What is the surface area of a triangular with 6, 7cm 4cm 12cm
The surface area of the given triangle is approximately 33.74 square centimeters.
To calculate the surface area of a triangle, we need the lengths of two sides and the included angle between them. However, in this case, you provided the lengths of all three sides (6 cm, 7 cm, and 12 cm).
To determine the surface area, we can use Heron's formula, which is applicable to triangles with all three side lengths known.
Heron's formula states that the surface area (A) of a triangle with side lengths a, b, and c is given by:
[tex]A = \sqrt(s \times (s - a) \times (s - b) \times (s - c))[/tex]
where s is the semi perimeter of the triangle, calculated as:
s = (a + b + c) / 2
Plugging in the given side lengths, we have:
s = (6 cm + 7 cm + 12 cm) / 2 = 25 / 2 = 12.5 cm
Now we can substitute the values into Heron's formula:
[tex]A = \sqrt(12.5 cm \times (12.5 cm - 6 cm) \times (12.5 cm - 7 cm) \times (12.5 cm - 12 cm))[/tex]
[tex]= \sqrt(12.5 cm \times 6.5 cm \times 5.5 cm \times 0.5 cm)[/tex]
= √(1137.5 cm^4)
≈ 33.74 cm^2
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Find the surface area of the regular pyramid shown to the nearest whole number.
to scale.
13 m
6.5-√3 m
9m
Please answer ASAP I will brainlist
Using Gauss-Jordan method, the value of x, y and z are 0, -2 and 1
What is the solution of the system of equation?To solve the system of equations using the Gauss-Jordan method, we'll perform row operations to transform the augmented matrix into row-echelon form and then further transform it into reduced row-echelon form. Here are the steps:
1. Write the augmented matrix for the system of equations:
[1 -2 4 | 20]
[1 1 13 | -31]
[-2 6 -1 | -69]
2. Perform row operations to transform the matrix into row-echelon form:
R2 = R2 - R1
R3 = R3 + 2R1
[1 -2 4 | 20]
[0 3 9 | -51]
[0 2 7 | -29]
3. Perform row operations to further transform the matrix into reduced row-echelon form:
R2 = R2 / 3
R3 = R3 - 2R2
[1 -2 4 | 20]
[0 1 3 | -17]
[0 0 1 | 1]
4. Perform row operations to obtain a diagonal of 1s from left to right:
R1 = R1 + 2R2 - 4R3
R2 = R2 - 3R3
[1 0 0 | 0]
[0 1 0 | -2]
[0 0 1 | 1]
The resulting matrix corresponds to the system of equations:
x = 0
y = -2
z = 1
Therefore, the solution to the given system of equations is x = 0, y = -2, and z = 1.
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Christina is buying a $170,000 home with a 30-year mortgage. She makes a $20,000 down payment.
Use the table to find her monthly PMI payment.
A. $51.25
B. $37.50
C. $23.75
D. $42.50
The monthly PMI Payment for Christina's loan is $37.50.The correct answer is option B.
To determine Christina's monthly PMI (Private Mortgage Insurance) payment, we need to find the corresponding interest rate for her loan-to-value (LTV) ratio. The LTV ratio is calculated by dividing the loan amount by the property value.
The loan amount can be calculated by subtracting the down payment from the property value:
Loan amount = Property value - Down payment
= $170,000 - $20,000
= $150,000
Now we can calculate the LTV ratio:
LTV ratio = Loan amount / Property value * 100
= $150,000 / $170,000 * 100
= 88.24%
Since Christina is obtaining a 30-year mortgage, we need to look at the interest rates for LTV ratios between 85.01% and 90%. According to the table, the interest rate for this range is 0.30%.
To calculate the PMI payment, we multiply the loan amount by the PMI rate and divide it by 12 months:
PMI payment = (Loan amount * PMI rate) / 12
= ($150,000 * 0.30%) / 12
= $450 / 12
= $37.50
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The Probable question may be:
Christina is buying a $170,000 home with a 30-year mortgage. She makes a $20,000 down payment.
Use the table to find her monthly PMI payment
Base to loan% = 95.01% to 97%,90.01% to 95%,85.01% to 90%,80.01% to 85%.
30-year fixed-rate loan = 0.55%,0.41%,0.30%,0.19%
15-year fixed-rate loan = 0.37%,0.28%,0.19%,0.17%.
A. $51.25
B. $37.50
C. $23.75
D. $42.50
Use the following models to show the equivalence of the fractions 35 and 610 a) Set model
Answer:
0
Step-by-step explanation:
Use the following models to show the equivalence of the fractions 35 and 610 a) Set model
Read the following conditional statement:
If one of the angles of a triangle equals 90º, then the triangle is classified as a right triangle.
Which of the following choices is the first step of an indirect proof?
If the triangle is a right triangle
If the triangle is not a right triangle
If the triangle equals 90º
None of these choices are correct.
Answer/Step-by-step explanation:
C., the first proof we would be given if a little box is shown, which indicates a 90 degree angle at the place where to lines touch in a T kind of manor. So C is the answer.
Select the correct answer.
Mr. Miller owns two hotels and is ordering towels for the rooms. He ordered 27 hand towels and 48 bath towels for a bill of $540 for the first hotel. He
ordered 50 hand towels and 24 bath towels for a bill of $416 for the other hotel.
What is the cost of one hand towel and one bath towel?
O A.
OB.
OC.
O D.
The cost of one hand towel is $4 and the cost of one bath towel is $9.
The cost of one hand towel is $9 and the cost of one bath towel is $4.
The cost of one hand towel is $5 and the cost of one bath towel is $8.
The cost of one hand towel is $8 and the cost of one bath towel is $5.
Answer: D: The cost of one hand towel is $8 and the cost of one bath towel is $5.
Step-by-step explanation:
Let's assume the cost of one hand towel is 'x' dollars and the cost of one bath towel is 'y' dollars.
For the first hotel, Mr. Miller ordered 27 hand towels and 48 bath towels, resulting in a bill of $540. This can be expressed as the equation:
27x + 48y = 540 ...(equation 1)
For the second hotel, Mr. Miller ordered 50 hand towels and 24 bath towels, resulting in a bill of $416. This can be expressed as the equation:
50x + 24y = 416 ...(equation 2)
To solve this system of equations, we can use any suitable method such as substitution or elimination. Let's use the elimination method:
Multiplying equation 1 by 2 and equation 2 by 3, we get:
54x + 96y = 1080 ...(equation 3)
150x + 72y = 1248 ...(equation 4)
Now, subtracting equation 4 from equation 3, we have:
(54x + 96y) - (150x + 72y) = 1080 - 1248
-96x + 24y = -168
Dividing both sides of the equation by -24, we get:
4x - y = 7 ...(equation 5)
Now, we have a system of equations:
4x - y = 7 ...(equation 5)
50x + 24y = 416 ...(equation 2)
Solving this system of equations, we find that x = 8 and y = 5.
Therefore, the cost of one hand towel is $8 and the cost of one bath towel is $5.
So, the correct answer is option D: The cost of one hand towel is $8 and the cost of one bath towel is $5.
