Answer:
Question 32
Scale Factor = 3/8Ratio of Perimeters = 8 : 3Ratio of Areas = 64 : 9Area of smaller figure = 144 mm²Question 33
Scale Factor = 10/7Ratio of Perimeters = 7 : 10Ratio of Areas = 49 : 100Area of smaller figure = 196 in²Step-by-step explanation:
Scale Factor: A number used as a multiplier when scaling an object.
Perimeter: The total distance around the outside of a 2D shape.
Area: The space occupied by a flat shape, measured in two dimensions.
Question 32Scale Factor
To find the scale factor from the shaded figure to the unshaded figure, divide the given side length of the unshaded figure by the given side length of the shaded figure:
\(\implies \sf \dfrac{unshaded}{shaded}=\dfrac{9}{24}=\dfrac{3}{8}\)
Ratio of Perimeters
Perimeters are measured in one dimension (length). To find the ratio of the perimeters, divide the given side length of one figure by the given side length of the other:
\(\sf \implies\dfrac{shaded}{unshaded}=\dfrac{24}{9}=\dfrac{8}{3}\)
Therefore:
\(\sf \implies shaded:unshaded=8:3\)
Ratio of Areas
Area is measured in two dimensions. To find the ratio of the areas, divide the square of the given side length of one figure by the square of the given side length of the other:
\(\sf \implies\dfrac{shaded}{unshaded}=\dfrac{24^2}{9^2}=\dfrac{64}{9}\)
Therefore:
\(\sf \implies shaded:unshaded=64:9\)
Area of the smaller figure (unshaded)
Area of shaded figure = 1024 mm²
Let x = area of unshaded figure
Use the ratio found above:
\(\begin{aligned}\implies \sf \dfrac{shaded\:area}{unshaded\:area} & =\sf \dfrac{64}{9}\\\\\sf \dfrac{1024}{x} & =\sf \dfrac{64}{9}\\\\\sf 1024 \cdot 9 & = \sf 64x\\\\\sf x & = \sf \dfrac{1024 \cdot 9}{64}\\\\\implies \sf x & = \sf 144\:\:mm^2\end{aligned}\)
Question 33Scale Factor
To find the scale factor from the shaded figure to the unshaded figure, divide the given side length of the unshaded figure by the given side length of the shaded figure:
\(\implies \sf \dfrac{ushaded}{shaded}=\dfrac{20}{14}=\dfrac{10}{7}\)
Ratio of Perimeters
Perimeters are measured in one dimension (length). To find the ratio of the perimeters, divide the given side length of one figure by the given side length of the other:
\(\sf \implies\dfrac{shaded}{unshaded}=\dfrac{14}{20}=\dfrac{7}{10}\)
Therefore:
\(\sf \implies shaded:unshaded=7:10\)
Ratio of Areas
Area is measured in two dimensions. To find the ratio of the areas, divide the square of the given side length of one figure by the square of the given side length of the other:
\(\sf \implies\dfrac{shaded}{unshaded}=\dfrac{14^2}{20^2}=\dfrac{49}{100}\)
Therefore:
\(\sf \implies shaded:unshaded=49:100\)
Area of the smaller figure (shaded)
Area of unshaded figure = 400 in²
Let x = area of shaded figure
Use the ratio found above:
\(\begin{aligned}\implies \sf \dfrac{shaded\:area}{unshaded\:area} & =\sf \dfrac{49}{100}\\\\\sf \dfrac{x}{400} & =\sf \dfrac{49}{100}\\\\\sf x& = \sf \dfrac{400 \cdot 49}{100}\\\\\implies \sf x & = \sf 196\:\:in^2\end{aligned}\)
May I have help on This question I’ll give you brainliest
Answer: 460 miles is the answer ( give me brainliest thanks)
look at the image for the solution
Step-by-step explanation:
What is the image of H (-2,6) after the translation defined by (x,y)—> (x+2y, y-1)
Answer:
H'(10,5)Step-by-step explanation:
GivenPoint H(-2, 6)Translation rule (x, y) → (x + 2y, y -1)SolutionImage of H is H' with coordinates of:
x → -2+2*6 = -2 + 12 = 10y → 6 - 1 = 5H'(10,5)An automobile purchased for $38000 is worth $2300 after 7 years. Assuming that the car's value depreciated steadily from year to year, what was it worth at the end of the third year?
The value 3 years after it was purchased is
Answer:
11422.46
Step-by-step
2300=38000x⁷
x=.669872323
38000*.669872323³=11422.4614
The expected probability of rolling an even number in 1 roll of a fair cube with faces numbered 1 through 6 is 1/2.
When the cube was rolled 20 times, an even number came up 15 times, or 3/4 of the time. When the same cube was rolled 100 times, an even number came up 51 times, or almost 1/2 the time. Why are the actual results closer to the expected probability of 1/2 when rolling the cube 100 times?
Select one:
a. A larger sample size was used.
b. The 100 tosses were controlled better.
c. The expected probability changed when the cube was rolled 100 times.
d. The thrower considered only the even rolls, and disregarded the odd rolls.
After considering the given set of options we conclude that a large sample was used in the evaluation, which means the correct option is Option A.
1/2 is the evaluated expected probability for the given case under the condition that when the die was rolled an even number came out with face number 1 out of 6.
In the event that the cube was rolled 20 times, an even number came up 15 times, or 3/4 of the time. Now the same cube was again rolled 100 times, an even number came up on the recent throw which showed 51 times even, or almost 1/2 the time.
Therefore we can say that the actual results are closer to the expected probability of 1/2 when rolling the cube 100 times because a larger sample size was used.
Hence we are dealing with larger sample size, this means that the actual results will be much closer to the expected probability.
This is due to the law of large numbers which states that as the sample size increases, the average of the results will get closer and closer to the expected value .
Therefore, option (a) is correct.
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i need some help asap no rocky
Answer:
This is way out of my level sorry. Thanks me
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
math
The equation C = 75h + 29 represents the total
cost, C, to rent a boat for h hours. If Greg
rented a boat at 7:30 a.m. and paid $385.25
for the rental, what time did he return the
boat?
The line plots represent data collected on the travel times to school from two groups of 15 students.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 4,6,14, and 28. There are two dots above 10, 12, 18, and 22. There are three dots above 16. The graph is titled Bus 47 Travel Times.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 8, 9,18, 20, and 22. There are two dots above 6, 10, 12,14, and 16. The graph is titled Bus 18 Travel Times.
Compare the data and use the correct measure of variability to determine which bus is the most consistent. Explain your answer.
Bus 18, with an IQR of 16
Bus 47, with an IQR of 24
Bus 18, with a range of 16
Bus 47, with a range of 24
The bus that is the most consistent, given the data collected on travel times to school from two groups of students is C Bus 18, with a range of 10
How to find the consistent bus ?To determine which bus is the most consistent, we should use the interquartile range (IQR) as the measure of variability. The IQR measures the spread of the middle 50% of the data, which makes it less sensitive to outliers compared to the range.
Bus 47:
Median (Q2): 16
Q1: 10
Q3: 22
IQR = Q3 - Q1 = 22 - 10 = 12
Bus 18:
Median (Q2): 12
Q1: 8
Q3: 18
IQR = Q3 - Q1 = 18 - 8 = 10
Bus 18 has a smaller IQR than Bus 47 (10 vs. 12), which means the travel times for Bus 18 are more consistent.
Note: Figures might be different due to options being for different variant but Bus 18 is the most consistent.
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4x + 5 + 5x + 6 = 29. Whats X?
Answer:
9x
Step-by-step explanation:
the full answer is 9x+11=29
Answer:
X=2
Step-by-step explanation:
Add the numbers
4+5+5+6=29
4x+{\color{#c92786}{5}}+5x+{\color{#c92786}{6}}=29
4x+5+5x+6=294+11+5=29
4x+{\color{#c92786}{11}}+5x=29
4x+11+5x=29
Combine like terms
Subtract
1
1
11
11
from both sides of the equation
Simplify
Divide both sides of the equation by the same term
Simplify
Solution
=
2
2
Let g(x) = x + 4x-7.
What is g(x) in graphing form?
(x + 2) - 7 = 4
O g(x) = (x + 2)²-7
Onone of the answer choices
x² + 4x-7=0
O g(x) = (x + 2)² - 11
The graphing form of the function g(x) is: C) none of the answer choices.
The function g(x) = \(x^2 + 4x - 7\)is already in the standard form of a quadratic equation. In graphing form, a quadratic equation can be represented as y =\(ax^2 + bx + c,\) where a, b, and c are constants.
Comparing the given function g(x) =\(x^2 + 4x - 7\)with the standard form, we can identify the coefficients:
a = 1 (coefficient of x^2)
b = 4 (coefficient of x)
c = -7 (constant term)
Therefore, the graphing form of the function g(x) is:
C) none of the answer choices
None of the given answer choices (A, B, D, or E) accurately represents the graphing form of the function g(x) =\(x^2 + 4x - 7\). The function is already in the correct form, and there is no equivalent transformation provided in the answer choices. The given options either represent different equations or incorrect transformations of the original function.
In graphing form, the equation y = \(x^2 + 4x - 7\) represents a parabolic curve. The coefficient a determines the concavity of the curve, where a positive value (in this case, 1) indicates an upward-opening parabola.
The coefficients b and c affect the position of the vertex and the intercepts of the curve. To graph the function, one can plot points or use techniques such as completing the square or the quadratic formula to find the vertex and intercepts. Option C
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Which graph represents the function f (x) = StartFraction 1 Over x EndFraction minus 1?
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 0, and the horizontal asymptote is at y = 1.
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 1, and the horizontal asymptote is at y = 0.
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = negative 1, and the horizontal asymptote is at y = 0.
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 0, and the horizontal asymptote is at y = negative 1.
Mark this and return
The correct answer is Option C. The graph represents the function f (x) = StartFraction 1 Over x EndFraction minus 1 is On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = negative 1, and the horizontal asymptote is at y = 0.
On a coordinate plane, the graph of a hyperbola is shown.
In quadrant 1, one curve opens up and to the right, while in quadrant 3, the other curve opens down and to the left.
The vertical asymptote is at x = -1, and the horizontal asymptote is at y = 0. This hyperbola is symmetrical across both the x and y axes.
The function f(x) = 1/x - 1 has a vertical asymptote at x = 0 because the denominator approaches zero as x approaches zero.
A fraction with a denominator of zero cannot exist.
The horizontal asymptote of this function is y = -1 because as x approaches infinity or negative infinity, f(x) approaches -1.
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fill in the mission numbers to make the fractions equivalent. 1/2 and /8= 4/12 and /60= 2/3 and /12= 4/4 and /8=
To make the fractions equivalent, we need to find the missing numerators that would make them equal. Let's fill in the missing numerators:
1/2 and __/8
To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 4:
1/2 and 4/8
Now, the fractions are equivalent.
---
4/12 and __/60
To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 5:
4/12 and 20/60
Now, the fractions are equivalent.
---
2/3 and __/12
To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 4:
2/3 and 8/12
Now, the fractions are equivalent.
---
4/4 and __/8
To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 2:
4/4 and 8/8
Now, the fractions are equivalent.
In the equation 11z = 66 - 11, what is the next step in the equation solving sequence?
In the equation 11z=66-11, what is the next step in the equation solving sequence?
Two possibilities: You can subtract 66–11 then divide both sides by 11 OR you can divide both sides by 11 and do the subtraction as 6–1. I would usually do it the first way, but some might prefer the second.
how would i anwser this? help pls!
Answer:
Step-by-step explanation:
To get the y values all you need to do is substitute the x value in the equation y=-2/3x+7.
For example:
y=-2/3(-6)=7
-2/3x6=-4
-4+7=3
(-6,3)
You can double check your work by filling the x and y coordinates in the equation and when solved if it it true you know you were correct.
To get the x value, you need to fill in the y in the equation y=-2/3x+7
for example:
5=-2/3x+7
-2=-2/3x
3=x
(3,5)
y=-2/3x+7
y=-2/3(15)+7
y=-10+7
y=-3
(15,-3)
y=-2/3x+7
15=-2/3x+7
8=-2/3x
-12=x
(-12,15)
As a technical engineer, you must calculate the elevation of a Point marked on a topographic map. The distance between the 420-foot and 440-foot contour lines is 0.5 inches, and the marked point between them is 0.2 inches from the 420-foot contour. What is the elevation, in feet, of the marked point?
A.100
B.424
C.428
D.430
E432
Answer:
The correct answer is C, 428 feet.
To calculate the elevation of the marked point, we need to interpolate between the two contour lines. The difference in elevation between the two contour lines is 20 feet (440 - 420 = 20). And since the distance between the two contour lines is 0.5 inches, each 0.1 inch increment represents a 4-foot change in elevation (20 feet ÷ 0.5 inches = 40 feet per inch ÷ 10 = 4 feet per 0.1 inch).
Since the marked point is 0.2 inches from the 420-foot contour, the elevation of the marked point can be calculated by adding 8 feet (4 feet x 0.2 inches) to the 420-foot contour line: 420 + 8 = 428 feet.
The amount Troy charges to mow a lawn is proportional to the time it takes him to mow the lawn. Troy charges 30 to mow a lawn that took him 1.5 hours to mow.
Which equation models the amount in dollars, d, Troy charges when it takes him h hours to mow a lawn?
The amount Troy (D, in dollars) charges to mow a lawn is proportional to the time (H, in hours) it takes him to mow the lawn.
Hence, we can write \(\text{D = kH}\) ......... (1), where k is a constant.
Now, given that Troy charges $30 to mow a lawn that took him 1.5 hours to mow.
So, from equation (1) we get
\({30 = 1.5\text{k}\)
\(\rightarrow \text{k = 20}\).
Therefore, equation (1) becomes
\(\boxed{\bold{D = 20H}}\) (Answer)
Sergey is solving 5x2 + 20x – 7 = 0. Which steps could he use to solve the quadratic equation by completing the square? Select three options. 5(x2 + 4x + 4) = –7 + 20 x + 2 = Plus or minus StartRoot StartFraction 27 Over 5 EndFraction EndRoot 5(x2 + 4x) = 7 5(x2 + 4x + 4) = 7 + 20 5(x2 + 4x) = –7
The steps Sergey could use to solve the quadratic equation by completing the square is 5(x2 + 4x) = –7
How to use the completing the square method?We should know that in completing the square method both sides of the equation are made perfect squares.
The given equation is 5x²+20x-7=0
Solving this equation by completing the square method we have
5(x²+4x+4)=-7
This means that (x+2)=±√27/5
Simplifying further we have
5(x²+4x)=7
Then expanding to make ²HS a perfect square we have
5(x²+4x+4)=7+20
This means that 5(x²+4x)=-7
Therefore the step he could use is 5(x²+4x)=-7\
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At a local high school, 40% of the students drink soda regularly, 30% of the students drink coffee regularly, and 10% of the students drink both regularly. If a
student is randomly selected from this school, what is the probability that the student drinks soda or coffee regularly?
A. 70%
B. 20%
C. 80%
D. 60%
Answer:
c he is your answer dear friend♀️♀️
Probability that the student drinks soda or coffee regularly is 60%
Option D is correct
Percentage of students that drink soda regularly, P(s) = 40%
Percentage of the students that drink coffee regularly, P(c) = 30%
Percentage of students that drink both coffee and soda regularly,
P(s and c) = 10%
Percentage of students that drink coffee or soda regularly is:
P(s or c) = P(s) + P(c) - P(s and c)
P(s or c) = 40 + 30 - 10
P(s or c) = 70 - 10
P(s or c) = 60
Probability that the student drinks soda or coffee regularly is 60%
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54. f(x) = ln (x + 1)
What is the end behavior?
The function end behavior of ln(x + 1 ) is \(\quad \mathrm{as}\:x\to \:+\infty \:,\:f\left(x\right)\to \:+\infty \:\)
How to determine the end behavior of the functionFrom the question, we have the following parameters that can be used in our computation:
f(x) = ln(x + 1)
The end behavior of a function f(x) describes the behavior of the function as x approaches \(+\infty\) and as :x approaches \(-\infty\)
Calculate f(∝) and f(-∝)
So, we have
f(∝) = ln(∝ + 1) = +∝
f(-∝) = ln(-∝ + 1) = +∝
Using the above as a guide, we have the following:
The function end behavior of ln(x + 1 ) is \(\quad \mathrm{as}\:x\to \:+\infty \:,\:f\left(x\right)\to \:+\infty \:\)
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Two bicycle trails were developed in a new housing development. One trail is
3 1/2 miles long. The other trail is 3/4 as long. How long is the second trail?
The length of the second trial will be equal to 2(⁵/₈) miles.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that two bicycle trails were developed in a new housing development. One trail is 3¹/₂ miles long. The other trail is 3/4 as long.
The length of the second trial will be calculated as,
Length = 3/4 x ( 3¹/₂ )
Length = 2(⁵/₈)
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PLEASE HELP! SHOW YOUR WORK. DON’T PUT A LINK AS AN ANSWER!
A 32 ounce bag of brown rice costs $3.49 cents. What is the price per ounce? ( be sure to round to the nearest cent - or the hundredths place)
Answer:
9.2
Step-by-step explanation:
When you divided 32 by 3.49 you get 9.16905444126. Look at the second number after the decimal you see that it's bigger than 5, so you round the number before that up.
When you round 2 up, it goes to 2. So your answer is 9.2
using 0-9 as digits,
which 2 digit number has order rotational of 2
which 3 digit number also has order rotational of 2
The value of 2 digit number has order rotational of 2 is, 16
And, The value of 3 digit number has order rotational of 2 is, 931
Now, For a two-digit number with an order rotational of 2, it means that if you flip the digits, you get a different but still valid number.
Hence, There are a few such numbers, but one example is 16 which becomes 61 when you flip the digits.
And, For a three-digit number with an order rotational of 2, it means that if you rotate the digits, you get a different but still valid number.
And, There are also a few such numbers, but one example is 319 which becomes 931 when you rotate the digits.
Thus, The value of 2 digit number has order rotational of 2 is, 16
And, The value of 3 digit number has order rotational of 2 is, 931
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Please help!!!! I will give points to correct answer !!!
The equation that shows the Pythagorean identity is true for θ = 270° and is in the form sin²θ + cos²θ = 1 is option B. 0² + (-1)² = 1
The Pythagorean identity is a fundamental trigonometric identity that relates the sine and cosine functions. It states that for any angle θ, the sum of the squares of the sine and cosine of that angle is equal to 1: sin²θ + cos²θ = 1.
We are given θ = 270° and we need to select the equation that satisfies the Pythagorean identity in the given form.
Let's evaluate each option:
A. 0² + 1² = 1
In this case, sin²θ = 0² = 0 and cos²θ = 1² = 1. Adding them together, we get 0 + 1 = 1, which satisfies the Pythagorean identity.
B. 0² + (−1)² = 1
Here, sin²θ = 0² = 0 and cos²θ = (−1)² = 1. Adding them, we have 0 + 1 = 1, which satisfies the Pythagorean identity.
C. (−1)² + 0² - 1
In this equation, sin²θ = (−1)² = 1 and co
s²θ = 0² = 0. However, the equation does not satisfy the Pythagorean identity because 1 + 0 - 1 ≠ 1.
D. 1² + 0² = 1
For this option, sin²θ = 1² = 1 and cos²θ = 0² = 0. Adding them together, we get 1 + 0 = 1, which satisfies the Pythagorean identity.
Based on our evaluation, options A and B both satisfy the Pythagorean identity for θ = 270°. Therefore, either A or B can be selected as the correct equation.The correct answer is b.
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The Question was Incomplete, Find the full content below :
Which equation shows that the Pythagorean identity is true for θ = 270°?
Select the equation that is in the form sin²θ+ cos²θ = 1.
A. 0² + 1² = 1
B. 0² + (−1)² = 1
C. (-1)² + 0² - 1
D. 1² + 0² = 1
First one to answer gets brainlest
Square root of 42.25
Answer:
Square root of 42.25 is 6.5
The square root of 42.25 is 6.5.
To find the square root of 42.25, we need to determine the number that, when multiplied by itself, equals 42.25. In this case, the square root of 42.25 is 6.5 because 6.5 multiplied by itself (6.5 x 6.5) equals 42.25.
Mathematically, it can be represented as:
√42.25
= 6.5
The square root (√) is the inverse operation of squaring a number.
When we square a number, we multiply it by itself.
In this case, squaring 6.5 (6.5 x 6.5) gives us the original value of 42.25.
Therefore, the square root of 42.25 is 6.5.
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Is this correct or not?
If not please provide correct answer
Answer:
It is correct please I do not want yo sound rude can you give me brainliest answer.
Answer:
correct steps
Step-by-step explanation:
if asked to find angles in terms of the ratios, then don't forget to shift sin / cos / tan across the equal sign and change it to arc sin / cos / tan.
Type your answer into the box and choose the correct answer. Gifts are packaged in cylinders. Each cylinder is 12 cm high with a diameter of 8 cm. Calculate the volume of each cylinder. Use 3 as a value for TT Give your answer using the correct units. Select...
Answer:
volume of a cylinder
V= TTr² h
V= volume
TT= pie
h= height
Step-by-step explanation:
Note: radius is 2times diameter ... if you are given diameter and to convert to radius, divide the diameter by 2
V=TTr²h
r= 8/2 =4cm
V= 3×4²×12
V=3×16×12=576cm³
can anyone help me identify the center and radius on these 3 pls , brainly
Answer:
See below
Step-by-step explanation:
Circle equation standard form
(x-h)^2 + ( y-k)^2 = r^2 h, k is the center
All are centered at 0,0
radii are sqrt(225) = 15 sqrt 49 = 7 and sqrt 178
The slope is 60. It represents the rate at which the amount of water changes each hour.
True
False
Answer:
True
Step-by-step explanation:
Slope:
The slope of an equation represents how the y value changes as the x values changes, defined as: \(\frac{\text{change in y}}{\text{change in x}}\), so the slope of 60 can be represented as: \(\frac{60}{1}\), which tells us the amount of water (y-axis) increases by 60 units each hour (x-axis), or in other words, the rate at which the amount of water changes each hour.
What number needs to be added to both sides of the equation to complete the square?
x^2−3x=10
Enter your answers in the boxes.
x^2−3x + ?= 10 + ?
Answer:
10.444444444 OR 10.44 dots above 44
Step-by-step explanation:
(x-2/3)^2 = 10 (x-2/3)^2 = - 0.444444444 10- - 0.444444444 = 10+ 0.444444444 = 10.444444444
find the size of angle x
Answer: 14 is bigger than 8 and x is smaller than 8 so x would be a small number, i bet that x is = to 3 cm
Step-by-step explanation:
I don't know for SURE though :)