Let us Represent the Line A in the Standard form : y = mx + c
where : m is the Slope of the Line and c is the y-intercept
Given : Equation of Line A is 2x + 3y = 10
[tex]\bf{\implies y = \frac{-2}{3}x + \frac{10}{3}}[/tex]
Comparing with the Standard form, We can notice that :
Slope of Line A [tex]\bf{= \frac{-2}{3}}[/tex]
We know that : Parallel lines have Same Slope
Given : Line A and Line B are Parallel
⇒ Slope of Line B [tex]\bf{= \frac{-2}{3}}[/tex]
Given : Line B passes through the Point (-6 , 8)
We know that : Equation of a Line passing through a Point (x₀ , y₀) and having Slope 'm' is given by : y - y₀ = m(x - x₀)
Here : x₀ = -6 and y₀ = 8 and Slope(m) [tex]\bf{= \frac{-2}{3}}[/tex]
Equation of Line B is :
[tex]\bf{\implies y - 8 = \frac{-2}{3}(x + 6)}[/tex]
⇒ 3y - 24 = -2x - 12
⇒ 2x + 3y = 12
PLEASE HELP ASAP!!! CORRECT ANSWERS ONLY PLEASE!!
Simplify.
Answer:
(B): (x - 2)/(x + 1)
Step-by-step explanation:
The numerator is x^2 + 5x - 14. That is equal to (x - 2)(x + 7).
The denominator is x^2 + 8x + 7. That is equal to (x + 1)(x + 7).
You can then eliminate (x+7) to get (x - 2)/(x + 1).
Answer: B
Step-by-step explanation:
[tex]\dfrac{x^{2}+5x-14}{x^{2}+8x+7}[/tex]
[tex]=\dfrac{(x+7)(x-2)}{(x+7)(x+1)}[/tex]
[tex]=\dfrac{(x-2)}{(x+1)}[/tex]
The sides of a hexagon are 2, 3, 2, 4, 7, and 6. Find the perimeter of a similar hexagon with two sides of length 3.
The first hexagon: 2, 2, 3, 4, 6, 7
The second hexagon: 3, 3, a, b, c, d
The hexagons are similar. Therefore the sides are in proportion.
[tex]\dfrac{a}{3}=\dfrac{3}{2}[/tex] multiply both sides by 3
[tex]a=\dfrac{3}{2}=4.5[/tex]
[tex]\dfrac{b}{4}=\dfrac{3}{2}[/tex] multiply both sides by 4
[tex]b=\dfrac{3}{2}\cdot4=6[/tex]
[tex]\dfrac{c}{6}=\dfrac{3}{2}[/tex] multiply both sides by 6
[tex]c=\dfrac{3}{2}\cdot6=9[/tex]
[tex]\dfrac{d}{7}=\dfrac{3}{2}[/tex] multiply both sides by 7
[tex]d=\dfrac{21}{2}=10.5[/tex]
The perimeter:
[tex]P=4.5+6+9+10.5=30[/tex]
Answer:
36
Step-by-step explanation:
The previous answerer forgot to add the two 3's to the sum so the correct answer it 36
Gina opened a bank account with $40. She plans to add $20 per week to the account and not make any withdrawals. After how many weeks will Gina have exactly $700 in her account, excluding interest?
Answer:
After 33 weeks.
Step-by-step explanation:
Let w be number of weeks.
We have been given that Gina opened a bank account with $40. She plans to add $20 per week to the account and not make any withdrawals. So the balance after w weeks will be 20w+40.
To figure out number of weeks Gina will have exactly $700 in her account, we will equate the balance after w weeks to 700.
[tex]20w+40=700[/tex]
Let us subtract 40 from both sides of equation.
[tex]20w+40-40=700-40[/tex]
[tex]20w=660[/tex]
Upon Dividing both sides of our equation by 20 we will get,
[tex]\frac{20w}{20}=\frac{660}{20}[/tex]
[tex]w=\frac{660}{20}[/tex]
[tex]w=33[/tex]
Therefore, after 33 weeks Gina will have exactly $700 in her account, excluding interest.
Which Expression are equivalent to -12(2-3x)-5x
Answer:
-24-36x-5x
-24-41x
or -41x-24
Step-by-step explanation:
Can someone please help with these 2 math questions? :)
Answer:
4. 8.8 years
5. 8.6 meters
Step-by-step explanation:
4. The process of solving the equation f(x) = g(x) gives rise to a 4th-degree equation. Those are best solved using some sort of machine solver. A graphing calculator is often a good place to start. If you're going to do that anyway, you may as well start with a graphical solution to the question.
