A flagpole 12 meters tall casts a 24-meter shadow. Nearby, luke stands and is 4 meters tall. Determine the length of luka's shadow. Include all labels.
Answer:
8 meters
Step-by-step explanation:
This is a question that deals with Proportion
Height of flagpole/Shadow of flagpole = Height of Luke/Shadow of Luke
Length of the shadow of Luke = x
= 12/24 = 4/x
We cross Multiply
12 × x = 24 × 4
x = 24 × 4/12
x = 8 meters
Hence, the length of the shadow of Luke = 8 meters
Oak Street intersects with Mill Avenue. The traffic light on Oak Street follows a cycle. It is green for 35 seconds, yellow for 5 seconds, and red for 20 seconds. As you travel along Oak and approach the intersection, what is the probability that the first color you see is red? Write the probability as a simplified fraction. Incorrect feedback has been removed from the screen. Fill in the blank text field 1
Answer:
1/3
Step-by-step explanation:
20/60 simplified is 1/3
20 for the red light
60 all of them added
. David drives 40 miles in one hour. How many miles does he drive in 1.5 hours?
Answer:
60 miles in 1.5 hours
Step-by-step explanation:
40 miles times 1 hour = 40 mph
40(1.5)= 60 mph
Answer:
60 miles on 1.5 hours
Step-by-step explanation:
Just do 40*1.5
Show your work and solve 10w=6+24
Answer:
w=3
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
10w=6+24
10w=(6+24)(Combine Like Terms)
10w=30
10w=30
Step 2: Divide both sides by 10.
10w /10= 30 /10
w=3
The cubic polynomial below has a double root at x=-4 and one root at x=6 and passes through the point (2,36) as shown. Algebraically determine it’s equation in factored form.
Answer: P(x) = (-1/4)*(x + 4)*(x + 4)*(x - 6)
Step-by-step explanation:
The factored form of a polynomial is:
P(x) = A*(x - r₁)*(x - r₂)*(x - r₃)....
Where:
A is a real number.
r₁, r₂,.... etc
are the roots.
In this case, we know that the roots are:
-4, -4, and 6.
Then the polynomial will be:
p(x) = A*(x + 4)*(x + 4)*(x - 6)
Now we also know that this polynomial passes through the point (2, 36)
This means that:
P(2) = 36 = A*(2 + 4)*(2 + 4)*(2 - 6) = A*6*6*(-4) = A*(-144)
36 = A*(-144)
-36/144 = A
-0.25 = -1/4 = A
Then the polynomial is:
P(x) = (-1/4)*(x + 4)*(x + 4)*(x - 6)
given the equation 9x+3Y=7 which equation is perpendicular to an equation with a y intercept of 12
When x = 3, y = 4. What is y when x = 12?
Group of answer choices
A)3
B)4
C)12
D)16
Answer:
A)3
Step-by-step explanation:
if im wrong tell me and i will do it again
HOPE THIS HELPS:::)))
Find the unknown length given that the triangles are similar.
Answer:
20 is the answer.Step-by-step explanation:
1. Make a proportion.
Set the numbers equal to each other.
I chose the numbers 9, 12, 15, and of course x.
Make the fractions in a way that the x is in the numerator if you want to make your life easier.
15/9 = x/12
2. Simplify
Cross multiply the numbers.
This will give you the equation of
9*x and 15*12
3. Make an equation
Simplify the numbers by mulitplying them
9x = 180
4. Divide both sides by 9
9x = 180
/9 /9
x = 20Hope this helped,
Kavitha Banarjee
HELPPPPPPP PLEASE!!!!!
Answer:
i am so sorry that i dont know
what is 76.385 + 8.93
The stopping distance, d ( in feet) for a van moving at a velocity (speed) v miles per hour is modeled by the equation:
d = 0.04v + 1.1v
What is the stopping distance for a velocity of 10 miles per hour?
a. 10 ft
b. 7 ft
c. 15 ft
d. 13 ft
Note: The must be [tex]0.04v^2[/tex] instead of [tex]0.04v[/tex].
Given:
The stopping distance, d ( in feet) for a van moving at a velocity (speed) v miles per hour is modeled by the equation:
[tex]d=0.04v^2+1.1v[/tex]
To find:
The stopping distance for a velocity of 10 miles per hour.
Solution:
We have,
[tex]d=0.04v^2+1.1v[/tex]
where, d is stopping distance and v is velocity.
Substitute v=10 in the given equation to find the stopping distance for a velocity of 10 miles per hour.
[tex]d=0.04(10)^2+1.1(10)[/tex]
[tex]d=0.04(100)+11[/tex]
[tex]d=4+11[/tex]
[tex]d=15[/tex]
So, the stopping distance for a velocity of 10 miles per hour is 15 ft.
Therefore, the correct option is c.
A circular garden has a diameter of 8 feet, and a rectangular garden has side lengths of 5 feet by 9 feet.
which garden is larger
Answer:
rectangular garden
Step-by-step explanation:
A young couple purchases their first new home in 2011 for $95,000. They sell it to move into a bigger home in 2018 for $105,000. First, we will develop an exponential model for the value of the home. The model will have the form
Given:
The value of home in 2011 is $95,000.
The value of home in 2018 is $105,000.
To find:
The exponential model for the value of the home.
Solution:
The general exponential model is
[tex]y=ab^x[/tex] ...(i)
where, a is initial value and b is growth factor.
Let 2011 is initial year and x be the number of years after 2011.
So, initial value of home is 95,000, i.e., a=95,000.
Put a=95000 in (i).
[tex]y=95000b^x[/tex] ...(ii)
The value of home in 2018 is $105,000. It means the value of y is 105000 at x=7.
[tex]105000=95000b^7[/tex]
[tex]\dfrac{105000}{95000}=b^7[/tex]
[tex]\dfrac{21}{19}=b^7[/tex]
Taking 7th root on both sides, we get
[tex]\left(\dfrac{21}{19}\right)^{\frac{1}{7}}=b[/tex]
Put [tex]b=\left(\dfrac{21}{19}\right)^{\frac{1}{7}}[/tex] in (ii).
[tex]y=95000\left(\left(\dfrac{21}{19}\right)^{\frac{1}{7}}\right)^x[/tex]
[tex]y=95000\left(\dfrac{21}{19}\right)^{\frac{x}{7}}[/tex]
Therefore, the required exponential model for the value of home is [tex]y=95000\left(\dfrac{21}{19}\right)^{\frac{x}{7}}[/tex], where x is the number of years after 2011.
A triangle with side lengths of 8, 15, and 17.5 form a right triangle.
I would appreciate the help
9514 1404 393
Answer:
false
Step-by-step explanation:
You can check to see if the sum of squares of the smaller two numbers is equal to the square of the larger.
8² +15² vs 17.5²
64 +225 vs 306.25
At this point, you need go no further. The sum of two integers will not have a fractional part, so cannot be equal to 306.25.
289 vs 306.25 . . . . the long side is too long for a right triangle.
__
If you were familiar with some of the Pythagorean triples, you would know that the closest triple is {8, 15, 17}, so (8, 15, 17.5) does not represent a right triangle.
A few common Pythagorean triples are ...
{3, 4, 5}, {5, 12, 13}, {7, 24, 25}, {8, 15, 17}, {9, 40, 41}
The numerator of a rational number is 7 less than the denominator .If the denominator is increased by 9 and the numerator by 2, we again get the same rational number. Find the Number
Answer:
5/3
Step-by-step explanation:
Let
Denominator = x
Numerator = x - 7
New
Denominator = x + 9
Numerator = x - 7 + 2
= x - 5
x / x-7 = x -5 / x + 9
Cross product
x * x + 9 = x-7 * x-5
x² + 9x = x²- 5x - 7x + 35
x² + 9x - x² + 5x + 7x - 35 = 0
21x = 35
divide both sides by 21
x = 35 / 21
= 5 / 3
x = 5/3
The rational number is 5/3
There are 50 animals in a shelter. Sixty percent of the animals are dogs. Which equation can be used to find the number of dogs in the shelter?
11 points
Answer:
60/100 divided by 2
Step-by-step explanation:
60%= 60/100
100 divided by 2 is 50
( what you do to the top you do to the bottom)
60 divided by 2 is 30
60/100= 30/50
So the answer is 30
HOPE THIS HELPS o(≧o≦)o ◑﹏◐Polka Dot Boutique is having a sale of 15% off previously marked down items. Gwen finds a pair of jeans originally priced at $45.00 and marked down 25%. She must pay a 6% sales tax on the final prices of the jeans. How much does Gwen spend at Polka Dot Boutique? Group of answer choices
Answer:
$30.41
Step-by-step explanation:
Given that:
Discount off = 15%
Original price = $45
Mark down on item = 25%
Sales tax on final price = 6%
Cost of Jean will be ;
Mark down price :
Original price - (Original price * markdown %)
$45 - ($45 * 0.25) = $33.75
Discounted price :
Markdown price - (markdown price * discount %(
$33.75 - (33.75 * 0.15)
= $28.6875
Final price :
Discounted price + (sales tax * discounted price)
28.6875 + (0.06 * 28.6875)
= $30.40875
= $30.41
What two consecutive integers have a sum of 39?
19 & 20 are the reqd. integers.
By what is given, x + ( x + 1 ) = 39 .
∴ 2 x + 1 =39.
∴ 2 x = 39 − 1 = 38 .
∴ x = 19 , so, x + 1 = 20 .
Thus, 19 & 20 are the reqd. integers.
NEED HELP ASAP
A rectangle is labeled truck. A vector that goes down and to the right is labeled 7,500 pounds and the terminal point is labeled tow truck 2. A vector that goes up and to the right is labeled 10,000 pounds and the terminal point is labeled tow truck 1. The angle between the vectors is 110 degrees. The angle between tow truck 2 and the x-axis is 60 degrees.
A pair of tow trucks are pulling on a trailer that is stuck in mud. The first truck pulls with a force of 10,000 pounds at a 110° angle from the second truck, which is pulling with a force of 7,500 pounds. What is the magnitude of the resultant force?
9,821 pounds
10,244 pounds
14,405 pounds
24,226 pounds
Answer:
10,244 pounds
Step-by-step explanation:
|R|= √(7,500+10,000cos110)²+(10,000sin110)²
|R|= about 10,244 pounds
thats how i did it :I
Answer:
B
Step-by-step explanation:
Edge 2021
Find A. Round to the nearest tenth:
Answer:
24.0
SinA = sinB
a b
Sin150 = Sin12
a 10
cross multiplication:
Sin(150) x 10
Sin(12)
5
sin 12 = 24.0
I hope I got it correct
Answer:
Step-by-step explanation:
[tex]\frac{10}{sn12}[/tex] = [tex]\frac{a}{sin150}[/tex]
a = [tex]\frac{10sin150}{sin12}[/tex] ≈ 24.0
I'll give Brianiest for the first answer if correct pleaseee!!
Answer:
its b
Step-by-step explanation:
they have the same slope
1)-4/-6=2/3
2)-2/-3=2/3
BUT different y-int
1)-6/-26=1/4
2)-3/-6=1/2
so no solution
what is the slope of the line that passes through the points (2,1) and (17,-17)
hi
You have two points A ( X;Y) and B ( X ; Y)
slope is : ( Yb -Ya) / (Xb -Xa )
A(2 ; 1) and B (17 ; - 17)
so : (-17 - 1 ) / (17 -2) = -18/ 15 = - 6*3 / 5*3 = -6/5
I NEED HELP ASAP FOR BRAINLIEST
Answer:
y=x+4
Step-by-step explanation:
slope intercept form: y=mx+b
m is the slope of the line and b is the y-intercept
slope: 1
y-intercept: 4
hopefully this helps :)
Answer:
y=x+4
Step-by-step explanation:
y=mx+b
m-is the slope and b-is the y-intercept
(x, y) = (0,4)
4=0+b so b =4
substitute in the equation
y=x+4
Will mark brainliest pls help
Answer:
18
Step-by-step explanation:
Add all the sides. But you are missing two sides. Soo since the top is 4, the bottom is two bc half is two. then the right side is 5 and the left, half is 2 so the other half is 3. 3+2=5! soooo the perimeter is 18.
Answer:
18
Step-by-step explanation:
We add up the side lengths,
[tex]5+4+3+2+2+2= 18[/tex]
by finding missing side lengths with subtraction and logic
and I'm pretty sure this is correct, but I like double-checking things.
This figure is made out of 2 rectangles,
2x5 and 3x2
The perimeter of each is 14 and 10
[tex]14+10-3-3=18[/tex]
the two 3's are the over lapping sides
We also get 18.
What is the answer for A B and X (geometry)
Answer:
a=8
b=5
x=13
Step-by-step explanation:
Use Pythagoras's Theorem to find A
h²=y²+z²
10²=a²+6²
100=a²+36
∴a²=64
∴a=8
Use Pythagoras's Theorem to find A
h²=y²+z²
9²=b²+6²
81=b²+36
∴b²=45
∴b=3√5
x=a+b
=8+3√5
Answer:
a = 8
b = ∛5
x = 8 + ∛5
Step-by-step explanation:
I think here we have to do pythagorean theorem a² + b² = c² or c =√a² + b²
Now just plug in the numbers for 9, 6 and b
6² + b² = 9²
36 + b² = 81
b² = 45
b = 6.70820....
b = ∛5
∛5 = 6.70820..
Now plug in 6, 10, a
a² + 6² = 10²
a² + 36 = 100 (subtract 36 on both sides)
a² = 64
√64 = 8
a = 8
NOW X
8 + √45 = 14.708203
8 + ∛5 = 14.708203
x = 8 + ∛5
Hope this helps ya!!!
The ratio of women to men at a college is 9 to 8. If there are 5,644 students in the school, how many more women are there than men?
A) 332
B) 2988
C) 2656
D) 705
Answer:
332
Step-by-step explanation:
Since there is a ratio of 9:8 (women to men), the total should be 17. So even if there were 81 women and 72 men, the total ratio should still be 17. (In simplifiest form.)
So, 5,644 divided by 17=332
Since 9 is 1 more than 8, there are 332 more women than men.
Hope this made sense! I wasn't sure how to explain this.
Answer:
332
Step-by-step explanation:
a mixture calls for 1 cup of lemonade and 3 cups of iced tea ratio of lemonade to iced tea
Guys I really need help pls!!
Answer:
No, yes, yes, no
Step-by-step explanation:
23.6/4.02=5.87
2.36/40.2=0.0587
2360/402=5.87
2.36/0.402=5.87
236/4020=0.0587
Systems of equations, solve by substitution please!
x + 7y = -37
4x - 3y = 7
Step-by-step explanation:
make the coefficients same
then if sign are same subtract the one you wanna cancel it then here it goes
lam gonna start making coefficient of x sam like this:
4.X+7y= -37
1.4X-3y=7
then i will subtract all x or cancel to each other then
4X+28y= -148
-
4X-3y=7
and then -×-=+
add all y
31y=141
y= 4.55 then we take one of the equation then substitute y to 4.55 so i chose first equation
X+7(4.55)=-37
X+31.85=-37
so take 31.85 to the side it will become -31.85
then X=-37-31.85
X=68.85
i hope that it will help you
The equation of the graphed line is x+2y=5. What is the x-intercept of the graph?
Answer:the x intercept is 5
Step-by-step explanation: