Complete the following statement. Use the integers that are closest to the number in the

middle.

<-√14<

The slope-intercept form of the given equation is y = -3/5x - 5

From the question, we are to write the given equation in the slope-intercept form

From the given information,

The given equation is

3x + 5y = -25  

The general form for the slope-intercept form of the equation of a line is

y = mx + b

Where m is the slope

and b is the y-intercept

Writing the equation in the slope-intercept form of a line

3x + 5y = -25

5y = -3x - 25

Divide through by 5

5y/5 = -3/5x - 25/5  

y = -3/5x - 5

The equation is y = -3/5x - 5

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The slope of a line f(x) exceeds the slope of a line g. (x). As a result, option A is the right response.

A line's slope or gradient is a number that defines both its direction and its steepness. The slope may be calculated using the following formula: slope = (y2-y1)/ (x2-x1). The coordinate points on the equation of line g(x) are (0, 2), (5, 4) and (10, 6) while the coordinate points on the equation of line f(x) are (3, 1) and (0, -1).

The slope of the line g(x) is now (4-2)/(5-0) =2/5.

The slope of a line f(x) is (-1)/. (0-3)

=2/3

The slope of a line f(x) exceeds the slope of a line g. (x). As a result, option A is the right response.

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The eight interior angle based on the information given will be 728°.

From the information, the sizes of seven of the exterior angles of an octagon are 42˚, 110˚, 13˚, 67˚, 55˚, 11˚ and 53˚ and.we.wany to eork out the size of each of the eight interior angles

In this case, it should be noted the octagon has with sides. This will be Illustrated as:

= (n - 2) × 180

= (8 - 2) × 180

= 1080

The eight interior angle will be:

= 1080 - (42 + 110 + 13 + 67 + 55 + 11 + 54)

= 1080 - 352

= 728

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1 kilograms is equal to 2.205 pounds, which leads to the conversion factor of 2.205. The conversion factor is based on both the Avoirdupois system of measurement, which is used in the United States and the United Kingdom to measure weight or mass, and the International System of Units (SI).

  The basis for the Avoirdupois system is the pound, which is equal to 0.45359237 kilos. Consequently, 0.45359237 kilograms equal one pound.

  Finding the weight in pounds of 1 kilograms is necessary to convert kilograms to pounds. We can divide 1 kilograms by 0.45359237 kilograms/pound to get this equivalent weight.

1 kg / 0.45359237 kg/lb = 2.20462262 lb

 This is the kilograms to pound conversion factor. The value is rounded to the widely regarded and employed value of 2.205.

 Therefore, to convert kilograms to pounds, we multiply the weight in kilograms by 2.205.

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Answer:

You can use the second equation to substitute the value of x in the first equation and solve for y.

x = y - 4

-10(y - 4) + 3y = 5

-10y + 40 + 3y = 5

-7y = 35

y = 5

Now that you have the value of y, you can use the second equation to find the value of x.

x = y - 4

x = 5 - 4

x = 1

So the solution of the system of equations is x = 1 and y = 5

Step-by-step explanation:

If Sarah has a 20% discount, her total cost after the discount in dollars and cents be 31.40.

Therefore the answer is $31.40

Sarah has a 20% discount, so the percentage of the cost she needs to pay is

100 - 20 = 80%.

To calculate the total cost after the discount, we need to multiply the original total cost by the percentage of the cost Sarah needs to pay:

= $39.25 x 0.8

= $31.40

So, after the discount, Sarah would pay $31.40 before tax.

To round it to the nearest cent we have $31.40 so the answer is 31.40

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On solving the provided question, we can say that the value of the expression will be as - [tex]1/ ( 36a^4b^{10} )[/tex]

In mathematics, it is possible to multiply, divide, add, or remove. The construction of an expression is as follows: Expression, number, and mathematical operator Numbers, variables, and functions are the building blocks of a mathematical expression (such as addition, subtraction, multiplication or division etc.) Expressions and phrases can be contrasted. Any mathematical statement with variables, numbers, and an arithmetic operation between them is called an expression or an algebraic expression. For instance, the expression 4m + 5 has the terms 4m and 5 as well as the variable m of the supplied expression, all of which are separated by the arithmetic sign +.

here,

the expression is -

[ [tex][( 2a{-3}b^4)^2 / (3a^5b){-2}]^{-1}[/tex] ]

[tex][( 1 /2a{-3}b^4)^2 (3a^5b){2}]^{-1}[/tex]

[tex]1/ ( 36a^4b^{10} )[/tex]

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As per the remainder that the greatest possible value of 17

The term remainder in math defined as if a number is not completely divisible by another number  then we are left with a value once the division is done

Here we have if x is a positive integer, then r is the remainder when x is divided by 4 and r is the remainder when x is divided by 9.

As we all know that the remainder is always smaller than the divisor.

Here we have also know that it will be 0 if the dividend is evenly divisible or a positive integer less than the divisor.

So, when we divided by 4 then the largest remainder will be 3 and then here we have to  divided by 9, then the largest remainder will be written as

=> r² + R = 32 + 8

=> 9 + 8 = 17

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Answer:

Step-by-step explanation:

The constant of proportionality from the number of bottles of juice bought to the total cost is 1.15 dollars and cents.

Answer:Volume of Pipe Formula. The pipe volume formula is: Volume = pi x radius² x length. To do piping size calculation, follow these steps: Find the inner diameter and length of the pipe, in inches or millimeters. Calculate the inner diameter of the pipe by measuring

Step-by-step explanation:

The answer is CalcETS 1.1.058.

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a) The maximum Height of Projectile is 843.75 m

b) The projectile reach its maximum at t= 12.5 sec.

A quadratic equation is a second-order polynomial equation in a single variable x ax²+bx+c=0. with a ≠ 0 .

It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem.

Given:

h(t) = -5t² +120t + 125

a) For the maximum height, h= 0

-5t² +120t + 125 = 0

t²  - 24 t - 25 = 0

t²  - 25t + t - 25 = 0

t( t- 25) + 1(t-25)= 0

(t-25)(t+1)=0

t= 25, -1

So, Max height is reached after half the total flight time, t= 25/2

So, h(25/2 )= -5(25/2)² +120(25/2) + 125

= -5 x 156.25 + 1500+ 125

= 843.75 m

b) The projectile reach its maximum at t= 12.5 sec.

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The drone has flown a total distance of 4 units, as it has travelled the same distance as the two cars (2 units each).

Perimeter is the total length of a two-dimensional shape's boundary. It is the sum of all the sides of a shape. Perimeter is used in many areas such as geometry, architecture, landscaping, and more. Perimeter is a measure of the distance around a shape and is often used to measure the size of a space or area.

As the cars have completed a full circuit of the square $abcd$, the drone has also completed a full circuit of the square. The perimeter of the square is 2, so the drone has flown a total distance of 4 units.

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The drone has flown a total distance of 4 units, as it has travelled the same distance as the two cars (2 units each). This can be solved by applying the concept of perimeter.

Perimeter is the total length of a two-dimensional shape's boundary. It is the sum of all the sides of a shape. Perimeter is used in many areas such as geometry, architecture, landscaping, and more. Perimeter is a measure of the distance around a shape and is often used to measure the size of a space or area.

As the cars have completed a full circuit of the square abcd, the drone has also completed a full circuit of the square. The perimeter of the square is 2, so the drone has flown a total distance of 4 units.

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(a) The 6 a.m. temperature in montreal was 84 Fahrenheit lower than in atlanta.

(b) by noon, the temperature in milwaukee was 3 Fahrenheit.

In mathematics, it deals with numbers of operations according to the statements.

The process in mathematics to operate and interpret the function to make the function simple or more understandable is called simplifying and the process is called simplification.

Given that,

    City                Temperature table (°F)

   Montreal                -16

   Atlanta                   68

   Dayton                   36

  milwaukee               -5

   Juneau                   -31

Part A- Temperature difference in Atlanta and Juneau

= (-16) - 68

= -84 F

Part B- temperature in milwaukee raise by 8 F at noon

Temperature in noon = - 5 + 8 = +3 F

Thus,

(a) The 6 a.m. temperature in montreal was 84 Fahrenheit lower than in atlanta.

(b) by noon, the temperature in milwaukee was 3 Fahrenheit.

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Applying proportions, the amount of money Bob saved is $18.

Proportions can also be used to express a relationship between two or more values in the form of a ratio, such as a:b, where a and b are values being compared.

We can start the problem by using the proportion of saving to earning, which is 9/16.

If for every $16 he earns babysitting, he saves $9, then for $32 that he earned babysitting, he saved:

$9 / (16/32) = $9 * 2 = $18

So Rob saved $18 from the money he earned babysitting on Saturday

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Answer: To graph an inequality, treat the <, ≤, >, or ≥ sign as an = sign, and graph the equation. If the inequality is < or >, graph the equation as a dotted line. If the inequality is ≤ or ≥, graph the equation as a solid line.

Step-by-step explanation:

Answer: The answer is 4

Step-by-step explanation: Firstly you want to convert the whole number into a fraction, the fraction will be 24/1. Then you multiply 1/6 by 24/1 or 1x24/6x1 which equals 26/6. This fractio can be simplified, by finding the greatest common factor. The GCF of 24 and 6 is 6.

24/6 = 4

6/6 = 1

So our full answer is 4/1 which simplifies to 4

Answer:

4

Step-by-step explanation:

take 24 divided by 6 you'll get

By solving a linear equation we will see that there are 20 games left.

We know that there is a total of 100 games, and the ratio of wins to loses for the rockets is:

3:2

The ratio for the rangers is:

7:13

We know that if the rockets loses all the remaining games, and the rangers win all the remaining games then both teams will win the same number of games.

Let's define X as the number of games left, the number of games won by the rockets is:

(100 - X)*(3/5)

The number of games won by the rangers is:

(100 - X)*(7/20)

We know that if the rangers win the X games left, they will have the same number of wins than the rockets (if the rockets don't win any more game)

Then we can write the linear equation:

(100 - X)*(7/20) + X = (100 - X)*(3/5)

we can solve this for X.

X = (100 - X)*(3/5) - (100 - X)*(7/20)

X = (100 - X)*(3/5 - 7/20)

X = (100 - X)*(12/20 - 7/20)

X = (100 - X)*(5/20)

(20/5)*X = 100 - X

4*X = 100 - X

4*X + X = 100

5*X = 100

X = 100/5

X = 20

There are 20 games left for the rockets.

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An integral in calculus is a mathematical concept that can be used to represent an area or an expanded version of an area. The basic components of calculus are integrals and derivatives is[tex]-1/2*(t^2/2+18ln(t)-81/(2t^2))+C\\[/tex].

The terms antiderivative and primal are additional terms for integral. Something that is essential is crucial or required. If you are an essential member of the team, it signifies that you are necessary for the team to work. To complete the whole, an essential component is required. The term "essential" is almost a synonym in this context.

The set of functions (the antiderivative) whose derivative is the integrand is represented by the integral, which is referred to as an indefinite integral. Calculus' fundamental theorem connects the assessment of definite integrals to that of indefinite integrals.

From 1 to 3:

[tex]sqrt(x^2+9)=t+x\\x=(9-t^2)/(2*t)\\anddx=-(t^2+9)/(2t^2)dt\\= 1/2int (t^2+9)^2/t^3dt\\= -1/2int (t+18/t+81/t^3)dt\\= -1/2*(t^2/2+18ln(t)-81/(2t^2))+C\\[/tex]

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The simplified form of the given expression is, [tex]\frac{81x^5}{125y^1^8}[/tex].

What is simplifying an expression?

To simplify an expression, create an equivalent expression without any terms that are similar. The expression will then be rewritten using the fewest terms possible.

Solving a math problem is the same thing as simplifying an expression. You basically try to write an expression as simply as you can when you simplify it. At the conclusion, there shouldn't be any more multiplying, dividing, adding, or removing to do.

Consider, the given expression:

[tex](\frac{3x^3y^0}{x^-2} )^4*(\frac{y^2x^-^4}{5xy^-^8} )^3[/tex]

Using the rule:  [tex](\frac{a}{b} )^m = \frac{a^m}{b^m}[/tex]

⇒  [tex](\frac{3x^3y^0}{x^-2} )^4*(\frac{y^2x^-^4}{5xy^-^8} )^3 = (\frac{81x^1^2y^0}{x^-^8})(\frac{y^6x^-^1^2}{125x^3y^2^4} ) = \frac{81y^6}{125x^-^5y^2^4} = \frac{81y^-^1^8}{125x^-^5}= \frac{81x^5}{125y^1^8}[/tex]

Hence, the simplified form of the given expression is, [tex]\frac{81x^5}{125y^1^8}[/tex].

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Answer:

The total number of pencils is 76 x 3 = 228 pencils

If each teacher receives an equal amount of pencils, we can divide the total number of pencils by the number of teachers to find how many pencils each teacher receives:

228 pencils / 4 teachers = 57 pencils/teacher

Each teacher receives 57 pencils.

The length of the side overline(FH) when Triangle FGH is formed by connecting the midpoints of the side of triangle CDE is 5.

This problem can be solved using the Median Line theorem. The Median Theorem states that the medians of a triangle intersect at a point called the centroid which is two-thirds of the distance from the vertices to the midpoint of the opposite sides. This is what we will use to solve the given problem.

From the problem, we can conclude that points H and F are the midpoints of the sides CE and CD respectively. Hence, line HF is the median line of the triangle CDE. So, the length of the line HF/FH is going to be -

= (1/2)*ED

= 5

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The slope of the line that passes through (-4, 7) and (-6, 5) is 1.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The formula to find the slope of a line is slope = (y₂-y₁)/(x₂-x₁).

The given coordinate points are (-4, 7) and (-6, 5).

Now, slope m=(5-7)/(-6+4)

m=-2/(-2)

m=1

Substitute m=1 and (x, y)=(-4, 7) in y=mx+c, we get

7=1(-4)+c

c=11

Substitute m=1 and c=11 in y=mx+c, we get

y=x+11

Therefore, the slope of the line that passes through (-4, 7) and (-6, 5) is 1.

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A polynomials is a mathematical statement made up of real number coefficients and a sum of power in one or so more parameters (indeterminates) having non-negative integer exponents.

SOLUTION:

Three terms with non-negative integers exponents (x2, x1) make up Option "polynomial, "'s which has real numbers (x3, -2x3, and 3) as coefficients.

Option "c" x+1/x is a rational function; it is not a polynomials because of the fraction in it. It consist of one polynomials divided by another polynomial. 1/x

Option "d" is a polynomial that has real numbers (5, -3, and 2) as coefficients and terms with non-negative integers exponents (x2, x1) as its exponents.

Consequently, option "b" 3x3/2-5x2-1/2x-1 is not a polynomial due to the fraction and non-integer exponent (3/2).

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Option "b" 3x3/2-5x2-1/2x-1 is not a polynomial due to the fraction and non-integer exponent (3/2). A polynomials is a mathematical statement made up of real number coefficients and a sum of power in one or so more parameters (indeterminates) having non-negative integer exponents.

Three terms with non-negative integers exponents (x2, x1) make up Option "polynomial, "'s which has real numbers (x3, -2x3, and 3) as coefficients.

Option "c" x+1/x is a rational function; it is not a polynomials because of the fraction in it. It consist of one polynomials divided by another polynomial. 1/x

Option "d" is a polynomial that has real numbers (5, -3, and 2) as coefficients and terms with non-negative integers exponents (x2, x1) as its exponents.

Consequently, option "b" 3x3/2-5x2-1/2x-1 is not a polynomial due to the fraction and non-integer exponent (3/2).

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Tomas drove the fastest with the speed of 70 miles per hour.

What is speed?

The distance travelled in relation to the time it took to travel that distance is how speed is defined. Since speed simply has a direction and no magnitude, it is a scalar quantity.

The formula for calculating speed is -

Speed = Distance / Time

Maren travels 60 miles in 1 hour.

Speed of Maren = 60/1

Speed of Maren = 60 miles per hour

Safiya travels 120 miles in 3 hour.

Speed of Safiya = 120/3

Speed of Safiya = 40 miles per hour

Tomas travels 84 miles in 1.2 hour.

Speed of Tomas = 84/1.2

Speed of Tomas = 70 miles per hour

Cam travels 75 miles in 1.5 hour.

Speed of Cam = 75/1.5

Speed of Cam = 50 miles per hour

Therefore, the fastest driver is Tomas.

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The inequality describing how much she can withdraw is x < 3550

An equation is a expression that shows the relationship between numbers and variables.

Inequalities are used in expression for non equal comparison of variables.

Let x represent the amount of money that can be withdrawn.

Tabitha’s account balance is $3,800. Of this, $750 is for rent. Hence:

Money remaining = 3800 - 750 = 3050

Tabitha wants to keep a balance greater than $500. Hence:

3050 - x > 500

x < 3550

The inequality is x < 3550

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The number of the books owed by Tara which she has not read would be = 152 books.

Percentage is defined as the part of the value that can be expressed as per 100 of the whole given value. This can be represented with a symbol such as %..

The number of books owned by Tara = 160 books

The percentage of books read by Tara = 95%

Therefore, 95% of her books = 95/100 × 160

= 15200/100

= 152 books.

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The solutions are x = ±1.73, ±3.87.

Given equation: x4 − 10x2 + 9 = 0

Rewrite equation as (x2 - 9)(x2 + 1) = 0

Set each factor equal to 0 and solve for x

x2 - 9 = 0

⇒ x2 = 9

⇒ x = ±3.87

x2 + 1 = 0

⇒ x2 = -1 ⇒

x = ±1.73

The given equation is x4 − 10x2 + 9 = 0. This can be rewritten as (x2 - 9)(x2 + 1) = 0. By setting each factor equal to 0 and solving for x, we get x2 - 9 = 0 which implies x2 = 9 and x = ±3.87. Similarly, x2 + 1 = 0 implies x2 = -1 and x = ±1.73. Therefore, the solutions of x4 − 10x2 + 9 = 0 are x = ±1.73, ±3.87.

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Answer:

54 cm^2

Step-by-step explanation:

calculate the area of each of the 2 rectangles and add them .

area of rectangle = l × w

so let the area of the big rectangle be A1 and the area of the small one A2 :

A1 = l × w = 11 × 4 = 44 cm^2

A2 = l × w = 5 × 2 = 10 cm^2

then , the area of the shape is = A1 + A2 = 44 + 10 = 54 cm^2