The coordinates of a centroid of a triangle with vertices [tex](x_1,y_1),(x_2,y_2),(x_3,y_3)[/tex] are [tex](\frac{x_1+x_2+x_3}{3}, \frac{{y_1+y_2+y_3} }{3})[/tex].
Centroid of a triangle
For a triangle, the centroid is obtained by the intersection of its medians. The line segments of medians join vertex to the midpoint of the opposite side. All three medians meet at a single point (concurrent). The point of concurrency is known as the centroid of a triangle.
Let KLM be a triangle with the vertex coordinates [tex](x_1,y_1),(x_2,y_2),(x_3,y_3)[/tex] as K,L and M respectively.
Let the midpoints of the side LM, KL and KM are D, E, and F, respectively. The centroid of a triangle is represented as “G.”
As D is the midpoint of the side LM, we can write,
D = ((x2+x3)/2, (y2+y3)/2)
Now, we know that, G intersects AD in the ratio 2:1 , we get
Hence, using section formula we can write,
The x-coordinates of G will be:-
x = (2(x2+x3)/2 + 1.x1 )/ (2+1) = (x2+x3+x1)/3 = (x1+x2+x3)/3
The y-coordinates of G will be :-
y =(2(y2+y3)/2 + 1.y1 )/ (2+1) = (y2+y3+y1)/3 = (y1+y2+y3)/3
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12 eggs cost $2.56. How much is one egg? (unit rate)
x² - 6 = 54
I don’t understand
Answer:x squared = 60
Step-by-step explanation:
x2-6=54, first you have to cancel out the 6 on the left side by adding 6 to -6 after doing that you are left with
x2-(-6+6)=54
but since you did +6 on the right side you have to do +6 on the left so after that you are left with
x2=54+6
now you just do 54+6=60 so after all of that you get
x2=60
(you can use a calculator to find the square root of 60)
A number x divided by 36
Answer:
x/36 is what you're looking for my guy
The hypotenuse of a right triangle measures 20 cm and one of its legs measures 7 cm. Find the measure of the other leg. If necessary, round to the nearest tenth.
Answer:
19
Step-by-step explanation:
The square value of the measure of hypotenuse is equal to the square measure of sum of two legs.
Let x represent the missing leg:
[tex] {20}^{2} = {7}^{2} + {x}^{2} [/tex]
400 = 49 + x^2 subtract 49 from both sides
351 = x^2 find the root for both sides
The root of 351 is between 18 and 19 but it is closer to 19 since 19×19 = 361 and since we are asked to round to the nearest tenth the answer is 19.
solve for missing length, round to nearest if necessary. (check if all of these are correct) if it’s not correct say the number and the answer
Answer:
2. 14.42
3. 17.69
6. 12.8
9. 10.29 (I cant see your answer)
Rest is correct ;D
Step-by-step explanation:
Please help me I need help
Answer:
16 and -16
Step-by-step explanation:
Answer: D. 16 and -16
Step-by-step explanation: I dont think you need an explanation because it is multiple choice.
Milly measured a cereal box It is two inches wide six inches long and twelve inches tall what is the volume of the cereal box
The volume of the cereal box is 144 square inches its width is two inches, its length is six inches and its height is 12 inches.
What is the volume of a rectangular prism?The top, bottom, and lateral faces of a rectangular prism are all rectangles, and all the pairs of opposing faces are congruent. A rectangular prism is a three-dimensional structure with six faces.
The rectangular prism's base area is equal to lw (using the area of a rectangle formula)
The height of the rectangle prism is equal to h.
Thus, V = lw ×h = lwh is the formula for the rectangular prism's volume.
Given,
width = 2 inches
length = 6 inches
height = 12 inches
The volume of a rectangular prism is simply length× width× height.
Volume = 6× 2× 12
= 144 square inches.
Therefore, the volume of the cereal box is 144 square inches.
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867,000 rounded to the nearest ten thousand is
Answer:
870,000
Step-by-step explanation:
Ten thousand is 10,000.
The ten thousand value here is 6
The thousand value here is 7.
Using rounding rules, 5 and up goes up therefore the ten thousand value becomes 7.
867,000 --> 870,000
Hope that helps
|−4| Choose... equal to |4|. |−4| is the distance from −4 to Choose... on a number line.
A pancakes recipe needs 6 eggs to make 16 servings. If Ms. Moon wants to make a pancakes that serves 24 people, how many eggs will she need?
Identify the GCF of the following terms; 18a^4b^9c^2 and 34a^6b^5 and 22a^8bc^7
The greatest common factor of the given terms is 2a⁴b
Greatest Common Factor (GCF)From the question, we are to determine the greatest common factors of the given terms
The given terms are
18a^4b^9c^2 and 34a^6b^5 and 22a^8bc^7
That is,
18a⁴b⁹c² and 34a⁶b⁵ and 22a⁸bc⁷
We will express each of the given terms as a product of their factors
18a⁴b⁹c² = 2 × 3 × 3 × a⁴ × b⁸ × b × c²
34a⁶b⁵ = 2 × 17 × a⁴ × a² × b⁴ × b
22a⁸bc⁷ = 2 × 11 × a⁴ × a⁴ × b × c⁷
Hence, the GCF is 2 × a⁴ × b = 2a⁴b
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what is the equivalent fraction?
The equivalent fraction of 1 2/3 + 1 1/2 is 1 4/6 + 1 3/6
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators.
How to evaluate the fraction expression?The fraction expression is given as
1 2/3 + 1 1/2
Express the mixed numbers as improper fractions
So, we have
1 2/3 + 1 1/2 = 5/3 + 3/2
Rewrite as equivalent fractions
1 2/3 + 1 1/2 = 10/6 + 9/6
Express the improper fractions as mixed numbers
So, we have
1 2/3 + 1 1/2 = 1 4/6 + 1 3/6
Hence, the value of the expression is 1 4/6 + 1 3/6
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Find the equation of a line perpendicular to y=3x+3 that passes through the point (3,2)
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]y = \stackrel{\stackrel{m}{\downarrow }}{3} x + 3\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{3\implies\cfrac{3}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{3}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{3}}}[/tex]
so we're really looking for the equation of a line whose slope is -1/3 and that is passes through (3 , 2)
[tex](\stackrel{x_1}{3}~,~\stackrel{y_1}{2})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{1}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{- \cfrac{1}{3}}(x-\stackrel{x_1}{3}) \\\\\\ y-2=- \cfrac{1}{3}x+1\implies {\Large \begin{array}{llll} y=- \cfrac{1}{3}x+3 \end{array}}[/tex]
What is the name of the line of reflection for the pair of figures?
Enter your answer in the box.
line
Answer: r
Step-by-step explanation:
The figures are symmetrical about line r.
4 2/5 divide 1 1/5 need answer
Answer:
5 3/5
Step-by-step explanation:
assuming you are dividing fractions, here are your steps
A scale drawing of an elephant is shown. The actual
elephant that the model is based on is 216 inches long.
What is the scale factor for the model?
A. 1:30
B. 30:1
C. 208.8
D. 1555.2
The scale factor for the model of the elephant is 1 : 30 (option A).
What is the scale factor?A scale drawing is either a smaller or a larger version of an original image. For example, a map is a smaller version of a city, country or area.
A scale factor provides information on the relationship that exists between the scale drawing and the actual image. The scale factor shows the rate of reduction or enlargement of the original image.
Scale factor = actual length of the elephant / length of the elephant in the model
216 / 7.2 = 30
The scale factor is 1 : 30
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Tony went on holiday to Canada.
His flights cost a total of £1600
Tony stayed for 12 nights.
His hotel cost $184 per night.
Tony used wifi for 9 days.
Wifi cost $6 per day.
Tony took a taxi 6 times costing a mean average of $27 per taxi journey.
The exchange rate was $1.83 to £1
Work out the total cost of the flights, the hotel room, the wifi and 6 taxi journeys.
Give your answer in pounds.
Answer:
Step-by-step explanation:
(12 nights)($184) = $2208
(9 nights)($6) = $54
(6 taxi rides)($27) = $162
$2208 + $54 + $162 = $2424
We will use a ratio to calculate American dollars to pounds
2424/x = 1.83/1
Cross multiply
1.83x=2424
Divide
= ~£1324.59
£1324.59 + £1600 = £2924.59
The answer is ~2924.59 pounds
The total cost of the flights, the hotel room, the wifi, and 6 taxi journeys for Tony's holiday in Canada is approximately £2925.13.
Given that Tony is vacationing in Canada, his flight cost is £1600, he stayed for 12 nights, his hotel cost $184 per night, Tony used wifi for 9 days. Wifi cost $6 per day. Tony took a taxi 6 times costing a mean average of $27 per taxi journey.
The exchange rate was $1.83 to £1.
We need to find the total cost his spend in the vacation.
To calculate the total cost of Tony's holiday, we need to convert all the expenses to pounds and then sum them up.
Flights cost: £1600
Hotel cost per night: $184
Hotel cost for 12 nights: 12 nights x $184/night = $2208
Wifi cost per day: $6
Wifi cost for 9 days: 9 days x $6/day = $54
Taxi cost per journey (mean average): $27
Total taxi cost for 6 journeys: 6 journeys x $27/journey = $162
Now, we need to convert the costs from dollars to pounds using the exchange rate of $1.83 to £1.
Flights cost in pounds: £1600
Hotel cost in pounds: $2208 / $1.83 = £1207.10
Wifi cost in pounds: $54 / $1.83 = £29.51
Taxi cost in pounds: $162 / $1.83 = £88.52
Finally, we can calculate the total cost in pounds:
Total cost = Flights cost + Hotel cost + Wifi cost + Taxi cost
Total cost = £1600 + £1207.10 + £29.51 + £88.52
Total cost = £2925.13
So, the total cost for Tony's holiday in Canada is approximately £2925.13.
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figure 1 and figure 2 below are similar. which point corresponds to point S.
Both figures 1 & 2 are similar
Point S in figure 1 corresponds to Point P in fugure 2
Let a and b be real numbers where a b 0. Which of the following functions could represent the graph below?
#y
○_f(x) = x(x − a)²(x −b)4
f(x) = x(x − a)³(x − b)²
f(x) = x²(x-a)(x - b)²
O f(x) = x²(x-a)5(x - b)
X
Answer: C
f(x)= x^4(x-a)(x-b)^2
Answer:
[tex]f(x)=x^4(x-a)(x-b)^2[/tex]
Step-by-step explanation:
The graph of a polynomial function will:
touch the x-axis at zeros with even multiplicities. cross the x-axis at zeros with odd multiplicities.The zero at the origin (0, 0) touches the x-axis and so it has an even multiplicity (exponent). Therefore, we can immediately discount the first two answer options as both have x as a zero (x = x¹ so its exponent is odd).
The end behavior of the graphed function means the leading coefficient is positive and the degree of the polynomial is odd.
The sum of the multiplicities is the degree of the polynomial function.
[tex]f(x)=x^4(x-a)(x-b)^2 \implies \textsf{Sum of multiplicities}: 4+1+2=7[/tex]
[tex]f(x)=x^2(x-a)^5(x-b) \implies \textsf{Sum of multiplicities}: 2+5+1=8[/tex]
Therefore, the only function that could represent the given graph is
[tex]\boxed{f(x)=x^4(x-a)(x-b)^2}[/tex]
as its degree is odd and it has a zero at the origin with even multiplicity.
Estimate the percentage of engineers that are chemical engineers using the following data
-Total number of engineers listed in this figure is approximately 1,326,800.
-chemical engineers: 27,860
Show work and type formulas Speed=distance=
Time
Based on the number of people who are engineers and those who are chemical engineers, the percentage who are chemical engineers is 2.01%
How to find the percentage?To find the percentage of something out of the total number, the formula is:
= Number of selected variables / Total number of variables x 100%
The selected variable here is chemical engineers so the percentage of chemical engineers out of the total number of engineers is:
= Number of chemical engineers / Total number of engineers x 100%
= 27,860 / 1,326,800 x 100%
= 2.01%
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how to solve please
The reasons that proves the congruency of the triangles are;
2.7 [tex] \Delta EDF \cong \Delta FGE[/tex] by SSS congruency postulate
2.8 [tex] \Delta AOB \cong \Delta COB[/tex], by SAS congruency rule
[tex] \Delta AOB \cong \Delta COB[/tex], by ASA congruency rule or postulate
What are the triangle congruency rules?The rules that proves two triangles to be congruent is if they satisfy any of the 5 rules of congruency, which are; Side–side–side, or SSS, side–angle–side, or SAS, side–angle–angle, or SAA, angle–side–angle, or ASA, and right angle–hypotenuse–side, or RHS
2.7 The given parameters of the two triangles are;
DE = GF, and DF = GE
Required;
To prove that
[tex] \Delta EDF \cong \Delta FGE[/tex]
Solution;
From the given diagram, we have;
[tex]EF \cong FE[/tex]
Reflexive property
Therefore;
[tex] \Delta EDF \cong \Delta FGE[/tex]
Side–Side–Side, SSS rule of congruency
The Side–Side–Side congruency postulate states that if the three sides of one triangle are congruent to three sides of another triangle, then both triangles are congruent.
2.8 The circle information are;
The midpoint (center) of the circle = Point O
Segment OB is perpendicular to segment AC, [tex] OB \perp AC [/tex]
OB bisects AC
Required;
To prove that [tex] \Delta AOB \cong \Delta COB[/tex]
Solution;
Segment OA and OC are the radius of circle O
Therefore;
[tex] OA \cong OC[/tex] by the properties of the radius of a circle
The angle [tex] \angle OAB \cong \angle OCB [/tex] ; Base angles of isosceles triangle ∆OAC
[tex] AB \cong BC[/tex], Segments formed by the perpendicular bisector OB
Given that AB, [tex] \angle OAB [/tex] and OA in [tex] \Delta AOB [/tex] are congruent to BC, [tex] \angle OCB [/tex] and OB in [tex] \Delta COB [/tex], we have;
[tex] \Delta AOB \cong \Delta COB[/tex] by Side–Angle–Side, SAS congruency postulateSecond proof;
Given that OB is the perpendicular bisector of AC, we have;
[tex] \angle OBA \cong \angle OBC = 90^{\circ} [/tex], definition of angles formed by perpendicular lines
[tex] AB \cong BC[/tex]
Therefore;
[tex] \Delta AOB \cong \Delta COB[/tex] by Angle–Side–Angle, ASA, congruency postulateLearn more about the triangle congruency here:
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Jeffrey invests $500 every month and earns interest at a rate of 12% p.a, compounded monthly.
a. Jeffrey wants to buy a car worth $41000 after five years. Can he afford it? If not, how much does he need? (2.d.p)
b. How much is the fund worth after 20 years? (2.d.p)
c. How much interest did he earn over 20 years? (2.d.p)
a) Jeffrey needs an extra amount of $40,357.5 for buying a car.
b) After 20 years fund is worth $1364.
c) After 20 years $1200 interest had been earned.
a) P = $500
r = 12% = 12 ÷ 100 = 0.12
n = 12 because it was compounded 12 times in a year.
t = 5 years
Therefore,
A = 500 × [tex](\frac{1 + 0.12}{12})^{60}[/tex]
A = 500 × [tex](\frac{1 + 0.12}{12})^{60}[/tex]
A = 500 × 1.285
A = $ 642.5
Jeffrey needs an extra $40,357.5 for buying a car.
b) P = $500
r = 12% = 12 ÷ 100 = 0.12
n = 12 because it was compounded 12 times in a year.
t = 20 years
Therefore,
A = 500 × [tex](\frac{1 + 0.12}{12})^{240}[/tex]
A = 500 × [tex](\frac{1 + 0.12}{12})^{240}[/tex]
A = 500 × 2.728
A = $1364
After 20 years fund is worth $1364.
c) Simple interest = P × R × T ÷ 100
Simple interest = 500 × 12 × 20 ÷ 100
Simple interest = $1200
After 20 years $1200 interest had been earned.
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Assume that TUVE AWXY. Which of the following congruence statements
are correct? Check all that apply.
A. TU = YX
B. ZULT
C.LY/V
D. ZW= LT
E. ZX=ZT
☐ F. VU = WX
2 odd numbers that are a factor of 30 and multiples of 5
Answer:
Step-by-step explanation:
The required two odd numbers are 3 and 5.
We have to determine, It is a factor of 30 and a multiple of 3 what are 2 numbers.
To obtain the factor of 30 and 2 numbers is calculated in the following steps.
The Factors of 30 are,
30 = 2 , 3 , 5 ,
And multiply the terms by 2,
After multiply by 2 all the term become even.
Then,
The 2 odd numbers are: 3, 5
Hence, The required two odd numbers are 3 and 5.
X
3
2
1
0
-1
-2
-2
Y
12
10
8
6
4
2
0
Find the domain and range
Answer:
domain: all x-values
Step-by-step explanation:
(3, -5)(7,-5)(7,2)(3,3)
Find the area of the rectangle
Answer: The answer could be 28 but I need to know what is the length and what is the height.
Step-by-step explanation:
I will just name the points for simplicity:
A - (3, -5)
B - (7, -5)
C - (7, 2)
D - (3, 3)
A to B - 4
B to C - 7
C to D - 4.1231
***
Distance (d) = √(3 - 7)^2 + (3 - 2)^2
= √(-4)^2 + (1)^2
= √17
= 4.1231056256177
***
D to A - 8
4 * 7 = 28
Answer the 2 question in the photo ( easy points + brainliest )
Answer:
I think the first number is 45 and the second number is 81.
Step-by-step explanation:
45 > 42 but 45 < 55 81 > 80 but 81 < 89
Consider a goodness-of-fit test with a computed value of chi-square27. 385 and a critical value13. 388, the appropriate decision would be to __________.
Since the chi-square 27.385 is greater than 13.388 at the provided critical value level value, the null hypothesis is accepted.
What is conclusion of hypothesis testing?The hypothesis test makes an announcement the outcome of an assumption in five to six fundamental phases. The technique to be used is based on the idea of correlating the standardized sample equivalent of a parameter to the critical boundary that allows the null hypothesis to be accepted.For the given question;
27. 385 is the chi-square value.13.388 is the critical value.The hypotheses for the goodness of fit test are as follows:
Null: a expected value does not differ significantly from the observed values.Alternative: the expected value differs significantly from the observed values.The chi-square test has one tail.
The criterion is as follows:
The null hypothesis is dismissed if the test statistic exceeds the critical value.If the test statistic is less than the critical value, this same null hypothesis is rejected.Thus, the null hypothesis is accepted at the provided level of critical value because the chi-square 27.385 is more than 13.388.
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What are the domain and range of this relation? pt2
Answer:
Domain: { -5, -1, 1, 3, 4}
Range: { -2, 1, 5}
Step-by-step explanation:
Domain = X-Values
Range = Y-Values
Every possible X-Value is the domain, and likewise with the Range.
Meaning if it was a line that went on forever through Y-1 the the Domain would be X = {-[infinity], +[infinity]} and the range would be Y = {1}
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a large national study finds that 10% of pregnant women deliver prematurely. a local obstetrician is seeing 20 pregnant women in the next week at their clinic. (round answers to 3 decimal places)
The probability that fewer than 3 women will deliver prematurely is 1/20.
What is probability?Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution. The total number of positive outcomes as well as the probability of any given event depend on each other. The probability is typically defined as the proportion of favorable outcomes to all outcomes in the sample space. Probability of an event P(E) = (Number of favorable outcomes) ÷ (Sample space).So, 10% of 20:
20/100 × 10 = 2 (Which is less than 3)Then, Premature delivery (Of fewer than 3 women) = 1Total events = 20P(E) = favourable/total events1/20Therefore, the probability that fewer than 3 women will deliver prematurely is 1/20.
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The correct question is given below:
A large national study finds that 10% of pregnant women deliver prematurely. a local obstetrician is seeing 20 pregnant women in the next week at their clinic. what is the probability that fewer than 3 of them will deliver prematurely?