After evaluating the algebraic expression we can infer that both students were correct.
An algebraic expression in mathematics is one that was produced utilizing integer variables, constants, and algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number)
On the other hand, transcendental numbers, such and e, are not algebraic because they are not generated from integer constants and algebraic operations. While the definition of e necessitates an infinite number of algebraic operations, the creation of is frequently done as a geometric expression .
If an expression can be converted into a rational fraction using the characteristics of the arithmetic operations, it is said to be rational expression (commutative properties and associative properties of addition and multiplication, distributive property and rules for the operations on the fractions).
The expression 5a/2a+3 is the quotient of the terms as it can be written as 5a ÷ ( 2a+3 ).
Again the expression 2a +3 is a sum with only two terms.
Hence both students were correct.
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After evaluating the algebraic expression we can infer that both students were correct.
An algebraic expression in mathematics is one that was produced utilizing integer variables, constants, and algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number)
On the other hand, transcendental numbers, such and e, are not algebraic because they are not generated from integer constants and algebraic operations. While the definition of e necessitates an infinite number of algebraic operations, the creation of is frequently done as a geometric expression .
If an expression can be converted into a rational fraction using the characteristics of the arithmetic operations, it is said to be rational expression (commutative properties and associative properties of addition and multiplication, distributive property and rules for the operations on the fractions).
The expression 5a/2a+3 is the quotient of the terms as it can be written as 5a ÷ ( 2a+3 ).
Again the expression 2a +3 is a sum with only two terms.
Hence both students were correct.
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An angle measures 27.8° less than the measure of its supplementary angle. What is the measure of each angle?
Answer:
∠1 = 103.9° ; ∠2 = 27.8°
Step-by-step explanation:
Supplementary angles = 180°
So, Let the angles be 'x'
Then, x + x -27.8° = 180°
2x - 27.8° = 180°
2x = 180° + 27.8°
2x = 207.8°
x = 207.8°/2
x = 103.9°
Therefore ∠1 = 103.9° ; ∠2 = 27.8°
I hope the answer is correct and has helped you!!!
PLS Heeeeeeelp!!!!!!!!!!
Answer 9 3/7
Step-by-step explanation:
[tex] \frac{30}{7} \times \frac{11}{5} \\ = \frac{330}{35} \\ = 9 \frac{15}{35} [/tex]
SIMPLIFIED WE GET:
[tex]9 \frac{3}{7} [/tex]
THE LAST OPTION IS THE ANSWER
HELP ME I DONT UNDERSTAND THIS
Answer:
[tex]4r - 9s = k \\ ➪4r = 9s + k \\➪ r = \frac{9s + k}{4} [/tex]
Hope it helps
What is the least common multiple of 8, 11, and 20?
PL help
Answer: 40
Step-by-step explanation:
The smallest number that all three numbers go into evenly is 40.
Therefore the LCM of 8, 11, and 20 is 40.
Answer:
440
Step-by-step explanation:
To find the Least common multiple (L.C.M) of 8, 11 and 20, it means that:
you list the first several multiples of each number, look for multiples common to both lists, Look for the smallest number common in both sides, the number is the LCM you are looking for.8 = 2,2,2
11 = 1, 11
20= 2,2,5
LCM of 8,11,20 = 2× 2 × 2 × 11 × 5
= 440
A bowl is used to serve punch for a party.
Which figure would be best to use to estimate the volume of the punch bowl?
C
Semicircle is the best figure to use to estimate the volume of the punch bowl.
What is meant by volume?Every three-dimensional object requires some amount of space. The volume of this space is measured. Volume is defined as the space occupied by an object within the boundaries of three-dimensional space. It is also known as the object's capacity. The liquid state has a definite volume but no definite shape. A solid state has a definite volume and a definite shape. Even if the containers are changed, the solid's shape and volume remain constant. Volume is a measurement of an object's capacity. For example, the volume of a cup is 100 ml if it can hold 100 ml of water up to the brim.To learn more about volume, refer to:
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a 100 gram chocolate bar is shared equally between 5 students while a separate 100 gram chocolate bar is shared equally between 20 students. which group of students receives the larger amount of chocolate per student?
Answer:
The 5 students receive the larger amount.
100:5= 20 gram per student
100÷20= 5 gram per student
Step-by-step explanation:
prove me wrong
a shorter solution that probably will get full pts :
Because each group has the same mass of the chocolate bar, whichever group has less students will get a larger amount of chocolate per student (as there are less people receiving)
and here's if you think it is kinda not too detailed :
The first group has each student receiving 100 : 5 = 20 grams of chocolate per student
The second group has each student receiving 100 : 20 = 5 grams of chocolate per student
Both solutions give us a conclusion of : The group with 5 students have each of the receiving a larger amount of chocolate.
what is the value of cos 360
Simplify the exponential expression (2x^2y^4)^3
Answer:
8x6y12
Step-by-step explanation:
Please answer the two questions in the photo ( will mark brainliest if correct )
Answer: The rhombus below has two lines of symmetry, and the shape below has two lines of symmetry.
Step-by-step explanation:
Symmetry is when we split an object in half, in which both sides are equivalent. This definition must explain how the rhombus was most plausibly split, as well as the letter "H".
Given ΔRST is similar to ΔUVW with RT = 9 inches, UW = 5.4 inches, and RS = 6 inches.
Which is the length of UV¯¯¯¯¯¯¯¯
?
Responses
3.6 inches
3.6 inches
2.4 inches
Because triangle SRT and VUW are similar, all sides of triangle SRF are scaled up by an amount.
We calculate the scale factor : 9/5.4 = 5/3
-> The corresponding side of SR (UV) is scaled down 5/3 times from the length of SR
-> UV = 6 : 5/3 = 3.6 (inches).
The volume of this cylinder is 6480π cm3.
Find the length of the radius,
The sides are equal to 180cm.
Answer:
The length of the radius is 10.7cm
Step-by-step explanation:
[tex]v = \pi {r}^{2} h[/tex]
6480=(22r*180)/7
6480*7=3960r
r=
[tex]r = \sqrt{45360 \div 396} [/tex]
radius=10.7Lisa walked 10,560 feet in 30 minutes. She walked at a constant rate.
At what rate did Lisa walk in miles per hour
convert feet to miles;
10,560 = 2 miles
30 minutes to miles;
2; therefore,
in 1hr she walked 4 miles
4 miles/hour
Answer:
Step-by-step explanation:
UGH I HATE MATH HELP
Hello!
What is the slope-intercept form:
[tex]y = mx + b[/tex]
m: is the slope[tex]m = \dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-1-4}{0--2} =\dfrac{-5}{2}[/tex]
⇒ where (x₂,y₂) and (x₁,y₁) are random points on the line
b: y-intercept or the point that has an x-coordinate value of '0'⇒ thus our y-intercept is '-1'
Thus our line's equation in slope-intercept form:
[tex]y= -\dfrac{5}{2}x -1[/tex]
Hope that helps!
(EASY POINTS)
Solve for x in this figure.
x=
Answer:
x = 132°
Step-by-step explanation:
Sum of interior angles = (n - 2) x 180, where n is number of sides of the polygon.
Sum = (6 - 2) x 180 = 720°
sum = 160 +75 + 132 + 113 + 108 + x
sum = 588 + x
720 = 588 + x
x = 720 - 588
x = 132°
:)
What is the slope-intercept form of the equation of the line that contains the points (1, 4)and (0, 1)?
Answer:
3
Step-by-step explanation:
m=y2-y1÷x2-x1
4-1÷1-0=3÷1=3
Given: -3(4x + 1) = 21
Prove: x = -2
Answer:
-3(4x + 1) = 21 given
4x + 1 = -7 Division Property of Equality
4x = -8 Subtraction Property of Equality
x = -2 Division Property of Equality
Answer:
see explanation
Step-by-step explanation:
prove by solving the equation
- 3(4x + 1) = 21 ( divide both sides by - 3 )
4x + 1 = - 7 ( subtract 1 from both sides )
4x = - 8 ( divide both sides by 4 )
x = - 2
thus solution is x = - 2
Find the midpoint of each line segment
1) (4, 8)
2) (4, 8)
The midpoints are already given to you.
Answers:
(-1, 26) for problem 1(14, 12) for problem 2=======================================================
Explanation:
A = (9, -10)
B = (4,8)
C = (x,y)
A and C are the endpoints. B is the midpoint of segment AC.
The x coordinates of A and C are 9 and x respectively. Add them up and divide in half to get (9+x)/2. This is set equal to the x coordinate of point B and we solve for x.
(9+x)/2 = 4
9+x = 2*4
9+x = 8
x = 8-9
x = -1
The x coordinate of point C is -1.
