Answer:
Step-by-step explanation:
If the distance from M to N is 80 miles and we want to find the coordinates of the point 60 miles into the trip, we are looking for the point 3/4 of the way from M to N, since 60 is 3/4 of 80. This is the process:
First we need to consider that MN is a directed vector. We first find the components of the directed vector, which is found in the change in x and the change in y. First step, then, looks like this:
<Δx, Δy> = <9-3, 13-2> = <6, 11> We will call those the x and y components of the vector (which comes from vector study in both physics and math, so if you don't understand that, it's ok! Just follow the process here and you'll be fine). Knowing that 60 is 3/4 of the way from M to N, we find 3/4 of both the x and y components, like this:
[tex]<\frac{3}{4}(6), \frac{3}{4}(11)>[/tex] which will give us 3/4 of the change in x and 3/4 of the change in y:
[tex]<\frac{18}{4},\frac{33}{4}>=<4.5,8.25>[/tex]
Since we are going 3/4 of the way from M to N, we add that component to the x and y coordinates of M, giving us 3/4 of the way from M to N, which translates to 60 miles of the 80 mile trip:
(3 + 4.5, 2 + 8.25) = (7.5, 10.25)
Those are the coordinates of the point that represents 60 miles into the 80 mile trip.
In In 5x + In In (x - 1) = 2
Answer:
exact form: x=-1/2
decimal form: x=-0.5
P(x) is a polynomial. here are a few values of p(x).
P(-5) = - 2
P(-3) = 6
P(3) = 7
P(5) = -1
What is the remainder when P(x) is divided by (x+5)?
What is the remainder when P(x) is divided by (x-3)?
Given:
Values of a polynomial P(x).
[tex]P(-5)=-2[/tex]
[tex]P(-3)=6[/tex]
[tex]P(3)=7[/tex]
[tex]P(5)=-1[/tex]
To find:
The remainder when P(x) is divided by (x+5).
The remainder when P(x) is divided by (x-3).
Solution:
If a polynomial P(x) is divided by (x-a), then the remainder is P(a).
If the polynomial P(x) is divided by (x+5), then the remainder is P(-5).
[tex]P(-5)=-2[/tex]
Therefore, the remainder is -2 when P(x) is divided by (x+5).
If the polynomial P(x) is divided by (x-3), then the remainder is P(3).
[tex]P(3)=7[/tex]
Therefore, the remainder is 7 when P(x) is divided by (x-3).
plz help me with this math and also explain
Step-by-step explanation:
[1]SI = $250Rate (R) = 12[tex] \sf \dfrac{1}{2}[/tex] %Time (t) = 4 years[tex]\longrightarrow \tt { SI = \dfrac{PRT}{100} } \\ [/tex]
[tex]\longrightarrow \tt { 250 = \dfrac{P \times 12\cfrac{1}{2} \times 4}{100} } \\ [/tex]
[tex]\longrightarrow \tt { 250 = \dfrac{P \times \cfrac{25}{2} \times 4}{100} } \\ [/tex]
[tex]\longrightarrow \tt { 250 = \dfrac{P \times 25 \times 2}{100} } \\ [/tex]
[tex]\longrightarrow \tt { 250 = \dfrac{P \times 50}{100} } \\ [/tex]
[tex]\longrightarrow \tt { 250 \times 100 = P \times 50} \\ [/tex]
[tex]\longrightarrow \tt { 25000 = P \times 50} \\ [/tex]
[tex]\longrightarrow \tt { \dfrac{25000}{50} = P } \\ [/tex]
[tex]\longrightarrow \underline{\boxed{ \green{ \tt { \$ \; 500 = P }}}} \\ [/tex]
Therefore principal is $500.
__________________[2]2/7 of the balls are red.3/5 of the balls are blue.Rest are yellow.Number of yellow balls = 36Let the total number of balls be x.
→ Red balls + Blue balls + Yellow balls = Total number of balls
[tex]\longrightarrow \tt{ \dfrac{2}{7}x + \dfrac{3}{5}x + 36 = x} \\ [/tex]
[tex]\longrightarrow \tt{ \dfrac{10x + 21x + 1260}{35} = x} \\ [/tex]
[tex]\longrightarrow \tt{ \dfrac{31x + 1260}{35} = x} \\ [/tex]
[tex]\longrightarrow \tt{ 31x + 1260= 35x} \\ [/tex]
[tex]\longrightarrow \tt{ 1260= 35x-31x} \\ [/tex]
[tex]\longrightarrow \tt{ 1260= 4x} \\ [/tex]
[tex]\longrightarrow \tt{ \dfrac{1260 }{4}= x} \\ [/tex]
[tex]\longrightarrow \underline{\boxed{ \tt { 315 = x }}} \\ [/tex]
Total number of balls is 315.
A/Q,
3/5 of the balls are blue.
[tex]\longrightarrow \tt{ Balls_{(Blue)} =\dfrac{3 }{5}x} \\ [/tex]
[tex]\longrightarrow \tt{ Balls_{(Blue)} =\dfrac{3 }{5}(315)} \\ [/tex]
[tex]\longrightarrow \tt{ Balls_{(Blue)} = 3(63)} \\ [/tex]
[tex]\longrightarrow \underline{\boxed{ \green {\tt { Balls_{(Blue)} = 189 }}}} \\ [/tex]
solve the simultaneous equation: x-y=2
xy=36
Answer:
Y= –7.08, 5.08
Step-by-step explanation:
hope ya ready bro.
X=36/Y
replace 36/y instead of X
36/Y–Y=2===> 36–Y²=2Y===> Y²+2Y–36=0
Y1= –1+√37≈ –7.08
Y2= –1–√37≈ 5.08
In which section of the number line is 32−−√?
where's the number line?
maybe u can attach it at the comments:)
Answer:
Section B
Step-by-step explanation:
What is 6.273 rounded to the nearest thousandths?
Answer:
6.270
Step-by-step explanation:
3 is below 5 so you just turn it into a 0. If it was 5 or above you would just add a number to the 7.
Find the measure of the missing angle using the exterior angle sum theorm.
Answer:
85°
Step-by-step explanation:
The exterior angle of a triangle is=sum of the opposite interior angles
So
? °=45°+40°
If f(x) = 2x2 + 1, what is f(x) when x = 3?
Answer:
18
Step-by-step explanation:
f(x)=2x(2+1)
f(3)=2(3)(2+1)
=6(2+1)
=12+6
=18
Need help ASAP !!!when creating a question for a survey , the way a question is written:
Answer:
The third one i think
Step-by-step explanation:
Since a survey shouldn't be biased or anything.
a^2×c^2/c^2×d^2+bc/ad reduce the algebraic
Answer:
[tex]\frac{a^2*c^2}{c^2*d^2}+\frac{bc}{ad}= \frac{a^3 + bcd}{ad^2}[/tex]
Step-by-step explanation:
Given
[tex]\frac{a^2*c^2}{c^2*d^2}+\frac{bc}{ad}[/tex]
Required
Simplify
We have:
[tex]\frac{a^2*c^2}{c^2*d^2}+\frac{bc}{ad}[/tex]
Cancel out [tex]c^2[/tex]
[tex]\frac{a^2*c^2}{c^2*d^2}+\frac{bc}{ad}= \frac{a^2}{d^2}+\frac{bc}{ad}[/tex]
Take LCM
[tex]\frac{a^2*c^2}{c^2*d^2}+\frac{bc}{ad}= \frac{a^3 + bcd}{ad^2}[/tex]
A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid ₹27 for a book kept for seven days, while Susy paid ₹21 for the book she kept for five days. Find the fixed charge and the charge for each extra day.
Answer:
Ji Gud afternoon.
I'm fine
what about you madam.
Hope u r fine and stay safe and healthy
The equation d = m/v can be used to calculate the density,d, of an object with mass,m, and volume,V. Which is an equivalent equation solver for V?
Answer:
v = m/d
Step-by-step explanation:
since
[tex]d = \frac{m}{v} \: \\ \\ v = \frac{m}{d} [/tex]
If
5
3 cosα = in the first quadrant, what does cot α
equal?
Answer:
5/4
Step-by-step explanation:
To Find :-
cot a .Solution :-
By question ,
=> cos a = 5/3 = b/h
=> p = √ 5² - 3² = √ 25 -9 = 4
Therefore ,
=> cot a = b/p = 5/4
The sum of three consecutive odd numbers is 63. What are the numbers?
Answer:
19, 21 and 23
Step-by-step explanation:
→ Make an algebraic expression for the 3 consecutive numbers
2x + 1, 2x + 3 and 2x + 5
→ Add the expressions together and make it equal to 63
2x + 1 + 2x + 3 + 2x + 5 = 63
→ Simplify
6x + 9 = 63
→ Minus 9 from both sides
6x = 54
→ Divide both sides by 6
x = 9
→ Resubstitute x = 9 into the 3 expressions
x = 9 into 2x + 1 is 19
x = 9 into 2x + 3 is 21
x = 9 into 2x + 5 is 23
I would raise it to 1grand but I’m very broke
Answer:
ITS A LOL
Step-by-step explanation:
help help help pls :)
Answer:
[tex]opposite\approx 70.02[/tex]
Step-by-step explanation:
The triangle in the given problem is a right triangle, as the tower forms a right angle with the ground. This means that one can use the right angle trigonometric ratios to solve this problem. The right angle trigonometric ratios are as follows;
[tex]sin(\theta)=\frac{opposite}{hypotenuse}\\\\cos(\theta)=\frac{adjacent}{hypotenuse}\\\\tan(\theta)=\frac{opposite}{adjacent}[/tex]
Please note that the names ([tex]opposite[/tex]) and ([tex]adjacent[/tex]) are subjective and change depending on the angle one uses in the ratio. However the name ([tex]hypotenuse[/tex]) refers to the side opposite the right angle, and thus it doesn't change depending on the reference angle.
In this problem, one is given an angle with the measure of (35) degrees, and the length of the side adjacent to this angle. One is asked to find the length of the side opposite the (35) degree angle. To achieve this, one can use the tangent ([tex]tan[/tex]) ratio.
[tex]tan(\theta)=\frac{opposite}{adjacent}[/tex]
Substitute,
[tex]tan(35)=\frac{opposite}{100}[/tex]
Inverse operations,
[tex]tan(35)=\frac{opposite}{100}[/tex]
[tex]100(tan(35))=opposite[/tex]
Simplify,
[tex]100(tan(35))=opposite[/tex]
[tex]70.02\approx opposite[/tex]
Find (a) the mean, (b) the median, and
(c) the mode of the number of verses in
the first eight chapters of Proverbs.
Proverbs 1 23 4 5 6 7 8
Verses 33 22352723352736
(a)
(b)
(c)
Answer:
Mean = 33+ 22+35+27+23+35+27+36 = 238/8 = 29.75
Median = 27+23 = 50/2 = 25
Mode = 35
Range = 36 - 22 = 14
Step-by-step explanation:
Stay Blessed
Arvin has $10000 to invest. He invests part in a term deposit paying 5%/year, and the remainder in Canada savings bonds paying 3.4%/year. At the end of the year, he earned simpler interest of $413. How much did he invest at 5%/year?
Answer:
$4,562.5
Step-by-step explanation:
The amount Arvin has to invest, P = $10,000
The interest paid on the investment in the term deposit = 5%/year
The interest paid om the investment in Canada savings bonds = 3.4%/year
The amount Arvin earned at the of the year as simple interest, A = $413
Let, x, represent the amount Arvin invested in the term deposit and let, y, represent the amount he invested in Canada savings bonds, we can get the following system of equations
x + y = 10,000...(1)
0.05·x + 0.034·y = 413...(2)
Making y the subject of equation (1) and substituting the value in equation (2), we get;
From equation (1), we get, y = 10,000 - x
Plugging the above value of y in equation (2) gives;
0.05·x + 0.034 × (10,000 - x) = 413
∴ 0.05·x - 0.034·x + 340 = 413
x = (413 - 340)/(0.05 - 0.034) = 4,562.5
Therefore, the amount Arvin invested in the term deposit at 5%, x = $4,562.5
(y = 10,000 - x
∴ y = 10,000 - 4,562.5 = 5,437.5
The amount Arvin invested in Canada savings bonds, y = $5,437.5.)
find the volume of the rectangular prism. plz answer this lol
Answer:
.....how when the dimensions are not even clear lol
Answer:
48 cm³
Step-by-step explanation:
the volume of a rectangular prism= length × breadth × height
= 8× 3 × 2
= 48 cm³
Find the value of y
Help please
Answer:
6
Step-by-step explanation:
Set your formula up as
15 = 2y+3
15 - 3 = 2y
12 = 2y
12 / 2 = y
6 = y
The measure of an angle is eight times the measure of its supplementary angle. What is the measure of each angle?
Answer:
160°
Step-by-step explanation:
Let one angle be x
Let second angle be 8x
Sum of supplementary angles = 180°
x+ 8x = 180°
9x = 180
x = 180/9 = 20
First angle= x= 20°
Second angle = 8x = 8*20 = 160°
The polygons are similar, but not necessarily drawn to scale. Find the value of x. PLEASE HELPPPP
Answer:
x = 27.5.
Step-by-step explanation:
There are given numbers on each side. If the figures are similar, then they have a set ratio for each value.
So, 55:8 and x:4. If you want to, you can flip it, so that it is 8:55 and 4:x.
With that in mind, it is easy to see what the ratio is. Because 4 is half of 8, x is half of 55. 55 divided by 2 is 27.5.
Therefore, x = 27.5.
if u help me i will give you brainliest <3
Answer:
a) 6
b) 12:35 ( not so sure about this one)
Step-by-step explanation:
a)
distance = speed * time
ruths distance = 4* 1.5 (because it takes her 1h 30 mins)
distance = 6miles
b) 1/4 here is quarter so, 15mins
10:30 and then add 50 mins to that.
she leaves at 11:20 and takes 1h and 15 mins ( 75mins) to walk home
so 11:20 + 1h 15min
= 12:35
hope this helps :)
Answer:
a) 6 miles
b) 12:35 pm
Step-by-step explanation:
a) 9 am to 10:30 am = 1 hour and 30 mins = 1.5 hours
4mph x 1.5 = 6miles
b) 10:30 am + 50 mins = 11:20 am
1 hour = 60 mins
60/4 = 15 mins
1 1/4 = 1 hour 15 mins
11:20 am + 1 hour 15 mins = 12:35 pm
Someone please help me ASAP
Step-by-step explanation:
a vector multiplied by a scalar is equal to it's image. The expression above gives an equation and after solving, it gives you the image
Does anyone know the answer to this question?
For the function G defined by G(x)=5x+3, find G(r+5)
Given function:
g(x) = 5x + 3Find
g(r+5)Substitute x with r = 5:
g(r + 5) = 5(r + 5) + 3 = 5r + 25 + 3 = 5r + 28
Answer:
G ( r + 5 ) = 5r + 28
Step-by-step explanation:
Given ;
G ( x ) = 5x + 3
To Find :-
G ( r + 5 )
Solution :-
plug r + 5 as x in the function.
G ( r + 5 ) = 5 ( r + 5 ) + 3distribute 5
G ( r + 5 ) = 5r + 25 + 3combine like terms
G ( r + 5 ) = 5r + 28what is the value of b in this equation?
A. -20
B. -6
C. 6
D. 20
Answer:
Step-by-step explanation:
a- 12
b- 2
c- 11
and the next part is
x- 6
y- 18
Answer:
B
Step-by-step explanation:
Using the rules of exponents
[tex](a^m)^{n}[/tex] = [tex]a^{mn}[/tex]
[tex]a^{-m}[/tex] = [tex]\frac{1}{m}[/tex]
Then
[tex](y^b)^{4}[/tex] = [tex]\frac{1}{y^{24} }[/tex]
[tex]y^{4b}[/tex] = [tex]y^{-24}[/tex]
Equate the exponents
4b = - 24 ( divide both sides by 4 )
b = - 6 → C
log8-log4 ÷ log4-log2=
Which point is in the solution set of this system inequalities?
A. (0,0)
B. None of these
C. (5,1)
D. (3,7)
Answer:
B
Step-by-step explanation:
To find which ordered pairs are solutions to the inequalities we can simply plug in the x and y values of the ordered pairs into the inequalities and if the equation is true for both inequalities then the ordered pair is a solution to the inequalities.
For (0,0)
x = 0
y = 0
y > x + 5
Substitute 0 for y and x
0 > 0 + 5
Simplify right side
0 > 5
The inequality is not true as 5 is greater than 0, not less than. So immediately we can eliminate answer choice A.
For (5,1).
x = 5
y = 1
y > x + 5
Substitute 5 for x and 1 for y
1 > 5 + 5
Simplify right side
1 > 10
Again, the equation is not true as 1 is not greater than 10. This means that c cannot be the answer
For (3,7)
x = 3
y = 7
y > x + 5
Substitute 3 for x and y for 7
7 > 3 + 5
Simplify right side
7 > 8
7 is not greater than 8 meaning that (3,7) cannot be a solution to the inequalities
None of the ordered pairs created true equations hence the answer is B
a 10 foot ladder rests against a vertical wall if the bottom of the ladder slides away from the wall at a speed of 2 ft/s how fast is the angle betwween the top of the ladder and the wall changing when that angle is
Answer:
d∅/dt = √2/5 Rad/sec
Step-by-step explanation:
According to the Question,
Given That, a 10-foot ladder rests against a vertical wall if the bottom of the ladder slides away from the wall at a speed of 2 ft/s how fast is the angle between the top of the ladder and the wall changing when that angle is π/4.Solution,
Let x be the Distance between the base of the wall and the bottom of the ladder.
and let ∅ be the angle between the top of the ladder and the wall.
Then, Sin∅ =x/10 so, x=sin∅ *10
Differentiating with respect to time t we get,
dx/dt = 10 * cos∅ * d∅ /dt
We have given that dx/dt = 2 ft/s and ∅ =π/4Now, Put these value we get
2 = 10 *(cos(π/4))* d∅/dt
2 = 10/√2 * d∅/dt
d∅/dt = √2/5 Rad/sec