminate x
we get
2x - 3y = 13
2x + 4y = -8 ( subtracting the two equations)
-7y = 21
y = -3
To get x we substitute y with -3 in one of the equation
x = -4 -2y
x = -4 - 2(-3)
x = 2
Therefore, the value of x = 2 and y =-3
Question 3
The first thing is to get a table of values for each of the equation using at least three values of x, this gives you at least three coordinates that can be used to plot the lines on the Cartesian plane.
That is;
For; y = (1/2)x + 3
x y
(2 , 4)
(4, 5)
(6, 6)
And for -3x +y = -2 which is the same as y =-2 +3x
x y
(0, -2)
(1, 1)
(2, 4)
Then, plot the two lines on the plane using the above coordinates,
The solution will be the point of intersection of the two lines (where the two lines plotted meet)
Which expression represents the number of sides in the polygon for the nth member of the pattern? A) n + 3 B) n3 C) n + 2 D) 3n
Answers
2nd member has 6 sides (3x2)
3rd member has 9 sides' (3x3)
Therefore, i think for nth member
the appropriate expression for n th member will be 3n
Which list shows all the factors of 18?
1, 2, 3, 4, 6, 9, 18
1, 2, 3, 6, 9, 18
2, 3, 4, 6, 9
2, 3, 6, 9
Answers
Instructions:Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
is parallel to . and are perpendicular to and .
The ratio of the lengths of and is
:
.
Answers
Answer:
The ratio of the lengths of PR and QS is 1 : 1
Step-by-step explanation:
If your question is based on this exercise:
PQ Is parallel to RS. PR and QS are perpendicular to PQ and RS
Here is why
Joan has 45 marbles . MARY HAS m marbles if Joan has 15 times as many marbles , write an equation that shows how many marbles mary has
Answers
Mary has 3 marbles.
Explanation:To find out how many marbles Mary has, we can use the information that Joan has 45 marbles and Joan has 15 times as many marbles as Mary. So, we can set up an equation:
45 = 15m
To solve for m, we divide both sides of the equation by 15:
m = 45/15
Simplifying the expression, we get:
m = 3
Therefore, Mary has 3 marbles.
Determine the number of possible triangles, ABC that can be formed given angle A=30 degrees, a=4 and b=6
Answers
Answer:
One possible triangle
Step-by-step explanation:
Given that in a triangleABC given one angle A =30 , two sides a and b
We can use sine angle formula for triangles
[tex]\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}[/tex]
Substitute to get
[tex]\frac{4}{sin30} =\frac{6}{sin B} =\frac{c}{sinC}[/tex]
[tex]sin B = 0.75\\B=48.6[/tex]
C=[tex]180-30-48.6\\= 101.4[/tex]
[tex]c=8sin 101.4\\c=7.842[/tex]
There can be only one triangle
helppppppppppppppppppppp
Answers
f (a) = 5 + a ^ 2
g (a) = root (a-5) -2
By making the composition we have:
g (f (a)) = root ((5 + a ^ 2) -5) -2
Rewriting the function:
g (f (a)) = root (5 + a ^ 2-5) -2
g (f (a)) = root (a ^ 2) -2
g (f (a)) = lal-2
Answer:
The functions are:
f (a) = 5 + a ^ 2
g (a) = root (a-5) -2
option 3
Which is the ratio for sin a written as a fraction in simplest form
Answers
your Answer issss:
√3/2
A group of college students are volunteering for Help the Homeless during their spring break. They are putting the finishing touches on a house they built. Working alone, Irina can paint a certain room in 9 hours. Paulo can paint the same room in 8 hours. Write an equation that can be used to find how long it will take them working together to paint the room. How many hours will it take them to paint the room? If necessary, round your answer to the nearest hundredth
Answers
Since Paulo can paint 1 room in 8 hours, that means he paints 1/8 of the room in 1 hour. His portion of the equation would be 1/8x, with x being the number of hours he works and 1/8 of a room per hour being his speed.
The equation would then be 1/9x + 1/8x = 1 (Irina's portion of the room, plus Paulo's portion of the room, equal to one whole room).
Find a common denominator. 72 is the first number that both 9 and 8 divide evenly into. Since 9*8 = 72, we multiply the top of 1/9 by 8 to convert the fraction and get 8/72x. Since 8*9 = 72, we multiply the top of 1/8 by 9 to convert the fractio and get 9/72x. We now have 8/72x+9/72x=1
17/72x=1
Divide both sides by 17/72:
17/72x ÷ 17/72 = 1÷17/72
x=1/1 ÷ 17/72
x=1/1 * 72/17
x=72/17=4.24
Together it should take them 4.24 hours.
The combined work rate can be found by using the equation for combined rate.
The correct responses;The time it will take them working together is; [tex]\displaystyle \underline{\frac{1}{t_b} = \frac{1}{t_1} + \frac{1}{t_2} }[/tex]The number of hours it will take them working together to paint the room is approximately 4.24 hours. The method by which the above responses are obtained:The time it takes Irina to paint the room alone, t₁ = 9 hours
Time it takes Paulo to paint the room, t₂ = 8 hours
Required:
To write the equation for the combined rate of Irina and Paulo
Solution:The equation that gives the time, [tex]\mathbf{t_b}[/tex], it will take both Irina and Paulo to paint the room together is given by the combined rate formula, as follows;
[tex]\displaystyle \underline{ \frac{1}{t_b} = \frac{1}{t_1} + \frac{1}{t_2}}[/tex]Required:The duration it will take them to paint the room when working together.
Solution:The time it will take them to paint the room together is found as follows;
[tex]\displaystyle \frac{1}{t_b} = \mathbf{\frac{1}{9} + \frac{1}{8}}[/tex]
Which gives;
[tex]\displaystyle \frac{1}{t_b} = \frac{8 + 9}{9 \times 8} = \mathbf{\frac{17}{72}}[/tex]
Therefore;
[tex]\displaystyle t_b = \frac{72}{17} \approx \mathbf{4.24}[/tex]
The time it takes Irina and Paulo to paint together, [tex]t_b[/tex] ≈ 4.24 hrs.Learn more about combined rate of work here:
https://brainly.com/question/25312135