A plot of the two curves finds they intersect at about x = 8.8. (See the first attachment.) This avoids the extraneous solutions introduced by the process of eliminating the radical.
___
5. Analytical solution is simpler here, but the graphing calculator is faster yet. It shows the two rocks are at the same height at 8.6 meters (if they're launched at the same time).
... f(x) = g(x)
... -4.9x^2 +17 = -4.9x^2 +13x
... 17 = 13x . . . . . add 4.9x^2
... 17/13 = x . . . . time when rocks meet
... f(17/13) = -4.9(17/13)^2 +17 = -1416.1/169 +17 ≈ 8.62071
... f(17/13) ≈ 8.6 . . . . height at which rocks meet
What is the perimeter of a triangle with the given side lengths? s1 = x + 4 cm s2 = 3x + 1 cm s3 = 7x + 3 cm P = x + cm
Answer:
11x+8 cm = Perimeter
Step-by-step explanation:
A triangle has 3 sides. We add up all three sides to get the perimeter.
s1+s2+s3 = Perimeter
(x+4) +( 3x+1) + (7x+3) = Perimeter
Combine like terms
11x+8 = Perimeter
Answer:
P = 11x + 8 cm
Step-by-step explanation:
The perimeter of a triangle is the sum of the lengths of the three sides.
... P = s1 + s2 + s3
... P = (x +4 cm) +(3x +1 cm) +(7x +3 cm) . . . . substitute for s1, s2, s3
... P = x(1 +3 +7) + cm(4 + 1 + 3) . . . . . . collect terms
... P = 11x + 8 cm
Can someone help me with 1-3
You have 10 batteries sitting on your desk, three of which are dead. You choose 2 batteries are random for you calculator. What is the expected number of good batteries that you get?
A) 0
B) 1
C) 1.4
D) 2
Answer:
C) 1.4
Step-by-step explanation:
The probability of choosing 2 good ones is 7/10·6/9 = 42/90.
The probability of choosing 1 good one is 7/10·3/9 +3/10·7/9 = 42/90.
The probability of choosing 0 good ones is 3/10·2/9 = 6/90
The expected value is the sum of the product of number of good ones and their probability:
... 2·42/90 +1·42/90 +0·6/90 = (2+1)·42/90 = 42/30 = 1.4
1. What is the radical form of the expression 4 2/3?
2. What function equation is represented by th graph?
Answer:
1. [tex]\sqrt[3]{4^2}[/tex]
2. Answer A
Step-by-step explanation:
1. A fraction exponent can be represented using a radical. The base number is the number in the radical. The numerator of the fraction is the exponent inside the radical. The denominator is the type of radical.
[tex]4^{\frac{2}{3} }[/tex]
[tex]\sqrt[3]{4^2}[/tex]
2. An exponential always crosses at (0,1) This function crosses at (0.6) meaning it has shifted up 5 units or +5. These means only answer options A and D are possible solutions. Also, since the graph starts high and ends low and leveling out, this means the base is less than 1. Only 3/4 is less than 1. Answer A is the solution.
Tommy notices that he reads 2/3 page in a minute. At the rate, how long will it take him to read 12 pages
Answer:
18 minutes
Step-by-step explanation:
To do this, you need to divide 12 by the two thirds to find out how many 2/3 there are in 12, giving the amount of minutes it takes:
12 ÷ 2/3 = 18
So it would take him 18 minutes!
Which ordered pair is the solution to the system of linear equations -5x+y=26 and 2x-7y=16?
(–4, 6)
(6, –4)
(–4, –6)
(–6, –4)
Answer:
(–6, –4)
Step-by-step explanation:
After converting the two equations from standard form to slope -int form I graphed the two equations on a coordinate plane and found the intersection (in this case solution) of the equation to be (–6, –4)
Answer:
(–6, –4)
Step-by-step explanation:
This pair of linear equations may be solved simultaneously by using the elimination method. This will involve ensuring that the coefficient of one of the unknown variables is the same in both equations.
It may be solved by substitution in that one of the variable is made the subject of the equation and the result is substituted into the second equation.
