Given:
The difference between two numbers is 22.
The sum of twice the smaller number and 3 times the greater number is 246.
Required:
To find the two numbers.
Explanation:
Let the two numbers be x and y.
Let y be the smaller number.
The difference between two numbers is 22.
[tex]x-y=22[/tex]The sum of twice the smaller number and 3 times the greater number is 246.
[tex]2y+3x=246[/tex]Now
[tex]\begin{gathered} 2y+3(22+y)=246 \\ 2y+66+3y=246 \\ 5y=246-66 \\ 5y=180 \\ y=\frac{180}{5} \\ y=36 \end{gathered}[/tex]Now x is,
[tex]\begin{gathered} x-36=22 \\ x=22+36 \\ x=58 \end{gathered}[/tex]Final Answer:
The two numbers are 58 and 36.
1. is the √15 rational or irrational?
2) Is the point you graphed an estimated or exact answer? Explain why.
(1) √15 is an irrational number.
(2) The point graphed on the number line is estimated.
Any number that cannot be stated as a fraction of any integer is considered to be irrational. The decimal expansions of irrational numbers are neither periodic nor do they come to an end. Every number that is transcendental is illogical.
When multiplied by itself, the square root of 15 produces the original integer 15. The square root of 15 is an irrational number since it cannot be expressed in the form of p/q.
Therefore, √15 is an irrational number.
The value of √15 in decimal is 3.87298334621 and hence, the point graphed on the number line is estimated but not an exact answer.
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Find the domain of f and write your answer in interval notation. f(x) = 9/10 + 4x + 6
The domain of a function is the set of all posible values that its input can take.
To find it, we should analyze the rule of correspondence of the function to see if it includes restrictions over the variable that works as input. In this case, we can see that x appears inside a square root. The expression inside the square root must be greater or equal to 0. Then:
[tex]\begin{gathered} 10+4x\ge0 \\ \Rightarrow4x\ge-10 \\ \Rightarrow x\ge-\frac{10}{4} \\ \Rightarrow x\ge-\frac{5}{2} \end{gathered}[/tex]The domain of f is the set of all real numbers x such that:
[tex]-\frac{5}{2}\le x[/tex]In interval notation:
[tex]x\in\lbrack-\frac{5}{2},\infty)[/tex]Therefore, the domain of the function is:
[tex]\lbrack-\frac{5}{2},\infty)[/tex]AcellusWhat is the measure of m?n20m5m == [?]Give your answer in simplest form.Enter
1) Examining that right triangle, and deriving from the similarity ratios, we can write down the following formulas:
[tex]\begin{gathered} n^2=20\cdot5 \\ n^2=100 \\ \sqrt[]{n^2}=\sqrt[]{100} \\ n=10 \end{gathered}[/tex]Note that in this equation, we are not taking into consideration the negative 10 as a possible result since dimensions can only be written as positive numbers.
2) Now, with the length of the height (n) we can find the length of that hypotenuse m using this formula:
[tex]\begin{gathered} m^2=25\cdot5 \\ \sqrt[]{m^2}=\sqrt[]{25\cdot5} \\ m=\sqrt[]{125} \end{gathered}[/tex]And that is the answer.
7 1/4 dividend by 1 2/3
Answer:
6.2
Step-by-step explanation:
i got this answer by guessing, srry.
- One leg of a right triangle is 4 inches longer than the other leg. The hypotenuse is 20 inches long. What is thelength of the shortest side?
Let's name the a, b, c
let side a = x
let side b = 4+x
Let side c = hypotenuse = 20
Using the law of pythagoras
opposite² + adjacent² = hypotenus²
x² + (x+4)² = 20²
open the parenthesis
x² + x² + 4x +16 = 400
2x² + 4x + 16 = 400
2x² + 4x + 16 - 400 = 0
2x² + 4x - 384 = 0 --------------------------------(1)
The is now a quadratic equation
so we will solve and find x
Using the formula method
Quadratic formula is
[tex]x\text{ = }\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]Comparing equation (1) with ax² + bx + c = 0
a = 2 b = 4 and c= -384
Inserting the values into the formula
[tex]x\text{ = }\frac{-4\text{ }\pm\sqrt{4^2\text{ - 4(2)(-384)}}}{2(2)}[/tex]simplifying the above
[tex]x\text{ = }\frac{-4\pm\sqrt{16\text{ + 3072}}}{4}[/tex][tex]undefined[/tex]The lengths of two sides of a triangle are 8 and 17. What is one possible length of the third side?
One possible length of the third side of the given triangle is 15
Determining a possible length of a side of a triangleFrom the question, we are to determine a possible length of the third side of the triangle
From one of the properties of a triangle, we know that
The sum of any two sides of a triangle is greater than the third side and the positive difference of any two sides of a triangle is lesser than the third side.
Thus,
8 + 17 is greater than the third side
25 is greater than the third side
and
17 - 8 is lesser than the third side
9 is lesser than the third side
If the third side of the triangle is x,
Then,
9 < x < 25
Hence, a possible value of x is 15
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Table:x y1 172 212 233 264 34Part A:When Hana goes to the mall, she always buys the same lunch and also buys some books. The table shows the number of books she buys x and the total amount of money she spends y. Choose the type of correlation that this data shows.Correlation: negative, positve, or none
PART A.
The data in the table shows a POSITIVE CORRELATION , an increase in variable x is associated with an increase in the variable y.
PART B
complete the two way relative frequencies using decimels, and round to three places.
To complete the second table, you need to divide all cells in the first table by 41. obtaining:
is 10% greater than or less than 1/8
is 10% greater than or less than 1/8 ?
Convert both of the given to decimals
So, 10% = 10/100 = 0.1
And 1/8 = 0.125
so, 10% is less than 1/8
are these data discrete or continuous explain a. the dangerous discreet because they are finite or countable numbers of valuesb. today is continuous because if recorded 40 consensus Saturday c. the days are continuous because they are finite or countable number of valued. Edina and discreet because if recorded 40 consistence Saturdays
Answer:
A. The data are discrete because there are a finite or countable number of values.
Explanation:
In continuous data there are infinite possibilities for the values, on the other hand, discrete data has a limited number of possibilities for its values.
In this case, the number of customers waiting is a discrete value, there is a limit and it will be an integer number. Therefore, the answer is
A. The data are discrete because there are a finite or countable number of values.
f(x) = |x+1|-1; vertical stretch by a factor of 3
The image of the function after vertically stretched by a factor of 3 is f'(x) = 3|x + 1| - 3
How to determine the equation of f(x) after the transformation?From the question, the given parameters are:
f(x) = |x + 1| - 1
The transformation is given as
Vertical stretch by a factor of 3
This implies that we stretch the function f(x) by a factor of 3 across the origin
Mathematically, this transformation can be represented as
(x, y) = (x, 3y)
When represented as a function, we have
f'(x) = 3 * f(x)
Substitute the equation f(x) = |x + 1| - 1 in the equation f'(x) = 3 * f(x)
So, we have the following equation
f'(x) = 3 * (|x + 1| - 1)
Remove the bracket
So, we have
f'(x) = 3 * |x + 1| - 3 * 1
Evaluate the products
So, we have
f'(x) = 3|x + 1| - 3
Hence, the equation of f'(x) is f'(x) = 3|x + 1| - 3
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(7, 17)
(-4,0)
(-3,-13)
(2,2)
(5,10)
write your answer in exponential form. 8^5 multiply 8^-2
Answer: 8^3
Explanation:
We want to multiply 8^5 multiply 8^-2
We would apply the rule of exponent;
a^b * a^c = a^(b + c)
By comparing both expressions,
a = 8
b = 5
c = - 2
Thus, we have
8^5 * 8^-2 = 8^(5 + - 2) = 8^(5 - 2)
= 8^3
A new energy drink advertises 120 calories for 5 oz. How many calories are in 15 oz of drink
A new energy drink advertises 120 calories for 5 oz.
How many calories are in 15 oz?
We can set up a proportion to solve this problem
[tex]\frac{120}{5}=\frac{x}{15}[/tex]Where x is the number of calories in 15 oz
Let us solve the above equation for x
[tex]\begin{gathered} \frac{120}{5}=\frac{x}{15} \\ \frac{x}{15}=\frac{120}{5} \\ x=\frac{120}{5}\cdot15 \\ x=120\cdot3 \\ x=360 \end{gathered}[/tex]Therefore, there are 360 calories in 15 oz of drink.
Camelle manages her soccer team. She needs to order 4 practice jerseys for each player. There are y players.
Camelle should buy a total of 4y practice jerseys for the team
How to determine the total number of practice jerseys?From the question, the given parameters are:
Number of players in the team = y players
Number of practice jersey for each player = 4 practice jerseys for each player
The total number of practice jerseys is the product of the number of players in the team and the number of practice jersey for each player
This is represented as
Total number of practice jerseys = Number of players in the team x Number of practice jersey for each player
Substitute the known values in the above equation
So, we have the following equation
Total number of practice jerseys = y players x 4 practice jerseys for each player
Evaluate the products
Total number of practice jerseys = y x 4 practice jerseys
This gives
Total number of practice jerseys = 4y practice jerseys
Hence, the number of jerseys is 4y
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Step-by-step explanation:
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My son is in 6th grade and he doesn’t understand why the base is 1/2
Given:
[tex]16\text{ inches}\times\frac{1}{8}\text{ inches}[/tex][tex]16\text{ inches}\times\frac{1}{8}\text{ inches}=2\text{ square inches}[/tex]A rectangle has an area ofx2+ 10x + 21Find the expressions that represent the dimensions of the rectangle.O (x - 3) and (x + 7)O (x + 1) and ( x + 21)O 3 and 7O (x + 3) and ( x + 7)
Answer:
The expressions that represent the dimensions of the rectangle are:
(x+3) and (x+7)
Explanation:
The area of the said rectangle is
[tex]x^2+10x+21[/tex]To find an expression that represents the dimensions of the rectangle, we need to factorize the expression for the area.
[tex]\begin{gathered} x^2+10x+21 \\ =x^2+3x+7x+21 \\ =(x^2+3)+(7x+21) \\ =x(x+3)+7(x+3) \\ =(x+3)(x+7) \end{gathered}[/tex]Therefore, the expressions we are looking for are
(x+3) and (x+7)
Find the distance between the two points:(7,12), (1,4)
In order to find the distance between the given points, use the following formula:
[tex]d=\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]where (x1,y1) and (x2,y2) are the given points,
In this case, you have:
(x1,y1) = (1 , 4)
(x2,y2) = (7 , 12)
By replacing the previous values into the formula for d, you obtain:
[tex]\begin{gathered} d=\sqrt[]{(12-4)^2+(7-1)^2} \\ d=\sqrt[]{8^2+6^2^{}} \\ d=\sqrt[]{64+36} \\ d=\sqrt[]{100} \\ d=10 \end{gathered}[/tex]Hence, the distance between the given points is 10
The equation y = 461.19x + 3,492 represents the value of awork of art from 1964 to 2005. What does the number461.19 represent?o yearly increase in valueo yearly decrease in valueO value of the work of art in 2005o value of the work of art in 1964
we have, in
[tex]y=461.19x+3492[/tex]then 461.19 represents the yearly increase in value
answer: the first one, yearly increase in value
Please answer with a detailed explanation.
From a tee box that is 6 yards above the ground, a golfer hit a ball. The Domain of the function is [0,230].
Given that,
In the picture there is a question with a graph.
From a tee box that is 6 yards above the ground, a golfer hit a ball. The graph displays the height of the golf ball above the ground in yards as a quadratic function of x, the golf ball's horizontal distance from the box in yards.
We have to find the domain of the function in the situation.
The domain is nothing but All of a function's x-values, or inputs, make up the domain, and all of a function's y-values, or outputs, make up the range.
The domain of a graph is every value in the graph, from left to right. The graph's entire range, from lower to higher numbers, represents the range.
Therefore, the Domain of the function is [0,230].
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match each playing with the option that correctly fills in that blank.
SOLUTION
One way to find the blank 1: least common multiple of two numbers is to list their multiples and find the first number that appears in both list.
Another way is to blank 2: multiply the numbers together, and then divide by their blank 3: greatest common factor.
I am doing calculus and I am supposed to use the tips it gives us and write it step by step and get explain each step. I can not use L hospitals rule, but I don’t know where to start
The value is 1
From the question, we have
lim_(K→0) ((sin(AK))^2)/((sin(BK))^2 )
Differentiate the above form, we get
=lim_(K→0) ((2cos(AK)))/((2cos(BK)) ) (Applying l hospital rule)
Now substitute the limit,
=2/2 = 1
L’Hospital’s Rule :
An input value that a function approaches and yields some result is referred to as a limit. Calculus and mathematical analysis depend on limits, which are also used to determine integrals, derivatives, and continuity. A general technique for assessing indeterminate forms like 0/0 or / is the L'Hospital rule. L'Hospital's rule is applied to calculate the limits of indeterminate forms for calculus derivatives. It is possible to use the L Hospital rule many times. This rule is still valid after being applied, and it will take any indefinite form. L'Hospital's Rule cannot be applied if the issue is not of the indeterminate types.
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Understanding Ratios
Eliza is a chef at a restaurant. She is making spaghetti sauce and put 21 tomatoes and 6 onions in the pot. Wh
tomatoes to onions in the pot?
Answer: The Answer is 7:2
Step-by-step explanation:
is 7:2
The perimeter of a square is equal to four times the length of its side. Write the direct variation equation that represents this situation.
Let y be the dependent variable and let x be the independent variable.
The linear equation representing this situation will be y = 4x, where y is the dependent variable and x is the independent variable.
As per the question statement, it is given that the perimeter of a square is equal to four times the length of its side and we are supposed to write the direct variation equation that represents this situation.
Also given that we have to use "y" and "x" which are dependent and independent variables respectively.
Perimeter = 4*side
So we conclude that perimeter is dependent on the independent value of side of the square.
Therefore, y = 4x would be the appropriate linear equation depicting the situation given.
Linear equation: An equation is said to be linear if the maximum power of all the variables are consistently 1.Dependent Variable: A quantity whose value relies on how the independent variable is altered is referred to as a dependent variable.Independent variable: A variable that indicates a quantity being altered in an experiment is known as an independent variable.To learn more about the concept of linear equations and dependent / independent variables, click on the link given below:
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Write an equation for this phrase "2 cubed is equal to the square root of x"
2 cubed means that you have to make the axponent of 2 by 3, symbolically:
[tex]2^3[/tex]The square root of x can be symbolized:
[tex]\sqrt[]{x}[/tex]If both terms are equal then you can put them together as:
[tex]2^3=\sqrt[]{x}[/tex]This is the expression that sumbolizes the phrase.
help meeee please !!
thank you
Answer:
i'm wath
Step-by-step explanation:
in whatwhat because wich
Factor problem and I'm having difficulty of setting up the problem.
The factor of the given polynomial is (m - 2n)(m - 5n).
What is termed as the factors of polynomial?Factors of polynomials are zeros of polynomials depicted in the form of some other linear polynomial. If we divide a given polynomial by any of its factors after factorisation, the remainder would be zero. We also factor the polynomial in this process by locating its greatest common factor.For the given question, the polynomial is -
= m² - 7mn + 10n²
We know that 10 = 5×2, thus break the equation like.
= m² - 2mn - 5mn + 10n²
Take m common from first two terms and -5n common from last two terms.
= m(m - 2n) - 5n(m - 2n)
Take common, (m - 2n).
= (m - 2n)(m - 5n)
Thus, the required factors of the given polynomial is (m - 2n)(m - 5n).
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Order the following math expressions from least to greatest. 100 = 22 = 02 = = 32
First, we need to simplify the expressions, as follows:
[tex]\begin{gathered} \sqrt[]{100}=10 \\ \sqrt[]{9}=3 \\ 2^2=4 \\ \sqrt[]{4}=2 \\ -4^2=-16 \\ 0^2=0 \\ \sqrt[]{1}=1 \\ 3^2=9 \\ (-4)^2=16 \end{gathered}[/tex]Then, the ordered list is:
[tex]\begin{gathered} -16,0,1,2,3,4,9,10,16 \\ or \\ -4^2,0^2,\sqrt[]{1},\sqrt[]{4},\sqrt[]{9},2^2,3^2,\sqrt[]{100},(-4)^2 \end{gathered}[/tex]In rectangle ABCD, ∡BAC=30° and AD=50. What is the length of side DC?25.028.943.386.6
With the informationabout the rectangle, we can say the angle between the diagonal and the longest side (unknown) is 30°. While the shortest side is 50.
Then, to estimate the length of the remaining side (DC, which is equal to AB), we can state the following relationship:
[tex]\tan 30^o=\frac{50}{AB}=\frac{50}{DC}[/tex]Then:
[tex]DC=\frac{50}{\tan30^o}=\frac{50}{\sqrt[]{3}/3}=\frac{3\cdot50}{\sqrt[]{3}}[/tex]We can multiply numerator and denominator by square root of 3 to simplify:
[tex]DC=\frac{3\cdot50}{\sqrt[]{3}}=\frac{\sqrt[]{3}\cdot3\cdot50}{\sqrt[]{3}\cdot\sqrt[]{3}}=\frac{\sqrt[]{3}\cdot3\cdot50}{3}=50\sqrt[]{3}\approx86.6[/tex]The length of side DC is approximately 86.6. The correct answer is the fourth option.
Flo measures the amount of water her high pressure sprayer uses and finds that it uses 20 gallons of water in 4 minutes and 30 gallons in 6 minutes. Complete the table, Then describe whether it makes sense to use a constant rate to describe the relationship . Explain I need help I’m confused
Given, 20 gallons per 4 minutes, let's find the unit rate:
[tex]\frac{20}{4}=5\frac{\text{gal}}{\min }[/tex]Also, given 30 gallons per 6 minutes, that also has an unit rate of:
[tex]\frac{30}{6}=5\frac{\text{gal}}{\min }[/tex]Thus, the constant of proportionality is 5.
Let's complete the table:
Yes, it does make sense. Because a high pressure sprayer should ideally be using a constant rate of water.
