How far from the base of the house do you need to place an 18’ ladder so that it exactly reaches the top of a 14’ wall?
Answer:
Length of Ladder(Hypotenuse)=18
Height of wall(Opposite) =14
How far from the base... This talks about the adjacent or distance between the wall and the base.
You can get your answer from Pythagoras theorem
Which states
The square of the hypotenuse is = to the squares of the adjacent and Opposite sides
H² = O² + A²
We're looking for the adjacent "A"
Making A the subject
A² = H² - O²
A= √H² - O²
A= √18² - 14²
A=√128
A= 8√2'
What is an equation of the line that passes through the point(-1,-3) and is perpendicularly to the line x-2y=14
Answer:
the equation will be
Step-by-step explanation:
2x+y+5=0
Answer:
2x + y + 5 = 0
Step-by-step explanation:
The equation of line is x-2y = 14 and we need to find the equⁿ of line which passes through (-1,-3) and is perpendicular to given line.
Find the slope of given line by converting it into slope intercept form.=> x - 2y = 14
=> 2y = x - 14
=> y = x-14/2
=> y = x/2 - 7
Comparing to y = mx + c ,=> Slope (m) = 1/2 .
Now the slope of line perpendicular to it , will have a slope ,
=>[tex] m_{perp}[/tex] = -1/m
=>[tex] m_{perp}[/tex] = -1/½
=> [tex] m_{perp}[/tex] = -2
Using point slope form ,=> m = (y - y₁) / ( x - x₁)
=> -2 = { y - (-3) } / { x - (-1) }
=> -2 = y + 3/x + 1
=> -2(x + 1) = y + 3
=> -2x -2 = y + 3
=> y + 2x +3+2 = 0
=> 2x + y + 5 = 0
Hence the equation of line perpendicular to it is 2x + y + 5 = 0 .Josie makes fruit punch by mixing fruit juice and lemonade in the ratio 1:3
She needs to make 28 litres of punch for a party,
How much of each ingredient does she need?
Fruit juice = 7 litres Lemonade = 21 litres [4]
During the party Josie decides to make some more.
She has 3 litres of fruit juice left and plenty of lemonade,
How much extra punch can she make?
litres
To make the second batch of punch go further Josie
adds 3 more litres of lemonade,
What is the ratio of fruit juice to
lemonade in the second batch?
it takes 3 cups of flour to make 1 batch of cookies how many cups of flour will it take to make 6 batches of cookies
Answer:
6*3=18 cups
Step-by-step explanation:
3 cups of flour to make 1 batch
so to make 6 batches = 3*6 = 18
Find the volume of the solid
Answer:
V = 2784 mm^3
Step-by-step explanation:
The base of this prism is a right triangle. We can use the formula:
A = bh/2
to find the area of the base. A is area, b is base, and h is height. We can substitute what we have:
A = 16 * 12 / 2
A = 96
The volume of a prism is represented by the formula:
V = Bh
Where V is the volume, B is the base, and h is the height.
We have the area of the base as 96 and the height as 29, so we can substitute them in:
V = 96 * 29
V = 2784 mm^3
Marcie Ann Weber, age 32, takes out $15,000 of a term insurance for a ten year term.
annual premium: $
quarterly premium: $
Answer:
Annual premium = $1,500 per year
Quarterly premium = $375 per quarter
Step-by-step explanation:
Given:
Insured amount of term insurance plan = $15,000
Number of year = 10 year
Find:
Annual premium
Quarterly premium
Computation:
Annual premium = Insured amount of term insurance plan / Number of year
Annual premium = $15,000 / 10
Annual premium = $1,500 per year
Quarterly premium = Insured amount of term insurance plan / Number of quarter in 10 year
Quarterly premium = 15,000 / (10 x 4)
Quarterly premium = 15,000 / 40
Quarterly premium = $375 per quarter
A rectangle is removed from a right triangle to create the shaded region shown below. Find the area of the shaded region. Be sure to include the correct unit in
your answer.
00
alyd
yd
yde
yoo
3yd
х
3
?
2yd
4yd
2yd
A ranger spots a forest fire while on a 30-meter observation tower. The angle of depression from the tower to the fire is 14°. To the nearest meter, how far is the fire from the base of the tower?
a. 7 meters
b. 4 meters
c. 124 meters
d. 120 meters
The fire from the base of the tower is at 120 m and Option D is the correct answer.
What is Angle of Depression ?The angle of depression is an angle formed between the horizontal line and the line of sight when an observer looks downwards at an object is known as an angle of depression.
The formula is
[tex]\rm sin\;\theta = y/z\\\\\\cos\; \theta = x/z\\\\\\tan\; \theta = y/x[/tex]
where x is the distance between the point of the ground and the object , horizontally,
y is the perpendicular distance between the surface to the object
and z is the measure of line of sight
[tex]\rm \theta[/tex] is the angle of depression = 14°
It is given in the question that y= 30 m
x= ?
To determine we will substitute the value
[tex]\rm tan\; \theta = y/x\\\\\\tan \;14^{o} = 30/ x\\\\\\0.25 = 30/x\\\\\\\x= 30/0.25\\\\\\x= 120 m\\[/tex]
Therefore the fire from the base of the tower is at 120 m and Option D is the correct answer.
To know more about Angle of depression
brainly.com/question/13514202
#SPJ2
what is 1+1-(3x3)-(1x9)
You go to the ice cream shop and you can choose from 3 different flavors and 2 different toppings? What is the
probability that you will pick an ice cream with sprinkles?
Answer:
I Think C is correct
Gary's stock dropped 3 points in value every day for 4 days. Find the integer that represents the change in value of his stock during that time.
Answer:
- 12 points
Step-by-step explanation:
He's dropping three points each day for four days, ie 4 * 3 , which is equal to 12.
How many solutions exist for the given equation?
1/2(x + 12) = 4x - 1
zero
one
two
O infinitely many
Answer: X = 2
Step-by-step explanation:
Step 1: Simplify both sides of the equation!
Step 2: Subtract 4x from both sides.
Step 3: Subtract 6 from both sides.
Step 4: Multiply both sides by 2/(-7).
Analyze the table below and complete the instructions that follow.
A. A = 11, B = 39, C = 3, D = 8, E = 54
B. A = 22, B = 11, C = 5, D = 28, E = 54
C. A= 32, B= 17, C = 3, D= 8, E = 54
D. A = 22, B = 39, C = 3, D = 8, E = 54
pls, be honest. 20 points
Answer:
it is 5.7 so it should be in between the 5 and 6 but closer to the 6.
Step-by-step explanation:
Hope this helps have a great day! :)
Answer: 5.7
Step-by-step explanation:
Because it’s closer to six but still In the 5 range.
2x+y=3
x-y= 1
solve the equation
Answer:
x = 4/3
y = 1/3
Step-by-step explanation:
System of equations! This is set up really well to make the second equation equal x then substitute.
x - y = 1
x = 1 + y
and then our substitution:
2 (1+y) + y = 3
and solve:
2 + 2y + y = 3
3y + 2 = 3
3y = 1
y = 1/3
And now we can substitute that value into one of our equations:
x - (1/3) = 1
x = 4/3
Next we should check by substituting these values into both of our equations:
2 (4/3) + (1/3) = 3
9 / 3 does equal 3 !
(4/3) - (1/3) does equal 1 !
Therefore, x = 4/3 , and y = 1/3
Tom and Susan park at different lots.
To see which lot is busier, they count the numbers of cars in the lots each day as they arrive.
Their data are shown in the box plots.
the questions to compare the variabilities of the data sets.
1. What is the interquartile range for Tom's data? Explain how you found the interquartile range.
Write your answer in the space below.
1
Answer:
Tom = 5
Susan = 3
Step-by-step explanation:
FROM THE BOXPLOT :
Tom's IQR :
IQR = Q3 - Q1
Q3 = third quartile (value at the endpoint of the box)
Q1 = 1st quartile (value at the beginning of the box)
IQR = 9 - 4
IQR = 5
SUSAN :
IQR = Q3 - Q1
Q3 = third quartile (value at the endpoint of the box)
Q1 = 1st quartile (value at the beginning of the box)
IQR = 8 - 5
IQR = 3
which of these fractions is greater and by how much? 3/5 or 3/8
Answer:
3/5
Step-by-step explanation:
Answer:
Step-by-step explanation:
3/5 is greater than 3/8 I’m not sure by how much tho
Which of the following grids correctly graphs the points A (3, 1), B (0, 3), and C (1, 3)?
First quadrant grid with points A, B, and C labeled
First quadrant grid with points A, B, and C labeled
First quadrant grid with points A, B, and C labeled
First quadrant grid with points A, B, and C labeled
Answer:
First quadrant grid with points A, B, and C labeled
Step-by-step explanation:
Because that is the only option and I also don't see the graph
15 31/40 to the nearest whole number
Answer:
16
Step-by-step explanation:
Because the number is closer to 16, it can be rounded off to that. 15 31/40 is the same as 15.78. When the decimal is over .50 it is rounded up to the next whole number, but when it is under .50 it si rounded down to the nearest whole number. ex. since this one is over the .50, it's rounded up, but if it were 15.36 then it would be rounded down to 15. hope this helps :D
in desperate need of help please :/
Answer:
since 13 miles is 68640 i wood say 189 inches long from bumper to bumper. A mile is 5,280 feet (or 63,360 inches).
If 335 of these cars were parked with their bumpers touching, they would be almost exactly a mile long.
If your question refers to traffic jams, the answer will be a bit different, since cars in traffic jams don’t get that close together. I’m going to take a wild guess here, but let’s assume that there is a 4-foot gap between cars in our hypothetical traffic jam. now put that in to 13 miles
Step-by-step explanation:
please help me out please
Answer:
DCB = 44 degree
Step-by-step explanation:
DAB (given = 100
(180-100 ) / 2 = 40
ADB = ABD = 40 degree (each)
ADC (given = 108
BDC = DBA = 108-40 = 68 degree;
(subtracting angle inscribed within another triangle)
Triangle DBC = 180- 68+68 = 180 - 136 = 44 degree
Find DCB We have found BDC and DBA by deducting ADB from ADC
to get BDC
Then we deduct BDC from ADC to get DCB
what is the answer to x+2y=2 and
3x+4y=-4
Answer:
x = − 8 and y = 5 or (-8, 5)
Step-by-step explanation:
please draw out the rectangular prism parts
PLEASE HELP
Answer:
280
Step-by-step explanation:
3
Find the value of a
in the equation,(3+4√3)(2-a√3)=-18+2√3
Given:
The equation is:
[tex]\left(3+4\sqrt{3}\right)\left(2-a\sqrt{3}\right)=-18+2\sqrt{3}[/tex]
To find:
The value of a.
Solution:
We have,
[tex]\left(3+4\sqrt{3}\right)\left(2-a\sqrt{3}\right)=-18+2\sqrt{3}[/tex]
On simplification, we get
[tex](3)(2)+(4\sqrt{3})(2)+(3)(-a\sqrt{3})+(4\sqrt{3})(-a\sqrt{3})=-18+2\sqrt{3}[/tex]
[tex]6+8\sqrt{3}-3a\sqrt{3}-4a(3)=-18+2\sqrt{3}[/tex]
[tex]6+8\sqrt{3}-3a\sqrt{3}-12a=-18+2\sqrt{3}[/tex]
[tex](6-12a)+(8-3a)\sqrt{3}=-18+2\sqrt{3}[/tex]
On comparing both sides, we get
[tex]6-12a=-18[/tex]
[tex]-12a=-18-6[/tex]
[tex]a=\dfrac{-24}{-12}[/tex]
[tex]a=2[/tex]
And,
[tex]8-3a=2[/tex]
[tex]-3a=2-8[/tex]
[tex]a=\dfrac{-6}{-3}[/tex]
[tex]a=2[/tex]
Therefore, the value of a is 2.
Plz help me well mark brainliest if correct.....????
Answer:
The answer would be C. 31
Step-by-step explanation:
Answer:
Hello There!!
Step-by-step explanation:
15 Girls like fantasy books and 16 boys like fantasy books so in total the students that like fantasy books are 31.
hope this helps,have a great day!!
~Pinky~
4 When Janelle was born, her grandmother put $200 into a college savings account for her.
Each month, her grandmother adds $50 to the account. Which inequality can be used to find
m, the number of months it will take for Janelle's savings account to have more than $1,250
in savings?
A 200m + 50 > 1,250
B 200 + 50m > 1,250
C 200 + 50m < 1,250
D 200m + 50 < 1,250
Answer:
B
Step-by-step explanation:
200+50m >1250
This means that for every month her grandmother gives 50 for an unknown amount of months along with the first 200 dollars.
The greater than 1250 shows that until she is greater than 1250 she'll keep getting money
please help me (no links or you are reported)
Answer:
whats the qestion??
Step-by-step explanation:
What is the solution to the inequality below?
√x>5
O A. No solutions
O B. O< x< 25
O C. x> 25
O D. x>10
Answer:
Quadratic Equations
A quadratic equation is one of the form ax2 + bx + c = 0, where a, b, and c are numbers, and a is not equal to 0.
Factoring
This approach to solving equations is based on the fact that if the product of two quantities is zero, then at least one of the quantities must be zero. In other words, if a*b = 0, then either a = 0, or b = 0, or both. For more on factoring polynomials, see the review section P.3 (p.26) of the text.
Example 1.
2x2 - 5x - 12 = 0.
(2x + 3)(x - 4) = 0.
2x + 3 = 0 or x - 4 = 0.
x = -3/2, or x = 4.
R.
A circle has a diameter of 6 inches.
Show your work to find the following (use
3.14 for pi):
A) Area of the circle
B) Circumference of the circle
FIND THE VALUES FOR ANGLES A, B, C,
CuOUL/CYPLAIN YOUR
Answer: A IS CORRECT
Step-by-step explanation:
question in pictures
Answer:
V = 252 m³
Step-by-step explanation:
Formula for volume of a triangular prism = base area × height of prism
We are given the height (H) of the prism = 9 m
Let's find the base area using the figure of the base that is shown above with the dimensions:
Base area = ½*bh
b = 14 m
h = 4 m
Base area = ½*14*4
= 28 m²
✅Volume of the triangular prism = 28 × 9
= 252 m³