Using the substitution method, make y the subject in the first equation
y = 5x + 26
substitute into the second equation
2x -7(5x + 26) = 16
-33x - 182 = 16
-33x = 16 + 182
-33x = 198
x = 198/-33
x = -6
since y = 5x + 26
y = 5(-6) + 26
= -30 + 26
= -4
hence (x,y) = (-6,-4)
Please answer quickly, more might be coming soon. 50 Points!
Answer:
2) ∠SDH and ∠SDT are right angles because SD ⊥ HT.
3) [tex]\bar{SH}\cong \bar{ST}[/tex] as it is given in the question.
4) [tex]\bar{SD}\cong \bar{SD}[/tex] is the reflexive property.
5) ΔSHD ≅ ΔSTD by RHS congruency.
Step-by-step explanation:
Given in the question:
[tex]\bar{SH}\cong \bar{ST}\\\bar{SD}\perp \bar{HT}[/tex]
In ΔSHD and ΔSTD
[tex]\bar{SH}\cong \bar{ST}[/tex] (Given)
[tex]\angle SDH\cong \angle SDT=90^o[/tex] (SD ⊥ HT)
[tex]\bar{SD}\cong \bar{SD}[/tex] (Common)
Therefore, [tex]\Delta SHD\cong \Delta STD[/tex] (By RHS rule)
Reflexive property of congruency is defined as the property in which something is equal to itself. Hence, the reflexive property of these two triangles is [tex]\bar{SD}\cong \bar{SD}[/tex]
Which equation is a quadratic model for the data set? Hint: Use a graphing calculator or a spreadsheet program.
Data table
Answer:
Equation for the quadratic model for the data set is;
[tex]y = 1.0774x^2-0.9393x+0.6905[/tex]
Step-by-step explanation:
A Quadratic regression is the process of finding the equation of the parabola that best fits the set of data.
An equation is in the form of: [tex]y=ax^2+bx+c[/tex] where a≠0.
You just enter the x-coordinates and y-coordinates in your graphing calculator and
then do a quadratic regression.
The equation of the parabola that best approximates the points is
:
[tex]y = 1.0774x^2-0.9393x+0.6905[/tex]
Now, plot the graph of the above equation as shown below in the figure.
Also you can see that the [tex]R^2[/tex] value for the above data is, 0.994
A graph is translated according to the following rule. Describe the translation.
(x, y) → (x, y – 3)
The graph is translated three units to the right.
The graph is translated three units to the left.
The graph is translated three units down.
The graph is translated three units up.
Answer:
The graph is translated three units down.
Step-by-step explanation:
We know that, a 'Translation' is an transformation where the figure or graph is shifted in any direction.
According to our question (x,y) becomes (x, y-3) , this means that the graph value of 'x' co-ordinate remains same and the value of 'y' co-ordinate is decreased by 3 units.
So, the graph is shifted three units downwards i.e. it is translated three units down.
Light travels at a speed of 1.17 × 107 miles per minute. Pluto's average distance from the Sun is 3,670,000,000 miles. On average, how long does it take sunlight to reach Pluto? Enter your answer in scientific notation, and, if necessary, round your multiplier to the nearest hundredth.
Speed is the rate of change of distance over time.
It will take [tex]\mathbf{2.20 \times 10^{2}}[/tex] minutes to get to Pluto.
The given parameters are:
[tex]\mathbf{Speed = 1.17 \times 10^7 miles/mins}[/tex]
[tex]\mathbf{Distance = 3670000000 miles}[/tex]
Speed is calculated as:
[tex]\mathbf{Speed = \frac{Distance}{Time}}[/tex]
Make Time the subject
[tex]\mathbf{Time = \frac{Distance}{Speed}}[/tex]
Substitute values for Speed and Distance
[tex]\mathbf{Time = \frac{3670000000\ miles}{1.17 \times 10^7 miles/mins}}[/tex]
[tex]\mathbf{Time = \frac{3670000000\ mins}{1.17 \times 10^7 }}[/tex]
Rewrite as:
[tex]\mathbf{Time = \frac{3.67\times 10^9\ mins}{1.17 \times 10^7 }}[/tex]
Apply law of indices
[tex]\mathbf{Time = \frac{3.67\times 10^{9 - 7}\ mins}{1.17}}[/tex]
Divide
[tex]\mathbf{Time = 2.20 \times 10^{2}\ mins}[/tex]
Hence, it will take [tex]\mathbf{2.20 \times 10^{2}}[/tex] minutes to get to Pluto.
