Answer:
the red car is traveling at 102.44 ft/s along the road
Step-by-step explanation:
From the given information:
Let consider p be how far the car is up the road and q be how far the police is off the road.
Also, suppose that r is the distance between the police and the car.
Then, we can have a right triangle in which we can use the Pythagorean Theorem to calculate the r (distance between the cop and the car)
NOW,
p² + q² = r²
r² = 40² + 180²
r² = 1600 + 32400
r² = 34000
r = [tex]\sqrt{34000}[/tex]
r = 184.39
If we consider q' to be how fast the car is traveling down the road.
And, p' be how fast the police is traveling toward the road.
r' be how fast the distance between the police and the car is changing.
then , the derivative of our equation, p² + q² = r² with respect to time can now be:
2p(p') +2q(q') = 2r(r')
p(p') +q(q') = r(r')
By replacing our values; we have:
40(0) +180(y') = [tex]\sqrt{34000} \times 100[/tex] (given that the police is not moving p' =0)
180(y') = [tex]\sqrt{34000} \times 100[/tex]
[tex](y') = \dfrac{\sqrt{34000} \times 100}{180}[/tex]
[tex](y') = \dfrac{184.39 \times 100}{180}[/tex]
[tex]\mathbf{(y') = 102.44 \ ft/s}[/tex]
the red car is traveling at 102.44 ft/s along the road
The perpendicular bisector of the line segment connecting the points $(-3,8)$ and $(-5,4)$ has an equation of the form $y = mx + b$. Find $m+b$.
Answer:
m = -1/2 and b = 6.5
Step-by-step explanation:
To find the slope of the original line segment, we have to do the change in y/the change in x:
(4-8)/(-5--3) = -4/-2 = 2
2 is the slope of the original line segment, but since this is the perpendicular bisector, we have to take the negative reciprocal of 2 so m = -1/2
To find b we substitute the values of x, y, and m into the equation. Let's use the x value of -3 and the y value of 8:
y = mx + b
8 = -1/2(-3) + b
8 = 3/2 + b
6.5 = b
Which of the following best represents the average rate at which the human hair grows (1 point)
a
0.25 inches per second
b
0.25 meters per hour
с
0.25 meter per month
d
0.25 inches per month
Answer:
D.0.25 inches per months
Step-by-step explanation:
The average rate or speed of human hair growth is about 0.25inches per month.
Complete the square.
3x^2-12x=96
Answer:
x = 8 and -4
Step-by-step explanation:
3x² - 12x = 96
3(x² - 4x + 4 = 32 + 4)
3[(x - 2)² = 6²]
x - 2 = +/- 6
x = 8
x = -4
A gear ratio is the ratio of the teeth on the rear sprocket. If a bike has 36 teeth on the front and 12 teeth on the rear sprocket, what is the gear ratio for the bike?
Answer: the ratio of the bike is 3
Step-by-step explanation:
its simply easy all you have to do is divide 36/12
Hey There!!
The answer to this is: (3:1) 36:12. 36 is the teeth on the front socket and 12 is the teeth on the rear socket. All you need to do is simplify by finding the greatest common factor (GCF) of 36 and 12-which is 12, then divide by the GCF. This gives you 3:1. The gear ratio for the bike is 3 teeth on the front socket for every 1 teeth on the rear socket (3:1).
Hope It Helped!~ ♡
ItsNobody~ ☆
Point M is on line segment LN. Given LM=7 and MN=10, determine the length LN.
Answer:
[tex]\huge \boxed{17}[/tex]
Step-by-step explanation:
Point M is on the line segment LN.
LM = 7
MN = 10
LN = LM + MN
LN = 7 + 10 = 17
The value of the line segment LN is 17.
What is a line segment?A line segment in geometry is a section of a line that has two clearly defined endpoints and contains every point on the line that lies within its confines.
Given that point, M is the online segment LN. Given LM=7 and MN=10,
The value of the line segment will be calculated as:-
Point M is on the line segment LN.
LM = 7
MN = 10
LN = LM + MN
LN = 7 + 10 = 17
Therefore, the value of the line segment LN is 17.
To know more about line segments follow
brainly.com/question/3573606
#SPJ5
24. Three minus four times a number is equal to ten times a number plus ten.
25. Four times the quantity of three times c plus 5 is equal to 8.
26. Six less than two thirds of a number is negative ten. Find the number.
27. Twenty-nine is thirteen added to four times a number. What is the number.
Answer:
(24) 3 - 4b = 10c + 10
(25) 4(3c+5) = 8
(26) - 6
(27) 4
Step-by-step explanation:
These questions require that words are translated into equations and then may be solved.
(24) Three minus four times a number is equal to ten times a number plus ten.
let the first number be b.
(a)Three minus four times a number ... can be represented as:
3 - (4 x b) = 3 - 4b
(b) ...ten times a number plus 10
let the other number be c. Therefore we have;
(10 x c) + 10 = 10c + 10
Now, three minus four times a number is equal to ten times a number plus ten means that expressions in (a) and (b) above are equal. i.e
3 - 4b = 10c + 10
(25) Four times the quantity of three times c plus 5 is equal to 8.
(a) four times the quantity of three times c plus 5 can be represented as
4 x (3 x c + 5) = 4(3c + 5)
(b) ... is equal to 8. This means that the expression in (a) is equal to 8.
4(3c + 5) = 8
(26) Six less than two thirds of a number is negative ten. Find the number.
(a) six less than can be represented as:
- 6
(b) two thirds of a number can be represented as
([tex]\frac{2}{3}[/tex])x [where x is the number]
(c) six less than two thirds of a number can thus be written as;
([tex]\frac{2}{3}[/tex])x - 6
(d) ... is negative 10 means that the expression is (c) above is equal to -10. i.e
([tex]\frac{2}{3}[/tex])x - 6 = -10
(e) Find the number.
The number can be found by solving for x in the expression in (d) above.
([tex]\frac{2}{3}[/tex])x - 6 = -10 [multiply through by 3]
2x - 18 = -30 [collect like terms]
2x = -30 + 18
2x = -12 [divide both sides by 2]
x = - 6
Therefore, the number is -6
(27) Twenty-nine is thirteen added to four times a number. What is the number.
(a) ... thirteen added to four times a number can be written as:
13 + 4b [where the number is b]
(b) Twenty-nine is thirteen added to four times a number means that the 29 is equal to the expression in (a) above. i.e
29 = 13 + 4b
(c) Find the number.
The number can be found by solving for b in the expression in (b) above. i.e
29 = 13 + 4b [collect like terms]
4b = 29 - 13
4b = 16 [divide both sides by 4]
b = 4
Therefore, the number is 4.
Use the quadratic formula to solve x - 5x+3 = 0.
Answer:
(D) [tex]\begin{array}{*{20}c} {x=\frac{{ 5 \pm \sqrt {13} }}{{2}}} \end{array}[/tex]
Step-by-step explanation:
The quadratic formula is:
[tex]\begin{array}{*{20}c} {\frac{{ - b \pm \sqrt {b^2 - 4ac} }}{{2a}}} \end{array}[/tex]
Assuming that a is our x² term, b is our x term, and c is the constant, we can substitute inside the equation.
[tex]\begin{array}{*{20}c} {\frac{{ - (-5) \pm \sqrt {5^2 - 4\cdot1\cdot3} }}{{2\cdot1}}} \end{array}[/tex]
[tex]\begin{array}{*{20}c} {\frac{{ 5 \pm \sqrt {25 - 12} }}{{2}}} \end{array}[/tex]
[tex]\begin{array}{*{20}c} {\frac{{ 5 \pm \sqrt {13} }}{{2}}} \end{array}[/tex]
So the answer is D, [tex]\begin{array}{*{20}c} {x=\frac{{ 5 \pm \sqrt {13} }}{{2}}} \end{array}[/tex].
Hope this helped!
Write the equation of a circle with a center at (12, 6) and a radius of 6.
Answer:
(x-12)² + (y-6)² = 36 (Option C)
Step-by-step explanation:
use circle formula
(x-h)² + (y-k)²= r²
h= 12 and k= 6 and r= 6
(x-12)² + (y-6)² = 6²
6 squared = 36 (6·6)
(x-12)² + (y-6)² = 36
In circle O, AC and BD are diameters. Circle O is shown. Line segments B D and A C are diameters. A radius is drawn to cut angle C O C into 2 equal angle measures of x. Angles A O C and B O C also have angle measure x. What is mArc A B?
Answer:
120
Step-by-step explanation:
Got it right on the assigment
Answer:
c. 120
Step-by-step explanation:
Which one of these relations are functions ?
Please helpppp fast
Answer:
the 4th and 6th one
Step-by-step explanation:
A function is when there are x- and y-values but each x value has only 1 y-value
Simple: If the x-value is repeated its not a function
Answer:
Step-by-step explanation:
1,2,3
Micha is playing a game with five cards numbered 1 through 5. He will place the cards in a bag and draw one card at random three times, replacing the card each time. To win a prize, he must draw the number 5 all three times. What is the probability he will draw the number 5 all three times?
Answer: 0.008
Step-by-step explanation:
We have 3 experiments.
Each experiment is exactly the same: "Drawing the card with the number 5, out of a bag with five cards".
in a random selection all the cards have exactly the same probability of being drawn, so the probability of drawing the 5, is equal to the quotient between the number of cards with the 5 (only one) and the total number of cards in the bag (5) then the probability is:
p = 1/5.
And we want this event to happen 3 consecutive times, then the total probability is equal to the product of the probabilities for each event:
P = (1/5)*(1/5)*(1/5) = 1/125 = 0.008
Identify the type of function represented by f(x) = 3/8(4)^x
A. Exponential decay
B. Exponential growth
C. Linear
D. Quadratic
variable is in power so it exponential.
the constant and coefficient both are positive so it is exponential Growth.
two years ago a woman wad 7 times as old as her daughter, but in 3 years time she would be x times as old as the girl. how old are they now?
Answer:
The present age of the woman is 37 years and her daughter is 7 years
Step-by-step explanation:
two years ago a woman was 7 times old as her daughter, but in 3 years time she would be 4 times old as the girl. how old are they now
Two years ago a woman wad 7 times as old as her daughter
Let her daughter=x-2
The woman=y-2
x-2
7(y-2)=7y-14
x-2=7y-14
x-7y=-14+2
x-7y= -12 (1)
but in 3 years time she would be 4 times as old as the girl.
x+3
y+3
x+3
4(y+3)=4y+12
x+3=4y+12
x-4y=12-3
x-4y=9. (2)
x-7y= -12 (1)
x-4y=9. (2)
Subtract (1) from (2)
4y-(-7y)=9-(-12)
-4y+7y=9+12
3y=21
y=21/3
y=7
Substitute
y=7 into (1)
x-7y= -12
x-7(7)=-12
x-49=-12
x= -12+49
=37
The present age of the woman is 37 years and her daughter is 7 years
Julio is paid 1.3 times his normal hourly rate for each hour he works over 31 hours in a week. Last week he worked 42 hours and earned $548.13. Enter and solve an equation to find Julio's normal hourly rate, r. Complete the explanation how you know that your answer is reasonable.
Step-by-step explanation:
Answer:
$12.10 / hour
Step-by-step explanation:
42 - 31 =
1.3(11)r + 31r = 548.13
14.3r + 31r = 548.13
45.3r = 548.13
r = 12.1 / hour
Find the height of the triangle by applying formulas for the area of a triangle and your knowledge about
triangles.
9 in
9 in.
Xin
6 in
Answer:
8.5
Step-by-step explanation:
Applying pythagora's theorem,
hypotenuse^2 = opposite^2 + adjacent^2
but, hypotenuse = 9
opposite = X
adjacent = 1/2(base of triangle)= 1/2(6)
adjacent = 3
9^2 = X^2 + 3^2
X^2 = 81 - 9
X^2 = 72
X = 8.5
PLEASE help me with this question!!! REALLY URGENT!
Answer:
The third table is the correct answer
Step-by-step explanation:
Here in this question, we are concerned with determine which of the tables correctly represents what an exponential function is.
An exponential function is a function of the form;
y = x^n
where the independent variable x in this case is raised to a certain exponent so as to give the results on the dependent variable axis (y-axis)
In the table, we can see that we have 2 segments, one that contains digits 1,2 and so on while the other contains purely the powers of 10.
Now, let’s set up an exponential outlook;
y = 10^x
So we have;
1 = 10^0
10 = 10^1
1/10 = 10^-1
1000 = 10^3
1/100 = 10^-2
We can clearly see here that we have an increase in the value of y, depending on the value of the exponent.
However it is only this table that responds to this successive correctness as the other tables in the answer do have a point where they fail.
For example;
10^-2 is not 10 which makes the fourth table wrong
10^4 is not 100 which makes the first table wrong
we have same error on second table too
Another way to write g(h(x)) is
Answer:
((x)h)g
Step-by-step explanation:
Hope this helps and if this is wrong then please comment the right answer and I will edit it thanks :)
Sophie is making a copy of an angle. The original angle will be labeled G and the new angle will be labeled B. She has just finished using a compass, with the point on G, to draw an arc that intersects both rays of angle G. Which of the following should she do next
Answer:
The next step is;
Label the two intersection points
Step-by-step explanation:
To make a copy of an angle, the steps are;
1) Draw the rays of the original angle passing through the point B
2) Open the compass slightly and place the compass point on the vertices G where the two rays meet to draw an arc that intersect both rays
3) Label the point of intersection of both rays points C and D
4) With the compass still opened to the same width, move the compass to the point B on the line the angle is to be copied and draw a similar arc intersecting the ray at J
5) Open the compass to the width of C and D on the original angle and place the compass at point J to mark the arc on the copied angle location at M
6) Draw a line from B passing through M to complete the second ay of the copied angle.
How do I find DG. A. 3 B. -7 c. 16 d. 13
Answer:
x = -7
Step-by-step explanation:
DE + EF + FG = DG
2x+17 + 8+2 = x+20
Combine like terms
2x+ 27 = x+20
Subtract x from each side
2x+27-x = x+20-x
x+27 = 20
Subtract 27 from each side
x+27-27 = 20-27
x = -7
In a naval engagement, one-third of the fleet was captured, one-sixth was sunk, and two ships were destroyed by fire. One-seventh of the surviving ships were lost in a storm after the battle. Finally, the twenty-four remaining ships sailed home. How many ships were in the fleet before the engagement?
Answer:
60 ships.
Step-by-step explanation:
Let the total number of ships in the naval fleet be represented by x
One-third of the fleet was captured = 1/3x
One-sixth was sunk = 1/6x
Two ships were destroyed by fire = 2
Let surviving ships be represented by y
One-seventh of the surviving ships were lost in a storm after the battle = 1/7y
Finally, the twenty-four remaining ships sailed home
The 24 remaining ships that sailed home =
y - 1/7y = 6/7y of the surviving fleet sailed home.
Hence
24 = 6/7y
24 = 6y/7
24 × 7/ 6
y = 168/6
y = 28
Therefore, total number of ships that survived is 28.
Surviving ships lost in the storm = 1/7y = 1/7 × 28 = 4
Total number of ships in the fleet(x) =
x = 1/3x + 1/6x + 2 + 28
Collect like terms
x - (1/3x + 1/6x) = 30
x - (1/2x) = 30
1/2x = 30
x = 30 ÷ 1/2
x = 30 × 2
x = 60
Therefore, ships that were in the fleet before the engagement were 60 ships.
Find the constant of proportionality (r) in the equation y = r x
Answer:
r = 11Step-by-step explanation:
y = r x
r is the constant of proportionality
To find r pick any values of x and y provided and substitute it into the above formula and solve for r.
That's
using
x = 2
y = 22
We have
22 = 2r
Divide both sides by 2
r = 11Therefore the constant of proportionality is 11
Hope this helps you
The quotient of x^2+x-6/x^2-6x+5*x^2+2x-3/x^2-7x+10 has ___ in the numerator and ______ in the denominator.
Answer:
So the quotient of [tex]\frac{x^{2} + x - 6}{x^{2} -6x + 5} X \frac{x^{2} + 2x - 3}{x^{2} -7x + 10}[/tex] has (x + 3)² in the numerator and (x + 5)² in the denominator.
Step-by-step explanation:
[tex]\frac{x^{2} + x - 6}{x^{2} -6x + 5} X \frac{x^{2} + 2x - 3}{x^{2} -7x + 10}[/tex]
Factorizing the expressions we have
[tex]\frac{x^{2} + 3x -2x - 6}{x^{2} -x - 5x + 5} X \frac{x^{2} + 3x - x - 3}{x^{2} -2x -5x + 10}[/tex]
[tex]\frac{x(x + 3)- 2(x + 3)}{x(x -1) - 5(x - 1)} X \frac{x(x + 3) - 1(x + 3)}{x(x - 2) - 5(x - 2)}[/tex]
[tex]\frac{(x + 3)(x - 2)}{(x - 5)(x - 1)}X\frac{(x + 3)(x - 1)}{(x - 2)(x - 5)}[/tex]
Cancelling out the like factors, (x -1) and (x - 2), we have
[tex]\frac{(x + 3)(x + 3)}{(x - 5)(x - 5)}[/tex]
= [tex]\frac{(x + 3)^{2} }{(x + 5)^{2} }[/tex]
So the quotient of [tex]\frac{x^{2} + x - 6}{x^{2} -6x + 5} X \frac{x^{2} + 2x - 3}{x^{2} -7x + 10}[/tex] has (x + 3)² in the numerator and (x + 5)² in the denominator.
suppose we want to choose 6 letters without replacement from 13 distinct letters. A) how many ways can this be done if order does not matter? B) how many ways can this be done if order of choices matters
Answer: A) 1716 B) 1235520
Step-by-step explanation:
If order doesn't matter , then we use combinations, where the number of combinations of selecting r things from n is given by :-[tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]
If order matters , then we use permutations, where the number of permutations of selecting r things from n is given by :-[tex]^nP_r=\dfrac{n!}{(n-r)!}[/tex]
Given, Total distinct letters = 13
To choose = 6 letters
A) Number of ways to choose (if order does not matter)=[tex]^{13}C_6[/tex]
[tex]=\dfrac{13!}{6!7!}=\dfrac{13\times12\times11\times10\times9\times8\times7!}{(720)\times 7!}\\\\= $$1716[/tex]
B) Number of ways to choose (if order matters)=[tex]^{13}P_6[/tex]
[tex]=\dfrac{13!}{7!}=\dfrac{13\times12\times11\times10\times9\times8\times7!} 7!}\\\\= $$1235520[/tex]
Hence, A) 1716 B) 1235520
use the formula S = 40,000 (1.06)t to calculate your salary after 4 years. Round your answer to the nearest dollar.
a. $42,400
b. $44,944
c. $47,641
d. $50,499
Answer:
d. $50,499
Step-by-step explanation:
Given:
S = 40,000 (1.06)^t
Where,
t=4 years
S=40,000(1.06)^4
=40,000(1.26247696)
=50,499.0784
To the nearest dollar
S=$50,499
The answer is d. $50,499
Please answer this question now
Answer:
65.94 square inches
Step-by-step explanation:
Surface area of a cone=πr(r+√h^2+r^2)
π=3.14
r=diameter/2
=14/2
=7 in
h=?
h=a
To find h using Pythagoras theorem
c^2 = a^2 + b^2
14^2 = a^2 + 7^2
14^2 - 7^2= a^2
196-49=a^2
147=a^2
Square root both sides
√147=√a^2
12.12=a
a=12.12 in
Surface area of a cone=πr(r+√h^2+r^2)
=3.14(7+√12.12^2+7^2)
=3.14(7+√147+49)
=3.14(7+√196)
=3.14(7+14)
=3.14(21)
=65.94 square inches
Which of the following shows the correct solution steps and solution to 7x-4= -18?
Answer:
x = -2
Step-by-step explanation:
To solve for x always get x on one side
First add 4 on each side, 4 + 7x - 4 = -18 + 4
Next subtract 18 from 4, making it -14 7x = -14
Now divide 7 on each side, x = -2
Someone please help me!! Tyy
Answer:
x² = 900
Step-by-step explanation:
ΔABC is an equilateral triangle because its sides are equal lengths
this means their angles are also equal.
180 / 3 = 60
∠BCA and ∠DCA are supplementary angles - add up to 180º
if ∠BCA = 60º, then ∠DCA = 120º
ΔACD is an isosceles triangle because two sides are equal lengths. this means their angles are equal.
∠CAD ≅ ∠CDA
180 - ∠DCA = 2(∠CAD)
180 - 120 = 60
60 / 2 = 30º
x = 30º
x² = 900
Temperature can be measured in two different common units: degrees Celsius and degrees Fahrenheit. fff represents the temperature in degrees Fahrenheit as a function of the temperature ccc in degrees Celsius. f=32+1.8cf=32+1.8cf, equals, 32, plus, 1, point, 8, c Water freezes at 000 degrees Celsius. What is the freezing temperature of water in degrees Fahrenheit?
Answer:
Water freezes at 32 °F.
What is the value of w? inscribed angles (Image down below)
Answer:
w = 100°
Step-by-step explanation:
Opposite angles in an inscribed quadrilateral in a circle are supplementary.
Therefore, [tex] w + 80 = 180 [/tex]
Subtract 80 from both sides
[tex] w + 80 - 80 = 180 - 80 [/tex]
[tex] w = 100 [/tex]
The value of w = 100°
what is the discriminant and how many solutions?
Step-by-step explanation:
[tex]\text{Discriminant} =\Delta = b^2-4ac\\
\implies \Delta = 7^2-4(1)(10)=49-40=9\\
\therefore \Delta >0\\[/tex]
Since the discriminant is greater than zero, there are two real solutions.
Also, the solutions are $x=5$ and $x=2$
