Step-by-step explanation:
FV = PV ( 1 + i)^n FV = future value ....what you are looking for
PV = present value = $ 6000
i = decimal periodic interest = .07/12
n = periods = 5 yr * 12 monts/yr = 60 periods
FV = $ 6000 ( 1 + .07/12)^60 = $ 8505.75
for each situation, determine taxable income, assuming pretax accounting income is $100 million
Answer:
Temporary Differences Reported First on: The Income Statement The Tax Return Revenue Expense Revenue Expense1) $272) $273) $274) $275) $22 $276) $27 $227) $22 $27 $178) $22 $27 $12 $17Taxable Income assuming pretax accounting income is $100 million1) Pretax Income - Revenue = $100m - $27m = $73m2) Pretax Income + Expense = $100m + $27m = $127m3) Pretax Income + Revenue Return = $100m + $27m = $127m4) Pretax Income - Expense Return = $100m - $27m = $73m5) Pretax Income - Revenue + Expense = $100m - $22m + $27m = $105m6) Pretax Income + Expense + Revenue Return = $100m + $27m + $22m = $149m7) Pretax Income - Revenue + Expense - Expense Return = $100m - $22m + $27m - $17m = $88m8) Pretax Income - Revenue + Expense + Revenue Return - Expense Return = $100m - $22m + $27m + $12m- $17m = $100m
Step-by-step explanation:
First, return is added to differentiate revenue and expense from the tax return from that of the income statement.Temporary difference is defined as the difference between the tax and financial reporting bases of assets and liabilities. These differences can result in taxable or deductible amounts in future years (deferred tax assets or liabilities).For each scenario, temporal difference of revenue reported first in the income statement is deducted from the pretax accounting income while expenses are added back to the pretax accounting income.For temporal differences from the tax return, the revenue is added to the pretax accounting income while expenses are deducted.
Researchers comparing the effectiveness of two pain medications randomly selected a group of patients who had been complaining of a certain kind of joint pain. They randomly divided these people into two groups, then administered the pain killers. Of the 112 people in the group who received medication A, 84 said this pain reliever was effective. Of the 108 people in the other group, 66 reported that pain reliever B was effective.
(a)Find a 95% confidence interval for the difference in the proportions of people who may find these medications effective. Interpret your interval.
(b) Does this interval contain zero? What does that mean for the hypothesis test of the difference in proportions?
(a) The 95% confidence interval for the difference in proportions of people who may find these medications effective is 0.029 to 0.231, which suggests that medication A is more effective than medication B in relieving joint pain.
(b) No, the interval does not contain zero, which means that the difference in proportions is statistically significant and supports the hypothesis that medication A is more effective than medication B.
Use the distributive property to solve 4 2/5 x 10. Where 4 2/5 is a fraction. Please show work so I can explain. Thank you.
Answer:
Step-by-step explanation:it will be 44/1 = 44
Since 4 2/5 x 10
We will use 10 as 10/1
and 4 2/5 as 22/5 so
22/5 x 10/1 we cross out the 5 and 10 since there a factor of each other
then it will be 22/1 x 2/1 it will be much easier
Then 22 x 2 = 44
1x1 = 1
=44/1 = 44
Ice cream is packaged in cylindrical gallon tubs. A tub of ice cream has a total surface area of 183.69 square inches.
If the diameter of the tub is 6 inches, what is its height? Use π = 3.14.
A 2.25 inches
B 4.5 inches
C 6.75 inches
D 12.75 inches
Answer:
6.75 inches.
Step-by-step explanation:
[tex]183.69 = 2*3.14*3^2 + 2*3.14*3*h[/tex]
[tex]= 56.52 + 18.84h[/tex]
[tex]183.69 - 56.52 = 18.84h[/tex]
[tex]127.17 = 18.84h[/tex]
[tex]=\frac{127.17}{18.84}[/tex]
[tex]=6.75[/tex]
11). Evaluate the definite integral.
The value of the definite integral is determined as -1/28.
