Answer:
y = 1/3x - 3
Step-by-step explanation:
We can find the equation of the line, by finding the slope and combine with our y-intercept (-3).
We need to use the slope formula to find the slope.
Thus, we have (-3 - (-2)) / 0 - 3 = -1/-3 = 1/3
So our equation is y = -1/3x - 3
The product of a number and 3 less than the number is 40. Find the number.
By solving a quadratic equation we will see that the number can be:
8 or -5.
How to find the number?The product of a number N, and 3 less than the number, is equal to 40.
This is written as:
[tex]N*(N - 3) = 40[/tex]
Now we need to solve this for N.
[tex]N^2 - 3N = 40[/tex]
[tex]N^2 - 3N - 40 = 0[/tex]
Then we need to solve this quadratic equation:
[tex]N = \frac{-(-3) \pm \sqrt{(-3)^2 - 4*1*(-40)} }{2} \\\\N = \frac{3 \pm 13 }{2}[/tex]
Then we have two solutions:
N = (3 - 13)/2 = -5N = (3 + 13)/2 = 8These are the two possible solutions.
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The length of a certain rectangle is 6 meters more than twice its width. What is the perimeter of the rectangle if the area of the rectangle is 260 square meters?
Answer:
Perimeter = 72 meters
Step-by-step explanation:
Let L be the length and W the width of the rectangle
We have the following relationship
L = 2W + 6
Area of the rectangle = LW = (2W+6)W by substituting for L
Area =
2W² + 6W =260 ==> 2W² + 6W -260 = 0
Dividing both sides by 2 yields
W² + 3W -130 = 0
This is a quadratic equation which can be solved using the formula for the roots of the equation ie the values of W which satisfy the above equation
However in this case it is easier to solve by factorization
W² + 3W -130
= W² + 13W - 10W - 130
= W(W + 13) -10(W + 13)
= (W+13)(W-10) = 0
This means W is either -13 or W = 10
Since W cannot be negative, we get W = 10 and
L = 2(10) + 6 = 26
Perimeter of a rectangle is given by
2(L + W) = 2(26 + 10) = 2(36) = 72 Answer
Question 19 (5 points) ✔ Saved
Order the following temperatures from coolest to warmest.
1
>
>
>
>
3°C
-7°℃
2°F
262 K
Question 20 (5 points)
The order of temperature values become -16.7°C > -11.15°C > -7°C > 3°C And -16.7°C is the coolest temperature and 3°C is the warmest as compare to others.
According to the statement
we have given that the some values of the temperatures and we have to write it in the order from the coolest to the warmest means in increasing order.
So, For this purpose,
The given values of temperatures are:
3°C , -7°C , 2°F, 262 K
Firstly convert into one form
So, convert all values in Celsius form,
3°C = 3°C
-7°C = -7°C
2°F = -16.7°C
262 K = -11.15°C
Now arrange into the order from coolest to warmest
So, it will become
-16.7°C > -11.15°C > -7°C > 3°C
So, -16.7°C is the coolest temperature and 3°C is the warmest as compare to others.
The order of temperature values become -16.7°C > -11.15°C > -7°C > 3°C And -16.7°C is the coolest temperature and 3°C is the warmest as compare to others.
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2. One day at Coffee Town a customer asks for exactly 300 ml of coffee. To this 300 ml of
coffee,
the customer wants pure cream added until the cream represents 20% of the total volume of
the drink (cream and coffee. Not just 20% of the 300 ml). How much pure cream should the
barista add?
Answer:60 ml
Step-by-step explanation:20 % of 300 = 60 and snce the rest of the the l are coffee thats 20%
Instructions: Find the value of the trigonometric ratio. Make sure to simplify the fraction if needed.
Sin A= Answer
Check the picture below.
100 POINTS!!!!!!!!!!!!!!1 PLEASE SOLVE THESE PROBLEMS QUICKLY WITH AN EXPLANATION
In triangle ABC, if m∠B = 90°, BH = AH, and the ratio of m∠A to m∠C is 1:2, then m∠BHA = 120° (C).
In the next given equilateral triangle ABC, y = 70°.
Finding m∠BHA:
In triangle ABC, it is given that,
∠B = 90°
And m∠A : m∠C = 1:2
Let us assume m∠A is x. Then, m∠C = 2x
According to the angle sum property of a triangle,
∠A + ∠B + ∠C = 180°
90° + x + 2x = 180°
90° + 3x = 180°
3x = 90°
x = 30°
⇒ In triangle ABC, ∠A = 30° and ∠C = 60°
Now, in triangle AHB, it is also given that,
BH = AH
⇒ ∠ABH = ∠A = 30°
Thus, according to the angle sum property of a triangle,
∠ABH + ∠A + ∠BHA = 180°
30° + 30° + ∠BHA = 180°
∠BHA = 180° - 60°
∠BHA = 120°
Finding y in the Second Triangle:
Since triangle ABC is equilateral,
∠A = ∠B = ∠C = 60°
∴ x + 2x + 3x = 60°
6x = 60°
x = 10°
In triangle ABD, using angle sum property of triangle,
x + ∠B + ∠BDA = 180°
10° + 60° + ∠BDA = 180°
∠BDA = 180° - 70°
∠BDA = 110°
Now, since, ∠BDA and y are linearly adjacent angles,
∠BDA + y = 180°
110° + y = 180°
y = 180° - 110°
y = 70°
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HELP PLS!!!!!!!!!!!!
Answer:(3+3)(1+3) = 24
Step-by-step explanation: There is a 1 and 3 3's. We know that added up, the sum is not 24. So it can't be all addition. But, 3 is a factor of 6 which is a factor of 24. There are 2 3's, so we add them up to get 6. Then, we have a 1 and a 3 left. we add these up to get 4. 6x4= 24.
Which of the following are true statements about a 30 69 90 triangle? Check all that apply
By the 30 - 60 - 90 theorem the right options of the multiple choice question is:
A. The hypotenuse is twice as long as the shorter leg.
D. The longer leg is √3 times as long as the shorter leg.
What are the properties of a 30 - 60 - 90 right triangles
In this problem we must look for the right choices in a multiple choice question. According to the Euclidean geometry, 30 - 60 - 90 have the following properties:
The length of the hypotenuse is √3 / 2 times as long as the longer leg.The length of the hypotenuse is twice as long as the shorter leg.The length of the longer leg is √3 times as long as the shorter leg.Thus, the right options of the multiple choice question is:
A. The hypotenuse is twice as long as the shorter leg.
D. The longer leg is √3 times as long as the shorter leg.
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Triangle ABC is a non-right triangle with Angle C = 117, a = 12, and b = 18. Find Angle B to the nearest tenth.
Using the law of cosines and sines, the measure of angle B is: 38.4°.
What is the Law of Cosines and Sines?Law of cosines is: c = √[a² + b² ﹣ 2ab(cos C)]
Law of sines is: sin A/a = sin B/b = sin C/c
Use the law of cosines to find c:
c = √[12² + 18² ﹣ 2(12)(18)(cos 117)]
c ≈ 25.8
Use the law of sines to find angle B:
sin B/b = sin C/c
sin B/18 = sin 117/25.8
sin B = (sin 117 × 18)/25.8
sin B = 0.6216
B = sin^(-1)(0.6216)
B = 38.4°
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Which relation is also a function?
A.
A dot plot graph shows on a coordinate plane passes through (4, minus 8), (2, minus 4), (2, minus 3), (1, minus 1), (0, 1), (minus 1, 2), (minus 1, 4), (minus 3, 5), and (minus 4, 7)
B. (,)
C. circle graph
A nonlinear function on a coordinate plane vertex at (minus 3, minus 2) passes through (minus 7, 0), and (minus 6, minus 4).
D.
x y
The relation that is also a function is described as follows:
A nonlinear function on a coordinate plane vertex at (minus 3, minus 2) passes through (minus 7, 0), and (minus 6, minus 4).
When a relation is a function?A relation is a function if each value of the input is mapped to only one value of the output.
In this problem, we have that:
For the dot plot graph, input 2 is mapped to -3 and -4, hence it is not a function.In a circle graph, each value of x is mapped to two values of y, hence it is not a function.Hence a function is given by:
A nonlinear function on a coordinate plane vertex at (minus 3, minus 2) passes through (minus 7, 0), and (minus 6, minus 4).
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A photograph is 3 in. longer than it is wide. When a 2-in. border is placed around the photograph, the total area of the photograph and the border is 108 in^2. Find the dimensions of the photograph.
width = 7
length = 10
Step-by-step explanation:
solve for the one letter that gets talked about the most
which is w or width
width = w
length = 3 + w
2 inch border means
width = w + 2
length = 3 + w + 2
area = length times width
area = ( 3 + w + 2 ) times (w + 2 )
108 = ( 3 + w + 2 ) times (w + 2 )
108 = ( w + 5 ) times (w + 2 )
( w + 5 ) times (w + 2 ) = 108
w^2 + 7w +10 = 108
w^2 + 7w - 98 = 0
going to make w = x
x^2+7x-98=0
(x-7)(x+14)
x = 7
x = -14
w=7
w= -14
cant have a negative measurement so w=7 is used
width = w
length = 3 + w
width = 7
length = 3 + 7 = 10
Bags of chips cost $4 each. Write a direct
proportion equation using (b) for bags of
chips and (t) for total cost.
Answer:
t = 4b
Step-by-step explanation:
Each bag costs 4 dollars.
hope this helps! <3
The table gives a partial set of values of a polynomial h(x), which has a leading coefficient of 1. x –2 0 1 2 3 h(x) 0 –12 0 8 0 If every x-intercept of h(x) is shown in the table and has a multiplicity of one, what is the equation of the polynomial function?
Using the Factor Theorem, the equation of h(x) is given as follows:
h(x) = -2(x³ - 2x² - 5x + 6)
What is the Factor Theorem?The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
In which a is the leading coefficient.
Looking at the table, considering the values of x when h(x) = 0, the roots of h(x) are given as follows:
[tex]x_1 = -2, x_2 = 1, x_3 = 3[/tex]
Then the rule is:
h(x) = a(x + 2)(x - 1)(x - 3)
h(x) = a(x² + x - 2)(x - 3)
h(x) = a(x³ - 2x² - 5x + 6)
The h-intercept is of -12, as when x = 0, h = -12, hence this is used to find a as follows:
6a = -12
a = -12/6
a = -2.
Hence the function is given by:
h(x) = -2(x³ - 2x² - 5x + 6)
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Can u guys please give me the correct answe
angle at y and w are equal
hence, 54°=w
54°+w+x =180°
x=180-(54°+54°)
x=72°
A company reports cost of goods manufactured of $918,700 and cost of goods sold of $955,448. Compute the average manufacturing cost per unit assuming 18,374 units were produced.
If the cost of goods manufactured of $918,700 and cost of goods sold is $955,448. The average manufacturing cost per unit assuming 18,374 units were produced is $102 per unit.
Average manufacturing cost per unitUsing this formula to determine the average manufacturing cost per unit
Average manufacturing cost per unit= Total cost/Number of units produced
Where:
Total cost=$918,700+$955,448=$1,874,148
Number of units produced=18,374 units
Let plug in the formula
Average manufacturing cost per unit=$918,700+$955,448/18,374
Average manufacturing cost per unit=$1,874,148/18,374
Average manufacturing cost per unit=$102 per unit
Therefore the average manufacturing cost per unit assuming 18,374 units were produced is $102 per unit.
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A container manufacturer plans to make rectangular boxes whose bottom and top measure 2x by 3x. The container must contain 12in.3 The top and the bottom will cost $2.60 per square inch, while the four sides will cost $4.30 per square inch. What should the height of the container be so as to minimize cost? Round your answer to the nearest hundredth.
The height of the container be so as to minimize cost will be 1.20. inches.
How to calculate the height?The volume of the box will be:
= 2x × 3x × h
= 6x²h
Volume = 6x²h
12 = 6x²h
h = 2x²
The cost function will be:
C = 2.60(2)(6x²) + 4.30(12x)h
C = 31.2x² + 51.6xh
Taking the derivative
62.4x + 51.6h
h = 1.20
Therefore, the height of the container be so as to minimize cost will be 1.20 inches.
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Which features are present
in this polar graph?
The features that exist present in this polar graph is that D. Symmetry about the polar axis θ = 0.
What is polar graph?A polar curve exists as a form constructed utilizing the polar coordinate system. Polar curves exists determined by points that exist at a variable distance from the origin (the pole) depending on the angle calculated off the positive x-axis.
