Answer:
The coordinates of point P along the segment AB is (-1, 6).
Step-by-step explanation:
It is known that ratio of AP to PB is:
[tex]\frac{AP}{PB} = \frac{2}{3}[/tex]
Or vectorially speaking:
[tex]\overrightarrow{AP} = \frac{2}{3}\overrightarrow{PB}[/tex]
The vector that represents the segment AB is:
[tex]\overrightarrow{AB} = \vec B -\vec A[/tex]
If [tex]\vec A = (-7,4)[/tex] and [tex]\vec B = (8,9)[/tex], then:
[tex]\overrightarrow{AB} = (8,9)-(-7,4)[/tex]
[tex]\overrightarrow {AB} = (8+7,9-4)[/tex]
[tex]\overrightarrow{AB} = (15,5)[/tex]
But [tex]\overrightarrow{AB} = \overrightarrow{AP} + \overrightarrow{PB}[/tex], then:
[tex]\overrightarrow{AB} = \frac{2}{3}\overrightarrow{PB} +\overrightarrow{PB}[/tex]
[tex]\overrightarrow{AB} = \frac{5}{3}\overrightarrow{PB}[/tex]
[tex]\overrightarrow{PB} = \frac{3}{5}\overrightarrow{AB}[/tex]
[tex]\overrightarrow{PB} = \frac{3}{5}(15,5)[/tex]
[tex]\overrightarrow{PB} = \left(9, 3\right)[/tex]
The location of [tex]\vec P[/tex] is derived of this formula:
[tex]\overrightarrow{PB} = \vec B - \vec P[/tex]
[tex]\vec P = \vec B - \overrightarrow{PB}[/tex]
If [tex]\vec B = (8,9)[/tex] and [tex]\overrightarrow{PB} = \left(9, 3\right)[/tex], then:
[tex]\vec P = (8,9) - (9,3)[/tex]
[tex]\vec P = (8-9,9-3)[/tex]
[tex]\vec P = (-1, 6)[/tex]
The coordinates of point P along the segment AB is (-1, 6).
Solve this problem T=u+v/2 solve for u
Answer:
u = 2T - v[tex]T = \frac{u + v}{2} [/tex]
Cross multiply
We have
2T = u + v
u + v = 2T
Move v to the right side of the equation to make u stand alone
We have the final answer as
u = 2T - vHope this helps you
A line contains the point (8,-5). If the slope of the line is write the equation of the line using point-slope form
Answer:
[tex]\bold{y+5=\frac57(x-8)}[/tex]
Step-by-step explanation:
[tex]y-y_1=m(x-x_1)[/tex] - point-slope form of Equation of the Line
[tex](8,-5)\ \ \implies x_1=8\,,\ y_1=-5\\\\m=\frac57\\\\equation:\\{}\qquad\qquad y-(-5)=\frac57(x-8)\\\\{}\qquad\qquad y+5=\frac57(x-8)[/tex]
Can someone help me with this question please?
Answer:
a.) (0,4) b.) (-4,0)
Step-by-step explanation:
a.) Let x=0 and solve for y: y=0+4=4. Since we let x=0 the first number will be 0 and we found y to be 4, so our coordinates are (0,4)
b.) Let y=0 and solve for x: 0=x+4, x=-4. Since x=-4 our first number is -4, since y is 0 our second number is 0, so our coordinates are (-4,0)
Hope this helps!
If AC =4.5 what is the measure of AB
Answer:
f
Step-by-step explanation:
f
Answer:
[tex]\boxed{AB = 9}[/tex]
Step-by-step explanation:
AB = 2(AC) {Because a line segment drawn from a center of a circle bisect the chord opposite to it}
So,
AB = 2(4.5)
AB = 9
Solve the system of equations by substitution.
y=-1/2x-7
2 x - y = -16
Answer:
Point Form:
( − 46 /3 , − 44 /3 )
Equation Form:
x = − 46 /3 , y = − 44 /3
Step-by-step explanation:
Combine 1 /2 and x .
y = x /2 − 7
2 x − y = − 16
Replace all occurrences of y in 2 x − y = − 16 with x /2 − 7 .
y = x /2 − 7
2 x − ( x /2 − 7 ) = − 16
Simplify
2 x − ( x /2 − 7 ) .
y = x /2 − 7
3 x /2 + 7 = − 16
Solve for
x
in the second equation.
y = x /2 - 7
x = − 46 /3
Replace all occurrences of x in y = x /2 − 7 with − 46 /3 .
y = − 46 /3 /2 − 7
x = − 46 /3
Simplify − 46 /3 /2 − 7 .
y = − 44 /3
x = − 46 /3
The solution to the system of equations can be represented as a point.
( − 46 /3 , − 44 /3 )
The result can be shown in multiple forms.
Point Form:
( − 46 /3 , − 44 /3 )
Equation Form:
x = − 46 /3 , y = − 44 /3
The question i want to know is linked below. Please help :)
Answer:
Hey there!
To solve this problem, we want to find the LCM (least common multiple) of the two numbers.
The numbers are 25 and 30.
25=5x5
30=2x3x5
LCM is 5x5x2x3, or 150.
Thus, in 150 minutes is when the next bus will leave.
150 mins is equal to 2 hours and 30 mins, or 2.5 hours.
8 AM + 2.5 hrs = 10:30 AM.
Thus, the next time the busses leave together would be at 10:30 AM.
Let me know if this helps :)
Dave ran 3.52 miles in the same time
that Eric ran 2.44 miles. How much
further did Dave run than Eric?
I need to find the derivative of d). Can someone please fine y’ please.
Answer:
= -2x/ ( x^2+5) ^2
Step-by-step explanation:
y = 1/ ( x^2 +5)
y = ( x^2+5) ^ -1
dy/dx = -1 * (x^2 + 5) ^-2 * d/dx (x^2 + 5)
-1 * (x^2 + 5) ^-2 * 2x
= -2x/ ( x^2+5) ^2
The question i want to know is linked below, please help!!
Answer: 250 metre
Step-by-step explanation:
The radius of the semi circle will be:
Radius r = diameter/ 2
Where diameter = 140
r = 140/2 = 70m
The radius is also equal to the width of the diameter.
Find the quarter of the circumference of a circle.
Circumference of a circle = 2πr
Substitute for r in the formula
Circumference = 2 × 22/7 × 70
Circumference = 44 × 10 = 440 m
Divide the circumference by 4
440/4 = 110 m
The perimeter P of the shaded region will be
P = 110 + 70 + 70
Perimeter = 250 m
Therefore, the perimeter of the shaded region is 250 m
At the beginning of the season, MacDonald had to remove 555 orange trees from his farm. Each of the remaining trees produced 210210210 oranges for a total harvest of 417904179041790 oranges. Write an equation to determine the initial number of orange trees (t)(t)(, t, )on MacDonald's farm. Find the initial number of orange trees on MacDonald's farm. orange trees
Answer:
Initial number of trees (t)=204
Step-by-step explanation:
t = initial number of trees
Subtract 5 trees from the initial number of trees
we have,
t-5
each remaining tree made 210 oranges for a total of 41,790 oranges
We have,
(t-5) * 210=41790
Solve the equation
(t-5) * 210=41790
Open the bracket
210t-1050=41790
210t=41790+1050
210t=42840
Divide both sides by 210
210t/210=42840/210
t=204
The initial number of trees on MacDonald farm orange trees (t)=204
If 5 is removed from the initial trees
t-5=204-5
=199 trees
199 trees produce 210 oranges
We have,
199*210=41790 oranges
Answer:
Equation: 210t - 1050 = 41790
204 orange trees
Step-by-step explanation:
answer is from khan academy
pls brainliest :|
are the triangles similar?
Answer:
Yes.
Step-by-step explanation:
The angles of the triangles add up to be 180. 180 - 114 - 31 = 35. 180-114-35 = 31. Since the angles of the triangles correspond and are congruent, the triangles are similar, with PQR corresponding to TUS.
Hope this helps !
what is the slope of the line that contains these points (-2 2) and (3 3)
Answer:
[tex]\bold{m=\dfrac15}[/tex]
Step-by-step explanation:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}\\\\(-2,\,2)\ \implies\ x_1=-2\,,\ y_1=2\\(3,\,3)\ \implies\ x_2=3\,,\ y_2=3\\\\m=\dfrac{3-2}{3-(-2)}=\dfrac{1}{3+2}=\dfrac15[/tex]
(-30) x ______ = (-270)
Find the slope of a line parallel to each given line and graph.
y=9x+5
Answer:
9
Step-by-step explanation:
This equation is in slope intercept form
y = mx+b where m is the slope and b is the y intercept
y = 9x+5
The slope is 9
Parallel lines have the same slope so a line parallel would have a slope of 9
Answer:
i think the slope is 9.
because y= 9x+5 is in the form of slope intercept form.
as y=mx + c (where m is the slope of the equation.)
therefore, the slope (m )= 9....ans
hope it helps....
A linear function has the same y-intercept as x + 4y = 8 and its graph contains the point (4, 3). Fill in the blank to find the y-intercept.
Answer:
The y - intercept is (0, 4)
Step-by-step explanation:
The equation x + 4y = 8 is in 'standard form.' Any line parallel to this line has an equation that looks exactly the same EXCEPT for the constant.
So, let's write out x + 4y = 8 and replace the 8 with C.
x + 4y = C
Now take the coordinates of the given point (4, 3) and substitute them into the above equation: 4 + 4(3) = C = 16
Thus, the equation of the line passing through (4, 3) is x + 4y = 16.
To find the y-intercept, set x = 0 and calculate y:
0 + 4y = 16, or y = 4
The y - intercept is (0, 4)
Please answer this question now in two minutes
Answer:
67 degrees.
Step-by-step explanation:
The two quadrilaterals are congruent, with angle T corresponding to angle F, angle U corresponding to angle C, angle V corresponding to angle D, and angle W corresponding to angle E.
A quadrilateral's interior angles add to be 360 degrees.
x + 138 + 67 + 88 = 360
x + 293 = 360
x = 67
So, angle D is 67 degrees.
Hope this helps!
Amanda teaches violin lessons for $21.30 per hour. How many hours of lessons must Amanda give to make no less than $894.60?
No less than 42 lessons
No less than 35 lessons
No less than 45 lessons
No less than 33 lessons
Answer:
No less than 42 lessons
Step-by-step explanation:
To find the total numbers of hours needed to teach, divide the total amount of money needed by the amount of money made an hour.
$894.60/$21.30 = 42
Can someone please help me I really need help please help me thank you
Answer:
97
Step-by-step explanation:
the shape leans a little so it's more than 90
Which system below has no solution? y = 4x and y = 2x - 3 y = -4x and y = 2x - 3 y = -4x and y = 2x + 3 y = -4-x and y = 2x - 3
Answer:
y=4x
Step-by-step explanation:
this is because all other systems are defined and can be solved simultaneously...
pls lime and follow me ...i follow back...thanks
Please help me!
30g of cornflakes contain 2.5g of fat
How many grams of fat are there in 566g of cornflakes?
Give your answer to 1 dp
Answer:
47 .2 Grams 0f FatStep-by-step explanation:
[tex]30g ----> 2.5g -fat\\566g ----> xg -fat\\30x = 1415\\\frac{30x}{30} =\frac{1415}{30} \\\\x = 47.1666\\\\x = 47.2g of Fat[/tex]
Find equation of the line.
Answer:
-1+9
Step-by-step explanation:
-1 divide by -1 =1
so the answer is -1+9
I hope that helped and can you do my answer as a Brainliest PLEASE
If it helped don't forget to thanks
Find the area of this triangle..
Answer:
Step-by-step explanation:
For this problem, we have to use Heron's Formula.
S= (a + b + c)
over 2
And then √S( S-a) (S-b) (S-c)
That's the formula, now to plug in the numbers.
S= 12+12+21.2
over 2
that equals 45.2/ 2= 22.6'
Now we found s, so we can plug in the second step of the formula...
√22.6 ( 22.6 - 12 ) ( 22.6 - 12 ) ( 22.6 - 21.2 )
This equals √ 22.6 (10.6) (10.6) (1.4)
and that equals...
59.624411 = or rounded it up to 60.
3
8
9
10
TIMEI
01:
C D
When simplified and written in standard form, which quadratic function is equivalent to the polynomial shown?
2 + 7c-4c2 – 30 + 4
4c2 + 4c + 6
-7c2 + 10C + 6
O4c2 + 4C + 8
0-7c2 + 70 +6
Answer:
A. -4c^2+4c+6
Step-by-step explanation:
2+7c-4c^2-3c+4
-4c^2+7c-3c+4+2
-4c^2+4c+6
Gwen and Bryn drive to work.
Gwen drives 65 miles in 2.5 hours.
Bryn drives 76 km in 1 hour 15 min.
Work out the difference between their average speeds in km/h
Answer: 18.96 km/h
Step-by-step explanation:
Gwen:
65 miles = 104.6 km
104.6 km / 2.5 h = 41.84 km/h
Bryn:
15 min = 0.25 h
76 km / 1.25 h = 60.8 km/h
Difference:
60.8 - 41.84 = 18.96 km/h
Hope this helps!
find the exact length of the third side
Answer:
8
Step-by-step explanation:
We will the pythagorian theorem :
let x be the third side x²+6²= 10²x²= 100-36 x=[tex]\sqrt{64}[/tex] x=8Answer:
b=8
Step-by-step explanation:
We can use the Pythagorean theorem since this is a right triangle:
a^2+ b^2 = c^2 where a and b are the legs and c is the hypotenuse
a=6 and b = 10
6^2 + b ^2 = 10^2
36+ b^2 = 100
b^2 = 100-36
b^2 = 64
Taking the square root of each side
sqrt(b^2) = sqrt(64)
b = 8
i need help from uh all..
Answer:
Step-by-step explanation:
Given expression is,
[tex]\text{cot}A=\frac{1}{2}(\text{cot}\frac{A}{2}-\text{tan}\frac{A}{2})[/tex]
To prove this identity we will take the right side of the identity,
[tex]\frac{1}{2}(\text{cot}\frac{A}{2}-\text{tan}\frac{A}{2})=\frac{1}{2}(\frac{1}{\text{tan}\frac{A}{2}}-tan\frac{A}{2})[/tex]
[tex]=\frac{1}{2}(\frac{1-\text{tan}^2\frac{A}{2}}{tan\frac{A}{2}})[/tex]
[tex]=\frac{1}{2}[\frac{2(1-\text{tan}^2\frac{A}{2})}{2tan\frac{A}{2}}][/tex]
[tex]=\frac{1}{2}(\frac{2}{\text{tan}A} )[/tex] [Since [tex]\text{tan}A=\frac{2\text{tan}\frac{A}{2}}{1-\text{tan}^2\frac{A}{2}}[/tex]]
= cot A
Hence right side of the equation is equal to the left side of the equation.
what is the measure of x? 68 degrees 70 degrees
Answer:
x = 138°
Step-by-step explanation:
Since the sum of all angles in a triangle is 180°, we find ∠BAC:
m∠BAC = 180 - (68 + 70) = 42°
Since ∠x and ∠BAC are Supplementary Angles, they add up to 180°:
180 - 42 = x
x = 138°
Answer:
138
Step-by-step explanation:
1. 68 + 70 = 138
2. 180 - 38 = 42
3. 180 - 42 = 138
4. X = 138
In the diagram below, AB is parallel to CD. What is the value of x?
Answer:
A. 120 degrees.
Step-by-step explanation:
The two angles are alternate angles, which means they are congruent. So, x is also 120 degrees.
Hope this helps!
How are the graphs of the functions f(x) = . 16and g(x) = 3/64 related?
The functions f(x) and g(x) are equivalent.
The function g(x) increases at a faster rate.
The function g(x) has a greater initial value.
The function g(x) decreases at a faster rate.
Answer: A there are equivalent.
Step-by-step explanation:
f(x) = [tex]\sqrt{16}^x[/tex] reduces to f(x)=[tex]4^{x}[/tex]
g(x)= [tex]\sqrt[3]{64}^{x}[/tex] also reduces to g(x) = [tex]4^{x}[/tex]
The function g(x) equal to f(x).
What is the exponent?A quantity representing the exponent to which a given number or letter is to be raised is usually expressed as a raised symbol beside the number or letter. It is expressed as aˣ is a variable and a is constant.
Given are two functions, f(x) = √16ˣ and g(x) = ∛64ˣ,
We need to find the relation between the function,
So,
√16 = 4
∛64 = 4
Functions can be written as, f(x) = 4ˣ and g(x) = 4ˣ,
It is clear that g(x) equal to f(x) because g(x) is having power equal than f(x).
Thus, It is clear that g(x) is equal to f(x).
More about the exponent link is given below.
brainly.com/question/5497425
#SPJ7
Draw a circle with center A and a radius of your choice. Create three well-spaced points, B, C, and D, on the circle in clockwise alphabetical order. Draw two radii, AB and AC , and draw two chords, DB and DC . Measure and record m∠CAB and m∠CDB. Take a screenshot of your diagram with the measurements, and paste it below.
Answer:
Please find attached the required circle
It is observed that the angle subtended by the arc CB which are m∠CAB and m∠CDB is such that the angle arc CB subtends at the center, m∠CAB is two times the angle that the arc CB subtends at the circumference
The measured angle subtended by the arc CB at the center m∠CAB = 64° and the measured angle subtended by the arc CB at the circumference m∠CDB = 32°
Step-by-step explanation:
T
Answer:
from edmentum
Step-by-step explanation: