The distributive property also combines subtraction and multiplication for example, 3 x (5 — 2) = (3 x 5) —(3 x 2). Explain how you could use the Distributive Property and mental math to find 5 x 198.
After using distributive property we find the solution of 5 × 198 is 990.
What is Distributive property?
By the rule of distributive property, multiplying the sum of two or more addends by a number gives the same result as when each addend is multiplied individually by the number and the products are added together.
The expression is given as;
5 × 198
Now, By using distributive property we calculate as;
5 × 198 = 5 × ( 200 - 2 )
= (5 × 200) - (5 × 2)
= 1000 - 10
= 990
Hence, After using distributive property we find the solution of 5 × 198 is 990.
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Find a counterexample to show that the conjecture is false.
The sum of two numbers is always greater than their difference.
The statement is false, a counterexample is given by using the numbers 1 and -1.
How to find the counterexample?Here we have the statement:
"The sum of two numbers is always greater than their difference"
So we just need to find two numbers such that the statement is false.
This is really trivial, for example, we can propose the numbers 0 and 0.
The sum gives 0 + 0 = 0
The difference is 0 - 0 = 0
The sum is not greater than the difference.
Now, I will propose a less trivial counterexample, let's use the numbers 1 and -1.
The sum gives 1 + (-1) = 1 - 1 = 0
The difference gives: 1 - (-1) = 1 + 1 = 2
The difference is larger than the sum, so we found a counterexample for the given statement.
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carlos jogged 5 3 4 laps around the school track in 8 minutes. what was his average speed in laps per minute? lap(s) per minute how to solve step by step
Average Speed is 23/32 laps per minute.
In the given statement is:
Carlos jogged 5 3/4 laps around the school track in 8 minutes.
What is Average speed?
Average Speed is calculated by dividing the total distance travelled by the time interval. For example, Someone who takes 40 minutes to drive 20 miles north and then 20 miles south (to end up at the same place), has an average speed of 40 miles divided by 40 minutes, or 1 mile per minute (60 mph)
Now, According to the Question:
5 3/4laps = 23/4 laps
23/4 ÷8
=23/4 × 1/8
=23/32
So, 23/32 laps per minute
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Stephanie is a taxi driver. She rents her taxi for $300/week. She feels she can take in $120/day in fares. Let D be the number of days she drives her taxi in a week and T be the total earnings she expects after subtracting the rental charge.
a. Identify four ordered pairs (D,T).
b. Write an equation that gives T as a function of D.
c. What is the most she can earn in a year at this rate?
Answer: a. (0, -300), (1, -180), (2, -60), (7, 540)
b. T=120D-300
c. $28080
Step-by-step explanation:
a. T=120D-300 ==> per week
D=0: T=120(0)-300
D=0: T=-300 ==> (0, -300)
D=1: T=120(1)-300
D=1: T=120-300
D=1: T=-180 ==> (1, -180)
D=2: T=120(2)-300
D=2: T=240-300
D=2: T=-60 ==> (2, -60)
D=7: T=120(7)-300
D=7: T=840-300
D=7: T=540 ==> (7, 540)
b. T=120D-300
c. T=120(7)-300
T=840-300
T=$540 per week
1 year = 52 weeks
540*52=$28080
What is 5 divided by 1900 ?
If you know the answer please write steps
Answer:
i think the answer is 0.00263157895
Write the expression n ⋅ n ⋅ p ⋅ p ⋅ r ⋅ r ⋅ r using exponents.
Answer:
n² p²r³
Step-by-step explanation:
n ⋅ n ⋅ p ⋅ p ⋅ r ⋅ r ⋅ r
Write using exponents
There are 2 n terms
n²⋅ p ⋅ p ⋅ r ⋅ r ⋅ r
There are 2 p terms
n² p²⋅ r ⋅ r ⋅ r
There are 3 r terms
n² p²r³
need help with this work it is 6th grade
Answer:
1/4
Step-by-step explanation:
You jumped rope of 1/3 of 3/4 hour.
In math, "of" usually means times.
