The difference between whole numbers and integers is that whole numbers do not include negative numbers, whereas integers do. Therefore, the same rule used by integers can be used with whole numbers, so long as negative numbers are not used.
The rule for subtracting integers applies to whole numbers because whole numbers are integers. In subtraction, we change the sign of the subtracted number and then add, a principle that works with both negative and whole numbers.
The rule for subtracting integers can indeed be used to subtract whole numbers because whole numbers are a subset of integers. Integers include all positive whole numbers, zero, and their negative counterparts. When we look at the subtraction of integers, for example, 5 - 3 = 2, we can also see this as adding the opposite, 5 + (-3) = 2. Similarly, if you subtract a negative number, like subtracting -6 from 2, it becomes 2 - (-6) = 2 + 6 = 8. Hence, even with whole numbers, we are using the same principles.
When subtracting whole numbers, you follow the same process: change the sign of the number being subtracted and proceed with addition. If the numbers have different signs, you subtract the smaller number from the larger and retain the sign of the larger number. The basic principle to use in working with addition and subtraction of integers is changing subtraction into addition and the paying attention to the signs.
The universality of mathematical rules applies regardless of where or when, meaning subtraction of whole or negative numbers follow the same fundamental principles.
Find the product. -2 x ( x2 - 3) -2 x3 - 6 x -2 x3 + 6 x -2 x2 + 6 x 6 x3
[tex]-2x(x^2-3)\qquad|\text{use distributive property}\\\\=(-2x)(x^2)+(-2x)(-3)=-2x^3+6x[/tex]
Does this graph represent a function?Why or why not?
No, it does not have a straight line. (A)
Hello, floresvanexel4pejp1p
Your question: Does this graph represent a function?Why or why not?
My answer: No, Because there are no straight lines so in that order your answer will be A
Important:I hope my answer helped if it did please mark me as brainliest thank you and have the BEST day ever!
A high definition radio station charges $200 per year in addition to $50 per month for the first 3 months to receive its broadcast. Write a function using function notation to describe the situation.
Let's assume
number of months =x
A high definition radio station charges $200 per year
so, we get point as (0,200)
Assume
f(x) is the total amount of charges in a year
we can see that this is linear relationship
so, we can use formula
[tex]f(x)=mx+b[/tex]
in addition to $50 per month for the first 3 months to receive its broadcast
so, m=50
we can plug it
[tex]f(x)=50x+b[/tex]
we can use point as (0,200)
[tex]200=50*0+b[/tex]
[tex]b=200[/tex]
now, we can plug it back
and we get
[tex]f(x)=50x+200[/tex]...............Answer
200 kids came to a fundraiser. He found out that 60 people like rap. What percent of people like rap?
I believe it is 30% because you can divide 200 in half to get it out of 100, and then divide 60 in half to make it even! (i’m sorry if this doesn’t make sense)
Final answer:
To calculate what percent of people like rap out of 200 who came to a fundraiser, divide the 60 people who like rap by 200 and multiply by 100, resulting in 30% of people liking rap.
Explanation:
The question asks us to calculate what percent of people like rap out of 200 kids who came to a fundraiser. To find the percentage of people who like rap, we use the basic formula for finding percentages: (Part / Whole) × 100. Here, the 'Part' is the number of people who like rap, and the 'Whole' is the total number of kids who came to the fundraiser.
Given:
Part (people who like rap) = 60
Whole (total kids at the fundraiser) = 200
Using the formula, we calculate the percentage as follows:
(60 / 200) × 100 = 0.3 × 100 = 30%.
Therefore, 30% of the people at the fundraiser like rap.
mx=n-p solve this equation for x
x = [tex]\frac{n-p}{m}[/tex]
isolate x by dividing both sides by m
x = [tex]\frac{n-p}{m}[/tex]
Evaluate the following expression when n = -7.
-9|n + 5|
Answer:
-18
Step-by-step explanation:
The tall sticks around n+5 are absolute value signs. Basically, all you need to do is work out what the answer to the problem is inside the signs, then make whatever the answer is positive, then multiply by -9.
