Answer:
105.72 meters
Step-by-step explanation:
We can set up a system of equations to represent the information given in the problem, and then use algebra to solve for the length of the blue rope. Let x be the length of the red rope.
According to the problem statement:
blue rope = 3 * red rope = 3x
green rope = 4 * blue rope = 4 * 3x = 12x
we know that:
red rope + blue rope + green rope = 563.84
x + 3x + 12x = 563.84
then we can solve for x:
16x = 563.84
x = 35.24
So the length of the red rope is 35.24 meters.
The length of the blue rope is 3x = 3 * 35.24 = 105.72 meters.
Goran invested his savings in two investment funds. The amount he invested in Fund A was 7000 less than the amount he invested in Fund B. Fund A returned a 4% profit and Fund B returned a 2% profit. How much did he invest in Fund B, if the total profit from the two funds together was 500?
If Goran invested his savings in two investment funds. The amount that Goran invest in Fund B, if the total profit from the two funds together was 500?
How to find the amount invested?Amount Invested in Fund A = x
Amount invested in Fund B = x+7000
Profit from fund A = 0.04x
Profit from fund B = 0.02(x+7000)
0.04x +0.02(x+7000) = 500
0.04 +0.02x + 140 =500
Combine like terms
0.06 x =360
Divide both side by 0.06x
x = 360 /0.06
x = 6,000
Amount Invested in Fund A = x =6,000
Amount invested in Fund B = x+7000
Amount invested in Fund B = 6,000 + 7,000
Amount invested in Fund B = 13,000
Therefore the amount invested in Fund A 6,000 and the Fund B is 13,000.
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Click on a factor pair of 32
Factor pair of 32 are (1, 32) ; (2, 16) ; (4, 8)
⇒ Firstly find the factors of 32
How Do You Work Out Factors of 32?
Step 1: Let's start with the whole number 1 and work our way up to the factors of 32. 32 ÷ 1= 32
Step 2: Now divide 32 by two. 32 ÷ 2= 16
Step 3: Then we get. 32 ÷ 4= 8
Step 4: Similarly, we calculate all the 32 factors.
32 factors = 1, 2, 4, 8, 16, and 32.
⇒ Secondly, find factor pairs of 32
The two numbers that, when multiplied together, give 32 are the factors of 32 in pairs. The factors of 32 are listed below in pairs.
Products of 32 Factor pair of 32
1 × 32 = 32 (1, 32)
2 × 16= 32 (2 ,16)
4 × 8 = 32 (4, 8)
∴Therefore, factor pair of 32 are (1, 32) ; (2, 16) ; (4, 8)
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Michael bakes a soft pretzel and a loaf of bread. Use the system of equations to find c, the amount of flour, in cups, needed for the soft pretzel, and b, the amount of flour, in cups, needed for the loaf of bread. Show your work.
b = 24c
(1/4)b + 4c = 5/4
The amount of flour needed for soft pretzel is c = 1/8 and the amount of flour needed for the loaf of bread is b = 3.
What are Linear Equations?Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.
Linear equations may include one or more variables.
Given system of equations,
b = 24 c and
[tex]\frac{1}{4}[/tex] b + 4c = [tex]\frac{5}{4}[/tex]
Substitute b = 24 c in the second equation.
[tex]\frac{1}{4}[/tex] (24 c) + 4c = [tex]\frac{5}{4}[/tex]
6c + 4c = [tex]\frac{5}{4}[/tex]
10 c = [tex]\frac{5}{4}[/tex]
c = [tex]\frac{5}{4}[/tex] × [tex]\frac{1}{10}[/tex] = [tex]\frac{1}{8}[/tex]
b = 24c = 24 / 8 = 3
Hence c = 1/8 and b = 3 in cups.
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how are algebraic expressions used to represent and solve problems
Answer:
How are algebraic expressions used to represent and solve problems?
The purpose of solving an algebraic expression in an equation is to find the unknown variable. When two expressions are equated, they form an equation, and therefore, it becomes easier to solve for the unknown terms. To solve an equation, place the variables on one side and the constants on the other side.
Step-by-step explanation:
How can you use algebraic expressions to solve problems?
To solve an algebraic word problem:
1. Define a variable.
2.Write an equation using the variable.
3.Solve the equation.
4.If the variable is not the answer to the word problem, use the variable
to calculate the answer.
How are algebraic expressions applied in real life situations?
utilizing linear algebra, and this uniqueness starts to expose a lot of applications. Other real-world applications of linear algebra include ranking in search engines, decision tree induction, testing software code in software engineering, graphics, facial recognition, prediction and so on.
What is algebraic expression why it is used in mathematics?
In mathematics, an algebraic expression is an expression built up from integer constants, variables, and the algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number). For example, 3×2 − 2xy + c is an algebraic expression.
find the nth term of the following sequence :
5, 20, 45, 80, 125
The nth term of the following sequence is: 5n²
What is arithmetic sequence?Arithmetic sequence is a sequence where each consequtive term has a common constant difference.
An arithmetic sequence, therefore, is defined by two parameters, viz. the starting term and the common difference.
We are given the sequence are;
5, 20, 45, 80, 125
The quadratic sequence formula : an²+bn+c
2nd difference 2a = 10
a = 5
1st difference 3a+b = 15
Then substitute 5
3(5)+b = 15
b = 0
The nth term rule : a + b + c = 5
Now substitute a and b values into equation
5 + 0 + c = 5
c = 0
The nth term is: 5n²
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What is the equation of a line with a slope of 3 and a point (3. 1) on the line? Express the equation in the form of y Enter your answer in the box mz+ b where m is the slope and b is the y-intercept
A line with a slope of three and the point three on the line have the equation y=3 z+1. The equation of a straight line can be found using the formula y = mx + b.
What do you meant by y-intercept ?If a line has a slope of 3 and a y intercept of 1, you need to determine its equation. Remember the line's equation by first going back: when y=mz+b , M is the slope, and Y-intercept b is the value.
In order to solve for y in the equation y=m z+b, all you need to do is swap out m for 3, the slope you provided, and b for 1, the y-intercept. The line's equation is given by y=3 z+1, where z represents the line's y-intercept and slope. If you are aware of the slope of the line being studied and the provided point is also the y intercept, you can utilise the slope intercept formula, y=mx+b (0,b).
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Katrina buys a 76-ft roll of fencing to make a rectangular play area for her dogs. Use
2({+w) = 76 to write a function for the length, given the width. Graph the function.
What is a reasonable domain for the situation? Explain.
Therefore , As a result 5, 10, and 15 make up the reasonable domain for the function 2 (l + w) = 64..
The definition of functionA connection between a group of sources and one output for each input is referred to as a function. A function is, to put it simply, a collection of equation connected to a single, unique output. In mathematics, a function is a statement, rule, or law that describes the connection between two variables (the dependent variable). One input leads to one output when a rule of this type is used. by Alex Federspiel, the photographer. This statement gives an example of y=x2. There is just one output for y from any input for x. According to our definition, y is a function of x since x is the input value.
Here,
We have the following for the rectangle's perimeter:
2 ( l + w ) = 64
Here,
W = width, and L = length.
We must determine the length and breadth values necessary to make the rectangle's perimeter 64.
Now,
2 ( l + w ) = 64
l + w = 32
Thus, the sum of the length and breadth measurements must equal 32.
The possible widths are 5, 10, 15, 20, and 25.
Now,
l + 5 = 32
l = 27
l + 10 = 32
l = 22
l + 15 = 32
l = 17
l + 20 = 32
l = 12
l + 25 = 32
l = 7
We think about
The domain has widths of 5, 10, 15, 20, and 25.
The range for length is: 27, 22, 17, 12, and 7.
Values for width and length are used as the x- and y-axes, respectively.
Below is a graph of the data.
The following is the reasonable domain for the aforementioned situation:
5, 10, 15, 20, and 25
Below is a graph of the function 2 (l + w) = 64.
Therefore , As a result, 5, 10, and 15 make up the reasonable domain for the function 2 (l + w) = 64.
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What is the solution of the inequality shown
below?
a+5>-7
The required solution for the inequality a + 5 > -7 is (-12, ∞).
What is inequality?Inequality shows relation between two expression which are not equal to each others.
The given inequality is,
a + 5 > -7
To find the solution for the inequality,
Simplify the inequality,
a + 5 > - 7
a > - 7 - 5
a > -12
The value of a is greater than -12, implies that,
The solution for the value of the given inequality is (-12, ∞).
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an altitude is drawn from the vertex of an isosceles triangle forming a right angle and two congruent triangles. as a result, the altitude cuts the base into two equal segments. the length of the altitude is 30 inches, and the length of the base is 10 inches. find the triangles perimeter. round to the nearest tenth of an inch.
The perimeter of the isosceles triangle with altitude 30 inches and base 10 inches is calculated to be 70.82 inches
How to find the perimeter of the isosceles trianglePerimeter of a triangle refers to the surface dimensions, this is calculated by the formula
Perimeter, P = a + b + c
where
a, b, c are sides of the triangle
The third side of the triangle will be calculated using Pythagoras theorem given by the the formula
hypotenuse² = opposite² + adjacent²
The right triangle consist 1/2 the isosceles triangle base = 5 inches and the altitude = 30 inches
plugging the values as in the problem
let x be the required distance
x² = 30² + 5²
x² = 900 + 25
x² = 925
x = √925
x = 30.41 inches
Perimeter of the isosceles triangle
= 30.41 + 30.41 + 10
= 70.82 inches
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Pls help! Step by step
Answer:
x = 4[tex]\sqrt{3}[/tex]
Step-by-step explanation:
using the cosine ratio in the right triangle and the exact value
cos30° = [tex]\frac{\sqrt{3} }{2}[/tex] , then
cos30° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{8}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )
2x = 8[tex]\sqrt{3}[/tex] ( divide both sides by 2 )
x = 4[tex]\sqrt{3}[/tex] ( exact value )
Step-by-step explanation:
SOHCAHTOA
CAH-
Cosine●= adj/hyp
cos30= y/8
0.8660=y/8
Cross multiply
0.8660×8=y
y=8×0.8660
y=6.928
x−2y=3
Determine the missing coordinate in the ordered pair (−4,?) so that it will satisfy the given equation.
Answer:
y=-3.5
Step-by-step explanation:
substitute -4 for x
add 4 on both sides to get rid of the -4
divide -2 on both sides to isolate y
and you get 3.5 for y
The value of y that will satisfy the equation given is -3.5.
What is an equation?Mathematically, an equation can be defined as a statement that supports the equality of two expressions, which are connected by the equals sign “=”.
Given that, the missing coordinate in the ordered pair (−4, ?), we need to find the missing value that will satisfy the equation x-2y = 3,
To find the same, just replace the value of x by -4,
-4-2y = 3
-2y = 7
y = -3.5
Hence, the value of y that will satisfy the equation given is -3.5.
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(1/a)^3 Help simplify please
Answer:
1/a³
Step-by-step explanation:
(1/a)³ = 1³/a³ = 1/a³
Physical Fitness Dino works out regularly. When he first started exercising, he
could do 10 push-ups. After the first month he could do 14 push-ups. After the
second month he could do 19, and after the third month he could do 25. Predict
the number of push-ups Dino will be able to do after the fifth month of
working out. How confident are you of your prediction? Explain.
Answer:
he will do 34 the next month
please answer this is due at 11:59PM!!!
Answer:
Step-by-step explanation:
An explanatory variable is what you manipulate or observe changes in while a response variable is what changes as a result (e.g., reaction times). The words “explanatory variable” and “response variable” are often interchangeable with other terms used in research.
how many times does 12 go into 72
Answer:
Step-by-step explanation:
6
The value of z varies inversely with the value of w. The constant of variation is 2. Which are possible values for z
3
and w? Check all that apply.
Oz=.
z = 1+₁ w = 2/1/201
O z = 2, w = 3
O z=
z = -1/₁w=2
O z
4,
= 1/5, w = 2/1/201
z = 1/2/3₁, w = 2/1/201
Answer:A,C,D
As a result of the inverse relationship between z and w, their product is constant.
What does "inverse connection" actually mean?There is an inverse relationship between two parameters when they are connected, where the value of one parameter tends to decrease as the value of the other parameter increases. It's often described as a "bad friendship" in conversation.
According to the information:z * W is equal to 1.
The statement indicates that the constant's value is 2/3, so:
z * w = 2/3
The result of solving for any of the variables is:
either w = (2/3) / z or z = (2/3) / w
The following values fit that relation:
z w = (2/3) / z
-8/9 (2/3) / (-8/9)
= - (2/3) * (9/8) = -3/4
- 4/9 (2/3) / (-4/9)
= - (2/3) * (9/4) = - 3/2
- 2/9 (2/3) / (-2/9)
= - (2/3) * (9/2) = - 3
2/9 (2/3) / ( 2/9)
= (2/3) * (9/2) = 3
4/9 (2/3) / (4/9)
= (2/3) * (9/4) = 3/2
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The label on Masao's breakfast cereal said that
one serving of cereal provides 85 milligrams (mg) of
potassium, which is 2% of the recommended daily
amount. What is the total recommended daily
amount of potassium?
Nutrition Facts
Serving Size: 1 cup (47g)
Servings Per Container: About 7
Amount Per Serving
Calories
Calories from Fat
Total Fat 1g
Saturated Fat Og
Trons Fat og
Polyunsaturated Fat 0.5g
Monounsaturated Fat 0.5g
Cholesterol Omg
Sodium 190mg
Potassium 85mg
Total Carbohydrate 40g
Dietary Fiber 1g
Sugars 8g
Protein 3g
Cereal With Milk
180
2:30
20
10
% Daily Value
2%
0%
0%
8%
2%
13%
4%
2%
0%
|
0%
11%
8%
15%
4%
STAR
22
Find the unit rate: 406 miles to 14.5 gallons of gas.
Find the unit rate: 423 miles to 18 gallons of gas.
The grocery store charges $3.99 for a case of 24
bottles of water. What is the unit price?
Paul is shopping for laundry detergent. At the grocery
store, the liquid detergent is priced at $14.99 for 64
loads of laundry and the same brand of powder
detergent is priced at $15.99 for 80 loads. Which is
the better buy, the liquid, or the powder
Therefore , the solution of the given problem of percentage comes out to be 4250 mg, or 4.25 g and the percentage increase is 50%.
A percentage is what?A% is a number that can be expressed as a decimal or a fraction and indicates what proportion of 100 it is. Put 100 in the denominator and the percentage amount in the numerator to turn a percentage into a fraction.
Here,
This "Nutritional Facts" table indicates that 85 mg of potassium, or 2% of the daily recommended value, corresponds to the row "Potassium".
By using the unitary method, (85/2) mg of potassium will represent 1% of the daily required intake.
As a result, 4250 mg of potassium, or 100% of the daily allowance, will be required: (85/2 * 100).
The entire quantity of potassium that is advised for daily consumption is 4250 mg, or 4.25 g.
(New value) − (Initial value) / (Initial value) = percent change. * 100%.
Here,
Initial value: $1.50 (the 1995 fare).
New value equals $2.25 for the 2008 fare.
Therefore,
percentage variation
= [(2.25 - 1.50) / 1.50] .50] * 100%
= (0.75 / 1.50) * 100%
= 0.5 * 100%
= 50%.
Positive indications of the transition point to an increase in fare.
The percentage increase is therefore 50%.
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A project requires you to figure out the area of a triangular lot. You take measurements and find that the lot has a base of 32 ft., while the altitude of the triangle, or height is 24 ft. What's the area of this lot?
is 0.2/2.6 0.3/3.6 proportional or not proportional
Answer:
not proportional
Step-by-step explanation:
0.2/2.6 is 1:13
0.3/3.6 is 1:12
Write an equation and solve for b using the diagram
below. YOU MUST WRITE THE EQUATION IN
ORDER TO GET CREDIT.
(3b + 18)°
93°
Step-by-step explanation:
hope this is right hehe.....
10. Matt has twice as many stickers as David. If David has d stickers, and Matt gives David 10 stickers, how many stickers does each have in terms of d?
Therefore, the number of stickers David has in terms of d is d+10 and the number of stickers Matt has in terms of d is 2d-10.
Define term.A term is a phrase or statement that is used to convey a certain meaning. Rap, punk, grunge, and heavy metal are examples of words used to characterize certain musical genres. To the majority of people, at least, "sweetie" is a word of affection.
What are phrases and statements?A phrase is a collection of words with significance but which is not usually a complete sentence. A set of words that form a sentence must have a topic.
We know that Matt has twice as many stickers as David, so if David has d stickers, then Matt has 2d stickers.
When Matt gives David 10 stickers, David has d+10 stickers and Matt has 2d-10 stickers.
So the number of stickers David has in terms of d is d+10 and the number of stickers Matt has in terms of d is 2d-10.
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What is the slope of the line that passes through the points (-4, -6) and (1, -6)? Write your answer in simplest form
The slope of the line that passes through the points (-4, -6) and (1, -6) is zero and hence the line is parallel to the x-axis.
What is slope?The slope is the rate of change of the y-axis with respect to the x-axis.
The equation of a line in slope-intercept form is y = mx + b, where
slope = m and y-intercept = b.
We know the greater the absolute value of a slope is the more steeper is its graph or rate of change is large.
We know slope(m) = (y₂ - y₁)/(x₂ - x₁).
Therefore, The slope of the line that passes through the points (-4, -6) and (1, -6) is,
m = (- 6 + 6)/(- 4 - 1).
m = - 0/5.
m = 0.
As the slope is equal to zero the line is parallel to the x-axis.
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The coordinates of cd are C(-7,-2) and D (-3,-5) Point E is the midpoint of cd What are the coordinates of the midpoint E?
The coordinates of the midpoint of CD with endpoint at C(-7,-2) and D(-3,-5) is E(-5, -3.5)
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Let (x, y) represent the coordinate of the midpoint E. Point E is the midpoint of CD, hence:
x = [(-7) + (-3)] / 2 = -5
y = [(-2) + (-5)] / 2 = -3.5
Therefore the coordinates of the midpoint of CD with endpoint at C(-7,-2) and D(-3,-5) is E(-5, -3.5)
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Question 5 of 10
Mackenzie took out a payday loan for $1100 that charged a $95 fee. If the
loan matures in 2 weeks, what is the approximate effective interest rate of the
loan?
OA. 862%
OB. 86%
OC. 76%
OD. 762%
\int (2)/(\sqrt(5x^(2))+3)dx and steps
Answer:
Step-by-step explanation:
XYZ Company
Balance Sheet
Assets
Cash
$45,000
Inventory $41,000
Property $134,000
Total Assets:
Liabilities
Notes
Wages
Equity
Stock
$55,000
$56,000
$50,000
Investment $59,000
Total Liabilities + Equity:
Using the balance
sheet, calculate XYZ
Company's total
assets - liabilities.
Total Assets - Liabilities = $ [?]
Enter
PH
Skip
On solving the provided question, we can say that - by formula of simple interest we have SI = [tex]2200 X 2 X 4/100 = > 17600/100 = > 176[/tex]
what is interest ?Multiplying the principal by the interest rate, time, and other factors yields simple interest. Simple return equals principle times interest times hours is the marketed formula. It is easiest to compute interest using this formula. A percentage of the principle balance is how interest is most commonly computed. For instance, he will only pay his portion of the 100% interest if he borrows $100 from a buddy and promises to pay it back with 5% interest. $100 (0.05) = $5. When you borrow money, you must pay interest, and when you lend money, you must charge interest. Most of the time, interest is expressed as a yearly percentage of the loan amount. The interest rate on the loan is known as this percentage.
here,
principal, p = 2200
rate, r = 2%
time, t = 4 rs,
so SI = P X R X T/100
SI -
[tex]2200 X 2 X 4/100\\17600/100\\176[/tex]
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Clare has $150 in her bank account. she buys a bike for $200. what is Clare's account balancenow?
Answer:
-50
Step-by-step explanation:
Answer:
Step-by-step explanation:
if she had $150 in he bank account and buys a bike that costs 200 she possibly can't afford it since she is $50 dollars short so even if she borrows $50 dollars she has to repay the person 50 dollars before she starts earning another money so i think it is -50. if it doesn't help am sorry I hope you got this answer correct. goodluck
Which lines are parallel. 1.) The blue and green 2.) blue and red 3.) Red and green 4.) blue,red,green
Answer: 2.) Blue and red
Step-by-step explanation:
The slope of the red and blue ones is - 3 while the green one's slope is -4
Select the answer with the correct number of significant figures for each calculation. 31.580 + 4.26 = 35.8 35.84 35.840
Answer:
35.84
Step-by-step explanation:
What's the inverse of ƒ(x) = x – 20?
Therefore , the solution of Inverse function comes out to be of x-20 equals to x+20
What is the inverse symbol?A function f has an inverse function only if for every y in its range there is only one value of x in its domain for which f(x)=y. This inverse function is unique and is frequently denoted by f−1 and called “f inverse.” For an overview into the idea of an inverse function, see the function machine inverse.Steps for finding the inverse of a function fReplace f(x) by y in the equation describing the function. Interchange x and y. In other words, replace every x by a y and vice versa.
Here,
Solve for y.
Replace y by f-1(x).
y=x-20
x=y-20
Solve for y,x = y-20
x+20
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Answer:
ƒ^(-1)(x) = x + 20
Step-by-step explanation:
To find the inverse of the function ƒ(x) = x - 20, we need to switch the roles of x and y and solve for y.
Let's start by replacing ƒ(x) with y:
y = x - 20
Next, swap x and y:
x = y - 20
Now, solve for y by isolating it:
x + 20 = y
Therefore, the inverse of the function ƒ(x) = x - 20 is given by:
ƒ^(-1)(x) = x + 20