Step-by-step explanation:
Using the section formula , if a point ( x , y ) divides the line joining the points ( x1 , y1 ) and ( x2 , y2 ) into the ratio m : n , then
( x , y ) = ( mx2 + nx1 / m + n , my2 + ny1 / m + n)
Let the points be A(-8,−2) and B(6,19). Let a point P(x,y) divides AB in the ratio 5:2
Therefore, we have
[tex]P(x,y) =( \frac{5 \times 6 + 2 \times - 8}{5 + 2} , \: \frac{5 \times 19 + 2 \times - 2}{5 + 2}) [/tex]
[tex]P(x,y) = ( \frac{30 + ( - 16)}{7} , \: \frac{95 + ( - 4)}{7} )[/tex]
[tex] P(x,y) = (2, 13)[/tex]
Answer:
(2, 13)
Step-by-step explanation:
Let P be the point that partitions the segment.
Let M = (-8, -2)
Let N = (6, 19)
If point P partitions the segment MN in a 5 : 2 ratio, then to calculate the x and y values of point P:
divide the difference of the x (or y) values of the two endpoints by the sum of the ratiosmultiply this by 5, since P partitions the segment at 5 : 2add this to the x (or y) value of point Mx-value of P:
[tex]\sf \implies \left(\dfrac{x_N-x_M}{5+2}\right)\cdot5+x_N[/tex]
[tex]\sf \implies \left(\dfrac{6-(-8)}{5+2}\right)\cdot5+(-8)=2[/tex]
y-value of P:
[tex]\sf \implies \left(\dfrac{y_N-y_M}{5+2}\right)\cdot5+y_N[/tex]
[tex]\sf \implies \left(\dfrac{19-(-2)}{5+2}\right)\cdot5+(-2)=13[/tex]
[tex]\sf P=(2,13)[/tex]
What is the slope-intercept form of 11x-13y=39?
Answer:
Step-by-step explanation:
y=11/13x−3
hope this helps and mark me brainliest as well please.
In the equation, y=4x-1, what does the 4 mean? What does the -1 mean?
Answer:
The equation is written in slope-intercept (y = mx + b) form. Therefore, the '4' represents the slope of the line, and the '-1' represents the y-intercept.
An 18 ft. tree casts a 15 ft. long shadow as shown in the following figure.
Which of the following is the angle formed by the sun's rays and the ground?
A.30
B.40
C.50
D.60
Answer:
The answer should be C=50
Step-by-step explanation:
The diameter of a circle is 12 ft. Find its area to the nearest whole number. Answer: A =
Answer:
113 ft²
Step-by-step explanation:
π = 3.14
r = 6
Use the formula for the area of a circle:
A = πr²
A = 3.14*6²
A = 3.14*36
A = 113.04
A = 113
Hope this helps :)
Answer:
Area = 113 ft²
Step-by-step explanation:
The formula to find the area of a circle is:
Area = π × r²
r is the radius that can be found by taking half of the diameter.
r = [tex]\frac{12}{2}[/tex] = 6
Area = π × 6²
Area = π × 36
Area = 113.09 = 113 [ to the nearest whole number ]
A log is partly buried in the mud. One third of the log is buried and 8 meters of the log are above ground. What is the total length of the log?
Answer:
12
Step-by-step explanation:
The answer is 12 because if 1/3 of the log is buried then 2/3 of the log is 8 meters. 8 divided by 2 is 4 so you know that 1/3 of the log is 4 meters. Then you just multiply 4 times 3 or add 4 and 8.
Answer:
12 meters
Step-by-step explanation:
see image. If 1/3 log is buried, then 2/3 (the rest of it) log is above ground. If 8meters of log is 2/3 of the log, that is 8 meters is 2 parts, then each part is 4 meters.
2 parts (thirds!) above ground:
8 meters
1 part (one-third) below ground:
4 meters
Total is 8 + 4 =12
or 3×4 = 12
The whole log is 12 meters.
Which expression represents 25 times the sum of m and 3?
Answer:
25(m+3)
Step-by-step explanation:
25 is multiplied by (m+3)
'the sum of m and 3' is a quantity which must be indicated using parentheses
Hello!
The sum of means we add:
m+3
Multiply it times 25:
25(m+3)
The answer is Option C.
Now, the option you selected is wrong for the following reasons:
If you translate it into a verbal phrase, this is what it means:
25 plus the product of m and 3
Hence, Option C is correct.
Hope everything is clear.
Let me know if you have any questions!
Always remember: Knowledge is power! :-)
You are calculating the volume of a box which has a width ofx inches, a
length 1 inch less than the width, and a height 2 inches less than the width.
What is the end behavior of the polynomial function that models the volume
as a function of x?
and down
C. down and down
B. down and up
D. up and up
А. up
Using limits, it is found that the end behavior of the polynomial function for the volume of the rectangular box is:
B. down and up.
What is the volume of a rectangular prism?The volume of a rectangular prism of length l, width w and heigth h is given by:
V = lwh.
In this problem, we have that the dimensions are given by:
w = x.l = x - 1.h = x - 2.Hence the volume is given by:
[tex]V = x(x - 1)(x - 2) = x(x^2 - 3x + 2) = x^3 - 3x^2 + 2x[/tex]
What is the end behavior of a function?It is given by it's limits as x goes to infinity.
Hence:
[tex]\lim_{x \rightarrow -\infty} V(x) = \lim_{x \rightarrow -\infty} x^3 - 3x^2 + 2x = \lim_{x \rightarrow -\infty} x^3 = -\infty[/tex]
[tex]\lim_{x \rightarrow \infty} V(x) = \lim_{x \rightarrow \infty} x^3 - 3x^2 + 2x = \lim_{x \rightarrow \infty} x^3 = \infty[/tex]
Which means that option B is correct.
More can be learned about limits at brainly.com/question/22026723
Parallelogram P Q S R is shown. The length of P Q is (4 x minus 1) centimeters and the length of R S is (3 x + 7) centimeters.
The perimeter of parallelogram PQSR is 74 cm. What is QS?
4 cm
6 cm
8 cm
12 cm
The opposite sides PQ and RS of the parallelogram PQRS are congruent
The value of the length QS is 6 cm
How to determine the length QS?The given parameters are:
PQ = 4x - 1
RS = 3x + 7
Opposite sides are congruent.
So, we have:
4x - 1 = 3x + 7
Collect like terms
4x - 3x = 1 + 7
Evaluate the expressions
x = 8
The perimeter is calculated using:
Perimeter = 2(QS + RS)
This gives
2(QS + RS) = 74
Divide by 2
QS + RS = 37
Substiute RS = 3x + 7
QS + 3x + 7 = 37
Substitute 8 for x
QS + 3*8 + 7 = 37
This gives
QS + 31 = 37
Subtract 31 from both sides
QS = 6
Hence, the value of the length QS is 6 cm
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Answer:
6cm or b
Step-by-step explanation:
How many sides does a regular polygon have if each interior angle measures 150°?
Answer:
12
Step-by-step explanation:
Its interior angle has measure 150∘. Therefore, the exterior angle has measure 180∘−150∘=30∘. Therefore, the number of sides of the regular polygon with interior angle 150∘ is 12.
100 POINTS!!!!!!!
Part A: What is a coterminal angle of θ such that 0 ≤ θ ≤ 2π?
Part B: What are the exact values of all six trigonometric functions evaluated at θ?
Answer:
A. coterminal angle = 4π/3
B. sin(θ) = -√3/2; csc(θ) = -2√3/3; cos(θ) = -1/2;
sec(θ) = -2; tan(θ) = √3; cot(θ) = √3/3
Step-by-step explanation:
A.Any angle that is a multiple of 2π added to the given angle will be coterminal. You want one in the range [0, 2π], so we need to add 4π to the given angle
coterminal angle = -8π/3 +4π = -8π/3 +12π/3
coterminal angle = 4π/3
__
B.The reference angle is 4π/3 -π = π/3. θ is a quadrant III angle, so both the sine and cosine are negative.
sin(θ) = -√3/2 . . . csc(θ) = -2√3/3
cos(θ) = -1/2 . . . sec(θ) = -2
tan(θ) = √3 . . . cot(θ) = √3/3
Choose true or false:
y = 9 is the solution of y + 9 = 0
Please help. this is a end- of- year school test.
I appreciate it! ^^
Answer:
False.
Step-by-step explanation:
y+9=0
y=-9
hope you have a good day/night! :)
Elise drinks 2 cups of water per hour on Friday. At a certain time, she has already had 4 cups of water. On Friday, Jacob drinks 3 cups of water per hour, and at the same time of day, he has only had 2 cups of water for the day.
Write a system of equations that can be used to determine when Elise and Jacob will have drank an equal amount of water after drinking water for the same number of hours after 10:00 am.
How many hours will it take for Elise and Jacob to drink an equal amount of water?
By finding and solving a system of equations, we will see that after 2 hours they will drink the same amount of water.
How to write and solve the system of equations?For Elise, the number of cups consumed after the 10:00 am is:
y = 2*x + 4
Where x is the number of hours after 10:00 am.
For Jacob, the number is:
J = 3*x + 2
Then the system of equations is:
y = 2x + 4
y = 3x + 2
To solve it, we use the fact that the variable y is already isolated in both equations, so we can write:
2x + 4 = y = 3x + 2
2x + 4 = 3x + 2
Solving for x we get:
4 - 2 = 3x - 2x
2 = x
After 2 hours, Elise and Jacob drink the same amount of water.
If you want to learn more about systems of equations, you can read:
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When asked to factor the trinomial 4x^2 + 12x + 9, a student gives the answer (2x - 3)(2x - 3). What is one thing wrong with this answer?
A. There is nothing wrong with the answer
B. The minus signs should be plus signs
C. 4 is also a factor of this trinomial
D. The factors are not simplified
The one thing wrong with the answer is option B. The minus signs should be plus signs.
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
Given quadratic is 4x²+12x+9
Taking common 4
4(x²+3x) + 9
=4(x² + 3x + 9/4) + 9 - 9
=4(x + 3/2)²
=(2x+3)²
=(2x+3)(2x+3)
So, the minus sign must be a plus sign. option B is correct.
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A triangle has side lengths of 18 in., 22 in., and 29 in. Is the triangle acute, obtuse, or right?
Acute
Obtuse
Right
None of the above
========================================================
Explanation:
We have a triangle with these side lengths
a = 18b = 22c = 29Computing a^2+b^2 gets us
a^2+b^2 = 18^2+22^2 = 808
Compare this to c^2
c^2 = 29^2 = 841
Because 808 < 841, this means a^2+b^2 < c^2
-------------------
We have three cases:
If a^2+b^2 > c^2, then the triangle is acuteIf a^2+b^2 = c^2, then we have a right triangleIf a^2+b^2 < c^2, then the triangle is obtuseFor more information, check out the converse of the Pythagorean Theorem.
Miko has 3 cakes.
She cuts each cake into 4 equal pieces.
How many pieces of cake does Miko have?
Answer:
12 pieces of cake
Step-by-step explanation:
4 pieces for each cake
there is a total of three cakes
needed to find total pieces of cakes
multiply 4 by 3 and you will get 12 pieces of cake.
Answer:
Miko has 12 pieces of cake
Jemima was arranging 400 packets of biscuits for a sale. She put 52 packets into a basket and displayed 25% of the remaining packets on the shelves. What percentage of all the packets of biscuits did Jemima display on the shelves?
Answer:
87% of all the packets of biscuits Jemima displayed on the shelves.
Step-by-step explanation:
400-52=348
so, 348*25%
348*25/100
87
9×4 - 10 fours - ? fours
Answer:
9×4 - 10 fours - 26 fours
Step-by-step explanation:
9×4 - 10 fours - 26 fours
Hi what is a+3squared /56
Answer:
well friend you answer is
Step-by-step explanation:
a+ 3/56
i hope this helped
Answer:
Step-by-step explanation:
The appropriate symbolic expression would be
a + 3²
---------
56
A large pizza at Palanzio’s Pizzeria costs $6.80 plus $0.90 for each topping. The cost of a large cheese pizza at Guido’s Pizza is $7.30 plus $0.65 for each topping. How many toppings need to be added to a large cheese pizza from Palanzio's Pizzeria and Guido's Pizza in order for the pizzas to cost the same, not including tax?
Answer:
2 toppings need to be added to a large cheese pizza from Palanzio's Pizzeria and Guido's Pizza in order for the pizzas to cost the same
Step-by-step explanation:
t=toppings
6.80 +0.90t = 7.30+0.65t
0.25t = 0.5
t = 2
The collection of all equally likely outcomes is known as the
Answer:
The Sample space
Step-by-step explanation:
The collection of all equally likely outcomes is known as the- the sample space.
For the function f(x)=−7x2+8x−8, find f(4).
Answer:
- 88
Step-by-step explanation:
[tex]f(x ) = - 7 {x}^{2} + 8x - 8 \\ plug \: x = 4 \\ \\ \implies \: f(4 ) = - 7 {(4)}^{2} + 8(4) - 8 \\\\ \implies \: f(4 ) = - 7 \times 16 + 32 - 8 \\\\ \implies \: f(4 ) = - 112+ 32 - 8 \\ \\ \implies \: f(4 ) = - 120+ 32 \\\\ \implies \: f(4 ) = - 88 \\[/tex]
Find the values of x for which the denominator is equal to zero for 5x+6/x^2+6x+9 . none
x = −3
x = 3
x = −3, x = 3
The denominator would be x = -3.
Option (A) is correct.
What is the denominator?
A denominator is a bottom number in a fraction. It represents the divisor or the number by which the numerator is being divided.
In this case, the denominator is x^2+6x+9. To find the values of x for which the denominator is equal to zero, we need to set the denominator equal to 0 and solve for x. The equation would be x^2+6x+9=0. By factorizing the denominator we get (x+3)^2=0.
x + 3 = 0
x = -3
Hence, the denominator would be x = -3.
Option (A) is correct.
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Factor the equation k^2 + 25
Answer:
k^2+25
Step-by-step explanation:
Factor k^2+25
=k^2+25
Doesn't factor
A unicycle wheel has a diameter of 12 inches. How many inches will the unicycle travel in 6 revolutions? Round your answer to the nearest hundredth of an inch. this is just for anyone who is having trouble with this question and want the answer the answer to this question is 188.4 or 188.40
Answer:
226.19 in.
Step-by-step explanation:
circumference = πd
circumference = 3.14159 × 12 in.
circumference = 37.70 in.
In one revolution of the wheel, the unicycle travels a distance equal to the circumference of the wheel, or 37.70 in.
In 6 revolutions, the unicycle travels 6 times the circumference of the wheel.
6 × circumference = 6 × 37.70 in. = 226.19 in.
Answer: 226.19 in.
Find the area of the figure.
Pls help
It's a trapezoid
Base=15+5=20cmAnother side=15cmHeight=12cmNow
Area:-
1/2(Sum of parallel sides)(Height)1/2(15+20)(12)6(35)210cm^2An American roulette wheel has 38 spaces, labeled using the numerals 1 through 36, 0, and 00. In a random spin of the wheel, what is the probability that the ball will land on 2?
This is because there's one space labeled "2" out of 38 spaces total.
This fraction is approximately equal to 1/38 = 0.0263 meaning there's roughly a 2.63% chance of landing on this space.
The probability is 0.0263 that the ball will land on 2 in a random spin of the wheel.
What is probability?The probability is defined as the possibility of an event is equal to the ratio of the number of outcomes and the total number of outcomes.
Assuming an unbiased wheel.
The probability of an event = number of favourable outcomes/ number of total outcomes.
The total number of outcomes is 38
The number of favourable outcomes is one because there's one space labeled "2" out of 38 spaces total.
The probability of an event = 1/38 = 0.0263
Hence, the probability is 0.0263 that the ball will land on 2 in a random spin of the wheel.
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What type of function is f(x) = 2x3 – 4x2 + 5?
it's a cubic function
The given function f(x) = 2x³ – 4x² + 5 is a cubic function.
What is a cubic polynomial?A polynomial in mathematics is an expression made up of coefficients and indeterminates and involves only the operations of multiplication, addition, subtraction, and non-negative integer exponentiation of variables.
A cubic polynomial is a sort of polynomial that is based on the variable's largest exponent, or degree, in mathematical terms. As a result, a cubic polynomial is one in which the degree or maximum power of the variable is 3.
It is observed that the given function is a cubic function as its highest power of the variable is three.
Therefore, the given function f(x) = 2x³ – 4x² + 5 is a cubic function.
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Find the Perimeter
Length - 152 cm
Breadth- 120 cm
Step-by-step explanation:
Perimeter=2(l+b)
=2(152+120)
=544 cm
write 14,689 in word form what is the answer like identify the thousand group and the ones group
Answer:
fourteen thousand six hundred and eighty nine
Step-by-step explanation:
1 is in the ten thousand group, four is in the thousands, six is in the hundreds, eight is in the tens, nine is in the ones. i hope this helped :)
Answer:
Fourteen-thousand and six-hundred eighty nine.
solve step by step
1/x-1+1/y-2=1
3/x-1+5/y-2=4