Use the same idea for the y coordinates.
(-10+y)/2 = 8
-10+y = 2*8
-10+y = 16
y = 16+10
y = 26
Point C is located at (-1, 26)
The midpoint between (9, -10) and (-1, 26) is (4, 8)
Use the midpoint formula to confirm this.
------------------------
The steps for the second problem are going to follow the same outline.
A = (-6,4)
B = (4,8)
C = (x,y)
(-6+x)/2 = 4 solves to x = 14
(4+y)/2 = 8 solves to y = 12
Point C is located at (14, 12)
The midpoint between (-6, 4) and (14, 12) is (4, 8)
tell wheter the lines through the given points are parallel, perpendicular or neither.
a. Line 1: (2,-3), (-4, -6)
Line 2: (-3, 2), (2, -8)
b. Line 1: (-4, -5), (4, 1)
Line 2: ( 6, 10), (-3, -2)
c. Line 1: (0, -4), (-2, -8)
Line 2: (-1, 5), (1, 9)
Help I need this by tomorrow :c
Answer:
a. Perpendicular
Make sure to read the step-by-step explanation to figure out how to do the other 2.
Step-by-step explanation:
I will not be providing answers to all three, but I will answer the first one (this is, so you don't depend on people to solve this for you).
Parallel lines have one thing in common, their slope. Two lines that have the same slope never intersect because they are both facing the same direction and moving the same distance. So, you can find the slope of two lines by using the slope formula.
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m_1=\frac{-6-(-3)}{-4-2}=\frac{-3}{-6}=\frac{1}{2}\\m_2=\frac{-8-2}{2-(-3)}=\frac{-10}{5}=-2[/tex]
This is evidence that the two lines are not parallel. But, by finding the slope, we can conclude that it is perpendicular.
This brings me to how to identify perpendicular lines. The slope of perpendicular lines is negative reciprocals. A reciprocal is just a fraction that is flipped, and it's negative. For example, [tex]\frac{-2}{3}[/tex]'s negative reciprocal would be [tex]\frac{3}{2}[/tex]. The negative of -2/3 is a positive, and the reciprocal of 2/3 is 3/2. So, the negative reciprocal is 3/2.
How does this apply to what I said earlier?Well, [tex]-2[/tex] is the negative reciprocal of [tex]\frac{1}{2}[/tex]. The reciprocal of [tex]\frac{1}{2}[/tex] is 2, and the negative of 2 is -2. So, simply, lines 1 and 2 are perpendicular.
Use this method to solve the other questions. If they don't have the same slope and aren't negative reciprocals, then they are neither.
Answer:
Step-by-step explanation:
To solve this problem, we use the following formula:
[tex]\displaystyle\\\boxed {\frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1} }[/tex]
a) (2,-3) (-4,-6)
[tex]x_1=2\ \ \ \ x_2=-4\ \ \ \ y_1=-3\ \ \ \ y_2=-6[/tex]
[tex]\displaystyle\\\frac{x-2}{-4-2} =\frac{y-(-3)}{-6-(-3)} \\\\\frac{x-2}{-6}=\frac{y+3}{-6+3} \\\\\frac{x-2}{-6} =\frac{y+3}{-3}[/tex]
Multiply both parts of the equation by -3:
[tex]\displaystyle\\\frac{x-2}{2}=y+3\\\\0.5x-1=y+3\\\\0.5x-1-3=y+3-3\\\\0.5x-4=y\\[/tex]
⇔ Line 1: y=0.5x-4 m₁=0.5
(-3,2) (2,-8)
[tex]\displaystyle\\\frac{x-(-3)}{2-(-3)}=\frac{y-2}{-8-2} \\\\\frac{x+3}{2+3} =\frac{y-2}{-10} \\\\\frac{x+3}{5} =\frac{y-2}{-10} \\\\[/tex]
Multiply both parts of the equation by -10:
[tex]-2(x+3)=y-2\\-2x-6=y-2\\-2x-6+2=y-2+2\\-2x-4=y[/tex]
⇔ Line:y=-2x-4 m₂=-2
[tex]\displaystyle\\m_1=-\frac{1}{m_2}[/tex]
⇒ The given lines are perpendicular
b)
(-4,-5) (4,1)
[tex]\displaystyle\\\frac{x-(-4)}{4-(-4)}=\frac{y-(-5)}{1-(-5)} \\\\\frac{x+4}{4+4}=\frac{y+5}{1+5} \\\\\frac{x+4}{8} =\frac{y+5}{6} \\[/tex]
Multiply both parts of the equation by 6:
[tex]\displaystyle\\\frac{6(x+4)}{8} =y+5\\\\\frac{3}{4} x+3=y+5\\\\\frac{3}{4} x+3-5=y+5-5\\\\\frac{3}{4} x-2=y\\[/tex]
⇔ Line 1: y=(3/4)x-2 m=3/4
(6,10) (-3,-2)
[tex]\displaystyle\\\frac{x-6}{-3-6} =\frac{y-10}{-2-10} \\\\\frac{x-6}{-9} =\frac{y-10}{-12} \\\\[/tex]
Multiply both parts of the equation by -12:
[tex]\displaystyle\\\frac{-12(x-6)}{-9} =y-10\\\\\frac{4}{3}x-8=y-10 \\\\\frac{4}{3}x-8+10=y-10+10\\\\\frac{4}{3}x+2=y[/tex]
⇔ Line 2: y=(4/3)x+2 m=4/3
⇒ The given lines are neither perpendicular and neither parallel
c)
(0,-4) (-2,-8)
[tex]\displaystyle\\\frac{x-0}{-2-0} =\frac{y-(-4)}{-8-(-4)} \\\frac{x}{-2}=\frac{y+4}{-8+4} \\\\\frac{x}{-2}=\frac{y+4}{-4}[/tex]
Multiply both parts of the equation by -4:
[tex]2x=y+4\\2x-4=y+4-4\\2x-4=y[/tex]
⇔ Line 1: y=2x-4 m₁=2
(-1,5) (1,9)
[tex]\displaystyle\\\frac{x-(-1)}{1-(-1)} =\frac{y-5}{9-5} \\\\\frac{x+1}{1+1} =\frac{y-5}{4}\\\\\frac{x+1}{2} } =\frac{y-5}{4} \\[/tex]
Multiply both parts of the equation by 4:
[tex]2(x+1)=y-5\\2x+2=y-5\\2x+2+5=y-5+5\\2x+7=y[/tex]
⇔ Line 2: y=2x+7 m₂=2
m₁=m₂
⇒ The given lines are parallel
Use the digits 1, 2, 3 and 4 to fill in each rectangle in order to
create the sum closest to 50. Each digit may only be used once.
+
Manewering the Middle 110
The sum will be 46 which is the nearest combinational value that could be deduced from the digits 1, 2, 3, and 4.
Let's check all the combinations which can be possibly used,
34 + 21 = 46, which is 4 numbers less than 50 so far the nearest.
43 + 12 = 55, which is 5 numbers more than 50.
32 + 41 = 73, which is 23 numbers more than 50.
32 + 14 = 46, which is 4 numbers less than 50 so far the nearest.
23 + 41 = 64, which is 14 numbers more than 50.
So the two combinations are deduced after permutation and a combination of numbers that are 3 and 4 + 2 and 1 and another is 3 and 2 + 1 and 4.
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Amari bought three chicken wings for $4.80 if Morris spent $27.20 how many chicken wings did she buy
Answer:
24 wings
Step-by-step explanation:
Answer:
17 wings
Step-by-step explanation:
1. first we multiply 3 by 27.20 you get 81.6
2. then we divide 81.6 by 4.80 and we get 17
17 wings
Which of the following are rational numbers?
5.48
78.541
97
42.111...
Answer:
5.48, 78.541 and 97
Step-by-step explanation:
A rational number by definition refers to a number that is in the form of k/m and in which k and m are integers and m is not equal to 0.
Let me give you some examples:
1/32/41/59/3From our question,
5.48 = 137/25 hence rational number78.541 = 78541/1000; rational 97 = 97/1; rational 42.111..... = 4211111*/100000: irrational number. It is recurring hence not a rational number.Therefore 5.48, 78.541 and 97 are rational numbers
The black triangle in the first quadrant is the original figure. Label each other triangle with its
transformation.
A. Translation of 6 to the left
B. Translation of 6 to the left and down 4
C. X-axis reflection
D. Y-axis reflection
E. Translation of 3 to the left and down 6
The Hu family goes out for lunch, and the price of the meal is $59. The sales tax on the meal is 6%, and the family also leaves a 15% tip on the pre-tax amount. What is the total cost of the meal? The total cost of the meal is $ .
Answer:
$71.39
Step-by-step explanation:
So we can go ahead and add the extra money they paid (sales tax and tip).
15% + 6% = 21%
Then we can find 21% of 59 then that will be our extra money we're paying.
59 × 0.21 = 12.39
Then we add that amount to our 59 to get the total amount.
59 + 12.39 = 71.39
Help quick!! I need someone to answer this for me.
If T is the midpoint of SU,find x. ( ST=14x-6 and TU= 12x+5). What is the value of x?
the numerical value of x in fraction and decimal form are 11/2 and 5.5 respectively.
What is the numerical values of x?A midpoint is simply a point that divides a line segment into two equal halves.
Given the data in the question;
T is the midpoint of SUSegment ST = 14x - 6Segment TU = 12x + 5Numerical value of x = ?Since that T is the midpoint of segment SU, segment ST and segment TU are two equal halves of of segment SU.
Segment ST = Segment TU
Plug in the given values and solve for x
14x - 6 = 12x + 5
14x - 12x = 5 + 6
2x = 11
x = 11/2
x = 5.5
Therefore, 11/2 or 5.5 is the numerical value of x.
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John held a garage sale. He priced all the items at a dime or a quarter. His sales totaled
less than $5. Write an linear inequality that describes this situation.
John held a garage sale. He priced all the items at a dime or a quarter, his sales totaled less than $5, the solution is shaded region in quadrant I.
What is a slope?In mathematics, line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction. The letter m is frequently used to represent the slope; reason for this usage is unclear, but it can be found in O'Brien's (1844) and Todhunter's (1888) formulations of equation for a straight line as "y = mx + b" and "y = mx + c," respectively.
He priced all items at a dime or a quarter. His sales totaled less than $5
Since dime =$ 0.10=$0.10 and the quarter =$0.25=$0.25
Let x=x= the number of the items sold for a dime
Let y=y= the number of the items sold for a quarter
0.10x+0.25y<5
0.10x+0.25y<5
Inequality in the slope-intercept form
0.10x+0.25y Subtract 0.10x from both sides
0.25y<-0.10x+5 Divide both sides by 0.25
Subtract 0.10x from both sides
[tex]y= -\frac{2}{5}x+20\\[/tex]
The slope is, [tex]-\frac{2}{5}[/tex] and the y- intercept is 20
Since inequality sign is << so, draw a dashed line
Test point (0,0)(0,0)
Substituting the values 0 for x and 0 for y,
[tex]y < -\frac{2}{5}x+20\\\\0 < -\frac{2}{5}(0)+20\\\\0 < +20[/tex]
Since inequality is true
So, (0,0)(0,0) is solution of the inequality
Shade region containing (0,0)(0,0).
The graph below shows all possible solutions
Since boundary line is dashed and the number of items is always positive
The solution is shaded region in quadrant I
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I need help. What are the answers????
Answer:
5) a) x=55
Step-by-step explanation:
x=55
2x + 15 = 110 + 15
=125
Write the negation of the following statement: No one has a pet water buffalo.
SOMEONE HAS A PET WATER BUFFALO.
THE GIVEN STATEMENT IS INDICATING THAT NOT EVEN ONE PERSON HAS A PET WATER BUFFALLO SO THE NEGATION SHOULD INDICATE THERE IS SOMEONE WHO DOES HAVE A PET WATER BUFALLO.
HOPE THIS HELPS
b) A different pattern is made using 20 straight lines
and 14 arcs.
The straight lines and arcs are made from metal.
20 straight lines cost £12
cost of one straight line: cost of one arc = 2:3
Work out the total cost of metal in the pattern.
26.4
total cost of metal in the pattern is £24.6
What is ratio and proportion ?To compare two values is to use a ratio. A proportion is formed when two ratios have the same value. Choose whether the ratio is part-to-part or part-to-whole before you write it.
Calculation20 straight line cost £12
12 ÷ 20 = 0.6 per straight line
straight line : cost of one arc = 2:3
arc = 0.6 x (3/2) = 0.9
total = 12 + 14 x 0.9
= 12 + 12.6
= 24.6
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-3(3-8j) answer pls i need to make up my grade , what’s the answer?
Answer: if the j is supposed to be there, the answer is -9+24j. if the j is not there then just -9+24.
Step-by-step explanation: we distribute the -3 to the 3 and the -8. (-3x3=-9) and (-3x-8=24). when you multiply for divide by a single negative it is negative. when there are two negatives the answer will come out positive.