Answer:
The equation in the slope-intercept form is
y = -5x - 41
Step-by-step explanation:
The given equation in the question is;
y = -5x + 2
The equation of a straight line graph can be written in the form;
y = mx + c
where m is the slope and c is the intercept
From here, we can see that the slope m is -5
Since the line is parallel to the new line we are trying to write its equation, it means that they have the same value of intercept.
Hence, the slope of the new line is also -5
Now, we can write the equation of the new line as;
y = -5x + c
we need to get the value of c here however
To get the value of c, we need to input the value of x and y
From the graph, x = -7 and y = -6
Substituting these values, we have;
-6 = -5(-7) + c
-6 = 35 + c
c = -6 -35
c = -41
So the equation of the new line will be;
y = -5x - 41
If 12 cats can catch 6 rats in 2 hours, how many hours would it take 50 cats to catch 75 rats?
Answer:
50 cats would take 6 hours to catch 75 rats.
Step-by-step explanation:
After reading the statement we noticed the existence of two relationships:
1) The amount of cats is directly proportional to the quantity of caught rats.
2) The amount of cats is inversely proportional to time taken to catch rats.
That is to say:
[tex]n \propto \frac{x}{y}[/tex]
[tex]n = k\cdot \frac{x}{y}[/tex] (Eq. 1)
Where:
[tex]n[/tex] - Amount of cats, dimensionless.
[tex]x[/tex] - Amount of caught rats, dimensionless.
[tex]y[/tex] - Time, measured in hours.
[tex]k[/tex] - Proportionality ratio, measured in hours.
Then, we obtain the following relationship by eliminating the proportionality ratio in (Eq. 1):
[tex]\frac{n_{1}\cdot y_{1}}{x_{1}} = \frac{n_{2}\cdot y_{2}}{x_{2}}[/tex] (Eq. 2)
Where:
[tex]n_{1}[/tex], [tex]n_{2}[/tex] - Initial and final amounts of cats, dimensionless.
[tex]x_{1}[/tex], [tex]x_{2}[/tex] - Initial and final amounts of caught rats, dimensionless.
[tex]y_{1}[/tex], [tex]y_{2}[/tex] - Initial and final times, measured in hours.
Now we clear final time in (Eq. 2):
[tex]y_{2} = y_{1}\cdot \left(\frac{n_{1}}{n_{2}} \right)\cdot \left(\frac{x_{2}}{x_{1}} \right)[/tex]
By knowing that [tex]y_{1} = 2\,h[/tex], [tex]n_{1} = 12[/tex], [tex]x_{1} = 6[/tex], [tex]n_{2} = 50[/tex], [tex]x_{2} = 75[/tex], then we get that time taken by 50 cats to catch 75 rats is:
[tex]y_{2} = (2\,h)\cdot \left(\frac{12}{50} \right)\cdot \left(\frac{75}{6}\right)[/tex]
[tex]y_{2} = 6\,h[/tex]
50 cats would take 6 hours to catch 75 rats.
In the month of June, the temperature in Johannesburg, South Africa, varies over the day in a periodic way that can be modeled approximately by a trigonometric function. The lowest temperature is usually around 3^\circ C3 ∘ C3, degrees, C, and the highest temperature is around 18^\circ C18 ∘ C18, degrees, C. The temperature is typically halfway between the daily high and daily low at both 10\text{ a.M.}10 a.M.10, start text, space, a, point, m, point, end text and 10\text{ p.M.}10 p.M.10, start text, space, p, point, m, point, end text, and the highest temperatures are in the afternoon.
Answer:
The answer is "[tex]\bold{T = - 7.5 \cos \frac{\pi}{12}( t - 4 )+ 10.5}[/tex]"
Step-by-step explanation:
Given value:
Temp-maximum=[tex]18^{\circ}[/tex]
Temp. minimum = [tex]3^{\circ}[/tex]
It is halfway between 10 am and 10 pm to 4 am.
The sinus and cosine roles could be used throughout the year to predict fluctuations in climate models. Its type of formula that can be used to model such information is:
[tex]T = A \cos B(t-C) + D,[/tex] where parameters are A, B , C, D, T is the ° C temperature and t is the time (1-24)
[tex]A = amplitude = \frac{(T_{max} - T_{min})}{2}\\\\[/tex]
[tex]= \frac{(3 - 18)}{2}\\\\= - \frac{15}{2}\\\\ = -7.5[/tex]
[tex]B = \frac{2 \pi}{24}\\\\[/tex]
[tex]= \frac{\pi}{12}[/tex]
[tex]C = \text{ units translated to the right}= 4[/tex]
[tex]D = y_{min} + amplitude = units \ translated \ up\\\\[/tex]
D = 7.5 + 3 = 10.5
Its trigonometric function equation that model temperature T hours after midnight in Johannesburg t.
