Mathematics High School

if 5a = 20b, then b/a=

A. 4

B. 1/4

C. 4/1

D. 10

Answers

Answer 1
5a = 20b divide both sides by 5
a= 4b
b/a = b/4b
= 1/4
Answer 2

The ratio b/a is found by dividing both sides of the equation 5a = 20b by 5a, resulting in b/a being B) 1/4.

The question asks us to solve for the ratio b/a given the equation 5a = 20b. To find b/a, we can divide both sides of the equation by 5a:

5a = 20b
(5a) / (5a) = (20b) / (5a)
1 = 4b/a

From this, we can see that b/a must be 1/4, since 4 multiplied by 1/4 equals 1. Therefore, the correct answer is B. 1/4.

Related Questions

Add 21 1/2 in. 10 9/16 in.

Answers

First convert 1/2 into 8/16 then add your fractions. You should get 17/16 then make it a mixed number. 1 & 1/16. Now add 21+10+1 and you should get 32. So your awnser is 32 1/16 in.
Answer:

The addition is:

      [tex]=\dfrac{513}{16}\ in.[/tex] or   [tex]32\frac{1}{16}\ in.[/tex]

Step-by-step explanation:

We are asked to add the expression :

[tex]21\frac{1}{2}\ in.[/tex] and [tex]10\frac{9}{16}\ in.[/tex]

both the numbers are in mixed fraction .

We will first change both the numbers into simple fraction as follows:

[tex]21\frac{1}{2}=\dfrac{21\times 2+1}{2}\\\\\\21\frac{1}{2}=\dfrac{43}{2}\ in.[/tex]

and

[tex]10\frac{9}{16}=\dfrac{10\times 16+9}{16}\\\\10\frac{9}{16}=\dfrac{169}{16}\ in.[/tex]

Hence, the addition of the two numbers is calculated as follows:

[tex]\dfrac{43}{2}+\dfrac{169}{16}\\\\\\=\dfrac{43\times 8+169}{16}[/tex]

( Since, on taking lcm of 2 and 16)

Hence, we get:

[tex]=\dfrac{513}{16}\ in.[/tex]

which in mixed fraction is:

          [tex]32\frac{1}{16}\ in.[/tex]

Which pair of variables has a clear causal link between the two named variables?
the number of hats sold and the number of mittens sold in a city
the amount of butter and the amount of bread consumed by a family
the number of notebooks sold and the number of pens sold in a stationery store
the number of air conditioners sold per day in a city and the daily temperature
the number of hours a person can swim and the depth of the pool
NextReset

Answers

Answer: The number of air conditioners sold per day in a city and the daily temperature

Step-by-step explanation:

We know that if there is a causal relationship between two variables then one variable is responsible for causing the other variable.

the number of hats sold and the number of mittens sold in a city.

there is no causal relationship between the variables since both are independent variables.

the amount of butter and the amount of bread consumed by a family .

there is no causal relationship between the variables since both are independent variables.

the number of notebooks sold and the number of pens sold in a stationery store .

there is no causal relationship between the variables since both are independent variables.

the number of air conditioners sold per day in a city and the daily temperature .

there can be causal relationship between the variables since by increasing  or decreasing temperature the the number of air conditioners sold per day in a city can be increased or decreased respectively.

the number of hours a person can swim and the depth of the pool.

there is no causal relationship between the variables since both are independent variables.

A, 4, D, H, 16, M, 25, _, _ What are the next two in the sequence?

Answers

I would say that the new two in sequence are S and 36.
There are two numbers between A and D, three between D and H, four between H and M, which means that S is the fifth number after M.
I think you are missing number 9 between D and H, which means that 4 + 5 =9, 9 + 7 = 16, 16 + 9 = 25, and 25 + 11 = 36, 2 is added to each number. 

The sequence alternates between letters and squares of integers. The letters seem to follow a particular positional increment pattern, and the numbers are squares of consecutive positive integers. The missing elements in the sequence are R and 36.

The given sequence is: A, 4, D, H, 16, M, 25, _, _. This sequence appears to have two separate patterns interleaved. One pattern is a sequence of letters and the other is a sequence of numbers. For the letters part, A (1st letter), D (4th letter), H (8th letter), M (13th letter), so the next letters might follow an increasing pattern with the position of the letters in the alphabet. For the numbers, we have 4, 16, 25 which are squares of 2, 4, and 5 respectively. To solve for the next elements in the pattern, we would have to decipher the rule that connects the letters with their positions and the next squares of numbers.

The numbers are squares of consecutive positive integers: 2², 4², 5². The next number is 6² which is 36. Following the pattern in letters, after M (the 13th letter), the next letter should be the letter that is five positions ahead because the interval between the previous letters increased by 3 each time (D is 3 letters after A, H is 4 letters after D, M is 5 letters after H), so the next letter should be R (the 18th letter, which is 5 letters after M).

Therefore, the sequence should continue with R, 36.

TRUE or FALSE. If chord AB Is 3 inches from the center and chord CD is 5 inches from the center of the same circle, then chord CD is the longer chord.

Answers

The answer is false.

Answer:

False.

Step-by-step explanation:

Given,

Chord AB Is 3 inches from the center and chord CD is 5 inches from the center of the same circle,

Since, the distance of a chord is inversely proportional to the length of the chord,

That is, the chord that has the smallest distance from the center is largest.

3 < 5

⇒ The distance of chord AB from center < The distance of Chord CD from center

By the above statement,

⇒ The length of chord AB > The length of chord CD.

Hence, the given statement is FALSE.

you have a full job that pays 2400 per month you decide to take a part time job delivering newspapers that pay 200 per week if 15% is withheld for taxes from both jobs how much would you make in a year after taxes

Answers

ft (full time)= $2,400/ monthpt (part time)= $200/ week15% taken from taxes------------------------- 1 year= 12 months; 1 month= 4 weeks (12*2,400) + (4*12*200)= $38,400 you made in a year I set up the problem this way because you want to know how much you made that whole year, so if there are 12 months in a year, and you get paid $2,400 a month, then from your full time job you ear (12*2,400). From your PT job you make $200 a week, there are 4 weeks in a month and 12 months in a year, so to calculate what you earned from your PT job, you do: 4*12*200 15% of what you made is deducted from taxes:0.15(38,400)= $5,760 After taxes, you made:$38,400-$5760= $32,640 

Juanita is 15 years old and her brother is 5. what is the ratio of juanita's age to her brother's age?

Answers

15:5 and you can also say it as 3:1

Answer:  The required ratio is 3 : 1.

Step-by-step explanation:  Given that Juanita is 15 years old and her brother is 5 years old.

We are to find the ratio of Juanita's age to her brother's age.

Let x and y represents the ages of Juanita and her brother respectively in years.

Then, according to the given information, we have

[tex]x=15,\\\\y=5.[/tex]

Therefore, the ratio of Juanita's age to her brother's age is given by

[tex]x:y\\\\=\dfrac{x}{y}\\\\\\=\dfrac{15}{5}\\\\\\=\dfrac{3}{1}\\\\=3:1.[/tex]

Thus, the required ratio is 3 : 1.

Alex has 520 yards of fencing to enclose a rectangular area.

A retangle that maximises the enclosed area has a length of _ yards and a width of _ yards.

The maxium area is _____ yards

Answers

Perimeter =2w+2L= 520.
We can solve this by understanding that the area is maximized by a square
Therefore L=w.

p=2w+2w=520=4w
w=130

Area
 
A=wL=130(130)= 16900 square yards

The first thing we are going to do for this case is define variables.

We have then:

w: width

l: length

The perimeter is given by:

[tex] 2w + 2l = 520
[/tex]

The area is given by:

[tex] A = w * l
[/tex]

The area as a function of a variable is:

[tex] A (w) = w * (260-w)
[/tex]

Rewriting we have:

[tex] A (w) = -w ^ 2 + 260w
[/tex]

To obtain the maximum area, we derive:

[tex] A '(w) = -2w + 260
[/tex]

We equal zero and clear the value of w:

[tex] -2w + 260 = 0

2w = 260
[/tex]

[tex] w = \frac{260}{2}

w = 130
[/tex]

Then, the length is given by:

[tex] l = 260 - w

l = 260 - 130

l = 130
[/tex]

Finally, the maximum area obtained is:

[tex] A = w * l

A = 130 * 130

A = 16900
[/tex]

Answer:

A retangle that maximizes the enclosed area has a length of 130 yards and a width of 130 yards.

The maxium area is 16900 square yards

What is y=5/6x-3 in standard form

Answers

The answer is negative 2.5 why because...

take out any common factors
so..
5/ 2(3×-1)

Discuss the continuity of the cosine, cosecant, secant and cotangent functions,
...?

