Reason:
a+b = 15+24 = 39 is NOT larger than c = 39
Since a+b > c is false, a triangle is NOT possible.
The sum of any two sides must exceed the third side for a triangle to be possible. For more information, check out the triangle inequality theorem.
a bond is worth 100$ and grows in value by 4 percent each year. f(x) =
To represent the value of the bond after x years, we can use the function:f(x) = 100 * (1 + 0.04)^xwhere x is the number of years the bond has been held.The expression (1 + 0.04) represents the growth factor of the bond per year, since the bond grows in value by 4 percent each year. By raising this factor to the power of x, we obtain the cumulative growth of the bond over x years.Multiplying the initial value of the bond, 100$, by the growth factor raised to the power of x, gives us the value of the bond after x years. This is the purpose of the function f(x).
what are the null and alternative hypotheses? let the probability the shares held will be worth more after the split.
Null hypothesis: No statistically significant relationship between stock splits and the value of shares held
Alternative Hypothesis: Statistically significant relationship between stock splits and the value of shares held
Probability of the shares held being worth
The null and alternative hypotheses are as follows:Null Hypothesis (H0): There is no statistically significant relationship between stock splits and the value of shares held.Alternative Hypothesis (Ha): There is a statistically significant relationship between stock splits and the value of shares held.The probability that the shares held will be worth more after the split can be determined through statistical analysis. The null hypothesis assumes that there is no relationship between stock splits and the value of shares held, while the alternative hypothesis suggests that there is a statistically significant relationship between the two variables.Therefore, the probability of the shares held being worth more after the split is based on the results of the statistical analysis of the null and alternative hypotheses.
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you flip a coin 4 times and get 4 heads in a row what is the probability that the 5th coin flipped is a head
The probability of flipping a coin 4 times and getting 4 heads in a row is 0.0625, and the probability of getting a head on the 5th coin flip is 0.5.
The probability of getting a head on the 5th flip is still 50%. This is because each coin flip is an independent event, and each coin flip is not affected by the outcome of the previous coin flips. Thus, the probability of getting a head on the 5th coin flip is 0.5, regardless of the previous 4 coin flips.
To summarize, the probability of flipping a coin 4 times and getting 4 heads in a row is 0.0625, and the probability of getting a head on the 5th coin flip is 0.5.
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what is the probability of getting all tails? express your answer as a simplified fraction or a decimal rounded to four decimal places.
The probability of getting all tails when flipping a coin three times can be calculated using the multiplication rule of probability. For each flip of the coin, there are two possible outcomes: heads or tails.
Assuming the coin is fair, both outcomes are equally likely, so the probability of getting tails on any one flip is 1/2.
To calculate the probability of getting all tails in three flips, we need to multiply the probabilities of getting tails on each individual flip. Since the flips are independent events (i.e. the outcome of one flip does not affect the outcome of another flip), we can simply multiply the probabilities together:P(all tails) = P(tails on first flip) x P(tails on second flip) x P(tails on third flip)
= (1/2) x (1/2) x (1/2)
= 1/8
Therefore, the probability of getting all tails when flipping a coin three times is 1/8 or 0.125 when expressed as a decimal rounded to four decimal places.
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THIS IS URGENT AM I CORRECT PLEASE HALP!!!!!!
The total time that it took the fireman to be ready and aboard the firetruck can be obtained by summing all of the time spent. When summed, the total figure will be 32 seconds.
How much time did it take?The total time taken to board the firetruck can be calculated by summing all the time given in seconds. We start by getting the time it took the firefighter to reach the fire pole which is 9.5 seconds.
Next is the time it took him to slide down the pole which is 3.2 seconds. Next is 13.6 seconds for sliding down the pole and 5.7 seconds for climbing aboard. The sum of all these is 32 seconds.
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the admission fee at an amusement park is $4.25 for children and $7.00 for adults. on a certain day, 303 people entered the park, and the admission fees collected totaled 1824 dollars. how many children and how many adults were admitted?
