Answer:
The 1st and the 5th tables represent the same function
Step-by-step explanation:
* Lets explain how to solve the problem
- There are five tables of functions, two of them are equal
- To find the two equal function lets find their equations
- The form of the equation of a line whose endpoints are (x1 , y1) and
(x2 , y2) is [tex]\frac{y-y_{1}}{x-x_{1}}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
* Lets make the equation of each table
# (x1 , y1) = (4 , 8) and (x2 , y2) = (6 , 7)
∵ x1 = 4 , x2 = 6 and y1 = 8 , y2 = 7
∴ [tex]\frac{y-8}{x-4}=\frac{7-8}{6-4}[/tex]
∴ [tex]\frac{y-8}{x-4}=\frac{-1}{2}[/tex]
- By using cross multiplication
∴ 2(y - 8) = -1(x - 4) ⇒ simplify
∴ 2y - 16 = -x + 4 ⇒ add x and 16 for two sides
∴ x + 2y = 20 ⇒ (1)
# (x1 , y1) = (4 , 5) and (x2 , y2) = (6 , 4)
∵ x1 = 4 , x2 = 6 and y1 = 5 , y2 = 4
∴ [tex]\frac{y-5}{x-4}=\frac{4-5}{6-4}[/tex]
∴ [tex]\frac{y-5}{x-4}=\frac{-1}{2}[/tex]
- By using cross multiplication
∴ 2(y - 5) = -1(x - 4) ⇒ simplify
∴ 2y - 10 = -x + 4 ⇒ add x and 10 for two sides
∴ x + 2y = 14 ⇒ (2)
# (x1 , y1) = (2 , 8) and (x2 , y2) = (8 , 5)
∵ x1 = 2 , x2 = 8 and y1 = 8 , y2 = 5
∴ [tex]\frac{y-8}{x-2}=\frac{5-8}{8-2}[/tex]
∴ [tex]\frac{y-8}{x-2}=\frac{-3}{6}=====\frac{y-8}{x-2}=\frac{-1}{2}[/tex]
- By using cross multiplication
∴ 2(y - 8) = -1(x - 2) ⇒ simplify
∴ 2y - 16 = -x + 2 ⇒ add x and 16 for two sides
∴ x + 2y = 18 ⇒ (3)
# (x1 , y1) = (2 , 10) and (x2 , y2) = (6 , 14)
∵ x1 = 2 , x2 = 6 and y1 = 10 , y2 = 14
∴ [tex]\frac{y-10}{x-2}=\frac{14-10}{6-2}[/tex]
∴ [tex]\frac{y-10}{x-2}=\frac{4}{4}======\frac{y-10}{x-2}=1[/tex]
- By using cross multiplication
∴ (y - 10) = (x - 2)
∴ y - 10 = x - 2 ⇒ add 2 and subtract y in the two sides
∴ -8 = x - y ⇒ switch the two sides
∴ x - y = -8 ⇒ (4)
# (x1 , y1) = (2 , 9) and (x2 , y2) = (8 , 6)
∵ x1 = 2 , x2 = 8 and y1 = 9 , y2 = 6
∴ [tex]\frac{y-9}{x-2}=\frac{6-9}{8-2}[/tex]
∴ [tex]\frac{y-9}{x-2}=\frac{-3}{6}======\frac{y-9}{x-2}=\frac{-1}{2}[/tex]
- By using cross multiplication
∴ 2(y - 9) = -1(x - 2) ⇒ simplify
∴ 2y - 18 = -x + 2 ⇒ add x and 18 for two sides
∴ x + 2y = 20 ⇒ (5)
- Equations (1) and (5) are the same
∴ The 1st and the 5th tables represent the same function
Answer:The 1st and the 5th tables represent the same function!!!!!!!
If 100 dollars in one year gain 3 1/2 dollars interest, what sum will gain $38.50 cents in a year and a quarter
Answer:
10,300?
Step-by-step explanation:
Given: m∠1 = 140°, find m∠6.
A) 40°
B) 50°
C) 90°
D) 140°
Answer:
The answer is A
Step-by-step explanation:
When two parallel lines are crossed by another line the angle of 1 will be equal to 4, 5, and 8. The angle 2 will be equal to 3, 6, and 7. Since a straight line has a degree of 180, the subtracted degree of 180-140=40 which would mean 2=40 which 2=6 so 6=40.
Answer:
40°, A
Step-by-step explanation:
What are we going to do to figure out measure 6?
First of all, we know that measure 5 and measure 6 are equal to 180 degrees.
Second of all, we know that measure 1 and measure five are corresponding angles, which means they are congruent. If measure one is 140 degrees, measure 5 would also be 140 degrees.
So we know that measure 5 and measure 6 are equal to 180 degrees. We can now make an equation...
Let x = measure 6
140° + x = 180° x = 40°Complete the synthetic division below.
Answer:
The quotient is (x+7)
Step-by-step explanation:
Given the synthetic division problem
2|1 5 -14
we have to complete the synthetic division to find the quotient.
The steps are
Step 1: Set up the synthetic division
Step 2: Bring down the leading coefficient to the last row.
Step 3: Multiply the value which is written on the top left by the value just written on the bottom row.
Step 4: Add the column created in above step.
Step 5: continue until we reached last column.
The synthetic division is shown in attachment.
The quotient is (x+7)
Option D is correct
Find the greatest common factor
6x^2y^4+18x^3y^5-12x^5y^3
Answer:
6x^2y^3
Step-by-step explanation:
6x^2y^4+18x^3y^5-12x^5y^3
Lets check the coefficients first:-
6, 18, 12 - The GCF is 6.
x terms:- x^2, x^3 and x^5 . The GCF is x^2.
y terms:- y^4, y^5 and y^3. The GCF is y^3.
Answer:
6x^2y^3
Step-by-step explanation:
6x^2y^4+18x^3y^5-12x^5y^3
Lets break each term into prime factors
6x^2y^4 =3*2*x*x*y*y*y*y
18x^3y^5 = 9*2^3y^5 = 3*3*2*x*x*x*y*y*y*y*y
12x^5y^3 = 4*3x^5y^3 = 2*2*3*x*x*x*x*x*y*y*y
Each has one 2, one 3, two x's and three y's
So the greatest common factor is
2*3*x*x*y*y*y
6x^2y^3
Five added to twice Jeff’s age is the same as 3 times his age minus 2. How old is Jeff
Answer:
21
Step-by-step explanation:
To find Jeff's age, we set up an algebraic equation based on the problem given. By isolating the variable and solving the equation, we determine that Jeff is 7 years old.
The problem presented is a basic algebraic equation that can be translated to: 5 + 2 * Jeff's age = 3 * Jeff's age - 2. To solve for Jeff's age, we follow these steps:
First, let's define Jeff's age as the variable x. So we can rewrite the equation as 5 + 2x = 3x - 2.Next, we want to get all the x terms on one side and the constant terms on the other to isolate x. We can do this by subtracting 2x from both sides of the equation, which gives us: 5 = x - 2.Finally, by adding 2 to both sides of the equation, we get Jeff's age, x = 7.Jeff is 7 years old.
How many times can 25 go into 212
25 can go into 212 a total of 8 times with a remainder.
To determine how many times 25 can go into 212, we perform the division of 212 by 25.
This is a simple division problem where we are looking for the quotient, which represents the number of times 25 can be subtracted from 212 before the remainder is less than 25.
Let's perform the division:
[tex]\( \frac{212}{25} = 8 \)[/tex] with a remainder of 12.
This means that 25 can be multiplied by 8 to get as close as possible to 212 without exceeding it.
The difference between 212 and 200 is 12, which is the remainder.
Therefore, 25 can go into 212 a total of 8 times with a remainder of 12."
A road construction crew paves 1/5 mile every day. How much would they pave in 2 days?
Answer: 0.4 miles
Step-by-step explanation:
You can use the equation y=1/5x to help you figure it out where x is the days and y is the length. y=1/5(2). y=2/5 or 0.4 miles. Please vote my answer as brainliest
The road construction crew would pave 2/5 of a mile in 2 days, as they pave 1/5 mile every day.
Explanation:The road construction crew paves 1/5 mile each day. If they were to work for 2 days, to find out how much they would pave, you would simply multiply the pace per day by the number of days. So, 1/5 mile * 2 days = 2/5 miles. Therefore, the crew would pave 2/5 of a mile in 2 days.
To find out how much the road construction crew would pave in 2 days, we need to multiply the amount they pave in 1 day by 2. So, if they pave 1/5 mile every day, they would pave 1/5 * 2 = 2/5 mile in 2 days.
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A bookcase in a classroom contains textbooks that weigh 0.8 pound each. The bookcase alone weighs 22.2 pounds. If the total weight of the books and the bookcase is 31.8 pounds, how many books are in the bookcase?
Answer:
It should be 12 because:
31.8 - 22.2 = 9.6
9.6 ÷ 0.8 = 12
A 12-ounce bottle of soda costs $3.60. If the unit price remains the same how much would a 20-ounce bottle of soda cost?
A) $3.00
B) $5.50
C) $6.00
D) $6.50
For this, simply set up a proportion. If 12 oz. costs $3.60, then this means $3.60 per oz, or [tex]\frac{3.6}{12}[/tex]. Now letś make a proportion for 20 oz. Itś asking for how much it would cost if the unit price was the same, which means that the two should have a similar ratio. Because we don´t know how much it costs yet, this means x dollars for a 20 oz. bottle, or [tex]\frac{x}{20}[/tex]. I´ve already mentioned that they two are proportional, so write [tex]\frac{3.6}{12} = \frac{x}{20}[/tex].
To solve, cross multiply.
⇒[tex]12*x=3.6*20[/tex]
⇒[tex]12x=72[/tex]
Isolate variable x.
⇒[tex]\frac{12x}{12} = \frac{72}{12}[/tex]
⇒ x = 6: $6.00 for 20 ounces of soda.
Checking your work:
3.6/12 = 0.3
6/20 = 0.3
This means that theyŕe proportional, and that your answer is correct. Hope this was helpful.
find the nonpermissible for a in this expression a^2/2a+6
Answer:
The value not permissible for a is -3.
Step-by-step explanation:
Considering real numbers, the expression is undefined for any value a for which the denominator expression is zero.
[tex]\frac{a^2}{2a+6}, \,\,\,2a+6\neq 0\implies a\neq -3[/tex]
The expression is valid for all real numbers, except -3.
Answer:
a≠-3
Step-by-step explanation:
We cannot divide by zero, so the denominator cannot be zero
2a+6≠ 0
Subtract 6 from each side
2a+6-6≠ 0-6
2a ≠-6
Divide each side by 2
2a/2 ≠-6/2
a≠-3
the ages of three men are in the ratio 3:4:5.if the difference between the age of the oldest and the youngest is 18years, fine d the sum of the age of the three men
Answer:
108
Step-by-step explanation:
Givens
let the oldest one = 5xLet the youngest one = 3xLet the middle one = 4xEquation
3x + 18 = 5xSolution
3x + 18 = 5x Subtract 3x from both sides3x - 3x + 18 = 5x - 3x Combine18 = 2x Divide by 218/2 = 2x/2 Dividex = 9Answer
3x = 3*9 = 275x = 5*9 = 454x = 4*9 = 36The sum is 108Comment
This is a very tricky problem. It is not the usual way that 3 part ratios are handled. Thanks for posting.
If reyna drives 120 miles at a speed of 60mph how long will it take her to get home
Answer: 2 hours
Step-by-step explanation:
3 pounds of peaches cost $6. how many pounds of peaches could be bought for $24. find the algebraic equation
Answer:
Step-by-step explanation:The algebraic equation is 24/6*3 which will give you 12 pounds
Answer:
Equation
2x = 24
Step-by-step explanation:
3 pounds of peaches cost $6
so each pound = $6/3 = $2
so if you have $24 then $24/ 2 = 12 pounds
Let x = # of pounds of peaches
Equation
2x = 24
If m(x) = x2 + 3 and n(x) = 5x + 9, which expression is equivalent to (mn)(x)? A. 5x3 + 9x2 + 15x + 27 B. 25x2 + 90x + 84 C. x2 + 5x + 12 D. 5x2 + 24
Answer: A
Step-by-step explanation:
m(x) = x² + 2
n(x) = 5x + 9
(m*n)(x) = (x² + 3)(5x + 9)
= x²(5x + 9) + 3(5x + 9)
= 5x³ + 9x² + 15x + 27
Answer:
[tex]5x^3 +9x^2 +15x+27[/tex]
Step-by-step explanation:
If m(x) = x2 + 3 and n(x) = 5x + 9,
(mn)(x) is (m times n)(x)= m(x) times n(x)
m(x) * n(x)
Plug in m(x) and n(x). then multiply it
m(x) * n(x)
(x^2 + 3)(5x+9)
Apply FOIL method to multiply it
x^2 * 5x = 5x^3
x^2 * 9 = 9x^2
3*5x= 15x
3*9 = 27
[tex]5x^3 +9x^2 +15x+27[/tex]
a number m plus 4 is greater than or equal to 7
What is the equation of this line
A) y=2x-3
B) y=-1/2x-3
C) y=-2x-3
D) y= 1/2x-3
Answer:
A) y=2x-3
Step-by-step explanation:
I looked at the first 2 points that were perfectly on the x and y axis, so (3,3) and (5,7). I then put the numbers into their correct spots. When they were plugged in, both of the answers came back correct, so that is the correct equation.
Answer:
A. y=2x-3
Step-by-step explanation:
Since we have it in slope intercept form y=mx+b. B is our y intercet which we know is -3. Next we can find the slope which rise over run. This gives up 2 and our answer.
Solve for x.
−6 = 3/8x
Answer:
-16 =x
Step-by-step explanation:
−6 = 3/8x
Multiply each side of the equation by 8/3 to isolate x
-6 *8/3 = 8/3* 3/8 x
-48/3 = x
-16 =x
Answer:
Step-by-step explanation:
-6=3/8x
To make this easier to visualize:
3/8= 0.375
-6=.375x
Divide both sides by .375
The right side cancels.
-6/.375=-16
So x=-16
carlose has 38 apples .he put 8 apples in each bag.if he fills as many bags as possible ,how many apples are left.
plezz hurry
Answer:
he can fill 4 bag
i think he will have 4 or 6 left
Step-by-step explanation:
38/8= 4.75
.75/8=6
Answer:
4 bags and 6 apples
or
4.75 bags of apples
Step-by-step explanation:
First, take 38 divided by 8. You get 4.75. That means 4 bags have been filled up.
Next take 8 times 4. you get 32. then take 38-32 and you get 6.
That means there is 4 bags of apples and 6 left over. You could also say 4.75 bags are filled.
This was a different way of awnsering it so I hope this helps. This is how I do it.
Evaluate 2(11-5)+9÷3
Answer:
2(11-5)+9÷3 = 15
Step-by-step explanation:
the correct answer is: 15
To Solve:
11 - 5 = 6
6 x 2 = 12
9 / 3 = 3
12 + 3 = 15
The value of the expression is; 15
Evaluation of expressions;The given expression is; 2(11-5)+9÷3
By first solving the expression within the parenthesis, and then the division operator ; we have;
2(6) + 3By taking care of the parenthesis; we have;
12 + 3= 15Read more on arithmetic expressions;
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Which fraction is bigger 7/8 or 13/15
Answer:
7/8
Step-by-step explanation:
Step 1: Change the denominators so that they are the same for both fractions
7/8 x 15 = 105/120
13/15 x 8 = 104/120
Step 2: Compare
104/120 < 105/120 = 13/15 < 7/8
The fraction 7/8 is bigger than 13/15.
Explanation:To determine which fraction is bigger between 7/8 and 13/15, we need to find a common denominator. The least common multiple of 8 and 15 is 120. Now, we can convert both fractions to have the same denominator:
7/8 = 105/120
13/15 = 104/120
Since 105/120 is larger than 104/120, the fraction 7/8 is bigger than 13/15.
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On a scale model of a building, 1 4 inch represents 3 8 foot. What length on the model represents 1 foot? 3 32 in. 2 3 in. 1 1 1 in. 10 2 3 in.
Answer:
2/3 in
Step-by-step explanation:
We can use ratios to solve this problem.
1/4 inch x inches
-------------- = ---------------------
3 /8 ft 1 ft
Using cross products
1/4 * 1 = 3/8 * x
Multiply each side by 8/3 to isolate x
1/4 * 8/3 = 3/8*8/3 x
2/3 = x
Chole wants to build a storage container in the shape of a cube to hold 15.625 cubic meters of hay for her horse. Slove the equation 15.625 =s3 find the length of oneside of the container
Answer:
The length of each side is 2.5 m
Step-by-step explanation:
A cube has a volume of 15.625 m^3 of hay
We want to find the length of one side
V= s^3 where s is the length of one side
15.625 = s^3
Take the cube root of each side
15.625 ^ (1/3) = s^3 ^(1/3)
15.625 ^ (1/3) = s
2.5 = s
The length of each side is 2.5 m
find the value of x and show your work
Answer:
x = 10
Step-by-step explanation:
2.1 Adding a fraction to a whole
Rewrite the whole as a fraction using 10 as the denominator :
7x 7x • 10
7x = —— = ———————
1 10
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
2.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
7x • 10 + 1 70x + 1
——————————— = ———————
10 10
Final result :
70x + 1
———————
10
Processing ends successfully
what is the function f(x) = 2(x + 6), find x if f(x) = 22
Answer:
x = 5Step-by-step explanation:
f(x) = 2(x + 6)
f(x) = 22
thereofre we have the equation:
2(x + 6) = 22 use distributive property
2x + 12 = 22 subtract 12 from both sides
2x = 10 divide both sides by 2
x = 5
Determine whether the lines are parallel. Use slope to explain your answer. Use the graph shown below.
The slope is of the red line is ___
The slope is of the blue line is ___
The lines do/do not have the same slope so they are/are not parallel.
Please it's my third time trying to figure it out!
Answer:
red 1/2,
blue 2/5
The lines do not have the same slope so they are not parallel
Step-by-step explanation:
We can find the slope of the red line by using the formula
m = (y2-y1)/(x2-x1)
We have the points (0,1) and (2,2)
m= (2-1)/ (2-0)
= 1/2
We can find the slope of the blue line by using the formula
m = (y2-y1)/(x2-x1)
We have the points (0,-5) and (5,-3)
m= (-3--5)/ (5-0)
= (-3+5)/(5-0)
= 2/5
The lines do not have the same slope so they are not parallel
Allison is rolling her hula hoop on the playground. The radius of her hula hoop is 35 cm.
Answer:
The hula hoop rolls 879 \text{ cm}879 cm.
Step-by-step explanation:
Give a counter example to the following statement.
All quadrilaterals are rectangle
You can buy 3 apples at the Quick Market for $1.29.You can buy 5 of the same apples from the Stop and Save for $2.50.Which place is the better buy?
Answer: Quick market
Step-by-step explanation:
At quick market each apple is .43 each
At Stop and Save they are .50 each
PLZ HELP NEEED ASAP
Which equation shows y=−1/2x+4 is in standard form? First multiply each term by 4 to remove the fractions, 2. Then move the x value to the other side
A. 2x + y = 8
B. x+2y=−8
C. x + 2y = 8
Answer:A
Step-by-step explanation:
because standard form is ax+by=c
so multiply one half to both side and it cancancel
THIS IS MATH IS eASY PLZ SOLVE!!!!!!!!!!!!!!! POINTS HERE WILL GIVE BRAINLIEST!!!!!!!!!!!!
Answer:
The exact answer is 27 * pi
or the approximate answer is 27 * 3.14 = 84.78
Step-by-step explanation:
First step is to find the area of the circle
A = pi * r^2
A = pi * 6^2
A = 36* pi
We are missing 90 degrees of the circle or 90 out of 360.
That means we keep 360 - 90 = 270 or 270/360
The fraction we are keeping simplifies to 3/4 (divide top and bottom by 90)
Multiply the area by the fraction that we kept.
36 pi * 3/4 = 27 * pi
The exact answer is 27 * pi
or the approximate answer is 27 * 3.14 = 84.78