Answer:
Step-by-step explanation:
Total cost of hand towels for first hotel = 27 * $5 = $135
Total cost of bath towels for first hotel = 48 * $8 = $384
Total cost of hand towels for second hotel = 50 * $5 = $250
Total cost of bath towels for second hotel = 24 * $8 = $192
Total cost of all hand towels = $135 + $250 = $385
Total cost of all bath towels = $384 + $192 = $576
Total number of hand towels = 27 + 50 = 77
Total number of bath towels = 48 + 24 = 72
Average cost of one hand towel = $385 / 77 = $5
Average cost of one bath towel = $576 / 72 = $8
For the sequence -27,-12, 3, 18,..., the expression that defines the nth term where a, = -27 is
Answer:
-27+15 (N-1)
Step-by-step explanation:
-27, -12, 3, 18
Take the second term and subtract the first term to find the common difference
-12 - (-27)
-12+27 = 15
The common difference is +15
We are adding 15 each time
The formula for an arithmetic sequence is
an = a1+d(n-1)
an = -27 +15(n-1)
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Answer:
[tex]\textsf{12)} \quad \text{a.}\;\;m \angle 1 = 107^{\circ}, \quad \text{b.}\;\;m \angle 2 = 107^{\circ}, \quad \text{c.}\;\;m \angle 3 = 73^{\circ}[/tex]
[tex]\textsf{13)} \quad EC = 6[/tex]
[tex]\textf{14)}\quad \text{a.}\;\;x = 33, \quad \text{b.}\;\; x = 8[/tex]
Step-by-step explanation:
Question 12As the base angles of an isosceles trapezoid are congruent, the measures of angles E and J are the same. Therefore:
[tex]m\angle 3 = 73^{\circ}[/tex]
The opposite angles of an isosceles trapezoid sum to 180°. Therefore:
[tex]\implies m\angle 1 + m\angle 3 = 180^{\circ}[/tex]
[tex]\implies m\angle 1 + 73^{\circ} = 180^{\circ}[/tex]
[tex]\implies m\angle 1 = 107^{\circ}[/tex]
Since the base angles of an isosceles trapezoid are congruent, the measures of angles A and N are the same. Therefore:
[tex]m\angle 2 = 107^{\circ}[/tex]
[tex]\hrulefill[/tex]
Question 13The diagonals of isosceles trapezoid ABCD are AC and BD.
Point E is the point of intersection of the diagonals. Therefore:
[tex]BE + ED = BD[/tex]
[tex]AE + EC = AC[/tex]
As the diagonals of an isosceles trapezoid are the same length, BD = AC. Therefore:
[tex]AE + EC = BD[/tex]
Given BD = 20 and AE = 14:
[tex]\implies AE + EC = BD[/tex]
[tex]\implies 14 + EC = 20[/tex]
[tex]\implies 14 + EC - 14 = 20 - 14[/tex]
[tex]\implies EC = 6[/tex]
[tex]\hrulefill[/tex]
Question 14The midsegment of a trapezoid is a line segment that connects the midpoints of the two non-parallel sides (legs) of the trapezoid.
The formula for the midsegment of a trapezoid is:
[tex]\boxed{\begin{minipage}{6 cm}\underline{Midsegment of a trapezoid}\\\\$M=\dfrac{1}{2}(a+b)$\\\\where:\\ \phantom{ww}$\bullet$ $M$ is the midsegment.\\ \phantom{ww}$\bullet$ $a$ and $b$ are the parallel sides.\\\end{minipage}}[/tex]
a) From inspection of the given trapezoid:
M = xa = 18b = 48Substitute these values into the midsegment formula and solve for x:
[tex]x=\dfrac{1}{2}(18+48)[/tex]
[tex]x=\dfrac{1}{2}(66)[/tex]
[tex]x=33[/tex]
Therefore, the value of x is 33.
b) From inspection of the given trapezoid:
M = 15a = 22b = xSubstitute these values into the midsegment formula and solve for x:
[tex]15=\dfrac{1}{2}(22+x)[/tex]
[tex]30=22+x[/tex]
[tex]x=8[/tex]
Therefore, the value of x is 8.
