y = x + 6 and 3x - 3y = -18 will have no solution (parallel lines)
y = −4x + 11 and −6x + y = 11 will have unique solution (intersecting lines)
y = -2x + 5 and 2x + y = -7 will have no solutions (parallel lines)
taking first set of equations,
y = x + 6 and 3x - 3y = -18
rearranging it in the ax+by=c form we get,
x - y = 6
3x - 3y = -18
a1=1, b1= -1, c1= 6
a2=3, b2= -3, c2= -18
now comparing,
1/3 = 1/3 ≠ 6/(-18) 0r -1/3
thus, we get a1/a2=b1/b2≠c1/c2, which satisfies the condition for parallel lines, thus there will be no solution.
taking second set of equations,
y = −4x + 11 and −6x + y = 11
rearranging it in the ax+by=c form we get,
4x+y=11
-6x+y=11
a1=4, b1= 1, c1= 11
a2=-6, b2= 1, c2= 11
4/6 or 2/3≠1/1
thus, we get a1/a2≠b1/b2, which satisfies the condition for intersecting lines, so there will be a unique solution.
taking third set of equations,
y = -2x + 5 and 2x + y = -7
rearranging it in the ax+by=c form we get,
2x+y=5
2x+y=-7
a1=2, b1= 1, c1= 5
a2=2, b2= 1, c2= -7
2/2 or 1/1 =1/1≠ -5/7
thus, we get a1/a2=b1/b2≠c1/c2, which satisfies the condition for parallel lines, thus there will be no solution.
What are intersecting and parallel lines?
Parallel lines never cross, always have distinct ends, and are always spaced at the same distance from one another. Lines that intersect are lines that have a common point and do cross.
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let f(x)=x^2+3x and g(x)=2x-1 find each function value f(g(-2))
The composite result function of f( g(-2) ) in the given functions f( x ) = x² + 3x and g( x ) = 2x - 1 is 10.
What is the composite result function of f( g(-2) ) in the given function?A function is simply a relationship that maps one input to one output..
Given the data in the question;
f( x ) = x² + 3xg( x ) = 2x - 1f( g(-2) ) = ?First, set up the composite result function f( g(x) )
f( x ) = x² + 3x
f( g(x) ) = f( 2x - 1 ) = ( 2x - 1 )² + 3( 2x - 1 )
f( g(x) ) = ( 2x - 1 )² + 3( 2x - 1 )
Simplify
f( g(x) ) = ( 2x - 1 )( 2x - 1 ) + 3( 2x - 1 )
f( g(x) ) = 2x( 2x - 1 ) -1(2x - 1 ) + 3( 2x - 1 )
f( g(x) ) = ( 4x² - 2x - 2x + 1 ) + 3( 2x - 1 )
f( g(x) ) = ( 4x² - 4x + 1 ) + 6x - 3
f( g(x) ) = 4x² - 4x + 1 - 6x - 3
f( g(x) ) = 4x² - 4x + 6x + 1 - 3
f( g(x) ) = 4x² + 2x - 2
Now, replace all the occurrence of x with -2 in the function and simplify.
f( g(-2) ) = 4(-2)² + 2(-2) - 2
f( g(-2) ) = 4×4 - 4 - 2
f( g(-2) ) = 16 - 4 - 2
f( g(-2) ) = 10
The composite result function of f( g(-2) ) in the given functions is 10.
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can a percent of change be greater than 100%?
A line with a slope of – 1/6 passes through the points (1,3) and (7,f). What is the value of f?
Answer:
[tex]{ \tt{ - \frac{1}{6} = \frac{f - 3}{7 - 1} }} \\ \\ { \tt{6(f - 3) = - 6 }} \\ \\ { \tt{f - 3 = - 1}} \\ \\{ \tt{f = 2}}[/tex]
Answer:-2
Step-by-step explanation:
A student states that a triangle can be formed with side lengths 4 in, 5 in, and 8 in. Is the student correct? Why, or why not?
A) Yes, because 4 + 5 > 8
B) Yes, because 5 + 8 > 4
C) No, because 4 + 5 > 8
D) No, because 5 + 8 > 4
Answer: Yes, because 4 + 5 > 8
Step-by-step explanation: The sum of 4 + 5 must be more than 8 to be a triangle
Answer:
The answer is A) Yes, because 4 + 5 > 8
Step-by-step explanation:
I got it right loves <3
Lines AB and CD are parallel. Find the measure of the three angles in triangle FAB.
136⁰
71⁰
For the given parallel lines AB and CD, the measure of the angle of the triangle ∠FAB = 25°.
What is defined as the corresponding angles?Corresponding angles are generated when two parallel lines have been intersected by a transversal.The definition of corresponding angles states that when two parallel lines intersect with a third, the angles that occupy the very same relative position at every intersection are said to be corresponding angles to one another."The two lines are considered to be parallel if indeed the corresponding angles inside the two intersection areas are congruent."For the given question;
Line AB || Line CD
From the given diagram,
∠CFD = ∠AFB = 110 (corresponding angles)
Now, in triangle ABF
By the property of triangle; sum of all interior angles of triangle is 180.
Thus,
∠AFB + ∠ABF + ∠FAB = 180°
Put the values;
110° + 45° + ∠FAB = 180°
∠FAB = 180° - 155°
∠FAB = 25
Thus, the measure of the angle ∠FAB = 25° in triangle FAB.
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I’m sorry i need at least twenty letters so pleas tell me
What is
13.1×3.70
Answer:
44.77
Step-by-step explanation:
13.1x3.70=13.1x3.7
37x131=4477
get back the decmial point 44.77
△PGH is an equilateral, PG=x+5, GH=2x-5 and PH=3x-15. Find the value of x and the perimeter of the triangle.
The value of x is 10
The perimeter of the triangle is 30 units
What is an equilateral triangle?An equilateral triangle can be defined as a triangle which has all its sides equal or congruent to each other.
The properties of an equilateral triangle includes;
From the information given, we have the sides as;
PG=x+5 GH=2x-5 PH=3x-15Since all of its sides are equal, we have to equate two side, we have;
x + 5 = 2x - 5
collect like terms
x - 2x = -5 - 5
subtract the like terms
-x = -10
make 'x' the subject
x = 10
But the perimeter of an equilateral triangle = 3a = 3(10) = 30 units
Thus, the value is 10
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find one seventh of the sum of 19 and the product of 4 and 11
Answer: One seventh of the sum of 19: 2.714
Product of 4 and 11: 44
Step-by-step explanation:
4x11=44
One seventh times 19 equal 2.714.
1/7 x 19/1 = 19/7
Simpified 2 5/7
2 5/2 as decimals is 2.714
Determine the slope of the function as a unit rate for the linear situation. y = − 4 4/5x + 13 1/2
The slope of the function as a unit rate for the linear situation. y = [tex]-4\frac{4}{5}[/tex]x + [tex]13\frac{1}{2}[/tex] can be viewed as [tex]-4\frac{4}{5}[/tex] by taking the derivative of the first term of the equation.
What is the slope of a function?The slope m=y/x of a straight-line y=mx+b quantifies the change in y for every unit change in x. This can also be interpreted as a kind of measure of "sensitivity''.
Finding the slope of a function is like finding the rate at which the value of y (the dependent variable) changes in relation to x is what this method entails (independent variable).
How to find the slope of a function?To find the slope of a line that is given with the equation of the line, first you have to write the equation of the line in a slope-intercept form.
Then use inverse operations in order to solve for y so that it is written as y=mx+b. Thereafter you can easily spot the slope since the slope is the coefficient of the x variable, or in other words, the number in front of x.
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Between 10 P.M. and 7:45 A.M., the water level in a swimming pool decreased by
3/8 in. Assuming that the water level decreased at a constant rate, how much did the water level drop each hour?
Please help asap
The water level drop each hour by 0.0384 inch
Firstly, the deacrease in water level is takes as per the question
Decrease = 3/8 inches
Decrease=0.375 inches
Then the time interval is calculated
From 10 pm to 7:45 hours will be 9.45 hours
Time interval= (9 + 45/60) hours
Time interval=9.75 hours
Now, the drop in water level per hour is determined, to do so, total water level decreased is divided by the time taken to decrease that water level
that is 0.375/9.75 inches/hour
= 0.03846 inches/hour
Therefore, if between 10 P.M. and 7:45 A.M., the water level in a swimming pool decreased by 3/8 inches and the water level decreased at a constant rate, the water level drop each hour is 0.03846
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If 1/4 gallon of paint covers 1/3 of a wall in Luna's bedroom, how many gallons of paint does she need to cover 1 wall?
Answer: 3/4 of a gallon
Step-by-step explanation:
1/4 times 1/3 is 3/4 so she would need to buy a gallon of paint
evaluate 3x - 2 when x =
a) 0
b) +3
c) -2
Answer:
- 2, 7 , - 8
Step-by-step explanation:
substitute the given values of x into the expression
(a)
x = 0 : 3(0) - 2 = 0 - 2 = - 2
(b)
x = 3 : 3(3) - 2 = 9 - 2 = 7
(c)
x = - 2 : 3(- 2) - 2 = - 6 - 2 = - 8
Help me please :((((((
100 keed lol keed lol keed
Find three equivalent rational numbers for 81/24 PLEASE ...
Answer:
3.375
3[tex]\frac{375}{1000}[/tex]
[tex]\frac{27}{8}[/tex]
Step-by-step explanation:
The first answer divide 81 by 24 and you will get the decimal answer of 3.375.
0.375 is [tex]\frac{375}{1000}[/tex]
[tex]\frac{81}{24}[/tex] Divide the top and the bottom by 3 to get [tex]\frac{27}{8}[/tex]
1.the difference of six and two divided by four
2.eighteen divided by the sum of two and seven
3.the difference of eleven and four times five
4.the sum of two and four and six times eight
Answer:
1. 4
2. 2
3. 35
4. 96
Step-by-step explanation:
1. (6-2)÷4=4
2. 18÷(2+7)=2
3. (11-4)×5= 35
4.(4+2+6)×8= 96
Answer:
1. 1
2. 2
3. 35
4. 96
The question is asking “Rewrite in simplest terms: 7(9y+2y-6)-9y
Answer:
[tex]68y-42[/tex]Explanation:
Here, we want to rewrite the given expression
What we have to do is to start by opening up the bracket
To do this, we have to multiply the term on the left with each term inside the bracket
Then we collect the like terms and perform the necessary arithmetic operation
We have this as follows:
[tex]\begin{gathered} \text{ =7(11y-6)-9y} \\ =\text{ 77y-42-9y} \\ =\text{ 77y-9y-42} \\ =\text{ 68y-42} \end{gathered}[/tex]Answer:
68y-42
Step-by-step explanation:
7(9y+2y-6)-9y
Find the expression in simplest terms
Combine like terms
7(11y-6)-9y
Distribute
77y -42-9y
Combine like terms
68y-42
In a recent year, 32.2% of all registered doctors were female. If there were 53,600 female registered doctors that year, what was the total number of registered
doctors?
Round your answer to the nearest whole number.
Answer:
166,460 doctors registered.
Step-by-step explanation:
32.2% -------- 53,600 female doctors
100% -------- X
X * 32.2% = 100% * 53,600
X = (100% * 53,600) / 32.2%
X = 166,460 doctors
mark receives a score report detailing his performance on a statewide test. on the math section, mark earned a raw score of 39, which placed him at the 68th percentile. this means that
Mark receives a scale report and on the Math section, he earned a raw score of 39 which is at the 68th percentile, meaning that the total raw score on the Math section is 57
Find out the total score of the Math score, 100th percentile
Given; raw score- 39 which is at the
68th- percentile
For someone to be at the 100th percentile, he or she must have scored all the questions right.
In Mark's case, he had a score of 68 percentile with a score of 39
Total raw score for the Math section;
state; If score of 39 = 68 percentile
? 100 percentile
Cross multiply to solve for the unknown
Thus; 39 * 100 / 68
= 57
Therefore, total raw score on the Math section is 57, which is at the 100th percentile.
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In the isosceles triangle. if <A = 55 find the m<B.
Isosceles triangle
Answer:
62.5
Step-by-step explanation:
Given m
||n, find the value of x.
m
102°
xº
x=102°(Corresponding angles are equal m || n)
HOPE THIS HELPS
One km is equal to _______.
a.
0.62 ft
b.
3280.8 ft
c.
1.61 ft
d.
5280 ft
When we try to convert the value of one kilo meter to feet, the value that we obtain is 3280.8 ft.
How do you convert?We know that there are several units that we could use for calculations. t is often common that we need to convert the units from one unit to the other so that we can be able to carry out calculations. The number that allows us to be able to carry out such a a conversion is what we call the conversion factor for that particular operation.
Given that;
1 foot = 0.0003048 kilo meter
We can see that if we seek to convert a value of One km to feet we would have 3280.8 ft
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The figure above is rotated 270° counterclockwise about the origin. What are the coordinates of W'?
Answer: The coordinates W' after a rotation 270° counterclockwise about the origin is (3,-1)
In AJKL, JL is extended through point L to point M,
m/JKL = (3x – 16)°, m/LJK = (2x + 15)°, and
m/KLM = (8x – 19)°. Find m/LJK.
The value of x is 6 and the measure of angle LJK is 27°.
According to the triangle's "angle sum property," a triangle's interior angles add up to 180°.
We have the measure of the following angles,
m∠JKL = ( 3x - 16 )°
m∠LJK = ( 2x + 15 )°
m∠KLM = ( 8x - 19)°
In ΔJKL, JL is extended through point L to point M.
At point L, the measure of angle JLK will be as,
m∠KLM + m∠JLK = 180°
m∠JLK = 180° - m∠KLM
m∠JLK = 180° - ( 8x - 19)°
m∠JLK = ( 199 - 8x )°
Now,
In triangle JKL,
By angle sum property:
m∠JKL + m∠LJK + m∠JLK = 180°
(3x – 16)° + (2x + 15)° + ( 199 - 8x )° = 180°
- 3x + 198 = 180
- 3x = - 18
x = 6°
Therefore,
m∠LJK = ( 2x + 15 )°
m∠LJK = ( 2(6) + 15 )°
m∠LJK = ( 12 + 15 )°
m∠LJK = 27°
The measure of angle LJK is 27°.
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give this answer please
Answer:
<KLC
Step-by-step explanation:
Alternate angles are angles that occur on opposite sides of the transversal line and have the same size.
Both are obtuse angles and are on the opposite side of the transversal line
Answer:
∠KLC is the alternate angle of ∠BKL
Step-by-step explanation:
Alternate angles are angles that are opposite of one another and on two different parallel lines created by an intersecting line (also known as a transverse line).
In this case, the parallel lines are lines A↔B and C↔D, and the transverse line is M↔N. Therefore, the alternate angle from ∠BKL is ∠KLC.
Help again :').. sorry for the spam of questions lol
29 points will b givin
Answer:
A
Step-by-step explanation:
Do long division. See the attached image for work.
Answer:
B
Step-by-step explanation:
[tex]\frac{56}{90}[/tex]
= 56 ÷ 90
= 0.6222222..
= 0.62 ( with a bar above the 2 , indicating the 2 is repeating )
A students cost for last semester was 2000 she spent 320 on books. What percent of last semester was cost in books
The percentage of money spent on books to that of cost for last semester is 16%
The cost for last semester was 2000.
The cost books was 320.
The percentage formula = part/whole × 100
Part = 320
Whole = 2000
Equation = 320/2000× 100
= 32/20
= 16%
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which of the following options result in a graph that shows expoential decay
The option that results in a graph that shows exponential decay is Option(b) f(x) = 3(0.7)ˣ.
What is the Exponential Decay Formula?The exponential decay formula helps to determine the rapid decline over time or exponential decline. The exponential decay formula is used to calculate various types of decay, including radioactivity decay, half-life, and population decay.The exponential decay formula is f(x) = abˣ, where a is the initial amount, b is the decay factor and x is the time interval.According to the question, we have to determine the function that results in a graph that shows exponential decay.
The function will show an exponential decay if the value of b was less than 1 and greater than 0.
As we can notice in the second option, f(x) = 3(0.7)ˣ, where b is equal to 0.7 which is less than one.
So, f(x) = 3(0.7)ˣ shows exponential decay.
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The complete question is: "Which of the following options results in a graph that shows exponential decay?
a. f(x) = 0.6(2)ˣ
b. f(x) = 3(0.7)ˣ
c. f(x) = 0.4(1.6)ˣ
d. f(x) = 20(3)ˣ."
Need help!!! ASAP!!!!
g(x)×h(x) means we will have to multiply the two functions.
[tex]g(x) \times (h(x) = (3 {x}^{2} - 1)( {x}^{2} - x) \\ = 3 {x}^{2} ( {x}^{2} - x) - 1( {x}^{2} - x) \\ = 3 {x}^{4} - 3 {x}^{3} - {x}^{2} + x \\ g(x) \times h(x) = 3{x}^{4} - {x}^{3} - {x}^{2} + x[/tex]
ATTACHED IS THE SOLUTION
help me please help me
Step-by-step explanation:
we sadly need to do all the multiplications for the whole polynomial in standard form.
the other 3 things we get out of the given form :
we multiply 3 terms, each in x. the result will be x³.
so, we have the 3rd degree.
the leading coefficient is 1, as for the x³ term we get x×x×x = x³. no other number is involved.
the constant term is the extreme on the other end. it is 4×2×1 = 8.
so, now for the full multiplications, that should also show you, why I could make the conclusions above.
(x+4)(x-2)(x+1)
we do this by multiplying first 2 terms with each other, and then we multiply that result by the third term.
remember, we need to multiply every item of one term with every item in the other term.
(x+4)(x-2) = x² -2x + 4x - 8 = x² + 2x - 8
now
(x² + 2x - 8)(x+1) = x³ + x² + 2x² + 2x - 8x - 8 =
= x³ + 3x² - 6x - 8
so, that is already the standard form
f(x) = x³ + 3x² - 6x - 8
show work
Solve.
−2/5x −9 < 9/10
Answer:
X>-99/4
Step-by-step explanation:
Let's solve your inequality step-by-step.
−2/5x−9<9/10
Step 1: Add 9 to both sides.
−2/5x−9+9<9/10+9
−2/5x<99/10
Step 2: Multiply both sides by 5/(-2).
(5/−2)*(−2/5x)<(5/−2)*(99/10)
x>−99/4
Answer:
x>−99/4