Answer:
39 feet
Step-by-step explanation:
From the question;
let length of ladder =x feet
height of ladder will be=x-3 feet
ground distance of ladder bottom to building=15 feet
Applying Pythagorean relation
a²+b²=c²
where a=15 feet b=x-3 feet and c=x feet thus
x²-15²=(x-3)²
x²-225=x²-6x+9
collect like term
x²-x²-225-9=-6x
-234= -6x
x= 39 feet length of ladder
distance from ground to top of ladder= 39-3=36 feet
The length of the ladder is 39 feet.
Explanation:Let's denote the length of the ladder as x. According to the problem, the distance from the ground to the top of the ladder is 3 feetless than the length of the ladder. So, the height from the ground to the top of the ladder is x - 3 feet. The distance from the bottom of the ladder to the building is given as 15 feet. We can set up a right triangle where the ladder is the hypotenuse and solve for x using the Pythagorean Theorem:
x^2 = (x - 3)^2 + 15^2
Expanding and simplifying, we get:
x^2 = x^2 - 6x + 9 + 225
Combining like terms, we have:
0 = -6x + 234
Now, let's solve for x:
6x = 234
x = 39
Therefore, the length of the ladder is 39 feet.
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1+2-3-4+5+6-7-8+...-60
A) -60
B) -30
C) 0
D) 36
E) 60
Answer and explanation please!
Answer:
I'm not sure you put the right information for this one, because
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 36
so, to find the next number that equals 60, we have to subtract 60 to 36.
60 - 36 = 24
The answer to this question is zero 0
Please please help me I am struggling !
Solve 20/15 = n/18 for the unknown quantity n
Answer:
n = 24Step-by-step explanation:
[tex]\dfrac{20}{15}=\dfrac{n}{18}\qquad\text{cross multiply}\\\\15n=(20)(18)\\\\15n=360\qquad\text{divide both sides by 15}\\\\n=24[/tex]
What is the final amount if 1920 is increased by 5% followed by a further 15% increase? Give your answer rounded to 2 DP.
2318.4 is the correct wander
Work the following financial transactions. Your station charges $15.95 for a lubrication job. As a promotion you sell six coupons for lubrication jobs for $80. What percentage discount are you offering for customers who purchase the 6-coupon lube book? Discount (to the nearest tenth) = _____.
Answer:
16.4%
Step-by-step explanation:
We know that a station charges $15.95 for a lubrication job and as a promotion sell six coupons were sold for lubrication jobs for $80.
We are to find the percentage discount that was being offered on purchase of 6 coupon lube book.
Original price of 6 coupons = 6 × 15.95 = $95.7
Difference in prices = 95.7 - 80 = $15.7
Percentage discount = 15.7/95.7 = 16.4%
Answer:
16.4%
Step-by-step explanation:
59 =7r+3 what is the answer
Answer:
r = 8
Step-by-step explanation:
59 = 7r + 3
Switch sides:
7r + 3 = 59
Subtract 3 from both sides:
7r = 56
Divide both sides by 7:
r = 8
Answer:
r = 8
Step-by-step explanation:
59 = 7r+3
subtract both sides by 3
56 = 7r
divide both sides by 7
8 = r
Which expression is equivalent 219 X minus 6X +2 And why?
19x - 6x + 2
Two terms have an X in them, so you can combine them :
19x -6x = 13x
You now have 13x +2, which can be rewritten as 2 + 13x
The 3rd answer is correct.
Hey there!
The correct choice is C. 2 + 13x
Like the answer says, all you have to do is combine the x’s and rearrange: 13x +2 can be rearranged as 2 + 13x
Hope this helps you!
God bless ❤️
xXxGolferGirlxXx
What is the equation of the graphed function?
Enter your answer in the box.
f(x)=
F(x)=(x+1)^2 that’s the answer
Answer:
[tex]f(x)=(x+1)^2[/tex]
Step-by-step explanation:
We have been given graph of a function. We are asked to find the equation of the graphed function.
Upon looking at our given graph, we can see that the graph represents a parabola.
We know that vertex form of a parabola is: [tex]y=a(x-h)^2+k[/tex], where, (h,k) represents the vertex of parabola.
We can see that vertex of our given parabola is at point [tex](-1,0)[/tex], so substituting the coordinates of vertex of parabola, we will get:
[tex]y=a(x--1)^2+0[/tex]
[tex]y=a(x+1)^2[/tex]
Now we will find the value of a using coordinates of point (0,1) in above equation.
[tex]1=a(0+1)^2[/tex]
[tex]1=a(1)^2[/tex]
[tex]1=a*1[/tex]
[tex]1=a[/tex]
Therefore, the equation of our graphed function would be [tex]f(x)=(x+1)^2[/tex]
A triangle has side lengths measuring 20 cm, 5 cm, and n cm. Which describes the possible values of n? 5 < n < 15 5 < n < 20 15 < n < 20 15 < n < 25
Answer:
15 < n < 25
Step-by-step explanation:
According to the triangle inequality theorem, any two sides lengths' sum should be greater than the third side. This also implies that to find the possible length of the 3rd side given other two sides (let two given sides be x and y), we can say that the 3rd side length will be between x+y and x-y.
Hence, we can say that n should be between 20+5 and 20-5.
So, 20 - 5 < n < 20 + 5, which is
15 < n < 25
This is the correct answer.
Answer:
15 < n < 25 which on ed is D
Step-by-step explanation:
According to the triangle inequality theorem, any two sides lengths' sum should be greater than the third side. This also implies that to find the possible length of the 3rd side given other two sides (let two given sides be x and y), we can say that the 3rd side length will be between x+y and x-y.
What segments are parallel on the attached diagram?
Answer:
From the given figure we get,
DC║AB
Step-by-step explanation:
It is given that,
<DCB and <CBA are supplementary, that means
<DCB + <CBA = 180
If these two angles are on the same side of a traversal CB.
<DCB and CBA are same side interior angles.
CB is the traversal of AB and DC
Therefore we get DC║AB
The correct answer is DC║AB
Solve the equation, , using the quadratic formula.
Question 4 options:
x = -1 or
x = -1 or x = 2
x = 1 or
x = 1 or
Answer:
[tex]x=1\ or\ x=-\frac{1}{2}[/tex]
Step-by-step explanation:
To solve the given quadratic equation [tex]2x^2-x-1=0[/tex] you can apply the Quadratic formula, which is shown below:
[tex]x=\frac{-b\±\sqrt{b^2-4ac}}{2a}[/tex]
Where:
[tex]a=2\\b=-1\\c=-1[/tex]
Therefore, when you substitute values into the Quadratic formula shown above, you obtain the following solution:
[tex]x=\frac{-(-1)\±\sqrt{(-1)^2-4(2)(-1)}}{2*2}[/tex]
[tex]x=1\ or\ x=-\frac{1}{2}[/tex]
The dot plot below represents a set data. Which set of data does this represent?
Answer:
The correct answer would be (1, 3, 3, 4, 5, 6)
Step-by-step explanation:
The reason why it is this answer is because there is one X above 1, two X's above 3, one X above 4, one X above 5, and one X above six. Moving up in the numbers, depending on how many X's there are above each number, you can easily tell that the dot plot shows the data of 1, 3, 3, 4, 5, and 6.
Answer is D
Step-by-step explanation:
Write down each number there is a X on and you get the numbers for answer choice D
a triangle has side lengths of 11 cm, 60 cm, and 61 cm. which is the correct equation to verify whether the side lengths form a right triangle
PLEASE HELP
➷ Pythagoras' theorem:
a^2 + b^2 = c^2
'c' is the hypotenuse and also the longest length
Taking this into consideration, the correct option would be:
C) 11^2 + 60^2 = 61^2
✽➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
↬ ʜᴀɴɴᴀʜ ♡
Answer:
its c
Step-by-step explanation:
2(a-1) (a+6) Please Is important
Answer:
2a² + 10a - 12
Step-by-step explanation:
To expand 2(a - 1)(a + 6), first expand the parenthesis
= 2(a² + 6a - a - 6)
= 2(a² + 5a - 6) ← distribute the terms in the parenthesis by the 2 outside
= 2a² + 10a - 12
I need help with 11 please I will give 10 points
a. true
b. true
c. true
John shot a toy rocket into the air. Consider the graph below which shows the relationship between the height of the rocket from ground level and the time elapsed.
Which statement best interprets information provided by the graph?
A. The height of the rocket changes at a constant rate for the entire time.
B. The height of the rocket increases for some time and then decreases for some time.
C. The height of the rocket remains constant for some time.
D. The height of the rocket decreases for some time and then increases for some time.
The height from the ground increases from 4 to 26, then decreases from 26 to 0.
Why the others are wrong.
A. The height of the rocket changes at a constant rate for the entire time.
The graph is a curve. This means the rate is not constant. If it were constant, the graph would be linear - a straight line.
C. The height of the rocket remains constant for some time.
The graph is a curve. This means the rate is not constant. If it were constant, the graph would be linear - a straight line.
D. The height of the rocket decreases for some time and then increases for some time.
This implies the graph decreases first then increases. However, the rocket will increase, then decrease.
The students at the engineering conference ate more than 20 pizzas. The inequality x > 20 represents the situation. Which graph represents the inequality?
Answer:
The graph in the attached figure
Step-by-step explanation:
Let
x----> the number of pizzas
we know that
The inequality that represent the situation is
[tex]x>20[/tex]
The solution is all real numbers greater than 20
In a number line the solution is the shaded area to the right of the dashed line at x=20 (open circle)
see the attached figure
Answer:
A
Step-by-step explanation:
Hope this helps Bai! I did it on edg btw! <3
P and a are on points on the line 4x+2y=8. What are the coordinates?
Answer:
The answer is P(0,4) , Q(2,0)
Step-by-step explanation:
Points P and A are any coordinates where y = 4 - 2x. For example, P might be the point (1, 2).
Explanation:The given equation is 4x + 2y = 8. To find the coordinates of points P and A, we can rearrange and simplify the linear equation. Divide the whole equation by 2, we get 2x + y = 4, or y = 4 - 2x. Therefore, the line has the slope-intercept form of y = mx + b, where m is the slope and b is the y-intercept. This line passes through all points (x, y) where y = 4 - 2x. Therefore, P and A can be any points satisfying this equation. For example, if x = 1, then y = 2, so one possible coordinate is P(1, 2).
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Solve for m.t=mr^2/3
t = mr^2/3
Divide both sides by r^2/3
m = t / r^2/3
Answer:
[tex]\large\boxed{m=\dfrac{3t}{r^2}}[/tex]
Step-by-step explanation:
[tex]\dfrac{mr^2}{3}=t\qquad\text{multiply both sides by 3}\\\\mr^2=3t\qquad\text{divide both sides by}\ r^2\\\\m=\dfrac{3t}{r^2}[/tex]
so far she has saved $30, which is three-fifth of the total cost of game. How much does the game cost?
Answer:
$50
Step-by-step explanation:
3/5=30/x
x is the total cost of the game
You can see that 3×10 =30
So, 5×10 would be x.
Therefore, x equals to 50.
Please help in 23 & 24
Answer:
In order to answer 23, you have to include 22 in the picture. The answer to 24 is 3 times 11+6, and Kayla earns $351.
Step-by-step explanation:
Answer: $351
Step-by-step explanation:
f(x) = 3x + 6 g(x) = x - 2
(f · g)(x) = (3x + 6)(x - 2)
= 3x² - 6x + 6x - 12
= 3x² - 12
(f · g)(11) = 3(11)² - 12
= 3(121) - 12
= 363 - 12
= 351
NOTE: Q23 cannot be answered because the information from Q22 is needed.
70×40 I need to no 70×40 can you please help me??
Answer:
2800
Step-by-step explanation:
since 7 x 4 is 28 , 70 x 40 is 2800 because 70 is 7 x 10 and 40 is 4 x 10,
so 7 x 10 x 4 x 10 can be moved to get 7 x 4 x 10 x 10. if we do this we get 28 x 100 therefore 2800
Answer:
2800
Step-by-step explanation:
hear is a tip do the butterfly method
The unit rate comparing dollars earned to cars washed is 6. If the fundraiser earned $318, how many cars were washed? Explain
Answer: 53 cars were washed.
Step-by-step explanation:
Given : The unit rate comparing dollars earned to cars washed is 6.
i.e. The fundraiser can earn $6 per car wash.
If the fundraiser earned $318, then the number of car wash he did is given by :-
[tex]\dfrac{318}{6}=53[/tex]
Hence, 53 cars were washed.
25= a/5 what is that?
Answer:
hi there
your answer is A=125
Step-by-step explanation:
Step 1 :A=25 = a/5 - a/5
Step 2 :A=25-(a/5) = 0
Step 3 : A= 25-1/5×a = 0 - 25
Step 4 :A= -1/5×a = -25 -1/5
Step 5 :a = -25/(-1/5)
Step 6 : a = 125
i hope this helps out
Have a great morning
FaithRawlins14
Which graph represents a bike traveling at a constant rate of 12 miles per hour
The graph that represents the line (y = 12x) is option C) and this can be determined by using the point-slope form of the line.
Given :
Bike traveling at a constant rate of 12 miles per hour.
The following steps can be used to determine the graph that represents a bike traveling at a constant rate of 12 miles per hour:
Step 1 - All the graphs in the option pass through the point (0,0). So, (0,0) is the point through which a line is pass through.
Step 2 - Another point is (1,12) through which line passes because it is given that bike traveling at a constant rate of 12 miles per hour.
Step 3 - The equation of the line that passes through the points (0,0) and (1,12) is given by:
[tex]\dfrac{y-0}{x-0}=\dfrac{12-0}{1-0}[/tex]
y = 12x
So, the graph that represents the line (y = 12x) is option C).
For more information, refer to the link given below:
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find the perimeter of the shape below:
The answer would be 11
darlene wants to buy martian invader video game. The video game price is $100. Darlene has a coupon for 25%. What is the price of the video game with the coupon?
Answer:
$75
Step-by-step explanation:
100 ÷ 25=75
Hope this helps!☺
To find the price of the video game with the coupon, subtract the discount amount from the original price.
Explanation:To calculate the price of the video game with the coupon, we first calculate the discount amount. The coupon is for 25% off, so the discount amount is 25% of $100. Using the formula discount = (percentage / 100) * original price, the discount amount is (25 / 100) * $100 = $25.
To find the price of the video game with the coupon, we subtract the discount amount from the original price. The price of the video game with the coupon is $100 - $25 = $75.
Therefore, the price of the video game with the coupon is $75.
5x−2y=305, x, minus, 2, y, equals, 30
Complete the missing value in the solution to the equation.
(8,(8,left parenthesis, 8, comma
))right parenthesis
Answer:
The missing value is 5
The solution is (8,5)
Explanation:
The given equation is:
5x - 2y = 30
An order pair is written as (x , y). We are given (8 , ?)
This means that we want to find the y value that corresponds to x=8
To do this, we will substitute with x=8 in the given equation and solve for y
This is done as follows:
5x - 2y = 30
5(8) - 2y = 30
40 - 2y = 30
2y = 10
y = 5
This means that at x=8 and y=5, the equation is satisfied
(8,5) is a solution to the given equation
Hope this helps :)
Answer:
(8, 5)
Step-by-step explanation:
The given equation is:
5x - 2y = 30
We have to complete the given incomplete solution set (8, ?)
The first point in the ordered pair is always the x-value. So we are given an x-value and we have to find the corresponding y-value from the function.
Using x = 8 in the given function, we get:
5(8) - 2y = 30
40 - 2y = 30
- 2y = 30 - 40
- 2y = -10
y = 5
So, the value of y for x = 8 is 5. The complete ordered pair that satisfy the equation will be (8, 5)
Which graph shows a graph of a circle with equation x 2 + (y+3) 2 =9
The graph of the circle is given in the image attached
To graph the circle represented by the equation x^2 + (y+3)^2 = 9, identify the center at (0,-3) and radius 3, then plot the center and draw the circle on a graph.
Explanation:The student's question relates to the equation of a circle in Cartesian coordinates and how to graph it. Given the equation x2 + (y+3)2 = 9, we can determine the center and the radius of the circle it represents. To graph the circle, first identify the center, which in this case is at (0, -3), because the equation can be written in the standard form (x - h)2 + (y - k)2 = r2 where (h, k) is the center and r is the radius. Then find the radius by taking the square root of the right side of the equation, which is 3 in this case.
Plot the center on the Cartesian graph, and draw a circle around it with a radius of 3 units, ensuring that possible points on the circle follow the equation such as (0,0), (-3,-3), and (3,-3) for instance.
What could be the area of a face of the rectangular prism?
A.)5m^2
B.)6m^2
C.)7m^2
D.)9m^2
The answer is B.
This is because the formula is length × width.
So the 3 formulas we would have are 2 × 4, 4 ×3, and 3 × 2.
This means your possible answers are 8, 12 and 6.
The only answer that matches up is 6 or B.
The area of a rectangular prism is [tex]6m^{2}[/tex] since option B is correct.
Definition of area of rectangular prism:The surface area of a rectangular prism may be determined using the following formula because all of its faces are rectangles and opposite faces are equal: 2 (width x length) + (length x height) + (width x height) = Surface Area
How to calculate the area of the rectangular prism?Because the formula is length x width, this is the case.2×4, 4×3, and 3×2 are the three formulas we'd have.As a result, your options are 8, 12, and 6.The only answers that are correct are 6 or B.
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