To answer this question, we can proceed as follows:
As we can see from the above figure, the triangles PQR and MQN are similar triangles. If they are similar, then their corresponding sides are in proportion. Then, we have:
\(\frac{PR}{MN}=\frac{RQ}{NQ}\Rightarrow\frac{15}{MN}=\frac{10}{2}\)Then, we need to solve the equation for MN, then we have:
\(\frac{15}{MN}=5\Rightarrow\frac{MN}{15}=\frac{1}{5}\Rightarrow MN=\frac{15}{5}\Rightarrow MN=3\operatorname{cm}\)Therefore, the value for the side MN is 3 cm (option b).
As the CAPS document outlines, the Content Specification and Content Clarification for Patterns, Functions, and Algebra shows sequenced mathematics content topics and a content area spread. In the Intermediate Phase, select one topic and report on the topic sequence and content area spread. Your report should demonstrate mathematics concepts and procedures’ hierarchical and logical progression.
Answer:
Step-by-step explanation:
In the Intermediate Phase of mathematics education, one topic that demonstrates a hierarchical and logical progression in patterns, functions, and algebra is the concept of "Linear Equations."
The topic of Linear Equations in the Intermediate Phase builds upon the foundation laid in earlier grades and serves as a stepping stone towards more advanced algebraic concepts. Here is an overview of the topic sequence and content area spread for Linear Equations:
Introduction to Variables and Expressions:
Students are introduced to the concept of variables and expressions, learning to represent unknown quantities using letters or symbols. They understand the difference between constants and variables and learn to evaluate expressions.
Solving One-Step Equations:
Students learn how to solve simple one-step equations involving addition, subtraction, multiplication, and division. They develop the skills to isolate the variable and find its value.
Solving Two-Step Equations:
Building upon the previous knowledge, students progress to solving two-step equations. They learn to perform multiple operations to isolate the variable and find its value.
Writing and Graphing Linear Equations:
Students explore the relationship between variables and learn to write linear equations in slope-intercept form (y = mx + b). They understand the meaning of slope and y-intercept and how they relate to the graph of a line.
Systems of Linear Equations:
Students are introduced to the concept of systems of linear equations, where multiple equations are solved simultaneously. They learn various methods such as substitution, elimination, and graphing to find the solution to the system.
Word Problems and Applications:
Students apply their understanding of linear equations to solve real-life word problems and situations. They learn to translate verbal descriptions into algebraic equations and solve them to find the unknown quantities.
The content area spread for Linear Equations includes concepts such as variables, expressions, equations, operations, graphing, slope, y-intercept, systems, and real-world applications. The progression from simple one-step equations to more complex systems of equations reflects a logical sequence that builds upon prior knowledge and skills.
By following this hierarchical progression, students develop a solid foundation in algebraic thinking and problem-solving skills. They learn to apply mathematical concepts and procedures in a systematic and logical manner, paving the way for further exploration of patterns, functions, and advanced algebraic topics in later phases of mathematics education.
Find the tangent of the smaller acute angle in a right triangle with side lengths 5, 12, and 13.
Write your answer as a fraction.
The tangent of the smaller acute angle is ____?_______
The tangent of the smaller acute angle in a right triangle is tanФ = 0.42.
What are trigonometric ratios in terms of a right-angle triangle?We know a right-angled triangle has three sides they are -: Hypotenuse,
Opposite and Adjacent.
We can remember SOH CAH TOA which is,
sin = opposite/hypotenuse, cos = adjecen/hypotenuse and
tan = opposite/adjacent.
Given, A right triangle with side lengths 5, 12, and 13.
tanФ = 5/12.
tanФ = 0.42.
Ф = tan⁻¹(0.42).
Ф = 22.8°.
learn more about trig ratios here :
https://brainly.com/question/14977354
#SPJ1
Drag a statement or reason to each box to complete this proof. If3x−4=14, thenx=6
Answer
Statement Reason
1. 3x - 6 = 14 Given
2. 3x - 4 + 4 = 14 + 4 Addition Property of Equality
3. 3x/3 = 18/3 Division Property of Equality
4. x = 6 Given
A bicycle wheel has diameter 66 cm. Find how many turns the wheel makes when the bicycle travels 400 metres.
The number of turns the wheel makes is 1.93 ≈ 2.
What is Turns?
This is referred to as a cycle. It is a unit of plane angle measurement that is equivalent to 2π radians, 360 degrees, or 400 gradians.
formular for calculating Turns:
Turns = Lenght
Circumference
Circumference of a circle, C= πD
Where,
Diameter=D
π =22/7
Calculating Circumference;
C= 22 * 66
7
=207.4
From the question:
D= 66cm
L =400m
Calculating Turns:
Turns = Lenght
Circumference
= 400m
207.4
Turns =1.93
Turns =1.93≈ 2
Learn more about Turns on
https://brainly.com/question/28638630
#SPJ1
Below is a table for f(x) = 3x + 1. Using the table, determine the value of x when f(x) = 13
In this question, use CAN $1.00 = JA $72.00.
1) On a vacation in Canada, Steve used his credit card to buy a camera for CAN $25.00.
What is the value of the camera in jamaican dollars?
2) Steve's credit card limit is JA $30,000.00. After buying the camera, how many Canadian does he have left on his credit card for spending?
Which comparisons are true? Select all that apply.
7.34 > 7.304
1.628 > 1.63
4.05 < 4.055
9.103 < 9.13
2.29 < 2.129
I NEED ANSWER NOW ITS A MAJOR GRADE
Answer:
7.34 > 7.304 is true
4.05 < 4.055 is true
9.103 < 9.13 is true
Step-by-step explanation:
Because you need it quick, i wont explain
solutions: greater than, less than, equals to:
7.34 > 7.304 ↔ True1.628 > 1.63 ↔ False4.05 < 4.055 ↔ True9.103 < 9.13 ↔ True2.29 < 2.129 ↔ False
Giving brainliest for CORRECT awnser.
Answer: x - 8
Step-by-step explanation:
Factor it and you'll be fine.
Solve for x using the quadratic formula x^2-6x +9=0
Answer:
3 both ways x = 3
EXPLANATION:
plug in inputs and do a little simplifying we get
x = 6 ± √(36-36) all of that over 2
So we simplify and we get 6±sqrt(0) / 2
Then we get 6/2 = 3
x-0 = x+0
thats why there is only one answer
Answer:
The value of X is 3
Step-by-step explanation:
x²-6x+9=0
x²- 3x - 3x + 9= 0
X(x-3) -3(x-3)=0
(x-3) (x-3)=0
(x-3)²=0
(x-3)=0
x-3 = 0
X= 3
Five quarts of a latex enamel paint will cover about 200 square feet of wall surface. How many quarts are needed to cover 165 square feet of kitchen wall and 115 square feet of bathroom wall?
Answer:
25
Step-by-step explanation: just like that
Points A and B are on opposite sides of a lake. Another point, C. is 94.4 meters from Angle A. The measure of Angle A is 72° and the measure of Angle C is 30°. Find the distance between A and B.
To find the distance between points A and B, we can use trigonometry and the given information.
Let's label the distance between A and B as "d". We know that point C is 94.4 meters away from point A. From angle A, we have the measure of 72°, and from angle C, we have the measure of 30°.
Using trigonometry, we can use the tangent function to find the value of "d".
tan(72°) = d / 94.4
To solve for "d", we can rearrange the equation:
d = tan(72°) * 94.4
Using a calculator, we can evaluate the expression:
d ≈ 4.345 * 94.4
d ≈ 408.932
Therefore, the distance between points A and B is approximately 408.932 meters.
Mr. Mares' class has 28 students. If five people can work together on a group project, estimate the number of groups that there will be by rounding the larger number.
28/5 = 5.6
then round it up so it would be 6
connie poured 200 milliliters of juice into a glass from a juice carton. She then poured 225 milliliters into a second glass. What is the final change in the volume of the carton?
Answer:
A reduction of 450ml
Step-by-step explanation:
Given
\(V_1 = 200ml\) -- To glass 1
\(V_2 = 250ml\) --- To glass 2
Required
The final change to the carton
To do this, we simply add V1 and V2
So, we have:
\(Total = V_1 + V_2\)
\(Total = 200ml + 250ml\)
\(Total = 450ml\)
This implies that the changes is a reduction of 450ml
Find the midpoint of the segment with the given endpoints.
(-7,10) and (6.-10)
Answer:
c
Step-by-step explanation:
cc
Choose the correct option from the following about the effect of increase in the cut-off value of a logistic regression model? The True Positives will decrease, and the True Negatives will increase. The change in cut-off should have no effect on the number of true positives and true negatives of the model, if we do not change the variables in the fitted logistic regression model. Both False Negatives and True Negatives will decrease. The False Positives will increase, and the False Negatives will decrease.
There will be a rise in false positives and a fall in false negatives.This is because the true positives and true negatives are determined by the values of the variables in the logistic regression model.
When the cut-off value is increased, the False Positives will increase, meaning that more observations will be incorrectly classified as positives. The False Negatives will decrease, meaning that fewer observations will be incorrectly classified as negatives. At the same time, the True Positives and True Negatives will remain unchanged, as long as the variables in the fitted logistic regression model remain the same.When the cut-off value is increased, the logistic regression model will be more stringent in its classification of observations. This means that the model will classify more observations as false positives (incorrectly classifying them as positives) and fewer as false negatives (incorrectly classifying them as negatives). On the other hand, the model will not be affected by the change in cut-off value when it comes to true positives and true negatives. This is because the true positives and true negatives are determined by the values of the variables in the logistic regression model, which remain unchanged when the cut-off value is changed.
Learn more about regression here
https://brainly.com/question/28178214
#SPJ4
find two numbers whos diffrence is 16 and the product is 720
Answer:
the numbers who's difference is 16 and the product is 720 is
36 &20
Explanation:
to finding numbers you have to express the equation in a quadratic equation then Factor it.
since the two numbers have a difference of 16 you can say that the first number is x and the second number is x -16 then their product is 720.
x(x-16)=720
x²-16x=720
x²-16x-720=0
(x-36)(x+20)
there are two possible value of x but since you are looking for the positive value of x, choose the positive value of x the first number is 20.
To find the second number
x-16=20
x=20+16
x=36
the second number is 36
Now to check
36-20=16
20*36=720
which expression is equivalent to -2-7?
Find the value of x such that the line containing (1,2) and (5,3) is perpendicular to the line containing (x,4) and (3,0)
The value of x that makes the line containing (1,2) and (5,3) perpendicular to the line containing (x,4) and (3,0) is x = 2.
To determine the value of x such that the line containing (1,2) and (5,3) is perpendicular to the line containing (x,4) and (3,0), we need to find the slope of both lines and apply the concept of perpendicular lines.
The slope of a line can be found using the formula:
slope = (change in y) / (change in x)
For the line containing (1,2) and (5,3), the slope is:
slope1 = (3 - 2) / (5 - 1) = 1 / 4
To find the slope of the line containing (x,4) and (3,0), we use the same formula:
slope2 = (0 - 4) / (3 - x) = -4 / (3 - x)
Perpendicular lines have slopes that are negative reciprocals of each other. In other words, if the slope of one line is m, then the slope of a line perpendicular to it is -1/m.
So, we can set up the equation:
-1 / (1/4) = -4 / (3 - x)
Simplifying this equation:
-4 = -4 / (3 - x)
To remove the fraction, we can multiply both sides by (3 - x):
-4(3 - x) = -4
Expanding and simplifying:
-12 + 4x = -4
Adding 12 to both sides:
4x = 8
Dividing both sides by 4:
x = 2
For more such questions on line.
https://brainly.com/question/280216
#SPJ8
The new bed I want is 3/4 by 1/2. How much of the room will it take up?
Answer:
the rooms want is 4 so this is answer
1.5
Step-by-step explanation:
3/4 divided by 1/2 = 1.5
Solve for x
-1/5(5x+3)= 2/15
Simplify 7-(3x+5y)+6(2x-3y)+8y
Answer:
Step-by-step explanation:
First get rid of the parentheses. Distribute the - sign and the +6 to each one.
\(7-3x-5y+12x-18y+8y\\7+9x-5y-18y+8y\\7+9x-15y\)
Determine if the equation given in slope-intercept form represents the graph. If the equation is correct support your reasoning with why it is correct. If the equation is incorrect, give the correct slope-intercept form equation explaining how you determined it.
The equation of the line would be y = (4/5)x + 4 which in slope-intercept form represents the graph.
The graph is given in the question.
As per the given line, we take two points (0, 4) and (5, 8)
Let the required line would be y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]
x₁ = 0, y₁ = 4
x₂ = 5, y₂ = 8
⇒ y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]
Substitute values in the equation, we get
⇒ y - 4 = (8 - 4)/(5-0 )[x -0]
⇒ y - 4 = (4/5)x
⇒ y = (4/5)x + 4
The given equation of the line y = 4x + 5 is incorrect because its slope is not correct.
So, the equation of the line would be y = (4/5)x + 4.
Learn more about the Slope of the Line here:
brainly.com/question/14511992
#SPJ1
the Grand Canyon has the average death of 4000 ft with some sections going to 6000. If you drop an object from a Section 3300 above, how long (in seconds) will it take the object to hit the bottom?
the Grand Canyon has the average depth of 4000 ft with some sections going to 6000.
i.e. distance = 4000 ft
goind speed = 6000ft/sec
If the object is fall from the 3300 feet above the bottom
Thus total distance travelled by the object = 4000-3300
Distance travelled = 700 feet
Speed = Distance/Time
Substitute the value
6000=700/time
Time = 700/6000
Time= 0.116 second
Answer: it take the object to hit the bottom in 0.11 seconds
Find the quotient of 10^-4/10^2
The quotient of 10⁻⁴/10² is 10⁻⁶
How to Find the quotient of 10⁻⁴/10²?Quotient is the result obtained by dividing one quantity by another. It represents the value that is obtained after division.
For example, if you divide 20 by 2, the quotient is 10 because 20 divided by 2 equals 10.
Division law states that:
10ᵃ / 10ᵇ = 10ᵃ⁻ᵇ
In this case have:
10⁻⁴/10² = 10⁻⁴⁻² (Division law)
10⁻⁴/10² = 10⁻⁶
Learn more about quotient on:
brainly.com/question/27862246
#SPJ1
What is the solution to this equation? 9^x– 1 = 2 Α. 1/2 B. 1 C. 2 D. -1/2
Answer:
for 9^(x)-1=2 the answer is 1/2 or .5
The solution to this equation 9ˣ - 1 = 2 is 1/2.
The correct option is A.
What is an equation?Two algebraic expressions having same value and symbol '=' in between are called as an equation.
Given:
An equation:
9ˣ - 1 = 2
Simplifying,
9ˣ = 3
3²ˣ = 3
Comparing, we get,
2x = 1
x = 1/2
Therefore, the solution is x = 1/2.
To learn more about the equation;
https://brainly.com/question/12788590
#SPJ2
4(1-x)<16 solve and graph
Answer: (x > -3).
Step-by-step explanation:
To solve the inequality 4(1 - x) < 16, we will simplify and solve for x:
4(1 - x) < 16
Distribute the 4:
4 - 4x < 16
Subtract 4 from both sides:
-4x < 12
Divide both sides by -4. Note that when dividing by a negative number, the inequality sign flips:
x > -3
The solution to the inequality is x > -3. This means that x must be greater than -3 for the inequality to hold true.
To graph the solution on a number line, we mark a shaded region to the right of -3, indicating that all values greater than -3 satisfy the inequality:
The open circle at -3 indicates that -3 is not included in the solution since the inequality is strict (x > -3).
here's the graph for 4(1-x)<16
12, 60, 300, ...
Find the 9th term.
The _ function calculates the repayment for a loan; the _ function calculates the interest portion of the loan repayment
Part 1:
The PMT Function in Excel is used to calculate the repayment of a loan. The PMT Function calculates the amount of loan repayment.
The generic formula for PMT Function is as follows:
=PMT(rate,nper, pv,[fv],[type])
Now let us understand each of the components of the PMT Function:
rate: The interest rate for the loan
per: Total number of payments of the loan repayment.
PV: Present Value of a series of Future Payments ie. the Principal of the Loan
VF: The future value of the loan or the cash balance that an individual wants to obtain after the loan is paid. This can be omitted, if omitted its value will be taken as zero ie the value of the loan in the future will be zero.
Type: The numbers 0 and 1 indicate when the payment of the loan is due. This is optional and can be omitted If it is 0 or omitted then payments are considered to be due at the end of the period(ie. end of month or quarter or end of year as the case may be). If it is 1 then payments are considered to be due at the beginning of the period((ie. beginning of month or quarter or end of the year as the case may be)
Part 2:
The Excel IPMT Function can be used to calculate the interest portion of loan repayment for a given period.
The generic formula for Excel IPMT Function is as follows:
=IPMT(rate,per,nper,pv,fv,[type])
Now let us understand each of the components of the IPMT Function:
rate: The interest rate for the loan
per: The period for which the interest payment has to be determined and should range between 1 and per
per: Total number of payments of the loan
PV: Present Value of a series of Future Payments ie. the Principal of the Loan
VF: The future value of the loan repayment or the cash balance that an individual wants to obtain after the loan is paid . This can be omitted, if omitted its value will be taken as zero ie the value of the loan in the future will be zero.
Type: The numbers 0 and 1 indicate when the loan repayment is due. This is optional and can be omitted If it is 0 or omitted then payments are considered to be due at the end of the period(ie. end of month or quarter or end of year as the case may be). If it is 1 then payments are considered to be due at the beginning of the period((ie. beginning of the month or quarter or end of the year as the case may be).
Learn more about loan repayment at
https://brainly.com/question/25696681
#SPJ1
5% of a number is 23
1% of a number is 4.6
work out 16% of the number
Given the equation y=2x+3, write a second equation that would create an independent consistent linear system
Two equations will be called independent if their graphs touch only on one point (they have one solution for the x-value and one solution for the y-value), and two equations will be dependent if they touch at every point (there is an infinite number of solutions).
This definition of independent and dependent equations is shown in the following diagram. Consider that there are two lines, one red line and one blue line:
They are independent if they touch only on one point and dependent if they touch at every point (they are the same line).
In our case, we are asked to write an equation in order to create an independent consistent linear system.
Note: Consistent means that the system has a solution.
First, we graph the given equation:
\(y=2x+3\)There are many different equations that will form an independent consistent linear system with this equation.
We are going to choose the following line equation:
\(y=-x+1\)Because when we graph this equation next to the previous line:
We can see that they touch at one point, thus there is a solution and the system is independent --> we have created an independent consistent linear system.
Answer:
\(y=-x+1\)