Since Xavier states that the decay rate of the value of the car is 40%, an answer option that accurately describes Xavier's statement is: A) Xavier correctly determined the decay rate of the value of the car.
What is an exponential function?In Mathematics, an exponential function can be modeled by using this mathematical expression:
f(x) = a(b)^x
Where:
a represents the base value or y-intercept.x represents time.b represents the rate of change (decay rate).In this scenario, we can logically deduce that values of a certain type of car x years after it is purchased can be modeled by the following exponential function:
f(2) = 19,400(0.40)^2
By comparison, we have:
Decay rate (r) = 0.40, which simply means Xavier correctly determined it.
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What's the difference between right circular cylinder and cylinder?
The difference between a right circular cylinder and a cylinder is that a right circular cylinder has a circular base and is perpendicular to the base, whereas a cylinder can have any shaped base and the sides do not have to be perpendicular to the base.
A right circular cylinder has a circular base and its sides are perpendicular to the base, forming a right angle. This means that the axis of the cylinder is at a right angle to the base.
On the other hand, a cylinder can have any shaped base, such as a rectangle or an ellipse, and the sides do not have to be perpendicular to the base. This means that the axis of the cylinder can be at any angle to the base.
In summary, the main difference between a right circular cylinder and a cylinder is the shape of the base and the angle of the sides to the base. A right circular cylinder has a circular base and perpendicular sides, while a cylinder can have any shaped base and the sides can be at any angle to the base.
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A triangle has side lengths measuring 2x + 2 ft, x + 3 ft,
and n ft.
Mark this and return
Which expression represents the possible values of n,
in feet? Express your answer in simplest terms.
O x-1
On = 3x + 5
On=x-1
O 3x+5
Save and Exit
Next
Submit
The possible value of n in the triangle given is, n < 3x+5
What is a triangle?The triangle is a polygon with three side, vertex, and angles.
Given that, a triangle has side lengths measuring 2x + 2 ft, x + 3 ft,
and n ft.
We asked to find the expression that represents the possible values of n.
We know that,
The sides of a triangle rule assert that the sum of the lengths of any two sides of a triangle has to be greater than the length of the third side.
Therefore,
2x+2+x+3 = 3x+5
Thus, the possible value of n is,
n < 3x+5
Hence, the possible value of n in the triangle given is, n < 3x+5
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suppose that a classroom has 4 light bulbs. the probability that each individual light bulb works is 0.25. suppose that each light bulb works independently of the other light bulbs. what is the probability that all four of the light bulbs work?
The Probability that all four of the light bulbs work is 0.004 approx.
The probability that all four light bulbs work can be calculated by taking the product of the probability that each individual light bulb works. If each light bulb works independently of the other light bulbs, then the probability that all four light bulbs work is:
P(all 4 bulbs) = P(bulb 1) * P(bulb 2) * P(bulb 3) * P(bulb 4)
P(all 4 bulbs) = 0.25 * 0.25 * 0.25 * 0.25
P(all 4 bulbs) = 0.25^4
P(all 4 bulbs) = 0.00390625
So, the probability that all four light bulbs work is 0.00390625 or approximately 0.004.
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4. If m/3 = 54°, find the measure of each missing angle.
a. m<1=
b. m<2=
c. m<4=
d. m<5=
e. m<6=
f. m<7=
g. m<8=
h. m<9=
i. m<10=
j. m<11 =
k. m<12 =
l. m<13 =
m. m<14 =
Note that if m/3 = 54°, then the measure of each missing angle are given as follows:
a. m<1= 36°
b. m<2= 90°
c. m<4= 36°
d. m<5= 90°
e. m<6= 45°
f. m<7= 126°
g. m<8= 54°
h. m<9= 126°
i. m<10= 45°
j. m<11 = 36°
k. m<12 = 144°
l. m<13 = 36°
m. m<14 = 144°
What is the rationale for the above response?We are given three clues from which we solve the missing angles.
Clue 1: m∠3 given as 54°
Clue 2: m∠ 2 given as 90°
The two lines that (are now labeled AB and CD are parallel to one another. Thus:
a) ∠1, ∠2, and ∠3 are complimentary, ∠1 = 180 - (90+54) = 36°
b) ∠2 = 90° (given)
c) ∠4 = 36° (Opposite angles) ∠1 ≅ ∠4
d) ∠5 =90° (Opposite angles) ∠2 ≅ ∠5
e) ∠6 = 54° (Opposite angles) ∠13≅ ∠6
f) ∠7 = ∠1+∠2 (since Line EF is perpendicular to GH, (∠1+∠2) are corresponding angles to ∠7
g) ∠8 = 54° (∠3 and ∠8 are corresponding angles)
h) ∠9 = 126° (∠9 corresponds to ∠5 and ∠4; an alternate explanation is the angle on straight line (∠8 and ∠9) (180-54 = 126°)
i) ∠10 = 54° (∠6 and ∠10 are corresponding angles)
j) ∠11 = 36° (∠11 and ∠1 are corresponding angles)
k) ∠12 = 144° (∠12 corresponds to (∠2+∠3)
l) ∠13 = 36° ( ∠12 and ∠13 are supplementary angles)
m) ∠14 = 144° (∠12 and ∠14 are opposite angles)
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A 2-column table with 5 rows. The first column, number of snapdragons, x, has the entries 11, 12, 13, 14. The second column, number of daisies, y, has the entries 34, 33, 32, 31.
Hans is planting a garden with snapdragons and daisies. The table shows some possible combinations of the two plants. If Hans plants 29 daisies, how many snapdragons will he plant?
The equation
models the scenario.
Hans will plant
snapdragons.
Use the drawing tool(s) to form the correct answer on the provided graph.
Draw the resulting image after the given triangle is rotated 90° counterclockwise about the origin.
Drawing Tools
Select
Point
Line Segment
Click on a tool to begin drawing
Reset
<+
Delete Undo
10
A graph of the resulting image after the given triangle is rotated 90° counterclockwise about the origin is shown in the image below.
What is a rotation?In Geometry, the rotation of a point 90° about the center (origin) in a counterclockwise (anticlockwise) direction would produce a point that has these coordinates (-y, x).
By applying a rotation of 90° counterclockwise to the vertices of triangle ABC, the coordinates of the vertices of the image are as follows:
(x, y) → (-y, x)
Ordered pair A = (-5, 7) → Ordered pair A' = (-(7), -5) = (-7, -5).
Ordered pair B = (-8, 3) → Ordered pair B' = (-(3), -8) = (-3, -8).
Ordered pair C = (-2, 6) → Ordered pair C' = (-(6), -2) = (-6, -2).
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Truman's father is designing a toy car ramp for him. His dad determined that the measure of angle x needs to be increased by 200 .
What is the measure of the new angle?
__ °
The measure of angle x needs to be increased by 200, the new angle would be the original measure of angle x plus 200 degrees.
What is the angle measurement?
A radian is the length of an arc formed by an angle that, when shown as a central angle, equals the length of the circle's radius.
If the measure of angle x needs to be increased by 200, we can simply add 200 to the original measure of angle x to find the new angle.
So, if the original measure of angle x is, for example, 30 degrees, the new angle would be:
New angle = 30 degrees + 200 degrees
New angle = 230 degrees
Therefore, if the measure of angle x needs to be increased by 200, the new angle would be the original measure of angle x plus 200 degrees.
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$47,000 a year is how much an hour?
A yearly salary of $47,000 is equivalent to an hourly rate of approximately $22.60 per hour.
To convert a yearly salary to an hourly rate, you need to divide the annual salary by the number of working hours in a year.
Assuming a typical workweek of 40 hours and 52 weeks in a year, the total number of working hours in a year is:
40 hours/week x 52 weeks/year = 2,080 hours/year
To calculate the hourly rate for a yearly salary of $47,000, you can divide the annual salary by the total number of working hours in a year:
$47,000 / 2,080 hours = $22.60 per hour
Therefore, a yearly salary of $47,000 is equivalent to an hourly rate of approximately $22.60 per hour.
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Jon tossed a standard die several times. He got the number "4" on 5 of the tosses. Based on theoretical probabilities, what is the best estimate of the total number of times he tossed the cube? A) 20 times B) 60 times C) 30 times D) 10 times
Based on theoretical probabilities, the best estimate of the total number of times Jon tossed the cube would be 60 times. The probability of rolling a "4" on a standard die is 1/6. If Jon got "4" on 5 of the tosses, then the total number of tosses would be 5/ (1/6) = 30 tosses. To find the best estimate of the total number of tosses, it is common to round up to the nearest multiple of 10, which in this case would be 60. Therefore, the best estimate would be 60 times (Option B).
Classify each polynomial by degree and number of terms -4
Based on degree, polynomials can be classified as follows:
Constant: A polynomial of degree 0, with a single term containing only a constant coefficient.Linear: degree 1, with two terms, one of which is a variable raised to the first power.Quadratic: A polynomial of degree 2, with three terms, one of which is a variable raised to the second power.Then for number of terms, there are monomials with a single term, binomials with two terms, trinomials with three terms and multinomials with more than three terms.
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A rectangle is twice as long as it is wide. If the width is w, the length is 2w. The area of the rectangle can be found using the expression 2w to the power of 2
If the rectangle is 10 centimeters wide, what is its area in square centimeters?
The area of the rectangle is 200 square centimeters
Area of rectangleThe area of a rectangle can be found by multiplying its length and width. In this case, the width is given as w and the length is given as 2w.
Therefore, the area of the rectangle can be found using the expression 2w^2.
If the width of the rectangle is 10 centimeters, we can substitute this value into the expression for the area to find the area in square centimeters.
Area = 2w^2
= 2(10)^2
= 2(100)
= 200 square centimeters
Therefore, the area of the rectangle is 200 square centimeters
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The diameter C of the top of a randomly selected large drink cup at a fast-food restaurant follows a Normal distribution with a mean of 3.96 inches and a standard deviation of 0.01 inch.
The diameter Lof a randomly selected large lid at this restaurant follows a Normal distribution with mean 3.98 inches and standard deviation 0.02 inch.
Assume that Land Care independent random variables. Let the random
variable D = L - C be the difference between the lid's diameter and the
cup's diameter.
For a lid to fit on a cup, the value of L has to be bigger than the value of C, but not by more than 0.06 inch. Find the probability that a randomly selected lid will fit on a randomly selected cup.
Interpret this value. Justify your answer.
The required probability that a randomly selected lid will fit on a randomly selected cup is 0.9772, or 97.72%.
What is a normal distribution?Normal distributions can be altered to standard normal distributions by the formula:
Z = (X - μ)/σ
The difference in diameter between the lid and cup, D = L - C, is also a normal distribution with mean μ(D) = μ(L) - μ(C) = 3.98 - 3.96 = 0.02 inches and standard deviation σ(D) = √(σ² (L)+ σ²(C)) = 0.03 inches.
The probability that a randomly selected lid will fit on a randomly selected cup is the probability that D is between 0 and 0.06 inches. To find this probability, we can standardize D using the z-score formula and find the corresponding area under the standard normal curve.
Let z = (D - μ) / σ.
Then, the required probability is,
P(0 < D < 0.06) = P(0 < z < (0.06 - 0.02) / 0.03) = P(0 < z < 2).
We can use a standard normal table or a calculator to find the area under the standard normal curve between 0 and 2. This area represents the required probability. For example, using a standard normal table, we can find that P(0 < Z < 2) = 0.9772.
Therefore, the probability that a randomly selected lid will fit on a randomly selected cup is 0.9772, or 97.72%.
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Write the prime factorization of 35. Use exponents when appropriate and order the factors from least to greatest (for example, 2².3.5).
The prime factorization of 35 is 5 * 7
How to determine the prime factorization of 35From the question, we have the following parameters that can be used in our computation:
Number = 35
Express 35 as the product of its factors
So, we have the following representation
Number = 5 * 7
None of the factors 5 and 7 can be further simplified
This means that the prime factorization of 35 is 5 * 7
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PLEASE ANSWER ASAP I need help
Answer:
6
Step-by-step explanation:
F = 4 x 6 / 2^2
= 6
Estimate the product by rounding each number to the nearest 10 88 x 304
After rounding off the numbers product of the given numbers is 27000.
What is multiplication?Multiplication is an operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication of two or more numbers is known as the product of those numbers.
The given number are 88 and 304.
Rounding each number to the nearest 10
That is, 88 to 90 and 304 to 300
Now, 88×304 can be written as
90×300
= 27000
Therefore, after rounding off the numbers product of the given numbers is 27000.
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y - 10 + 9y - 3 what is the answer?
Answer:
10y - 3
Step-by-step explanation:
(y + 9y) + (-10 - 3)
(1 + 9) x y + (-10 - 3)
10y - 13
An equilateral triangle shares a single side with a kite to form a new
quadrilateral, as shown below.
Calculate the size of angle p.
Give your answer in degrees (°).
In the given figure , the measure of angle p is 41 degrees.
What is Quadrilateral ?A quadrilateral is a closed figure that has four sides, four vertices, and four angles. It is a form of polygon. In order to create it, four non-collinear points are joined. Quadrilaterals always have a total internal angle of 360 degrees.
It is given that the kite is shares a side with an equilateral triangle to form a new quadrilateral.
The side of kite which is attatched to triangle contains an angle of 79 degree.
the other end of side which is attatched to the triangle contains angle of 120 degree because it is attatched to the side of triangle which makes a straight line and the triangle is having each angle of 60 degrees.
So, the angle opposite to it will also be of 120 degrees.
Now in the kite, the angles are,
79+120+p+120=360
p=360-319
p=41 degrees
Hence, the measure of angle p is 41 degrees.
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9/16 divided by 7/ 10
Answer: 15/7
Step-by-step explanation:
9/16 / 7/10 = 9/6 * 10/7 multiply by recipricol to find answer
90/42
15/7 simplify
I need help from anyone!
Answer:
h = 10.0708 cm
Area of shaded region = 8.1841 [tex]cm^{2}[/tex]
Step-by-step explanation:
r = radius of circle
= 14 cm
h = perpendicular height of triangle
Use SinФ trigonometric function to determine h
SinФ = [tex]\frac{Opposite}{Hypotenuse}[/tex]
Sin46° = [tex]\frac{h}{14}[/tex]
Cross-multiplication is applied:
∴h = (14)(Sin46°)
h = 10.0708 cm (Rounded to four decimal places)
Area of sector = [tex]\frac{AngleOfSector}{360^{o}}[/tex] × ([tex]\pi r^{2}[/tex])
= [tex]\frac{46}{360}[/tex] × [tex]\pi (14^{2})[/tex]
= [tex]\frac{9016}{360} \pi[/tex] [tex]cm^{2}[/tex]
= 78.68 [tex]cm^{2}[/tex]
Area of triangle = [tex]\frac{1}{2}[/tex] × (Base of triangle) × h
= [tex]\frac{1}{2}[/tex] × (14 cm) × [(14)(sin46°)]
= (98)(sin46°)
= 70.50 [tex]cm^{2}[/tex]
∴Area of yellow shaded region = Area of sector - Area of triangle
= {[[tex]\frac{9016}{360} \pi[/tex]] - [(98)(sin46°)]} [tex]cm^{2}[/tex]
= 8.1841 [tex]cm^{2}[/tex] (Rounded to four decimal places)
Solve. Please i need help with this.
The value of x and y in the equations are as follows:
x = -8
y = -1
How to solve system of equation?System of equation can be solved using different method such as elimination method, substitution method and graphical method. Therefore, let's use elimination method to solve the equation.
Therefore,
8x - 8y = -8
-3x + 4y = -4
multiply equation(ii) by 2
8x - 8y = -8
-6x + 8y = -8
add the equations
2x = -16
x = -16 / 2
x = -8
Let's find y
-8y = -8 - 8x
-8y = -8 - 8(-8)
-8y = -8 + 16
-8y = 8
y = 8 / -8
y = -1
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Please answer this question for me
Thanks!
According to hing theorem, the following inequalities describe each triangle:
x < 2x > 3x < 8How to use the hing theorem in geometrical systemsAccording to Euclidean geometry, the hing theorem states that if two triangles with two pairs of congruent sides and the former triangle has larger internal angle, then the third side of the former triangle is longer than the third side of the latter triangle.
Mathematically speaking, the relationship between the third can be expressed in terms of inequalities. Now we proceed to express the inequalities in terms of variable x for each case below:
3 · x + 4 < 10The letter e has been eliminated from hing[e] due to profanity detector.
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Find the circumcenter of the triangle
The circumcenter of the triangle is (-3, -4), units.
What is the circumcenter of a triangle?
The circumcenter is the intersection point of the perpendicular bisectors of sides of a triangle. It is the Centre of a triangle's circumcircle.
For a right-angled triangle, the circumcenter lies on the hypotenuse.
The middle of the horizontal length of the triangle = - 3
The middle of the vertical length of the triangle = - 4
The circumcenter of the triangle is located at (x, y ) = ( -3, -4 )
Thus, the circumcenter of the triangle is determined from the interception point of the horizontal length and vertical length.
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The process standard deviation is 0. 15, and the process control is set at plus or minus one standard deviation. Units with weights less than 9. 85 or greater than 10. 15 ounces will be classified as defects. If required, round your answer for the probability of a defect to four decimal places and for the number of defects to the nearest whole number.
The probability of a defect units is 0.3174 by calculating the z-score of the greater than and less than value.
When the distribution is normal, we use the z-score formula.
Z = (X - μ)/σ
We have σ = 0.15 and units with weights less than 9.85 or greater than 10.15 ounces will be classified as defects.
μ = 10.15 - 0.15 = 9.85 + 0.15 = 10
Now, the probability that a unit is defective.
P(X ≥ 10.15)
1 subtracted by the pvalue of Z when X = 10.15
[tex]Z = \frac{10.15-10}{0.15}[/tex]
Z = 1 has a pvalue of 0.8413
1 - 0.8413 = 0.1587
P(X ≤ 9.85)
[tex]Z = \frac{9.85-10}{0.15}[/tex]
Z = -1 has a pvalue of 0.1587
P = P(X ≥ 10.15) + P(X ≤ 9.85)
P = 0.1587 + 0.1587
P = 0.3174
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Review the graph of a piece wise function.
At which value of x does the function have a jump discontinuity?
Given piecewise function has a jump discontinuity at 0 or x=0 i.e. B.
What exactly is a piecewise function?
A piecewise function is one that has multiple definitions in different x intervals. A piecewise function's graph is divided into parts that correspond to each of its definitions. A very excellent example of a piecewise function is the absolute value function. Let us investigate why it is thus named. We know that an absolute value function is defined as f(x) = |x|.
f(x)=(x if x≥0 ,
-x if x><0)
This piecewise function should be interpreted as
When x is higher than or equal to 0, f(x) equals x.
When x is less than zero, f(x) equals -x.
Now,
As jump discontinuity is defined as where the endpoint of one segment and the start of the following segment may have the same x coordinate but have different values of f(x). In the piecewise linear function, such a difference is known as a jump discontinuity.
and in the given graph that happened at x=0 or 0.
Hence,
Given piecewise function has a jump discontinuity at 0.
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What is 164lbs to kg ?
164 pounds is equal to 74.389 kilograms (kg). To convert pounds to kilograms, you can use the conversion factor of 0.45359237, which is the number of kilograms in one pound.
To convert 164 pounds to kilograms, you can use the conversion factor of 0.45359237, which represents the number of kilograms in one pound. Multiplying 164 pounds by this conversion factor gives the result in kilograms. Using this method, 164 pounds is equivalent to 74.389 kilograms. This conversion is useful in many situations, such as when traveling to countries that use the metric system, or when working with scientific measurements that use metric units. Understanding the relationship between pounds and kilograms can help to make conversions easier, and allow for more accurate and consistent measurements across different systems of measurement.
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The following are characteristics of a normal curve except for three. Determine which of the following are not characteristic of a normal curve. I. The mode and median occur at µ. II. The curve is symmetric about the vertical axis through the mean µ. III. The normal curve is asymptotic to the vertical axis on both sides. IV. The total area under the curve and above the vertical axis is equal to 1. V. The probability that the normal random variable is equal to a specific discrete value is always zero, since the normal random variable is continuous. VI. The probability that the normal random variable is between two values is given by the area under the curve between the two given values and the vertical axis. A. VI,I,II B. III,IV,VI C. I,V,II D. II,IV,VI
The statements that are not characteristics of a normal curve are III, IV, and VI. The answer is B.
A normal curve is a bell-shaped probability distribution that is commonly used in statistics. It has several key characteristics that make it useful in modeling real-world data. These include the fact that the mode and median occur at the mean, the curve is symmetric about the mean, and the total area under the curve and above the horizontal axis is equal to 1.
In addition, the normal curve is asymptotic to the horizontal axis on both sides. However, not all normal curves are asymptotic to the horizontal axis on both sides, as this is only true for curves with a finite standard deviation.
Finally, the probability that a normal random variable is equal to a specific discrete value is always zero, since the normal variable is continuous, and the probability that the variable is between two values is given by the area under the curve between those values and the horizontal axis.
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Alonso has x quarters and y dimes. He has no less than 18 coins worth a maximum of $3.60 combined. Solve this system of inequalities graphically and determine one possible solution.
Answer: A quarter is worth $0.25 and a dime is worth $0.10, so the total amount of money Alonso has can be represented by the expression 0.25x + 0.1y. To find one possible solution to the system of inequalities, we need to find the values of x and y that satisfy both the inequality 0.25x + 0.1y ≥ 3.60 and the inequality y ≥ 0.
The inequality 0.25x + 0.1y ≥ 3.60 represents all points (x, y) that are on or above the line 0.25x + 0.1y = 3.60. The inequality y ≥ 0 represents all points (x, y) that are above or on the x-axis. The intersection of these two regions is the solution set of the system of inequalities, which represents all points (x, y) that satisfy both inequalities.
To graph the solution set, we can start by plotting the line 0.25x + 0.1y = 3.60 and shading the region above the line. Then, we can plot the x-axis and shade the region above the x-axis. The intersection of the two shaded regions is the solution set.
One possible solution to the system of inequalities is the point (14, 4). This means that Alonso has 14 quarters and 4 dimes, which total $3.60. However, there may be other solutions to the system of inequalities that would also satisfy the conditions.
Step-by-step explanation:
In 1846 the depth of the river was 5 feet deep.
In 1847 it dropped to 4.9 feet.
This year, 1848, it rose to 6.4 feet.
Answer:
Step-by-step explanation:
Based on the information given, we can calculate the change in the depth of the river between the years 1846, 1847, and 1848.
Change in depth between 1846 and 1847:
The depth of the river dropped from 5 feet in 1846 to 4.9 feet in 1847. The change in depth can be calculated as:
Change in depth = 4.9 - 5 = -0.1 feet
So, the depth of the river dropped by 0.1 feet between 1846 and 1847.
Change in depth between 1847 and 1848:
The depth of the river rose from 4.9 feet in 1847 to 6.4 feet in 1848. The change in depth can be calculated as:
Change in depth = 6.4 - 4.9 = 1.5 feet
So, the depth of the river increased by 1.5 feet between 1847 and 1848.
Solve for x please help show proofs
The value of x from the right triangle is x = 3√11
What is a Triangle?A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
if a² + b² = c² , it is a right triangle
if a² + b² < c² , it is an obtuse triangle
if a² + b² > c² , it is an acute triangle
Given data ,
Let the first triangle be ΔABC
Let the second triangle be ΔDBC
Now , BD is perpendicular to AC
So , the triangles ΔABC and ΔDBC are similar
The measure of BD = x
The measure of AD = 9
The measure of DC = 20
Now , AD / AB = AB / DC
Substituting the values in the equation , we get
9/a = a/20
On simplifying the equation , we get
a² = 180
So , a = 3√20
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
Now , the measure of x = √ ( 3√20 )² - ( 9 )²
So , the measure of x = √ ( ( 180 ) - 81 )
The measure of x = √ 99
The measure of x = 3√11
Hence , the measure of x of triangle is 3√11
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26. Which function is increasing and decreasing over the same intervals as the function in the graph?
Answer:
B.y=(x+2)
Step-by-step explanation