At the library, Newton borrows 8 books and Descartes borrows 4 books. 7 of their books are nonfiction. The rest are fiction. How many fiction books did they borrow together?​

Answer:

1.  2550

2.  1600

Step-by-step explanation:

Even Integer: A whole number that can be positive, negative, or zero, and that can be divided exactly by 2.

Even integers between 1 and 101:  

This forms an arithmetic sequence with:

Sum of the first n terms of an arithmetic series:

[tex]\boxed{S_n=\dfrac12n[2a+(n-1)d]}[/tex]

There are 50 even integers between 1 and 101.  

Therefore, to find the sum of the even integers between 1 and 101, substitute n = 50 and the found values of a and r into the formula:

[tex]\begin{aligned}\implies S_{50} & =\dfrac{1}{2}(50)[2(2)+(50-1)2]\\\\& =25[4+(49)2]\\\\& =25[4+98]\\\\& =25[102]\\\\& = 2550\end{aligned}[/tex]

Therefore, the sum of the even integers between 1 and 100 is 2550.

Given arithmetic sequence:

From inspection of the given arithmetic sequence:

Sum of the first n terms of an arithmetic series:

[tex]\boxed{S_n=\dfrac12n[2a+(n-1)d]}[/tex]

To find the sum of the first 25 terms of the given arithmetic sequence, substitute n = 25 and the found values of a and r into the formula:

[tex]\begin{aligned}\implies S_{25} & =\dfrac{1}{2}(25)[2(4)+(25-1)5]\\\\& =\dfrac{25}{2}[8+(24)5]\\\\& =\dfrac{25}{2}[8+120]\\\\& =\dfrac{25}{2}[128]\\\\& = \dfrac{3200}{2}\\\\& = 1600\end{aligned}[/tex]

Therefore, the sum of the first 25 terms of the given arithmetic sequence is 1600.

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The equation of the function after translation: [tex]$y=\frac{|x|}{4}$[/tex]

The y values advance toward the x-axis as they are multiplied by a value between 0 and 1. This is known as a vertical shrink and tends to flatten the graph.

When a base graph is multiplied by a particular factor larger than 1, vertical stretch happens. As a consequence, the graph is stretched outward while keeping the input values (or x). We anticipate that the y values in a function's graph will be further away from the x-axis when it is vertically extended.

The y-values are multiplied by a value between 0 and 1, which causes them to travel in the direction of the x-axis. This is known as a vertical shrink and tends to flatten the graph. A point (a,b) on the graph of y=f(x) y = f (x) shifts to a point (a,kb) (a, k b) on the graph of y=kf(x) y = k f (x) in both scenarios.

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Amount while opening account at rate of 4% for 6 months and earn simple interest $37 is $1850.

As given,

Simple interest amount earned by Elsa = $37

Annual interest rate R= 4%

Time T =6 months

Let P be the principal amount she put while opening account

Simple interest = (P × R × T) / 100

⇒37 ={P × 4 × (6/12)}/100

⇒P =(37 × 100) / 2

     = $1850

Therefore, amount while opening account at rate of 4% for 6 months and earn simple interest $37 is $1850.

The complete question is:

Elsa opens an account to save money for a family vacation. The account earns an annual interest rate of 4%. She earns $37 in simple interest after  6 months. How much money did she put in the account when she opened it?

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Holy will take 13/5 or 2.6 hours to finish the bookcase.

The relation between time and work is

Work Done = Time Taken × Rate of Work ·

or, Rate of Work = 1 / Time Taken ·

or, Time Taken = 1 / Rate of Work ·

Now it is given that,

Time taken by Fritz to build a bookcase =  8 hours

So, Bookcase build by Fritz in 1 hour = 1/8

Similarly,

Time taken by Holly to build a bookcase =  10 hours

So, Bookcase build by Holly in 1 hour = 1/10

So, bookcase build in 3 hours

Fritz = 3/8

Holly = 3/10

Total bookcase build in 3 hours =  3/8 + 3/10 =  27/40

So. remaining work =  1 - 27/40 =  13/40

Thus, Time taken by Fritz to complete the bookcase =  8 * (13/40) hours

                                                                                         =  13/5 or 2.6 hours

Thus, Holy will take 13/5 or 2.6 hours to finish the bookcase.

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Answer:

C. y = 2x + 2

Step-by-step explanation:

There are 2 points on the line (0,2) and (-3,-4)

from (-3,-4) to (0,2), rise over run is 6/3 so slope is 2

You can calculate it too

m = (y2-y1)/(x2-x1)

m = (-4 - 2)/(-3 - 0) = -6/-3 = 2

Using m = 2, x = 0, y = 2

y = mx + b

2 = 2(0) + b

b = 2

therefore

y = 2x + 2

[tex]111.2[/tex]

Step-by-step explanation:

As per the question, 15 times 15 i.e. 225

[tex]15 \times 15 = 225[/tex]

225 divide by 20 i.e. 11.25

[tex] \frac{225}{20} = 11.25[/tex]

take away five from the 11.25 then it will be 11.2

Add 100 to 11.2 i.e

[tex]11.2 + 100 = 111.2[/tex]

Answer: 115

Step-by-step explanation:

[tex]\displaystyle\\\frac{15*15}{20-5} +100=\\\\\frac{15*15}{15} +100=\\\\15+100=\\\\115[/tex]

If the interior angles in the octagon is (4x-80)°, (4x-80)°,(2x+50)°,(2x+50)°,(4x-80)°,(4x-80)°,(2x+50)°,(2x+50)° then the value of x is equal to 50.

Given that the interior angles in the octagon is (4x-80)°, (4x-80)°,(2x+50)°,(2x+50)°,(4x-80)°,(4x-80)°,(2x+50)°,(2x+50)°,(4x-80)°.

We are required to find the value of x that are used in the angles of the given octagon.

Octagon is the shape that has eight sides,eight vertices,eight angles. Sum of all the interior angles of octagon is equal to 1080°.

(4x-80)°+ (4x-80)°+(2x+50)°+(2x+50)°+(4x-80)°+(4x-80)°+(2x+50)°+(2x+50)°=1080

24x-120=1080

24x=1080+120

24x=1200

x=1200/24

x=50

Hence if the interior angles in the octagon is (4x-80)°, (4x-80)°,(2x+50)°,(2x+50)°,(4x-80)°,(4x-80)°,(2x+50)°,(2x+50)° then the value of x is equal to 50.

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Answer:

please demonstrate how tha triangle looks like

An algebraic expression to represent the number of kilometres John ran in June month last year is 30a.

Given that, John runs the same number of kilometres each day.

We need to find an algebraic expression to represent the number of kilometres John ran in June month last year

An algebraic expression (or) a variable expression is a combination of terms by the operations such as addition, subtraction, multiplication, division, etc.

Let us assume that john is running 'a' kilometres per day.

We know that June month composed of total 30 days

So the algebraic expression for the number of kilometres John ran in June last year = Number of kilometres running per day × Number of days in the month of June

=a × 30=30a

Therefore, an algebraic expression to represent the number of kilometres John ran in June month last year is 30a.

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The sum will be negative.

The product of two negative numbers is always positive and if we add two numbers, the sign of the greater number is used in the result.

Here, we are given an expression 4a + (-3b)

Also we are told that a < b and b is a negative number

Mow, since b is a negative number, (-3b) will always be positive. This is because the product of two negative numbers, here -3 and b, will always be positive.

Now, a can be positive or negative. If a is positive, the sum will always be positive. However, if it is negative, the sum can be either positive or negative.

Here, in fact, since a < b, a will always be negative only

Let us take an example, say a = -3 and b = -2

Then the sum becomes 4(-3) + (-3)(-2)

= -12 + 6

= -6

If we observe closely since a and be are both negative and a < b, in absolute terms a will always be greater than b since for negative numbers higher the value, smaller is the number.

Thus, we can conclude that 4a > (-3b) for all values of a and b

and since 4a will always be negative, the sum will also be negative.

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The original amount borrowed was $517.

Simple Interest is the method to calculate the interest charged for a given number of years and given rate , in simple interest the principle remains same for each year.

Simple interest =[tex]\frac{P*R*T}{100}[/tex]

where P= principle, R=rate in % , T= time

We know that Amount= Principle+ Simple Interest........(1)

According to the question

Amount=$610.06

Rate=18%

time = 1yr

Substituting the value in equation (1) we get

[tex]610.06=P+\frac{P*18*1}{100}[/tex]

[tex]610.06=\frac{100P+18P}{100}[/tex]

[tex]610.06=\frac{118P}{100}[/tex]

[tex]61006=118P[/tex]

[tex]P=\frac{61006}{118}[/tex]

[tex]P=517[/tex]

Therefore  , The original amount borrowed was $517.

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The height of the cylinder is 20 meters.

The density of a cylinder is determined by its volume, which represents how much material may be immersed in it or carried inside of it. The formula r2h, where r is the radius of the circular base and h is the height of the cylinder, determines the volume of a cylinder. Any substance that can fill the cylinder consistently with liquid or another material may be used as the material. Check the shape's volume here.

Formula= V = π r² h

According to the given value,

The formula for the volume of a cylinder is V=πr²h.

The cylinder to the right has an exact value of 500π cubic meters.

Its radius is given as 5 meters in the figure.

volume of the cylinder.

V = π r² h

We have,

V = 500π cubic meters

500π cubic meters = πr²h

Find the height of the cylinder.

We have,

500π cubic meters = πr²h

Divide both sides by π

500cubic meters = r²h

We have,

r = 5

500 cubic meters = 5² square meters x h

500cubic meters =  25 square meters x h

Divide both sides by 25

20 meter = h

h = 20 meters

Thus the height of the cylinder is 20 meters.

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Answer:the graph is not linear

Step-by-step explanation:

Answer:

x = 1/2, y = 1

Step-by-step explanation:

Let's change the equation,

→ 6x - y = 2

→ y = 6x - 2

Then the value of x will be,

→ -4x + 3y = 1

→ -4x + 3(6x - 2) = 1

→ -4x + 18x - 6 = 1

→ 14x = 1 + 6

→ x = 7/14

→ [ x = 1/2 ]

Hence, the value of x is 1/2 (or) 0.5.

Now the value of y will be,

→ y = 6x - 2

→ y = 6(1/2) - 2

→ y = 3 - 2

→ [ y = 1 ]

Hence, the value of y is 1.

Answer:

x = ¹/₂

y = 1

Step-by-step explanation:

Given system of equations:

[tex]\begin{cases}-4x+3y=1\\\:\:\:\:\:\:6x-y=2 \end{cases}[/tex]

Multiply the second equation by 3:

[tex]\implies 3 \cdot 6x-3 \cdot y = 3 \cdot 2[/tex]

[tex]\implies 18x-3y=6[/tex]

Add this to the first equation to eliminate the term in y:

[tex]\begin{array}{lrr}&-4x+3y & = 1\\+ & 18x-3y& = 6\\\cline{2-3} & 14x \phantom{-3x)} & = 7\end{array}[/tex]

Solve for x:

[tex]\begin{aligned}\implies 14x & = 7\\\\\dfrac{14x}{14} & = \dfrac{7}{14}\\\\\implies x & = \dfrac{1}{2}\end{aligned}[/tex]

Substitute the found value of x into the first equation and solve for y:

[tex]\begin{aligned}-4x+3y & =1\\x=\dfrac{1}{2}\implies -4\left(\dfrac{1}{2}\right)+3y & =1\\-\dfrac{4}{2}+3y & =1\\-2+3y & =1\\-2+3y+2 & =1+2\\ 3y & =3\\\dfrac{3y}{3} & =\dfrac{3}{3}\\\implies y & =1\end{aligned}[/tex]

Therefore, the solution to the given system of equations is:

x = ¹/₂ and y = 1

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Answer:

88 [tex]cm^{2}[/tex]

Step-by-step explanation:

We need to find the area of the rectangle and the triangle.

Area of the rectangle:

a = length x width

a = 11 x 6 = 66

Area of the triangle:

a = [tex]\frac{ b x h}{2}[/tex]  We need to find the base and height of the triangle.  The base is the same length as the length of the rectangle: 11 and the height is 10 - 6 or 4

a = [tex]\frac{11 x 4}{2}[/tex]

a = [tex]\frac{44}{2}[/tex]

a = 22

Add the area of the rectangle and the triangle together.  66 + 22 = 88

Answer:

f(6) = - 10 and g(- 4) = 125

Step-by-step explanation:

substitute x = 6 into f(x) , that is

f(6) = - 2(6) + 2 = - 12 + 2 = - 10

substitute x = - 4 into g(x) , that is

g(- 4) = - 2(- 4)³ - 3 = - 2(- 64) - 3 = 128 - 3 = 125

Answer: Find step-by-step Probability solutions and your answer to the following textbook question: The velocity (v metres per second) of a body is known to be proportional to the square root of its kinetic energy (e j.) I don't know if this will help

Step-by-step explanation:

Answer: B (18.5b-21.2)

The required expression −18.5b − 21.2 is equivalent to the given expression which is the correct answer that would be option (A).

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.

We have been given the expression below as

5(−2.3b − 4.1) − (7b + 0.7)

Open the parentheses and apply the distributive property of multiplication,

⇒ −2.3b × 5 − 4.1 × 5 − 7b - 0.7

⇒ -11.5 - 20.5 − 7b - 0.7

Rearrange the likewise terms and apply the arithmetic operation,

⇒ −18.5b − 21.2

Hence, the required expression −18.5b − 21.2 is equivalent to the given expression.

Thus, the correct answer would be an option (A).

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Answer: Ali is correct because all of the negatives are mostly in quadrant 2.

Step-by-step explanation:

The sentence that represents the equation (7p + 23) = 102 is Seven times the sum of p and twenty-three is the same as one hundred two.

It is given that (7p + 23) = 102

Now, we have to write this equation in a sentence or to translate it in  words.  

As we can see in the given equation that seven is multiplied by p and then twenty three is added in the multiplication of seven and three, after that their addition is equal to one hundred two.  

So, the Option A will be the correct answer which is Seven times the sum of p and twenty-three is the same as one hundred two.

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Answer:

(5² - 8) x 2 doesn't belong

Step-by-step explanation:

this is because this answer is the only one with parintisies around the 5²

Answer: y=[tex]\frac{5-9x}{2}[/tex]

s=-30+10t

Step-by-step explanation:

9x + 2y = 5; y

9x-9x+2y = 5-9x

2y=5-9x

y=[tex]\frac{5-9x}{2}[/tex]

1/15s - 2/3t = -2; s

(1/15s - 2/3t = -2)*15     ==> Get rid of fraction by multiplying both sides by 15

s - 30/3 t=-30

s-10t=-30

s=-30+10t

Answer:

horizontal shift 5 units left

Vertical shift 1 unit down

reflection on the x-axis: Reflected

Vertical stretch: stretched

Step-by-step explanation:

Answer:

x= 2/7

Step-by-step explanation:

Multiply both sides by the common denominator

3x^2 +6x−2=3x^2 −x

Move everything to the left side.

3x^2+6x-2-3x^2+x=0

Simply.

7x-2=0

Separate the cosntants and variables.

7x=0+2

Add or subtract zero

7x=2

Then divide both sides by 7.

7x/7=2/7

Cancel out common factors in the numerator and denominator

x=2/7

Answer:

  x = 2/7

Step-by-step explanation:

You want to solve the equation 3x/(3x-1) + 2/x = 1.

It works nicely to subtract 1 from both sides, then simplify.

  [tex]\dfrac{3x}{3x-1}+\dfrac{2}{x}=1\\\\\dfrac{3x}{3x-1}\cdot\dfrac{x}{x}+\dfrac{2}{x}\cdot\dfrac{3x-1}{3x-1}-\dfrac{x(3x-1)}{x(3x-1)}=0\\\\\dfrac{3x^2+6x-2-3x^2+x}{x(3x-1)}=0\qquad\text{combine terms}\\\\\dfrac{7x-2}{x(3x-1)}=0\qquad\text{simplify}\\\\7x-2=0\qquad\text{expression is 0 when numerator is 0}\\\\\boxed{x=\dfrac{2}{7}}\qquad\text{add 2, divide by 7}[/tex]

__

Additional comment

The values x=0 and x=1/3 would make the denominator zero, so are excluded from the domain of the equation. By working the problem this way, we ensure that extraneous solutions do not present themselves.

Answer:

4 [tex]\sqrt{10}[/tex]

Step-by-step explanation:

Simplify

[tex]\sqrt{160}[/tex]

We can rewrite this as

[tex]\sqrt{16 * 10}[/tex]

Breaking this up

[tex]\sqrt{16} \sqrt{10}[/tex]

We know the square root of 16 is 4

4 [tex]\sqrt{10}[/tex]

sqrt(10) cannot be simplified so

Answer:

[tex]4\sqrt{10}[/tex]

Step-by-step explanation:

160 = 16 * 10

[tex]\sqrt{160} = \sqrt{16 \cdot 10} = \sqrt{16} \cdot \sqrt{10} = 4\sqrt{10}[/tex]

we cannot simplify further as 10 is 2*5, there are no more squares to simplify.