Answer:
Phil is 16 inches tall and his shadow is 8 inches tall
Step-by-step explanation:
this is an algebra word problem.
1. Find the unknown and label it x.
Let Phil's shadow be x inches.
2. find other unknown quantities and define them with
Phil's height= 2x (phil is shadow is half as long as Phil is tall)
3. FInd the equation
if he was 4 inches taller (2x+4)
and his shadow was three inches shorter (x-3)
his height ( 2x+4) times the shadow's height (x-3) would be 100 square inches.
(2x+4) ×(x-3)=100
(2x+4)(x-3)=100
this is a quadratic equation and there are a number of ways to solve these. the two main ways are
1. quadratic equation
2. expanding and factorising
3. graphing
we will use 2. expanding and factorising for this problem. We need to make the right hand side = 0 by first factorising then rearranging.
(2x*x)+(2x*-3)+(x*4) +(4*-3)=100
2x^2 -6x+4x-3x-12=100
2x^2 -2x=112
2x^2 -2x-112=0
once factorised take out the common factor of 2
2(x^2-x-56)=0
now factorise what's in the brackets ( two numbers multiply to make 56 but add to make -1.
2(x-8)(x+7)=0
x-8=0 => x=8
x+7=0 x=-7 not possible
the shadow is 8 inces long. Phil is 16 inches tall.
Hope this is of help :)
Phil's height is 16 inches, and the length of his shadow is 8 inches.
To solve the problem, we will let Phil's height be denoted by h (in inches) and the length of his shadow be s (in inches).
1. Phil's shadow is half as long as Phil is tall.
2. If Phil were 4 inches taller and his shadow were 3 inches shorter, the product of his height and his shadow's length would be 100 square inches.
From the first condition:
[tex]\[ s = \frac{h}{2} \][/tex]
From the second condition, we can write the equation involving the modified height and shadow:
[tex]\[ (h + 4) \times (s - 3) = 100 \][/tex]
Next, substitute [tex]\( s = \frac{h}{2} \)[/tex] into the equation:
[tex]\[ (h + 4) \times \left(\frac{h}{2} - 3\right) = 100 \][/tex]
Simplify inside the parentheses:
[tex]\[ (h + 4) \left(\frac{h - 6}{2}\right) = 100 \][/tex]
Multiply both sides by 2 to eliminate the fraction:
[tex]\[ 2(h + 4) \left(\frac{h - 6}{2}\right) = 2 \times 100 \][/tex]
[tex]\[ (h + 4)(h - 6) = 200 \][/tex]
Expand the left-hand side:
[tex]\[ h^2 - 6h + 4h - 24 = 200 \][/tex]
[tex]\[ h^2 - 2h - 24 = 200 \][/tex]
Move 200 to the left side to set the equation to zero:
[tex]\[ h^2 - 2h - 224 = 0 \][/tex]
Now, we solve the quadratic equation using the quadratic formula [tex]\( h = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \) where \( a = 1 \), \( b = -2 \), and \( c = -224 \):[/tex]
[tex]\[ h = \frac{-(-2) \pm \sqrt{(-2)^2 - 4(1)(-224)}}{2(1)} \][/tex]
[tex]\[ h = \frac{2 \pm \sqrt{4 + 896}}{2} \][/tex]
[tex]\[ h = \frac{2 \pm \sqrt{900}}{2} \][/tex]
[tex]\[ h = \frac{2 \pm 30}{2} \][/tex]
This gives us two potential solutions:
[tex]\[ h = \frac{32}{2} = 16 \][/tex]
[tex]\[ h = \frac{-28}{2} = -14 \][/tex]
Since height cannot be negative, we discard ( h = -14 ).
Thus, Phil's height is:[tex]\[ h = 16 \text{ inches} \][/tex]
Using [tex]\( s = \frac{h}{2} \)[/tex]:
[tex]\[ s = \frac{16}{2} = 8 \text{ inches} \][/tex]
Drag each tile to the correct box. Not all tiles will be used.
Calculate the interest earned on each simple interest account given the original principal, annual interest rate, and length of time the account
was held. Match each amount to the corresponding account description.
$124.74
$99.66
$105.60
$126.72
$143.50
$106.60
$1,100 at 3.2% for 3 years
$990 at 3.15% for 4 years
$1,025 at 2.8% for 5 years
Answer:
$1,100 at 3.2% for 3 years -> $105.60
$990 at 3.15% for 4 years -> $124.74
$1,025 at 2.8% for 5 years -> $143.5
Step-by-step explanation:
Simple interest formula is:
A = P*(1 + r*t)
where A if final account, P is principal, r is annual interest rate (as decimal) and t is time in years
Interest earned is A - P, then:
I = P*(1 + r*t) - P = P(1 + r*t - 1) = P*r*t
If P = $1100, r = 0.032 and t = 3, then:
I = 1100*0.032*3 = $105.6
If P = $990, r = 0.0315 and t = 4, then:
I = 990*0.0315*4 = $124.74
If P = $1025, r = 0.028 and t = 5, then:
I = 1025*0.028*5 = $143.5
Answer:
Picture below
Step-by-step explanation:
Enter the value of the exponential expression 5^0
Answer:
1
Step-by-step explanation:
whenever something is to the power of 0, it equals 1
Write the word sentence as an equation. Then solve.
The difference between a number p
and 6 is −14.
Answer:
p - 6 = -14
p = -8
If someone confuses the order, p might be 20, But here I am going to choose p= -8
Step-by-step explanation:
The difference between a number p
and 6 is −14.
The difference between a number p and 6 = -14
I replace "is" with an equal sign
p - 6 = -14
so
p = 6 - 14
p = -8
it can be confused as 6 - p = -14, p = 20
Answer:
The difference between a number p
and 6 is −14.
The difference between a number p and 6 = -14
I replace "is" with an equal sign
p - 6 = -14
so
p = 6 - 14
p = -8
it can be confused as 6 - p = -14, p = 20
Step-by-step explanation:
can someone help please?
Answer: 19
Step-by-step explanation:
в та
If B = 49°13' and b - 10 find a
a. 4.6
b. 8.6
C.
d.
5.4
6.5
Answer:
A
Step-by-step explanation:
Answer quick please.
Answer:
V = (1/2) mile per (5/10) hour, multiply both mile and hour by 2, => V = 1 mile per 1 hour (1 mile/hour)
Hope this helps!
:)
Answer:
1
Step-by-step explanation:
find the distance bewtween the points (3,3) and (-1,-2)
Answer:
[tex]\sqrt{41}[/tex]
Step-by-step explanation:
[tex]\sqrt{(3-(-1))^2+(3-(-2))^2}=\sqrt{16+25}=\sqrt{41}[/tex]
Hope this helps!
clarissa has 3 pints of ice tea that she divides into 1/2-pint servings. how Many 1/2 -pints servings does she have?
Answer:
6
Step-by-step explanation:
1 pint of tea will produce 2 half pints
So since there are 3 pints of tea it will produce 6 half pints of tea
Can you please help me
Answer:
B 6/13 times 5/12 equals 5/26
Step-by-step explanation:
if the total marbles are 13, then 13 has to be the denominator
they said that 2 orange marbles are selected
then it is 6/13 times 5/13
Hopes this helps
Answer:
I think it is C
Step-by-step explanation:
I am right
What is the measure of an angle whose sine is√3/2 ? 60 45 30
please I need entire explanation, and how do I use my calculator to fin the answer.
Answer:
60
Step-by-step explanation:
sin(theta) = sqrt(3)/2
On the calculator:
Press shift
Press sin
(It will show sin^-1)
Then enter sqrt(3)/2
Press =
It will give you an output of 60
Step-by-step explanation:
Step 1: Find the answer
To find sine, that means we need to find the y-value where it equals √3/2.
If you know the unit circle, you know that the long side is √3/2 and the short side is 1/2. So... in order to have the long side to be a y-value, that means that we need to have a long vertical triangle. The angle that will fit this will be 60 degrees.
On you calculator, you should have a sin and you just type in something like this: sin(60) and it should give you √3/2.
Answer: Option A, 60
Given: A = 1 −1 −2 3 B = 1 5 8 −8 C = 1 2 3 4 Solve: AX + B = C X =
Answer:
-5 3, -5 6
Step-by-step explanation:
just did it
Answer:
1st row: [-5 3] 2nd row: [-5 6]
Step-by-step explanation:
Edge 2020
Number five Please I really need it
Hello! I really need help with this problem!
Answer: No, yes, yes, no, yes, no, yes
Step-by-step explanation: When you graph the two functions together you can determine the verity of the differnt statements and the relation between the functions such as when and where they will collide, x and y intercepts, etc
Answer:
e
Step-by-step explanation:
what is f^7 . f^1 please help
Answer:
is f^8
Step-by-step explanation:
HIGH POINT QUESTION
A shape is rotated 180 degrees about the origin and then its image is reflected in the Y-axis. Describe fully the single transformation that would have the same result as the two transformations described above.
Answer:
Reflection in the x-axis
Step-by-step explanation:
If the point (x, y) of the shape is rotated 180° about the origin, it will be transformed into the point (-x, -y).
If the point (-x, -y) is reflected in the Y-axis, it will be transformed into the point (x, -y). This transformation is equivalent to the reflection of (x, y) in the x-axis.
After a 35% discount, a book costs 11.21, what is the normal undiscounted price of the book?
Answer:
$17.25
Step-by-step explanation:
First, we know that $11.21 is 65% of the original price, so divide 11.21 by 65 to find 1% of the original price
Then just multply your result of .17246 by 100 to get 17.246, which rounded to 17.25
The normal undiscounted price of the book is $17.24.
Explanation:To find the normal undiscounted price of the book, we need to calculate the original price before the discount. Let's assume the original price of the book is 'x'. After a 35% discount, the book costs $11.21. We can set up the equation:
x - 0.35x = 11.21
Simplifying the equation, we get:
0.65x = 11.21
Dividing both sides by 0.65, we find:
x = 11.21 / 0.65
Using a calculator, we get:
x ≈ $17.24
Therefore, the normal undiscounted price of the book is $17.24.
Learn more about calculating undiscounted price here:https://brainly.com/question/16322266
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Rate the following bank accounts from most to least liquid: CD, savings account, checking account, money market account.
a CD, savings account, checking account, money market account
b. Savings account, checking account, CD, money market account
C. CD, money market account, savings account, checking account
d. Checking account, savings account, money market account, CD
Please select the best answer from the choices provided
Mark this and return
Save and Exit
Next
Submit
Answer:
d
Step-by-step explanation:
Answer:
d. Checking account, savings account, money market account, CD
Ben needs to mix 1.5 cups of lemonade concentrate with 4 cups or water to make lemonade. He has 6 cups of concentrate. How much water does he need?
Answer:
24
Step-by-step explanation:
To get your answer, you need to multiply 1.5 and 6.
1.5 x 6 = 9
Then you multiply 4 and 6.
4 x 6 = 24
Which is your final answer.
I hope this helps you! Good Luck!Find the radius of a circle with area equal to 153.86 square feet.
R = ?
Answer:
7 feet
Step-by-step explanation:
The area of a circle can be found using:
a=3.14*r^2
We know that the area is 153.86 square feet, so we can substitute 153.86 in for a.
153.86=3.14*r^2
Now, we have to solve for r. To do this, we need to get r by itself. First, divide both sides by 3.14
153.86/3.14=3.14*r^2/3.14
153.86/3.14=r^2
49=r^2
Now, r is being squared. The opposite of squared is the square root. So, take the square root of both sides .
√49=√r^2
√49=r
7=r
The radius is 7 feet
The radius of the circle with an area of 153.86 square feet is approximately 7 feet.
How to determine the radius of a circle with area equal to 153.86 square feet.To find the radius of a circle given its area, you can use the formula:
Area = π * r^2
In this case, we are given the area as 153.86 square feet.
153.86 = π * r^2
To solve for the radius (r), we need to isolate it. Divide both sides of the equation by π:
153.86 / π = r^2
Now, take the square root of both sides to find r:
r = √(153.86 / π)
Using a calculator or approximating the value of π as 3.14, we can calculate:
r ≈ √(153.86 / 3.14) ≈ √49.0401 ≈ 7
Therefore, the radius of the circle with an area of 153.86 square feet is approximately 7 feet.
Learn more about radius at https://brainly.com/question/27696929
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What is the set of all x values called? *
The domain of a relation is the set of all the x-terms of the relation.
If an x-term appears twice in a relation, only list in once in the domain.
A cylinder with height 9 inches and radius 6 inches. What is the exact volume of the cylinder? Cylinder V=Bh V = 54 pi inches cubed V = 108 pi inches cubed V = 324 pi inches cubed V = 486 pi inches cubed
Answer:
V=324 pi inches cubed
Step-by-step explanation:
The formula for the volume of a cylinder is πr²h
π(6)²(9)
π(324)
Answer:
c : 324 pi in cubed. on edge 2020
Step-by-step explanation:
Please answer for a chance to be entered in the iphone 11 pro giveaway!!!
Sponsered by Beyonce Carter !!!!!!!!!!!!!!!!!!!!!
Answer:
5.8<x<6.0 I think
Step-by-step explanation:
why?
when a trend line is drawn on a scatter plot, there are four points above the trend line. about how many points should be below the trend line?
a. 0
b. 2
c. 4
d. 8
Answer:4
Step-by-step explanation:
$5 PAYPAL + BRAINLIEST TO ANSWER THS
1) Please Rewrite this quadratic equation to
Standard Form: 3x^2=2x +5
2) Using your answer from 1): Assign values of a, b and c based on the
Standard Form of a Quadratic Equation
3) Find the value of the discriminant by substituting a,b and c from 2) and evaluating **Discriminant: ( )^2-4( )( ) = ?? **
4) Based on the discriminant, what type of solutions can we expect for this quadratic equation? Use complete sentences and proper grammar
IF ANSWERED PROPERLY I WILL MESSAGE YOU ASKING FOR YOUR PAYPAL EMAILING ADDRESS THANK YOU!
Answer:
Quadratic Equation:
[tex]3x^2=2x +5[/tex]
[tex]\text{Standard Form: } 3x^2-2x-5=0[/tex]
From the standard form of a Quadratic Function, we get:
[tex]a=3,\:b=-2,\:c=-5[/tex]
Discriminant:
[tex]\Delta=\left(-2\right)^2-4\cdot \:3\left(-5\right)[/tex]
[tex]\Delta=\left(-2\right)^2+4\cdot \:3\cdot \:5[/tex]
[tex]\Delta=64[/tex]
From the discriminant, we conclude that the equation will have two real solutions.
State that:
[tex]b^2-4ac <0:\text{The equation has no real solutions, the solutions are complex}[/tex]
[tex]b^2-4ac =0:\text{The equation has 1 real solution}[/tex]
[tex]b^2-4ac >0:\text{The equation has 2 real solutions}[/tex]
By the way, solving the equation given:
[tex]$x=\frac{2\pm\sqrt{64}}{2\cdot \:3}$[/tex]
[tex]$x=\frac{2\pm\sqrt{64}}{6}$[/tex]
[tex]$x=\frac{2\pm8}{6}$[/tex]
[tex]$x_{1} =\frac{10}{6}=\frac{5}{3} $[/tex]
[tex]$x_{2}=\frac{-6}{6} =-1$[/tex]
Evaluate each expression
Use the values a = 5 and b = 3
3(a+b)
(a+b)-7
4(2a+b)
6( a- b )+5
( a + b) ( a -b )
(2a + b ) (2a - b)
3 ( b + a )
4 (b + 2a
Answer:
Answers are all the way to the right
Step-by-step explanation:
3(a+b) 3(5 + 3) 3(8) 24
(a+b)-7 (5 + 3) - 7 8 - 7 1
4(2a+b) 4(2*5 + 3) 4(10 + 3) 4(13) 52
6( a- b )+5 6(5 - 3) + 5 6(2) + 5 12 + 5 17
( a + b) ( a -b ) (5 + 3)(5 - 3) 8(2) 16
(2a + b ) (2a - b) (2*5 + 3)(2*5 - 3) (10 + 3)(10-3) 13(7) 91
3 ( b + a ) 3(3 + 5) 3(8) 24
4 (b + 2a) 4(3 + 2*5) 4(3 + 10) 4(13) 52
If these answers are correct, please make me Brainliest!
an umbrella at a shop was marked for $6. during a slae a discount of 10% was given. A further 8% discount was given to senior citizens. how much would a senior citizen need to pay for the umbrella during the sale? Round you answer to the nearest cent.
Answer:
75
Step-by-step explanation:
Answer:
5.52
Step-by-step explanation:
this is because if you do
6 * 0.08 it would equal 0.48
then subtract 0.48 from 6
How should the decimal point in 948.921 change to get the correct answer to 948.921 ÷ 10 to the power of 4?
move it 4 places to the left
move it 4 places to the right
move it 5 places to the left
move it 5 places to the right
Answer:
move it 4 places to the left
Step-by-step explanation:
10 to 4th power is basically 10000 so 948.921 divided by 10000 so its obvious it will not move to the right, making the number bigger.
Red box weighs 50 pounds, blue box weighs 60 pounds, and yellow box weighs 115 pounds. What is the average weight in pounds?
Answer: 75
Step-by-step explanation:
Add the three factors and divide by three.
YO Gang i need yo help pleaseeeeee!!
1. What is 5/6 of an hour?
2. What is 2/3 of an hour?
3. What is 0.25 of an hour?
Answer:
5/6 of an hour is 50 minutes.
2/3 of an hour is 40 minutes.
0.25 of an hour is 15 minutes.
Solve 14x + 1 = 36.
Round to the nearest ten-thousandth.
Answer:
x≈ 3.2056
Step-by-step explanation:
Set both sides by log. Then, solve for x.
1. 14^(x + 1) = 36
(x + 1)log(14) = log(36)
x + 1 = log(36)/log(14) . . . Divide both sides by log(14)
x = log(36)/log(14) - 1 . . . . Subtract both sides by 1.
x ≈ 0.3579 . . . . . . . . . . . .Use calculator to simplify the expression.
Note that the second problem is similar to the first.
2. 12^(y - 2) = 20
(y - 2)log(12) = log(20)
y - 2 = log(20)/log(12)
y = log(20)/log(12) + 2
y ≈ 3.2056
Answer:
X=2.5
Step-by-step explanation:
14x +1 =36
14x + 1 =36
- 1 = 36
14x = 35
14x / 2 = 35 / 2
x = 2.5