Answers
Equation of the first line = [tex]y=-\frac{1}{2} x+1[/tex]
Equation of the second line = [tex]y=-\frac{5}{2} x -1[/tex]
What is the equation of the first line?
Co-ordinates of the first line (x, y) = (-2,2), (0,1), (2,0), (4,-1)
We know that,
[tex]\text{slope }=m=\frac{y_2-y_1}{x_2-x_1}\\\\= > \frac{1-2}{0+2} \\\\=-\frac{1}{2}[/tex]
The slope -intercept form of a line is given by,
y = mx + b ---(1)
Let us substitute ( x, y )= (-2, 2) in (1)
2=(-1/2)*-2+b
2-1= b
b = 1 ----(2)
Let us substitute m and b in the slope-intercept equation (1)
[tex]y=-\frac{1}{2} x+1[/tex]
What is the equation of the second line?
Co-ordinates of the second line (x, y)=(-4,9), (-2,4), (0,-1), (2,-6)
We know that,
[tex]\text{slope }=m=\frac{y_2-y_1}{x_2-x_1}\\\\= > \frac{4-9}{-2+4} \\\\=-\frac{5}{2}[/tex]
The slope -intercept form of a line is given by,
y = mx + b ---(3)
Let us substitute ( x, y )= (-4, 9) in (1)
9 = (-5/2)*-4+b
2 - 1 = b
b = - 1 ----(4)
Let us substitute m and b in the slope-intercept equation (3)
[tex]y=-\frac{5}{2} x -1[/tex]
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Related Questions
The table shows information about the masses of some dogs. a) Work out the minimum number of dogs that could have a mass of more than 27 kg. b) Work out the maximum number of dogs that could have a mass of more than 27 kg. Mass, x (kg) 0≤x≤10 10≤x≤20 20≤x≤30 30≤x≤40 Frequency 3 9 13 4
Answers
Information regarding various dogs' masses is displayed in the table.
(a) 4 bare minimum number of dogs that could weigh more than 27 kg.
(b) 17 dogs, in total, may weigh more than 27 kg.
Given that,
Information regarding various dogs' masses is displayed in the table.
(a)Calculate the bare minimum number of dogs that could weigh more than 27 kg.
(b)Calculate how many dogs, in total, may weigh more than 27 kg.
(a) 4 bare minimum of dogs that could weigh more than 27 kg.
Because the minimum number so lets assume that all dogs in 20≤x<30 are less then 27.
Therefore, 4 bare minimum of dogs that could weigh more than 27 kg.
(b) 17 dogs, in total, may weigh more than 27 kg.
Because the maximum number so lets assume that all dogs in 20≤x<30 are more then 27.
4+13=17
Therefore,17 dogs, in total, may weigh more than 27 kg.
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Answer:
Step-by-step explanation:
nathan eats 2 pounds of lunch meat every 8 days how much meat does he eat per day
Answers
the volume of a cube shaped crate i 27 cubic feet. what is the length of one edge of the crate?
Answers
Answer: The length of the edge of the crate is 3 feet.
Step-by-step explanation:
The formula of the volume of a cube is the cube of edge length.
The volume of the cube (V) = (edge)³ ...................................(1)
In the given question volume is 27 cubic feet.
So, V = 27 cubic feet
Now we replace the Volume with the edge using equation (1)
i.e. (edge)³ = 27
or we can say that the cube root of the edge is equal to 27
i.e. edge = ∛27
which is equal to 3
hence, edge = 3 feet
To calculate the cube root write prime factors of 27 and group them in groups of three
i.e. ∛27 = ∛(3×3×3) = ∛ (3)³ = 3
squared root 50 x squared root 8
surds
Answers
Answer:
20
Step-by-step explanation:
using the rule of radicals
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] = [tex]\sqrt{ab}[/tex] , then
[tex]\sqrt{50}[/tex] × [tex]\sqrt{8}[/tex]
= [tex]\sqrt{50(8)}[/tex]
= [tex]\sqrt{400}[/tex]
= 20
please HELP!! thank you
Answers
13.4 dollars.
This is the total amount Kelly deposit when she opened the account.
What is simple interest?Simple interest is a quick and easy way to calculate the interest on a loan. Simple interest is calculated by multiplying the daily interest rate by the principal multiplied by the number of days between payments.Here,
The total amount is determined by:
F=I(1+rt)
Where
I is the initial sum.r is the interest rate. t stands for time interval.F represents the total amount.Here given ,
r = 1.2%
t = 7
F = $126
As a result,
I = F/(1+rt)
= 126/1+1.2*7
= 13.4 dollars.
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Marking for BRAINLIEST!!!
A maximum number of 4 points are available for this question. Part A is worth 1 point. Part B is worth 1 point. Part C is worth 2 points.
Greg is shopping at a bicycle store. The store is having a sale and discounting all bicycles by 20% of the marked price. He decides to buy a bicycle with a marked price of $199.75.
Part A: Set up a proportion that can be used to find the dollar amount of the discount (d).
Part B: Given that the sales tax in Greg's state is 7%, what is the final cost of the bicycle he buys?
Part C: Greg's brother, Max, lives in a different state with a 5.5% sales tax rate. Max found the same bicycle discounted 25% from a regular price of $215.99. If Max buys the bicycle, who pays the lower total cost? Justify your answer.
Answers
Help with this need to turn please help
Answers
Based on the graph given on the height of the helicopter, the slope and y-intercept of the function would be:
0 = Neither 5 = Neither 10 = Slope 50 = y-intercept 100 = Neither How to find the slope and y-intercept?To find the slope of the line om the height of the helicopter, the formula is:
= Change in y / Change in x
= (100 - 50) / (5 - 0)
= 50 / 5
= 10
The y-intercept takes the form b in the linear equation model:
y = mx + b
100 = 10(5) + b
b = 100 - 50
b = 50
The slope is 10 and the y-intercept is 50.
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The length of a rectangular sign is 12 ft less than twice its width. Its perimeter is 144 ft. Find the length and the width of the sign.
Answers
The rectangular sign is 30 feet in length and 42 feet in width.
The perimeter of the rectangular sign = 144 ft
Let the width of the rectangular sign be x, and the length of the sign will be x-12
The formula for the perimeter of the rectangle:
P = 2(l+w)
where P = perimeter of the rectangle
l = length of the rectangle
w = width of the rectangle
Substituting the values in the formula we get:
144 = 2(x-12+x)
144 = 2(2x-12)
144 = 4x -24
168=4x
x= 42
So, the length is 30ft and the width is 42ft
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as soon as possible please!
Answers
Answer:
C). [tex]1 - sec^{2} A[/tex]
Step-by-step explanation:
Lets say the bottom side is X, right side is Y, and hypotenuse is H.
[tex]tan A = \frac{Y}{X}[/tex]
[tex]tan B = \frac{X}{Y}[/tex]
[tex]\frac{tan A}{tan B} = \frac{\frac{Y}{X}}{\frac{X}{Y}} = \frac{Y}{X} * \frac{Y}{X} = \frac{Y^{2} }{X^{2}} = (\frac{Y}{X})^{2} = tan^{2} A= 1 - sec^{2} A[/tex]
Given m||n, find the value of x.
need help
Answers
Using the alternate exterior angles theorem, the value of x is: 127°.
What is the Alternate Exterior Angles Theorem?When two parallel lines are intersected by a transversal to form alternate exterior angles that lie outside on each of the parallel lines, the alternate exterior angles theorem states that both angles are equal or congruent to each other.
From the diagram given, we are told that line m is parallel to line n. transversal t crosses both lines and n. The angles, x and 127 degrees are alternate exterior angles that lie on each parallel lines.
Therefore, the alternate exterior angles theorem states that, both angles would be equal.
Thus, we can conclude that, x = 127°.
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The scale on a map is 1 : 30000
What is the actual distance represented by 1 centimetre?
Answers
When the scale on a map is 1 : 30000, the actual distance represented by 1 centimetre is 300 meters.
How to calculate the distance?It should be noted that in order to get the distance, we have to convert 1cm to meter. It should be noted that;
100cm = 1 meter
1cm = 1/100 = 0.01 meters.
Therefore, when the scale on a map is 1 : 30000, the actual distance represented by 1 centimetre will be:
= (0.01 × 300000)
= 300 meters.
Therefore, the distance is 300m
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I don't understand what I'm doing, I'm confused irritated and I just need some help
Answers
Answer:
See explanation
Step-by-step explanation:
Slope: 4 since $4 was made per ticket. $4/1=$4.
Equation: y=mx+b
0=4(0)+b ==> the function has a point on the origin, (0,0).
0=0+b
b=0
y=4x+0
y=4x ==> equation of line
Answer:
day 1: $4
day 2: $8
day 3: $12
day 4; $16
Step-by-step explanation:
y= 4x
cuz you add 4 each time
What is the equation of the line that passes through the point (-3,2) and has a slope of 2/3
Answers
Answer: y = 2/3 -2
Step-by-step explanation: using a graph you can plot the point (-3, 2).
After this, you can use the slope of 2/3 to graph the starting point. You go 3 to the left and 2 up going through the y axis of -2. using y = mx + b, you can plug in the slope of 2/3 and the starting point of -2.
in the game of hearts, four players are each dealt 13 cards from a deck of 52. is this a function? if so, what are the domain and codomain? is the function injective, surjective, both (bijective), or neither?
