Дробово раціональне рівняння
[tex]\frac{x+1}{x-2}-\frac{x-3}{x+2}=0[/tex]

No. of pennies and nickels are 53 and 29 respectively

Let the number of pennies be x

Let the number of nickels be y

Value of pennies = $0.01x

Value of nickels = $0.05y

It is given that value of pennies and nickels = $1.98

Therefore the equation will be,

0.01x + 0.05y = 1.98

x + 5y = 198------(1)

Also, the number of pennies is five less than twice of nickels

x = 2y - 5

2y - x = 5 -------(2)

Adding equations (1) and (2) we get,

(x + 5y) + (2y - x) = 203

7y = 203

y = 29

Substituting the value of y in equation (1) we get,

x = 53

Therefore, the no. of pennies is 53 and the no. of nickels is 29

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Answer:

399

Step-by-step explanation:

Factor the polynomial, and that will give you 399.

Using factor (156 + 243), can be rewritten as  3.(52+81).

Factor is a number  that devides any other number and does not leave any remainder.

The given term is,

(156 + 243)

The factor of 156 = 2×2×3×13

The factor of 243 = 3×3×3×3×3

The common factor is 3,

So (156 + 243) can be rewritten as,

3(2×2×13+3×3×3×3)= 3.(52+81).

So, the required term is 3.(52+81).

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Answer:

6f-15

Step-by-step explanation:

First distribute 3/2.

3/2(4) =6

3/2(-10) =15

So, the answer should be 6f-15.

Let me know if you do not understand or need further explanation :)

Answer:

The answers are below

Step-by-step explanation:

The greater sign is > and the less then symbol is <

Using the red arrows on the number line, you can tell which one is bigger or less. The dot is colored in so it has to have a line under it. So for the first one (top, left), The red arrow is pointing to the right side meaning x is bigger than 3. Therefore x ≥ 3.

In the next one (top, right) the arrow is pointing to the negative side so that one must be less than 3. The dot is also colored in meaning it is: x ≤ 3

In the next one (bottom, left) the arrow is pointing to the right, the dot not colored in, so it has no line. Therefore it is  x > 3

Last one (bottom right) the arrow is pointing left, dot is white meaning that the answer is x < 3

If you're wondering what the open dots and closed dots mean:

An open dot is used to show that the ray's endpoint is not a component of the solution when the inequality is "strict" ( < or >).

A closed dot is used to denote that the endpoint is a component of the solution for the other types of inequalities (≥ and ≤ ).

Answer:

x = -1

Step-by-step explanation:

5x + 3y = 26

- (6x + 7y = 21)

_________

-x - 4x = 5

-5x = 5

x = -1

The term in the given expression is -3x − 7(x + 4) (A) -3x.

Term:

Therefore, the term in the given expression is (A) -3x.

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The correct question is given below:
Which choice is a term in this expression? -3x − 7(x + 4)

The total amount in the bank account after 7 years will be $1490

Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time. The principal amount in simple interest is constant.

The formula for simple interest = (P*R*T)/100

where P = principal amount

R = rate of interest

T = time in years

As per the question,

P = 1000

R = 7%

T = 7 Years

Simple interest will be = (1000*7*7)/100 = $490

The amount of money in the savings account at the end of 7 years will be $1000 + $490 = $1490

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Answer:

it's x+3

Step-by-step explanation:

it seems to go up by one so if you go down by you the input of 1 would be the output of 4 also known as (1,4)

and go again down by 1 and get (0,3)

so we know we have to add 3 each time so it is x+3

Answers to Question 6: m∠1 = 92, m∠2 = 88

    The sum of a linear pair's angles is 180°, so we will set up an equation to solve.

(x + 67) + (3x + 13) = 180

4x + 80 = 180

4x = 100

x = 25

    -

(x + 67) ➜ (25 + 67) ➜ 92

(3x + 13) ➜ (3(25) + 13) ➜ 88

Answer to Question 7: m∠2 = 56

    Vertical angles are congruent, or equal, so we can set up an equation to solve.

(5x + 16) = (4x + 24)

x = 8

    -

(5x + 16) ➜ (5(8) + 16) ➜ 56

(4x + 24) ➜ (4(8) + 24) ➜ 56

The slope of a plot of the natural log of the vapor pressure of a substance versus 1/t is  - e.

What is slope?

[tex]l_{n} P = \frac{- Delta H_{vol} }{R} ( 1 T ) + C[/tex]

Yy = mx + c

[tex]m = \frac{- Delta H_{vol} }{R}[/tex]

m = slope

Ans = - e

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Answer:

9

Step-by-step explanation:

Let the ratio's unit be x. We have:

3x:2x:x. We add these up to get 6x. 6x=18, so x=3. 3*3 (since the wins is 3 in the ratio 3:2:1) is 9, so there's your answer! We can double check because 3*2 = 6 losses, and 3*1 = 3 draws, and 9:6:3=3:2:1, and 9+6+3=18!

The expression that uses an additive inverse and represents his net calorie intake 200 + (- 200) = 0.

In mathematics, the additive inverse of a number a is the number that, when added to a, yields zero. This number is also known as the opposite (number), sign change, and negation.

Now it is given that,

Calories burned by Greg = -200

Calorie taken from protien shake = + 200

Thus, Net calorie intake =  Calorie taken + Calories burned

⇒ Net calorie intake = 200 + (-200) = 0

Thus, the expression that uses an additive inverse and represents his net calorie intake 200 + (- 200) = 0.

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Answer: Total cost for her would be $8.05

Step-by-step explanation:

Given:

Berry Ice charges $6.25 a cup

$0.60 for each topping (x) you add

since she wants a cup with 3 toppings.

then

total cost = 6.25 (cost of 1 cup) + 0.60*3 ($0.60 for each topping then for 3 topping 3*cost of 1 topping)

=$8.05

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Answer:

Step-by-step explanation:

[tex]f(x)=-x^3-7x^2-7x+15\\Prove:\ x_1=-5\ \ \ \ x_2=-3\ \ \ \ x_3=1\ at\ f(x)=0\\\\-x^3-7x^2-7x+15=0[/tex]

Multiply both parts of the equation by -1:

[tex]x^3+7x^2+7x-15=0\\x^3+5x^2+2x^2+7x-15=0\\x^2*(x+5)+(2x^2+7x-15)=0\\x^2*(x+5)+(2x^2+10x-3x-15)=0\\x^2*(x+5)+(2x*(x+5)-3*(x+5))=0\\x^2*(x+5)+(x+5)*(2x-3)=0\\(x+5)*(x^2+2x-3)=0\\x+5=0\\x=-5\\x^2+2x-3=0\\x^2+3x-x-3=0\\x*(x+3)-(x+3)=0\\(x+3)*(x-1)=0\\x+3=0\\x=-3\\x-1=0\\x=1[/tex]

D) 2.65 gallons of gas left in his car after taking both friends home when 1.05 gallons of gas is used to take one friend home and three tenths gallon to take the other friend home.

Manny used 1.05 + 0.3 = 1.35 gallons of gas to take his friends home.

Since he originally had 4 gallons of gas, he had 4 - 1.35 = 2.65 gallons of gas left in his car after taking both friends home.

So the answer is D.

Here is the solution in more detail:

Manny started with 4 gallons of gas.

He used 1.05 gallons of gas to take one friend home.

He used 0.3 gallons of gas to take the other friend home.

The total amount of gas he used was 1.05 + 0.3 = 1.35 gallons.

Therefore, he had 4 - 1.35 = 2.65 gallons of gas left in his car.

I hope this helps! Let me know if you have any other questions.

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Answer:

5 and 6, 3 and 10

Step-by-step explanation:

that's all I can think of

Answer: 1/7 or 0.142857

Step-by-step explanation:

Answer:

1/7 :)

Step-by-step explanation:

Answer:

Answer: mark me brainlest

Step-by-step explanation:

Answer is A.

Answer:

  The given point satisfies both equations of a line, hence is common to the two lines.

Step-by-step explanation:

Given two lines, one joining the points (6,-7,0) to (16,-19,-4), and the other joining the points (0,3,-6) to (2,-5,10), you want to show that the point (1, -1, 2) is common to those lines.

The equation of a line through points (x1, y1, z1) and (x2, y2, z2) can be written:

  (x -x1)/(x2 -x1) = (y -y1)/(y2 -y1) = (z -z1)/(z2 -z1)

For the first pair of points, the equation of the line is ...

  (x -6)/(16 -6) = (y +7)/(-19 +7) = (z -0)/(-4 -0)

  (x -6)/10 = -(y +7)/12 = -z/4 . . . . . line 1

For the second pair of points, the equation of the line is ...

  (x -0)/(2 -0) = (y -3)/(-5 -3) = (z +6)/(10 +6)

  x/2 = -(y -3)/8 = (z +6)/16 . . . . . line 2

If the given point is on each of these lines, then it will satisfy each of the equations.

Line 1: (1 -6)/10 = -(-1 +7)/12 = -2/4   ⇒   -5/10 = -6/12 = -2/4 . . . true

The given point is on Line 1.

Line 2: (1)/2 = -(-1-3)/8 = (2+6)/16   ⇒   1/2 = 4/8 = 8/16 . . . true

The given point is on Line 2.

The given point is common to both lines.

__

Alternate solution

For points A and B and parameter p, we can write the parameterized equation of each line as ...

  (x, y, z) = A +p(B -A)

Using parameters t and s for the two lines, we get ...

  Line 1: (x, y, z) = (6, -7, 0) +t(16 -6, -19 +7, -4 -0) = (6 +10t, -7 -12t, 0 -4t)

  Line 2: (x, y, z) = (0, 3, -6) +s(2 -0, -5 -3, 10 +6) = (0 +2s, 3 -8s, -6 +16s)

A common point will be found where (x, y, z) for some value of t matches (x, y, z) for some value of s. We can find those values of s and t by solving simultaneous equations for any pair of the variables (x, y, z). The equations are ...

By any of your favorite methods, these equations have the solution (t, s) = (-0.5, 0.5). The point the lines have in common is ...

  (6 +10(-0.5), -7 -12(-0.5), 0 -4(-0.5)) = (6 -5, -7 +6, 2) = (1, -1, 2)

The common point to the two lines is (1, -1, 2).

The correcting answer is - Since 5/6 is a repeating decimal, Miguel should convert the decimal -0.6 to a fraction and multiply the fractions.

Fractions represent the parts of a whole or collection of objects.

A fraction has two parts. The number on the top of the line is called the numerator and the number on the top of the line is called the denominator.

Now the given mixed fraction is,

-0.6(5/6)

Now since 5/6 is a repeating decimal,

Therefore converting 0.6 into fraction, we get

0.6 = 6/10

Therefore, -0.6(5/6) = -(6/10)*(5/6)

Rearranging we get,

-0.6(5/6) = -(6/6)*(5/10)

⇒ -0.6(5/6) = -1*(5/10)

or, -0.6(5/6) = -(5/10)

simplifying 5/10 we get,

-0.6(5/6) = -(1/2)

Thus, the correcting answer is - Since 5/6 is a repeating decimal, Miguel should convert the decimal -0.6 to a fraction and multiply the fractions.

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Answer:

26,000,000

Step-by-step explanation:

I had that question before

Answer:

26,000,000

Step-by-step explanation:

9 is the hundred thousand digit starting from behind .

So, you start rounding up from 9.

The value of y for the given input x=7 is 15.

The given function is  y=2x+1.

We need to graph the given function.

Graphing functions is the process of drawing the graph (curve) of the corresponding function. Graphing basic functions like linear, quadratic, cubic, etc is pretty simple, graphing functions that are complex like rational, logarithmic, etc, need some skill and some mathematical concepts to understand.

Now,

Graph the line using the slope and y-intercept, or two points.

Slope: 2

y-intercept: (0, 1)

Plot the points (0, 1) and (1, 3)

The value of y for x=7 is y=2(7)+1=15

Therefore, the value of y for the given input x=7 is 15.

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I just think this way if it is wrong sry but at least I try

The length between the two points is 9.2 units.

Given points are:

Q(1,₋5)

P(₋5,2)

Let the two points be denoted as

Q(1,₋5) as (x₁,y₁)

P(₋5,2) as (x₂,y₂)

Distance between two points is calculated as:

d = √(x₂ ₋ x₁)² ₊ (y₂ ₋ y₁)²

d = √(₋5 ₋ 1)² ₊ (2 ₋ (₋5))²

d =  √(₋6)² ₊ (7)²

d =  √36 ₊ 49

d =  √85

d = 9.2

Hence the length of QN is 9.2 units.

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domain = { 3,1,4,6} and range = { 2, 2 , 3 ,-2} are each relation is a function.

Describe domain.

Describe Range?

Range is the difference between the largest and lowest values in a dataset in statistics and mathematics. One indicator of data dispersion is the range.

function = ((3, 2), (1,2), (4,3), (6, -2)}

domain = { 3,1,4,6}

range = { 2, 2 , 3 ,-2}

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Determine the conditions for when a function has an inverse. Use the horizontal line test to recognize when a function is one-to-one. Find the inverse of a given function.

It is simple to establish whether the inverse of a function is also a function using the horizontal line test.

Because it fails the vertical line test, a function's inverse might not actually be a function.

Graph of the line

f\left( x \right) = - x + 2

f(x)=−x+2.

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Answer:

$31.44

Step-by-step explanation:

$125.76 ÷ 4 = $31.44

Lauren $31.44

Friend 1 $31.44

Friend 2 $31.44

Friend 3 $31.44

+ ________

$125.76

Answer:

75%

Step-by-step explanation:

15 over 20 is equal to 3/4 and 3/4 is 75%