Suppose a and b are positive integers such that lcm(a,b) = 90 and gcd(a,b) = 3. If b is three more than a, then what are the values of a and b?
Given:
LCM(a,b) = 90 and GCD(a,b) = 3.
b is three more than a.
To find:
The values of a and b.
Solution:
We have,
LCM(a,b) = 90
GCD(a,b) = HCF(a,b) = 3
According to the question,
[tex]b=a+3[/tex]
If a and b are two positive integers, then
[tex]a\times b=HCF(a,b)\times LCM(a,b)[/tex]
[tex]a\times (a+3)=3\times 90[/tex]
[tex]a^2+3a=270[/tex]
[tex]a^2+3a-270=0[/tex]
Splitting the middle terms, we get
[tex]a^2+18a-15a-270=0[/tex]
[tex]a(a+18)-15(a+18)=0[/tex]
[tex](a+18)(a-15)=0[/tex]
Using zero product property, we get
[tex]a+18=0[/tex] and [tex]a-15=0[/tex]
[tex]a=-18[/tex] and [tex]a=15[/tex]
a is a positive integer so it cannot be negative. So, a=15.
Now,
[tex]b=a+3[/tex]
[tex]b=15+3[/tex]
[tex]b=18[/tex]
Therefore, the value of a is 15 and the value of b is 18.
I need help :(
Figure ABCD is a rhombus. Find the value of x.
The value of x is 32 degrees.
Rhombus
A rhombus is a special case of a parallelogram. In a rhombus, opposite sides are parallel and the opposite angles are equal. The rhombus is also called a diamond or rhombus diamond.
It is given in the question that there is a rhombus ABCD with ∠ DAC = 58 degrees.
We have to find the angle x or ∠ ADB.
We know the property that the diagonals of the rhombus perpendicularly bisect each other.
Hence, the rhombus is divided into 4 right triangles.
Hence,
∠DAC + ∠ADB = 180 - 90 = 90 degrees
58 + x = 90 degrees
x = 90 - 58
x = 32 degrees.
To learn more about rhombus, here:-
https://brainly.com/question/27870968
#SPJ1
Solve the equatuon
x/2-(2/(x+1))=1
x=?
[tex]\frac{x}{2}-\frac{2}{x+1}=1[/tex]
We have 2 denominators that we need to get rid of. Whenever there are the denominators, all we have to do is multiply all whole equation with the denominators.
Our denominators are both 2 and x+1. Therefore, we multiply the whole equation by 2(x+1)
[tex]\frac{x}{2}[2(x+1)]-\frac{2}{x+1}[2(x+1)] = 1[2(x+1)][/tex]
Then shorten the fractions.
[tex]\frac{x}{2}[2(x+1)]-\frac{2}{x+1}[2(x+1)] = 1[2(x+1)]\\x(x+1)-2(2)=1(2x+2)[/tex]
Distribute in all.
[tex]x^2+x-4=2x+2[/tex]
We should get like this. Because the polynomial is 2-degree, I'd suggest you to move all terms to one place. Therefore, moving 2x+2 to another side and subtract.
[tex]x^2+x-4-2x-2=0\\x^2-x-6=0\\[/tex]
We are almost there. All we have to do is, solving for x by factoring. (Although there are more than just factoring but factoring this polynomial is faster.)
[tex](x-3)(x+2)=0\\x=3,-2[/tex]
Thus, the answer is x = 3, -2
question is in the picture.
Answer: About 16 snaps
Step-by-step explanation:
In a box and whisker plot, the rightmost line in the "box" of the plot is the third quartile, which represents the 75th percentile.
In this graph, although it is difficult to pinpoint the EXACT number of snaps sent, the 75th percentile would be marked at about 16 snaps.
What fraction is equivalent to the expression
21
16
÷
7
4
?
Answer:
3/4
Step-by-step explanation:
21/16 ÷ 7/4
21/16 × 4/7
3/4
Leonardo draws a cookie on graph paper using the scale shown below. The cookie has a diameter of 12.5 cm in the drawing. Which of the following drawings best represents the diameter of the cookie at the scale Leonardo chose?
Answer:
Where's the drawing at because I don't see anything man
-60+x-23=70
Need help
Answer:
x-83=70
x = 70 + 83
x= 153
Let f(x) = 2x^2-2x+ 7 and g(x) = x^2 + 9x -6z Find f(x) - g(x).
A. X^2-11x+13
B. X^2-11x+1
C. X^2+7x+1
D. X^2+7x+13
Heres the answer welcome btw
The cube of the product of 8 and a number.
The unknown number will be equal to 64.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the cube of the product of 8 and the number is 512. The unknown number will be calculated as,
8 x = 512
x = 512 / 8
x = 64
The number which is the product of 8 will be equal to 64.
The complete question is given below.
The cube of the product of 8 and the number is 512. What is the number?
To know more about an expression follow
https://brainly.com/question/1713767
#SPJ2
PLEASE HELP ME!!!!! WILL GIVE BRAINLIESTTTTTTTTTT!!!!!!!
Answer:
Domain: -3 ≤ x ≤ 3
Range: -2 ≤ y ≤ 4
General Formulas and Concepts:
Algebra I
Domain is the set of x-values that can be inputted into function f(x) Range is the set of y-values that are outputted by function f(x)Step-by-step explanation:
According to the graph, our x-values span from -3 to 3. Since both are closed dot, they are inclusive in the domain:
[-3, 3] or -3 ≤ x ≤ 3
According to the graph, our y-values span from -2 to 4. Since both are closed dot, they are inclusive in the range:
[-2, 4] or -2 ≤ y ≤ 4
Help? Will give brainliest!
Answer:
Top one
Step-by-step explanation:
It is more appropriate to measure the speck of dust using millimeters because that is most similar to the scale of the speck's size.
A wading pool holds 30 gallons. How many pints of water would be equivalent?
Answer:
240 Pints
Step-by-step explanation:
To convert 30 gallons into pints you need to multiply 30 by the conversion factor in order to get the volume amount from gallons to pints.
Answer: 240 pints
Step-by-step explanation:
One pint is equal to 0.125 gallons.
-2 1/3 - (-5) =
Solve please
Answer:
2 2/3
Step-by-step explanation:
1. If 5 lbs of apples cost $2.99, How much would 3 lbs cost?
Which graph represents an even function?
Answer:
one that looks like triangle
Step-by-step explanation:
WILL MARK BRAINLIEST IF CORRECT ANSWER! How many solutions??
Answer: infinite
Step-by-step explanation: since they have the same slope and y interscept it is a coincident line and has infinite solutions
y= 4-x
y= 4-x
Answer:
infinitely many
Step-by-step explanation:
when you simplify, you get the following two equations:
y=-x+4
y=-x+4
those two equations are the same, therefore it is many
2x<6 solve the following inequality
Answer:
x<3
Step-by-step explanation:
2x<6
/ /
2 2
x<3
The average daily maximum temperature in Syracuse is 21.85°C, and the average daily minimum temperature is -4.7°C. The average daily maximum temperature is BLANK °C higher than the average daily minimum temperature.
Answer:
The average daily maximum temperature is
26.56 °C higher than the average daily minimum temperature
Step-by-step explanation:
Here, we simply want to calculate how higher is the average daily maximum temperature to average daily minimum temperature
We simply proceed to subtract the two
Mathematically, that will be;
21.85 - (-4.7)
= 21.85 + 4.7
= 26.56 °C
9-3x/9=-11 what is x and how you did it in a way that isn’t complicated please
What is the volume of a cylinder, in cubic ft, with a height of 9ft and a base diameter
of 16ft? Round to the nearest tenths place
Answer:
Volume of cylinder is: Volume=1808.64 ft³
Step-by-step explanation:
Height of cylinder = 9 ft
Base diameter of cylinder = 16 ft
We need to find volume of cylinder .
The formula used is: [tex]Volume=\pi r^2h[/tex]
We need radius:
The radius = diameter/2 = 16/2 = 8 ft
Putting values and finding volume of cylinder
[tex]Volume=\pi r^2h[/tex]
[tex]Volume=3.14\times (8)^2\times (9) \\Volume=3.14\times 64\times (9) \\Volume=1808.64 \: ft^3[/tex]
So, Volume of cylinder is: Volume=1808.64 ft³
Need this ASAP thanks
Answer:
In Step 2.
Step-by-step explanation:
They should have distributed the 2 to the x and 1 instead of subtracting it.
I can write linear equations
1. Through: (-1,3), Slope=2
2.Through: (3,3), slope= -2
Anna's favorite pool toys are the beach balls. If the radius of one of the beach balls
is 6 inches, to the nearest whole number, what is the volume of the beach ball?
Leave your answer in terms of a.
Inches Cubed
Answer:
288
Step-by-step explanation:
please review the attachment for step by step soluation
An artist can draw 3 illustrations in 3.5 hours. How many hours will it take to
draw 15 illustrations? Explain or show how you found your answer.
Answer:
17.5 hours
Step-by-step explanation:
divide 15 by 3 to get 5,
multiply 5 by the amount of hours it takes to draw 3 illustrations so 5 x 3.5, the answer is 17.5
Determine the intercepts of the line.
x-intercept ( , )
y-intercept ( , )
Answer:
y-100
x-250
Step-by-step explanation:
because the lines are insecting the other lines on that line
I can't seem to figure this one out. Could someone show how to do it and the answer? Thanks in advance!
Answer:
[tex]\displaystyle (-\infty, -\frac{1}{6})[/tex]
Step-by-Step explanation:
We have the function:
[tex]\displaystyle y=\int_{1}^{x}\frac{1}{3+t+3t^2}\, dt[/tex]
And we want to find the interval for which y is concave upwards.
Therefore, we will need to find the second derivative of y, find its inflection points (where y''=0), and test for values.
So, let's take the derivative of both sides with respect to x. So:
[tex]\displaystyle y^\prime=\frac{d}{dx}\Bigg[\int_{1}^{x}\frac{1}{3+t+3t^2}\, dt\Bigg][/tex]
By the Fundamental Theorem of Calculus:
[tex]\displaystyle y^\prime=\frac{1}{3+x+3x^2}[/tex]
So, we will take the derivative again. Hence:
[tex]\displaystyle y^\prime^\prime=\frac{d}{dx}\Big[\frac{1}{3+x+3x^2}\Big]=\frac{d}{dx}\Big[(3+x+3x^2)^{-1}\Big][/tex]
We will use the chain rule. Let:
[tex]\displaystyle u=x^{-1}\text{ and } v=3+x+3x^2[/tex]
Differentiate:
[tex]\displaystyle y^\prime^\prime=-(3+x+3x^2)^{-2}(1+6x)[/tex]
Rewrite:
[tex]\displaystyle y^\prime^\prime=-\frac{6x+1}{(3+x+3x^2)^2}[/tex]
So, points of inflection, where the concavity changes, is whenever the second derivative is 0 or undefined.
We can see that the second derivative will never be undefined since the denominator can never equal 0.
So, our only possible inflection points are when it's equal to 0. Hence:
[tex]\displaystyle 0=-\frac{6x+1}{(3+x+3x^2)^2}[/tex]
Multiplying both sides by the denominator gives:
[tex]0=-(6x+1)[/tex]
Then it follows that:
[tex]\displaystyle x=-\frac{1}{6}[/tex]
So, our only possible point of inflection is at x=-1/6.
We will test for values less than and greater than this inflection point.
Testing for x=-1, we see that:
[tex]\displaystyle y^\prime^\prime=-\frac{6(-1)+1}{3+(-1)+3(-1)^2}=1>0[/tex]
Since the result is positive, y is concave up for all values less than -1/6.
And testing for x=0, we see that:
[tex]\displaystyle y^\prime^\prime=-\frac{6(0)+1}{3+(0)+3(0)^2}=-\frac{1}{3}[/tex]
Since the result is negative, y is concave down for all values greater than -1/6.
Therefore, the interval for which y is concave up is:
[tex]\displaystyle (-\infty, -\frac{1}{6})[/tex]
Note that we use parentheses instead of brackets since at exactly x=-1/6, our graph is neither concave up nor concave down.
Julius earns $47,800 a year working for a delivery service. He is single and pays $2,152.60 in state income
tax each year. He claims no dependents. What is the tax rate of Julius' state?
The tax rate is 4.50% if Julius earns $47,800 a year working for delivery service. He is single and pays $2,152.60 in state income tax each year.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
It is given that:
Julius earns $47,800 a year working for delivery service. He is single and pays $2,152.60 in state income tax each year.
To find the tax rate:
tax rate = (2152.60/47800)×100
tax rate = (0.045)×100
tax rate = 4.50%
Thus, the tax rate is 4.50% if Julius earns $47,800 a year working for delivery service. He is single and pays $2,152.60 in state income tax each year.
Learn more about the percentage here:
brainly.com/question/8011401
#SPJ5
Bonnie filled her car’s gas tank. She put in 10 1/2 gallons and paid $15.36.
Write the ratio in fractional form to determine the cost of gasoline per gallon.
What is the cost of gasoline per gallon?
Answer:
1: 2 and $3.072
Step-by-step explanation:
According to the question, the data provided is as follows
10 half gallons
For this she paid $15.36
Based on the above information,
The ratio in fractional form is
= 1 ÷ 2
= 1 : 2
And, the cost of gasoline per gallon is
Since half of 10 gallons is 5
And, the amount paid is $15.36
So, the cost of gasoline per gallon is
= $15.36 ÷ 5
= $3.072
Step-by-step explanation:
what if you use 24 cups of water. how much sugar do you need.
Make a ratio table
Answer:
24:?
Step-by-step explanation:
it depends on the ratio of cups of water to sugar.
For example: if there is one cup of sugar for every 12 cups of water. the ratio would be 24:2
The winner of a 50 mile race drove his car to victory at a rate of 112.9094 mph. What was his time (to the nearest thousandth of an hour)?
His time was
hours.
(Round to the nearest thousandth.)
Answer:
0.443 hours
Step-by-step explanation:
time = total distance / mph
time = 50 / 112.9094
time ≈ 0.443 hours
Answer:
0.443 hours
Explanation:
Given following:
speed: 112.9094 mphdistance: 50 milesFormula:
[tex]\sf time \ taken = \dfrac{distance}{speed}[/tex]
Substitute values to find time taken:
[tex]\sf \rightarrow time = \dfrac{50}{112.9094 }[/tex]
evaluate
[tex]\sf \rightarrow time = 0.4428329262[/tex]
rounded to nearest thousandth
[tex]\sf \rightarrow time = 0.443[/tex]