Answers
Answer:
standard form: Ax + By = C
Slope-intercept form: y=mx+b
where m is the slope and b is the y intercept.
first lets put this into intercept form:
y=-5x+b
(4, 0) is the x intercept.)
To find what b is plug in the point 4, 0 for the x and y of the equation:
0=-5(4)+b
0=-20+b
20=b
b=20
Now that we have the slope, m, and the y intercept, b, we can make our equation
y=-5x+20
Now we need to transform this equation into standard form like so:
y=-5x+20
5x+y=20 - this is your answer
Step-by-step explanation:
Related Questions
Find the area of a right isosceles triangle with hypotenuse 10\sqrt{2}10
2 units
Answers
Answer:
A = 50 square units
Step-by-step explanation:
Right Triangles
A right triangle is identified because it has one internal angle of 90°.
The longest side is called hypotenuse and the other two sides are called legs. Being c the hypotenuse and a and b the legs, the Pythagora's theorem relates the with the equation:
[tex]c^2=a^2+b^2[/tex]
If the triangle is also isosceles, then both legs have the same measure or a=b:
[tex]c^2=a^2+a^2=2a^2[/tex]
Since we know the hypotenuse has a measure of 10\sqrt{2}:
[tex](10\sqrt{2})^2=2a^2[/tex]
Operating:
[tex]100*2=2a^2[/tex]
Dividing by 2:
[tex]a^2=100~~\Rightarrow a=\sqrt{100}[/tex]
a = 10 units
The area of the triangle is:
[tex]\displaystyle A=\frac{a.b}{2}[/tex]
[tex]\displaystyle A=\frac{10*10}{2}[/tex]
A = 50 square units
2. Mr Alison fill ups his car at the gas station. He also gets a car wash at the station and visits with the manager, Then he drives to the next town on buisness
Which graph did you not choose for exercise 1 and 2?
Answers
Answer:
Hmm graph 3, i think.
Step-by-step explanation:
Express 45% as a ratio in its simplest form.
Answers
Answer:
4:5 is the ratio in it simplest form
How do you do these questions?
Answers
I'll do the first problem to get you started.
Part (a)
We have a separable equation. Get the y term to the left side and then integrate to get
[tex]\frac{dy}{dt} = ky^{1+c}\\\\\frac{dy}{y^{1+c}} = kdt\\\\\displaystyle \int\frac{dy}{y^{1+c}} = \int kdt\\\\\displaystyle \int y^{-(1+c)}dy = \int kdt\\\\\displaystyle -\frac{1}{c}y^{-c} = kt+D\\\\\displaystyle -\frac{1}{c*y^{c}} = kt+D\\\\[/tex]
I'm using D as the integration constant rather than C since lowercase letter c was already taken.
Let's use initial condition that [tex]y(0) = y_0[/tex]. This means we'll plug in t = 0 and [tex]y = y_0[/tex]. After doing so, solve for D
[tex]\displaystyle -\frac{1}{c*y^{c}} = kt+D\\\\\displaystyle -\frac{1}{c*(y_0)^{c}} = k*0+D\\\\\displaystyle D = -\frac{1}{c*(y_0)^{c}}\\\\[/tex]
Let's plug that in and isolate y
[tex]\diplaystyle -\frac{1}{c}y^{-c} = kt+D\\\\\\\diplaystyle -\frac{1}{c}y^{-c} = kt-\frac{1}{c*(y_0)^{c}}\\\\\\\diplaystyle y^{-c} = -ckt+\frac{1}{(y_0)^{c}}\\\\\\\diplaystyle y^{-c} = \frac{1-c*(y_0)^{c}kt}{(y_0)^{c}}\\\\\\\diplaystyle \frac{1}{y^{c}} = \frac{1-c*(y_0)^{c}kt}{(y_0)^{c}}\\\\\\\diplaystyle y^{c} = \frac{(y_0)^{c}}{1-c*(y_0)^{c}kt}\\\\\\\diplaystyle y = \left(\frac{(y_0)^{c}}{1-c*(y_0)^{c}kt}\right)^{1/c}\\\\\\\diplaystyle y = \frac{y_0}{\left(1-c*(y_0)^{c}kt\right)^{1/c}}\\\\\\[/tex]
-------------------------
We end up with [tex]\displaystyle y(t) = \frac{y_0}{\left(1-c*(y_0)^{c}kt\right)^{1/c}}\\\\[/tex] as our final solution. There are likely other forms to express this equation.