What is a definite integral?A definite integral is a mathematical concept that represents the area under a curve between two specific points, called the limits of integration. The definite integral is denoted by the symbol ∫, and the limits of integration are written as a and b, where a is the lower limit and b is the upper limit.
To evaluate the definite integral, we will use the following method:
[tex]\int\limits^2_0 {- \frac{6x}{(3x + 2)^2} } \, dx ; u = 3x^2 + 2[/tex]
We can start by substituting [tex]$u=3x^2+2$[/tex], which gives us [tex]$du/dx=6x$[/tex], or [tex]$x,dx=du/6$[/tex].
Using this substitution, we can rewrite the integral as:
[tex]\int\limits^2_0 - \frac{6x}{(3x^2 + 2)^2} , dx &\\\\\\\=\ \int\limits^{u(2)}{u(0)} -\frac{1}{u^2},du/6\\\\\\&= \left[ \frac{1}{6u} \right]^{u(2)}{u(0)} \\\\\\&= \frac{1}{6}\left(\frac{1}{u(2)} - \frac{1}{u(0)}\right)\\\\\\\&= \frac{1}{6}\left(\frac{1}{3(2)^2 + 2} - \frac{1}{3(0)^2 + 2}\right) \\\\\\\&= \frac{1}{6}\left(\frac{1}{14} - \frac{1}{2}\right)\\\\\\\ &= \frac{1}{6}\left(-\frac{6}{28}\right) \\\\\\\\&= \boxed{-\frac{1}{28}}\end{align*}[/tex]
Learn more about definite integral here: https://brainly.com/question/31166438
#SPJ1
A rectangular box has a length that is 4 feet longer than its width, w.
Write an algebraic expression, in simpliest form, to find the perimeter of the box.
Step-by-step explanation:
The length of the rectangle is 4 feet longer than its width w, which means the length is w + 4
The perimeter of a rectangle is the sum of the lengths of all four sides which can be expressed as:
Perimeter = 2(length + width)
Substituting w + 4 for length and w for width, we get:
Permiter = 2(w + 4 + w)
Simplifying this expression, we get:
Perimeter = 2(2w + 4)
Perimeter = 4w + 8
Therefore, the algebraic expression to find the perimeter of the rectangular box is 4w + 8
The gasoline gauge on a van initially read
1/4 full. When 12 gallons were added to the tank, the gauge read 3/4 full. How many more gallons are needed to fill the tank?
Initially, 1/4 of the tank was filled.
After adding 12 gallons, it was 3/4 full.
Increase in fuel filled portion =
[tex]\dfrac{3}{4} -\dfrac{1}{4} =\dfrac{3-1}{4} =\dfrac{2}{4}[/tex]
So 2/4 of the tank = 12 gallons
1/4 of tank [tex]= 12 \div 2 = 6[/tex] gallons
4/4 of tank [tex]= 6\times4 = 24[/tex] gallons
____________________
Portion remaining to be filled =
[tex]1-\dfrac{3}{4} =\dfrac{4-3}{4} =\dfrac{1}{4}[/tex]
Fuel needed [tex]= \dfrac{1}{4} \times 24 = 6[/tex] gallons
So you need 6 more gallons to fill the tank
(-8)-(-2) porfa lo necesito
Answer:
-6
Step-by-step explanation:
Henderson's Hardware has an ROA of 12%, a 8% profit margin, and an ROE of 19%. What is its total assets turnover? Do not round intermediate calculations. Round your answer to two decimal places. What is its equity multiplier? Do not round intermediate calculations. Round your answer to two decimal places.
Answer: We can use the DuPont Model to calculate the total assets turnover and equity multiplier:
ROE = ROA × Equity Multiplier
Equity Multiplier = Total Assets / Total Equity
Profit Margin = Net Income / Sales
Total Assets Turnover = Sales / Total Assets
Given:
ROA = 12%
Profit Margin = 8%
ROE = 19%
To find the Total Assets Turnover:
Profit Margin = Net Income / Sales
0.08 = Net Income / Sales
Net Income = 0.08 x Sales
ROA = 12%
ROA = Net Income / Total Assets
0.12 = 0.08 x Sales / Total Assets
Total Assets Turnover = Sales / Total Assets = 0.08 / 0.12 = 0.67
Therefore, the total assets turnover is 0.67.
