Answer:
y₁ - y₂ = (-7/9)(x₁ - x₂)
Step-by-step explanation:
The general structure for an equation in point-slope form is:
y₁ - y₂ = m(x₁ - x₂)
In this form, "m" represents the slope and the "x" and "y" values come from each point. To find "m", plug the values of each point into the equation.
Point 1: (4, -3) Point 2: (-5,4)
y₁ - y₂ = m(x₁ - x₂) <---- Original equation
-3 - 4 = m(4 - (-5)) <---- Plug values in for "x" and "y"
-7 = m(4 - (-5)) <---- Simplify left side
-7 = m(9) <---- Simplify within parentheses
-7/9 = m <---- Divide both sides by 9
I don't exactly understand what "fully simplified point-slope form" means because if all of the variables are plugged in, you wouldn't be left with an equation. It may just be asking for the slope, which in this case would make the equation look like this:
y₁ - y₂ = (-7/9)(x₁ - x₂)
It may want you to find the equation in slope-intercept form (y = mx + b), and you would have to find "b". Sorry I don't quite understand what exactly you are looking for.
At a certain college, 49% of the students are female, and 21% of the students major in civil engineering. Furthermore, 8% of the students both are female and major in civil engineering.
The probability that a student is a female or major in civil engineering is 62%
How to determine the probability?Let A represent Female and B represents civil engineering.
So, we have:
P(A) = 49%
P(B) = 21%
P(A and B) = 8%
The required probability is calculated as:
P(A or B) = P(A) + P(B) - P(A and B)
This gives
P(A or B) = 49% + 21% - 8%
Evaluate
P(A or B) = 62%
Hence, the probability that a student is a female or major in civil engineering is 62%
Complete questionAt a certain college, 49% of the students are female, and 21% of the students major in civil engineering. Furthermore, 8% of the students both are female and major in civil engineering. What is the probability that a randomly selected female student majors in civil engineering?
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please answer asap!!!
A timer is started and a few moments later a model airplane is launched from the ground. Its height (in feet) as a function of time (in
seconds after the timer was started) is given by the equation h (t) = -(t-14)² +74 Which of the following statements is true?
O The airplane reaches its minimum height of 14 feet in 74 seconds.
O The airplane reaches its minimum height of 74 feet in 14 seconds.
O The airplane reaches its maximum height of 14 feet in 74 seconds.
O The airplane reaches its maximum height of 74 feet in 14 seconds.
9
12 13 14 15 16 17
18
Next
10 11
Answer:
The airplane reaches its maximum height of 74 feet in 14 seconds.
Step-by-step explanation:
The easiest thing to do here is to plug in the two numbers given in the answer choices. Finding the height at 14 seconds and the height after 74 seconds is straightforward from here.
h (14) = -(14-14)²+ 74
h (14) = 0 + 74
h (14) = 74
h (74) = -(74-14)² + 74
h (74) = -(60)² + 74
h (74) = -3600 + 74
h (74) = -3,526
Now, we know that a height of an airplane won't be negative, as the height below the ground cannot be reached.
because our equation includes -(t-14)², any number greater than 14 will be a larger negative than 0--setting the height to an impossible number.
{However, we add +74 feet, so our t-14 could be any number that is less than 74 when squared (after first subtracting 14 from the number). Numbers like 15, (resulting in subtracting 1 from 74), 16 (resulting in -4 from 74), 17 (74-9), 18 (74-16), 19 (74-25), 20 (74-36), 21 (74-49), 22 (74-64) are still above the minimum input}
{So, our t could be up to 22, and any number above this maximum limit, such as 23, result in a height of 0}
for example: -(23-14)² + 74
-(9)² = -81
-81 + 74 = -7
All numbers below 14, which would end in an eventual negative outcome [ -(x)² = negative if x < 0 ]
are greater than a t of 14.
-(13-14)² = -1
; showing that t = 14 is our maximum height
(remember that if you have -(x)² you get the negative version of x² [pemdas. the negative outside of the parenthesis is equivalent to multiplying the parenthesis by -1. (E)xponents comes before (M)ultiplication].)
Seeley takes home $4800 per month. What is the maximum amount he can
spend each month on loan and credit card payments without being in danger
of credit overload?