The admission fee at an amusement park is $4.25 for children and $7.00 for adults. on a certain day, 303 people entered the park, and the admission fees collected totaled 1824 dollars. There are 108 children and 195 adults were admitted
Let the number of children admitted = C and the number of adults admitted = A
Total number of people admitted = 303
We can form two equations from the given information.
The first equation is to represent the number of people admitted in terms of children and adults.
So, the equation will be
C + A = 303 ------(1)
The second equation represents the total amount collected from admission fees.
So, the equation will be
4.25C + 7A = 1824 ------(2)
Multiplying equation (1) by 4.25, we get
4.25C + 4.25A = 1289.25 ------(3)
Subtracting equation (3) from equation (2), we get:
7A - 4.25A = 1824 - 1289.25
Simplifying, we get:
2.75A = 534.75
Dividing by 2.75, we get:
A = 195
Putting A = 195 in equation (1), we get:
C + 195 = 303
Simplifying, we get:
C = 108
So, there were 108 children and 195 adults admitted on that day.
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What is the measure of each interior angle of a regular 20-gon?
Answer:
162°
Step-by-step explanation:
the sum of the interior angles of a polygon is
sum = 180° (n - 2) ← n is the number of sides
here n = 20 , then
sum = 180° × (20 - 2) = 180° × 18 = 3240°
The interior angles of a regular polygon are congruent
then each interior angle = 3240° ÷ 20 = 162°
data is gathered on the number of reviews for every app in the play store. the median number of reviews is 1,359 and the mean number of reviews is 453,058. what would explain the difference between these two numbers?
Answer:
The median and mean are two different measures of central tendency that provide different information about a data set. The median is the middle value in a data set, where half of the values are above and half are below. The mean, on the other hand, is the sum of all values divided by the total number of values.
In this case, the median number of reviews is much lower than the mean number of reviews, indicating that there are likely a few very high review counts that are skewing the data towards the higher end. This is because the mean is more affected by extreme values, while the median is not. It is possible that there are a few apps with an extremely large number of reviews, which are driving up the mean.
The mean number of reviews would be significantly higher than the median.
The difference between the median and mean number of reviews can be explained by the fact that some apps have very large numbers of reviews, whereas others have very few. The median is the middle value of the dataset, and does not take into account the outliers, which can have a large effect on the mean. For example, if there is one app with 1 million reviews, the mean number of reviews would be significantly higher than the median.
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A cylinder and a cone have the same diameter: 8 inches. The height of the cylinder is 3 inches. The height of the cone is 18 inches.
Use π = 3.14.
What is the relationship between the volume of this cylinder and this cone? Explain your answer by determining the volume of each and comparing them. Show all your work. (10 points)
Answer:
The formula for the volume of a cylinder is V = πr²h, where r is the radius and h is the height.
Given the diameter of both the cylinder and the cone is 8 inches, the radius is 8/2 = 4 inches.
The volume of the cylinder is Vcyl = π(4)²(3) = 48π cubic inches.
The formula for the volume of a cone is V = (1/3)πr²h.
The volume of the cone is Vcone = (1/3)π(4)²(18) = 96π/3 = 32π cubic inches.
Therefore, the relationship between the volume of the cylinder and the cone is that the volume of the cone is exactly two-thirds of the volume of the cylinder.
We can see this by dividing the volume of the cylinder by the volume of the cone:
Vcyl/Vcone = (48π) / (32π) = 3/2
So, the volume of the cylinder is 1.5 times greater than the volume of the cone.
Four cities recorded the temperature at midnight.
*Delway’s temperature was –8°C.
*Hickory’s temperature was –10°C.
*Midway’s temperature was –2°C.
*Ridgemonte’s temperature was 3°C.
Which list shows the cities in order from warmest to coldest?
A Delway, Hickory, Midway, Ridgemonte
B Hickory, Delway, Midway, Ridgemonte
C Midway, Ridgemonte, Hickory, Delway
D Ridgemonte, Midway, Delway, Hickory
How much plastic wrap will be needed to completly cover and ice cream cone with the slant height of 4. 25 inches and a diameter of 2 inches
The amount of plastic wrap required to cover the entire cone will be 16.575 square inches.
To calculate how much plastic wrap is required to completely cover an ice cream cone with a slant height of 4.25 inches and a diameter of 2 inches, we must use the surface area of the cone.
Here, the ice cream cone can be visualized as a cone-shaped object with an added circular base.
We must use the following formula to calculate the surface area:
Surface area = πr2 + πrl
Where r is the radius and l is the slant height of the cone.
As we know the diameter of the ice cream cone is 2 inches, and its radius can be calculated by dividing it by
2.r = d/2 = 2/2 = 1 inch.
Substitute the values of r and l in the formula, and then calculate the surface area of the cone.
π = 3.14r = 1 inchl = 4.25 inches
Surface area = πr2 + πrl
= 3.14 × 1² + 3.14 × 1 × 4.25
= 3.14 + 13.435
= 16.575 square inches
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a local county has an unemployment rate of 4%. a random sample of 19 employable people are picked at random from the county and are asked if they are employed. round answers to 4 decimal places.
The probability that exactly 8 of the 19 people in the random sample are employed is 27.93%.
We need to calculate the probability that exactly 8 of the 19 people in the random sample are employed. The probability of a single person being employed is 4%, or 0.04.
To calculate the probability of 8 people being employed out of the 19, we can use the binomial distribution formula:
P(X=8) = nCx * (p^x) * (1-p)^(n-x) Where n = 19, x = 8, p = 0.04, and 1-p = 0.96
So, P(X=8) = 19C8 * (0.04^8) * (0.96^11) = 0.2793 or 27.93%.
Therefore, the probability that exactly 8 of the 19 people in the random sample are employed is 27.93%.
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A triangle has an area of 19.68 sqaure millimeteres and a height of 4.8 millimeteres. What is the length of the base?
Answer:
8.2mm
Step-by-step explanation:
Formula for area of triangle is 1/2 base x height
Since we are trying to find base, we must work in reverse.
19.68mm / 4.8 = 4.1mm (1/2 the base)
To find base we must multiply by 2
2 x 4.1mm = 8.2mm
Base = 8.2mm
The figure below is made of 2 rectangular prism.
What is the volume of this figure?
Total volume of the shape is 124 cm³
What is a cuboid?A cuboid is a three-dimensional solid shape that has six rectangular faces or sides, where each face meets at a right angle with its adjacent faces.
The formula for the volume of a cuboid is:
Volume = Length x Width x Height
So, the Volume of first cuboid = 3 × 4 × 5 = 60 cm³
and the Volume of second cuboid = 2 × 4 × 8 = 64 cm³
Total volume of the shape = Volume of first cuboid + Volume of second cuboid
Total volume of the shape = 60 cm³ + 64 cm³
Total volume of the shape = 124 cm³
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Jessica went deep sea diving. She make the first stop on her descent at 25 meters below the surface of the water. From that point she dives down further, stopping every 5 meters. If she makes 4 additional stops, which number represents her position, relative to the surface of the water?
*
A 45
B 20
C -20
D -45
Jessica's position relative to the surface of the water after making 4 additional stops is 45 meters below the surface.Option(A) is correct.
What is sea diving?Divers who engage in scuba diving use breathing apparatus that is entirely independent of a surface air source. Christian J. Lambert-sen came up with the moniker "scuba," which stands for "Self-Contained Underwater Breathing Apparatus," in a 1952 trademark application.
According to question:Jessica's position relative to the surface of the water can be represented by the following arithmetic sequence:
[tex]$$25, 30, 35, 40, 45$$[/tex]
where the first term is 25 and the common difference is 5 (the distance between each stop).
To find the fifth term (her position after making 4 additional stops), we can use the formula for the nth term of an arithmetic sequence:
[tex]$$a_n = a_1 + (n-1)d$$[/tex]
where [tex]$a_1$[/tex] is the first term, d is the common difference, and n is the term number.
Plugging in the values we know, we get:
[tex]$$a_5 = 25 + (5-1)5 = 45$$[/tex]
Therefore, Jessica's position relative to the surface of the water after making 4 additional stops is 45 meters below the surface.
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Find the area of the shaded region.
11 yd
22 yd
5 yd
The shaded region of the provided number is 214.5 yards, according to the given statement.
Rectangle: What does that mean?A rectangular shape is an illustration of a trapezoid with proportionate and matched opposite sides. It has four sides, four 90-degree borders, and is shaped like a rectangular. Any shape with only two sides is said to be rectangular.
Calculating Area by Subtracting Area from Two as well as More Regions: To determine the area for combined figures consisting of basic forms that overlap, deduct the area of the unshaded figure from the total area to obtain the area of the shaded region.
For illustration, let's calculate the size of the shaded section in the provided picture.
It is clear from the provided picture that a triangular and a rectangle have overlapped. We must deduct the triangular area from the size of the parallelogram in order to determine the area about the shaded figure. Area of the shaded figure =
Area of the rectangle −
Area of triangle
=l×b−12×b×h
=22×11−12×11×5
=214.5yd2
Hence, the area of the shaded figure is 214.5yd2
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Prove that the two triangles are congruent. Be sure to include each step in the proof.
Triangle ABC and triangle DEF are congruent, according to the Side-Angle-Side (SAS) postulate.
Congruent Sides Angles: What Are They?If the matching sides and angles of two triangles are the same length, then the triangles are said to be congruent. Congruent sides angles are what these are called.
Triangle ABC must be shown to be congruent with triangle DEF.
By demonstrating that the two triangles have a single pair of congruent sides, we can get started. We can observe that AB and DE are both 6 cm long.
The congruent angle between the two triangles can be demonstrated. As BAC and EDF are both right angles, we can see that they are equivalent.
Thus, according to the Side-Angle-Side (SAS) hypothesis Triangle ABC is consistent with triangle DEF, we can say.
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what is the 1ooth digit to the right of the decimal point in the decimal representation of (1 .fi.)3000 ?
The 100th digit to the right of the decimal point in the decimal representation of (1 .fi.)3000 is 0.
First, let's convert the number (1 .fi.)3000 into its decimal representation. This is done by dividing 3000 by 10 raised to the power of the number of digits following the decimal point, which in this case is 3. We get the answer 1000, or 1.000.
Now, we can look at the 100th digit to the right of the decimal point. This will be the 0th digit from the right of the decimal point, which is 0. Therefore, the 100th digit to the right of the decimal point in the decimal representation of (1 .fi.)3000 is 0.
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a cylindrical tank with radius m is being filled with water at a rate of . how fast is the height of the water increasing?
The height of the water is increasing at the rate of 3 meters per minute.
We know that a cylindrical tank with radius r and height h has a volume of V = πr²h.
The rate at which the water is being filled in the tank is given as dV/dt = 2πr²( dh/dt).
On rearranging the above equation we get dh/dt = (dV/dt) ÷ (2πr²)
Given: Radius of the cylindrical tank, r = 3 m
Rate at which the water is being filled,
dV/dt = 54π cubic meters per minute.
we
Height of the cylindrical tank, h = ?
We need to find out how fast is the height of the water increasing.
This can be calculated using the formula.
dh/dt = (dV/dt) ÷ (2πr²)
Substitute the values of dV/dt and r in the above formula,
we get,
dh/dt = (54π) ÷ (2π x 3²)
dh/dt = 54/18
dh/dt = 3 m/min
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Can someone pls help me with this
A. The equation of the line is expressed as: y = (-5/2)x + 13.
B. The x-intercept of the equation is calculated as: 26/5.
How to Find the Equation of a Line?A. We can use the point-slope form of a linear equation:
y - y1 = m(x - x1), where m is the slope and (x1, y1) is the given point, to find the equation of a line passing through the point (4,3) with a slope of -5/2.
Substituting the values, we get y - 3 = (-5/2)(x - 4), which simplifies to y = (-5/2)x + 13 by expanding and adding 3 to both sides.
B. To find the x-intercept of the equation y = (-5/2)x + 13, we set y to 0 and solve for x. 0 = (-5/2)x + 13, which simplifies to x = 26/5 by multiplying both sides by -2/5 and adding (26/5) to both sides.
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for what mileages will company a charge less than company b? use for the number of miles driven, and solve your inequality for .
Company A will charge less than Company B for any mileage greater than 70 miles. For mileages less than 70 miles, Company B will be cheaper. The inequality solved is m > 70.
To determine for what mileages Company A will charge less than Company B, we can set up an inequality with m representing the number of miles driven.
Let's start by finding the total cost for each company based on the number of miles driven:
Company A: $138 (unlimited mileage)
Company B: $75 + $0.90m (where m is the number of miles driven)
To find the mileage for which Company A will charge less than Company B, we need to set up an inequality by equating the total cost for Company A to the total cost for Company B and then solving for m:
138 < 75 + 0.90m
Subtracting 75 from both sides, we get:
63 < 0.90m
Dividing both sides by 0.90, we get:
m > 70
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Complete question is:
Latoya is going to rent a truck for one day. There are two companies she can choose from, and they have the following prices.
Company A charges $138 and allows unlimited mileage.
Company B has an initial fee of $75 and charges an additional $0.90 for every mile driven.
For what mileages will Company A charge less than Company B? Use m for the number of miles driven, and solve your inequality for m .
he square quilt block shown is made from nine unit squares, some of which have been divided in half to form triangles. what fraction of the square quilt is shaded? express your answer as a common fraction.
To find the fraction of the square quilt block that is shaded, we need to count the number of shaded unit squares and divide it by the total number of unit squares in the quilt block. Let us begin by counting the number of shaded unit squares.
We notice that there are a total of 6 unit squares that are shaded. The unit squares that are shaded are the 2 squares that are completely shaded and the 4 squares that are half shaded due to the presence of triangles.
Next, we need to count the total number of unit squares in the quilt block. We notice that the quilt block is made up of 9 unit squares, each of which can be divided into 4 smaller unit squares. Thus, the total number of unit squares in the quilt block is 9 x 4 = 36.
Therefore, the fraction of the square quilt block that is shaded is 6/36 or 1/6.
To summarize, the shaded portion of the quilt block consists of 6 unit squares out of a total of 36 unit squares. Thus, the fraction of the square quilt block that is shaded is 1/6.
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Make a graph of kinetic energy versus mass for the bikers. Label each biker on your
graph. (4 points)
See Below
HAVE A NICE DAY !
Geometry, and Slope. Worth 15 Points
Please Explain
The equation of the line perpendicular to the line QR in slope intercept is y= [tex]\frac{1}{2}x+\frac{7}{2}[/tex].
Given,
x+2y=2
y = 1 - [tex]\frac{x}{2}[/tex]
Slope = -1/2 = [tex]m_{1}[/tex]
Let Slope of line perpendicular to line x+2y=2 is [tex]m_{2}[/tex]
⇒ [tex]m_{1}[/tex] * [tex]m_{2}[/tex] = -1
Then [tex]m_{2}[/tex] = 1/2
Equation of line perpendicular is given by
[tex]y = \frac{1}{2}x + c[/tex]
Since it contains point (5,6)
6 = [tex]\frac{1}{2} (5) + c[/tex]
c= [tex]\frac{7}{2}[/tex]
Then the equation of line is:
[tex]y = \frac{1}{2}x+ \frac{7}{2}[/tex].
Therefore, the equation of the line perpendicular to the line QR in slope intercept is y= [tex]\frac{1}{2}x+\frac{7}{2}[/tex].
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the process mean can be adjusted through calibration. to what value should the mean be adjusted so that 99% of the cans will contain 12 oz or more?
The value of mean should be adjusted to 12 + 2.576σ so that 99% of the cans will contain 12 oz or more.
The process mean can be adjusted through calibration. The mean is a measure of central tendency in a dataset that represents the average value of a group of data. The population standard deviation is denoted by σ. The formula for the population mean is as follows: μ = (Σ xi) / n, where xi represents the data values and n represents the total number of data values.
Here we can use the formula of confidence interval as,μ±z σ/√n, Where μ is the mean, z is the z-score, σ is the standard deviation is the sample size. Given,The required confidence level is 99%. So,α = 1-0.99α = 0.01. We can find z from the z-score table at α/2 = 0.005 as, z = 2.576.
Now, we need to find out the value of μ when the mean will be 12 ounces so that 99% of cans will contain 12 ounces or more. So,μ ± z σ/√n = 12. We know that, P(X > 12) = 0.99. The formula for standardization is, Z = (X - μ) / σHere, X = 12, σ is given and we need to find the value of μ.z = (X - μ) / σ2.576 = (12 - μ) / σμ - 12 = 2.576 × σμ = 12 + 2.576 × σ.
Now, the value of μ should be adjusted to 12 + 2.576σ so that 99% of the cans will contain 12 oz or more.
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Determine whether it is possible to find values of L 0 so that the given boundary-value problem has precisely one nontrivial solution, more than one solution, no solution, and the trivial solution. (Let k represent an arbitrary integer. If an answer does not exist, enter DNE.) y" + 16y=0, y(0)= 1, y(L) = 1 (a) precisely one nontrivial solution (b) more than one solution (c) no solution (d) the trivial solution
There is no solution if the boundary conditions are inconsistent, i.e., if y(0) ≠ y(L) = 1.
We are given the boundary-value problem:
y" + 16y = 0, y(0) = 1, y(L) = 1
The characteristic equation is r^2 + 16 = 0, which has roots r = ±4i.
The general solution to the differential equation is then y(x) = c1cos(4x) + c2sin(4x).
Using the boundary conditions, we get:
y(0) = c1 = 1
y(L) = c1cos(4L) + c2sin(4L) = 1
Substituting c1 = 1 into the second equation, we get:
cos(4L) + c2*sin(4L) = 1
Solving for c2, we get:
c2 = (1 - cos(4L))/sin(4L)
Thus, the general solution to the differential equation that satisfies the given boundary conditions is:
y(x) = cos(4x) + (1 - cos(4L))/sin(4L)*sin(4x)
Now, we can answer the questions:
(a) To have precisely one nontrivial solution, we need the coefficients c1 and c2 to be uniquely determined. From the above expression for c2, we see that this is only possible if sin(4L) is nonzero. Thus, if sin(4L) ≠ 0, there exists precisely one nontrivial solution.
(b) If sin(4L) = 0, then c2 is undefined and we have a family of solutions that differ by a constant multiple of sin(4x). Hence, there are infinitely many solutions.
(c) There is no solution if the boundary conditions are inconsistent, i.e., if y(0) ≠ y(L) = 1.
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PLEASE HELP ASAP!!!!!!!!!!!!!!
Rewrite each of the following expressions without using absolute value
1.|x-1| if x>1
2. |x-y| if x>y
3. |3-[tex]\sqrt{4}[/tex]
4. |4r -12| if r<3
5. |[tex]\sqrt{15} -5+1[/tex]
6. |4-[tex]\sqrt{7}[/tex]
7. |7m-56| if m<8
8. |z-7|-|z-9| if z<7
Answer:
1 4(3-r) or 12-4r
2. 7( 8-m) or 56-7m
3. -2
Step-by-step explanation:
1) |4r−12| , if r<3
|4r-12|
Factor out a 4
4|r-3|
|r-3| will be less than 0 since r is less than 3
So we can rewrite it as 3-r to remove the absolute value signs and make it positive
4 (3-r)
12 -4r
2. |7m–56| , if m<8
Factor out a 7
7| m-8|
|m-8| will be less than 0 since m is less than 8
So we can rewrite it as 8-m to remove the absolute value signs and make it positive
7( 8-m)
56-8m
3) |z−7|−|z−9| , if z<7
|z-7| will be less than 0 since z is less than 7 and |z-9| will be less than 0 since z is less than 7
So we can rewrite it as 7-z and 9-z to remove the absolute value signs and make it positive
7-z - (9-z)
Distribute the minus sign
7-z-9+z
-2
A pharmacist mixes 10 grams of a 15% medicine solution with 25 grams of a 10% medicine solution. Suppose we know that after she adds the x grams of pure medicine the pharmacists mixture is 25% medicine solution. Write an equation
The equation that represents the situation is (4 + x) / (10 + 25 + x) = 0.25
Let's start by finding the amount of medicine in the original mixture before adding any pure medicine.
The amount of medicine in the 10 grams of 15% solution is
0.15 × 10 = 1.5 grams
The amount of medicine in the 25 grams of 10% solution is
0.10 × 25 = 2.5 grams
So the total amount of medicine in the original mixture is,
1.5 + 2.5 = 4 grams
Now let x be the amount of pure medicine added.
The total amount of medicine in the final mixture is,
4 + x
The total amount of solution in the final mixture is,
10 + 25 + x
So the concentration of the final mixture is,
(4 + x) / (10 + 25 + x)
We know that this concentration is 25%, so we can write:
(4 + x) / (10 + 25 + x) = 0.25
This is the equation that represents the situation.
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The given question is incomplete, the complete question is:
A pharmacist mixes 10 grams of a 15% medicine solution with 25 grams of a 10% medicine solution. Suppose we know that after she adds the x grams of pure medicine the pharmacists mixture is 25% medicine solution. Write an equation that represents the situation
Find the value of x in a triangle, 142 degrees and 112 degrees
The value of x in the triangle can be found by using the fact that the sum of all angles in a triangle is 180 degrees. Simplifying the equation 142 degrees + 112 degrees + x = 180 degrees, we get x = 26 degrees.
To find the value of x in the triangle, we use the fact that the sum of all angles in a triangle is 180 degrees.
Let's call the third angle of the triangle "x".
Then, we have:
142 degrees + 112 degrees + x = 180 degrees
Simplifying this equation, we get:
x = 180 degrees - 142 degrees - 112 degrees
x = 26 degrees
Therefore, the value of x in the triangle is 26 degrees.
Learn more about triangle here: brainly.com/question/2773823
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The third term of a sequence is 14. Term to term rule is square, then subtract 11. Find the first term of the sequence
The third term of a sequence is 14. Term to term rule is square, then subtract 11. The first term of the sequence is 6.
The given information is about the third term of a sequence which is 14, and the term to term rule is square, then subtract 11.
We have to find the first term of the sequence. The sequence can be calculated using the following formula:
An = A1 + (n-1)d
Where, An is the nth term of the sequence A1 is the first term of the sequence d is the common difference between the terms of the sequence. Let's solve the problem by finding the value of the common difference between the terms of the sequence.
Using the given information, we can write: A3 = 14=> A1 + (3 - 1)d = 14=> A1 + 2d = 14 ----- (i)
Also, the term to term rule is square, then subtract 11.So, we can write, A2 = A1 + d = (A1)² - 11 ---- (ii)
Substituting the value of d from equation (ii) in equation (i),
we get: A1 + 2 [(A1)² - 11] = 14 Simplifying this equation, we get: A1² - 2A1 - 12 = 0 On solving this quadratic equation
we get: A1 = -2 or A1 = 6 Ignoring the negative value of A1, we get the first term of the sequence to be 6.
for such more question on sequence
https://brainly.com/question/7882626
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