To find the Equity Multiplier:
ROE = ROA x Equity Multiplier
0.19 = 0.12 x Equity Multiplier
Equity Multiplier = 0.19 / 0.12 = 1.58
Therefore, the equity multiplier is 1.58.
Note: The total assets turnover and equity multiplier are related to each other through the DuPont model. The product of these two ratios should be equal to the ROE. In this case, 0.67 x 1.58 = 1.06, which is approximately equal to 1.9 (ROE in decimal form). This confirms that our calculations are correct.
Step-by-step explanation:
A quadratic function passes through the points (-2,5) and (-8,5) and has a graph in the xy-plane that opens downward. Which of these could be the coordinates of the highest point of the graph?
O (5, 1)
O (5, 8)
O (5, 1)
O (5, 8)
The highest point of the quadratic equation that opens down can be (-5, 8)
Which of these could be the coordinates of the highest point of the graph?We have a quadratic equation whose graph opens downwards, and we know that it also passes through the points (-2,5) and (-8, 5).
The highest point will be of the form (x, y).
Such that y is larger than 5, and the value of x is right between the two values above:
x = (-2 - 8)/2
x = -5
So the point is of the form (-5, y) where again y > 5.
From the given options the only of this form is (-5, 8)
Learn more about quadratic equations at:
https://brainly.com/question/1214333
#SPJ1
To amend a country’s constitution, 7/9 of the 84 states in that country must approve the amendment. If 66 states approve the amendment, will the constitution be amended?
Answer:
Since only 66 states approve the amendment, it falls short of the required 7/9 majority. Therefore, the constitution will not be amended.
Step-by-step explanation:
To determine whether the constitution will be amended, we need to compare the number of states that have approved the amendment to the required number of states needed for approval.
The requirement is that 7/9 of the 84 states must approve the amendment. So, we need to calculate 7/9 of 84 to find out how many states need to approve the amendment:
(7/9) x 84 = 66.67
Rounding up, we see that 66.67 is equivalent to 67 states. This means that in order for the amendment to be approved, at least 67 states must approve it.
Since only 66 states approve the amendment, it falls short of the required 7/9 majority. Therefore, the constitution will not be amended.
Factor by substitution: (3y−2)2−(3y−2)−2.
The simplification of the polynomial using factor by substitution is: ((3y - 2)⁴ - 1)/(3y - 2)²
How to factor Polynomial by substitution?Factoring polynomials simply means separating a polynomial into its component polynomials.
Sometimes, in the event that polynomials are particularly complicated, it is usually easiest to substitute a simple term and factor down.
We have the equation:
(3y - 2)² - (3y - 2)⁻²
Let 3y - 2 be denoted by S and as such we have:
S² - S⁻²
= S² - 1/S²
Using the denominator as factor, we have:
= (S⁴ - 1)/S²
Plugging 3y - 2 for S gives us:
((3y - 2)⁴ - 1)/(3y - 2)²
Read more about Polynomial at: https://brainly.com/question/17517586
#SPJ1
If 9x+10=20
, what is the value of 18x+1
?
Answer:
21
Step-by-step explanation:
9x + 10 = 20
9x = 10
x = 10/9
What is the value of 18x + 1?
18(10/9) + 1
= 20 + 1
= 21
So, the value of 18x + 1 is 21
Question 7 of 10
AFGH is a right triangle.
9
6
G
√45
H
A. True
OB. False
Yes, it is true that Triangle FGH is a right triangle.
How can this be determined?We check whether the Pythagorean theorem holds true for these sides to determine if this triangle is a right triangle. According to the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the squares of the right triangle's legs.
a² + b² = c²
If this is a right triangle, the hypotenuse will be the longest side, and the other two sides will be the legs. We have these when we incorporate the Pythagorean theorem.
