Using cosine rule, the largest angle In the triangle is
C. 117. 3°How to find the measure of the largest angleThe angle is found first using cosine rule by the formula
cos A = (b² + c² - a²) ÷ 2bc
Solving for the largest angle
substituting the values
cos γ = (2² + 1.5² - 3²) ÷ 2 * 1.5 * 2
< γ = arc cos ( -0.4583 )
< γ = 117.28 degrees
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You roll a 6-sided die two times.
What is the probability of rolling a number greater than 1 and then rolling a number less than
3?
Answer:
Step-by-step explanation:
The possible outcomes of rolling a fair six-sided die are the numbers 1, 2, 3, 4, 5, and 6, each of which has an equal probability of $\frac{1}{6}$ of appearing.
The probability of rolling a number greater than 1 is $\frac{5}{6}$, since there are five out of six possible outcomes that satisfy this condition (namely, 2, 3, 4, 5, and 6).
The probability of rolling a number less than 3 is $\frac{2}{6}=\frac{1}{3}$, since there are two out of six possible outcomes that satisfy this condition (namely, 1 and 2).
To find the probability of both events happening (rolling a number greater than 1 and then rolling a number less than 3), we can multiply their respective probabilities:
$\frac{5}{6}\cdot\frac{1}{3}=\frac{5}{18}$
Therefore, the probability of rolling a number greater than 1 and then rolling a number less than 3 is $\boxed{\frac{5}{18}}$.
The height of three basketball players is 210 cm, 220 cm and 191 cm.
What is their average height?
Answer:
Average height = 207 cmStep-by-step explanation:
It's given that, The height of three basketball players is 210 cm, 220 cm and 191 cm.
h₁ = 210 cm
h₂ = 220 cm
h₃ = 191 cm
Total number of observations = 3.
Average = Sum of all observations/Total number of observations.
↠ Average = h₁ + h₂ + h₃/3
↠ Average = 210 +220 + 191 /3
↠ Average = 430 + 191/3
↠ Average = 621/3
↠ Average = 207
Therefore, The required average height is 207 cm.
As as you approach zero from the left on a number line the integers ____ , but the absolute values of those integers ___?
As you approach zero from the left on a number line, the integers become increasingly negative, but the absolute values of those integers remain positive.
A number line is a visual representation of numbers placed in order on a straight line. It is a graphical tool used to represent the real numbers, starting from negative infinity on the left side and extending to positive infinity on the right side. The number line is divided into equal intervals, and each point on the line corresponds to a specific value or number. The distance between any two points on the number line represents the numerical difference between the corresponding numbers. The number line is a fundamental tool in mathematics for understanding the order and magnitude of numbers, as well as for performing operations such as addition, subtraction, and comparison.
As you approach zero from the left on a number line, the integers become increasingly negative, but the absolute values of those integers remain positive.
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Choose the correct answer.
Find the quadratic equation given the points (6,0), (-1,0), and (7,4).
h(x) = 1/2(x + 1)(x − 6)
h(x) = 2(x+6)(x − 1)
h(x) = 2(x + 1)(x - 6)
h(x):1/2(x+6) (x - 1)
The quadratic equation given the points (6,0), (-1,0), and (7,4).
The correct answer is h(x) = 1/2(x + 1)(x - 6).
To find the quadratic equation given the points (6,0), (-1,0), and (7,4), we can use the general form of a quadratic equation, which is [tex]h(x) = ax^2 + bx + c.[/tex]
First, let's substitute the coordinates of the given points into the equation to create a system of equations:
For the point (6,0):
[tex]0 = a(6)^2 + b(6) + c ---- (1)[/tex]
For the point (-1,0):
[tex]0 = a(-1)^2 + b(-1) + c ---- (2)[/tex]
For the point (7,4):
[tex]4 = a(7)^2 + b(7) + c ---- (3)[/tex]
We now have a system of three equations with three unknowns (a, b, c). We can solve this system to find the values of a, b, and c.
Solving the system of equations (1), (2), and (3), we find:
a = 1/2
b = -3/2
c = 0
Thus, the quadratic equation that satisfies the given points is:
h(x) = 1/2(x + 1)(x - 6).
