what is the solution to 7ln(x+2.8)=11.2
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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.
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Length: 80+x
p=2(l+w)
320=2(80+x+x)
320=2(80+2x)
320=160+4x
320-160=4x
160=4x
160/4=x
40yd=x
The width is 40 yds and the length is 80+40=120 yards
Hope I helped :)
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 statements are true ?
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D. the segment DE is bisects segment AC
----------------
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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PLEASE HELP!!
What is the length of the midsegment of this trapezoid?
Enter your answer in the box.
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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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If 3cot^2x - 5cotx = -2, then cotx = _____.
A. -2, -1/3
B. -1, -2/3
C. 1, 2/3
D. 2, 1/3
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Lets pretend cotx = t
3t² - 5t = -2
3t² - 5t + 2 = 0
factor polynomial
(3t-2)(t-1) = 0
3t-2 = 0
t-1 = 0
then "t" which is also cotx is equal to 1 or 2/3
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?
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ax+by=z
where
a - number of times she played arcade
x- prize of arcade
b- number of times of Ferris wheel
y- prize of Ferris
z- the whole allowance
so in order to make it a two-variable equasion we need to know the value of three more variables.
If let's say we know a, b, and z we could solve the problem of how much cheaper/more expensive the arcade is than ferris wheel (we could find something like x=2y, for example ( we don't know yet, we need more variables) so we'd know that one game is more expensive than the other.
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
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
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First, let's calculate the total cost of the peaches.
18.4 pounds × $1.75/pound = $32.20
Now, divide by the number of people who were contributing to the cost of the peaches (there are 4) -
$32.20 ÷ 4 = $8.05
The correct answer is $8.05.
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?
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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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Is this true 1/2 >0.25
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The sum of three consecutive integers is -255. what are they?
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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
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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
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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.
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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
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Hope this helps :)
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.
Which of the following inequalities is shown in the graph
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Check It
0≤(5/2)0+5
0≤0+5
0≤5
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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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
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5000g-600g=4400g
4400g/4=1100g
So your answer is 1,100 grams.
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?
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I hope this helps!!!
(If I’m wrong plz tell me)
what is 3 divided by 7.71?
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You could round to 0.4 or 0.39 , etc.
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.
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The vertex for the second equation is a minimum because the parabola opens upward.
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.
Please help! Thank you!
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The dilatation inverse direction : scale factor k is negative.
k*12=-3==>k=-3/12=-1/4=-0.25
Answer B
Kanisha has x green apples and y red apples.
Which statement explains why x + y and y + x will each find the total number of apples that Kanisha has?
In addition, the order of the variables matters in the expression.
The expressions are not equivalent because there are two variables.
The first expression has a greater value than the second expression.
In addition, the order of the variables does not matter in the expression.
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its the one because it makes the most sense
Answer:
the answer is in addition the order of the variables does not matter in the expression
Step-by-step explanation:
i took the test
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
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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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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?
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Writing are the equations m + 3 = -5 and m = -2 equivalent? explain
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m = -5 - 3
m = - 8
and m = -2
no, they are not equivalent because they do not equal.
What's the answer of the photo I just sent you
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You would just add 26 and 69.
What is x if rs= 6, st=9, tu=7, uv=15,vr=14
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When I leave home to walk to school2And what I think I've seen3Now, what can I say4And I've kept careful track5Just a broken down wagon6When Isay that i saw it on Mulberry St7The story would really be better to hear8A reindeer is better; he's fast and he's fleet9To pull a thing that runs on wheels10Jack or Fred of Joe or NAT-11Say! That makes a story that no one can beat12But he'd look simply grand13If a man sits and listens while hitched on behind14But now what worries me is this...15To guide them through where's traffic's thick-16And he raises his hat as they dash by the stand.17With a roar of its motor an airplane appears18A big magician doing tricks..19For I had a story that NO ONE could beat!20There was so much to tell, I JUST COULDN'T BEGIN!21"Nothing," I said, growing red as a beet
Solve by substitution-5x+4y=22 x - 3y = 0A) No solution.
b. (6, 2)
c. Infinitely many solutions.
d. (-6, 2)
e. (-6, -2)
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-5x + 4y = 22 (1)
x - 3y = 0 (2)
From (2), obtain
x = 3y (3)
Substitute (3) into (1).
-5(3y) + 4y = 22
-15y + 4y = 22
-11y = 22
y = -2
From (3), obtain
x = 3y = 3*(-2) = -6
Answer: e. (-6, -2)
the sum of twice a number x and 13 is two less than three times x
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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.
Find the slope of the line.
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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!
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
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the answer is -14
Hope this helps : )
A customer wants you to enlarge a photo to 2 3/4 its current height. The photo’s current height is 3 1/4 inches. What should its enlarged height be, in inches?