Answers
5. The value of x = 15
6. The converse that must be used is: C. Same-side exterior ∠s converse.
7. The proof is completed in the explanation part.
8. Slope of AB = 7/4; Slope of CD = -4/7, they are perpendicular.
What is the Same-Side Exterior Angles Theorem?The same-side exterior angles theorem states that same-side exterior angles that are on the same side of a transversal are supplementary to each other. Its converse states that if same-side interior angles are supplementary, then the lines they lie on are parallel to each other.
5. 10x - 22 + 3x + 7 = 180 [same-side exterior angles theorem]
13x - 15 = 180
13x = 180 + 15
13x = 195
x = 15
6. The converse that must be used to show that lines y and x are parallel to each other is: C. Same-side exterior angles converse.
7.
Statements Reasons
1. ∠6 ≅ ∠8 1. Given
2. y║z 2. Corresponding ∠s converse
3. ∠2 and ∠3 are supplementary 3. Same Side Interior ∠s
8. Given:
A(-3, 8)
B(1, 15)
C(10, -9)
D(3, -5)
Slope = change in y / change in x
Slope of AB = (8 - 15)/(-3 - 1) = -7/-4 = 7/4
Slope of CD = (-9 -(-5))/(10 - 3) = -4/7
-4/7 is the negative reciprocal of 7/4. Perpendicular lines have slope that are negative reciprocals of each other.
Therefore, CD and AB are perpendicular.
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Related Questions
a = 5.2 cm and B = 67°.
Work out the area of the triangle. Round
your answer to 1 DP.
Answers
The area of the triangle for the given parameter is 12.4 squared cm.
How to calculate the area of the triangle?
In mathematics, the area of the triangle is classified into three forms isosceles, scalene and equilateral. Depending upon the sides of the triangle, it is classified. That means, when the two sides are equal then the triangle is isosceles triangle.
According to the question, the given parameters for the calculation of the area of the triangle is as written below:
Side of the triangle(a) = 5.2 cm. Angle of a triangle(B) = 67°.
Using standard formula for the area of the triangle, we get:
Area of the triangle = (1/2)(5.2)(5.2)sin(67°) = 12.4384 = 12.4 squared cm.
Hence, the area of the triangle for the given parameter is 12.4 squared cm.
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If a construction crew paved 9680
yards of road, how many miles of road
did they pave? (1760 yards = 1 mile)
Answers
Answer: m = 5.5
Step-by-step explanation:
9680 / 1760 = m
m = 5.5
Graph the function identify the vertex and axis of symmetry f(x)=x^2+4x-2
A. axis of symmetry:x=2
(2,6)
B. axis of symmetry: x= -2
(-2,6)
C. axis of symmetry: x= 2
(2,-6)
D. axis of symmetry: x=-2
Vertex: (-2,-6)
Answers
The vertex and the axis of symmetry are (-2, -6) and x = -2, respectively
How to determine the vertex and the axis of symmetry?The equation of the function is given as
f(x) = x^2 + 4x - 2
The above equation is a quadratic equation
Next, we plot the equation on a graph (see attachment)
The vertex of the graph is the minimum or the maximum of the graph
In this case, we have
Minimum= (-2, -6)
This means that
Vertex = (-2, -6)
The axis of symmetry is the x-coordinates of the vertex
So, we have
x = -2
Hence, the vertex is (-2, -6) and the axis of symmetry is x = -2
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Answer the following. If needed, round your answers to two decimal places.
Roza and Rina are in the same maths class. On their unit test, Roza scored 70 out of 75
marks and Rina got a 92%.
Express Roza's mark as a simplified fraction.
Express Rina's mark as a simplified fraction.
By what percentage is Roza's mark higher?
%
Answers
Answer:
1) 14/15
2)23/25
3) 1.33%
Step-by-step explanation:
The simplest form for 2(x + 3) + 3(2x -3)
Answers
Answer: 8x-3
Step-by-step explanation
2x + 6 + 6x - 9
8x - 3
Answer:
8x - 3
Step-by-step explanation:
2(x+3) + 3(2x-3)
2x+6 + 6x-9
2x+6x + 6-9
= 8x - 3
f(x) = 3 x + 1 and g (x) = 2x - 3. find g (f(x))
Answers
Answer:
6x -- 1
Step-by-step explanation:
To Solve for g(f(x)), bear in mind
f(x) = 3x + 1
g(x) = 2x -- 3
g(f(x)) = 2x -- 3. (Calm down right?)
Let x = f(x).
if you recheck g(x) = 2x -- 3 so we got the (x) from it (do you get?)
g(f(x)) = 2(3x + 1) -- 3
g(f(x)) = 6x + 2 -- 3
g(f(x)) = 6x -- 1
#AllonGod
Answer:
Step-by-step explanation:
To find g(f(x)), first, understand that this means we are going to use the function of f(x) where the x would be in g(x).
1. First, identify the x in g(x) and replace it with the function of f(x)
g(x)=2x-3; so g(f(x))= 2(3x+1) -3
2. Simplify the equation by distributing the 2 and combining like terms.
2*3x=6x and 2*1=2, so we are left with 6x+2-3. After, just do 2-3 to end up with
g(f(x))=6x-1
(2^3×2^4) simplify and expression 7th grade.
Answers
The simplified expression of (2^3×2^4) is 2^7
How to evaluate the expression?The expression is given as
(2^3×2^4)
The base of the above expression are the same
i.e. Base = 2
This means that we can apply the law of indices
When the law of indices is applied, we have the following equation:
(2^3×2^4) = 2^(3 + 4)
Evaluate the sum in the above equation
So, we have
(2^3×2^4) = 2^7
Hence, the simplified expression of the expression given as (2^3×2^4) is 2^7
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a researcher is interested in the travel time of utrecht university students to college. a group of 50 students is interviewed. their mean travel time in 16.7 minutes. for this study the mean of 16.7 minutes is an example of a:
Answers
For this study, the mean of 16.7 minutes is an example of a (B) Statistic.
What do we mean by Statistic?As opposed to methods for gathering statistical data, mathematical statistics is the application of probability theory, a subfield of mathematics, to statistics. Mathematical analysis, linear algebra, stochastic analysis, differential equations, and measure theory are some of the specific mathematical methods used in this. Due to the abstract concepts and ideas that you will encounter later in your study, statistics stands out as the more challenging area of math. When you actually try to understand what's happening in a statistics equation or problem, you'll discover that the concepts are very challenging.So, the appropriate choice is an option (B).
In this case, a researcher is interested in how long it takes Utrecht University students to get to class. For this study, a sample of 50 students was gathered, and the sample mean for travel time was found to be 16.7 minutes.Since the sample means is a sample statistic, option (B) is the right choice.Therefore, for this study, the mean of 16.7 minutes is an example of a (B) Statistic.
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The correct question is given below:
A researcher is interested in the travel time of Utrecht University students to college. A group of 50 students is interviewed. Their mean travel time in 16.7 minutes. For this study, the mean of 16.7 minutes is an example of a(n)
A. Parameter
B. Statistic
C. Population
D. Sample.
Exercises
Write an algebraic expression for each verbal expression.
Four times a number?
Answers
The mathematical expression is as follows.
1) 4(v +3)
2) 15v -7
What is algebraic expression?An algebraic expression is one that has been constructed using integer constants, variables, and algebraic operations. A good example of an algebraic expression is 3x 2 2xy + c.
Given Data
Suppose the number is v
1) To obtain: four times the product of v and 3.
Accordingly, we must first add v and 3, and then multiply the result by 4.
The mathematical expression is as follows.
= 4(v+3)
2) Assume that v is the given integer.
What we're aiming for is: 7 less than 15 times v.
This calls for multiplying the v by 15 and then taking 7 out of the result.
The expression in algebra would be as follows:
= 15v - 7
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7653x213, please help me....
Answers
Answer:
Step-by-step explanation:
1630089 is the answer
an elevator can carry 15 adults or 20 children at one time. During the course of a day, the elevator carries a full passenger load 52 times. if all the passengers were children, how many more people would the elevator carry then if all the passengers were adults
Answers
Answer:
Step-by-step explanation:
20(kids per ride) x 52(number of rides) = 1040. 15(adults per ride) x 52(number of rides) = 780. 1040-780= 260 more kids than adults.
-0.6 as a fraction in simplest form
Answers
By dividing and multiplyinh the decimal by 10, we will see that:
-0.6 = -6/10
How to write the decimal as a fraction?Here we have the following decimal: -0.6
And we want to write it as a fraction.
To do so, we just need to multiply it and divide it by 10 as many times as digits we have after the decimal point. In this case we have only one digit after the decimal point, so we multiply and divide by 10 only once.
-0.6 = -0.6*(10/10) = (-0.6*10)/10 = -6/10
That is the fraction form of the given decimal.
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A 5oz jar of jam costs $2.50. How much is the unit price per ounce?
Answers
The unit price per ounce of the jar of jam is $0.50
How to determine the unit price per ounce for the jam?From the question, the given parameters are
Volume = 5 oz
Cost of jam = $2.50
The unit rate of the jam is calculated as
Unit rate = Cost of jam/Volume
Substitute the known values in the above equation
So, we have the following equation
Unit rate = 2.50/5
Evaluate the quotient
So, we have the following equation
Unit rate = 0.5
Hence, the unit price per ounce is $0.50
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2-b/3= -5/2 if you guys can help me thank you very much.
Answers
Answer:
b = 13.5
Step-by-step explanation:
2-b/3 = -5.2Multiply both sides of the equation by 6, the least common multiple of 3,212 - 2b = -15Subtract 12 from both sides-2b = -15 - 12Subtract 12 from -15 to get -27-2b = -27Divide both sides by -2b = -27/-2You can simplify -27/-2 by dropping off the negative sings making it b = 27/2Divide 27/2 to get 13.5 Or you can just simplify 27/2 to 13 1/2There are different ways you can solve this equation. Let me know if you'd like to know a different way.
Have a Good Rest of Your Day.
3.
Find the area of sector AOB. Round to the nearest tenth.
2
1.
A
18 cm
0
70°
4 ft
쏭
What is the answer for all three of those help
40%
1 mm
A
B
Area
Area =
C
Area =
mm²
Answers
What is the total number of Goals Scored in all 10 games combined? *
Number of goals
0
1
2
3
Your answer
Frequency
3
4
2
1
Answers
Based on the information given, the total number of Goals Scored in all 10 games combined is 11 goals.
How to illustrate the information?It should be noted that in Mathematics, frequency simply has to do with the number of occurence that an event has based on the data or the information that's illustrated.
Based on the information given, it should be noted that the number of goals as well as the frequency are given. This will be illustrated we:
Total number of goals will be:
= (0 × 3) + (1 × 4) + (2 × 2) + (3 × 1)
= 0 + 4 + 4 + 3
= 11 goals
Therefore, 11 goals are scored.
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please look at the pic
Answers
By using internal angles of the triangles and the definition of supplementary angles, the measure of the angle MNP is equal to 54°.
How to determine a missing angle in a geometric systemHerein we find a geometric system formed by two common semirrays with a common vertex at point N and a line segment MP such that triangle MPN is a right triangle. By Euclidean geometry we know that the sum of the measures in the internal angles equals 180°:
m ∠ NMP + m ∠ MNP + m ∠ MPN = 180° (1)
And the two angles at point P are supplementary angles:
24 · x + m ∠ MPN = 180° (2)
Then, by (1):
90° + 9 · x + m ∠ MPN = 180°
m ∠ MPN = 90° - 9 · x
By (1) in (2):
24 · x + 90° - 9 · x = 180°
15 · x = 90°
x = 6
Then, the measure of the angle MPN is equal to:
m ∠ MNP = 9 · x
m ∠ MNP = 9 · 6
m ∠ MNP = 54°
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Please help me, I am very confused, I have no idea what to do.
Answers
50 POINTS__ Solve for z and graph the solution.
–7 ≥ z–10 ≥ –14
Plot the endpoints. Select an endpoint to change it from closed to open. Select the middle of a segment, ray, or line to delete it.
Answers
Answer:
Step-by-step explanation:
Separate the compound inequality into two inequalities
7-10<-7
7-10>-14
Solve the inequality for z
7≤3
7-10>-14
Z<3
7>-4
Solution
Z [-4,3]
Alternative Form
{zI-4≤z≤3}
alex has a circular rug the radius of the rug is 5 1/4 feet which is closest to the area of the rug use 22/7
Answers
The area when Alex has a circular rug the radius of the rug is 5 1/4 feet is 86.625 feet².
How to calculate the area?It should be noted that the area of a circle is given the formula:
Area of a circle = πr²
where π = 22/7
r = radius = 5 1/4
Therefore, the area will be:
Area = πr²
Area = 22/7 × (5 1/4)²
Area = 22/7 × 25 1/16
Area = 86.625 feet²
The area is 86.625 feet².
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Which number sentence is true? OA. 2 3/4 >2.68 2² OB. 7.895 x 10² > 5.43 x 10³ OC. √63>811 OD. 1-151> 13.21
Answers
All the expressions like (a), (b) and (c) are true sentences in the form of inequality.
What is inequality expression?
The inequality expression in a sentence consist of two algebraic expression with the inequality symbols. And the solution of an inequality is a number which when substituted for the variable to makes the inequality as a true statement.
According to the question, the given inequality expressions in the form of the sentence is as follows:
(a) 2(3/4) > 2.68;
(b) 7.895 x 10² > 5.43 x 10³;
(c) √63 > 8.11;
(d) |-1.5| > |3.2|
In this, all the expressions like (a), (b) and (c) are true sentences in the form of inequality.
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Area of a triangle with a vertical height of 1/2 m and base of 1/4 m.
Answers
Answer:
1/16 squared meters
Step-by-step explanation:
The formula to find the area of a triangle is [tex]\frac{Base * Height}{2}[/tex]
We can form an equation if we substitute the values (base and height).
[tex]\frac{1/2*1/4}{2}[/tex]
1/2 * 1/4 = 1/8
and [tex]\frac{1/8}{2}[/tex] = 1/16
Therefore, the area of a triangle with a vertical height of 1/2 m and a base of 1/4 m is 1/16 meters squared.
Pls help me and show steps too, I’m so lost. I’m giving a lot of points
Answers
Answer:
x=16
Step-by-step explanation:
I apologize I have not done geo in a while so I am not sure what the theorem is, but there is a theorem that states that when a transversal intersects with two parallel lines, two angles that are facing the same direction are the same angle. (the two white angles that i have marked are equal)
next, two lines that intersect each other will have the same angle measurements on opposite sides (the green marked angles are equal)
so that means 3x - 8 = x + 24
and when you simplify that, you get 2x = 32 ---> x = 16
-2x + 3y = -6 and -3x - 2y = 11
Answers
Step-by-step explanation:
-2x + 3y = -6
-3x - 2y = 11
-5x + y = 5
y = 5 + 5
y = 10
-2x + 3(10) = -6
-2x + 30 = -6
-2x = -6 - 30
-2x = -36
x = -18
i have no idea
-12/x = 24/8 what does x equal
Answers
Simply 24/8 to 3.
-12/x = 3
Since x is the number being divided, we take the divisor and divide it by the quotient.
x = -12/3 = -4.
you make 12 equal payments. you pay a total of $1224. How much is each payment
Answers
I need help with this
Answers
Answer:
convert 10 hours 30 minutes to hours= 10.5
683/10.5
=65.04km/h
Solve for x: (1 point) negative 9 over 8, multiplied by x minus 7 equals negative 25
Answers
Answer:
Step-by-step explanation:
what is 1+1x3/2+10x3450/2+300-500 I don't know what is it
Answers
Answer:
17052 1/2
You're Welcome
A cash discount of 8% is allowed on an item which costs £45. How much money is saved if a customer decides to pay in cash?
Answers
If a costumer decides to pay in cash then saved £3.6.
What is mean by Percentage?
A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
To Calculate the percent of a number , divide the number by whole number and multiply by 100.
Given that;
A cash discount of 8% is allowed on an item which costs £45.
Now, The amount of Saved money calculated as;
Since, A cash discount of 8% is allowed on an item which costs £45.
Hence,
Saved money = 8% of £45
= 8 x 45 / 100
= 3.6
Thus, Saved money = 3.6
Therefore, If a costumer decides to pay in cash then saved £3.6.
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