Answers
Based on the fact the game of hearts, four players are each dealt 13 cards from a deck of 52
The domain is the deck of 52 cardscodomain is 4 playersfunction, f(k) maps a card to each playerIt is surjectiveThis is further explained below.
What is a surjective Function?A surjective function is a kind of function that exists in mathematics that ensures that any element y may be transferred to element x in such a way that f(x) equals y.
To put it another way, each element that makes up the function's codomain is the mirror image of at least one element that makes up the domain.
Generally, function, f(k) maps a card to each player
And since each player is dealt 13 cards st 13 of the cards are mapped to each player.
It is a function as one card is mapped to one and only one player.
The function is not injective because 13 cards 1 are mapped to one player so it is a many-one function but the injective function does not map two elements to a common clement.
In conclusion, It is surjective as each player is dealt 13 cards. the function is not injective hence rot bijective.
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You and a friend are going to the movies. Tickets cost $5 each and you both buy popcorn and soda. Each costs a different amount. Write an algebra expression to represent the cost of your friends and your trip to the movies.
Answers
Answer:
2(5)+2x+2y
Step-by-step explanation:
since you both have the tickets the amount of the prize is going to double. You both also bought popcorn and soda if we take 1 popcorn as "x" it is also going to multiple 2 times same with the soda except different variable.
Find the midpoint of each line segment
Answers
Answer:
(10, -3)
Step-by-step explanation:
It is stated in the given information.
Please list the number below least to greatest.PLEASE
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27/4 , -3.2, -∛60 ,√48, 7.05 when arranged in ascending order we get:
-3.2 , -∛60 , 27/4 , √48, 7.05
How to order numbers from least to greatest?Determine the number of digits in each number.The number with the fewest digits is the smallest, so write it first.The number with the most digits is the largest, so it is placed last.
Given list of numbers,
27/4 , -3.2 , -∛60 , √48 , 7.05.
simplifying each numbers ,
=> 27 / 4 = 6.75
=> -∛60 = - ∛(2 × 2 × 3 × 5)
= -3.9149.
=> √48 = √(2 × 2 × 2 × 2 × 2)
= 4√3
= 6.928
So the list after simplification is ,
6.75 , -3.2 , -3.9149 , 6.928 , 7.05
Now arrange the numbers from least to greatest,
-3.2 , -3.91 , 6.75 , 6.928 , 7.05
= -3.2 , -∛60 , 27/4 , √48, 7.05.
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what is 2/3 times 1/16
Answers
Answer:
1/24
Step-by-step explanation:
Answer:
1/24
Step-by-step explanation:
so first you cross out the 2 and 16 because 2*8=16
then you multiply the numerator and the denominator.
then bam! your answer!
1/24
In a given country, the average price of a gallon of unleaded gasoline in 1995 was $2.54. In 2010, the average price was $3.18. Find and interpretThe average rate of change in the price of a gallon of gasoline per year. The average rate of change is $ ___ per year.(Type an integer or a decimal. Round to the nearest cent as needed.)
Answers
The rate of change is found using the slope formula
m = ( y2-y1)/(x2-x1)
We have two points
( 1995, 2.54) ( 2010, 3.18)
m = (3.18-2.54) / (2010-1995)
=.64/15
$.042666666 per year
Rounding to the nearest cent
$.04 per year
We know that the price went up from 1995 to 2010 so the price increased
It increased an average of $.04 each year
A. The price of a gallon of gasoline increased by an average of $_.04__ per year from 1995 to 2010
A triangle is dilated by a factor of 2 and then rotated clockwise Which statement about the triangle's image and pre-image is correct?
Answers
Answer:
what are th e statements though
Which of the following numbers is a whole number? A −2 C 4.1 B 3 D \pi
Answers
Answer: B
Step-by-step explanation: A whole number is a number that is not a decimal or a fraction and is over 0.
Which transformation
does not always preserve distance?
1 (x,y) → (x + 2, y)
2 (x,y) → (-y, -x)
3 (x,y) → (2x, y - 1)
4 (x,y) → (3-x, 2-y)
Answers
From Option 1,2,3 and 4.
Option 3 transformation is A dilation does not always preserve distance.
Give that,
We have to find which transformation does not always preserve distance.
1 (x,y) → (x + 2, y)
2 (x,y) → (-y, -x)
3 (x,y) → (2x, y - 1)
4 (x,y) → (3-x, 2-y)
Option 3 is A dilation does not always preserve distance.
Dilation means a modification of this kind that alters the size of the image is called a dilatation. How much larger or smaller the image is is determined by the scale factor, often known as the scalar factor. A picture of each type of dilatation is shown below (one that gets larger and one that gest smaller).
Therefore, Option 3 transformation is A dilation does not always preserve distance.
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Please answer ASAP and thank you
Answers
Answer:
The last answer is correct.
Step-by-step explanation:
The plant start at 4 inches (0,4) and then grows 1 inch each week.
(1,5), (2,6).(3,7) and so on.
15/14 multiplied by 4/3
Answers
Hope this help
The function a(t) = 44,000(1.045)^t models Johanna’s annual earnings a, in dollars, t years after she starts her job.
Which of the following statements are true about Johanna’s salary?
Johanna initally earns $44,000 per year. True or False
Johanna initially earns $45,980 per year. True or False
Johanna’s salary increases by 1.045% per year. True or False
Johanna’s salary increases by 4.5% per year. True or False
Johanna’s salary increases by 104.5% per year. True or False
This represents an exponential growth. True or False
This represents exponential decay. True or False
Answers
Step-by-step explanation:
true.
false.
true.
true
.true.
false.
true..
please mark me as brainlist
given that f(x) =3x+7 and g(x) x2/2 what is the value of f(g(4))
Answers
Given the following functions:
[tex]\begin{gathered} f(x)=3x+7 \\ g(x)=\frac{x^2}{2} \end{gathered}[/tex]to find f(g(4)), we can start by finding g(4) first:
[tex]\begin{gathered} x=4 \\ \Rightarrow g(4)=\frac{(4)^2}{2}=\frac{16}{2}=8 \\ g(4)=8 \end{gathered}[/tex]now that we know that g(4) = 8, we can calculate the composition f(g(4)):
[tex]undefined[/tex]Answer:
f(g(4) ) = 31
Step-by-step explanation:
evaluate g(4) then substitute the value obtained into f(x)
g(4) = [tex]\frac{4^2}{2}[/tex] = [tex]\frac{16}{2}[/tex] = 8 , then
f(8) = 3(8) + 7 = 24 + 7 = 31
The cat rescue is selling cat beds as a fundraiser. If its goal is to raise $1300, how many cat beds must be sold at $15.00 each to meet the goal?
Answers
The cat rescue must sell 87 beds to meet the goal
How calculate the number of beds that must be sold ?The car rescue is selling cat beds as a fundraiser
The goal is to raise $1300
Each cat bed is sold at $15
The number that must be sold to reach the goal can be calculated as follows
= 1300/15
= 86.6
= ≅ 87
Hence 87 cat beds must be sold to reach the goal
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write 14/3 as a decimal.if necessary,use a bar to include which digit pr group of digits repeats.
Answers
To convert a fraction to a decimal, we simply divide.
Shown below:
This is never ending decimal with the "6" repeating.
Thus, we can put a bar over "6".
So,
[tex]\frac{14}{3}=4.\bar{6}[/tex]the length of Michelle's room is shown. The ratio of length to width is 4:3. What is the width of Michelle's room?
it is 111
Answers
The width of Michelle's room is 111 inches.
How to find the width of a rectangle?The ratio of the length to the width is 4:3.
The width of her room can be calculated as follows:
Therefore,
length = 12 ft 4 inches
Hence.
1 ft = 12 inches
12 ft = 144 inches
Hence,
length = 144 + 4 = 148 inches
Therefore,
x = length + width
4 / 7 × x = 148
4x / 7 = 148
cross multiply
4x = 148 × 7
4x = 1036
x = 1036 / 4
x = 259
Hence,
width of the rectangle = 259 - 148
width of the rectangle = 111 inches
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given : AD is perpendicular to DC, <1 and <2 are complementary Proven: <1 is congruent to <3
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When two straight lines or rays intersect at a single endpoint, an angle exists formed. If 2 and 3 exists complements, and m2= 55°, then m3 = 90 - 55 = 35 degrees.
What is meant by angle?When two straight lines or rays intersect at a single endpoint, an angle exists formed. The vertex of an angle is the location where two points come together. The Latin word "angulus," which means "corner," is where the term "angle" originates.
An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.
Complements sum to 90 degrees.
If 1 and 2 are complements and m1 = 35°, then
m2 = 90 - 35 = 55 degrees.
Now if 2 and 3 are complements, and m2= 55°,
then m3 = 90 - 55 = 35 degrees.
The complete question is:
Given: 1 and 2 are complements, 2 and 3 are complements, and m1 = 35°. Prove: m3 = 35° Complete the missing parts of the paragraph proof. By then, we know that angle 1 is congruent to angle 3. The measure of angle 1 equals the measure of angle 3 by the definition of angles. Then, using the property, the measure of angle 3 is the degree.
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