Answers

Final answer:

The cosine, cosecant, secant, and cotangent functions are all trigonometric functions. They are continuous everywhere except where the denominator is zero.

Explanation:

The cosine, cosecant, secant, and cotangent functions are all trigonometric functions. These functions are defined for all real numbers except when the denominator becomes zero. Therefore, they are continuous everywhere except where the denominator is zero.

For example, the cosine function, denoted as cos(x), is continuous for all real numbers. It has a periodic nature and oscillates between -1 and 1.

Similarly, the cosecant function, denoted as csc(x), is continuous everywhere except at the points where sin(x) is equal to zero. The secant function, denoted as sec(x), is continuous everywhere except at the points where cos(x) is equal to zero. The cotangent function, denoted as cot(x), is continuous everywhere except at the points where tan(x) is equal to zero.

Solve the Inequality.

-5r + 6 ≤ -5(r+2)

Answers

There is no solution.
There is no values that make the inequality true, the inequality has no solution.

To solve the inequality -5r + 6 ≤ -5(r+2), the answer is that this inequality has no solution.

Solve the Inequality:

-5r + 6 ≤ -5(r+2)

Distribute the -5 on the right side: -5r + 6 ≤ -5r - 10

Combine like terms: 6 ≤ -10

Since 6 is not less than or equal to -10, the inequality has no solution.

Which of the symbols correctly relates the two numbers below? Check all that apply.

55?35

A. less than or equal to
B. more than or equal to
C.<
D. not equal to
E.=
F.>

Answers

Based on the given numbers above, the answer would be options F and D. The symbols that correctly relates the two numbers above would be the greater than symbol and not equal to symbol. Obviously, we can see that number 55 has a greater value than 35 so these numbers cannot be equal. Hope this answer helps.

Answer:

>

Step-by-step explanation:

Given : [tex]55?35[/tex]

To Find: Which of the symbols correctly relates the two numbers below?

Solution:

We are given that [tex]55?35[/tex]

Since we know that 55 is greater than 35 .

So, sign of greater than (>)should replace ?

So, [tex]55>35[/tex]

Hence Option F is correct.

So, [tex]55?35[/tex] = [tex]55>35[/tex]

Option F : >

11/9 converted to a mixed number is

Answers

To write an improper fraction as a mixed number, divide the denominator into the numerator.

Image is provided.

Therefore, the improper fraction 11/9 can be written as the mixed number 1 and 2/9.

Antarctica comprises about 10.5% of the total land area on Earth. Antarctica has a surface area of about 5,400,000 square miles. What is the total land area on Earth?

Answers

Solution
(5.4 x 10^6)/10.5 = 514285.71
514285.71 x 100 = 51,428,571 square miles

The border line of the linear inequality 4x-2y<1 is solid.

true or false?

Answers

It is actualy false because
Solid =

either ≤ or ≥

Dash = < or >
Hope it helps you

Integrate sin^-1(x) dx

please explain how to do it aswell ...?

Answers

If you're using the app, try seeing this answer through your browser:  https://brainly.com/question/2264253

_______________


Evaluate the indefinite integral:

[tex]\mathsf{\displaystyle\int\!sin^{-1}(x)\,dx\qquad\quad\checkmark}[/tex]


Trigonometric substitution:

[tex]\mathsf{\theta=sin^{-1}(x)\qquad\qquad\dfrac{\pi}{2}\le \theta\le \dfrac{\pi}{2}}[/tex]


then,

[tex]\begin{array}{lcl} \mathsf{x=sin\,\theta}&\quad\Rightarrow\quad&\mathsf{dx=cos\,\theta\,d\theta\qquad\checkmark}\\\\\\ &&\mathsf{x^2=sin^2\,\theta}\\\\ &&\mathsf{x^2=1-cos^2\,\theta}\\\\ &&\mathsf{cos^2\,\theta=1-x^2}\\\\ &&\mathsf{cos\,\theta=\sqrt{1-x^2}\qquad\checkmark}\\\\\\ &&\textsf{because }\mathsf{cos\,\theta}\textsf{ is positive for }\mathsf{\theta\in \left[\dfrac{\pi}{2},\,\dfrac{\pi}{2}\right].} \end{array}[/tex]


So the integral [tex]\mathsf{(ii)}[/tex] becomes

[tex]\mathsf{=\displaystyle\int\! \theta\,cos\,\theta\,d\theta\qquad\quad(ii)}[/tex]


Integrate [tex]\mathsf{(ii)}[/tex] by parts:

[tex]\begin{array}{lcl} \mathsf{u=\theta}&\quad\Rightarrow\quad&\mathsf{du=d\theta}\\\\ \mathsf{dv=cos\,\theta\,d\theta}&\quad\Leftarrow\quad&\mathsf{v=sin\,\theta} \end{array}\\\\\\\\ \mathsf{\displaystyle\int\!u\,dv=u\cdot v-\int\!v\,du}\\\\\\ \mathsf{\displaystyle\int\!\theta\,cos\,\theta\,d\theta=\theta\, sin\,\theta-\int\!sin\,\theta\,d\theta}\\\\\\ \mathsf{\displaystyle\int\!\theta\,cos\,\theta\,d\theta=\theta\, sin\,\theta-(-cos\,\theta)+C}[/tex]

[tex]\mathsf{\displaystyle\int\!\theta\,cos\,\theta\,d\theta=\theta\, sin\,\theta+cos\,\theta+C}[/tex]


Substitute back for the variable x, and you get

[tex]\mathsf{\displaystyle\int\!sin^{-1}(x)\,dx=sin^{-1}(x)\cdot x+\sqrt{1-x^2}+C}\\\\\\\\ \therefore~~\mathsf{\displaystyle\int\!sin^{-1}(x)\,dx=x\cdot\,sin^{-1}(x)+\sqrt{1-x^2}+C\qquad\quad\checkmark}[/tex]


I hope this helps. =)


Tags:  integral inverse sine function angle arcsin sine sin trigonometric trig substitution differential integral calculus

Arrange the following polynomial into descending order for x, then interpret the degree of the 2nd term.

7x3y3 + 4 − 11x5y2 − 3x2y

Answers

Answer:

Always double check first but I am pretty sure that it is 6


The sum of two numbers is 66 and the difference is 12 . What are the numbers?

Answers

66-54=12. So, 54+12 = 66.
one of them is 27 and the other is 39

What are the x- and y- intercepts for the line y−3=3(x+5)



Enter your answers in the boxes. please help me

Answers

The y intercept is found when you substitute a zero for x. y-3=3(0+5) would find the y intercept. when you solve that you find that the y intercept is 18. The x intercept is the other way around, and when you do it, you find out that the x intercept is -6.

which of the following represents the most accurate estimation if 75-33?

Answers

40 is the most accurate.
You could round 75 to 80 and 33 to 30. Then subract to get 50

ln 1/sqrt e = -1/2 write in exponential form pls show steps ln 1/sqrt e = -1/2 write in exponential form pls show steps

Answers

Here is the answer to the given expression above.
According to what I have researched,
1/sqrt e is e^-1/2, or conversely, 1/sqrt a is a^-1/n.
1a≡a−1 and
√a ≡ a^1/2

therefore: 1/√a = a^−1/2

Whereas:
n√a ≡ a^1/n and thus: 1/n√a = a −1/n
Hope this the answer that you are looking for.
Thanks for posting your question.

What is the expression in radical form?

(5x4y3)^2/5



Enter your answer, in simplest form, in the box.

Answers

5^400x^2y^2 answer to question

If a(x) and b(x) are linear functions with one variable, which of the following expressions produces a quadratic function?
(ab)(x)
(a/b)(x)
(a – b)(x)
(a + b)(x)

Answers

I hope this helps you

Answer:

Option (a) is correct.

a(x)b(x) = (ab)(x)

To produce a quadratic equation the two linear equation must be multiply.

Step-by-step explanation:

Given :  a(x) and b(x) are linear functions with one variable.

We have to choose from the given option the correct expression that will produce a quadratic equation.

Quadratic equation is an equation which is in the form of [tex]ax^2+bx+c[/tex] where [tex]a\neq0[/tex]

Since given a(x) and b(x)  are linear equation in one variables so to get square term we must multiply the two linear equations.

Let a(x)=3x+1

and b(x)= 8x+1

then when we multiply we get,

[tex]a(x)\times b(x)=(3x+1)\times (8x+1)=24x^2+11x+1[/tex]

Thus, To produce a quadratic equation the two linear equation must be multiply.

Thus, a(x)b(x) = (ab)(x) is correct.

Option (a) is correct.

multiplicative inverse of -3.4

Answers

multiplicative inverse of -3.4 is -1/3.4

What are the least common multiples of 7 and 11

Answers

I think is the least common number is 77 because it multiple of 7 and 11 both

34 - 2(x + 17) = 23x - 15 - 3x what is x.

Answers

x= 15/22. Hope this helps :)

Your poor health causes you to miss one work day every two weeks. You do not get paid when you are out sick. You normally work 8 hours a day and get paid $9.29 per hour. How much pay are you losing each year

Answers

Final answer:

The annual loss of income due to missing one work day every two weeks at $9.29 per hour, working 8 hours per missed day, is $1,932.32.

Explanation:

To calculate the amount of pay being lost each year due to missing one work day every two weeks, we need to consider the weekly work schedule and hourly wage.

Step-by-Step Calculation


 First, determine the hourly wage and the number of hours missed per day. In this case, the hourly wage is $9.29 and each missed day accounts for 8 hours of work.
 Second, calculate the daily loss of income due to illness. Multiply the hourly wage by the number of hours missed: $9.29 x 8 = $74.32.
 Third, calculate how many work days are missed per year. Since one work day is missed every two weeks, and there are 52 weeks in a year, there would be a total of 52 / 2 = 26 missed work days per year.
 Finally, multiply the daily loss of income by the number of missed work days per year to find the annual loss: $74.32 x 26 = $1,932.32.

The annual loss of income due to missing one day of work every two weeks at an hourly wage of $9.29 is $1,932.32.

solve the exponential equation 9^8x = 27

Answers

The answer is x=3/16

Answer:

[tex]x=\frac{3}{16}[/tex]

Step-by-step explanation:

Given : Exponential function [tex]9^{8x}=27[/tex]

We have to solve the given exponential equation.

Consider the given exponential function [tex]9^{8x}=27[/tex]

[tex]\mathrm{Convert\:}9^{8x}\mathrm{\:to\:base\:}3[/tex]

[tex]9^{8x}=\left(3^2\right)^{8x}[/tex]

Function becomes,

[tex]\left(3^2\right)^{8x}=27[/tex]

Convert 27 to base 3, we have,

[tex]\left(3^2\right)^{8x}=3^3[/tex]

Apply exponent rule, [tex]\left(a^b\right)^c=a^{bc}[/tex]

We have, [tex]3^{2\cdot \:8x}=3^3[/tex]

[tex]\mathrm{If\:}a^{f\left(x\right)}=a^{g\left(x\right)}\mathrm{,\:then\:}f\left(x\right)=g\left(x\right)[/tex]

We have,

[tex]2\cdot \:8x=3[/tex]

Simplify, we have,

[tex]16x=3[/tex]

Thus, [tex]x=\frac{3}{16}[/tex]

PLEASE HELP
A line has slope -5/3. Through which two points could this line pass?

A. (12,13), (17,10)

B. (16,15), (13,10)

C. (0,7), (3,10)

D. (11,13), (8,18)

Answers

m = -5/3

slope formula:
m = y2 - y1 / x2 - x1

A) m = 10-13 / 17-12 = -3/5
B) m = 10-15 / 13-16 = -5/-3
C) m = 10-7 / 3 -0 = 3/3 = 1
D) m = 18-13/8-11 = 5/-3 or -5/3  

D. (11,13); (8,18) are the two points the line could pass

Please help !!
Answer correct for a brainliest and also a thanks ! Don't answer if you don't know it .

Answers

b) between one and two months....
....................................................
look on graph and you see it....
I'd say between 1 and 2 months

What is the range of the function h(x) = -8x?

Answers

Final answer:

The range of the function h(x) = -8x is all real numbers, as there are no restrictions on the output the function can produce. This is typical of a linear function.

Explanation:

The range of a function refers to the possible outputs it can produce. In the case of the function h(x) = -8x, it is a linear function, and there are no restrictions on the values that x can take, meaning x can be any real number between -∞ and +∞. The output, h(x), therefore, can be any real number, also between -∞ and +∞, given that it will be the result of -8 multiplied by x. Therefore, the range of the function h(x) = -8x is all real numbers from -∞ to +∞.

Learn more about range of a function here:

https://brainly.com/question/29145252

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