the distance between two cities is 4 kilometeres. how many meters apart are the two cities

Answer:

z=38

Step-by-step explanation:

Using the fact that angles on a straight line add to 180°, the interior angles of the triangle are 86°, (180-3z)°, and (180-4z)°.

Angles in a triangle add to 180°, so:

[tex]86+180-3z+180-4z=180 \\ \\ 86-3z+180-4z=0 \\ \\ 266-7z=0 \\ \\ 7z=266 \\ \\ z=38[/tex]

Answer:

A. (10x^2) / (5x + 4y)

B. (8xy) / (4y + 5x)

Step-by-step explanation:

A. Factor the numerator and denominator, then cancel out like terms

(10x^2(2a + 3b)) / (2a(5x + 4y) + 3b(5x + 4y))

(10x^2(2a + 3b)) / ((2a + 3b)(5x + 4y))

(10x^2) / (5x + 4y)

B. Factor the numerator and denominator, then cancel out like terms.

(8xy(3p - 4q)) / (3p(5x + 4y) - 4q(4y + 5x))

(8xy(3p - 4q)) / ((3p - 4q)(4y + 5x))

(8xy) / (4y + 5x)

The polynomial function that has the degree of 5 is written as f(x) = 2x⁵ + 26x⁴ + 128x³ + 296x² + 320x + 128

Polynomial function:

The equations formed with variables, exponents and coefficients are known as the polynomial equations. And it can have different exponents, where the higher one is called the degree of the equation.

Given,

Here we have the following things,

Degree = 5

Root of multiplicity 2 is x = -4

Root of multiplicity 1 at x = -1

Root of multiplicity 2 at x = -2

y-intercept of (0, 128)

Here we need to find the polynomial equation of the function.

According to the given roots of multiplicity, we have the factors of the polynomials are,

=> (x + 4)² (x + 1) (x + 2)²

So, the general form of the polynomial function can be written as,

=> f(x) = A (x + 4)² (x + 1) (x + 2)²

In order to find the 5 degree polynomial function, we have to calculate the value of A.

To Find the value of A, we have to apply the y - intercept point on the equation then we get,

=> 128 = A (0 + 4)² (0 + 1) (0 + 2)²

=> 128 = A (4)² (1) (2)²

=> 128 = A (16 x 1 x 4)

=> 128 = 64A

=> A = 2

Now, the polynomial function is written as,

=> f(x) = 2 (x + 4)² (x + 1) (x + 2)²

When we expand this one then we get,

=> f(x) =2 [x⁵ + 13x⁴ + 64x³ + 148x² + 160x + 64]

Therefore, the resulting polynomial function is,

=> f(x) = 2x⁵ + 26x⁴ + 128x³ + 296x² + 320x + 128

To know more about Polynomial function here.

https://brainly.com/question/12914312

#SPJ1

For give expression Ben's work is correct.

In this question, Ben and Jerry both simplified the expression √24x⁵y³

where x > 0, y > 0

We need to determine which student is correct.

First we simplify given expression.

√24x⁵y³

= √(2)(2)(2)(3)(x)(x)(x)(x)(x)(y)(y)(y)

= √(2²)(2)(3)(x²)(x²)(x)(y²)(y)

= √(2²) * √(2) * √(3) * √(x²) * √(x²) * √(x) * √(y²) * √(y)    ...(seperate the radical symbol)

= 2 * √(2) * √(3) * x * x * √(x) * y * √(y)            ...........exponent rule

= 2x²y√(2)(3)(x)(y)                     ........(combine terms with same powers)

= 2x²y √6xy

So, Ben's work is correct.

We observe that by rule of exponents, the fourth step in Jerry's work is incorrect.

Therefore, Ben's work is correct.

Learn more about the expression here:

https://brainly.com/question/1859113

#SPJ1

Answer: School is 10 blocks north and 2 blocks west of Megan's house. A straight line from Megan's house to school is 10.2 blocks long, Northwest

Step-by-step explanation:

5 blocks north, then 4 east, then 5 north is a total of 10 blocks north.  The last turn is 6 blocks west. So she walks 4 blocks west to get her back to due north of her house then an additional 2 more blocks west.

