Given: PRST square
PMKD is a square
PR = a, PD = a
Find the area of PMCT.
PLEASE HELPP
Answers
Answer:
7a²/16
Step-by-step explanation:
Area of the triangle PTS
½ × a × a
a²/2
Length of PS:
sqrt(a² + a²)
asqrt(2)
Length of MS:
¼asqrt(2)
Triangles MCS and TPS are similar
With sides in the ratio:
¼asqrt(2) : a
sqrt(2)/4 : 1
Area of triangle SMC:
A/(a²/2) = [(sqrt(2)/4)]²
2A/a² = 1/8
A = a²/16
Area of PTMC
= a²/2 - a²/16
= 7a²/16
Step-by-step explanation:
This is a much more interesting problem than what we usually see here.
Let's just start by assuming a=1 so we have two unit squares.
PMC and PTC are two congruent triangles, each right triangles with one leg of length 1 and a shared hypotenuse PC.
We'll put it on the grid at P(0,0), T(1,0).
Angle TPM is 45 degrees and PM=1 so
M(cos 45, sin 45) = M(1/√2, 1/√2)
MK has slope -1, thru M, so is
y = -x + √2
C's on that line at x=1, so C's x coordinate is 1, so its y coordinate is √2 - 1
C(1, √2 - 1)
OK, that's enough to compute the area.
P(0,0), T(1,0), C(1, √2 - 1), M(1/√2, 1/√2)
area(PMCT) = area(PTC) + area(PCM)= 2 area(PTC)
The area of a right triangle is half the product of its legs.
area(PMCT) = 2 (1/2) (1) ( √2 - 1)
area(PMCT) = √2 - 1
When we have sides a, the area scales by a²,
Answer: a²(√2 - 1)
Related Questions
The data plots represent the hours students study each week in two different classrooms.
The mean number of hours a student in Mr. Hart’s class studies is hours.
The mean number of hours a student in Ms. Perry’s class studies is hours.
A typical student in Mr. Hart’s class studies a typical student in Ms. Perry’s class.
Poop
Answers
Answer:
The data plots represent the hours students study each week in two different classrooms
The mean number of hours a student in Mr. Hart’s class studies is (4.6) hours.
Answer: 4.6
The mean number of hours a student in Ms. Perry’s class studies is (2.8) hours.
Answer: 2.8
A typical student in Mr. Hart’s class studies a typical student in Ms. Perry’s (more than) class.
Answer: More than
Hope this helps
Final answer:
This inquiry involves comparing mean study times and understanding statistical concepts like the 30th percentile and hypothesis testing. The analysis includes determining if study habits have changed and interpreting the implications of percentile ranks among students.
Explanation:
The student's question pertains to statistics, specifically the comparison of mean study times between two classrooms and understanding of percentiles and hypothesis testing in the context of education research. When comparing the mean study times of students in Mr. Hart’s class to those in Ms. Perry’s class, it’s important to gather the numerical data representing the average weekly study hours for each class – which seems missing in the provided details. To understand the 30th percentile, in the context provided, it refers to the number of hours below which 30 percent of the students fall. Thus, thirty percent of students in the high school study seven or fewer hours per week, implying that the majority study more. To conduct a hypothesis test about whether study times have changed, one would set a null hypothesis stating that there has been no change in study time (with the mean study time equal to 2.5 hours), and an alternative hypothesis suggesting that the mean study time has increased. A statistical test (such as a t-test) would then be conducted to assess these hypotheses.
When planning a collaborative exercise for measuring student work habits, it is advisable to incorporate data collection and statistical analysis practices to allow students to understand real-world application of statistical concepts. The example given where students are asked to record their hourly activities over the course of a week is an excellent practice in self-monitoring and time management.
Given the equation of the parabola -36y = x^2 The focus of the parabola is
Answers
Which of the following shows that polynomials are closed under addition when two polynomials 4x + 6 and 2x2 − 8x − 4 are added? 2x2 − 4x + 2; will be a polynomial 2x2 − 4x + 2; may or may not be a polynomial 2x2 − 12x − 10; will be a polynomial 2x2 − 12x − 10; may or may not be a polynomial
Answers
Answer:
The answer is a
Step-by-step explanation
2x2 - 4x + 2 will be a polynomial
(4x + 6) + (2x² - 8x - 4)
= 4x + 6 + 2x² - 8x - 4
= 2x² + (4x - 8x) + (6 - 4)
= 2x² - 4x + 2
And it is polynomial (it has more than 1 term)
Answer:
A. [tex]2x^{2} - 4x + 2[/tex] ; will be a polynomial
Step-by-step explanation:
(4x + 6) + (2x² - 8x - 4)
= 4x + 6 + 2x² - 8x - 4
= 2x² + (4x - 8x) + (6 - 4)
= 2x² - 4x + 2
Polynomial (it has more than 1 term)
Hope that help!
Lilly constructed a box in the shape of a rectangular prism. The amount of space inside of the box is 180 cubic inches. What is the height of Lilly’s box?
Answers
3 inches
Explanation:
10x 6 x H = 180
60 x h = 180 divide
/60 /60
the Height is 3 in
Answer:
B
Step-by-step explanation:
3 in.
P is the set of factors of 20
Answers
The elements of set P={1,2,4,5,10,20}
Hope it will help you...
Answer:
P = {1 , 2 , 5 , 10 , 20}.
Step-by-step explanation:
20÷2
=10
10÷2
=5
5÷5
=1
then the prime factors of 20 are 2 and 5
all factors of 20 :1
and
2
and
5
and
5×2
=10
and
5×2^2
=20
to summarize the factors of 20 :P = {1 , 2 , 5 , 10 , 20}.
________________________________________
:)
Which of the following pair of right triangles cannot be proven to be congruent? Select all that apply.
Answers
Find the volume of the sphere whose radius is 0.8 cm
Answers
Answer:
2.14 cm^3
Step-by-step explanation:
V = 4/3 pi r^3
V = 4/3 pi 0.512
V = 2.14
Using this formula, you just plug in your current values into a calculator and out comes the answer!
[tex]\frac{4}{3}[/tex]πr³
[tex]\frac{4}{3}[/tex]π(0.512)
^ (do 0.8³, which equals 0.512)
ANSWER: 2.14
5(2x + 4) = 50 (Given)
10x + 20 = 50 (Distributive Property)
10x = 30 (?)
x = 3 (Division Property)
Fill in the missing reason for the argument shown.
Answers
Answer:
The answer is: D.) subtraction property
Step-by-step explanation:
The missing reason in the algebraic equation is the Subtraction Property of Equality, which involves subtracting the same number from both sides of an equation to maintain equality.
The missing reason for the argument shown is the Subtraction Property of Equality.
When we go from the step 10x + 20 = 50 to 10x = 30, we are subtracting 20 from both sides of the equation. This property states that if you subtract the same number from both sides of an equation, the two sides remain equal.
Therefore, the complete series of steps with their corresponding properties is:
5(2x + 4) = 50 (Given)
10x + 20 = 50 (Distributive Property)
10x = 30 (Subtraction Property of Equality)
x = 3 (Division Property)
how many different outcomes are possible from rolling a six sided cube four times
Answers
Answer:
1296 different outcomes
Step-by-step explanation:
Each cube has 6 possible values (from 1 to 6), and for each additional cube rolled, we have 6 more possible values, and the final number of different outcomes is the product of all the number of possible values for each cube.
So, if we roll the cube four times, the total number of different outcomes is:
6 * 6 * 6 * 6 = 1296
We have 1296 different outcomes from rolling the six sided cube four times.
James and two friends are going bowling. It costs them six dollars to rent the lane and
three dollars for each game they bowl. In interval form, how many games can they play
if they brought twenty five dollars?
(0,6]
(0,6)
(0,8]
(0,8)
Answers
Answer:
answer is c
Step-by-step explanation:
Answer:
(0,8}
Step-by-step explanation:
PLEASE HELP! CORRECT ANSWERS ONLY! 20 POINTS
In two or more complete sentences discuss the advantages and disadvantages of investing in a 529 plan versus investing in a money market account.
Answers
Answer:
1.) In 529 plan, Your account earns interest and you can contribute as much as you want. But Your investment options are limited and the money must be used for college
2.) While in money market account, the account pays higher interest than traditional savings accounts, but limited to writing no more than three checks a month. Some banks limit your cash withdrawals.
Step-by-step explanation:
Money market deposit accounts are better choices than 529 plan for money you might need to tap at a moment’s notice to cover an emergency or an unexpectedly large expense. They pay higher interest than ordinary savings accounts and give you immediate access to your money
While in 529 savings plan, If you don’t use the money invested for college tuition, you will be penalized 10 percent when you withdraw the money to use it for something else. In addition, both your state and the federal government will tax the earnings on your account in your current tax bracket.
The function ƒ(x) = x is transformed to g(x) = 2x. What type of transformation has occurred?
Question 6 options:
A)
Reflection
B)
Vertical translation
C)
Rotation
D)
Can't be determined
Answers
Answer:
Scaling
Step-by-step explanation:
Scaling was the type of transformation used on f(x), such that:
[tex]g (x) = 2 \cdot f(x)[/tex]
Simplify. Express your answer as a single term using exponents. 6689x 6689
Answers
Answer:
(6689)^2
Step-by-step explanation:
6689x 6689
There are 2 terms multiplied together and they are identical
a*a = a^2
6689x 6689 = (6689)^2
Solve the quadratic equation for x.
3x2+12x=0
x =
or x =
Answers
Answer:
x=0, x=-4
Step-by-step explanation:
Answer:
x=0, x=4
Step-by-step explanation: yes
What is the value of a if the point (a, 2) is also on the line?
Answers
Answer:
i think -7
Step-by-step explanation:
but im not sure
What is the length of a diagonal of a cube with a side length of 3 cm?18 cm
27 cm
33 cm
138 cm
Answers
What is the equation that represents the line?
Answers
Answer: -7-4
Step-by-step explanation:
If u could answer this u would be magical
Answers
Answer:
12r^2 +r -7
Step-by-step explanation:
9r^2 +4r -7 +3r^2 -3r
Combine like terms
9r^2 +3r^2 +4r -3r -7
12r^2 +r -7
Which graph shows the information in the table?
Minutes in Hours
Number of Minutes Number of Hours
30 0.5
60 1
90 1.5
120 2
Answers
Answer:
The last graph
Step-by-step explanation:
In the first and third one the labels are switched. And the minutes should be on the x axis while the hours should be on the y axis.
The second one is incorrect because it literally says that 0 minutes= 0.5 hour
Answer:
A (the first graph on edge)
Step-by-step explanation:
Looking at the graph, we can see that the graph that has the line pass through (30, .5) is going to be the correct one.
I need help! Please answer below on card A
Answers
Answer:
x = 8
DBC = 32
Step-by-step explanation:
The sum of the two smaller angles is the larger angle
23+4x = 55
Subtract 23 from each side
23+4x-23 =55-23
4x = 32
Divide each side by 4
4x/4 = 32/4
x = 8
Then we want to find DBC = 4x = 4*8 = 32
The Fahrenheit measure of temperature is a function of the Celsius measure. The Fahrenheit measure is 32 more than StartFraction 9 Over 5 EndFraction times the Celsius measure. Which equation best fits the situation? Use g to represent the function. a. x (g) + 32 = StartFraction 9 Over 5 EndFraction (x) b. x (g) = StartFraction 9 Over 5 EndFraction (x) + 32 c. g (x) + 32 = StartFraction 9 Over 5 EndFraction (x) d. g (x) = StartFraction 9 Over 5 EndFraction (x) + 32
Answers
Answer:
D. [tex]g(x) = \frac{9}{5}\cdot x + 32[/tex]
Step-by-step explanation:
The mathematical transcription of the statement is:
[tex]g(x) = \frac{9}{5}\cdot x + 32[/tex]
Which corresponds with option D.
Special Segments, Please help!
x= 1, 3, 7
Answers
Answer:
x=3
Step-by-step explanation:
Secant-Secant Formula:
(whole secant) x (external part) = (whole secant) x (external part)
9*4 = 12*x
36 = 12x
Divide each side by 12
36/12 = 12x/12
3 =x
How many solutions exist for the given equation?
1/2(x + 12) = 4x – 1
1.zero
2.one
3. two
4. infinitely many
Answers
Answer:
one
Step-by-step explanation: you cant simplify the equation so that both sides can be divided to get the same equation, if you graph it theres not a parabola so the only thing left is one.
Answer:
One solution
Step-by-step explanation:
To solve this problem, isolate x.
1/2(x + 12) = 4x - 1
Dividing 1/2 from both sides, we get x + 12 = 8x - 2
Subtracting 12 from both sides, we get x = 8x - 14
Subtracting 8x from both sides, we get -7x = -14
Dividing -7 from both sides, we get x = 2
Since this problem is able to be solved with only one answer, there is one solution: x = 2.
Miriam took a survey, asking each family in her neighborhood how many pets they have. She made a graph showing the results: [asy] size(5.5cm); draw((0,30)--(0,0)--(41,0)); for(int i=1; i<7; i+=1) {draw((0.6,5*i)--(-0.6,5*i)); draw((0.6,5*i)--(41,5*i),black+0.5+dashed); }; path a=(3,0)--(3,30)--(9,30)--(9,0)--cycle; path b=(9,0)--(9,15)--(15,15)--(15,0)--cycle; path c=(15,0)--(15,15)--(21,15)--(21,0)--cycle; path d=(21,0)--(21,30)--(27,30)--(27,0)--cycle; path e=(27,0)--(27,5)--(33,5)--(33,0)--cycle; path f=(33,0)--(33,5)--(39,5)--(39,0)--cycle; fill(a,gray); fill(b,gray); fill(c,gray); fill(d,gray); fill(e,gray); fill(f,gray); draw(a); draw(b); draw(c); draw(d); draw(e); draw(f); label(rotate(-45)*scale(0.8)*"0 pets",(5,-1),SE); label(rotate(-45)*scale(0.8)*"1 pet",(11,-1),SE); label(rotate(-45)*scale(0.8)*"2 pets",(17,-1),SE); label(rotate(-45)*scale(0.8)*"3 pets",(23,-1),SE); label(rotate(-45)*scale(0.8)*"4 pets",(29,-1),SE); label(rotate(-45)*scale(0.8)*"5 pets",(35,-1),SE); label(scale(0.8)*"1",(-0.6,5),W); label(scale(0.8)*"2",(-0.6,10),W); label(scale(0.8)*"3",(-0.6,15),W); label(scale(0.8)*"4",(-0.6,20),W); label(scale(0.8)*"5",(-0.6,25),W); label(scale(0.8)*"6",(-0.6,30),W); label(scale(0.8)*rotate(90)*"Number of families",(-3.5,15),W); [/asy] What is the average number of pets per family?
Answers
Answer:
1.8
Step-by-step explanation:
The graph of the problem is plotted using Asymptote and attached.
From the graph:
6 Families had 0 Pets3 Families had 1 Pets3 Families had 2 Pets6 Families had 3 Pets1 Family had 4 Pets1 Family had 5 PetsThere are a total of 20 families.
Average Number of Pets
[tex]=\dfrac{6*0+3*1+3*2+6*3+1*4+1*5}{20} \\\\=\dfrac{36}{20}\\\\=1.8[/tex]
The average number of pets per family is 1.8.
Answer:
1.8
Step-by-step explanation:
The bar chart tells us that:
6 families each have 0 pets,
3 families each have 1 pet,
3 families each have 2 pets,
6 families each have 3 pets,
1 family has 4 pets, and
1 family has 5 pets.
The total number of pets in all these families is (6 ∙ 0) + (3 ∙ 1) + (3 ∙ 2) + (6 ∙t 3) + (1 ∙ 4) + (1 ∙ 5) = 36. The number of families is 6 + 3 + 3 + 6 + 1 + 1 = 20. Therefore, the average number of pets per family is 38/20 = 1.8.
Select the points that are solutions to the system of inequalities. Select all that apply
Answers
Answer:
(-10, 10) and (0,10).
Step-by-step explanation:
For a point to be a solution to the system of inequalities, you will need to see which of the points falls into the shaded area.
When we test out each of the points, we can see that only:
(-10, 10) and (0,10) fall into the blue-shaded area.
Answer:
-10,10 and 0,10
Step-by-step explanation:
alvs verified 100% correct
In a right triangle, 0 is an acute angle and cos0= 6/11. Evaluate the other five trigonometric functions of 0.
Answers
Answer:
sin O = √85/11, csc O = 11/√85
cos O = 6/11, sec O = 11/6
tan O = √85/6, cot = 6/√85.
Step-by-step explanation:
cos = adjacent / hypotenuse = 6/11, so the opposite side to angle O
= √(11^2 - 6^2)
= √85.
csc O = 1/sin O
sec O = 1/cos O
cot O = 1/tan O.
Candita uses 1 of an ounce of green paint each time she draws a green line on her painting. She draws a total of 7 green
lines. Which expression represents the amount of green paint that Candita used drawing green lines on the painting? Check
all that apply.
1+1+1+1+1+1+1
0 1 2 + 1 2 + 1 2 + 2 / 2
Answers
This results in the total amount of 7/8 ounce of green paint used.
The amount of green paint that Candita used for drawing seven green lines on her painting can be represented by the expression 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8. Each 1/8 ounce of green paint is used for one green line, and she draws a total of 7 green lines. So, we simply add up seven times the fraction 1/8.
The sum can be calculated as:
1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8Which equals:
7/8 ounce of green paintThis is the total amount of paint she used to draw all the green lines.
Write two numbers that multiply to the value on top and add to the value on bottom.
Answers
(1,20),(2,10),(5,4)
The pair that also adds up to 20 is (2,10). So these are the two numbers you need.
The models all represent a real-world problem. How would you match the models to a problem? Find a problem with the same variables and the same relationship between the quantities. Find a problem that has the same numbers. Find a problem that has the same variables. Find a problem that has the same x-values.
Answers
Answer A
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
hope this helps!
Mrs. Zimmerman’s students build letter of their names out of wood. Holly builds an H using rectangles with the dimensions shown.
Answers
Answer:
you have to show us a clip so that we can see & so that we can help