The equation of the line is y = -0.35x – 3.55
Given,
The gradient of the line between two points (x₁, y₁) and (x₂, y₂) is m = (y₂ - y₁)/(x₂ - x₁).
Since the line passes through the points (7,-6) and (3,8),
• (x₁, y₁) = (7,-6) and
• (x₂, y₂) = (3,8).
So, substituting the values of the variables into the equation, we have
m = (y₂ - y₁)/(x₂ - x₁).
m = (8 - (-6))/(3 - 7).
m = (8 + 6)/ -4
m = 14/-4
m = -3.5
The equation of the line passing through the point (x₁, y₁) in point-slope form is given by
y - y₁ = m(x - x₁) where
• m = gradient =- 0.35 and
• (x₁, y₁) = (7, -6)
So, substituting the values of the variables into the equation, we have
y - y₁ = m(x - x₁)
y - (-6) = -0.35(x - 7)
y + 6 =-0.35 (x - 7)
y = (-0.35x + 2.45 – 6)
y = -0.35x – 3.55
So, the equation of the line is y = -0.35x – 3.55
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a newborn kitten weights about 1/4 pound. There are 0.45 kilograms in 1 pound. If a mother cat has a litter of 6 kitten. What is the approximate total weight of the litter of 6 kittens in kilograms.
The approximate total of weight of the litter of 6 kittens 0.675kg
What is Weight ?
The force exerted on an object by gravity is known as its weight. The gravitational force acting on the item is referred to as weight in several common textbooks. Some people refer to weight as a scalar quantity that measures the gravitational force's strength.
Given,
The weight of one newborn kitten = 1/4 pounds
The value of pound in kilograms = 1pound = 0.45kg
convert the weight from pound to kilograms = 1/4 x 0.45
= 0.1125kg
Now, to find out total weight of litter of 6 kitten in kilograms
= 0.1125 x 6
= 0.675kg
Hence, The approximate total weight of the litter of 6 kittens in kilograms is 0.657kg
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Write a function store_digits that takes in an integer n and returns a linked list where each element of the list is a digit of n.
def store_digits(n):
"""Stores the digits of a positive number n in a linked list.
>>> s = store_digits(1)
>>> s
Link(1)
>>> store_digits(2345)
Link(2, Link(3, Link(4, Link(5))))
>>> store_digits(876)
Link(8, Link(7, Link(6)))
"""
"*** YOUR CODE HERE ***"
1 = Link.empty
while n > 0:
1 = Link(n % 10, 1)
n //= 10
return 1
Store Digits
In some programming languages you have to declare a variable before using them or define the information that will be stored in it, e.g., a number. However, in Python we just need to type the name of our variable, followed by an equals sign and a value to assign to it.
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simplify - (5+√2) (3+√5)
HELP PLS,
Alexandra signed up for a streaming music service where there's a fixed cost for monthly membership and a cost per song downloaded.
Answer:
D.
Step-by-step explanation:
7.99 is the basic fixed cost per month. this is charged, even if there are no songs (x = 0) downloaded.
and so, 1.75 is the cost per downloaded song in addition to the basic fixed cost. so, yes, the number of downloaded songs has to be multiplied by the cost for a single song to get the total.
and so, 1.75 is the change in the total cost for every automakers download (every time x is increased by 1).
Which table represents a proportional relationship?
Responses
x 1 2 3 4 5
y 4 5 6 7 8
r 2 3 4 5 6
s 3 5 6 8 9
b 2 3 8 9 14
c 4 6 16 18 28
I don't know.
The tables that represent a proportional relationship are :
x 1 2 3 4 5
y 4 5 6 7 8
b 2 3 8 9 14
c 4 6 16 18 28
Which tables have a proportional relationship?Two variables have a proportional relationship when the ratios of the rate of change of the variables are constant.
