Answer:
the common difference of the sequence (d) = -3
Step-by-step explanation:
Given sequence is 1st term, 2nd term, 3rd term
= 5, 2, -1
It is an arithmetic sequence.
The common difference (d) = second term - first term
d = 2 - 5
d = -3
Therefore, the common difference of the sequence (d) = -3
Hope this will helpful.
Thank you.
Solve x2 + 6x + 7 = 0.
Answer:
[tex]x=-3+\sqrt{3}[/tex] , [tex]x=-3-\sqrt{3}[/tex]
Step-by-step explanation:
x2 + 6x + 7 = 0
Solve the equation for x
To solve this we apply quadratic formula
[tex]x=\frac{-b+-\sqrt{b^2-4ac} }{2a}[/tex]
a= 1 , b= 6 , c= 7
Plug in all the values in the formula
[tex]x=\frac{-6+-\sqrt{6^2-4(1)(7)} }{2(1)}[/tex]
[tex]x=\frac{-6+-\sqrt{36-28} }{2(1)}[/tex]
[tex]x=\frac{-6+-\sqrt{8} }{2(1)}[/tex]
[tex]x=\frac{-6+-2\sqrt{2} }{2}[/tex]
Divide each term by 2
[tex]x=-3+- \sqrt{3}[/tex]
so we got two value for x
[tex]x=-3+\sqrt{3}[/tex] , [tex]x=-3-\sqrt{3}[/tex]
What is the surface to a rectangular playing surface with 44 feet and 77 feet?
Which linear inequality is represented by the graph
Option B is correct, y≤1/3x-4 is the linear inequality which is represented by the graph
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
The equation of line passing through points (3, -3) and (0, -4)
Slope = -4+3/0-3
=1/3
Now let us find y intercept
-4=1/3(0)+b
b=-4
Equation is y=1/3x-4
y≤1/3x-4 is the required inequality of the graph
Hence, y≤1/3x-4 is the linear inequality which is represented by the graph
To learn more on slope of line click:
https://brainly.com/question/16180119
#SPJ7
What should you do to both sides of the inequality in order to solve x + (-2) > 3?
Subtract 2.
Add 2.
Add 3.
Subtract 3.
The Frostburg-Truth bus travels on a straight road from Frostburg Mall to Sojourner Truth Park. The mall is 4 miles east and 4 miles north of the City Center. The park is 2 miles west and 4 miles south of the Center. How far is it from the mall to the park to the nearest tenth of a mile?
11.1 miles
5.7 miles
10.0 miles
4.5 miles
Answer:
10.0 is the correct answer
Step-by-step explanation:
During a soccer game, Erin scored 1 out of 3 goals attempted. Lauren scored 2 out of 8 goals attempted. Write the fraction that represents each and compare. Who was most successful?
A: 1/3<2/8;Erin
B: 1/3>3/8;Erin
C: 1/3<2/8;Lauren
D: 1/3>2/8;Lauren
NEED HELP ASAP PLZ
Rank and alice are penguins. at birth, frank's beak was 1.95 inches long, while alice's was 1.50 inches long. homework help ✎ frank's beak grows by 0.25 inches per year and alice's grows by 0.40 inches per year. write an equation to represent the length of each penguin's beak in x years. how old will they be when their beaks are the same length?
) compute $x+y$ and $\sqrt{x^2+y^2}$ when $x=5$ and $y=12.$
b.when is \[x+y=\sqrt{x^2+y^2}?\]when is
sin x°= 4/15 round to nearest tenth find x
explain how you can compare the cost of two items that are different sizes
Answer:
First find the unit price for each. Then compare the unit prices. The item that has the lesser unit cost is the better buy.
Step-by-step explanation:
When comparing the costs of two items that are different sizes, use ratios to make a comparison and consider the unit size.
Explanation:When comparing the costs of two items that are different sizes, you can use ratios to make a comparison. Let's say Item A costs $10 and Item B costs $20. Item A is twice as expensive as Item B. To make the comparison fair, you can also consider the size or quantity of the items. For example, if Item A is twice as expensive but also twice as large as Item B, then the cost per unit size is the same. However, if Item A is half the size of Item B, then Item B is a better deal in terms of size.
Find the maximum rate of change of f(xy)=ln(x2+y2) at the point (-1, -5) and the direction in which it occurs.
Solve to the equation for y
4x+2y=6
Calculate 6¾% tax on $2,305 a.$15.56 b.$145,22 c.$146,14 d.$155,59.
A weather forecaster predicts that the temperature in antarctica will decrease 8 degreesf each hour for the next 6 hours how long will it take to go down 36 degrees
LeAnn wants to gift wrap a present she got for her little brother. How many square inches of gift wrap will be needed to cover a box that is 4in x 6in x 2in?
List two advantages of buying and two advantages of renting
Answer:
advantages of buying:
-you own your own property
-the value of your property may increase over time
-you can improve or decorate your house as you wish
advantages of renting:
-your landlord is responsible for repairs
-you need to pay fewer up-front cost
-paying rent on time helps you build a good credit history
-renting is better if you dont plan to stay long
-you can have roomates to share costs
4.Thirty percent of the liquid evaporated. If 560 milliliters remain, how many milliliters evaporated?
Eliza Savage received a statement from her bank showing a checking account balance of $324.18 as of January 18. Her own checkbook shows a balance of $487.38 as of January 29. The bank returned all of the cancelled checks but three. The amounts of these three checks are $15.00, $77.49, and $124.28. How much did Eliza deposit in her account between January 18 and January 29?
A. $197.24 B. $379.97 C. $54.44 D. $201.12
Answer:
b
Step-by-step explanation:
What method can be used to write the equation of a line in slope-intercept form given two points?
To write the equation of a line in slope-intercept form given two points, calculate the slope from the points, use one point and the slope to find the y-intercept, then write the equation as y = mx + b.
Explanation:To write the equation of a line in slope-intercept form, given two points, follow these steps:
Calculate the slope (m) using the formula m = (Y2 - Y1) / (X2 - X1), where (X1, Y1) and (X2, Y2) are the coordinates of the two given points.Once you have the slope, choose one of the two points to substitute into the slope-intercept form equation, y = mx + b, along with the slope you calculated. This will allow you to solve for the y-intercept (b).With both the slope and y-intercept, you can write the final equation of the line: y = mx + b.For example, if the two points given are (1, 3) and (4, 11), the slope would be (11 - 3) / (4 - 1) = 8 / 3. Then choosing the point (1, 3), we would substitute to find the y-intercept: 3 = (8/3)(1) + b, resulting in b = 3 - 8/3 = 1/3. So the equation of the line is y = (8/3)x + 1/3.
A rectangle has an area of 126 m2 and a width of 7 m. What is its length?
An astronaut who weighed 150 pounds on Earth found that his weight on Jupiter was 400 pounds. He captured an alien that weighed 120 pounds on Jupiter. What is the alien's weight on Earth?
Answer:
45 pounds
Step-by-step explanation:
In the measurement 0.503 l, which digit is the estimated digit? the 0 immediately to the left of the 3 5 the 0 to the left of the decimal point 3
Answer:
3.
Step-by-step explanation:
We are asked to find the estimated digit in the measurement 0.503 L.
We know that in each measurement the estimated digit is always the last digit.
We can see that the first digit in the given measurement is 5, the second digit is 0 and the last digit is 3.
Since the last digit is in our given measurement 3, therefore, the estimated digit is 3.
Artaud noticed that if he takes the opposite of his age and addes 40 he gets the number 28 how old is artaud
Answer:
Artaud is 12 years old
Step-by-step explanation:
What is the best answer???
m is the set of integers that are greater than -1 and less than 4
The domain for f(x) and g(x) is the set of all real numbers. Let f(x) = 3x + 8 and g(x) = x2. Find (f • g)(x).
A. x2 − 3x − 8
B. 3x2 + 8
C. 3x3 + 3x2 + 8
D. 3x3 + 8x2
Solve for x.
13(x - 3) = 39
x = 1
x = 4
x = 6
x = 10
log(w^2+21)=log(10w)
[tex]\[ w = 7 \][/tex]
Explanation:The given equation is [tex]\(\log(w^2+21)=\log(10w)\)[/tex]. To find the solution, we can set the arguments of the logarithms equal to each other, giving [tex]\(w^2 + 21 = 10w\)[/tex].
Rearranging, we get a quadratic equation [tex]\(w^2 - 10w + 21 = 0\).[/tex] Factoring or using the quadratic formula yields the solutions
However, we need to check for extraneous solutions. Substituting [tex]\(w = 3\)[/tex] back into the original equation results in taking the logarithm of a negative number, which is undefined in the real number system. Therefore, [tex]\(w = 3\)[/tex] is extraneous, and the valid solution is [tex]\(w = 7\).[/tex]
In the detailed explanation, we used the property of logarithms that states [tex]\(\log(a) = \log(b)\)[/tex] implies [tex]\(a = b\)[/tex]. By setting the arguments of the logarithms equal to each other, we obtained a quadratic equation.
Factoring or applying the quadratic formula allowed us to find the solutions. However, we must always check for extraneous solutions by substituting them back into the original equation and ensuring the logarithms are defined for the real number system.
In this case, only [tex]\(w = 7\)[/tex] satisfies the equation without resulting in undefined logarithms.
The measure of the angle's supplement is 40° more than three times that of its complement. find the measure of the angle described
LaTonya has 16 photos on her phone , and Luis has p photos in his wallet.
Which algebraic expression represents the total number of photos that LaTonya and Luis have ?
Answer:
The expression is 16 + p
Step-by-step explanation:
Algebraic expression is a mathematical phrase that contains numbers and variables with an operation ( addition or subtraction etc. )
Given,
The number of photos Latonya has on her phone = 16,
While p represents the number of photos Luis has in his wallet,
Where p is a variable,
So, the total number of photos = Latonya's photos + Luis's photos
= 16 + p
Hence, the required expression is '16 +p'