========================================================
Part (b)
We want y(t) to approach positive infinity.
Based on the solution in part (a), this will happen when the denominator approaches 0 from the left.
So [tex]y(t) \to \infty[/tex] as [tex]1-c*(y_0)^{c}kt \to 0[/tex] in which we can effectively "solve" for t showing that [tex]t \to \frac{1}{c*(y_0)^{c}k}[/tex]
If we define [tex]T = \frac{1}{c*(y_0)^{c}k}[/tex] , then approaching T from the left side will have y(t) approach positive infinity.
This uppercase T value is doomsday. This the time value lowercase t approaches from the left when the population y(t) explodes to positive infinity.
Effectively t = T is the vertical asymptote.
========================================================
Part (c)
We're told that the initial condition is y(0) = 5 since at time 0, we have 5 rabbits. This means [tex]y_0 = 5[/tex]
Another fact we know is that y(3) = 35 because after three months, there are 35 rabbits.
Lastly, we know that c = 0.01 since the exponent of dy/dt = ky^(1.01) is 1.01; so we solve 1+c = 1.01 to get c = 0.01
We'll use y(3) = 35, c = 0.01 and [tex]y_0 = 5[/tex] to solve for k
Doing so leads to the following:
[tex]\displaystyle y(t) = \frac{y_0}{\left(1-c*(y_0)^{c}kt\right)^{1/c}}\\\\\\\displaystyle y(3) = \frac{5}{\left(1-0.01*(5)^{0.01}k*3\right)^{1/0.01}}\\\\\\\displaystyle 35 \approx \frac{5}{\left(1-0.0304867k\right)^{100}}\\\\\\\displaystyle 35\left(1-0.0304867k\right)^{100} \approx 5\\\\\\\displaystyle \left(1-0.0304867k\right)^{100} \approx \frac{1}{7}\\\\\\[/tex]
[tex]\displaystyle \left(1-0.0304867k\right)^{100} \approx 7^{-1}\\\\\\\displaystyle 1-0.0304867k \approx \left(7^{-1}\right)^{1/100}\\\\\\\displaystyle 1-0.0304867k \approx 7^{-0.01}\\\\\\\displaystyle k \approx \frac{7^{-0.01}-1}{-0.0304867}\\\\\\\displaystyle k \approx 0.63211155281122\\\\\\\displaystyle k \approx 0.632112\\\\\\[/tex]
We can now compute the doomsday time value
[tex]T = \frac{1}{c*(y_0)^c*k}\\\\\\T \approx \frac{1}{0.01*(5)^{0.01}*0.632112}\\\\\\T \approx \frac{1}{0.00642367758836}\\\\\\T \approx 155.674064621806\\\\\\T \approx 155.67\\\\\\[/tex]
The answer is approximately 155.67 months
18 ÷ x = -2
what is x PLEASE HELP FAST AS YOU CAN!!!!!!!!!!!!!!! I WILL GIVE BRAINLIEST TO WHOEVER ANSWERS FIRST AND CORRECTLY 10 POINTS!!!!!!!!!
Answers
Answer: x=-9
Step-by-step explanation:
18/x=-2
multiply x
18=-2x
divide by -2
-9=x
x=-9
Answer:
[tex]18 \div x = - 2 \\ \frac{18}{x} = - 2 \\ x = \frac{18}{ (- 2)} \\ \boxed{x = - 9}[/tex]
-9 is the right answerWhich of the following is an equation of a proportional relationship?
Group of answer choices
y = 25x
y = 5x + 25
Describe what the equation you chose above could represent. In other words, what real-world situation could this equation be used?
Answers
Answer:
Both are proportional, because as the value of x change (increases or decreases), the value of y changes (increases or decreases).
The first equation (y = 25x) could represent that amount of teachers per students. If x = teachers (let's say there is 1 teacher), then y = students (1 teacher would teach a class of 25 students).
The second equation (y = 5x + 25) could represent the amount of money you could earn babysitting. The starting/base amount would be $25, and you would earn $5 more for every hour you babysat.
Step-by-step explanation:
an arts academy requires there to be 6 teachers for every 132 students and 3 tutors for every 27 students . how many students does the academy have per teacher ? per tutor ? how many tutors does the academy need if it has 72 students ?
Answers
Answer:
3
Step-by-step explanation:
The number of necessary tutors when you divide 27 into 72, is 2.6; therefore the necessary number of tutors is 3 because you can’t have .6 of a tutor. Hope this helps!
Johnny made 8 benches in 2 hours. At this rate, how
many benches will he make in 9 hours.
plzzzzzzzzzz!!!!!!!! help on thissss
Answers
Answer:
36
Step-by-step explanation:
4 benches in 1 hour
? benches in 9 hours
36 benches
HOPE THIS HELPS
PLZZ MARK BRAINLIEST
Answer:
36 is the answer :)
Step-by-step explanation:
producto de (10x+7)(10x-7)
Answers
Answer:
(10x−7)^2
Step-by-step explanation:
(10x+7)(10x-7)
i stead of making it a "100" since they are both the same but positive and negative () and bring it to the power of 2
1,682 inches rounded to the narest tenth is 1.6 inches?
Answers
Answer:
yes
Step-by-step explanation:
Souvenir hats, t-shirts, and jackets are sold at a rock concert. Two hats, two t-shirts, and one jacket cost $141. Three hats, three t-shirts, and two jackets cost $239. One hat, three t-shirts, and three jackets cost $262. Find the prices of the individual items.
Answers
Answer:
Step-by-step explanation:
jjkk[
(-3,6] to inequality
Answers
Answer:
-3 < x ≤ 6
Step-by-step explanation:
Left side is exclusive, right side is inclusive, hence the < and ≤, respectively.
Vance used the associative property to write (4.5 m + StartFraction 7 Over 8 EndFraction) minus 9 as the equivalent expression 4.5 m (StartFraction 7 Over 8 EndFraction minus 9). Did Vance apply the associative property correctly? Why or why not?
Yes, the terms with variables should be written first.
Yes, the terms can be regrouped and still be equivalent.
No, the order of the terms should have been changed.
No, the addition symbol was dropped in the second expression.
Answers
Answer: D
Step-by-step explanation:
No, the addition symbol was dropped in the second expression is not correct.
What is Expression?An expression is combination of variables, numbers and operators.
No, Vance did not apply the associative property correctly.
The associative property states that the grouping of terms in an expression can be changed without affecting the value of the expression.
However, in this case, Vance changed the order of the terms, but did not actually group them in a different way.
Additionally, Vance dropped the subtraction symbol in the second expression, which is incorrect.
The correct equivalent expression using the associative property would be:
(4.5 m + 7/8) - 9 = 4.5 m + (7/8 - 9)
From there, we could simplify the expression further, if needed.
Hence, No, the addition symbol was dropped in the second expression.
To learn more on Expressions click:
https://brainly.com/question/14083225
#SPJ3
If line lis parallel to line m, find the value of x and y. (please help taking a test)
(7x + 12)
(12x - 28)
(9y - 77)"
O x = 10.3 and y = 17.9
O x = 8 and y = 21
O x = 7 and y = 12
x = 12 and y = 7
Answers
Answer:
x=8 and y=21
Step-by-step explanation:
12x-28=7x+12 (the 2 angles are equivalent)
12x-7x=12+28
5x=40
x=8
9y-77 + 12x-28 =180 (the sum of those 2 angles is a flat angle (180°))
9y-77+12*8-28=180
9y=180+28+77-96
9y=189
y=21
Are the two hearts congruent? How do you know?
Answers
Answer:
yes they are congruent
Step-by-step explanation:
they both the same shape and size
4598÷101 =? write your answer as a whole number and remainder
Answers
Answer:
45 R53
Step-by-step explanation:
Hope This Helps
Solve for x in this equation: 3/4+|5-x| = 13/4
step 1: 3/4
step 2: -5/2
step 3: 5-x= 5/2
step 4: 5
step 5: 5/2
I just did the equation on edgeinuity 2020
Answers
Answer: X =5/2, 15/2 x=2.5, 7.5
Step-by-step explanation:
Can anyone show me how to figure this out.
Answers
Answer:
Option A (5, 0)
Step-by-step explanation:
Step 1: Determine what is a solution
To find a solution of two lines, it has to be in the area where both of the colors intersect. As you can see the red line goes up and the blue line goes down, but there is a shaded region where there is just white, just blue, just red, and the red and blue. The shaded region where both red and blue is, that is where the solutions are.
(5, 0) -> This means that the x-value is 5 and the y-value is 0 meaning that it is in the area where there is both red and blue.
(1, -3) -> This means that the x-value is 1 and the y-value is -3 meaning that it is in the area where there is only red.
(3, 3) -> This means that the x-value is 3 and the y-value is 3 meaning that it is in the area where there is only blue.
(2, 1) -> This means that the x-value is 2 and the y-value is 1 meaning that it is in the area where there is only blue.
Answer: Option A (5, 0)
Find the area of this
Answers
Answer:
616
Step-by-step explanation:
A fashion designer wants to know how many new dresses women buy each year. Assume a previous study found the variance to be 2.89. She thinks the mean is 5.6 dresses per year. What is the minimum sample size required to ensure that the estimate has an error of at most 0.11 at the 98% level of confidence?
Answers
Answer:
The minimum sample required = 1296.65
Step-by-step explanation:
Given that:
Variance [tex]\sigma^2 = 2.89[/tex]
Standard deviation [tex]\sigma = \sqrt{2.89}[/tex]
Standard deviation [tex]\sigma = 1.7[/tex]
Margin of error = 0.11
Confidence Interval = 98%
Level of significance = 1 - 0.98 = 0.02
The critical value = [tex]Z _{\alpha//2} = Z_{0.02/2} = Z_{0.01}[/tex]
= 2.33
Thus, the minimum sample size is given by the formula:
[tex]n = \bigg ( \dfrac{Z_{\alpha/2} \times \sigma }{E} \bigg)^2[/tex]
[tex]n = \bigg (\dfrac{2.33 \times 1.7 }{0.11} \bigg)^2[/tex]
n = 1296.65
What is the product of = 4/9 and 1/11?
4/99
5/99
9/44
1/4
Answers
4/9 and 1/11
product means multiplying
4 times 1
4*1=4
9 times 11
9*11=99
answer: 4/99
8y-2x=-72 in slope form
Answers
Answer:
y=1/4x-9
Step-by-step explanation:
Slope-intercept form is y=mx+b.
8y-2x=-72
Add 2x to both sides
8y=2x-72
Divide both sides by 8.
y=1/4x-9
HTH :)
Carmen is an engineer making plans to run a rail line, represented by the transversal t, through a city. Parallel lines v and w are crossed by transversal t. Clockwise from top left, the angles formed with line v are 155 degrees, blank, blank, blank; with line w are 1, 2, 3, 4. Examine Carmen’s rail plans to identify the measure of ∠1. The streets represented by lines V and W are parallel. What is the mAngle1? 25° 35° 145° 155°
Answers
Answer:
155
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
I took the quiz
Been trying to get this one answered for months, will make the first one to answer a brainliest :D Please explain how you did it so I can do the next one? Thanks in advance
Answers
Answer:
[tex]\frac{2}{7}[/tex]
Step-by-step explanation:
In order to find the slope of a line you must find where the points intersect, use the formula for slope, substitute values, and simplify if needed.
In this case we were already given the points for slope:
[tex]P1=(-4,-4) = (x1,y1)[/tex]
[tex]P2=(-2,3)=(x2,y2)[/tex]
Slope formula:
[tex]slope = \frac{y2-y1}{x2-x1}[/tex]
Now substitute:
[tex]\frac{-2--4}{3--4}[/tex]
Solve using KCC: (Keep, Change, Change)
[tex]-2+4=2[/tex]
[tex]3+4=7[/tex]
=[tex]\frac{2}{7}[/tex]
Because the slope isn't a negative you do not need to simplify the answer.
Hope this helps.
PLEASE HELP OMG calculate the slope of the graph below at the point (-1,5)
f(x) = x^5 + 1/x^3 +7
Answers
Answer:
The slope of the graph at x=-1 is 2
Step-by-step explanation:
Instant rate of change
Given a real function f(x), the instant rate of change with respect to x is defined as the derivative of f which coincides with the instant value of the slope of the tangent line in the point (x,y).
We have the function:
[tex]\displaystyle f(x) = x^5+\frac{1}{x^3}+7[/tex]
Prepare the function to apply the power rule of the derivative:
[tex]\displaystyle f(x) = x^5+x^{-3}+7[/tex]
Recall the power rule:
[tex](x^n)' = nx^{n-1}[/tex]
Also, the derivative of a constant is zero.
Taking the derivative:
[tex]\displaystyle f'(x) = 5x^4-3x^{-4}[/tex]
Evaluating for x=-1:
[tex]\displaystyle f'(-1) = 5(-1)^4-3(-1)^{-4}[/tex]
[tex]\displaystyle f'(-1) = 5*1-3*1=2[/tex]
The slope of the graph at x=-1 is 2
Garrett reflects points A and B across the y-axis to make the images of the points A' and B'. If the distance between points A and B is 10 units, what is the distance between points A' and B'? Explain your answer.
Answers
Answer:
A'B' = AB = 10Step-by-step explanation:
Reflection of points across y-axis doesn't change the distance between the points so AB = A'B' = 10 units
Let the coordinates be:
A = (x1, y1) and B(x2, y2)Reflection:
A'= (-x1, y1) and B(-x2, y2) as per ruleLets compare distances:
AB = √(x2-x1)² + (y2 - y1)²and
A'B' = √(-x2 - (-x1))² + (y2 - y1)² = √(-(x2 - x1))² + (y2-y1)² = √(x2-x1)² + (y2 - y1)²As we see the results are same
Answer:
Reflection of points across y-axis doesn't change the distance between the points so AB = A'B' = 10 units
Step-by-step explanation:
ADD NOTE
QUESTION GUIDE
EXIT TEST
6.
Raul spent 2
hours shopping for new clothes on Saturday,
1
O
Raul spent
hours shopping for shoes.
10
3
• He spent hour shopping for pants
2
• He spent
hour shopping for shirts
3
• He spent the rest of the time shopping for shoes
о
Raul spent
5
7
hours shopping for pants and shirts.
Raul spent the same amount of time shopping for shoes
as he spent shopping for pants.
O
Based on this information, which statement is true?
о
1
Raul spent
hours more time shopping for shoes than
6
he spent shopping for shirts.
e
CLEAR ALL
Answers
Answer:
D. Raul spent the same amount of time shopping for shoes as he spent shopping for pants
Step-by-step explanation:
just trust me :)
Easy Car Corp. is a grocery store located in the Southwest. It paid an annual dividend of $2.00 last year to its shareholders and plans to increase the dividend annually at the rate of 4.0%. It currently has 2,000,000 common shares outstanding. The shares currently sell for $13 each. Easy Car Corp. also has 30,000 semiannual bonds outstanding with a coupon rate of 10%, a maturity of 23 years, and a par value of $1,000. The bonds currently have a yield to maturity (YTM) of 8%. What is the weighted average cost of capital (WACC) for Easy Car Corp. if the corporate tax rate is 30%?
When answering this problem enter your answer using percentage notation but do not use the % symbol and use two decimals (rounding). For example, if your answer is 0.10469 then enter 10.47; if your answer is 10% then enter 10.00
Answer:_____
Answers
Answer:
Since the instruction in the question indicates that the % symbol should not be used, the weighted average cost of capital (WACC) for Easy Car Corp is therefore 12.07.
Step-by-step explanation:
This can be calculated using the following steps:
Step 1: Calculation of the current bond price
Semiannual coupon amount = Bond face value * Semiannual coupon rate = $1000 * (10% / 2) = $50
Semiannual coupon discount factor = ((1 - (1 / (1 + r))^n) / r) .......... (1)
Where;
r = Semiannual yield to maturity (YTM) = 8% / 2 = 0.08 / 2 = 0.04
n = number of semiannuals = 23 years * 2 = 46
Substituting the values into equation (1), we have:
Semiannual coupon discount factor = ((1-(1/(1 + 0.04))^46) / 0.04) = 20.8846535613106
Present value of coupon = (Semiannual coupon amount * Semiannual coupon discount factor) = $50 * 20.8846535613106 = $1,044.23
Present value of the face value of the bond = Face value / (1 + r)^n = $1,000 / (1 + 0.04)^46 = $164.61
Therefore, we have:
Current bond price = Present value coupon + Present value of the face value of the bond = $1,044.23 + $164.61 = $1,208.84
Step 2: Calculation of weights of each finance source
Market value of common shares outstanding = Number common shares outstanding * Current price per share = 2,000,000 * $13 = $26,000,000.
Market value of bond = Number of bonds * Current bond price = 30,000 * $1,208.84 = $36,265,200
Total financing market value = Market value of common shares outstanding + Market value of bond = $26,000,000 + $36,265,200 = $62,265,200
Weight of Market value of common shares outstanding = Market value of common shares outstanding / Total financing market value = $26,000,000 / $62,265,200 = 0.42
Weight of Market value of bond = Market value of bond / Total financing market value = $36,265,200 / $62,265,200 = 0.58
Step 3: Calculation of return on equity
Current year dividend = Last year dividend * (1 + Dividend growth rate) = $2 * (1 + 4.0%) = $2.08
Next year dividend = Current year dividend * (1 + Dividend growth rate) = $2.08 * (1 + 4.0%) = $2.1632
The return on equity can now be calculated using the following formula:
Current share price = Next year dividend / (Return on equity – Dividend growth rate) ………………….. (2)
Where;
Current share price = $13
Next year dividend = $2.1632
Return on equity = ?
Dividend growth rate = 4.0%, or 0.04
Substituting the values into equation (2) and solve for return on equity, we have:
13 = 2.1632 / (Return on equity - 0.04)
13 * (Return on equity - 0.04) = 2.1632
(13 * Return on equity) – (13 * 0.04) = 2.1632
(13 * Return on equity) – 0.52 = 2.1632
13 * Return on equity = 2.1632 + 0.52
Return on equity = 2.6832 / 13
Return on equity = 0.21
Step 4: Calculation of Weighted average cost of capital
Weighted average cost of capital = (WS * CE) + (WD * CD * (1 – T)) ………………… (4)
Where;
WS = Weight of Market value of common shares outstanding = 0.42
WD = Weight of debt = Weight of Market value of bond = 0.58
CE = Cost of equity = Return on equity = 0.21
CD = Cost of debt = YTM = 8%, or 0.08
T = Tax rate = 30%, or 0.30
Substituting the values into equation (3), we have:
Weighted average cost of capital = (0.42 * 0.21) + (0.58 * 0.08 * (1 - 0.30)) = 0.12068, or 12.068%
Rounding to two decimal places, we have:
Weighted average cost of capital = 12.07%
Since the instruction in the question indicates that the % symbol should not be used, the weighted average cost of capital (WACC) for Easy Car Corp is therefore 12.07.
Brittany buys 2.55 pounds of turkey for $5.96 per pound and 3.7 pounds of
cheese for $3.35 per pound. She gave the clerk twenty dollars. How much
more money does Brittany need? Include your units.
Answers
Answer:
Brittany needs another $3.7405.
Step-by-step explanation:
Per pound Cost of turkey = $5.96 per pound
The amount Brittany buys the turkey = 2.55 pounds
Brittany's cost for turkey = 2.55 × $5.96 = $15.198
Per pound cost for cheese = $3.35 per pound
The amount Brittany buys the cheese = 3.7 pounds
Brittany's cost for cheese = 2.55 × $3.35 = $8.5425
So,
Brittany's total cost = Turkey cost + Cheese cost
= $15.198 + $8.5425
= $23.7405
As brittany gave the clerk 20 dollars.
So, the amount she further needs will be:
$23.7405 - $20 = $3.7405
Therefore, Brittany needs another $3.7405.
If the temperature changes - 5/8 degrees per hour for 8 hours, what is the total change in temperature?
Answers
Answer:
I think it is 5.
Step-by-step explanation:
5/8 in decimal form is 0.625. 0.625 x 8 = 5. I hope this helps/ sorry if it didn't.