Ratio = change in the value of y / change in the value of x
First table:
(5 - 4) / (2 - 1) = 1
(6 - 5) / (3 - 2) = 1
(7 - 6) / (4 - 3) = 1
(8 - 7) / (5 - 4) - 1
Second table:
(5 - 3) / (3 - 2) = 2
(6 - 5) / (4 - 3) = 1
(8 - 6) / (5 - 4) = 2
(9 - 8) / (6 - 5) = 1
Third table:
(6 - 4) / (3 - 2) = 2
(16 - 6) / (8 - 3) = 2
(18 - 16) / (9 - 8) = 2
(28 - 18) / (14 - 9) = 2.
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1. Find the value of x and the perimeter of the square.
2X
7x - 15
A square has 4 congruent side lengths. This means that each side will be the same length. Therefore, we can set the two lengths equal to each other.
[tex]S=S[/tex]
[tex]7x-15=2x[/tex]
Isolating a variable: rearranging an equation so that the variable is by itself
done by performing inverse operations3 Step Solving process:
1. Collect like terms
2. Perform inverse operations
3. Simplify if necessary
[tex]7x-2x-15=0[/tex]
[tex]5x=15[/tex]
[tex]\frac{5x}{5}=\frac{15}{5}[/tex]
[tex]x=3[/tex]
The value of x = 3
The perimeter can be found by adding all of the side lengths. A square has 4 sides.
a + a + a + a = P
However, we know that a square has congruent sides so we can manipulate this formula:
4a = P - where a is equal to the side length
Using a previous equation we know that a side length is equal to 2x and we know the value of x, to be 3. Therefore, a side length must be 6.
we can now input the value of the side length into the formula.
[tex]4(6)=P[/tex]
[tex]24=P[/tex]
The perimeter of the square is 24.
Justin is playing tennis. When serving, he stands 12 feet away from the net, which is 3 feet tall. The ball is served from a height of 7.5 feet. Justin thinks the ball travels about 21.4 feet before it hits the ground 8 feet from the net on the opposite side.
a) How far does the ball travel?
b) What assumptions did you make to solve the distance the ball travels?
c) What mathematical practice did you use to solve this problem?
Considering Justin's serve, it is found that:
a) The ball traveled 21.4 feet, which means that Justin's estimate is correct.
b) An assumption regarding the angle of Justin's serve was made.
c) The Pythagorean Theorem was used to solve this mathematical problem.
Pythagorean TheoremThe Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle(triangle which has an angle of 90º between the two legs) with the length of the hypotenuse h, stating that the hypotenuse squared is the sum of the legs squared, according to the following rule:
[tex]h^2 = l_1^2 + l_2^2[/tex]
Assuming that the ball was served at an angle of 90º, the situation can be summarized as follows:
Distance of the serve: hypotenuse of the triangle.Bottom leg: horizontal change, of 20 feet, 12 feet on one side of the net and 8 feet on the other side of the net. Top leg: vertical change, of 7.5 feet, as the serve was made at a height of 7.5 feet, and hit the ground, where the height is of 0.Hence the Pythagorean Theorem is applied and the distance is calculated as follows:
d² = 7.5² + 20²
d = sqrt(7.5² + 20²)
d = 21.4 feet.
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please help asap for 50 points. The Smith and Jones manufacturing company keeps a third of its cash in the bank, which pays 0.5% interest, and the other two-thirds in long-term investments that give 3.5% interest. If the company earned a total of $37,500 in interest last year, how much cash did they keep in the bank?
Based on the calculation below, the amount of cash that the Smith and Jones manufacturing company kept in the bank was $500,000.
How do we calculate amount kept in the bank?Let x represents the amount of cash that Smith and Jones manufacturing company has.
Therefore, we have:
Interest amount from bank = Cash * A third * Bank interest rate = x * (1/3) * 0.5% = x0.0017
Interest amount from long-term investments = Cash * Two-third * Long-term investments interest rate = x * (2/3) * 3.5% = x0.023
Total interest earned = Interest amount from bank + Interest amount from long-term investments = $37,500 ...................... (1)
Substituting all the relevant values into equation (1) and solve for x, we have:
x0.0017 + x0.023 = $37,500
x0.025 = $37,500
x = $37,500 / 0.025
x = $1,500,000
Amount kept in the bank = Cash * A third = $1,500,000 * (1 / 3) = $500,000
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What is the expanded form of this number?
