Answers
The area of the triangle is 1500ft²
What is area of triangle?A triangle is a polygon with three sides having three vertices.
The area of a figure is the number of unit squares that cover the surface of a closed figure.
The area of a triangle is expressed as;
A = 1/2bh
where b is the base and h is the height.
Though the triangle consist of two right angle triangle, we have to calculate area of each and add them together.
The base of the small triangle
= √55²-25²
= √ 3025 - 625
= √ 2400
= 49.0( 1 dp)
The area of small triangle = 1/2bh
= 1/2 × 49 × 25
= 612.5 ft²
The area of the big triangle
= 1/2 × 71 × 25
= 887.5 ft²
Therefore the area of the triangle
= 612.5 + 887.5
= 1500ft²
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A triangle is a polygon with three sides having three vertices.
The area of a figure is the number of unit squares that cover the surface of a closed figure.
The area of a triangle is expressed as;
A = 1/2bh
where b is the base and h is the height.
Though the triangle consist of two right angle triangle, we have to calculate area of each and add them together.
The base of the small triangle
= √55²-25²
= √ 3025 - 625
= √ 2400
= 49.0( 1 dp)
The area of small triangle = 1/2bh
= 1/2 × 49 × 25
= 612.5 ft²
The area of the big triangle
= 1/2 × 71 × 25
= 887.5 ft²
Therefore the area of the triangle
= 612.5 + 887.5
= 1500ft²
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Related Questions
Which equation and solution can be used to solve this problem?
Twenty-two less than a number is twenty-four.
A:q+22=24: Subtract 22 from both sides. The answer is 2.
O B:24+q=22: Subtract 22 from both sides. The answer is 2.
O C:q-24 22: Add 24 to both sides. The answer is 46.
O D:q-22-24: Add 22 to both sides. The answer is 46.
4
Answers
The equation that could be used to solve the problem q -22 = 24. The answer is 46. The correct option is D
Linear expressionsFrom the question, we are to determine which equation could be used to solve the given word problem.
The statement is
Twenty-two less than a number is twenty-four
If the number is q, twenty-two less than a number is
q -22
Thus,
Twenty-two less than a number is twenty-four means
q -22 = 24
This is the equation that could be used to solve the problem
Solving the problem
q -22 = 24
Add 22 to both sides
q -22 +22 = 24+22
q = 46
Hence, the equation that could be used to solve the problem q -22 = 24. The answer is 46. The correct option is D
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If m varies directly with n and m=12 when n=3 what is the value of m when n=4?
Answers
Step-by-step explanation:
Itni show data tatoo ko max plus one common 9 - 245
Use each of the three corresponding base and height pairs to find the area of the triangle. Why is the area the same for each calculation?
Answers
Answer:
The three correct corresponding pairs that gives the same area are;
\(\begin{gathered} A=\frac{1}{2}\times10\times3.5=17.5cm^2 \\ A=\frac{1}{2}\times5\times7=17.5cm^2 \\ A=\frac{1}{2}\times14\times2.5=17.5cm^2 \end{gathered}\)The areas are the same in each case because the product of each pair is the same.
Explanation:
Given the base and height pairs in the question.
Let us use the corresponding pairs that gives the same area.
Firstly, for the first pair;
\(\begin{gathered} A=\frac{1}{2}\times10\times3.5=17.5cm^2 \\ A=\frac{1}{2}\times10\times7=35cm^2 \\ A=\frac{1}{2}\times10\times2.5=12.5cm^2 \end{gathered}\)Secondly, the second pair is;
\(\begin{gathered} A=\frac{1}{2}\times5\times7=17.5cm^2 \\ A=\frac{1}{2}\times5\times3.5=8.75cm^2 \\ A=\frac{1}{2}\times5\times2.5=6.25cm^2 \end{gathered}\)Thirdly, the third pair;
\(\begin{gathered} A=\frac{1}{2}\times14\times3.5=24.5cm^2 \\ A=\frac{1}{2}\times14\times7=49cm^2 \\ A=\frac{1}{2}\times14\times2.5=17.5cm^2 \end{gathered}\)Therefore, the three correct corresponding pairs that gives the same area are;
\(\begin{gathered} A=\frac{1}{2}\times10\times3.5=17.5cm^2 \\ A=\frac{1}{2}\times5\times7=17.5cm^2 \\ A=\frac{1}{2}\times14\times2.5=17.5cm^2 \end{gathered}\)The areas are the same in each case because the product of each pair is the same.
Triangle abc gets translated and reflected prove its congruent to a"b'c"
A. AA postulate
B. HL Postulate
C.ASA throem
D.SSA Theroem
Answers
Answer: the answer is b
Step-by-step explanation: since i helped can i have brainlist please it would be greatly apperacited. :D
what is the bank routing number on the check? a sample check. responses 204.67 204.67 856425785 856425785 403 403 2146578212
Answers
The bank routing number on a check is a 9-digit code used to identify a financial institution in a transaction. It is also known as an ABA routing number, an RTN, and a routing transit number.
In order to determine the routing number on a check:
Look at the bottom left corner of the check, where the routing number is printed in magnetic ink. The first nine digits of the MICR (Magnetic Ink Character Recognition) line, located at the bottom of the check, represent the routing number.The routing number may also be printed on the check in a different location, such as the top or bottom right. One could also find their bank routing number by searching online or contacting their bank directly.Learn more about bank number here: brainly.com/question/25642105
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The center of a normal curve is a. cannot be negative b. always equal to zero c. is the mean of the distribution d. is the standard deviation
Answers
The center of a normal curve is the mean of the distribution, making option C the right choice.
A normal distribution—also known as the bell curve or De Moivre distribution—occurs naturally in a variety of circumstances. Bell curve symmetry is present. The data will split in two, falling half to the left and half to the right of the mean.
The characteristics of a normal curve are as follows:
Bell-like symmetrical form.The distribution's mean and median, both of which are situated in their center, are equal. ≈ 68% of the data is within one standard deviation of the mean. ≈ 95% of the data is within two standard deviations of the mean. ≈ 99.7% of the data is within three standard deviations of the mean.Thus, the center of a normal curve is the mean of the distribution, making option C the right choice.
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# An aeroplane flies a distance of 450km in 3/4h. At what speed does it travel?
Answers
If an airplane flies a total distance of 450km in 3/4 hours, the plane is traveling at an average speed of 600 kilometers per hour.
What is the average speed?The average speed refers to the quotient of the total distance divided by the total time used by the airplane to cover the distance.
Based on the distance, time, and speed equation, we can state that there exists an equation relationship, which is given as distance = time x speed.
The total distance flown by airplane = 450 kilometers
The total time used by the airplane to travel the distance = ³/₄ hours or 0.75 hours
Thus, the average speed of the airplane is 600 kilometers per hour (450 ÷³/₄).
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which of these points is closest to the point (7,1)? (4,1), (7,-1), (7,4), (11,1)
Answers
Answer:
(4 , 1) ; (7 , 4) ; (11 , 1)
Step-by-step explanation:
Each of these are 3 points away from the original point, ( 7 , 1)
(7 - 3, 1) = (4 , 1)
(7 , 1 + 3) = (7 , 4)
(7 + 3 , 1) = (11 , 1)
~
The circumference of a circle is 8.88cm. Find the length of the diameter. Give your answer rounded to 2 DP.
Answers
Answer:
2.82
Step-by-step explanation:
The formula for the circumference of a circle is given as:
π × D
Where D represents the Diameter of the circle.
From the question:
The circumference of a circle is 8.88cm.
The Length of the Diameter is calculated as:
8.88cm = π × D
D = 8.88 cm/π
D = 2.8265917893 cm
Approximately to 2 decimal places = 2.83cm
Therefore, the length of the diameter = 2.83 cm
Evaluate the following expression if x=3: 2^x *
Answers
Answer:
x = 8
Step-by-step explanation:
This question is pretty simple. You already know the value of x, we substitute what x equals and find the number 2 cubed.
2^3 = ?
2x2x2 = 8
Find the measures of angles x and y in the figure.
Answers
Answer:
x = y = 60°
Step-by-step explanation:
The angle adjacent to 120° inside the triangle is
180° - 120° = 60°
The triangle is isosceles ( 2 congruent legs ) with the 2 base angles being congruent , then
y = 60°
The vertex of the triangle = 180° - (60 + 60)° = 180° - 120° = 60°
x is vertically opposite the vertex and is congruent , so
x = 60°
A culture of bacteria has an initial population of 8600 bacteria and doubles every 5
hours. Using the formula P = Po 24, where P, is the population after t hours, Po
is the initial population, t is the time in hours and d is the doubling time, what is the
population of bacteria in the culture after 7 hours, to the nearest whole number?
Answers
Answer: The formula for population growth of bacteria with a constant doubling time is P = Po*2^(t/d), where P is the population after t hours, Po is the initial population, t is the time in hours, and d is the doubling time.
Given the initial population of 8600 bacteria and a doubling time of 5 hours, we can substitute these values into the formula:
P = 8600 * 2^(7/5)
To find the population after 7 hours, to the nearest whole number, we can use a calculator to calculate 2^(7/5) which is approximately 3.7 and then multiply it with the initial population.
P = 8600*3.7
P = 31420
So, the population of bacteria in the culture after 7 hours will be around 31420.
Step-by-step explanation:
1. what is the height of the cone? Explain how you found the height.
2. Now that you have the height of the cone, how can you solve for the slant height, s?
3. Now that you have the height of the cone, how can you solve for the slant height, s?
Answers
1. The height of the cone is equal to
2. You can solve for the slant height, s by applying Pythagorean's theorem.
3. To get from the base of the cone to the top of the hill, an ant has to crawl 29 mm.
How to calculate the volume of a cone?In Mathematics and Geometry, the volume of a cone can be calculated by using this formula:
Volume of cone, V = 1/3 × πr²h
Where:
V represent the volume of a cone.h represents the height.r represents the radius.By substituting the given parameters into the formula for the volume of a cone, we have the following;
8792 = 1/3 × 3.14 × 20² × h
26,376 = 3.14 × 400 × h
Height, h = 26,376/1,256
Height, h = 21 mm.
Question 2.
In order to solve for the slant height, s, we would have to apply Pythagorean's theorem since the height of the cone has been calculated above.
Question 3.
By applying Pythagorean's theorem, we have the following:
r² + h² = s²
20² + 21² = s²
400 + 441 = s²
s² = 841
Slant height, s = √841
Slant height, s = 29 mm.
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Tony who is 6 ft tall is looking at a mirror on the ground 12 feet in front of him and he can see the top of the
flagpole. He knows the distance from the mirror to the flagpole is 18 ft and that the 2 triangles are similar.
Determine the height of the flagpole. Record your answer on your answer document on the griddable.
Answers
Answer:
splurg i need this answered aswell sum1 help us out
When graphing on the complex plane , which quadrant will the complex number 10 - 13i be found in ?
Answers
Answer:
The complex number would be in the 4th quadrant.
Step-by-step explanation:
We know that a complex number is a number that can be expressed in the form of a + bi,
where
'\(a\)' and b are real numbers, and '\(i\) represents the imaginary unitGiven the complex number
10 - 13i
Here,
Coefficient of the real part of the complex number = 10Coefficient of the imaginary part of complex number = -13As the coefficient of the imaginary part holds a negative sign, and the real part holds a positive sign.
Thus, the complex number would be in the 4th quadrant.
Problem 10: Find the equivalent polar equation and sketch its graph for rectangular equation \( y=x-3 . \)
Answers
The given rectangular equation is.
(y = x - 3\)
We know that the polar coordinate system uses r and θ instead of x and y.
In the rectangular coordinate system,
y = x - 3.
we can substitute y with (r sin θ) and x with (r cos θ) to obtain the equivalent polar equation.
=r sin θ = r cos θ - 3
Plot the origin (0, 0)2. Draw a line at an angle of
= (π/4 radians) from the x-axis.
Draw a circle with radius 3 centered at the origin.4.
Wherever the line intersects the circle is a point on the graph of the polar equation.
Repeat steps 2-4 for angles 45° to 225°.6.
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Mr. Wilkerson bought frozen treats for 34 children. Each child picked either a popsicle or an ice cream bar. Each popsicle cost $2 and each ice cream bar cost $5. If Mr. Wilkerson spent a total of $128, how many of each type of treat did he buy?
Answers
Answer: He bought 20 ice cream bars and 14 popsicle
Step-by-step explanation:
To solve this I used the elimination method, you could use substitution as well
Here are our two equations
x+y=34 Because the total number of ice creams bought must be given to 34 children and no more
2x+5y=128 because that is the cost for each ice cream and the amount he spent
For the elimination method we have to cancel out one of the variables, I decided to cancel out the x, so I multiplied the top equation by -2. So i got -2x-2y=-68
2x+5y=128 Then we get
3y=60 so
y=20
Now we can go back to the first equation and plug in y.
x+20=34
-20 -20
x=14
So he bought 14 popsicles and 20 ice cream bars.
Find the real solutions of the equations 7x to the fourth =56. Round your answers to two decimal places. Explain.
Answers
The equation 7x^4 = 56 can be rewritten as x^4 = 8. To find the real solutions of the equation, we take the fourth root of both sides:
What does a math equation mean?
Algebraically speaking, an equation is a statement that shows the equality of two mathematical expressions. For instance, the two equations 3x + 5 and 14, which are separated by the 'equal' sign, make up the equation 3x + 5 = 14.
x = ∛8 = 2.
So the real solutions of the equation are x = 2.
Note: since the fourth root of 8 is 2, we can check that the equation holds true. i.e 7*2^4 = 56
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* Ono 3 b) P and are the subsets of universal set U. If n (p) = 55% n (Q) = 50% and n(PUO)complement = 15% find: (i) n(PUQ) (ii) n(PDQ) (iii)n(only P) iv. n(only Q).
Answers
The probability of the sets are solved and
a) n(P U Q) = 85%
b) n(P ∩ Q) = 20%
c) n(only P) = 35%
d) n(only Q) = 30%
Given data ,
P and are the subsets of universal set U
And , n (p) = 55% n (Q) = 50% and n(PUO)complement = 15%
Now , we'll use the formula for the union and intersection of sets:
n(P U Q) = n(P) + n(Q) - n(P ∩ Q)
n(P ∩ Q) = n(P) + n(Q) - n(P U Q)
n(only P) = n(P) - n(P ∩ Q)
n(only Q) = n(Q) - n(P ∩ Q)
We're given that:
n(P) = 55%
n(Q) = 50%
n(P U Q)' = 15%
To find n(P U Q), we'll use the complement rule:
n(P U Q) = 100% - n(P U Q)'
n(P U Q) = 100% - 15%
n(P U Q) = 85%
Now we can substitute the values into the formulas above:
(i)
n(P U Q) = n(P) + n(Q) - n(P ∩ Q)
n(P ∩ Q) = n(P) + n(Q) - n(P U Q)
n(P ∩ Q) = 55% + 50% - 85%
n(P ∩ Q) = 20%
(ii)
n(P ∩ Q) = 20%
(iii) n(only P) = n(P) - n(P ∩ Q)
n(only P) = 55% - 20%
n(only P) = 35%
(iv)
n(only Q) = n(Q) - n(P ∩ Q)
n(only Q) = 50% - 20%
n(only Q) = 30%
Hence , the probability is solved
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Gwen and her sister started watching a cartoon movie at 11:00 A.M. The movie was 2 hours and 5 minutes long. After the movie, they played a card game for 1 hour and 15 minutes and then played soccer in the backyard for 50 minutes. What time was it when Gwen and her sister finished playing soccer?
Include A.M. or P.M. in your answer (for example, 11:58 A.M.).
Answers
Answer: 2:10 PM
Step-by-step explanati
Help me please, I need to pass this class
Answers
Answer:
Step-by-step explanation:
20
Answer: KL IS 3 + 9 THEN 5 MINUS NINE
Step-by-step explanation: FIND KL
The graph represents the fees in thousands of dollars, y, depending on the amount invested in millions, x, with one financial investment firm.
Over what interval is the change constant?
[0, 5)
[1, 5)
[0, 20)
[1, 20)
Answers
help me with this, please
Answers
Answer:
Correct Answer: Option A
Step-by-step explanation:
cos(x + 25o) = sin 45o
using cos θ = sin(90 - θ)
cos(x + 25o) = cos(90 - 45)
cos(x + 25o) = cos 45
x + 25 = 45
x = 45 - 25
x = 20o
Hope it helps ♡＾▽＾♡
Chance has hired a construction crew to renovate his kitchen. They charge $3.57 per square foot for materials and $122.22 per day
of labor. Chance spent $3,411.87 on the renovation. If the number of square feet is 251 more than the number of days it took for the
renovation, how long did the renovation take?
Answers
The graph of part of linear function p is shown on the grid.
Which inequality best represents the domain of the part shown?
−7≤x<2
−7
−5≤p(x)<3
−5
Answers
Answer:
A
Step-by-step explanation:
The domain of a function is the span of x-values covered by the graph.
From the graph, we can see that it stretches from x=-7 to x=2.
