base= 5+h
height= h
area= 1/2bh, so since our area us 18cm^2
therefore 18=1/2*b*h
18*2=(5+h)*h
36=5h+h^2
h^2+5h-36=0 ( for quadratic equation)
h^2+9h-4h-36=0
(h^2+9h)(-4h-36)=0
h(h+9)-4(h+9)=0
(h-4)(h+9)=0
h=4 or h= -9
i need help plzzzzzzzzzzzzzzzzzzzzzzzzzzzz
Answer:
The answer is 7
Step-by-step explanation:
Q11-4=7
Hope this helped!!!
b is two-fifth of c
4a = 3c
work out the ratio a:b:c
give your answer in its simplest form where a,b and c are integers
Answer:
8a:15b:6c
a:b:c = 8:15:6
A train is spotted 10 miles south and 8 miles west of an observer at 2:00 pm. At 3:00 pm the train is spotted 5 miles north and 16 miles east of the observer. a. How far did the train travel in the first hour? b. If the train continues at this pace where will it be in relation to the observer at 5:00 pm? Write a function that will give the train's position at any given time c. d. At 2:00 pm a cyclist is traveling due east and is next to the observer. If the cyclist is traveling at 10 mph, do they collide with the train when the bike goes over the train tracks?
Answer:
a. The distance the train travelled in the first hour is approximately 28.3 miles
b. The location of the train at 5:00 p.m. is 53 miles east, and 46 miles west
c. The location of the train at any given time by the function, f(t) = (-8 + 24·t, -10 + 15·t)
d. The train does not collide with the cyclist when the bike goes over the train tracks
Step-by-step explanation:
a. The given information on the train's motion are;
The location south the train is spotted = 10 miles south and 8 miles west
The time the observer spotted the train = 2:00 pm
The location the train is spotted at 3:00 p.m. = 5 miles north and 16 miles east
Therefore, the difference between the two times the train was spotted, t = 3:00 p.m. - 2:00 p.m. = 1 hour
Making use of the coordinate plane for the two locations the train was spotted, we have;
The initial location of the train = (-10, -8)
The final location of the train = (5, 16)
Therefore the distance the train travelled in the first hour is given by the formula for finding the distance, 'd', between two points, (x₁, y₁) and (x₂, y₂) as follows;
[tex]d = \sqrt{\left (x_{2}-x_{1} \right )^{2}+\left (y_{2}-y_{1} \right )^{2}}[/tex]
Therefore;
[tex]d = \sqrt{\left (5-(-10) \right )^{2}+\left (16-(-8) \right )^{2}} = 3 \cdot\sqrt{89}[/tex]
The distance the train travelled in the first hour, d = 3·√89 ≈ 28.3 miles
b. The speed of the train, v = (Distance travelled by the train)/Time
∴ v ≈ 28.3 miles/(1 hour) = 28.3 miles per hour
The speed of the train in the first hour, v ≈ 28.3 mph
The direction of the train, θ, is given by the arctangent of the slope, 'm', of the path of the train;
[tex]\therefore The \ slope \ of \ the \ path \ of \ the \ train, \, m =tan(\theta) = \dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
∴ m = tan(θ) = (5 - (-10))/(16 - (-8)) = 0.625
c. Distance = Velocity × Time
At 5:00 p.m., we have;
The time difference, Δt = 5:00 p.m. - 3:00 p.m. = 2 hours
The distance, d₁ = (28.3 mph × 2 hours = 56.6 miles
Using trigonometry, we have the horizonal distance travelled, 'Δx', in the 2 hours is given as follows;
Δx = d₁ × cos(θ)
∴ Δx = 56.6 × cos(arctan(0.625)) ≈ 48
The increase in the horizontal position of the train, relative to the point (5, 16), Δx ≈ 48 miles
The vertical distance increase in the two hours, Δy is given as follows;
Δy = 56.6 × sin(arctan(0.625)) ≈ 30
The increase in the vertical position of the train, relative to the point (5, 16), Δy ≈ 30 miles miles
Therefore; the location of the train at 5:00 p.m. = ((5 + 48), (16 + 30)) = (53, 46)
The location of the train at 5:00 p.m. = 53 miles east, and 46 miles west
c. The function, 'f', that would give the train's position at time-t is given as follows;
The P = f(28.3·t, θ)
Where;
28.3·t = √(x² + y²)
θ = arctan(y/x)
Parametric equations
y - 5 = 0.625·(x - 16)
∴ y = 0.625·x - 10 + 5
The equation of the train's track is therefore, presented as follows;
y = 0.625·x - 5
d = 28.3·t
The y-component of the velocity, [tex]v_y[/tex] = 3*√89 mph × sin(arctan(0.625)) = 15 mph
Therefore, we have;
y = -10 + 15·t
The x-component of the velocity, vₓ = 3*√89 mph × cos(arctan(0.625)) = 24 mph
Therefore, we have;
x = -8 + 24·t
The location of the train at any given time, 't', f(t) = (-8 + 24·t, -10 + 15·t)
d. The speed of the cyclist next to the observer at 2:00 p.m., v = 10 mph
The distance of the cyclist from the track = The x-intercept = 5/0.625 = 8
The distance of the cyclist from the track = 8 miles
The time it would take the cyclist to react the track, t = 8 miles/10 mph = 0.8 hours
The location of the train in 0.8 hours, is f(0.8) = (-8 + 24×0.8, -10 + 15×0.8)
∴ f(0.8) = (11.2, 2)
At the time the cyclist is at the track along the east-west axis, at the point (8, 0), the train is at the point (11.2, 2) therefore, the train does not collide with the cyclist when the bike goes over the train tracks.
If the cyclist is travelling at 10 mph the train does not collide with the cyclist when the bike goes over the train tracks.
The location south the train is spotted = 10 miles south and 8 miles west
The time the observer spotted the train = 2:00 pm
The location of the train is spotted at 3:00 p.m. = 5 miles north and 16 miles east
Thus, the difference between the two times the train was spotted,
t = 3:00 p.m. - 2:00 p.m. = 1 hour
What is the distance?The distance is the product of velocity and time.
Distance = Velocity × Time
The initial location of the train = (-10, -8)
The final location of the train = (5, 16)
Therefore the distance the train travelled in the first hour
[tex]d = \sqrt{(x_{2} -x_{1} )^{2} +(y_{2} -y_{1} )^{2} } \\d = \sqrt{(5 -(-10) )^{2} +(16-(-8) )^{2} }[/tex]
d = 3√89
The distance the train travelled in the first hour, d = 28.3 miles
b. The speed of the train, v = (Distance travelled by train)/Time
∴ v ≈ 28.3 miles/(1 hour) = 28.3 miles per hour
The speed of the train in the first hour, v ≈ 28.3 mph
The direction of the train, θ, is given by the arc tangent of the slope, 'm', of the path of the train;
∴ m = tan(θ) = (5 - (-10))/(16 - (-8))
m = 0.625
c. Distance = Velocity × Time
At 5:00 p.m., we have;
The time difference, Δt = 5:00 p.m. - 3:00 p.m. = 2 hours
The distance, d₁ = (28.3 mph × 2 hours = 56.6 miles
Using trigonometry, we have the horizontal distance travelled, 'Δx', in the 2 hours is given as follows;
Δx = d₁ × cos(θ)
∴ Δx = 56.6 × cos(arctan(0.625)) ≈ 48
The increase in the horizontal position of the train, relative to the point (5, 16), Δx ≈ 48 miles
The vertical distance increase in the two hours, Δy is given as follows;
Δy = 56.6 × sin(arctan(0.625)) ≈ 30
The increase in the vertical position of the train, relative to the point (5, 16), Δy ≈ 30 miles miles
Therefore; the location of the train at 5:00 p.m. = ((5 + 48), (16 + 30)) = (53, 46)
The location of the train at 5:00 p.m. = 53 miles east, and 46 miles west
c. The function, 'f', that would give the train's position at time-t is given as follows;
The P = f(28.3·t, θ)
28.3·t = √(x² + y²)
θ = arctan(y/x)
Parametric equations
y - 5 = 0.625·(x - 16)
∴ y = 0.625·x - 10 + 5
The equation of the train's track is, therefore, presented as follows;
y = 0.625·x - 5
d = 28.3·t
The y-component of the velocity,
= 3 × √89 mph × sin(arctan(0.625)) = 15 mph
Therefore, we have
y = -10 + 15·t
The x-component of the velocity,
vₓ = 3 × √89 mph × cos(arctan(0.625))
= 24 mph
Therefore, we have;
x = -8 + 24·t
The location of the train at any given time, 't',
f(t) = (-8 + 24·t, -10 + 15·t)
d. The speed of the cyclist next to the observer at 2:00 p.m., v = 10 mph
The distance of the cyclist from the track = The x-intercept
= 5/0.625 = 8
The distance of the cyclist from the track = 8 miles
The time it would take the cyclist to reach the track, t = 8 miles/10 mph = 0.8 hours
The location of the train in 0.8 hours, is f(0.8)
= (-8 + 24×0.8, -10 + 15×0.8)
∴ f(0.8) = (11.2, 2)
therefore, If the cyclist is travelling at 10 mph the train does not collide with the cyclist when the bike goes over the train tracks.
Learn more about distance;
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i don't understand this can someone help me please
Answer:
Total interest to be paid: $210
Total amount to be repaid: $3,710
Step-by-step explanation:
You can ignore the monthly payment for this problem.
For simple interest, the formula is I = PRT where I = interest earned, P = principal amount borrowed/deposited, R = rate as a decimal, and T = time in years.
I = (3,500)(0.06)(1)
I = 210
Then add that to the amount borrowed ($3,500) and you're done.
3,500 + 210 = $3,710
Please let me know if you have questions.
I cant do this please help me i will give brainliest
Answer:
Here, I graphed this especially for you.
Check attachment.
What is the length of EF in the right triangle below?
A: 54
B: 24
C: 1296
D: 585
E: 36
F: square root of 576
-9+3y=24 write an equivalent equation in slope intercept form
ig hanganaahajssislaalalla
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP HELP I NEED HELP ASAP
HELP I NEED HELP ASAP HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
Answer:
a.
Step-by-step explanation:
please click the heart and rate excellent and pa brainleist po please ☻❤☺️☺️❤☻
LOOK AT THE PICTURE!! I REALLY NEED HELP SOMEONE PLEASE HELP ME OUT
Answer: B
Step-by-step explanation: Hope this help :D
Can anyone help me with this math question please I will give brainlist!!
Answer:
b. (6, 4)
Step-by-step explanation:
i hope this helps :)
Answer:
B. (6,4)
Step-by-step explanation:
The point is inside the triangle.
Tamia is getting balloons for her father's birthday party. She wants each balloon string to be 6 feet long. At the party store, string is sold by the yard. If Tamia wants to get 59 balloons, how many yards of string will she need?
Answer:
118 yards
Step-by-step explanation:
Tamia is getting balloons for her father's birthday party
She wants each balloon to be 6 feet long
Tamia wants to get 59 balloons
Therefore the yards of string needed can be calculated as follows
= 59×6
= 354 feet to yards
= 118 yards
Hence the number of yards needed is 118 yards
I need this question really badly
Answer:
yeah same for me but with ice cream
Answer both parts with all of the numbers for both sides please
Answer:
the answer is in the photo above
the temperature is dropping -3.75 degrees per hour. how many hours will the temperature drop for 4.5 hours
Answer:
It will drop 16.875 degrees
Step-by-step explanation:
3.75 × 4 = 15
.5 × 3.75 1.875
Answer:
-16.875
Step-by-step explanation:
This equation is quite simple and will only require one equation to solve. This is the equation,
-3.75×4.5=-16.875
The final answer is -16.875
How to add 12.50, 18.50, 20, 20, 13, 12
Answer:
96
Step-by-step explanation:
12.50 + 18.50 + 20 + 20 + 13 + 12 = 96
help with this nth term homework please answer true of false
x on the top and 24 on the bottom 11 on the top 6 on the bottum
Answer:
x = 44
Step-by-step explanation:
this is a proportion which you can solve by cross-multiplying:
6x = 24·11
6x = 264
x = 264/6
x = 44
Answer:
c
Step-by-step explanation:
Can you please tell me the table of 12?
Answer:
you have the table of the 12in the photo
Step-by-step explanation:
Answer:
12×1=12
12×2=24
12×3=36
12×4=48
12×5=60
12×6=72
12×7=84
12×8=96
12×9=108
12×10=120
In your question
the table of 12 is correct
hope it is helpful to you ☺️☺️☺️☺️☺️
6^1-x=10^x how do I solve for x?
Answer:
x = -3, x = 2
Step-by-step explanation:
re-order the terms to get this quadratic: x² + x - 6 = 0
factor: (x + 3)(x-2) = 0
x = -3, x = 2
Mr. Thomsen is buying two types of gift
cards to give as prizes to employees at a
company meeting. He will buy restaurant
gift cards that each cost $50. He will also
buy movie theater gift cards that each
cost $20. He has $450 to buy a total of
15 gift cards. How many of each type of gift cards can he buy?
Answer:
he can buy 6 gift cards, 7 theatre cards with a remainder of $10.
Step-by-step explanation:
What is mU?
A. 17
B. 29
C. 46
D. 134
Answer:
I think its A
Step-by-step explanation:
because it's a tighter angle than 29,46,and 134 degrees i might not be right but i hope it is :)
Kevin knit scarves for his friends. Altogether, the scarves had a total length of
442.8 in. If he knit 9 scarves, and each scarf was the same length, how long
was each scarf? Write your answer in feet.
Kevin knit 9 scarves, and each scarf was 49.2 inches long.
Converting this length to feet, we find that each scarf is 4.1 feet long.
Let's use the variable "L" to represent the length of each scarf in inches. Since Kevin knit 9 scarves, we can write the equation for the total length of all scarves as:
[tex]\(L_{\text{total}} = L \times 9\)[/tex]
We are given that the total length of all scarves is 442.8 inches. So, we can write:
[tex]\(442.8 \text{ inches} = L \times 9\)[/tex]
To find the length of each scarf, we need to isolate "L" on one side of the equation. To do that, we can perform the following steps:
Divide both sides of the equation by 9 to get:
[tex]\(\frac{{442.8 \text{ inches}}}{{9}} = \frac{{L \times 9}}{{9}}\)[/tex]
Simplifying, we get:
[tex]\(49.2 \text{ inches} = L\)[/tex]
Now, we have found the length of each scarf in inches (49.2 inches). To convert this length to feet, we know that 1 foot is equal to 12 inches. So, to find the length in feet, we divide the length in inches by 12:
[tex]\(L_{\text{feet}} = \frac{{L_{\text{inches}}}}{{12}}\)[/tex]
Substituting the value of [tex]\(L_{\text{inches}}\)[/tex] with 49.2 inches:
[tex]\(L_{\text{feet}} = \frac{{49.2 \text{ inches}}}{{12}}\)[/tex]
Now, let's perform the division:
[tex]\(L_{\text{feet}} = 4.1 \text{ feet}\)[/tex]
So, each scarf is 4.1 feet long.
Kevin knit 9 scarves, and each scarf was 49.2 inches long.
Converting this length to feet, we find that each scarf is 4.1 feet long.
To know more about Length here
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Please Help, Please Help, Please Help
Answer:
a=76 b=83
Step-by-step explanation:
for a. we divide 6688(area) by 88 to find the width bc 88*w=6688
6688/88 is 76 so a=76
Since 312 is perimeter we have to subtract 73 twice and then divide that by 2 bc 73+73+L+L=312
(312-73-73)/2=83 so b=83
Smo answer these and show work plz
Answer:
Step-by-step explanation:
1) multiply the three dimension
V = 7 x 2 x 4 = 56 cm^3
2) find the base area
base area = (9 x 3)/2 = 13,5 km^2
multiply the base area for the height
V = 13,5 x 5 = 67,5 km^3
3) find the trapezoid area
trapezoid area = [(base 1 + base 2) x h]/2 = [(4+6) x 1.7]/2 = 8.5 cm^2
mutiply the trapezoid area for the height that the priam would assume if the base will touch the ground
V = 8.5 x 4 = 34 cm^3
4) find the base area
base area = radius^2 x pi = 2^2 x pi = 12,57 yd^2
multiply the base area for the height
V= 12.57 x 6 = 75.40 yd^3
5) find the base area
base area = 9^2 x pi = 81 x pi = 254.47 ft^2
multiply the base area for the height
V = 254.47 x 5 = 1272.35 ft^3
6) multiply the three dimensions
V = 12 x 11 x 9 = 1188 yd^3
7) find the trapezoid area
trapezoid area = [(12+6) x 6.3]/2 = [20 x 6,3]/2 = 63 in^2
mutiply the trapezoid area for the height that the priam would assume if the base will touch the ground
V = 63 x 16 = 1008 in^3
8) find the base area
base area = (leg1 x leg 2)/2 = (4 x 3)/2 = 6 m^2
multiply the base area for the height
V = 6 x 9 = 54 m^3
Answer:
hope this helps you out good luck with your math
URGENT!!!!!!!! PLEASE HELP ASAP TIMED!!!!!!!!!!!!!!! HELP!!!!!!!!!!!!!!!!!
Answer:
Height of building = 86.9 ft
Step-by-step explanation:
I've drawn a triangle image to depict this question and I have attached it.
From the attached image, we can see that ABC is the height of the building.
We can see the distance from your eye to the ground indicated and also the distance from the horizontal distance from the building to you indicated.
We can use pythagoras theorem to find AB.
AB/57 = tan 55°
AB = 57 × 1.4281
AB = 81.4 ft
Now, total height of the building is AB + BC.
BC = 5.5 ft since B is parallel to your eye and height from there to the ground is 5.5 ft.
Thus;. Height of building = 81.4 + 5.5 = 86.9 ft
louis created a square garden with a side length of 5 feet. what is the total area of the garden
Answer:
the answer of the question is 25
HELP ASAP TIMED!!!!!!!!!!!!!!!
Step-by-step explanation:
1 ans 35/37
2 ans 0.95
3 ans 12/37
4 ans 0.32
answer for brainlest for 25 points
Answer:
1. 23/4 , 2. 5.555... , 3. 5 1/2 , 4. √28
you want to make them all into decimals so you can compare then easier
23/4 would be 5.75
√28 (just put it in a calculator) would be 5.29
5 1/2 would be 5.5 (make it into a improper fraction 11/2 then do 11/2 and you get 5.5)
and you have 5.555.
so...
5.75
5.29
5.5
5.55555
first is 5.75 it's bigger because of the .(75)
then 5.555 because it's .(55)
then 5.5 because it's .(50)
and the last one 5.(29)
I WAS IN THE HOSPITAL AND MISSED A MATH LESSON HELP PLZZZ
Answer:
30 ft
Step-by-step explanation:
[tex]C=\frac{n^2}{5} +175\\\\355=\frac{n^2}{5} +175\\\\180=\frac{n^2}{5}\\\\n^2=900\\\sqrt{n^2} =\sqrt{900} \\n=30[/tex]
The price of tire is $45.50. The store marks it Up 60%. What is the total?
Answer:
$72.80
Step-by-step explanation:
1.) Find 60% of 45.50
0.60 * 45.50 = 27.3
2.) Add this to the cost
27.30 + 45.50 = 72.80