Answer:
Jack needs 6 hours and Jill needs 3 hours.
Step-by-step explanation:
Let's define the variables:
X = rate at which Jack can write a holiday card.
Y = rate at which Jill can write a holiday card.
Each of them will need a given time to write a card, such that:
X*T = 1 card
We know that Jack needs 3 more hours to write a card than Jill, then Jill needs 3 hours less than Jack, so if Jack needs T hours, Jill will need T - 3 hours
Then we have the equation:
Y*(T - 3 hr) = 1 card
And we also know that when they work together, they need 2 hours, then:
(X + Y)*2 hr = 1 card.
So we have 3 equations:
X*T = 1 card
Y*(T - 3 hr) = 1 card
(X + Y)*2 hr = 1 card.
Now let's ignore the card part just for the equations, then we get:
X*T = 1
Y*(T - 3 hr) = 1
(X + Y)*2 hr = 1
To solve it, we first need to isolate one variable in one of the equations, let's isolate T in the first equation, we get:
T = 1/X
Now we can replace this in the second equation to get:
Y*((1/X) - 3hr) = 1
So now we have two equations:
(X + Y)*2 hr = 1
Y*((1/X) - 3hr) = 1
We need to do the same, isolate one variable in one of the equations, let's isolate Y in the above one:
Y*2hr = 1 - X*2hr
Y = (1 - X*2hr)/2hr
Now we can replace this in the other equation to get:
((1 - X)/2hr)*((1/X) - 3hr) = 1
Now we can solve this for X:
((1 - X)/2hr)*((1/X) - 3hr) = 1
(1 - X)*((1/X) - 3hr) = 2 hr
1/X - 3hr - X*2hr/X + X*2hr*3hr = 2hr
1/X - 3hr - 2hr + X*6hr^2 = 2hr
1/X + X*6hr^2 = 2hr + 3 hr + 2 hr = 7hr
1/X + X*6hr^2 = 7hr
Now we can multiply all by X to get:
X/X + X*(X*6hr^2) = 7hr*X
Now we have the quadratic equation:
(6hr^2)*X^2 - (7hr)*X + 1 = 0
We can find the solutions of this equation if we use the Bhaskara's formula, the solutions are:
[tex]X = \frac{-(-7hr) +- \sqrt{(-7hr)^2 - 4*(6hr^2)*1} }{2*6hr^2} = \frac{7hr +- 5hr}{12 hr^2}[/tex]
Then we have two solutions:
X = (7hr + 5hr)/12hr = 1 hr^-1
And this is the rate at which Jack writes a card, so the actual units are:
X = 0.167 card/hr
Then Jill's rate will be:
Y = (1 - X*2hr)/2hr = (1 - 1card/hr*2hr)/2hr = -0.5 card/hr
So we have a negative rate, this makes no sense, so we can discard this option. The other solution for X is:
X = (7hr - 5hr)/12hr = 0.166... hr^-1
And this is the rate at which Jack writes a card, so the actual units are:
X = 0.166... card/hr
If we have this, then the rate for Jill will be:
Y = Y = (1 - X*2hr)/2hr = (1 - 0.167card/hr*2hr)/2hr = 0.333 card/hr
Then we have:
X = 0.167 card/hr
If we use the first equation, we get:
(0.166... card/hr)*T = 1 card
T = 1 card/((0.166... card/hr)) = 6 hours
Then Jack needs 6 hours to write a card.
And we know that Jill needs 3 hours less than that, then Jill needs 3 hours.
Answer these 3 questions if not able to answer all try question 10 thank you
3. Solve: 5 x 4+ (1+1) + 5 = *
Your answer
Answer:
27
Step-by-step explanation:
We can solve by using order of operations (PEMDAS), which shows us the order in which we're supposed to perform mathematical operations:
Parentheses,Exponents,Multiplication/DivisionThe / comes from the fact that you do these operations from left to right as multiplication and division have the same level of priority in an equation/operation.
and Addition/Subtraction.Like multiplication/division, the / comes from the fact that you do these operations from left to right as addition and subtraction also have the same level of priority in an equation/operation.
