In parallelogram DEFG, DH = x + 3, HF = 3y, GH = 3x – 3, and HE = 5y + 4. Find the values of x and y.
x = 5, y = 12
x = 5, y = 9
x = 4, y = 9
x = 9, y = 4
Answers
DH = HF
x + 3 = 3y
GH = HE
3x - 3 = 5y + 4
We then have the following system of equations:
x-3y = -3
3x-5y = 7
Resolving the system graphically we obtain the following values:
x = 9
y = 4
Note: see attached image.
Answer:
The values of x and y are:
x = 9, y = 4
Final answer:
In parallelogram DEFG, DH = x + 3, HF = 3y, GH = 3x – 3, and HE = 5y + 4. Solving the equations yields x = 9, y = 4.
Explanation:
To find the values of x and y in parallelogram DEFG, we'll use the properties of parallelograms. In a parallelogram, opposite sides are equal in length.
Given that DH = x + 3 and HF = 3y, and that DH is opposite to HF, we have:
x + 3 = 3y ...(1)
Similarly, given GH = 3x - 3 and HE = 5y + 4, and that GH is opposite to HE, we have:
3x - 3 = 5y + 4 ...(2)
Now, we have a system of two equations (1) and (2) to solve for x and y.
From equation (1):
x = 3y - 3 ...(3)
Substitute equation (3) into equation (2):
3(3y - 3) - 3 = 5y + 4
9y - 9 - 3 = 5y + 4
9y - 12 = 5y + 4
4y = 16
y = 4
Now, substitute the value of y into equation (3):
x = 3(4) - 3
x = 12 - 3
x = 9
So, the values of x and y are x = 9 and y = 4. Thus, the correct answer is x = 9, y = 4.
Related Questions
Find the simplified form of (-3)^-4
A. 12
B. -81
C. 1/81
D. -1/81
Answers
the answer is C
= 1 / (-3)^4
= 1/81
answer
C. 1/81
Nathan is building a toolshed with a rectangular floor. The area of a rectangle is given by the formula l⋅w, where l represents the length, and w represents the width. The floor of the shed will have measurements of either l=8 and w=6 or l=7 and w=7. What is the area of the larger floor?
Answers
Answer:
Here, l is the length of the rectangle and w is the width of the rectangle
To Compare the values, you must calculate each given situation.
Area of a rectangle is equal to length times width.
i.e, [tex]A = l \times w[/tex]
(A)
if l = 8 units and w= 6 units,
then;
[tex]A = l \times w[/tex] = [tex]8 \times 6 = 48 unit^2[/tex]
(B)
if l =7 units and w = 7 units
[tex]A = l \times w[/tex] = [tex]7 \times 7 = 49 unit^2[/tex]
Therefore, the Part B would yield a larger area.
If l -7 units and w = 7 units , the area of larger floor is 49 square units.
Strangely, she lifted us up like a feather on a breeze.
This sentence uses which TWO types of figurative language?
A)simile and onomatopoeia
B)metaphor and onomatopoeia
>>>C)personification and simile<<<
D)personification and metaphor
please check my answer i said C but i'm not sure if that is correct,
Answers
This is because “like a” is a simile and “feather on a breeze” is personification
Hope this helped!
i put C and it was correct !
The area of a rectangular deck can be modeled by f(x) = 2x3 + 30x2 6x 90. If x + 15 represents the width, which expression represents the length?
2x^2 21
2x^2 6
2x^2 + 9
2x^2 + 45,
Answers
Solve the system algebraically.
2x + y - 10 = 0
x - y - 5 = 0
What is the value of y?
-5/3
0
5
Answers
We can just add the numbers together to create an equation we can solve.
2x+y-10=0
x-y-5=0
3x-15=0 <== expression added together
3x=15
Divide both sides by 3.
x=5
Now, plug that in to solve for y.
x-y-5=0
5-y-5=0
Add 5 to both sides.
5-y=5
Subtract 5.
y=0
y=0
I hope this helps!
~kaikers
Given that ABCD is a parallelogram, solve for k. A. 4 B. 7 C. 8 D. 11
Answers
The answer is 7 on e2020.
