[tex]\large\underline{\bf \red{Step \:by\: Step \:Explanation:}}[/tex]
Let us take ,
First integer be x .Second integer be y .Also let us consider x > y .
According to first Condition :-
⇒ x - y = 1.
⇒ x = y + 1. .............(i)
According to second Condition :-
⇒ x × y = 30 .
⇒ ( y + 1 )y = 30 . [ From (i) ]
⇒ y² + y = 30.
⇒ y² + y - 30 = 0 .
⇒ y² + 6y - 5y -30 = 0.
⇒ y ( y + 6 ) -5 ( y + 6 ) = 0 .
⇒ ( y + 6 ) ( y - 5 ) = 0 .
[tex]\red{\bf \longmapsto y = 5 , (-6)}[/tex]
Here y can sustain both values 5 and minus 6 as y is an integer.
So , x = -6 , 5 .
Hence possible answers are ,
[tex]\boxed{\purple{\bf x = -6 , y = -5 }}[/tex]
[tex]\qquad\qquad\qquad \bf Or [/tex]
[tex]\boxed{\purple{\bf x = 6 , y = 5 }}[/tex]
.
When multiplying the factors 2/3 and 4/7 what is the product of the denominators
Answer:
21
Step-by-step explanation:
When multipling fractions you go straight across so, all you have to do in the furture is multiply the demonators, anyways all i had to was 3x7 which is 21. Hope this helps and have a wonderful day!
Answer:
21
Step-by-step explanation:
2/3+4/7= 8/21
the top number is the numerator and the bottom number is the denominator.
The graph below shows the amount of money Janet earned at her new job.
Janet's Earnings
у
80
70
60
50
Money Earned ($)
40
30
20
10
0
2 4 6 8 10 12 14 16
Hours Worked
How much does Janet earn per hour?
Answer:
b
Step-by-step explanation:
The amount of money Janet earns per hour is given by the slope of the line m = $ 7.50
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the first point be P ( 4 , 30 )
Let the second point be Q ( 8 , 60 )
Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = amount of money Janet earns per hour
So , slope m = ( 60 - 30 ) / ( 8 - 4 )
On simplifying , we get
The amount of money Janet earns per hour = 30/4
The amount of money Janet earns per hour = $ 7.50
Hence , the amount of money Janet earns = slope = $ 7.50
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Calculate the area of the trapezoid.
12 mm
5 mm
9 mm
________square millimeters
Answer:
52.5 square millimeters.
Step-by-step explanation:
Area of a Trapezoid = (a+b/2)h
= (9+12/2)•5
=(21/2) • 5
= 10.5 • 5
= 52.5 square millimeters
hope this helps!
Answer:
52.5 mm^2 (square millimeters)
Step-by-step explanation:
Just split the figure into two sections to make a rectangle, and a right triangle (This whole figure can be thought of as a composite figure)
Once that is done, you will notice that the length and width of the rectangle is 9mm by 5mm, and the triangle is 3mm by 5mm (because 12mm - 9mm is 3 mm, and the height of the triangle is shared with the width of the rectangle).
The area of a triangle is 1/2(base×height) [just as a triangle is half of a rectangle], so the area of the rectangle is (length × width).
Therefore the 9mm by 5mm rectangle has an area of 9×5 mm = 45 mm^2, and the 3mm by 5mm triangle has an area of 1/2(5×3) = 15/2 = 7.5 mm^2.
Add both areas to find the total area:
45mm^2 + 7.5mm^2 = 52.5 mm^2.
____________________________
Or using the formula for the area of a trapezoid: A = h (b1 + b2) / 2
Where A is the area, b1 is the first base, b2 is the second base, and h is the height of the figure.
Given that our first base is 9, second base is 12, and our height is 5.
A = h ( b1 + b2 ) / 2 → A = 5 ( 9 + 12 ) / 2 → 5 ( 21 ) / 2 → 105 / 2 → 52.5
Then just put this quantity in mm^2 because it is the area of the figure in that unit.
→ 52.5 mm^2
_____________________________
the martin family‘s truck gets an average of 25 miles per gallon. Predict how many miles they can drive using 7 gallons of gas.
Answer:
175
Step-by-step explanation:
7 times 25=175
you just purchased a new hooded sweatshirt for $24. the total cleaning cost is $2 total because it will be washed with other sweatshirts. you will wear the sweatshirt 18 times this winter. calculate the cost per wearing.