-7 + 5 = -2 (that turns into 2)
-9 x 2 = -18
Alexis has a rectangular piece of red paper that is 4 centimeters wide. It’s length is twice it’s width. She glued a rectangular piece of blue paper on top of the red piece measuring 3 centimeters by 7 centimeters. How many square units of red paper will be visible on top?
for the rectangular red paper :
w₁ = width of the red paper = 4 cm
L₁ = length of red paper = 2 w = 2 x 4 = 8 cm
A₁ = area of the red paper = L₁ w₁ = 8 x 4 = 32 cm²
for the rectangular blue paper :
w₂ = width of the blue paper = 3 cm
L₂ = length of blue paper = 7 cm
A₂ = area of the blue paper = L₂ w₂ = 7 x 3 = 21 cm²
area visible is given as
A = A₁ - A₂ = 32 cm² - 21 cm² = 11 cm²
so 11 square units of red paper will be visible on top
rewrite, differentiate and simplify:
3/(2x)^3
[tex]\frac{dy}{dx}[/tex] = - [tex]\frac{9}{8x^{4} }[/tex]
let y = [tex]\frac{3}{(2x)^{3} }[/tex] = [tex]\frac{3}{8}[/tex] [tex]x^{-3}[/tex]
differentiate using the power rule
[tex]\frac{d}{dx}[/tex] ([tex]ax^{n}[/tex] ) = na[tex]x^{n-1}[/tex]
[tex]\frac{dy}{dx}[/tex] = - [tex]\frac{9}{8}[/tex][tex]x^{-4}[/tex] = - [tex]\frac{9}{8x^{4} }[/tex]
Will give brainliest. Some one please help your mans out please.
Identify the range of the function.
A)
R:{y| 0 ≤ y < 5}
B)
R:{y| 0 < y ≤ 5}
C)
R:{y| −4 ≤ y < 4}
D)
R:{y| −4 < y ≤ 4}
Answer:
a) R: { y | 0 ≤ y < 5 }
Step-by-step explanation:
The lowest point on the graph (-4, 0) - point painted over ( ≤ ).
The highest point of the chart - close (4, 5) - point not painted over ( < ).
In two weeks, your class collected more than 380 cans of food for the annual food drive. In the first week, 145 cans were collected. How many cans c of food were collected in the second week? Write and solve an inequality.
145 + c = 380
145 - 145 + c = 380 - 145 -Subtract 145 from both sides of the equation
c = 235
So, they collected 235 cans in the second week.
Hope this helps!
To find out how many cans of food were collected in the second week, subtract the number of cans collected in the first week from the total number of cans collected in two weeks. The inequality representing the problem is c + 145 > 380. Solving the inequality, we find that more than 235 cans were collected in the second week.
Explanation:To find out how many cans of food were collected in the second week, we can subtract the number of cans collected in the first week from the total number of cans collected in two weeks. Let's assign a variable, c, to represent the number of cans collected in the second week. The inequality that represents the problem is: c + 145 > 380. To solve this inequality, we need to isolate the variable by subtracting 145 from both sides: c > 380 - 145. Simplifying further, we get c > 235. So, more than 235 cans of food were collected in the second week.
Learn more about Inequality here:https://brainly.com/question/32625151
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Sylvie finds the solution to the system of equations by graphing. y = 2/3 x + 1 and y = -2/3x – 1
Which graph shows the solution to Sylvie’s system of equations?
Remark
One of the ways you could solve this is to go to a place like Desmos and graph it for yourself. Then at least you would know what the answer looked like. Another way is to solve for the x value by equating the equations since the y has to be the same. We'll do both.
Solve For X
(2/3)x + 1 = -(2/3)x - 1 Add 1 to both sides
(2/3)x + 1 + 1 = - 2/3x Subtract (2/3x) from both sides.
2 = (-2/3)x - (2/3)x
Show the graph and comment
Notice that there is only one graph given that has a value of x = - 3/2 Normally you are not that lucky. Thanks for putting the graphs in. We are usually not that lucky and have to guess at the answer if it is a graph.
2 = - 4/3x Multiply both sides by 3
2 * 3 = - 4x
6 = - 4x Divide by - 4
6/-4 = x Reduce
-3/2 = x
Remark
The x value is wrong for the one on the left. It is also wrong for the third one from the left. And the last graph is also incorrect. Only the second from the left gives the right answer.
what is 7.08 as mixed number
7 8/100 or 7 2/25 in lowest terms
7 2/25 is your answer
your welcome
-12(x+2)=6(-4-2x)+4x
-12(x+2)=6(-4-2x)+4x
-12x-24=-24-12x+4x
x=0
x is equal to zero. Distribute The -12 to x and 2. Then distribute the 6 to -4 and -2.
That gives you -12-24=-24-12x+4x
combining like terms gives you -12-24=24-8x
next you should get x by itself. that gives you 0 as the final answer
In the diagram shown, ∠a and ∠h are______. A) vertical angles B) linear pair angles C) corresponding angles D) alternate exterior angles
Answer:
The correct answer is D) Alternate Exterior Angles
Answer: D) Alternate Exterior Angles
Step-by-step explanation: Did it on USATP !
what is the sum: (1−5q)+2(2.5q+8)
The answer is seventeen
The equation 3.3x − 6.6 = 2.7x can be transformed to form which of the following expressions?
a. 6.0x = 6.6
b. 0.6x = 6.6
c. 6.0x = −6.6
d. 0.6x = −6.6
Answer:
3.3x − 6.6 = 2.7x ⇔ 0.6x = 6.6
B is correct
Step-by-step explanation:
The equation 3.3x − 6.6 = 2.7x can be transformed to another form.
Given
3.3x − 6.6 = 2.7x
Move all variable same side. using subtraction property of equality
subtract 2.7x both sides
3.3x -2.7x − 6.6 = 0
0.6x - 6.6 = 0
Addition property of equality
0.6x = 6.6
Hence, The equivalent equation is 0.6x = 6.6
Answer:
Step-by-step explanation:
3.3x - 2.7x = 6.6
0.6x = 6.6
answer is B
answer is also 11
need help with apex im not good at algebra at all
g(x) = ax²
We have a point (1, 5).
Substitute x = 1 and g(x) = 5
a(1²) = 5
a = 5
Answer: B. g(x) = 5x²
PLEASE HELP!!
At 6:00 p.m. the temperature was -5*F outside. By midnight the temperature had dropped 12 degrees. What was the temperature at midnight?
A) -7*F
B) -17*F
C) 17*F
-5-12=-17 so it is b)
What is 4,396.92 rounded to the. Nearest whole number
Answer:
4397
Step-by-step explanation:
Because 9 is closer to another 0, so you would round the 6 to a 7.
A coffee merchants want to make 6 pounds of a blend of coffee costing five dollars per pound. The blend is made using a six dollar per pound grade coffee and a three dollar per pound grade of coffee. How many pounds of each of these grades should be used?
Answer:
We should use 4 pounds of $6 coffee and 2 pounds of $3 coffee for the blend.
Step-by-step explanation:
The blend should,
Cost = $5
Weigh = 6 pounds.
Lets take the weight of $6 coffee as [tex]x[/tex] pounds
And lets take the weight of $3 coffee as [tex]y[/tex] pounds.
Lets write an equation for the weight of the blend,
[tex]x+y=6[/tex] <---------- 1st equation.
[tex]\frac{6x+3y}{x+y} =5[/tex]
=[tex]6x+3y=5x+5y[/tex]
=[tex]x=2y[/tex] <---------- 2nd equation
We can substitute to x in 1st equation from 2nd equation,
⇒[tex]2y+y=6[/tex]
=[tex]2y+y=6[/tex]
=[tex]3y=6[/tex]
=[tex]y=2[/tex]
We can substitute y value to 2nd equation to find x,
⇒[tex]x=2y[/tex]
=[tex]x=2*2[/tex]=[tex]x=4[/tex]
Therefore, we should use 4 pounds of $6 coffee and 2 pounds of $3 coffee for the blend.
25 points! Please help!
I need help! You have 5 attempts and if you are wrong, I will let you know so you can make corrections and I get the right answer.
Obviously, if he were to only maximize his income he would put all money on the higher interest. But to reduce the risk he will balance the investment. He will put a fraction a (between 0 and 1) of the 710000 on 1% and the rest (1-a) on the 4.5%. Both interests together must then satisfy to add up to 18000.
So written as an equation:
[tex]710000\cdot a\cdot 0.01 + 710000\cdot(1-a)\cdot 0.045 = 18000[/tex]
I am not going to solve step by step assuming you can solve for a (if not let me know) but the solution is
[tex]a = 279/497[/tex]
So that means he should put
[tex]710000\cdot \frac{279}{497} \approx 398571[/tex] on the 1% account, and the rest 311429 on the riskier 4.5% account.
I need help with this.
10 POINTS!
there are 24 people at a party twice many female as males and 5 times children as adults how many males are there and how many children are at the party
Answer: There are 4 adults. Two males. 16 children.
Step-by-step explanation:
2 x 2 = 4
4 adults
4 x 5 = 20
20 + 4 = 24
24 = 24
Answer:
Exact same way:
4 adults,
2 males & 2 females,
and 16 children
Step-by-step explanation:
Exactly as his!
247x82 using in area model
247x82=534 5 go in the hundreads place 3 go in the tens place and 4 go in the ones place
3x567 estimate rounding?
567 would round out to 600. If you are also rounding the three, then that is one. The answer to that would be 600. If you aren't rounding the three, the answer would be 1800.
Answer:
1800
Step-by-step explanation:
567 = 600 rounded to nearest hundred
3 * 600 = 1800
Angle(<)K and <L are complementary angles. If m<K = 3x+3 and m<L = 10x-4, find the measures of both angles.
3x+3 + 10x-4 +90 (because complementary angle add up to 90)
13x-1+90 (add 1)
13x/13=91 (divide 13 on both sides)
x=7
now you fill in 7 for x
m<K=24 and m<L=66
hope i helped
The measures of both angles are 24° and 66°.