14.702
here is confusing it wont paste right but try to help tysm
(1×10)+(4×1)+(7×110)+(2×1100)
left parenthesis 1 times 10 right parenthesis plus left parenthesis 4 times 1 right parenthesis plus left parenthesis 7 times 1 over 10 right parenthesis plus left parenthesis 2 times 1 over 100 right parenthesis
(1×10)+(4×1)+(7×110)+(2×11,000)
left parenthesis 1 times 10 right parenthesis plus left parenthesis 4 times 1 right parenthesis plus left parenthesis 7 times 1 over 10 right parenthesis plus left parenthesis 2 times 1 over 1000 right parenthesis
(1×10)+(4×1)+(7×1100)+(2×1100)
left parenthesis 1 times 10 right parenthesis plus left parenthesis 4 times 1 right parenthesis plus left parenthesis 7 times 1 over 100 right parenthesis plus left parenthesis 2 times 1 over 100 right parenthesis
(1×10)+(4×1)+(7×1100)+(2×11,000)
The expanded form of this number 14.702 will be (1 × 10) + (4 × 1) + (7/10) + (2/1000)
How to illustrate the information?It should be noted that expanded form simply means breaking down of the number given into different units.
Therefore, based on the information illustrated. This will be:
14.702 will be:
= (1 × 10) + (4 × 1) + (7/10) + (2/1000)
= 10 + 4 + 0.7 + 0.002
Note that your options aren't written well.
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What is the probability of obtaining a sum of at least nine when rolling a pair of dice (enter the probability as a fraction )
Total number of possible outcomes:
[tex]6\cdot6=36[/tex]From those 36 possible outcomes the next 10 sum of at least 9 ( a number greather than or equal to 9):
[tex]\lbrace(3,6),(4,5),(4,6),(5,4),(5,5),(5,6),(6,3),(6,4),(6,5),(6,6)\rbrace[/tex]Then, the probability of obtaining a sum of at least nine when rolling a pair of dice is:
[tex]P=\frac{10}{36}=\frac{5}{18}[/tex]I REALLY NEED HELP PLEASE!!!!!!!!!!!!!!!!!!!!!
The area of the rectangles A,B, C are 8 cm , 3cm and 15 cm , whereas the area of the enlarged rectangle A,B,C are 32 cm ,12 cm and 60cm
The relation between the area of the both original and the enlarged is the area of the enlarged rectangle is 4 times the area of the original rectangle.The problem we are dealing with is area what is referred to as the amount of space occupied by a two-dimensional figure, it is the amount that measures the number of unit squares that surround the surface of a closed figure. The standard unit of the region is square units which are generally spoken to as square inches, square feet. For the area of the rectangle we multiply the length of the rectangle by the width of the rectangle.
Area= l x b
for rectangle A : 4 x2 = 8 cm, for B : 3 x 1 = 3 cm and for C: 5 x 3 = 15 cm
As we increase each dimension by 2 times:
For the enlarged rectangle A : 8 x4 = 32 cm ,B : 6 x 2 = 12 cm and C: 10 x 6 = 60 cm .
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How long is the hypotenuse?
Answer:70 cm
Step-by-step explanation:a^2+b^2=c^2
All side lengths of ΔJKL equal 2 units. A transformation maps ΔJKL to ΔJ'K'L'. The length of side J'K' is 5 units. Is this a rigid transformation?
No, there is no one-to-one mapping of all the points of the pre-image to the image.
No, at least one segment length is not preserved, making this a nonrigid transformation.
Yes, the vertices of the pre-image map to the vertices of the image.
Yes, all of the side lengths of the pre-image are proportionate to the image.
Answer: No, at least one segment length is not preserved, making this a nonrigid transformation.
Step-by-step explanation: A rigid transformation implies that both the shape and size are not changed. The second answer is right because the length of segment JK (2 units) is not preserved when mapped onto J'K' (5 units).
Diane deposits the same amount of money into a bank account every month. The table below shows the amount of money in the account after different amounts of time.
Giv the table below:
Time (Months) 6 8 10 12
Money (Dollars) 476 606 736 866
(a) We are asked to find the amount that is alreafy in the account when Diane started depositing.
The amount that will be in the account before Diane started depositing will be
86 dollars.
(b) To get the rate if the money increase or decrease:
606 - 476
2
= 130/2
= 65
The money increases by 65
the true average diameter of ball bearings of a certain type is supposed to be .5 in. a one-sample t test will be carried out to see whether this is the case. what conclusion is appropriate in each of the following situations? a. n
The null hypothesis should not be rejected. There is insufficient evidence that the true diameter differs from 0.5 inches.
We are given that,
n = 15
t-value = 1.66
Significance level;α = 0.05
So, DF = n - 1 = 15 - 1 = 14
In the attached one-sample t-table, we can see that the p-value of 0.06
corresponds to a t-value of 1.66 and a DF of 14
Due to the P-value of 0.06, it is greater than the significance level of 0.05. Based on the results, we are not rejecting the null hypothesis. There is insufficient evidence to conclude that the true diameter in active attachment is different from 0.5
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(3+5),2y=(5x8)-(2x4)
Answer:
Answer down below!
Step-by-step explanation:
y = 2
Drag and drop the answer into the box to match each point to its coordinates. Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. Point A Point B Point C
The answer should be dragged and dropped into the box to match each point to its coordinates as follows;
Point A ⇔ (2 1/4 , 1 1/2).
Point B ⇔ (-1 1/4 , 1 1/2).
Point C ⇔ (-2 1/2 , 1/4).
What is an ordered pair?In Mathematics, an ordered pair is sometimes referred to as a coordinate and it can be defined as a pair of two (2) elements or data points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate (abscissa) and the y-coordinate (ordinate) on the coordinate plane of any graph.
How to identify the coordinates points and quadrants?In Mathematics and Geometry, a quadrant simply refers to the area that is occupied by the values on the x-coordinate (x-axis) and y-coordinate (y-axis) of a cartesian coordinate.
Based on the cartesian coordinate (grid) below, the coordinates points and quadrants should be identified as follows;
Point A ⇔ (2 1/4 , 1 1/2) → quadrant 1.
Point B ⇔ (-1 1/4 , 1 1/2) → quadrant 2.
Point C ⇔ (-2 1/2 , 1/4) → quadrant 2.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Sariah bought a magazine for $3.95 and 5 packs of gum. She spent $18.75. How much did it cost for 1 pack of gum?
Answer: $2.96
Step-by-step explanation:
$18.75 - $3.95 = $14.80
$14.80 / 5 = $2.96
A projectile is launched in the air. The function h(t) = -16t^2 + 32t + 128 gives the height, h, in feet, of the projectile t seconds after it is launched. After how many seconds will the projectile land back on the ground?
Help is always greatly appreciated. :)
Answer:
4 seconds
===========================
Given is the
quadratic function
, which has a graph of parabola.
It has two
x-intercepts
, with the greater one representing the
projectile on the ground, at h(t) = 0
.
Let's
solve
the equation:
- 16t² + 32t + 128 = 0
t² - 2t - 8 = 0
t² - 2t + 1 - 9 = 0
(t - 1)² = 9
t - 1 = 3 and t - 1 = - 3
t = 4
and t = - 2
The root with the greater value is
t = 4
, which represents the time we need.
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:4 \:\: sec [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
height of an object projected in air with time is represented by the given equation :
[tex]\qquad\displaystyle \tt \rightarrow \: h(t) = - 16 {t}^{2} + 32t + 128[/tex]
The height when the object hits the ground will be 0
so, just equate the equation with 0, and we will get the value of t (time) when the projectile will be back to ground.
[tex]\qquad\displaystyle \tt \rightarrow \: - 16 {t}^{2} + 32t + 128 = 0[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: - 16( {t {}^{2} - 2t}^{} - 8) = 0[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: t {}^{2} - 2t - 8 = 0[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: t {}^{2} - 4t +2 t - 8 = 0[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: t(t - 4) + 2(t - 4) = 0[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: (t - 4)(t + 2) = 0[/tex]
So,
[tex]\qquad\displaystyle \tt \rightarrow \: t = 4 \: \: \: \: or \: \: \: \: t = - 2[/tex]
but since time can't be negative, t = 4 seconds
The object will be back on ground after 4 seconds.
find the upper and lower bounds of the total weight of 3 boxes each weighing 5.7 kg to the nearest 0.1kg
Answer:
while using a calculator we need it for solving problems and practice and analysis of reference to be able to answer
Step-by-step explanation:
according to which unit are we calculating
Please help me!! I was absent when class learned this but teacher is still making me do homework!!! I have no idea how to do this!! Please help!! Need now!!
Answer:
a. (2x−9)(x+3)
b. (2x+11)(2x−11)
c. (3x−2)(2x+5)
d. (3x+4)(x+1)
e. (5x+3)(x−9)
f. (2x+5)(2x−7)
g. 4(3x+5)(3x−5)
h. 3(2x+5)(2x+5)
Step-by-step explanation:
Answer:
Lol, I recommend you ask your teacher later how to factor :]
It's kinda hard to explain. Tell me if I got any wrong :]
Step-by-step explanation:
Ouch. Well, here I go:
a) (2x-9)(x+3)
b) (2x-11)(2x+11)
c) (3x-2)(2x+5)
d) (x+1)(3x+4)
e) (x-9)(5x+3)
f) (2x-7)(2x+5)
g) (6x-10)(6x+10)
h) (6x+15)(2x+5)
:]
simplify + 3 root 20 +4root5
Answer:
Step-by-step explanation:
[tex]3\sqrt{20} + 4\sqrt{5}[/tex]
1st: Split up the numbers under the radical into possible factors.
[tex]3\sqrt{5*4} + 4\sqrt{5}[/tex]
2nd: Take out the perfect square (in this case 4)
[tex]3*2\sqrt{5} + 4\sqrt{5}[/tex]
3rd: simplify
[tex]6\sqrt{5} + 4\sqrt{5}[/tex]
4th: Combine like terms
[tex]10\sqrt{5}[/tex]
Answer:
[tex]\sf 10\sqrt{5}[/tex]
Step-by-step explanation:
Simplifying the radicals:Prime factorize 20 and simplify 3√20
[tex]\sf 3\sqrt{20} = 3\sqrt{2*2*5}=3*2*\sqrt{5}=6\sqrt{5}[/tex]
[tex]\sf 3\sqrt{20}+4\sqrt{5}=6\sqrt{5}+4\sqrt{5}[/tex]
[tex]\sf = 10\sqrt{5}[/tex]
Melika Yasin's gross pay for this week is $355.00. She is married and claims no allowances. According to the table below, what amount will be withheld from Ms. Yasin's pay for FIT?
Based on the gross pay for Melika Yasin, and the fact she claims no allowances and is married, the amount withheld from her pay for Federal Income Tax is $43.
How to find the amount withheld for federal income tax?Melika Yasin had a gross pay of $355.00 for the week. This amount is more than $350 but less than $360.
Melika Yasin therefore falls into the bracket of "At least $350 but less than $360."
She also claims no allowances in this bracket. This means that the amount that would be withheld for Federal Income Tax according to the table would be $43.
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Torque is a measure of how much to tighten a bolt. The torque specification for a
small-block Chevy V8 is 70 foot-pounds with an error of 0.02 foot-pounds. Write
and solve an absolute value equation to find the minimum and maximum torque
required for the bolts.
The absolute value equation is |x - 70| = 0.02, while the minimum and maximum torque are 69.98 and 70.02 foot pounds
How to determine the absolute value equation?From the question, the given parameters are:
Specification = 70 foot pounds
Margin of error = 0.02 foot pounds
The absolute value equation of the scenario is then calculated as
|x - Specification| = Margin of error
Substitute the known values in the above equation
So, we have
|x - 70| = 0.02
Solving the equation, we have
x - 70 = 0.02 and x - 70 = -0.02
Add 70 to all sides
x = 70.02 and x = 69.98
Hence, the range is 69.98 to 70.02
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Greg charges a flat fee of $140 to mow a lawn plus $45 and hour. Greg charges a flat fee of 100 to mow the lawn plus $25 an hour. After how many hours do they make the same amount
We need to know how to write linear equation to solve the problem. The number of hours when they make the same amount is 2 hours.
Linear equation is when a value of one variable is dependent on only one other variable. In the given question we know that Greg charges a flat fee of $140 and another $25 for every hour and Greg charges a flat fee of $100 and $45 for every hour. We need to find out the number of hours when both of them have the same amount, we can consider number of hours to be x and form equations accordingly.
140+25x=100+45x
20x=40
x=2
Therefore both of them will make the same payment when number of hours is 2.
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-6(6x - 1) +9=36x + 18
Answer:
x = - 1 / 24
Step-by-step explanation:
-6 ( 6x - 1 ) + 9 = 36x + 18
First, solve the brackets.
-36x + 6 + 9 = 36x + 18
Then, subtract 36x by both sides.
-36x - 36x + 6 + 9 = 18
-72x + 15 = 18
Now, Subtract 15 by both sides.
-72x = 18 - 15
-72x = 3
Now divide both sides -72 by both sides.
x = - 3 / 72
x = - 1 / 24
Mark walked 21,129 feet in one hour. At that speed about how many miles will he walk in two hours?
Answer:
8.00340909
Step-by-step explanation:
since 21129 was walked in one hour the in two hours 42258 wouldve been walked so that means mark walked a little over 8 miles
hope this helped
have a good day^^
A student writes the inequality representing the graph as y ≥ –2(x – 10)2 + 200.
The inequality is
because testing the point (5, 100) simplifies to the inequality
Answer:
A student writes the inequality representing the graph as y ≥ –2(x – 10)2 + 200.
The inequality is
✔ incorrect
because testing the point (5, 100) simplifies to the inequality
✔ 100 ≥ 150
.
Step-by-step explanation:
A student writes the inequality representing the graph as y ≥ –2(x – 10)2 + 200.
The inequality is
✔ incorrect
because testing the point (5, 100) simplifies to the inequality
✔ 100 ≥ 150
.
The inequality is incorrect because testing the point (5, 100) simplifies to the inequality 100 ≥ 150.
What is an inequality?An inequality can be defined as a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an equation based on any of the following arguments (symbols):
Greater than (>).Greater than or equal to (≥).Less than (<).Less than or equal to (≤).Next, we would evaluate and simplify the given inequality in order to determine its solution as follows:
y ≥ –2(x – 10)² + 200.
At point (5, 100), we have:
100 ≥ –2(5 – 10)² + 200.
100 ≥ –2(-5)² + 200.
100 ≥ –2(25) + 200.
100 ≥ –50 + 200.
100 ≥ 150 (incorrect and false).
In conclusion, the given inequality is incorrect because 100 cannot be greater than or equal to 150.
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Compete Question;
A student writes the inequality representing the graph as y ≥ –2(x – 10)² + 200.
The inequality is ______ because testing the point (5, 100) simplifies to the inequality _____.
Determine the value of y in the inequality.
18 + 3y < 27
y > 3
y < 3
y > −9
y < −9
Answer:
y < 3
Step-by-step explanation:
The Smith and Jones manufacturing company keeps a third of its cash in the bank, which pays 0.5% interest, and the other two-thirds in long-term investments that give 3.5% interest. If the company earned a total of $37,500 in interest last year, how much cash did they keep in the bank?
The amount of cash that as kept in the bank is $937500.
How to calculate the amount?Let's have x represent the amount of cash.
One portion of it pays 0.5%, so 0.005x; the other portion pays 3.5%, so 0.035x. This gives us:
0.005x + 0.035x = 37500
Combining like terms:
0.040x = 37500
Solve for x:
x = (37500)/(0.04)
x = 937500
Therefore, the company started with $937,500.
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