Answer:
T(6,5)
Step-by-step explanation:
Solution,
Let the coordinate of T be T(a,b), where T divides a line AB internally in the ratio 5:2. Given that A is (-4,10) and B is (10,3).
From the section formula,
[tex]x=\frac{m_1x_2+m_2x_1}{m_1+m_2},y=\frac{m_1y_2+m_2y_1}{m_1+m_2}[/tex]
Let,
(x,y)=(a,b)
(x₁,y₁)=(-4,10)
(x₂,y₂)=(10,3)
m₁:m₂=5:2
Now substitute the values.
[tex]\hookrightarrow x=\frac{m_1x_2+m_2x_1}{m_1+m_2},y=\frac{m_1y_2+m_2y_1}{m_1+m_2}\\\\\hookrightarrow a=\frac{5\times10+2\times(-4)}{5+2},b=\frac{5\times3+2\times10}{5+2}\\\\\hookrightarrow a=\frac{42}{7},\: b=\frac{35}{7}\\\\\hookrightarrow a=6, \:b=5[/tex]
Find the area of the trapezoid
Answer:
A = 7.5 units^2
Step-by-step explanation:
A = (a+b)/2 * h
A and B are both bases of the trapezoid (top and bottom)
H is the height
A is 1
B is 4
H is 3
Plug that into the trapezoid equation and we get
(1+4)/2 * 3 = 7.5 units ^2
4 people are going to a dinner party. Each person at the party will eat 5/6 pound of salad but you can only buy in pounds.If you can only buy whole pounds of salad, how many pounds should you buy?
A teacher randomly chooses a two-person leadership team from a group of four qualified students. Three of the
students, Sandra, Marta, and Jane, are girls. The fourth student, Franklin, is a boy.
Using the sample space of possible outcomes listed below, where each student is represented by the first letter
of his or her name, answer each of the following questions.
What is P(A), the probability that the first student is a girl?
What is P(B), the probability that the second student is a girl?
What is P(A and B), the probability that the first student is a girl and the second student is a girl?
Answer:
what is P(A), the probability that the first student is a boy? 3/5
what is P(B), the probability that the second student is a girl? 3/4
what is P(A and B), the probability that the first student is a boy and the second student is a girl? 1/2
No, évents A and B are not independent events
Step-by-step explanation:
The probability that the first student is a girl P(A)= 3/4.
The probability that the second student is a girl P(B)= 3/4.
The probability that the first student is a girl and the second student is a girl P(A and B)=9/16.
Given that there are three girls (Sandra, Marta, Jane) and one boy (Franklin), and the sample space of possible outcomes is:
{SA, SM, SJ, SF, MA, MS, MJ, MF, JA, JS, JM, JF, FA, FS, FM, FJ}
P(A): Probability that the first student is a girl (Sandra, Marta, or Jane).
Number of favorable outcomes where the first student is a girl: 3 (Sandra, Marta, Jane)
Total outcomes: 4 (total number of students)
P(A) = Number of favorable outcomes / Total outcomes = 3 / 4
P(B):
Probability that the second student is a girl (Sandra, Marta, or Jane).
Number of favorable outcomes where the second student is a girl: 3 (Sandra, Marta, Jane)
Total outcomes: 4 (total number of students)
P(B) = Number of favorable outcomes / Total outcomes = 3 / 4
P(A and B):
Probability that the first student is a girl and the second student is a girl.
Number of favorable outcomes where both students are girls: 3 (Sandra, Marta, Jane)
Total outcomes: 4 (total number of students)
P(A and B) = P(A).P(B)
= 3/4 × 3/4
=9/16
Hence, P(A)=3/4
P(B)=3/4
P(A and B)=9/16
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What is the Volume! ~
Answer:
108
Step-by-step explanation:
Volume of a Square Pyramid :
V = 1/3 x Base Area x HeightSolving :
V = 1/3 x (6)² x 9V = 36 x 3V = 108 cubic centimetersAnswer: Volume = 108 cm ³
Explanation:
For a square pyramid, the volume can be calculated as follows:
Volume = * area of base * height
Volume = * side² * height
We have:
side length = 6 cm
height = 9 cm
Therefore:
Volume = * 36 * 9 = 108 cm ³
Hope this helps :)
What is the perimeter of the parallelogram?
Step-by-step explanation:
b×h1÷2 use this formulae
Can someone help me with this please thank you.
Answer:
1) 104
2) 132
3) 110
4) 112
5) 105
Step-by-step explanation:
These questions involve the sum of interior and exterior angles.
for the first 4 questions,
Use the formula: (n-2)*180-(sum of remaining angles)
For example q1, it has 4 angles
So substitute 4 into n
(4-2)*180=360
64+99+93+x=360
x=104°
(Do the same for q2-4)
For q5,
Sum of exterior angles of ANY polygon=360°
Therefore,
88+75+92+x=360
x=105°
Pls double check the answers yourself with a calculator, hope you find it helpful! :)
Simplify 12 raised to 2/5 into 5 raised to 2/5
Answer:
60^2/5
Step-by-step explanation:
2^2/5 × 5^2/5
=(12×5)^2/5
=60^2/5
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textsf{12}}^ \mathsf{^ {\dfrac{2}{5}}}\ \huge\boxed{\times}\ \huge\textsf{5}^\mathsf{^ \dfrac{2}{5}}[/tex]
[tex]\huge\boxed{=}\huge\textsf{ 2.70192 }\huge\boxed{\times}\huge\textsf{ 1.903654}[/tex]
[tex]\huge\boxed{= }\huge\textsf{ 60}^\mathsf{\dfrac{2}{5}}[/tex]
[tex]\huge\boxed{\approx}\huge\textsf{ 5.143521}[/tex]
[tex]\huge\text{Therefore, the answer is: \boxed{\textsf{60}^\mathsf{^\dfrac{2}{5}}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Complete the standard form equation representing the quadratic relationship displayed above, where a, b, and c are constants.
HELP!!! Simplify the expression.
3√25t²
Answer:
15t
Step-by-step explanation:
if you do the sqrt of 25 you get five than multiply that by 3 to get 15 then do the sqrt of t to get t
Hope this helps! ;-)
Aldo is a software salesperson. His base salary is $2500 and he makes $80 more for every copy of English is Fun he sells. His total pay, p (in dollars), after selling c copies is given by the following.
p=80c+2500
Answer the following questions.
(a)
If Aldo's total pay is $5140, how many copies did he sell?
? copies
(b)
What is Aldo's total pay if he sells 23 copies?
$
Answer:
A: He sold 33 copies
B: $4340
Step-by-step explanation:
A: p=80(33) + 2500
p=2640+ 2500
p=5140
B: p = 80(23) + 2500
p=1840+ 2500
p=4340
Sum interior angle on a regular pentagon
Answer:
540°
Step-by-step explanation:
Formula: note that n means nr of sides
(n-2)×180°
(5-2)×180°=3×180=540°
Where each angle are 540°÷5=108°
Answer:
540
Step-by-step explanation:
108 is one interior angle from a regular pentagon
And a pentagon has 5 interior angles
So 180x5=540
I have no clue, I have asked others and they don't know either.
To find the point of symmetry:
⇒ must find where the distance between the original point and the
line of symmetry and reflected point and the line of symmetry are
equally distant from each other
Based on that knowledge:
⇒ the image appears to be entirely reflected horizontally
⇒ when the line of symmetry is the y-axis
⇒ A, A' equal distant from line of symmetry
⇒ B, B' equal distant from line of symmetry
⇒ C, C' equal distant from line of symmetry
Answer: y- axis
Hope that helps!
40 POINTS!!!
Find the volume of this irregular figure.
Hint: Find the volume of the whole rectangular prism, then subtract the volume of the missing piece, which is also a rectangular prism.
Answer:
470 cm³
Step-by-step explanation:
Volume of rectangular prism = width × length × height
⇒ Volume of whole rectangular prism = 9 cm × 10 cm × 8 cm
= 720 cm³
Side lengths of the missing piece:
width = 5 cmlength = 10 cmheight = 8 cm - 3 cm = 5 cm⇒ Volume of the missing piece = 5 cm × 10 cm × 5 cm
= 250 cm³
⇒ Volume of irregular figure = 720 cm³ - 250 cm³
= 470 cm³
I need help with this math question please!
Answer:
x < 0
( x is less than 0 )
Explaination:
That open circle point means the answer will not be equal to, which would be options including <(less than) or >(greater than).
If the circle was closed you would use these symbols, ≤(less than or equal to) and ≥(greater than or equal to)
The open circle lands on 0 and the arrow points to the left into the negative numbers. The answer should be x<0 or x is less than 0.
A way to help remember less than vs greater than on a line like this is that the arrow points in the same direction as the symbol! For example, your question shows an arrow going to the left, and the symbol used for it is less than (<) which also looks like a left pointing arrow.
Hope this helps out! :D
he tables represent the functions f(x) and g(x). A table showing g(x) equals 2 x plus 15 with 2 columns and 7 rows. The first column, x, has the entries, negative 15, negative 12, negative 9, negative 6, negative 3, 0. The second column, g(x), has the entries, negative 15, blank, blank, blank, blank, 15. Which input value produces the same output value for the two functions? x = –12 x = –9 x = –6 x = –3
Answer:
Answer:
C
Step-by-step explanation:
Answer:
x=-6
Step-by-step explanation:
i got a hundred on the test
It is believed that the best angle to fly a kite is 30 degrees. If you fly a kite at this angle and let out 200 feet of string, approximately how high above the ground will the kite be?
Answer:
200 feet of the ground at a thirty degrees angle does not make a difference .
u need to know whether it is the top or bottom of it, the kite
help! Solve each triangle (find all missing sides and angles) Round each answers to the nearest tenth
Answer:
D.
Step-by-step explanation:
sin 67 = b / 2.4
b = 2.4 sin 67
= 2.2
cos 67 = a / 2.4
a = 2.4 cos 67
= 0.9
M < A = 90-67 = 23 degrees.
express x^2-8x+5 in the term (x-a)^2-b where a and b are integers
Answer:
(x-4)² -11 where a = 4, b = 11
Step-by-step explanation:
The final form (x-a)² - b evaluates to x² - 2ax + a² -b
Matching
x² - 8x + 5
x² - 2ax + a² -b
This gives us -2ax = -8x or -2a = -8 or a = 4
and a² - b = 11 ==> 16 - b = 11 or b =5
Rewritten form is
(x-4)² -11
I NEED HELP!!!!
[tex]3(7+7i)+i(7+7i)[/tex]
Thanks!:)
Solve the equation:-
[tex]3(7 + 7i) + i(7 + 7i) \\take \: common \: (7 + 7i) \: out\\ (7 + 7i) (3 + i) \: is \: your \: answer [/tex]
Open the equation:-
[tex]3(7 + 7i) + i(7 + 7i) \\ 21 + 21i + 7i + 7 {i}^{2} \\ 7 {i}^{2} + 28i + 21 \: \: answer[/tex]
help 30 points for all ansers
The answers to the problem are:
a) The value of x is : 8
b) ∠ZRB and ∠BTS are not supplementary angles.
c) ∠BST and ∠RSB are complementary angles.
d) ∠ABT is an acute angle
e) SA is not the bisector of the angle ∠ZSY.
Types of AnglesAngles are formed when two lines meet and they are of different types.
acute: this is an angle less than 90°
obtuse: this angle is greater than 90° but less than 180°
reflex: this angle is greater than 180° but less than 360°
Analysis:
∠BRS = 180 - (20X - 22) = 202 - 20X
a) To find x, sum of angles in the triangle = 202-20x + 2x+32 + 5x+10 + 120-10x = 180
364 -23x = 180
23x = 364-180
23x = 184
x = 8
b) ∠ZRB = 20x-22 = 20(8) - 22 = 138°
∠BTS = 2x+32 = 2(8)+32 = 48°
138°+48° = 186° [tex]\neq[/tex] 180°
They are not supplementary
c) ∠BST = 120-10X = 120 - 10(8) = 40°
∠RSB = 5x+10 = 5(8)+10 = 50°
50+40 = 90°. They are complementary
d) ∠ABT = 180 - ∠ABR = 180 - 100 - x = 88°
It is acute since it is less than 90°
e) SA is not an angle bisector, since it dived the angles as 40° and 50° and not equal.
In conclusion, the solution to the questions are:
a) The value of x is : 8
b) ∠ZRB and ∠BTS are not supplementary angles
c) ∠BST and ∠RSB are complementary angles
d) ∠ABT is an acute angle
e) SA is not the bisector of the angle ∠ZSY
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need this answered ASAP
type the correct answer in the box.
Mitten crabs are an invasive species in North America. A coastal ecosystem has a population of 320 mitten crabs. The population is predicted to increase by 50% per year. The population will reach an estimated 1,620 crabs in ___ years.
Answer:
10 1/8 years?
I hope this is right!
Step-by-step explanation:
Answer: 2.5
Step-by-step explanation:
OC is perpendicular to AB. What is the length of AB?
A. 8.8 units
B. 4.4 units
C. 13.2 units
D. 2.2 units
Answer:
A.8.8 units
Step-by-step explanation:
Answer:
The correct answer is 8.8 units
Step-by-step explanation:
I just got it correct.
8 ft
6 ft
Find the area of this figure. Round your
answer to the nearest hundredth. Use
3.14 to approximate i.
A = [? ] ft2
Answer:
49.12 ft squared
Step-by-step explanation:
1/2(6*8) = 24
1/2(16)pi = 8pi = 25.12
total: 49.12
7.) Find the center and radius of a circle with the equation (x − 4)² + (y − 2)² = 100.
Answer:
Centre is (4,2) and radius is 10
Step-by-step explanation:
The circle equation is of form,
=> (x - a)² + (y - b)² = r²
where the centre is (a,b) and radius is 'r'.
Find the number that belongs
in the green box.
4
? 1°
29°
10
Round your answer to the nearest tenth.
Answer:
16.6°
Step-by-step explanation:
The triangle can be solved using the Law of Cosines to find the side opposite the given angle, then the Law of Sines to find the missing angle from the given sides.
__
We choose to use a=10, b=4, C=29°.
c² = a² +b² -2ab·cos(C) . . . . . law of cosines
c² = 10² +4² -2·10·4·cos(29°) ≈ 46.0304
c ≈ √46.0304 ≈ 6.78457
Then angle B (opposite side b) is ...
sin(B)/b = sin(C)/c . . . . . . . . . law of sines
sin(B)/4 = sin(29°)/6.78457
B = arcsin(4/6.78457×sin(29°)) ≈ 16.6085°
The missing acute angle is about 16.6°.
Which function can be used to model the graphed geometric sequence? f(x 1) = five-sixthsf(x) f(x 1) = six-fifthsf(x) f(x 1) = five-sixths superscript f (x) f(x 1) = six-fifths superscript f (x)
The function that can be used to model the graphed geometric sequence is y = 1555.2(5/6)^x
Exponential functionsThe standard exponential function is expressed as y = ab^x
Using the coordinates (3, 900) and (4, 750)
Create the equations
900 = ab^3 ............. 1
750 = ab^4 ................. 2
Divide
900/750 = 1/b
b = 75/90
b = 5/6
Determine the value of "a"
900 = a(5/6)^3
900 = (125/216)a
a = 1555.2
Determine the required equation
y = 1555.2(5/6)^x
Hence the function that can be used to model the graphed geometric sequence is y = 1555.2(5/6)^x
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Answer:
a
Step-by-step explanation:
This figure shows the dimensions of an A frame house.
What is the volume of the house?
Enter your answer in the box.
V =
ft³
the distance lesley walks from home to school is 120 meters and 80 meters when he goes to church from home. gusion estimates that the distance lesley walks when he goes directly to church. coming frim school is 180 meters. guinevere's estimation is 210 meters which etimation is feasible? make a map of lesley ways from home to school and church justify.
Find the area of the rhombus
[tex]60cm^{2}[/tex]
Step-by-step explanation:
A=pq/2
shorter diagonal= 8cm
longer diagonal = 15cm
15*8 = 120
120/2 = 60
A = [tex]60cm^{2}[/tex]
25(-7)= ?
what type of equation is this?? division, multiplication, addition, or subtraction??
Answer:
multiplication
Step-by-step explanation:
the () means to multipy
