Final answer:
The midsegment of a triangle is a line segment connecting the midpoints of two sides of the triangle, parallel to the third side and half its length.
Explanation:
In geometry, the midsegment of a triangle is a line segment that connects the midpoints of two sides of the triangle. By definition, this segment is parallel to the third side of the triangle, and its length is half that of the third side. When we think about a triangle, we must consider it as a three-sided figure on a plane, with three angles adding up to 180 degrees. Within this triangle, the midsegment represents a special relationship between its sides and angles.
An example of a midsegment would be if you have a triangle ABC with points D and E being the midpoints of AB and AC, respectively. The midsegment DE would connect these midpoints and have properties that relate to side BC, the side of the triangle to which it is parallel.
The concept of the midsegment is useful in various geometric proofs and problems because it establishes proportional relationships within the triangle. It aids in solving problems by applying these inherent ratios and proportions.
Et f(x) = 9x − 2 and g(x) = −x + 3. find f(g(x)). −9x − 2 −9x + 5 −9x + 25 −9x + 27
Answer:
its a on edg
Step-by-step explanation:
im 100%
Please help :)))) ( attachment )
KL = 4x+7 and LM= 5x-4
One day a store sold 17 sweatshirts. white ones cost $10.95 and yellow ones cost $ 11.50. in all, $192.75 worth of sweatshirts were sold. how many of each color were sold?
Allison practices her violin for at least 12 hours per week. She [practices for three fourths of an hour each session. If Allison has already practiced 3 hours this week, how many more sessions remain for her to meet or exceed her goal?
Please show the Inequality
Answer:
[tex]3+\frac{3}{4}x\geq 12[/tex]
Step-by-step explanation:
Given,
The number of hour he already practiced in this week = 3,
Also, she practices for three fourth of an hour each session,
If x be the number of remaining session,
So, the additional number of hours he practiced in this week = [tex]\frac{3x}{4}[/tex]
Thus, the total number of hours he practiced in this week = [tex]3+\frac{3x}{4}[/tex]
According to the question,
Total number of hours ≥ 12 hours
[tex]\implies 3+\frac{3x}{4}\geq 12[/tex]
Which is the required inequality.
Can anybody help me with this? It's geometry
Sophia used the digits 6, 3, and 8 to write a number less than 6 and greater than 5. Her number has three digits, and the digit in the tenths place is odd. She used each digit only once in the number. What is Sophia's number?
The measure of a supplement of angle is 12 more than three times the measure of a complement. find the measure of the angle.
Which correctly applies the distributive property to show an equivalent expression to (–2.1)(3.4)?
Answer:
(–2.1)(3) + (–2.1)(0.4)
Step-by-step explanation
It's D
Planes X and Y are perpendicular. Points A, E, F, and G are points only in plane X. Points R and S are points in both planes X and Y. Lines EA and FG are parallel.
Based on this information, which lines could be perpendicular to RS? Check all that apply.
EA,ER,EF,FG,FS
Answer:
Step-by-step explanation:
The area of this parallelogram is 24 square units the base is 8 units what is the height of the figure
Two people bought 48 oranges pat bought five times as many as chris. how many oranges did chris buy
Chris bought [tex]8[/tex] Oranges.
What is reasoning ?Reasoning is the process of using existing knowledge to draw conclusions, make predictions, or construct explanations.
We have,
Chris and Pat bought [tex]48[/tex] oranges.
Let,
Oranges bought by Pat [tex]= x[/tex]
Oranges bought by Chris [tex]= y[/tex]
Now,
According to the question;
As Pat bought five times as many as bought by Chris.
i.e.
[tex]x=5y[/tex] [tex]........(i)[/tex]
And,
Chris and Pat bought [tex]48[/tex] oranges.
i.e.
[tex]x+y=48[/tex] [tex]........(ii)[/tex]
Now,
Substituting value of [tex]x[/tex] from equation [tex](i)[/tex] in equation [tex](ii)[/tex];
We get,
[tex]5y+y=48[/tex]
[tex]6y=48[/tex]
[tex]y=8[/tex]
Now,
Substituting value of [tex]y[/tex] in equation [tex](i)[/tex];
[tex]x=5y[/tex]
[tex]x=5*8[/tex]
[tex]x=40[/tex]
Hence, we can say that Chris bought [tex]8[/tex] Oranges and Pat bought [tex]40[/tex] Oranges.
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If p(x) = 2x2 – 4x and q(x) = x – 3, what is (poq)(x)
What is the equation of the line that passes through (5, -2) and (-3, 4)?
Answer: [tex]4y=-3x-7[/tex]
Step-by-step explanation:
The equation of a line passing through (a,b) and (c,d) is given by :-
[tex](y-b)=\dfrac{d-b}{c-a}(x-a)[/tex]
The equation of a line passing through (5, -2) and (-3, 4) is given by :-
[tex](y-(-2))=\dfrac{4-(-2)}{-3-5}(x-5)\\\\\Rightarrow\ y+2=\dfrac{6}{-8}(x-5)\\\\\Rightarrow\ y+2=\dfrac{-3}{4}(x-5)\\\\\Rightarrow\ 4(y+2)=-3(x-5)\\\\\Rightarrow\ 4y+8=-3x+15\\\\\Rightarrow\ 4y=-3x-7[/tex]
Peter wants to put 2 coats of paint on both the inside and outside of the walls. There are 5 walls, each side having 45 ft2 of paintable surface. A gallon of paint covers x ft2. Explain how to write an expression to represent the number of gallons of paint Peter needs.
To calculate the number of gallons Peter needs, multiply the surface area of one side of the wall (225 ft2) by 2 for both sides, and then by 2 again for two coats, totaling 900 ft2. Then divide 900 ft2 by the coverage per gallon x to get the expression 900 / x.
To determine the number of gallons of paint Peter needs, we must first calculate the total paintable surface for both the inside and outside of the walls and then factor in the two coats of paint. Peter has 5 walls, with each side having 45 ft2 of paintable surface, so the total paintable surface for one side is 5 walls imes 45 ft2/wall = 225 ft2. Since he wants to paint both sides, we double this to get 450 ft2. For two coats, we need to double this again, resulting in 900 ft2. Now, if a gallon of paint covers x ft2, the number of gallons needed is total square footage divided by coverage per gallon, which is 900 ft2 / x ft2/gallon.
Therefore, the expression to represent the number of gallons Peter needs is 900 / x.
what are rational numbers
Sum or difference for (6xy + 2y + 6x) + (4xy -x)
If AB is parallel to CD and the slope of CD is -8, what is the slope of AB
Choose the graph that matches the following system of equations 4x +2y=-2 x-3y=24
The solutions of the above system of equations is x = 3 and y = -7 and the graph of above system of equations is as shown below.
What is system of equations?"It is a finite set of equations for which we find the solution."
For given question,
We have been given a system of equations.
4x +2y = -2 ................(i)
x - 3y = 24 ................(ii)
From equation (ii),
x = 24 + 3y .............(iii)
Substitute this value of x in equation (i)
⇒ 4(24 + 3y) +2y = -2
⇒ 96 + 12y + 2y = -2
⇒ 14y = -98
⇒ y = -7
Substitute this value of y in equation (iii)
⇒ x = 24 + 3(-7)
⇒ x = 24 - 21
⇒ x = 3
Therefore, the solutions of the above system of equations is x = 3 and y = -7 and the graph of above system of equations is as shown below.
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5q + 3 = 3h solve for q (literal equations)
Consider the diagram and the paragraph proof below.
Given: Right △ABC as shown where CD is an altitude of the triangle
Prove: a2 + b2 = c2
Because △ABC and △CBD both have a right angle, and the same angle B is in both triangles, the triangles must be similar by AA. Likewise, △ABC and △ACD both have a right angle, and the same angle A is in both triangles, so they also must be similar by AA. The proportions and are true because they are ratios of corresponding parts of similar triangles. The two proportions can be rewritten as a2 = cf and b2 = ce. Adding b2 to both sides of first equation, a2 = cf, results in the equation a2 + b2 = cf + b2. Because b2 and ce are equal, ce can be substituted into the right side of the equation for b2, resulting in the equation a2 + b2 = cf + ce. Applying the converse of the distributive property results in the equation a2 + b2 = c(f + e).
Which is the last sentence of the proof?
A. Because f + e = 1, a2 + b2 = c2.
B. Because f + e = c, a2 + b2 = c2.
C. Because a2 + b2 = c2, f + e = c.
D. Because a2 + b2 = c2, f + e = 1.
In the right angle triangle ABC [tex]\rm a^2+b^2=c^2[/tex] because (e + f = c) and this can be determined by using the Pythagorean theorem.
Given :
Right △ABC is shown where CD is an altitude of the triangle.
The following steps can be used in order to prove that [tex]a^2+b^2=c^2[/tex]:
Step 1 - According to the Pythagorean theorem, the sum of the square of the shorter side is equal to the square of the longer side.
Step 2 - The Pythagorean theorem is given below:
[tex]\rm H^2=B^2+P^2[/tex] --- (1)
where H is the hypotenuse, B is the base, and P is the perpendicular.
Step 3 - So, according to the given diagram:
H = e + f
B = a
P = b
Step 4 - Substitute the values of the known terms in the expression (1).
[tex]\rm a^2+b^2=(e+f)^2[/tex]
Step 5 - According to the diagram, (e + f = c). So, the above expression becomes:
[tex]\rm a^2+b^2=c^2[/tex]
Therefore, the correct option is C).
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Which of the following is irrational?
A. 7.51... x -4
B. root 16 + 3/4
C. root 3 + 8.486
D. 8 2/3 x 17.75
Option (C) √3 + 8.486 is an irrational number.
What is an irrational number?An irrational number is a type of real number which cannot be represented as a simple fraction. It cannot be expressed in the form of a ratio. Those real numbers that are not rational numbers are known as irrational numbers.
For the given situation,
We need to check the options, that is irrational.
Option A: 7.51... x -4
⇒ [tex](7.51 ) (-4)[/tex]
We can express this as fraction. So it is not an irrational number.
Option B: root 16 + 3/4
⇒ [tex]\sqrt{16} +\frac{3}{4}[/tex]
⇒ [tex]4+\frac{3}{4}[/tex]
We can express this as fraction. So it is not an irrational number.
Option C: root 3 + 8.486
⇒ [tex]\sqrt{3} +8.486[/tex]
⇒ [tex]\sqrt{3}[/tex] is an irrational number, so the sum is also an irrational number.
Option D: 8 2/3 × 17.75
⇒ [tex](8\frac{2}{3})(17.75)[/tex]
We can express this as fraction. So it is not an irrational number.
Hence we can conclude that option (C) √3 + 8.486 an irrational number.
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What is radical 64/8 simplified
Answer:
2^(6-3) = 2^3 = 8
Step-by-step explanation:
To simplify radical 64/8
We will express 64 and 8 in powers of 2
64 = 2×2×2×2×2×2= 2^6
8 = 2×2×2=2^3
From the law of indices,
a^5 / a^3 = a^ (5-3) = a^2
Applying this law of indices to the given radical,
64/8 = 2^6/ 2^3
= 2^(6-3)
= 2^3 = 8
Also, we can try another way. since
64 = 2×2×2×2×2×2= 2^6
8 = 2×2×2=2^3
64/8 = 2×2×2×2×2×2 / 2×2×2
2×2×2 cancels out 2×2×2 and
It remains 2×2×2 = 8
So which ever way we do it,
radical 64/8 simplified is 2^3 = 8
A movie theater sold a total of 390 adult and child tickets on a certain day. The theater sold 2.25 times as many adult tickets as child tickets. Each adult ticket cost $7 and each child ticket cost $3. How much revenue did the theater generate in ticket sales that day?
The Revenue generated by theater is $2,250.
What is simplification?Simply put, to simplify is to make something simpler. Simplifying an equation, fraction, or issue in mathematics entails taking something complex and making it simpler. The issue is made simpler by calculations and problem-solving strategies. We can simplify fractions by removing all common elements from the numerator and denominator and putting the fraction in its simplest/lowest form.
It is possible to simplify mathematical formulas by merging and grouping related terms. This makes it easy to understand and decipher the puzzle.
Given total ticket sold = 390
adult ticket + child ticket = 390
and 2.25 times as many adult tickets as child tickets
so adult ticket = 2.25 child tickets
Let child ticket be x
adult ticket = 2.25x
equation will be
2.25x + x = 390
3.25x = 390
x = 120
adult ticket = 390 - 120 = 270
cost of 1 adult ticket = $7
cost of 270 adult ticket = 7 x 270 = $1890
cost of 1 child ticket = $3
cost of 120 child ticket = 3 x 120 = $360
Total revenue = $1890 + $360
Total revenue = $2,250
Hence the total collection of theater is $2,250.
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A=12h(a+b)
Solve for h.
A. h=2Aa+b
B.h=a+b2A
C.h=A2(a+b)
D.h=2(a+b)A
Answer:
h = 2A/a+b
or 1st answer
Step-by-step explanation:
Mia is three years older than twice for Sister Brooke’s age. The sum of their ages is less than 30. What is the greatest age Brooke could be? 7, 10, 8, or 9?
Answer:
the greatest age is 8
Step-by-step explanation:
i took the test
Which property justifies that 4.37.25=4.25.37?
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 19 inches.
The length of the picture frame is 17 inches, which is found by substituting the given width and perimeter into the perimeter formula and solving for the length.
The question asks to calculate the length of a picture frame using the perimeter formula P = 2l + 2w, where P stands for the perimeter, l is the length, and w is the width. Given that the width (w) is 19 inches and the perimeter (P) is 72 inches, we can substitute these values into the formula:
P = 2l + 2w
72 = 2l + 2(19)
72 = 2l + 38
2l = 72 - 38
2l = 34
l = 34 / 2
l = 17 inches
So, the length (l) of the frame is 17 inches.
How many different combinations of a 4-member debating team can be formed from a group of 10 qualified students?
Simply x squared over Y plus Y squared over X all over Y squared minus XY plus X squared