The comparison of the volume of a cone relative to the volume of a cylinder with the same dimensions is given as follows:
4 The volume of the cone is 1/3 as large.
How to obtain the volume a cone?The volume of a cone of radius r and height h is given by the equation presented as follows, which the square of the radius is multiplied by π and the height, and then divided by 3.
V = πr²h/3.
For the volume of the cylinder, the equation is given as follows:
V = πr²h.
The volume of the cylinder is triple the volume of the cone, hence the volume of the cone is one third of the volume of the cylinder.
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If 4a² + 9b² = 25 and ab = 8, find the value of (2a + 3b)²
Answer:
(2a + 3b)² = 121
Step-by-step explanation:
given 4a² + 9b² = 25 and ab = 8
(2a + 3b)² ← expand using FOIL
= 4a² + 6ab + 6ab + 9b²
= 4a² + 9b² + 12ab ← substitute given values from above
= 25 + 12(8)
= 25 + 96
= 121
What does the three lined equal sign mean
Answer: identical to/same as
Step-by-step explanation:
Answer:
The ≡ sign means identical to, similar but not exactly the same as, equals
Step-by-step explanation:
Hope this helps! =D
Mark me brianliest and Have a good day! =D
sophie is a barber at a barber shop. she earns a different amount of money each day depending on what task she does. she earns $115 for the day if she works at the reception desk. she earns dollars per hour for doing haircuts. the table shows the tasks she does this week.
Table:
Thursday, 2 hours cutting hair
Friday, reception desk
Saturday, 5 hours cutting hair
Question: which expression represents the total amount of money sophie earns this week.
Expressions:
2c + 115 + 5
2c + 115c + 5c
2c + 115 + 5c
2 + 115c + 5
Answer:
Step-by-step explanation: The answer is 115+2c+5c.
Friday the reception desk which gives her 115 dollars.
Thursday and Saturday she cut hair for 2 hrs and 5 hrs respectively.so if she earns ‘c’ dollars per hour for cutting hair it is 2c and 5c respectively.
so the total amount of money is 2c+115+5c
Is △ABC ≅ △DEF? Explain. Options - AAS, NO, HL, ASA, Are, Are not, SAS, Yes
________; the triangles __________ congruent by ___________
No; the triangles are not congruent by any of the congruence criteria.
To determine if two triangles are congruent, we must use one of the five congruence criteria: Side-Angle-Side (SAS), Angle-Angle-Side (AAS), Angle-Side-Angle (ASA), Side-Side-Side (SSS), and Hypotenuse-Leg (HL). To be congruent, the triangles must have three pairs of congruent sides and three pairs of congruent angles.
In the case of △ABC and △DEF, we can compare their sides and angles to determine if they are congruent. We can see that the sides of the two triangles are not equal in length, nor do the angles have the same measure. Therefore, △ABC is not congruent to △DEF.
In order to prove that the two triangles are not congruent, we can use the formula for determining the measure of the angles in a triangle, known as the Law of Cosines. This formula states that c² = a² + b² - 2ab cos γ, where c is the length of the longest side of the triangle, a and b are the lengths of the other sides of the triangle, and γ is the measure of the angle opposite the side c.
Using this formula, we can calculate the measure of the angles in both triangles. For △ABC we have angle A = arccos ( (b² + c² - a²) / 2bc ) and for △DEF we have angle D = arccos ( (e² + f² - d²) / 2ef ). The measure of angle A is not equal to the measure of angle D, so we can conclude that △ABC ≠ △DEF
Therefore, based on the calculation of the angles and the lengths of the sides, it can be concluded that △ABC is not congruent to △DEF.
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What is the image of (−5,−9) after a dilation by a scale factor of
3 centered at the origin?
The image of (-5,-9) after dilation by a scale factor of 3 centered at the origin is (-15,-27).
What is the image of (−5,−9) after a dilation by a scale factor of 3 centered at the origin?To find the image of the point (-5,-9) after dilation by a scale factor of 3 centered at the origin.
We can use the following formula:
(x', y') = (kx, ky)
Where (x', y') are the coordinates of the dilated point, (x, y) are the coordinates of the original point, and k is the scale factor.
In this case, k = 3, and the coordinates of the original point are (-5,-9).
So we have:
x' = 3(-5) = -15
y' = 3(-9) = -27
Therefore, the image after dilation is (-15,-27).
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Nora made 3 gallons of lemonade.
Which of the following can be used to find the number of pints of lemonade that Nora made?
A 3x2x2
B 3x4x2
C 3x3x2
D 3x4x3
This is a new version of the question. Make sure you start new workings.
Select all of the shapes below that are nets of a pentagonal-based pyramid.
Back to task
A
D
Watch video
B
Answ
The shapes that are nets of a pentagonal-based pyramid are shapes A and D.
What are properties of a pentagonal-based pyramid?A net of a pentagonal-based pyramid is a 2-dimensional pattern that can be folded into a 3-dimensional pentagonal-based pyramid. The net of a pentagonal-based pyramid has the following properties:
It consists of a regular pentagon as the base of the pyramid and five triangles that form the sides of the pyramid.The five triangles are congruent isosceles triangles.The apex of the pyramid is located at the center of the regular pentagon.Each triangle has one vertex at the apex of the pyramid and two vertices on the edges of the regular pentagon.The sum of the angles of each triangle is 180 degrees, and the sum of the angles of the regular pentagon is 540 degrees.The perimeter of the base of the pyramid is equal to five times the length of one side of the regular pentagon.The height of the pyramid is the perpendicular distance from the apex to the base, which can be found using the Pythagorean theorem.Learn more on pentagonal-based pyramid here: https://brainly.com/question/28226952
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The area of a rectangle is found using the formula A=lw
, where l
is the length of the rectangle and w
is the width. Multiply each pair of factors and express the area of each rectangle as a single polynomial in terms of x
.
Question
l=x+14; w=3x+1
Answer:
The area of the rectangle is given by the formula A = lw. Substituting the given values, we get:
A = (x+14)(3x+1)
Expanding the expression, we get:
A = 3x^2 + x + 42x + 14
A = 3x^2 + 43x + 14
Therefore, the area of the rectangle is given by the polynomial expression 3x^2 + 43x + 14.
Construct a polynomial function of least degree possible using the given information.
Real roots: −1 (with multiplicity 2), 1 and (2,
f(2)) = (2, 7)
The polynomial function of least degree possible using the given information.
Real roots: −1 (with multiplicity 2), 1 and (2,
f(2)) = (2, 7) is f(x) = x³ - 3x² + 3x - 1.
How to explain the polynomialSince the polynomial function has real roots at -1 (with multiplicity 2) and 1, we know that the factors of the polynomial are (x + 1)² and (x - 1).
Let the polynomial be of the form f(x) = ax³ + bx² + cx + d. We know that f(2) = 7, so:
a(2³) + b(2²) + c(2) + d = 7
8a + 4b + 2c + d = 7
Now we need to use the fact that the roots are -1 (with multiplicity 2) and 1. Since the polynomial has factors of (x + 1)² and (x - 1), we can write the polynomial as:
f(x) = a(x + 1)²(x - 1)
Expanding this expression, we get:
f(x) = a(x² - 2x + 1)(x - 1)
f(x) = ax³ - 3ax² + 3ax - a
Now we can equate the coefficients of this expression with the coefficients of our assumed polynomial f(x) = ax³ + bx² + cx + d:
a = a
-3a = b
3a = c
-a = d
Therefore, our polynomial function is:
f(x) = x³ - 3x² + 3x - 1
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Here is the graph for one equation in a system of equations. (picture below)
Write a second equation for the system so it has infinitely many solutions.
Write a second equation whose graph goes through (0,2) so that the system has no solutions.
Write a second equation whose graph goes through (2,2) so that the system has one solution at (4,3).
After answering the provided question, we can conclude that which slope equals m = 1/2. As a result, the second line's equation is y - 2 = (1/2)(x - 2), or y = (1/2)x + 1.
what is slope intercept?In mathematics, the slope-intercept form of a linear equation is an equation of the form y = mx + b, where m is the line's gradient and b is the más, which is the point on the line where it intersects the y-axis. Because it allows you to speedily see the line and ascertain its slope and y-intercept, the slope-intercept form is a useful way to represent a line's equation. The slope of the line indicates its steepness, while the esta indicates in which the line intersects the y-axis.
To answer these questions, we must first determine the equation of the line depicted in the graph. Assume the line is in slope-intercept form, y = mx + b, with m representing the slope and b representing the y-intercept.
where m is the slope to be found. Because we want this line to intersect the given line at (4, 3), we can plug those values into both equations and solve for m: Because y = (1/4)x + 1, we get 3 = (1/4)(4) + 1 = 2 + 2m, which equals m = 1/2. As a result, the second line's equation is y - 2 = (1/2)(x - 2), or y = (1/2)x + 1.
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please help me!!!!!!!!
The mean of the data is X = 85. The variance is 187.5. The standard deviation is σ = 13.7
Describe Standard Deviation?Standard deviation is a measure of the amount of variability or dispersion of a set of data points from the mean value. It is calculated by finding the square root of the variance, which is the average of the squared differences between each data point and the mean. The standard deviation indicates how far the data points are from the mean on average, with larger values indicating greater variability and smaller values indicating less variability. The standard deviation is a commonly used measure of spread in statistics and is often used to describe the distribution of a dataset. It is denoted by the symbol σ (sigma) for a population and s for a sample.
To find the mean of the data, we add up all the values and divide by the total number of values:
X = (90 + 75 + 60 + 85 + 65 + 80 + 70 + 75) / 8
= 680 / 8
= 85
So the mean of the data is X = 85.
To find the variance, we need to first find the deviation of each value from the mean, square each deviation, and then take the average of the squared deviations:
deviation of 90 from mean = 90 - 85 = 5
deviation of 75 from mean = 75 - 85 = -10
deviation of 60 from mean = 60 - 85 = -25
deviation of 85 from mean = 85 - 85 = 0
deviation of 65 from mean = 65 - 85 = -20
deviation of 80 from mean = 80 - 85 = -5
deviation of 70 from mean = 70 - 85 = -15
deviation of 75 from mean = 75 - 85 = -10
Now, we square each deviation and find the average:
variance = [(5)² + (-10)² + (-25)² + (0)² + (-20)² + (-5)² + (-15)² + (-10)²] / 8
= (25 + 100 + 625 + 0 + 400 + 25 + 225 + 100) / 8
= 1500 / 8
= 187.5
So the variance is 187.5.
Finally, the standard deviation is the square root of the variance:
σ = √(187.5)
= 13.7 (rounded to the nearest tenth)
Therefore, the standard deviation is σ = 13.7 (rounded to the nearest tenth).
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The rectangular board below is to be cut at an angle of 36 and 32 as shown.When you cut out ABC,what is the measure of A
The measure of angle A is 112 degrees. Hence, option d is correct.
What is a rectangle?Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral, A closed, four-sided rectangle is a two-dimensional shape. A rectangle's opposite sides are equal and parallel to one another, and all of its angles are exactly 90 degrees.
Similarly, since the angle of the cut is 36 degrees, the angle opposite it (angle BCD) is also 36 degrees. Since angles BCD and BDC add up to 90 degrees (because triangle BCD is a right triangle), angle BDC measures 54 degrees (90 - 36 = 54).
Now, we can find angle BDA by subtracting angle ADB and angle BDC from 180 degrees:
angle BDA = 180 - angle ADB - angle BDC
= 180 - 58 - 54
= 68
Finally, we can find angle A by subtracting angle BDA from 180 degrees:
angle A = 180 - angle BDA
= 180 - 68
= 112
Therefore, the measure of angle A is 112 degrees. Hence, option d is correct.
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Complete question:
The sixth-grade art students are making a mosaic using tiles in the shape of right triangle. The two sides that meet to form a right angle are 7 centimeters and 5 centimeters long. If there are 20 tiles in the mosaic, what is the area of the mosaic ?
Answer: The area of the mosaic is 175 cm². To calculate this, multiply the two sides of each triangle together (7 cm * 5 cm = 35 cm²) and then multiply that by the number of tiles (35 cm² * 20 = 175 cm²).
Step-by-step explanation:
Scale factors,
For 19 would it be 5/4 since the polygon is free trying bigger and for 20 would it be 4/5 since it is getting smaller?
All my friends are writing it the other way around but I’m confused because how can it get bigger if it’s less than 1?
The answers of the following questions are mentioned below respectively.
What is scale factor?Scale factor is the ratio of the lengths of corresponding sides of two similar figures. Two figures are considered similar if they have the same shape, but not necessarily the same size.
19.To find the scale factor of PQRS to JKLM, we can use the fact that the corresponding sides of similar figures are proportional. Thus, we have:
PQ/JK = QR/KL = RS/LM
Substituting the given values, we get:
w/25 = 12/15 = 10/x
Simplifying, we get:
w = 5/3 * 25 = 41.67 (approx)
x = 15/2 = 7.5
y = 25 * 7.5 / 15 = 12.5
Therefore, the scale factor of PQRS to JKLM is PQ/JK = w/25 = 41.67/25 = 1.6667 (approx).
20. To find the scale factor of JKLM to PQRS, we can take the reciprocal of the scale factor of PQRS to JKLM. Thus, we have:
JK/PQ = 1/(PQ/JK) = 1/1.6667 = 0.6 (approx)
Therefore, the scale factor of JKLM to PQRS is JK/PQ = 0.6 (approx).
21. To find the values of ti.. .r. and v, we need more information or equations.
22. To find the perimeter of each polygon, we can add up the lengths of the sides. Thus, we have:
Perimeter of JKLM = KJ + JM + ML + LK = 25 + y + x + 15 = y + x + 40 = 20 + 7.5 + 40 = 67.5
Perimeter of PQRS = PQ + QR + RS + SP = w + 12 + 10 + 16 = w + 38 = 41.67 + 38 = 79.67 (approx)
Therefore, the perimeter of JKLM is 67.5 and the perimeter of PQRS is 79.67 (approx).
23. To find the ratio of the perimeter of PQRS to the perimeter of JKLM, we can divide the perimeter of PQRS by the perimeter of JKLM. Thus, we have:
Ratio of perimeter of PQRS to perimeter of JKLM = Perimeter of PQRS / Perimeter of JKLM = 79.67 / 67.5 = 1.18 (approx)
Therefore, the ratio of the perimeter of PQRS to the perimeter of JKLM is 1.18 (approx).
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19. The scale ratio of PQRS to JKLM is PQ/JK = 1.6667. (approx).
20. JK/PQ is the scale factor of JKLM to PQRS is = 0.6 (approx).
22. The JKLM perimeter is 67.5 and the PQRS perimeter is 79.67 (approx).
23. The PQRS perimeter's ratio to the JKLM perimeter is 1.18. (approx).
What is scale factor?The ratio of the lengths of the respective sides of two similar figures is known as the scale factor. When two figures share the same shape but not necessarily the same height, they are said to be similar.
19. We can use the knowledge that the corresponding sides of comparable figures are proportional to determine the scale factor of PQRS to JKLM.
So, here we are:
[tex]\frac{PQ}{JK}=\frac{QR}{KL}=\frac{RS}{LM}[/tex]
Replace the specified numbers in the aforementioned equation,
[tex]\frac{w}{25}=\frac{12}{25}=\frac{10}{x}[/tex]
Simplifying, we get:
w = 5/3 * 25
= 41.67 (approx)
x = 15/2 = 7.5
y = 25 * 7.5 / 15
= 12.5
As a result, PQ/JK = w/25 is the scale factor for PQRS to JKLM.
= 41.67/25
= 1.6667 (approx).
20. We can take the inverse of the scale factor of PQRS to JKLM to determine the scale factor of JKLM to PQRS. So, here we are:
JK/PQ = 1/(PQ/JK)
= 1/1.6667
= 0.6 (approx)
As a result, JK/PQ is equal to 0.6 when converting JKLM to PQRS. (approx).
21. To find the values of ti.. .r. and v, additional details or formulae are required.
22. We can sum up the side lengths of each polygon to determine its perimeter. So, here we are:
Perimeter of JKLM = KJ + JM + ML + LK
= 25 + y + x + 15
= y + x + 40
= 20 + 7.5 + 40
= 67.5
Perimeter of PQRS = PQ + QR + RS + SP
= w + 12 + 10 + 16
= w + 38
= 41.67 + 38
= 79.67 (approx)
As a result, the JKLM perimeter is 67.5 and the PQRS perimeter is 79.67 (approx).
23. By dividing the perimeters of the two systems, we can determine the percentage of the perimeters of PQRS and JKLM. So, here we are:
Ratio of the PQRS periphery to the JKLM perimeter = Perimeter of PQRS / Perimeter of JKLM = 79.67 / 67.5 = 1.18 (approx)
As a result, the PQRS perimeter's relationship to the JKLM perimeter is 1.18. (approx).
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Ms. Mazzei has a farm on 12 acres of land. She wants to create animal pens that are each 3/11 of an acre. How many pens can Ms. Mazzei have in the 12 acres?
Ms. Mazzei can have 44 animal pens in her 12 acres of land.
Describe Algebra?Algebra is a branch of mathematics that deals with the manipulation and properties of mathematical expressions, including variables and symbols representing numbers, as well as the rules governing their relationships and operations.
Algebraic equations typically involve variables, which are represented by letters or symbols, and are used to express relationships between different quantities or unknowns. These equations can be manipulated using algebraic operations such as addition, subtraction, multiplication, division, and exponentiation to solve for the value of the variables.
The study of algebra includes a wide range of topics, including linear algebra, abstract algebra, number theory, and algebraic geometry. It is a fundamental part of mathematics and plays a crucial role in many areas of modern science and technology.
To find the number of animal pens Ms. Mazzei can have in 12 acres of land, we need to divide the total area by the area of each pen:
Number of pens = Total area / Area of each pen
Total area = 12 acres
Area of each pen = 3/11 acres
Number of pens = 12 / (3/11)
Number of pens = 44
Therefore, Ms. Mazzei can have 44 animal pens in her 12 acres of land.
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If 6x + 2y = 18, but 8x + 3y also equals 25, what are the values of x and y?
Answer: x=1 y=6
Step-by-step explanation:
What is the gradient of the blue line?
The blue line is the tangent line that passes through the point (0.75, 0.25). The point on the tangent line is (3, 4). The gradient of the curve is approximately 0.6.
Answer:
gradient = [tex]\frac{1}{4}[/tex]
Step-by-step explanation:
calculate the gradient m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (4, 2) and (x₂, y₂ ) = (8, 3) ← 2 points on the line
m = [tex]\frac{3-2}{8-4}[/tex] = [tex]\frac{1}{4}[/tex]
About 61% of students at a certain high school take the SATs. What is the probability of sampling five successive students at random until you find the first student to take the SATs?
Answer: The probability of a student taking the SATs is p = 0.61. Let's consider the first student we sample. The probability that this student does not take the SATs is q = 1 - p = 0.39.
If the first student does not take the SATs, we need to sample another student. The probability that the second student does not take the SATs, given that the first student did not take the SATs, is still q = 0.39.
Similarly, if the second student also does not take the SATs, we need to sample a third student. The probability that the third student does not take the SATs, given that the first two students did not take the SATs, is still q = 0.39.
We continue this process until we find the first student who takes the SATs. Let X be the number of students we sample until we find the first student who takes the SATs. Then X can take on the values 1, 2, 3, and so on.
The probability that we find the first student who takes the SATs on the first try is p = 0.61. The probability that we find the first student who takes the SATs on the second try is (q)(p) = (0.39)(0.61) = 0.238.
Similarly, the probability that we find the first student who takes the SATs on the third try is (q)(q)(p) = (0.39)(0.39)(0.61) = 0.147.
In general, the probability that we find the first student who takes the SATs on the kth try is (q)^(k-1)(p).
Therefore, the probability that we find the first student who takes the SATs in exactly k tries is:
P(X=k) = (q)^(k-1)(p)
We want to find the probability of sampling five successive students at random until we find the first student to take the SATs. So we want to find:
P(X=1) ∗ P(X=2) ∗ P(X=3) ∗ P(X=4) ∗ P(X=5)
= p ∗ (q)(p) ∗ (q)(q)(p) ∗ (q)(q)(q)(p) ∗ (q)(q)(q)(q)(p)
= (0.61) ∗ (0.39)(0.61) ∗ (0.39)(0.39)(0.61) ∗ (0.39)(0.39)(0.39)(0.61) ∗ (0.39)(0.39)(0.39)(0.39)(0.61)
= 0.61 ∗ 0.238 ∗ 0.147 ∗ 0.0905 ∗ 0.0554
≈ 0.00028
Therefore, the probability of sampling five successive students at random until you find the first student to take the SATs is approximately 0.00028 or 0.028%.
Step-by-step explanation:
Simplify the expression. .
2. 3h( 6 – k)
Step by step please
1874
2365
Fold this paper so that
1 is on top of 2,
2 is on top of 3,
3 is on top of 4, ...
Numbers can
be upside down
or backwards.
1
Answer:
Fold the paper in half lengthwise. Unfold it, then fold it in half again widthwise. Unfold it, then fold it in thirds lengthwise. Unfold it and then fold it in half again widthwise. You should now have a paper with 8 sections, with 1 on top of 2, 2 on top of 3, 3 on top of 4, etc. You can flip the numbers upside down or backwards as desired.
Step-by-step explanation:
answer i will give u a lot of points 100
Answer:
25.1
Step-by-step explanation:
formula for circumfrance is 2piR
so (2pi)(4)= 25.1
:)
Shawnee bought a shirt on sale that was 20% off of the original price. The original price was $5 more than the sale price. What was the original price? Use a model and check your work using the 80/20 rule.
It takes 4 people 8 days to paint a wall. How long will it take for 8 people to finish the same wall?
Answer: 4 days
Step-by-step explanation:
If it takes 4 people 8 days to paint a wall. We can only assume that doubling the number of people would be 2 times as fast. So divide 8/2=4.
HELP PLEASEEEE ENOUGH POINTS I REALLY NEED HELP
Answer:
Step-by-step explanation:
. A pile of bottle caps is located at (4, -10). find the length of the most direct path between Ann and the bottle caps?
Thus, the most direct path between the bottle caps and Ann is found as:
d = 10.63 units.
Define about the distance formula:The algebraic phrase known as the distance formula, which provides the distances between two places in terms of respective coordinates (in coordinate system).
The distance formulas with points in rectangular coordinates in two- through three-dimensional Euclidean space are based here on Pythagorean theorem.
The formula used to calculate the distance between both the points (x1, y1) and ((x2, y2)
d = √[(x2 - x1)² + (y2 - y1)²]
Coordinates of pile of bottle caps -:(x1, y1) = (4, -10).
Coordinates of ANN - (x2, y2) = (-4, 3).
Using the distance formula:
d = √[(x2 - x1)² + (y2 - y1)²]
d = √[(-4 - 4)² + (-3 + 10)²]
d = √[(64) + 49]
d = 10.63 units
Thus, the most direct path between the bottle caps and Ann is found as:
d = 10.63 units.
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complete question
A pile of bottle caps is located at (4, -10). find the length of the most direct path between Ann and the bottle caps?
The graph for the question is given.
Q1 The following diagram represents the positions and bearings
of two helicopters. Helicopter B is 1.2km away from
helicopter A on a bearing of 122°. How far north is
helicopter A from helicopter B?
N
Helicopter A1220
1.2km
N
Helicopter B
The distance north of Helicopter A from helicopter B is 1. 03 km.
The shortest distance between the polar bear and the conservationists is 9.36 km.
How to find the distance ?To find the distance from Helicopter A to Helicopter B in the north direction, we can use trigonometry. We can create a right triangle with the north direction as one side, the distance between the helicopters as the hypotenuse, and the angle of 122° between them.
Let N be the north distance between A and B. We can use the sine function:
sin(angle) = opposite side / hypotenuse
sin(122°) = N / 1.2 km
Now, solve for N:
N = 1.2 km x sin (122°) = 1.03 km
The polar bear's position is given as 3 km eastward and on a bearing of 104°. To find the shortest distance between the polar bear and the conservationists, we need to consider the right triangle formed by the eastward direction, the north direction, and the distance between the polar bear and the conservationists as the hypotenuse.
Let D be the shortest distance between the polar bear and the conservationists. We can use the cosine function:
cos(angle) = adjacent side / hypotenuse
cos(104°) = 3 km / D
Now, solve for D:
D = 3 km / cos(104°) = 9.36 km
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Select the expression that represents this real-world situation.
Josie has 12 yards of fabric. She is making identical dresses for d dolls. What is the length of fabric used for each doll?
12 + d
12 − d
12 x d
12 ÷ d
you order a cell phone case and 2 screen protectors online for a total of $18.95. your friend orders 2 cell phone cases and 5 screen protectors at the same unit prices for a total of $41.40. what is the cost of each cell phone case? each screen protector?
Answer:
Step-by-step explanation:
The cost of each cell phone case is $7.15, and the cost of each screen protector is $2.25.
To solve this problem, we can create a system of equations.
Let x represent the cost of one cell phone case and y represent the cost of one screen protector.
Then, we can write the following equations:
1x + 2y = 18.95 (equation 1)
2x + 5y = 41.40 (equation 2)
We can solve for x and y by multiplying equation 1 by 2 and subtracting it from equation
2.2x + 5y = 41.40(2 x 1x + 2 x 2y = 2 x 18.95)2x + 5y = 41.4002x + 4y = 37.90
Subtracting equation 1 from equation 2 gives us:
2x + 5y = 41.400- (0.2x + 0.4y = 3.790)
1.8x + 4.6y = 37.61
Now we can solve for y.
1.8x + 4.6y = 37.61
=> 46y = 46.29
=> y = 1.05
Then we can solve for x using equation
1.1x + 2y = 18.95
=> 1x + 2(1.05) = 18.95
=> x = 7.15
For similar question on cost
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Question:
You order a cell phone case and 2 screen protectors online for a total of $18.95. Your friend orders 2 cell phone cases and 5 screen protectors at the same unit prices for a total of $41.40. What is the cost of each cell phone case? Each screen protector?
find the slope of a line perpendicular to y=- 1/2x+7
Answer:
perpendicular slope = 2
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - [tex]\frac{1}{2}[/tex] x + 7 ← is in slope- intercept form
with slope m = - [tex]\frac{1}{2}[/tex]
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{1}{2} }[/tex] = 2
!!!help please I’ll mark BRAINLIEST!