The equation of the line in point-slope form, which passes through the pair of points located at (0 , 0) and (-4 , -5), is y + 5 = 5/4(x + 4).
The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.
The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).
Getting the slope of the two points: (0 , 0) and (-4 , -5)
m = (y2 - y1)/(x2 - x1)
m = (-5 - 0)/(-4 - 0)
m = -5/-4
m = 5/4
Using the point slope form, plug in the values of the slope and Point A to set up the equation.
(y - y1) = m(x - x1)
where m = 5/4 and (x1 , y1) = (-4 , -5)
(y - -5) = 5/4(x - -4)
y + 5 = 5/4(x + 4)
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Sergei runs a bakery. He needs at least 175 kilograms of flour in total
to complete the holiday
orders he's received. He only has 34
kilograms of flour, SO he needs to buy more.
The flour he likes comes in bags that each contain 23 kilograms of flour. He wants to buy the
smallest number of bags as possible and get the amount of flour he needs.
Let F represent the number of bags of flour that Sergei buys.
Answer:
Step-by-step explanation: Using proportions, it is found that Sergei needs to buy 7 bags.
-----------
This question is solved by proportions, using a rule of three.
He has 34 kilograms of flour.
He needs 175 kilograms.
Thus, he needs to buy 175 - 34 = 141 kilograms.
Each bag contains 23 kilograms. How many bags are needed for 141 kilograms?
1 bag - 23 kilograms
x bags - 141 kilograms
Applying cross multiplication:
[tex]23x = 141[/tex]
[tex]x = \frac{141}{23}[/tex]
[tex]x = 6.1[/tex]
Rounding up, he needs to buy 7 bags
Evaluate each
a. -4+|-5|-4
b. -3•-8
c. 32 divided by -2
Answer:
A is -3 B is 24 and c is -16
Step-by-step explanation:
|x+1|+|3x-2|=2
Solve each equation
Answer:
2
Step-by-step explanation:
x+1 +3x-2=2 group them in like terms
3x-x+2+1=2 then subtract the variable and add the number
2x=3-2 arrange them
2x=1 divide both side by 2
therefore x=2
A classroom has 48 seats. There are 6 seats in each row, which are arranged In this order:
Wall 5A 5B 5C aisle 5D 5E 5F wall
Four students are already sitting in their seats in the 5th row. Lina decides to sit by the wall, as she likes to have only one person sitting next to her and be close to the windows. Alex is sitting next to the aisle, as he needs to rush out of the classroom as soon as the lesson ends. Ken and Rue are best friends and are sitting in the adjacent seats, but Rue is not sitting by the wall. Maria and Ted enter the classroom, and there are only two available seats left in the classroom in the 5th row. Maria and Ted were hoping to sit next to each other.
What are the chances that their expectations will not be met?
Answer: 6%
Step-by-step explanation:
I just baised it off of how many students were in the equation. at the end thier is only 6 seats left
Identify each sequence as arithmetic, geometric, or neither. Then find the next two terms. 2,1,0.5,0.25, . . . . . .
It is a geometric sequence. The next two terms are: 0.125, 0.0625
The given sequence is:
2, 1, 0.5, 0.25, . . . .
Let a(n) be the nth term, then in the above sequence
a(1) = 2
a(2) = 1
a(3) = 0.5
a(4) = 0.25
Notice that:
a(2) = a(1) x 0.5
a(3) = a(2) x 0.5
a(4) = a(3) x 0.5
A sequence, of which its next term is obtained by multiplying the previous term by a constant is called a geometric sequence. The constant is called the ratio.
Therefore this is a geometric sequence with r = 0.5
To find the next two terms, continue the multiplication process:
a(5) = a(4) x 0.5 = 0.25 x 0.5 = 0.125
a(6) = a(5) x 0.5 = 0.125 x 0.5 = 0.0625
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what is the answer to b?
Answer:35
Step-by-step explanation:because x equals 3y +2 so if x=11 then just mutlipy 11x3 thats 33 then plus 2 is 35
hope that helps :}
43 43. The area of a circle is 100 cm². Calculate its radius.
Answer:
About 5.6 cm
Step-by-step explanation:
The formula for the radius of a circle (based on the area) is [tex]\sqrt{\frac{A}{\pi } }[/tex], where [tex]A[/tex] is the area of the circle?
Francisco’s game involves a bag of 3 green, 2 yellow, 4 red, and 3 black marbles. andrew wants to increase the likelihood of selecting a yellow marble. how can the game be modified to make drawing a yellow marble more likely? select all that apply. andrew should add more green marbles to the bag. andrew should add more yellow marbles to the bag. andrew should remove from the bag 1 green, 1 black, and 2 red marbles. andrew should add more black marbles to the bag. andrew should triple the number of yellow marbles in the bag.
From the options given, the options that can increase the likelihood of selecting a yellow marble can be determined by finding out the probability of selecting the yellow marble.
Probability is method of determining a numerical occurrence of a outcome from the set of all possible outcomes of an events. The value is expressed from zero to one.
Probability (Event)= Favorable Outcomes(x)/Total Outcomes(n)
Hence,
n=total number of marbles=3+2+4+3=12
x=no of yellow marbles=2
Probability=2/12=1/6
In order to increase the probability of choosing a yellow marble, let consider the options.
Andrew should add more green marbles to the bag.
Increasing green by say 2
Probability=2/14=1/7<1/6
Andrew should add more yellow marbles to the bag.
Increasing yellow by say 3
Probability=5/15=1/3>1/6
Andrew should remove from the bag 1 green, 1 black, and 2 red marbles.
Decreasing the said marbles
Probability=2/8=1/4>1/6
Andrew should add more black marbles to the bag.
Increasing black by 2
Probability=2/14=1/7<1/6
Andrew should triple the number of yellow marbles in the bag.
Increasing yellow marble by 2x3=6
Probability=6/16=3/8>1/6
Hence, the options of making the likelihood of yellow drawing more would be Andrew should add more yellow marbles to the bag, Andrew should remove from the bag 1 green, 1 black, and 2 red marbles and Andrew should triple the number of yellow marbles in the bag.
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A bag contains 3 red chips, 5 green chips, 2 yellow chips, 4 brown chips, and 6 purple chips. One chip is chosen at random, the color noted, and the chip returned to the bag.
a. Suppose two trials of this experiment are conducted. Are the events independent or dependent? Explain.
Both can be seen as individual events. thus the events are independent.
Which pair of events are called independent events?When one event's occurrence or non-occurrence doesn't affect occurrence or non-occurrence of other event, then such events are called independent events.
Symbolically, we have:
Two events A and B are said to be independent iff we have:
[tex]P(A \cap B) = P(A)P(B)[/tex]
Given that; A bag contains 3 red chips, 5 green chips, 2 yellow chips, 4 brown chips, and 6 purple chips. One chip is chosen at random, the color noted, and the chip returned to the bag.
The probability of selecting the chip is green;
= 5/20
= 1/4
The probability of selecting the chip is brown;
= 4/20
= 1/5
the probability that the first chip is green and the second is brown
= 1/4 x 1/5
= 1/20
Both can be seen as individual events. thus the events are independent.
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FIFTY POINTS
y=-16t^2+40t+2
For what interval or intervals of time will the projectile be
above 18 feet?
a.) Between 1 and 1.5 seconds
b.) Less than 1 second and greater than 1.5 seconds
c.) Between 0.5 and 2 seconds
d.) Less than 0.5 second and greater than 2 seconds
Answer:
To find when the projectile is above 18 feet, we need to find the values of time when the height of the projectile is greater than 18. The height of the projectile can be found by plugging the value of time into the equation y = -16t^2 + 40t + 2.
So, we need to find the values of t when y > 18.
y = -16t^2 + 40t + 2 > 18
-16t^2 + 40t - 16 > 0
To solve this inequality, we can use the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / 2a
where a = -16, b = 40, and c = -16.
So, t = (40 ± √(40^2 - 4(-16)(-16))) / 2(-16)
t = (40 ± √(40^2 + 256)) / -32
t = (40 ± √(1616)) / -32
t = (40 ± 40) / -32
t = (80 / -32) / 2 or (0) / 2
t = -1.25 or 0
Since t has to be positive (time cannot be negative), we can only use the positive value, t = 0.5. So, the interval of time when the projectile is above 18 feet is between 0.5 and 2 seconds, which is (c).
Which shows 0.00234 written in scientific notation?
A 2.34 ×10⁵
B 2.34× 10³
C 2.34 × 10⁻²
D 2.34 × 10⁻³
32^10-33x^5+1 find the real roots
By algebra properties, the roots of the quintic equation are approximately 541.159 with a multiplicity 5.
How to find the roots of polynomial by algebraic proceduresIn this problem we find a quintic equation, whose roots have to be found by using algebra rules:
33¹⁰ - 33 · x⁵ + 1 = 0
33 · x⁵ = 33¹⁰ + 1
x⁵ = (33¹⁰ + 1) / 33
x⁵ = 33⁹ + 33⁻¹
x = [tex]\sqrt[5]{33^{9}+33^{- 1}}[/tex]
x ≈ 541.159
By using algebra properties, the roots of the quintic equation are approximately 541.159 with a multiplicity 5.
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8=3x+6y. I need help on how to find Y?
Answer:y =20
Step-by-step explanation:8 = 3x + 6y.
subtract 3x from both sides:
8-3x = 6y,
Divide both sides by 6:
8/6 - 3x/6 = Y,
4/3 - x/2 = Y.
Determine the total number of roots of each polynomial function. f (x) = (3x4 + 1)2[
The total number of roots will be 8.
We have a function f(x) = [tex](3x^{4}+1 )^{2}[/tex].
We have to determine the total number of roots for this function f(x).
What is function ?A function in mathematics is a relation involving two variables, such that one variable is dependent on the other for its value.
According to the question, we have function -
[tex](3x^{4}+1 )^{2}[/tex]
We can rewrite it after expanding as follows -
[tex](3x^{4}) ^{2} + 1 + 6x^{4}[/tex]
[tex]9x^{8}+6x^{4} +1[/tex]
Now, the maximum degree of the polynomial is 8. The number of roots are equal to the maximum degree of a polynomial.
Hence, the total number of roots will be 8.
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Write an equation for the line on the graph below:
Answer:
y= - 6
Step-by-step explanation:
the coordinate- y of every point on the line will be - 6
Write the equation of the line in slope-intercept form
2y=-12x-16
The equation of the line in slope-intercept form is y = (-6)x + (-8) .
The equation of a line in slope-intercept form can be written as follows,
y = mx + c equation 1
m in the above equation represents slope of the line and c represents the intercept.
The given equation is 2y = -12x -16 .
To get the equation of the line in slope-intercept form we need to convert the given equation in the format of equation of a straight line i.e., equation1. So, now we will rearrange the given equation as
2y = -12x -16
On dividing both sides of above equation by 2, we will get
y = (-6)x + (-8) equation 2
On equating equation 1 and equation 2, we will get
Slope of the line = m = -6
Intercept = c = -8
The equation of the line in slope-intercept form is y = (-6)x + (-8) .
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need help please find the height of a cylinder with a volume of 500 cubic meters
Answer:
height = 20 cm
Step-by-step explanation:
the volume (V) of a cylinder is calculated as
V = πr²h ( r is the radius and h the height )
here r = 5 and V = 500π , then
π × 5² × h = 500π
25πh = 500π ( isolate h by dividing both sides by 25π )
h = [tex]\frac{500\pi }{25\pi }[/tex] = 20 cm
Does anyone know the answers to these?
The results for each case of congruence are listed below:
9) Congruent
10) No congruent
11) No congruent
12) Congruent
13) Congruent
14) No congruent
Are two line segments congruent to each other?
There are several ways to determine if two line segments are congruent to each other. One form consists in finding the vector associated with each line segment and the length is found by the Pythagorean theorem:
Now we proceed to show how to apply the vector criterion:
9) AB = (- 4, 8) - (- 4, 5) = (0, 3), CD = (2, 0) - (2, - 3) = (0, 3).
AB = 3, CD = 3. Congruent
10) AB = (1, - 1) - (6, - 1) = (- 5, 0), CD = (4, - 3) - (2, - 3) = (2, 0).
AB = 5, CD = 2. No congruent
11) AB = (- 1, 3) - (8, 3) = (- 9, 0), CD = (5, 3) - (5, 10) = (0, - 7).
AB = 9, CD = 7. No congruent
12) AB = (6, 1) - (6, - 8) = (0, 9), CD = (- 2, - 2) - (7, - 2) = (- 9, 0).
AB = 9, CD = 9. Congruent
13) AB = (- 5, - 1) - (- 5, 6) = (0, - 7), CD = (3, 3) - (- 4, 3) = (7, 0).
AB = 7, CD = 7. Congruent
14) AB = (3, - 4) - (10, - 4) = (- 7, 0), CD = (- 1, 5) - (- 1, 2) = (0, 3).
AB = 7, CD = 3. No congruent
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me i don't now this help please
Frequency is measured in Hertz, which is one per second. If the wave vibrated 10 times in 10 seconds, it would have a frequency of 1Hz According to the graph, the frequency is increasing to 2Hz then 3Hz.
This is further explained below.
What is Frequency?Generally, The number of instances of a recurring event that takes place in a certain amount of time is referred to as its frequency.
In conclusion, Hertz is the unit of measurement for frequency, and one Hertz equals one second. If the wave vibrated once per second for a whole minute, its frequency would be one hertz (Hz).
The graph indicates that the frequency will reach 2Hz, and eventually 3Hz, in the near future.
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The trail mix that you are making requires 4 cups of raisins for every 10 cups total of trail mix. If you use 24 cups of peanuts (the other ingredient), how many total cups will you have?
Answer:
40 cups
Step-by-step explanation:
4/10 is raisin
6/10 is peanuts
24/40 is peanuts
The local gym holds two 45-minute workout sessions and four 30-minute sessions each week. Judy attended all of the sessions this week but left 5 minutes early during the 30-minute sessions and 10 minutes early during the 45-minute sessions. How many total minutes did Judy work out for the week?
170 minutes
190 minutes
65 minutes
75 minutes
Answer: 75
Step-by-step explanation:
The total number of minutes Judy worked out for the week was 170 minutes. The correct option is the first option 170 minutes
Calculating timeFrom the question, we are to determine the total number of minutes Judy worked out for the week
From the given information,
The gym holds two 45-minute workout sessions and four 30-minute sessions each week
Thus,
The total number of minutes the gym holds workout sessions is
2 × 45 + 4 × 30
= 90 + 120
= 210 minutes
Also, from the information,
Judy left 5 minutes early during the 30-minute sessions and 10 minutes early during the 45-minute sessions
The total number of minutes Judy didn't attend is
2 × 10 + 4 × 5
= 20 + 20
= 40 minutes
Then,
The total number of minutes Judy worked out for the week was
210 minutes - 40 minutes
= 170 minutes
Hence, the total number of minutes Judy worked out for the week was 170 minutes. The correct option is the first option 170 minutes
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Aileen sold 42 MP3 players last
month at $125 per MP3 player. If
she earns $2130 per month in
base pay and makes an 18%
commission on all MP3 sales,
how much did she earn last
month?
By adding the base salary and the commissions, we conclued that Aileen did make 3,075 dollars last month.
how much did she earn last month?
She sold 42 MP3 for $125 each, and she gets a 18% commission on this, so what she wins in commissions is:
0.18*42*$125 = $945
If we add that to the base that she earns per month, which is $2,130, it gives:
$945 + $2,130 = $3,075
In this way, we conclued that Aileen did make 3,075 dollars last month.
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Solve the following problem for x. If there is more than one solution include all solutions in your answer.
|3z-6|=9
X=
X=
Answer:
z = - 1 , z = 5
Step-by-step explanation:
| 3z - 6 | = 9
the absolute value function always gives a positive result, however, the expression inside can be positive or negative, that is
3z - 6 = 9 ( add 6 to both sides )
3z = 15 ( divide both sides by 3 )
z = 5
or
- (3z - 6) = 9
- 3z + 6 = 9 ( subtract 6 from both sides )
- 3z = 3 ( divide both sides by - 3 )
z = - 1
As a check
substitute these values into the left side of the equation and if equal to the right side then they are the solutions.
x = 5
| 3(5) - 6 | = | 15 - 6 | = | 9 | = 9 = right side
x = - 1
| 3(- 1) - 6 | = | - 3 - 6 | = | - 9 | = 9 = right side
then solutions are z = - 1 , z = 5
please help me with this
Answer: Angle R is 15.8 and angle S is 15.4.
Step-by-step explanation: Equal 3x + 5 to 9x - 17, to each other and get 3.6 and 3.6 equals x. Q and R are congruent. for 3x +5, multiply 3.6 by three and add 5. Multiply 3.6 by 9 and subtract 17. I hope this helps :)
Millie and kim both entered a pumpkins in the county fair. Millie's pumpkin weighs 52 1/4 lbs. Kim's pumpkin is 90% as big as Millie's pumpkin. How much does Kim's pumpkin weigh? Give your answer as a decimal
I dont know if its adding, subtracting, dividing, or multiplication. Please include the answer and how you got it!!
Step-by-step explanation:
Millies pumpkin: 52.25 lbs. (25 is one quarter of 100)
Kims is 90% as heavy.
We know in percentage, it only goes up to 100%.
Concept #1Dividing
We can divide 100% into 10 chunks of 10%. In this instance, 52.25 lbs is 100%. So we divide 52.25 lbs into 10 chunks of 5.225 lbs.
Concept #2
Multiplying
90% is 9 times those little chunks of 10%. In this instance, 1 chunk is 5.225 lbs. So we simply multiply that by 9 because it's 90%.
Concept #3
Actually multiplying it
5.225 x 9 = 47.025 lbs
So 47.025 lbs is 90% of 52.25 lbs which is Millie's pumpkin.
Therefore your answer for "how much does kims pumpkin weigh" is
47.025 lbs
hoped this helped
Write an equation of each line in standard form with integer coefficients. y=-7 x-9
The equation of the given line y = -7x - 9 in standard form is 7x + y + 9 = 0
Equation of a line in standard form can be expressed as:
Ax + By + C = 0
Where:
A and B are coefficients.
x and y are variables of degree 1 or linear variables.
C is a constant.
All coefficients and constant term should be integers, not fractions or decimals. Furthermore, A should be a positive number.
The given equation is:
y = -7x - 9
Add both sides by 7x
7x + y = -7x +7x -9
7x + y = -9
Add both sides by 9
7x + y + 9 = -9 + 9
7x + y + 9 = 0
This is the standard form of the given line equation.
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A refrigerator that originally costs $ 1,200 it's on sale for 15% off. Tax is 8%. What would be the sale price of this refrigerator be including tax
The sale price of this refrigerator be including tax $1101.6 .
The value on the label of associate article/product is termed the marked price or asking price. this is often the worth at that product is meant to be sold-out. However, there will be some discount given on this value and therefore the actualof the merchandise could also be but the marked price. it's typically denoted by MP.When Discount is obtainable, M.P. > S.P.When Discount isn't offered, M.P. < S.P.Discount is outlined because the quantity of rebate given on the label value (marked price) of a piece. it's given by merchants/shopkeepers for attracting customers for increasing their sales.Discount = Marked value – priceIt is given that a refrigerator that originally costs $ 1,200 it's on sale for 15% off.
Discount percentage = [(Discount)/(Marked price)]× 100
15 = Discount / 1200 × 100
15 = Discount / 12
Discount = 15 × 12
= $ 180
Selling price = marked price - discount
= 1200 - 180
= $ 1020
The selling tax is given by = 8% 1020
= 8 / 100 ×1020
= $ 81.6
The total amount one has to pay to buy a refrigerator is = 1020 + 81.6
= $ 1101.6
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Please help me understand this problem!
Answer:
30 degrees.
Step-by-step explanation:
I included a picture to solve for X. Once you have X, we know that angle a=A= x + 39.
Doing the math on the paper, we know that X= - 9, therefore - 9 + 39 = 30.
Thus, angle A is equal to 30 degrees.
a boy has a metal of density 14000kg/m3 .He intends to use it to make a rectangular pipe with external dimension of 18 cm by 10 cm and internal dimension of 15 cm by 8 cm .The length of the pipe is150 cm .Calculate the mass of the pipe in kg
Mass of the pipe= 100.8kgs
Mass is, in effect, the resistance that a body of matter offers to a change in its speed or position upon the application of a force. The greater the mass of a body, the smaller the change produced by an applied force.
mass= density x volume
given that, the area of cross- section of the pipe is rectangular ring with area,
A=(10x10) - (15x8)
=180-120
=60 cm²=0.006 m²
length of the pipe = 150 cm=h
volume= A. h
= 0.006x150x10⁻²
= 0.720x10⁻²
= 0.0072 m³
Density =14000kg/m³
mass= density x volume
= 14000 x 0.0072
= 14 x 7.2
= 100.8 kg
we got that the mass of the pipe in kgs is = 100.8kgs
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Answer:
The pipe weighs 100.8 kg.
Step-by-step explanation:
Mass is essentially a body of matter's resistance to having its speed or position change when a force is applied. The change caused by an applied force is smaller the more mass a body has.
density x volume equals mass.
Considering that the pipe's cross-section is a rectangular ring of area,
A=(10x10) - (15x8)
=180-120
=60 cm²=0.006 m²
length of the pipe = 150 cm=h
volume= A. h
= 0.006x150x10⁻²
= 0.720x10⁻²
= 0.0072 m³
Density =14000kg/m³
mass= density x volume
= 14000 x 0.0072
= 14 x 7.2
= 100.8 kg
we got that the mass of the pipe in kgs is = 100.8kgs
54 x 10 to the power of 4
Answer: 54*10^4=540000
Step-by-step explanation:
