the scale of dilation is 2.5 for the triangle ABC.
We are given the coordinates of triangle ABC as:
A(0, 0), B(0, 4), and C(6, 0)
Coordinates of dilated triangle A'B'C' is:
A' (10, 0), B'(0, 10), and C' (15, 0).
The scale of dilation can be calculated as:
k · ( 0, 0 ) = ( 0 , 0 )
k · ( 0 , 4 ) = ( 0 , 10 )
k · ( 6, 0 ) = ( 15, 0 )
k = 15 / 6 = 10 / 4 = 2.5
The scale of dilation is 2.5 for the triangle.
Therefore, the scale of dilation is 2.5 for the triangle ABC.
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Write a two-column proof.
Given: ∠ K ≅ ∠M, KP⊥ PR, MR ⊥ PR
Prove: ∠K P L ≅ ∠ M R L
∠KPL ≅ ∠MRL as perpendicular always makes an angle of 90°.
What specifically is meant by "triangle congruency"?When two triangles' three corresponding sides and angles are the same sizes, they are said to be congruent.These triangles can be moved, rotated, flipped, and turned to look exactly the same.They will coincide if they are moved.Congruence exists when two triangles satisfy the five congruence conditions.They are the side-side-side (SSS), the side-angle-side (SAS), the angle-side-angle (ASA), the angle-angle-side (AAS), and the right angle-hypotenuse-side (RHS).So,
Given: ∠ K ≅ ∠M, KP⊥ PR, MR ⊥ PR
To Prove: ∠KPL ≅ ∠MRL
As MR ⊥ PR (Given), then: ∠MRL = 90°Similarly, KP⊥ PR (Given), then: ∠KPL = 90°So, ∠KPL ≅ ∠MRL.
Therefore, ∠KPL ≅ ∠MRL as perpendicular always makes an angle of 90°.
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Solve √5-4 x-6=7 .
(F) -44
(G) -41
(H) 41
(J) 44
The answer for this equation is -2.69.
Given,
Equation, [tex]\sqrt{5}[/tex] - 4x - 6 = 7
We have to find x using Order of Operations.
That is,
[tex]\sqrt{5}[/tex] - 4x - 6 = 7
[tex]\sqrt{5}[/tex] - 4x = 7 + 6
[tex]\sqrt{5}[/tex] - 4x = 13
-4x = 13 - [tex]\sqrt{5}[/tex]
-4x = 10.76
x = 10.76 / -4
x = -2.69
Therefore, the answer for the given equation [tex]\sqrt{5}[/tex] - 4x - 6 = 7 is -2.69
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Doy muchos puntos. Ayuda pls
Answer:
Ava had a greater percentage of change because her allowance increased by 150%, while Joey's only increased by 133%
Step-by-step explanation:
To find the percentage of change, you'll divide.
For Ava:
18 ÷ 12 = 1.5
This means her percentage of change is 150%
For Joey:
24 ÷ 18 = 1.33333... (Round to 1.33)
This means his percentage of change is 133%
150% > 133%, so Ava has the greater percentage of change.
Showing results for stan works as a customer service representative. he know that the amount in dollars of his yearly bonus is represented by the expression -1.5x + 546 where x is the number of complaints customer had about him during the year. to find his bonus if he gets 20 complaints he substitutes 20 for x. what should be his next step? what would his bonus be?
As a customer service representative Stan's yearly bonus would be 516 dollars.
What is Bonus ?A bonus is a financial compensation that is above and beyond the normal payment expectations of its recipient. Bonuses may be awarded by a company as an incentive or to reward good performance.
We have given that the amount of his yearly bonus in expression which is -1.5x + 546 dollars.
Where, 'x' = Number of complaints customer
We know that Stan gets 20 complaints,
To find his bonus we will solve this expression -1.5x + 546 by substituting 20 for x.
Bonus of Stan = -1.5x + 546
= (-1.5×20) + 546
= -30 + 546 = 516
Hence, the yearly bonus of Stan is 516 dollars.
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Write a coordinate proof to prove that the large triangle in the center of the flag is isosceles. The dimensions of the flag are 4 feet by 6 feet and point B of the triangle bisects the bottom of the flag.
ΔACD ≅ ΔBCE so DC = EC therefore the triangle will isosceles triangle.
What is a triangle?A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.
The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.
There are many types of triangles such that right-angle triangles, equilateral triangles, and much more.
In the given figure
AC = CB , DA = EB and ∠A = ∠B
So,
ΔACD ≅ ΔBCE
Now corresponding sides of a congruent triangle are the same.
So,
DC = EC therefore the triangle will isosceles triangle.
Hence "ΔACD ≅ ΔBCE so DC = EC, therefore, the triangle will isosceles triangle".
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At an amusement park, 360 visitors rode the roller coaster in 3 hours. Write and solve a proportion to find the number of visitors at this rate who will ride the roller coaster in 7 hours.
Answer:
840
Step-by-step explanation:
360 divided by 3 = 120 Visitors per Hour
Now you do you 120 x 7 which equals to 840
Hope this helps ^^
Step-by-step explanation:
360 visitors in 3 hours.
that gives us the ratio
360/3
and because a ratio is nothing else than a fraction with a special meaning, we cab simplify this like any other fraction too :
360/3 = 120/1 = 120
in other words, out of the 3-hour ratio we know that there are 120 visitors in 1 hour.
and now it is easy to use it to find the number of visitors for 7 hours.
remember, if we multiply one part of the fraction by something, we need to multiply also the other part by the same number so that the value of the fraction stays the same.
in other words, we can only do
a/b × c/c
so, if we multiply the bottom part of our ratio by 7 (to go to 7 hours), we also have to multiply the top part by 7 to keep the ratio :
120/1 × 7/7 = 840/7
that tells us that there are 840 visitors in 7 hours.
A cone 4.5 centimeters high with a radius of 3 centimeters. Label B is pointing to the circular base of the cone.
The volume of the cone isV = 42.41[tex]Cm^{3}[/tex].
In order to calculate the volume of the solid, you use the following formula:
where
r: radius of the circular base of the cone = 3 cm
h: height from the circular base to the peak of the cone = 4.5 cm
You replace the values of r and h in the formula for the
volume V = [tex]\frac{1}{3}[/tex] [tex]\pi[/tex] [tex](3cm)^{2}[/tex]4.5 =42.411 [tex]cm^{3}[/tex] = 42.41 [tex]cm^{3}[/tex]
Hence, the volume of the cone is 42.41 [tex]Cm^{3}[/tex]
Volume may be a measure of occupied three-dimensional space. it's often quantified numerically using SI derived units (such as the cubic meter and liter) or by various imperial units (such as the gallon, quart, cubic inch). The definition of length (cubed) is interrelated with volume. the quantity of a container is generally understood to be the capacity of the container; i.e., the quantity of fluid (gas or liquid) that the container could hold, instead of the amount of space the container itself displaces.In past , volume is measured using similar-shaped natural containers and afterward , standardized containers. Some simple three-dimensional shapes can have its volume easily calculated using arithmetic formulas. Volumes of more complicated shapes are often calculated with integral calculus if a formula exists for the shape's boundary.
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Explain why only like radicals can be added or subtracted while unlike radicals can be multiplied or divided, Under what conditiones can unlike radicals not be multiplied on divided?
Answer:
To multiply radicals with different indices, we need to find a common denominator, which is the lowest common multiple (LCM) between the roots. Once we obtain the LCM, we can multiply each root and exponent in the radicand to obtain the LCM, and rewrite as one radical
When we multiply two radicals with the same type of root (both square roots, both cube roots, and so on), we simply multiply the radicands (the expressions under the radical signs) and put the product under a radical sign
Two vertices of rectangle ABCD are located at A(-4,-2) and B(5,-2). If the
midpoint of AD is located 5 units down from A, what are the coordinates of the
vertices C and D?
By using the definition of a rectangle on a Cartesian plane, the coordinates of the vertices C and D are C(x, y) = (5, - 12) and D(x, y) = (- 4, - 12).
What are the missing coordinates of two vertices of rectangles?
Rectangles are quadrilaterals with two pairs of parallel sides of equal length and four right internal angles. On a Cartesian plane, we find define the locations of the vertices of the rectangle below:
A(x, y) = (a, c), B(x, y) = (b, c), C(x, y) = (b, d), D(x, y) = (a, d)
If we know that a = - 4, b = 5, c = - 2, d = - 12, then the coordinates of the vertices C and D are C(x, y) = (5, - 12) and D(x, y) = (- 4, - 12).
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San Diego, California is about 2,683,824 feet away from San Francisco, California. Los Angeles is about 700,000 feet closer to San Francisco than San Diego is. Which of the following could be the actual distance between Los Angeles and San Francisco?
The actual distance between Los Angeles and San Francisco is 19,83,824 feet.
Given that, the distance between San Diego and San Francisco is 2,683,824 feet away and Los Angeles is about 700,000 feet closer to San Francisco than San Diego.
What is the distance?Distance is the total movement of an object without any regard for direction. We can define distance as how much ground an object has covered despite its starting or ending point.
The actual distance between Los Angeles and San Francisco = The distance between San Diego and San Francisco - The difference in distance.
= 2,683,824-700,000
= 19,83,824
Therefore, the actual distance between Los Angeles and San Francisco is 19,83,824 feet.
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If f(x)=x-5, then match each of the following.
1.-5
2.0
3.-6
4.-3
5.3
6.-4
f(1)
f(-1)
f(2)
f(0)
f(5)
f(8)
Answer:
Step-by-step explanation:Given f(x)=x-5
f(-1)= -1-5
= -6
f(0)=0-5
= -5
f(1)=1-5
= -4
f(2)=2-5
= -3
f(5)=5-5
=0
f(8)=8-5
= 3
Marvel consists of calcium, carbon, and oxygen in the ratio 10:3:12
a) How much carbon would you find in a 300kg piece of marvel?
b) what percentage of marble is calcium
How do I work with these ratios I'm confused
Using proportions, it is found that:
a) You would find 36 kg of carbon is a 300 kg piece of marvel.
b) 40% of marble is Calcium.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
For this problem, the ratio 10:3:12 of calcium, carbon and oxygen means that:
Calcium is 10/25 of the total.Carbon is 3/25 of the total.Oxygen is 12/25 of the total.Hence for item a, the amount is given as follows:
300 x 3/25 = 36.
You would find 36 kg of carbon is a 300 kg piece of marvel.
For item b, the percentage is found as follows:
10/25 = 40%.
40% of marble is Calcium.
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Write an equation of each line in standard form with integer coefficients.
the line through (1,2) with slope 4/5
The equation of the line in standard form passing through point (1 , 2) with slope equal to 4/5 is 4x - 5y = -6.
The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.
The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).
Using the point slope form, plug in the values of the slope and the point to set up the equation.
(y - y1) = m(x - x1)
where m = 4/5 and (x1 , y1) = (1 , 2)
(y - 2) = 4/5(x - 1)
y - 2 = 4/5 x - 4/5
To express it in standard form, arrange the variables in one side and the constants on the other.
y - 2 = 4/5 x - 4/5
4/5 x - y = -2 + 4/5
4/5 x - y = -6/5
Multiply both sides by 5 to have integer coefficients.
5(4/5 x - y) = 5(-6/5)
4x - 5y = -6
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What is the ratio of 5 days to 60 hours?
Answer:
12:1
Step-by-step explanation:
Answer:
2:1
Step-by-step explanation:
An employee earns $
20.25
per hour after receiving a
8
% raise. What was the employee's hourly pay before raise? Round your answer to the nearest cent.
The employee's pre-raise salary was $ ____
The employee's pre-raise salary was $18.75
What was the employee's hourly pay before raise?The given parameters are
New hourly pay = $20.25
Raise = 8%
The new hourly pay of the employee is calculated using
New hourly pay = Pre-raise salary * (1 + raise)
This gives
20.25 = Pre-raise salary * (1 + 8%)
Divide both sides by 1 + 8%
Pre-raise salary = 18.75
Hence, the employee's pre-raise salary was $18.75
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sunil has 40 counters
Answer:
Question:
Sunil has 40 counters. 9 of Sunil's counters are red. (c) What fraction of Sunil's counters are not red?
Answer: 0.775 or 77.5%
Step-by-step explanation:
Based on the given conditions, formulate: (40 - 9) / 40
Calculate the sum or difference: 31/40
= 31/40 = 77.5% or 0.775
The equation d = 4 - (1/15)t represents your distance from home d for each minute you walk t .
b. Are you walking towards or away from your home? Explain. points on the line.
The graph of the equation is showing that we are walking towards our home. If the equation d = 4 - (1/15)t represents your distance from home d for each minute you walk t .
What is a slope of line?A line's steepness and direction are determined by the slope of the line. Without actually using a compass, determining a line's slope in a coordinate plane allows one to anticipate whether a line is parallel, perpendicular, or not.
The change in a line's y coordinate relative to its change in x coordinate is referred to as the line's slope. Δy is the net change in the y coordinate, while Δx is the net change in the x coordinate.
Therefore,
m = y₂-y₁/x₂-x₁ (where m denotes the slope) can be used to express how the y coordinate changes in relation to the x coordinate.
Be aware that tan ∅ = y/x
We also refer to this tan as the line's slope
We have given d = 4 - (1/15)t
We will use the graph tool and determine the coordinates
(see the attached image)
When t = 0, d = 4 (y-intercept)
This provide the info that at the time t = 0 the house was four units away.
When t = 60 min, d = 0 (x-intercept)
This provide the info that he was already at home at the time t = 60 minutes.
Thus, this slope proves that he was walking towards the house.
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In the diagram below, DGL DF. Use the diagram for questions 1-7.
1. Name the sides of 24.
2. Name the vertex of 22.
3. Give another name for 23.
4. Classify 25.
5. Classify LCDE.
6. If m25 = 42° and m/1 = 117°, find m/CDF.
7. If m/3 = 73°, m/FDE.
H5
D
4
3
G
tay
E
1.
2.
3.
4.
5
Answer:
1. Sides of ∠4 are DC and DG
2. Vertex of ∠2 = Point D
3. Another name for ∠3 = ∠EDG
4. ∠5 is an acute angle
5. ∠CDE is a straight angle
6. m ∠CDF = m∠5 + m∠1 = 42 + 117 = 159°
7. m ∠FDE = 17°
Step-by-step explanation:
For # 7 note that since DG is perpendicular to DF, m ∠GDF = 90°
m ∠GDF = m ∠3 + m ∠FDE
Since m ∠3 = 73°, m∠FDE = 90 - 73 = 17°
two companies sell custom t shirts company a charges $5 per shirt plus a one time $20 service fee company b charges $7 per shirt plus a one time $10 service fee what is the number of shirts were both companies would cost the same
The number of shirts produced by each company to have the same cost are 5 shirts.
We have that:
For Company A:
Fixed cost will be = $ 20
Cost per shirt = $ 5
For company B:
Fixed cost will be = $ 10
Cost per shirt = $ 7
Let the number of shirts be x.
Equation for cost for company A:
Cost = 20 + 5 x
Equation for cost for company B:
Cost = 10 + 7 x
Now, put both the companies cost equal, we get that:
10 + 7 x = 20 + 5 x
7 x - 5 x = 20 - 10
2 x = 10
x = 10 / 2
x = 5
Therefore, the number of shirts produced by each company to have the same cost are 5 shirts.
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Five years ago, Lucia’s age was 1/3 the age she will be in eleven years. How old is Lucia now? Enter an integer.
Answer:
13 years old
Step-by-step explanation:
Let the age now be = [tex]x[/tex]
Age 5 years ago = [tex]x - 5[/tex]
Age 11 years from now = [tex]x + 11[/tex]
[tex]x - 5 = \frac{1}{3}(x+11)[/tex]
[tex]x - 5 = \frac{1}{3}x + \frac{11}{3}[/tex]
[tex]x - \frac{1}{3}x = \frac{11}{3} + 5[/tex]
[tex]\frac{2}{3}x = \frac{26}{3}[/tex]
[tex]x = \frac{26}{3}/\frac{2}{3}[/tex]
[tex]x = 13[/tex]
Identify a pattern and find the next three numbers in the pattern.
2,6,10,14, . . .
The difference between 6 and 2 is 4
The difference between 10 and 6 is 4
The difference between 14 and 10 is 4
for each number we just add 4 to the previous number.
14+4 = 18
18+4 =22
22+4 =26
The next 3 numbers in the pattern are 18, 22, 26.
What is Arithmetic sequence?
In an Arithmetic Sequence the difference between one term and the another could be a constant. In other words, we just include the same value each time infinitely. An arithmetic sequence is an ordered set of numbers that have a common difference between each consecutive term.
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Clara is building a triangular garden. She wants the length of the longest side to be three more than twice as long as the length of the shortest side, and the third side will be twelve feet long.
What expression could she write to determine the perimeter of the triangle if s represents the length of the shortest side? (Recall that perimeter is the distance around a shape.)
what is 0.5835 centimeter rounded to the nearest tenth
Answer:
0.6 centimeter
Step-by-step explanation:
The picture below should help you see the tenth place, or where we are rounding to! Since, the number after the tenth place is above 4, we are going to round the tenth place up :)
0.5835 cen. → 0.6 cen.
Hope this Helps! :)
Have any questions? Ask below in the comments and I will try my best to answer.
-SGO
The relation between degrees Fahrenheit F and degrees Celsius C is described by the function F = (9/5)C+32 In the following ordered pairs, the first element is degrees Celsius and the second element is its equivalent in degrees Fahrenheit. Find the unknown measure in each ordered pair.
c. (p,12)
5:9 is degrees Celsius and the second element is its equivalent in degrees Fahrenheit.
What does a temperature in Fahrenheit mean?
Water freezes at 32 degrees Fahrenheit and boils at 212 degrees Fahrenheit on the Fahrenheit scale, which is used to measure temperature. It is denoted by the °F sign. The temperature had risen to 100 degrees Fahrenheit by mid-morning.F = (9/5)C+32
F = C x 9/5 + 32
C = (F - 32) x 5/9
The above equations could easily be derived by the following relationships:
Freezing Point = 0C or 32F and Boiling Point = 100C or 212F
Range from freezing point to boiling point = 100C or 180F,
i.e. C : F = 100:180 = 5:9
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Briefly explain how to get the next term in the Fibonacci Sequence
PLS HELPP
Answer:
The Fibonacci sequence is defined by , for all , when and . In other words, to get the next term in the sequence, add the two previous terms. The notation that we will use to represent the Fibonacci sequence is as follows: f1=1,f2=1,f3=2,f4=3,f5=5,f6=8,f7=13,f8=21,f9=34,f10=55,f11=89,f12=144,…
A battery with 20% of its full capacity is connected to a charger. Every minute that passes, an
additional 5% of its capacity is charged. Graph
Answer:
25
Step-by-step explanation:
just count by five
then that your answer
tate whether each sentence is true or false. If false, replace the underlined word or phrase to make a true sentence.
Extended ratios can be used to compare three or more quantities.
Given statement 'Extended ratios can be used to compare three or more quantities.' is True.
We know that an extended ratios are ratios that compare more than two quantities.
If we're comparing values x, y and z, then we would express this using the extended ratio x : y : z.
For example, suppose a triangle has side lengths of 15, 45, and 10.
The extended ratio that compares the side lengths of the triangle is:
15 : 45 : 10
We can simplify this ratio by factoring each of 15, 45, and 10 and cancelling out any factors that are common to all three quantities.
(5 × 3) : (5 × 9) : (5 × 2)
5 is a common factor of all three quantities, so cancel it out.
3 : 9 : 2
Therefore, given statement 'Extended ratios can be used to compare three or more quantities.' is True.
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A group of hikers is descending the mountain at a rate of 250 feet per hour. What is the change in elevation of hiker after 4 hours?
Answer: 1000 ft
Step-by-step explanation:
Its pretty simple, 250 ft per hour, if they go for 4 hours theyll be at 1000 feet i guess
Answer:
1000 ft
Step-by-step explanation:
you multiple 250 by 4 and the is the change in elevation
Im begging y’all 33 to 36
Answer:
33a. 7^6
33b. 3^-4
34a. 6^4
34b. 11^0
34c. 5^4
35a. 144
36a. 5^7
36b. 2^8
36c. 3^7
give brainliest
Step-by-step explanation:
Using laws of indices
put all no to the same base
33a. 4+3-1 =6
7^6
33b.-2+8-10=-4
3^-4
34a. 7+2-5=4
6^4
34b. 2-1+3=4
11^4
34c. 6-2=4
5^4
35a. 3^2×4^2
9×16=144
35c. 5*2-6
10-6=4
3^4
36a. Remember 5^3=125
4+3=7
5^7
36b. 5+3=8
2^8
36c. 5+2=7
3^7
In question 35b, I don't think I know it but please give me brainliest.
Hope it helps, for more explanation ask in the comment section.
6/7 x (-3/13) + 3/13 - 3/13 x 8/7
[tex]\frac{6}{7} \times(\frac{-3}{13} )+\frac{3}{13}-\frac{( \frac{3}{13} \times8)}{7}[/tex]
By simplifying answer is [tex]\frac{-3}{13}[/tex] in decimals -0.230769
Here, we have done addition, subtraction, multiplication and division.
[tex]\frac{6}{7} \times(\frac{-3}{13} )+\frac{3}{13}-\frac{( \frac{3}{13} \times8)}{7}\\[/tex]
First, We will do Multiplication
Adding a number to itself as many times as the value of the other number is equivalent to multiplying two numbers by their sum.
[tex]\frac{-18}{91} +\frac{3}{13}-\frac{\frac{24}{13} }{7}[/tex]
Now, We will do the division
Basically, dividing is the act of dividing anything into equal sections or groups.
[tex]\frac{-18}{91} +\frac{3}{13}-\frac{24 }{91}[/tex]
Now, We will do the subtraction and Addition
When objects are collected together, addition, a mathematical operation, describes how many total items there are in the collection.
The reverse of adding in mathematics is called subtraction. When a specific number of objects from a group are removed, subtraction is used to determine how many objects are still present in the group.
[tex]\frac{3}{13}-\frac{6 }{13}\\\frac{-3}{13} \\[/tex]
Therefore, the simplified answer is [tex]\frac{-3}{13}[/tex] in decimals -0.230769.
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