The domain of a function refers to the set of all possible input values. We can easily find the domain of the given function h(t) using the following rules:
Since the denominator cannot be zero, we must exclude the value t = -3 from the domain. This means that the domain is {t | t ≠ -3}.
Furthermore, the expression inside the square root cannot be negative since the square root of a negative number is undefined. Thus, we have t^2 - 16 ≥ 0, which implies t ≤ -4 or t ≥ 4.
Therefore, the domain of the function h(t) is given by {t | t ≠ -3, t ≤ -4 or t ≥ 4}. This can also be written in set-builder notation as {t : t ≤ -4 or t ≥ 4, t ≠ -3}.
Hence, the correct option is {\color{Red}\boxed{(-\infty,-4] \cup[4, \infty) \text { or }{x \mid x \leq-4 \text { or } x \geq 4}}}
For further information on Function, refer below:
https://brainly.com/question/12431044
#SPJ11
The runways at an airport are arranged to Intersect and are bordered by fencing. A security guard needs to patrol the outside fence of the
runways once per shift. What is the estimated distance she walks every shift?
Х
5,000 ft
4,000 ft
OA. 5,830 ft
OB. 18,000 ft
OC. 11,660 ft
OD. 23,320 ft
22 Edmentum. All rights reserved.
She logs 18,000 feet of walking each shift based on perimeter of the rectangle field.
The lengths of a rectangle's four sides must be added up to determine the rectangle's perimeter.
The perimeter (P) of a rectangle of length L and width W can be calculated using the following formula:
P = 2L + 2W
For instance, the perimeter of a rectangle with dimensions of 10 metres in length and 5 metres in width would be:
[tex]P = 2(10) plus 2(5) equals 20 plus 10 metres.[/tex]
Hence, the rectangle's perimeter is 30 metres.
The fencing has a length and a width and is rectangular in design.
Size: 5000 feet
width is 4000 feet.
She will walk a distance equal to the length of the rectangular fence's perimeter.
Perimeter = 2 (length + width) = 2 (5000 + 4,000) = 2 (9000) = 18,000 ft.
She logs 18,000 feet of walking each shift.
Learn more about perimeter here:
https://brainly.com/question/6465134
#SPJ1
The table of values represents a relationship between the number of cupcakes, x, and the total cost, y. What is the slope of the line that best represents this relationship?
The slope of the line that best represents the relationship between the number of cupcakes and the total cost is 3.
To find the slope of a line that represents the relationship between two variables, we can use the formula: slope = (change in y) / (change in x).
Let's choose the first and last points from the table:
x1 = 0, y1 = 0
x2 = 3, y2 = 9
Using the slope formula:
slope = (y2 - y1) / (x2 - x1)
= (9 - 0) / (3 - 0)
= 3
Therefore, the slope of the line that best represents the relationship between the number of cupcakes and the total cost is 3.
Learn more about slope :
https://brainly.com/question/14511992
#SPJ4
which of the following data sets would most likely have a negative association and a correlation coefficient between 0 and -1? a.) number of miles driven; number of radio stations listened to b.) average annual temperature in the united states; annual sweater sales by an american retailer c.) number of minutes spent exercising; number of calories burned d.) age of baby; weight of baby
The most likely data sets to have a negative association and a correlation coefficient between 0 and -1 are: number of minutes spent exercising; number of calories burned, which is option C.
The correlation coefficient, a numerical measure of the strength and direction of the relationship between two variables, is used to describe the association between two data sets. It ranges from -1 to +1, where a correlation coefficient of -1 indicates a negative correlation and +1 indicates a positive correlation.
Number of minutes spent exercising and the number of calories burned while exercising have a negative association. That is, as the number of minutes spent exercising increases, the number of calories burned decreases.
Therefore, the most likely data sets to have a negative association and a correlation coefficient between 0 and -1 are "number of minutes spent exercising; number of calories burned."
Hence, the correct answer is C.
To know more about data sets, refer here:
https://brainly.com/question/22210584#
#SPJ11
Answer: Average Annual Temperature in the US; Annual sweater sales by an American retailer
Step-by-step explanation:
What appears true about these two triangles? Please provide a true hypothesis?
The two triangles are similar using the AA criteria of similarity.
