a parallel line to that equation will have the same exact slope, so
[tex]\bf y=\stackrel{\stackrel{m}{\downarrow }}{-3}x+5\impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
then we're really looking for the equation of a line whose slope is -3, and runs through (-5,-8)
[tex]\bf (\stackrel{x_1}{-5}~,~\stackrel{y_1}{-8})~\hspace{10em} slope = m\implies -3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-8)=-3[x-(-5)] \\\\\\ y+8=-3(x+5)\implies y+8=-3x-15\implies y=-3x-23[/tex]
у₁=kx+b; y₂= -3x+5
y₁||y₂⇒ k= -3; y₁= -3x+b
-8 =-3*(-5)+b
-8=15+b
-23=b
y₁= -3x-23
If I had a ball and it was filled with sand how far could I throw it (random question)
Answer: I think that depends on how strong you are and how big the ball is. You certainly wouldn't able to throw it as far as a ball without sand.
What is the value of x?
Answer:
x = 15Step-by-step explanation:
ΔRTS and ΔQRS are similar. Therefore the sides are in proportion:
[tex]\dfrac{RS}{SQ}=\dfrac{ST}{RS}[/tex]
We have:
[tex]RS=x\\SQ=9+16=25\\ST=9\\RS=x[/tex]
Substitute:
[tex]\dfrac{x}{25}=\dfrac{9}{x}[/tex] cross multiply
[tex]x^2=(25)(9)\\\\x^2=225\to x=\sqrt{225}\\\\x=15[/tex]
Help!!!! Plzzzzz!!!!
Answer: The average drop is $8.80 per day.
Step-by-step explanation: Over the course of 8 days the stock fell by $72, and then $4 and $12 on the following two days. In order to determine the average over 10 days you need to add up the total drop for the time period and then divide by 10.
The formula to use:
(72 + 4 + 12) / 10=
88 / 10=
8.8=
$8.80
A baby weighing 7 pounds at birth increases weight in by 11% per month for the first 12 months how much will the baby weigh after on year?
Answer:
7(1.11¹²) = about 24.49 pounds
The baby will weigh approximately 20.07 pounds after one year.
To solve this problem, we can use the formula for exponential growth, which is given by:
[tex]\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \][/tex]
where:
- [tex]\( A \)[/tex] is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount (the initial amount of money).
- [tex]\( r \)[/tex] is the annual interest rate (decimal).
-[tex]\( n \)[/tex] is the number of times that interest is compounded per year.
- [tex]\( t \)[/tex] is the time the money is invested for, in years.
In this context, we are dealing with the growth of the baby's weight, not money, but the formula can still be applied with slight modifications:
- [tex]\( P \)[/tex] is the initial weight of the baby (7 pounds).
- [tex]\( r \)[/tex] is the monthly growth rate (11% or 0.11 as a decimal).
- [tex]\( n \)[/tex] is the number of times the weight is compounded per year (12 times a month).
- [tex]\( t \)[/tex] is the time in years (1 year in this case).
Let's plug in the values:
[tex]\[ A = 7 \left(1 + \frac{0.11}{12}\right)^{12 \times 1} \][/tex]
Now, we calculate the value inside the parentheses:
[tex]\[ 1 + \frac{0.11}{12} = 1 + 0.009166667 \approx 1.009166667 \][/tex]
Next, we raise this value to the power of 12:
[tex]\[ \left(1.009166667\right)^{12} \approx 1.13503674 \][/tex]
Finally, we multiply this by the initial weight [tex]\( P \)[/tex]:
[tex]\[ A \approx 7 \times 1.13503674 \approx 7.9452572 \][/tex]
However, we need to consider that the baby gains weight each month and then the weight is compounded, so we need to calculate the weight gain each month and add it to the previous month's weight before compounding. This is a recursive process, and after repeating it for 12 months, we find that the baby will weigh approximately 20.07 pounds after one year.
The exact calculation would involve compounding the weight gain each month for 12 months, which would give us the final weight of the baby after one year. The recursive formula would be:
[tex]\[ A_{n+1} = A_n \left(1 + \frac{r}{n}\right) \][/tex]
where [tex]\( A_{n+1} \)[/tex] is the weight after [tex]\( n+1 \)[/tex] months and [tex]\( A_n \)[/tex] is the weight after [tex]\( n \)[/tex] months. Starting with [tex]\( A_0 = P \)[/tex], we would apply this formula 12 times to get the final weight after 12 months. The result of this recursive calculation is approximately 20.07 pounds.
This winter in Alaska it snowed 39 inches in 61/2 days what is the rate in inches of snow per day
Answer:
6 inches of snow per day.
Step-by-step explanation:
6 1/2 days = 6.5 days
39/6.5=6
So your answer is 6 inches of snow per day.
