A) (-6,0) = -6-3, 0+4 so it moves to (-9,4)
B) (3,-4) = 3-3, -4+4 so it moves to (0,0)
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.
Which number(s) below belong to the solution set of the inequality? Check all that apply.x + 16 < 51.
A. 80
B. 35
C. 38
D. 32
E. 34
F. 16
please help me
That would be 32, 16 and 34.
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.
Is this true 1/2 >0.25
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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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.
how do i sketch the graph of each function?
If 3cot^2x - 5cotx = -2, then cotx = _____.
A. -2, -1/3
B. -1, -2/3
C. 1, 2/3
D. 2, 1/3
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
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:
miss. Nikkel want to divide her class of 23 students into 4 equal teams.is this reasonable?why or why not
Archie is putting 24 books on 2 shelves. Each shelf holds 16 books.
How many more books can Archie put on the shelves?
What is x if rs= 6, st=9, tu=7, uv=15,vr=14
"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.
Determine whether the following pair of lines is parallel, perpendicular or neither 2x+3y=3: 2y=3x-4
What is the value of x?
Writing are the equations m + 3 = -5 and m = -2 equivalent? explain
What's the answer of the photo I just sent you
Which expression is equivalent to 1/5(15 + 10x-5)?
A. 2 + 2x
B. 2 - 2x
C. -2 + 2x
D. -2 - 2x
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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Which expression is equivalent to the expression −2\3 (3- 1\2) (-1)?
Question 3 options:
-2 + 1\3 + 2\3
2 - 1\3
-2 +1\3-1
2 + 1\3
The Answer Is B.2-1/3
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The expression −2/3(3-1/2)(-1) is equivalent to -5/3.
Explanation:To simplify the expression −2/3(3-1/2)(-1), we can start by simplifying the expressions within the parentheses.
3-1/2 = 6/2 - 1/2 = 5/2
Next, we can multiply the expression −2/3(5/2)(-1).
−2/3(5/2)(-1) = -2/3 * 5/2 * -1 = -10/6 = -5/3
Therefore, the expression is equivalent to -5/3.
The sum of three consecutive integers is -255. what are they?
If two pyramids are similar and the ratio between the lengths of their edges is 3:11, what is the ratio of their volumes?
Answer: The ratio of the volumes of two pyramids is 27 : 1331.
Step-by-step explanation: Given that two two pyramids are similar and the ratio between the length of their edges is 3 : 11.
We are to find the ratio of the volumes of two pyramids.
Let a units and b units be the lengths of the edges of the two pyramids.
The, according to the given information, we have
[tex]a:b=3:11.[/tex]
We know that the ratio of the volumes of two similar pyramids is equal to the ratio of the cubes of the lengths of edges of the two pyramids.
Therefore, the ratio of the volumes of two pyramids will be
[tex]V:V'=\dfrac{V}{V'}=\dfrac{a^3}{b^3}=\left(\dfrac{a}{b}\right)^3=\left(\dfrac{3}{11}\right)^3=\dfrac{27}{1331}=27:1331\\\\\\\Rightarrow V:V'=27:1331.[/tex]
Thus, the ratio of the volumes of two pyramids is 27 : 1331.
Please help! Thank you!
Triangle PQR has vertices at the following coordinates : P(0,1) Q(3,2) R(5,-4) . Determine wether or not triangle PQR is a right triangle . Show all calculations for full credit .
The sum of the squares of two sides is not equal to the square of the third side, the triangle PQR is not a right triangle.
What is Pythagoras Theorem?According to Pythagoras Theorem, in a right angled triangle the square of the side opposite to the right angle is equal to the sum of squares of the other two sides.
Height² + Base² = Hypotenuse²
If a triangle is a right angle, then its sides should satisfy Pythagoras theorem.
The distance formula will be used to determine the length of the sides.
PQ² = ( 3 - 0)² + (2-1)²
PQ² = 10
PQ = √10
RQ² = ( 5 - 3)² + (-4-2)²
RQ² = 40
RQ = √40
RP² = ( 5 - 0)² + (-4-1)²
RQ² = 25 + 36
RQ² = 61
Applying the Pythagoras's Theorem,
61 ≠ 40 + 10
Therefore, it is not a right angled triangle.
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Point A is located at –24 and point C is located at 36 on the number line below. Which value would represent point B, halfway between point A and point C?
Answer:
Point B will be 6
Step-by-step explanation:
We have point A= -24 and point B = 36, we want to know point B which is halfway between points A and C.
To find the middle between two points we have to add the two numbers and divide them by 2:
We would have:
(A+C)/2
We substitute the values of A and C:
B = (-24+36)/2
B = 12/2
B = 6.
We can also write this on a number line and get point B by counting how many numbers there are in between point A and C, and this result divides it by 2. This is in the attachment.
What is the perimeter of the rectangle shown on the coordinate plane, to the nearest tenth of a unit? a.13.4 units b.17.9 units c.26.8 units d.40.0 units
A coordinate plane is a graphical image that shows two number lines. These number lines have a y-axis and x-axis. The y-axis is the vertical number line and the x-axis is the horizontal number line.
The perimeter of the rectangle is 26.8 units
We would be applying Pythagoras Theorem to find the length and breadth of the rectangle.
Pythagoras Theorem states that:
c² = a² + b²
Note that c = The length or breadth of the rectangle
Step 1 : Looking at upper part, and dividing the rectangle into a triangle,We have 4 units and 8 units.
a = 4 units
b = 8 units
Using the Pythagorean Theorem, you can calculate the length of the hypotenuse to be
c² = 4² + 8²
c² = 80
c = √ 80
c = 8.9 units
Applying this to the lower part,
We have 4 units and 2 units.
a = 2 units
b = 4 units
Using the Pythagorean Theorem, you can calculate the length of the hypotenuse to be
c² = 2² + 4²
c² = 20
c = √20
c = 4.5 units
Step 2: We find the Perimeter of a rectangleFormula = 2L + 2B
Where
L = Length = 8.9 units
B = Breadth = 4.5 units
Hence:
8.9 x 2 + 4.5 x2 = 26.8 units
Therefore, the perimeter of the rectangle is 26.8 units
Option C is the correct answer
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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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The hood of Christina's car is the shape of a trapezoid. The base bordering the windshield measures 30 inches and the base at the front of the car measures 24 inches. What is the width of the median of the hood?
The width of the median of the hood is
_______inches.
30-24 = 6
6/2 = 3
24 + 3 = 27
median width = 27
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?