Answers
The inverse matrix of the given matrix is
[tex]\left[\begin{array}{ccc}3/2&-2\\-1/2&1\end{array}\right][/tex]
What is meant by inverse matrix?
If A is a non-singular square matrix, then A^-1, often known as the inverse matrix of A, must exist if it is to satisfy the following property:
AA^-1 = A^-1A = I, Where I is the Identity matrix
Now, we will first find the determinant of the given matrix, whichis as follows:
Determinant = 6-4 = 2
Since, the determinant is not zero, this means that the inverse matrix exists.
Now, let's find the inverse matrix i.e. A^-1
[tex]A^{-1} = \frac{1}{D} \left[\begin{array}{ccc}d&-b\\-c&a\end{array}\right][/tex]
[tex]A^{-1} = \frac{1}{2} \left[\begin{array}{ccc}3&-4\\-1&2\end{array}\right][/tex]
[tex]A^{-1} = \left[\begin{array}{ccc}3/2&-4/2\\-1/2&2/2\end{array}\right][/tex]
[tex]A^{-1} = \left[\begin{array}{ccc}3/2&-2\\-1/2&1\end{array}\right][/tex]
Hence, the inverse matrix of the given matrix is as under
[tex]\left[\begin{array}{ccc}3/2&-2\\-1/2&1\end{array}\right][/tex]
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Related Questions
Express 12.7% as a decimal
Answers
Answer:
Step-by-step explanation:
12.7% = 12.7/100 = 0.127
Brad has five pieces of wood each measuring the exact same number of inches in length.
If three inches are cut off each piece, which expression represents the new total length of all five pieces of wood?
Answers
If three inches are cut off each piece, the expression represents the new total length of all five pieces of wood will be 5 x (initial length) - 15 .
To derive the expression:
Multiply 5 (the number of pieces) times the initial length of each piece
5 x (initial length)
Subtract 3 (the amount cut off each piece) times 5 (the number of pieces)
5 x (initial length) - (3 x 5)
Simplify
5 x (initial length) - 15
New total length of all five pieces of wood:
5 x (initial length) - 15
Hence the required expression is 5 x (initial length) - 15.
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A food truck did a daily survey of customers to find their food preferences. The data is partially entered in the frequency table. Complete the table to analyze the data and answer the questions: Likes hamburgers Does not like hamburgers Total Likes burritos 49 92 Does not like burritos 75 38 Total 81 205
Answers
30.6% of survey respondents do not like both hamburgers and burritos, with the strongest association being that customers who like hamburgers are more likely to not like burritos.
Part A: The number of survey respondents that do not like hamburgers is 205 - 81 = 124.
Of these 124 respondents, 38 do not like burritos as well, so the percentage of respondents that do not like both hamburgers and burritos is 38 / 124 * 100% = 30.6%.
Part B: The marginal relative frequency of all customers who like hamburgers is 81 / (81 + 205) = 28.2%.
Part C: The conditional relative frequency of customers that like burritos given they like hamburgers is 49 / 81 = 60.5%.
The conditional relative frequency of customers that do not like burritos given they like hamburgers is 32 / 81 = 39.5%.
The conditional relative frequency of customers that like hamburgers given they like burritos is 49 / 141 = 34.8%.
The conditional relative frequency of customers that do not like hamburgers given they like burritos are 92 / 141 = 65.2%.
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I'm stuck any help? About Understanding Linear Functions.
Answers
Answer:
No.
Step-by-step explanation:
A linear function can be identified if the function is a line when graphed or if the x is to the first power. X is to the third power, so it's not linear.
Hope it helped!
(b) find the probability that the eia test result is positive. round your answer to 3 decimal places. leave your answer in decimal form. 0.0159 (c) given that the eia test is positive, find the probability that the person has the hiv antibody. round your answer to 3 decimal places. leave your answer in decimal form.
Answers
(b) The probability of a positive test result is 0.0159.
(c) The probability that a person has the HIV antibody, given a positive test result, is 0.735. In this case, that would be 0.8 x 0.9 = 0.72.
This means that, if someone tests positive for the HIV antibody, there is a 73.5% chance that they actually have the HIV antibody. This number is determined by taking into account the false positive rate and true positive rate of the test.
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Decide whether or not each equation represents a proportional relationship. Volume measured in cups (c) vs. The same volume measured in ounces (z): c=18z Area of a square (A) vs. The side length of the square (s): A=s2 Perimeter of an equilateral triangle (P) vs. The side length of the triangle (s): 3s=P Length (L) vs. Width (w) for a rectangle whose area is 60 square units: L=60w
Answers
The equations c = 18z, 3s = P, and L = 60w represent a proportional relationship, but A = s² does not represent a proportional relationship.
The equation that represents a proportional relationship, or a line, is y = kx, where k is the constant of proportionality.
If we take the first equation, Volume measured in cups (c) vs The same volume measured in ounces (z): c = 18z
Here, 18 is a constant
∴It is a proportional relationship.
If we take the second equation, the Area of a square (A) vs The side length of the square (s): A = s²
This is a quadratic equation.
∴It is not a proportional relationship.
If we take the third equation, Perimeter of an equilateral triangle (P) vs The side length of the triangle (s): 3s = P
Here, 3 is a constant
∴It is a proportional relationship.
Finally, If we take the fourth equation, Length (L) vs Width (w) for a rectangle whose area is 60 square units: L = 60 w
Here, 60 is a constant
∴It is a proportional relationship.
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A square rotated about its center by 360º maps onto itself at
2
different angles of rotation. You can reflect a square onto itself across
different lines of reflection.
Answers
A square rotated about its center by 360º maps onto itself at 4 different angles of rotation. You can reflect a square onto itself across 4 different lines of reflection.
How to find the angles of rotation.?It is important to note that a square has 4 angles of rotation and 4 lines of symmetry.
The 4 angles of rotation implies that you can tend to rotate it 4 times so as to have it line up with its main image before hitting 360°.
The 4 lines of symmetry which are:
T lines which are the horizontal lines and vertical line through the center. Two diagonal lines of symmetry through the center.Therefore the first and second blank is both 4.
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it is statement of quality of two ratios A.fraction B.ratio C.proportion D.rate
Answers
Answer: C. proportion
Reason:
A fraction or ratio is something like [tex]\frac{2}{3}[/tex]
Something like [tex]\frac{2}{3} = \frac{4}{6}[/tex] is a proportion that ties together two fractions.
Answer:
C. proportion
Step-by-step explanation:
It is statement of equality of two ratios
A. fraction
B. ratio
C. proportion
D. rate
(I think the word should be "equality", not "quality".)
The ratio of a to b can be written as:
a to b, a:b, a/b
When you set a ratio equal to another ratio, then you have a proportion.
If ratio a/b is equal to ratio c/d, then you can write
a/b = c/d,
and now you have a proportion.
conditions for rhombuses rectangles and squares practice
Answers
Conditions which help us to differentiate the properties of rectangle, rhombus , and square are:
Rectangle : Opposite sides are congruent with measure of each of the angle 90°.
Rhombus : Parallelogram whose diagonals are perpendicular.
Square: All four sides are congruent with measure of each of the angle 90°.
Different conditions of rectangle , rhombus, and square are:
Rectangle, rhombus, and square are all type of quadrilateral.Rectangle is a type of quadrilateral whose opposite sides are congruent to each other.All the four angles in a rectangle are of 90 degrees.Rhombus is a type of quadrilateral whose all four sides are congruent to each other.Diagonals of the rhombus are perpendicular to each other.Square is a type of quadrilateral with all four congruent sides and measure of all the four angles is 90 degrees.The given question is incomplete, I answer the question in general according to my knowledge:
What are the conditions which differentiate rhombus, rectangle, and square from each other?
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the ratio of strawberries to grapes in the fruit salad is 3:9. the ratio of strawberries to honeydew is 6:14. if there are 36 grapes. how many strawberries and how much honeydew is there?
Answers
Answer:
12 strawberries
28 honeydew
Step-by-step explanation:
[tex]\frac{strawberries}{grapes}[/tex] = [tex]\frac{3}{9}[/tex] = [tex]\frac{x}{36}[/tex]
9 x 4 = 36
so, 3 x 4 = 12
There are 12 strawberries
[tex]\frac{strawberries}{honeydew}[/tex] = [tex]\frac{6}{14}[/tex] = [tex]\frac{12}{x}[/tex]
6 x 2 = 12
so, 14 x 2 = 28
There are 28 honeydew
for the differential equation a. find all equilibrium solutions and use the first derivative test to draw the phase line for the de. b. classify each equilibrium solution as asymptotically stable , unstable or semi-stable. c. use the second derivative test for concavity and the phase line to produce a phase portrait and sketch one typical solution curves in each region determined by the equilibrium solutions.
Answers
An autonomous first order ordinary differential equation is any equation of the form: dy/dt = f(y).
1. Stable: The equilibrium solution y(t) = c is stable if all solutions with initial conditions y0 ‘near’
y = c approach c as t → ∞.
2. Unstable: The equilibrium solution y(t) = c is unstable if all solutions with initial conditions y0 ‘near’ y = c do NOT approach c as t → ∞.
3. Semi-stable: The equilibrium solution y(t) = c is semistable if initial conditions y0 on one side of c lead to solutions y(t) that approach c as t → ∞, while initial conditions y0 on the other side of c do NOT approach c.
Find the equilibrium points for the differential equation (1) and determine whether each is asymptotically stable, semistable, or unstable.
The graph of y0 as a function of y, and the phase line. (It’s important that α is positive – if it were negative, we’d have very different behavior).
We can see that there are two equilibrium solutions: y = 0, which is unstable, and y = 1, which is stable.
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PLEASE HELP!! 100 POINTS
Answers
Answer:
y = - [tex]\frac{1}{3}[/tex] x + [tex]\frac{5}{3}[/tex]
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 )
here m = - [tex]\frac{1}{3}[/tex] and c = [tex]\frac{5}{3}[/tex] , then
y = - [tex]\frac{1}{3}[/tex] x + [tex]\frac{5}{3}[/tex] ← equation of line
In triangle ABC, the measure of angle A is 35º and the measure of angle B is 20°. In triangle
DEF, the measure of angle D is 35º and the measure of angle F is 125. Are triangles ABC
and DEF similar? Explain or show your reasoning.
Answers
ΔABC and ΔDEF are not similar because corresponding angles are not equal.
Now, According to the question:
In triangle ABC :
The measure of angle A is 35º and
The measure of angle B is 20°.
In triangle DEF:
The measure of angle D is 35º and
The measure of angle F is 125
We know that :
Sum of interior angles of triangle is 180°
Now, In ΔABC:
∠A + ∠B + ∠C = 180°
35 + 20 + ∠C = 180°
55° + ∠C = 180°
∠C = 180° - 55°
∠C = 125°
Now, In ΔDEF:
∠D + ∠E + ∠F = 180°
35 + ∠E + 125 = 180°
160 + ∠E = 180°
∠E = 180° - 160°
∠E = 20°
So, ∠C ≠ ∠E as ∠C = 125° and ∠E =20°
Hence, No, Triangles are not similar .
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What is this answer for this page
Answers
Answer: 24x+ (-12y)= -36
Step-by-step explanation:
What is the solution to this system? Enter the solution as an ordered pair, (x, y).
Answers
The solution to the system of equations is (7.5, 1)
How to determine the solution to the systemFrom the question, we have the following parameters that can be used in our computation:
2x−3y=12
−12y+8x=48
divide the first equation by 2
So, we have
x - 1.5y = 6
This gives
x = 6y + 1.5
By substitution, the second equation becomes
-12y + 8 (6y + 1.5) = 48
So, we have
-12y + 48y + 12 = 48
Evaluate
36y = 36
Divide by 36
y = 1
So, we have
x = 6 + 1.5
x = 7.5
Hence, the solution is (7.5, 1)
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Complete question
What is the solution to this system?
2x−3y=12
−12y+8x=48
Enter the solution as an ordered pair, (x, y).
To create the flower gardens, Wendell bought six pieces of wood. Pieces A and B are 6 feet long, pieces C and D are 8 feet long, piece E is 3 feet long and piece F is 2 feet long.
Part A
Can Wendell make a triangular garden using pieces A, B, and F? Why or why not?
Part B
Can Wendell make a triangular garden using pieces D, E, and F? Why or why not?
Part C
Can Wendell make a rectangular garden with the pieces of wood he has? if yes, which pieces can he use?
Part D
Describe how Wendell can use all six pieces of wood to create either two rectangular gardens or two triangular gardens. Assume the gardens do not share a common side.
Part E
Wendell's dog. Jordan, was getting in his way as he worked in the backyard. So, Wendell chained him to a pole. If the chain is 12 feet long, about how much area does Jordan have to walk around?
Answers
Part E: The area that Jordan can walk around is equal to the area of a circle with a radius of 6 feet is 113 square feet.
Making triangular and Rectanglar garden with woods of different lengthsPart A: Wendell cannot make a triangular garden using pieces A, B, and F because the sum of the lengths of the two shorter sides of a triangle (in this case, pieces A, B, and F) must be greater than the length of the longest side (in this case, piece F, which is 2 feet long) in order for the triangle to be a valid one. Since the sum of the lengths of pieces A and B is 12 feet, which is greater than the length of piece F, it is not possible to make a triangular garden using these pieces.
Part B: Wendell cannot make a triangular garden using pieces D, E, and F because the sum of the lengths of the two shorter sides of a triangle (in this case, pieces D, E, and F) must be greater than the length of the longest side (in this case, piece D, which is 8 feet long) in order for the triangle to be a valid one. Since the sum of the lengths of pieces E and F is 5 feet, which is less than the length of piece D, it is not possible to make a triangular garden using these pieces.
Part C: Wendell can make a rectangular garden with the pieces of wood he has by using pieces A and C or pieces B and D. He cannot use pieces E and F because they are not long enough to make up one of the sides of a rectangle.
Part D: Wendell can not create two triangular gardens using all six pieces of wood as the sum of the lengths of the two shorter sides of a triangle must be greater than the length of the longest side, and he only have 3 pieces with length greater than 3 feet which is required to create one triangle.
Wendell can create two rectangular gardens using all six pieces of wood by using pieces A and C, and pieces B and D.
Part E: The area that Jordan can walk around is equal to the area of a circle with a radius of 6 feet (since the chain is 12 feet long).
The formula to calculate the area of a circle is πr^2
where π is approximately 3.14 and
r is the radius of the circle,
so the area that Jordan has to walk around is approximately
3.14 x 6² =113 square feet.
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9 ≥ 15 - x
What would x be
Answers
Answer:
Step-by-step explanation:Math
(4,0)
(5,3)
(6,0)
Identify the values of the variables in the equation when it is written in vertex form: y = a (x - h)² + k
1. What is the value of a?
2. What is the value of h?
3. What is the value of K?
Answers
Answer:
VALUES (5,6,12)
Step-by-step explanation:
Solve each trigonometric function for ALL POSSIBLE VALUES IN DEGREES
2 sin cos + cos = 0
Answers
Answer:
sin-1(-1/2), 180 + sin-1(-1/2), 360 + sin-1(-1/2)
What is 87 1/2% as a fraction?
Answers
Answer:
87.5/100
Step-by-step explanation:
Percents are parts of a whole. So if we imagine that the whole is 100, then 87 1/2% would be 87.5/100
how many distinct lines represent altitudes medians interior angle bisecrots of a isosceles triangle but not equilateral
Answers
The altitudes, the medians, and the angle-bisectors are distinct for the congruent sides but coincident for the base. Hence, 7 lines.
Now, According to the question:
Altitude. A line segment joining a vertex of a triangle with the mid-point of the opposite side. An altitude is a perpendicular line segment drawn from a vertex of a triangle to the opposite side. It divides the opposite sides into two equal parts.
A Median of a triangle is a straight line segment which is drawn from the vertex of a triangle to the middle point of the opposite side. It splits the opposite side of the triangle into two equal line segments. That means we know that it's a median if we have got those equal line segments.
The altitudes, the medians, and the angle-bisectors are distinct for the congruent sides but coincident for the base. Hence, 7 lines.
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A snail traveled 48 cm in 2/3h
Suppose the snail moved at a constant
speed and made no stops. How far
would the snail travel in 1 h?
Answers
10.8 m = 10*(8/10)=54/5 m
1.5 h = 3/2 h
distance = 54/5
time = 3/2 h
Speed = distance /time
= 54/5 ÷ 3/2 = 7.2 m/h
how far will the snail travel in 5 minute ?
5 min = 5/60 = 1/12 h
In 1/12 h the snail will travel
7.2 * 1/12 m = 0.6 m = 60 cms
a represents pounds of apples and b represents pounds of bananas. guillermo and cara are finding and interpreting the solution. is either correct? explain your reasoning.
Answers
Both Guillermo's and Cara's solutions are incorrect due to the incorrect substitution of values of a variable to find the dependent one.
Guillermo's solution is incorrect because he did not substitute the value of 'b' from the first equation into the second equation. Instead, he directly added 0.49b to both sides and solved for a, which gives an incorrect result.
Cara's solution is also incorrect because she did not substitute the value of 'a' from the first equation into the second equation. Instead, she used the equation a + b = 7 to solve for the value of b, which gave her an incorrect result.
We can find the correct solution as follows -
The system of equations is,
⇒ a + b = 7 .. (i)
And 1.29a + 0.49b = 6.63 .. (ii)
Now, we will solve the system of equations as follows -
⇒ a + b = 7
⇒ a = 7 - b .. (i)
And, ⇒ 1.29a + 0.49b = 6.63 .. (ii)
Substitute the value of a from (i) in (ii), we get;
⇒ 1.29a + 0.49b = 6.63
⇒ 1.29(7 - b) + 0.49b = 6.63
⇒ 9.03 - 1.29b + 0.49b = 6.63
⇒ - 0.8b = 6.63 - 9.03
⇒ - 0.8b = - 2.4
⇒ 0.8b = 2.4
⇒ b = 2.4 / 0.8
⇒ b = 3
And, From (i);
⇒ a = 7 - b .. (i)
⇒ a = 7 - 3
⇒ a = 4
Hence, 4 pounds of apples and 3 pounds of bananas were bought.
Thus, both of their solutions are incorrect.
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The complete question is -
FIND THE ERROR In the system a + b = 7 and 1.29a + 0.49b = 6.63, a represents pounds of apples and b represents pounds of bananas a person bought. Guillermo and Cara are finding and interpreting the solution. Is either correct? Explain your reasoning.
a. Guillermo: 1.29a + 0.49b = 6.63 ⇒ 1.29a +0.49(a + 7) = 6.63 ⇒ 1.29a + 0.49a + 3.43 = 6.63 ⇒ 1.78a = 3.2 ⇒ a = 1.8
a + b = 7, so b = 5.2. The solution (1.8, 5.2) means that 1.8 pounds of apples and 5.2 pounds of bananas were bought.
b. Cara: 1.29a + 0.49b = 6.63 ⇒ 1.29(7-b) + 0.49b = 6.63 ⇒ 9.03- 1.29b + 0.49b = 6.63 ⇒ -0.8b = -2.4 ⇒ b=3
The solution b = 3 means that 3 pounds of apples and 3 pounds of bananas were bought. volunteers. The ratio of boys to girls is 7:5.
The table represents a proportional relationship. Write an equation to represent the relationship.
Answers
For the table of values gives, the equation of line is obtained as y = 1/3x.
What is an equation?
A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").
The coordinate points for cups of flour, x and loaves of bread y is given in the table.
The slope-intercept form of an equation is - y = mx + b
To find the slope m use the formula -
(y2 - y1)/(x2 - x1)
Substituting the values in the equation -
(3 - 2)/(9 - 6)
1/3
So, the slope point is obtained as m = 1/3.
The equation becomes - y =1/3 x + b
To find the value of b substitute the values of x and y in the equation -
2 = 1/3(6) + b
2 = 2 + b
b = 2 - 2
b = 0
So, the value for b is 0.
Now, the equation becomes -
y = 1/3x + 0
y = 1/3x
The graph is plotted for the equation.
Therefore, the equation is y = 1/3x.
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given four sets: a, b, c and d. each set has 15. the pair-wise intersections have 4 elements. the three-way intersections have 3 elements. there are 2 elements in the intersection of all sets. how many elements are there in total?
Answers
There are 46 elements in total for 4 sets A, B, C, and D.
Consider 4 sets A, B, C, and D.
Each set has 15 elements.
The pair-wise intersection has 4 elements.
The three-way intersection has 3 elements.
There are 2 elements in the intersection of all sets.
So,
P(A) = P(B) = P(C) = P(D) = 15
P(A ∩ B) = P(A ∩ C) = P(A ∩ D) = P(B ∩ C) = P(B ∩ D) = P(C ∩ D) = 4
P(A ∩ B ∩ C) = P(A ∩ B ∩ D) = P(A ∩ C ∩ D) = P(B ∩ C ∩ D) = 3
P(A ∩ B ∩ C ∩ D) = 2
The total number of elements are:
P (A U B U C U D) = P(A) + P(B) + P(C) + P(D) - P(A ∩ B) - P(A ∩ C) - P(A ∩ D)- P(B ∩ C) - P(B ∩ D) - P(C ∩ D) + P(A ∩ B ∩ C) + P(A ∩ B ∩ D) + P(A ∩ C ∩ D) + P(B ∩ C ∩ D) - P(A ∩ B ∩ C ∩ D).
P (A U B U C U D) = 15 + 15 + 15 + 15 - 4 - 4 - 4 - 4 - 4 - 4 + 3 + 3 + 3 + 3 - 2
= 60 - 24 + 12 - 2
= 60 + 12 - 24 - 2
= 72 - 26
= 46
Therefore there are 46 elements.
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Consider a force F = 〈–1, 3〉 applied to an object that is moving from the point (3, –9) to the origin. Find the displacement vector of the object.
Answer:
d = 〈 -3 , 9 〉
W = 30 Joules
Answers
The displacement vector of the object is (-3, 9) and the work done is 30 Joules
The term called vector in math is defined as a quantity or phenomenon that has two independent properties such as magnitude and direction.
Here we know that the value of force F is (-1, 3) and the point is (3, -9)
Then the displacement from origin to (3, -9) is calculated as,
=> d = (0-3, 0-(-9))
Then the value of d is ( -3, 9)
Here the formula to Work done is written as,
=> F x d
=> (-1, 3) x (-3, 9) = 3 + 27
=> 30 joules.
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Ella invested $4,900 in an account paying an interest rate of 3% compounded monthly. Assuming no deposits or withdrawals are made, how long would it take, to the nearest tenth of a year, for the value of the account to reach $5,920?
Answers
Answer:
To solve this problem we can use the formula for future value of an investment, which is:
FV = PV(1+r)^t
Where PV is the present value, r is the interest rate, t is the number of years, and FV is the future value.
In this case, we know that PV = $4,900, r = 3% = 0.03, and FV = $5,920.
So we can rearrange the formula to solve for t:
t = log(FV/PV) / log(1+r)
t = log($5,920 / $4,900) / log(1+ 0.03)
t ≈ 10.3 years
Therefore, it would take approximately 10.3 years for the account to reach $5,920.
8. At a fund raising event, a booth was set up to sell handmade cards and photo
frames. On the first day, 3 cards and 9 photo frames were sold for a total of $75.
The next day, 8 cards and 5 photo frames were sold for a total of $67.
Find the selling price of a card and the selling price of a photo frame.
Answers
We can start solving this problem by using a system of equations. Let x be the selling price of a card and y be the selling price of a photo frame.
From the information given, we know that on the first day:
3x + 9y = 75 (1)
And on the second day:
8x + 5y = 67 (2)
Now we have two equations with two variables. To find the value of x and y, we can use either substitution or elimination method.
One possible way to solve for x and y is to use substitution method:
Solve equation (1) for x in terms of y:
x = (75 - 9y) / 3
Substitute this expression into equation (2) to eliminate x:
8((75 - 9y) / 3) + 5y = 67
Solving this equation for y:
y = 3
Now we can substitute this value of y back into equation (1) or (2) to find the value of x:
3x + 9(3) = 75
3x = 48
x = 16
So the selling price of a card is $16 and the selling price of a photo frame is $3.
Answer:
Photo frame = $7
Card = $4
Step-by-step explanation:
Define the variables:
Let c = the selling price of a handmade card (in dollars).Let p = the selling price of a handmade photo frame (in dollars).Given information:
On the first day, 3 cards and 9 photo frames were sold for a total of $75.On the next day, 8 cards and 5 photo frames were sold for a total of $67.Create a system of linear equations using the given information and defined variables:
[tex]\begin{cases}3c + 9p = 75\\ 8c + 5p = 67\end{cases}[/tex]
Rearrange the first equation to isolate c:
[tex]\implies 3c+9p=75[/tex]
[tex]\implies 3(c+3p)=75[/tex]
[tex]\implies \dfrac{3(c+3p)}{3}=\dfrac{75}{3}[/tex]
[tex]\implies c+3p=25[/tex]
[tex]\implies c+3p-3p=25-3p[/tex]
[tex]\implies c=25-3p[/tex]
Substitute the expression for c into the second equation and solve for p:
[tex]\implies 8c+5p=67[/tex]
[tex]\implies 8(25-3p)+5p=67[/tex]
[tex]\implies 200-24p+5p=67[/tex]
[tex]\implies 200-19p=67[/tex]
[tex]\implies 200-19p-200=67-200[/tex]
[tex]\implies -19p=-133[/tex]
[tex]\implies \dfrac{-19p}{-19}=\dfrac{-133}{-19}[/tex]
[tex]\implies p=7[/tex]
Therefore, the selling price of a handmade photo frame was $7.
Substitute the found value of p into the expression for c and solve for c:
[tex]\implies c=25-3p[/tex]
[tex]\implies c=25-3(7)[/tex]
[tex]\implies c=25-21[/tex]
[tex]\implies c=4[/tex]
Therefore, the selling price of a handmade card was $4.
Joe graphed y = -1/2 x + 2 in his graph below.
Joe made a mistake
What is his mistake? How should he fix the mistake?
Answers
Answer:
Joe graphed the wrong y-axis. The y-axis is (0,2) Also the x-axis is wrong, its supposed to be (4,0).
Step-by-step explanation:
Line F passes through points (2, 8) and (9, 3). Line g passes through points (1, 8) and (10, 1). Are line f and line g parallel or perpendicular? Pls help I’m getting frustrated
Answers
The linear functions f(x) and g(x) are neither parallel nor perpendicular.
How to obtain if the lines are parallel or perpendicular?To obtain whether they are parallel of perpendicular, first we must obtain the slope of each line.
Given two points, the slope of a line is calculated as the change in y divided by the change in x.
Hence, the slope for each line is obtained as follows:
Line F: m = (3 - 8)/(9 - 2) = -5/7.Line G: m = (1 - 8)/(10 - 1) = -7/9.They would be:
Parallel if they have the same slope.Perpendicular if the product of the slopes was of -1.Hence they are neither.
More can be learned about linear functions at https://brainly.com/question/24808124
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