A 15 ft long cable is connected from a hook to the top of a pole that has an unknown height. The distance from the hook to the base of the pole is 3 ft shorter than the height of the pole.
a. What can you use to find the height of the pole?
b. Write and solve a quadratic equation to find the height of the pole.
c. How far is the hook from the base of the pole?
Answers
a. What can you use to find the height of the pole?
solution: We can use Pythagoras theorem to find the height of the pole.
b. Write and solve a quadratic equation to find the height of the pole.
solution:
a² + b² = c²
[tex]\sf (x)^2 + (x-3)^2 = 15^2[/tex]
[tex]\sf x^2 + x^2 - 6x + 9 = 15^2[/tex]
[tex]\sf 2x^2 -6x + 9 = 225[/tex]
[tex]\sf 2x^2 -6x -216=0[/tex]
[tex]\sf 2x^2 -24x +18x -216 = 0[/tex]
[tex]\sf 2x(x-12)+18(x-12) = 0[/tex]
[tex]\sf (2x + 18)(x-12) = 0[/tex]
[tex]\sf x = 12, -9[/tex]
[tex]\sf x = 12[/tex]
height of the pole: 12 ft
c. How far is the hook from the base of the pole?
solution: (x-3) → (12-3) → 9
Related Questions
Solve the quadratic equation below by Completing the Square STEP-BY-STEP:
x^2+6x=0
Answers
Suppose you roll a number cube. What is the probability that you roll a number greater than 1?
Answers
Answer:
Ok a cube has 6 sides and the choices are 1,2,3,4,5,6. As you can see you need to know the probability getting greater than 1. So 2,3,4,5,6 are greater so, the answer would be 5/6 into percentage around 83% of getting greater than 1.
Step-by-step explanation:
A manager at a shopping mall counts 244 males and n females as they enter the mall. The manager realizes that 25% of all males and 25% of all females are children. She writes the expression 0.25n + 61 to represent the number of children who enter the mall. Is the manager correct?
Answers
Answer:
Step-by-step explanation:
The manager is not correct in her calculation.
Step-by-step explanation:
There are 244 males and n females who entered the mall as the manager at the shopping mall counts.
If 25% of all males are children, then the number of male children are .
Again, the 25% of all female are children, then the number of female chilfren are .
Therefore, the total number of children will be (60 + 0.25n).
But the manager gives the number of children to be 0.25n + 61 who entered the mall.
So, the manager is not correct in that calculation. (Answer)
Please help with this question I’m stuck
Answers
Answer:
53 degrees
Step-by-step explanation:
because its at a right angle and measure 1 is 37 so 90-37 would equal 53
Step-by-step explanation:
because it is on a corner the hole corner = 90
1 + 2 = corner so
1+ 2 = 90
1 is 37
37 + 2 = 90
rearrange
90 - 37 = 2
so 2 = ???
Please solve in subtraction method! Will give brainliest!!!
Answers
The value of x and y is 1 and 4.
how would you solve it's for algebra 2B I'm just a little stuck thanks so much for your help hope it's not a waste of time
Answers
Answer: [tex]\frac{2x^2+s^2}{x(x+s)}[/tex]
This is the fraction of 2x^2+s^2 all over x(x+s)
==============================================
Explanation:
Currently the denominators are not the same, so we cannot subtract the fractions just yet.
We need to get the denominators equal to the LCD (lowest common denominator).
In this case, the LCD is x(x+s). Often the LCD is the product of the denominators, but not always.
To get the first fraction to have the LCD, we multiply top and bottom by x.
[tex]\frac{3x}{x+s} = \frac{x*3x}{x(x+s)} = \frac{3x^2}{x(x+s)}[/tex]
To get the second fraction to have the LCD, we multiply top and bottom by x+s
[tex]\frac{x-s}{x} = \frac{(x+s)(x-s)}{x(x+s)} = \frac{x^2-s^2}{x(x+s)}[/tex]
I used the difference of squares rule to go from (x+s)(x-s) to x^2-s^2.
-----------------------------------------
At this point, we have x(x+s) in both denominators and we can subtract
[tex]\frac{3x}{x+s} - \frac{x-s}{x}\\\\\frac{3x^2}{x(x+s)} - \frac{x^2-s^2}{x(x+s)}\\\\\frac{3x^2-(x^2-s^2)}{x(x+s)}\\\\\frac{3x^2-x^2+s^2}{x(x+s)}\\\\\frac{2x^2+s^2}{x(x+s)}\\\\[/tex]
Optionally, you can distribute the x through in the denominator, but I'll leave it factored.
HELP! WHAT DID I DO WRONG?!
PLEASE PROVIDE THE CORRECT SOLUTION ALONG WITH STEP-BY STEP EXPLANATION!
Answers
Answer:
1256
Step-by-step explanation:
You added the diameter for r and not the radius
3.14(20)^2
3.14(400)
1256
What is this
F(x)=-x^2-3. 7x-6. 5
Find the maximum value
Round to the nearest hundredth
Answers
"Find the maximum value" or namely find the value of f(x) at the vertex point, like the one in the picture below.
[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ f(x)=\stackrel{\stackrel{a}{\downarrow }}{-1}x^2\stackrel{\stackrel{b}{\downarrow }}{+-3.7}x\stackrel{\stackrel{c}{\downarrow }}{+-6.5} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{ -3.7}{2(-1)}~~~~ ,~~~~ -6.5-\cfrac{ (-3.7)^2}{4(-1)}\right)\implies \stackrel{maximum~value}{(-1.85~~,~~\stackrel{\downarrow }{-3.08})}[/tex]
9. The area of a circle is 706.97 in2. Find the radius.
Answers
Answer:
15
Step-by-step explanation:
Using the formula
A=πr2
Solving
r=√A/π
r=√706.97/22/7
r≈15.00118
Rodrigo works for a company that ships orders from two different locations—location A and location B. He wonders if the same proportion of orders arrive late from each location. He takes a random sample of orders from each location to test if there is a significant difference in the proportion of orders that arrive late from each location.
Which of the following is an appropriate set of hypotheses for Rodrigo's significance test?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
\begin{aligned} &H_0: p_\text{A} - p_\text{B}=0\\ &H_\text{a}: p_\text{A} - p_\text{B} <0 \end{aligned}
H
0
:p
A
−p
B
=0
H
a
:p
A
−p
B
<0
(Choice B)
B
\begin{aligned} &H_0: p_\text{B} - p_\text{A}=0\\ &H_\text{a}: p_\text{B} - p_\text{A} <0 \end{aligned}
H
0
:p
B
−p
A
=0
H
a
:p
B
−p
A
<0
(Choice C)
C
\begin{aligned} &H_0: p_\text{A} - p_\text{B}=0\\ &H_\text{a}: p_\text{A} - p_\text{B} \neq 0 \end{aligned}
H
0
:p
A
−p
B
=0
H
a
:p
A
−p
B
=0
(Choice D)
D
\begin{aligned} &H_0: p_\text{B} - p_\text{A}\neq0\\ &H_\text{a}: p_\text{B} - p_\text{A} =0 \end{aligned}
H
0
:p
B
−p
A
=0
H
a
:p
B
−p
A
=0
Answers
According to the described situation, the appropriate set of hypotheses for Rodrigo's significance test are given by:
[tex]H_0: p_A - p_B = 0[/tex]
[tex]H_1: p_A - p_B \neq 0[/tex]
What are the hypothesis tested?At the null hypothesis, it is tested if there is no difference between the locations, that is:
[tex]H_0: p_A - p_B = 0[/tex]
At the alternative hypothesis, it is tested if there is a difference, that is:
[tex]H_1: p_A - p_B \neq 0[/tex]
More can be learned about hypothesis tests at https://brainly.com/question/26454209
Maria had some candy to give to her four children.She first took three pieces for herself and then evenly divided the rest among her children.Each child received five pieces.With how many pieces did she start?
Answers
Step-by-step explanation:
her and 4 children
she had 3
rest divided by 4
each child had 5
and 4 children
so
4 * 5 = 20
20 for children and 3 for her
20 + 3 =
answer in comments
please mark brainest
Answer:
23
Step-by-step explanation
5 pieces of candy for each of the 4 children plus the 3 she took equals 23
Find the area of the
shaded region.
8m
12m
Answers
Answer:
96m^2
Step-by-step explanation:
To find the area you must multiply length times width (l*w).
8*12 = 96
So 96 m^2
Ben is 4 times as old as Ishaan and is also 6 years older than Ishaan.
How old is Ben?
Answers
✪According to question:-
Ben is 6 years older than Ishaan
So :-
Ben age - Ishaan age = 6 yearsput supposed values
4x - x = 63x = 6x = 6 ÷ 3x = 6/3x = (2 × 3)/3x = 2/1x = 2Original Ages :-
Ishaan age = xIshaan age = 2 yearsBen age = 4xBen age = 4(2)Ben age 4 × 2Ben age = 8 years✪Verification :
1st condition:-
Ben age - Ishaan age = 6 yearsput original ages
8 - 2 = 66 = 6LHS=RHS
Hence verified !
Required answer :-Ben's age = 8 years
please help this is due tomorrow
Answers
Answer:
2.35
Step-by-step explanation:
divide by 1000
Which equation can be used to find x, the length of the hypotenuse of the right triangle? A triangle has side lengths 18, 24, x. 18 24 = x 18 squared 24 = x (18 24) squared = x squared 18 squared 24 squared = x squared.
Answers
Answer:
18 squared + 24 squared = x squared
Step-by-step explanation:
As we know from Pythagorean theorem:
a^2=b^2+c^2, where a -s hypotenuse and b&c are adjacent sides of right angle.
Here we should have: x^2=18^+24^2
Please help Ill mark and worth 40 points.
a.) What is the measure of ZB ? (just write the numerical answer in the blank below, do not type in the word degrees) (
b.) Are the two triangles shown similar? (write yes or no in the second blank) (5 points)
Answers
WILL GIVE BRAINLIST .
which function is equivalent to y =5 (x+3 ^2) -8 ?
A) y = 5x^2 +30x +37
B) y=5x^2 + 6x - 2
C) y=5x^2 +30x +5
D) y= 5x^2 + 1
Answers
Answer: Below
Step-by-step explanation:
So we can start off by solving this equation.
(x + 3)² = x² + 6x + 9
5(x² + 6x + 9) = 5x² + 30x + 45
5x² + 30x + 45 - 8 = 5x² + 30x + 37
Going off of this, we can already see that A is our answer.
How do I describe the end behavior, determine if it's an odd or even degree, and the real number of zeros? Please help me.
Answers
Answer:
1. Even Degree
2. 6 zeros
Step-by-step explanation:
Determine if it’s an odd or even degree:—
- The graph is shown approach positive infinity when both sides of x-values, negative and positive, both approach their respective infinity sides.
To put it simply, see when both negative x-values and positive x-values approach their negative or positive infinity, the y-values will always be positive, even if negative x-values approach negative infinity.
For a polynomial function to be an even degree, it must satisfy the following:—
[tex]\displaystyle \large{ \lim_{x \to \pm \infty} f(x) = \infty}[/tex]
As an odd degree, either negative or positive x-values will approach positive infinity or negative infinity, depending on the function itself.
From the graph, we can say that the function is an even degree.
__________________________________________________________
Summary I
Even-Odd Degree
Even Degree, when both sides of x-value approach their respective infinity, y-value will always approach positive infinity.
Odd Degree, one side of y-value will approach positive infinity and another will approach negative infinity.
__________________________________________________________
Determine numbers of zeros:—
- We can determine numbers of zeros by examining x-axis and the graph. How many times does the graph intersect or pass through x-axis? Count and you should get 6 intercepts.
Therefore, there are 6 real solutions/zeros for this function/equation.
__________________________________________________________
Summary II
Determine zeros
To determine or check how many solutions or zeros do the graph/function/equation has, you can use the graph method. Simply count how many times does the graph pass through x-axis and x-intercepts are zeros.
__________________________________________________________
If you have any doubts regarding my answer or explanation, do not hesitate to ask in comment!
The ratio to boys to girls is 3:5 there are 40 children in the class how many children are boys
Answers
Answer:
15 boys and 25 girls in the class
One of the legs of a right triangle measures 19 cm and its hypotenuse measures 13 cm, Find the measure of the other leg. If necessary, round to the nearest tenth.
Answers
not possible, the hypotenuse must be the longest side of a right triangle
Find the co-ordinate of the point where y-4x=1 crosses the y-axis
Answers
Answer: (0,1)
Step-by-step explanation:
When a line crosses the y-axis, the x-coordinate must equal to 0.
Now we can plug in x = 0 into the equation given:
y - 4*0 = 1
y- 0 = 1
y = 1
Therefore, the point where the line crosses the y-axis is (0,1)
HELPPPPPPPPPPPPPP!!!!!!!! PLEASEEEEEEE
Answers
Answer:
No solution
Step-by-step explanation:
The slopes of both equations are identical (both being 2/3), therefore the only possible answers would be "infinitely many solutions" and "no solution". Because of the fact that the y-intercepts of the equations are different (-10 and 10) they two lines will never cross, meaning there is no solution.
Answer:
no solution
Step-by-step explanation:
[tex]\frac{2}{3} x - 10 = \frac{4}{6} x + 10[/tex]
Reduce the fraction:
[tex]\frac{2}{3} x - 10 = \frac{2}{3} x + 10[/tex]
Rearrange variables to the left side of the equation:
[tex]\frac{2}{3} x - \frac{2}{3} x = 10 + 10[/tex]
Apply the inverse property of addition
0 = 10 + 10
0 = 20
Based on the given conditions, the system of equations has no solution.
hope this helps!! p.s. i really need brainliest :)
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP MEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
Answers
Place them in the correct place on the diagram (rational,integers, and whole) view the image
Answers
Answer:
rational: 4¾, ¼, -0.9
whole: 8
integers: 8, -16
Step-by-step explanation:
rational numbers are numbers that can be expressed as a fraction. (-0.9 = -9/10)
whole numbers are numbers that do not have a fraction but they do not include negative numbers.
integers are numbers that can be expressed as a whole number with no fractions.
estimate 33.2 x 21 fast please
Answers
Please can you guys help me
Answers
Answer:
Calculator
Step-by-step explanation:
Literally all you have to do is multiply every number on one tow
iygm
it's actually easier than you might think
good luck!
Find the volume of the box
Answers
Answer:200
Step-by-step explanation:
Volume formula: length x width x height
5x4x100=200
A plane is descending from an altitude of 8,000 feet. The plane
descends at a constant rate of 500 feet per minute.
Which function can be used to determine the height, H, of the plane
after m minutes?
Answers
The linear function that can be used to determine the height, H, of the plane after m minutes is given by:
H(m) = 8000 - 500m
What is a linear function?A linear function is modeled by:
[tex]y = mx + b[/tex]
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value.In this problem:
The plane is descending from an altitude of 8,000 feet, hence the y-intercept is b = 8000.The plane descends at a constant rate of 500 feet per minute, hence the slope is of m = -500.Thus, the equation is:
H(m) = 8000 - 500m.
More can be learned about linear functions at https://brainly.com/question/24808124
Emily’s bedroom ceiling needs to be repainted due to a leak in the ceiling. How many square feet will she be painting
Answers
Answer:
64
Step-by-step explanation:
5*8+6*4
what is the area of this face
Answers
explanation: 12 x 18 = 216
216 - (6 x 6)
216 - 36 = 180