The equation of a line is -2x+5y = -20
What’s the x-intercept of the line?
Answer each question below.
14. In angle LMN, the exterior angle adjacent to angle L has a measure of 5x+12. If the measure of angle M= 3x-2 and the measure of angle N= 50. Find the measure of angle L.
Answer:
[tex]\huge\boxed{\sf L = 78\°}[/tex]
Step-by-step explanation:
Given that:Exterior angle of L = 5x + 12
M = 3x - 2
N = 50
Statement:Exterior angle is equal to the sum of non-adjacent interior angles.So, the exterior angle that is adjacent to L is equal to the sum of non-adjacent sides (M and N) of the triangle.
Here,
Exterior angle of L = M + N
5x + 12 = 3x - 2 + 50
5x + 12 = 3x + 48
Subtract 12 to both sides
5x = 3x + 48 - 12
5x - 3x = 36
2x = 36
Divide 2 to both sides
x = 18
So,
Measure of angle M:= 3x - 2
= 3 (18) - 2
= 54 - 2
= 52°
Now,
Measure of angle L:We know that,
Sum of all the interior angles of triangle is 180 degrees.L + M + N = 180°
L + 52 + 50 = 180
L + 102 = 180
Subtract 102 to both sides
L = 180 - 102
L = 78°
[tex]\rule[225]{225}{2}[/tex]
The star shape is made from a regular hexagon and six congruent equilateral triangles The area of the star shape is 96cm squared Work out the area of the regular hexagon.
Answer:
48 Square Centimeters
Step-by-step explanation:
The red triangular exterior pieces are all equilateral triangles with some side length.
We don't need to know what that side length is. It doesn't matter.
The area of one red equilateral triangle is some area A.
There are 6 of these red triangles, so the red exterior triangular parts combine to a total area of 6*A.
The hexagon is composed of equilateral triangles as well.
Each of these blue equilateral triangles is congruent to any outer red triangle because the side length is the same.
Therefore, the 6 blue equilateral triangles composing this hexagon combine to get a total area of 6*A
The area of the star overall is 12*A because we have 6 blue triangles combining with the 6 red triangles.
There is a total of 12 triangles.
The table of values represents a linear function g(x) where c is the number of days that have passed and g(x) is the balance in the bank account
After 7 days, the balance will be Rs. 628.
(A) The slope of the given function is 40.
(B) In point - slope form it is y - 600 = 40x
In Slope - intercept form it is y = 40x + 600
In Standard form it is 40x - y + 600 = 0
(C) g(x) = 4x + 600
(D) After 7 days, the balance will be Rs. 628
Let g(x) = y
(A) We know slope = change in y/change in x
= 720-600/3-0
= 120/3
= 40
Therefore, the slope of the given function is 40.
(B) We know that the equation of a line
in point - slope form is y - y₁ = m(x - x₁)
where ( x₁, y₁ ) is a point on the line
where m is the slope
Therefore, substituting the values, we get,
y - 600 = 40(x - 0)
=> y - 600 = 40x --(i)
What is the Slope - intercept form?
Slope - intercept form is y = mx + b
where m is the slope
and b is the y-intercept
To find y intercept, we substitute x = 0 in equation (i)
=> 40*0 - y + 600 = 0
=> -y + 600 = 0
=> y = 600
Therefore, substituting the values, we get,
y = 40x + 600
in Standard form is ax + by = c
where a, b, and c is constant
Converting the equation found above into the standard form
=> y = 40x + 600
=> 40x - y + 600 = 0
(C) As we had assumed g(x) to be y
=> From equation (i),
y - 600 = 40x
can be written as g(x) - 600 = 4x
=> g(x) = 4x + 600 --(ii)
(D) We need to find the balance in the bank account after 7 days
=> Balance [g(x)] when x = 7
Therefore, substituting the value of x in equation (ii)
=> g(x) = 4*7 + 600
= 28 + 600
= 628
Therefore, after 7 days, the balance will be Rs. 628.
To learn more about the Slope - intercept form visit:
https://brainly.com/question/1884491
#SPJ1
Exponential function f is represented by the table. x -2 -1 0 1 2 f(x) -46 -22 -10 -4 -1 Function g is represented by the equation. Which statement correctly compares the two functions on the interval [-1, 2]? A. Both functions are increasing, but function f increases at a faster average rate. B. Only function f is increasing, but both functions are negative. C. Both functions are increasing, but function g increases at a faster average rate. D. Only function f is increasing, and only function f is negative.
The statement that describes better about function is "Both functions are increasing, but function g increases at a faster average rate." since option (c) is correct.
Given the table
x f(x)
-2 -46
-1 -22
0 -10
1 -4
2 -1
We have to choose which statement describes better about function
Let us assume [tex]f(x)=ab^x+c[/tex]
at x=0, f(0)=-10
So, -10 =a+c
Similarly, by satisfying the above table in the f(x)
[tex]f(x)=\frac{33}{5} (\frac{1}{11})^x-\frac{17}{5}[/tex]
[tex]f'(x) > 0[/tex]
So we can say that f(x) is an increasing function.
[tex]g(x) = - 18 (\frac{1}{3} )^ x + 2[/tex]
[tex]g^ \prime (x) = - 18 (\frac{1}{3} )^ x ln(1/3)[/tex]
ln(1/3) < 0
So, g^ \prime (x) > 0
So, g(x) is an increasing function.
For any x∈f(x) and x∈g(x) [tex]g'(x) > f'(x)[/tex]
So, g increases at a faster average rate
Thus, Both functions are increasing, but function g increases at a faster average rate.
Learn more about increasing functions here: brainly.com/question/12940982
#SPJ10
What is the gradient of the line y = -7x + 13?
Answer:
y = 7 x - 13. y=7x−13. Swap sides so that all variable terms are on the left hand side. Swap sides so that all variable terms are on the left hand side.7x-13=y. 7x−13=y. Add 13 to both sides. ... 7x=y+13. 7x=y+13. Divide both sides by 7. ... \frac{7x}{7}=\frac{y+13}{7} 77x=7y+13 Dividing by 7 undoes the multiplication by 7.
Step-by-step explanation: hope this helps
Answer:
-7
Step-by-step explanation:
The fuel for a lawn mower is a mixture of 8 parts petrol to one part oil. How much oil is required to make 1 litre of fuel?
The amount of oil required for 1 liter of fuel is 111.11 mL.
Fraction is the portion of a total amount where the above part of the fraction is the denominator and the bottom part of the fraction is called the numerator.
Given that the fuel is the mixture where 8 parts are petrol and 1 part is oil in the whole part of the fuel.
The total part of the fuel is 8+1=9
the portion of the petrol is = parts of petrol/total parts of the fuel= 8/9
the portion of the oil = parts of oil /total parts of the fuel= 1/9
Now we have to calculate the amount of oil required for 1 liter of fuel.
As discussed before, 1/9 parts of the fuel is oil.
So the amount of oil is= (1/9)*1 liter= (1/9)litre= 1/9* 1000 mL= 111.11 mL
Similarly, we can calculate the amount of petrol which will be
the amount of petrol= (8/9)*1 liter= (8/9) liter= 8/9*1000 mL= 888.88 mL
Therefore the amount of oil required for 1 liter of fuel is 111.11 mL.
Learn more about fraction
here: https://brainly.com/question/5091
#SPJ10
What decimal is equivalent to ?
7-25
The ratio table shows the numbet of miles karen can drive for 1,2,3 and 4 gallons of gasoline.Based on the table, How far would she be able to drive on 8 gallons of gasoline
Using a proportional relationship, it is found that she would be able to drive 240 miles on 8 gallons of gasoline.
What is a proportional relationship?A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:
y = kx
In which k is the constant of proportionality.
Researching the problem on the internet, it is found that she drives 30 miles per gallon, hence the function for the distance driven considering the number of gallons in the tank is given by:
D(n) = 30n.