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Please help with 23a and 24a
Answer:
perimeter = 75 cm , area ≈ 28.3 in²
Step-by-step explanation:
23 (a)
since the figure is being enlarged by a scale factor of 5
then the perimeter is increased by a factor of 5.
perimeter of larger shape = 5 × 15 = 75 cm
24
the area (A) of the sector is calculated as
A = area of circle × fraction of circle
= πr² × [tex]\frac{90}{360}[/tex]
= π × 6² × [tex]\frac{1}{4}[/tex]
= 36π × [tex]\frac{1}{4}[/tex]
= 9π
≈ 28.3 in² ( to 1 decimal place )
Need help with the vector page
Answer:
Only one scalene triangle with side lengths of 12 in, 15 in, and 18 in exists. Therefore, exactly one unique triangle exists with the given side lengths.
Step-by-step explanation:
a/(2x - 3) + b/(3x + 4) = (x + 7)/(6x ^ 2 - x - 12)
Answer:
[tex] \frac{a}{2x - 3} + \frac{b}{3x +4} = \frac{x + 7}{ 6{x}^{2} - x - 12} [/tex]
[tex](3x + 4)a + (2x - 3)b = x + 7[/tex]
3a + 2b = 1---->9a + 6b = 3
4a - 3b = 7---->8a - 6b = 14
--------------- ----------------
17a = 17
a = 1, b = -1
Which statement can be concluded using the true statements shown?
If two angles in a triangle measure 90° and x degrees, then the third angle measures (90-x) degrees.
In triangle ABC, angle A measures 90 degrees and angle B measures 50°.
Angle C must measure 50 degrees.
Angle C must measure 40 degrees.
O Angle C must measure (90 - 40) degrees.
O Angle C must measure (90-30) degrees.
Answer:
Angle C must measure 40 degrees.
Step-by-step explanation:
All angles in a triangle add up to 180 degrees
(90-50)=40 degrees
We can check our answer by adding all the angles up
90+50+40=180
Angle C must be 40 degrees
Deacon Company is a merchandising company that is preparing abudget for the three-month period ended June 30th. The followinginformation is availableDeacon CompanyBalance SheetMarch 31AssetsCash$60,200 Accounts receivable $30,800Inventory $60,400Buildings and equipment, net of depreciation $124,000Total assets$295,400Liabilities and Stockholders’EquityAccounts payable$71,100Common stock 70,000Retained earnings $134,300Total liabilities and stockholder...
The total liabilities and stockholders' equity for Deacon Company as of March 31st is $275,400.
To calculate the total liabilities and stockholders' equity, we need to add the amounts of accounts payable, common stock, and retained earnings. Accounts Payable: The balance sheet provides the information that the accounts payable is $71,100.
Common Stock: The balance sheet states that the common stock is $70,000.
Retained Earnings: The balance sheet shows that the retained earnings are $134,300.
Calculate the total liabilities and stockholders' equity: Add the amounts of accounts payable, common stock, and retained earnings.
Total liabilities and stockholders' equity = Accounts payable + Common stock + Retained earnings
= $71,100 + $70,000 + $134,300
= $275,400
Therefore, the total liabilities and stockholders' equity for Deacon Company as of March 31st is $275,400.
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How to make 1001 from nine 9. Use can use 9 in any way
Using the given operations and nine 9s, you can make 1001.
How to make 1001 from nine 9. Use can use 9 in any wayTo make 1001 using nine 9s, you can use the following mathematical operations:
1. (9 + 9 + 9) * 9 * 9 - 9 - 9 - 9 = 1001
- Adding three 9s together: (9 + 9 + 9) = 27
- Multiplying the sum by two 9s: (27 * 9 * 9) = 2187
- Subtracting three 9s: (2187 - 9 - 9 - 9) = 2160
- Adding one 9: (2160 + 9) = 2169
- Adding 832 (which is (9 * 9 * 9 + 9 * 9 + 9)) to 2169: (2169 + 832) = 3001
- Subtracting two 9s: (3001 - 9 - 9) = 2983
- Adding nine 9s: (2983 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9) = 1001
Therefore, using the given operations and nine 9s, you can make 1001.
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8.5 x 10[2] my assignment is about exponents
Answer:
850
Step-by-step explanation:
Our given expression is [tex]8.5*10^{2}[/tex]
To solve, simply use PEMDAS as it applies to the expression.
First, you do the exponent(s): [tex]10^2 = 100[/tex]
Then, you do multiplication: [tex]8.5*100=850[/tex]
So, your answer is 850.
representa graficamente los vectores 2u, -3v y 1/4 usando los vectores dados A -1,3
B -2,4 C 0,-2 D 8,1
Para representar gráficamente los vectores 2u, -3v y 1/4, necesitamos utilizar los vectores dados A(-1,3), B(-2,4), C(0,-2) y D(8,1).
Vector 2u:
El vector 2u se obtiene al multiplicar el vector u por 2. Si conocemos las coordenadas de u, podríamos multiplicar cada componente por 2. Sin embargo, no se proporciona información sobre las coordenadas de u, por lo que no podemos realizar este cálculo específico.
Vector -3v:
Similar al caso anterior, para obtener el vector -3v, debemos multiplicar el vector v por -3. Sin información sobre las coordenadas de v, no podemos realizar este cálculo específico.
Vector 1/4:
El vector 1/4 se obtiene al multiplicar cada componente de los vectores A, B, C y D por 1/4. Podemos calcular las nuevas coordenadas de estos vectores:A' = (-1/4, 3/4)
B' = (-1/2, 1)
C' = (0, -1/2)
D' = (2, 1/4)
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PLS HELP WILL GIVE BRAINLIEST IF ANSWER IS CORRECT (NO LINKS)
Identify the value of b and the length of each chord.
Answer: C
b = 6; JG = 34; HF = 29
find AB using segment addition prostulate 2x-3 24 5x+6
Answer:
To find the length of AB using the segment addition postulate , we need to add the lengths of segments AC and CB.
AC + CB = AB
Substituting the given lengths:
2x-3 + 24 = 5x+6
Simplifying and solving for x:
21 = 3x
x = 7
Now that we know x, we can substitute it back into the expression for AB:
AB = 2x-3 + 24 = 2(7)-3 + 24 = 14-3+24 = 35
Therefore, the length of AB is 35.
Step-by-step explanation:
Giraffe jack is 19ft tall, and ostrich Jim is 9ft tall. What percent of Jim’s height is jacks height?
Answer:
211%
Step-by-step explanation:
percent = part/whole × 100%
percent = 19/9 × 100%
percent = 211%
What function has the same range as f(x) = -2 x - 3 + 8
Answer:
Any equation that has the power of x at 1
Step-by-step explanation:
Since the function f(x) = -2x -3 +8 has an infinite range, so any other equation that only contains x^1 would work
Algebra Question
Jasmine played outside today. She asked her mother if she could play outside tomorrow. Her mother said she could play outside only if the difference between today’s temperature and tomorrow’s temperature is less than 10 degrees. If today’s temperature was 93, what is the range of temperatures that would allow Jasmine to play outside tomorrow?
Address each of these parts:
a. Define the variable for the situation.
b. Write an absolute value inequality to represent the situation (tolerance).
c. Solve the inequality.
Referring back to the last question, using words, write the interpretation of the solution in terms of the range of temperatures that will allow Jasmine to play outside. Then, graph the solution.
Answer:
a. Let tomorrow's temperature be x
b.
[tex] |93 - x | < 10[/tex]
c.
[tex] - 10 < 93 - x < 10 \\ - 103 < - x < - 83 \\ 103 > x > 83[/tex]
Snow Fall (Inches)
2.75
2.5
2.25
2
1.75
1.5
1.25
1
0.75
0.5
0.25
0
4
O A. 1.25
OB. 0.75
O C. 2.5
O D. 1.5
●
1
2
3
4
Time (hours after Midnight)
5
12. The graph above depicts the amount of snow accumulation from midnight to 5:00 a.m. The x-axis represents time (hours after midnight), and the y-axis represents the number of
inches of snow on the ground. How many inches of snow accumulated between 2:00 a.m. and 5:00 a.m.?
The amount of snow accumulated between 2 am and 5 am is: 1.25 inches
How to Interpret Linear Equation Graphs?The general formula for the equation of a line in slope intercept form is:
y = mx + c
where:
m is slope
c is y-intercept
From the given graph attached, we see that the y-axis gives the amount of snow at different specific times.
Meanwhile the x-axis gives the time in hours after midnight
At 2am, the y-axis value is 1.25 inches, and as such at 2am snow accumulation was 1.25 inches.
At 5 am, the y-axis value reads 2.5 inches, and as such at 5am snow accumulation was 2.5 inches.
The difference in both snow accumulations is: 2.5 - 1.25 = 1.25
Hence, 1.25 inches snow accumulated between 2 am and 5 am.
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In the figure, m<1 = (x+6)°, m<2 = (2x + 9)°, and m<4 = (4x-4)°. Write an
expression for m<3. Then find m<3.
A. 180° -(x+6)°
B. 180° -(4x-4)°
C. 180° - [(2x+9)° + (x+6)°]
D. 180° + (x+6)°
m<3=
The expression for m<3 is 349° - 7x.
To find the measure of angle 3 (m<3), we need to apply the angle sum property, which states that the sum of the angles around a point is 360 degrees.
In the given figure, angles 1, 2, 3, and 4 form a complete revolution around the point. Therefore, we can write:
m<1 + m<2 + m<3 + m<4 = 360°
Substituting the given angle measures, we have:
(x + 6)° + (2x + 9)° + m<3 + (4x - 4)° = 360°
Combining like terms:
7x + 11 + m<3 = 360°
To isolate m<3, we subtract 7x + 11 from both sides:
m<3 = 360° - (7x + 11)
m<3 = 360° - 7x - 11
m<3 = 349° - 7x
Therefore, the expression for m<3 is 349° - 7x.
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Calculate:
1+2-3+4+5-6+7+8-9+…+97+98-99
The value of the given expression is 1370.
To calculate the given expression, we can group the terms in pairs and simplify them.
We have the following pattern:
1 + 2 - 3 + 4 + 5 - 6 + 7 + 8 - 9 + ... + 97 + 98 - 99
Grouping the terms in pairs, we can see that each pair consists of a positive and a negative term. The positive term increases by 1 each time, and the negative term decreases by 1 each time. Therefore, we can rewrite the expression as:
(1 - 3) + (2 + 4) + (5 - 6) + (7 + 8) + ... + (97 + 98) - 99
The sum of each pair in parentheses simplifies to a single term:
-2 + 6 - 1 + 15 + ... + 195 - 99
Now, we can add up all the terms:
-2 + 6 - 1 + 15 + ... + 195 - 99 = 1370
As a result, the supplied expression has a value of 1370.
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How do you find the approximate circumference of a circle with a diameter of 6 inches.use 3.14 as estimate of tt that is correct to two decimal places.
Answer:
18.84 in
Step-by-step explanation:
The circumference of a circle = pi * diameter = 6*3.14 = 18.84 in.
de un grupo de 75 alumnos se sabe que 20 estudian mate y física determina la probabilidad que al escoger un alumno estudie a) estudie solo mate b) estudie mate o fisica c) que no estudié ninguna de las dos d) que estudie mate y fisica
A) The probability that a randomly selected student studies only mathematics would be 20/75.
B) The probability that a randomly selected student studies mathematics or physics would be (20 + X) / 75.
C) The probability that a randomly selected student does not study either of the two subjects would be (75 - (20 + X)) / 75.
D) The exact probability that a student studies mathematics and physics cannot be determined without knowing the number of students who study both subjects.
To determine the requested probabilities, we will use the information provided about the group of 75 students.
a) Study only mate:
We know that there are 20 students studying mathematics and physics, so the number of students studying only mathematics would be the total number of students studying mathematics (20) minus the number of students studying both subjects. Since no information is provided on the number of students studying both subjects, we will assume that none of the students study both subjects. Therefore, the number of students studying only mathematics would be 20 - 0 = 20.
The probability that a randomly selected student studies only mathematics would be 20/75.
b) Study math or physics:
To determine this probability, we need to add the number of students who study mathematics and the number of students who study physics, and then subtract the number of students who study both subjects (we again assume that none of the students study both subjects).
Number of students studying mathematics = 20
Number of students studying physics = X (not given)
Number of students studying both subjects = 0 (assumed)
Therefore, the number of students studying mathematics or physics would be 20 + X - 0 = 20 + X.
The probability that a randomly selected student studies mathematics or physics would be (20 + X) / 75.
c) That he does not study either:
The number of students not studying either subject would be the complement of the number of students studying mathematics or physics. So it would be 75 - (20 + X).
The probability that a randomly selected student does not study either of the two subjects would be (75 - (20 + X)) / 75.
d) To study math and physics:
Since no information is provided on the number of students studying both subjects, we cannot determine the exact probability that a student will study mathematics and physics.
In summary:
a) The probability that a randomly selected student studies only mathematics would be 20/75.
b) The probability that a randomly selected student studies mathematics or physics would be (20 + X) / 75.
c) The probability that a randomly selected student does not study either of the two subjects would be (75 - (20 + X)) / 75.
d) The exact probability that a student studies mathematics and physics cannot be determined without knowing the number of students who study both subjects.
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Determine the range of the following graph:
Answer:
The range of this graph is (-4, 6], or
-4 < y < 6.
The range of the graph is [-4, 6].
What is a range?In Mathematics and Geometry, a range is the set of all real numbers that connects with the elements of a domain.
This ultimately implies that, a range simply refers to the set of all possible output numerical values (real numbers), which are shown on the y-coordinate (y-axis) of a graph.
Based on the information provided in this scenario, the domain and range of the graph of this equation can be determined are as follows:
Domain = [1, 10] or 1 ≤ x < 10
Range = [-4, 6], or -4 < y ≤ 6.
Therefore, the range can be rewritten as [-4, 6].
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Graph the ellipse, Plot the foci of the ellipse 100pts
Answer:
Step-by-step explanation:
The general equation for an ellipse with center (h, k) is:
[tex]\boxed{\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1}[/tex]
If a > b, the ellipse is horizontal.
If b > a, the ellipse is vertical.
Given equation:
[tex]\dfrac{(x-5)^2}{4}+\dfrac{(y+5)^2}{9}=1[/tex]
As b > a, the ellipse is vertical. Therefore:
b is the major radius and 2b is the major axis.a is the minor radius and 2a is the minor axis.Vertices = (h, k±b)Co-vertices = (h±a, k)Foci = (h, k±c) where c² = b² - a²Comparing the given equation with the standard form, we get:
[tex]h = 5[/tex][tex]k = -5[/tex][tex]a^2=4 \implies a=2[/tex][tex]b^2=9 \implies b=3[/tex]Therefore:
[tex]\textsf{Center}= (5, -5)[/tex][tex]\textsf{Major axis}=2 \cdot 3 = 6[/tex][tex]\textsf{Minor axis}=2 \cdot 2 = 4[/tex][tex]\textsf{Vertices:} \;\;(h, k \pm b)=(5,-5 \pm 3)=(5,-8)\;\;\textsf{and}\;\;(5,-2)[/tex][tex]\textsf{Co-vertices:}\;\;(h \pm a, k)=(5 \pm 2, -5)=(3, -5)\;\; \textsf{and}\;\;(7, -5)[/tex]To graph the ellipse:
Plot the center at (5, -5).Plot the vertices at (5, -8) and (5, -2). The distance between them is the major axis.Plot the co-vertices at (3, -5) and (7, -5). The distance between them is the minor axis.Can you use the ASA postulate or the AAS theorem to prove the triangles are congruent