A 45 foot ladder is set against the side of a house so that it reaches up 27 feet. If Nicole grabs the ladder at its base and pulls it 4 feet farther from the house, how far up the side of the house will the ladder reach now? (The answer is not 23 ft.) Round to the nearest tenth of a foot.
The ladder will reach a height of 20.6 feet
The given parameters are:
Length = 45-footHeight = 27 feetStart by calculating how far (d) the ladder is, from the bottom of the house using the following Pythagoras theorem
[tex]45^2 = 27^2 +d^2[/tex]
Collect like terms
[tex]d^2= 45^2 -27^2[/tex]
[tex]d^2= 1296[/tex]
Take square roots of both sides
[tex]d= 36[/tex]
When the ladder is moved 4 feet farther, the new distance becomes
[tex]d= 36+4[/tex]
[tex]d= 40[/tex]
The new height (h) of the ladder is then calculated using the following Pythagoras theorem
[tex]45^2=40^2 + h^2[/tex]
Collect like terms
[tex]h^2 = 45^2-40^2[/tex]
[tex]h^2 = 425[/tex]
Take the square roots of both sides
[tex]h = 20.6[/tex]
Hence, the ladder will reach a height of 20.6 feet
Read more about Pythagoras theorem at:
https://brainly.com/question/654982
the difference of two numbers is 13/24. if 11/12 of the reciprocal of one number is equal to 5/9 of the reciprocal of the other, what are the 2 numbers?
Answer:
The two numbers are 11/8 and 5/6
Step-by-step explanation:
Let the unknown numbers be x and y
Given that the difference of two numbers is 13/24
x - y = 13/24
and that 11/12 of the reciprocal of one number is equal to 5/9 of the reciprocal of the other
11/12 * 1/x = 5/9 * 1/y
11/12x = 5/9y
cross multiply
12x * 5 = 11* 9y
60x = 99y
x = 99y/60
= 33y/20
substitute into x - y = 13/24
33y/20 - y = 13/24
13y/20 = 13/24
24y = 20
y = 20/24
= 5/6
x = 33y/20
= 33 *5/20*6
= 11/8
What is the value of x?
Answer:
67.5
Step-by-step explanation:
The sum of the interior angles is 540, therefore
540 = 90 + 4y
540 - 90 = 4y
450 = 4y
450 / 4 = y
112.5 = y
X and Y together equal 180, therefore
180 = x + 112.5
180 - 112.5 = x
67.5 = x
can anyone help with this? find st and rt
Answer:
ST= 5.2
RT= 23.6
Step-by-step explanation:
Answer:
ST= 5.2
RT= 23.6
Step-by-step explanation:
Please help me on this problem, im struggling
Answer:
a
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
in fact if we look at the graph we can see that sausages are 7.5 % and mushrooms 5%, while in the table this datas are inverted.
Question and choices are in the photo please explain the answer
Step-by-step explanation:
but sorry i can't get the answer of (2x-1) =3 (x+5) because the answer of this came -16
pls pls pls help don't ignore imma fail
Answer:
6 as b
7 as a
Step-by-step explanation:
if indeed the scale is 3 to 1, this is correct! the answer is B
1. Find the numbers a, b, c such that
2x4 + 2x3 +5x2 + 3x + 3 = (x2 + x +1)(ax2+bx+c)
for all values of x.
Answer:
a = 2
b = 0
c = 3
Step-by-step explanation:
if I understand correctly the problem should look like
2x⁴ + 2x³ + 5x² + 3x + 3 = (x² + x + 1)(ax² + bx + c)
let's calculate the right side
ax⁴ + ax³ + ax² + bx³ + bx² + bx + cx² + cx + c
as there is only one term of x⁴, we know a = 2
as there is only one term without any x, we know c = 3
now we get
2x⁴ + 2x³ + 2x² + bx³ + bx² + bx + 3x² + 3x + 3
remember, that is equal to
2x⁴ + 2x³ + 5x² + 3x + 3
after subtracting 2x⁴ and 3 from both sides we get
2x³ + 5x² + 3x = 2x³ + 2x² + bx³ + bx² + bx + 3x² + 3x
we subtract 2x³ and 3x from both sides and get
5x² = 2x² + bx³ + bx² + bx + 3x² = 5x² + bx³ + bx² + bx
we subtract 5x² from both sides and get
0 = bx³ + bx² + bx
=> b must be 0 to make this true for all values of x
work out the m and c for the line: y=x-7
Answer:
Step-by-step explanation:
Compare the given y = x - 7 to the general slope-intercept formula
y = mx + b
Here the slope is 1 and the y-intercept, b, is -7.
Answer:
Step-by-step explanation:
Slope - y intercept form : y = mx +c
y = x - 7
m = 1
c = -7
Logx-1(343)=3 solve for base x
Answer:
should be 8 !
Step-by-step explanation:
it just is
What does b stand for in this equation?
3b=12
A 1
B 2
C 3
D 4
Answer:
4
Step-by-step explanation:
3b=12
Divide each side by 3
3b/3 =12/3
b =4
Answer:
D. 4Step-by-step explanation:
Given,
3b = 12
=> b = 12 ÷ 3
=> b = 4 (Ans)
What is the length of Line segment A C?
3 ft
4 ft
18 ft
12 ft
On edge unity pls help
Answer:
4
Step-by-step explanation:
because its 4
The length of Line segment AC is 12ft.
Similar trianglesThe given triangle ABC is similar to triangle BMN
The length of AM = BM = 4ft
The length AB = BM + AM = 4 ft + 4ft = 8ft
The length of Line segment AC is calculated by using similar triangle proportions as follows;
[tex]\frac{AB}{BM} = \frac{AC}{MN} \\\\\frac{8}{4} = \frac{AC}{6} \\\\2 = \frac{AC}{6}\\\\AC = 2(6)\\\\AC = 12 \ ft[/tex]
Learn more about similar triangles here: https://brainly.com/question/11899908
first answer gets most brainley
Answer:
What are we supposed to do on this
Step-by-step explanation:
Answer: the dilated point will be 2 units at the right of P, and 3 units above P.
Step-by-step explanation:
Jenna sells apples and pears. If 20 apples and 60 pears re sold every hour, there will be 80 pears when all the apples are sold. If 60 apples and 20 pears are sold every hour, there will be 400 pears when all the apples are sold. How many pears are there at the stall?
Answer:
There are 1,360 pears.
Step-by-step explanation:
Suppose that there are P pears and A apples.
We know that:
"If 20 apples and 60 pears are sold every hour, there will be 80 pears when all the apples are sold."
Suppose that all of these are sold after N hours, then:
20*N = A
80*N = P - 80
We also know that:
"if 60 apples and 20 pears are sold every hour, there will be 400 pears when all the apples are sold."
60*N = A
20*N = P - 400
Then we have four equations:
20*N = A
80*N = P - 80
60*N = A
20*N = P - 400
From the first one and the second one, we get:
20*N = A = 20*N = P - 400
A = P - 400
Now we have 3 equations:
80*N = P - 80
60*N = A
A = P - 400
Now we can just replace the third equation into the second one, then we get:
60*N = A = P - 400
Now we have two equations:
80*N = P - 80
60*N = P - 400
Now, remember that we want to find the number of pears, so we want to find the value of P.
To do it, we can take the quotient of the two equations, so we get:
(80*N)/(60*N) = (P - 80)/(P - 400)
8/6 = (P - 80)/(P - 400)
Now we can solve this for P
(8/6)*(P - 400) = P - 80
(8/6)*P - (8/6)*400 = P - 80
(8/6)*P - P = (8/6)*400 - 80
(2/6)*P = (8/6)*400 - 80
P = (6/2)*( (8/6)*400 - 80 )
P = 3*( (8/6)*400 - 80 ) = 1,360
There are 1,360 pears.
Write as a single fraction in its simplest form.
how do you do this?
Answer:
(-12x - 25) / (x + 3) (x - 5)
Step-by-step explanation:
1 - 2x/(x+3) + (x+3)/(x - 5)
= {(x + 3)(x - 5) - 2x(x - 5) + (x + 3)(x - 3)} / (x + 3) (x - 5)
= {(x² -5x + 3x - 16) - (2x² + 10x) + (x² - 3x + 3x - 9)} / (x + 3) (x - 5)
= x² - 2x - 16 - 2x² - 10x + x² - 9 / (x + 3) (x - 5)
= x² - 2x² + x² - 2x - 10x - 16 - 9 / (x + 3) (x - 5)
= (-12x - 25) / (x + 3) (x - 5)
Please help me with this question...
Answer:
my answer is in this picture. sorry about my presentation and English
What is the equation of the line
What additional information is needed to prove the triangles congruent by SSS
Answer:
Angle a = Angle D
Answer:
A: Angle A Angle D
Step-by-step explanation:
Berto has $12 to put gas in his car. If gas costs $3.75 per gallon, which ordered pair relating number of gallons of gas, x, to the total cost of the gas, y, includes the greatest amount of gas Berto can buy?
(__,__ )
Answer:
If gas costs $3.75 per gallon and Berto has $12, then he can purchase 12/3.75 gallons. This is approximately 3.2 gallons. So the coordinate on this line would be (3.2, 12).
Actually... It's from web
I need it fast plss help someone help
56 over 15
hope this help yoooooooooooooooooooo
Answer:
22/15
Step-by-step explanation:
(1/3 + 2/5) x (2 - 1/2) ÷ 3/4
=(5/15 + 5/15) x (4/2 - 1/2) ÷ 3/4
=11/15 x 3/2 ÷ 3/4
=11/15 x 3/2 x 4/3
=22/15
Hope this helps! Have a nice day!
Evaluate the expression 4 to the power of 3 ÷ (7 − 3) × 2.
Answer:
5.0625 is 1.5 to the fourth power
Answer:
8
Step-by-step explanation:
4 to the power of 3 is 64.
64 ÷ (7 − 3) × 2
64 ÷ (4) × 2
64 ÷ 8
8
Your answer is 8.
I hope this helps, have a nice day.
Gianna draws a rectangle on a piece of grid paper. She wants to know the side length of each grid square. Which equation can Gianna use to find the side length, s , of one square.
Answer: the answer is 213.4
Stepby-step explanation:
First you multiply 10.8 and 19.8 then your done
Answer:
10.8 ÷ 6
1.8
Step-by-step explanation:
–6(2 + a) = –48 please answer
Answer:
a = 6
Step-by-step explanation:
–6(2 + a) = –48
Divide each side by -6
–6(2 + a) / -6 = –48/-6
2+a = 8
Subtract 2 from each side
2+a-2 = 8-2
a = 6
How many feet is it from goal line to goal line on a regulation football field
that is 100 yards long? It is measured in the
A. tens
B. thousands
C. millions
D. hundreds
Answer:
D. hundreds
Step-by-step explanation:
if a football field is 100 yards long then it is 300 feet long and that is in the hundreds
Write an equation that passes through the points (3, 6) and (1,-1)
Answer:
y = 7/2x - 9/2
Step-by-step explanation:
y2 - y1 / x2 - x1
-1 - 6 / 1 - 3
-7 / -2
7/2
y = 7/2x + b
-1 = 7/2(1) + b
-1 = 7/2 + b
-9/2 = b
Which is NOT a proposition
A. Marlon is eating his lunch
B. Will you be at school tomorrow.
C. The earth is rectangular
D. 10 + 5 = 15
Answer:the answer is b
Step-by-step explanation:reason being that the question will you be at school tmrw?cat be given a choice to say wether it’s true or false so Yh...I don’t know if that helped
Using laws of exponents,
The answer is :
- i
I hope this helps
Answer:
-i
Step-by-step explanation:
just did it on edg 2021
Write the number 10 000 000 as a power of 10.
Answer:
10⁷
Step-by-step explanation:
Just count the number of zero and raise the counted number of zero.
If the equation 2x2+bx+5=0 has no real solutions, which of the following must be true?
Answer:
There are no choices but in order to qudratic equation not to have real roots the discriminant must be negative.
d = b² - 2*2*5 = b² - 20If d < 0, we get:
b² - 20 < 0b² < 20b < |√20|- √20 < b < √20or
-2√5 < b < 2√5or
b = (-2√5, 2√5)15 cm
10 cm
o
10 cm
Diagram NOT accurately drawn
The diagram shows a sector of a circle, centre 0, radius 10 cm.
The arc length of the sector is 15 cm.
Calculate the area of the sector.
Answer:
221cm squre
Step-by-step explanation:
