Answer:
[tex] \large \boxed{y = - \frac{1}{9} x - \frac{5}{9} }[/tex]
Step-by-step explanation:
In order to find an equation of a line with two given ordered pairs. We have to find a slope first which we can do by using the formula below.
[tex] \large \boxed{m = \frac{y_2 - y_1}{x_2 - x_1} }[/tex]
m-term is defined as slope in y = mx+b form which is slope-intercept form.
Now we substitute these ordered pairs (x, y) in the formula.
[tex] \large{m = \frac{1 - ( - 2)}{ -14 - 13} } \\ \large{m = \frac{1 + 2}{ - 27} } \\ \large{m = \frac{3}{ - 27} = - \frac{1}{9} }[/tex]
After we calculate for slope, we substitute m-value in slope-intercept form. The slope-intercept form is
[tex] \large \boxed{y = mx + b}[/tex]
We already know m-value as we substitute it.
[tex] \large{y = - \frac{1}{9} x + b}[/tex]
We are not done yet because we need to find the b-term which is our y-intercept. (Note that m-term is slope while b-term is y-intercept)
We can find the y-intercept by substituting either (-14,1) or (13,-2) in the equation. I will be using (13,-2) to substitute in the equation.
[tex] \large{y = - \frac{1}{9} x + b} \\ \large{ - 2 = - \frac{1}{9} (13) + b} \\ \large{ - 2 = - \frac{13}{9} + b} \\ \large{ - 2 + \frac{13}{9} = b} \\ \large{ - \frac{5}{9} = b}[/tex]
Finally, we know b-value. Then we substitute it in our equation.
[tex] \large{y = - \frac{1}{9} x + b} \\ \large{y = - \frac{1}{9} x - \frac{5}{9} }[/tex]
A teacher is four times as old as a student. In 28 years, the student's age will be half of the teacher's age. How old are they now?
The age of the teacher is
years.
The age of the student is
years
Compound Interest: You deposit $100 in an account that earns 3% annual interest compounded continuously. How long does it take the balance to reach the following amounts? (A = Pe^(rt). NO LINKS
a. $110
b. $150
c. $200
9514 1404 393
Answer:
a) 3.18 years
b) 13.52 years
c) 23.10 years
Step-by-step explanation:
Solving for t, we find ...
A = Pe^(rt)
A/P = e^(rt)
ln(A/P) = rt
t = ln(A/P)/r
For P=100 and r=.03, the times are ...
a. $110: t = ln(110/100)/.03 ≈ 3.18 years
b. $150: t = ln(150/100)/.03 ≈ 13.52 years
c. $200: t = ln(200/100)/.03 ≈ 23.10 years
Translate this sentence into an equation. The sum of 16 and Delia's height is 74. Use the variable d to represent Delia's height.
The Clothes Barn is having a 65% off sale on all the dresses. Jennifer paid $43.75 for a dress that was on
sale. What was the original price of the dress?
1. $125.00
2. $28.44
3. $15.31
4. $105.00
Answer:A
Step-by-step explanation:
I used the process of elimination. I did, 125 x .65 to get 81.25. Then, I subtracted 81.25 to 125. To get 43.75.
The original price of the dress was $125.00.
What is the percentage?A percentage is a number or ratio that can be expressed as a fraction of 100 in mathematics. If we need to calculate the percentage of a number, divide it by the whole and multiply by 100. As a result, the percentage denotes a part per hundred.
How to solve this problem?Given that the discount = 65%
Sale price = $43.75
Let the original price of the dress is $x.
Now, sale price = x - x * 65% = x - x * 65/100 = (100 - 65)x/100 = 35x/100
We can write
35x/100 = 43.75
i.e. x = (43.75 * 100)/35 = 4375/35 = 125
Therefore, the original price of the dress was $125.00. So, option 1 is correct.
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using a positive and negative integer, write an addition expression that equals -9
Answer:
-13 + 4
Step-by-step explanation:
For the sum to be negative, the absolute value of the negative integer has to be 9 more than the positive integer. There are an infinite number of equations, but here is one:
-13 + 4
what is the angle of d
Answer:
115°
Step-by-step explanation:
65 +65 = 130
360-130= 230
230÷2= 115
5.
Which value of x would satisfy this inequality?
V3
4
2
A А.
С
D
000
4
10
Answer:
C) 4/5
Step-by-step explanation:
pi/4 = 0.7853981634
[tex]\frac{\sqrt{3} }{2}[/tex] = 0.8660254038
3/4 = 0.75. It's less than pi/4, so not correct
9/10 = 0.9. It's more than 0.866, so not correct
4/5 = 0.8. It's right for both condition
8/9 = 0.888. It's more than 0.866, so not correct.
Please help me find 'x' your help would be much appreciated
-Thanks
Answer:
x=25.
Step-by-step explanation:
We know because of corresponding angles, the sum of the angle adjacent to (2x-5) and (2x-5) is 180 degrees
2x-5+5x+10=180
7x+5=180
7x=175
x=25
3. 8.F.1.3
Which of the following equations represents
a linear function?
A. y = 3x2
B. y = 2-
C. y = 4x+6
D. y = -x + 3
A lock has a 3-number code made up of 15 numbers. If none of the numbers are allowed to repeat, how many different ways can you choose three different numbers in order for a unique code?
Answer:2730
Step-by-step explanation:
The number of ways we can choose three different numbers in order for a unique code for this case is 2730
How many ways k things out of m different things (m ≥ k) can be chosen if order of the chosen things doesn't matter?We can use combinations for this case,
Total number of distinguishable things is m.
Out of those m things, k things are to be chosen such that their order doesn't matter.
This can be done in total of [tex]^mC_k = \dfrac{m!}{k! \times (m-k)!}[/tex] ways.
If the order matters, then each of those choice of k distinct items would be permuted k! times.
So, total number of choices in that case would be:
[tex]^mP_k = k! \times ^mC_k = k! \times \dfrac{m!}{k! \times (m-k)!} = \dfrac{m!}{ (m-k)!}\\\\^mP_k = \dfrac{m!}{ (m-k)!}[/tex]
This is called permutation of k items chosen out of m items (all distinct).
Given that:
The considered lock as a 3 number codeThere are 15 numbers available.None of the number can repeat.In a lock, the order of the way numbers are arranged matters.
Because of no repetition allowed, we can simulate this situation as:
The number of ways we can choose 3 numbers out of 15 numbers with order = The number of different ways we can choose three different numbers in order for a unique code.
And we have:
The number of ways we can choose 3 numbers out of 15 numbers with order = [tex]^{15}P_3 = \dfrac{15!}{(15-3)!} = \dfrac{15 \times 14 \times 13 \times 12!}{12!} = 2730[/tex]
Thus, the number of ways we can choose three different numbers in order for a unique code for this case is 2730
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what is 1+1-(3x3)-(1x9)
If the door to the library is at (2, 4), the door to the mall is at (8, 2), and one square unit equals one square mile, the approximate distance between the library and the mall is miles, when measured door to door.
Please help best answer will get brainly
Answer:
https://ihomeworkhelpers.com/mathematics/question512843765
Step-by-step explanation:
MRK ME BRAINLIEST PLZZZZZZZZZZZZZZ
that link is not fake its is a homework helper site if it doesn't works let me know
Answer: 126.66 m²
Step-by-step explanation: The pertinent area formula is a = πr², where r is the radius. here, a = π(6.35 m)² = 40.32π, or approximately 126.66 m²
Each day 1/2 of the money that is in a bank is removed .no money is added to the vault .which of the following models the situation
A rectangle is graphed on a coordinate plane. The rectangle’s two lines of symmetry are the x-axis and the y-axis. Evie says that means the vertices are reflections of each other over the x-axis and y-axis. Is she correct? Explain your reasoning NO LINKS worth 50 points
Answer:
Can you add a picture if there are any?
Step-by-step explanation:
In
any
School there are 7000
students 45%. are boys. How many
boys are there? How
many girls
are there
Answer: there are 3150 boys and 3850 girl
Step-by-step explanation:
45÷100×7000= 3150 and 7000- 3150 = 3850
Hope this helps!!
The water level at a local pier rises and falls with the tide. Yesterday, the maximum depth of the water at the pier was 8 feet, and the minimum depth was 4 feet. High tide occurred at 12:00 am and low tide occurred at 12:20 pm. Which function models the depth, in feet, of the water at the pier yesterday, as a function of the time t in minutes past high tide?
Answer: C, Bottom Left
Step-by-step explanation:
The function that models the depth, in feet, of the water at the pier yesterday, as a function of the time t in minutes past high tide is: 2 cos(π/740t)+6.
What is function model?Amplitude
A = 8 - 6
A = 2 ft
Average depth
A = (4 + 8)/2
A = 6 ft
Hence:
A+B=8
-A+B=4
1/2t=12×60×20=740
w=2π/t=π740
When t=0
d=2sin4+6=8
4=π/2
Hence:
d(t)=2 sin(π/740t + 4)+6
2 cos(π/740t)+6
Therefore the function that models the depth, in feet, of the water at the pier yesterday, as a function of the time t in minutes past high tide is: 2 cos(π/740t)+6.
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25 PTS PLEASE HELP QUICK
(not related to the question but please add thx i want friends)
OK THX THE QUESTION IS BELOW
Answer:
-3
Step-by-step explanation:
just plug in the points on the line into y2-y1/x2-x1
Order from least to greatest.
18.186; 18.1806; 18.085; 18.0728; 18.1472
Triangle ABC is graphed in the coordinate plane with vertices A(1, 1); B(3, 4) and C(- 1, 8) as shown in the figure.
Answer:
(-4,-2)
Step-by-step explanation:
B(3,4)
x=3 , y=4
(3-7,4-6)
(-4,-2)
Transformation involves changing the position of a shape.