[tex]T = - 7.5 \cos \frac{\pi}{12}( t - 4 )+ 10.5[/tex]
Answer:
Hope this helps.
Step-by-step explanation:
there are no 43 people in the cafeteria what is the inequality
Answer:
Step-by-step explanation:
if you have the option, you can say
# of people ≠ 43
How can I solve this? 32 1/4 x 1/8
convert 32 1/4 into an improper fraction
100 POINTS!!!!!!!!!!! ( I NEED FAST ANSWERS ) Find the slope of the line that contains the points:(-6, 3) and (-4,5).
Answer:
slope = -4/5
Step-by-step explanation:
-16 - (-t) = -45 how do you solve this please help
Answer:
- 29
Step-by-step explanation:
Step 1:
- 16 - ( - t ) = - 45 Equation
Step 2:
- 16 + t = - 45 Open Parenthises
Step 3:
t = - 45 + 16 Add 16 on both siddes
Answer:
t = - 29
Hope This Helps :)
Answer:
t = -29
Step-by-step explanation:
Step 1: Write equation
-16 - (-t) = -45
Step 2: Solve for t
Simplify: -16 + t = -45Add 16 to both sides: t = -29Step 3: Check
Plug in t to verify it's a solution.
-16 - (-(-29)) = -45
-16 - 29 = -45
-45 = -45
khan academy graph from the linear standard form.
Graph -14x + 21y = 84
Answer:
16
Step-by-step explanation:
because i am smort
16/7 - 1/14 subtracting fractions
Answer:
31/14
Step-by-step explanation:
We first need to get common denominators, so we multiply the 16 and the 7 by 2, to get 32/12. Now we can subtract since the fractions have common denominators. After subtracting we get 31/14 or 2 3/14. Hope this helps!
This is really confusing can someone help?
Answer:
D.780.8
Step-by-step explanation:
multiply 244 and 3.2 and you get D. hope this helps.
Answer:
B (780 4/5)
Step-by-step explanation:
He’s buying 24 boxes, and each box weighs 3 1/5 pounds. So we need to multiply 24 x 3 1/5, resulting in 780 4/5
So sorry if I’m wrong. Have a good day!
~Louella Marie Smith♥️
plllsssssssssss I needddd ansswwerss
Answer:
9/4 or 2¼
Step-by-step explanation:
have the number be represented by x2/3s OF x (of means to mulitply); 3 INCREASED BY (increased by means to add); 1/2 OF x (again, of means to multiply)so we can write the equation like this:2/3x=3+1/2xnow we need to get x by itselfmultiply both sides of the equation by 2/1 (the reciprocal of 1/22/3(2/1)=4/3 ; 1/2(2/1)=1now our equation look like 4/3x=3multiply both sides of the equation by 3/4 (the reciprocal of 4/3)4/3(3/4)=1 ; 3(3/4)=9/4x = 9/4 or 2¼Ian measures 9 kg of rice. One kilogram is approximately equal to 2.2 pounds. Which measurement represents the number of pounds of rice?
Answer:
19.8 poundsStep-by-step explanation:
9 kg x 2.2 pounds
1 kg
= 19.8 pounds
Answer:
19.8
Step-by-step explanation:
Duncan is excited to begin diving lessons. He starts on the diving board, 5 feet above the surface of the pool. Then, Duncan dives off the board and ends up 7 feet below the surface of the pool. What is the total distance from Duncan's start on the diving board to his lowest point beneath the surface of the pool?
Answer:12
Step-by-step explanation:
Answer:
12
Step-by-step explanation:
3.The snow starts at a depth of 10 inches and melts to 2 inches over the span of 4 hours. Determine the rate of change over the interval 0≤x≤4A.4 inches per hour
B.2 inches per hour
C.8 inches per hour
D.12 inch per hour
4.The population in a neighborhood increased from 120 to 156 people from 1990 to 1994. Find the rate of change over the interval 1990≤x≤1994.
A.1/9 of a person per year
B.9 people per year
C.36 people per year
D.4 people per year
5.The temperature increases from 60 degrees Fahrenheit to 84 degrees Fahrenheit from 8 in the morning to 12 in the afternoon. Find the rate of change over the interval 8≤x≤12
A.16 of a degree Fahrenheit per hour
B.4 degrees Fahrenheit per hour
C.6 degrees Fahrenheit per hour
D.24 degrees Fahrenheit per hour
If you answer, answer with all of the questions listed thank you.
3. B: 2 inches
4. C: 9 people
5. B: 6 degrees
HURRY!! THIS ASSIGNMENT IS DUE IN 5MIN!!! THANK YOU!!!!!!
Find the discounted price.
flashlight: $18.00 discount: 25%
Answer:
You can also calculate how much you save by simply moving the period in 25.00 percent two spaces to the left, and then multiply the result by $18 as follows: $18 x . 25 = $4.50 savings.
Cleo and jandi are having a Halloween party. They have 3 1/2 pounds of candy to divide into 14 goodie bags. How much candy will be in each bag?
Answer:
1/4 pound(s) of candy in each bag
Step-by-step explanation:
3 1/2 (pounds of candy) ÷ 14 (goodie bags) = ?
To make this easier let's turn 3 1/2 into a improper fraction and flip 14/1 (14/1 to 1/14):
3 1/2 = 7/2 14/1 = 1/14
Now we multiply:
7/2 x 1/14 = 7/28 = 1/4
(When you divide fractions, you can flip the second fraction and multiply and get your answer. Remember to simplify once you get your answer!)
Hope I helped! Sorry if wrong!
Answer:
1/4 pounds
Step-by-step explanation:
Write 5.77 x 10 in standard form.
5.77 x 10–2
Answer:
The answer is 57.7 x.
Step-by-step explanation:
Select the prime factors of 204.
A. 2 x 17
B. 6 x 17
C. 2 x 3 x 17
D. 2 x 2 x 3 x 17
Solve each quadratic equation by completing the square.
6x2 – 28x = - 16
Answer:
There is no real solutionStep-by-step explanation:
[tex]6x^2-28x = - 16\\\\6x^2-28x + 16=0\\\\3x^2-7x+8=0\\\\9x^2-21x+24=0\\\\(3x)^2-2\cdot3x\cdot\frac72+(\frac72)^2-(\frac72)^2+24=0\\\\(3x-\frac72)^2-\frac{49}4+24=0\\\\(3x-\frac72)^2-12\frac{1}4+24=0\\\\(3x-\frac72)^2+12\frac{3}4=0\\\\(3x-\frac72)^2=-12\frac{3}4[/tex]
Which property does this show? 4(3 - x) = 12 - 4x
Answer:
Distributive property
Step-by-step explanation:
when you distribute the left sid dit equals the right
Shelby wants to buy 10 yards of fabric that costs $2.49 per yard. How much money will Shelby need to purchase all the fabric? $2.49 $4.01 $12.49 $24.90
Answer:
$24.90
Step-by-step explanation:
Answer:
24.90
Step-by-step explanation:
9. PRODUCTION Brown Pencil factory can
produce 150 gross of pencils in a quarter of an
hour. At this rate, how many gross of pencils
can the factory produce in seven and a half
hours?
Please hurry
Answer:
4500
Step-by-step explanation:
Use the vertical line test to determine whether or not the graph is a graph of a function.
If you have a negative slope how do you graph it?
What is the sum of the first 21 even numbers? FAST!!!
Answer:
462
Step-by-step explanation:
Sum = n/2 x (a + Tn)
= 21/2 x (2 + 42)
= (21 x 44)/ 2
= 924/2
2 + 4 + 6 + 8 + 10 + 12 + . . . . + 42 = 462
can ya smart people solove ths
Answer:
[See Below]
Step-by-step explanation:
____________________
✦ Solve:
Divide: [tex]6[/tex] ÷ [tex]2=3[/tex]Add: [tex]1+2=3[/tex]Multiply: [tex]3*3=9[/tex]____________________
So your answer would be:
[tex]\bold9[/tex]____________________
~Hope this helps Mate. If you need anything feel free to message me.
[tex]-Your~ Friendly~ Answerer,~Shane[/tex] ☺
Use the function to fill in the table.
g(x)=-3x+1
leila decides to save for 6 years. she opens a saving account with $800. the account pays simple interest at an annual rate of 2%. she doesn’t make any more deposits how much total interest will leila earn?
Answer:
time =T=6 years
principal = P=$800
rate = R= 2%
interest = (P*T*R)/1000
= 800*6*2/100
= 96
Step-by-step explanation:
Sorry but what is “ 6(-5n + 7) “ equal ?
Answer:
-30n+42
Step-by-step explanation:
6(−5n+7)
=(6)(−5n+7)
=(6)(−5n)+(6)(7)
=−30n+42
Answer: − 30 n + 42
Step-by-step explanation:
(5x² + 8x - 3) + (2x² - 7x + 13x)
Answer:
Simplify the expression.
7x2+14x−3
Step-by-step explanation:
The required simplification can be given as 7x²+ 14x - 3
What is simplification?
The operation in mathematics to process and interpret the relation to make function simple or more simple is called simplify and the phenomenon is called simplification.
We have,
= (5x² + 8x - 3) + (2x² - 7x + 13x)
= 5x²+ 2x²+ 8x - 7x + 13x - 3
= 7x²+ 14x - 3
Thus, the required simplification can be given as 7x²+ 14x - 3
Learn more about simplification here:
https://brainly.com/question/12501526
#SPJ2
A(x) = x² +10x - 75
rewrite in factored form
Step-by-step explanation:
A(x) = x² + 10x -75
= (x + 15)(x - 5)
Answer:
(x+15)(x-5)
Step-by-step explanation: