A building meets the ground at a right angle. The top of a 10-foot ladder is placed against the bottom edge of a window in the building, and the base of the ladder is placed 6 feet from where the building meets the ground. Draw diagram that represents this situation. How far up from the ground is the bottom edge of the window?
Answers
Answer:
8 ft
Step-by-step explanation:
Use pythagorean theorem. [tex]a^{2}+b^{2}=c^{2}[/tex]. Put 10 and 6 into the equation as b and c.
[tex]a^{2}+6^{2}=10^{2}[/tex]
[tex]a^{2} =100-36\\a^{2}=64\\a=8[/tex]
Therefore, the answer is 8ft.
A diagram is attached. Sorry it's kinda messy.
Pythagoras' theorem, is a basic relationship between the three sides of a right triangle in Euclidean geometry. The height of the window from the ground or the base of the building is 8 feet.
What is Pythagoras theorem?The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between the three sides of a right triangle in Euclidean geometry. The size of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides, according to this rule.
Given the length of the ladder is 10 feet, while the distance between the base of the ladder and the building is 6 feet. Therefore, the height of the window from the base is,
(Length of the ladder)² = (Length between the two)² + (Height)²
(10 feet)² = (6 feet)² + (Height)²
(Height)² = 100 - 36
Height = 8 feet
hence, the height of the window from the ground or the base of the building is 8 feet.
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Related Questions
What’s the slope for this graphed?
A.1/2
B.-2
C.2
D.-3
Answers
Answer:
the answer is just 2
Step-by-step explanation:
start at the -3 and move right 3 and up 6 this is a inclined line so the answer will be positive the fraction put the numbers into a rise over run fraction which will be 6/3 which will reduce to 2/1 which is 2.
-----------------> 10x - 3 - 2x = 4
Answers
Answer:
[tex]x=\frac{7}{8}[/tex]
Step-by-step explanation:
[tex]10x-3-2x=4[/tex]
First, collect and rearrange the like terms.
[tex]10x-3-2x=4[/tex]
[tex]8x-3=4[/tex]
[tex]8x=4+3[/tex]
Then, solve the equation:
[tex]8x=4+3[/tex]
[tex]8x=7[/tex]
[tex]x=\frac{7}{8}[/tex]
So, the answer is [tex]x=\frac{7}{8}[/tex]. Hope my solution and explanation can help you. Thank you!
If you still cannot get the point, you can ask me anytime.
Answer:
x=7/8
Step-by-step explanation:
10x-3-2x=4
collect like term
8x-3=4
move constant to the right-hand side and change its sign
8x-3=4 into 8x=4+3
add up the number : 8x=4+3
8x=7 divide both sides of the equation by 8
x = 7/8
Help needed urgently explain how to do for each and everyone, please
Answers
Answer:
1) a0.1 = 1/10
b).0.64 = 64/ 100 = 16/25
2).a0.7841 = 7841 / 10,000
b).0.67 = 67/100
3). a0.53 = 53/100
b).0.26 = 26/100 = 13/50
4). a0.6 = 6/10 = 3/5
b.0.42 = 42/100 = 21/50
Hope this helps you
Graph the image of this figure after a dilation with a scale factor of 2 centered at (2, 2).
Answers
Answer:
(-6,6), (0,12), (4,8)
Step-by-step explanation:
To dilate an object, we need to multiply the x and y values by the given scale factor.
In this case the scale factor is 2 --> 2(x, y)
Before-> After dilation
2(-3,3) = (-6,6)
2(0,6) = (0,12)
2(2,4) = (4,8)
Please leave a 'thanks' if this helps!
You spend 1/5 of your income on car payment. You spend 3/8 of the remainder of your income on rent. What fraction of income is spent on rent?
Answers
Answer:
3/10
Step-by-step explanation:
1/5 of total income - spent on car
remainder income = 4/5
3/8 of remainder = 3/8 ×4/5 = 3/10(of total income spent on rent)
the word "of" means you can find it by multiplication
e.g. 2 of 1/2 means 2 × 1/2 which is 1
Write ln (4∕9) in terms of ln 2 and ln 3. Question 13 options: A) 3(ln 2 – ln 3) B) 2ln 2 – 2ln 3 C) 4ln 2 – 4ln 3 D) ln2 2 – 4ln 3
Answers
Answer:
The answer is option B
Step-by-step explanation:
2ln 2 - 2ln3
= ln ( 2²/3²)
= ln (4/9)
Hope this helps you
Answer:
B) 2ln 2 – 2ln 3
Step-by-step explanation:
hi there plz help me
Answers
Answer:
for every 3 tomato plants there will be 1 squash plants
Step-by-step explanation:
9 divided by 3 = 3. That will find the tomatoes
then you have to divide all the other plants by 3. Squash will be the only one with 1 plant per 3 tomato plants.
The answer is B
Answer:
B. Squash
Step-by-step explanation:
There are 9 tomato plants and there are 3 squash plants.
9 ÷ 3 = 3
3 tomato plants = 1 squash plants
3 × 3 = 1 × 3
9 = 3
9 tomato plants = 3 squash plants
Mark scored an 89 on his first
test, an 85 on his second test, a
95 on his third test, and an 83 on
his fourth test. What is Mark's
average test score for all 4 tests?
Answers
Answer:
88
Step-by-step explanation:
89+85+95+83= 352,
352/4 = 88
which equation is correct?
arccsc(x)=1/cos(x)
Answers
Answer:
arccsc(x)=1/cos(x)
Step-by-step explanation:
Answer:
the answer to your question is D
Step-by-step explanation:
Krista was assigned a homework problem that stated there were 45 stamps purchased for $18.75. Some stamps were 40 cents, and some stamps were 55 cents. To solve this problem, she wrote the system of equations that is shown below. 0.40 x + y = 45. x + 0.55 y = 18.75. Which explains the error that Krista made? Krista put 0.40 in the first equation meant for the number of stamps. Krista put 0.55 in the second equation meant for the value of stamps. Krista did not use the correct decimal to represent the total cost of the stamps. Krista mistakenly put 45 in the first equation when it should have been in the second equation.
Answers
Answer:
Option A.
Step-by-step explanation:
there were 45 stamps purchased for $18.75. Some stamps were 40 cents, and some stamps were 55 cents.
Let x and y be the number of stamps of 40 cents and 55 cents respectively.
Total number of stamps is 45. So
[tex]x+y=45[/tex]
Total cost of stamps is $18.75. So
[tex]0.40x+0.55y=18.75[/tex]
But Krista wrote the system of equations as
[tex]0.40x+y=45[/tex]
[tex]x+0.55y=18.75[/tex]
Krista put 0.40 in the first equation meant for the number of stamps.
Krista did not write 0.40 in the second equation meant for the value of stamps.
Therefore, the correct option is A.
Answer:
The answer is A
Step-by-step explanation:
TOOK THE TEST!
Find the.equation of the line through point (-4,1) and parallel to y=-1/2x -2
Answers
Answer: y = -1/2x -1
Step-by-step explanation: since the new line is parallel to the given line the slope of both the lines world be same. Therefore putting the new values in the equation
y-y1=m(x-x1)
y-1=-1/2(x+4)
y-1=-1/2x -2
y=-1/2x-1
Please hurry!!!
The fraction bars represent which equation?
A fraction bar is labeled 1. Underneath the bar, 4 boxes are labeled 1/4. Underneath the 4 boxes, boxes are labeled 1/8. 6 of those boxes are circled.
A. 1/4 ÷ 1/8 = 6
B. 3/4 ÷ 1/8 = 6/8
C. 1/4 ÷ 1/8 = 6/8
D. 3/4 ÷ 1/8 = 6
Answers
Answer:
Answer- 3/4 divided by 1/8 = 6/8
Which of the following functions represent exponential growth? f(x)=.0001(1.77)^x f(x)=2(1.5)^x/2 f(x)=5(0.5)^-x f(t)=5e^-t
Answers
Answer:
Hello There. ☆~\《`°---_●£●__---`°》\~☆
An exponential growth function is represented by
f(x)=a(b)^{x},a>0,b>1.
The given functions can be written as,
A)f(x)=.001(1.77)^x,0.001>0,1.77>1
B)f(x)=2(1.5)^{x/2}=2(\sqrt{1.5} )^x,2>0,\sqrt{1.5} >1
C)f(x)=5(0.5)^{-x}=5(2)^x,5>0,2>1
D) f(t)=5e^{-t}=5(\frac{1}{e} )^x,5>0,1/e.
So the function f(t)=5e^{-t}=5(\frac{1}{e} )^x,5>0,1/e violates the conditions for an exponential growth function. It is an exponential decay function.
The correct choices are (A), (B), (C).
Hope It Helps!~ ♡
ItsNobody~ ☆
The functions that represent exponential growth are choices (A), (B), and (C). The correct option is A, B, and C.
What is exponential growth?Exponential growth is the process of gradual increase of quantity over time.
An exponential growth function is represented by
[tex]\rm f(x)=a(b)^{x}[/tex], a>0,b>1
The given functions can be written as,
A)[tex]f(x) = .001(1.77)^x[/tex], 0.001>0,1.77>1
B) [tex]f(x) = 2(1.5)^{x/2} = 2(\sqrt{1.5} )^x,[/tex] 2>0, [tex]\sqrt{1.5}[/tex] >1
C)[tex]f(x) = 5(0.5)^{-x}=5(2)^x[/tex], 5>0, 2>1
D) [tex]f(t) = 5e^{-t}=5(\frac{1}{e} )^x[/tex], 5>0, 1/e.
So, the function [tex]f(t)=5e^{-t}=5(\frac{1}{e} )^x,5 > 0,1/e[/tex] violates the conditions for an exponential growth function. It is an exponential decay function.
The correct choices are (A), (B), and (C).
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Solve for x: 4x - 2 > 6x + 8. (5 points)
x<-5
x>5
x<5
x>-5
Answers
Answer:
x<-5 is the correct answer
Answer:
x<-5 is the answer
Step-by-step explanation:
The formula for any geometric sequence is an = a1 · rn - 1, where an represents the value of the nth term, a1 represents the value of the first term, r represents the common ratio, and n represents the term number. What is the formula for the sequence 2, -6, 18, -54, ...? an = 2 · 3n - 1 an = 2 · (-3)n - 1 an = 3 · 2n - 1 an = -3 · 2n - 1
Answers
Answer:
The second choice
Step-by-step explanation:
So first we would plug in the first term which is 2 so we would get [tex]an=2[/tex] times [tex]rn-1[/tex] so next we would see that the common ration is -3 since every time the number is being multiplied by -3. so then our equation would be [tex]an= 2[/tex] times [tex]-3n-1[/tex]. Now we would just find the choice that matches and it would be the second choice.
Answer:
option 2
Step-by-step explanation:
First term [tex]a_{1} = 2\\[/tex]
common ratio = r = second term ÷ first term
= -6 ÷2 = -4
Plug in the values of [tex]a_{1}[/tex] & r in the formula
[tex]a_{n} = a_{1}*r^{n-1}\\\\\\a_{n}=2 * (-3)^{n-1}[/tex]
What is the range of the function for the given domain? y = 2x − 5 D: {-2, 0, 2, 4}
Answers
Answer:
Range of Function : { - 9, - 5, - 1, 4 }
Step-by-step explanation:
We know that y = 2x - 5 provided the domain ( x - values ) { - 2, 0, 2, 4 }. Let us substitute each element in this set of domain as x in the equation "y = 2x - 5" as to solve for the y - values, otherwise known as the range of the function.
{ - 2, 0, 2, 4 }
y = 2( - 2 ) - 5 = - 9,
y = 2( 0 ) - 5 = - 5,
y = 2( 2 ) - 5 = - 1,
y = 2( 4 ) - 5 = 4
We have the set of y - values as { - 9, - 5, - 1, 4 }. This is the range of our function.
David is making rice for his guests based on a recipe that requires rice, water, and a special blend of spice, where the rice-to-spice ratio is 15:115:115, colon, 1. He currently has 404040 grams of the spice blend, and he can go buy more if necessary. He wants to make 101010 servings, where each serving has 757575 grams of rice. Overall, David spends 4.504.504, point, 50 dollars on rice. How many servings can David make with the current amount of spice he has
Answers
Answer:
8 servings
Step-by-step explanation:
At the ratio of 15:1, the 75 grams of rice in one serving will require 75/15 = 5 g of spice. David's inventory of 40 g of spice is enough for ...
40 g/(5 g/serving) = 8 servings
Only 8 servings can be made with the available spice.
Rice to spice ratio = 15 : 1
Number of grams per serving = 75 grams
Grams of spice available = 40 grams
Grams of rice, r required for available spice :
15 grams of rice = 1 gram of spice
r grams of rice = 40 grams of spice
Cross multiply :
r = (40 × 15)
r = 600 grams
The grams of rice which can go with the available spice :
Number of servings = grams of rice / grams per serving
Number of serving = 600 grams / 75 grams
Number of grams per serving = 8
Hence, The number of servings which can be made with the available spice is 8 servings
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Experiment consist of drawing one card from a standard 52 card deck. What is the probability of drawing a black 10?
Answers
Answer:
2/52 or 1/26 or 0.0385 or 3.85%
Step-by-step explanation:
There are 2 black 10's in a standard 52 card deck.
2/52 or 1/26 or 0.0385 or 3.85% (depending on how your teacher wants it expressed)
out of 40 coins, 16 are dimes. half of the remaining coins are quarters and the rest are pennies and nickles. these are 2 nickles for every penny. how many pennies are there?
Answers
===========================================
Work Shown:
40 coins total
16 are dimes
40-16 = 24 coins are not dimes
Half of this is 24*(1/2) = 12 which are quarters. The other half (12) are pennies and nickels
n = number of nickels
p = number of pennies
This means n+p = 12 so that we have 12 pennies and nickels combined.
"There are 2 nickels for every penny", so we can write n = 2p. If p = 1, then n = 2. If p = 2, then n = 4, etc. Whatever p is, we double it to get n.
So,
n+p = 12
2p+p = 12
3p = 12
p = 12/3
p = 4, we have 4 pennies
n = 2p
n = 2*4
n = 8 and 8 nickels
-----------------------------------------
Here are all the coin counts
16 dimes12 quarters8 nickels4 pennies16+12+8+4 = 40 coins total
Answer:
Option (B) is correct, 4 pennies.
Jan is solving the equation shown below. Which of the following represents the solution to Jan’s equation?
a. x = 3
b. x = -3
c. x = 27
d. x = -33
Answers
Answer:
C. X=27
Step-by-step explanation:
-11+1/3x+9=7
1/3x=7+11-9
1/3x=9
x=9x3
x=27
Given the lengths of two sides of a triangle, find the range for the length of the third side. (Range means find between which two numbers the length of the third side must fall.) Write an inequality. 22 and 15
Answers
Answer:
7 < (third side length) < 37
Step-by-step explanation:
Add these two side lengths together. We get 37. Unless the 3rd side is LESS than 37, we cannot form a triangle.
Next, subtract 15 from 22, obtaining 7. The 3rd side has to be GREATER than 7 in order for the sides 7+, 15 and 22 to form a triangle.
7 < (third side length) < 37
Answer:
26.63 ??
Step-by-step explanation:
I think you use pythagorean theorum to solve.
do 22^2 and 15^2 and get 709.1569
sqrt of that is 26.63
The coordinates of rhombus ABCD are A(–4, –2), B(–2, 6), C(6, 8), and D(4, 0). What is the area of the rhombus? Round to the nearest whole number, if necessary.
Answers
Answer:
The rhombus ABCD has an area of 22 square units.
Step-by-step explanation:
The coordinates of rhombus ABCD are shown in the image attached below. The area of the rhombus can be found in terms of their diagonals, which are now calculated by Pythagorean Theorem:
[tex]AC = \sqrt{[6-(-4)]^{2}+[8-(-4)]^{2}}[/tex]
[tex]AC = 15.620[/tex]
[tex]BD = \sqrt{(4-6)^{2}+[0-(-2)]^{2}}[/tex]
[tex]BD \approx 2.828[/tex]
The area of the rhombus is: ([tex]AC = 15.620[/tex] and [tex]BD \approx 2.828[/tex])
[tex]A = \frac{AC\cdot BD}{2}[/tex]
[tex]A = \frac{(15.620)\cdot (2.828)}{2}[/tex]
[tex]A = 22.087[/tex]
The rhombus ABCD has an area of 22 square units.
Answer:
22 units
Step-by-step explanation:
Find the surface area of this rectangular prism. Be sure to include the correct unit in your answer.
Answers
Answer:
72cm2 (2 means squared)
Step-by-step explanation:
you add all the sides once you get the are for each side. To do that you multiply l(w)
Answer:
The surface area of the rectangular prism is [tex]136cm^{2}[/tex]
Step-by-step explanation:
What is surface area?
Surface area is the amount of space covering the outside of a three-dimensional shape.
What is rectangular prism?
A rectangular prism can be defined as a 3-dimensional solid shape which has six faces that are rectangles. A rectangular prism is also a cuboid.
Given, length l= 7cm
breadth b=6cm
height h=2cm
The surface area of the cuboid is,
=2(lb+bh+lh)
=2(7*6+6*2+2*7)
=2(42+12+14)
=2*68
=136 [tex]cm^{2}[/tex]
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[tex]solve for x if 4 x+1-9(2 ^{2} +2=0[/tex]
Answers
Answer:
mark my answer as the brainliest
Step-by-step explanation:
x = 53/4
Answer:
4×+1-9 (2^)+2)=0
4×+1-9 (4+2)=0
4×+1(-36-18)=0
4×+1 (-54)=0
4×-54=0
4×=54
×=54÷4
×=13.5
Suppose that f(x)=4x+5. What is f^-1 (f^-1(9)) ?
Answers
Step-by-step explanation:
the inverse of the inverse of a function is the function itself
It's like going and coming back
f^-1(f^(-1)9) = f(9) f(9) = 4*9+5f(9) = 36+5 f(9) = 41Answer:
9
Step-by-step explanation:
The inverse of the inverse is the input
f^-1 (f^-1(9)) = 9
As a proof
f(x) = 4x+5
y = 4x+5
Exchange x and y
x = 4y+5
Solve for y
(x+5) = 4y
(x+5)/4 = y
f^-1 (x) = ( x-5)/4
Then find the inverse of this function
y = ( x-5) /4
Exchange x and y
x = (y-5)/4
4x = y-5
4x+5 = y
Which gives us the original function back
f^-1( input) = 4x+5
Using the value given
f^-1 (9) = ( 9-5)/4=4/4 =1
Using the 1 from the previous part as the input
f^-1( 1) = 4*1+5 = 4+5 = 9
PLEASE HELPPPP Wilson is thinking about buying a house for $249,000. The table below shows the projected value of two different houses for three years. Number of years 1 2 3 House 1 (value in dollars) 253,980 259,059.60 264,240.79 House 2 (value in dollars) 256,000 263,000 270,000 Part A: What type of function, linear or exponential, can be used to describe the value of each of the houses after a fixed number of years? Explain your answer. (2 points) Part B: Write one function for each house to describe the value of the house f(x), in dollars, after x years. (4 points) Part C: Wilson wants to purchase a house that would have the greatest value in 45 years. Will there be any significant difference in the value of either house after 45 years? Explain your answer, and show the value of each house after 45 years. (4 points) (10 points)
Answers
Part A
House 1: we make exponential can be used to describe the
value of house 1. After 1 year, 253480 = 249000 x 1.02
After 2 years, 259059.6 = 25398×1.02. After 3 years 264240.79 =259059.60x1.02.
House 1: we make linear. 256000=249000 + 1000.263000 = 256000 +7000.270000=263000 + 1000.
Part B.
House 1: f(x)=249000 1.02x [genometic sequence]
House 2: f(X) = 24900 + 1000x [arithmetic progression]
Part C
House 1: f(45)=249000×1.02 45 = 607025.697
House 2: f(45) = 249000 +7000x45 = 564000
"House 1 is an arithmetic sequence that increases in price each year while House 2 is an arithmetic sequence that only increases by 1000 per year.
What are word problems in mathematics?
In computational mathematics, a word problem is a problem of deciding whether two given expressions are equivalent with respect to a set of rewriting identities. A prototypical example is the word problem for groups, but there are many other instances as well.
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In the circle below, O is the center and mĞ= 128° What is the measure of angle HIG?
Answers
Answer:
HIG=28°
Step-by-step explanation:
HI is a diameter therefore it's measure is 180°
HI-IG=HG
180-128=HG
52°=HG
HIG=1/2HG
HIG=1/2(56°)
HIG=28°
please solve these questions for me. i am having a difficult time understanding.
Answers
Answer:
1) AD=BC(corresponding parts of congruent triangles)
2)The value of x and y are 65 ° and 77.5° respectively
Step-by-step explanation:
1)
Given : AD||BC
AC bisects BD
So, AE=EC and BE=ED
We need to prove AD = BC
In ΔAED and ΔBEC
AE=EC (Given)
[tex]\angle AED = \angel BEC[/tex] ( Vertically opposite angles)
BE=ED (Given)
So, ΔAED ≅ ΔBEC (By SAS)
So, AD=BC(corresponding parts of congruent triangles)
Hence Proved
2)
Refer the attached figure
[tex]\angle ABC = 90^{\circ}[/tex]
In ΔDBC
BC=DC (Given)
So,[tex]\angle CDB=\angle DBC[/tex](Opposite angles of equal sides are equal)
So,[tex]\angle CDB=\angle DBC=x[/tex]
So,[tex]\angle CDB+\angle DBC+\angle BCD = 180^{\circ}[/tex] (Angle sum property)
x+x+50=180
2x+50=180
2x=130
x=65
So,[tex]\angle CDB=\angle DBC=x = 65^{\circ}[/tex]
Now,
[tex]\angle ABC = 90^{\circ}\\\angle ABC=\angle ABD+\angle DBC=\angle ABD+x=90[/tex]
So,[tex]\angle ABD=90-x=90-65=25^{\circ}[/tex]
In ΔABD
AB = BD (Given)
So,[tex]\angle BAD=\angle BDA[/tex](Opposite angles of equal sides are equal)
So,[tex]\angle BAD=\angle BDA=y[/tex]
So,[tex]\angle BAD+\angle BDA+\angle ABD = 180^{\circ}[/tex](Angle Sum property)
y+y+25=180
2y=180-25
2y=155
y=77.5
So, The value of x and y are 65 ° and 77.5° respectively
pls asap its not 128......In how many ways can you put seven marbles in different colors into four jars? Note that the jars may be empty.
Answers
Answer:
hope it helps
this is my best
please tell me if I'm wrong
ordered pair please help
Answers
Answer:
PLS PLS DO MARK MY ANSWER AS THE BRAINLIEST......
Step-by-step explanation:
P - ( 2, -3) - 4TH QUADRANT
Q - (-3,-2) - 3RD QUADRANT
R - (1,3) - 1ST QUADRANT
S -(-2,2) - 2ND QUADRANT
Answer:
P - ( 2, -3) - 4TH QUADRANT
Q - (-3,-2) - 3RD QUADRANT
R - (1,3) - 1ST QUADRANT
S -(-2,2) - 2ND QUADRANT