However, note that at x=-7, the dot is closed (shaded in). In other words, x=-7 is in our domain.
On the other hand, at x=2, the dot is not shaded. So, x=2 is not included in our domain.
Therefore, our domain all are numbers between -7 and 2 including -7 (and not including 2).
As a compound inequality, this is:
\(-7\leq x<2\)
So, our answer is A.
Also note that we use x instead of p(x) because the domain relates to the x-variable. If we were to instead find the range, then we would use p(x).
YOOO PLZ HELP ASAP!!! simplify this expression. 4^9/4^3
Answers
Answer: 4096
Step-by-step explanation:
4^9/4^3
4^(9-3)
4^6=4096
Answer:
\(4^{6}\)
Step-by-step explanation:
\(4^{9}\) ÷ \(4^{3}\) is equal to . This is because \(4^{9}\) is basically 4 · 4 · 4 · 4 · 4 · 4 · 4 · 4 · 4, while \(4^{3}\) is 4 · 4 · 4. When dividing you take out 3 of the fours in \(4^{9}\) to get \(4^{6}\).
Solve the formula h = 54t + 1/2 * a * t ^ 2 for a.
Answers
The initial equation is:
\(h=54t+\frac{1}{2}at^2\)First, we subtract 54t on both sides as:
\(\begin{gathered} h-54t=54t+\frac{1}{2}at^2-54t \\ h-54t=\frac{1}{2}at^2 \end{gathered}\)Multiplying by 2, on both sides:
\(\begin{gathered} 2\cdot(h-54t)=2\cdot\frac{1}{2}at^2 \\ 2h-108t=at^2 \end{gathered}\)Dividing by t^2, we get:
\(\begin{gathered} \frac{2h-108t}{t^2}=\frac{at^2}{t^2} \\ \frac{2h}{t^2}-\frac{108}{t}=a \end{gathered}\)Answer:
\(a=\frac{2h}{t^2}-\frac{108}{t}\)The ratio of boy to girl who play kickball at rece i 6 to 2. There are 18 girl on the team. What i the nu
mber of boy who play kickball at rece?
Answers
The ratio of boy to girl who play kickball at race is 6 to 2. There are 18 girl on the team. the number of boys who play kickball at race is 12 boys.
The ratio of boy to girl who play kickball at race is 6 to 2
6 boys: 2 girls
Multiply the number of girls by the ratio:
18 girls x (6 boys / 2 girls) = 18 x 3 = 54
Subtract the number of girls from the total to get the number of boys:
54 - 18 = 36
Therefore, there are 12 boys who play kickball at race.
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consider a buffer made by adding 132.8 g of nac₇h₅o₂ to 300.0 ml of 1.23 m hc₇h₅o₂ (ka = 6.3 x 10⁻⁵)
Answers
The addition of 132.8 g of NaC₇H₅O₂ to 300.0 ml of 1.23 M HC₇H₅O₂ forms a buffer solution to maintain the pH of the solution
The addition of 132.8 g of NaC₇H₅O₂ to 300.0 ml of 1.23 M HC₇H₅O₂ (Ka = 6.3 x 10⁻⁵) results in the formation of a buffer solution.
In the given scenario, NaC₇H₅O₂ is a salt of a weak acid (HC₇H₅O₂) and a strong base (NaOH). When NaC₇H₅O₂ is dissolved in water, it dissociates into its ions Na⁺ and C₇H₅O₂⁻. The C₇H₅O₂⁻ ions can react with H⁺ ions from the weak acid HC₇H₅O₂ to form the undissociated acid molecules, maintaining the pH of the solution.
The initial concentration of HC₇H₅O₂ is given as 1.23 M. By adding NaC₇H₅O₂, the concentration of C₇H₅O₂⁻ ions in the solution increases. This increase in the concentration of the conjugate base helps in maintaining the pH of the solution, as it can react with any added acid.
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2 Which of the following is the equation of the straight line with slope of 2 and with the same y-
intercept as that of the line represented by the equation y = 4x - 2?
F
1
y = 2x +
G
1
y = 4x -
2
Hy = 4x + 2
Jy = 2x - 2
Answers
Answer:
y = 2x-2
Step-by-step explanation:
Generally, we have the equation of a straight line as;
y = mx + b
where m is the slope and b is the y-intercept
For the second equation, we can see that the y-intercept value is -2
So using the slope 2, we write the complete equation as;
y = 2x - 2