OAA', OBB', and OCC' are straight lines. Triangle ABC is mapped onto Triangle A'B'C' by an enlargement with center O. What is the scale factor of enlargement.
Answers
Answer:
(D) 2
Step-by-step explanation:
The scale factor of the enlargement of ΔABC to ΔA'B'C' is given by the ratio of the length of the corresponding sides of ΔA'B'C' and ΔABC
Therefore, we have;
[tex]The \ scale \ factor = \dfrac{Length \ of \overline {B'C'}}{Length \ of \overline {BC}} = \dfrac{Length \ of \overline {A'C'}}{Length \ of \overline {AC}} = \dfrac{Length \ of \overline {A'B'}}{Length \ of \overline {AB}}[/tex]
[tex]\dfrac{Length \ of \overline {B'C'}}{Length \ of \overline {BC}} = \dfrac{2 \ units}{1 \ unit} = 2[/tex]
[tex]\dfrac{Length \ of \overline {A'C'}}{Length \ of \overline {AC}} = \dfrac{4 \ units}{2 \ units} = 2[/tex]
[tex]\dfrac{Length \ of \overline {A'B'}}{Length \ of \overline {AB}} = \dfrac{2 \cdot \sqrt{5} \ units}{\sqrt{5} \ units} = 2[/tex]
Therefore, the scale factor = 2
Related Questions
Find all solutions to the equation
in the interval [0, 21). Enter the
solutions in increasing order.
sin 2x = 2 sin x
x = [?],[1]
TT
Remember: sin 20 = 2 sin 0 cos 0
Answers
Answer:
[tex]x=0, \\x=\pi[/tex]
Step-by-step explanation:
Recall the trigonometric identity [tex]\sin 2x=2\sin x\cos x[/tex].
Therefore, given [tex]\sin 2x=2\sin x[/tex], rewrite the left side of the equation:
[tex]2\sin x\cos x=2\sin x[/tex]
Subtract [tex]\sin x[/tex] from both sides:
[tex]2\sin x\cos x-2\sin x=0[/tex]
Factor out [tex]2\sin x[/tex] from both terms on the left:
[tex]2\sin x(\cos x-1)=0[/tex]
We now have two cases:
[tex]\begin{cases}2\sin x=0, x=k\pi\text{ for }k\in \mathbb{Z}\\\cos x-1=0,x=k2\pi\text{ for }k\in \mathbb{Z}\end{cases}[/tex]
Since the problem stipulates that [tex]x[/tex] is in the interval [tex][0, 2\pi)[/tex], we have:
[tex]\text{For }x\in [0, 2\pi):\\\sin x=0\rightarrow \boxed{x=0, x=\pi}\\\cos x-1=0\rightarrow \boxed{x=0}[/tex]
Recall that square brackets mean inclusive and parentheses mean exclusive. Therefore, [tex]2\pi \notin [0, 2\pi)[/tex].
ASAP !!
If using the method of completing the square to solve the quadratic equation x^2+3x-17=0x
2
+3x−17=0, which number would have to be added to "complete the square"?
Answers
Answer:
17
Step-by-step explanation:
need help w question in this pic thanks!!
Answers
Given:
A figure of a circle.
To find:
The value of x.
Solution:
First label the given figure as shown below.
In triangle ABO,
[tex]OA=OB[/tex] (Radii of same circle)
[tex]\Delta ABO[/tex] is an isosceles triangle. (By the definition of isosceles triangle)
[tex]\angle OAB\cong \angle OBA[/tex] (Base angles of an isosceles triangle)
[tex]m\angle OAB=m\angle OBA[/tex]
[tex]42^\circ=m\angle OBA[/tex]
In triangle ABO,
[tex]m\angle AOB+m\angle OAB+m\angle OBA=180^\circ[/tex] (Angle sum property)
[tex]m\angle AOB+42^\circ+42^\circ=180^\circ[/tex]
[tex]m\angle AOB=180^\circ-42^\circ-42^\circ[/tex]
[tex]m\angle AOB=96^\circ[/tex]
Now,
[tex]m\angle AOB+m\angle BOC=180^\circ[/tex] (Linear pair)
[tex]96^\circ+x=180^\circ[/tex]
[tex]x=180^\circ-96^\circ[/tex]
[tex]x=84^\circ[/tex]
Therefore, the value of x is 84 degrees.
The sum of two numbers is 50. The larger number is 20 more than the smaller number. What are the numbers?
Answers
Answer:
the smaller number is 15 and the larger number is 35
Step-by-step explanation:
x+y=50
x=smaller number y=larger number
y=x+20
x+(x+20)=50
2x+20=50
2x=30
x=15
smaller number=15
larger number= 15+20=35
Answer:
Smaller: 15
Larger: 35
Step-by-step explanation:
1. Finding the two equationsLarger: y
Smaller: x
[tex]x+y=50[/tex]
[tex]y=20+x[/tex]
2. Plugging it in[tex]x+20+x=50\\2x=50-20\\2x=30\\x=15[/tex]
[tex]15+y=50\\y=50-15\\y=35[/tex]
x=15; y=35
Hope this helped! Please mark brainliest :)
P=A+B+C What is B? You can get 50 points.
Answers
Answer:
I guess B=C
Step-by-step explanation:
If it's correct then please mark me brainliest
Given f(x)= 2^x and g(x)=x^2 answer the questions that follow
a. Your friend claims the graph of f(x)=2x increases at a faster rate than the graph of g(x)=x2 when x ≥ 0. Is your friend correct? Explain your reasoning.
b. How are the 2 functions different?
PLEASE HELP
Answers
Answer:
a. Yes it's correct, reasons;
I) let x=1, f(1)=2^1=2, g(x)=1^2=1 this proves that when a higher number is used the value of f(x) will be higher than g(x).
ii) As x approaches zero f(x) approaches 1, but g(x) approaches 0. Which will make the rate at which the graph of f(x) increase be faster than g(x)
b. f(x) has an infinite degree but g(x) has a finite degree of 2.
Determine whether each sequence is arithmetic or geometric. Sequence 1: –10, 20, –40, 80, ... Sequence 2: 15, –5, –25, –45, ...
A. Sequence 1 is arithmetic and Sequence 2 is geometric.
B. Both sequences are geometric.
C. Sequence 2 is arithmetic and Sequence 1 is geometric.
D. Both sequences are arithmetic.
sequence 2 may be arithmetic because -20 but I can't find out what sequence 1 is
Answers
Answer:
Step-by-step explanation:
C-10,20,-40,80,...[tex] u_{n+1}=(-2)*u_{n}[/tex]. is geometric1
Triangle MNO is isosceles. Find the value of y and the measure of Angle O. Y=______
Angle O=_______degrees
Answers
Answer:
y = -5
o = 35 degrees
Step-by-step explanation:
If you replace y with -5, the statement 7y = 4y - 15 is correct. You get -35 = -35. Hope this helped!
Which of the following is the explicit rule for a geometric sequence defined by
a recursive formula of a, - 138-1 for which the first term is 7?
Answers
Answer:
C
Step-by-step explanation:
What you wrote is not the same thing as what the question is, or at least I don't think so. I'll answer the printed question.
First of all, the 13 is what separates each of the terms. In other words 7 is the first term. 13 must be raised to the n - 1 power.
It is written like this
an = 7 * 13^(n - 1)
you want a1 to be 7. The only way that can happen is if 13^0 which gives you 1.
So the correct answer is C
If A - B = {2,4,6}, B - A = {0,1,3}, and A∪B = {0,1,2,3,4,5,6,7,8}. What is A∩B?
Answers
Answer:
{5,7,8}
Step-by-step explanation:
A-B = {2,4,6} => A={2,4,6}
B - A = {0,1,3} => B= {0,1,3}
A∪B = {0,1,2,3,4,5,6,7,8}
=> A = {2,4,5,6,7,8}
B= {0,1,3,5,7,8}
=> A∩B = {5,7,8}
ABCD is a quadrilateral.
a) Calculate the value of x.
b) When ABCD is drawn to scale, would the lines AD and BC be parallel or not? A You must justify your answer without using a scale drawing.
Answers
Answer:
A) 45=x
B) Yes, since both A and B are 90°
6x+90=360
6x=270
x=45
No lines are not parallel
Problem: Construct a triangle with interior angle measures of 60° and 60°. Let one of the side lengths be 10. What are the lengths of the other sides?
Answers
Answer:
The lengths of the other sides would be 10, as well.
Step-by-step explanation:
Since we already know two of the three angles, we can subtract to find the other angle. The interior angles of a triangle will always add up to 180°. We have 60° and 60°, giving us 120°. 180 - 120 is equal to 60°, so that's the missing angle. Because all of the angles are the same, this is an equilateral triangle, which means the sides also have to be the same length. If one of the sides is 10, all of the sides are 10.
The triangle with sides 10 , 10 and 10 and all angles at 60° is an equilateral triangle
What is an Equilateral Triangle?An equilateral triangle is a triangle in which all three sides have the same length.
Let the triangle be ΔABC , and
∠A = ∠B = ∠C = 60° and AB = BC = CA
Given data ,
Let the triangle be represented as ΔABC
Let the side length of the triangle be AB = 10
Now , the measure of ∠ABC = 60°
And , the measure of ∠BAC = 60°
So , the total sum of all the angles in a triangle = 180°
And , the measure of ∠ACB = 180° - ( 60° + 60° ) = 60°
Therefore , all the angles of the triangle are 60°
So , it is an equilateral triangle
And , the measure of side lengths of the triangle is 10
Therefore , AB = BC = CA = 10
Hence , it is an equilateral triangle
To learn more about equilateral triangle click :
https://brainly.com/question/17824549
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algebra 1 solve − 0.32 + 0.18 = 0.25 − 1.95
Answers
Answer:
Step-by-step explanation:
Add 0.32 and 0.18 to get 0.5.
0.5=0.25 - 1.95
subtract 1.95 from 0.25 to get —1.7.
0.5=—1.7
compare 0.5 and —1.7.
flase
Easy
a) -2,-5.-8.-11,...
Answers
Step-by-step explanation:
???????? what is easy??
could someone help me with this ASAP?
Answers
Answer:
just draw a circle that connects all of the 10's on the graph.
a circle is NOT a function
Step-by-step explanation:
Find the measure of the third angle of a triangle if the measures of the other two angles are given.
31.8 and 89.8
Answers
The three angles of a triangle equal 180
Third angle = 180 - 31.8 - 89.8 = 58.4
Answer: 58.4
Pier is a teacher
There are 13 boys and 17 girls in the class
Pier chooses one student at random
Workout the probability the student is a boy
Answers
Answer:
I think its 43%
Explanation
math
The probability of Pier choosing a boy is 0.43 or 43%.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
Example:
The probability of getting a head in tossing a coin.
P(H) = 1/2
We have,
The total number of students in the class is:
13 boys + 17 girls
= 30 students
The probability of Pier choosing a boy is the number of boys in the class divided by the total number of students:
Probability of choosing a boy.
= number of boys / total number of students
Probability of choosing a boy.
= 13 / 30
Probability of choosing a boy.
= 0.4333 or approximately 0.43
Therefore,
The probability of Pier choosing a boy is 0.43 or 43%.
Learn more about probability here:
https://brainly.com/question/14099682
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Which equation in slope-intercept form represents a line that is parallel to y=1/2x-2 and passes through the point (-8,1)?
Answers
Answer:
[tex]\displaystyle y=\frac{1}{2}x+5[/tex]
Step-by-step explanation:
We want to find the slope in slope-intercept form of a line that is parallel to:
[tex]\displaystyle y=\frac{1}{2}x-2[/tex]
And passes through the point (-8, 1).
Recall that parallel lines have equivalent slopes.
Since the slope of our given line is 1/2, the slope of our new line must also be 1/2.
We are also given that it passes through the point (-8, 1). Since we are given a slope and a point, we can use the point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]
Substitute 1/2 for m and (-8, 1) for (x₁, y₁). Hence:
[tex]\displaystyle y-(1)=\frac{1}{2}(x-(-8))[/tex]
Since we want the equation in slope-intercept form, we can isolate y. Distribute:
[tex]\displaystyle y-1=\frac{1}{2}x+4[/tex]
Therefore, our equation is:
[tex]\displaystyle y=\frac{1}{2}x+5[/tex]
What is 240 : 60 in its simplest form
Answers
Answer:
4:1
Step-by-step explanation:
Explanation: To solve this equation, you need to divide each number to the lowest value, using the same number to divide each term. Let’s use your equation as an example. 240 and 60 can each be divided by 10, by simply removing the zero. This would leave the radio as 24: 6. However, the numbers can still be further simplified. Each number can still be divided by 6. This would change the radio to 4:1. Since 1 cannot be divided by any number other than itself while still remaining a whole number, this is our final answer.
Someone tell me where everyone is going right please !!
Answers
Answer:
1min = 0.25miles
5.25miles / 0.25miles = 25 = 25minutes
Step-by-step explanation:
Hope this is right I'm not the best at worded time/distance math questions.
9514 1404 393
Answer:
0 ≤ t < 52.5 minutes
Step-by-step explanation:
Riko will be behind Yuto until her distance traveled matches his. That is, she will be behind for ...
0.35t < 5.25 +0.25t
0.10t < 5.25
t < 52.5
Riko will be behind Yuto on the interval 0 ≤ t < 52.5 minutes.
_____
Additional comment
distance = speed × time
Here, time is measured from when Riko starts riding. In addition to the 5.25 miles that Yuto has already gone, his distance will be the product of his speed (0.25 mi/min) and the travel time (t min). Then Yuto's total distance is 5.25+0.25t miles. The speed×time product is also used to find Riko's distance traveled. In her case, it is 0.35t miles.
How many triangles are there in the picture?
Answers
five I think I am not sure
Find the size of each of the unknown angles. Help me plz.
The answer is a=b=60 degree and c=120 degree. Give me solution plz
Answers
Answer:
a=60 b=60 c=120 is the answer
Write a phrase in words to match each expression.
5+3
——
n
Answers
Answer:
sum of five and 3 is divided by n
someone help me now?
Answers
Answer:
answer of given question is 200 miles
for this answer give me brilliant tag
Answer:
200 miles
Step-by-step explanation:
this is really not difficult.
just solve the equation as it is already written there.
130 = 0.5m + 30
100 = 0.5m = m/2
m = 200 miles
that is all that is to it.
putting this in here as question costs way more time than just doing this.
true or false,the diagonal of a rectangle is longer than any of its sides. I want the answer with explanation If u don't I will report
Answers
Answer:
True
Step-by-step explanation:
Yes! The diagonal of a rectangle is longer than any of its sides.
Consider PQRS as a rectangle. It is known to us that each interior angle of a rectangle measures 90°. Now, after making the diagonal of the rectangle PQRS, the rectangle has been split into 2 right-angled triangles i.e, ∆PRS and ∆RPQ. In the right angled triangle, hypotenuse is always the longest side. Here, in ∆PRS and ∆RPQ, the bases are RS and QP ; perpendiculars are PS and QR and both triangles' hypotenuse is PR. As, hypotenuse is always the longest side, so PR will be longer than RS,QP,PS and QR. Clearly, the diagonal of a rectangle is longer than any of its sides.
The side of an equilateral triangle is 22. Find the exact length of the altitude.
Use the exact value, meaning leave your answer with a radical.
PLEASE HELP THE TEST IS DUE IN 5 MINS
Answers
Step-by-step explanation:
here's the answer to your question
suppose 2 standard 6 sided dice are rolled at the same time. what is the smaple space for the multiplication of the values for the 2 die
Answers
Answer:
Step-by-step explanation:
Following is the sample space for all the possible outcomes when 2 standard 6-sided dice are rolled simultaneously:
1 2 3 4 5 6
1 1,1 1,2 1,3 1,4 1,5 1,6
2 2,1 2,2 2,3 2,4 2,5 2,6
3 3,1 3,2 3,4 3,4 3,5 3,6
4 4,1 4,2 4,3 4,4 4,5 4,6
5 5,1 5,2 5,3 5,4 5,5 5,6
6 6,1 6,2 6,3 6,4 6,5 6,6
Therefore the sample space for the multiplication of the two values in each possible outcome:
elements of the set are:
1*1=1
1*2=2
1*3=3
...........
2*1=2
2*2=4
2*3=6
.............
so on...
Therefore the complete set:
S={ 1, 2, 3, 4, 5, 6, 2, 4, 6, 8, 10, 12, 3, 6, 9, 12, 15, 18, 4, 8, 12, 16, 20, 24, 5, 10, 15, 20, 25, 30, 6, 12, 18, 24, 30, 36 }
What is the value of the power? Negative StartFraction 9 Over 12 EndFraction Negative StartFraction 27 Over 64 EndFraction StartFraction 9 Over 12 EndFraction StartFraction 27 Over 64 EndFraction
Answers
Answer:
[tex](\frac{-3}{4})^3 = -\frac{27}{64}[/tex]
Step-by-step explanation:
Given
[tex](\frac{-3}{4})^3[/tex]
Required
Evaluate
The expression can be represented as:
[tex](\frac{-3}{4})^3 = (\frac{-3}{4})*(\frac{-3}{4})*(\frac{-3}{4})[/tex]
So, we have:
[tex](\frac{-3}{4})^3 = \frac{-3*-3*-3}{4*4*4}[/tex]
[tex](\frac{-3}{4})^3 = \frac{-27}{64}[/tex]
Rewrite as:
[tex](\frac{-3}{4})^3 = -\frac{27}{64}[/tex]
Answer:
B -27/64
Step-by-step explanation:
The graph plots four equations, A, b,c,and d
Which pair of equations has (0.8) as its solution?
Equation A and Equation C
Equation B and Equation
Equation C and Equation D
Equation B and Equation D
Answers
Answer:
equation A and equation c
Answer:
Equation A and Equation C
bobby drove 110 miles and his car used 5 gallons of gas. How many miles can he drive with 16 gallos of gas
Answers
Answer:
Bobby can drive 352 miles with 16 gallons of gas.
Step-by-step explanation:
110 miles uses 5 gallons of gas.To find how many miles can be driven with one gallon we divide 110 by 5.
110 ÷ 5 = 22
Therefore to find the amount of miles that can be driven with 16 gallons we multiply 16 × 22 = 352