Use the pythagorean theorem to calculate the straight line if Megan were able to take a straight path there:

Answer:

x^25

Step-by-step explanation:

The simplified expression is x²⁵.

Given is an expression (x⁵)⁵, we need to simplify the expression.

To simplify the expression (x⁵)⁵, we need to apply the exponentiation rules.

The exponent outside the parentheses should be distributed to each term inside the parentheses.

In this case, the exponent outside is 5, and the term inside the parentheses is x⁵.

To distribute the exponent, we multiply the exponents together.

Applying the rule, we get:

(x⁵)⁵ = x⁵⁽⁵⁾ = x²⁵

Therefore, the simplified expression is x²⁵.

Learn more about expression click;

https://brainly.com/question/28170201

#SPJ6

Answer:

slope = (1/3)

Step-by-step explanation:

(-8, 2), (-11, 3)

(x₁, y₁)   (x₂, y₂)

m = slope

        y₂ - y₁          3 - 2              1              1

m = ------------ = -------------- = ----------- = -------

        x₂ - x₁         -11 - (-8)       -11 + 8        3

I hope this helps!

Answer:

$205.6

Step-by-step explanation:

20.56hours × $10/hour = $205.6

Answer:

[tex] \huge{ \bold{y = - 43x - 25}}[/tex]

Step-by-step explanation:

Equation of a line in slope-intercept form is given by

[tex]y = mx + c[/tex]

where

m is the slope

c is the y intercept

From the question

m = - 43

In order to find c we substitute the point (0,−25) into the equation y = mx + c

That's

[tex] - 25 = - 43(0) + c \\ - 25 = 0 + c \\ c = - 25[/tex]

We now substitute m and c into the equation

We have the final answer as

[tex] \bold{y = - 43x - 25}[/tex]

Hope this helps you

77 is 0.7% of 11000

this number is a lot greater than 77.

Let 77 is 0.7% of m

0.7 percent of m = 77

(0.7/100) * m = 77

m = 77 * (100/0.7)

m = 11000

Therefore, 77 is 0.7% of 11000

this number is a lot greater than 77.

Learn more about percentage here:

https://brainly.com/question/16797504

#SPJ1

Answer:

46.9

Step-by-step explanation:

sin54=x/58

58sin54=46.922

Answer:

Below

Step-by-step explanation:

x^2 + 32 + 116 = 12x         1st intermediate step: put everything on one side

x^2 -12x + 148 = 0      2nd intermediate step : re-arrange with constant on R

x^2 -12x = -148            3 rd intermediate step : take 1/2 of the 'x' coefficient

                                            square it and add to both sides

x^2 -12x + 36 = -148 + 36    4th intermediate step :   simplify

(x-6)^2  = -112

The equvalent fractions of 5/7 using 35 as a common denominator is 25/35.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

In this case, it should be noted that the fraction given is 5/7.

The equivalent fraction will be:

= 5/7 × 5/5

= 25/35

Learn more about fractions on:

brainly.com/question/17220365

#SPJ1

Complete question

Write the equvalent fraction of 2/5 using 35 as a common denominater

Answer:

NOT CONGRUENT

Step-by-step explanation:

There are several types of congruence:

ASA - Angle Side Angle

AAS - Angle Angle Side

HL - Hypotenuse Leg

This image shows two triangles which have 2 congruent sides and one congruent angle.

Is it ASA?

There is only one congruent angle, so this cannot be congruent by ASA

Is it AAS?

By the same reasoning, it cannot be congruent by AAS.

Is it HL?

Although there are 2 congruent sides, neither one is the hypotenuse. Is is not congruent by HL.

There is no such thing as SSA congruence, because it is actually possible to have 2 non-congruent triangles who have 2 congruent sides and 1 congruent angle. Therefore, these are NOT CONGRUENT

The slope for the following question is = 4.

acc to our question-

hence the value of slope=4

learn more about slope click here:

https://brainly.com/question/3493733

#SPJ1

The selling price of the two washing machies are

I will buy the first because it has a lower selling price

The question is a percentage problem

The first washing machine has a mark down by ​40%

= 40 percent

= 40 / 100

= 0.4

marked down factor = 1 - 0.4 = 0.6

selling price of the first machine = 550 * 0.6 = 330

the second washing machine has mark down of 30%

30% = 0.3

marked down factor = 1 - 0.3 = 0.7

selling price of the second washing machine at first mark down

= 550 * 0.7 = 385

marked down again

10% = 0.1

the  factor here is = 1 - 0.1 = 0.9

selling price of the second washing machine at second mark down

= 385 * 0.9 = 346.5

Learn more about percent here:

https://brainly.com/question/29325921

#SPJ1

According to the volume of cylinder formula, an aluminum can with a 2 3/5 diameter and 5 1/4 in height are in 27.86 cubic inches.

Volume of Cylinder

The formula to calculate the volume of the cylinder is

Volume of a cylinder = πr²h cubic units.

where

r refers the radius

h refers the height.

Given,

Here we have an aluminum can with a 2 3/5 diameter and 5 1/4 in height and now we have to find the volume in cubic inches.

While we looking into the given question, we know the following values,

Diameter = 2 3/5

When we simplify it, then we get the value of diameter as

d = 13/5 or 2.6

Similarly, the value of height is rewritten as,

h = 5.25

So, based on the formula of volume of cylinder,

We get the value as,

=> V = π x (2.6/2)² x 5.25

Apply the value of π as 3.14, then we get,

=> V = 3.14 x (1.3)² x 5.25

=> V = 16.485 x 1.69

Therefore, the volume in cubic inches is 27.86 cubic inches.

To know more about Volume of cylinder here.

https://brainly.com/question/17106541

#SPJ1

The amount his account will have after 3 months be $ 759.38.

Given, Angel Garcia deposited his $750 federal income tax refund check into his savings account. The account pays 5% and he made no other deposits or withdrawals.

we have to find the amount in the account after 3 months,

So, the amount he made is,

Amount = 750(1 + 5/100)^0.25

Amount = 759.38

So, the amount his account will have after 3 months be $ 759.38.

Learn more about Compound Interest here https://brainly.com/question/24274034

#SPJ1

The simple interest owned for the use of the money is $2625.

What is Simple Interest?

Simple interest is a quick and simple way to figure out how much money has accrued interest. Interest is always applied to the original principal amount and is calculated at the same rate for each period of time. Any bank where we deposit money will pay us interest on that amount. Simple interest is one of many forms of interest that banks charge. Now, let's first clarify what a loan is before delving further into the idea of simple interest. A loan is a sum of money that someone borrows from a bank or other financial institution to cover expenses. Home loans, auto loans, student loans, and personal loans are a few instances of loans.

In the given question we have:

Principal amount  = ​7000$​,

Rate of interest r​ = ​7.5%,

Time t​ =  15 months;

So, applying the formula to calculate simple Interest:

S.I = [tex]\frac{PRT}{100}[/tex]

S.I = [tex]\frac{7000 \times 7.5 \times 15}{ 12 \times 100}[/tex]

S. I =  $2625;

Hence, The Simple Interest owed for the use of the money.  is $ 2625.

To learn more about: Simple Interest, visit:
https://brainly.com/question/25793394
#SPJ1

The value of f(x+h)-f(x)  = h.

Given function:

f(x) = x + 7

difference quotient = f(x+h) - f(x)

= (x+h) - 7 - (x - 7)

= x + h - 7 - x + 7

= x - x + 7 - 7 + h

= 0 + 0 + h

= h

Therefore the value of f(x+h)-f(x)  = h.

