The two triangles formed by trimming the peaks of the house with the 7-ft pieces of molding are congruent.
Explanation:To determine if the two triangles formed by trimming the peaks of the house with the 7-ft pieces of molding are congruent, we can use the concept of the Side-Angle-Side (SAS) congruence criterion.
In the first case, the carpenter uses three 7-ft pieces of molding to trim the first triangular peak. This means that each side of the triangle is 7 feet long.
In the second case, the carpenter uses 21 ft of molding to trim the second triangular peak. Since the total length of molding used is 21 ft, we know that each side of the triangle is still 7 feet long.
So, in both cases, the triangles are formed by sides of the same length, which is 7 feet, and they have a common angle at the peak of the house.
This satisfies the SAS congruence criterion, which states that if two triangles have two sides of equal length and the included angle is the same, then the triangles are congruent.
Therefore, the two triangles formed by trimming the peaks of the house with the 7-ft pieces of molding are congruent.
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I need help learning how to do these problems some how whenever I do them I always get it wrong please help I have a test Wednesday!
Which symbol creates a true sentence when x equals 6? 42 + (x – 3)2 __ 28
Which side has an equal measure to BC?
A.DE
B.AB
C.EF
D.DF
PLEASE HELP
In the given diagram, we are given two triangles, triangle ABC and triangle DEF.
And we are given a line or reflection l.
Triangle DEF is the mirror image of triangle ABC.
Therefore, all sides of the triangle ABC would be congruent to sides of triangle DEF.
AB = DF
AC = DE and
BC = EF.
We can see than BC is the smallest side of triangle ABC and EF is the smallest side of triangle DEF.
Therefore, correct option is C option.C.EFThe image shown has two triangles sharing a vertex:
What is the measure of ∠WZX, and why?
A. y over 2, because Triangle UVW is congruent to triangle WXZ
B. y, because Triangle UVW is similar to triangle ZXW
C. y + 50 degrees, because Triangle UVW is similar to triangle ZXW
D. 130 degrees − y, because Triangle UVW is congruent to triangle WXZ
The measure of ∠WZX is B; y, because Triangle UVW is similar to triangle ZXW.
What is vertically opposite angles?The vertically opposite angles are those angles that are opposite one another at a specific vertex and are created by two straight intersecting lines.
We can see that Angles UVW ad ZXW are congruent,
Then because of the vertical angle theorem; angles UWV and XWZ are congruent.
So if there are 2 angles in each triangle which are congruent to each other, then the triangle angle sum theorem state that the third angle also has to be congruent in each.
BUT congruent angles do not make the triangles congruent due to the length of the sides can change and the measures of the angles remain unchanged.
Hence, The measure of ∠WZX is B; y, because Triangle UVW is similar to triangle ZXW.
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If the length of side a is 6 centimeters, the length of side b is 4 centimeters, and the length of side c is 7 centimeters, what is the measure of ? Round your answer to two decimal places.
Answer:
34.77
Step-by-step explanation:
The area of a triangle with sides of length 6 cm, 4 cm, and 7 cm is approximately 11.95 cm² when calculated using Heron's formula and rounded to two decimal places.
The original question appears to be incomplete as there's no clear indication of which measure is being sought for the triangle with sides of length 6 cm, 4 cm, and 7 cm. However, if the goal is to use these sides to determine the area of a triangle, we can use Heron's formula, since the lengths given do not form a right triangle.
First, calculate the semiperimeter (s):
(s) = (a + b + c) / 2
(s) = (6 + 4 + 7) / 2
(s) = 17 / 2
(s) = 8.5 cm
Now, apply Heron's formula which is Area [tex](A) = \sqrt{[ (s)((s)-a)((s)-b)((s)-c) ][/tex]:
[tex]A = \sqrt{[8.5(8.5-6)(8.5-4)(8.5-7)]}\\A = \sqrt{[8.5(2.5)(4.5)(1.5)]}\\A = \sqrt{[8.5 \times 2.5 \times 4.5 \times 1.5]}\\A \approx 11.95 cm^2 after\ calculating\ the\ square\ root[/tex]
Thus the area of the triangle is approximately [tex]11.95 cm^2[/tex] (rounded to two decimal places). Note that the question's original instructions to round to two significant figures would result in an answer of [tex]12 cm^2[/tex].
can someone please help?
Mike wants to make meatloaf. His recipe uses a total of 6 pounds of meat. If he uses a 3 to 1 ratio of beef to pork how much pork will he use? Enter your answer as a mixed number in simplest terms
Mike will use 1 1/2 pounds of pork for his meatloaf recipe, which calls for a 3 to 1 ratio of beef to pork and a total of 6 pounds of meat.
Mike's meatloaf recipe has a total of 6 pounds of meat and uses a 3 to 1 ratio of beef to pork. To find out how much pork he will use, we can express the total amount of meat as the sum of beef and pork parts.
First, we know that there are 3 + 1 = 4 parts in total because of the given ratio. Since the ratio is 3 to 1, for every 4 parts of meat, 1 part is pork. Therefore, we calculate the weight of each part by dividing the total weight by the number of parts:
6 pounds ÷ 4 parts = 1.5 pounds per part
Since one part is pork, Mike will use 1.5 pounds of pork for his meatloaf. Expressed as a mixed number, that's 1 1/2 pounds of pork in simplest terms.
Solve 2x2 + 5x + 5 = 0. Round solutions to the nearest hundredth.
Rounded to the nearest hundredth, they are:
[tex]\[x_1 \approx -0.63 + 1.35i\][/tex]
[tex]\[x_2 \approx -0.63 - 1.35i\][/tex]
To solve the quadratic equation [tex]\(2x^2 + 5x + 5 = 0\)[/tex], we can use the quadratic formula:
[tex]\[x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}\][/tex]
where [tex]\(a = 2\), \(b = 5\)[/tex], and [tex]\(c = 5\)[/tex].
Substituting the values into the quadratic formula:
[tex]\[x = \frac{{-5 \pm \sqrt{{5^2 - 4 \cdot 2 \cdot 5}}}}{{2 \cdot 2}}\][/tex]
[tex]\[x = \frac{{-5 \pm \sqrt{{25 - 40}}}}{{4}}\][/tex]
[tex]\[x = \frac{{-5 \pm \sqrt{{-15}}}}{{4}}\][/tex]
Since the discriminant [tex](\(b^2 - 4ac\))[/tex] is negative, the solutions will involve imaginary numbers.
Using the imaginary unit [tex]\(i\)[/tex], where [tex]\(i^2 = -1\),[/tex] we can rewrite [tex]\(\sqrt{{-15}}\)[/tex] as [tex]\(i\sqrt{{15}}\):[/tex]
[tex]\[x = \frac{{-5 \pm i\sqrt{{15}}}}{{4}}\][/tex]
So, the solutions to the equation [tex]\(2x^2 + 5x + 5 = 0\)[/tex] are complex numbers. Rounded to the nearest hundredth, they are:
[tex]\[x_1 \approx -0.63 + 1.35i\][/tex]
[tex]\[x_2 \approx -0.63 - 1.35i\][/tex]
These solutions represent the points where the graph of the quadratic equation intersects the x-axis. They lie on the complex plane.
Given that the two triangles are similar, solve for x if AU = 20x + 108, UB = 273, BC = 703, UV = 444, AV = 372 and AC = 589.
Ue can wash a car in 1 hour. steve can wash a car twice as fast as sue. how long will it take them to wash a car if they work together, but sue starts 30 minutes before steve?
The number of hours (H) that a candle will burn increases when the length of the candle (L) increases. Write the correct equation for this scenario, and solve for the number of hours when the length is 2. Length Hours 15 3 20 4
Answer:
H = .2L; H = .4
Step-by-step explanation:
There are 10 runners in race. in how many ways can the first, second and third place finishes occur
Thank you very much for your help!
The Jonas school district gives awards to its schools based on overall student attendance. The data for attendance are shown in the table, where Low represents the fewest days attended and High represents the most days attended for a single student.
School High School M High School N High School P
Low - 128 131 140
High - 180 180 180
Range- 52 49 40
Mean- 141 159 153
Median- 160 154 165
IQR- 55.5 48.5 32.5
σ- 41.5 36.5 31.5
Part A: If the school district wants to award the school that has the most consistent attendance among its students, which high school should it choose and why? Justify your answer mathematically. (5 points) Part B: If the school district wants to award the school with the highest average attendance, which school should it choose and why? Justify your answer mathematically. (5 points)
Which expression is equivalent to (2x^4y)^3
The equivalent expression to the given expression is [tex]8x^12y^3[/tex].
We have given that,
The expression (2x^4y)^3
We have to determine the,
Which expression is equivalent to (2x^4y)^3
What is the equivalent expression?
Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value(s) for the variable(s).
The answer is D.
2^3 is 8.
(x^4)^3 is x^12 and y^3 is simply y^3.
Put them together to get the final answer.
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The length l of a rectangle is 4 inches greater than its width w. The area of the rectangle is 252 square inches.Using the method of completing the square, what are the length and width of the rectangle? Show your work.
Shyla used a probability simulator to pull 3 colored marbles from a bag and flip a coin 50 times. The results are shown in the tables below:
16 blue
20 green
14 yellow
heads 18
tails 32
Using Shyla's simulation, what is the probability of pulling a blue marble and the coin landing tails up?
Answer:
512/2500
Step-by-step explanation:
Find the radius of a circle with an area of 615.75 sq kilometers?
area = pi x r^2
615.75 = 3.14 x r^2
r^2 = 615.75/3.14 =196.0987 round to 196.1
r = sqrt(196.1) = 14.00357 round to 14
radius = 14 kilometers
A photo that is 3 inches wide by 5 inches long is being enlarged so that it is 12 inches long. How wide will the enlarged photo be
12/5 = 2.4 times larger
3 x 2.4 = 7.2 inches wide
. The total cost of gasoline varies directly with the number of gallons purchased. Gas costs $1.77 per gallon. Write a direct variation to model the total cost c for g gallons of gas.
A . c=g/1.77
B. c=1.77g
C. g=1.77c
D. c=g+1.77
Which of the following are the coordinates of the vertex of y=3x^2+3?
PLEASE HELP ASAP ILL GIVE BRAINLIEST IF YOURE RIGHT!!
Find the greatest possible error for each measurement.
9 g
a.
1/2 g
b.
1/4 g
c.
1/6 g
d.
1/8 g
gpe = 1/2 of the unit measures
since 9 is a whole number the gpe would be 1/2 g
A ball is thrown from an initial height of 7 feet with an initial upward velocity of 23/fts. The ball's height h (in feet) after t seconds is given by the following.
h=7+23t-16t^2
Find all values of t for which the ball's height is 15 feet.
Round your answer(s) to the nearest hundredth. (If there is more than one answer, use the "or" button.)
As per quadratic equation, all values of 't' for which the ball's height is 15 feet are 33.25 and (- 31.813).
What is a quadratic equation?"Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax² + bx + c = 0 where a, b, c, ∈ R and a ≠ 0. It is the general form of a quadratic equation where 'a' is called the leading coefficient and 'c' is called the absolute term of f (x)."
Given, [tex]h = 15[/tex] feet.
Therefore, the quadratic equation for [tex]h = 15[/tex] will be:
A ball is thrown from an initial height of 7 feet with an initial upward velocity of 23 feet per second.
The ball's height h (in feet) after t seconds is:
[tex]h = 7+23t-16t^{2}[/tex]
[tex]15 = 7+23t-16t^{2}[/tex]
⇒ [tex]15-7-23t+16t^{2} = 0[/tex]
⇒ [tex]16t^{2} -23t - 8 = 0[/tex]
⇒ [tex]t = [- (-23)[/tex] ± [tex]\sqrt{(23)^{2} - 4(16)(- 8)}[/tex] ]/(2 × 16)
⇒ [tex]t =[/tex] [23 ± 1041]/32
⇒ [tex]t =[/tex] [23 + 1041]/32, [23 - 1041]/32
⇒ [tex]t =[/tex] 33.25, - 31.813
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Let x+3, 2x+1, and 5x+2 be consecutive terms of an arithmetic sequence. find the absolute value of the common difference of the terms.
Find the value of two numbers if their sum is 12 and the difference is 4
x+y=12
x-y=4
x=y-4
y-4+y=12
2y-4=12
2y=16
y=8
x=8-4=8
8+4=12
the 2 numbers are 8 & 4
how many solutions does this system have -3x+6y=10 -3x+6y= -4
PLEASE HELP
graph and completely describe the function f (x)= 4^x
I already graphed this on desmos
An equilateral triangle and a square have the same perimeter of 12 inches. what is the ratio of the side length of the triangle to the side length of the square? express your answer as a common fraction.
Which has a greater area, a square with sides that are x - 1 units long or a rectangle with a length of x units and a width of x - 2 units?
What's the slope of the line that passes through (2,14) and (-1,-1)?