in 10 minutes, a heart can beat 700 times.At this rate, in how may mintues will a heart beat 140 times? At what rate can a heart beat?

Answer:

B. The equations have the same solution because the second equation can be obtained by multiplying both sides of the first equation by −3.

Statement B is true. The equations have the same solution because the second equation can be obtained by multiplying both sides of the first equation by −3.

A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.

Equation 1;

-2x=14

Equation2;

6x=-42

Multiply equation 2 on both sides by -3.

-2x=14

-2x×3=14×3

6x= - 42

Because the second equation can be found by multiplying both sides of the first equation by 3, the equations have the same solution.

Hence, statement B is true

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The total cost for 53 people attending the school banquet is $1,665.

Given the parameter:

The cost of a school banquet is expressed as:

$75 + 30n, as n is the number of people attending.

To determine the cost for 53 people attending the school banquet, you can plug the value of n (which is 53) into the given cost function:

Cost = $75 + 30n

Plug in n = 53

Cost = $75 + 30( 53 )

Cost = $75 + 1590

Cost = $1,665

Therefore, the total cost will be $1,665.

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Answer 1:

[tex]\frac{x^{2} -x+1}{x^{2} +x+1}[/tex]

Here given that, x is real that is the domain

Range of the given expression is :

[tex]\frac{1}{3} \leq y\leq 3[/tex]  

Write it interval form.

[tex][\frac{1}{3},3][/tex]       Option (2)

Answer 3:

[tex]\frac{11x^{2} +12x+6}{x^{2} +4x+2}[/tex]

Here domain is all real x.

Range is :

{y ∈ R : y ≤ -5 or y ≥ 3}

In interval form:

(-∞, -5] ∪ [3, ∞)

So, y can't lies between -5 to 3                Option (2)

Answer 5 :

[tex]\frac{x^{2} -3x+4}{x^{2} +3x+4}[/tex]

Here domain is :

x is real

And range is :

{y ∈ R : [tex]\frac{-1}{7}[/tex] ≤ y ≤ 7}

We see that maximum y value is 7.

So, maximum value is 7.                      Option (4)

Answer 6:

[tex]\sqrt{9x^{2}+6x+1 } < (2 -x)[/tex]

Solve for x .

Square both the side

9x² + 6x + 1 =  4 + x² - 4x

8x² + 10x - 3 < 0

(2x + 3)(4x - 1) < 0

2x + 3 = 0                           &                    4x - 1 = 0

x = [tex]\frac{-3}{2}[/tex]      &                    x = [tex]\frac{1}{4}[/tex]

So,

[tex]\frac{-3}{2} < x < \frac{1}{4}[/tex]

x ∈ [tex](-\frac{3}{2} , \frac{1}{4} )[/tex]                     Option (1)

a4b2 + 2a4 - 12a3b - 2ab3 - 4b2  

 ———————————————————————————————

               2a2              

Answer:

Likely

Step-by-step explanation:

The answer is likely, its really close to certain but certain is 100%. Likely is the odds are for it but not confirmed.

Answer:

Likely is the answer hope this helps

Step-by-step explanation:

The given pentagon can be divided into two figures : a triangle and rectangle as shown in figure.

Let us find area of each figure separately.

Triangle:

Area of triangle is given by:

[tex]A=\frac{1}{2}*b*h[/tex]

where b=base and h=height

Height of triangle :

h=(3x+5)-(2x+1)

h=x+4

Base = 2x-2

[tex]A=\frac{1}{2}*(x+4)(2x-2)[/tex]

Area of triangle= (x-1)(x+4) = x²+3x-4

Area of rectangle:

Area of rectangle is given by:

A=l*b

[tex]A=(2x-2)(2x+1)[/tex]

Area of rectangle = 4x²-2x-2

Area of pentagon = Area of triangle + Area of rectangle

Area of pentagon = x²+3x-4 + 4x²-2x-2

Area of pentagon = 5x²+x-6

If area of pentagon is 42 cm², then solving for x,

[tex]42=5x^{2}+x-6[/tex]

[tex]5x^{2}+x-48=0[/tex]

Factorising to get x,

x=-3.2 and x=3

If we take x as negative the side will be negative, so we neglect x=-3.2

So x=3 is the answer.