Step 1: Simplify inside the parentheses:
5 * 4 + (1 + 1) + 5
5 * 4 + 2 + 5
Step 2: Multiply 5 and 4:
20 + 2 + 5
Step 3: Add 20 and 2:
22 + 5
Step 4: Add 22 and 5 to get your answer:
27
Thus, 5 *4 + (1 + 1) + 5 = 27
I will give all my points and mark as brainliest (((())))pls
Find the regression equation. Round your answer to the nearest hundredth.
The equation shows that the point total in the 10th level is predicted to be 514.4.
How to calculate the valueThe equation given is: y= 48.2x + 32.4
where y is the point total and x is the level.
In order to predict the point total in the 10th level, I will substitute x=10 into the equation:
y=48.2(10) + 32.4 = 482 + 32.4 = 514.4
Therefore, the point total in the 10th level is predicted to be 514.4.
Learn more about equations on
https://brainly.com/question/2972832
#SPJ1
Four points are plotted on the number line. Which point best represents 33 1/3% of the distance between zero and one
The point Y best represents 33 1/3% of the distance between zero and one.
We know that if the mixed fraction a b/c can expressed as improper fraction in below way:
a b/c = (a*c + b)/c
Here the given the mixed fraction is = 33 1/3 = (33*3 + 1)/3 = 100/3
The distance between the point 0 and 1 is given by = 1 - 0 = 1
So the required percentage of the distance = 1*(33 1/3%) = 1*(100/3 %) = 100/(3*100) = 1/3.
From the number line given we can see that the distance between 0 and 1 is divided in to 12 equal parts.
So, 33 1/3% stands at = 12*(1/3) = 4 th parts that is point Y.
Hence the point Y best represents 33 1/3% of the distance between zero and one.
To know more about number line here
https://brainly.com/question/25230781
#SPJ1
The question is incomplete. The complete question will be -
Need help Which of the following is not an expression?
• A. 3x+4 = 7
O B. x+8
ㅇ G0-품
O D. 2x -
The answer is A, because it includes an equals sign and a statement of equality.
A. 3x + 4 = 7 is not an expression, but an equation because it includes an equals sign and a statement of equality.
B, C, and D are all expressions. Expression refers to a mathematical phrase that can include numbers, variables, and mathematical operations, but does not contain an equals sign or a statement of equality.
B. x + 8 is a simple expression that includes a variable and a constant.
C. 6 - x/5 is also an expression that involves a constant and a variable, and uses a division operation.
D. 2x-3 is another expression that includes a variable and a constant, and uses a subtraction operation.
Therefore, the answer is A, since it is not an expression.
Learn more about Expression:
https://brainly.com/question/723406
#SPJ1
Consider a sample with six observations of 16, 11, 13, 22, 15, and 19. Compute the z-score for each observation.
The z-scores for the observations 16, 11, 13, 22, 15, and 19 are approximately 0, -1.37, -0.82, 1.64, -0.27, and 0.82, respectively.
To compute the z-scores for each observation in the sample, we need to first calculate the mean and standard deviation of the data set.
Given the sample with observations: 16, 11, 13, 22, 15, and 19.
Calculate the mean (μ):
Add up all the observations and divide by the total number of observations.
Mean (μ) = (16 + 11 + 13 + 22 + 15 + 19) / 6 = 96 / 6 = 16.
Calculate the standard deviation (σ):
Subtract the mean from each observation.
Deviation = Observation - Mean
Square each deviation.
Squared Deviation = Deviation²
Calculate the average of the squared deviations.
Average Squared Deviation = (Squared Deviation1 + Squared Deviation2 + ... + Squared Deviation6) / 6
Take the square root of the average squared deviation.
