Answers
Exterior angle theorem and properties of the isosceles triangles are used
prove the specified relations.
Correct responses:
9. ΔPAT ~ ΔPTB by AA similarity postulate
15. [tex]\overleftrightarrow{HM}[/tex]║[tex]\overleftrightarrow{JK}[/tex] by basic proportionality theorem
Detailed methods used to prove response9. A two column proof is presented as follows;
Statement [tex]{}[/tex] Reasons
1. ∠PTA = ∠B [tex]{}[/tex] 1. Given
2. ∠PAT = ∠ATB + ∠B [tex]{}[/tex] 2. Exterior angle of a triangle theorem
3. ∠BTP = ∠ATB + ∠PTA [tex]{}[/tex] 3 Angle addition postulate
4. ∠BTP = ∠ATP + ∠B [tex]{}[/tex] 4. Substitution property of equality
5. ∠PAT = ∠BTP [tex]{}[/tex] 5. Substitution property
6. ΔPAT ~ ΔPTB [tex]{}[/tex] 6. AA similarity postulate
The Angle-Angle, AA, similarity postulate states that two triangles are similar if two angles in one triangle are each equal to two angles in the other triangle.
15. A two column proof is presented as follows;
Statement [tex]{}[/tex] Reasons
[tex]\displaystyle 1. \hspace{0.3 cm} \frac{GJ}{HK} = \frac{GK}{GM}[/tex] [tex]{}[/tex] 1. Given
2. ∠1 ≅ ∠G [tex]{}[/tex] 2. Given
3. ΔKHG is an isosceles triangle[tex]{}[/tex] 3. Definition
4. HK = HG [tex]{}[/tex] 4. Legs of an isosceles triangle
[tex]\displaystyle 5. \hspace{0.3 cm} \frac{GJ}{HG} = \frac{GK}{GM}[/tex] [tex]{}[/tex] 5. Substitution property
6. [tex]\overleftrightarrow {HM}[/tex] ║ [tex]\overleftrightarrow{JK}[/tex] [tex]{}[/tex] 6. BPT, Basic Proportionality Theorem
Basic Proportionality Theorem, BPT, states that if a line parallel to one of the sides of a triangle, intersects the other two sides, then the line divides the other two sides in the same proportion.
Learn more about basic proportionality theorem, AA similarity postulate here:
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Related Questions
Find the slope of the line
Answers
Answer:
-1
Step-by-step explanation:
A housepainter mixed 4 gal of red paint with every 3 gal of blue paint in order to make a purple paint. Which
ratio of gallons of red paint to gallons of blue paint will make the same shade of purple paint?
28: 15
15:20
28:21
12:3
Answers
Reason:
The purple paint has 4 parts red and 3 parts blue.
The ratio of red to blue is 4:3
Multiply both parts of that ratio by 7 and we end up with 28:21
The two ratios 4:3 and 28:21 will produce the same shade of purple.
Kate father is 50 years old and kate is 24 years old now. How many years ago was kates father three times as old as her
Answers
Answer:
11
Step-by-step explanation:
50-x=3(24-x)
50-x=72-3x
2x=22
x=11years ago when kate's father was 3 times as old as kate=11
f(x)=4- 2x - x^3
Show that the graph of y=f(x) has no turning points.
Answers
Answer:
It would be F(0)=4
Step-by-step explanation:
Step-by-step explanation:
for a turning point the first derivative of the function must have zero points (= there must be some values of x that make the derivative function to have 0 as result).
the first derivative is the function that calculates the slope of the tangent at every x. so, if that function result is 0, it means the tangent slope is 0 at this point (a horizontal line), and this could be a real candidate for a turning point.
and then, left and right of such a point, the slope of the tangent must have different signs (+ to - or the other way around).
but if there is no real zero point of the first derivative, then there is no turning point anyway.
the first derivative f'(x) = -2 - 3x²
so,
-2 - 3x² = 0
-3x² = 2
x² = -2/3
x = sqrt(-2/3)
now, the square root of a negative number has no real number solution. so, on our grid of real number coordinates there is no point with a horizontal tangent (with the slope of the tangent = f'(x) = 0).
therefore, there cannot be any turning points.
through: (3,-1), slope =-1
3.
Answers
Answer:
What is the question
Step-by-step explanation:
Are these lines parallel?
Find the slope to determine the answer.
Yes
No
Answers
Answer:
yes, because they are side to side
Step-by-step explanation:
Answer:
Yes these lines are parallel because like the person before me said they are side by side
Step-by-step explanation: If they weren't side by side they would be perpendicular. Perpendicular lines are lines that intersect at a right angle of 90°. Parallel lines are lines that are side by side and do not intersect.
Hope this helps ╰(*°▽°*)╯
Here is some information 20= a+b, b is two more than a, what are the values of a and b?
Please can someone explain to me how I would go about solving this?
Answers
Answer:
a= 9, b= 11
Step-by-step explanation:
20= a +b
Let's rewrite this so that the variables are on the left-hand side of the equation:
a +b= 20 -----(1)
I have also labelled the equation as equation (1).
Since b is two more than a,
b= a +2 -----(2)
Label the equation as equation (2).
Substitute (2) into (1):
a +(a +2)= 20
2a +2= 20
-2 on both sides of the equation:
2a= 20 -2
2a= 18
Divide both sides by 2:
a= 18 ÷2
a= 9
Substitute a= 9 into (2):
b= a +2
b= 9 +2
b= 11
Lolo typed 1,125 words in 15 minutes. Let w represent the numbers of words Type each minute. If Lolo typed the same number of words each minute, how many words did she type in 1 minute?
Answers
PLEASE HELP ILL GIVE BRAINLIEST
Answers
Answer:
Um I'm just guessing
Step-by-step explanation:
2)congruent
3)noncongruent
4)noncongruent
5)noncongruent
6)congruent
7)noncongruent
8)noncongruent
9)noncongruent
10)congruent
my answers might have a high chance it is incorrect but maybe this might still help give a hint or small step on solving the problem?
Help Me With My Question.
Answers
Step-by-step explanation:
$30 bonus was already given to her, so I don't think we need to count that.
CAN SOMEONE HELP ME PLEASE ASAP!?
Answers
Answer:
108°
Step-by-step explanation:
∠4 and ∠2 are vertical angles meaning they have the same value.
Please help
This is due soon and I can’t find the answer!
Answers
Answer:
[tex]\frac{18z-2}{3} [/tex]
Step-by-step explanation:
see attached for step-by-step
Step-by-step explanation:
[tex] \frac{20z - 1}{3} - \frac{8z + 4}{12} \\ = \frac{12(20z - 1) - 3(8z + 4)}{12 \times 3} \\ \frac{240z - 12 - 24z - 12}{36} \\ = \frac{216z - 24}{36} \\ = 6z - \frac{2}{3} [/tex]
Clear picture
Solve for x.
Answers
Answer:
x = 9
Step-by-step explanation:
Since you have parallel lines intersected by a transversal, the angles are congruent so set them equal to each other and solve for x.
7x + 17 = 80
Subtract 17 from both sides
7x + 17 - 17 = 80 - 17
7x = 63
Divide by 7
7x/7 = 63/7
x = 9
For Brand B, the cost y can be represented by the equation y=1.99x , where x represents the number of bags.
Which brand costs less for 6 bags of compost?
Answers
The cost of the brand less than 6 bags is less than 11.94
Functions and equationsIf the cost y of a brand can be represented by the equation y=1.99x
where
x represents the number of bags.For a brand that costs less than 6 bags, we will substitute x = 6 into the function
y = 1.99(6)
y = 11.94
Hence the cost of the brand less than 6 bags is less than 11.94
Learn more on cost and functions here: https://brainly.com/question/25109150
Kala needs to make a total of 40 deliveries this week. So far she has completed 34 of them. What percentage of her total deliveries has Kala completed?
Answers
Answer:
85%
Step-by-step explanation:
The answer is 85% . 34/40 = 0.85 and as a percentage that is 85%
In a cafeteria,38of the students are eating salads , and14are eating sandwiches. There are 24 students in the cafeteria. How many students are eating lunches other than salads or sandwiches?
Answers
Answer:
9 students.
Step-by-step explanation:
Assuming you meant 3/8 & 1/4
3/8 students are eating a salad and 1/4 are eating a sandwich
Add these two fractions to get 5/8
(3/8 + 1/4 -> 3/8 + 2/8 = 5/8)
This means that 5/8 of the students are eating one of the above options & 3/8 are not eating these options
Then we need to find 3/8 of 24
1/8 of 24 = 3
3 x 3 = 9
Find the scale factor of the Simla r polygons
Answers
Compare two similar sides:
24:32 this reduces to 3:4
Answer: D) 3:4
What is the next fraction in this sequence? Simplify your answer.
7/15, 2/5,1/3, 4/15,...
Answers
Answer:
3/15 or 1/3
Step-by-step explanation:
Convert each fraction to a common denominator of 15:
7/15 7/15
2/5 6/15
1/3 5/15
4/15 4/15
Each step subtracts 1/15. so the next step would be 3/15 or 1/3.
A salesman's commission is 6% of his total sales. His total sales last month were $24,000. How much was his commission last month?
Answers
His commission last month was $1,440.
A new pair of ski boots cost $85. You have a coupon for 15% off. What is the price of the boots after the coupon?
Answers
Answer:
the price would be $72.25 after the coupon
Step-by-step explanation:
(85)(.15)=12.75
85-12.75=72.25
have a nice day.
Answer:
$72.25
Step-by-step explanation:
The original price is 100% of the price since 100% means the entire thing.
The discount is 15%.
100% - 15% = 85%
After taking off the discount, the price is 85% of the original price.
85% of $85 =
= 85/100 × $85
= 0.85 × $85
= $72.25
Answer: $72.25
Sketch the graph of the exponential function.
f(x)=(0.2)^x
Answers
Answer:
[tex] \frac{1}{0.2} = \frac{ \frac{1}{1} }{ \frac{2}{10} } = \frac{10}{2} = 5 \: and \: 1 \: and \: 0.2 [/tex]
Step-by-step explanation:
f(x) = (0.2)^x
x = -1
f(-1) = 0.2^-1 = 1/0.2 = 1/1/2/10 = 10/2 = 5
x = 0
f(0) = 0.2^0 = 1
x = 1
f(1) = 0.2
These would be the values for y, then you need to make a graph using them and the ones for,
Solve the inequality. Graph the solution.
Answers
Which of the following functions has a zero of x=-3 and x=1? Select all that apply.
Answers
A because when you try to find x you can do x +3 =0 and then do x - 1 =0 giving you x = -3, 1
Explain how to use a number's greatest square factor to
write the square root of that number in simple radical
form.
Answers
Now, let’s find all the factors of 40 .
1, 2, 4, 5, 8, 10, 20, 40.
Now, let’s pick the greatest factor that is also a perfect square, meaning that if we took the square root of it, we would get a nice whole number.
In this case, the greatest factor that is a perfect square is 4.
Now, we can write the radical as
root4 • root10
Because 4 • 10 is 40, our original radical
Now we can simplify this to 2•root10.
What is the product of 2v3 and 4V 18 in simplest radical form?
Answers
Answer:
a x n = n √ a = n = √ a a x = n = √ a a 144 v ⋅ 3 ⋅ V = 432 v V
Step-by-step explanation:
n = √ a a Multiply 3 by 144 . 432 v V
List all of the solutions. a x n = n √
a = n = √ a
a x = n = √ a a 144 v ⋅ 3 ⋅ V = 432 v V
Answer: 24[tex]\sqrt{6}[/tex]
Step-by-step explanation:
1. Identify that 4[tex]\sqrt{18}[/tex] is equal to 4 times [tex]\sqrt{2}[/tex] times [tex]\sqrt{3^2}[/tex]. [tex]\sqrt{3^2}=3[/tex]. Our rational numbers are now 4 and 3. 4 times 3 equals 12, and we have a remainder of [tex]\sqrt{2}[/tex]. Knowing [tex]4\sqrt{18}=12\sqrt{2}[/tex] makes the second step much easier.
2. A fast approach for these types of problems is to multiply the rational numbers together and multiply the irrational numbers separately until the last step. 2 times 12 equals 24. [tex]\sqrt{3}[/tex] times [tex]\sqrt{2}[/tex] equals [tex]\sqrt{6}[/tex].
3. Now we must simply multiply the whole number with the irrational number. 24 times [tex]\sqrt{6}[/tex] equals 24[tex]\sqrt{6}[/tex].
solve the system of equations using substitution
Answers
Answer:
Yeah,I don't see the question
A certain forest covers an area of 4900 km². Suppose that each year this area decreases by 7.25%. What will the area be after 8 years?
Answers
Answer:
4618.25 sq.km.
Step-by-step explanation:
After 1 year, the forest has shrunk from 4900 sq.km to 4900*(1-0.0575) = 4900*(0.9425)
What is the answer to this question
Answers
Because the original format is y = mx + b
m = slope
b = y-intercept
Problem-Solving Practice
Measures of Variation
Answers
Write the expression in simplest form
Answers
Answer: the numbers are different
Step-by-step explanation: in the form