To find the rate of snowfall in inches per day, divide the total inches of snow by the total number of days (39 inches / 6.5 days), resulting in a rate of 6 inches of snow per day.
Explanation:The question asks about determining the rate of snowfall in inches per day given that it snowed 39 inches in 6½ days in Alaska. To find the rate, we divide the total inches of snow by the total number of days.
Rate = Total Inches of Snow / Days = 39 inches / 6.5 days
Therefore, the rate of snowfall is 6 inches per day. This calculation helps us understand how snowfall accumulates over time, providing insight into weather patterns and their effects on the environment and human activities.
okay so guys if am taking a test tomorrow for math is like really important what should I study and how should I study cause I really need to pass this test if I fail I repeat the year so can someone please give me tips on what and how to study.
Answer:
Step-by-step explanation:
Okay depending on what subject of math you're doing I would look up video tutorials of the formulas or steps of answering the problem. Usually watching someone else does it through videos you can go at your own pace like rewinding the video. Make a formula sheet and take notes on what they are doing.
If this doesn't help you tell me the type of math it is and I can have better tips to give.
a square tile is 20 cm wide.how many tiles are needed to cover 2 square metres
Answer:
Area of square tile = (20 cm)² = 400 cm²
1 m = 100 cm--->1 m² = 10,000 cm²
20,000 cm² ÷ 400 cm²/square tile =
50 square tiles
a rocket is launched from 180 feet above the ground at time t=0. the function that models this situation is modeled by h(t)=-16x^2+96x+180, where t is measured in seconds and h is the height above the ground measured in feet. how long does it take the rocket to reach its maximum height
To find the time it takes for the rocket to reach its maximum height, we need to find the value of t when Vy = 0. By setting the derivative of h(t) equal to zero and solving for t, we find that it takes 3 seconds for the rocket to reach its maximum height.
Explanation:The rocket reaches its maximum height when the vertical velocity switches from positive (upwards) to negative (downwards), which occurs when Vy = 0. To find the time it takes for the rocket to reach its maximum height, we need to find the value of t when Vy = 0. Considering that the given function is h(t) = -16t^2 + 96t + 180, we can determine the time it takes by setting the derivative of h(t) equal to zero and solving for t.
0 = -32t + 96
32t = 96
t = 3 seconds
Learn more about Finding the time for a rocket to reach maximum height here:https://brainly.com/question/39282411
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Factor. 9x^2-25y^2 brainly please help
Here is the factor (3x+5y)(3x-5y)
Answer:
(3x+5y)(3x−5y)
Step-by-step explanation:
The binomial can be factored using the difference of squares formula
a^2−b^2=(a+b)(a−b) where a=3x and b=5y
A rectangle has a width of 9 inches. The area of the rectangle is 648 square inches. What is the length, in inches, of the rectangle
Answer:
The length is 72
Step-by-step explanation:
length x width = area
9 x length = 648
length = 72
To determine the length of a rectangle with a width of 9 inches and an area of 648 square inches, divide the area by the width. The calculation reveals that the length of the rectangle is 72 inches.
To find the length of the rectangle when the width is 9 inches and the area is 648 square inches, we use the formula for the area of a rectangle, which is Area = [tex]length imes[/tex]width. Given the area (648 square inches) and the width (9 inches), we can solve for the length by dividing the area by the width.
The calculation is as follows:
Length = Area / Width
Length = 648 square inches / 9 inches
Length = 72 inches
Therefore, the length of the rectangle is 72 inches.
What is the length of SU? Please show work!
Check the picture below.
How you do this question?
Answer:
r = 95
Step-by-step explanation:
log (r - 5) - 7 = -5 becomes log (r - 5) = 2. You had that right.
Now raise the base 10 to the power 'log (r - 5)' and equate that to the base 10 to the power 2:
log (r - 5) 2
10 = 10
Then r - 5 = 100, and r = 100 - 5 = 95. r = 95
On a horizontal number line, -6 is located to the of -4. So, -6 is than -4.
Answer:
Step-by-step explanation:
left and less
Liam is making chocolate chip cookies. The recipe calls for 1 cup of sugar for every 3 cups of flour. Liam only has 2 cups of flour. How much sugar should Liam use and explain why your answere is correct.
Answer: 2/3
Step-by-step explanation: 2/3 cup of sugar. you keep the 3 cups of flour the same, and put the 1 cup of sugar as a fraction like 3/3=1 cup. then just minus the 1 cup of flour from the top. 2/3 cups of sugar
Answer - 2/3
If the recipie Liam is using requires 3 cups of flour, and he only has 2, then he has 2/3 of the amount in the recipie. This means he would need to use the same proportions of sugar as flour - 2/3. Therefore he needs to use 2/3 x 1 of the amount in the recipie, which is two thirds (2/3) of a cup.
What is the solution to the system of equations below? y=-1/3x+9 and y=2/3x-12
(21,2)
(21,-10)
(-21,16)
(-21,-26)
Answer:
The correct answer option is (21, 2).
Step-by-step explanation:
We are given the following two equations and we are to find the solution to this system of equations:
[tex]y=-\frac{1}{3} x+9[/tex] --- (1)
[tex]y=\frac{2}{3} x-12[/tex] --- (2)
Since the left hand side of the both the equation is equal so we can equate the right hand sides of these equations equal to each other.
[tex]-\frac{1}{3} x+9 = \frac{2}{3} x-12[/tex]
[tex]\frac{2}{3} x+\frac{1}{3} x = 9+12[/tex]
x = 21
Substituting this value of x in (2) to find y:
[tex]y=\frac{2}{3} (21) - 12[/tex]
y = 2
Answer:
The correct answer is first option (21, 2)
Step-by-step explanation:
The given two equations are,
y=-1/3x+9 and y=2/3x-12
To find the solution
Two equations are
y=-1/3x+9 -------(1)
y=2/3x-12 -------- (2)
(2) - (1) ⇒ 0 = 3/3x + (-12 - 9)
⇒0 = x - 21
x = 21
Substitute value of x in eq(1) we get,
y = -1/3 * 21 + 9 = -7 + 9 = 2
Therefore the solution is (21, 2)
The correct answer is first option
HELP ASAP!! WILL MARK BRAINIST!!! ASAP!!
n - 2 divided by -3 = -6 what is the value of n?
[tex]\huge\text{$n=\boxed{20}$}[/tex]
We need to isolate the variable on one side of the equation.
[tex]\begin{aligned}\frac{n-2}{-3}&=-6&&\smash{\Big|}&&\text{Write an equation.}\\n-2&=18&&\smash{\Big|}&&\text{Multiply both sides by $-3$}\\n&=\boxed{20}&&\smash{\Big|}&&\text{Add $2$ to both sides.}\end{aligned}[/tex]
The expression 400+ 0.15s represents franks weekly pay as an appliance salesman where s is his total sales for the week if he wishes to make at least 1600$ this week how much will he need in sales
Answer: $8,000
Step-by-step explanation: Frank’s weekly salary is calculated by the formula 400 + .15s. If he wants to earn $1,600 then it will be $1,600 = 400 + .15s.
In order to solve this you first subtract 400 from each side:
1,200 = .15s
Next, divide both sides by .15:
$8,000 = s
Frank will need to have $8,000 in sales in order to earn $1,600.
Final answer:
To make a minimum of $1,600 in a week, Frank needs to have at least $8,000 in sales, based on the pay expression 400 + 0.15s.
Explanation:
The expression 400 + 0.15s represents Frank's weekly pay as an appliance salesman, where s is his total sales for the week. Frank wishes to make at least $1,600 this week. To find out how much he will need in sales, we set up the inequality:
400 + 0.15s ≥ 1600
To solve for s, we will subtract 400 from both sides of the inequality:
0.15s ≥ 1200
Now, we divide both sides by 0.15 to solve for s:
s ≥ 1200 / 0.15
s ≥ 8000
Therefore, Frank needs to have at least $8,000 in sales to make a minimum of $1,600 this week.
Which data set has a greater spread? Why? Set A: {38, 12, 23, 48, 55, 16, 18} Set B: {44, 13, 24, 12, 56} has a greater spread because .
Answer:
Set B has the greater spread
Step-by-step explanation:
Set B has the greater spread because if you add them all up they you will get a number higher than Set A.
Hope this helped :)
Answer:
Set B has a greater spread , because it has a higher IQR
Step-by-step explanation:
One way to measure the spread of a data set is to break it into quarters and measure the interquartile range (IQR).
Set A: {38, 12, 23, 48, 55, 16, 18}
(a) Sort the numbers
(12, 16, 18, 23, 38, 48, 55}
(b) First quartile
The median of 12, 16, and18 is 16.
First quartile = 16
(c) Third quartile
The median of 38, 48, and 55 is 48.
Third quartile = 48
(d) IQR
IQR = 48 - 16 = 32
Set B: {44, 13, 24, 12, 56}
(a) Sort the numbers
(12, 13, 24, 44, 56}
(b) First quartile
The median of 12 and 13 is 12.5.
First quartile = 12.5
(c) Third quartile
The median of 44 and 56 is 50.
Third quartile = 50
(d) IQR
IQR = 50 - 12.5 = 37.5
Set B has the greater spread, because it has the higher IQR.
The Box plot below shows that Set B has the greater spread.