OA. $1600
OB. $1200
OC. $960
OD. $480
Answer:
1200
Step-by-step explanation:
I'm not 100% sure but that seems like the most reasonable answer
Diana put $8000 in a 10-year CD
paying 5% interest compounded
monthly. After 2 years, she
withdrew all her money, and as an
early withdrawal penalty, she paid
back all the interest she made
during the first year. How much
money was Diana left with?
Th amount of money that Diana is left with is $8,430.23.
How much is Diana left with?The first step is to determine the interest earned in the first year and the total amount that was made in the 2 years.
The formula used to determine the future value with monthly compounding is:
P(1 + r)^( n x m)
Where:
P = present value r = periodic interest rate n = number of years m = frequency of compoundingTotal amount made in 2 years = $8000 x ( 1 + 5% / 12)^(12 x 2) = 8839.53
Interest earned in the first year = [ $8000 x ( 1 + 5% / 12)^(12) ] - 8000 = $409.29
Amount she is left with = 8839.53 - $409.29 = $8430.23
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A graph shows the number of texts, numbered 10 to 100, on the x-axis, and the total cost in dollars, numbered 3 to 27, on the y-axis. A straight red line with a positive slope, labeled Emilia, begins at (0, 10), and a straight blue line with a positive slope, labeled Hiroto, begins at (0, 20). Both lines intersect at point (50, 22.5).
Hiroto’s texting plan costs $20 per month, plus $0.05 per text message that is sent or received. Emilia’s plan costs $10 per month and $0.25 per text. Using the graph below, which statement is true?
Hiroto’s plan costs more than Emilia’s plan when more than 50 texts are sent.
Both plans cost the same when 22 texts are sent.
Emilia’s plan costs more than Hiroto’s plan when more than 22 texts are sent.
Both plans cost the same when 50 texts are sen
Answer:
Both plans cost the same when 50 texts are sent
Step-by-step explanation:
Both the plans cost the same amount $22.5 when 50 texts are sent:
[tex]20+0.05*50 = 10+0.25*50[/tex]✔️
Have a nice day! :)
HELP (WORTH 20 POINTS)
Answer:
1 matter
2 atoms
3 molecules
4 matter and energy
5 solid liquid and gas
6 mass
i dont know the rest to be honest
Step-by-step explanation:
Euler's formula, V – E + F = 2 relates the number of vertices V, the number of edges E, and the number of faces F of a polyhedron. How many faces does a polyhedron with 5 vertices and 8 edges have?
Answer:
5 faces
Step-by-step explanation:
V – E + F = 2
We know that V = 5 and E = 8
Substitute these into the equation
5 -8+F = 2
-3+F =2
Add 3 to each side
-3+F+3 = 2+3
F=5
How many cups are there in 3/8 gallon?
Answer:
6 cups
Step-by-step explanation:
Answer:
That would be 6 cups I believe
Juniper measured his bed twice: once in meters and once in
millimeters. Which is true?
A) The number of meters will be greater.
B) The number of millimeters will be greater.
C) They will both be the same.
Answer:
B
Step-by-step explanation:
millimeter means one-thousandth of a meter meaning the number of millimeters will be larger by a factor of 1000.
Answer:
B
Step-by-step explanation:
Millimetres is A LOT smaller than meters, meaning the individual number of millimetres is larger than the individual number of meters.
Chelsea collected 12 containers each with 3 grams of sand and Pierre collected 8 containers each with sand. They collected the same amount of sand every day for 4 days. How many grams of sand did Chelsea and Pierre have altogether?
Answer:
288 grams
Step-by-step explanation:
Chelsea
12 × 3 = 36
48 × 4 = 192
Pierre
8 × 3 = 24
24 × 4 = 96
together
192 + 96 = 288 grams
What is the domain of the function shown in this graph?
Answer:
[tex] - \infty < x < \infty [/tex]
Step-by-step explanation:
On the right hand side of the y axis, the x values will continue to increase. They will go to positive Infinity. On the left hand side of the y axis, the x values will continue to decrease, this means that they will become more negative. They will go to negative Infinity.Select the action you would use to solve x-3= 12. Then select the property
that justifies that action.
Select all that apply.
A. Action: Add 3 to both sides.
B. Action: Multiply both sides by 3.
C. Action: Subtract 3 from both sides.
D. Property: Addition property of equality
E. Property: Multiplication property of equality
OF. Property: Subtraction property of equality
← PREVIOUS
Answer:
Add 3 to both sides
Property: Addition property of equality
Step-by-step explanation:
Action: Add 3 to both sides.