Learn more about the function here:

https://brainly.com/question/5975436

#SPJ1

The total cost of the shoe after tax is $79.50

From the question, we are to determine the total cost of the shoes after tax.

From the given information,

Jason bought new shoes priced at $75

and

The sales tax is 6%

The total cost of the shoe = Price of the shoe + Sales tax

Sales tax = 6% of $75

Sales tax = 0.06 × $75

Sales tax = $4.50

Thus,

Total cost of the shoe = $75 + $4.50

Total cost of the shoe = $79.50

Hence, the total cost is $79.50

Learn more on Calculating total cost after sales tax here: https://brainly.com/question/13283182

#SPJ1

The expression of the given statement is  [tex]\frac{2x}{5}[/tex] .

What is algebraic expression?

  When terms are combined using operations like addition, subtraction, multiplication, division, etc., the result is an algebraic expression (or variable expression). Let's look at the formula 5x + 7 as an illustration. Consequently, we can state that 5x + 7 is an illustration of an algebraic statement. Here are some more examples: 5x + 4y + 10

Here the given product of two and a number. Lets us take number as x. Then ,

=> 2*x= 2x

Product of two and a number divided by 5. Then,

=> [tex]\frac{2x}{5}[/tex]

Hence the algebraic expression of the given statement is  [tex]\frac{2x}{5}[/tex] .

To learn more about algebraic expression refer the below link

https://brainly.com/question/4344214

#SPJ1

The sales tax rate of the cocktail table is 0.055

A sales tax is a consumption tax imposed by the government on the sale of goods and services

The cocktail table sold for $250 and the sales tax amount was $13.75. The sales tax rate can be calculated as follows:

Sales tax = list price * sales tax rate

Therefore,

sale tax rate = sales tax / list price

sales tax = $13.75

list price = $250

sale tax rate = 13.75 / 250

sales tax rate = 0.055

learn more on sale tax here:https://brainly.com/question/858105

#SPJ1

The expression that represents the quotient of given model is x + 5

The correct answer is an option (C)

In this question, we have been given a synthetic division of x^2 + 5x and x

We need to find the quotient.

    x  + 1  + 1 + 1 + 1 + 1        

x) x^2    x   x   x   x   x

 - x^2                                  

    0      x

         -  x                            

            0   x

             -  x                    

                  0  x

                  -  x                

                      0    x

                       -    x            

                             0  x

                             -    x      

                                   0

Therefore, the expression that represents the quotient of given model is x + 5

The correct answer is an option (C)

Learn more about an expression here:

https://brainly.com/question/1859113

#SPJ1

slope= -3/2, y-intercept=8

y=mx+b m is the slope while b is the y-inteecept

Answer:

y-intercept (0,-3)

x-intercept (3,0)

Step-by-step explanation:

Let x = 0

-y =3

y = -3

(0,-3)

Let y = 0

x = 3

(3,0)

Answer:

150

Step-by-step explanation:

I had this on one of my quizzes, hope this helps :D

The percent increase in the median monthly rent prices is 14.3%

From the information, the median monthly rent in 2005 was $694 and $810 in 2010.

The increase in the amount will be:

= $810 - $694.

= $116

The percent increase in the median monthly rent prices from 2005 to 2010 will be:

= Increase in amount / Old rent × 100

= 116/810 × 100

= 14.3%

Learn more about percentages on:

brainly.com/question/24304697

#SPJ1

Answer: 5 is the ancer

Step-by-step explanation:!

The number of highway routes from A to D is 560

Number of highway routes from A to B = 7 highways

Number of highways routes from B to C = 8 highways

Number of highways routes from C to D = 10 highways

Number of routes from A to D = Number of highway routes from A to B × Number of highways routes from B to C × Number of highways routes from C to D

Here we have to use multiplication

Substitute the values in the equation

Number of routes from A to D = 7 × 8 × 10

= 560 highways

Hence, the number of highway routes from A to D is 560

Learn more about multiplication here

brainly.com/question/14667283

#SPJ1