The polar graph can be said to contain a symmetry about the polar axis which indicates that theta or θ exists equivalent to 0.
This exists because the graph is symmetric about the x-axis. This indicates that all the lines of symmetry can be seen intersecting the graph at x = 0. This demonstrates that there exists indeed symmetry in the polar graph.
Therefore, the correct answer is option D. symmetry about the plane θ = 0
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Given the following exponential function, identify whether the change
represents growth or decay, and determine the percentage rate of increase or
decrease.
y = 540(1.04)
Step-by-step explanation:
We can determine whether the change represents exponential growth or decay by seeing whether the number being raised to x is between 0 and 1, or greater than 1.
In the equation [tex]y = 540(1.04)^x[/tex], y will increase every time that x increases, as we are multiplying by a number greater than 1 every time.
Hence, this exponential function represents exponential growth.
The percentage rate of increase for this function would be how much the y-value increases each time. Since we are multiplying by 1.04, each time the new value is 104% the original y-value. Hence, the percentage increase is 4%.
Find the length indicated
Answer:
23
Step-by-step explanation:
if you have 8 apples in a box, and then you put 15 additional apples into the box - how many apples are in the box ?
you see that is the same problem as the symbolized scenario with 2 lines being connected.
you have a string (e.g. for a kite) of 8 meters. and then you tie another string of 15 meters to it - how long is the new combined string ?
you really need help with that ?
8 + 15 = 23
What are the x- and y- coordinates of point E, which partitions the directed line segment from J to K into a ratio of 1:4?
The x- and y- coordinates of point E, which partitions the directed line segment from J to K into a ratio of 1:4 is (17, 11)
Midpoint of coordinate pointsThe midpoint of a line is the point that bisects or divides the line into two equal parts
If the line JK is partitioned into the ratio 1:4 with the following coordinates
J(-15, -5) and K(25, 15)
Using the expression below;
M(x, y) =[mx1+nx2/m+n, my1+ny2/m+n]
Substitute the ratio and the coordinates
M(x, y) =[1(-15)+4(25)/4+1, 1(-5)+4(15)/1+4]
M(x, y) = [(85)/5, 55/5]
M(x, y) = (17, 11)
Hence the x- and y- coordinates of point E, which partitions the directed line segment from J to K into a ratio of 1:4 is ((17, 11)
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A four-person committee is chosen from a group of eight boys and six girls.
If students are chosen at random, what is the probability that the committee consists of all boys?
Answer:
7.....gggggggggggggggh
If a translation maps point A(-3,1) to point A′(5,5), the translation is:
A. (x+2,y+4)
B. (x+8,y+6)
C. (x+2,y+6)
D. (x+8,y+4)
Answer:
D is the correct answer -3+8=5 ,1+4=5
HELP PLEASE
What is the area of the kite below?
Answer:
Area = 33 inches squared
Step-by-step explanation:
The formula for the area of a kite is:
Area = ½ × (d)1 × (d)2
To find the first diagonal (d1):
d1 = 7 in + 4 in = 11 in
To find the second diagonal (d2):
The triangles on the right of the kite must be 3 4 5 triangle since it is a right triangle with a hypotenuse of 5 and a side of 4, we know half of a diagonal would be 3 inches.
d2 = 3 in + 3 in = 6 in
Now we can plug the diagonals into the area formula.
Area = ½ × 11 × 6 = 33 inches squared
Answer: A = 33 in²
Step-by-step explanation:
Given information:
Longer side = 7 in
Shorter side = 4 in
Shorter Hypotenuse = 5 in
Given formula:
A = (1/2) × (d₁) × (d₂)
A = aread₁ = The longer line (horizontal)d₂ = The shorter line (vertical)Please refer to the attachment below for a graphical understanding
Determine the length of the shorter side (vertical) through the Pythagorean theorem
a² + b² = c² (Pythagorean theorem)
(4)² + b² = (5)² (Substitute values into the equation)
16 + b² = 25
b² = 25 - 16
b² = 9
b = 3 or b = -3 (rej)
Substitute values into the given formula
A = (1/2) × d₁ × d₂
A = (1/2) × (7 + 4) × (3 + 3)
Simplify values in the parenthesis
A = (1/2) × 11 × 6
Simplify by multiplication
A = (11/2) × 6
[tex]\Large\boxed{A=33}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
If R={(1,2),(2,3),(3,9),(4,5)} find R-1
Answer:
R-1={(2,1),(3,2),(9,3),(5,4)
Step-by-step explanation:
R-1={(2,1),(3,2),(9,3),(5,4) because (- 1) means reverse in relation
i need help quick, everything is in the image
Answer:
x = 3
Step-by-step explanation:
see image. Instead of distributive property, let's multiply by 2 to get rid of the fraction and also the parenthesis on the left. See image.
Then subtract 5 and finally, divide by 3 to solve. See image.
Simply the expression a = -3; b = 9
-7a + 4b
46?
-15?
15?
57?
Answer:
57
Step-by-step explanation:
-7a + 4b
Let a = -3 b = 9
Substitute the values in
-7(-3) + 4(9)
Multiply
21 + 36
Add
57
Let σ(n) be the sum of all positive divisors of the integer n and let p be any prime number.
Show that σ(n) < 2n holds true for all n of the form n = p²
The statement that "σ(n) < 2n holds true for all n of the form n = p²" has been proved.
Let p be any prime number, and let σ(n) be the sum of all positive divisors of the integer n.
As p is a prime number, and 2 is the smallest prime number, so, p[tex]\geq[/tex]2
So, the positive divisors of the integer n are: 1,p,p².
As σ(n) represents the sum of all positive divisors of the integer n.
σ(n)=1+p+p²
In order to prove that σ(n) < 2n,for all n of the form n = p².
1+p+p²<2p²
p²-p-1>0
It is know that, p[tex]\geq[/tex]2.
So, p²-p-1[tex]\geq[/tex]1
Thus, σ(n) < 2n holds true for all n of the form n = p².
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In a certain school 70% of the students in first-year chemistry have had algebra. If there are 290 students in first-year chemistry, how many of them have had algebra?
The number of the students in the school that have had algebra is 203
How to determine the number of students?The given parameters in the question are
Proportion of students taking algebra, p = 70%Number of students in the school, n = 290The number of students that had algebra in the school is calculated as:
Algebra = Proportion of students taking algebra * Number of students in the school
The above equation can be represented as:
Algebra = np
Substitute values for n and p in the above equation
So, we have
Algebra = 290 * 70%
Express 70% as decimal i.e. 0.70
So, we have
Algebra = 290 * 0.70
Evaluate the product i.e. multiply 290 and 0.70
So, we have
Algebra = 203
Hence, the number of the students in the school that have had algebra is 203
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Caisse can download a maximum of 1000 mb of songs or movies to her smartphone each month. the file of each movie is 85mb, and the file of each song is 4mb. write an inequality that represents the number of movies(M) and songs(S) that Caisse downloads each month?
If Caisse can download a maximum of 1000 mb of songs or movies then the inequality that represents the number of movies and songs that Caisse downloads each month is 85x+4y<1000.
Given that Caisse can download a maximum of 1000 mb of songs or movies to her smartphone each month. the file of each movie is 85mb, and the file of each song is 4mb.
We are required to find the inequality that represents the number movies and songs that Caisse downloads each month.
Inequality is like an equation that shows the relationship between variables that are expressed in greater than, less than , greater than or equal to , less than or equal to sign.
let the number of movies be x and the number of songs be y.
According to question Caisse cannot download more than 1000 mb, so we will use less than towards equation.
It will be as under:
85x+4y<1000.
Hence if Caisse can download a maximum of 1000 mb of songs or movies then the inequality that represents the number of movies and songs that Caisse downloads each month is 85x+4y<1000.
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Suppose that a and b are integers with a < b How many numbers are in the list a, a+1, a+2.... b?
So I thought about doing a-(a-1) to get the first number to one so the list becomes 1,2,3 but i soon realized that does not work
The count of numbers in the list a, a+1, a+2.... b is b - a + 1
How to determine the count of numbers in the list a, a+1, a+2.... b?The list of numbers is given as:
a, a+1, a+2.... b
From the above list, we can see that the numbers are consecutive numbers.
This means that, the count of numbers in the list is
Count = Highest - Least + 1
Where
Highest = b
Least = a
Substitute the known values in the above equation
Count = b - a + 1
Hence, the count of numbers in the list a, a+1, a+2.... b is b - a + 1
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