The coordinates of B after the translation is (-4,-2)
The vertices are given as:
[tex]\mathbf{A =(1,1)}[/tex]
[tex]\mathbf{B =(3,4)}[/tex]
[tex]\mathbf{C =(-1,8)}[/tex]
The translation rule is given as:
[tex]\mathbf{(x-7,y-6)}[/tex]
So, the coordinates of B' is calculated using:
[tex]\mathbf{(x,y) \to (x-7,y-6)}[/tex]
This gives
[tex]\mathbf{(3,4) \to (3-7,4-6)}[/tex]
[tex]\mathbf{(3,4) \to (-4,-2)}[/tex]
Rewrite as:
[tex]\mathbf{B' = (-4,-2)}[/tex]
Hence, the coordinates of B after the translation is (-4,-2)
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pls helpppppppp meee i dont wanna faillll
Answer:
D, No trend or association
volume of a cube with side length of 5.2 cm.
Answer:
140.608
Step-by-step explanation:
Please help me fast!
Find the surface area of this cone. Show your work.
Answer:
The answer is 628 meters.
Step-by-step explanation:
The area for surface of a cone is pi times the radius (radius plus the square root of the height squared plus the radius squared).
Lol, i know this is really confusing, just look up surface area of a cone formula.
Height squared = 15 * 15 = 225
Radius squared = 8 * 8 = 64
225 + 64 = 289
The square root of 289 is 17
17 + 8 = 25
3.14 * 8 = 25.12
25.12 * 25 = 628 meters.
Could I get Brainliest please?!?!
Assume that 200 babies are born to 200 couples treated with the XSORT method of gender selection that is claimed to make girls more likely. Preliminary results from a test of the XSORT method of gender selection involved 200 couples who gave birth to 115 girls and 85 boys. At significance level of 0.1, test whether the proportion of girl births after the treatment is greater than the 50% that occurs without any treatment (optional: show your work of the hypothesis testing in paper). Answer the next three questions
a. test statistic =
b. p-value =
c. What is your decision?
Answer:
a) test statistic = 2.12
b) p-value = 0.017
c) we reject the Null hypothesis
Step-by-step explanation:
Given data :
N = 200
girls (x) = 115 , Boys = 85
p = x / n = 115 / 200 = 0.575
significance level ( ∝ ) = 0.1
aim : test whether the proportion of girls births after the treatment is greater than 50% that occurs without any treatment .
A) Determine the test statistic
H0 : p = 0.5
Ha : p > 0.5
to determine the test statistic we will apply the z distribution at ( ∝ ) = 0.1
Z - test statistic = ( 0.575 - 0.5) / [tex]\sqrt{0.5*0.5 / 200}[/tex] = 2.12
b) determine the p-value
The P-value can be determined using the normal standard table
P-value = 1 - p(Z< 2.12 ) = 1 - 0.9830 = 0.017
c) Given that the p value ( 0.017 ) < significance level ( 0.1 )
we will reject the H0 because there is evidence showing that proportion of girls birth is > 50%
PLEASE HELP ME WITH THIS
Gabriela is solving the following equation. Her steps are shown:
Gabriella is not sure she has solved the problem correctly. How can you convince Gabriella if she has solved the problem correctly / incorrectly? If she has solved the problem incorrectly, solve it and convince her of the solution
Answer:
Solution given:
5(9x-8)=4(x+2)
45x-40=4x+8
45x-4x=40+8
41x=48
x=[tex] \frac{48}{41} [/tex]
Gabriella is not correct:
she has done in distribution
5(9x-8)=4(x+2)
45x-40=4x+8 not 45x-8=4x+2.
No, Gabriela is not solving correctly because her second step is wrong.
What is a fraction?In a fraction the upper part is known as numerator and the lower part is known as denominator.
How to solve the problem?The problem is as under
(9x-8)/4=(x+2)/5
The above problem is solved as
5(9x-8)=4(x+2)
45x-40=4x+2
41x=42
x=42/41
Hence the value of x is 42/41 therefore the solution of Gabriella is wrong.
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if there 10 students and 2/5 play soccer how many students play soccer?
Answer:
4
Step-by-step explanation:
2 out of 5 play so if there is 10 students 10*2/5 = 4 students
Answer:
4 students would play soccer
Step-by-step explanation:
To make the total students 10 instead of 5 we multiply the information by 2. 2/5 times 2 equals 4/10. So 4 out of 10 studento play soccer
Please, Please help! :(
Answer:
first blank is 3
second blank is 126
Step-by-step explanation:
the ratio is 2:3 so you must keep that the same in the table
The one for chocolates is 3 and the one for peppermints is 126
HELP! PLEASEEEEE
IMAGE BELOW!
Answer:
Quadrant I and Quadrant II
Step-by-step explanation:
Quadrant I has both positive x and y coordinates,Quadrant II has a negative x coordinate but the y coordinate is positive.
What is the measure of the angle in standard position 30 330 -60 -30
find the area of this parallelogram with the measurements 5.2cm and 8.4cm
Answer:
43cm square
Step-by-step explanation:
A= bh
A=8.4cm x 5.2cm
A=43.68cmsqr
ILL GIVE BRAINLIEST PLSSSS HELP BASICALLY EVERYTHING IS IN THE PICTURE IF YOU ANSWER THIS WRONG OR PUT RANDOM WORDS OR A LINK I WILL REPORT YOU FASTER THAN THIS IS DUE