If g(x) is the graph of f(x) where f(x) and g)(x) both are functions and f(x) is shifted up 2 units, then the formula for g(x) is g(x)= f(x) + 2
What is a function?A function from one set X to another allocates exactly one element of the other set Y to each element of X. The set X is known as the function's domain, while the set Y is known as the function's codomain. Initially, functions were just an idealized representation of the relationship between two changing quantities.
Here, we have
Given: If g(x) is the graph of f(x) shifted up 2 units. Here f(x) and g(x) are functions.
We have to write the formula for g(x).
Shifting up 2 units means you add 2 to f(x).
Shifted right 0 unit means you subtract 0 from the argument of the function f(x) (i.e. from x).
g(x) = f(x - 0) + 2
g(x) = f(x) + 2
Hence, the formula is g(x) = f(x) + 2
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The area of a rectangular field is equal to the area of a square. The length of the
rectangular field is 4 times the width. The cost of rope per metre is Tk 7. The
cost of the rope to make fence twice around the field is Tk 5600.
a) What will be the perimeter of the rectangular field?
b)
If you sow a papaya plant in every 4 m2 area how many papaya plants will
be needed?
Let's assume that the area of the rectangular field is x square meters, and the width of the field is y meters. Then we know that:
x = y * 4 (since the length of the rectangular field is 4 times the width)
And we also know that the area of the rectangular field is equal to the area of a square. Therefore:
x = y^2
Combining these two equations, we get:
y^2 = y * 4
y = 4 meters
So the width of the rectangular field is 4 meters. Using this, we can find the length:
x = y * 4 = 4 * 4 = 16 square meters
Now, to find the perimeter of the rectangular field:
Perimeter = 2 * (length + width) = 2 * (16 + 4) = 40 meters
Therefore, the perimeter of the rectangular field is 40 meters.
Next, we need to find the number of papaya plants that can be sown in the area of the field. The total area of the field is 16 square meters. If one papaya plant is sown in every 4 square meters, then the number of plants required would be:
Number of plants = Total area / Area per plant
Number of plants = 16 / 4 = 4 plants
Therefore, 4 papaya plants can be sown in the rectangular field.
laney walks 0.23 miles to school each day. how many miles does she walk total to and from school in 5 days
Answer:
1.15
Step-by-step explanation:
To figure out how many miles she walked in 5 days, we can multiply the number from just one day and multiply that by 5 and we will get our answer!
0.23 * 5 = 1.15
Write the equation of
the circle with diameter
endpoints of (-6, 3) and
(-14, 13).
The midpoint of the line segment connecting the endpoints of the diameter is the center of the circle. We can find the midpoint by averaging the coordinates of the endpoints:
$\sf\implies\:Midpoint\:=\:\left(\frac{-6\:-\:14}{2},\:\frac{3\:+\:13}{2}\right)\:=\:(-10,\:8)$
The radius of the circle is half the length of the diameter, which we can find using the distance formula:
$\sf\implies\:Radius\:=\:\frac{\sqrt{(-6\:-\:(-14))^2\:+\:(3\:-\:13)^2}}{2}\:=\:\frac{\sqrt{160}}{2}\:=\:4\sqrt{10}$
Thus, the equation of the circle is
$\sf\implies\:(x\:+\:10)^2\:+\:(y\:-\:8)^2\:=\:(4\sqrt{10})^2$
Simplifying and rearranging, we get:
$\sf\implies\red\bigstar\:(x\:+\:10)^2\:+\:(y\:-\:8)^2\:=\:160$
[tex]\huge{\colorbox{black}{\textcolor{lime}{\textsf{\textbf{I\:hope\:this\:helps\:!}}}}}[/tex]
[tex]\begin{align}\colorbox{black}{\textcolor{white}{\underline{\underline{\sf{Please\: mark\: as\: brillinest !}}}}}\end{align}[/tex]
[tex]\textcolor{blue}{\small\textit{If you have any further questions, feel free to ask!}}[/tex]
[tex]{\bigstar{\underline{\boxed{\sf{\textbf{\color{red}{Sumit\:Roy}}}}}}}\\[/tex]
what is the largest of 3 consecutive positive integers if the product of the two is smaller integers is 8 more times the largest integer
The three successive positive numbers are 3, 4, and 5.
The largest of these 5.
What are integers?Integers are made up of zeros, natural numbers, and their additive inverses. Except for the fractional part, it can be represented on a number line.
Let's call the smallest of three successive positive numbers x. The following two consecutive integers would then be x + 1 and x + 2.
The product of the two smaller integers (x and x + 1) is eight times that of the largest integer (x + 2). This can be written as an equation:
x(x + 1) = 8 + (x + 2)
By enlarging and simplifying the left side, we get:
[tex]x^2 + x = x + 10[/tex]
When we subtract x and 10 from both sides, we get:
[tex]x^2 - 9 = 0[/tex]
After factoring in, we get:
(x - 3)(x + 3) = 0
As a result, x = 3 or x = -3. We can disregard the negative solution because we're seeking positive integers and infer that x = 3.
As a result, the three successive positive numbers are 3, 4, and 5.
The largest of these 5.
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An African elephant has a mass of
8139
kg
8139 kg8139, start text, space, k, g, end text.
Choose the best approximation of the mass of an African elephant.
Choose 1 answer:
Choose 1 answer:
(Choice A)
8
⋅
1
0
3
kg
8⋅10
3
kg8, dot, 10, cubed, start text, space, k, g, end text
A
8
⋅
1
0
3
kg
8⋅10
3
kg8, dot, 10, cubed, start text, space, k, g, end text
(Choice B)
8
⋅
1
0
4
kg
8⋅10
4
kg8, dot, 10, start superscript, 4, end superscript, start text, space, k, g, end text
B
8
⋅
1
0
4
kg
8⋅10
4
kg
Best approximation of the mass of an African elephant is 8 ×10³kg
Define massIn physics, mass is a fundamental property of matter that measures the amount of substance in an object. It is a scalar quantity that describes an object's resistance to acceleration when a force is applied. Mass is usually measured in kilograms (kg) and can be calculated by dividing an object's weight by the acceleration due to gravity.
Given;
Mass of elephant=8139kg
Dividing the mass by 1000 and multiplying it by 10³, we get
Mass of elephant=8.139 ×10³kg
Estimating the mass of elephant, we get
Mass of elephant=8 ×10³kg
hence, best approximation of the mass of an African elephant is 8 ×10³kg.
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STATS
When a truckload of apples arrives at a packing plant, a random sample of 125 apples are selected and examined for bruises and other defects. In reality, 14% of the apples on a particular truck are bruised or otherwise unsatisfactory.
(a) How many standard errors away from 0.14 would you need to go to contain 89% of the sample proportions of bad apples you might expect to find? (3 decimal places)
Number of Std errors away from 0.12 one need to go = 1.227
What does standard deviation mean?Standard deviation (or σ) is a measure of how far the data are from the mean. A low standard deviation means that the data are clustered around the mean, and a high standard deviation means that the data are more scattered. Standard deviation shows how the data are distributed. This is a measure of how far each observation is from the mean.
The variance is the mean squared deviation from the mean and the standard deviation is the square root of that number. Both measures reflect the variability of the distribution, but in different units. The standard deviation is expressed in the same units as the original value (minutes, meters, etc.).
A. for 89% ; critical z value = 1.227
89% = 0.89
Critical z value = 0.89 × 0.14
= 1.227
Therefore number of Std errors away from 0.12 one need to go = 1.227
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find local maximum values.
The local maximum values of the graph is determined as 3, 4, and 5.
What is local maximum values?A local maximum value is a point in the domain of a function where the value of the function is greater than or equal to the values of the function at all neighboring points. In other words, a local maximum is a point where the function reaches a peak, but only in the immediate vicinity of that point.
It's important to note that a local maximum need not be the maximum value of the function over its entire domain. There may be other points in the domain where the function attains higher values.
For the given function, the local maximum values are;
{3, 4, 5}.
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Find the midpoint, M, of AB.
A = (-3,-1) B = (-7,-7)
Answer:
M=(-5,-4)
Step-by-step explanation:
The midpoint of the line segment AB with coordinates A = (-3, -1) and B = (-7, -7) is (-5, -4).
Explanation:To find the midpoint of a line segment AB, we can use the midpoint formula. The midpoint formula states that the x-coordinate of the midpoint is the average of the x-coordinates of A and B, and the y-coordinate of the midpoint is the average of the y-coordinates of A and B.
Given A = (-3, -1) and B = (-7, -7), we can use the midpoint formula as follows:
x-coordinate of M = (x-coordinate of A + x-coordinate of B) / 2 = (-3 + -7) / 2 = -5y-coordinate of M = (y-coordinate of A + y-coordinate of B) / 2 = (-1 + -7) / 2 = -4Therefore, the midpoint M of AB is (-5, -4).
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3. Daniel and his mom are working together to paint his bedroom The paint store is currently offering the following sales Item sale pricematte paint 7.56 4 pints for $7.56 Glossy Paint 2 gallons for $26.16 Paint Brushes 4 for $18 = 4.5 per Brish Calculate the unit rate of these items, and use that information to select all of the following statements that are correct. If necessary, round to the nearest penny. A) Daniel will spend $21.68 on matte paint if he buys 1 y gallons. B)Daniel will spend $19.62 on glossy paint if he buys 6 quarts. c) Daniel's total cost will be $24.12 if he buys 2 paint brushes and 1 gallon of matte paint.Daniel can buy 13 pints of glossy paint for $20.
Answer:
Options B and C
Step-by-step explanation:
First, we have to find out the unit rates
Matte Paint
7.56 ÷ 4
= $1.89 per paint
Glossy Paint
26.16 ÷ 2
= $13.08 per gallon
Paint Brushes
18 ÷ 4
= $4.5 per brush
Now we have to check for each statement.
Option A
If he buys 1 [tex]\frac{1}{2}[/tex] gal on matte paints
1 [tex]\frac{1}{2}[/tex] = 1.5 gal
1.5 × 1.89 = $2.84
So therefor statement A is not true.
Option B
We have to convert quart to gal
1 quart = 0.25 gal
6 quarts = 1.5 gal
1.5 × 13.08 = $19.62
so statement B is true
Option C
They got 2 paintbrushes so we have to mutiply
2 × 4.5=$9
1 gal matte paint
We have to convert gal to pint
1 gal = 8 pint
8 × 1.89 = $15.12
Then we add them
15.12 + 9 = $24.12
Which means statement C is true
Option D
13 pints of glossy paint
$13.08 per gallon
1 gal =8 pint
13 pints = [tex]\frac{13}{8}[/tex] gal
[tex]\frac{13}{8}[/tex] × 13.08 = $21.26
so statement D is not true
That leaves us with Option B and C
There are two right circular cylinders. The radius of the first cylinder is 3 centimeters, and its height is 5 centimeters. The radius of the second cylinder is 15 centimeters, but its height is also 5 centimeters. What is the ratio of the volume of the second cylinder to the volume of the first cylinder? A. 9:1 B. 16:1 C. 36:1 D. 25:1
Answer:
D) 25 : 1
Step-by-step explanation:
[tex]\boxed{\bf Volume \ of \ cylinder = \pi r^2h}[/tex]
Cylinder 1:
[tex]h_1 = 5 \ cm\\\\r_1 = 3 \ cm[/tex]
Cylinder 2:
[tex]h_2 = 5 \ cm\\\\r_2 = 15 \ cm[/tex]
[tex]Volume \ of \ cylinder2 : Volume \ of \ cylinder1 = \dfrac{\pi * 15 * 15 * 5}{\pi *3*3*5}[/tex]
= 25 : 1
What is 1/5+2/5+3/5
:):):):):):):)
Answer:
Step-by-step explanation:
What you'll want to do is add the three numbers on top to get 6/5. If you need the answer in decimal form, it's 1.2, and if you need it as a mixed number, your answer will be 1 1/5 :)M Hope this helped.
Jasmine invests $2,658 in a retirement account with an annual interest rate of 9%
compounded continuously. What will the account balance be after 15 years?
Maria invests $6,154 in a savings account with an annual interest rate of 8% compounded
continuously. What will the account balance be after 10 years?
If $17,000 is invested at a rate of 6.25% per year for 39 years, find the value of the
investment to the nearest penny if the interest is compounded continuously.
If $20,000 is invested at a rate of 6.5% per year compounded continuously, find the value
of the investment at each given time and round to the nearest cent.
(a) 8 months (b) 18 months (c) 21 years (d) 100 years
Joe invests $10,000 in an account that earns 12.3% interest annually. What is the balance
of the account after 8 years?
If principal is $2,658 and rate of interest 9% then the value of the account balance is approximately $10,253 by using continuous compound interest formula.
What is the Continuous Compound Interest ?Recurring interest is interest calculated on principal plus all interest and other interest. The idea is that lenders always receive interest, not individually at specific times.
The formula for continuous compound interest :
A= Peˣⁿ
Where,
A =Amount of money after a certain amount of time
P= principal or the amount of money you start with
e =Napier's number, which is approximately 2.7183
x =Interest rate
n =Amount of time in years.
Use the continuous compound interest formula :
Given P= 2658
x =9% = = 0.09
n = 15
e = 2.7183
By using
A= Peˣⁿ
A= (2658)(2.7183)⁰°⁰⁹¹⁵
A =10,253 (approximately)
Hence, the value of account balance after 15 years is approximately $10,253
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I need to know what is the step in finding the answer
Answer:
z = -1.5
6.68%
More than 2.5 standard deviations: X > 125 mg/dl
Less than 2.5 standard deviations: X < 75 mg/dl
Step-by-step explanation:
If a continuous random variable X is normally distributed with mean μ and variance σ², it is written as:
[tex]\boxed{X \sim\text{N}(\mu,\sigma^2)}[/tex]
Given:
Mean μ = 100 mg/dlStandard deviation σ = 10 mg/dlTherefore, if the blood sugar levels are normally distributed:
[tex]\boxed{X \sim\text{N}(100,10^2)}[/tex]
where X is the blood sugar level in milligrams per deciliter.
Converting to the Z distribution:
[tex]\boxed{\textsf{If }\: X \sim\textsf{N}(\mu,\sigma^2)\:\textsf{ then }\: \dfrac{X-\mu}{\sigma}=Z, \quad \textsf{where }\: Z \sim \textsf{N}(0,1)}[/tex]
If David has a blood sugar of 85 mg/dl then X = 85:
[tex]\implies Z=\dfrac{85-100}{10}=-1.5[/tex]
To calculate the percentile, find the area associated with the z-score on the Z Table (attached). Multiply the area by 100 and add a percentage sign:
[tex]z=-1.5 \implies 0.0668=6.68\%[/tex]
The calculations of the blood sugar readings that would be more than or less than 2.5 standard deviations from the mean are:
[tex]\implies \mu + 2.5 \sigma=100+2.5(10)=100+25=125[/tex]
[tex]\implies \mu -2.5 \sigma=100-2.5(10)=100-25=75[/tex]
The blood sugar readings that would be more than 2.5 standard deviations from the mean are:
Readings that are more than 125 mg/dl: X > 125The blood sugar readings that would be less than 2.5 standard deviations from the mean are:
Readings that are less than 75 mg/dl: X < 75Find the inverse of each of the given functions.
f(x) = 4x-12
ƒ¹(x) =
what is the area of this shape
Step-by-step explanation:
Assuming 18 cm and 12 cm sides are parallel ( you are not told this) , this is just a trapezoid
area = height * averge of bases = 7 * ( 12+18)/2 = 105 cm^2
Answer:
Step-by-step explanation:
What quadrant is -0.5 , -1.5
Answer:
third
Step-by-step explanation:
both the points are negative therefore they would be in the third quadrant
Factor the following polynomial.
After applying the difference of squares procedure , the factors we get =(7y + 5z)(7y - 5z)
Describe factor?Finding the factors of a given statement is a procedure known as factoring.
For instance, the factors of 12 are 1, 2, 3, 4, 6, and 12 are. The components of x²+ 5x + 6 are (x + 2) and (x + 3), respectively.
What is the square formula difference?Factorization of polynomials is a specific instance of the difference of squares formula. It claims that the product of two squares' sum and differences may be calculated using their difference.
A difference of squares expression is, for instance, a² - b² = (a + b)(a - b).
the phrase 49y² - 25z² can be factored, where
a² - b² = (a + b).(a - b).
Where a=49 , b = 25
After applying the difference of squares procedure, the phrase 49y² - 25z² can be factored, where a² - b² = (a + b).(a - b).
Consequently, 49y - 25z
= 7y + 5z(7y - 5z).
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What is the y-intercept of the function y=-cos(x)?
0 ( - 1/1/1₁0)
0 (0-1)
O
O
(0, 2/7)
0 (2.0)
O
What is a collection of objects or people from whom we gather information?
Give a “teacher’s explanation” of why 4/5 = 8/10 using a model and sentences.
The shaded area is the same in both circumstances, implying that 4/5 equals 8/10.
What is the model representation of the fraction?We can use a visual representation of a rectangle divided into five equal segments to understand why 4/5 equals 8/10.
If we shade four of those portions, we have shaded four-fifths of the rectangle.
Let's now divide the same rectangle into ten equal sections, each half the size of one of the five parts we started with.
If we shade in eight of these smaller areas, we will have shaded eight-tenths of the rectangle.
We can observe that the shaded area is the same in both circumstances, implying that 4/5 equals 8/10.
In other words, when we divide a whole into equal parts, we can always discover a fraction of those parts.
another fraction that is equivalent to it by splitting the same total into more or less equal-sized parts. In this scenario, 4/5 and 8/10 represent the same portion of the entire rectangle, simply divided into a different number of portions.
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Ed is a farmer who changes $3.75 for 5 pounds of cabbage. This table shows the rates charged for cabbage by some other farmers.
Determine whether the unit rate charged for cabbage by the other farmers is less than, equal to, or greater than the unit rate charged by Ed.
The table in the attachment compares the unitary-method prices for cabbage charged by Ed ($0.75 per unit) and other farmers.
Farmer-A:Greater than Ed
Farmer-B:Equal to Ed
Farmer-C:Less than Ed
Farmer-D:Equal to Ed
What is unitary-method?Unitary technique refers to the process of figuring out the cost of the necessary items. The value of a multiple is typically used to determine the value of one item, and the value of the desired number of articles can subsequently be determined from the value of one. This method primarily uses both division and multiplication.
Considering that Ed fixed the price for 5 pounds of cabbage at $3.75
5 pounds cabbage= $3.75
1 pound cabbage=$3.75 ÷ 5
Unit rate set by Ed = $ 0.75
Charges Set by Farmer-A= $ 0.50 for 1/2 pound
Unit rate set by Farmer-A = $ 0.50 x 2
= $1
Charges Set by Farmer-B= $ 0.75 for 1 pound
Unit rate set by Farmer-B = $ 0.75
Charges Set by Farmer-C= $ 1.75 for 2 1/2 pound
= $ 1.75 ÷ 5/2
Unit rate set by Farmer-C = $ 1.75 x 2/5
=$ 0.70
Charges Set by Farmer-D= $ 6 for 8 pound
= $ 6 ÷ 8
Unit rate set by Farmer-D = $ 0.75
Based on the above calculation:
Farmer-A charges:Greater than Ed
Farmer-B charges:Equal to Ed
Farmer-C charges:Less than Ed
Farmer-D charges:Equal to Ed
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Cameron invests $11000 in two different accounts. The first account paid 14 %, the second account paid 7 % in interest. At the end of the first year he had earned $1120 in interest. How much was in each account?
$ ___ at 14 %
$ ___ at 7 %
Cameron invested $5000 at 14% and $6000 at 7%.
Define interest.Interest is the amount of money that is paid or earned on a sum of money that has been borrowed or invested. It is usually expressed as a percentage of the original amount, and it can be calculated using various formulas depending on the type of interest and the frequency of compounding.
Let's assume that Cameron invested x dollars in the first account, which earns an interest rate of 14%, and y dollars in the second account, which earns an interest rate of 7%.
According to the problem, the total amount invested was $11,000. So, Equation is
x + y = 11000
We also know that at the end of the first year, Cameron had earned $1120 in interest.
The interest earned on the first account can be calculated as 0.14x, and the interest earned on the second account can be calculated as 0.07y.
0.14x + 0.07y = 1120
We now have two equations with two unknowns. Here, we will use substitution:
x = 11000 - y
0.14(11000 - y) + 0.07y = 1120
1540 - 0.14y + 0.07y = 1120
0.07y = 420
y = 6000
Substituting y = 6000 into the equation x + y = 11000, we get:
x + 6000 = 11000
x = 5000
Therefore, Cameron invested $5000 at 14% and $6000 at 7%.
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Evaluate:
n+2m;m=12,n=2
HURRY!!! Will give Brainliest!!
Answer:
26
Step-by-step explanation:
n+2m m = 12, n = 2
2 + 2(12)
2 + 24
26
Orange sell in a marketplace for $50.95 per box. One box contain 114 orange. How much would you pay to buy 14 orange?
The cost of 14 peaches will be 14/114 the of the price of 114 peaches. Therefore, the answer is 14/114 x 50.95 ≈ $6.26.
A certain shampoo is available in two sizes. A 10.1-ounce bottle costs $2.53. A 23.7-ounce bottle costs $5.48. Find the unit price for each size. Then state which size is the better buy based on the unit price.
Based on the unit price, the 23.7-ounce bottle is the better buy, since it costs less per ounce than the 10.1-ounce bottle.
What is meant by unit price?
Unit price refers to the cost of one unit of a product or service. It is calculated by dividing the total cost of the item by the number of units and is used by consumers to compare the prices of different products or by businesses to determine their pricing strategies.
What is an ounce?
An ounce is a unit of measurement used to express weight or mass. It is equal to 1/16th of a pound or approximately 28.35 grams. Ounces are commonly used to measure the weight of food, liquids, and precious metals.
According to the given information
To find the unit price for each size of shampoo, we need to divide the cost of each bottle by its size in ounces.
For the 10.1-ounce bottle, the unit price is:
Unit price = cost / size = $2.53 / 10.1 oz = $0.25 per ounce
For the 23.7-ounce bottle, the unit price is:
Unit price = cost / size = $5.48 / 23.7 oz = $0.23 per ounce
So, based on the unit price, the 23.7-ounce bottle is the better buy, since it costs less per ounce than the 10.1-ounce bottle.
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The hypotenuse of a right triangle is 1 cm longer than the longest leg. The shorter leg is 7 cm shorter than the longest leg. Find the dimensions of the triangle.
Answer:
The hypotenuse is 13 cm
The longest leg is 12 cm
The shortest leg is 5 cm
Step-by-step explanation:
Given:
A right triangle
Let's assume, that the longest leg is x, the shortest leg is y and the hypotenuse is z
Let's write 2 equations according to the given information and put them into a system (use the Pythagorean theorem):
[tex]z = \sqrt{ {x}^{2} + {y}^{2} } [/tex]
{√(x^2 + y^2) = x + 1,
{x - y = 7;
Let's make x the subject from the 2nd equation:
x = 7 + y
Replace x in the 1st equation with its value from the 2nd one:
[tex] \sqrt{( {7 + y)}^{2} + {y}^{2} } = (7 + y) + 1[/tex]
[tex] \sqrt{49 + 14y + {2y}^{2} } = 8 + y[/tex]
Square both sides of the equation:
[tex]2 {y}^{2} + 14y + 49 = {(8 + y)}^{2} [/tex]
[tex]2 {y}^{2} + 14y + 49 = 64 + 16y + {y}^{2} [/tex]
Move the expression to the left and collect like-terms:
[tex] {y}^{2} - 2y - 15 = 0[/tex]
a = 1, b = -2, c = -15
Solve this quadratic equation:
[tex]d = {b}^{2} - 4ac = ({ - 2})^{2} - 4 \times 1 \times ( - 15) = 64 > 0[/tex]
[tex]y1 = \frac{ - b - \sqrt{d} }{2a} = \frac{2 - 8}{2 \times 1} = \frac{ - 6}{2} = - 3[/tex]
y must be a natural number, since the length of a triangle's side cannot have negative units
[tex]y2 = \frac{ - b + \sqrt{d} }{2a} = \frac{2 + 8}{2 \times 1} = 5[/tex]
We found the length of the shortest leg
Now, we can find the rest of the dimensions:
x = 7 + 5 = 12
[tex]z = \sqrt{ {12}^{2} + {5}^{2} } = \sqrt{144 + 25} = \sqrt{169} = 13[/tex]
a diver dove to a location 6 3/5 meters below sea level. He then dove to a second location 8 1/5 meters below sea level. How many meters are there between the two locations?
Answer:
[tex]1\frac{3}{5}[/tex] meter is the difference in depths of locations diver dove.
Step-by-step explanation:
Can someone help pls it’s math!!!!!!!!!!!!!!!!!!!!!!!
The expression for the total combined profit that John made from the sales of MP3 and DVD players last week is: 18x + 35(128 - x) dollars.
How to obtain the equationTo arrive at the expression, we should first note that if x is the number of DVD players sold by John last week, then the number of MP3 players sold by John last week would amount to:
(128 - x), because the total number of players sold for both MP3 and DVD was 128.
Next, the total profit made by John from selling x DVD players is 18x dollars, since he makes a profit of $18 for a unit of DVD player sold.
In the same vein, the total profit made by John from selling (128 - x) MP3 players is 35(128 - x) dollars, since he makes a profit of $35 for each MP3 player sold.
In conclusion, the expression for the total combined profit John made from selling the DVD and MP3 players last week is: 18x + 35(128 - x) dollars.
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1)
Find the value of x in
the triangle below:
17
A) 20.2
B) 18.7
C) 19.5
D) 21.1
E) 22.6
K
84⁰
65°
Mrs. Wilson
Mrs. Crane
Mr. Haynes
Ms. Lindstrom
Mr. Swasey
O Gina Wilson (All Things Algebra), 2014
The correct option is A) 20.2.
What is triangle sum?
The triangle sum is a property of triangles that states that the sum of the interior angles of a triangle is always equal to 180 degrees. In other words, if you add up the measures of the three angles inside a triangle, the result will always be 180 degrees.
Using the given information and the fact that the angles in a triangle sum to 180 degrees, we can find the value of x as follows:
Start by finding the measure of angle K by subtracting the measures of angles A and B from 180 degrees:
K = 180 - A - B
= 180 - 84 - 65
= 31 degrees
Use the law of sines to set up an equation relating the side lengths and corresponding angle measures:
sin(A)/x = sin(K)/17
Substitute the values we know into the equation and solve for x:
sin(84)/x = sin(31)/17
x = sin(84)*17/sin(31)
Using a calculator, we get:
x ≈ 20.2
Therefore, the value of x in the triangle is approximately 20.2.
So, the correct option is A) 20.2.
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PKEASEEEE I NEEED YALL HELPPPPP
The value of x by the use of the laws of trigonometry is 94 degrees.
What are vertically opposite angles?Vertically opposite angles are a pair of angles formed by the intersection of two straight lines. When two lines intersect at a point, four angles are formed, and the angles that are opposite each other and not adjacent are called vertically opposite angles. Vertically opposite angles are always equal in measure, which means that they have the same angle degree or radian measure.
We know that the interior angle is vertically opposite to 39 degrees and the exterior angle is equal to the sum of the opposite interior angles.
Hence;
55 + 39 = 94 degrees
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