30 Points! Please Help!
Answers
Suppose ruth ann has 5 routes she can choose from to get from school to the library, and 6 routes from the library to her home. how many routes are there for ruth anns school to her home with a sop at the library?,
Answers
This is my last quiz question, Please help <3
Triangle PQR has two known interior angles of 24°, and 100°.
Triangle RST has two known interior angles of 24°, and 56°.
What can be determined about whether trianglesPQR and RST are similar?
Similarity cannot be determined from the given information.
The triangles are similar.
The triangles are not similar.
All interior angles must be given to determine similarity.
Answers
This is true of all triangles.
You have two given angles of triangle PQR.
They are 24 degree and 100 degree.
What do those measures add up to?
What is 100 + 24? = 124
When you add the measure of the third angle to 124, you must get 180.
To find the measure of the third angle, just do 180 - 124.
What do you get?
180 - 124 = 56
That means the third angle of triangle PQR measures 56 deg.
Now we know the measures of all three angles of triangle PQR: 24, 100, 56.
Triangle RST has two angles that measure 24 deg. and 56 deg.
Since two angles of triangle PQR are congruent to two angles of triangle RST, the triangles are similar.
Simplify: 1/3x(6x - 1) A) 5 3 x B)2x - 1 C)2x - 1 3 D)2x2 - 1 3 x
Answers
2x^2 -(1/3)x . . . . . . matches selection D
Answer is D Use the distributive property to simplify.
I get stuck whit these I don’t get how to do them
Answers
[tex]y \leq 2x-2[/tex]
[tex]y +2 \leq 2x[/tex]
[tex] \frac{y+2}{2} = x [/tex]
Plug that into the second equation for x:
[tex]y \leq ( \frac{y+2}{2})^2-3(\frac{y+2}{2})[/tex]
[tex]\frac{y^2+4y+4}{4}- \frac{3y-2}{2} = \frac{y^2+4y+4}{4}- \frac{6y-4}{4} [/tex]
[tex]y \leq\frac{y^2-2y}{4} [/tex]
[tex]0 \leq y^2-2y-4y[/tex]
[tex]0 \leq y(y-6) [/tex]
[tex]6 \leq y[/tex]
Now, plug this back into the first equation to solve for x:
[tex]6 \leq 2x-2[/tex]
[tex]8 \leq 2x[/tex]
[tex]4 \leq x[/tex]
So, the solution to that system is (4, 6) which looks like the D.
The sum of two consecutive even integers is −34−34. find the two integers.
Answers
x+2= second integer
Add the integers together set equal to -34.
x + (x+2)= -34
combine like terms
2x + 2= -34
subtract 2 from both sides
2x= -36
divide both sides by 2
x= -18 first integer
Substitute x= -18 to find second integer.
=x+2
= -18 + 2
= -16 second integer
CHECK:
-18 + -16= -34
-34= -34
ANSWER: The first integer is -18 and the second consecutive even integer is -16.
Hope this helps! :)
K is the midpoint of JL. If: JK = 5x + 1 and KL = 7x - 3. Find JL
Answers
To find JL, we simply add the lengths of JK and KL together which gives us 22 units.
If K is the midpoint of JL, it means that JK is equal in length to KL.
Thus, we can set up the equation 5x + 1 (for JK) equal to 7x - 3 (for KL) since these expressions represent the lengths of JK and KL respectively.
Solving the equation 5x + 1 = 7x - 3 for x, we find that x = 2. Substituting x back into the expression for either JK or KL yields the length of one segment, which in this case is 11 units for both JK and KL.
Use a calculator to find the approximate value of arccos(0.63).
Answers
if cos(∅)=x----------------> arccos (x)=∅
then
cos(∅)=0.63
∅=arccos(0.63)-------------> ∅=50.95°
The question does not specify in which quadrant the angle is, since the cosine function is positive, the angle must be in the first quadrant or in the fourth quadrant
if it is in the first quadrant the angle is 50.95°
and
if it is in the fourth quadrant the angle is (360°-50.95°)=309.05°
(a + b - c)(a + b + c) I need help asap
Answers
Hope this helps :)
Write an expression to represent: One minus the quotient of one and a number x
Answers
Hope this helps!
Please help me...
