the roots of the function are[tex]x = 1[/tex] and [tex]x = 3.[/tex] These are also the x-intercepts of the parabola.
What is the polynomial of degree?This polynomial is a quadratic function and can be graphed as a parabola. a polynomial of degree two.
[tex]f(x) = x^2 - 4x + 3[/tex]
The coefficient of the x^2 term is positive, which means that the parabola opens upwards. The vertex of the parabola is at (2, -1) and the y-intercept is at (0, 3).
The roots of the function can be found by setting f(x) = 0 and solving for x:
[tex]x^2 - 4x + 3 = 0[/tex]
[tex](x - 3)(x - 1) = 0[/tex]
[tex]x = 1, 3[/tex]
Therefore, the roots of the function are[tex]x = 1[/tex] and [tex]x = 3.[/tex] These are also the x-intercepts of the parabola.
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Proctor & Gamble claims that at least half the bars of Ivory soap they produce are 99. 44% pure (or more pure) as advertised. Unilever, one of Proctor & Gamble's competitors, wishes to put this claim to the test. They sample the purity of 146 bars of Ivory soap. They find that 70 of them meet the 99. 44% purity advertised.
What type of test should be run?
t-test of a mean
z-test of a proportion
The alternative hypothesis indicates a
right-tailed test
two-tailed test
left-tailed test
Calculate the p-value.
Does Unilever have sufficient evidence to reject Proctor & Gamble's claim?
No
Yes
The test that should be run on the claim by Proctor & Gamble should be B. z-test of a proportion.
The alternative hypothesis indicates a c. left-tailed test.
The p - value is 0.2665. Unilever does not have sufficient evidence to reject Proctor & Gamble's claim, so A. no.
How to test the claim ?Conducting a z-test of a proportion is necessary in light of the proportion-based nature (at least half of the bars being 99.44% pure) of the inquiry, instead of means. Proctor & Gamble had asserted that over fifty percent of their bars exhibit 99.44% purity or better; Unilever wishes to investigate this assertion's accuracy.
Consequently, we run our test under null-hypothesis framework that considers fifty percent of bars possessing sufficient purity level and alternative hypothesis positing <50% do. The resultant course of action entails carrying out a left-tailed test.
The p - value. Find the test statistic:
z = ( 0. 4795 - 0.5) / √ ( ( 0.5 x (1 - 0.5) ) / 146)
z = - 0. 6236
z- table shows the p - value is 0. 2665 as a result.
With the p - value being higher than the normal significant level of 0. 05, Unilever should not reject Proctor & Gamble's claim.
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Find the measure of each labeled angles in the rhombus below:
The measure of each labeled angles in the rhombus are ∠1 = 49°, ∠2 = 90°, ∠3 = 49° and ∠4 = 41°
Finding the measure of each labeled angles in the rhombusFrom the question, we have the following parameters that can be used in our computation:
The rhombus
By corresponding angles, we have
∠3 = 49°
∠1 = 49°
The diagonals of a rhombus bisect each other at right angles
So, we have
∠2 = 90°
Ths sum fo angles in a triangle is 180
So, we have
∠4 = 180 - 90 - 49°
Evaluate
∠4 = 41°
Hence, the measure of the angles in the rhombus are ∠1 = 49°, ∠2 = 90°, ∠3 = 49° and ∠4 = 41°
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Question 2(Multiple Choice Worth 4 points) (05.03 MC) Solve the system of equations using elimination. 2x + 3y = -8 3x+y=2 O(-4,0) (2,-4) (5.-6) (8-8)
Answer:
(2,-4)
Step-by-step explanation:
In order to solve by elimination, coefficients of one of the variables must be the same in both equations so that the variable will cancel out when one equation is subtracted from the other.
2x+3y=−8,3x+y=2
To make 2x and 3x equal, multiply all terms on each side of the first equation by 3 and all terms on each side of the second by 2. Then simplify
6x+9y=−24,6x+2y=4
Add 6x to −6x. Terms 6x and −6x cancel out, leaving an equation with only one variable that can be solved, add 9y to −2y, add −24 to −4, and divide both sides by 7.
y=−4
Substitute −4 for y in 3x+y=2. Because the resulting equation contains only one variable, you can solve for x directly. Add 4 to both sides of the equation and divide both sides by 3.
x=2
in a survey among 2500 people it was found that 720 people like only milk 880 liked only curd and 400 of them didnot like both milk and curd.find the number of people who liked both milk and curd.also,find the number of people who liked at least one of the drink
The number of people who liked both milk and curd is 500.
Here's how you can calculate it:
- The number of people who liked only milk is 720.
- The number of people who liked only curd is 880.
- The number of people who did not like either milk or curd is 400.
- Let x be the number of people who liked both milk and curd.
- We can use the formula: Total = Group 1 + Group 2 - Both + Neither.
- Substituting the values, we get: 2500 = 720 + 880 - x + 400.
- Solving for x, we get: x = 500.
- Therefore, 500 people liked both milk and curd.
The number of people who liked at least one of the drinks is 2100.
Here's how you can calculate it:
- The number of people who liked only milk is 720.
- The number of people who liked only curd is 880.
- The number of people who liked both milk and curd is 500.
- Therefore, the total number of people who liked at least one of the drink is: 720 + 880 + 500 = 2100.
Answer:
liked both milks: 900
liked at least 1: 2100
Step-by-step explanation:
there are 2500 people
ONLY LIKE 1 type- 1600 people
400 don't like milk
2500-1600=900
2500-400=2100
Mrs. Rambo got a YMCA membership for her family. The pass has a onetime fee of $30 and then $5 for every visit to the YMCA. Her bill the first month was $150. How many times did her family visit the YMCA?
They visited ------------- times last month. Way to go Rambo family!
Answer:
Step-by-step explanation: Solution:
Total cost: 150
150-30=120
120 divided by 5 = 24
They visited 24 times in a month.
Question 11 Σ Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If it diverges to infinity, state your answer as "oo" (without the quotation marks). If it diverges to negative infinity, state your answer as "-00". If it diverges without being infinity or negative infinity, state your answer as "DNE". 10 10 dc 2 6
The given integral is ∫₁₀ (10/(x-2)) dx.
The given integral is divergent and the answer is "oo".
To see why the integral is divergent, we can use the following limit comparison test:
∫₁₀ (10/(x-2)) dx ~ ∫₁₀ (1/x) dx, as x → 2.
The symbol "~" means "is asymptotic to". We can use this comparison because as x approaches 2 from the right, the function 10/(x-2) approaches positive infinity.
Now, we know that the integral ∫₁₀ (1/x) dx diverges because the improper integral of 1/x from 1 to infinity diverges. Therefore, by the limit comparison test, the original integral is also divergent.
Hence, the given integral ∫₁₀ (10/(x-2)) dx is divergent, and the answer is "oo".
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The unit cube is divided into identical rectangular prisms. What is the volume of one of the identical prisms?
Note that the Volume of one prism = (1/16) unit³
How did we reach the above conclusion?
The given volume of the cube, v₁ = 1 unit cube
The height of the unit cube, h₁ = 1 unit
The length of the unit cube, w₁ = 1 unit
The height of the unit cube, l₁ = 1 unit
The number of identical prism located along the height = 2 identical prism
The number of identical prism located along the width = 2 identical prism
The number of identical prisms located along the length = 4 identical prism
Therefore;
The height of each identical rectangular prism that make up the unit cube, h₂ = h₁/2 = 1/2 unit
Similarly, for each identical rectangular prism, we have;
The width, w₂ = w₁/2 = 1/2 unit
The length, l₂ = l₁/4 = 1/4 unit
The volume of each one of the identical rectangular prism, v₂ = h₂ × w₂ × l₂
⇒ v₂ = 1/2 unit × 1/2 unit × 1/4 unit = 1/16 unit³
So it is correct to state that the volume of one of the identical rectangular prisms = (1/16) unit³.
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Full Question:
Although part of your question is missing, you might be referring to this full question:
See attached image.
find the value of x.
Answer:
x ~= 61.0°
Step-by-step explanation:
This is a trig question. The marked angle is unknown so we will use an inverse trig function to find a missing angle. On your calculator you may need to use the 2nd button or shift to get not just "cos" but the inverse cos. It might look like cos with a -1 exponent or "arccos" or "acos"
So the triangle is a right triangle. The angle is next to one of the given sides. "Next to" is called "adjacent" these mean the same thing. One side is adjacent to the angle. The other given side is the hypotenuse.
The trig function that puts together Adjacent and Hypotenuse is cosine.
cos (angle) = adj/hyp
We know the two sides. Fill them in.
cos (angle) = 31/64
We are looking for the angle.
cos x = 31/64
Use the inverse cos to find the angle.
cos^-1 (31/64) = x
This is a calculator activity. Unless your teacher has given you tables of values (this is how it was done before calculators) you have to use a calculator.
x = 61.0284677763
round to the nearest tenth.
x ~= 61.0
Question 3 of 10
What property does the equation show?
32 19
14
56
1 3
+
=
A. The associative property
B. The commutative property
OC. The distributive property
32 19
14 56
D. The identity property of multiplication
5 8
1 3
+
32
14
19
56
4
7
Answer:
C. The distributive property
Item #1 - Which set of data points could be modeled by a
decreasing linear function?
A. {(0, 0), (1, 8), (2, 15), (3, 22), (4, 30)}
B. {(0, 5), (1, 6), (2, 10), (3, 16), (4, 28)}
C. {(0, 50), (1, 42), (2, 33), (3, 25), (4, 16)}
D. {(0, 64), (1, 60), (2, 52), (3, 39), (4, 22)}
A set of data points could be modeled by a decreasing linear function include the following: C. {(0, 50), (1, 42), (2, 33), (3, 25), (4, 16)}.
What is a linear function?In Mathematics, a linear function is a type of function whose equation is graphically represented by a straight line on the cartesian coordinate.
For any given function, y = f(x), if the output value (range or y-value) is decreasing when the input value (domain or x-value) is increased, then, the function is generally referred to as a decreasing function.
By critically observing the set of data points, we can reasonably infer and logically deduce that it set C is decreasing as follows 50, 42, 33, 25, 16.
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pls some help with this question!
Luis tiene una mochila de ruedas
que mide 3.5 pies de alto cuando se extiende el mango.Al hacer rodar
su mochila, la mano de Luis se
encuentra a 3 pies del suelo. ?Que ángulo forma su mochila con el suelo? Aproxima al grado más cercano
As a result, the angle formed by Luis's backpack and the ground is roughly 53 degrees (rounded to the nearest degree).
what is function ?A function in mathematics is a relationship between a set of potential outputs and a number of potential inputs, with the feature that each input is associated to only one possible output. It is a principle or set of guidelines that allots a different output value towards each input value. Equations, graphs, and tables are frequently used to depict functions in order to explain how the output changes as the input does. They are employed to express relationships between various quantities, such as the length of time it takes for an automobile to drive a certain distance or the height of an object in relation to its weight. The concept of a function is crucial to many departments of science and math, and it is widely applied in areas like engineering,
given
We can use trigonometry to determine the angle that Luis's backpack creates with the ground.
Consider the backpack's handle to represent the hypotenuse of a right triangle, with the vertical leg being Luis's hand's distance from the ground (3 feet) and the horizontal leg being the backpack's height (3.5 feet).
The angle can be determined using the inverse tangent function (tan-1):
53.13 degrees at tan-1(3.5/3)
As a result, the angle formed by Luis's backpack and the ground is roughly 53 degrees (rounded to the nearest degree).
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Based on the experiment if the spinner is spun 150 times how many times would you expect to get an even number?
Answer:
60
Step-by-step explanation:
((sum of frequency of even numbers)/(total number of tries))(150)
Find the equation of the line that
is perpendicular to y = -8x + 2
and contains the point (-4,1).
Help
=
y = (?)X +
X
8
Enter the correct symbol, + or -, that
belongs in the green box
The equation of the line that is perpendicular to y = -8x + 2 and contains the point (-4, 1) is y = (1/8)x + (3/2).
To find the equation of the line that is perpendicular to y = -8x + 2 and contains the point (-4, 1), first, determine the slope of the given line. The slope is -8. Perpendicular lines have slopes that are negative reciprocals of each other, so the slope of the new line will be 1/8.
Now, use the point-slope form of a linear equation, y - y1 = m(x - x1), where m is the slope and (x1, y1) is the given point (-4, 1). Plug in the values: y - 1 = (1/8)(x - (-4)).
Simplify the equation: y - 1 = (1/8)(x + 4). Distribute the 1/8: y - 1 = (1/8)x + (1/2). Finally, add 1 to both sides: y = (1/8)x + (1/2) + 1.
So, the equation of the line that is perpendicular to y = -8x + 2 and contains the point (-4, 1) is y = (1/8)x + (3/2).
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The radius of a circle measures 7 inches. A central angle of the circle measuring 4π15 radians cuts off a sector.
What is the area of the sector?
Enter your answer, as a simplified fraction
The area of sector is 14π/3 square inches for a circle having a radius of 7 inches and measures an angle of 4π/15 radians.
Radius of circle = 7 inches
Angle of circle = 4π/15 radians
The area of a sector of a circle can be calculated by using the formula:
A = (θ/2) × [tex]r^2[/tex]
A = The area of the sector
θ = central angle in radians
r = radius of the circle.
Substituting the given values in the formula:
Area = (θ/2) × [tex]r^2[/tex]
Area = (4π/15 × 1/2) × [tex]7^2[/tex]
Area= (2π/15) × 49
Area = 14π/3
Therefore, we can conclude that the area of the sector is 14π/3 square inches.
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Write a note to your pen pal about the kinds of music you like best. In addition, write about any instruments you might play. Be sure you use at least 5-6 complete Spanish sentences in your response. Find the values of x, y, and z. Round answers to the nearest hundredths place, if necessary
Answer:
Querido/a [Pen pal's name],
¡Hola! Espero que estés bien. Quería escribirte sobre mis gustos musicales. Me encanta la música de todo tipo, pero mis géneros favoritos son el pop y el rock. Me gusta escuchar artistas como Taylor Swift, Ed Sheeran, Coldplay y Queen. También disfruto escuchar música latina como el reggaetón y la salsa.
Además de escuchar música, también me gusta tocar algunos instrumentos. Toco la guitarra y el piano desde hace algunos años y me encanta aprender nuevas canciones y melodías en ambos instrumentos.
Creo que la música es una forma maravillosa de expresión y me encanta poder hacer música yo mismo.
¿Y tú? ¿Qué tipo de música te gusta? ¿Tocas algún instrumento? Me encantaría saber más sobre tus gustos musicales y si tienes algún hobby musical.
Espero tu respuesta pronto. ¡Cuídate mucho!
Saludos cordiales,
[Your name]
x = 4.56
y = 8.24
z = 12.99
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which angle is adjacent to TOU
A watch designer claims that men have wrist breadths with a mean equal to 9 cm. A simple random sample of wrist breadths
of 72 men has a mean of 8.91 cm. The population standard deviation is 0.36 cm.
Assume a confidence level of a = 0.01. Find the value of the test statistic z using
formula below
Z=
X-H
σ
O2.12
O-1.27
O 0.06
O-2.12
The value of the test statistic z is approximately -2.12. The Option D is correct.
What is the value of the test statistic z?To test the hypothesis that the mean wrist breadth of men is equal to 9 cm, we will use a one-sample z-test.
The null hypothesis is: H0: µ = 9 cm
The alternative hypothesis is: Ha: µ ≠ 9 cm
We are given a sample of n = 72 men with a sample mean of x = 8.91 cm and a population standard deviation = 0.36 cm.
The test statistic for a one-sample z-test is given by: z = (x - µ) / (o / sqrt(n))
Substituting the given values, we get:
= (8.91 - 9) / (0.36 / sqrt(72))
z = -2.119
At a significance level of a = 0.01, the critical values for a two-tailed test are ±2.576.
Since our test statistic (-2.119) falls outside of this range, we reject the null hypothesis and conclude that there is sufficient evidence to suggest that the mean wrist breadth of men is not equal to 9 cm.
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You are building a fence for your pasture. the length is three more than four times the width
The perimeter of the fence for the pasture is 10W + 6.
To find the perimeter of the fence, we need to add up the lengths of all four sides. Let's start by using the given information to find the length and width of the pasture.
Let's say the width of the pasture is W. Then, according to the problem, the length of the pasture is 3 more than 4 times the width, which can be expressed as:
Length = 4W + 3
Now that we have the length and width, we can find the perimeter by adding up all four sides:
Perimeter = 2(Length + Width)
Perimeter = 2(4W + 3 + W)
Perimeter = 2(5W + 3)
Perimeter = 10W + 6
Therefore, the perimeter of the fence is 10W + 6.
Note: The question is incomplete. The complete question probably is: You are building a fence for your pasture. The length is three more than four times the width. What is the perimeter of the fence.
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A can is to be made to hold a litre of oil. Find the radius of the can that will minimize the cost of the metal to make the can. (1L = 1000 cm)
The problem involves finding the radius of a cylindrical can that will minimize the cost of the metal to make the can, given that the can must hold one liter of oil.
Specifically, we need to find the radius of the can that will minimize the surface area, and hence the cost, of the metal required to make the can.
To solve the problem, we need to first write an expression for the surface area of the can in terms of its radius, and then differentiate this expression with respect to the radius to find the critical point. We then need to check that the critical point corresponds to a minimum value of the surface area, which will give us the optimal radius for the can. Optimization problems like this one are used in many fields, including engineering, economics, and physics, to find the best course of action given certain constraints and objectives.
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You sold a total of 320 student and adult tickets for a total of $1200. Student
tickets cost $3 and adult tickets cost $8. How many adult tickets were sold?
Answer:
48 adult tickets were sold.
Step-by-step explanation:
Let's use algebra to solve this problem:
Let's define:
x: the number of student tickets soldy: the number of adult tickets soldFrom the problem statement, we know:
x + y = 320 (the total number of tickets sold is 320)3x + 8y = 1200 (the total revenue from ticket sales is $1200)We can use the first equation to solve for x in terms of y:
x = 320 - y
Substituting this expression for x into the second equation, we get:
3(320 - y) + 8y = 1200
Expanding the left side, we get:
960 - 3y + 8y = 1200
Simplifying, we get:
5y = 240
Solving for y, we get:
y = 48
Therefore, 48 adult tickets were sold.
Additional:
To find the number of student tickets sold, we can substitute y=48 into the first equation:
x + 48 = 320
x = 272
Therefore, 272 student tickets were sold.
In 2012, the population of a city was 6.47 million. the exponential growth rate was 2.91% per year.
The population of the city after 5 years is approximately 7.94 million.
How to find the population of the city?Assuming that the population of the city grows exponentially, we can use the formula:
P(t) = [tex]P0 * e^(^r^t^)[/tex]
Where:
- P(t) is the population after time t
- P0 is the initial population
- r is the annual growth rate expressed as a decimal
- t is the time elapsed in years
Using the given information:
- P0 = 6.47 million
- r = 2.91% = 0.0291
Let's calculate the population after 1 year:
[tex]P(1) = 6.47 million * e^(^0^.^0^2^9^1 ^* ^1^)[/tex]
= 6.66 million (rounded to two decimal places)
So, the population of the city after one year is approximately 6.66 million.
We can also calculate the population after 5 years:
[tex]P(5) = 6.47 million * e^(^0^.^0^2^9^1 ^* ^5^)[/tex]
= 7.94 million (rounded to two decimal places)
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Suppose a bus arrives at a bus stop every 26 minutes. If you arrive at the bus stop at a random time, what is the probability that you will have to wait at least 4 minutes for the bus?
The time between buses arriving at the stop follows an exponential distribution with a mean of 26 minutes.
To find the probability of waiting at least 4 minutes for the bus, we can use the cumulative distribution function (CDF) of the exponential distribution:
P(waiting at least 4 minutes) = 1 - P(waiting less than 4 minutes)
The probability of waiting less than 4 minutes can be calculated using the CDF:
P(waiting less than 4 minutes) = 1 - e^(-4/26) ≈ 0.146
Therefore, the probability of waiting at least 4 minutes for the bus is:
P(waiting at least 4 minutes) = 1 - 0.146 ≈ 0.854
So the probability of having to wait at least 4 minutes for the bus is about 85.4%.
After burning half of a cylindrical candle, the surface area is 176 square inches. The radius of the candle is 2 inches. What was the original height of the candle? Round your answer to the nearest inch
The original height of the candle was approximately 26 inches. Rounded to the nearest inch, it will be 27 inches.
Formula for the surface area of a cylinder:
S = 2πrh + 2πr^2
where S is the surface area, r is the radius, and h is the height.
The radius is 2 inches and that the surface area after burning half the candle is 176 square inches. Substitute this values in the equation for surface area:
176 = 2π(2)(h/2) + 2π(2)^2
Simplifying:
176 = 2πh + 8π
168 = 2πh
h = 168/(2π)
h ≈ 26.75
So the original height of the candle was approximately 26 inches. Rounded to the nearest inch, the original height is 27 inches.
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More help please????
The value of sin(θ) = √15/4
The value of csc(θ) = [tex]\sqrt[4]{\frac{15}{15} }[/tex]
The value of sec(θ) = 4
The value tan(θ) = ±√15
The value of cot(θ) = ±√15/15
How to find the value using the trigonometric ratioWe can use the identity sec²(theta) - 1 = tan²(theta) to find the value of tan(theta).
Given sec(θ) = 4, we have:
sec²(θ) = 4² = 16
Then, using the identity:
tan²(θ) = sec²(θ) - 1 = 16 - 1 = 15
Taking the square root of both sides, we get:
tan(θ) = ±√(15)
Since sec(θ) is positive, we know that cos(theta), which is the reciprocal of sec(θ), is also positive. This tells us that θ is in the first or fourth quadrant, where sin(θ) is also positive.
Therefore:
sin(θ) = √(1 - cos²θ))
= √(1 - (1/16))
= √15/16)
= √(15))/4
Using the reciprocal identities, we can find the values of csc(θ) and cot(θ):
csc(θ) = 1/sin(θ)
= 4√(15)
[tex]\sqrt[4]{\frac{15}{15} }[/tex]
cot(θ)
= 1/tan(θ)
= ±√(15)/15
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In two or more complete sentences, describe the steps a consumer can take to become more knowledgeable.
uploa
There are several steps a consumer market can take to become more knowledgeable like research and asking questions.
Research The first step is to probe the product or service that you're interested in. This involves looking at reviews, product descriptions, and comparing prices. You can also look for information from dependable sources similar as consumer reports or government websites. Ask questions If you have any dubieties or enterprises, don't vacillate to ask the dealer or service provider.
Ask them about their experience and qualifications, and make sure to clarify any terms or conditions that are unclear. Get a alternate opinion If you're doubtful about a product or service, seek the advice of someone you trust or who has moxie in that area. They can help you make an informed decision grounded on their knowledge and experience.
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The letters of the word "MOBILE" are arranged at random. Find
the probability that the word so formed i) starts with M ii) starts
with M and ends with E.
The probability that the word so formed starts with M is 1/6, and the probability that it starts with M and ends with E is 1/30.
i) To find the probability that the word starts with M, we need to consider the total number of possible arrangements of the letters and the number of arrangements that start with M. The word "MOBILE" has 6 letters, so there are 6! = 720 possible arrangements of the letters. To find the number of arrangements that start with M, we can fix the M in the first position and arrange the remaining 5 letters in the remaining positions, which gives us 5! = 120 arrangements. Therefore, the probability that the word starts with M is:
P(starts with M) = number of arrangements that start with M / total number of arrangements
= 120 / 720
= 1/6
ii) To find the probability that the word starts with M and ends with E, we can fix the M in the first position and the E in the last position, and then arrange the remaining 4 letters in the remaining positions. This gives us 4! = 24 arrangements. Therefore, the probability that the word starts with M and ends with E is:
P(starts with M and ends with E) = number of arrangements that start with M and end with E / total number of arrangements
= 24 / 720
= 1/30
Thus, the probability that the word so formed starts with M is 1/6, and the probability that it starts with M and ends with E is 1/30.
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The original selling price of a jacket was
s
s dollars. The selling price was then changed on two occasions by the store owner. Its price is now represented by
0. 85
(
1. 4
s
)
0. 85(1. 4s). Which expression could explain what happened to the price of the jacket?
The expression 0.85(1.4s) represents the final selling price of the jacket after two price changes: an initial 15% decrease in price, followed by another 15% decrease in price.
Find out which expression could explain the happened price of the jacket?The expression 0.85(1.4s) represents the final selling price of the jacket after two price changes. We can break it down into its constituent parts to understand what happened to the price.
Factor 1.4s represents the original selling price of the jacket. This means that the store owner started with a price of 1.4s dollars.
The factor 0.85 represents the first price change. When the store owner lowered the price by 15%, the new price became 0.85 times the original price.
The second factor of 0.85 represents the second price change. After the first price change, the new price was 0.85(1.4s) dollars. When the store owner lowered the price again by 15%, the final selling price became 0.85 times the price after the first price change.
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How can you find the value of x in the expression 5x = 20?
Answer:
x = 4
Step-by-step explanation:
5x = 20 Divide both sides by 5
[tex]\frac{5x}{5}[/tex] = [tex]\frac{20}{5}[/tex]
x = 4
Helping in the name of Jesus.
KLM has vertices K 4,-5 L 2,2 and M 7,3 which translation move the triangle so that point K lies on the Y axis
To move triangle KLM so that point K lies on the Y-axis, you need to apply a translation that shifts the entire triangle horizontally. By translating triangle KLM using the vector (-4, 0), point K now lies on the Y-axis.
To move the triangle so that point K lies on the Y axis, we need to perform a translation. First, we need to determine how far point K is from the Y axis. We can do this by finding the x-coordinate of point K, which is 4. This means that point K is 4 units away from the Y axis.
Next, we need to determine the direction of the translation. Since we want to move point K onto the Y axis, we need to move the triangle in the negative x direction. Therefore, the translation that will move the triangle so that point K lies on the Y axis is a horizontal translation of -4 units. We can express this translation as follows:
T(-4, 0)
This means that we need to move each point of the triangle 4 units to the left (negative x direction) to achieve the desired position of point K on the Y axis.
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