Read more about speed and rates at:
https://brainly.com/question/359790
What is the vertex and axis of symmetry for y=4x^2-12x+9?
Answer:
axis of symmetry x=3/2
vertex (3/2, 0)
Step-by-step explanation:
to find the axis of symmetry we use h = -b/2a
where ax^2 + bx+c
h = -(-12)/2(4)
h= 12/8
h = 3/2
the axis of symmetry is x = 3/2
the x coordinate of the vertex is h x=3/2
to find k, the y coordinate of the vertex, substitute x=3/2 into the equation
y=4x^2-12x+9
y=4(3/2) ^2-12(3/2)+9
= 4 (9/4) - 6*3 +9
= 9-18+9
= 0
the vertex (3/2, 0)
For the following functions, (a) describe the domain and range, and (b) sketch the graph.
f(x)=(1/2)^x(-3)
Indicate the method you would use
Answer:
SSS can be used to prove that the given triangles are congruent.
Step-by-step explanation:
In the given two triangles ΔADC and ΔABC,
AD = AB = 7 units,CD = BC = 8 units,AC is common to both triangles,Hence, ΔADC ≅ ΔABC by Side-Side-Side (SSS) congruence.
SSS congruence-
If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.
Someone help plz (20 points)
Answer:
The answer is C)
Step-by-step explanation:
In order to fully solve a system of equations, you need both variables, x And y. Therefore he has to go back and solve for x
Write an explicit formula for the sequence -13, -6, 1, 8, ...
a) an = -13n+7
b) an = -13+(n+7)
c) an = -13+7(n-1)
d) an = -13n+7
Answer:
c) an = -13+7(n-1)
Step-by-step explanation:
We can use the formula for arithmetic sequences
an =a1+d(n-1)
where a1 is the first term in the sequence
d is the common difference
and n is the term number
a1 is -13
d is found by taking the second term and subtracting the first term
d = -6--13
= -6+13
d=7
We are adding 7 each time
Substituting what we know,
an = -13 + 7(n-1)
The answer is:
c) [tex]a_{n}=-13+7(n-1)[/tex]Help please !Algebra Two!!
Answer:
a. -1, odd; 2, even
b. [tex](x+1)(x-2)^2[/tex]
c. odd likely 3
Step-by-step explanation:
A polynomial graph has several features we look for to determine the equations.
The zeros of the function are the x-intercepts. If the x-intercepts touch but do not cross then the intercepts have an even multiplicity like 2, 4, 6, etc. If the x-intercepts cross over then they have an odd multiplicity. Degree is the exponent or multiplicity of each zero. Therefore if we know the multiplicity of each zero we can add them together to find or make an educated guess for the degree of the entire polynomial. The shape of the graph tells us what type of polynomial. Odd degrees have a backwards S shape. Even degrees have a W shape. The shape can even tell us the if the equation has a positive or negative leading coefficient. Upside down W or an M shape is negative. While a sideways S shape is negative.In this graph, there are two real zeros: -1,2
We can write them in intercept or factored form as (x+1) and (x-2).
Because the graph crosses the x-axis at -1, it's multiplicity is odd likely 1. However, the graph does not cross at 2 and has an even multiplicity likely 2.
The graph is ends up and is a sideways s so is positive with an odd degree.
This means the function has a degree of 3 or higher with the degree being odd.
A total of 17,100 seats are still available for the next hockey game. If 62% of the tickets are sold, how many seats are in the arena? A. 7,100 seats B. 7,900 seats C. 45,000 seats D. 27,900 seats
Answer:
We have
seats x ( 62 / 100 ) = (seats - 17,100);
seats x 62 = 100 x (seats - 17,100);
seats x 62 = seats x 100 - 1710000;
1,710,000 = seats x 38;
seats = 1,710,000 ÷ 38;
seats = 45,000;
The correct answer is c. 45,000 seats;
Step-by-step explanation:
45, 000 A for plato users
Step-by-step explanation:
Trust me im Master chief
Dana can jump a rope 264 times in 4 minutes. How many jumps can Dana make in one minute?
A) 55 jumps
B) 60 jumps
C) 66 jumps
D) 72 jumps
Whoever can answer it right, gets brainliest too!
Answer:
66
Step-by-step explanation:
divide 264/4=66
Answer:
C) 66 jumps
Step-by-step explanation:
Dana can jump 264 times in 4 minutes
Divide 364 by 4 to see how many times she can jump in one minute
264/4 = 66
Given h(x)=5(x-6)^2+2 what transformations were done compared to the parent function f(x)=x^2?
Answer:
1. Translation 6 units to the right.
2. Stretch by a factor 5.
3. Translation 2 units up.
Step-by-step explanation:
Consider parent function [tex]f(x)=x^2.[/tex]
1. Translate the graph of the function 6 units to the right. Then you get the function [tex]f_1(x)=(x-6)^2.[/tex]
2. Stretch the graph of the function [tex]f_1(x)=(x-6)^2[/tex] by a factor 5 and get the function [tex]f_2(x)=5(x-6)^2.[/tex]
3. Translate the graph of the function [tex]f_2(x)=5(x-6)^2[/tex] 2 units up to fet the function [tex]h(x)=5(x-6)^2+2.[/tex]
Brooke has to set up 70 chairs in equal rows for the clas talent show. But, there is not room for more than 20 rows. What are the possible number of rows that Brooke could set up?
Which is equivalent to 80 1/4 ?
Hey there!
"Which is equivalent to [tex]80\frac{1}{4}[/tex]?"
In order for you to solve this particular equation, you multiply the front number from the denominator, then whatever that outcome is, add to the nominator
So,
[tex]80\frac{1}{4}[/tex]
[tex]80(4) = 320[/tex]
[tex]320 +1 = 321[/tex]
[tex]4[/tex] stays the same
[tex]\boxed{Answer: \frac{321}{4}}[/tex]
If you want the decimal form, simplify the the mixed to a improper then you should get a outcome of: [tex]80.25[/tex]
For percentage do the fraction out of [tex]100[/tex] then solve it from there ([tex]0.8025[/tex]) would be the percentage form
Good luck on your assignment and enjoy your day!
~[tex]LoveYourselfFirst:)[/tex]
[tex]80\frac{1}{4}[/tex] is equivalent to the decimal number 80.25, which can also be expressed as the improper fraction 321/4.
The question asks for an equivalent of the number [tex]80\frac{1}{4}[/tex]. To find this, we can convert the mixed number to an improper fraction or decimal. Since 1/4 is a standard fraction that is equivalent to 25 percent, we can express 1/4 as 0.25. Adding this to 80, we get an equivalent decimal number of 80.25. Another way to express 80 1/4 would be as an improper fraction, which would be [tex]\frac{321}{4}[/tex] because 80 times 4 equals 320, plus the numerator 1 equals 321.
The bus comes at 6:55. It takes meg 19 minutes to get to the bus stop. What time would she have to leave at to catch the bus?
Answer:
6 hrs 36 mins
Step-by-step explanation:
Bus at 6:55
Minutes to get to the bus 19.
deduct 19 Minutes from 6:55 = 6 hrs 36 mins
solve f(x)=x²+7x+12/-x²-3x+4
[tex]x^2+7x+12=x^2+4x+3x+12=x(x+4)+3(x+4)=(x+4)(x+3)\\\\-x^2-3x+4=-(x^2+3x-4)=-(x^2+4x-x-4)\\\\=-[x(x+4)-1(x+4)]=-(x+4)(x-1)\\\\f(x)=\dfrac{x^2+7x+12}{-x^2-3x+4}=\dfrac{(x+4)(x+3)}{-(x+4)(x-1)}\\\\\text{The domain:} x\neq-4\ and\ x\neq1\\\\canceled\ (x+4)\\\\f(x)=\dfrac{x+3}{-(x-1)}=-\dfrac{x+3}{x-1}\ for\ x\neq-4\ and\ x=1[/tex]
[15 POINTS] A rectangle has a width w and a length that is two more than its width. what is the perimeter of the rectangle? Write and simplify an expression.
Answer: P = 4w + 4
Step-by-step explanation:
width (w) = w
length (L) = w + 2 (2 more than its width)
Perimeter (P) = 2L + 2w
P = 2L + 2w
= 2(w + 2) + 2(w)
= 2w + 4 + 2w
= 4w + 4
Find the exact values of the six trigonometric functions for angle in standard position if a point with the coordinates (-6, 6) lies on its terminal side.
Answer:
sin = √2/2, cos = -√2/2, tan = cot = -1
csc = √2, sec = -√2
Step-by-step explanation:
Angle runs around unit circle (where x^2+y^2=1)
from (1,0) to (-√2/2,√2/2)