A student solved the following problem and made an error:
Triangles ABC and DEF. Angles A and F are congruent and measure 63 degrees. Coordinates for the vertices are at A 1, 2 and B 1, 4 and C 3, 3 and D 5, 1 and E 3, 2 and F 5, 3.
Line 1 segment AB equals 2, segment FD equals 2, segment AB is congruent to segment FD
Line 2 ∠A ≅ ∠F
Line 3 Length of segment AC.
A (1, 2)
C (3, 3)
d equals square root of quantity x sub 2 minus x sub 1 squared plus quantity y sub 2 minus y sub 1 squared, then d equals square root of quantity 1 minus 3 all squared plus quantity 2 minus 3 all squared, then d equals square root of negative 2 squared plus negative 1 squared, then d equals square root of 4 plus 1, then d equals square root of 5
segment AC = 2.23
Line 4 Length of segment EF.
E (3, 2)
F (5, 3)
d equals square root of quantity x sub 2 minus x sub 1 squared plus quantity y sub 2 minus y sub squared then d equals square root of quantity 3 minus 5 all squared plus quantity 2 minus 3 all squared, then d equals square root of negative 2 squared plus negative 1, then d equals square root of 4 plus 1, then d equals square root of 5
segment EF= 2.23
Line 5 segment AC is congruent to segment FE
Line 6 triangle ABC is congruent to triangle EFDby SAS
In which line did the student make the first mistake?
Line 1
Line 5
Line 6
Line 2
A flower bed has the shape of a rectangle 9 yards long and 3 yards wide. What is its area in square feet?
Answer:
243 ft2
Step-by-step explanation:
9*3= 27
3*3= 9
27*9=243 ft2
The area of the rectangular flower bed is 243 square feet.
What is an area?The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the rectangle in a two-dimensional plane is called the area of the rectangle.
A rectangle is a quadrilateral having four sides and the sum of the angles is 180 in the rectangle the opposite two sides are equal and parallel and the two sides are at 90-degree angles.
Given that a flower bed has the shape of a rectangle 9 yards long and 3 yards wide.
Length = 9 yards = 9 x 3 feet = 27 feet
Width = 3 yards = 3 x 3 feet = 9 feet
The area of the rectangular flower bed will be calculated as,
Area = L x W
Area = 27 x 9
Area = 243
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for f(x)=5x+1 find f(x) when x=2 and when x=3
Answer:
f(x)=11 and f(x)=16
Step-by-step explanation:
f(x)=5(2)+1
f(x)=11
f(x)= 5(3)+1
f(x)=16
The sum of four consecutive odd integers is 176
The numbers are 41,43,45,47.
Given that,
The sum of four consecutive odd integers is 176.Based on the above information, the calculation is as follows:
x + x + 2 + x + 4 + x + 6 = 176
4x + 12 = 176
4x = 164
x = 41
So, the four consecutive odd numbers are 41, 43, 45, 47
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The main cable of a suspension bridge forms a parabola, described by the equation y = a(x - h)2 + k, where y is the height in feet of the cable above the roadway, x is the horizontal distance in feet from the left bridge support, a is a constant, and (h, k) is the vertex of the parabola. At a horizontal distance of 30 ft, the cable is 15 ft above the roadway. The lowest point of the cable is 6ft above the roadway and is a horizontal distance of 90 ft from the left bridge support.Which quadratic equation models the situation correctly?
The main cable attaches to the left bridge support at a height of ft.
The main cable attaches to the right bridge support at the same height as it attaches to the left bridge support. What is the distance between the supports?
Answer:
26.25 ft.
Step-by-step explanation:
The general form of a parabola is [tex]y = a(x - h)^2 + k[/tex], where the vertex of the parabola is (h,k).
The equation of the parabola is [tex]y = 0.0025(x - 90)^2 + 6[/tex].The distance between the supports at a vertical height of 26.25 is 180ftGiven that
[tex]y = a(x - h)^2 + k[/tex]
A. The quadratic equation
The lowest point (which stands for the vertex) is given as:
[tex](h,k) = (90,6)[/tex]
So, we have:
[tex]y = a(x - 90)^2 + 6[/tex]
From the question, we understand that:
At a horizontal distance of 30ft, the cable is at 15ft. This means:
[tex](x,y) = (30,15)[/tex]
Substitute these values in: [tex]y = a(x - 90)^2 + 6[/tex]
So, we have:
[tex]15 = a(30 - 90)^2 + 6[/tex]
[tex]15 = a(- 60)^2 + 6[/tex]
[tex]15 = a \times 3600 + 6[/tex]
Collect like terms
[tex]3600a = 15 - 6[/tex]
[tex]3600a = 9[/tex]
Make a, the subject
[tex]a = \frac{9}{3600}[/tex]
[tex]a = 0.0025[/tex]
Substitute [tex]a = 0.0025[/tex] in [tex]y = a(x - 90)^2 + 6[/tex].
[tex]y = 0.0025(x - 90)^2 + 6[/tex]
B. The horizontal distance at a height of 26.25ft.
This means that, y = 26.25
So, we have:
[tex]26.25 = 0.0025(x - 90)^2 + 6[/tex]
Collect like terms
[tex]-6 + 26.25 = 0.0025(x - 90)^2[/tex]
[tex]20.25= 0.0025(x - 90)^2[/tex]
Divide both sides by 0.0025
[tex]8100 = (x - 90)^2[/tex]
Take square roots of both sides
[tex]\±90 = x - 90[/tex]
Solve for x
[tex]x = 90 \± 90[/tex]
To the left of the cable, the horizontal distance is:
[tex]x_1 = 90 - 90[/tex]
[tex]x_1 = 0[/tex]
To the right of the cable, the vertical distance is:
[tex]x_2 = 90 + 90[/tex]
[tex]x_2 = 180[/tex]
So, the coordinates of the left and right support at a height of 26.25 is:
(0,26.25) and (180, 26.25)
The distance (d) between them is calculated using:
[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 -y_1)^2}[/tex]
[tex]d = \sqrt{(180- 0)^2 + (26.25-26.25)^2}[/tex]
[tex]d = \sqrt{180^2 + 0^2}[/tex]
[tex]d = \sqrt{180^2}[/tex]
[tex]d = 180[/tex]
The distance between them is 180ft
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number 8 d+3n=1 solve for n
The digit with the greatest value 6789
differentiation. questions 1 and 2
Which is greater 1/3 or 0.33
The greater number between 1/3 and 0.33 is 1/3
How to determine which fraction is greaterFrom the question, we have the following parameters that can be used in our computation:
1/3 or 0.33
Express them as decimals
So, we have
1/3 = 0.333..
0.33 = 0.33
By comparison
0.333.. is greater than 0.33
This means that the greater number is 1/3
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The Johnsons framed a family picture to hang on the wall. The perimeter of the frame is 72 inches. Use the formula p= 2l ÷ 2w to find the length of the frame if the width is 14 inches
A triangle has one angle measuring 3X degrees the second angle measures 2X +20° and the third angle measures 4X -20° what is the value of X
Answer:
[tex]x=20[/tex]
Step-by-step explanation:
We have been a triangle has one angle measuring [tex]3x[/tex] degrees the second angle measures [tex]2x+20[/tex] degrees and the third angle measures [tex]4x-20[/tex] degrees. We are asked to find the value of x.
We know that all interior angles of a triangle add up-to 180 degrees.
[tex]3x+2x+20+4x-20=180[/tex]
Combine like terms:
[tex]3x+2x+4x-20+20=180[/tex]
[tex]9x=180[/tex]
Divide both sides by 9:
[tex]\frac{9x}{9}=\frac{180}{9}[/tex]
[tex]x=20[/tex]
Therefore, the value of x is 20 for our given triangle.
click on the graph until the graph of a line with undefined slope appears
please help! picture is above!
The slope is undefined for figure 2.
In general, when the x-values or x-coordinates is the same for both points, the slope is undefined.
For example, let us try to get the slope for a line passing through the points (1, 3) and (1, 9)
Let x₁ = 1 , y₁ = 9 and x₂ = 1 and y₂ = 3
Slope, m = (y₂ − y₁)/((x₂ − x₁)
m = (3 − 9)/(1 − 1)
m = -6/0, which is undefined.
What's -2x-x+8
?? Thanks
Evaluate -2/3 to the 4th power
HELP ME PLEASE!!!!
Construct the perpendicular bisector of each side of the given triangle. What do you observe about these bisectors?
What is the equivalent decimal to 1/2?
Please help! All the questions.
What is 4 3/4 times 2 1/8 5 simplified? Helppppp
The hot dog eating champion eats 27.5 hot dogs in 4 minutes. At that rate, how many does he eat in to 10 minute competition
3x - 2 (x + 3) = 4x - 7
A cafeteria sells 30 drinks every 15 minutes.How many drinks would they sell in 1 hour?
Sara recorded the height of the ocean at low tide, with respect to sea level, for four days.
Time Low Tide (inches)
Monday a.m. −4
Monday p.m. −6
Tuesday a.m. −3
Tuesday p.m. −1
Wednesday a.m. 0
Wednesday p.m. 2
Thursday a.m. −1
Thursday p.m. −3
What is the average height of the ocean at low tide with respect to sea level?
The average height of the ocean is -2.
What is Average?Average The arithmetic mean is calculated by adding a set of integers, dividing by their count, and then taking the result.
For instance, the result of 30 divided by 6 is 5, which is the average of 2, 3, 3, 5, 7, and 10.
Averages are used to condense a vast number of data points into a single value. It is a visual depiction of all the data set's accessible numbers.
Given data:
Monday a.m.: −4
Monday p.m.: −6
Tuesday a.m.: −3
Tuesday p.m.: −1
Wednesday a.m.: 0
Wednesday p.m.: 2
Thursday a.m.: −1
Thursday p.m.: −3
So, the average height of the ocean at low tide
=(-4 + (-6)+ (-3)+ (-1) + 0+ 2 + (-1) + (-3))/8
= (-18 + 2 ) / 8
= -16 /8
= -2
Hence, the average height of the ocean is -2.
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Rodrigo researched the number of pets owned in the U.S. and displayed his results in the bar graph shown. in his research, he found that $7,737.6 million was spent on annually on veterinary visits for the dogs and $5,913 million was spent annually on visits for cats. How much more was spent, on average, by each person for dogs than cats?
Answer:
$29 million is spent more by each person for dogs than cats.
Step-by-step explanation:
Amount spent on visits for the dogs = $7,737.6 millions.
Number of dogs owned = 31.2 millions (by bar graph)
∴ On average amount spent on each person = [tex]\frac{7,737.6}{31.2} = $248 millions [/tex]
Amount spent on visits for the cats = $7,737.6 millions.
Number of cats owned = 27 millions (by bar graph)
∴ On average amount spent on each person = [tex]\frac{5913}{27} = $219 millions [/tex]
Thus, on average, by each person amount spent for dogs than cats = $248 millions - $219 millions = $29 millions.
. Which numbers are all divisible by 5?
1. 124, 333, 315, 266, 391
2. 135, 205, 330, 275, 365
3. 135, 211, 330, 274, 252
4. 232, 250, 365, 225, 210
Write 28 as a product of its prime factors write the factors in order, from smallest to largest
Final answer:
To express 28 as a product of its prime factors, you would write [tex]28 = 2^2 \times 7[/tex], where 2*2 represents 2 multiplied by itself and 7 is a prime number.
Explanation:
To write 28 as a product of its prime factors, we begin by finding the smallest prime number that divides 28. Since 28 is an even number, we know it's divisible by 2. So we start with 2 and keep dividing:
28 ÷ 2 = 14
14 ÷ 2 = 7
Now, 7 is a prime number and cannot be divided further except by 1 and itself. So, we end up with:
28 = 2 × 2 × 7
We can also express this using exponents:
28 = 2² × 7
These are the prime factors of 28, written in order from smallest to largest.
if a doctor prescribes tablets with a strenght of 0.2 mg and 0.6 mg is ordered, how many tablets should the patient take?
Solve inequality.
x + 1 > -5(7 - 2x)
On Monday two hundred ninety students went on a trip to the zoo.All five buses were filled and only five students had to travel in cars.How many students were in each bus?
Patio covers 56 square yards find length of a side of patio to nearest tenth of yard
The length of a side of the patio, rounded to the nearest tenth of a yard, is 7.5 yards.
Explanation:To find the length of a side of the patio, we need to find the square root of the area. The area of the patio is given as 56 square yards.
To find the length of a side, let's take the square root of 56. The square root of 56 is approximately 7.48.
Therefore, the length of a side of the patio, rounded to the nearest tenth of a yard, is 7.5 yards.
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How many ways can you stack 77 books into equal piles