The equations will be 20x and 500w.
How to express the equation?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.
In this case, when offered a job in sales where you can choose to either make a salary $500 (constant) every week or commission of $20 per sale. This will be:
Let the sales be x
The equation will be:
= 20 × x
= 20x.
The second equation will be:
= 500 × w
where w = number of weeks.
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The density of grape juice is 1.07 grams per cm³.
The density of fruit syrup is 1.6 grams per cm³.
The density of carbonated water is 0.99 grams per cm³.
35 cm³ of grape juice are mixed with 25 cm³ of fruit syrup and
310 cm³ of carbonated water to make a drink with a volume of 370 cm³.
Work out the density of the drink.
Give your answer correct to 2 decimal places.
The density of the drink is 1.04 grams per cm³
How to work out the density of the drink?
Given:
density of grape juice = 1.07 grams per cm³, density of fruit syrup = 1.6 grams per cm³ and density of carbonated water = 0.99 grams per cm³
volume of grape juice = 35 cm³, volume of fruit syrup = 25 cm³ and volume of carbonated water = 310 cm³
First, find the mass of grape juice, fruit syrup and carbonated water using their volume and density:
density = mass / volume
=> mass = density × volume
mass of grape juice = 1.07 × 35 = 37.45 grams
mass of fruit syrup = 1.6 × 25 = 40 grams
mass of carbonated water = 0.99 × 310 = 306.9 grams
Total mass = 37.45 + 40 + 306.9 = 384.35 grams
Total volume = 35 + 25 + 310 = 370 cm³
density of the drink = Total mass / Total volume
density of the drink = 384.35 / 370 = 1.04 grams per cm³
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SOMEONE PLEASE HELP ME
7*2*4 = 56.
7 is the length, 2 is the height, 4 is the widght
Equation for volume is l*h*w
A circle of radius 5 is centered at the origin. The line x + 2y = −5 intersects this circle at the points A and B. Determine the length of the major arc AB.
The length of the major arc AB is 15.44 units
How to determine the length of the major arc?Given: line x + 2y = −5 and circle of radius 5 centered at the origin
The equation of a circle of radius r whose center is the origin O (0, 0) is given by x²+y² = r². Thus:
x²+y² = 5²
x²+y² = 25
To find the points where the line intersects the circle, we can substitute the equation of the circle into the equation of the line.
Substituting this into the equation of the line, we have;
x + 2y = -5
x²+y² = 25
Solving for x, we have
x = (-5 ±√(33))/2
Since the circle is centered at the origin, both of these points are on the circle. Thus, the coordinates of the points A and B are
A: (-5 +√(33))/2, (-5 - √(33))/4
B: (-5 - √(33))/2, (5 - √(33))/4
To find the length of the major arc AB, we can use the formula
length = θ/360 × 2πr
where r is the radius of the circle, and θ is the central angle formed by points A and B. The central angle can be found using the formula
θ= 180 - 2cos⁻¹((AB² + r² - AC²)/(2 × AB × r))
where AB is the distance between the points A and B, and AC is the distance between point A and the center of the circle (which is the origin)
We can use the Pythagorean Theorem to find AB and AC:
AB = √(((-5 + √(33))/2 - (-5 - √(33))/2)² + ((-5 - √(33))/4 - (5 - √(33))/4)²)
= √(66)
AC = √(((-5 + √(33))/2)² + ((-5 - √(33))/4)²)
= √(25 + 33)/2
= √(58)/2
Substituting these values into the formula for θ, we have
θ = 180 - 2cos⁻¹((√(66)² + 5² - (√(58)/2)²)/(2 × √(66) ×5))
= 180 - 2cos⁻¹((66 + 25 - 29)/(20))
= 180 -2cos⁻¹(62/20)
= 180 - 2cos⁻¹(3.1)
= 180 - 2 × 1.43
= 180 - 2.86
= 177.14
Finally, substituting this value into the formula for the length of the major arc, we have
length = 2 × π × 5 × (177.14/360)
= 2 × π 5 × (0.4925)
= 2 × 3.14 × 5 × (0.4925)
= 6.28 × 5 × (0.4925)
= 31.4 × (0.4925)
= 15.44 units
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What is the equation, in standard form, of a parabola that models the values in the table x-3 0 2 f(x) -8 -2 -28
The equation in the standard form of a parabola is y = -3x² - 7x - 2
What is the standard form of a parabola?
Another equation that, when graphed, produces a parabola is one written in standard form. Like the letters in the vertex form equation, each letter in the standard form equation provides a nugget of knowledge about the parabola.
Here, we have
The standard equation of a parabola is
y = ax² + bx + c
Substitute the given values in this equation
When x = - 3 and y = -8
-8 = a (-3)² + b (-3) + c
-8 = 9a - 3b + c …. (1)
When x = 0 and y = - 2
-2 = a (0)² + b (0) + c
c = -2....(2)
When x = 2 and y = -28
-28 = a (2)² + b (2) + c
-28 = 4a + 2b + c …. (3)
Equations (1) and (3) can be written as
9a - 3b + c = -8 …. (4)
4a + 2b + c = -28 …. (5)
Multiply equation (4) by 2 and equation (5) by 3 to eliminate 'b'
18a - 6b + 2c = -16
12a + 6b + 3c = -84
Subtracting these equations
30a + 5c = -100
Substitute the value of 'c' here
30a + 5(-2) = -100
30a = -100 + 10
30a = -90
a = -3
Substitute the value of a and c in equation (1)
-8 = 9a - 3b + c
-8 = -27 - 3b -2
-6 = -27 - 3b
3b = -21
b = -7
Here the value of a = -3, b = -7, and c = -2.
Hence, the equation in the standard form of a parabola is y = -3x² - 7x - 2
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A. Use the appropriate formula to determine the periodic deposit.
B. How much of the financial goal comes from deposits and how much comes from interest?
Periodic Deposit: $? at the end of each year
Rate: 6% compounded annually
Time: 18 years
Financial Goal: $130,000
The periodic deposit is? $
By using compound interest, it can be calculated that-
A) Deposit is $45544.69
B) Interest = $84455.31
What is compound interest?
If the interest on a certain principal at a certain rate over a certain period of time increases exponentially rather than linearly, the interest earned is called compound interest.
If p is the principal, r is the rate and n is the time in years, then amount is calculated by
[tex]A = p(1 + \frac{r}{100})^n[/tex]
The difference between the amount and the principal is the compound interest
A)Here,
Let the principal be $p
Rate = 6%
Time = 18 years
Amount = $130000
[tex]130000 = p(1 + \frac{6}{100})^{18}[/tex]
[tex]130000 = p(1 + \frac{3}{50})^{18}[/tex]
[tex]130000 = p(\frac{53}{50})^{18}[/tex]
[tex]130000 = p(1.06)^{18}[/tex]
[tex]p = \frac{130000}{1.06^{18}}[/tex]
p = $45544.69
B) Interest = $(130000 - 45544.69)
= $84455.31
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please help, it tells u to write the expression in simplified radical form
The given expression in simplified radical form is 2x⁴ y³ [tex]\sqrt[4]{2y^3}[/tex]
Define Radicals.
The term "radical" is used to represent the square root or nth roots.
Expression with a square root is referred to as a radical expression.
Radicand: The value or phrase contained within the radical symbol.
Given expression is,
[tex]\sqrt[4]{32x^1^6 y^1^5}[/tex]
Rewrite this expression,
we know, 2⁵ = 32
[tex]\sqrt[4]{(2x^4.y^3)^4 .y^3 .2}[/tex]
You see this expression is equal to given expression i.e, [tex]\sqrt[4]{32x^1^6 y^1^5}[/tex]
Take out the term from under the radical,
2x⁴ y³ [tex]\sqrt[4]{2y^3}[/tex]
Hence, the given expression in simplified radical form is 2x⁴ y³ [tex]\sqrt[4]{2y^3}[/tex]
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For the story problem below, make sure you have a
representation (circles), an answer and a number sentence.
I have 20 chocolate chip cookies that I want to put onto
plates. I can fit 4 cookies on each plate. How many plates
How many plates
will I need? Need help really please
Hannah wants to have $ 6500 to help pay for a new deck in 16 years. If she wants to put her money into an account earning 4.75% interest compounded continuously, how much should she invest now, so that she will have $ 6500 in 16 years?
Payment amount =
[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$6500\\ P=\textit{original amount deposited}\\ r=rate\to 4.75\%\to \frac{4.75}{100}\dotfill &0.0475\\ t=years\dotfill &16 \end{cases} \\\\\\ 6500=Pe^{0.0475\cdot 16} \implies \cfrac{6500}{e^{0.0475\cdot 16}}=P\implies 3039.83\approx P[/tex]
John earned $45.90 during the summer break. He used of the money to buy trading cards. Then, he used of the remaining amount to buy a sketchbook, and also spends $4.50 on comic books.
How much money does John have left after these purchases?
Answer:
Not possible with given
Step-by-step explanation:
twice the sum of the number and negative seven is eight. Find the number. Round your answer to the nearest integer, if necessary
The number that twice the sum of it and negative seven is eight is 11.
How to find the number ?Twice the sum of the number and negative seven is eight. The number can be found as follows:
let
the number = x
According to the word expression, twice the value of the addition of x and minus seven is equals to 8. Hence, we will find the value of x in the equation formed from the words expression.
The variable x is the required number.
Therefore,
2(x + (-7)) = 8
2(x - 7) = 8
open the brackets
2(x - 7) = 8
2x - 14 = 8
add 14 to both sides of the equation
2x - 14 = 8
2x - 14 + 14 = 8 + 14
2x = 22
divide both sides by 2
x = 22 / 2
x = 11
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The diagram below shows OAG, where RN, NE, and ER are mid-segments of the triangle. If OA = (4x + 3) units, NE = (2.5x) units, RN = 4.5 units, and ER = (2x) units, determine the measures below.
The measures are NE = 7.5 units, GO = 9 units, AG = 12 units, and the perimeter of the ΔOAG is 36 units.
What is the perimeter of the triangle?
A triangle's perimeter is measured in the same unit as its side lengths. If the lengths of its sides are measured in a different unit, first convert them to that unit.
We have,
OA = (4x + 3) .............(1)
NE = (2.5x) .............(2)
RN = 4.5 .............(3)
ER = (2x) .............(4)
Mid-point segment of the triangle
EN = 1/2(OA) .............(5)
from equations (1), (2), and (5)
2.5x = 1/2(4x + 3)
5x = 4x + 3
x = 3 .............(6)
OA = 4x + 3 = 15
NE = (2.5x) = 7.5
ER = (2x) = 6
RN = 1/2(GO)
GO = 2 * RN = 2 * (4.5)
GO = 9
ER = 2x = 2*3 = 6
AG = 2(ER) = 2 * 6 = 12
The perimeter of the OAG is OA + AG + GO = 15 + 12 + 9
= 36 units.
Hence, the asked measures are NE = 7.5 units, GO = 9 units, AG = 12 units, and the perimeter of the ΔOAG is 36 units.
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How does the graph of g(x) = (x − 8)3 + 3 compare to the parent function f(x) = x3?
The required given function is a translation of the parent function by 8 units left and 3 units up.
What are functions?Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Here,
Given function, g(x) = (x − 8)³+ 3
Parent function, f(x) = x³
From observation, it is seen that,
The given function is translated function of the parent function as,
As the parent function is translated left on the x-axis by 8 units, and 3 units up on the y-axis.
Thus, the required given function is a translation of the parent function by 8 units left and 3 units up.
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What is the volume of this rectangular prism?
Insert a monomial such that each expression can be rewritten as the square of a sum or the square of a difference.
36-12 x+
36-12 x+
The monomial that completes the expression is x²
How to determine the monomial that completes the expression?From the question, we have the following parameters that can be used in our computation:
36 - 12x + ...
Complete the expression with a variable
So, we have
36 - 12x + y
Rewrite as
y - 12x + 36
The given terms of the expression are factors of 6
By trial and error, we make use the following representation
y - 12x + 36 = (x - 6)²
Expand the expression
y - 12x + 36 = x² - 12x + 16
Evaluate the like terms
y = x²
Hence, the monomial is x²
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51. A company offers cable television at $29.95 per month plus a one-time installation fee. The total cost for the first six months of service is $214.70. a. Write an equation in point-slope form that represents the total cost you pay for cable television after x months.
The equation that represents the total cost you pay for cable television after x months is y = 35 + 29.95x.
What is an equation?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Given that a cable operator offers that buy a television at $29.95 per month plus a one-time installation fee.
The total cost that need to pay after 6 months is $214.70.
Assume that a be the cost one-time installation fee.
Then total cost that need to pay after 6 months is (6 × 29.95) + a = 179.7 + a
Therefore,
179.7 + a = $214.70
a = 35.
After x month, he needs to pay 35 + 29.95x.
Assume that y represents total cost after x months.
y = 35 + 29.95x
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Given: Given: 2 < a < 5, 3 < b < 7
Find: A-b
Using simple mathematical operations, we know that a-b can be -1, -2, and 0.
What are mathematical operations?A mathematical "operation" is the process of calculating a value utilizing operands and a math operator.
The supplied operands or integers must adhere to a set of predefined rules that are connected to the symbol of the math operator.
Parentheses, Exponents, Multiplication, Division, and Addition Subtraction are also known as PEMDAS (from left to right).
So, we have: 2 < a < 5, 3 < b < 7
Now, a - b will be:
the values of a can be 3 and 4
Similarly, the value of b can be 4 and 5.
So there are 4 possibilities as shown:
3 - 4 = -1
3 - 5 = -2
4 - 4 = 0
4 - 5 = -1
Therefore, using simple mathematical operations, we know that a-b can be -1, -2, and 0.
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Given h of x equals 2 times the square root x minus 5 end root, which of the following statements describes h(x)?
The function h(x) is increasing on the interval (–∞, 5).
The function h(x) is increasing on the interval (5, ∞).
The function h(x) is decreasing on the interval (–5, ∞).
The function h(x) is decreasing on the interval (–∞, –5).
Answer:
B
Step-by-step explanation:
x -5 ≥ 0
x ≥ 5
the function exists only in the interval [5, +oo) and it keeps growing
Answer the following.
Sukina wants to paint her dog's kennel a new colour.
Look at the diagram of the kennel.
What is the surface area she needs to cover if she paints
only the 4 walls of the kennel?
cm²
150cm
200cm
125cm
Answer:
200 b/c she will use 50cm² by Wall :)
Evaluate the function graphically.
Find f(-1)
The required value of the given function f(-1) is 2.
What is a function?
Exactly one value from the set of second components of the ordered pair is connected with each value from the set of first components of the ordered pairs in a relation known as a function.
For the given graph,
For x = -1, the exact y value will be 2.
So, f(-1) = 2
Hence, the required value of the given function f(-1) is 2.
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To prepare for his mountain biking trip, Rhyan bought four tire patches. Rhyan paid using a gift card that had $22.20 on it. After the sale, Rhyan’s gift card had $1.90 remaining.
Which equations could you use to find the price of one tire patch? Select all that apply.
4x – 1.9 = 22.2
4x – 22.2 = 1.9
4x + 1.9 = 22.2
4x + 22.2 = –1.9
22.2 – 4x = 1.9
Answer:
he paid 20.20 for the patch
Answer:
The equation could you use to find the price of one tire patch select all that apply 4x + 1.9 = 22.2 and 22.2-4x= 1.9
Yo guys I need help ASAP
Solve the equation 2x + 3y = 5 for x.
Step-by-step explanation:
[tex]2x + 3y = 5[/tex]
[tex]2x = 5 - 3y[/tex]
[tex]x = \frac{5 - 3y}{2} \\ [/tex]
Answer: Add 3y to both sides of the equation. 2x=5+3y Divide each term in 2x=5+3y by 2 and simplify.
PLEASE HELP ME!!! I WILL GIVE BRAINLIST!!!PLEASE
Answer: D. A'(-5,10) B'(-1,10) C'(-1,7) D'(-5,6)
Step-by-step explanation:
A(-5,5) B(-1,5) C(-1,2) D(-5,1)
A'(-5,5+5) B'(-1,5+5) C'(-1,2+5) D'(-5,1+5)
A'(-5,10) B'(-1,10) C'(-1,7) D'(-5,6)
x-6/2 = 10 help again pls
Answer:
30
Step-by-step explanation:
get the x by itself on one side to solve
x-6/2=10
multiply both sides by 2 and divide by 6 which cancels out s x is by itself
x=10*6/2
simplify
x=60/2
x=30
Answer:
x = 13
Step-by-step explanation:
Given equation,
→ x - (6/2) = 10
Now the value of x will be,
→ x - (6/2) = 10
→ x = 10 + (6/2)
→ x = 10 + 3
→ [ x = 13 ]
Hence, the value of x is 13.
A cylinder has a radius of 5 centimeters and a height of 10 centimeters. What is the volume of the cylinder to the nearest cubic
centimeter? Use 3.14 for
Answer: centimeters 3
a line passes through the point (-9,-8) and has a slope of 2/3
. Write a equation in slope intercept form for this line
Answer:
y=2/3x-2
Step-by-step explanation:
The equation is y = mx + b and m is the slope. You were already given the slope and you were even given a point. All you have to do is graph the point and use the slope until it intercepts the y-axis.
1. Plot the point (9,-8)
2. Go up 2, left 3 spots until the line hits the y-axis (the vertical one)
3. That point is what b will be equal to in y = mx + b
OR you can convert a point-slope equation into slope intercept
1. The formula for point slope is y – y1 = m(x – x1)
2. Plug in the given numbers and it will look like this: y+8=2/3(x+8)
3. Do the math and get a solution of y=2/3x-2
how manys pounds of mixed nuts that contain 20% peanuts must eugene add to 16 pounds of mixed nuts that contain 70% peanuts to make a mixture with 60% peanuts?
help
We can add 10 pounds of mixed nuts that contain 20% peanuts by solving equations.
What are equations?Algebraically speaking, an equation is a statement that shows the equality of two mathematical expressions.
For instance, the two equations 3x + 5 and 14, which are separated by the 'equal' sign, make up the equation 3x + 5 = 14.
So, the quantity of mixed nuts we need is x pounds.
There are 0.70 pounds of peanuts in this mixture.
3 pounds of peanuts make up the 20% mix, or 0.20*15.
We got the equation:
0.70 x + 3 = 0.40(x + 15)
Now, solve this equation as follows:
0.70 x + 3 = 0.40(x + 15)
0.70 x + 3 = 0.40(x + 15)
0.70x + 3 = 0.40x + 6
0.70x - 0.40x = 6 - 3
0.30x = 3
x = 10 pounds
Therefore, we can add 10 pounds of mixed nuts that contain 20% peanuts by solving equations.
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All the fudge machines at a chocolate factory work at the same rate. Six machines working simultaneously can complete a big order in 22 hours.
a
How many hours would it take to fill the order if the number of working machines increased by a factor of 2?
When the number of machines increased by factor 2 the order would have been finished in 11 hours,
Given that,
All the fudge machines at a chocolate factory work at the same rate. Six machines working simultaneously can complete a big order in 22 hours.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
Number of hours as of the current number of working machines = 22
The number of machinery now doubled so working hours = 22 / 2 = 11 hours.
Thus, When the number of machines increased by factor 2 the order would have been finished in 11 hours,
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Emma needs to order liquid fertilizer for her landscaping company. She plans to keep the fertilizer in a large cylindrical storage tank, but isn’t sure how much it will hold. The tank is 10 feet tall and the circular base has a radius of 5 feet. What is the volume of her storage tank?
785.4 cubic feet
Step-by-step explanation:Step 1: Start by calculating the area of the base of the storage tank. The area of a circle is calculated by: A = π*r², where r is the radius of the circle.
Step 2: For Emma’s cylindrical storage tank, the radius of the base is 5 feet. Substitute this value in the formula and calculate the area of the base, which is equal to: A = π*5² = 78.54 square feet.
Step 3: Now we need to calculate the volume of the cylindrical storage tank. The volume of a cylinder is calculated by: V = π*r²*h, where r is the radius of the circle and h is the height of the cylinder. For Emma’s tank, the height is 10 feet. Substitute these values in the formula and calculate the volume, which is equal to: V = π*5²*10 = 785.4 cubic feet.
Step 4: Therefore, Emma’s cylindrical storage tank has a capacity of 785.4 cubic feet.
If you have any additional questions or need further assistance, please let me know.
9. A bag contains marbles: 5 purple. 6 blue. 8 yellow. 1 green. You will draw a
marble, put it back, and then draw another. What is the probability that you will
draw a purple and a green? Make sure to simplify your answer. SHOW YOUR
WORK.
The probability of drawing purple and green marbles will be 1/80.
What is probability?The probability of an event occurring is defined by probability.
Probability is also called chance because if you flip a coin then the probability of coming head and tail is nothing but chances that either head will appear or not.
As per the given,
Number of purple marble = 5
Number of green marble = 1
Total marble = 5 + 6 + 8 + 1 = 20
Probability drawing a purple marble = 5/20
Probability of drawing a green marble = 1/20 (because the number of marble remain the same)
Probability of drawing a purple and green = 5/20 x 1/20 = 1/80
Hence "There is a 1/80 chance of drawing purple and green marbles.".
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use the midpoint formula to find the midpoint of a line segment with endpoints a (-3, 7) and b (1, 11).
The mid point of the line segment is (1,9)
The general formula to calculate the midpoint is written as
(x, y) = (x1+x2/2) , (y1 + y2)/2
Where (x1, y1) and (x2, y2) refers the end points.
Here we have given that line segment with endpoints a (-3, 7) and b (1, 11).
And we need to find the midpoint.
While we looking into the given question we have the end point of the line segment
Then the values of (x1, y1) is (-3, 7) and the value of (x2, y2) is (1, 11),
Then the midpoint is calculated by apply the values on the formula, then we get,
=> (1 - 3)/2 , (11 + 7)/2
When we do the appropriate mathematical operation, then we get
=> 2/2 , 18/2
Therefore, the midpoint is (1, 9).
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