Standard Deviation (σ) = √(Average Squared Deviation)
Let's calculate each step:
Deviation1 = 16 - 16 = 0
Deviation2 = 11 - 16 = -5
Deviation3 = 13 - 16 = -3
Deviation4 = 22 - 16 = 6
Deviation5 = 15 - 16 = -1
Deviation6 = 19 - 16 = 3
Squared Deviation1 = 0² = 0
Squared Deviation2 = (-5)² = 25
Squared Deviation3 = (-3)² = 9
Squared Deviation4 = 6² = 36
Squared Deviation5 = (-1)² = 1
Squared Deviation6 = 3² = 9
Average Squared Deviation = (0 + 25 + 9 + 36 + 1 + 9) / 6 = 80 / 6 = 13.33
Standard Deviation (σ) = √13.33 ≈ 3.65
Now that we have the mean (μ = 16) and standard deviation (σ ≈ 3.65), we can calculate the z-score for each observation.
The z-score (Z) for an observation (X) is calculated using the formula:
Z = (X - μ) / σ
Let's calculate the z-scores for each observation:
Z1 = (16 - 16) / 3.65 = 0 / 3.65 = 0
Z2 = (11 - 16) / 3.65 = -5 / 3.65 ≈ -1.37
Z3 = (13 - 16) / 3.65 = -3 / 3.65 ≈ -0.82
Z4 = (22 - 16) / 3.65 = 6 / 3.65 ≈ 1.64
Z5 = (15 - 16) / 3.65 = -1 / 3.65 ≈ -0.27
Z6 = (19 - 16) / 3.65 = 3 / 3.65 ≈ 0.82
So, the z-scores for the observations 16, 11, 13, 22, 15, and 19 are approximately 0, -1.37, -0.82, 1.64, -0.27, and 0.82, respectively.
for such more question on z-scores
https://brainly.com/question/15222372
#SPJ8
Type the correct answer in each box. Use numerals instead of words. Consider function h. h ( x ) = { 3 x − 4 , x < 0 2 x 2 − 3 x + 10 , 0 ≤ x < 4 2 x , x ≥ 4 What are the values of the function when x = 0 and when x = 4 ?
h(0)=
h(4)=
The value of function h (0) is,
h (0) = 10
And, The value of function h (4) is,
h (4) = 8
Given that;
The function is,
h (x) = { 3x - 4 , x < 0
= {2x² - 3x + 10, 0 ≤ x < 4
= { 2x , x≥ 4
Hence, The value of function h (0) is,
h (x) = 2x² - 3x + 10, 0 ≤ x < 4
h (0) = 2 (0) - 3 (0) + 10
h (0) = 10
The value of function h (4) is,
h (x) = 2x
h (4) = 2 (4)
h (4) = 8
Thus, The value of function h (0) is,
h (0) = 10
And, The value of function h (4) is,
h (4) = 8
Learn more about the function visit:
https://brainly.com/question/11624077
#SPJ1
[tex]f(x)=\frac{x-3}{x+7}[/tex] find the domain
The domain of the function f(x) is all real numbers except x = -7. In interval notation, we can express the domain as (-∞, -7) ∪ (-7, +∞).
To find the domain of the function f(x) = (x - 3)/(x + 7), we need to determine the values of x for which the function is defined.
The function is defined for all values of x except those that make the denominator, x + 7, equal to zero.
Division by zero is undefined in mathematics.
So, we set the denominator equal to zero and solve for x:
x + 7 = 0
x = -7
Hence, the only value that makes the denominator zero is x = -7. Therefore, the domain of the function f(x) is all real numbers except x = -7.
In interval notation, we can express the domain as (-∞, -7) ∪ (-7, +∞).
For similar question on domain.
https://brainly.com/question/26098895
#SPJ11
HELP ASAP PHOTO INCLUDED
I cannot solve that problem at the moment.
Step-by-step explanation:
But I will help you in the future
PLEASE HELP ASAP 25 POINTS
Answer:
A) Using Commutative property
Step-by-step explanation:
In step 1, it used distributive property when the number 5 is distributed inside of the equation in the parenthesis.
In Step 4, dividing both sides by 10 to further simplify the equation
In step 2, you combined like terms and it results to the equation in step 3
A box has 6 blue socks and 4 white socks. find the number of ways 2 socks can be drawn from the box where
a) There are no restriction
b) They are different colours
c) They are the same colours
The number of ways to draw the socks in each case is given as follows:
a) 90 ways.
b) 48 ways.
c) 42 ways.
What is the Fundamental Counting Theorem?The Fundamental Counting Theorem states that if there are m ways for one trial and n ways for another trial, then there are m x n ways in which the two trials can happen simultaneously.
This can be extended to more than two trials, where the number of ways in which all the trials can happen simultaneously is the product of the number of outcomes of each individual trial, according to the equation presented as follows:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
For item a, we have that there are no restrictions, hence there are 10 options for the first sock and 9 for the second, hence:
10 x 9 = 90.
For item b, we need one of each, hence the possible combinations are:
One of six(blue) and then one of four(white).One of four(white) and then one of six(blue).Hence:
6 x 4 + 4 x 6 = 48.
For item c, we can take 6 then five(two blue) or 4 then 3(two white), hence:
6 x 5 + 4 x 3 = 42.
More can be learned about the Fundamental Counting Theorem at https://brainly.com/question/15878751
#SPJ1
on a map, 1 inch equals 8.7 miles. If two cities are 2.5 inches apart on the map, how far are they actually apart?
The distance between the cities is ? miles
Answer:
the distance between the cities is 21.75 miles.
Step-by-step explanation:
1 inch = 8.7 miles.
2.5 inches x 8.7 miles/inch = 21.75 miles
The sin(n/4)equals ?
A. 0.0137
B. 0.7071
The value of function sin (π/4) is,
⇒ sin π/4 = 0.7071
We have to given that;
The expression is,
⇒ sin π/4
Now, We can simplify the expression as;
⇒ sin π/4
⇒ 1 / √2
⇒ 1 / 1.414
⇒ 0.7071
Thus, The value of function sin (π/4) is,
⇒ sin π/4 = 0.7071
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ1
Select all of the following that are quadratic equations. 5 x 2+ 15 x = 0 6 x - 1 = 4 x + 7 x 2 - 4 x = 4 x + 7 2 x - 1 = 0 3 x 2 + 5 x - 7 = 0 x 3 - 2 x 2 + 1 = 0
Answer:
Options A, C and E-----------------------
Quadratic equation has the form of:
ax² + bx + c = 0Analyze the given equations and see which has the same form:
A) 5x² + 15 x = 0, Yes, quadratic equation;B) 6 x - 1 = 4, No, it is a linear equation;C) x + 7x² - 4 x = 4, Yes, quadratic equation;D) x + 72x - 1 = 0, No, it is a linear equationE) 3x² + 5x - 7 = 0, Yes, quadratic equation;F) x³ - 2x² + 1 = 0, No, it is cubic equationPlease help me answer this question
For the function [tex]A(t)=4000e^0^.^0^4^t[/tex] the value of A'(8) is $220 and the value of [tex]A'(t)=160e^0^.^0^4^t[/tex]
The given function is [tex]A(t)=4000e^0^.^0^4^t[/tex] gives the balance after t years.
The initial investment is 8000
4% is the compounded interest.
Now differentiate with respect to t
[tex]A'(t)=0.04(4000)e^0^.^0^4^t[/tex]
[tex]A'(t)=160e^0^.^0^4^t[/tex]
Now let us find the value of A'(8)
Plug in t as 8
[tex]A'(8)=160e^0^.^0^4^(^8^)[/tex]
A'(8)=220.3
Hence, the value of A'(8) is $220 and the value of [tex]A'(t)=160e^0^.^0^4^t[/tex]
To learn more on Differentiation click:
https://brainly.com/question/24898810
#SPJ1
Given circle E with diameter CD and radius EA. AB is tangent to E at A. If AB=34 and EB=38, solve for EA. Round to the nearest tenth if necessary
The value of side EA is,
EA = 16.9
We have to given that;
Circle E with diameter CD and radius EA.
And, AB is tangent to E at A.
Here, AB = 34 and EB = 38
Hence, By using Pythagoras theorem we get;
AB² + AE² = EB²
34² + AE² = 38²
1156 + AE² = 1444
AE² = 1444 - 1156
AE² = 288
AE = √288
AE = 16.9
Thus, The value of side EA is,
EA = 16.9
Learn more about the circle visit:
https://brainly.com/question/24810873
#SPJ1
According to the table below, What is the domain of the data
Domain: {15, 17, 19, 21, 23}
Step-by-step explanation:The domain describes the x-values within a function.
Inputs
In a function, the inputs are the values that are plugged into a function, and the outputs are the resulting values. This means that the inputs represent the x-values and the outputs are the y-values. Since this is a function, each of the inputs has one output. So, each input is unique. We can use the input values to find the domain.
Domain
The domain of a data set is the x-values. Each x-value is one part of the domain. The domain is written as a list of values in numerical order with braces surrounding the values. Since the inputs represent the x-values, we can use the input values as the domain values. This means that the domain of the data is {15, 17, 19, 21, 23}.
Can someone please answer and provide an explanation for these problems?
(17) The length of the arc is 39.27 in
(18) The length of the arc is 70.7 cm
(19) The area of the sector is 395.84 in²
(20) The area of the sector is 38.5 cm².
What is the area of the sector?The area of each of the sector is calculated by using the following formula;
Area = πr² (θ/360)
Where;
r is the radiusθ is the angle subtended by the sectorThe formula for length of arc is given as;
length of arc = 2πr (θ/360)
(17) The length of the arc is calculated as;
L = 2π (10 in) (225/360)
L = 39.27 in
(18) The length of the arc is calculated as;
L = 2π (15 cm) (270/360)
L = 70.7 cm
(19) The area of the sector is calculated as;
A = π(12)² (315/360)
A = 395.84 in²
(20) The area of the sector is calculated as;
A = π(7)² (90/360)
A = 38.5 cm²
Learn more about area of sector here: https://brainly.com/question/22600628
#SPJ1
Need help with this homework
Answer:
Step-by-step explanation:
use gauth math it helps with maths
Consider the following symbolic logic statement: ¬ (∃x)(P(x) ∧ Q(x)) ∧ (∀y)(R(y) → P(y))
a) Translate the statement into English using proper syntax and semantics.
b) Identify and explain any potential ambiguities in the translated statement.
c) Rewrite the statement in a way that eliminates any ambiguities and maintains the original meaning.
(a). The statement can be translated into English as follows "Not exists x such that P(x) and Q(x), and for all y, if R(y) then P(y)." (b) The rewritten statement explicitly places the negation symbol "¬" only in front of the existential quantifier (∃x). (c). This clarifies that the negation applies to the existence of x such that P(x) and Q(x).
a) Translation into English:
The statement can be translated into English as follows:
"Not exists x such that P(x) and Q(x), and for all y, if R(y) then P(y)."
b) Potential ambiguities in the translated statement:
Ambiguity in the scope of negation: The placement of the negation symbol "¬" might lead to ambiguity. It is not clear whether the negation applies only to the existential quantifier (∃x) or to the entire statement. Specifically, it is unclear if the negation applies to both conjuncts separately or to their conjunction as a whole.
Ambiguity in the scope of quantifiers: The scope of the quantifiers (∃x) and (∀y) is not explicitly defined. It is unclear which variables the quantifiers bind to and how they relate to the predicates P(x), Q(x), R(y), and P(y).
c) Rewritten statement to eliminate ambiguities while maintaining the original meaning:
To eliminate the ambiguities, we can rewrite the statement as follows:
(¬∃x)(P(x) ∧ Q(x)) ∧ (∀y)(R(y) → P(y))
The rewritten statement explicitly places the negation symbol "¬" only in front of the existential quantifier (∃x). This clarifies that the negation applies to the existence of x such that P(x) and Q(x). Additionally, parentheses are used to explicitly define the scope of the quantifiers (∃x) and (∀y), making it clear which variables they bind to.
For more such questions on symbol , Visit:
https://brainly.com/question/30289310
#SPJ11
Percy's Desserts made a batch of fresh scones with 5/8 of a pound of butter and 1/2 of a
pound of sugar. How much more butter than sugar was used?
Write your answer as a fraction or as a whole or mixed number.
pounds
Answer:
Step-by-step explanation:
To find the difference between the amount of butter and sugar used, we need to subtract the weight of sugar from the weight of butter.
The weight of butter used is 5/8 pounds, and the weight of sugar used is 1/2 pounds. To subtract these fractions, we need to find a common denominator.
The common denominator for 8 and 2 is 8, so we can rewrite the fractions as follows:
5/8 pounds of butter
4/8 pounds of sugar
Now we can subtract the weight of sugar from the weight of butter:
5/8 - 4/8 = 1/8
Therefore, Percy's Desserts used 1/8 pound more butter than sugar.
Answer: Percy's Desserts used 1/8 pounds more butter than sugar in their batch of fresh scones.
Step-by-step explanation:
1. Identify the quantities of butter and sugar used: Percy's Desserts used 5/8 of a pound of butter and 1/2 of a pound of sugar.
2. Convert the quantities to a common denominator: To compare these quantities, we need to express them with a common denominator. The least common denominator of 8 and 2 is 8. So, we express 1/2 as 4/8.
3. Subtract the quantity of sugar from the quantity of butter: Now that both quantities are expressed in eighths of a pound, we can subtract them: 5/8 - 4/8 = 1/8.
4. Convert the result back to a decimal: 1/8 of a pound is equivalent to 0.125 pounds.
So, Percy's Desserts used 0.125 pounds more butter than sugar in their batch of fresh scones.
100 Points! Geometry question. Identify the similar triangles. Then find each measure. Photo attached. Please show as much work as possible. Thank you!
The triangles ABC and DBE are similar by the SAS similarity theorem
The measure of the side lengths AC is 16 units
How to identify the similar triangles.From the question, we have the following parameters that can be used in our computation:
The triangles ABC and DBE
These triangles have the following measures
Two similar corresponding sidesTwo equal corresponding anglesThis means that the triangles are similar by the SAS similarity theorem
How to find each measureUsing the SAS similarity theorem, we have the following equation
(x + 1)/12 = (x + 5)/15
Cross multiply the equation
15x + 15 = 12x + 60
So, we have
3x = 45
Divide by 3
x = 15
This means that
x + 1 = 15 + 1 = 16
x + 5 = 15 + 5 = 20
Hence, the measure of the side lengths are 16 and 20 units
Read more about similar triangles at
https://brainly.com/question/14285697
#SPJ1
Please help me find the perpendicular height
The perpendicular height of the pyramid is 83.65 cm
How to find the perpendicular height?To find the perpendicular height we can define a right triangle.
The perpendicular height is one leg, and the other leg will be half of the diagonal of the base.
The base is a square whose sidelength is 23cm, then the diagonal is:
D = √( (23cm)² + (23cm)²)
D = 32.527cm
Half of that is
D/2 = 32.527cm/2 = 16.26cm
Now, we know one side of the right triangle and the angle of 79°, for which the known cathetus is adjacent.
The perpendicular height is the opposite cathetus.
Then we can use the relation:
tan(79°) = H/16.26cm
Solving for H, the heigt, we will get.
H = tan(79°)*16.26cm = 83.65 cm
Learn moer about right triangles at:
https://brainly.com/question/2217700
#SPJ1
Please help answer theses questions
Answer:
Question 6 : True
Question 7: False
Step-by-step explanation:
To find g(f(x)) given f(x) and g(x), substitute the expression for f(x) for every x in g(x)
f(x) = 2x
g(x) = x²
g(f(x) = (2x)² = 4x²
So True
f(x) = x² + x
g(x) = 2x + 1
g(f(x)) = 2(x² + x) + 1 = 2x² + 2x + 1
So False
Alex washed 3/10 of his laundry yesterday. What fraction of his laundry does he have left to wash?
Answer:
7/10
Step-by-step explanation:
[tex]1 - \frac{3}{10} \\ = \frac{10}{10} - \frac{3}{10 } \\ = \frac{7}{10} [/tex]
#CMIIWPlease solve this question
Answer:
A.
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
id
mathmatically indication example with solution
A mathematically indication example would be to solve the equation 3x + 2 = 14 for the value of x. The solution would be 4.
How to solve the equation ?Looking for a mathematically indication example, we can consider a simple mathematical equation with one variable and solve it.
The equation would be 3 x + 2 = 14.
So we can solve for the equation to be :
3x + 2 - 2 = 14 - 2
3x = 12
3 x / 3 = 12 / 3
x = 4
In conclusion, the mathematically indication example would be 3x + 2 = 14 and the value of x would be 4.
Find out more on equation solutions at https://brainly.com/question/2228446
#SPJ1
A straw is placed inside a rectangular box that is 10 inches by 6 inches by 7 inches, as shown. If the straw fits exactly into the box diagonally from the bottom left corner to the top right back corner, how long is the straw? Leave your answer in simplest radical form.
100 Points! Geometry question. Photo attached. Determine whether the quadrilateral is a parallelogram. Justify your answer using a theorem. Please show as much work as possible. Thank you!
The prove of the statement is described below.
First of all ,
Labeling the given figure
And draw a diagonal,
In the quadrilateral PQRS,
The side PQ is equal to the side RS.
Therefore,
PQ = RS
And also, the side PQ is parallel to the side RS.
Then,
PQ || RS.
Now, draw the diagonal PR.
We know that a parallelogram's diagonal divides the parallelogram into two congruent triangles.
By the rule of Side-Angle-Side,
we can show that ∆ PQR ≅ ∆ RSP.
Therefore,
The side QR is parallel to PS
Then,
QR || PS.
Hence,
PQRS is a parallelogram.
To learn more about quadrilaterals visit:
https://brainly.com/question/11037270
#SPJ1
Investor C decided to purchase a home that costs $600,000 with a 40% down payment loan, a 3.00% annually fixed rate for a 30 year term, and one payment per month. What is the monthly payment for this mortgage?
Step-by-step explanation:
To calculate the monthly payment for a mortgage, you can use the formula for a fixed-rate mortgage:
Monthly Payment = (P * r * (1 + r)^n) / ((1 + r)^n - 1)
Where:
P = Loan amount (in this case, the home cost minus the down payment)
r = Monthly interest rate (annual rate divided by 12 and converted to decimal)
n = Total number of payments (number of years multiplied by 12)
Given:
Home cost = $600,000
Down payment = 40% of the home cost = 0.4 * $600,000 = $240,000
Loan amount = Home cost - Down payment = $600,000 - $240,000 = $360,000
Annual interest rate = 3.00%
Loan term = 30 years
First, calculate the monthly interest rate:
Monthly interest rate = (Annual interest rate / 100) / 12 = (3.00 / 100) / 12 = 0.0025
Next, calculate the total number of payments:
Total number of payments = Loan term * 12 = 30 * 12 = 360
Now, substitute the values into the formula:
Monthly Payment = ($360,000 * 0.0025 * (1 + 0.0025)^360) / ((1 + 0.0025)^360 - 1)
After performing the calculations, the monthly payment for this mortgage is approximately $1,520.06.
I hope I was helpful