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6.) Marissa's class is having a Read-a-Thon. The 34 students in her class have read a total of 817 books. On average, how many books has each student read? (5th grade answer)
Answer:
24 with a remainder of 1 (or Q.24 R.1)
Explanation:
divide the amount of books by the amount of students.
Apply the Distributive Property to the right side.
12
enter your response herex
enter your response here (Type integers or fractions.)
The rewritten expression of 12 using the distributive property is 3(2 + 2)
Rewriting the equation using the distributive property.From the question, we have the following parameters that can be used in our computation:
12 distributive property
This means that
12
Express as 6 + 6
So, we have
12 = 6 + 6
Factor out 3 from the equation
So, we have
12 = 3(2 + 2)
The above equation has been rewritten using the distributive property.
Hence, the rewritten expression using the distributive property is 3(2 + 2)
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Please help. The problem is found in the photo below, just please help.
Answer:
-4 = 5
0 = -1
2 = -4
4 = -7
(-4, 5)
(0, -1)
(2, -4)
(4, -7)
Step-by-step explanation:
First, let's identify what each term represents.
y-intercept: -1
slope: 3/2
Then, fill out the table.
x = -4
-1 - (3/2 · -4)
-1 - (-12/2)
-1 - (-6)
-1 + 6
y = 5
x = 0
-1 - (3/2 · 0)
-1 - 0
y = -1
x = 2
-1 - (3/2 · 2)
-1 - (6/2)
-1 - (3)
y = -4
x = 4
-1 - (3/2 · 4)
-1 - (12/2)
-1 - (6)
y = -7
Then, plot the points in the function on the graph.
(-4, 5)
(0, -1)
(2, -4)
(4, -7)
Consider the graph of function g
y4
If f(x)=x², which equation represents function g?
OA. g(z) f(27)
OB. g (2) f(42)
M
2
O C. g(z) = 2 f(z)
(2)
D. 9(2) -
Answer:
D
Step-by-step explanation:
Find a quadratic function that models the
number of cases of flu each year, where y is years since 2012. What is the coefficient of x? Round your answer to the nearest hundredth
Using regression analysis, we get the following quadratic function:
y = 557[tex]x^{2}[/tex] + 1,690x + 60,000
How to explain the functionWe can use the data given and fit a quadratic equation in the form of y = a[tex]x^{2}[/tex] + bx + c, where y represents the number of flu cases and x is the number of years since 2012.
x (years since 2012) y (number of flu cases)
0 60,000
1 62,000
2 63,000
3 64,000
4 65,000
5 66,000
6 67,000
7 68,000
8 69,000
9 70,000
10 71,000
11 72,000
12 73,000
13 74,000
14 75,000
15 76,000
Next, we can use this table to find the coefficients a, b, and c that give us the best-fit quadratic function.
Using a regression analysis, we get the following quadratic function:
y = 557[tex]x^{2}[/tex] + 1,690x + 60,000
Here, the coefficient of x is 1,690, which represents the linear term in the quadratic equation. It tells us how much the number of flu cases changes with each year since 2012, assuming a quadratic relationship.
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Year Number of Flu Cases
2000 20,000
2001 22,000
2002 25,000
2003 28,000
2004 32,000
2005 35,000
2006 38,000
2007 42,000
2008 45,000
2009 50,000
2010 55,000
2011 58,000
2012 60,000
2013 62,000
2014 63,000
2015 64,000
Find a quadratic function that models the number of cases of flu each year, where y is years since 2012. What is the coefficient of x?
Box and whisker plots
Answer: Box and whisker plots are plots on number lines with a box and two lines off the edges, called whiskers. The box has a line at the upper quartile(1), one at the lower quartile(2), and one in the center of the box at the median(3). The two lines go to the ends of the data, one at the minimum(4) and one at the maximum(5).
4 2 3 1 5
|-----[___|____]-----------|
₀__₁__₂__₃__₄__₅__₆__₇__₈
I hope this helps.
The profit from selling tickets to a musical can be modeled by the function P(x) = -100x2 + 2,400x - 8,000, where x is the price per ticket, in dollars. What ticket price will maximize the profit?
The profit is maximized at $16,400 when the ticket price is $12.
To find the ticket price that maximizes the profit, we used the fact that the maximum or minimum value of a quadratic function occurs at its vertex. For a quadratic function in the form of P(x) = ax^2 + bx + c, the x-coordinate of the vertex can be found using the formula x = -b / 2a.
In this case, we were given the function [tex]P(x) = -100x^2 + 2400x - 8000,[/tex]where x represents the price per ticket. The coefficient of [tex]x^2[/tex] is negative, which tells us that the graph of this function is a downward-facing parabola. The vertex of this parabola represents the maximum value of the function.
Using the formula x = -b / 2a, we found the x-coordinate of the vertex to be x = -2400 / 2(-100) = 12. This means that a ticket price of $12 will maximize the profit.
To verify that this is indeed the maximum profit, we substituted x = 12 into the profit function P(x):
[tex]P(12) = -100(12)^2 + 2400(12) - 8000 = 16,400[/tex]
We can see that the profit is maximized at $16,400 when the ticket price is $12.
In summary, to find the ticket price that maximizes the profit, we used the formula x = -b / 2a to find the x-coordinate of the vertex of the quadratic function representing the profit from selling tickets to a musical. The maximum profit occurs at the ticket price that corresponds to the x-coordinate of the vertex.
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Your local dry cleaners is running a special. The dry cleaner is offering a 13% discount for any drop off that is over $40. Also, they are running a neighborhood special of an additional 5% off. Given this information, determine the decay factor corresponding to each percent decrease. A. 34. 8; 33. 06 c. 0. 87; 0. 95 b. 0. 384; 0. 3306 d. 87; 95
The decay factor corresponding to each percent decrease is 0.87. The correct option is c. The customer would save a total of $17.35, or 17.35% off the original price.
To determine the decay factor corresponding to each percent decrease, we need to use the formula:
decay factor = (100% - percent decrease)/100%
For the first discount of 13%, the decay factor would be:
decay factor = (100% - 13%)/100% = 0.87
For the additional neighborhood discount of 5%, the decay factor would be:
decay factor = (100% - 5%)/100% = 0.95
So the correct answer is option C, with a decay factor of 0.87 for the 13% discount and 0.95 for the neighborhood discount.
These decay factors represent how much of the original price is left after the discount has been applied. For example, if the original price was $100, after the 13% discount, the price would be:
price after first discount = $100 x 0.87 = $87
Then, after the additional 5% discount, the final price would be:
final price = $87 x 0.95 = $82.65
So the customer would save a total of $17.35, or 17.35% off the original price.
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Chase was on his school’s track team and ran the 2400m race. He has been working on his pace and can run 1600m in 5. 5 minutes. If he keeps this pace through the entire race, how long will it take him to finish the 2400m race?
A. 8. 25 minutes
B. 7. 75 minutes
C. 8. 5 minutes
D. 8. 42 minutes
Find (A) f'(x). (B) the partition numbers for f', and (C) the critical numbers of f. f(x) = x³ - 75x - 2 (A) f'(x)= (B) Find the partition numbers for f' Select the correct choice below and, if necessary, fill in the answer box to complete your choice A. The partition number(s) is/are x = (Use a comma to separate answers as needed) B. There are no partition numbers (C) Find the critical numbers for f. Select the correct choice below and, if necessary, fill in the answer box to complete your choice A. The critical number(s) is/are x = (Use a comma to separate answers as needed) B. There are no critical numbers
The critical numbers of f are x = -5 and x = 5.
(A) To find the derivative f'(x), we differentiate f(x) = x³ - 75x - 2 with respect to x:
f'(x) = 3x² - 75
(B) There are no partition numbers for f' as partition numbers are related to integer partitions, which are not applicable in this context.
(C) To find the critical numbers of f, we set f'(x) equal to 0 and solve for x:
3x² - 75 = 0
x² = 25
x = ±5
So the critical numbers of f are x = -5 and x = 5.