⇒ x - 3 = 12
(cancel out)+ 3 + 3
------------------------ -----
x = 15
The property used:
Addition property of equality.→ equation is true and the same #is added to each side the resulting equation is true. for any #s a,b,c,if a=b then a+c=b+c.
God loves you Have an amazing day or night
Answer:
tha nks
Step-by-step explanation:
Which region represents the solution to the given system of inequalities? y<-1/2x and y>_2x+3
The region is C is the correct option because intersection region is on the region C after drawing on the coordinate plane.
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
The question is incomplete:
The complete question is:
Which region represents the solution to the given system of inequalities?
ABCDy < -1/2x and y ≥ 2x+3 and the missing figure is shown in the picture please refer to the picture.
We have two inequalities:
y < -1/2x
y ≥ 2x+3
After drawing the inequalities on the coordinate plane we see that the intersection region is on the region C.
Thus, the region is C is the correct option because intersection region is on the region C after drawing on the coordinate plane.
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Kyle wants to buy a television on a hire purchase agreement. the cash price of the television is R5600. she is required to pay a deposit of 15% and pay the remaining loan amount off over 24 months at an interest rate of 14% p.a. what are kyles monthly repayment? keep your answer to the nearest rand.
Kyles's monthly repayment on the television based on hire purchase agreement is R229
What is the monthly repayment?The monthly repayment is the amount paid monthly with interest on a particular loan or to recover from debt.
From the given information:
The price of the television = R5600Initial deposit = 15% of cash price = 0.15 × 5600 = 840Thus
principal amount left to be repaid = 5600 - 840 = 4760
Using the formula:
[tex]\mathbf{M=\dfrac{P( \dfrac{r}{12}) (1+\dfrac{r}{12})^n }{(1+\dfrac{r}{12})^n - 1}}[/tex]
[tex]\mathbf{M=\dfrac{4760( \dfrac{0.14}{12}) (1+\dfrac{0.14}{12})^{24} }{(1+\dfrac{0.14}{12})^{24} - 1}}[/tex]
M = R228.54
M ≅ R229
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Samples of size n = 60 are randomly selected from the population of numbers (0 through 9) produced by a random-number generator, and the mean is taken for each sample. What is the distribution of the sample means?
The distribution of the sample means when the samples of size n = 60 are randomly selected from the population is normal (approximately).
How is the sample explained?Calculating the sample mean is as simple as adding up the number of items in a sample set and then dividing that sum by the number of items in the sample set.
Here, the distribution of the sample means when the samples of size n = 60 are randomly selected from the population is normal (approximately).
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En un concurso de damas chinas hay 12 participantes, se premiaran 2 primeros lugarrs con medallas de oro y plata respectivamente. Calcula de cuantas maneras diferentes se pueden otorgar las medallas
Usando el teorema fundamental de conteo, se encuentra que 132 maneras diferentes de otorgar las medallas.
¿Qué es el teorema fundamental de conteo?Es un teorema que establece que si hay n cosas, cada una con [tex]n_1, n_2, \cdots, n_n[/tex] formas de hacer, cada cosa independiente de la otra, el número de formas en que se pueden hacer es:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
En este problema:
12 participantes pueden ganar la medalla de oro, o sea, [tex]n_1 = 12[/tex].11 participantes pueden ganar la medalla de plata, todos con excesion de lo que gano la medalla de plata, o sea, [tex]n_2 = 11[/tex].Así, el número de maneras diferentes en que se pueden otorgar las medallas es dado por:
[tex]N = n_1 \times n_2 = 12 \times 11 = 132[/tex]
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What is the simplest radical form of the expression? (8x5y3)2/3
The simplest radical form of the expression is [tex]\mathbf{40 ^{2/3}x^{{10}/{3}}y^2}[/tex].
What is the simplification of power indices?When we have indices in the form [tex]\mathbf{ax^{2/3}}[/tex], we are going to find the cube root of the (ax)². This can be mathematically expressed as:
[tex]\mathbf{=(\sqrt[3]{ax})^2 }[/tex]
From the given information:
[tex]\mathbf{=(8x^55y^3)^{2/3}}[/tex]
[tex]\mathbf{=(\sqrt[3]{8x^55y^3} } )^2[/tex]
[tex]\mathbf{=(\sqrt[3]{40x^5y^3} } )^2[/tex]
[tex]= (\sqrt[3]{40x^5} \times \sqrt[3]{y}^3)^2[/tex]
[tex]\mathbf{= 40 ^{2/3}x^{{5*2}/{3}}y^2}[/tex]
[tex]\mathbf{= 40 ^{2/3}x^{{10}/{3}}y^2}[/tex]
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The graph represents a person’s heart rate in beats per minute during 30 minutes of exercise.
A graph titled Cardiac Exercise. The horizontal axis shows time (minutes), numbered 3 to 30, and the vertical axis shows Heart Rate (b p m) numbered 15 to 150. The line starts at 75 b p m in 0 minutes, to 135 b p m from 6 to 25 minutes, and ends at 105 b p m at 30 minutes.
Which statement best describes the relationship between heart rate and time during exercise?
The heart rate increases for 6 minutes, remains constant for 19 minutes, and then gradually increases for 5 minutes.
The heart rate decreases for 6 minutes, remains constant for 19 minutes, and then gradually increases for 5 minutes.
The heart rate increases for 6 minutes, remains constant for 19 minutes, and then gradually decreases for 5 minutes.
The heart rate remains constant for 6 minutes, increases for 19 minutes, and then gradually decreases for 5 minutes.
Answer:
the heart rate increases for 6 minutes, remains constant for 19 minutes ,and then gradually decreases for 5 minutes
Two sides of an acute triangle measure 5 inches and 8 inches. The length of the longest side is unknown/ What is the greatest possible whole-number length of the unknown side?
8 inches
9 inches
12 inches
13 inches
The Triangle inequality theorem of a triangle says that the sum of any of the two sides of a triangle is always greater than the third side. The correct option is C.
What is the triangle inequality theorem?The Triangle inequality theorem of a triangle says that the sum of any of the two sides of a triangle is always greater than the third side.
Suppose a, b and c are the three sides of a triangle. Thus according to this theorem,
[tex](a+b) > c\\(b+c) > a\\(c+a) > b[/tex]
Given the length of the two sides of the triangle, therefore, we can write the inequalities,
8 + 5 > x ⇒ 13 > x
8 + x > 5 ⇒ x > - 3
5 + x > 8 ⇒ x > 3
Now, as per the inequality the value of x can lie between 3 to 13, but as the side needs to be greatest, therefore, the value of x will be 12.
Hence, the correct option is C.
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Answer:
12in
Step-by-step explanation:
The table represents a bicycle rental cost in dollars as a
unction of time in hours.
Bicycle Rental
Time
Cost
(hours)
($)
0
0
2
10
4
20
6
30
8
40
Which explains whether or not the function represents a
direct variation?
O This function represents a direct variation because it
passes through the origin and has a constant rate of
change of $5 per hour.
O This function represents a direct variation because it
has a positive, constant rate of change of $10 per
hour.
O This function does not represent a direct variation
because it does not represent the cost for 1 hour.
This function does not represent a direct variation
because the function rule for the cost is to add $10,
not multiply by a constant.
Answer:
(a) This function represents a direct variation because it passes through the origin and has a constant rate of change of $5 per hour.
Step-by-step explanation:
The equation of direct variation is ...
y = kx
for some constant k. Here, we have x in hours and y in dollars. We can see if k is constant for the values given in the table.
__
constant of variationSolving the direct variation formula for k, we have ...
k = y/x
Using the table values, we can see if this is constant:
k = dollars/hour = 10/2 = 20/4 = 30/6 = 40/8 = 5
The "rate of change" is constant at $5 per hour.
The function represents direct variation because it passes through the origin and has a constant rate of change of $5 per hour.
A school charges £5 for tickets to a show.
The school raises £x in total from ticket sales.
Write an expression for the total number of tickets sold by the school.
Answer:
x/5
Step-by-step explanation:
The revenue from sales is the product of the selling price of the ticket and the number of tickets sold.
__
If n represents the number of tickets sold, then the revenue from selling tickets for £5 each will be ...
(n)(£5) = £x
Dividing by the coefficient of n will given the number of tickets sold:
n = £x/(£5) = x/5
The number of tickets sold is x/5.
Type the expression that results from the following series of steps:
Start with
y
, subtract 7, multiply by 3, then add 6.
Answer:
3y-15
Step-by-step explanation:
(y-7)3=3y-21
3y-21+6=3y-15
What is the explicit formula for this geometric sequence?
64, 16, 4, 1,
Answer: [tex]a_{n}=64\left(\frac{1}{4} \right)^{n-1}[/tex]
Step-by-step explanation:
The common ratio is 16/64 = 1/4, so substituting into the formula, we get that [tex]a_{n}=64\left(\frac{1}{4} \right)^{n-1}[/tex]
find the x
please help me asap
Sum of two interiors=Exterior
[tex]\\ \rm\Rrightarrow 39+6x+11=11x-10[/tex]
[tex]\\ \rm\Rrightarrow 6x+50=11x-10[/tex]
[tex]\\ \rm\Rrightarrow 60=5x[/tex]
[tex]\\ \rm\Rrightarrow x=12[/tex]
Find the number of rectangles an and Squares in chess 8 by 8 board respectively.
Answer:
squares: 204
rectangle: 1,296
Step-by-step explanation:
Board Size: 8 x 8
The total number of squares is thus:
[tex]1^{2} + 2^{2} + ... + n^{2}[/tex]
sum = [tex]\frac{n(n + 1)(2n + 1)}{6}[/tex]
For a chess board, with n = 8,
sum = [tex]\frac{(8)((8) + 1)(2(8) + 1)}{6}[/tex]
sum = 204
the number of rectangles on a chess board,
to make a rectangle you need to pick any two of the vertical lines, and any two of the horizontal lines. There are 36 distinct pairs and the same number of vertical pairs, so the answer is 36 × 36 = 1,296.
1.___________a representation to show the total outcomes.
Study the situation and make a listing to solve for the answer.
Brilliant Spa offers a variety of uniform styles from which they can choose. Polo shirts come with yellow, red, and green. The pants come with black, blue, and white. Using the listing methods, how many possible uniforms are there?
Make a diagram to find the total number of possible outcomes.
As an opening promo, a café offers snack combos for P250.00. The meal includes a sandwich, a pasta, and a drink. The choices are below.
Sandwiches: chicken, tuna, bacon
Pasta: carbonara, fettuccine, seafoods
Drinks: iced tea, pineapple, calamansi
By using the listing method, the number of possible uniforms that Brilliant Spa can choose from is equal to 9 uniforms.
What is a listing method?In Mathematics, a listing method can be defined as a technique which is used to list all the elements or members of a data set, while separating each of them with a comma and enclosing the data set within curly braces.
From the information provided above, we have the following points:
Polo shirts come with color yellow, red, and green. The pants come with color black, blue, and white.By using the listing method, a list of all the elements in this data set is given by:
List = {(yellow, black), (yellow, blue), (yellow, white), (red, black), (red, blue), (red, white), (green, black), (green, blue), (green, white)}
Number of possible uniforms = 9 uniforms.
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Aleena cuts 3/8 part of ribbon for her project.then again she cuts 4/5 part of the remaining ribbon the next day.find the total length of the Ribbon ,if 6.5 m of ribbon still remain
The total length of the ribbon is 52 m.
Let x = the original length of the ribbonAleena initially cuts 3/8 of the ribbon, i.e. a length of (3/8)x.
How much is left?1 - (3/8)x = (5/8)x.
On the next day, she cuts 4/5 of the remaining ribbon.i.e. (4/5) * (5/8)x = (20/40)x = (1/2)x
How much of the ribbon has she now cut away?(3/8)x + (1/2)x = (3/8)x + (4/8)x = (7/8)x
That means 1 - (7/8)x = (1/8)x remains, and that is a length of 6.5 m.
We now need to determine the following:1/8 of what number is 6.5?
Let y = the unknown number.
(1/8)y = 6.5
Multiply both sides of the equation by 8 to clear the fraction.
y = 52 m
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A number cube is rolled. What is the probability
of rolling a number that is
less than 5 or odd?
Step-by-step explanation:
a complicated way to say "the probability to roll a number that is less or equal to 5".
and that is
5 desired cases over 6 total cases, and that means
5/6 = 0.833333333...
Which of these tables represent a linear function
Answer:
y=mx+c
Step-by-step explanation:
if any one of them have this form it's the linear function