The hole for the function f(x) = √(x-2) is x < 2.
What is a function?A function has an input and an output.
A function can be one-to-one or onto one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
A hole in a graph refers to a point where a function is undefined or missing.
Now,
f(x) = √(x-2)
Now,
To determine where this function is undefined, we need to consider the domain of the function, which is the set of all possible values of x that can be input into the function.
Since the square root function is defined only for non-negative numbers, The expression inside √(x-2) must be greater than or equal to zero:
i.e
x - 2 ≥ 0
Solving for x.
x ≥ 2
Therefore,
The function f(x) = √(x-2) is undefined for any value of x that is less than 2.
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The complete question.
what is the hole for this equation f(x) = √(x-2)?
Question: 7) How many significant figures are in the measured number 0.00208 m? A) six B) two C) three D) four E)
Number of significant figures are in the measured number 0.00208 m is option (C) three
The significant figures in a measured number are the digits that carry meaning or contribute to the precision of the measurement. In general, significant figures include all non-zero digits and any zeros between non-zero digits.
In this case, the measured number is 0.00208 m. The first two zeros in this number are not significant because they are only placeholders to indicate the decimal point's position. The first significant digit is 2, which is followed by two more significant digits, 0 and 8. Therefore, there are three significant figures in the measured number.
Therefore, the correct option is (C) three
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The height of an arch is modeled by the equation y=-x^(2)-6x+16. Which of the following gives the width of the arch at its base?
Answer:
Para encontrar el ancho del arco en su base, necesitamos encontrar las dos raíces de la ecuación cuadrática y = -x^2 - 6x + 16, que corresponden a los puntos donde la altura del arco es igual a cero.
Vaina
y = -x^2 - 6x + 16
0 = -x^2 - 6x + 16
x^2 + 6x - 16 = 0
Podemos resolver esta ecuación usando la fórmula cuadrática:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
donde a = 1, b = 6 y c = -16.
x = (-6 ± sqrt(6^2 - 4(1)(-16))) / 2(1)
x = (-6 ± sqrt(100)) / 2
x = (-6 ± 10) / 2
Esto nos da dos soluciones posibles:
x1 = (-6 + 10) / 2 = 2
x2 = (-6 - 10) / 2 = -8
La base del arco se extiende desde x = -8 hasta x = 2, por lo que el ancho del arco en su base es:
ancho del arco = 2 - (-8) = 10
Por lo tanto, el ancho del arco en su base es 10.
Step-by-step explanation:
espero te sirva, si no puedes español traducelo
The height h of the triangle is 8cm greater than its corresponding base. HELP PLSSS
The area of the triangle is 120 square centimeters.
A = 120 cm².
What is the area?The area is the amount of area occupied by an object's flat (2-D) surface or shape.
The area of the triangle = 1/2 x base x height.
Given:
The height h of the triangle is 8cm greater than its corresponding base.
That means
the height = 20 + 8 = 20 cm.
The area of the triangle,
= 1/2 x base x height
= 1/2 x 12 x 20
= 120 square centimeters.
Therefore, the area is 120 square centimeters.
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Express tan V as a fraction in simplest terms.
U
21
T
35
The value of tan V as a fraction in its simplest terms is 4/3.
What is the value of tan V?The figure in the image is a right triangle.
Angle θ = V Adjacent to angle V = 21Opoosite to angle V = UTtan V = ?First, we determine side UT using pythagoras theorem
UT = √( 35² - 21² )
UT = √784
UT = 28
Hence, using trigonometric ratio
Tangent = Opoosite / Adjacent
tanV = UT / UV
tanV = 28/21
tanV = 4/3
Therefore, the value of tanV is 4/3.
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What types of earned and unearned income do you think you'll have in 10 years?
Unearned income may vary depending on investment performance, interest rates, and changes in government policies.
What is Income?Income is the consumption and saving opportunity gained by an entity within a specified timeframe, which is generally expressed in monetary terms.
In 10 years, an individual's earned and unearned income may vary greatly depending on their career and investment choices, economic conditions, and personal circumstances.
Some individuals may see increases in earned income as they gain more experience or take on higher-paying positions, while others may see fluctuations or decreases in earned income due to changes in the job market.
Similarly, unearned income may vary depending on investment performance, interest rates, and changes in government policies.
Hence, unearned income may vary depending on investment performance, interest rates, and changes in government policies.
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Kaylee conducted a scientific experiment. For a certain time, the temperature of a compound rose 1 1/2 every 3/5 of an hour. What was the rate, in degrees per hour, that the temperature of the compound rose?
The rate, in degrees per hour, that the temperature of the compound rose was 5/2
In Kaylee's scientific experiment, she is interested in the rate at which the temperature of a compound is rising. To answer this question, we need to use mathematics to determine the rate, in degrees per hour, that the temperature of the compound rose.
Using the information provided, we can set up a proportion to solve this problem.
We can represent the rate of temperature rise during a certain time period as a/b, where a is the temperature rise and b is the time period.
We can then set this equal to the rate of temperature rise per hour, c/1. Therefore, we have a/b = c/1.
We are told that the temperature rose 1 1/2 every 3/5 of an hour, so a = 1 1/2 and b = 3/5.
Therefore, we can solve for c to get c = 5/2.
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Is 19 is a prime number or not?
The number 19 have only two factors. They are 1 and 19. So it is a prime number. The statement is true.
Prime numbers are the numbers having only two factors, 1 and the number itself. There are some conditions that should be satisfied if they are counted as prime numbers.
It must be greater than 1.
It must be a natural number, not a decimal fraction or negative number.
It must have only two factors.
It must not be a product of any two numbers other than 1 and the number.
So a number which is not divisible by any other number than 1, can be called a prime number. All other numbers are composite numbers.
So 19 is not divisible by any other numbers. So it is a prime number.
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Find the function of the graph
The rational function for the graph is defined as follows:
y = -8(x - 3)/(x² - x - 12)
How to define the rational function?A rational function is a function in which the variable x appears in both the numerator and the denominator of the function.
The function in this problem has a zero at x = 3, hence the numerator is given as follows:
a(x - 3).
In which a is the leading coefficient.
The function has vertical asymptotes at x = -3 and x = 4, hence the denominator is given as follows:
(x + 3)(x - 4) = x² - x - 12.
Hence the function is defined as follows:
y = a(x - 3)/(x² - x - 12)
When x = 0, y = -2, hence the leading coefficient a is obtained as follows:
-2 = 3a/12
3a = -24
a = -8.
Hence the function is defined as follows:
y = -8(x - 3)/(x² - x - 12)
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I don’t know how to solve
7x-y=16
y=7x-16
i need help....correct answer gets brainliest.
The area of given triangle whose base is 2 ft and height is 3/4 ft is [tex]\frac{3}{4} ft^2[/tex] .
Area of Triangle:The total area that is bounded by a triangle's three sides is termed as the triangle's area. In general, it is equal to 1/2 of the height times the base, or A = 1/2 b h. So, in order to get the area of a triangular polygon, we must first determine its base (b) and height (h).
In the given figure , we have,
Base = 2 ft
Height = 3/4 ft
Then , Area of Triangle,
[tex]=\frac{1}{2} *base *height\\\\=\frac{1}{2} *2 *\frac{3}{4}\\ \\=\frac{3}{4} ft^2[/tex]
So , Thus, the provided triangle's area is [tex]\frac{3}{4} ft^2[/tex] .
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Julie bought 3 ice creams and we give her back $3.25 change on a $10 bill. What is the price of an ice cream?
(Show your solution by using an equation)
The price of an ice cream is 2.21666666667 in other words, 2.21$
PLEASE !! HELP what is the slope of the line that contains the points ( -2, - 7/2) and (4,-4)
Work Shown:
-7/2 = -3.5
The two given points are (-2,-3.5) and (4,-4)
Let's use the slope formula.
[tex](x_1,y_1) = (-2,-3.5) \text{ and } (x_2,y_2) = (4,-4)\\\\m = \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}\\\\m = \frac{\text{y}_{2} - \text{y}_{1}}{\text{x}_{2} - \text{x}_{1}}\\\\m = \frac{-4 - (-3.5)}{4 - (-2)}\\\\m = \frac{-4 + 3.5}{4 + 2}\\\\m = \frac{-0.5}{6}\\\\m = \frac{-1/2}{6}\\\\m = \frac{-1/2}{6/1}\\\\m = \frac{-1}{2}\div\frac{6}{1}\\\\m = \frac{-1}{2}*\frac{1}{6}\\\\m = -\frac{1}{12}[/tex]
The slope is -1/12
It means "go down 1 unit, then go to the right 12 units".
You can use a tool like GeoGebra to confirm the answer is correct.
adding and subtracting rational expressions practice . what expression is equivalent to 3/x − 2 − 5/2 − 4/x − 2 ?
[tex]3/x - 2 -5/2 -4/x - 2[/tex] is equivalent to [tex](-15x + 40)/2(x-2)(x-2)[/tex]
[tex]3/x - 2 - 5/2 - 4/x - 2[/tex] can be simplified by finding a common denominator:
LCD = 2(x-2)
So we need to multiply the first fraction by 2/2 and the second fraction by (x-2)/(x-2):
[tex]3/x - 2 * 2/2 - 5/2 - 4/x - 2 * (x-2)/(x-2)[/tex]
[tex]= (6 - 2(x-2))/2(x-2) - 5/2 - (4x-8)/(x-2)(x-2)\\= (-2x + 14)/2(x-2) - 5/2 - (4x-8)/(x-2)(x-2)\\= (-2x + 14 - 5(x-2) - 2(4x-8))/2(x-2)(x-2)\\= (-2x + 14 - 5x + 10 - 8x + 16)/2(x-2)(x-2)\\= (-15x + 40)/2(x-2)(x-2)[/tex]
Therefore, [tex]3/x - 2 -5/2 - 4/x - 2[/tex] is equivalent to [tex](-15x + 40)/2(x-2)(x-2).[/tex]
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If x = -2, what is y = ?
In the curve of the sinusoidal curve when x = -2 y = 2
How to find the value y when x = -2 in the curve?A sinusoidal curve, also known as a sine wave, is a type of waveform that is commonly used to describe oscillations or periodic phenomena in various fields such as physics, engineering, mathematics, and electronics.
A sinusoidal curve is a graph of a function that oscillates between an upper value and a lower value, and repeats itself over a period of time.
In order to find the value of y when x = -2, from the x-axis at x = -2 trace it to touch the curve and then trace to the y-axis to get the y value (Check the attached).
Therefore, when x = -2, y = 2
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Which inequality
represents the values of x
for y ≤-6(x-18)-2
when y=46?
The inequality that represents the value of x is x ≥ -10.
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
We have,
y ≤ -6 (x - 18) - 2
Substitute y = 46
So,
46 ≤ - 6 (x - 18) - 2
46 ≤ - 6x + 108 - 2
46 ≤ 6x + 106
46 - 106 ≤ 6x
-60 ≤ 6x
-10 ≤ x
Thus,
The inequality of x is x ≥ -10.
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The weight, in pounds, of a baby in the first six months of life can be modeled by the function f(x) = 1.5x +7, where x is the age of the baby
in months. According to this model, what is the weight, in pounds, of a baby at age 5 months?
A. 8.5
B. 12.0
C. 13.5
D. 14.5
To find the weight of a baby at age 5 months, we can substitute x=5 in the given function:
f(5) = 1.5(5) + 7
f(5) = 7.5 + 7
f(5) = 14.5
Therefore, the weight of a baby at age 5 months is 14.5 pounds. Answer: D.
Which phase of the development process is where the most thorough testing
happens?
A. production
B. para-production
C. Opre-production
D. post-production
D. Post-production is the phase of the development process is where the most thorough testing happens.
What is the Phase of development:A phase of the development process is a distinct stage or step in the process of developing a software or product, from the initial idea or concept to the final delivery or deployment.
Each phase of the development process has a specific objective, and each phase typically requires the completion of certain activities or tasks before the development can progress to the next phase.
The phase of testing:
In this phase, the system or product is thoroughly tested to ensure that it meets all requirements and quality standards. This includes various types of testing such as unit testing, integration testing, system testing, acceptance testing, and user acceptance testing.
Post-production is the phase of the development process that occurs after the product or software has been developed and is ready for release. During this phase, thorough testing is performed to ensure that the product or software is functioning as intended and meets all quality standards.
Therefore,
D. Post-production is the phase of the development process is where the most thorough testing happens.
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what is linear interpolation formula
The formula of linear interpolation(y) = [tex]y_{1} +\frac{(x - x_{1}) (y_{2} -y_{1}) }{x_{2} -x_{1} }[/tex]
The formula to calculate linear interpolation is:
Linear Interpolation(y) = [tex]y_{1} +\frac{(x - x_{1}) (y_{2} -y_{1}) }{x_{2} -x_{1} }[/tex]
where,
[tex]x_{1}[/tex] and [tex]y_{1}[/tex] are the first coordinates[tex]x_{2}[/tex] and [tex]y_{2}[/tex] are the second coordinatesx is the point to perform the interpolationy is the interpolated value.It allows users to interpolate (interpolation is a mathematical technique for estimating any value between two known points) data points between the sets(two sets) of points or coordinates.
Take the two known points and calculate the value of the point that lies between them. This has been used in as many engineering applications as estimating the value of a point on a graph or table. This calculator helps in estimating the value of a point that lies between two known points on a line.
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Can somebody help me with these geometry problems (BTW these are not regular area this is trigonometry/ special right triangles area)
Answer: 1st 133
Step-by-step explanation: Hope this helps!
When computing the correlation coefficient, what is the effect of changing the order of the variables on r?Choose the correct answer below.A. It has no effect on r.B. It changes both the sign and magnitude of r.C. It changes the magnitude of r.D. It changes the sign of r
When computing the correlation coefficient, the effect of changing the order of the variables on r is option (A) It has no effect on r
The correlation coefficient is a measure of the strength and direction of the linear relationship between two variables.
Changing the order of the variables has no effect on the correlation coefficient, It has no effect on r.
This is because the correlation coefficient measures the degree of association between two variables, regardless of which variable is designated as the dependent variable or independent variable. The formula for the correlation coefficient is symmetrical, meaning that it yields the same result regardless of the order in which the variables are entered into the formula.
Therefore, the correct option is (A) It has no effect on r
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if d^n=24 square root of d
Answer:
1/24
Step-by-step explanation:
A lightbulb consumes 600 watts per day. How long does it take to consume 3450 watt hours
5.75 hours long to consume 33450 watt hours
The time it takes for a lightbulb to consume 3450 watt hours can be calculated using the formula: time = energy/power. In this case, the energy is 3450 watt hours and the power is 600 watts.
To find the time, we can plug the values into the formula:
time = 3450 watt hours / 600 watts
time = 5.75 hours
Therefore, it takes 5.75 hours for the lightbulb to consume 3450 watt hours.
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Tara and Veronica are making a parallelogram-shaped banner for a football game. They will paint the entire banner except for a rectangular section where a photo of the school's mascot will be placed. The photo of the mascot has an area of 6 square feet. If a 16-ounce bottle of primer covers 24 square feet, how many bottles of paint will they need?
The solution of the given problem of surface area comes out to be Tara and Veronica will need about 15.26 bottles of paint to cover the banner.
Describe Surface Area.Its surface area is a reliable indicator of its overall size. When figuring out the right triangle squared, the environment is taken into account. The surface area of everything determines its overall size. The total of the volumes from each of the twelve vertical sides makes up the water volume inside a cuboid. Utilize the following formula to get the box's dimensions: The region is represented by 2lh, 2lw, & 2hW. (SA). The area is represented by the flexible shape's entire surface area.
Here,
To calculate the number of paint bottles needed, we need to first find the area of the parallelogram-shaped banner.
Area = base × height
The apothem is given as 9.52 cm, which is also the height of one of the triangles. The base of each of these triangles is half of the length of the banner, which is 6.8/2 = 3.4 cm. Using the Pythagorean theorem, we can solve for the height "h" of each triangle:
h² = (9.52)² - (3.4)²
h ≈ 8.56 cm
So the total height of the parallelogram is twice this value, or approximately 17.12 cm. Therefore, the area of the banner is:
Area = b × 17.12
864 × 2.54² ≈ 5574.14 cm²
So the area of the banner is:
Area = b × 17.12 = 2(6.8 + b) × 8.56 - 5574.14
Simplifying this expression, we get:
Area = 17.12b - 226.67
Now we can solve for "b" by setting this expression equal to the area of the banner that can be painted:
16(24) = 384 square feet = 384 × 144 ≈ 55302.74 cm²
17.12b - 226.67 = 55302.74
17.12b = 55402.41
b ≈ 3232.87 cm
Finally, we can calculate the area of the painted portion of the banner:
Area painted = (6.8 + b) × 17.12 - 6
Area painted ≈ 5826.24 cm²
To find the number of paint bottles needed, we divide the area painted by the coverage of one bottle:
Number of bottles = Area painted / (16 × 24)
Number of bottles ≈ 15.26
So Tara and Veronica will need about 15.26 bottles of paint to cover the banner.
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You deposit $12,000 in an account that pays 6.5% interest compounded quarterly. Use the future value formula for simple interest to determine the effective annual yield.
Answer:
6.67%
Step-by-step explanation:
The formula for accrued value A on a deposit P for t years compounded n times annually at i% APR is
[tex]A = P\left(1 + \dfrac{r}{n}\right)^{nt}[/tex]
where r = i/100 i.e the interest rate as a decimal
We are given
P = $12,000
i = 6.5%
r = 6.5/100 = 0.065
n = 4 since interest is compounded annually
t = 1 year since we are interested in the annual yield
[tex]\begin{aligned}A &= 12000\left(1 + \dfrac{0.065}{4}\right)^{4\cdot 1}\\& = 12000(1 + 0.01625)^4\\&= 12000(1.01625)^4\\& = \$12,799.22\end{aligned}[/tex]
Effective Annual Interest = 12,799.22 - 12,000 = $799.22
This works out to an annual yield of 799.25/12000
= 0.0667
= 6.67%
you can compare two marginal distributions to see if the corresponding two variables are related. (True or False)
False. Marginal distributions describe the distribution of each variable separately, without considering any relationship between them.
Comparing the marginal distributions of two variables cannot determine whether the variables are related. Marginal distributions show the distribution of each variable separately and do not consider the relationship between them. To determine whether two variables are related, it is necessary to examine their joint distribution. This can be done through a scatter plot, which displays the relationship between the variables graphically, or through a correlation coefficient, which measures the strength and direction of the linear relationship between the variables. Therefore, comparing marginal distributions alone is not sufficient to determine whether two variables are related.
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how too convert kilometers to feet
We can convert Kilometer to feet by using the relation 1Km = 3280.83 ft.
A Kilometer is used as a standard unit of measuring distance between any two bodies.
As per the standard unit conversion rates 1 km is equal to 3280.83 ft.
So if we want to convert any quantity in km to feet. We can follow the above mentioned unit conversion rate in order to do so.
Let us say for example, we have to km and we have to converted into feet.
2 kilometer = 2 × 3280.83 ft
2 kilometer = 6561.66 ft.
So, we can convert any kind of distance given in kilometer to feet by using the same method as above.
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In ΔFGH, f = 55 cm, h = 99 cm and ∠H=169°. Find all possible values of ∠F, to the nearest degree.
The measure of angle F is 61.4° to the nearest degree and it can be found through Law of Sines.
What is Law of Sines?
The law of sines is a mathematical relationship between the lengths of the sides and the angles of a triangle. It states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant, regardless of the size or shape of the triangle. Using the law of sines, it is possible to calculate the length of any side of a triangle given the lengths of the other two sides and the measure of their included angle, or to calculate the measure of any angle given the lengths of the three sides. The law of sines can also be used to solve oblique triangles, which are triangles that are not right triangles.
The measure of angle F can be found using the Law of Sines, which states that:
a/sinA = b/sinB = c/sinC
Where a, b, and c are the sides of the triangle and A, B, and C are the angles opposite those sides.
In this case, a = h = 99 cm, b = f = 55 cm, and c = unknown. We are given the measure of ∠H = 169° and we are trying to find ∠F.
Rearrange the equation to solve for ∠F:
sinF = (a/c) * sinH
sinF = (99/c) * sin169
Now, let's solve for c:
c = (99/sin169) * sinF
Solve for sinF:
sinF = (99/c) * sin169
Solve for sinF. Plugging in the values we have (99/c) and sin169, we get sinF = 0.835.
To find the measure of angle F:
∠F = arcsin(0.835)
∠F ≈ 61.4°
Therefore, the measure of angle F is 61.4° to the nearest degree.
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Miss Richmond uses 4 tablespoons of cake mix and 2 tablespoons of water to make microwave mug cake. She wants to make a bigger amount to share with Mrs. St. Clair. If she uses 22 tablespoons of cake mix, how much water will she need to use? Select the 2 proportions that represent this situation.
1. 4/X = 2/22
2. x/2 = 22/4
3. 4/2 = 22/x
4. 2/22 = 4/x
Ans x/2 = 22/4
A word problem is a few sentences describing a "real-life" scenario where a problem needs to be solved using math.
To answer the question above, we equate the amount of cake mix initially to the amount of water needed to make a mug cake
4 tablespoons of cake mix = 2 tablespoons of water
we then equate the amount of cake mix in the final moment to the amount of water needed to make a mug cake
22 tablespoons of cake mix = X tablespoons of water
Now we divide both and these will give us the answer.
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Helen ran 12 miles. She ran 5 miles each hour.
True or False:
The equation 12h = 5 can be used to find h, the number hours that it took Helen to
complete her run.
Answer:
False, it took her 2 hours and 24 minutes
Step-by-step explanation:
The equation 12h = 5 is not correct because it would mean that Helen completed her run in 5 hours, which is not possible since she only ran 12 miles.
To find the correct number of hours, we can use the formula:
Distance = rate x time
Where distance is the total distance Helen ran (12 miles), rate is her speed (5 miles per hour), and time is the number of hours it took her to run.
We can rearrange the formula to solve for time:
Time = distance / rate
Plugging in the values we have:
Time = 12 miles / 5 miles per hour
Simplifying, we get:
Time = 2.4 hours
Therefore, it took Helen 2.4 hours (or 2 hours and 24 minutes) to complete her run.
I hope this helps! And if you could label my answer brainliest that would be awesome.
- Dante
Find the measures of AB and AC
Show all necessary calculations for full credit
The value of the segments AB and AC and for the similar triangles are 20 inches and 10 inches respectively.
How to calculate for AB and AC for the similar trianglesThe triangles ABC and EDC are similar, this implies that the length CD of the smaller triangle is similar to the length CB of the larger triangle
and the length AB of the smaller triangle is similar to the length ED of the larger triangle
and the length EC of the smaller triangle is similar to the length AC of the larger triangle
so;
12/15 = 16/AB
AB = (16 × 15)/12 {cross multiplication}
AB = 20
12/15 = 8/AC
AC = (8 × 15)/12 {cross multiplication}
AC = 10
Therefore, the value of the segments AB and AC and for the similar triangles are 20 inches and 10 inches respectively.
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