Answer:
Step-by-step explanation:
espera y termino y te ayudo vale que me falta poco vale
6m + 4n + 3m - 6
What are the terms? Separate them with a comma.
What is the sum of (2x2 + 5x -3) and (-3x2 -10 + x2)
Answer:5x-13
Step-by-step explanation:
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[tex](2 {x}^{2} + 5x - 3) + ( - 3 {x}^{2} + {x}^{2} - 10) = \\ [/tex]
[tex]2 {x}^{2} - 2 {x}^{2} + 5x - 3 - 10 = [/tex]
[tex]5x - 13[/tex]
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What is the value to the expression -2.1(4.7+(-7.4))
The quadratic function modeling the height of a ball over time is symmetric about the line , where t is time in seconds. Which statement is true about this situation?
A.
The height of the ball is the same after 1 second and 3 seconds.
B.
The height of the ball is the same after 0 seconds and 4 seconds.
C.
The height of the ball is the same after 0.5 second and 5.5 seconds.
D.
The height of the ball is the same after 1.5 seconds and 3.5 seconds.
Answer:
A. The height of the ball is the same after 1 second and 3 seconds.
Step-by-step explanation:
The quadratic equation function modeling is used to analyze the relationship between variables in the equation. If the ball is at height and t is time then the ball is on symmetric line which will move for initial 1 second then stabilizes at 3 seconds.
Water flows through a pipe at a rate of 8 pints per hour. Express this rate of flow in cups per week.
Answer:
2,688 cups per week
Step-by-step explanation:
Lets begin by figuring out the pints per week/pints per day. Multiplying 8 times 24, we get our daily total of 192 pints per day. Multiply this by 7 and we get a total of 1344 pints per week. We now must convert these pints into cups, which can be done by multiplying the total amount of pints by 2. 1344 times 2 = 2,688 cups
What is the z-score for Paula If she got 1400 on the SAT, the mean was 1100 and the
standard deviation was 275?
Express 610.47 in unit form.
Answer:
6 hundreds
1 tens
0 ones
4 tenths
7 hundredths
Use the figure to decide the type of angle pair that describes 4 and 5
Answer:
Alternate interior angles
Step-by-step explanation:
Angles 4 and 5 are alternate interior angles
A grocery store sells cheese for $0.48 a pound. What would be the price for 6 pounds of cheese?
Answer:
$2.88
Step-by-step explanation:
0.48×6=2.88
os the right answer
Eloise practiced piano for 25 of an hour. Sarah practiced piano for 34 of an hour.
How much longer did Sarah practice than Eloise?
Answer:
34 - 25 = 9
Step-by-step explanation:
If paper clips are 7/8 of an inch long and cost $0.02 to make, how much would it cost to produce enough paper clips to make a line, end to end, that stretches 56 inches?
Answer:
$1.12
Step-by-step explanation:
When you multiply 8/7 of 56, you get 64.
This shows that you will need 64 paperclips to make 56 inches worth of paper clips. If each paper clip costs two cents, you need to multiply 56 paperclips by 2 cents. 56x0.02=1.12 so it will cost you 1 dollar and twelve cents
Can you help me identify where I went wrong? I'm having trouble understanding this concept and I need to in order to understand what I will be learning next, thank you!
Step-by-step explanation:
Your work is correct. First, you graphed the region. The minimum or maximum is always at the corner, which you found to be (3.08, 3.64).
The value of C at this point is C = 14.
Between which pair of numbers is the of exact product
379 and 8
Answer:
3032
Step-by-step explanation:
379 x 8 = 3032
use math, also box method
Find the value of x. 4^3 = x
Answer:
x=64
Step-by-step explanation:
An automatic teller machine gives you $150 in five and ten-dollar bills. There are two more than twice as many five-dollar bills as there are ten-dollar bills. How many of each denomination are there?
Answer:
There are 7 ten-dollar bills and 16 five-dollar bills.
Step-by-step explanation:
Let's call:
T: Number of ten-dollar bills
F: Number of five-dollar bills
The amount of money withdrawn from the ATM is $150:
10T+5F=150
Dividing by 5:
[tex]2T+F=30\qquad\qquad [1][/tex]
We also know there are two more than twice as many five-dollar bills as there are ten-dollar bills:
[tex]F=2+2T\qquad\qquad [2][/tex]
Substituting [2] into [1]:
2T+2T+2=30
Rearranging:
2T+2T=30-2
Simplifying:
4T=28
Solving:
T=28/4=7
From [2]:
F=2+2*7=2+14=16
There are 7 ten-dollar bills and 16 five-dollar bills.
10
-25 please answer
Answer:
(-15)
Step-by-step explanation:
10-25 = (-15)
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grrrrrr please help i’ll give u a cookie :)
im only in 6th grade
Step-by-step explanation:
Use technology to solve the following problem: The lifetime of a certain type of automobile tire (in thousands of miles) is normally distributed with mean μ = 38 and standard deviation σ = 7. What proportion of tires have lifetimes between 36 and 46 thousand miles?
Answer:
0.4859
Step-by-step explanation:
The formula for calculating a z-score is is z = (x-μ)/σ,
where x is the raw score,
μ is the population mean, and
σ is the population standard deviation.
From the question:
mean μ = 38,000
standard deviation σ = 7,000
For.
36 ( thousand miles) = 36,000
z = (x-μ)/σ
z = 36,000 - 38,000/7000
z = -0.28571
Probability value from Z-Table:
P(x = 36000) = 0.38755
For 46 thousand miles = 46,000
z = (x-μ)/σ
z = 46,000 - 38,000/7000
z =1.14286
Probability value from Z-Table:
P(x = 46000) = 0.87345
The proportion of tires that have lifetimes between 36 and 46 thousand miles is calculated as:
P(x = 46000) - P(x = 36000)
0.87345 - 0.38755
= 0.4859
Dominique has $13.75 in her piggy bank. All of the money are quarters. How many quarters are in the piggy bank?
Answer: I think its 0.55
Step-by-step explanation: if you do 25 times 0.55 because quarter's are 25 cents it equals 13.75
The number of quarters in the piggy bag will be 55.
What is unit conversion?Multiplication or division by a numerical factor, selection of the correct number of significant figures, and unit conversion are all steps in a multi-step procedure. Unit conversion is the process of changing a quantity's measurement between different units, frequently using multiplicative conversion factors.
Given that Dominique has $13.75 in her piggy bank. All of the money is quarters.
The number of the quarters will be calculated as:-
1 dollar ⇒ 4 quarters
13.75 dollars ⇒ 13.75 x 4 quarters
13.75 dollars ⇒ 55 Quarters
Therefore, the number of quarters in the piggy bag will be 55.
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escribe el número igaul a 5 decenas y 13 unidades
Answer:
63
Step-by-step explanation:
what are the slopes of the two lines?
Step-by-step explanation:
The slopes of two lines are equal
The fastest doughnut machine can fry 9600 doughnuts per hour. Which is closest to the number
of doughnuts this machine can fry every second?
Answer:
9600/60 minutes = 9600/ 360 seconds = 26
Keep practicing :)
Step-by-step explanation:
Answer:
9.6
Step-by-step explanation:
The reason is because you divide this number by 1,000 which gives you 9.6
9600 divided by 1,000= 9.6
An experiment consists of determining the speed of automobiles on a highway using a radar equipment. The random variable in this experiment is a:
Answer:
the speed value that the radar equipment outputs.
Step-by-step explanation:
A random variable in an experiment is also (and most times the case) called a dependent variable. In this scenario, the random variable would be the speed value that the radar equipment outputs. This is because this value depends on the actual velocity of the cars that pass by the equipment. The faster the car is moving when it passes the radar the higher value will be displayed on the equipment. Therefore, depending completely on the vehicles.
Is 4.95 a terminating decimal
Answer:
Definitely
since the definition of a terminating decimal is one that has an ending, and a Repeating decimal is one that never ends.
Step-by-step explanation:
Find the remainder when f(x) is divided by g(x) given that f(x) = 4x3 − 5x2 − 3x + 2 and g(x) = x − 3.
Given:
[tex]f(x)=4x^3-5x^2-3x+2[/tex]
[tex]g(x)=x-3[/tex]
To find:
The remainder when f(x) is divided by g(x).
Solution:
According to remainder theorem, if f(x) is divides by (x-c), then remainder is f(c).
Using remainder theorem, if [tex]f(x)=4x^3-5x^2-3x+2[/tex] is divides by [tex]g(x)=x-3[/tex], then remainder is f(3).
Substitute x=3 in f(x).
[tex]f(3)=4(3)^3-5(3)^2-3(3)+2[/tex]
[tex]f(3)=4(27)-5(9)-9+2[/tex]
[tex]f(3)=108-45-7[/tex]
[tex]f(3)=56[/tex]
Therefore, the required remainder is 56.