1/3 of 3/4 hour = 1/3 × 3/4 hour = (1 × 3)/(3 × 4) hour = 3/12 hour = 1/4 hour
Answer: 1/4
rationalise the denominator and simplify the square root of 15 over the square root of 5
Answer:
[tex]\sqrt{3}[/tex]
Step-by-step explanation:
[tex]\frac{\sqrt{15} }{\sqrt{5} }[/tex]
to rationalise the denominator multiply numerator/ denominator by [tex]\sqrt{5}[/tex]
= [tex]\frac{\sqrt{15} }{\sqrt{5} }[/tex] × [tex]\frac{\sqrt{5} }{\sqrt{5} }[/tex]
= [tex]\frac{\sqrt{75} }{5}[/tex]
= [tex]\frac{\sqrt{25(3)} }{5}[/tex]
= [tex]\frac{5\sqrt{3} }{5}[/tex]
= [tex]\sqrt{3}[/tex]
Select all the expressions that are equivalent to –24 [tex]\frac{1}{2}[/tex] + 16.15 – 4.
The expressions that are equivalent to [tex]-24\frac{1}{2} +16.15-4[/tex] are (B)16.15 - 28.5 , (C)-28.5 + 16.15 and (E)[tex]12.15-24\frac{1}{2}[/tex] .
In the question,
the given expression is [tex]-24\frac{1}{2} +16.15-4[/tex] , solving further we get
= -49/2 + 16.15 - 4 ...(as [tex]24\frac{1}{2} = \frac{49}{2}[/tex] )
= -24.5 + 12.15
= -12.35
In option(A) we have ,
=[tex]24\frac{1}{2} -16.15+4[/tex]
= 49/2 -16.15 +4
= 24.5 -16.15 +4
= 8.35 + 4
= 12.35
In option(B) we have ,
= 16.15 - 28.5
= -12.35
In option(C) we have ,
= -28.5 + 16.15
= -12.35
In option(D) we have ,
[tex]=-20\frac{1}{2} +16.5[/tex]
= -41/2 + 16.5 ...( as [tex]20\frac{1}{2} = \frac{41}{2}[/tex] )
= -20.5 + 16.5
= -4
In option(E) we have ,
[tex]=12.15-24\frac{1}{2}[/tex]
= 12.15 - 49/2
= 12.15 - 24.5
= -12.35
As we can see that from all the option , only option(B), option(C) and option(E) matches with the given expression .
Therefore , The expressions that are equivalent to [tex]-24\frac{1}{2} +16.15-4[/tex] are (B)16.15 - 28.5 , (C)-28.5 + 16.15 and (E)[tex]12.15-24\frac{1}{2}[/tex] .
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73.69 in scientific notation
Answer:
see picture
Step-by-step explanation:
Please look at explaination
Algebra 2, Need help Fast
Answer:
[tex] - 2x - h[/tex]
Step-by-step explanation:
We are given a function [tex]g(x)=2-x^2[/tex]. We want to find [tex](g(x+h)-g(x))/h[/tex] To do so, first we need to work out the numerator
[tex]g(x+h)=2-(x+h)^2[/tex]. Therefore
[tex]g(x+h)-g(x)\implies 2-x^2-2xh-h^2-2x-x^2[/tex]
like terms cancel out leaving us with
-2xh-h²=h(-2x-h)So,
[tex] \displaystyle\frac{g(x + h) + g(x)}{h} = \frac{ h( - 2x - h )}{h} = \boxed{ - 2x - h}[/tex]
Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options.
2.3p – 10.1 = 6.4p – 4
2.3p – 10.1 = 6.49p – 4
230p – 1010 = 650p – 400 – p
23p – 101 = 65p – 40 – p
2.3p – 14.1 = 6.4p – 4
The equivalent equation for the given equation is 2.3p - 10.1 =6.49p - 4. Therefore, option B is the correct answer.
Given that, 2.3p – 10.1 = 6.5p – 4 – 0.01p.
We need to find which equations have the same solution as the given equation.
What is an equivalent equation?Equivalent equations are algebraic equations that have identical solutions or roots. Adding or subtracting the same number or expression to both sides of an equation produces an equivalent equation. Multiplying or dividing both sides of an equation by the same non-zero number produces an equivalent equation.
Now, 2.3p - 10.1 = 6.5p - 4 - 0.01p can be simplified as follows:
To add or subtract terms of algebraic equations group like terms add numerals and keep the variables the same.
That is, 2.3p - 10.1 = (6.5p - 0.01p) - 4
⇒2.3p - 10.1 =6.49p - 4
The equivalent equation for the given equation is 2.3p - 10.1 =6.49p - 4. Therefore, option B is the correct answer.
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The perimeter of a rectangular pool is more than 62 meters, and the width is at least 10 meters less than the length. Which system of inequalities represents the possible length in meters, l, and the possible width in meters, w, of the pool?
w ≤ 10 – l
2l + 2w ≥ 62
w ≤ 10 – l
2l + 2w > 62
w ≤ l – 10
2l + 2w ≥ 62
w ≤ l – 10
2l + 2w > 62
the system of inequalities that represents the possible length in meters, l, and the possible width in meters, w, of the pool is given as w ≤ l - 10 and 2 l + 2 w > 62.
Let the length of the pool be x.
So, ATQ, the width will be represented by the inequality:
x - 10 ≥ width
w ≤ x - 10
w ≤ l - 10
Also, it is given that, the perimeter of the pool is more than 62 m
So, we get that:
P > 62
Also, we know that:
P = 2 l + 2 w
So, we get that:
2 l + 2 w > 62.
Therefore, the system of inequalities that represents the possible length in meters, l, and the possible width in meters, w, of the pool is given as w ≤ l - 10 and 2 l + 2 w > 62.
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Answer:
D
Step-by-step explanation:
i’m pretty sure
helppppp plssssssssssssssssss
Answer:
x=3
Step-by-step explanation:
3x-7=2
+7 +7
3x=9
Divide by 3.
3x divided by 3 is x.
9 divided by 3 is 3.
x=3
Hope this helps.
(b) After his first month he had more than he expected to have due to interest the bank provided. This let
Rob come up with a better expression,
4,²
+45w+155, where w is the number of weeks. How much
25
will he have in 1 year?
Calculating the numeric value of the given function, it is found that Rob will have $2,603.16 in his account in one year.
How to find the numeric value of a function/expression?To find the numeric value of a function, we replace each instance of the variable by the desired value.
For this problem, the expression for the amount that he has into his account after w weeks is given by:
A(w) = 0.04w² + 45w + 155.
One year has 52 weeks, hence w = 52, and the amount is given finding the numeric value as follows:
A(52) = 0.04(52)² + 45(52) + 155 = $2,603.16.
Rob will have $2,603.16 in his account in one year.
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-6/25: 5 2/5 what is the answer i need help!!
The expression -6/25: 5 2/5 is simplified to -30/675
What is ratio?Ratio can be defined as the comparison of two numbers or elements indicating their sizes in relation.
It is represented using the symbol ':'
Example;
The ratio of 3: 5 is written as 3/ 5
Given the expression;
-6/25: 5 2/5
Convert 5 2/5 into an improper fraction = 27/5
We have
-6/ 25 : 27/ 5
Take the ratio
- 6/ 25 ÷ 27/ 5
Take the inverse of the divisor and multiply
- 6/ 25 × 5/ 27
-30/675
Thus, the expression -6/25: 5 2/5 is simplified to -30/675
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Please answer this math equation.
The interval where the function is nonlinear and decreasing is 0 < x < 4
How to determine the interval where the function is nonlinear and decreasing?The straight lines on the graph are the intervals where the graph is linear
This means that the straight lines on the graph will not be considered
Considering the curve, the graph decrease from x = 0 to x = 4
This can be rewritten as:
0 < x < 4
Hence, the interval where the function is nonlinear and decreasing is 0 < x < 4
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Type the correct answer in the box. Use numerals instead of words.
Consider this expression.
√x² - y²
When x = 3and y = -6, the value of the expression is
Reset
-33 is the value of √x² - y² at x = 3 and y = -6.
The expression given in the question is √x² - y² and we have to find the value of this expression when the value of x is 3 and the value of y is -6.
In order to evaluate √x² - y² simply put x = 3 and y = -6 and then solve accordingly.
Let's proceed to solve the expression,
√x² - y²
at x = 3 and y = -6. we have
= √3² - (-6)²
= √9-36
= 3-36
= -33
⇒√x² - y² = -33
∴ On solving, √x² - y² for x = 3 and y = -6 we get -33 as its evaluation.
Hence, -33 is the required answer.
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Find the value of f(-5)
Answer:
y=3 or just put 3
Step-by-step explanation:
The net below shows the dimensions of a triangular pyramid with equilateral base.
What is the lateral surface area of this triangular pyramid?
The Lateral surface of the triangular pyramid = 6 cm²
How to Find the Lateral Surface of a Triangular Pyramid?The lateral surface of a triangular pyramid is the area of the three triangular surfaces of the triangular pyramid, which excludes the area of the base.
The area of each triangular face = area of triangle = 1/2(base)(height).
Given the following as shown in the diagram:
Height of the triangular face = 7.2 cm
Base length of the triangular face = 5 cm
Lateral surface of the triangular pyramid = 3(1/2 × base × height)
Plug in the values
Lateral surface of the triangular pyramid = 3(1/2 × 5 × 7.2)
Lateral surface of the triangular pyramid = 3(18)
Lateral surface of the triangular pyramid = 6 cm²
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Given the linear functions f(x) = x-3 and g(x) = -2x + 4, determine (f g)(x).
O(f-g)(x) = -2x - 12
O(1-g)(x) = -2x² - 12
O(1-g)(x) = -2x2 - 2x - 12
O(f g)(x) = -2x2 + 10x - 12
!!!!!PLEASE HELP!!!!!
Answer:The answer would be 8
Step-by-step explanation:You would have to do 8/-2+2 and that would leave you with 8 because -2+2 is 0.
What is an equation of the line that passes through the points (−1,−7) and (−8,0)?
The equation of the line that passes through the points is y = -x - 8
What is an equation of the line that passes through the points?The points are given as:
(−1,−7) and (−8,0)
Calculate the slope (m) using
m = (y2 - y1)/(x2 - x1)
So, we have
m = (0 + 7)/(-8 + 1)
This gives
m = -1
The equation of the line that passes through the points is then calculated as
y = m(x - x1) + y1
So, we have
y = -1(x + 8) + 0
This gives
y = -x - 8
Hence, the equation of the line that passes through the points is y = -x - 8
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25 points plus brainliest
The largest integer is 0 (first option).
What is the largest integer?Integers are whole numbers. An integer is number that is not a fraction and not a decimal. Integers can either be positive, negative or zero. An example of an integer is 100, - 100 and 0.
An even number is a number that is divisible by 2 into two equal halves. An example is 2, 4, 6, 8. Consecutive even integers are whole even numbers that follow each other on the number line. An example is 2, 4, 6, 8.
If 0 is the largest number, the other three consecutive even integers would be : 0, -2, - 4, - 6. The sum of these numbers is -12.
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In a bag, there are numbered tiles 1 through 10. You will pick a tile, replace it, then pick another one. Find the following probabilities.
P (1, the 3)
P ( odd, then number less than 4 )
P ( even, then odd )
Please help, this paper is due tomorrow and I have no idea what I'm doing!
Answer:
Wait, can you explain the answer choices, I don't understand them.
Step-by-step explanation:
According to the 2010 census, the population of Nebraska was 1.8 × 106 people. Which state had a smaller population?
(1 point)
California: 3.7 × 107
Rhode Island: 1.1 × 106
Texas: 2.5 × 107
Missouri: 6 × 106
Rhode Island has a smaller population.
Here,
According to the 2010 census, the population of Nebraska was 1.8 × 106 people.
We have to find the smaller population.
What is Product?
The multiply of two or more number is called Product.
Now,
The population of Nebraska was 1.8 × 106 people.
1.8 x 106 = 190.8
And,
The population of California = 3.7 x 107 = 395.9
The population of Rhode Island = 1.1 x 106 = 116.6
The population of Texas = 2.5 x 107 = 267.5
The population of Missouri = 6 x 106 = 636
Hence, Rhode Island has a smaller population.
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The diagram represents two statements: p and q.
P
COD
A B
Which represents regions A, B, and C?
OpVq
Op-9
Ο g/p
O q-p
The regions is represented as :
A = p - p ∩ q , B = p ∩ q and C = q - p ∩ q
According to the question we have been given the Venn diagram with two regions p and q.
We need to find the representation of regions A, B and C.
As we can from the diagram,
region A is the area where the only p statement is there which exclude the B region . That is A is area of difference.
So it can be represented as
A = p - p ∩ q
region B is the intersection of p and q.
So it can be represented by
B = p ∩ q
region C is the area where only q statement is there and excludes the intersection region. That is C is area of difference
So it can be represented as
C = q - p ∩ q
Hence the regions is represented as
A = p - p ∩ q
B = p ∩ q
C = q - p ∩ q
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Solve each system by elimination.
For the given systems of equations, we have that:
1) The infinite solutions have the following format: (3y - 12, y, 10y - 31).
2) There is one solution: (1.58, -3.45, 3.89).
3) There is one solution: (3, 2, 4).
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
For item 1, the system is:
3x + y - z = -5.-4x + 2y + z = 17.-2x - 4y + z = -7.From the first equation, we have that:
z = 3x + y + 5.
Replacing on the second equation, we have that:
-4x + 2y + 3x + y + 5 = 17
-x + 3y = 12
x = 3y - 12.
Replacing on the third equation, we have that:
-2x - 4y + 3x + y + 5 = -7
x - 3y = -12
Since x = 3y - 12:
3y - 12 - 3y = -12
0 = 0.
Free variable, hence:
x = 3y - 12.y = y.z = 3x + y + 5 = 9y - 36 + y + 5 = 10y - 31.The infinite solutions have the following format: (3y - 12, y, 10y - 31).
For item 2, the system is:
x + 5y + 3z = -4.x + 2y - 3z = 8.-3x + 2y + 3z = -12.From the first equation:
x = -4 - 5y - 3z.
Replacing on the second equation:
-4 - 5y - 3z + 2y - 3z = 9.
-3y -6z = 13.
3y + 6z = 13.
Replacing on the third equation:
-3(-4 - 5y - 3z) + 2y + 3z = -12
12 + 15y + 9z + 2y + 3z = -12
17y + 12z = -14.
From the second equation, we have that:
z = (13 - 3y)/6.
Hence, replacing on the third again:
17y + 2(12 - 3y) = -14
11y + 24 = -14.
y = -3.45.
z = (13 - 3 x (-3.45))/6 = 3.89.
x = -4 - 5(-3.45) - 3(3.89) = 1.58.
Hence:
There is one solution: (1.58, -3.45, 3.89).
For item 3, the system is:
-4x - 2y + 5z = 4.5x + 2y - z = 15.5x - 2y - 3z = -1.From the second equation:
z = 5x + 2y - 15.
Replacing on the first:
-4x - 2y + 5(5x + 2y - 15) = 4
-4x - 2y + 25x + 10y - 75 = 4
21x + 8y = 79.
Replacing on the third:
5x - 2y - 3(5x + 2y - 15) = -1
5x - 2y - 15x - 6y + 45 = -1.
-10x - 8y = -46.
Adding both resulting equations, we have that:
11x = 33.
x = 3.
Then
21x + 8y = 79.
63 + 8y = 79
8y = 16
y = 2.
z = 5x + 2y - 15 = 5(3) + 2(2) - 15 = 4.
There is one solution: (3, 2, 4).
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Carly is playing her violin at a music festival and earns $8 for each song she plays. Maxwell is playing at a local coffee shop and earns $10 for each song he plays, but also has to pay a $50 fee to play there.
Problem
After how many songs will they have earned the same amount of money?
A.) 25
B.) 71
C.) 33
D.) 46
Answer:a
Step-by-step explanation: 25x8=200
(10x25)-50=200
Rewrite the following standard form linear equation into slope-intercept form. Write the answer starting with y=
12x-4y=-12
The equation of the line in the slope-intercept form is given y= 3x + 3 .
The graph of the equation y = mx + c is a line with m as the slope and m and c as the y-intercept. In the slope-intercept representation of the linear equation, the values of m and c are real numbers. A line's slope, expressed in m, indicates how steep it is. A line's gradient is also referred to as its slope occasionally. The y-coordinate of the point where the line's graph meets the y-axis is known as the y-intercept, or c, of a line.
The equation of the line is given by 12x - 4y = -12 .
This is the standard form of the line.
Now to represent the line in the slope-intercept form we need to write the equation for y in terms of x.
or, 12x-4y=-12
or, -4y = -12x - 12
or, y = (-12x - 12 ) ÷ (-4)
or, y = 3x + 3
Here the slope is 3 and the y-intercept is also 3.
Therefore the slope-intercept form of the line is given by y = 3x + 3
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