6²+(√45)² = 9²
36+45 = 81
which implies that right triangle because the assertion is true.
Learn more about right triangle at:
https://brainly.com/question/2217700
#SPJ1
A researcher is studying life Expectancy in different parts of the world. Using birth and death records, she randomly select a sample of 20 people from town A and a sample of 20 people from town B and record their lifespan in years.
The researcher wants to test the claim that there is a significant difference in life span for people in the two towns. What are the Noel and alternative hypotheses that should be used to test this claim?
Please see photo below for the options of answer , thank you!
Answer:
Null Hypothesis (H0): There is no significant difference in life span for people in the two towns.
Alternative Hypothesis (H1): There is a significant difference in life span for people in the two towns.
Answer:
The null and alternative hypotheses that should be used to test this claim are:
Null hypothesis: There is no significant difference in lifespan for people in the two towns. Symbolically, this can be represented as H0: μ1 = μ2, where μ1 and μ2 are the population mean lifespans of Town A and Town B, respectively.
Alternative hypothesis: There is a significant difference in lifespan for people in the two towns. Symbolically, this can be represented as Ha: μ1 ≠ μ2.
To test this claim, the researcher can conduct a two-sample t-test using the data collected from the two towns. The test statistic can be calculated as:
t = (x1 - x2) / (s1^2/n1 + s2^2/n2)^0.5
where x1 and x2 are the sample mean lifespans of Town A and Town B, respectively, s1 and s2 are the sample standard deviations of Town A and Town B, respectively, and n1 and n2 are the sample sizes of Town A and Town B, respectively.
Using the given data, the test statistic can be calculated as:
t = (78.5 - 74.4) / (11.2^2/20 + 12.3^2/20)^0.5 = 1.02
At a significance level of 0.05 with 38 degrees of freedom (df = n1 + n2 - 2), the critical value for a two-tailed test is ±2.024. Since the calculated t-value (1.02) falls within the acceptance region (-2.024 < t < 2.024), the null hypothesis cannot be rejected. Therefore, we do not have enough evidence to conclude that there is a significant difference in lifespan for people in the two towns.
Step-by-step explanation:
hope its help <:
Helppopppppppppppp image below
The value of angle Y (m∠Y) in the given parallelogram is determined as 112⁰.
What is the value of angle Y?The value of angle Y is determined by applying the principle of a quadrilateral for the given parallelogram as shown below.
The adjacent angles of a parallelogram are supplementary, that is they add up to 180 degrees, while the opposite angles are equal or congruent.
From the given diagram angle W = angle Y (opposite angles)
angle W + angle Z = 180 (adjacent angles )
angle W = 180 - angle Z
angle W = 180 - 68
angle W = 112
Therefore, angle Y (m∠Y) = 112⁰.
Learn more about opposite angles of parallelogram here: brainly.com/question/20526916
#SPJ1
Alan is going to sell eggs to a local market. Unfortunately, he dropped the box with the eggs and broke them all. He needs to figure out how many eggs he broke, but he forgot the exact number. This is what he does remember:
When he put all his eggs in groups of 2, one egg was left over.
When he put all his eggs in groups of 3, one egg was left over.
When he put all his eggs in groups of 4, one egg was left over.
When he put all his eggs in groups of 5, no eggs were left over.
How many eggs did he have before he broke them? Is there more than one answer? How do you know?
This is for extra credit and i need them. :) PLEASE
Step-by-step explanation:
It is an ODD number due to statement 1
it is a multiple of 5 due to the last statement
5 15 25 35 45 55 65 75 85 95 105 .....
When you divide by 3 there is a R 1
25 55 85 115 145
When you divide by 4 there is a R = 1
25 is the lowest number next possible number is 145 then another posssible is 265 etc
88.128 x 0.5 Multiplication question
Answer:
44.064x
Step-by-step explanation:
Answer: when you time 88.128 by 0.5, it gives you an answer of 44.064
Hope this helps :)
i’m begging can someone PLEASE help and hurry i have to turn this in soon
Given the diagram above, which is a combination of three right triangles,
27) m∠DGE = 45°
28) m∠EDG = 85°
29) FD = 10
30) GD = 14
31) EG = 19.
