Answer:
Maria can drive 400 miles.
Step-by-step explanation:
30 + 0.15x = 90
0.15x = 60
x = 60/0.15
x = 400
3. At noon Lan is in his blue mini-van 300 km north of Makenna in her Bugatti. Lan heads south
at a speed of 60km/h while Makenna heads west at 75km/h. At what rate is the distance between
them changing at 2:00 PM? Express your answer as an approximate value rounded to the nearest
hundredth. (4 marks)
Answer:
The rate at which the distance between them is changing at 2:00 p.m. is approximately 1.92 km/h
Step-by-step explanation:
At noon the location of Lan = 300 km north of Makenna
Lan's direction = South
Lan's speed = 60 km/h
Makenna's direction and speed = West at 75 km/h
The distance Lan has traveled at 2:00 PM = 2 h × 60 km/h = 120 km
The distance north between Lan and Makenna at 2:00 p.m = 300 km - 120 km = 180 km
The distance West Makenna has traveled at 2:00 p.m. = 2 h × 75 km/h = 150 km
Let 's' represent the distance between them, let 'y' represent the Lan's position north of Makenna at 2:00 p.m., and let 'x' represent Makenna's position west from Lan at 2:00 p.m.
By Pythagoras' theorem, we have;
s² = x² + y²
The distance between them at 2:00 p.m. s = √(180² + 150²) = 30·√61
ds²/dt = dx²/dt + dy²/dt
2·s·ds/dt = 2·x·dx/dt + 2·y·dy/dt
2×30·√61 × ds/dt = 2×150×75 + 2×180×(-60) = 900
ds/dt = 900/(2×30·√61) ≈ 1.92
The rate at which the distance between them is changing at 2:00 p.m. ds/dt ≈ 1.92 km/h
Given: ZDEF is a right angle. Using a paragraph proof, prove 41 is acute.
Let G be some point on the diagonal line away from point E.
Angle DEG represents angle 1.
We're given that angle DEF is a right angle which means it's 90 degrees. Angle DEG is some angle smaller than 90 degrees. By definition, that must mean angle 1 is acute. Any acute angle is smaller than 90 degrees. There's not much else to say other than this is just a definition problem.
----------------
Extra side notes:
If angle 1 was a right angle, then that would mean angle GEF would have to be 0 degrees; however the diagram shows this isn't the case.
If angle 1 was obtuse, then there's no way we'd be able to fit it into angle DEF. In other words, there's no way to have an angle larger than 90 fit in a 90 degree angle.
1. Write down the 3D shape each net make.
D to g.
Answer:
Step-by-step explanation:
D) Has a five sided shape as a base so its a pentagon-based pyramid
E)Two pentagons and retangular sides Pentagonal Prism
F)All sides and bases are rectangular so Rectangular Prism
G) Eight sided base and triangle shaped sides, Octogon-based Cone
what is the equation of the line that is perpendicular to the line y = − x / 5 + 4 / 5 and passes through the point ( − 3, 4 )?
pls answer quickly.
line y = − x / 5 + 4 / 5
slope( m1) = -1/5
Slope of required line( m2) = 5
[as it is perpendicular to given eqn of line
m1×m2= -1
m2=1/m1= 5]
y-4= 5(x+3)
y-4=5x+15
y=5x+19
Please help!! Find the scale factor dilation
Answer:
2
Step-by-step explanation:
take any point
i am taking F
coordinate of F is (5 , 3)
F' is (10,6)
so use formula
(x , y) = (kx , ky)
(5 , 3) = (5k , 3k) = (10 , 6)
compare corresponding elements
5k = 10
k = 10/5
k = 2
3k = 6
k = 6/3
k = 2
note here k means scale factor
What is the equation of a circle with a center (7, -3) and radius 4?
Answer:
see screenshot
general formula is
r² = (x - x-center)² + (y - y-center)²
Please I need help ASAP
Answer:
78.54
Step-by-step explanation:
[tex]A = \pi r^{2} \\A = \pi 5^{2} \\A = 78.54[/tex]
Jackson elementary will have 320 first grade students next year, each class can have 16 students using the equation 16x= 320 , how many first grade classes will the school need?
Answer:
20
Step-by-step explanation:
320 = 16x
Our objective here is to isolate the variable (x) using inverse operations
First we want to get rid of 16
16x is the same as 16 times x( which is multiplication)
The inverse of multiplication is division so to get rid of the 16 we divide by 16 ( but note: whatever you do to one side you must do to the other ) so we divide both sides by 16
320/16=20
16x/16 = x
We would be left with x = 20
This meaning that they would need 20 first grade classes
Answer:
The school will need 20 first grade classes
Step-by-step explanation:
So think about it. There are 320 first grade students and each class can have 16 students which represents the equation 16x=320
All you need to do is solve the equation 16x=320
The equation is multplication. To undo multiplication you need to do division
So, x=320/16
x=20
So overall, your awnser is 20.
What is the quotient of Negative StartFraction 3 over 8 EndFraction and Negative one-third?
Answer:
6
Step-by-step explanation:
Answer:
1/18
Step-by-step explanation:
I took the test :)
(9x2 + 9x2 + 5x + 1) = (3x+1)
A. 3x²+2x-2
B. 3x2 + 3x + 1
C. 3x2-3x-1
D. 3x2 + 2x+1
Answer:
2(13x – 7)
Step-by-step explanation:
You roll a six-sided number cube and flip a coin. What is the probability of rolling a number less than 2 and flipping heads? Write your answer as a fraction in simplest form. The probability is .
Answer:
[tex]\frac{1}{18}[/tex]
Step-by-step explanation:
As the six-sided number cube had six sides, there are six events which could occur. There is only one interger less than 2 (1), therefore the probability of rolling a number less than 2 is [tex]\frac{1}{6}[/tex].
There are two events which could occur when flipping a coin. This means the probability of flipping heads is [tex]\frac{1}{2}[/tex].
To find the probability of both of these happening, you must multiply the fractions together by multiplying together both the denominators and numerators, therefore:
[tex]\frac{1}{6}[/tex] × [tex]\frac{1}{2}[/tex] = [tex]\frac{1}{18}[/tex]
Answer:
1/12
Step-by-step explanation:
There is only one number less than two, which is 1, so you have 1/6 chance of getting a number less than two
Since a coin has two sides, you have 1/2, or 50% chance of landing on heads
If you multiply both of them, which is 1/6 times 1/2, you will get 1/12, since 1 times 1 is still 1, and 6 times 2 is 12.
80 25 x pls help me with this one
Answer:
25
Step-by-step explanation:
Answer:
x = 25
Step-by-step explanation:
Okay so as you can see there is an x shape and whenever you have that it means they are verticle angles. So we can conclude that 25 is verticle to x and so x is equal to 25.
Tiger is playing for the Masters Championships. His goal for the week is to average at most 68 for his rounds of golf. During his first three rounds he scores 69, 67, and 70. Which inequality could be used to determine what he must score on his fourth round is S represents the fourth round score?
Answer:
B
Step-by-step explanation:
4 scores add all together divided by 4 needs to be greater or equal to his goal
-2/3 × -7/5
please answer... i will follow the person who hives the ryt answer
Answer:
14/15 :]
Step-by-step explanation:
you dont have to follow me buts its appreciated!
Sue’s bakery sold 850 donuts last week this week the number of donuts sold increase 12% how many more donuts were sold this week
Answer:
952
Step-by-step explanation:
If you have anything else that has to do with donuts it goes straight to me.
Answer:
102 more donuts
Step-by-step explanation
when dealing with how much percent increase you multiply the amount by the percent in decimal form . So 850x0.12 is 102.
a²+b²+c²=138 and ab +bc+ca=3, Find a+b+c
[tex]a ^{2} + b {}^{2} + c { = 138} and \: ab + bc + ca \: find \: a + b + c[/tex]
ans pls?
Answer:
a + b + c = 12
Step-by-step explanation:
The given information are;
a² + b² + c² = 138
a·b + b·c + c·a = 3
The required data = a + b + c
Using an online tool, we have;
(a + b + c)² = (a + b + c) × (a + b + c) = 2·a·b + 2·b·c + 2·c·a + a² + b² + c²
∴ (a + b + c)² = 2·(a·b + b·c + c·a) + (a² + b² + c²)
Where;
a·b + b·c + c·a = 3, and a² + b² + c² = 138, we have;
(a + b + c)² = 2 × 3 + 138 = 144
(a + b + c)² = 144
(a + b + c) = √144 = 12
a + b + c = 12.
i need help, sleps plzz , i dont understand plzzz dont ignoree!!!!!!!!!!!!
Answer:
x = [tex]\frac{3+\sqrt{105} }{8} , \frac{3-\sqrt{105} }{8} x=1.655,-0.905[/tex]
Step-by-step explanation:
3x+6 = 4x^2
4x^2 -3x -6 = 0
x = [tex]\frac{3+\sqrt{105} }{8} , \frac{3-\sqrt{105} }{8} x=1.655,-0.905[/tex]
What is the answer to this question
Answer:
y = 1/4x
Step-by-step explanation:
pls help in the middle of my final lol
Answer:
b) 2
Step-by-step explanation:
both angles have the same values, they are technically opposites.
Set your formula up as
130 = 66x - 2
130 + 2 = 66x
132/66 = x
2 = x
Find f(-6)
FINAL EXAM PLEASE HELPPPP
f(-6) = 5
Just look at the graph when x= -6 , y = 5
Answer:
Step-by-step explanation:
See image -->Answer
Which expression is equivalent to this expression?
11
6
613
610
616
619
Answer:
6^10
Step-by-step explanation:
6^2 * 6^11
-----------------
6^3
First simplify the numerator. We know a^b*a^c = a^(b+c)
6^(2+11)
-----------------
6^3
6^(13)
-----------------
6^3
Then a^b / a^c = a^(b-c)
6^(13-3) = 6^10
Answer:
6^10
Step-by-step explanation:
To solve this you need to remember 2 things.
First off, multipication is addition with exponents.
And secondly, division is subtraction with expoinents.
So on the top we have 6^2*6^11
So this is really 6^11+2
=
6^13
Now we need to divide by 6^3:
6^13/6^3
And this would tecnically be:
6^13-3
=
6^10
So the expression 6^10 is your answer.
Hope this helps!
A banquet room is being carpeted. A floor plan of the room is shown below. Each unit represents 1 yard. The carpet costs $23.50 per square yard. How
much will is cost to carpet the room?
Area of the parallelogram -
square yards
Area of the rectangle =
square yards
Are of the triangle =
square yards
Area of the floor
square yards
Total cost of the carpet = 5
Answer: $775.50
explanation: I just looked it up and another website had the same question but also had the answer
What is the
measure of RK to the
nearest tenth if RQ is
7 in., QL is 24 in., and
LK is 3 in.?
R
Work:
Answer:
25.2 in.
Step-by-step explanation:
Given:
RQ = 7 in.
QL = 24 in.
LK = 3 in.
Required:
Length of diagonal RK
Solution:
Apply the extension of the Pythagorean theorem which is:
d² = x² + y² + z²
Where,
d = RK
x = RQ = 7 in.
y = QL = 24 in.
z = LK = 3 in.
Plug in the values
d² = 7² + 24² + 3²
d² = 634
d = √634
d = 25.1793566 ≈ 25.2 in. (nearest tenth)
How do you integrate
[tex](3x^{2} + 3) ^{3} [/tex]
?
Answer:
Since i don't know what formula is mentioned. I just used the easiest way to solve :)
Step-by-step explanation:
[tex](3x^2 + 3)^3 = (3x^2)^3 + 3^3 + 3((3x^2)^2)(3) + 3(3x^2)(3^2)[/tex]
[tex]= 27x^6 + 27 + 3(9x^4 \times 3) + 3(3x^2 \times 9)\\\\=27x^6 + 27 + 81x^4 + 81x^2\\\\=27x^6 + 81x^4 + 81x^2 + 27\\\\[/tex]
[tex]\int\limits {(3x^2+3)^3} \, dx = \int\limits {27x^6 + 81x^4+81x^2 + 27} \, dx[/tex]
[tex]= \frac{27}{7}x^7 + \frac{81}{5}x^5+\frac{81}{3}x^3 + 27x +C\\\\= \frac{27}{7}x^7 + \frac{81}{5}x^5+27x^3 + 27x +C\\\\[/tex]
Help,anyone can help me do this quetion and explain.
Answer:
[tex]x=100\\y=60[/tex]
Step-by-step explanation:
The shape of the figure is quadrilateral, that means overall it will be 360 degrees.....
Angle of straight line to find x:
[tex]x+80=180[/tex]
[tex]x=180-80[/tex]
[tex]x=100[/tex]
Now, both the values of x will be 100
Find the value of y:
[tex]y+100+120+80=360[/tex]
[tex]y+300=360[/tex]
[tex]y=360-300[/tex]
[tex]y=60[/tex]
Therefore, [tex]x=100[/tex] and [tex]y=60[/tex]
hope this helps, have a good day.....
See image for question. Show workings
Answer:
#85 men and 2 women = 7 people with no restriction
7P7 = 7!a) Two women must sit next to each other:
2!*5! = 2*120 = 240b) The two women must not sit next to each other:
7! - 2!5! = 4800#93 men and 5 women with no restriction:
8P8 = 8! = 40320Help please someone ans
Answer:
40
Step-by-step explanation:
the line in the middle shows the median
Find the degree of the polynomial function y=(x-5)(x+5)
Answer:
Step-by-step explanation:
y = (x + 5)(x - 5)
= x² - 5²
= x² - 25
Degree of this polynomial is 2.
Highest power of the variable x will be the degree of the polynomial.
Seven times a number minus the number is -48. Find the number.
Answer:
-8
Step-by-step explanation:
(7)*(-8) = -56
(-56) - (-8) = -48
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Simplify the radical expression.
Answer:
[tex]xy^3 \sqrt[4]{y^3}[/tex]
Step-by-step explanation:
Recall the exponent property [tex]a^b+a^c=a^{(b+c)}[/tex].
We can use this property to break the problem down:
[tex]\sqrt[4]{x^4y^{15}}=\sqrt[4]{x\cdot x\cdot x\cdot x\cdot y^3\cdot y^3\cdot y^3\cdot y^3\cdot y^3}=\boxed{xy^3 \sqrt[4]{y^3}}[/tex]
Answer:
[tex]xy^3\sqrt[4]{y^3}[/tex]
Step-by-step explanation:
[tex]\sqrt[4]{x^4y^{15}} =\sqrt[4]{x^4}*\sqrt[4]{y^{15}}\\\\=x\sqrt[4]{y^{15}}\\\\=x(\sqrt[4]{y^{12}} *\sqrt[4]{y^3})\\\\=xy^3\sqrt[4]{y^3}\\\\\\\sqrt[4]{y^{12}} =y^{12/4}=y^3 \\\\\sqrt[4]{x^4} =x^{4/4}=x[/tex]