What are vertically opposite angles?When two lines cross at a point, vertical angles are created. They are always on an equal footing. In other words, four angles are created anytime two lines cross or meet. It is evident that two opposed angles are equal and are referred to as vertical angles. They are also known as "Vertically opposed angles" due to the fact that they are perpendicular to one another.
In the given figure it is given that, AB is parallel to DF.
Thus, angle ABC = angle CDF
Also, the angle ACB and DCF form vertically opposite angles, and are equal.
Thus, the two triangles are similar using the AA criteria of similarity.
Learn more about AA criteria here:
https://brainly.com/question/29889759
#SPJ1
The graph of quadratic function k is shown on the grid. The coordinates of the x-intercepts,the y-intercepts,and the vertex are integers.what is the maximum value of k?
The maximum value of k is equal to 9.
What is a quadratic function?In Mathematics, a quadratic function refers to a mathematical equation which defines and represent the relationship that exists between two (2) or more variable on a graph, with a maximum exponent of two (2).
Generally speaking, the graph of a quadratic function would always form a parabolic curve (u-shaped). For this quadratic function, we can logically deduce that the graph is an upward parabola because the coefficient of x² is positive and the value of "a" is greater than zero (0).
In conclusion, the vertex of this quadratic function is at (2, 9) and as such, the maximum value of k is 9.
Read more on quadratic functions here: https://brainly.com/question/13911415
#SPJ1
14. Weather forecasts will often give reports on the pollen count. For people with
allergies, the pollen count indicates the severity of their symptoms. High pollen
count means bad symptoms. A medium pollen count is greater than 4 and less
than or equal to 8. Write an inequality for a high pollen count. Write another
inequality for a low pollen count?
The inequalities for each pollen count are given as follows:
High: p > 8.Low: p ≤ 4.What are the inequality symbols?The four inequality symbols, along with their meaning, are presented as follows:
> x: amount greater than x -> to the right of x with an open dot at the number line.< x: amount less than x. -> to the left of x with an open dot at the number line.≥ x: amount at least x. -> to the right of x with a closed dot at the number line.≤ amount at most x. -> to the left of x with a closed dot at the number line.A medium pollen count is greater than 4 and less than or equal to 8, hence:
A low pollen count is of amounts of 4 or less, hence: p ≤ 4.A high pollen count is an amount greater than 8, hence: p > 8.More can be learned about inequalities at brainly.com/question/25275758
#SPJ1
find x in a parallelogram ABCD.
Answer:
In a Parallelogram , opposite sides are parallel. => 3x = 30° . Hence, the required value of x is 10 degrees.
I need the X and Y for this please
Answer:
ما ان جميع زوايا. المثلث تساوي 180
x=180-90-57=27
y=3
The joint distribution of x and y are given as:
That is p(-1,-2)=1/8 ; p(1,2)=1/8 and so on… Determine the following
(a) P(???? < 0.5, ???? < 1.5); P(???? > 0.25, ???? < 4.5); P(???? ≤ 0.5)
(b) The conditional probability distribution of X given that Y =1 (c) E(Y)
(c) ????(????|???? = 1) (d) Are X and Y independent?
(a) 0, 1/2, 3/8.
(b) The conditional probability distribution of X is 1/3.
(c) the expected value of Y is 0.
(d) Yes, X and Y are independent.
What is Joint distribution?
Joint distribution is a probability distribution that describes the simultaneous behavior of two or more random variables. It specifies the probability of each possible combination of values for the random variables. In other words, it provides a way to calculate the probability of events that involve multiple random variables.
(a) To find the probabilities P(X < 0.5, Y < 1.5), P(X > 0.25, Y < 4.5), and P(X ≤ 0.5), we need to sum the joint probabilities over the appropriate ranges of X and Y.