What is the explanation for the above answers?27) m∠DGE = 45°
This is because m∠DGE is an alternate angle to m∠BAD which is = 45°. Recall that alternate angles are congruent.
28) m∠EDG = 85° because it is the vertical opposite of ∠ADC. Note that ∠ADC = 180 - 45 - 50
= 85°
29) and 30)
Given FG=10 and m∠DGE=45°,
FD = √DG² - FG²
Since we don't have FD
We use Cos Rule
GD = FG/cos(α)
GD = 10/Cos 45°
GD = 14.1421356237
GD [tex]\approx\[/tex] 14
Thus,
FD = √14.1421356237312 - 102
FD = √100
FD = 10
31)
EG = EF + 10
EF = √(GD² - FG²
EF = √(14² - 10²)
EF = √80.982478588641
EF = 8.99903
Hence,
EG = 8.99903 + 10
EG [tex]\approx[/tex] 19
Learn more about right triangles at:
https://brainly.com/question/30966657
#SPJ1
Of the 40 learners in the class, 12 walks to school, twice the number who walk, come by car or taxi and the remainder cycle to school. What fraction does not cycle to school? Answer must be simplest form.
The fraction of learners who do not cycle to school is equal to 9/10.
How to evaluate for the fraction of learners.Given that the total number of learners is 40, 12 of which walk to school and twice of the number of learners who walk, come to school by car or taxi, then the remainder of learners who cycle to school is calculated as;
40 - [12 +2(12)] = 4
The number of learners who do not cycle to school is;
12 + 2(12) = 36
fraction of learners who do not cycle to school = 36/40
by simplification;
fraction of learners who do not cycle to school = 9/10.
Therefore, the fraction of learners who do not cycle to school is equal to 9/10.
Know more about fraction here:https://brainly.com/question/1622425
#SPJ1
a rocket is launched from the top of a 30 foot cliff with an initial velocity of 170 feet per second. the height, h, of the rocket after t seconds is given by the equation h=-16t^2+170t+30. How long after the rocket is launched will it be 20 feet from the ground?
However, we need to choose the positive value for t, since time cannot equation be negative in this case. Therefore, the rocket will be 20 feet from the ground approximately 1.411 seconds after it is launched.
What is equation?An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the value "9." The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "x2 + 2x - 3 = 0." Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.
So we have:
[tex]-16t^2 + 170t + 30 = 20\\-16t^2 + 170t + 10 = 0\\8t^2 - 85t - 5 = 0\\t = (-b + \sqrt(b^2 - 4ac)) / 2a\\t = (-(-85) + \sqrt((-85)^2 - 4(8)(-5))) / 2(8)\\t = (85 + \sqrt(7225 + 160)) / 16\\t = (85 + \sqrt(7385)) / 16[/tex]
However, we need to choose the positive value for t, since time cannot be negative in this case. Therefore, the rocket will be 20 feet from the ground approximately 1.411 seconds after it is launched.
To know more about equation visit:
https://brainly.com/question/649785
#SPJ1
Determine whether the triangles can be proved similar. If they are similar, write a similarity statement. If they are not similar, explain why.
i’ll give brainlist
In response to the stated question, we may state that As a result, we can triangle only state that angle A is congruent to angle P, angle B to angle Q, and angle C to angle R.
What precisely is a triangle?A triangle is a closed, two-dimensional geometric shape made up of three line segments called sides that intersect at three points called vertices. Triangles may be identified by their sides and angles. Based on their sides, triangles might be equilateral (all sides equal), isosceles, or scalene. Triangles are classed as acute (all angles less than 90 degrees), right (one angle equal to 90 degrees), or obtuse (all angles more than 90 degrees) (all angles greater than 90 degrees). The area of a triangle may be calculated using the formula A = (1/2)bh, where A is the area, b is the base of the triangle, and h is the height of the triangle.
To demonstrate the similarity of two triangles, we must demonstrate that their respective angles are congruent and their corresponding sides are proportionate.
∆ABC ~ ∆PQR
We can see from the triangles that angle A is congruent with angle P, angle B is congruent with angle Q, and angle C is congruent with angle R. As a result, we have the angle-angle (AA) similarity:
∆ABC ~ ∆PQR
[tex]AC/PR = 13/16 \\AB/PQ = 5/8 \\BC/QR = 12/16 = 3/4 \\AC/PR = 13/16[/tex]
Because the matching side length ratios are not entirely equal, the triangles are not comparable according to the side-angle-side (SAS) similarity theorem. As a result, we can only state that angle A is congruent to angle P, angle B to angle Q, and angle C to angle R.
To know more about triangle visit:
https://brainly.com/question/2773823
#SPJ1
The measure of an angle is twice less than that of its supplement angle.
The supplementary angle will be 60°.
What are supplementary angles?
Supplementary angles are angles (only two) whose sum is equal to 180 degrees. In other words, if we add two angles together and the result is 180 degrees, those angles are considered supplementary.
For example, if we have angle A that measures 60 degrees, its supplement angle B will measure 120 degrees (180 - 60 = 120). Angles A and B are supplementary angles.
Supplementary angles can be adjacent, meaning they share a common vertex and side, or they can be non-adjacent. In either case, their sum will always be 180 degrees.
Supplementary angles are commonly used in geometry and trigonometry to solve problems related to angles and triangles.
Now,
Let x = measure of the angle.
Then, the supplement angle is 180 - x.
According to the problem, x is twice less than the supplement angle. In other words, the supplement angle is twice greater than x. We can write this as:
180 - x = 2x
Solving for x, we get:
180 = 3x
x = 60
Therefore, the angle measures 60 degrees.
To know more about supplementary angles visit the link
brainly.com/question/22960799
#SPJ1
Right Question:- The measure of an angle is twice less than that of its supplement angle. find that angle?
Based on historical data, an insurance company estimates that a particular customer has a 3.3% likelihood of having an accident in the next year, with the average insurance payout being $1500.
If the company charges this customer an annual premium of $120, what is the company's expected value of this insurance policy?
$
Based on this estimate, the insurance company's projected value of this probability insurance policy is negative, implying that the insurance company will lose money on this policy.
What is probability?Probabilistic theory is a branch of mathematics that calculates the chance of an event or a claim being true. A risk is a number between 0 and 1, where 1 represents certainty and a probability of about 0 shows how likely an event appears to be to occur. Probability is a mathematical term for the likelihood that a certain event will occur. Probabilities can also be expressed as numbers ranging from 0 to 1, or as percentages ranging from 0% to 100%. The proportion of occurrences among equally likely choices that result in a certain event in compared to all possible outcomes.
The total of the potential payouts multiplied by the odds of each payout occurring equals the anticipated value of the insurance policy. In this scenario, the possible compensation is the $1500 insurance payout, and the likelihood of the client being involved in an accident is 3.3%, or 0.033.
Expected value = (Payout if event happens) x (Probability of event happening) - (Annual premium)
($1500) x (0.033) - ($120) = expected value
Value expected = $49.50 - $120
-$70.50 is the expected value.
Based on this estimate, the insurance company's projected value of this insurance policy is negative, implying that the insurance company will lose money on this policy.
To know more about probability visit:
https://brainly.com/question/11234923
#SPJ1
What is 6% times 39%
Answer:
0.0234
Step-by-step explanation:
please give brainliest
Suppose you have two six-sided dice where each side is equally likely to land face up when rolled.
What is the probability that you will roll doubles?
(Give your answer as a number between 0 and 1. Round to 2 decimal places.)
What is the probability that you will roll a sum of twelve?
(Give your answer as a number between 0 and 1. Round to 2 decimal places.)
Answer:
12/12 and 1/12
Step-by-step explanation:
I couldn’t solve this and I was very confused, if anyone can please help me on this I will appreciate it, thank you so much
It is due tomorrow
no 1) what is the square root of 2? it's about 1.5
no 2) pi is 3.14 blah blahblah so just put somewhere around 3
no 3) do square root of 11, it's about 3.3 so put it a tiny bit after no 2.
all of these will be after the 0, not before because theyre positive
hope this helps x
ABCD is a trapezium. P is a point along AC such that AP=4PC. DC=1/4AB.
a) express PB in terms of a and b in its simplest form
b) express DP in terms of a and b in its simplest form
c) does DPB form a straight line?
Answer:
a) We can use similar triangles to find PB in terms of a and b. Let x be the length of AD. Then, using the fact that AP = 4PC, we have:
PC = CP = x - b
AP = 4(x - b)
Also, using the fact that DC = (1/4)AB, we have:
AD = x
AB = 4DC = x/4
BC = AB - AD = x/4 - x = -3x/4
Now, consider the similar triangles PBC and ABD:
PB/AB = BC/AD
PB/(x/4) = (-3x/4)/x
PB = -3/4(x/4) = -3x/16
Finally, substituting x = a + b, we have:
PB = -3(a + b)/16
b) Using the same similar triangles as in part (a), we have:
DP/DC = PB/BC
DP/(1/4)AB = PB/(-3x/4)
DP = -3/4(PB)(DC/BC)AB
DP = -3/4(PB)(1/4)/(AB - AD)AB
Substituting the expressions for PB, AB, and AD from part (a), we get:
DP = -3(a + b)/16 * 1/4 / (-3(a + b)/4) * (a + b)/4
DP = -3/16 * 1/4 * 4/(3(a + b)) * (a + b)
DP = -3/16
So, DP = -3/16(a + b)
c) To check if DPB forms a straight line, we need to verify if the slopes of DP and PB are equal. Using the expressions we found in parts (a) and (b), we have:
Slope of PB = Δy/Δx = (-3/16(a+b) - 0)/(0 - (-3(a+b)/16)) = 3/16
Slope of DP = Δy/Δx = (-3(a+b)/16 - (-3/16(a+b)))/(1/4 - 0) = -3(a+b)/4
Since the slopes are not equal, DPB does not form a straight line.
Find an equation of the line that passes through the pair of points (4,5) & (-1, -1). Write the equation in the form Ax+By=C
In response to the stated question, we may state that Hence the slope equation of the line passing through the points (4, 5) and (-1, -1) in the form Ax+By=C is: 6x - 5y = -1.
what is slope?Slope is just the curvature of a bend or line in mathematics. It is a measure of the manner in which the y-value of something like a function varies because when x-value changes. The slope of a line is commonly symbolized by the letter m and may be computed as follows: m = (y2 - y1) / (x2 - x1) (x1, y1) and (x2, y2) are any 2 options on the line. A bridge's slope might be negative, negative, zero, or unknown. A positive slope indicates that the line ascends to left to right, whereas a slope indicates that the line drops from left to right.
We must use the point-slope form of the equation of a line to obtain the equation of a line of the form Ax+By=C that goes through two points:
y - y1 = m(x - x1) (x - x1)
where (x1, y1) is the location of one of the points and m is the line's slope.
Then, we must determine the slope of the line.
[tex]m = (y2 - y1) / (x2 - x1) (x2 - x1)\\where (4, 5) = (x1, y1) and (x2, y2) = (-1, -1)m = (-1 - 5) / (-1 - 4) = -6 / (-5) = 6/5\\y - y1 = m(x - x1) (x - x1)\\y - 5 = (6/5)(x - 4) (x - 4)\\5y - 25 = 6x - 24\\6x - 5y = -1\\[/tex]
Hence the equation of the line passing through the points (4, 5) and (-1, -1) in the form Ax+By=C is: 6x - 5y = -1.
To know more about slope visit:
https://brainly.com/question/3605446
#SPJ1
What are the steps to solving the following problem,
5x+4=19
List at least 4 steps
Answer:
5x+4=19
5x=19-4
5x=15
5x÷5=15÷5
x=3