The scale factor for the dilation that maps △ABC to △DEF is 0.75.
What is triangle?A triangle is a geometric shape that consists of three line segments that connect to form three angles. These angles always add up to 180 degrees. A triangle has three sides and three vertices (corners). Triangles can have different shapes and sizes, and they are often classified based on the length of their sides or the size of their angles. Some common types of triangles include equilateral triangles (where all sides are equal in length and all angles are equal to 60 degrees), isosceles triangles (where two sides are equal in length), and right triangles (where one angle is a right angle, or 90 degrees). Triangles have many properties and are an important part of geometry and mathematics.
Here,
To determine the scale factor for the dilation that maps △ABC to △DEF, we need to find the ratio of the corresponding side lengths of the two triangles.
Since △ABC ∼ △DEF, we know that the corresponding angles of the two triangles are congruent. Therefore, angle B in △ABC corresponds to angle E in △DEF, and angle A in △ABC corresponds to angle D in △DEF.
Using the Pythagorean theorem, we can find the length of the missing side of △DEF:
DF² = DE² + EF²
6² =DE² + 4²
DE=√20
DE=2√5 units
3/4=2/2√5=√13/6=0.75
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2.5b +5r = 80
The given equation describes the relationship
between the number of birds, b, and the number of
reptiles, r, that can be cared for at a pet care business
on a given day. If the business cares for 16 reptiles on
a given day, how many birds can it care for on this
day?
The number of birds they can take care on that day is zero.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, An expression 2.5b + 5r = 80.
Where, b represents the number of birds and r represents the number of reptiles.
On a given day. If the business cares for 16 reptiles, Therefore,
2.5b + 5(16) = 80.
2.5b + 80 = 80.
2.5b = 0.
So, They can not take care of any birds during the day.
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substitution y=2y-2 and y=2x-5y=1
Answer:
We can solve for y in the equation y = 2y - 2 by substituting y = 2x - 5.
Starting with y = 2y - 2, we substitute y = 2x - 5:
2x - 5 = 2(2x - 5) - 2
Expanding the right side:
2x - 5 = 4x - 12
Next, we isolate y by subtracting 2x from both sides:
-2x - 5 = 4x - 12
Adding 2x to both sides:
-5 = 6x - 12
Adding 12 to both sides:
7 = 6x
Finally, we divide both sides by 6 to solve for x:
x = 7/6
So, y = 2x - 5 = 2(7/6) - 5 = 7/3 - 5 = -14/3.
Therefore, y = -14/3 is the solution to the system of equations y = 2y - 2 and y = 2x - 5.
Step-by-step explanation:
Lin rolls a six-sided number cube then chooses one card from a deck of three cards numbered 1 through 3. What is the probability that the number cube and the card have the same number?
The probability that the number cube and the card have the same number is 2/39.
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
Given:
Outcomes of cube = { 1, 2, 3, 4, 5, 6}
Outcome of Card = {1, 2, 3} from each group.
So, we have three number both in common as {1, 2, 3}
So, the probability that the number cube and the card have the same number is
= 1/6 x 16/52
= 8/156
= 2/39
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HELP ! A phone company offers two monthly plans. Plan A costs $30 plus an additional $0.03 for each minute of calls. Plan B has no initial fee but costs $0.18 for each minute of calls. What is the cost when the two plans cost the same for a set number of minutes?
Group of answer choices
$100
$200
$36
$30
The cost when the two plans cost the same for a set number of minutes is $36. Option C is correct.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Plan A costs $30 plus an additional $0.03 for each minute of calls.
This can be expressed in equation as
y=30+0.03x
Plan B has no initial fee but costs $0.18 for each minute of calls.
y=0.17x
Now we have to find the cost when the two plans cost the same for a set number of minutes
30+0.03x=0.18x
30=0.18x-0.03x
30=0.15x
Divide both sides by 0.15
x=200
when the number of minutes of calls is 200, the two plans cost the same.
To find the cost when the two plans cost the same,
we can substitute x = 200 into either expression for Cost_A or Cost_B:
Cost_A = 30 + 0.03(200) = $36
Cost_B = 0.18(200) = $36
Therefore, the cost when the two plans cost the same for a set number of minutes is $36. Option C is correct.
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Change each algebraic fraction into an equivalent fraction with the denominator of 24a^3b^2.
The algebraic fraction which is an equivalent fraction with the denominator 24a^3b^2 is 15b/24a^3.
To find an equivalent fraction with the denominator 24a^3b^2, we need to find a common denominator for the two fractions 5b and 8a^3. This common denominator is 24a^3b^2.
To find an equivalent fraction for 5b, we can multiply both the numerator and denominator by the same factor to obtain the desired denominator. To do this, we need to find a factor that would give us a denominator of 24a^3b^2 when multiplied with 8a^3.
The factor that would give us a denominator of 24a^3b^2 is 3.
So, the equivalent fraction for 5b with the denominator 24a^3b^2 is (5b * 3)/(8a^3 * 3) = 15b/24a^3.
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Help m please,,,,,,,,,,,,
Answer:
-2
Step-by-step explanation:
?
Which choice is equivalent to the expression below?
√50 -√2
The simplified form of the expression √50 - √2 is 4√2.
What is the simplified form of the expression?Given the expression in the question;
√50 - √2
To evaluate, first we simplify each term
√50 - √2
Factor out 25 from 50
√( 25(2) ) - √2
Now, rewrite 25 as 5²
√( 5²(2) ) - √2
Take the square root of 5² to pull it out of the radical
5√2 - √2
Now, subtract √2 from 5√2
4√2
Therefore, the simplified form is 4√2.
Option C) 4√2 is the correct answer.
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HELP DUE TONIGHT!
Find the volume of a cone with a base diameter of 6 in and a height of 6 in. Write the exact volume in terms of , and be sure to include the correct unit in your answer.
The volume of the cone with a base diameter of 6in and height of 6in is 6π in³.
What is the volume of the cone?The volume of a cone is expressed as;
V = (1/3)πr²h
Where r is radius of the base, h is the height of the cone and π is constant pi.
Given the data in the diagram;
Diameter d = 6inRadius r = diameter/2 = d/2 = 6in/2 = 3inHeight h = 6Volume V = ?Plug the given values into the above formula and solve for the volume of the cone.
V = (1/3) × π × r² × h
V = (1/3) × π × ( 3in )² × 6in
V = 18π/3 in³
V = 6π in³
Therefore, the volume of the cone is 6π cubic inches.
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Please answer with the work shown
The area and the perimeter of the various given figures above are listed below:
1.) area=70 cm²
perimeter = 29cm
2. area= 80mm²
perimeter = 36mm
3.) area=108m²
perimeter = 42m
4.) area=72cm²
perimeter = 34cm
How to calculate the area and perimeter of the given figures above?For figure 1;
The area of the given figure = length×width.
Where;
Length = 7cm, width = 10
area = 7×10 = 70 cm²
The perimeter = summation of the whole sides.
= 10+7+5+4+3
= 29cm
For figure 2;
The area of the given figure = length×width.
Where;
Length = 8 mm; width = 10mm
area = 8×10 = 80mm²
The perimeter = 6+8+6+10+(8-6)+(10-6)
= 6+8+6+10+2+4
= 36mm
For figure 3;
The area of the given figure = length×width.
Where;
Length= 6+3 = 9m
width ,= 8+5 = 12m
area = 9×12 = 108m²
The perimeter: 2( 9+12) = 42m
For figure 4;
The area of the given figure = length×width.
Where;
Length= 8cm
width = 4+5 = 9cm
area = 8×9 = 72cm²
The perimeter = 6+4+5+8+(5+4)+(8-6)
= 6+4+5+8+9+2
= 34cm.
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How many feet apart is 535 and -8
Answer:
543 fee
Step-by-step explanation:
The difference between 535 and -8 is the distance between them, but it is not specified in what unit this distance should be measured. If you meant to find the difference in feet, then:
535 - (-8) = 535 + 8 = 543
So the distance between 535 and -8 in feet is 543 feet.
The Beach Shack rents boats for $60 the first hour and $30 each hour after that. The Surf
Shop rents boats for $40 an hour. At what number of hours are the rental fees for a boat
from each shop equal?
Answer:
After 3 hours.
Step-by-step explanation:
60 + 30x = y
40x = y
Beach Shack:
60, 90, 120, 150, 180, 210
Surf Shop:
40, 80, 120, 160, 200
How to create the great paper outline templete?
First we need to select the subject to create the great paper outline template. Then follow the steps to create a paper.
Step 1: Choose the topic for the paper.
Step 2: Make a list of all the concepts you wish to discuss or incorporate.
Step 3: Separate similar concepts into smaller groupings.
Step 4: Put your concepts in order of importance: What ought the reader to discover first? What matters the most? Which conclusion will best suit your paper?
Step 5: Make good headers and subheadings for your documents.
Step 6: Format the outline in decimal, full-sentence, or alphanumeric form.
Step 7: State and review the paper by oneself first.
Follow all the steps to create the great paper outline template.
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find the angle of a sector if the radius is 14cm and area of the circle is 462cm^2
Answer: its 270.1087 degrees
Step-by-step explanation:
if the number of bacteria in a colony doubles every 384 hours and there is currently a population of 2,150 bacteria, what will the population be 1,152 hours from now?
The population be 1,152 hours from now will be 17200
What is exponential growth?Exponential growth is a process of increasing a quantity over time. It occurs when the rate of change of a quantity with respect to time is proportional to the itself.
Given that, the number of bacteria in a colony doubles every 384 hours and there is currently a population of 2,150 bacteria,
The exponential growth law for this problem is :-
p(t) = 2150(2)ⁿ/₃₈₄
where t is in hours. Plug t = 1152 into the equation and evaluate.
p(1152) = 2150(2)¹¹⁵²/₃₈₄
= 2150(2)³
= 17200
Hence, the population be 1,152 hours from now will be 17200
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the line pot shows the weight of 10 eggs laid by one head what is the total weight and an ounces of the four heaviest eggs
The total weight of the four heaviest eggs, in ounces, is 8 ³ / ₄ ounces .
How to find the total weight ?Given the line plot, the weights of the heaviest eggs are :
2 ¹ / ₂ , 2 ¹ / ₄ , 2, 2
This is because these are the highest numbers on the line plot.
The total weight of these four heaviest eggs is :
= 2 ¹ / ₂ + 2 ¹ / ₄ + 2 + 2
= 4 ³ / ₄ + 4
= 8 ³ / ₄ ounces
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Michelle sells ice cream bars at the beach. In addition to a fixed salary, she earns a commission for each ice cream bar she sells. The table shows Michelle's total earnings, y, from selling x bars of ice cream:
Ice Cream Sales and Earnings
Number of Bars Sold (x) Total Earnings (dollars) (y)
0
50
1
56
2
62
3
68
Which equation best shows the relationship between x and y? (1 point)
y = x + 50
y = 6x + 50
y = 6x + 56
y = x + 56
Answer:
y= 6x+50
Step-by-step explanation:
y= 6x+50
tell me the answer please how many students are vegetarian
Answer:
2 boys must be vegetarian.
If all 34 girls were vegetarian, there would have to be 2 boys to add up to 36.
Find the measure of
A. 63
The angle shown is 90 degrees, if you take 90 and subtract 27 you get 63.
What is 7 Roman numbers?
Answer:
VII
Step-by-step explanation:
HELP DUE TONIGHT!
Find the volume of a cone with a base radius of 4 m and a height of 12 m. Write the exact volume in terms of , and be sure to include the correct unit in your answer.
The volume of the cone is 64π
How to determine the volume of teh coneFrom the question, we have the following parameters that can be used in our computation:
Height, h = 12 m
Radius, r = 4 m
The volume is calculated s
V = 1/3πr²h
Substitute the known values in the above equation, so, we have the following representation
V = 1/3π * 4² * 12
Evaluate
V = 64π
Hence, the volume is 64π
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Hitler traveled 75 kilometers in 90 minutes. If he travels at the same speed, how
many kilometers would Hitler cover in 30 minutes?
A.20
B.24
C.25
D.30
Step-by-step explanation:
You can make a ratio. Put the first part of the question together and put the second part together.
[tex] \frac{75}{90} = \frac{x}{30} [/tex]
Next we cross multiply
[tex](75)(30) = 90x[/tex]
[tex]2250 = 90x[/tex]
Lastly we divide by 90
[tex]x = 25[/tex]
ILL GIVE BRAINLIEST PLS HELP The stem-and-leaf plot displays the distances that a heavy ball was thrown in feet.
2 0, 2, 5
3 1, 3, 4
4 1, 1, 5
5 0, 6
6 7
Key: 3|1 means 3.1
What is the mean, and what does it tell you in terms of the problem?
3.1 feet; The value means the furthest the ball went.
3.875 feet; The value means that a typical throw of the ball results in 3.875 feet.
4.1 feet; The value means this measurement had the most occurrences.
4.65 feet; The value means that a typical throw of the ball results in 4.65 fe
The mean distance that the ball was thrown is approximately 38.92/12 = 3.24 feet.
Ball throwing distancesTo find the mean distance that the heavy ball was thrown, we need to calculate the sum of all the distances and then divide by the total number of throws:
(20+25+25+31+33+34+41+41+45+50+56+67)/12 = 467/12 ≈ 38.92
So, the mean distance that the ball was thrown is approximately 38.92/12 = 3.24 feet.
This means that on average, the ball was thrown a distance of 3.24 feet. However, it's important to note that the mean can be influenced by outliers, which in this case is the one throw of 6.7 feet.
So, while the mean is a useful measure of central tendency, it's important to also consider other measures such as the median and mode to get a complete picture of the data.
The mean is the sum of all the values in a dataset divided by the total number of values. It provides an estimate of the central location of the data and can be a useful summary statistic for describing a dataset. However, the mean can be influenced by outliers, which are values that are significantly different from the rest of the data.
In this case, the one throw of 6.7 feet is an outlier because it is much further than any other throw, and it will increase the mean value.
For this reason, it's important to consider other measures of central tendency such as the median and mode. The median is the middle value in a dataset, and it's not affected by outliers. The mode is the value that appears most frequently in a dataset and can provide useful information about the typical or most common value in the data.
By considering all three measures (mean, median, and mode), we can get a more complete picture of the data and make better inferences or conclusions about it.
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Reese wants the find the equation of the line that passes through the point (-4, 8) and has a slope of 3. Help her complete the work below.
Reese will first need to use _______ Formula to plug in ________ for x1
, ________ for y1, and ________ for the m
. Reese's final answer will be _________, which is written in _________ Form.
Answers:
A. Slope
B. 3
C. y=3x+20
D. Standard
E. -4
F. y=3x+12
G. Slope Intercept
H. Point Slope
I. 8
J. y=3x+4
Answer:
Reese will first need to use point slope Formula to plug in- 4 for x1, 8 for y1, and 3 for the m
Reese's final answer will be y = 3x + 20, which is written in slope intercept Form.
Step-by-step explanation:
The answers in terms of the choices and order in which the blanks appear are
H. Point Slope
E. -4
I. 8
B. 3
C. y=3x+20
G. Slope Intercept
The point slope form for a line
y - y1 = m(x - x1)
Pugging in x1 = -4, y1= 8 and m = 3 gives
y -8 = 3(x - (-4))
y - 8 = 3x + 12 Move -8 to right side
y = 3x +12 + 8
y = 3x + 20
HELP PLEASE i need the answer for as may as possible o have done the first two!!( A1 and A2) WITH AN EXPLANATION PLEASE IM SO CONFUSED
1. The values of x in the equation are 1 and 10.
2. The values of x are 1 and -4.
How to calculate the valuesAn equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.
1. y = x²
y = 11x - 10
Combine both variables
x² - 11x + 10
x² - x - 10x + 10
x(x - 1) - 10(x - 1)
x - 10 and x - 1 = 0
x = 10 and 1
2. y = x².
y + 3x = 4
x² + 3x - 4
x² +4x - x - 4
x(x + 4) - 1(x + 4)
(x - 1)(x + 4)
x = 1 and -4
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what is 1.18x4?
PLEASE I NEED HELP
Answer:
4.72
Step-by-step explanation:
for essy calculation remove the decimal point
[tex] \frac{0.18}{100} [/tex]
=
[tex] \frac{18}{100} [/tex]
then multiply by 4
you will get
[tex] \frac{18 }{25} [/tex]
= 4.72
Compare / Contrast Exponential Equations
1.) 2 (1/5)x-5
2.) y=4x
The intersection point of the exponential and linear equation is at (3.748, 14.993).
What is the solution to the equation?An answer to a formula is any variable value that fulfills the equal outcomes, that is, it tends to make the Left Hand Side (LHS) and Right Hand Side (RHS) of the formula equal. To solve an equation, you must locate the feasible solution) to that formula.
The equations are given below.
[tex]\rm y = 2 \left ( \dfrac{1}{5} \right )^{x - 5}[/tex]
The graph of the exponential equation is drawn.
y = 4x
The graph of the linear equation is also drawn.
From the graph, the intersection point of the exponential and linear equation is at (3.748, 14.993).
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please help! it’s pretty easy I just am confused!
Answer:
since p is irrational it is not expressible as a ratio of two integers and has an infinite and nonrecurring expansion when expressed as a decimal
Step-by-step explanation:
so a
Camilla took a $23,500 secured auto loan that
allows her to make no payments for 18
months. If interest is still compounded
monthly at a rate of 6.3%, what will her
balance be in 18 months when she starts
making payments?
The graph shows a scuba diver's ascent over time. Use the graph to write an equation in slope-intercept
form that represents the diver's depth over time.
The equation that represents this situation is
The equation that represents the situation is m= 1/8s-10
What is a Graph?In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.
When
s= 0, m= -10
When
s= 80, m= 0
[tex]\frac{0-(0-10)}{80-0} = \frac{10}{80} = \frac{1}{8}[/tex]
m-0 = 1/8(s-80)
m= 1/8s-10. The equation
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Find the side length of a square with diagonals 18 cm long.
Answer:
162cm²
Step-by-step explanation:
Formula of square with diagonals=1/2*d²
=1/2*(18)²
=1/2*324cm²
we get,
=162cm²