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
If 2 < 20x - 13 < 3. what is one possible value for x?
Answer:
one possible value for x is 31/40
Step-by-step explanation:
Let's isolate the 20x term. Add 13 to all three terms:
2 + 13 < 20x - 13 + 13 < 3 + 13
and this simplifies to:
15 < 20x < 16
Dividing all three terms by 20, we get:
15/20 < x < 16/20
A fraction halfway between 15/20 and 16/20 is (31/20)/2, so
one possible value for x is 31/40.
Check by substituting this into the original equation and checking whether that equation is now true:
2 <20(31/40) - 13 < 3
or
2 < 31/2 < 16, or 2 < 15.5 < 16 (this is true, so 31/40 is a solution)
multiply 2x^2-4x 6c^2-5x
Answer:
a
Step-by-step explanation:
2x^2-4x 6x^2-5x
2x^2 times 6x^2= 12x^4
2x^2 times -5x= -10x^3
-4x times 6x^2= -24x^3
-4x times -5x= 20x^2
12x^4-10x^3-24x^3+20x^2
12x^4-34x^3+20x^2
(Also Brainliest if this helps pls)
The volume of a prism is the product of its height and area of its base, V = Bh. A rectangular prism has a volume of 16y4 + 16y3 + 48y2 cubic units. Which could be the base area and height of the prism?
a base area of 4y square units and height of 4y2 + 4y + 12 units
a base area of 8y2 square units and height of y2 + 2y + 4 units
a base area of 12y square units and height of 4y2 + 4y + 36 units
a base area of 16y2 square units and height of y2 + y + 3 units
Answer: 4. A base area of 16y^2 square units and height of y^2 + y + 3 units
Step-by-step explanation:
Using the distributive property; you can see that 16y^2(y^2+y+3)=
16y^4+16y^3+48y^2
Answer:
D. a base area of 16y2 square units and height of y^2 + y + 3 units
Step-by-step explanation:
Ed22
Given that ΔABC is a right triangle with the right angle at C, which of the following is true?
1. tan A = 1/(tan B)
2. tan A = sin B
3. cos A = 1/(cos B)
4. sin B = 1/(sin A)
Answer:
1. tan A = 1/(tan B)
Step-by-step explanation:
By definition,
tangent A = opposite / adjacent = a / b
and
tangent B = opposite / adjacent = b / a
Therefore tangent A = a/b = 1/tan(B)
Answer: Tan a=tan b
I belive
Step-by-step explanation:
for the function y= -2+5 sin [pi/12(x-2)], what is the maximum value
Answer:
The answer is 0. There is no minum or maxium vaule, it equals 0.
Step-by-step explanation:
PLEASE HELP ASAP
I WILL MARK BRAINLIEST
Answer:
Estimated 120 students
Step-by-step explanation:
Hi there!
The survey established that 3 out of the 75 students did not have social media accounts.
[tex]\displaystyle \frac{3}{75}[/tex]
Let [tex]x[/tex] be equal to the number of students in the entire school who does not have social media accounts.
[tex]\displaystyle\frac{x}{3000}[/tex]
Create a proportion:
[tex]\displaystyle \frac{3}{75}=\displaystyle\frac{x}{3000}[/tex]
Multiply both sides by 3000 to isolate [tex]x[/tex]:
[tex]\displaystyle \frac{3}{75}*3000=\displaystyle\frac{x}{3000}*3000\\\\\frac{9000}{75}=x\\\\120=x[/tex]
Therefore, the number of students in the entire school who do not have social media accounts is estimated to be 120.
I hope this helps!
can someone please please help me :/ I have to get this right. please help
Work Shown:
Solve for y. Then replace y with f(x).
[tex]680x + 10y - 1000 = 0\\\\10y - 1000 = -680x\\\\10y = -680x + 1000\\\\y = \frac{-680x + 1000}{10}\\\\y = \frac{-680x}{10} + \frac{1000}{10}\\\\y = -68x + 100\\\\y = 100 - 68x\\\\f(x) = 100 - 68x\\\\[/tex]
Effectively this involves adding 1000 to both sides and subtracting 680x from both sides, afterward we divide both sides by 10 to isolate y.
Answer:
choice B
Step-by-step explanation:
I did this problem like 6 months ago......
Question 8 If f (2) = (1 + 3) and g (2) VO+ 7, find g (f (x)). 9(f()) = 1 + 10 O g(f ()) = VI + 3 +7 Og(f (x)) = v= + 10 Og(f (2)) = 2? + 10
Answer:
x+10
Step-by-step explanation:
f(x) = (x+3)^2 and g(x) = sqrt(x)+7
g(f(x)) =
Replace f(x) in for x in the function g(x)
= sqrt((x+3)^2)+7
= x+3 +7
= x+10
simplify : 2(3+a)+4=36
(2.05 MC) Triangle PQR is transformed to Triangle P'Q'R'. Triangle PQR has vertices P(4,0), Q(0,-4) and R(-8,-4). Triangle P'Q'R' has vertices P'(1,0), Q'(0,-1), and R'(-2,-1). Part A: What is the scale factor of the dilation that transforms Triangle PQR to Triangle P'Q'R' Part B: Write The Coords of triangle P"Q"R" obtained after P'Q'R' is reflected about the y-axis Part C: Are the two Triangles PQR and P"Q"R" congruent?
Answer:
Part A: The scale factor of the dilation that transforms Triangle PQR to Triangle P'Q'R' is 1/4
Part B:
P''(-1, 0)
Q''(0, -1)
R''(2, -1)
Part C:
The two Triangles PQR and P''Q''R'' are not congruent
Step-by-step explanation:
The coordinates of triangle PQR are;
P(4, 0)
Q(0, 4)
R(-8, -4)
The coordinates of triangle P'Q'R' are;
P'(1, 0)
Q'(0, -1)
R'(-2, -1)
Part A:
The scale factor of the dilation that transforms Triangle PQR to Triangle P'Q'R' can be found from the ratio of the respective coordinates as follows;
The ratio of the x, and y coordinates of the points are;
P'/P = x'/x = 1/4, y'/y =0/0
R'/R = x'/x = -2/-8 = 1/4, y'/y =-1/-4 = 1/4
Therefore, the scale factor of the dilation that transforms Triangle PQR to Triangle P'Q'R' = 1/4
Part B: For reflection across the y-axis, we have;
Pre-image (x, y) becomes the image, (-x, y)
Therefore, we have;
Reflection of P'(1, 0) about the y-xis becomes P''(-1, 0)
Reflection of Q'(0, -1) about the y-xis becomes Q''(0, -1)
Reflection of R'(-2, -1) about the y-xis becomes R''(2, -1)
Part C:
The two Triangles PQR and P''Q''R'' are similar but they are not congruent as the dimensions of PQR are larger than the dimensions of the sides of triangle P''Q''R''.
(A) The scale factor of the dilation that transforms Triangle PQR to Triangle P'Q'R' is 1/4
(B) Coordinates of Δ P"Q"R"
P" (-1,0)
Q"(0,-1)
R"(2,-1)
(C) Triangles PQR and P"Q"R" are not congruent.
Given
ΔPQR is transformed into ΔP'Q'R'
Coordinates of P, Q, R are
P (4,0),
Q(0,-4)
R(-8,-4)
Coordinates of P'Q'R' are
P'(1,0)
Q'(0,-1)
R'(-2,-1)
(A) By Distance formula we can find the distance between P Q and P'Q'
Distance formula = [tex]D= \sqrt{(X_2-X_1)^2+(Y_2-Y_1)^2 }[/tex]
Where D = Distance between two points [tex](X_1.Y_1) \; and\; (X_2.Y_2)[/tex]
from distance formula we can write that
[tex]PQ = \sqrt{(0-4)^2+ (-4-0)^2} }\\[/tex]
PQ = [tex]4\sqrt{2}[/tex]
Similarly
P'Q'= [tex]\sqrt{2}[/tex]
PQ /P'Q' = 4
hence the scale factor of dilation is 1/4 (Compression)
(B )The Coordinates of Reflection about y axis can be written for a point
[tex](x,y ) \; as \; (-x,y)[/tex]
So the Coordinated of Δ P"Q"R" can be written as
P" (-1,0)
Q"(0,-1)
R"(2,-1)
(C) ΔPQR and ΔP"Q"R" are similar triangles but they are not congruent because their sides are not equal in size.
For more information please refer to the link below
https://brainly.com/question/12413243
how many are 1 raised to 3 ???
Answer:
1
Step-by-step explanation:
1^3
This is 1 multiplied by itself 3 times
1*1*1
1
Factorise : x^2+x-72 Step by Step
Answer:
(x + 9)(x - 8)
Step-by-step explanation:
f(x) = x^2 + x - 72
= x^2 - 8x + 9x - 72
= (x^2 - 8x) + (9x - 72)
= x(x - 8) + 9(x - 8)
= (x + 9)(x - 8)
Answer:
x² + x - 72 = (x + 9)(x - 8)
Step-by-step explanation:
[tex]x^2+x-72\quad \implies\quad a=1\,,\quad b=1\,,\quad c=-72\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x=\dfrac{-1\pm\sqrt{1^2-4\cdot1\cdot(-72)}}{2\cdot1}=\dfrac{-1\pm\sqrt{1+288}}{2}=\dfrac{17\pm\sqrt{289}}{2}\\\\x_1=\dfrac{-1-17}{2}=-9\quad,\qquad x_2=\dfrac{-1+17}{2}=8\\\\\\x^2+x-72=(x-(-9))(x-8)=(x+9)(x-8)[/tex]
or:
x² + x - 72 =
= x² + 9x - 8x - 72 =
= x(x + 9) - 8(x + 9) =
= (x + 9)(x - 8)
. Each side of this ice cube measures 3.3 millimetres. What is the volume of this ice cube?
The volume of the ice cube is 35.937 mm^3
We know that for a cube of side length L, the volume is defined as:
V = L^3
Here, we do know that each side of our ice cube measures 3.3 mm, so we have:
L = 3.3mm
Then the volume of the cube is just:
V = (3.3 mm)^3 = 35.937 mm^3
We can conclude that the volume of the ice cube is 35.937 mm^3
If you want to learn more, you can read:
https://brainly.com/question/14075019
Geometry, please answer question ASAP
Answer:
A,53.37°
360-306.63=53.37
Answer:
A
Step-by-step explanation:
a whole circle has 360 degrees (one time all around).
so, going from J over M to L is "using" already 306.63 degrees of that. going then from L to J just finishes the full trip of going one time around the whole circle.
so, LJ is just the missing "piece" to 360 degrees.
LJ = 360 - 306.63 = 53.37
Find the surface area of the pyramid.
A.)311.4
B.)230.4
C.)212.6
D.)200.4
Please someone help I am struggling with this
Answer:
A. 311.4 ft²
Step-by-step explanation:
Use the formula for the surface area of a square pyramid: SA = 2bs + b², where b is the length of a side of the base and s is the slant height.
Plug in the values and solve:
SA = 2(9)(12.8) + 9²
SA = 230.4 + 81
SA = 311.4 ft²
The surface area of the pyramid is 311.4 square units
The surface area of a pyramid is given by the formula:
Surface Area = 1/2 × base area × slant height + perimeter of base × slant height
The base area of the pyramid is 9 × 9 = 81 square units.
The slant height of the pyramid is the length of a line segment that connects a vertex of the pyramid to the midpoint of a side of the base.
We can find the slant height of the pyramid using the Pythagorean Theorem.
slant [tex]h^{2}[/tex] = [tex]h^{2}[/tex] + [tex](base/2)^{2}[/tex]
slant [tex]h^{2}[/tex] = [tex]12.8^{2}[/tex] + [tex]9/2^{2}[/tex] = 230.4
slant height = 15.2
Therefore, the surface area of the pyramid is:
Surface Area = 1/2 × 81 × 15.2 + 4 × × 15.2 = 311.4 square units
So the answer is A.
Learn more about surface area here: brainly.com/question/2773823
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pls help me ASAP !!!!!!!!!
arav spent 1 3/4 hours in studies and 2 1/2 hours in playing cricket. how much time did he spent at all ??
Answer:
[tex] \boxed{4 \frac{1}{4} \: \: hours}[/tex]Step-by-step explanation:
Time spent in studies = [tex]1 \frac{3}{4} [/tex]
Time spent in playing cricket = [tex]2 \frac{1}{2} [/tex]
Now, let's find the hours that he spent at all:
[tex] \mathsf {1 \frac{3}{4} + 2 \frac{1}{2} }[/tex]
Convert mixed fraction into improper fraction
[tex] \mathsf{ = \frac{7}{4} + \frac{5}{2} }[/tex]
Take the LCM
[tex] \mathsf{ = \frac{7 + 5 \times 2}{4} }[/tex]
Multiply the numbers
[tex] \mathsf{ = \frac{7 + 10}{4} }[/tex]
Add the numbers
[tex] \mathsf{ = \frac{17}{4} }[/tex]
Convert the improper fraction into mixed fraction
[tex] \mathsf{ = 4 \frac{1}{4} }[/tex] hours
Hope I helped!
Best regards!
plot the inequality on the number line
Answer:
Hope this helps!
what is this supposed to be bro pls help
Answer: 1
Step-by-step explanation:
so i put the amount of flour to servings into ratios (fractions)
28:14
9:12
10:13
then I put them into the same denominators
2184:1092
819/1092
840/1092
the first one is the greatest
find the volume of each figure. Round to the nearest tenth if necessary.
Answer:
1385.4
Step-by-step explanation:
Volume=pi*r^2*h=pi*49*9=1385.4
Which properties belong to all isosceles triangles? Check all that apply.
The base angles are congruent.
All three angles are congruent.
The two sides opposite the base angles are congruent.
All three sides are congruent.
The bisector of the vertex angle is the perpendicular bisector of the base.
=====================================================
Explanation:
Let's go through the answer choices to see which are true and which are false.
A) True. The base angles are the same measure, and they are opposite the congruent sides. Any isosceles triangle has exactly two congruent sides.B) False. This is describing an equilateral triangle (where all three angles are 60 degrees each).C) True. See choice A.D) False. This is describing an equilateral triangle where all sides are the same length. E) True. You can use the SAS (side angle side) congruence theorem to prove that the angle bisector is also the perpendicular bisector. Furthermore, this segment is also a median. This only applies to the vertex angle.Answer:
The base angles are congruent.
The two sides opposite the base angles are congruent.
The bisector of the vertex angle is the perpendicular bisector of the base.
Step-by-step explanation:
Scouts of ABC school made to run around a regular hexagonal ground fig 9, of perimeter 270 m .If they started running from point X and covered two fifth (2/5th) of the total distance.Which side of the ground will they reach?
Answer:
Scouts are on the third side in the sense they are running
Step-by-step explanation:
A regular hexagonal shape of perimeter 270 has each side of 270/6 = 45
Let´s call d the run distance then
d = 2/5 * 270 d = 108 m
We don´t have fig 9 available therefore if X is a vertex in the hexagon or at the middle point of one side, scouts are 108 m from the starting point which means they had run 2,4 sides of the hexagon. If X is not either a vertex or a middle point of a side then, we have two solutions for the question depending on the sense the scouts took when began the run (clockwise or counterclockwise)
solve for y. -y/3 = -23 simplify your answer as much as possible
Answer:
69
Step-by-step explanation:
-y/3 = -23
=> -y = -23 x 3
=> -y = -69
=> y = 69
Answer:
69
Step-by-step explanation:
We multiply both sides of the equation by 3 to cancel out the denominator. That gives us -y=-69. Since we cannot have a negative variable, we change the values on both sides, giving us y=69
What is – x4 + 2x3 + 6x2 – 10x – 4 divided by X – 2?
Answer:
-x^3 + 6x + 2
Step-by-step explanation:
Rochelle deposits $6,000 in an IRA. What will be the value (in dollars) of her investment in 15 years if the investment is earning 9% per year and is compounded continuously? (Simplify your answer completely. Round your answer to the nearest cent.)
Answer:
$ 23,145
Step-by-step explanation:
This is a compound interest question where the interest is compounded continuously. Hence, the formula for the value of total amount of investment is:
A = P×e^rt
Where:
A = Total value of investment after t years
P = Principal or Initial amount invested = $6,000
e = Exponential function
r = interest rate = 9% = 0.09
t = time in years = 15
So:
A = $6000 × e^15 × 0.09
A = $6000 × e^1.35
A = $23,144.553184
Approximately , A ≈$23,145
Therefore, the value (in dollars) to the nearest cent of Rochelle's investment in 15 years if the investment is earning 9% per year and is compounded continuously is $23,145.
what is the answer to -3/7 x -1 2/3
Answer:
-9x-35/21
Step-by-step explanation:
Answer:
[tex]\frac{5}{7}[/tex]
Step-by-step explanation:
[tex]\frac{-3}{7}* (-1\frac{2}{3})=\frac{-3}{7}*\frac{-5}{3}\\\\= \frac{5}{7}[/tex]
is 1/5 a rational or irrational number (20 points pls help)
Answer:
rational
Step-by-step explanation:
Answer:
it's Rational Number
Step-by-step explanation:
since each integer can't be written in the fraction form or for this example it would be thus 5 so it would be a rational number
A file that is 276 megabytes is being dowloaded . If the downloaded is 16.7% complete how many megabytes have been dowloaded? Round ur answer to the nearest tenth ( can ya please hurry and answer thank you)
Answer: 46.1 megabytes
Step-by-step explanation:
Can someone please help me I don’t know how to do this (Due today)
First go to the y intercept (or the b in y=mx+b) look for the slope and plot the points on the graph they're talking about e.g. #23 the y-intercept is 6 go to the 6 on the y axis, and then look at the slope (x), so it goes up and over to the right since it's positive by 1
I'm under the water on this problem, please help me:
question: f(x)=10x−3
answer choices:
A. f(−5)
B. f(0)
C. f(7)
D. f(t^2+2)
E. f(12−x)
F. f(x+h)
Answer:
See below
Step-by-step explanation:
Okay so...I might be interpreting the question wrong-if I am please comment! I'll fix it to the best of my ability.
A) Plug in -5 to all x values
f(-5)=10(-5)-3
==50-3
f(-5)= -53
B) f(0)=10(0)-3
f(0)= -3
C) f(7)=10(7)-3
=70-3
f(7)=67
D) f(t^2+2)=10(t^2+2)-3
=10t^2+20-3
f(t^2+2)=10t^2+17
E) f(12-x)=10(12-x)-3
=120-10x-3
f(12-x)=117-10x
F) f(x+h)=10(x+h)-3
=10x+10h-3