Given:
m<K = 3x + 3
m<L = 10x-4
Note:
Complementary angles are angles whose sum equals 90 degrees.
Therefore:
[tex]m \angle K + m \angle L = 90^{o}[/tex]
Substitute
[tex](3x+3) + (10x-4) = 90[/tex]
Solve for x
[tex]3x+3 + 10x-4 = 90\\[/tex]
Add like terms
[tex]13x-1 = 90\\[/tex]
Add 1 to both sides
[tex]13x = 90 + 1\\13x = 91[/tex]
Divide both sides by 13
[tex]x= 7[/tex]
Substitute the value of x in each of the expressions of the two given complementary angles.
[tex]m\angle K = 3(7) + 3 = 21 + 3\\m\angle K = 24^{o}[/tex]
[tex]m\angle L = 10(7) - 4 = 70 - 4 \\m\angle L = 66^{o}[/tex]
Therefore, the measures of both complementary angles are: 24° and 66°.
Learn more about complementary angles here:
https://brainly.com/question/17287188
Kelly and Greta are asked to write an equation for the scenario below. “One person was able to plant 4 trees in the same amount of time that 5 people working together were able to plant 20 trees.” The girls agree that x represents the number of people working and y represents the number of trees planted. Kelly wrote the equation , and Greta wrote the equation . Which person is correct, and why? Kelly is correct; each person plants more trees than the person before them. Kelly is correct; and . Greta is correct; each person plants 4 more trees than the person before them. Greta is correct; and .
Answer: Greta is correct.
Explanation:
Greta is correct sine you can substitute different number of people for each of the values of and y and check that each person will still plant 4 trees.
For example:
4x = 4(1) = 4 trees; and
4 x 5 = 20
but you should follow a certain pattern to increase the value of x, such that every foe every value of x, one person is able to plant 4 trees.
Answer:
the answer is D
Step-by-step explanation:
Augusta sells t-shirts at the school store. On Tuesday, Augusta sold 7 less than twice the number of t-shirts she sold on Monday. She sold 3 t-shirts on Tuesday. Write an algebraic equation to represent m, the number of t-shirts August sold on Monday.
Since it is true that 9=9, the answer x=2 works.
As equations get more complex it is important to use properties of equality to isolate the variable and solve the equation.
Here are the properties of equality you need to isolate terms and solve equations.
The Subtraction Property of Equality is used when you have an equation with addition in it. It states that you can subtract the same quantity from both sides of the equation without changing the equality.
The Addition Property of Equality is used when you have an equation with subtraction in it. It states that you can add the same quantity to both sides of the equation without changing the equality.
The Division Property of Equality is used when you have an equation with a variable multiplied by a number. It states that you can divide both sides of an equation by the same quantity (as long as that quantity is not equal to zero) without changing the equality.
The Multiplication Property of Equality is used when you have an equation with a variable divided by a number. It states that you can multiply both sides of an equation by the same quantity without changing the equality.
Let’s look at an example and use properties of equality to isolate the variable and solve the equation.
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You start at (8, 1). You move right 2 unit and left 3 units. Where do you end?
You should end around: (9,1) hope this helps!
if you move right 2 and left 3 one time you get 10.4, do it again you get 11.7 again 13.10
Susan uses 15 rolls of ribbon to decorate 10 wedding baskets. Each roll of ribbon is
[tex]5 \frac{3}{8} [/tex]
yards long. After she decorates the baskets, she decides to cut off another
[tex] \frac{3}{4} [/tex]
yard from the ribbons of each basket. Write and simplify an expression to find out how much ribbon was used on the baskets.
Answer:
Amount of ribbon used = [tex]73 \frac{1}{8} yards[/tex] = 73.125 yards.
Explanation:
Number of ribbon rolls = 15
Number of wedding basket = 10
Length of 1 ribbon roll = [tex]5\frac{3}{8}=\frac{5*8+3}{8} =\frac{43}{8}[/tex] yards.
Total length of 15 ribbon roll = [tex]15*\frac{43}{8} =\frac{645}{8}[/tex]yards.
Length of ribbon cutting from each basket = [tex]\frac{3}{4}[/tex]yards.
Total length of ribbon cutting from 10 baskets = [tex]10*\frac{3}{4}=\frac{15}{2}[/tex] yards
Amount of ribbon used
[tex]=\frac{645}{8}-\frac{15}{2}=\frac{645}{8}-\frac{15*4}{2*4}=\frac{645}{8}-\frac{60}{8}\\ \\ =\frac{585}{8} =73 \frac{1}{8} yards[/tex]
Amount of ribbon used = [tex]73 \frac{1}{8} yards[/tex] = 73.125 yards.