Writing are the equations m + 3 = -5 and m = -2 equivalent? explain
Four friends purchase 18.4 pounds of peaches. The peaches cost $1.75 per pound. The friends share the cost of the peaches equally. What amount does each person pay? $4.60 $8.05 $24.15 $32.20
The functions f(x) = –(x + 4)2 + 2 and g(x) = (x − 2)2 − 2 have been rewritten using the completing-the-square method. Is the vertex for each function a minimum or a maximum? Explain your reasoning for each function.
Final answer:
The completing-the-square method allows rewriting quadratic functions to determine the vertex. The coefficient of the squared term determines if the vertex is a minimum or maximum.
Explanation:
The completing-the-square method allows us to rewrite quadratic functions in a form that reveals the vertex of the parabola. To determine if the vertex is a minimum or a maximum, we need to consider the coefficient of the squared term. In the function f(x) = –(x + 4)² + 2, the coefficient is negative, indicating that the parabola opens downwards, and the vertex is a maximum. In the function g(x) = (x − 2)² − 2, the coefficient is positive, indicating that the parabola opens upwards, and the vertex is a minimum.
In the trivia bowl, each finalist must answer four questions correctly. each question is worth twice as much as the question before it. the fourth is worth $6000. how much is the first question worth? select the appropriate answer.
a. $750
c. $900
b. $500
d. $1000
Please help! Thank you!
"the sum of the squares of two consecutive odd integers is 2594. find the two integers."
Final answer:
To find two consecutive odd integers whose squares sum to 2594, a quadratic equation is set up and solved, revealing that the integers are 35 and 37.
Explanation:
To solve for two consecutive odd integers whose squares sum to 2594, we can set up equations based on the characteristics of odd integers. Let the smaller integer be n, then the next consecutive odd integer would be n + 2.
The equation based on the sum of the squares of the two numbers is then:
n2 + (n + 2)2 = 2594
Solving this equation:
n2 + n2 + 4n + 4 = 25942n2 + 4n - 2590 = 0n2 + 2n - 1295 = 0Solving the quadratic equation we find that n = 35 and n + 2 = 37. Hence, the two consecutive odd integers are 35 and 37.
Evaluate the expression 3(7 + 4)2 − 14 ÷ 7. (5 points)
50
361
363
586
Do not just give me the answer, walk me through it. I am literally so shallow minded when it comes to Algebra and I am trying really hard to understand it.
Which of the following statements are true ?
The true statements for the triangle ABC where DE is perpendicular to AC is given by option D. The segment DE bisects the segment AC.
In triangle ABC, B-D-C, and A-E-C, with E being perpendicular to AC and AE = EC.
A. The segment BD bisects the segment EC.
This statement is false. Since E is the midpoint of AC (AE = EC), and E is perpendicular to AC, B-D-C no relation.
B. The segment ED is congruent to the segment DC.
This statement is not necessarily true. We only know that AE = EC, which implies that DE = EC since E is the midpoint of AC. However, we don't have enough information to conclude that ED is congruent to DC.
C. The segment BD is perpendicular to the segment EC.
This statement is not necessarily true. While we know that E is perpendicular to AC, it does not imply that BD is perpendicular to EC.
The perpendicularity of BD and EC depends on the specific configuration of the triangle, and the given information is not sufficient to determine this relationship.
D. The segment DE bisects the segment AC.
This statement is true. Since E is the midpoint of AC (AE = EC), DE passes through E and will indeed bisect AC.
Therefore, the true statements for the given triangle is
option D. The segment DE bisects the segment AC.
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If 3cot^2x - 5cotx = -2, then cotx = _____.
A. -2, -1/3
B. -1, -2/3
C. 1, 2/3
D. 2, 1/3
How would I do this? I'll give brainliest!
Make a table of ordered pairs for the equation.
y = 1/2x − 3
Then plot two points to graph the equation.
Find the slope of the line.
We can use the points (-4, -1) and (0, -2) to solve.
Formula: y2-y1/x2-x1
= -2-(-1)/0-(-4)
= -1/4
Best of Luck!
which equation is an identity?
a. 11- (2v + 3) = -2v - 8
b. 5w + 8 - w = 6w - 2( w - 4)
c. 7m - 2 = 8m + 4 - m
d. 8y + 9 = 8y - 3
Answer:
Option b - [tex]5w + 8 - w = 6w - 2( w - 4)[/tex]
Step-by-step explanation:
To find : Which equation is an identity?
Solution :
Option a - [tex]11- (2v + 3) = -2v - 8[/tex]
If we open the parenthesis,
[tex]11- 2v -3 = -2v - 8[/tex]
[tex]-2v+8\neq -2v - 8[/tex]
No identity applied.
Option b - [tex]5w + 8 - w = 6w - 2( w - 4)[/tex]
If we apply distributive property, [tex]a(b+c)=ab+ac[/tex]
[tex]5w + 8 - w = 6w - 2w+8[/tex]
[tex]4w+8= 4w+8[/tex]
Distributive identity is applied.
Option c - [tex]7m - 2 = 8m + 4 - m[/tex]
Solve by subtracting in RHS
[tex]7m - 2 \neq 7m + 4[/tex]
No identity applied.
Option d- [tex]8y + 9 = 8y - 3[/tex]
This is not possible as [tex]8y + 9 \neq 8y - 3[/tex]
No identity applied.
Therefore, Option b is correct.
The sum of three consecutive integers is -255. what are they?
What's the answer of the photo I just sent you
Is this true 1/2 >0.25
a. Write an expression that represents the following expression using the variable b: "Billy's age in 8 years." b. Write an equation using the expression above if in 8 years Billy will be 21 years old. c. How old is Billy now? d. Write and solve a word problem that matches the equation: a - 6 = 10.
Answer:
"Billy's age in 8 years", this refers to a future age, which implies adding 8 years to the present age. The expression would be:
[tex]B+8[/tex]
"In 8 years Billy will be 21 years", this expression, using the first one too, would be:
[tex]B+8=21[/tex]
How old is Billy now?
The answer to this question is the solution of the second equation:
[tex]B+8=21\\B=21-8=13[/tex]
Billy is 13 years old now.
A problem for the expression [tex]A-6=10[/tex] could be:
Six years ago Adam was 10 years old.
The six years in the past refers subtracting, and the age back then is the result of that difference.
On wensday on a track myles run 7 laps for every 3 laps that elijah run on friday elijahrun 16 more laps than on wensday making the number of laps he run and myles run the same .how many laps did eligah run on wensday
the tour boats at the Laguna can carry 8 passengers. jacob watched 6 floats by. one of the board has 2 empty seats. the other were full. how many passengers were on the 6 boats?
Dr. Cheeks tries to run at least 45 rotations on her hamster wheel each week. She has already run 6 rotations. Which inequality shows how many more rotations, r, she would have to run to meet her weekly goal?
A. r-6>45
B. r-6>45
C. r+6>45
D.r+6<45
Answer: C. r+6>45
Step-by-step explanation:
Since, Dr. Cheeks tries to run at least 45 rotations on her hamster wheel each week.
If she runs r rotations then, for the value of r, [tex]45\leq r[/tex]
Since, If she has already 6 rotations
Therefore total rotation she has = r+6
Thus, if [tex]45\leq r[/tex] ⇒[tex]45<x+6[/tex]
So, Option C is the correct option.
The inequality of option C r+6 > 45 shows the rotations, r, she would have to run to meet her weekly goal.
What is inequality?Inequality is defined as the relation which makes a non-equal comparison between two given functions.
Dr. Cheeks tries to run at least 45 rotations on her hamster wheel each week.
She has already 6 rotations but if she runs r rotations then, for the value of r, 45 ≤ r
The total rotation she has = r+6
Thus, 45 ≤ r
= 45 < r + 6
or r+6 > 45
So, Option C is the correct option.
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What is x if rs= 6, st=9, tu=7, uv=15,vr=14
The probability that an individual is left-handed is 0.16. in a class of 10 students, what is the mean and standard deviation of the number of left-handers in the class?
Using the binomial distribution, it is found that:
The mean of the number of left-handers in the class is of 1.6.The standard deviation of the number of left-handers in the class is 1.16.For each student, there are only two possible outcomes, either they are left-handers, or they are not. The probability of a student being a left-hander is independent of any other student, hence the binomial distribution is used to solve this question.
Binomial probability distribution
Probability of exactly x successes on n repeated trials, with p probability.
The expected value is:
[tex]E(X) = np[/tex]
The standard deviation is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
In this problem:
The probability that an individual is left-handed is 0.16, hence [tex]p = 0.16[/tex].The class has 10 students, hence [tex]n = 10[/tex]Then:
[tex]E(X) = np = 10(0.16) = 1.6[/tex]
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{10(0.16)(0.84)} = 1.16[/tex]
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what is 3 divided by 7.71?
the sum of twice a number x and 13 is two less than three times x
This is a word problem which requires basic logic or understanding to solve. We can write the equation:
2 x + 13 = 3 x – 2
So calculate for x:
3 x – 2x = 13 + 2
x = 15
Therefore the number is 15.
PLEASE HELP!!
What is the length of the midsegment of this trapezoid?
Enter your answer in the box.
Answer:
7 units
Step-by-step explanation:
The length of the midsegment of this trapezoid will be 7 units.
What is mean by Rectangle?
A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Given that;
The coordinates of the vertices of the trapezoid are,
A = (-2, 4)
B = (4, 3)
C = (4 , -5)
D = (- 2, - 2)
Now,
Since, We know that;
The length of the midsegment of a trapezoid is always equal to the half of the sum of the parallel sides.
Here, Line AD and BC are parallel lines.
And, The length of AD = √(- 2 - (-2))² + (- 2 - 4)²
= √-6²
= 6
And, The length of BC = √(4 - 4)² + (- 5 - 3)²
= √-8²
= 8
Thus, The length of the midsegment of this trapezoid = (6 + 8)/2
= 14/2
= 7 units.
Therefore, The length of the midsegment of this trapezoid will be 7 units.
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The perimeter of a rectangular field is 320 yd. the length is 80 yd longer than the width. find the dimensions.
The dimensions of a rectangular field is width = 40 yd and length = 120 yd.
What is a rectangle?
A rectangle is one of the types of quadrilaterals in which all four angles are right angles or equal to 90 degrees. It is four-sided polygon in which the opposite sides are parallel and equal to each other.
For the given situation,
Let the width of the rectangle, w = x
The length is 80 yd longer than the width.
The length of the rectangle, l = x + 80.
The perimeter of a rectangular field = 320 yd.
The formula of perimeter of rectangle is
[tex]P=2(w+l)[/tex]
On substituting the above values,
⇒ [tex]320=2(x+x+80)[/tex]
⇒ [tex]320=2(2x+80)[/tex]
⇒ [tex]2x+80=\frac{320}{2}[/tex]
⇒ [tex]2x+80=160[/tex]
⇒ [tex]2x=160-80[/tex]
⇒ [tex]2x=80[/tex]
⇒ [tex]x=\frac{80}{2}[/tex]
⇒ [tex]x=40[/tex]
Thus width = [tex]40[/tex] and
length = [tex]40+80[/tex]
⇒ [tex]120[/tex]
Hence we can conclude that the dimensions of a rectangular field is width = 40 yd and length = 120 yd.
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Which of the following inequalities is shown in the graph
The inequality y ≤ [tex]\frac{5}{2}[/tex] x+5 represents the given graph. Therefore, option D is the correct answer.
What is an inequality?In mathematics, inequality refers to a relationship that makes a non-equal comparison between two numbers or other mathematical expressions.
From the graph the inequality intersect lines at (-2, 0) and (0, 5).
The graph is shaded below the line.
So, inequality y ≤ [tex]\frac{5}{2}[/tex] x+5.
The inequality y ≤ [tex]\frac{5}{2}[/tex] x+5 represents the given graph. Therefore, option D is the correct answer.
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What is the minimum value for P = x - 2y over the feasibility region defined by the constraints shown below?
A. 8
B. -2
C. -16
D. -14
the answer is -14
Hope this helps : )
A box containing 4 identical books weighs 5kg. if the weight of the box is 600g, what is the weight of each book? answer key
Answer:
1100 grams
Step-by-step explanation:
two chipmunks were collecting acorns for the winter months. the older chipmunk gathered three times as many acorns as the younger chipmunk. together they collected 28 acorns. how many acorns did each chipmunk save for winter?
Maya spent her allowance on playing an arcade game a few times and riding the Ferris wheel more than once.Write about what additional information you would need to create a two-variable equation for the scenario. What kind of problem could you solve with your equation?
To write a two-variable equation, I would first need to know how much Maya’s allowance was. Then, I would need the cost of playing the arcade game and of riding the Ferris wheel. I could let the equation be cost of playing the arcade games plus cost of riding the Ferris wheel equals the total allowance. My variables would represent the number of times Maya played the arcade game and the number of times she rode the Ferris wheel. With this equation I could solve for how many times she rode the Ferris wheel given the number of times she played the arcade game u welcome