The answer would be 12.5 ft
This is because you know that if you cast a shadow of 8 feet and you are 5 feet then a lamp post that is 12.5 feet will have a 20 foot shadow.
To solve for the height of the lamppost, we can use the equation h = (5/8) * 20, derived from the ratio of height to shadow length across similar triangles.
To determine the height of the lamppost using the shadow lengths, we apply the concept of similar triangles. Since the student's height and shadow form a right-angled triangle, and the lamppost and its shadow do as well, the two triangles are similar by the angle-angle similarity postulate. Thus, the ratio of the height to the shadow length is constant for similar triangles created by an object and its shadow under the same lighting conditions.
The relationship for the student can be expressed as student's height / student's shadow length, which is equal to 5 feet / 8 feet. For the lamppost, the relationship can be described as height of lamppost (h) / lamppost's shadow length, which is h / 20 feet. Therefore, the proportion can be set up as:
5/8 = h/20
Multiplying both sides of the proportion by 20 gives us the equation to solve for h, the height of the lamppost:
h = (5/8) * 20
the money used in eygpt is called the pound.The exchange rate is $5 to 29 pounds. Find how many Pounds you would recieve if you exchanged $15
87 Pounds would be the correct answer I believe.
5x=29x
x=3
87 pounds
Since $5 = 29. You can multiply both 5 and 29 to get 15=87 pounds
Solve for x.
−32>−5+9x
The inequality is
[tex]-32> -5+9x[/tex]
We need to isolate x and for that first we need to get rid of 5 by adding 5 to both sides.
[tex]-32+5 +-5+9x+5\\-27>9x\\[/tex]
Now we need to get rid of 9 and for that we divide both sides by 9 .That is
[tex]-\frac{27}{9}>\frac{9x}{9}[/tex]
[tex]-3>x[/tex]
[tex]x<-3[/tex]
Find each unit rate. Round your answer to the nearest hundredth.
1.) Teresa can buy 18 golf balls for $32.99.
2.) A 15 oz bottle of juice costs $2.75.
For unit rate, divide the total dollar amounts by the amount of the item you have.
in number 1:
18 golf balls equal $32.99
so divide 32.99 by 18
32.99
18
This tells us that 1 golf ball costs roughly $1.83
2. Do the same thing except put the ounces of juice under the total cost
2.75
15
This will tell us that 1 oz of juice costs $0.18.
Since this is in word form, it is a rule in higher math to answer in the same format.
The unit rate for one golf ball is $1.83, and it costs $0.18 per ounce of juice.
Factor completely 12x4 + 6x3 + 18x2.
Prime
3(4x4 + 2x3 + 6x2)
3x2(4x2 + 2x + 6)
3x(4x3 + 2x2 + 6x)
Answer:
B)3x^2 (4*x^2 + 2x + 6)
Step-by-step explanation:
Step 1: Find the Greatest common factor of the given expression.
12x^4 + 6x^3 + 18x^2
The above expression can be written as .
= 2*2*3*x^4 + 2*3*x^3 + 2*3*3*x^2
Here 3x^2 is prime factor
Step 2: Let's take out the 3[tex]x^{2}[/tex] and write the remaining terms in the parenthesis.
= 3x^2 (2*2*x^2 + 2x + 2*3)
= 3x^2 (4x^2 + 2x + 6)
Therefore, the answer is B)3x^2 (4*x^2 + 2x + 6)
Thank you.
Drag each expression to show whether it is equivalent to 36x + 9, 9(4x – 1), or (4 • 9x) + (4 • 2).
Start with expressions in blue boxes:
1st column) [tex]36x+9;[/tex]
2nd column) [tex]9(4x-1)=36x-9;[/tex]
3rd column) [tex](4\cdot 9x)+(4\cdot 2)=36x+8.[/tex]
You have 6 expressions. Consider all them:
1. [tex]36x+8[/tex] - 3rd column;
2. [tex](9\cdot 4x)+(9\cdot 1)=36x+9[/tex] - 1st column;
3. [tex](3\cdot 12x)-(3\cdot 3)=36x-9[/tex] - 2nd column;
4. [tex]9(4x+1)=36x+9[/tex] - 1st column;
5. [tex]36x-9[/tex] - 2nd column;
6. [tex]4(9x+2)=36x+8[/tex] - 3rd column.
Answer:
The equivalent expressions are:
[tex]36x + 9=(9\cdot 4x) + (9\cdot 1)=9(4x + 1)[/tex]
[tex]9(4x-1)=36x-9=(3\cdot 12x)-(3\cdot 3)[/tex]
[tex](4\cdot 9x)+(4\cdot 2)=4(9x+2)=36x+8[/tex]
Step-by-step explanation:
Consider the provided expressions.
[tex]36x + 9[/tex]
The expression [tex]36x + 9[/tex] can be written as:
[tex]36x + 9=(9\cdot 4x) + (9\cdot 1)[/tex]
[tex]36x + 9=(9\cdot 4x) + (9\cdot 1)=9(4x + 1)[/tex]
Consider the expression [tex]9(4x-1)[/tex]
The expression [tex]9(4x-1)[/tex] can be written as:
[tex]9(4x-1)=36x-9[/tex]
Take 3 common.
[tex]9(4x-1)=36x-9=(3\cdot 12x)-(3\cdot 3)[/tex]
Consider the expression [tex](4\cdot 9x)+(4\cdot 2)[/tex]
The expression [tex](4\cdot 9x)+(4\cdot 2)[/tex] can be written as:
Take out 4 common
[tex](4\cdot 9x)+(4\cdot 2)=4(9x+2)[/tex]
Open the parentheses.
[tex](4\cdot 9x)+(4\cdot 2)=4(9x+2)=36x+8[/tex]
If u help me out I will give a thanks...a hot air ballon are able to fly at a very high altitudes. A world record height of 68,997 feet was set in 1988. In 2005, a new record of 68,986 feet was set. How many feet higher was the 2005 record then 1988 record?
3 less than a product of two numbers
Let x= #1 number
let y= #2 number
We would get xy-3 as the answer
ab-3 is the required expression for the sentence "3 less than a product of two numbers". Here a and b are two numbers.
we need to write expression for 3 less than a product of two numbers
What is product of two numbers?The product is the multiplication of two integers.
Let a be one number
b be second number
Product of two numbers is ab.
as given 3 less than a product of two numbers
we get ab-3.
Therefore ab-3 is the required answer for 3 less than a product of two numbers.
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50 times the sum of 64 and 36
(64+36)x50= 5,000
Brainliest Please
50(64 + 36) = 5000
Hope this helps
-AaronWiseIsBae
a total of $9500 is invested, part at 10% simple interest and part at 9%. if the total annual return from the two investments is $914.00, how much is invested at each rate?
a total of $9500 is invested, part at 10% simple interest and part at 9%
if the total annual return from the two investments is $914.00
Amount invested = 9500
Total amount return means total yield = $914
Let x amount is invested at 10% simple interest
Interest for first part = 10 % times x = 0.10x
Remaining part invested is 9500 -x
Interest for remaining amount = 9% (9500 -x) = 0.09(9500-x)
Total interest yield is 914. Now we frame an equation
0.10x + 0.09(9500-x) = 914
0.10x +855 - 0.09x = 914 (combine like terms)
0.01 x + 855 = 914 (subtract 855)
0.01x = 59 ( divide both sides by 0.01)
So x = 5900
$5900 is invested in 10% simple interest
9500 - 5900 = $3600 is invested in 9% simple interest
Final answer:
To solve the problem, we set up a system of equations based on the provided information. After simplifying and solving the system, we find that $5900 is invested at 10% and $3600 is invested at 9%.
Explanation:
Investment Allocation Problem
Let's denote the amount of money invested at 10% as $x and the amount of money invested at 9% as $y. Since the total amount invested is $9500, we can write the first equation as:
x + y = 9500
The total annual return from the investments is $914. We know that the interest from the first investment is 0.10x and from the second investment is 0.09y. Thus, our second equation, based on the total interest earned is:
0.10x + 0.09y = 914
Now we can solve the system of equations:
x + y = 9500 (Equation 1)
0.10x + 0.09y = 914 (Equation 2)
Multiplying Equation 1 by 0.10 gives us a new equation:
0.10x + 0.10y = 950 (Equation 3)
Now, we subtract Equation 2 from Equation 3:
(0.10x + 0.10y) - (0.10x + 0.09y) = 950 - 914
0.10y - 0.09y = 36
0.01y = 36
y = 3600
Substitute y = 3600 into Equation 1 to find x:
x + 3600 = 9500
x = 5900
Therefore, $5900 is invested at 10% and $3600 is invested at 9%.
Simplify the expression. Write your answer as a power.
8^10⋅8^4
8^14 is the answer.
This is because since they both have the same base, the exponents could be added together if the numbers are multiplied together
Hello Tim!
[tex]8^1^0*8^4[/tex]
First you had to used apply exponent rule.
[tex]8^1^0*8^4=8^1^0^+^4=8^1^4[/tex]
[tex]=8^1^4[/tex]
Answer⇒⇒⇒8¹⁴
Hope this helps!
Thank you for posting your question at here on Brainly.
-Charlie
1. Estimate how many times larger 4 x 1015 is than 8 x 109 in the form of a single digit times an integer power of 10. 2. Estimate how many times larger 2 x 10-5 is than 4 x 10-12 in the form of a single digit times an integer power of 10.
Answer:
[tex]4*10^{15}[/tex] is [tex]5*10^5[/tex] times larger than [tex]8*10^9[/tex]
[tex]4*10^{15}[/tex] is [tex]5*10^6[/tex] times larger than [tex]4*10^{-12}[/tex]
Explanation:
Ratio between [tex]4*10^{15}[/tex] and [tex]8*10^9[/tex] = [tex]\frac{4*10^{15}}{8*10^9} =5*10^5[/tex]
So [tex]4*10^{15}[/tex] is [tex]5*10^5[/tex] times larger than [tex]8*10^9[/tex]
Ratio between [tex]2*10^{-5}[/tex] and [tex]4*10^{-12}[/tex] = [tex]\frac{2*10^{-5}}{4*10^{-12}} =5*10^6[/tex]
So [tex]4*10^{15}[/tex] is [tex]5*10^6[/tex] times larger than [tex]4*10^{-12}[/tex]
Heather eats a jelly sandwich every 5th day and drinks milk every 4th day. If she had a jelly sandwich and milk today, how many days will pass before she will have both again?
Follow below steps:
The question is asking to identify how many days will pass before Heather will have both a jelly sandwich and milk again, given that she eats a jelly sandwich every 5th day and drinks milk every 4th day. To find out when Heather will have both on the same day again, we need to find the Least Common Multiple (LCM) of the two numbers, 5 and 4.
The multiples of 5 are 5, 10, 15, 20, 25, and so on. The multiples of 4 are 4, 8, 12, 16, 20, and so on. The first common multiple of both 5 and 4 is 20. Therefore, Heather will have both a jelly sandwich and milk together on every 20th day after today.
So, after today, Heather will wait 19 more days before having both a jelly sandwich and milk on the same day again.
No scale is shown on this map of a wilderness area. The distance between Rose Lake and the main road is 3.5 mi. On the map it is 2 in. The distance from Rose Lake to the hiking trail is 4 in. What is the actual distance in miles between Rose Lake and the hiking trail?
Final answer:
To find the actual distance from Rose Lake to the hiking trail, a proportion is used based on the given information of the map scale, resulting in an actual distance of 7 miles.
Explanation:
The question involves solving for an actual distance on a map scale, which is a proportional relationship problem in mathematics. To find the actual distance between Rose Lake and the hiking trail, we can set up a proportion using the given distances: if 2 inches on the map equal 3.5 miles in reality, then 4 inches would represent the distance from Rose Lake to the hiking trail (since the relationship between inches on the map and actual miles should be consistent).
Set up the proportion as follows:
2 inches (map) / 3.5 miles (real) = 4 inches (map) / X miles (real)
Now, solve for X, which represents the unknown actual distance in miles. By cross-multiplying and solving for X, we get:
X = (4 inches * 3.5 miles) / 2 inches
Therefore, the actual distance between Rose Lake and the hiking trail is 7 miles.
Explain the distance formula. Then use it to calculate the distance between A(1,1) and B (7,-7)
The distance formula is given by:
[tex]d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} }[/tex]
We are given two points A and B as
A(1,1) and
B(7,-7)
so we have ,
x1 = 1 , y1=1
x2= 7 and y2=-7
Plugging these in the formula we have:
[tex]d=\sqrt{(7-1)^{2}+(-7-1)^{2} }[/tex]
d=√(36+64)
d=√100
d=10
Answer: The distance between A(1,1) and B(7,-7) is 10
Answer:
d=10 units
Step-by-step explanation:
Hello.
Step 1
the formula of the distance between two points is based on the Pythagorean theorem, which states that in a rectangle :
[tex]side^{2} +side^{2}=hypotenuse^{2}\\[/tex]
Now, suppose we have two points P1(X1,Y1) and P2(X2,Y2), the distance between the two points will be the hypotenuse of our triangle, the difference in x will be the adjacent leg, and the difference in coordinates in y will be our opposite leg.
adjacent side =X2-X1
opposite side=Y2-Y1
hypotenuse=distance between P1 and P2
replacing
[tex]adjacent\ leg^{2} +opposite\ leg^{2}=hypotenuse^{2}\\(x_{2}-x_{1}) ^{2} +(y_{2}-y_{1})^{2}=(distance between\ P1\ and\ P2)^{2}\\ distance between\ P1\ and\ P2=\sqrt{(x_{2}-x_{1}) ^{2} +(y_{2}-y_{1})^{2}} \\\\[/tex]
we take only the positive root because it is a distance, a negative distance makes no sense
Step 2
find the distance between A(1,1) and B (7,-7) using the formula
Let
P1=A(1,1)
P2=B(7,-7)
put the values into the formula
[tex]d=\sqrt{(x_{2}-x_{1}) ^{2} +(y_{2}-y_{1})^{2}} \\let\\\\x_{1}=1,y_{1}=1,x_{2}=7,y_{2}=-7\\d=\sqrt{(7-1) ^{2} +(-7-(1))^{2}}\\d=\sqrt{(6) ^{2} +(-8)^{2}}\\d=\sqrt{36 +64}\\d=\sqrt{100}\\ d=10[/tex]
d=10 units
Have a good day.
In a basketball game, the bulldogs make a total of 21 shots. Some of the shots are 2-pt shots while others are 3-pt shots. The bulldogs score a total of 50 points. How many 2-point and 3-point shots did they make?
Answer:
It is 8 3 pointers and 13 2 pointers
Step-by-step explanation:
8 x 3 = 24
13 x 2 = 26
24 + 26 = 50
The bulldogs made 13 2-pt shots and 8 3-pt shots.
Explanation:Let's assume that the bulldogs made x 2-pt shots and y 3-pt shots. Since each 2-pt shot is worth 2 points and each 3-pt shot is worth 3 points, we can set up the following equations: 2x + 3y = 50 (equation 1) and x + y = 21 (equation 2). To solve this system of equations, we can multiply equation 2 by 2 to get 2x + 2y = 42, and then subtract equation 1 from it. This gives us y = 8. Substituting y = 8 into equation 2, we get x + 8 = 21, which means x = 13. Therefore, the bulldogs made 13 2-pt shots and 8 3-pt shots.
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error analysis 7 3/4 divided 1/3
I don't really under stand what to do but the answer for 7 3/4 divided by 1/3 is 23 1/4.
Let me know what else is needed to figure out your question.
simplify final form.
[tex]\left(\dfrac{3}{\sqrt5}\right)\left(\dfrac{4}{\sqrt3}\right)=\dfrac{3\cdot4}{\sqrt5\cdot\sqrt3}=\dfrac{12}{\sqrt{5\cdot3}}=\dfrac{12}{\sqrt{15}}\\\\=\dfrac{12\cdot\sqrt{15}}{\sqrt{15}\cdot\sqrt{15}}=\dfrac{12\sqrt{15}}{15}=\dfrac{12\sqrt{15}:3}{15:3}=\dfrac{4\sqrt{15}}{5}[/tex]
[tex]Used:\\\\\sqrt{a}\cdot\sqrt{b}=\sqrt{ab}\\\\\sqrt{a}\cdot\sqrt{a}=a[/tex]
calculate the midpoint of a line segment with the endpoints 7,12 and -1,6
The formula of a midpoint:
[tex]M_{AB}\left(\dfrac{x_A+x_B}{2},\ \dfrac{y_A+y_B}{2}\right)[/tex]
We have:
[tex]A(7,\ 12)\to x_A=7,\ y_A=12\\B(-1,\ 6)\to x_B=-1,\ y_B=6[/tex]
Substitute:
[tex]\dfrac{7+(-1)}{2}=\dfrac{7-1}{2}=\dfrac{6}{2}=3\\\\\dfrac{12+6}{2}=\dfrac{18}{2}=9[/tex]
Answer: (3, 9).nick can read 3 pages in 1 minute. write the ordered pairs for nick reading 0,1,2, and 3 minutes.
(0, 0) 0 pages in zero minutes.
(3, 1) 3 pages in one minute.
(6, 2) 6 pages in two minutes.
(9, 3) 9 pages in three minutes.
What is the perimeter of the quadrilateral 9m 5m 7m 11m
The perimeter is 32m add all sides to find perimeter
What’s the derivative of sin^2(cos(x^2))
Answer:
[tex]\displaystyle \frac{dy}{dx} = -4x \sin x^2 \sin (\cos x^2) \cos (\cos x^2)[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationBasic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = \sin^2 (\cos x^2)[/tex]
Step 2: Differentiate
Basic Power Rule [Derivative Rule - Chain Rule]: [tex]\displaystyle y' = 2 \sin (\cos x^2) \Big( \sin (\cos x^2) \Big)'[/tex]Trigonometric Differentiation [Derivative Rule - Chain Rule]: [tex]\displaystyle y' = -2 \sin (\cos x^2) \cos (\cos x^2) (\cos x^2)'[/tex]Trigonometric Differentiation [Derivative Rule - Chain Rule]: [tex]\displaystyle y' = -2 \sin x^2 \sin (\cos x^2) \cos (\cos x^2) (x^2)'[/tex]Basic Power Rule: [tex]\displaystyle y' = -4x \sin x^2 \sin (\cos x^2) \cos (\cos x^2)[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
Write the expanded form for the decimal 24.56
Final answer:
The expanded form of the decimal 24.56 is 20 + 4 + 0.5 + 0.06, which breaks down each digit by its place value.
Explanation:
The expanded form of the decimal 24.56 is an expression that shows the value of each digit in the number. To write it in expanded form, we break down each digit according to its place value. For the number 24.56, the expanded form would look like this:
20 (which represents 2 tens, or 2 × 10)4 (which represents 4 ones, or 4 × 1)0.5 (which represents 5 tenths, or 5 × 0.1)0.06 (which represents 6 hundredths, or 6 × 0.01)Combining these values, the expanded form of 24.56 is:
20 + 4 + 0.5 + 0.06
Culinary Arts AGAIN!!! Please help me
Dived the price by the number of ounces and that should be your answer to the questions .
a piece of string is 3 yards long. How many 1 and a quarter yard long pieces can Julie cut from the string?
Answer:
2 pieces
Step-by-step explanation:
Julie wants to cut 1 and a quarter yard long pieces of a 3 yard string.
1 and a quarter yard = [tex]1\frac{1}{4}[/tex] yards = [tex]\frac{5}{4}[/tex] yards
= 1.25 yards
The total length of a piece of string = 3 yards
Julie can cut the number of pieces of 1.25 yards = [tex]\frac{3}{1.25}[/tex]
= 2.4 pieces
She can cut 2 pieces of 1.25 yard = 1.25 × 2 = 2.5 yard
3 yard - 2.5 yard = 0.5 yard would be leftover.
3/8 into a mixed number
Answer:
296
Step-by-step explanation:
111/3 = 37
37 * 8 = 296
Hope this helps :-)
What is 4 * 492 equal to the product
Answer:
1968
Step-by-step explanation:
I use the following method when it comes about products of big numbers
I grab the longer and put on the first line, below I put the smallest number.
492
x 4
Now, it is time to distribute the product, term by term, remember that when performing a product, if the result is greater or equal than 10, you need to carry a number for the following product.
492
x 4
--------------------
19 6 8
(end) (c3) (nc)
nc means: not carrying anything since 4x2=8 and 8 <10
c3 means: carrying 3 since 4x9= 32 and 32 >10
end means: put the whole number and sum it what you were carrying. 4*4+3=19
The product 492*4=1968
The product of 4 multiplied by 492 equals 1968. To find this, we used a step-by-step approach using basic multiplication and the distributive property.
To determine the product of 4 multiplied by 492, you can execute the following steps:
First, break down the problem into smaller, manageable parts. Let's use the fact that 4 = 2 x 2.Multiply 4 by 492 directly: 4 × 492.To perform this calculation step-by-step, you can apply the distributive property: (4 × 500) - (4 × 8).Calculate each part: 4 × 500 = 2000 and 4 × 8 = 32.Subtract the second product from the first: 2000 - 32 = 1968.Therefore, 4 × 492 = 1968.
if D is the midpoint of CE, CD =9X-7, and DE= 3X+17, find CE.
CE is equal to 58 units.
To find the length of CE, we'll use the fact that D is the midpoint of CE. The midpoint of a line segment divides it into two equal parts.
If CD is one part and DE is the other, then we can set up an equation:
CD=DE
9X−7=3X+17
Now, solve for X:
6X=24
X=4
Now that we have the value of X, substitute it back into either CD or DE to find the length of each part:
CD=9X−7=9(4) −7=36−7=29
DE=3X+17=3(4) +17=12+17=29
Now, since D is the midpoint, CD and DE are equal.
CD=DE=29
Finally, CE, the total length, is the sum of CD and DE:
CE=CD+DE=29+29=58
So, CE is indeed 58
Using graph paper determine the line described by the given point and slope (0,0) and -2/3
Answer:
your graph is gonna have a horizontal line crossing the y axis at (0,3)
outhside High School had a big basketball game Friday night. Six players contributed to their score. Three players scored 16 points each, 2 players made 21 points each and 1 player scored 8 points. Which expression would give you their final score?
A) (16 + 21 + 8) x 6
B) 3 x 16 + 2 x 21 +1
C) (3 x 16) + (2 x 21) + 8
D) (3 + 2 + 1) x (16 + 21 + 8)
*I hope this will help*
(3 x 16) + (2 x 21) + 8
3 people made 16, which is 48
2 made 21, making 42
and 1 made 8, making 8
The answer would be c. because there is 3 players with 16 points (3x16) and 2 with 21 points (2x21) so (3x16)+(2x21) and one player scored 8 points so (3x16)+(2x21)+8
I hope this helps have a nice day
Justin and Desiree each wrote a ratio comparing the numbers of students and tables in their classroom. There are 6 tables in the room with 4 students at each table.0
Answer: 4:1
Step-by-step explanation:
Given:- Number of tables in the classroom=6
Number of students on each table = 4
thus number of students in the classroom =6×4=24 students
Now ratio of numbers of students to the tables in the classroom= numbers of students/tables in the classroom=24/6=4/1=4:1
Ratio of numbers of students to the tables in the classroom= 4:1