She has n = 8 gallons, hence the distance is given by:
D(8) = 30 x 8 = 240 miles.
More can be learned about proportional relationships at https://brainly.com/question/10424180
#SPJ1
sara scores -4 marks if she got 3 correct answers how many were incorrect
The number of answers that were incorrect will be 7.
How to depict the information?From the information given, every correct answer will be +1 while and incorrect answer will be -1. The equation to represent the information will be:
3 - x = -4
where x = incorrect answer
3 - x = -4
-x - 4 - 3
-x = -7
x = 7
In conclusion, the number of answers that were incorrect will be 7.
Learn more about equations on:
brainly.com/question/2972832
#SPJ1
its math help me out
Answer:
60 minutes
Step-by-step explanation:
we can see that the number of minutes increases by 8 each day
(12 + 8 = 20, 20 + 8 = 28, 28 + 8 = 36...)
So, because we have the value for the previous day (day 6) we know that we can simply add 8
52 + 8 = 60
So, the predicted number of minutes for day 7 is 60
hope this helps!!
a man is 18 years older than his son. 3 years ago he was 4 times as old as his son how old is the man now
Answer:
The man is 27 years old.
Step-by-step explanation:
You can create a system of equations.
Let x = the age of the man
Let y = the age of his son
You can create the following equations based on what was given in the problem:
1. x = y + 18
2. (x - 3) = 4(y - 3)
You can simplify the second equation:
x - 3 = 4y - 12
x = 4y - 9
Then, solve the system of equations:
x = y + 18
-
x = 4y - 9
____________
0 = -3x + 27
The son's age is 9, therefore the father is 27 years old.
3x+2=0 i need the answer quick
Answer:
[tex]\huge\boxed{\sf x = -2/3}[/tex]
Step-by-step explanation:
Given equation:3x + 2 = 0
Subtract 2 to both sides
3x = 0 - 2
3x = -2
Divide 3 to both sides
x = -2/3
[tex]\rule[225]{225}{2}[/tex]
Hey guys need help here
Answer:
[tex]\boxed {D) -\frac{2y}{x}}[/tex]
Step-by-step explanation:
Solving :
[tex]\implies \mathsf {\frac{(-2xy^{2})^{3}}{4x^{4}y^{5}}}[/tex]
[tex]\implies \mathsf {\frac{-8x^{3}y^{6}}{4x^{4}y^{5}}}[/tex]
[tex]\implies \mathsf {\frac{-2y}{x}}[/tex]
if pound of cheese costs $3.43, what is the cost per pound?
PLS HELP
Answer:
can you rephrase it? how many pounds are there?
Step-by-step explanation:
What is the value of x/2 + 4 when x = 6?
Step-by-step explanation:
solution:
here,
x/2+4
= 6/2+4 ( x = 6 )
= 3+4
= 7
Answer:
7
Step-by-step explanation:
x/2 + 4
=> 6/2 + 4 (x=6)
=> 3 + 4
=> 7
Evaluate the function when x = - 2, 0 and 5.
[tex]h(x) = - x - 7 \\ \\ when \: x \: is \: - 2 \\ h(x) = - ( - 2) - 7 \\ h(x) = 2 - 7 \\ h(x) = - 5 \\ \\ when \: x \: is \: 0 \\ h(x) = 0 - 7 \\ h(x) = - 7 \\ \\ when \: x \: is \: 5 \\ h(x) = - 5 - 7 \\ h(x) = - 12[/tex]
Consider a political discussion group of 8 democrats, 8 republicans and 6 independent suppose the teo groups meme bet are randomly selected in succession to attend a policial convection find the probability of selecting two demo
Answer:
The probability of selecting two democrats is 1/380
Step-by-step explanation:
Probability is the branch of mathematics that deals with numerical descriptions of how likely an event is to occur.Probability of an event = Number of favourable outcomes / Total number of outcomes.Here we are given the people as,
8 democrats, 8 republicans and 6 independent.
So total number of people are: 8+6+6=20
Probability of choosing first democrat = 1/20
Probability of choosing first democrat = 1/19
Thus P( two democrats in succession ) = 1/20 ×1/19
= 1/380
#SPJ10
A line with slope 2 passes through the point (2, -4). Find the coordinates of another point on the line.
Answer:
(3, -2)
Step-by-step explanation:
We can view slope as: [tex]\frac{rise}{run}[/tex] (rise / run)
"rise" is the change in y from one point to another
"run" is the difference in x from one point to another
So, if the slope of a line is 2, it rises 2 every time it runs 1 (2 = 2/1)
So, we can find another point on the line by adding 2 to the y-value, and adding 1 to the x-value.
(x, y)
(2, -4)
+ 1 + 2
(3, -2)
So, another point on this graph is (3, -2)
0.84(7/6)^x Find the rate of growth/decay.
In accordance with the comparison of the given expression to the definition of exponential function, we conclude that the rate of growth is 1/6.
How to determine the rate of growth of an exponential function
In this question we need to analyze an exponential function of the form:
y = a · (1 + r)ˣ (1)
Where r is the growth rate. Please notice that there is a decay for r < 0. Thus, we find the following finding by comparing the given expression to (1):
y = 0.84 · (1 + 1/6)ˣ
In accordance with the comparison of the given expression to the definition of exponential function, we conclude that the rate of growth is 1/6.
To learn more on exponential functions: https://brainly.com/question/14355665
#SPJ1
This is a sketch of the curve with equation y = f(x).
The curve has a minimum point at M(-1, -3).
Write down the coordinates of the minimum point
of the curve with equation
y = f(x) - 2
Answer:
(-1, -5)
Step-by-step explanation:
Each point on a graph is the ordered pair (x, f(x)). Then the point M(-1 -3) is the ordered pair (-1, f(-1)) where f(-1) = -3.
A point on the shifted graph will be ...
(x, f(x) -2)
Then for x = -1, the point is ...
(-1, f(-1) -2) = (-1, -3 -2) = (-1, -5)
The minimum on the shifted curve is M'(-1, -5).
_____
Additional comment
f(x) is the y-coordinate of a point on a graph. Then f(x) -2 is the y-coordinate shifted down 2 units.
Where is the error in the proof? select all that aply
The correct answer is option D the error is that the linear pair of the theorem can not be used to say that ∠AOP is complementary to ∠POB
What is the Linear pair theorem?The linear pair postulate or linear pair theorem in mathematics states the same thing mathematically. The sum of the measurements of two angles that make up a linear pair is 180°.
In the proof of the given question, it is given that the ∠AOP and ∠POB are complementary angles by linear pair of theorem but the linear pair of the theorem is applied to the angles with the sum of 180.
Therefore the correct answer is option D the error is that the linear pair of the theorem can not be used to say that ∠AOP is complementary to ∠POB
To know more about the Linear pair theorem follow
https://brainly.com/question/5598970
#SPJ1
what is equivalent to the given equation -8(x+13)=2(x-7)+4x
(-8x-104=6x-14) is equivalent to the given equation (-8(x+13)=2(x-7)+4x).Option C is correct.
What is the equation?A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.
Given equation;
⇒-8(x+13)=2(x-7)+4x
⇒-8x-13×8 = 2x-2×7+4x
⇒-8x-104=2x-14+4x
⇒-8x-104=6x-14
(-8x-104=6x-14) is equivalent to the given equation (-8(x+13)=2(x-7)+4x).
Hence, option C is correct.
To learn more, about equations, refer;
https://brainly.com/question/10413253
#SPJ1
There are 130 people in a sport centre.
73 people use the gym.
62 people use the swimming pool.
58 people use the track.
22 people use the gym and the pool.
29 people use the pool and the track.
25 people use the gym and the track.
11 people use all three facilities.
Given that a randomly selected person
uses the gym and the track, what is
the probability they do not use the
swimming pool?
Given right triangle QRS, what is the value of sin(30°)?