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consider h(x)= 11x² - 6x calculate H (x) Fx 6.Xr1 유 11 6 3 (22.-6) 3 6 In(3) 11 A) 2 +1 (221 - 6)31 B) - (11r? - br)3*** In(3) 2 (3***") - 6 In(3) (221 - 63#* - (1142 – 63)3 (3***")" 2 +1 4 (221 - 63 - (1122 – 6x)3 In(3) i 1 D)
The answer is B) - (11x² - 6x)ln(3) + 2ln(3) - 6ln(x) + C, where C is the constant of integration.
To solve this problem, we are given a function h(x) and asked to find its antiderivative or indefinite integral, which is denoted by H(x) and is defined as the function whose derivative is h(x). We are also given a specific value of H(x) at x = 6 and asked to use it to find the constant of integration, denoted by C.
The given function is h(x) = 22x - 3x² - 6/x, and we want to find H(x), which is the antiderivative of h(x). Using the power rule of integration, we can integrate each term of h(x) separately:
∫ (22x - 3x² - 6/x) dx = ∫ 22x dx - ∫ 3x² dx - ∫ 6/x dx= 11x² - x³ - 6ln|x| + Cwhere C is the constant of integration. Note that we need to include an absolute value sign around x in the natural logarithm term because the function is not defined for x = 0.
Next, we are given that H(6) = 31, which means that when x = 6, the value of H(x) is 31. Substituting x = 6 and H(x) = 31 into the above equation, we get:
31 = 11(6)² - (6)³ - 6ln|6| + CSimplifying, we get:
31 = 132 - 216 - 6ln(6) + CC = 221/3 - 6ln(6)Therefore, the antiderivative of h(x) is:
H(x) = 11x² - x³ - 6ln|x| + 221/3 - 6ln(6)We can simplify the expression by using the identity ln|a/b| = ln|a| - ln|b|:
H(x) = 11x² - x³ - 6ln(3) - 6ln(x) + 2ln(3) + Cwhere C is the constant of integration. Thus, the final answer is:
B) - (11x² - 6x)ln(3) + 2ln(3) - 6ln(x) + C, where C is the constant of integration.To learn more about integration, here
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1. p(x)= f(x)+g(x)
Write the equation of p(x)
Answer:p(x)=3x+5
Step-by-step explanation:
f(x)=2x+3
g(x)=x+2
p(x)=(2x+2)+(x+2)= 3x+5
Answer:
p(x)=ax + b
Step-by-step explanation:
Omar Cuts A Piece of wrapping paper with the shape and dimensions as shown.Find The Area Of The Wrapping Paper.Round Your Answer To The Nearest Tenth Of Needed
Answer:
72.5 square inches
Step-by-step explanation:
See attachment.
The areas of the 2 shapes are in blue, but when added together:
60+12.5=72.5
Hope this helps!
What’s the answer I need help pls?
Answer:
A, C, F
Step-by-Step:
The amplitude is whatever the coefficient is behind the trig function
A.
kyle swam 4 laps in the pool on monday. he swam
6 times as many laps on tuesday. choose true or false
for each statement.
a. the expression 6 x 4 represents the number of
x
laps kyle swam on tuesday.
b. the words 6 times as many as 4 represents the
number of laps kyle swam on tuesday.
c. the number of laps kyle swam on tuesday can be
found by solving the equation ? = 6 x 4.
d. kyle swam 10 laps on tuesday.
A. Kyle swam 4 laps in the pool on Monday. He swam 6 times as many laps on Tuesday.
a. The expression 6 x 4 represents the number of laps Kyle swam on Tuesday.
b. The words "6 times as many as 4" represent the number of laps Kyle swam on Tuesday.
c. The number of laps Kyle swam on Tuesday can be found by solving the equation x = 6 x 4.
d. Kyle swam 10 laps on Tuesday.
a) True. Since Kyle swam 6 times as many laps on Tuesday as he did on Monday (4 laps), you would multiply 6 by 4 to find the number of laps he swam on Tuesday.
b) True. This phrase means that Kyle swam 6 times the number of laps he swam on Monday (4 laps), which gives you the number of laps he swam on Tuesday.
c) True. This equation represents the total number of laps Kyle swam on Tuesday. By solving the equation, you can determine that Kyle swam 24 laps on Tuesday.
d) False. Based on the information given and the calculations made, Kyle actually swam 24 laps on Tuesday, not 10.
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2. Mandy is walking in the woods. She completes 70% of her walk in 3 hours. She continues walking at that same rate. How much time, in hours, will Mandy's entire walk take?
A 3 4\5
B. 5
C. 6
D. 6 1\2
Answer:
If Mandy completed 70% of her walk in 3 hours, then we can find her walking rate as follows:
Let's assume that the entire walk takes t hours. Then, 70% of the walk would take 0.7t hours. We know that Mandy completes 70% of her walk in 3 hours, so we can set up the following equation:
0.7t = 3
Solving for t, we get:
t = 3 ÷ 0.7 ≈ 4.29
So, the entire walk will take approximately 4.29 hours. Since Mandy has already walked for 3 hours, the remaining time she needs to complete her walk is:
4.29 - 3 = 1.29 hours
Therefore, the answer is closest to option A, 3 4/5 hours.
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6. A football player throws a football. The function h given by h(t) = 6 + 75+ - 161
describes the football's height in feet † seconds after it is thrown.
A. The football is thrown from ground level.
B. The football is thrown from 6 feet off the ground.
C. In the function, - 167? represents the effect of gravity.
D. The outputs of h decrease then increase in value.
E. The function h has 2 zeros that make sense in this situation.
F. The vertex of the graph of h gives the maximum height of the foot
The correct options are:
The football is thrown from 6 feet off the ground. In the function, - 167? represents the effect of gravity.The vertex of the graph of h gives the maximum height of the footThe description of the football's heightOption B: The football is thrown from 6 feet off the ground.
when t = 0
h(t) = 6 * 75 * 0 + 16 * 0
= 6 feet
Option C : - 16t² represents the effect of gravity
we have
[tex]h = ut - \frac{1}{2}gt^2[/tex]
[tex]\frac{1}{2}gt^2=-16t^2[/tex]
F. The vertex of the graph of h gives the maximum height of the foot
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Please Help Fast!!!!!!!!!!!!!!!!!!!!!!!!!
The number of solutions that are there for the pair of equations for lines Q and S is zero solution (no solution) because the lines are parallel with no point of intersection.
What is no solution?In Mathematics and Geometry, no solution is sometimes referred to as zero solution, and an equation is said to have no solution when the left hand side and right hand side of the equation are not the same or equal.
This ultimately implies that, a system of equations would have no solution when the line representing each of the equations are parallel lines and have the same slope i.e both sides of the equal sign are the same and the variables cancel out.
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A baker has a small and large bag of sugar for making cakes. The large bag contains 30 cups of sugar and is 2. 5 times larger than the small bag. The small bag contains enough sugar to make 9 cakes and has 0. 75 cups of sugar remaining.
how many cakes can be made with a large bag of sugar?
After solving the word problem, the large bag contains enough sugar to make 40 cakes
Since the large bag is 2.5 times larger than the small bag, and the small bag contains enough sugar to make 9 cakes, the large bag contains enough sugar to make:
2.5 * 9 = 22.5 cakes
However, since there are only 30 cups of sugar in the large bag, and we don't know how much sugar is needed to make a single cake, we cannot determine the exact number of cakes that can be made with a large bag of sugar.
As for the small bag, if it had enough sugar to make 9 cakes and there are 0.75 cups of sugar remaining, then each cake requires:
(sugar in bag - remaining sugar) / number of cakes
= (9 - 0.75) / 9
= 0.75 cups of sugar
Therefore, the large bag contains enough sugar to make:
30 cups / 0.75 cups per cake
= 40 cakes
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Analyzing Solution Sets to Linear Equations with the Variable on Both Sides
2x + 5 = 3 + 2(x + 1)
Answer: it will need to be rewritten so that the variable is only on one side of the equation
Step-by-step explanation:f the equation contains fractions, you may elect to multiply both sides of the equation by the least common denominator
5. A 40-kg ornamental star is suspended by two chains fastened to
horizontal beams at different heights with angles as shown.
Determine the tension in each chain.
The diagram is shown below; I also know we have to split up the triangles to make two right angle triangles but I’m not sure where to go from there
Answer:We can start by resolving the forces acting on the ornamental star in the vertical direction and in the horizontal direction. Since the star is stationary, these forces must balance each other out.
Let's call the tension in the higher chain T1 and the tension in the lower chain T2. We can use trigonometry to find the vertical and horizontal components of each tension force.
For T1:
The vertical component is T1cos(40°) and the horizontal component is T1sin(40°).
For T2:
The vertical component is T2cos(30°) and the horizontal component is T2sin(30°).
Now, resolving the forces in the vertical direction, we have:
T1cos(40°) + T2cos(30°) - mg = 0
where m is the mass of the star and g is the acceleration due to gravity.
Substituting the values:
T1cos(40°) + T2cos(30°) - (40 kg)(9.81 m/s^2) = 0
T1cos(40°) + T2cos(30°) = 392.4 N
Next, resolving the forces in the horizontal direction, we have:
T1sin(40°) = T2sin(30°)
Now we have two equations with two unknowns:
T1cos(40°) + T2cos(30°) = 392.4 N
T1sin(40°) = T2sin(30°)
Solving these equations simultaneously, we get:
T1 = 266.4 N
T2 = 205.1 N
Therefore, the tension in the higher chain (T1) is 266.4 N and the tension in the lower chain (T2) is 205.1 N.
Step-by-step explanation:
A ball of radius 11 has a round hole of radius 4 drilled through its center.
Find the volume of the resulting solid.
The volume of the resulting solid is estimated 4,128.38 cubic units.
How do we calculate?
The volume of the ball isgitten as:
V_ball = (4/3)πr^3
r is the radius of the ball. In this scenario
r = 11, so:
V_ball = (4/3)π(11)^3
V_ball = (4/3)π(1331)
V_ball = 4,396.46 cubic units
The volume of the hole is gotten as :
V_hole = (4/3)πr^3
r is the radius of the hole.
In thisscenario, r = 4, so:
V_hole = (4/3)π(4)^3
V_hole = (4/3)π(64)
V_hole = 268.08 cubic units
In conclusion, the volume of the resulting solid is:
V_resulting_solid = V_ball - V_hole
V_resulting_solid = 4,396.46 - 268.08
V_resulting_solid = 4,128.38 cubic units
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Patty and Carol leave their homes in different cities and drive toward each other on the same highway.
• They start driving at the same time.
• The distance between the cities where they live is 300 miles.
• Patty drives an average of 70 miles per hour.
. Carol drives an average of 50 miles per hour.
Enter an equation that can be used to find the number of hours, t, it takes until Patty and Carol are at the same
location.
The equation to find the number of hours, t, until Patty and Carol are at the same location is: 70t + 50t = 300.
1. Patty and Carol start driving at the same time, towards each other on the same highway.
2. The distance between their cities is 300 miles.
3. Patty drives at an average speed of 70 mph, so in t hours she covers 70t miles.
4. Carol drives at an average speed of 50 mph, so in t hours she covers 50t miles.
5. As they drive towards each other, the sum of the distances they cover should equal the total distance between their cities.
6. Therefore, combining the distances covered by Patty and Carol, we get: 70t (Patty's distance) + 50t (Carol's distance) = 300 (total distance).
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Is there a relationship between the raises administrators at State University receive and their performance on the job? A faculty group wants to determine whether job rating (x) is a useful linear predictor of raise (y). Consequently, the group considered the straight-line regression model, (y) hat = (b) with subscript (1)x+ (b) with subscript (0). Using the method of least-squares regression, the faculty group obtained the following prediction equation, (y) hat=2,000x+ 14,000.
Interpret the estimated y-intercept of the line.
A)There is no practical interpretation, since rating of 0 is not likely and outside the range of the sample data.
B)For an administrator who receives a rating of zero, we estimate his or her raise to be $14,000.
C) The base administrator raise at State University is $14,000.
D) For a 1-point increase in an administrator's rating, we estimate the administrator's raise to increase $14,000
Yes, there is a relationship like a straight line between the raises administrators at State University receive and their performance on the job
The estimated y-intercept of the line in the given straight-line regression model is $14,000.The interpretation of this value is that for an administrator who receives a rating of zero, we estimate his or her raise to be $14,000. This value represents the base raise amount for the administrators at State University, regardless of their job performance rating.To obtain this interpretation, we consider the equation of the regression line, which relates the predicted raise amount (y hat) to the job performance rating (x). The y-intercept term in this equation is the value of y hat when x equals zero. Therefore, the estimated y-intercept of $14,000 represents the predicted raise amount for an administrator whose job performance rating is zero, which corresponds to the base raise amount at State University.
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Which triangle will always have the same area, no matter how it is drawn? A А a right triangle that has two 45° angles an obtuse triangle that has two 30° angles © a right triangle that has two 5-inch-long sides an obtuse triangle that has two 5-inch-long sides
The triangle that will always have the same area, no matter how it is drawn, is a right triangle that has two 45° angles. The correct answer is option A
This is because any right triangle with two 45° angles is a special type of triangle called an isosceles right triangle. In an isosceles right triangle, the two legs are congruent, which means they have the same length. Therefore, no matter how the triangle is drawn, its area will always be the same.
To see why this is true, let's use the formula for the area of a right triangle:
Area = (base x height) / 2
In an isosceles right triangle, the base and height are congruent, so we can write:
Area = (leg x leg) / 2
Simplifying this expression, we get:
Area = (leg^2) / 2
Since the legs of an isosceles right triangle are congruent, we can substitute leg for both legs in the formula:
Area = (leg^2) / 2 = (leg x leg) / 2
No matter how the triangle is drawn, the legs will have the same length, so the area of the triangle will always be the same.
Therefore, the correct answer is option A, a right triangle that has two 45° angles.
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7) Roy buys pizza for his friends. A whole pizza costs P 190. 00 and P 40. 00 for every
additional topping. If he spent P 1070 for pizza with 3 sets of additional toppings, how
many whole pizzas did he buy?
8) There are 4 large gifts. Inside each large gift are 2 medium-sized gifts and inside each
medium-sized gift are 3 small gifts. How many gifts are there altogether?
9) Mang Cardo has cows and chickens in his farm. If he counted 13 heads and 36 feet,
how many cows and chickens does he have?
10) Alexander travelled at 6:00 a. M. And started driving at an average speed of 70 km per
hour. After two hours of driving, he stopped for 30 minutes for a rest. He continued
driving and reach his hometown at 9:30 a. M. How far did he travel?
7) Roy buys 5 whole pizzas.
8) There are 36 gifts altogether.
9) There is 5 cows and 8 chickens.
10) He travel 210 km.
We have the four parts of question:
Now, We have the information:
7) A whole pizza costs P 190.00 and P 40. 00 for every additional topping.
If he spent P 1070 for pizza with 3 sets of additional toppings.
So, The formation of equation is:
=> (1070 - 3 × 40) ÷ 190
=> 5
8) Total gifts are : 4
and Inside each large gift are 2 medium-sized gifts and inside each
medium-sized gift are 3 small gifts.
So, the formation of equation;
=> 4 × 2 = 8
=> 8 × 3 = 24
The total is:
8 + 24 + 4 = 36
9) There are 13 heads and 36 feet .
We know:
Cows have (C) 4 legs
Chickens have (c) 2 legs
So, The equation will be:
C + c=13 ....eq.(1)
Multiply by 4, we get:
4C+2c=36
Then,
4C+4c=52
4C+2c=36
--------------- (-)
2c=16
c = 8 chickens
We put the value of c in eq.(1), we get
C=13 - 8
C = 5 cows
Hence, There is 5 cows and 8 chickens.
10) Alexander travelled at 6:00 a.m.
and, average speed is 70 km per hour.
So, He travelled 140 km in 2 hours.
After two hours of driving, he stopped for 30 minutes for a rest.
He continued driving and reach his hometown at 9:30 a.m.
So, therefore he continues driving at 8:30
then he arrived at his destination at 9:30
So after his break for driving he travels 1 more hour
So in total he travelled 3 hours to arrive at his destination
3 × 70 = 210.
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