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.
What’s the domain of the graph?
Answer:
(-10, 6)
Step-by-step explanation:
To find the domain of a function, you just look at where the x starts and the x ends. since there are points at either end you do the points. if it were to go on forever like a line then the domain would be from Infinity to a point or Infinity to Infinity and etc.
Which equation is quadratic in form?
© 2(x + 5)2 + 8x + 5+6 = 0
x6 + 6x +8=0
7x6 + 36x3 + 5 = 0
4x9 + 20x2 + 25 = 0
Answer: 2(x+5)2+ 8x + 5+6=0
Step-by-step explanation:
2(x + 5)2 + 8x + 5 + 6=0
2(x+5)(x+5) + 8x + 11=0
2(x^2+ 10x + 25) + 8x + 11=0
2x^2 +20x + 50 + 8x + 11=0
2x^2 +28x +66=0
This is a second-degree equation, the greatest power is two. Hence it is a quadratic equation.
None of the given equations are purely quadratic in form; they include terms of higher degrees or additional constant terms. Therefore, none of them fit the criteria.
To determine which equation is quadratic in form, we need to look for equations that can be written in the form [tex]\(ax^2 + bx + c = 0\)[/tex], where [tex]\(a\), \(b\), and \(c\) are constants and \(x\)[/tex] is the variable.
Let's analyze each given equation:
[tex]1. \(2(x + 5)^2 + 8x + 5 + 6 = 0\)[/tex]
This equation involves a quadratic term [tex]\((x + 5)^2\)[/tex], but it also includes linear and constant terms. Therefore, it is not purely quadratic in form.
2. [tex]\(x^6 + 6x + 8 = 0\)[/tex]
This equation contains a sixth-degree term [tex]\(x^6\)[/tex], making it a polynomial of degree 6. It is not quadratic in form.
[tex]3. \(7x^6 + 36x^3 + 5 = 0\)[/tex]
Similar to the previous equation, this equation contains a sixth-degree term [tex]\(x^6\)[/tex] and a third-degree term [tex]\(x^3\)[/tex].
It is not quadratic in form.
[tex]4. \(4x^9 + 20x^2 + 25 = 0\)[/tex]
This equation contains a ninth-degree term [tex]\(x^9\)[/tex] and a quadratic term[tex]\(20x^2\).[/tex]
However, it also contains a constant term. Therefore, it is not purely quadratic in form.
None of the given equations are purely quadratic in form.
For which rational expression is -which expression is equivalent to 2x^2+2x-4/2x^2-4x+2
Answer:
[tex]\frac{x+2}{x-1}[/tex]
Step-by-step explanation:
Factorise the numerator and denominator
2x² + 2x - 4 ← factor out 2 from each term
= 2(x² + x - 2)
= 2(x + 2)(x - 1) ← in factored form
2x² - 4x + 2 ← factor out 2 from each term
= 2(x² - 2x + 1)
= 2(x - 1)² ← in factored form
Thus
[tex]\frac{2x^2+2x-4}{2x^2-4x+2}[/tex]
= [tex]\frac{2(x+2)(x-1)}{2(x-1)^2}[/tex]
Cancel 2 and factor (x - 1) on numerator/ denominator, leaving
= [tex]\frac{x+2}{x-1}[/tex]
In 6th grade, the ratio of boys to girls is 4 to 5. If there are 145 girls,how many boys are there
Step-by-step explanation:
whrn you have a proble. you can tell me thank you have a nice day
To solve, find how many groups of 5 are in 145 girls (145 ÷ 5 = 29 groups of girls). Then, find how many boys are in these groups by multiplying the number of groups by the boys' ratio (4), thus 29 x 4 = 116 boys in the 6th grade.
Explanation:To determine the number of boys in the 6th grade, we will make use of the ratio provided, 4:5. This ratio means that for every 4 boys, there are 5 girls. To translate this into actual numbers, take the total number of girls (145) and calculate how many groups of 5 you have, because that's how many groups of boys you would have also. To determine the number of boys, you multiply the number of groups by 4.
First, Divide 145 by 5 to find out how many groups of girls there are: 145 ÷ 5 = 29. These equate to groups of students based on the ratio. Second, Multiply the number of groups by the boys’ ratio number (4) to find the number of boys. So, 29 x 4 = 116. That's the total number of boys in the 6th grade.
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5-0.852. What's is the answer
Answer:
4.148
Step-by-step explanation:
-3.3m=-1.1 please include how you solved it
Answer:
1/3
Step-by-step explanation:
-3.3m = -1.1
Divide both sides by -3.3
m = -1.1
-3.3
The solution to the equation -3.3m = -1.1 is m = 1/3 or approximately 0.33. This was determined by dividing both sides of the equation by -3.3.
Explanation:The problem -3.3m = -1.1 is a simple one-step equation which can be solved by isolating the variable. Here the variable is m. Dividing both sides of the equation by -3.3, we get m = (-1.1/-3.3). This simplifies to m = 1/3 ≈ 0.33. So, the solution to the equation is m = 0.33.
What we did here is an application of the principle that whatever you do to one side of an equation, you should do to the other side as well. This principle is essential in solving mathematical equations.
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The speed of a moving object equals
distance divided by time. If a bicycle
rider averages 7.5 mph for 6 h, how
far did he ride?
Answer:
45 Miles
Step-by-step explanation:
Speed = Distance / Time
Distance = Speed * Time
= 7.5 * 6 = 45 Miles
Final answer:
To find the distance traveled by the bicycle rider, multiply the average speed of 7.5 mph by the time of travel of 6 hours, resulting in a total distance of 45 miles.
Explanation:
Calculating Distance Traveled
To calculate the distance traveled by the bicycle rider, we use the formula that relates average speed, distance traveled, and time of travel:
Average speed = Distance traveled / Time of travel
In this scenario, the bicycle rider's average speed is given as 7.5 mph, and the time of travel is 6 hours. Therefore, the distance traveled can be calculated by multiplying the average speed by the time of travel:
Distance traveled = Average speed × Time of travel
Distance traveled = 7.5 mph × 6 h = 45 miles
Therefore, the bicycle rider traveled a total of 45 miles.
Find the solution of the system of equations.
–8x + 15y = –28
2x + 5y = -28
Step-by-step explanation:
To solve this system of equations, you can use either substitution or elimination. Let's use the elimination method.
First, multiply the second equation by 4 to make the coefficients of \( x \) in both equations opposites:
\( (2x + 5y) \times 4 = -28 \times 4 \)
This gives us:
\( 8x + 20y = -112 \)
Now, we'll subtract the first equation from this modified second equation:
\( (8x + 20y) - (-8x + 15y) = -112 - (-28) \)
Simplify:
\( 8x + 20y + 8x - 15y = -112 + 28 \)
\( 16x + 5y = -84 \)
Now we have a new equation:
\( 16x + 5y = -84 \)
And the first equation remains the same:
\( -8x + 15y = -28 \)
Now, we can solve this system of equations by elimination or substitution. Let's continue with elimination. Multiply the first equation by 2:
\( -16x + 30y = -56 \)
Now, add this equation to the second modified equation:
\( (-16x + 30y) + (16x + 5y) = -56 - 84 \)
\( 30y + 5y = -140 \)
\( 35y = -140 \)
Divide both sides by 35:
\( y = -4 \)
Now, substitute \( y = -4 \) into one of the original equations to solve for \( x \). Let's use the first equation:
\( -8x + 15(-4) = -28 \)
\( -8x - 60 = -28 \)
Add 60 to both sides:
\( -8x = -28 + 60 \)
\( -8x = 32 \)
Divide both sides by -8:
\( x = -4 \)
So, the solution to the system of equations is \( x = -4 \) and \( y = -4 \).
Mr. Hermans's class is selling candy for a school fundraiser. their goal is to raise $500 by selling C boxes of candy. for every box of candy they sell, they earn $2.75. Write and equation that the students could solve to figure out how many boxes they need to sell. Please answer quickly.
The equation to solve how many boxes of candy Mr. Hermans's class needs to sell to reach their goal of $500 is 2.75C = 500. To solve for C (number of boxes), divide 500 by 2.75.
Explanation:In order to figure out how many boxes of candy Mr. Hermans's class needs to sell, you can create an algebraic equation using your known values. Here you know that for each box of candy sold, the class earns $2.75 (represented in our equation as 2.75C) and that their fundraising goal is $500. This sets up the equation as 2.75C = 500. To solve this equation and find the number of boxes needed (represented by 'C'), you would divide each side of the equation by 2.75, which gives you C = 500 / 2.75.
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what is the value of the rational expression below when x is equal to 6? x-2/x-5
a. 3
b. 2/5
c. 8
d. 4
given
[tex] \frac{x - 2}{x - 5} [/tex]
put x = 6 into equation
[tex] \frac{6 - 2}{6 - 5} [/tex]
[tex] = \frac{4}{1} [/tex]
[tex] = 4[/tex]
Final answer:
The value of the rational expression (x-2)/(x-5) when x is 6 is 4.
Explanation:
To find the value of the rational expression x-2/x-5 when x is equal to 6, simply substitute the value of x into the expression:
((6-2)/(6-5) = 4/1 = 4)
So, the value of the expression when x is 6 is 4.
twice a number is less than or equal to the sum of a number and 15
Answer:
10+5
Step-by-step explanation:
It is the answer In my views
A company makes cones out of a solid foam. Each cone has a height of 9 inches, and it’s bade has a diameter of 5 inches. How much foam is needed to make 120 cones?
Final answer:
The volume of foam needed to make 120 cones, each with a 9-inch height and a 5-inch diameter base, is approximately 7,068.6 cubic inches.
Explanation:
The question involves finding the volume of a single cone and then calculating the total volume of foam needed for producing 120 cones. To find the volume of one cone, we use the formula V = (1/3)πr²h, where r is the radius of the base and h is the height. Given that the diameter of the base is 5 inches, the radius (r) would be half of that, which is 2.5 inches. The height (h) is given as 9 inches. Therefore, the volume of one cone is:
V = (1/3)π(2.5)²(9)
This simplifies to V ≈ 58.905 cubic inches (using 3.14159 for π). To find the volume for 120 cones, we multiply the volume of one cone by 120:
Total volume = 58.905 in³ × 120 ≈ 7,068.6 cubic inches.
This is the amount of foam needed to make 120 cones.
Find the derivative from the first principle y=×3
Does the phrase 20 more than a number indicate multiplication?
Answer:
No, the phrase 20 more indicates addition.
For instance, 20 more than 50 is 70.
Which equation represents the slope-intercept form of the line below?
y-intercept = (0, -6)
slope = -5
Answer:
y = - 5x - 6
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = - 5 and c = - 6, thus
y = - 5x - 6 ← equation in slope- intercept form
The slope intercept form is y = -5x-6
What is the required equation of line ?
Given, y-intercept = (0, -6) & slope of the line = -5
The general form of an equation of line is, y = mx+c
where, m is the slope of the line & c is the y intercept
So, when x = 0 , y = -6
So, the line above passes through the point (0, -6)
Therefore, The slope intercept form is, y = -5x-6
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45-2×(15-3) Please Help me figure this out because my calculator says the answer is 21 but I don't know why
Answer:
see explanation
Step-by-step explanation:
Following the order of operations as set out in PEMDAS
Given
45 - 2 × (15 - 3) ← evaluate parenthesis
= 45 - 2 × 12 ← evaluate multiplication
= 45 - 24 ← evaluate subtraction
= 21
0.2(x – 4.5) + 1.7 = 9.6
Answer:
44
Step-by-step explanation:
3dgenuity said so
100 POINTS please answer! ill give you brainliest but i rlly need help! (the circled ones!)
Hi there! I will try my best to help you. If the answers I give you are wrong, I am so sorry.
Answer:
1. <
2. <
3. >
7. Apricot sulphur, large orange sulphur, white-angled sulfur, great white
9. 8 (with the sign), 7/2 (with the sign), 2
10. pi, 12 (with the sign), 3.5
11. -20, 26 (with the sign), 35 (with the sign), 13.5
12. -5.25, 3/2, 6 (with the sign), 5
Answer:
lol this is a lot
Step-by-step explanation:
Idk idk idk idk help pls
Answer:
shade in 7 rectangles, than shade in 70 cubes
Step-by-step explanation:
Step-by-step explanation:
color 7 rectangles then 7 squares
3 people have 2 bananas to share how much banana does each person get
Answer:
1.5 bananas.
Step-by-step explanation:
1.5 x 2 = 3
Answer:
1.5
Step-by-step explanation:
3 divided by 2 is 1.5
Name the sets of numbers to which each number belongs. 192.0005
you should add me on snap connorpike2
Answer:
0.029
Step-by-step explanation:
"To write 29/1000 as a decimal you have to divide numerator by the denominator of the fraction.
We divide now 29 by 1000 what we write down as 29/1000 and we get 0.029"
-Solutions easy
if a basketball court is the shape of a rectangle and is 50 feet wide and 94 feet long what is the area
Answer:
4700
Step-by-step explanation:
Area for rectangle is length times width (lw) so it is 50*94 = 4700
Diana earns $8.50 an hour working as a life guard. Write a function to find Diana’s money earned m for any number of hours h. How much does she make in 9 hours ?
Answer:
76.5$
Step-by-step explanation:
8.5 x 9 = 76.5
x² - y² = z²
Express y in terms of x and z.
Answer:
y² = x² - z²
Step-by-step explanation:
x² - y² = z²
Transpose y the other side
x² - z² = y²
or
y² = x² - z²
Answer:
y= ± [tex]\sqrt{x^2-z^2}[/tex]
Step-by-step explanation:
Given
x² - y² = z² ( isolate y² by subtracting x² from both sides )
-y² = z² - x² ( multiply through by - 1 )
y² = x² - z² ( take the square root of both sides )
y = ± [tex]\sqrt{x^2-z^2}[/tex]
If you buy 15 bags of grass seed which cost $8.29 each, what is the total cost? $87.05 $82.90 $127.50 $124.35
Answer:124.35
Step-by-step explanation: if you times 8.25 by 15 you will get the answer of 124.35
In order to get the answer to this question you could rather multiply $8.29 by 15 or you could add 8.29 15 times.
[tex]1b=8.29[/tex]
[tex]15\times8.29=124.35[/tex]
[tex]=124.35[/tex]
Therefore your answer would be the fourth option "$124.35."
Hope this helps.
What is the decimal equivalent of 32/9
Answer:
3.55555555556
Step-by-step explanation:
-1+3m=2m+4
what is the answere to that?
Which ordered pair (c,d) is the solution to the given system of linear equations?
-C+2d=13
|-9c-4d=-15
Answer:
(-1, 6)
Step-by-step explanation:
{-c + 2d = 13
{-9c - 4d = -15
-⅑[-9c - 4d = -15]
{-c + 2d = 13
{c + 4⁄9d = 1⅔ >> New equation
______________
2 4⁄9d = 14⅔
______ _____
2 4⁄9 2 4⁄9
d = 6 [Plug this back into both equations to get the c-value of -1]; -1 = c
I am joyous to assist you anytime.
Answer:
(-1,6)
Step-by-step explanation:
We are given that system of linear equations
[tex]-c+2d=13[/tex]
[tex]-9c-4d=-15[/tex]
We have to find the value of ordered pair (c,d).
Equation first multiply by 2 then add to equation second
We get
[tex]-9c-4d-2c+4d=26-15[/tex]
[tex]-11c=11[/tex]
[tex]c=\frac{11}{-11}=-1[/tex]
Substitute the value of c in equation first then, we get
[tex]-(-1)+2d=13[/tex]
[tex]1+2d=13[/tex]
[tex]2d=13-1=12[/tex]
[tex]d=\frac{12}{2}=6[/tex]
Hence, the ordered pair (-1,6) is the solution of given system of linear equations.
How can I Factor the expression below 9x2-1
Answer:
Step-by-step explanation:9×2=18
18-1=17
Anwser 17
Answer:
(3x – 1)(3x + 1)
Step-by-step explanation:
Whats the place and value of each underlined digit for example whats the place and value of 5,291
I do not see the underlined digit, but I will do this for you. The 5 in the thousands place is worth 5000, the 2 in the hundreds place is worth 200, the 9 in the tens place is worth 90, and the 1 in the ones place is worth 1.
Hope this helped!
Nate
Final answer:
In the number 5,291, the digit 5 is in the thousands place (value of 5,000), the digit 2 is in the hundreds place (value of 200), the digit 9 is in the tens place (value of 90), and the digit 1 is in the ones place (value of 1).
Explanation:
The place value of a digit in a number indicates the value of the digit based on its position relative to the other digits. For example, in the number 5,291, the digit 5 is in the thousands place, which means its value is 5,000. Similarly, the digit 2 is in the hundreds place, so its value is 200; the digit 9 is in the tens place, so its value is 90; and the digit 1 is in the ones place, which means its value is simply 1.