I think its the third graph or the last .
correct me if im wrong
Answers
I believe the answer you are looking for - is the third graph.
Hope this helps!
~Alexa
The following data set shows the number of books checked out from a library during the first two weeks of the month:
36, 39, 40, 42, 45, 2, 38, 41, 37, 38, 35, 37, 35, 38
Which of the following statements is true based on the data set? (5 points)
There are two outliers, indicating very few books were checked out on those two days.
There are two outliers, indicating an abnormally large number of books were checked out on those two days.
There is one outlier, indicating an abnormally large number of books were checked out on that day.
There is one outlier, indicating very few books were checked out on that day.
Answers
There is one outlier, indicating very few books were checked out on that day.
Answer: There is one outlier, indicating very few books were checked out on that day.
Step-by-step explanation:
The given data of he number of books checked out from a library during the first two weeks of the month:
36, 39, 40, 42, 45, 2, 38, 41, 37, 38, 35, 37, 35, 38
Here , all the data value are near to each other except one i.e. 2.
Since 2 is very small value as compare to the other data values.
It means 2 is the outlier for the data.
It means only 2 books were checked out on that day, which is much lesser number of books than the other day.
Hence, the statements is true based on the data set :
There is one outlier, indicating very few books were checked out on that day.
10 POINTS + BRAINLIEST ANSWER!!
The table below shows the number of U.S. residents with health insurance in 2015, in thousands, categorized by age group and annual income. According to these results, if a U.S. resident with health insurance who was 35-64 in 2015 is selected at random, what is the approximate probability that this resident had an income between $50,000 and $79,999?
A. 0.20
B. 0.25
C. 0.40
D. 0.80
Answers
The approximate probability is 0.40 .
What is random selection?Random selection refers to how the sample is drawn from the population as a whole, while random assignment refers to how the participants are then assigned to either the experimental or control groups.
What is probability?Probability measures the chance of an event happening and is equal to the number of favorable events divided by the total number of events. The value of probability ranges between 0 and 1, where 0 denotes uncertainty and 1 denotes certainty.
Probability of an event P(E) = (Number of favorable outcomes) ÷ (Total outcomes ).
According to the question
The table below shows the number of U.S. residents with health insurance in 2015, in thousands, categorized by age group and annual income.
Now,
if a U.S. resident with health insurance who was 35-64 in 2015 is selected at random,
The probability that this resident had an income between $50,000 and $74,999
As
By using formula of probability
Probability of an event P(E) = (Number of favorable outcomes) ÷ (Total outcomes ).
where
Total outcomes = Total resident had an income between $50,000 and $74,999 = 56,908
Number of favorable outcomes = U.S. resident with health insurance who was 35-64 in 2015 and income between $50,000 and $74,999
= 7,185 + 14,978
= 22,163
Now,
Putting value in formula
Probability of an event P(E) = (Number of favorable outcomes) ÷ (Total outcomes ).
Probability of an event P(E) = [tex]\frac{22163}{56908}[/tex]
= 0.389
= 0.40 (approx.)
Hence, the approximate probability is 0.40 .
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The formula for the area of a regular polygon is A=1/2ap. What is the equation solved for a?
Answers
I'm pretty sure its this a=A/(1/2p)
Answer:a=2A/p
Step-by-step explanation:
Y=f(x) =-2^x. Find f(x) when x=0
Answers
Answer:
f(0) = -1
Step-by-step explanation:
Any scientific or graphing calculator can help you do this. According to the Order of Operations, the exponent is evaluated first, then the sign is applied:
f(0) = -2^0 = -(2^0) = -1
Write a recursive definition for the sequence 14, 10, 6, 2,… Common difference is 4 what do I do next?
Answers
a[n+1] = a[n] -4 . . . says each term is 4 less than the one before it
Since you're looking for a recursive definition, you simply need to do 2 things.
1. Define the function for some constant starting point(s).
2. Define the function in terms of itself for all other points.
For this question, I'll assume the first point is f(0). So we have f(x) = ?, with f(0) = 14
And we've handed the starting point by simply declaring that f(0) has the value of 14. Now for the recursive portion.
As you've noticed, each subsequent value is 4 less than the previous. So we can say f(x) = f(x-1) - 4. And with that, we can make the function.
f(x) = f(x-1) - 4, with f(0) = 14
As a side note, you are not restricted to just 1 starting value, nor just the immediate prior invocation of the function. For instance the definition of the Fibonacci sequence could be defined as
f(x) = f(x-1) + f(x-2), with f(0) = 0 and f(1) = 1
The local ice cream parlor has 20 different flavors of ice cream, 4 different types of cones, and 6 different types of toppings. how many different combinations of ice cream cones can be created?
Answers
The answer provides the total number of combinations of ice cream cones based on flavors, cone types, and toppings.
Explanation:The number of different combinations of ice cream cones that can be created considering different flavors of ice cream, types of cones, and toppings:
Calculate the total combinations by multiplying the number of flavors of ice cream, types of cones, and toppings: 20 * 4 * 6 = 480 different combinations of ice cream cones possible.the annual health insurance premium for Ms Everett is $12,304. her employer pays 70% of the premium and deducts the remainder from her paycheck. Ms Everett is paid monthly
what amount is deducted from Ms Everett's paycheck for her health insurance premium?
A.) $141.97
B.) $307.60
C.) $331.26
D.) $717.73
2.) The health insurance company that insures Peter pays 80% of nutritional counseling after Peter pays a $50 deductible. The cost of his counseling was $1060
How much did Peter pay for his nutritional counseling
A.) $202
B.) $212
C.) $252
D.) $262
3.) Mattie must pay a $15 co-pay for each of her visits to a chiropractor. the insurance company pays 60% of the cost of the visit. After her accident, she made 12 visits to the chiropractor, each costing $305.
How much, in total, did Mattie pay for her chiropractor visits?
A.) $1464
B.) $1644
C.) $2196
D.) $2376
Answers
Answer:
B.) $307.60 ; C.) $252 ; B.) $1644
Step-by-step explanation:
1.) Since the employer pays 70% of the premium, this leaves Ms. Everett with 100-70=30% of the cost.
30% = 30/100 = 0.3; this makes her part of the cost
0.3(12304) = 3691.2
She gets paid monthly, so we divide this by 12:
3691.2/12 = 307.6
This means she has $307.60 deducted monthly.
2.) Since the insurance company pays 80% of the costs, this leaves Peter with 100-80 = 20% of the cost.
We take his deductible out of the cost first:
1060-50 = 1010
20% = 20/100 = 0.2; this makes his part of the cost
0.2(1010) = 202+50 = 252, since we have to count the deductible as part of his cost.
3.) The total cost of all visits would be
305(12) = 3660
The insurance company pays 60% of the cost; this means she is left with 100-60 = 40%. 40% = 40/100 = 0.4;
0.4(3660) = 1464
Mattie also pays 12 $15 copays; this adds 12(15) = 180 to this:
1464+180 = $1644
Ms. Everett's monthly deduction for her health insurance premium is $307.60. Peter paid $202 for his nutritional counseling after accounting for the deductible and insurance payment. Mattie paid a total of $1,644 for her chiropractor visits, considering the co-pays and her share of the visit costs after insurance.
Explanation:Calculating Health Insurance Contributions and Costs1. To determine the amount deducted from Ms. Everett's paycheck for her health insurance premium, we calculate 30% of the total annual premium (since her employer pays 70%) and then divide by 12 to get the monthly deduction.
Total annual premium: $12,304
Employer's share (70%): $12,304 × 0.70 = $8,612.80
Ms. Everett's share (30%): $12,304 × 0.30 = $3,691.20
Monthly deduction: $3,691.20 / 12 = $307.60
2. To find out how much Peter paid for his nutritional counseling, we subtract the $50 deductible from the total cost and then calculate 20% of the remaining amount (since the insurance pays 80%).
Total cost of counseling: $1,060
Deductible: $50
Amount after deductible: $1,060 - $50 = $1,010
Peter's share (20%): $1,010 × 0.20 = $202
3. To determine the total amount Mattie paid for her chiropractor visits, we multiply the co-pay by the number of visits and add to it the total amount of her share for the visits after insurance contribution.
Cost per visit: $305
Insurance pays (60%): $305 × 0.60 = $183
Mattie's share per visit (40%): $305 × 0.40 = $122
Co-pay per visit: $15
Total co-pay: $15 × 12 = $180
Total Mattie's share for visits: $122 × 12 = $1,464
Total amount Mattie paid: $1,464 + $180 = $1,644
In the diagram, SR = 4 square root 2 and OR= square room of 10. What is the perimeter of the parallelogram PQRS?
Answers
Answer:
the perimeter is [tex]8\sqrt{2} +2\sqrt{10}[/tex]
Step-by-step explanation:
It is given that PQRS is a parallelogram
with sides SR=[tex]4\sqrt{2}[/tex] and QR = [tex]\sqrt{10}[/tex]
We know that the opposite sides in a parallelogram are equal
so we have
PQ= SR= [tex]4\sqrt{2}[/tex]
PS= QR= [tex]\sqrt{10}[/tex]
Now to find the perimeter of parallelogram we add all the sides
perimeter = [tex]PQ+SR+PS+QR[/tex]
=[tex]4\sqrt{2} +4\sqrt{2} +\sqrt{10} +\sqrt{10}[/tex] ( plug the values)
=[tex]8\sqrt{2} +2\sqrt{10}[/tex]
hence the perimeter is [tex]8\sqrt{2} +2\sqrt{10}[/tex]
A student club set a goal of donating 50 blankets to a local shelter. Two classes have participated so far. Ms. Carter’s class gathered 18 blankets and Mr. Moriarti’s class gathered 23 blankets. How many more blankets are needed to reach the goal of 50 blankets
What type of problem is this? How can you tell?
a part-whole problem because Ms. Carter’s class only gathered part of the number of blankets Mr. Moriarti’s class gathered
a part-whole problem because the unknown number of blankets that are still needed is part of the whole goal of 50 blankets
a comparison problem because the number of blankets gathered is compared to the number of blankets still needed
a comparison problem because the number of blankets Ms. Carter’s class gathered is compared to the number of blankets Mr. Moriarti’s class gathered
Answers
the whole value should be 50 blankets. Part of these blankets have already been collected, thats (18 +23) 41 blankets.
we have been given the whole that's 50 and we have been given the part thats 41 in total. we still have to find the other part that should be included to make the whole number of blankets. We can find the unknown number by subtracting the part given (41) from the whole (50) and the unknown is then 9 blankets.
Therefore this is a part whole problem to find out the missing part.
Final answer:
The students need 9 more blankets to reach their goal of donating 50 blankets. This is a part-whole problem because we are looking for the unknown number of blankets needed to complete the whole goal.
Explanation:
The student club set a goal of donating 50 blankets to a local shelter, with Ms. Carter’s class and Mr. Moriarti’s class contributing towards this goal. To determine how many more blankets are needed, we need to use addition and subtraction. We add the number of blankets collected by both classes then subtract that total from the goal. Ms. Carter’s class gathered 18 blankets and Mr. Moriarti’s class gathered 23 blankets. The sum of their contributions is 18 blankets + 23 blankets = 41 blankets. The goal is 50 blankets, so we subtract the number collected from the goal: 50 blankets – 41 blankets = 9 blankets. So, the answer is that the students need 9 more blankets to reach their goal of 50.
This is a part-whole problem because the unknown number of blankets that are still needed is part of the whole goal of 50 blankets. The problem does not compare the amounts collected by each class, nor does it compare the number still needed with the number collected; instead, it regards the collected blankets as part of the complete set, which is why we can dismiss the other options.
The cunninghams are moving across the country. mr. cunningham leaves 3 hours before mrs. cunningham. if he averages 55mph and she averages 75mph, how long will it take mrs. cunningham to overtake mr. cunningham?
Answers
Mrs. Cunningham travels at a speed that is 20mph faster than Mr. Cunningham. Given that Mr. Cunningham has a 165-mile head start, Mrs. Cunningham would need 8.25 hours to cover this distance and catch up with him.
Explanation:This question can be approached by analysing the relative speeds and the initial advantage Mr. Cunningham had. Mr. Cunningham travels for three hours at 55 mph before Mrs. Cunningham leaves, giving him a 165 mile head start. To determine how long it will take Mrs. Cunningham to overtake Mr. Cunningham, it's necessary to calculate how long it will take her to make up this 165-mile deficit at her faster speed.
Mrs. Cunningham travels 75mph, which is 20mph faster than Mr. Cunningham's speed. Thus, each hour, she closes the distance between them by 20 miles. To find out how many hours it takes her to close the 165 mile distance between them, divide this distance by her relative speed, so: 165miles / 20mph equals 8.25 hours.
Thus, it will take Mrs. Cunningham 8.25 hours to overtake Mr. Cunningham.
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The clock face in a famous clock tower has a radius of about 5 meters. What is the area of the clock face to the nearest square meter? Use 3.14 as an approximation for .
Answers
79 square meter when you round it up
Answer:
The area of the clock face is [tex]79\ m^{2}[/tex]
Step-by-step explanation:
we know that
The area of a circle is equal to
[tex]A=\pi r^{2}[/tex]
we have
[tex]r=5\ m[/tex]
[tex]\pi=3.14[/tex]
substitute
[tex]A=(3.14)(5^{2})=78.5\ m^{2}[/tex]
Round to the nearest square meter
[tex]78.5\ m^{2}=79\ m^{2}[/tex]
Ernest is purchasing a $175,000 home and is making 20% down payment toward the cost. He is also buying 2 points in order to lower his inteest rate. The appraisal fee is $400, the title is $300, and the processing fee is $575. Including the down payment, what are his total closing costs?
Answers
Answer: 39,075 is the answer
Step-by-step explanation:
How do I solve this 45-45-90 triangle?
Answers
Answer:
[tex]\large\boxed{\tt x \ and \ y = 4}[/tex]
Step-by-step explanation:
[tex]\textsf{We are asked to solve for x and y of a 45-45-90 degree triangle.}[/tex]
[tex]\large\underline{\textsf{What is a 45}^{\circ}\textsf{- 45}^{\circ} \textsf{- 90}^{\circ} \textsf{Triangle?}}[/tex]
[tex]\textsf{A 45}^{\circ} \textsf{- 45}^{\circ} \textsf{- 90}^{\circ} \ \textsf{triangle is a special right triangle with legs that are congruent.}[/tex]
[tex]\textsf{These kinds of Triangles are considered "Special Right Triangles" as first they're}[/tex]
[tex]\textsf{Right Triangles, and secondly they have special side lengths that can be figured}[/tex]
[tex]\textsf{out with only one side length given.}[/tex]
[tex]\underline{\textsf{What are the Ratios between the sides?}}[/tex]
[tex]\tt Leg : Leg : Hypotenuse[/tex]
[tex]\tt x : x : x \sqrt2[/tex]
[tex]\textsf{If we are given a leg, the other leg will equal the same since these kinds of triangles}[/tex]
[tex]\textsf{have 2 equal sides, which are considered \underline{Isosceles Triangles}. Given that 4 is one}[/tex]
[tex]\textsf{leg, this means that the other leg is 4, and the Hypotenuse is 4} \tt \sqrt 2. \ \textsf{The}[/tex]
[tex]\textsf{Hypotenuse is always multiplied by} \ \tt \sqrt 2 \ \textsf{to equal the sum of the legs. Finding}[/tex]
[tex]\textsf{the legs are different however, as we need to divide the Hypotenuse by} \ \tt \sqrt2.[/tex]
[tex]\large\underline{\textsf{Solving;}}[/tex]
[tex]\textsf{We are given the Hypotenuse, and a 45}^{\circ} \ \textsf{angle to show that it's a 45}^{\circ}\textsf{- 45}^{\circ} \textsf{- 90}^{\circ}[/tex]
[tex]\textsf{triangle. Let's divide the Hypotenuse by} \ \tt \sqrt 2 \ \textsf{to find the value of x and y. Remember}[/tex]
[tex]\textsf{that the legs are equal to each other.}[/tex]
[tex]\tt \frac{Hypotenuse}{\sqrt2} = Leg.[/tex]
[tex]\tt \frac{4 \sqrt{\not2}}{\sqrt{\not{2}}} = x \ and \ y.[/tex]
[tex]\large\boxed{\tt x \ and \ y = 4}[/tex]