The value of sin(30°) is 1/2.
What is Trigonometry?The branch of mathematics concerned with specific functions of angles and their application to calculations.
The diagram is attached below:
We know,
sin 30= Perpendicular/ Hypotenuse.
As, the hypotenuse is the opposite side of the right angle and the perpendicular is opposite to the given angle.
So,
sin 30 = 5/10
sin 30 = 1/2
Learn more about trigonometry here:
https://brainly.com/question/1152974
#SPJ1
Which phrase best describes the relationship indicated by the scatter plot?
OA constant correlation
B. negative correlation
C. positive correlation
D. no correlation
Phrase D best describes the relationship indicated by the scatter plot. There is no correlation.
What is a scatter plot?In an effort to demonstrate how much one variable is influenced by another, scatter plots are used to depict data points on a horizontal and vertical axis.
When there is no connection between two variables, it is called a zero correlation. For instance, there is no correlation between IQ level and the quantity of tea consumed.
Phrase D best describes the relationship indicated by the scatter plot. There is no correlation.
Hence option D is correct.
To learn more about the scatterplot refer to:
https://brainly.com/question/13984412
#SPJ1
Answer:
no correlation
Step-by-step explanation:
John, Johan, and Jonathan collect postage stamps. Johan and Jonathan have the same number of stamps. Two times Johan’s collection is eleven less than five times John’s collection, and three times Jonathan’s collection is three less than seven times John’s collection.
The number of postage stamps in John’s collection is 27.
We have given that,
John, Johan, and Jonathan collect postage stamps. Johan and Jonathan have the same number of stamps.
What is an elimination method?The elimination method is the process of eliminating one of the variables in the system of linear equations using the addition or subtraction methods in conjunction with the multiplication or division of coefficients of the variables.
Johan and Jonathan have the same number of stamps.
Let x be the Johan and Jonathan postal stamps.
Let y be the John postal stamps.
Two times Johan’s collection is eleven less than five times John’s collection.
2x = 5y - 11............(1)
Three times Jonathan’s collection is three less than seven times John’s collection.
3x = 7y - 3............(2)
Multiply equation 1 with 3
3(2x = 5y - 11)
⇒ 6x = 15y - 33.........(3)
Multiply equation 2 with 2
2(3x = 7y - 3)
⇒ 6x = 14y - 6.............(4)
Subtract equation 4 from equation 3
⇒ 6x - 6x = 15y - 33 - (14y - 6)
⇒ 0 = y - 27
⇒ y = 27
Hence, the number of postage stamps in John’s collection is 27.
Find more information about the elimination method here
brainly.com/question/13877817
#SPJ1
can someone please help mee(20 points and i will give brainliest!!!)
Answer:
(5,2)
Maximum
5
Step-by-step explanation:
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\texttt{\:Coordinates of vertex = (5,2)}[/tex]
[tex]\texttt{The graph has a maximum} [/tex]
[tex]\tt \: Axis\:\: of \:\; symmetry : x = 5\ [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
Coordinate of vertex is the point where there's a unique (only one) value of y for x :
[tex]\qquad \tt \rightarrow \: (5,2)[/tex]
Since it's a downward parabola, it doesn't have defined minima, as it's value reach [ - infinity ]
and hence, it has a maximum, at the vertex.
Axis of symmetry is the line that divides the parabola into two equal regions that are mirror images of each other.
it is the line passing through vertex and parallel to y - axis.
[tex]\qquad \tt \rightarrow \: x = 5[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
How many grains of Fermiun will remain after 15 days? 50 25 12.5 6.25
Answer:
0.00305 (rounded)
Step-by-step explanation:
this is a geometric sequence so the formula is
an=a×r×n-1
On a number line, 1.43 would be located ______. Choose all answers that make a true statement.
1.43
《--|----|----|----|----|----|----|----|----|----|--》
A. to the left of 1.41
B. between 1 and 2
C. between 1.42 and 1.44
D. to the right of 1.45
Answer:
B and C
Step-by-step explanation: