Answer:
15
Step-by-step explanation:
We can just make a ratio. 5:4 = x:12. We see x=15
The height of the tree = 15m.
let us say the height of the tree=h
in this problem,
the height of the sam can be treated as perpendicular of a right-angle triangle.
while his shadow can be treated as the base of the same triangle.
now, we need to calculate the angle of elevation α
what is the angle of elevation?it is the angle between the line of sight and the horizon.
hence,
the tangent of the angle of elevation α= height/length of the shadow
tanα= 5/4
tan α = height of the tree/length of the shadow of the tree
5/4 = h/12
h=15m
therefore, the height of the tree = 15m
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Graph the solution of y - 4 < 2 on a number line.
Answer:
y<6
Step-by-step explanation:
You will solve it like a one-step equation but just leave the less then symbol. so anything less then 6 is your answer
The solution of provided inequality equation y - 4 < 2 is y<6 and the number line for this is plotted below.
What is the number line?The number line is the way of representation of number and digits in a arranged form to understand the data batter.
Characteristics of the graph of the inequality-
Open circle- When the value of variable is equal the given number, then the graph of the inequality has a open circle.Closed circle-When the value of variable is not equal the given number, then the graph of the inequality has a closed circle.The ray will move to the right- When the, value of variable is greater then the number, then the ray will move to the right.The ray will move to the left- When the value of variable is less then the number, then the the ray will move to the left.The equation which need to be solve is,
[tex]y - 4 < 2[/tex]
Add 4 both side of the equation to solve it further,
[tex]y < 2+4\\y < 6[/tex]
This is the simplified form of the equation. This equation suggest that the value of y is less than the number 6.
Thus, the arrow should be point left side and the open circle is put on number 6 to make the number line for given equation as shown in figure attached below.
Thus, the solution of provided inequality equation y - 4 < 2 is y<6 and the number line for this is plotted below.
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Write the equation of the line in slope intercept from that is parallel given the equation and point.
Answer:
y = - 6x - 19
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - 6x - 4 ← is in slope- intercept form
with slope m = - 6
• Parallel lines have equal slopes, thus
y = - 6x + c ← is the partial equation
To find c substitute (- 3, - 1) into the partial equation
- 1 = 18 + c ⇒ c = - 1 - 18 = - 19
y = - 6x - 19 ← in slope- intercept form
Solve each inequality 3<-5n + 2n
Answer: -1>n
Step-by-step explanation:1) combine like terms (-5n+2n=-3n) so you have 3<-3n then you divide -3 on both sides and because it’s a negative you flip the sign so you end up with -1>n
Please help me..!!!:(
Answer:
NO Pick none :) Step-by-step explanation:
2 more than the product of -4 and a number x is less than 20 ?
Answer:
Step-by-step explanation:
Product of -4 and a number x is -4 * x = - 4x
-4x + 2 < 20
Answer:
Step-by-step explanation:
Turning the word problem into equations:
[tex]-4x+2 = 20[/tex]
Subtracting 2 on both sides
[tex]-4x+2 -2= 20 -2[/tex]
[tex]-4x = 18[/tex]
Dividing by -4
[tex] -4x/(-4) = 18/(-4)[/tex]
Considering that -4x/(-4) = x
Then the answer is x = -18/4 = - 9/2 = - 4 1/2
Part 1: Assume that a bacteria population triples every hour. Which of the following three tables of data, with
x representing time in hours and y the count of bacteria, could represent the bacteria population? Circle the
letter of your choice.
Answer:
Table C
If the bacteria population triples every hour, it must multiply by three each time.
Table C fits this pattern
y | 1 | 3 | 9 | 27 | 81 | 243 | 729
1×3=3, 3×3=9, 9×3=27 etc.
The fastest male marathon running time is 2 hours 2 minutes 57 seconds of a marathon is 26.2 miles how long in minutes and seconds would it take the same man to run 1 mile??
Answer:
B
Step-by-step explanation:
simply by dividing time and miles by number 2 until 6 miles comes to 1 mile
Factor completely: 9x3 - 9x2y + 4x - 4y A) (x + y)(9x2 - 4) B) (x - y)(9x2 + 4) C) (9x + y)(x - 2)(x + 2) D) (x + y)(3x - 2)(3x + 2)
9x3 - 9x2y + 4x - 4y A) (x + y)(9x2 - 4) B) (x - y)(9x2 + 4) C) (9x + y)(x - 2)(x + 2) D) (x + y)(3x - 2)(3x + 2)
Did I do this right or not?
Answer:
No
Step-by-step explanation:
[tex][x - 5][3x - 2] \\ \\ 3 {x}^{2} - 17x + 10[/tex]
F - Multiply the first terms in each set of parentheses FARTHEST TO THE LEFT
O - Multiply the first term in the first set of parentheses FARTHEST TO THE LEFT by the last term in the second set of parentheses FARTHEST TO THE RIGHT
I - Multiply the last term in the first set of parentheses FARTHEST TO THE RIGHT by the first term in the second set of parentheses FARTHEST TO THE LEFT
L - Multiply the last terms in each set of parentheses FARTHEST TO THE RIGHT
I am joyous to assist you anytime.
What is 15% of 75% of 80?
Final answer:
To find 15% of 75% of 80, calculate 75% of 80 first (0.75 imes 80 = 60), then find 15% of 60 (0.15 imes 60 = 9), resulting in an answer of 9.
Explanation:
The student has asked: What is 15% of 75% of 80?
To solve this problem, we'll need to follow these steps:
First, find 75% of 80.
Then, find 15% of the result from step 1.
Let's start with the first step:
75% of 80 is equivalent to 0.75 imes 80, which equals 60.
Now, for the second step:
15% of 60 is equivalent to 0.15 imes 60, which equals 9.
Therefore, 15% of 75% of 80 is 9.
4abc + (-9abc) + 10d?
Answer:5
Step-by-step explanation:
What is7766 rounded to the nearest thousands
7766 rounded ot the nearest thousands would be 8000, since the hundreds place value, 7, is going to be rounded up to 8000.
Hope this helped!
Nate
Answer:
8000
Step-by-step explanation:
|Thousands||Hundreds||Tens||Ones|
| 7 || 7 || 6 || 6 |
5 or more, raise the score (turn the 7 into an 8 and make the three other numbers 0)
4 or less, let it rest (leave the 7 as a 7 and make the other 3 numbers 0).
The number that we are looking at changing will be bold. The number that determines if we change that number will be underlined.
7766
The 5 or more, raise the score rule applies to 7.
So, we will make the 7 thousand (7000) 8 thousand (8000)
We will make the seven hundred sixty six (766) zero (0).
Our final answer is 8000.
The sum of two consecutive natural numbers is 475 find the numbers. Find the numbers
Step-by-step explanation:
Need to FinD :We have to find the numbers.[tex] \red {\frak{Given}} \begin{cases} & \sf{Two\ consecutive\ natural\ numbers.} \\ & \sf{The\ sum\ of\ the\ numbers\ is\ {\pmb{\sf{475}}}.} \end{cases}[/tex]
We know that,
The sum of the two consecutive natural numbers is 475 and we're asked to find out the numbers. So, let the two consecutive natural numbers be x and x + 1.Therefore,
[tex] \sf \dashrightarrow {x\ +\ x\ +\ 1\ =\ 475} \\ \\ \\ \sf \dashrightarrow {2x\ +\ 1\ =\ 475} \\ \\ \\ \sf \dashrightarrow {2x\ =\ 475\ -\ 1} \\ \\ \\ \sf \dashrightarrow {2x\ =\ 474} \\ \\ \\ \sf \dashrightarrow {x\ =\ \dfrac{\cancel{474}}{\cancel{2}}} \\ \\ \\ \dashrightarrow {\underbrace{\boxed{\pink{\frak{x\ =\ 237.}}}}_{\sf \blue {\tiny{First\ number}}}} [/tex]
∴ Hence, the first number is 237. Now, let us find out the second number.
[tex]\rule{200}{3}[/tex]
Second NumbeR :
x + 1237 + 1238∴ Hence, the second number is 238.
The two consecutive numbers whose sum is 475 are 237 and 238.
Let assume the two consecutive natural numbers as x and x+1.
According to the given information,
the sum of the two consecutive numbers is 475.
So, the equation can be set up as:
x + (x+1) = 475
Combining like terms, we get:
2x + 1 = 475
Subtracting 1 from both sides, we have:
2x + 1 - 1 = 475 - 1
2x = 474
Dividing both sides by 2, we find:
x = 237
Thus, the two consecutive numbers are 237 and 238.
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Mr zuro finds the mean height of all 14 students in his class to be 69.0 inches. Just as Mr Zuro finishes explaining how to get the mean, Danielle walks in late. Danielle is 70.5 inches tall. What is the mean height of the 15 students in the class?
Answer:
69.1
Step-by-step explanation:
Mean height of 14 students = 69.0 inches
Mean = sum of data/number of data
69 = sum of data/14
sum of data = 966
FOR NEW MEAN:
Height of additional student = 70.5
Mean = sum of data/ number of data
Mean = 966+70.5/14+1
Mean = 1036.5/15
Mean = 69.1
Therefore, the mean height of the 15 students in the class is 69.1
Final answer:
To find the new mean height after Danielle joins the class, calculate the total height of all students, add Danielle's height, and divide by the new number of students. The mean height increases to 69.1 inches.
Explanation:
Mr. Zuro finds the mean height of all 14 students in his class to be 69.0 inches. When Danielle, who is 70.5 inches tall, walks in late, we need to calculate the new mean height of all 15 students.
First, we find the total height of the initial 14 students by multiplying the mean height by the number of students: 69.0 inches × 14 = 966 inches. Next, we add Danielle's height to this total: 966 inches + 70.5 inches = 1036.5 inches. Finally, to find the new mean height, we divide this total by the number of students, now 15: 1036.5 inches ÷ 15 = 69.1 inches.
Therefore, the mean height of the 15 students in the class, including Danielle, is now 69.1 inches.
prove that 1÷loga ab + 1÷logb ab=1
Answer:
See below.
Step-by-step explanation:
1 ÷ loga ab + 1 ÷ logb ab
= 1 / (loga ab) + 1 / (loga ab / loga b) { change of log base)
= 1 / (loga ab) + loga b / (loga ab)
= (1 + loga b) / loga ab
= (1 + loga b) / (loga a + loga b) Now loga a = 1 so we have:
((1 + loga b) / (1 + loga b)
= 1.
José sets up computers. He has been working
on a job today for about six hours. He told his
boss the job was about 75% complete.
José needs approximately 2 more hours to complete his job.
We should calculate the total time required for 100% completion and then subtract the time he has already worked.
José has completed 75% of the job in 6 hours.To find the total time for 100%, we use the proportion: 6 hours / 0.75 = 8 hours.Therefore, the total time required to complete the job is 8 hours.José needs 8 hours - 6 hours = 2 more hours to finish the job.He needs approximately 2 more hours to complete the job.
Complete Question:
Jose sets up computers. He has been working on the job today for 6 hours. He told his boss the job was about 75% complete. Approximately how many more hours does he need to complete the job.
happy paws charges $19.00 plus $1.50 per hour to keep
-8(2r - 8)+ 6 = -3(r + 7)
Answer:
r = 7
Step-by-step explanation:
Use the distributive property by multipling the -8 to the 2r and the -8, do the same thing on the other side with the -3.
Afterwards, combine like terms by adding 64 and 6.
Next, add 3r to the left side, I usually choose the number with the variable (the letter) that looks like it will be easier to subtract. This leaves only 21 on the right side.
Next subtract 70 from both sides
Divide -13 by both sides
You should get the answer of r=7
2. Three times a number, increased by seventeen
A. 3(a + 17)
B 3a + 17
3xN
C. (17 +3)a
D. None of the above
3ya
The correct expression is 3a + 17.
Explanation:The correct expression that represents 'Three times a number, increased by seventeen' is 3a + 17. Option B is the correct answer.
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When deriving the quadratic formula by completing the square what expression can be added to both sides of the equation to create a perfect square trinomial x^+b/ax+_=-c/a+_
To convert the quadratic polynomial into the perfect square, the squared of half the value of the coefficient of degree one variable can be added to both sides of the equation. [tex]\dfrac{b^2}{4a^2}[/tex] can be added to both sides of the equation.
The given equation is [tex]x^2+\dfrac{b}{a}x+?=\dfrac{-c}{a}+?[/tex]
Now,
To change the quadratic equation into the perfect square, the squared of half the value of the coefficient of degree one variable can be added to both sides of the equation.
Therefore,
[tex]x^2+\dfrac{b}{a}x+\dfrac{b^2}{4a^2}=\dfrac{-c}{a}+\dfrac{b^2}{4a^2}[/tex]
Thus, [tex]\dfrac{b^2}{4a^2}[/tex] should be added to both sides of the equation to convert the above equation into the quadratic polynomial.
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Answer:
d
Step-by-step explanation:
edge
Which two whole numbers lies between the square root of 10
3 > √10 > 4
the answer would be 3 & 4
Answer: 3 & 4
Step-by-step explanation:
What is the answer to 6(-3-4y) simplifying algebriac expressions
Answer:
-18 - 24y.
Step-by-step explanation:
6(-3-4y)
We use the distributive law to give:
6 * -3 + 6* -4y
= -18 - 24y.
X is greater than or equal to -2
[tex]X \geq -2[/tex]
Please put these from greatest to least.
876.405, 887.053, 887.208
887.208
887.053
876.405
Hope this helps
What are the solutions to the equation (x – 6)(X + 8) = 0?
Answer:
x = - 8, x = 6
Step-by-step explanation:
Given
(x - 6)(x + 8) = 0
Equate each factor to zero and solve for x
x - 6 = 0 ⇒ x = 6
x + 8 = 0 ⇒ x = - 8
Answer:
x = -8, 6.
Step-by-step explanation:
(x– 6)(x + 8) = 0
Either factor can be zero:
x - 6 = 0 gives x = 6 and
x + 8 = 0 gives x = -8.
Thanks for any help provided to my question! <3
5m + 2(m + 8) + 3
Please help me, I'm stuck on this math problem. There is an attachment. Thank you!
Answer:
7
Step-by-step explanation:
Divide 427 and 61 to find the quotient.
427 ÷ 61
= 7
Angelina spend $50 on 16 packages of cookies for her club members. sugar cookies cost $2.50 per package and chocolate chip cookies cost $3.50 per package. how many packages of each cookie does Angelina buy?
Answer:
6 packs of sugar cookies and 10 packs of chocolate chip cookies.
Step-by-step explanation:
Let the quantity of sugar cookies be x packs and the quantity of chocolate chip cookies be y packs. Total packs are 16. Therefore: x + y = 16. This implies y = 16 - x (Equation 1).
It is given that a pack of sugar cookies is priced at $2.5 and a pack of chocolate chip cookies is priced at $3.5. It is also given that the student spends a total of $50 on the cookies. Since x packs of sugar cookies and y packs of chocolate chip cookies are to be bought, therefore:
2.5x + 3.5y = 50 (Equation 2).
Put equation 1 in equation 2.
2.5x + 3.5(16 - x) = 50.
2.5x + 56- 3.5x = 50.
-x = -6.
x = 6.
Put x = 6 in equation 1.
y = 16 - 6.
y = 10.
Therefore, Angelina will buy 6 packs of sugar cookies and 10 packs of chocolate chip cookies!!!
To shift a graph vertically and/or horizontally is to _____ it.
Answer:
Translate
Step-by-step explanation:
To shift a graph vertically and/or horizontally is to Translate it.
Step-by-step explanation:Translation--
A translation is a rigid transformation in which the graph of the original function is shifted some units to the left or to the right( i.e. horizontal shift) or some units up or down ( i.e. vertical shift ).
The horizontal shift of the function f(x) by k units is given by:
f(x) → f(x+k)
and the vertical shift of the function f(x) by k units is given by:
f(x) → f(x)+k