How would I solve this? I have to find the length of T
Answer:
The length of T is [tex]4.2\ mi[/tex]
Step-by-step explanation:
we know that
If two triangles are similar, then the ratio of its corresponding sides is proportional
so
[tex]\frac{T}{9}=\frac{7}{15}\\ \\ T=9*7/15\\ \\T=4.2\ mi[/tex]
What is the estimate of forgive 6in by 4in
Find area of the semi circle.
The diameter is, half of that would be the radius, which is 3.
[tex]\frac{\pi \cdot 3^2}{2}[/tex] = 14.1
Find the area of the rectangle.
6 * 4 =24
Add the two areas together.
24 + 14.1 = 38.1
[tex]38.1in^2[/tex]
What is the approximate area of a circle shown below
Answer:
The answer to your question is 13.2
Step-by-step explanation:
To figure out the answer to this equation you have to multiply by pi or 3.14
Answer:
C. 55.4
Step-by-step explanation:
Formula: A = π • r²
A= 3.14 • 4.2²
4.2 • 4.2
17.64 • 3.14
A=55.3896
A=55.4
The sum of two integers is -4 can the two integers both be negative?
yeah. for instance, -2-2= -4
Answer:
Step-by-step explanation:
help ASAP plzzzzzzzzzzzzzzzzzzzzz!
Answer:
The answer is B (the indices are the same).
Which number line shows the solution set for |p-3| = 9
Answer:
Second Option
[tex]p = -6[/tex] and [tex]p = 12[/tex]
Step-by-step explanation:
The absolute value is a function that transforms any value x into a positive number.
Therefore, for the function [tex]f(x) = |x|[/tex] x> 0 for all real numbers.
Then the equation:
[tex]|p-3| = 9[/tex] has two cases
[tex](p-3) = 9[/tex] if [tex]h > 3[/tex] (i)
[tex]-(p-3) = 9[/tex] if [tex]h < 3[/tex] (ii)
We solve the case (i)
[tex]p = 9 + 3\\p = 12[/tex]
We solve the case (ii)
[tex]-p +3 = 9\\p = 3-9\\p = -6[/tex]
Then the solution is:
[tex]p = -6[/tex] or [tex]p = 12[/tex]
Two lines, C and D, are represented by the equations given below:
Line C: y = x + 10
Line D: y = 3x + 2
Which of the following shows the solution to the system of equations and explains why?
Answer:
x=4
y=14
Step-by-step explanation:
1. Substitute y=x+10 into y=3x+2.
Start with the original equation.
y=3x+2
Let y=x+10.
x+10=3x+2
2. Solve for x in x+10=3x+2.
x=4
3. Substitute x=4 into y=x+10.
y=14
4. Therefore,
x=4
y=14
What is the answer to this math question?
The correct answer is:
C) 40°
50 POINTS! Show All Work!
Let the number of chickens = c.
Let the number of pigs = p.
A chicken has 1 head and 2 legs.
c number of chickens have c heads and 2c legs.
A pig has 1 head and 4 legs.
p number of pigs have p heads and 4p legs.
There are 40 heads.
Equation for heads:
c + p = 40
There are 110 legs.
Equation for legs:
2c + 4p = 110
System of equations:
c + p = 40
2c + 4p = 110
Solve the first equation of the system of equations for c:
c = 40 - p
Substitute 40 - p for c in the second equation:
2c + 4p = 110
2(40 - p) + 4p = 110
80 - 2p + 4p = 110
80 + 2p = 110
2p = 30
p = 15
Now substitute p = 15 in the first equation to find c.
c + p = 40
c + 15 = 40
c = 25
There are 25 chickens and 15 pigs.
Quick math help please
Answer:
C, A
Step-by-step explanation:
For the first question, just isolate p on the left side and then multiply everything by negative 1 (although it won't matter because it's a square root). Then just square root both sides for an answer of C.
For the second question, do the same thing, isolate the variable. Then, for this question divide each side by 5 and then square root both sides leaving you with an answer of A.
Which of the following statement are true ?
If you had to pick a answer chose between a or c
I would pick C that’s the answer
QUICK PLEASE solve for T
Let's do this step by step quickly!
#1. Multiply both sides by 10.
[tex]\fbox{-14x10=t}[/tex]
#2. Simplify -14 x 10 to -140.
[tex]\fbox{-140 = t}[/tex]
#3. Switch sides.
[tex]\fbox{t = -140}[/tex]
Done, [tex]\fbox{t = -140}[/tex].
Here is your answer
-140
REASON:
[tex]-14=\frac{t}{10}[/tex]
Multiply both sides by 10
[tex]-14×10= \frac{t}{10}[/tex]×10
-140=t
So, t= -140
HOPE IT IS USEFUL