The number line shows the graph of an inequality: A number line is shown from negative 5 to positive 5 with increments of 0.5. All the whole numbers are labeled on the number line. An empty circle is shown on the first mark to the left of 0. The region to the left of the empty circle is shaded. Which statement explains whether −1.5 can be a value in the shaded region? Yes it can, because −1.5 lies to the left of −0.5 Yes it can, because −1.5 lies to the right of −0.5 No it cannot, because −1.5 lies to the left of −0.5 No it cannot, because −1.5 lies to the right of −0.5
Answers
Answer:
Option A.
Step-by-step explanation:
Draw a number line from negative 5 to positive 5 with increments of 0.5. Make an empty circle on the first mark to the left of 0. It means mark an open circle at -0.5.
The region to the left of the empty circle is shaded. It means all the points lie on the left side of -0.5 at in the shaded region.
We need to find a statement that explains whether −1.5 can be a value in the shaded region.
Since −1.5 lies to the left of −0.5 , therefore -1.5 is in the shaded region.
Therefore, the correct option is A.
Answer:
C.)
Step-by-step explanation:
You have to use the line graph!
Please try to resist cheating and do the work!
Related Questions
On Monday Henry with drill $49 from his bank account on Wednesday he would do $78 how much did he withdraw in total
Answers
A student of one of the authors earned grades of 63, 91, 88, 84, and 79 on her five regular statistics tests. She earned a grade of 86 on the final exam and 90 on her
class projects. Her combined homework grade was 70. The five regular tests count for 60%
of the final grade, the final exam counts for 10%, the project counts for 15%, and homework
counts for 15%. What is her weighted mean grade? What letter grade did she earn (A, B, C, D,
or F)? Assume that a mean of 90 or above is an A, a mean of 80 to 89 is a B, and so on.
Answers
Answer:
Weighted mean grade: 81.2
Letter grade: B
Step-by-step explanation:
5 regular tests:
(63+91+88+84+79) / 5 * 60%
= 405 / 5 * 0.6
= 48.6
Final exam:
86 * 10% = 8.6
Project:
90 * 15% = 13.5
Homework:
70 * 15% = 10.5
So her weighted mean grade is
48.6 + 8.6 + 13.5 + 10.5 = 81.2
The student's weighted mean grade is 81.2, which corresponds to a letter grade of B.
Explanation:To calculate the student's weighted mean grade, we must apply the provided weights to each component. The five tests count for 60%, the final exam counts for 10%, the project counts for 15% and the homework counts for 15%.
First, find the mean of the five regular test scores: (63 + 91 + 88 + 84 + 79) / 5 = 81.
Then, calculate individual contributions by multiplying the scores by the corresponding weights:
Tests: 81 * 0.60 = 48.6Final exam: 86 * 0.10 = 8.6Project: 90 * 0.15 = 13.5Homework: 70 * 0.15 = 10.5Add these to find the student's weighted mean grade: 48.6 + 8.6 + 13.5 + 10.5 = 81.2. As her grade is above 80, her letter grade would be B.
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What is the value of x? Identify the missing justifications
Answers
Answer:
B. Angle Addition Postulate; Subtraction Property of Equality
Step-by-step explanation:
Given:
[tex]m\angle PQR=x+7\\ \\m\angle SQR=x+3\\ \\m\angle PQR+m\angle SQR=m\angle PQS=100^{\circ}[/tex]
Find: x
Solution:
1. [tex]m\angle PQR+m\angle SQR=m\angle PQS[/tex] - Angle Addition Postulate
2. [tex]x+7+x+3=100[/tex] - Substitution Property
3. [tex]2x+10=100[/tex] - Simplify
4. [tex]2x=90[/tex] - Subtraction Property of Equality
5. [tex]x=45[/tex] - Division Property of Equality
Larry claims that (14 + 12) × (8 + 12) and (14 × 12) + (8 × 12) are equivalent because they have the same digits and the same operations.
a. Is Larry correct? Explain your thinking.
b. Which expression is greater? How much greater?
Answers
Answer:
[tex](14+12)\times (8+12) > (14\times 12)+(8\times 12)[/tex]
Step-by-step explanation:
First let us evaluate the value of both the expressions.
[tex](14+12)\times (8+12) = 26\times 20 = 520[/tex]
[tex](14\times 12)+(8\times 12) = 168 + 96 = 264[/tex]
a) Hence, Larry's claim that both the expressions are equivalent is wrong.
The evaluation of the expressions have been shown above. The second expression was obtained by swapping the addition and multiplication order and that created the difference.
b) Clearly,
520 > 264
Therefore,
[tex](14+12)\times (8+12) > (14\times 12)+(8\times 12)[/tex]
[tex](14+12)\times (8+12)[/tex] is greater by the expression [tex](14\times 12)+(8\times 12)[/tex] by a value of 520 - 264 = 256.
Final answer:
Larry is incorrect; the expressions (14 + 12) × (8 + 12) and (14 × 12) + (8 × 12) are not equivalent. The first expression equals 520, and the second equals 264, with the first being greater by 256.
Explanation:
No, Larry is not correct. The expressions (14 + 12) × (8 + 12) and (14 × 12) + (8 × 12) are not equivalent because they do not follow the same mathematical rules. The former is calculated using the distributive property of multiplication over addition, while the latter is simply a sum of two products.
To illustrate, let's compute both expressions:
For the first expression, (14 + 12) × (8 + 12), first, we add the numbers inside the parentheses: 26 × 20. Then, we multiply the results: 26 × 20 = 520.For the second expression, (14 × 12) + (8 × 12), we compute the products first: 168 + 96. Finally, we add those products together: 168 + 96 = 264.Comparing the results, 520 is evident greater than 264. The difference between them is 256.
The rules of mathematics are universally valid, and incorrect application of these rules can lead to different outcomes, as shown in Larry's claim.
Prove that the triangle with vertices with (3,5), (-2,6), and (1,3) is a right triangle.
Answers
Answer:
The triangle with vertices with (3, 5), (-2, 6), and (1, 3) is a right triangle.
Solution:
Given that the vertices of triangle are (3, 5), (-2, 6) and (1, 3)
Let us consider A(3, 5) B(-2, 6) C(1, 3)
If the sum of square of distance between two vertices is equal to the square of distance between third vertices, then the triangle is a right angled triangle.
By above definition, we get
[tex]BC^{2} + CA^{2} = AB^{2}[/tex] ----- eqn 1
Where AB is the distance between vertices A and B
BC is the distance between vertices B and C
CA is the distance between vertices C and D
Distance between any two vertices of a triangle is given as
[tex]Distance = \sqrt{\left(x_{2} -x_{1}\right )^{2} + \left(y_{2} -y_{1}\right)^{2} }[/tex] ------- eqn 2
Step 1:
Let us find the distance between the vertices A(3,5) and B(-2,6)
By using equation 2, we get
[tex]x_{1} = 3, x_{2} = -2, y_{1} = 5 \text { and } y_{2} = 6[/tex]
Distance between vertices A and B =[tex]\sqrt{(-2-3)^{2}+(6-5)^{2}}[/tex]
= [tex]\sqrt{(-5)^{2} + (1)^{2}}[/tex]
= [tex]\sqrt{(-5)^{2} + (1)^{2}}[/tex]
= [tex]\sqrt{25+1}[/tex]
= [tex]\sqrt{26} units[/tex]
Step 2:
Let us find the distance between the vertices B(-2,6) and C(1,3)
By using equation 2, we get
[tex]x_{1} = -2, x_{2} = 1, y_{1} = 6 \text { and } y_{2} = 3[/tex]
Distance between vertices B and C = [tex]\sqrt{(1-(-2))^{2}+(3-6)^{2}}[/tex]
= [tex]\sqrt{(1-(-2))^{2} + (3-6)^{2}}[/tex]
= [tex]\sqrt{3^{2}+9}[/tex]
= [tex]\sqrt{9+9}[/tex]
= [tex]\sqrt{18} \text { units }[/tex]
Step 3:
Let us find the distance between the vertices C(1,3) and D(3,5)
By using equation 2, we get
[tex]x_{1} = 1, x_{2} = 3, y_{1} = 3 \text { and } y_{2} = 5[/tex]
Distance between the vertices C and A
= [tex]\sqrt{(3-1)^{2} + (5-3)^{2}}[/tex]
= [tex]\sqrt{2^{2} + 2^{2}}[/tex]
= [tex]\sqrt{4+4}[/tex]
= [tex]\sqrt{8} units[/tex]
Step 4:
By using equation 1,
[tex]BC^{2} + CA^{2} = AB^{2}[/tex]
[tex](\sqrt{18})^{2} + (\sqrt{8})^{2} = (\sqrt{26})^{2}[/tex]
18 + 8 = 26
26 = 26
Hence the condition is satisfied. So the given triangle with vertices with (3,5), (-2,6), and (1,3) is a right triangle.
{ (7+3) • 5-4} ÷2+2
Answers
Answer:
{ (7+3) • 5-4} ÷2+2
7 + 3 = 10
5 - 4 = 1
10 x 1 = 10
10 divided by 2 = 5
5 + 2 = 7
7 is your ansswer
Answer:
25
Step-by-step explanation:
For this, you would use PEMDAS.
PEMDAS stands for parenthesis, exponents, multiplication, division, addition and subtraction. That is the order that you would do those steps.
So first, you would do what is inside the parenthesis, 7+3 which is equal to 10.
So then, you would have { 10• 5-4} ÷2+2.
You next step would be to multiply 10 and 5. This would give you 50.
So your equation would be {50-4}÷2+2
The next step would be to subtract 4 from 50 which would give you 46. And the next step is to divide 46 by 2 which is 23. And the last step would be to add 2 to 23, which is 25.
So, your answer is 25.
Can someone help me with this word problem?
I know that you have to split up the money between the 3 based on how much work they have done, but I don't understand how to.
(If you answer, please include your work. Thx!)
FYI: I will mark anyone that offers me a useful answer the most brainiest
Answers
Answer:
10.56
Step-by-step explanation:add 1.25 and 6 then, add 6 and 1.5 together and last divide by 61
What is the equation of the line shown on the graph?
A. y=x
B. y=4x
C. y=-x
D. y=1/4x
Answers
Answer:
B. y = 4x
Step-by-step explanation:
** 4 blocks = 1 unit [vertically]
Starting from the origin, you do rise\run by moving four blocks north over one block east. This graph is an example of what is known as direct variation.
I am joyous to assist you anytime.
Answer:
It would be A y=x
Step-by-step explanation:
64y-4+2y=-2
solve the equation
Answers
Answer:33=y
Step 64u to 2y you get 66y the. -2+4 and you get 2 which is 66y=2. Now divide 66 by two to get 33=y
Anything that doesn’t have a ‘y’ is have to be moved which means the -4 will change to positive 4 and added to both sides.
64y -4 +2y = -2
(64y+2y) -4 = -2
+4 +4
Which crosses out the 4s on the left side and leaves 66y = 2.
Divide 66 on both sides.
66y/66 = 2/66
(2/66) / 2 = 1/33
Answer: y= 1/33
I hope this helps..
solve for x 2(x+2)+2x=4(x+1)
Answers
1.) distributive property
2x+4+2x=4x+4
2.) combine like terms
4x+4=4x+4
3.) subtract 4x from both sides to get
4=4.
Because 4=4 is a true statement the answer is infinite solutions. Hope this helps!!!!
Pete rides his motorcycle with a constant speed of 96 km/h. How far can he travel in 15 minutes?
Answers
Answer:
Step-by-step explanation:
In seven minutes jack types 511 words how many words does he type per minute
Answers
The number of words Jack can type in a minute is 73 words.
In seven minutes, Jack types 511 words. To calculate how many words he types per minute, you divide the total number of words by the total time taken:
Words per minute = Total words / Total time
Words per minute = 511 words / 7 minutes
Words per minute = 73 words
17. Prison Education In a federal prison, inmates can
select to complete high school, take college courses, or
do neither. The following survey results were obtained
using ages of the inmates.
High School College
Age
Courses Courses Neither
Under 30
107
450
30 and over
32
367
If a prisoner is selected at random, find these probabilities:
a. The prisoner does not take classes.
b. The prisoner is under 30 and is taking either a high
school class or a college class.
c. The prisoner is over 30 and is taking either a high
school class or a college class.
27
Answers
To find the probabilities in this scenario, we will use the information provided in the survey results.
Explanation:To find the probabilities in this scenario, we will use the information provided in the survey results. Let's go through each question one by one:
a. The prisoner does not take classes: We can find this probability by adding the number of prisoners who do not take high school or college classes and dividing it by the total number of prisoners. In this case, the number of prisoners who do not take classes is 107 + 32 = 139. The total number of prisoners is 107 + 450 + 32 + 367 = 956. So, the probability is 139/956.
b. The prisoner is under 30 and is taking either a high school class or a college class: We can find this probability by adding the number of prisoners who are under 30 and taking high school or college classes and dividing it by the total number of prisoners. In this case, the number of prisoners who are under 30 and taking high school or college classes is 107 + 450 = 557. So, the probability is 557/956.
c. The prisoner is over 30 and is taking either a high school class or a college class: We can find this probability by adding the number of prisoners who are over 30 and taking high school or college classes and dividing it by the total number of prisoners. In this case, the number of prisoners who are over 30 and taking high school or college classes is 32 + 367 = 399. So, the probability is 399/956.
what is the quontet for 1060 divided by 48
Answers
When you divide 1060 by 48, your answer will be 22.08333... (repeated decimal) but when rounded, it will either be 22, 22.1, or 22.08 (just for rounding, you do not have to put this in.)
Hope this helped!
Nate
Answer:
22.0833333333 or 22.083 with the line above 3
Step-by-step explanation:
22.0833333333 or 22.083 with a line above the 3 because 1060 divided by 48 is 22.0833333333 repeating 3s
A total that is divided into equal groups is called the
Answers
Greetings!
In division, the number being divided is considered the dividend, and the number dividing is called the divisor. The answer is the quotient.
A total that is divided into equal groups is called the dividend.
Hope this helps!
Last year, the school library had a total of x books. Over the summer, the library acquired another 46 books and now has a total of 1,191 books. Which equation could be used to find x, the number of books the library had last year?
Answers
Answer:
x+46=1,191 is the equation to solve it you need to do: x+46=1,191
-46 -46 and you would get
x=1145
To find the number of books the library had last year, we can set up an equation: x + 46 = 1,191. By isolating x, we find that the library had 1,145 books last year.
Explanation:To find the number of books the library had last year, we can set up an equation based on the given information. Let x represent the number of books the library had last year. Since the library acquired another 46 books over the summer, the total number of books is now 1,191. We can set up the equation:
x + 46 = 1,191
To find the value of x, we need to isolate it on one side of the equation. By subtracting 46 from both sides, we get:
x = 1,191 - 46 = 1,145
Therefore, the library had 1,145 books last year.
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Given: All snarfs are yelbs. All yelbs are blue.
Migs can be either green or pink. Some slokes
are snarfs. What conclusion can be drawn?
A. Some migs are snarfs.
B. Some snarfs are green.
C. Some slokes are yelbs.
D. All slokes are migs.
Answers
Answer:
C. Some slokes are yelbs.
Step-by-step explanation:
Given that ;
All snarfs are Yelbs
All Yelbs are Blue
Migs are Green or Pink
Some Slokes are Snarfs
We can see that some Slokes are related to snarfs hence connected to Yelbs
It will be correct to say that some slokes are yelbs
Answer:
The answer is: C. Some slokes are yelbs.
Step-by-step explanation:
Since all snarfs are yelbs. And some slokes are snarfs. Some slokes are yelbs, because all the yelbs are snarfs.
The answer is: C. Some slokes are yelbs.
How do you solve 11-.5y=3+6x for y
Answers
Answer:
y= 1.6
Step-by-step explanation:
First you make x=0 and then since x=0 you plug it in the equation
11-5y=3+6(0)
11-5y=3
now you swing the 11 to the other side
-5y=3-11
-5y=-8
now you divide -8 by -5 to isolate the variable
y= 1.6
HELP ME PLEASEEEEEEE
Answers
Step-by-step explanation:
You must first add 20 to all inqualies, leaving u with 0 is greater than or equal to 2x which is also greater than or equal to 40.
Divde everything by 2 to get rid of the 2 from the x
0 divided by 2 is 0, 2x divded by 2 is x, 40 divided by 2 is 20.
Thats the answers
factor 10c-25, please :)
Answers
10c - 25
Take 5 out
5.(2c - 5)
Therefore the factorized answer is: 5(2c-5)
what is the the reciprocal of 4/11
Answers
Answer: 11/4
Step-by-step explanation: When we are trying to find the reciprocal of a fraction, we just flip the fraction so that our numerator is on the bottom and our denominator is on the top.
In this case, we can change 4/11 to 11/4 by flipping the fraction.
Therefore, the reciprocal of 4/11 is 11/4.
How do you solve this problem? 3x(5+2)=
Answers
Answer:
21
Step-by-step explanation:
Add 5 and 2 together to get 7 and multiply it by 3
Simplify by combining like
terms:
3(4x + 5) + 2
Answers
Answer:
12x + 17Step-by-step explanation:
3(4x + 5) + 2 use the distributive property: a(b + c) = ab + ac
= (3)(4x) + (3)(5) + 2
= 12x + 15 + 2 combine like terms
= 12x + (15 + 2)
= 12x + 17
Answer: 12x + 17
Step-by-step explanation:
First, distribute the 3 to the values within the parentheses.
3 * 4x = 12x
3 * 5 = 15
The expression now becomes 12x + 15 + 2. Now you can combine like terms by adding 15 and 2, since they both have no variable.
12x + 15 + 2
12x + 17
Therefore, the final answer is 12x + 17.
Miss smith’s pay is directly proportional to the number of hours she work at the airport. Her pay for 22 hours is $297.How much should she earn in a 40 hour week
Answers
Answer:
$540
Step-by-step explanation:
You need first to calculate the hour rate that is payment divided to total number of hours done.
297/22 = 13.5
Now we know that she is earning $13.5/1 hour
We just need to multiply by 22 hours and we have 13.5*22 = $540
Answer:
Step-by-step explanation:
2,080
A rectangular field has an area of 162 m2.
The width of the field is 6 m.
What is the length of the field?
Answers
Answer:Length: 27m
Step-by-step explanation:
the formula of area of rectangle is : width*lengthso we just replace the values in the formula162=6*LengthLength=162/6Length=27mThe length of the rectangular field is 27 m.
Area of rectangleThe area of a rectangle is the product of length and width.
[tex]\rm{ Area\ of\ rectangle = Length \times width[/tex]
Given to usA rectangular field has an area of 162 m²The width of the field is 6 m.Length of the rectangular fieldAs given to us the shape of the field is rectangular, also, the width of the field is 6 m. therefore,
[tex]\rm{Area\ of\ rectangular\ field= Length \times width[/tex]
[tex]162\ m^2 = Length \times 6\ m\\\\\dfrac{162\ m^2}{6\ m} =Length\\\\ Length=\dfrac{162\ m^2}{6\ m}\\\\Length = 27\ m[/tex]
Hence, the length of the rectangular field is 27 m.
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[tex](6x+27) (12x-9)[/tex]
Answers
For this case we must apply distributive property term by term, to simplify the expression:
[tex](6x) (12x) + (6x) (- 9) + (27) (12x) + (27) (- 9) =[/tex]
We have to:
[tex]+ * - = -[/tex]
So:
[tex]72x ^ 2-54x + 324x-243[/tex]
Different signs are subtracted and the sign of the major is placed:
[tex]72x ^ 2 + 270x-243[/tex]
ANswer:
[tex]72x ^ 2 + 270x-243[/tex]
Solve the inequality: 4b-8 < 24
Answers
Answer:
4b < 32
b < 8 is the solution
classify each of the power functions based on their end behavior (increasing or decreasing) as x = ∞
[tex] f(x) = - 2 {x}^{2} [/tex]
[tex]g(x) = (x + 2 {)}^{3} [/tex]
[tex]h(x) = - 1 +x\frac{1}{2} [/tex]
[tex]j(x) = \frac{1}{2} ( - {x})^{5}[/tex]
Answers
Answer: right side behavior:
f(x) is Decreasing
g(x) is Increasing
h(x) is Increasing
j(x) is Decreasing
Step-by-step explanation:
The rules for end behavior are based on 2 criteria: Sign of leading coefficient and Degree of polynomial
Sign of leading coefficient (term with greatest exponent):
If sign is positive, then right side is increasingIf sign is negative, then right side is decreasingDegree of polynomial (greatest exponent of polynomial:
If even, then end behavior is the same from the left and rightIf odd, then end behavior is opposite from the left and rightf(x) = -2x²
Sign is negative so right side is decreasing Degree is even so left side is the same as the right side (decreasing)as x → +∞, f(x) → +∞ Decreasing
as x → -∞, f(x) → -∞ Decreasing
g(x) = (x + 2)³
Sign is positive so right side is increasing Degree is odd so left side is opposite of the right side (decreasing)as x → +∞, f(x) → +∞ Increasing
as x → -∞, f(x) → -∞ Decreasing
[tex]h(x)=-1+x^{\frac{1}{2}}\implies h(x)=x^{\frac{1}{2}}-1[/tex]
Sign is positive so right side is increasing Degree is an even fraction so left side is opposite of the right side as it approaches the y-intercept (-1)as x → +∞, f(x) → +∞ Increasing
as x → -∞, f(x) → -1 Decreasing to -1
[tex]j(x)=\dfrac{1}{2}(-x)^5\implies j(x)=\dfrac{1}{2}(-1)^5(x)^5\implies j(x)=-\dfrac{1}{2}x^5[/tex]
Sign is negative so right side is decreasing Degree is odd so left side is opposite of the right side (increasing)as x → +∞, f(x) → +∞ Decreasing
as x → -∞, f(x) → -∞ Increasing
what are examples ofcomplentary angles
Answers
Similarly, 70 degrees and 20 degrees are complementary because they add up to get 90 degrees. Hope this helps!!
Answer:
Examples are:
Angle ABC is 65 degrees and Angle DEF is 25 degrees.
Angle MNO is 50 degrees and Angle XYZ is 40 degrees.
Step-by-step explanation:
Complementary angles are any two angles that when added together equal 90 degrees. Complementary angles do not have to be next to each other, but they must total 90 degrees.
Mike watches a caterpillar climbing on a tree trunk. He writes the expression -5/8 - (-1/8 - 1/2) to show the change, in feet, of the caterpillar’s height on the tree trunk. Which of the following expressions are equivalent to
-5/8 - (-1/8 - 1/2) ?
Choose all that apply.
A. -5/8 + (1/8 + 1/2)
B. -5/8 + 5/8
C. -5/8 - (1/8 + 1/2)
D. -5/8 - (-1/8 + (-1/2))
E. -5/8 + (1/8 - 1/2)
F. -5/8 - 1/8 - 1/2
Answers
Answer:
A. [tex]\frac{-5}{8}+(\frac{1}{8}+\frac{1}{2})[/tex]
B. [tex]\frac{-5}{8}+(\frac{5}{8})[/tex]
D. [tex]\frac{-5}{8}-(\frac{-1}{8}+(\frac{-1}{2}))[/tex]
Step-by-step explanation:
- Mike watches a caterpillar climbing on a tree trunk
- He writes the expression [tex]\frac{-5}{8}-(\frac{-1}{8}-\frac{1}{2})[/tex]
- We need to find the equivalent expressions to this expression
A.
∵ The expression [tex]\frac{-5}{8}-(\frac{-1}{8}-\frac{1}{2})[/tex] has a
common sign negative in the bracket
∴ [tex]\frac{-5}{8}-(-)(\frac{1}{8}+\frac{1}{2})[/tex]
∵ (-)(-) = (+)
∴ [tex]\frac{-5}{8}+(\frac{1}{8}+\frac{1}{2})[/tex]
∵ The expression [tex]\frac{-5}{8}+(\frac{1}{8}+\frac{1}{2})[/tex] is
equivalent to the expression [tex]\frac{-5}{8}-(\frac{-1}{8}-\frac{1}{2})[/tex]
B.
∵ In the expression [tex]\frac{-5}{8}-(\frac{-1}{8}-\frac{1}{2})[/tex], lets
add the two terms in the bracket
[tex](\frac{-1}{8}-\frac{1}{2})=(\frac{-1}{8}-\frac{1(4)}{2(4)})=(\frac{-1}{8}-\frac{4}{8})=(\frac{-5}{8})[/tex]
∴ The expression = [tex]\frac{-5}{8}-(\frac{-5}{8})[/tex]
∵ (-)(-) = (+)
∴ The expression = [tex]\frac{-5}{8}+(\frac{5}{8})[/tex]
∴ The expression [tex]\frac{-5}{8}+(\frac{5}{8})[/tex] is equivalent to
the expression [tex]\frac{-5}{8}-(\frac{-1}{8}-\frac{1}{2})[/tex]
D.
∵ In the expression [tex]\frac{-5}{8}-(\frac{-1}{8}-\frac{1}{2})[/tex], we can
write the bracket as [tex](\frac{-1}{8}-\frac{1}{2})=(\frac{-1}{8}+(\frac{-1}{2}))[/tex]
because (+)(-) = (-)
∴ The expression [tex]\frac{-5}{8}+(\frac{5}{8})[/tex] is equivalent to
the expression [tex]\frac{-5}{8}-(\frac{-1}{8}+(\frac{-1}{2}))[/tex]
* The equivalent expressions are A , B and D
The equivalent expressions to [tex]-5/8 - (-1/8 - 1/2)[/tex] are [tex]-5/8 + (1/8 + 1/2)[/tex], [tex]-5/8 - (-1/8 + (-1/2))[/tex], and [tex]-5/8 + (1/8 - 1/2),[/tex] which correspond to options A, D, and E, respectively.
Explanation:The expression -5/8 - (-1/8 - 1/2) involves the subtraction of a negative number, which is equivalent to addition. We deal with the inner parentheses first, redistributing the minus sign to both terms inside. To find equivalent expressions, we change the subtraction of a negative to addition and check which options comply:
A. [tex]-5/8 + (1/8 + 1/2)[/tex]: This option correctly redistributes the minus sign, changing the subtraction of a negative to addition.D. [tex]-5/8 - (-1/8 + (-1/2))[/tex]: This option is equivalent by distributing the negative sign inside the parentheses properly.E. [tex]-5/8 + (1/8 - 1/2)[/tex]: This option reflects the correct sign change by changing the subtraction of a negative to an addition and adjusting the second term within the parentheses accordingly.Options B, C, and F are not equivalent to the original expression as they either do not adjust the signs correctly or do not respect the original arrangement of terms.
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