In triangle ABC, if m∠B = 90°, BH = AH, and the ratio of m∠A to m∠C is 1:2, then m∠BHA = 120° (C).
In the next given equilateral triangle ABC, y = 70°.
Finding m∠BHA:
In triangle ABC, it is given that,
∠B = 90°
And m∠A : m∠C = 1:2
Let us assume m∠A is x. Then, m∠C = 2x
According to the angle sum property of a triangle,
∠A + ∠B + ∠C = 180°
90° + x + 2x = 180°
90° + 3x = 180°
3x = 90°
x = 30°
⇒ In triangle ABC, ∠A = 30° and ∠C = 60°
Now, in triangle AHB, it is also given that,
BH = AH
⇒ ∠ABH = ∠A = 30°
Thus, according to the angle sum property of a triangle,
∠ABH + ∠A + ∠BHA = 180°
30° + 30° + ∠BHA = 180°
∠BHA = 180° - 60°
∠BHA = 120°
Finding y in the Second Triangle:
Since triangle ABC is equilateral,
∠A = ∠B = ∠C = 60°
∴ x + 2x + 3x = 60°
6x = 60°
x = 10°
In triangle ABD, using angle sum property of triangle,
x + ∠B + ∠BDA = 180°
10° + 60° + ∠BDA = 180°
∠BDA = 180° - 70°
∠BDA = 110°
Now, since, ∠BDA and y are linearly adjacent angles,
∠BDA + y = 180°
110° + y = 180°
y = 180° - 110°
y = 70°
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What equation of the line which passes through the point (-1, 2) and is parallel to the line y=x+4
Answer:
Thus, the equation of line for point (-1, 2) is y = x + 3.
Step-by-step explanation:
Answer:
The equation of the line is y = x + 3.
Step-by-step explanation:
A line that is parallel to y=x+4 and passes through the point (-1,2) will have the same slope as y=x+4. The slope of y=x+4 is 1, so the equation of the line will be in the form y = mx + b, where m=1. To find b, we can plug in x = -1 and y = 2 into the equation and solve for b.
y = mx + b
y = 1 * -1 + b
y = -1 + b
b = y + 1
b = 2 + 1
b = 3
A to D is an example of _____________?
A. reflection across the line y = 1
B. reflection across the line y = x
C. y-axis symmetry
D. x-axis symmetry
Answer:
D
Step-by-step explanation:
A and D are both equidistant from the x- axis, that is
A is 3 units above the x- axis and D is 3 units below the x- axis
then the x- axis is the line of symmetry
7 students are running for student council. how many different ways can their names be listed on the ballot
Step-by-step explanation:
7! = 5040 ways
−3x+6=39
What is the value of x?
Answer:
x=-11
Step-by-step explanation:
Answer:
X = -11 Hope this helps, work will be in comments
Find the sum! Help I don’t kno
if a circular pool with a radius of 16,what is the area
The area of a circular pool having radius 16 units is 804.24772 units².
What is area?
An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.
The circular pool has a radius of 16 units.
The formula for the area of circle is πr².
Here, r represents the radius of the circle.
Area = πr²
Substitute the values into the equation -
Area = π(16)²
Find the square of 16 -
Area = π × 256
Use the arithmetic operation of multiplication -
Area = 256 π
The value of π = 3.14159265359
Area = 256 × 3.14159265359
Use the arithmetic operation of multiplication -
Area = 804.24772
Therefore, the area is obtained as 804.24772 units².
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Linda and Rob open an online savings account that has a 2.89% annual interest rate, compounded
weekly. If they deposit $35 every week, how much will be in the account after 15 years?
Answer:
FV= $34,222.33
Step-by-step explanation:
First, we need to calculate the weekly interest rate:
Weekly interest rate= 0.0289/52= 0.00056
To calculate the future value (FV), we need to use the following formula:
FV= {A*[(1+i)^n-1]}/i
A= weekly deposit
n= 15*52= 780
A= $35
FV= {35*[(1.00056^780) - 1]} / 0.00056
FV= $34,222.33
What value of x is in the solution set of the inequality 2(3x – 1) ≥ 4x – 6? –10 –5 –3 –1
Answer: -1
Step-by-step explanation:
We will find the answer to this question by isolating the x variable.
Given:
2(3x – 1) ≥ 4x – 6
Distribute the 2 with multiplication:
6x – 2 ≥ 4x – 6
Add 2 to both sides of the equation, and subtract 4x from both sides of the equation:
2x ≥ – 4
Divide both sides of the equation by 2:
x ≥ -2
The only value given that is greater than or equal to -2 is -1, leaving us with an answer of;
-1
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The solution set of the inequality 2(3x - 1) ≥ 4x - 6 is [-2, ∞). So, -1 belongs to the solution set, i.e., -1 ∈ [-2, ∞).
Mathematically, an inequality is a mathematical assertion that compares the comparative size or order of two quantities. It shows that one quantity is greater than, less than, or not equal to another. The symbols often used to show inequalities are (≥), (≤), or (≠).
The given inequality is
2(3x - 1) ≥ 4x - 6
6x - 2 ≥ 4x -6
6x - 4x ≥ -6 + 2
2x ≥ -4
\(x \geq -\frac{4}{2}\)
x ≥ -2
x ∈ (-2, ∞).
The correct answer is -1, as -1 belongs to the solution set of the given inequality.
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An arc that measures 180 degrees is called a
help what is the answer for this
Which net represents the pyramid below?
The net which represents the pyramid is: B. A square with a triangle connected to each side with a dotted line.
What is a square pyramid?A square pyramid can be defined as a type of pyramid that has a square base, four (4) triangular sides, five (5) vertices, and eight (8) edges.
In this context, we can logically deduce that the net which represents the pyramid is a square with a triangle that is connected to each side with a dotted line as illustrated in the image attached below.
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Complete Question:
Which net represents the pyramid below? There are four squares attached left to right and a square above and below the last square. There are three rectangles connected vertically with dotted lines. There are triangles connected to the middle rectangle.
A. A hexagon with a triangle connected with a dotted line to each of the sides.
B. A square with a triangle connected to each side with a dotted line.
HELP ME ASAP!!!!!!!
Find the elapsed time: Start at 12:15 A.M. and end at 2:15 P.M.
31 POINTS!!!!
The elapsed time between 12:15 A.M. and 2:15 P.M. is 14 hours.
What is elapsed time?
Elapsed time is the amount of time that has passed between a starting point and an ending point. It is the difference between the ending time and the starting time. Elapsed time can be calculated for any duration of time, from seconds to hours, days, or even years.
To find the elapsed time between 12:15 A.M. and 2:15 P.M., we need to calculate the number of hours and minutes that have passed.
First, we need to convert the time to a 24-hour clock format.
12:15 A.M. can be represented as 00:15 and 2:15 P.M. can be represented as 14:15.
We can then subtract the start time from the end time to find the elapsed time:
14:15 - 00:15 = 14 hours
Therefore, the elapsed time between 12:15 A.M. and 2:15 P.M. is 14 hours.
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Need help ASAP will give brainly
Answer:
18) 50.43 m²19) 252 cm²11) 6Best decimal to represent 5 3/7
Answer:
to the nearest tenth: 5.4
to the nearest hundredth: 5.43
Step-by-step explanation:
Keep the whole number 5 by itself
divide 3 by 7 and add that as the decimal with 5
Answer:
5.4285714286
Step-by-step explanation:
Calculation:
5+3/7
= 5.4285714286
= 542.85714286%
1.2 Generate a three-column table where you evaluate how learning takes place according to: • Piaget • Vygotsky • Bruner (15)
While Piaget, Vygotsky, and Bruner have different perspectives on how learning occurs, they all emphasize the active role of the learner in constructing knowledge and the importance of social interaction and cultural influences in the learning process.
Here's a three-column table evaluating how learning takes place according to Piaget, Vygotsky, and Bruner:
Theorist Approach to Learning Key Concepts
Piaget Constructivism 1. Schema: Individuals actively construct their knowledge through assimilation and accommodation, organizing information into mental structures called schemas. 2. Stages of Development: Learning occurs through cognitive development stages, from sensorimotor to formal operational, where individuals progressively acquire more complex mental abilities. 3. Active Exploration: Children learn best through hands-on exploration and interactions with the physical world.
Vygotsky Sociocultural Theory 1. Zone of Proximal Development (ZPD): Learning takes place within the gap between a learner's actual developmental level and their potential level with guidance from a more knowledgeable other. 2. Social Interaction: Learning is facilitated through social interactions with peers and adults, such as cooperative learning and scaffolding. 3. Cultural Tools: The use of language, symbols, and cultural artifacts plays a central role in cognitive development and learning.
Bruner Constructivism 1. Scaffolding: Instruction should provide support and guidance tailored to the learner's current abilities to help them progress to higher levels of understanding. 2. Discovery Learning: Learners construct knowledge by actively exploring and discovering concepts and relationships on their own. 3. Spiral Curriculum: Learning is organized in a spiral manner, revisiting key concepts and building upon previous knowledge in a progressive and interconnected way.
While Piaget, Vygotsky, and Bruner have different perspectives on how learning occurs, they all emphasize the active role of the learner in constructing knowledge and the importance of social interaction and cultural influences in the learning process.
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Evaluate each expression.
Answer:
THIS DESERVES A BRAINLIEST BECAUSE I PUT ALL OF THE ANSWERS AND THE WORK TO IT
1: 6
2: 3
3: 5
4: 1
5: 3
6: -1
7: 8
8: 4
9: 3
10: 16
Step-by-step explanation:
Use PEMDAS
1. (2x2)+2
You do 2x2 first which is 4 so then you do 4+2 which is 6
2. 6 divided by (5-3)
You do 5-3 first which is 2 then 6/2 (that's 6 divided by 2) which is 3
3. 6/6 x5
so you do 6 divided by 6 which is 1 then you get 1x5 which is 5.
4. 2-(5-4)
5-4 is 1 and 2-1 is 1
5. 2+6/6
6 divided by 6 is 1 and 2+1 is 3
6. (-6)+5 is -1
7. 1-(-7) is the same as 1+7 which is 8
8. (-3)-7 is the same as -3+7 which is the same as 7-3 which is 4
9. 5+(-2) is the same as 5-2 which is 3
10. 8-(-8) is the same as 8+8 which is 16
Round to the nearest 10th if necessary
Answer:
Step-by-step explanation:
ah they are getting harder. :/ they didn't give any angles this time. so figure those out first, super hero math to the rescue :P oh and the question is just find angle C soo.
Angles C + B + A = 180
we can turn the law of cosines around and use it to find the angle, you are given the formula for that as well in the problem. it's nice of them to not expect you to memorize the formula I had to :/ your class is going easy on you. get out the ruler and smack some students , prof. Snape :D :D My prof. once threw an eraser at one person b/c they fell asleep in class :D when it hit him.. b/c it was all full of chalk.. the eraser.. it kinda "exploded" and he woke up coughing... :o anyway.. back to math :P
a= 28
b= 17
c = 15
C = arcCos [ (a^2 + b^2 - c^2) / (2 * a * b) ]
C = arcCos[ 28^2 + 17^2 - 15^2 / 2*28 *17 ]
C = arcCos[ 784 + 289 -225 / 952 ]
C = arcCos [ 848 / 952 ]
C = arcCos [0.8907563]
C = 27.03 °
rounded to nearest 10th then is
C = 27.0 °
:)
btw, does 27 seem right? to me it does b/c that angle is small
the price of fruit acid 1.65 for 11 ounces. Fruit B costs 2 cents more per ounce. What is the cost of 16 ounces of fruit B?
Answer: 2.72 i guess
y = -29.202x + 293.5.
Based on the line of best fit, approximately how many milliliters of juice will be in a glass with 7 ice cubes?
Answer:
17.7 inches.
Step-by-step explanation:
The equation of the line of best fit is y = - 0.368x + 18.483 .......... (1)
Based on the line of best fit, we have to approximate how many inches of snowfall during the month of January when the average temperature is 2°F.
So, here, x = 2 and we have to calculate y using the equation (1).
So, y = - 0.368 × 2 + 18.483 = 17.747 ≈ 17.7 inches. (Answer)
find all solutions of the systems of equations: x^2+y^2=53 x^2-y^2=45
The solutions to the equations are;
y = 2
x = 7
How to determine the valueFrom the information given, we have that the simultanoeus equation;
x² + y²=53
x²-y²= 45
Make 'x' the subject from equation 1, we have that;
x =√ 53 - y²
Substitute the values, we have;
(√53 - y²)² - y² = 45
find the square root, we have;
53 - y² - y² = 45
collect the like terms, we have;
-2y² = 45 - 53
subtract the values
-2y² = -8
y² = 4
y = 2
Substitute the value, we have;
x = √53 - (2)²
Find the value
x =√49
x = 7
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given the following matrix: find the matrix's inverse and enter it below: given the following syste, express the system in matrix form as below: use the result of to get the solution enter the solution below:
The matrix's inverse is \(\left[\begin{array}{ccc}1&2&3\\3&4&6\\7&8&9\end{array}\right]\)
To find the inverse of a matrix A, you can use the following formula:
A⁻¹ = (1/det(A)) * adj(A)
Where det(A) is the determinant of matrix A, and adj(A) is the adjugate of matrix A. The adjugate of a matrix is the transpose of the cofactor matrix of A.
Once you have found the inverse of matrix A, you can use it to solve a system of linear equations. To express a system of linear equations in matrix form, you can use the following notation:
Ax = b
Where A is the coefficient matrix, x is the vector of unknowns, and b is the vector of constants. In this case, the system of linear equations is:
x + 2y + 3z = 1
3x + 4y + 6z = 2
7x + 8y + 9z = 3
You can write this system in matrix form as:
A =\(\left[\begin{array}{ccc}1&2&3\\3&4&6\\7&8&9\end{array}\right]\)
x = [x; y; z]
b = [1; 2; 3]
Ax = b
Now, to solve for x, you can use the formula:
x = A⁻¹ * b
Where A⁻¹ is the inverse of matrix A, and b is the vector of constants. Once you have found x, you can substitute its values into the original system of linear equations to check your answer.
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Complete Question:
given the following matrix: find the matrix's inverse and enter it below: given the following system, express the system in matrix form as below:
A= [1 2 3
3 4 6
7 8 9]
use the result of to get the solution to enter the solution below
a dolphin in a aquaruim is 12 feet long. A scale model of the dolphin is 3 1/2 in long. What is the scale factor of the model
Answer:The scale factor= 1 : 41.14
Step-by-step explanation:
I did research on it
Find m∠1 and m∠2. and Tell which theorem you use in each case.
The angles in the parallel lines are as follows;
m∠1 = 42 degreesm∠2 = 42 degrees.How to find angles when parallel lines are cut by a transversal?When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate interior angles, alternate exterior angles, linear angles, vertically opposite angles etc.
Therefore, let's find the angles m∠1 and m∠2.
Hence,
138 + m∠1 = 180(angles on a straight line)
The sum of angles on a straight line is 180 degrees.
m∠1 = 180 - 138
m∠1 = 42 degrees
Therefore,
m∠1 = m∠2 (alternate exterior angles)
Alternate exterior angles are the pair of angles that are formed on th outer side of the parallel lines but on the opposite side of the transversal.
Alternate exterior angles are congruent.
Therefore,
m∠1 = m∠2 = 42 degrees.
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a car travels x km in 3 hours how far will it travel in 9 hours?
Answer:
distance traveled in 1 hour = x/3
To find the distance traveled in 9 hours, we can multiply the distance traveled in 1 hour by 9:
distance traveled in 9 hours = (x/3) * 9
Simplifying this expression gives:
distance traveled in 9 hours = 3x
Therefore, the car will travel 3 times the distance it travels in 3 hours when it travels for 9 hours.
Number of Computers
72
60
48
36
24
12
V
1 2 3 4 5 6 7 8 9 10 11 12
Number of Days
The graph shows a proportional relationship between
the number of computers produced at a factory per day.
In three days, 36 computers are produced; 48
computers are produced in 4 days; and 60 computers
are produced in 5 days.
Find the unit rate of computers per day using the graph.
Unit rate:
computers per day
The unit rate of computers per day using the graph is that 12 computers are made per day.
What is a unit rate?The unit rate is how many units of quantity correspond to the single unit of another quantity. We say that when the denominator in rate is 1, it is called unit rate. Unit rates is said to be the amount of something in each unit or per unit.
How to find the unit rate of computers per dayTo obtain the unit rate of computers sold per day using the graph, we need to obtain the slope of the graph, which is the change in y per change in x
So, it is given by:
\(\text{Slope} = \dfrac{\text{change in y}}{\text{change in x}}\)
\(\text{Slope} = \dfrac{\text{y}_2-\text{y}_1}{\text{x}_2-\text{x}_1}\)
\(\text{y}_2 = 60 , \ \text{y}_1 = 36 , \ \text{x}_2 = 5, \ \text{x}_1 = 3.\)
\(\text{Slope} = \dfrac{(60 - 36)}{(5 - 3)} = \dfrac{24}{2} = 12\)
\(\bold{Slope = 12}\)
Unit rate = 12 computers per day.
The attachment of the graph is given below.
Therefore, the unit rate of computers per day is 12.
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DQ2 Do all linear transformations have a matrix representation? If so, what theorem establishes this? If not, provide a counter-example
Yes, This is established by the Rank-Nullity Theorem, A counter-example would be a transformation that is not linear.
Yes, all linear transformations have a matrix representation. The theorem that establishes this is the Matrix Representation Theorem. This theorem states that given a linear transformation T : V → W where V and W are vector spaces over a field F, then there is a unique matrix A such that T(v) = Av for any v in V. This theorem proves that any linear transformation can be represented by a matrix.
A counter-example of a linear transformation that does not have a matrix representation is a transformation that maps a vector in one vector space to a vector in a different vector space. For example, if V is a vector space over the field F, and W is a vector space over another field K, then the linear transformation T : V → W does not have a matrix representation since the size of the matrix would need to be different for each vector in the different vector spaces.
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Use the model below to calculate
2
3
×
3
4
.
A rectangle is shown divided into 3 rows and 4 columns. 3 of the 4 columns are shaded blue.
A.
3
12
or
1
4
B.
12
12
or
1
C.
4
12
or
1
3
D.
6
12
or
1
2
Answer:
D
Step-by-step explanation:
i already did the test
Answer:
d
Step-by-step explanation:
2x+3y=12 solve for y
Answer:
y = (12-2x)/3
Step-by-step explanation:
Isolate the variable by subtracting -2x and dividing by 3
HELP ME PLEAS
What is the slope of the line on the graph?
The slope of the line that passes through the graph is -1/3
How to calculate the slope of the line?From the graph, the points are given as
(6, 2) and (-6, 6)
Rewrite the above points properly
So, we have the following ordered pairs
(x, y) = (6, 2) and (-6, 6)
The slope of the line is then calculated using the following slope equation
Slope = (y₂ - y₁)/(x₂ - x₁)
Where
(x, y) = (6, 2) and (-6, 6)
Substitute the known values in the above equation
So, we have the following equation
Slope = (6 - 2)/(-6 - 6)
Evaluate
Slope = -1/3
Hence, the slope of the line is -1/3
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Question 2
No calculations are necessary to answer this question.
3/01
3/02
$1.7420 $1.7360
Date
July GBP Futures
Contract Price
O long; long
Based on the closing prices of July GBP Futures Contract over the 3-day period in March 20XX as shown above, you shou
position on 3/01 and a position on 3/02.
O long; short
O short; short
3/03
short; long
$1.7390
The given information does not provide any clear indication for determining the position that should be taken on 3/01 and 3/02. Without additional information, it is not possible to make a decision. The table only displays the closing prices of the July GBP Futures Contract on different days, and it is unclear what trading strategy or what scenario is being considered. Additional information about the goals and objectives, the market conditions, and other relevant factors would be necessary to make a decision about trading positions.
Troy made $30,000 in interest by placing $40,000 in a savings account with simple interest for 5 years. What was the interest rate?
Answer:
the interest rate for the savings account is 15%
Step-by-step explanation:
We can use the formula for simple interest to solve this problem:
Simple Interest = Principal x Rate x Time
Where:
Principal is the amount of money invested
Rate is the interest rate (as a decimal)
Time is the length of time the money is invested
We know that Troy placed $40,000 in a savings account with simple interest for 5 years and earned $30,000 in interest. So we can plug these values into the formula to get:
$30,000 = $40,000 x Rate x 5 years
Simplifying this expression, we get:
Rate = $30,000 ÷ ($40,000 x 5 years)
Rate = 0.15 or 15%
Therefore, the interest rate for the savings account is 15%.