P(X < 0.5, Y < 1.5) = p(-1,-2) + p(-1,0) + p(-1,1) + p(0,-2) + p(0,0) + p(0,1) = 0
P(X > 0.25, Y < 4.5) = p(1,-2) + p(1,0) + p(1,1) + p(1,2) + p(2,-2) + p(2,0) + p(2,1) + p(2,2) = 1/2
P(X ≤ 0.5) = p(-1,-2) + p(-1,0) + p(-1,1) + p(0,-2) + p(0,0) + p(0,1) + p(0,2) + p(1,-2) + p(1,0) + p(1,1) = 3/8
(b) The conditional probability distribution of X given that Y = 1 can be found by dividing the joint probabilities by the marginal probability of Y = 1:
P(X = -1 | Y = 1) = p(-1,1) / ∑ p(-1,y) = 1/3
P(X = 0 | Y = 1) = p(0,1) / ∑ p(0,y) = 1/3
P(X = 1 | Y = 1) = p(1,1) / ∑ p(1,y) = 1/3
Therefore, the conditional probability distribution of X given that Y = 1 is:
X | P(X|Y=1)
--- | --------
-1 | 1/3
0 | 1/3
1 | 1/3
(c) To find E(Y), we need to sum the product of Y and its probability over all possible values of Y:
E(Y) = ∑ y p(x,y)
E(Y) = (-2)(1/8) + (-1)(1/4) + (0)(1/8) + (1)(1/4) + (2)(1/8) = 0
(d) To determine if X and Y are independent, we need to check if the joint distribution can be expressed as the product of the marginal distributions:
p(x,y) = p(x) * p(y)
We can find the marginal distributions by summing the joint probabilities over the appropriate values of X or Y:
p(x) = ∑ p(x,y)
p(-1) = p(-1,-2) + p(-1,0) + p(-1,1) = 1/4
p(0) = p(-1,0) + p(0,-2) + p(0,0) + p(0,1) = 1/2
p(1) = p(1,-2) + p(1,0) + p(1,1) + p(1,2) = 1/4
p(y) = ∑ p(x,y)
p(-2) = p(-1,-2) + p(1,-2)
To learn more about Joint distribution, visit the link:
https://brainly.com/question/29896953
#SPJ1
If angle A = 30 degree and AB =8 how long is bc
In a right angled triangle ABC, if angle A
= 30 degree and AB = 8 cm then the length of side BC is equals to the 4.62 cm.
As we see in figure, ∆ABC is an right angled triangle with side length of AB
= 8 cm and measure of angle A = 30°. Measure of angle B is 90°. So, measure of angle C = 180° - 90° - 30°
= 69°. So, AB is the opposite side for the angle C, AC is the opposite side for the angle B and BC opposite side for the angle A. We have to determine the length of side BC. Using the Trigonometric functions, tan x = height / base length
In ∆ABC, tan A = BC/AB
=> tan(30°) = BC/8
=> 1/√3 = BC/8 ( tan(30°) = 1/√3)
=> BC = 8/√3 = 4.62
Hence, required length of side BC is 4.62 cm.
For more information about right angled triangle, visit :
https://brainly.com/question/64787
#SPJ4
Complete question:
In triangle ABC, angle A=30 degrees and AB =8cm. Find the length of side BC? see the above figure.
Can someone pls help if they can:)
Step-by-step explanation:
Groceries 3% of $326.79
3/100 x 326.79/1 = 980.37/100
Ans $9.80
Other purchases 1.5% of $581.34
1.5/100 x 581.34/1 = 872.01/100
Ans $8.72
Total cash earned back $9.80 + $8.72 = $18.52
The radioactive substance cesium-137 has a half-life of 30 years. The amount A (t) (in grams) of a sample of cesium-137 remaining after + years is given by the following exponential function. A (t) = 647(1/2)^t/30
Find the initial amount in the sample and the amount remaining after 100 years.
Round your answers to the nearest gram as necessary.
In respοnse tο the questiοn, we may say that In 100 years, there will be functiοn arοund 125 grammes left.
what is functiοn?Mathematicians research numbers, their variants, equatiοns, assοciated structures, fοrms, and pοssible cοnfiguratiοns οf these. The wοrd "functiοn" describes the cοnnectiοn between a grοup οf inputs, each οf which has a cοrrespοnding οutput. A functiοn is a cοnnectiοn between inputs and οutputs where each input results in a single, distinct οutcοme. Each functiοn has a dοmain, cοdοmain, οr scοpe assigned tο it. Functiοns are usually denοted by the letter f. (x). An x is entered. On functiοns, οne-tο-οne capabilities, sο multiple capabilities, in capabilities, and οn functiοns are the fοur main categοries οf accessible functiοns.
Setting t = 0 in the prοvided functiοn will reveal the sample's οriginal quantity:
A(0) = 647
[tex](1/2)^{(0/30)}[/tex] = 647
As a result, there are 647 grammes οf starting material in the sample.
In οrder tο calculate the amοunt left after 100 years, we must enter t = 100 intο the supplied functiοn:
[tex]A(100) = 647(1/2)^{(100/30) }= 647(1/2)^{(10/3)}[/tex] ≈ 125.24
Thus, there will be arοund 125 grammes left after 100 years (rοunded tο the nearest gram).
There are 647 grammes οf starting material in the sample.
In 100 years, there will be arοund 125 grammes left.
To know more about function visit:
brainly.com/question/28193995
#SPJ1
The initial amount of the sample is 647 grams and the amount remaining after 100 years is 69 grams.
what is functiοn?
Mathematicians research numbers, their variants, equatiοns, assοciated structures, fοrms, and pοssible cοnfiguratiοns οf these. The wοrd "functiοn" describes the cοnnectiοn between a grοup οf inputs, each οf which has a cοrrespοnding οutput.
The given exponential function is:
A(t) = 647(1/2)^(t/30)
where t is the time in years.
To find the initial amount of the sample, we need to evaluate A(0):
A(0) = 647(1/2)^(0/30) = 647(1) = 647
Therefore, the initial amount of the sample is 647 grams.
To find the amount remaining after 100 years, we need to evaluate A(100):
A(100) = 647(1/2)^(100/30) ≈ 69.35
Rounding this to the nearest gram gives the amount remaining after 100 years as 69 grams.
Therefore, the initial amount of the sample is 647 grams and the amount remaining after 100 years is 69 grams.
To know more about function visit:
brainly.com/question/28193995
#SPJ1
list 5 values that are solutions to the inequality 3(x+4)<9
The given inequality will be satisfied by any value of x that is less than -1. Here are five potential remedies. x = -2, x = -2.5, x = -3, x = -1.2,x = -1.8. We can see that each of these values fulfils the given inequality.
What is the inequality formula?When x > Y and a > 0, the result is (x/a) > (y/a), and when x Y and a > 0, the result is (x/a) (y/a). On the other hand, if the inequality sign is reversed, the division of both sides of an inequality by a negative integer results in an equivalent inequality.
We can solve the inequality 3(x+4)<9 as follows:
3(x+4) < 9 (given inequality)
3x + 12 < 9 (distributing the 3)
3x < -3 (subtracting 12 from both sides)
x < -1 (dividing both sides by 3 and changing the direction of the inequality)
So, any value of x that is less than -1 will satisfy the given inequality. Here are five possible solutions:
x = -2
x = -2.5
x = -3
x = -1.2
x = -1.8
To know more about inequality visit:-
https://brainly.com/question/30231190
#SPJ1
George peels and eats 2 satsumas he then splits then into 6 equal parts and eats one of the parts how many satsumas does he eat in total give your answer as a improper fraction
George eats a total of 25/12 satsumas. This is an improper fraction, meaning the numerator is greater than the denominator, but it is the correct answer to the problem.
George starts with 2 satsumas, which he then splits into 6 equal parts, resulting in 12 parts in total. He eats one of these parts, which is 1/12 of a satsuma.
To find out how many satsumas he eats in total, we need to add the 2 whole satsumas he ate at the beginning to the fraction of a satsuma he ate later:
2 + 1/12
To add these together, we need to find a common denominator. The smallest common multiple of 12 and 1 is 12, so we can convert 2 to twelfths by multiplying it by 12/12:
2 + 1/12 = 24/12 + 1/12
Now we can add the two fractions together:
24/12 + 1/12 = 25/12
learn more about denominator here:
https://brainly.com/question/7067665
#SPJ4
which is an exponential decay function?
the second one, as the fraction (4/5) is less than 1
(-2x)² - (- 3x)²
simplify
Answer:
[tex]\boxed{5x^2}[/tex]
Step-by-step explanation:
[tex](-2x)^2-(-3x)^2[/tex]
Based in the order of operations (PEMDAS), we solve:
First, Parentheses or Brackets (Perform operations inside parentheses)next, Exponentsthen, Multiplication and divisionfinally, Addition and substraction[tex]4x^2-9x^2 =5x^2[/tex]
[tex]\text{-B$\mathfrak{randon}$VN}[/tex]
Answer: [tex]-5x^{4}[/tex]
Step-by-step explanation: add and boom
It’s argent
Suppose you invested $10,000 in an account that pays 5% simple interest. How much money will you have at the end of 5 years?
I will have $2500 at the end of 5 years
What is Interest Rate?Interest Rate is the amount of interest due per period, as a proportion of the amount lent, deposited, or borrowed. It is the percentage of principal charged by the lender for the use of its money.It is also percentage a lender charges on the amount of money borrowed.
Where, The principal is the amount of money loaned.
The formula = Principal * Rate * Time/100
Where Principal = $10000
Rate = 5%
Time = 5 years
Simple Interest = 10000 * 5 * 5/100
Simple Interest = 250000/100
Simple Interest = $2500
Read more about Simple Interest
https://brainly.com/question/2294792
#SPJ1
Select the correct answer from each drop-down menu.
The equation of a line is 2/5x + 1/10y = 2.
The x-intercept of the line is -blank-. and its y-intercept is -blank-.
The line with an equation (2/5)x + (1/10)y = 2 have an x intercept at (5, 0) and y intercept at (0, 20)
What is an equation?An equation is an expression that shows how two or more numbers and variables are related using mathematical operations of addition, subtraction, multiplication, division, exponents and so on.
The slope intercept form of a linear equation is:
y = mx + b
where m is the rate of change (slope) and b is the y intercept.
Given the equation:
(2/5)x + (1/10)y = 2
The x intercept is at y = 0, hence:
(2/5)x + (1/10)(0) = 2
(2/5)x = 2
x = 5
The x intercept is (5, 0)
The y intercept is at x = 0, hence:
(2/5)(0) + (1/10)(y) = 2
(1/10)y = 2
y = 20
The y intercept is (0, 20)
The line with an equation (2/5)x + (1/10)y = 2 have an x intercept at (5, 0) and y intercept at (0, 20)
Find more on equation at: https://brainly.com/question/2972832
#SPJ1
Rewrite in simplest term: -6(0.6w-3w-0.9)-0.9w
Answer:
13.5w + 5.4.
Step-by-step explanation:
Using the distributive property, we would write it out like
-6(0.6w-3w-0.9)-0.9w = -3.6w + 18w + 5.4 - 0.9w
Then we would combine like terms by adding the coefficients of the w terms:
-3.6w + 18w - 0.9w = 13.5w
Lastly we can add the constant terms.
13.5w + 5.4 = 13.5w + 5.4
factor w squared minus 81
Answer:
The answer is (w-9)(w+9).
Answer:
(w - 9)(w + 9)
Step-by-step explanation:
w² - 81 ← is a difference of squares and factors in general as
a² - b² = (a - b)(a + b)
then
w² - 81
= w² - 9²
= (w - 9)(w + 9)
3(x-5)+11= x + 2(x+5) ??
What is x ???
Mrs. Meyer is teaching a 5th grade class. She is standing 8 meters in front of Leslie.
Dalton is sitting 3 meters to Leslie's right. How far apart are Mrs. Meyer and Dalton? If
necessary, round to the nearest tenth.
The distance between Mrs. Meyer and Dalton would be = 8.5m
How to calculate the distance between Mrs. Meyer and Dalton?The shape that is being formed between the three individuals is the shape of a triangle.
Distance can be defined as the length that is covered by a moving object.
The distance between Mrs Meyer and Leslie =a= 8m(opposite)
The distance between Dalton and Leslie =b = 3 m (adjacent)
Therefore, the hypotenuse = ?
Using the Pythagorean theorem;
c² = a² + b²
C ² = 8²+3²
C = 64 + 9
c² = 73
C = √ 73
C = 8.5m
Learn more about triangle here :
https://brainly.com/question/28470545
#SPJ1
2 boxes combined weighed 155 pounds of flour. 20 pounds of flour was moved from the first box to the second. Now the first box has 12/19 of what is in the 2nd box. How much flour was in each box
The amount of flour in each box is given as follows:
1st box: 80 pounds.2nd box: 75 pounds.How to obtain the amount of flour in each box?The amount of flour in each box is obtained solving a system of equations.
The variables for the system of equations are given as follows:
Variable x: amount of flour on the first box.Variable y: amount of flour on the second box.2 boxes combined weighed 155 pounds of flour, hence:
x + y = 155
y = 155 - x.
20 pounds of flour was moved from the first box to the second. Now the first box has 12/19 of what is in the 2nd box, hence the ratio is:
(x - 20)/(y + 20) = 12/19.
Replacing the first equation into the second, the value of x is obtained as follows:
(x - 20)/(155 - x + 20) = 12/19
(x - 20)/(175 - x) = 12/19
19(x - 20) = 12(175 - x)
31x = 2480
x = 2480/31
x = 80 pounds.
Then the value of y is obtained as follows:
y = 155 - x
y = 155 - 80
y = 75 pounds.
More can be learned about a system of equations at https://brainly.com/question/30374328
#SPJ1
Solve for vertex algebraically 4x^2-8x+9
Answer: (1,5)
f(x)=4*x^2+-8x+9
f(x)=4*(x^2+-2x+9/4 ( Factor out )
f(x)=4*(x^2+-2x+(-1)^2+-1*(-1)^2+9/4) ( Complete the square )
f(x)=4*((x+-1)^2+-1*(-1)^2+9/4) ( Use the binomial formula )
f(x)=4*((x+-1)^2+1*5/4) ( simplify )
f(x)=4*(x+-1)^2+5 ( expand )
A shape is made of 6 right triangles of equal size. Each right triangle has a base of 6 cm and height of 5 cm. What is the total area, in square centimeters, of the 6 right triangles?
The total area of the shape is 90cm²
What is area of a Triangle?Area is defined as the total space taken up by a flat (2-D) surface or shape of an object. The area of a triangle is expressed as ;
A = 1/2 bh, where b is the base and h is the height if that triangle.
The base of the a triangle in the shape is 6cm and the height is 5cm.
A = 1/2 bh
A = 1/2 × 6 × 5
A = 3× 5
A = 15cm²
Since the size of the triangles are equal ,it means that all the triangles will have thesame area.
Therefore the area of six triangles =
6× 15 = 90cm²
Therefore the area of the shape is 90cm²
learn more about area of triangle from
https://brainly.com/question/17335144
#SPJ1
After she gave some stickers to her brother, Jenny’s dog ate three of her stickers now what fraction does Jenny have left of her original box of 15 stickers
Jenny has 7/15 of her original box of stickers left after giving some to her brother and after her dog ate three of them.
Jenny had an original box of 15 stickers. She gave some stickers to her brother and then her dog ate three of the remaining stickers. We can use fraction to represent what fraction of the original box of stickers Jenny has left.
Let's start by finding out how many stickers Jenny had left after giving some to her brother. If we don't know how many stickers she gave away, we can't know how many stickers she has left. So let's say Jenny gave away 5 stickers to her brother.
Jenny had 15 stickers - 5 stickers = 10 stickers left.
But then her dog ate three stickers, so she has 10 stickers - 3 stickers = 7 stickers left.
To find the fraction of the original box of stickers that Jenny has left, we need to divide the number of stickers she has left by the original number of stickers:
7 stickers ÷ 15 stickers = 7/15.
Therefore, Jenny has 7/15 of her original box of stickers left after giving some to her brother and after her dog ate three of them.
For more such questions on fractions
https://brainly.com/question/78672
#SPJ4
Find the area of the shaded segment of the circle
The area of the shaded segment in the given circle with radius 24cm and central angle 60° is approximately 301.5929 cm². This was calculated by subtracting the area of an equilateral triangle from that of a sector.
The area of the shaded segment can be calculated by subtracting the area of the triangle formed by the two radii from the area of the sector formed by the two radii.
First, let’s find the area of the sector. The formula for finding the area of a sector is A = (θ/360) * π * r², where θ is the angle at the center in degrees and r is radius. Substituting θ = 60° and r = 24cm, we get:
A = (60/360) * π * 24² A = 1/6 * π * 576 A = 96π
Next, let’s find the area of triangle. The formula for finding area of an equilateral triangle is A = √3/4 * a², where a is side length. Since all sides are equal to radius in this case, substituting a = 24cm, we get:
A = √3/4 * 24² A = √3/4 * 576 A = 144√3
Now we can find area of shaded segment by subtracting area of triangle from that of sector:
Area of shaded segment = Area of sector - Area of triangle = (96π) - (144√3) = 96π - 144√3 cm²
So, the area of shaded segment is approximately 301.5929 cm².
Learn more about circle here: brainly.com/question/29142813
#SPJ4
The missing figure is in the image below
A fence was installed around the edge of a rectangular garden. The length. I, of the fence was 5 feet less than 3 times its width. w. The amount of fencing used was 90 feet. Write a system of equations or write an equation using one variable that models this situation.
Determine algebraically the dimensions, in feet, of the garden.
Answer:
Width: w = 12.5 feet
Length: L = 32.5 feet
Step-by-step explanation:
Let's use two variables to represent the dimensions of the rectangular garden:
Let w be the width of the garden (in feet)
Let L be the length of the garden (in feet)
The problem tells us that the length of the fence is 90 feet, so we can write the equation:
2L + 2w = 90
We also know that the length of the fence (L) is 5 feet less than 3 times the width (w). We can write this as another equation:
L = 3w - 5
Now we have two equations with two variables. We can solve this system of equations using substitution or elimination.
Let's use substitution:
Substitute the expression for L in terms of w from the second equation into the first equation:
2(3w - 5) + 2w = 90
Simplify and solve for w:
6w - 10 + 2w = 90
8w = 100
w = 12.5
Now we can use this value of w to find L:
L = 3w - 5 = 3(12.5) - 5 = 32.5
Therefore, the dimensions of the rectangular garden are as follows:
Width: w = 12.5 feet
Length: L = 32.5 feet
1. Solve and check the following radical equations algebraically. Specify your solution set. a)2x−3−1=0b)3x 2+2= 5x 2−6c)6x+7=x+2d)x+1= x 2+9
Given equation 2x − 3 − 1 = 0.
Now, bring -1 to the right side of the equation:
2x − 3 = 1
Now, add 3 to both sides:
2x = 4
x = 2
Now, we need to check whether this is the correct solution or not. Putting the value of x in the given equation:
2(2) − 3 − 1 = 0
⇒ 1 − 1 = 0
⇒ 0 = 0
Hence, x = 2 is the solution to the given equation.
(a) The solution set of the equation 2x − 3 − 1 = 0 is {2}.
Given equation 3x² + 2 = 5x² − 6.
Now, bring 5x² − 6 to the left side of the equation:
-2x² + 2 = 0
Now, bring 2 to the right side of the equation:
-2x² = -2
⇒ x² = 1
⇒ x = ±1
Now, we need to check whether these are the correct solutions or not. Putting the value of x in the given equation:
3x² + 2 = 5x² − 6
For x = 1,
3(1)² + 2 = 5(1)² − 6
⇒ 3 + 2 = 5 − 6
⇒ -1 = -1
For x = -1,
3(-1)² + 2 = 5(-1)² − 6
⇒ 3 + 2 = 5 − 6
⇒ -1 = -1
Hence, x = 1 and -1 are the solutions to the given equation.
(b) The solution set of the equation 3x² + 2 = 5x² − 6 is {-1,1}.
Given equation 6x + 7 = x + 2.
Now, bring x to the left side of the equation:
6x − x + 7 = 2
Now, add 7 to both sides:
5x = -5
⇒ x = -1
Now, we need to check whether this is the correct solution or not. Putting the value of x in the given equation:
6(-1) + 7 = (-1) + 2
⇒ -6 + 7 = -1 + 2
⇒ 1 = 1
Hence, x = -1 is the solution to the given equation.
(c) The solution set of the equation 6x + 7 = x + 2 is {-1}.
Given equation x + 1 = x² + 9.
Now, bring x² to the left side of the equation:
x² − x + 1 = 9
Now, bring 9 to the right side of the equation:
x² − x − 8 = 0
Now, factorizing the given equation:
(x − 4)(x + 2) = 0
So, the solutions are x = 4 and x = -2.
Now, we need to check whether these are the correct solutions or not. Putting the value of x in the given equation:
x + 1 = x² + 9
For x = 4,
4 + 1 = 4² + 9
⇒ 5 = 25
For further information on factorization, refer below:
https://brainly.com/question/14209188
#SPJ11
Determine the domain of the following graph:
The domian of the graph is (-11, 11]
What is the domain of a graphThe domain of a graph is the set of all possible input values (or independent variable values) for which the function is defined and produces a valid output (or dependent variable value).
How to determine the domian of the graphFrom the question, we have the following parameters that can be used in our computation:
The graph
As stated above:
The domain of a graph is the set of input values of the graph
Using the above as a guide, we have the following:
The input values start from x = -11 (open circle)The input values end at x = 11 (closed circle)When this is represented as an interval, we have
(-11, 11]
Hence, the solution is (-11, 11]
Read more about domain at
https://brainly.com/question/2264373
#SPJ1