Answer:

every 20 days

Step-by-step explanation:

Exact Form: 2/7

Decimal Form:0.285714 (this is also a repeating decimals)

B and E with C and G

The minute hand is like an eight inch radius of a circle, whose circumference would equal 2 * PI * 8 = 50.265 inches.  By moving to 8 o'clock, it travels 2/3 of the circumference or 50.265 * 2/3 = 33.510 inches

if the minute hand is 8 inches long, it shows the radius of the circle of the clock.

thus, the circumference of the circle (boundary)= 2πr

= 2X 3.14 X 8    ( wherein, r= radius= 8; π= 22/7 or 3.14)

= 50.27 inches.

The length between each two consecutive no.s on the clock = 50.27/12 = 4.19

Thus, the length moved n=by the tip of the minute hand= 4.19X8

= 33.44 inches

Hope that this would be correct .

The answer is 51 remainder 4      because 51* 4 =408 and 412 + 4 = 412

at this rate, he will have attempted 27 passes. we can find this by setting the problem up into a proportion: 10/18=15/?

once we solve the proportion, we get that he attempted 27 passes in order to complete 15

Final answer:

To solve for the number of passes the quarterback will attempt to complete 15 passes, we set up a proportion based on the completed 10 out of 18 passes. By cross-multiplying and solving for the unknown, we find that the quarterback would need to attempt 27 passes.

Explanation:

The question is asking us to find out how many passes the Rams' quarterback will attempt if he is to complete 15 passes, given that he completed 10 out of 18 passes in his last game. This is a proportion problem in mathematics where we set up a ratio of completed passes to attempted passes and solve for the unknown.

We know the quarterback completed 10 passes out of 18 attempts, so the ratio of completed to attempted passes is 10/18. If we want the quarterback to complete 15 passes, we can set up the proportion as:

10/18 = 15/x

where x represents the number of passes that the quarterback will attempt. To solve for x, we cross-multiply:

10(x) = 18(15)

x = (18(15))/10

x = 27

Therefore, the quarterback will have to attempt 27 passes to complete 15 passes at the same completion rate.

y2-y1 / x2-x1

1 + 11 / 1 + 3

12 / 4

3 is the slope

Answer:

18 Tala.

Step-by-step explanation:

1. You have that Ming learned that the exchange rate is 6 Tala for $2. Therefore, if she exchanged $6, she would get:

[tex]\frac{6}{2}=\frac{x}{6}[/tex]

2. Now, you must solve for [tex]x[/tex], which is sthe amount of Tala:

[tex]x=\frac{(6)(6)}{2}\\x=\frac{36}{2}\\x =18[/tex]

3. Therefore, she would get 18 Tala.

The solution for the given inequality is x ≥ 10.

An inequality is an expression mathematical that represents a non-equal relationship between a number or another algebraic expression.  The solutions for inequalities can be given by: a graph in a number line or numbers.

Therefore, it is common to the use following symbols: ≤ (less than or equal to), ≥ (greater than or equal to), < (less than), and > (greater than).

The question gives the inequality  2x+4 ≥ 24. Thus, you should follow the next steps.

2x+4 ≥ 24

2x ≥ 24 -4

2x ≥ 20

x ≥ 10

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To solve the inequality 2x+4≥24, subtract 4 from both sides, simplify the expression, divide both sides by 2, and simplify again. The solution is x≥10.

Let's solve the inequality 2x+4≥24. The first step is to isolate the term with x on one side. We can do this by subtracting 4 from both sides, which results in 2x ≥ 20. Next, we want to solve for x, so we divide both sides by 2: x ≥ 10. This means that x is greater than or equal to 10. lets solve step-by-step.

To solve the inequality 2x+4≥24, we need to isolate the variable x.

Step 1: Subtract 4 from both sides of the inequality: 2x+4-4≥24-4

Step 2: Simplify: 2x≥20

Step 3: Divide both sides of the inequality by 2: 2x/2≥20/2

Step 4: Simplify: x≥10

The solution to the inequality is x≥10. This means that any value of x that is greater than or equal to 10 satisfies the inequality.

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Answer:

B

Step-by-step explanation:

Edge

We know that Company B will be less expensive at first, but Company A will become a better option as the miles rack up. Eventually, Company A will be less expensive. There will be a point where the price will be the same for each company.  

150 + .20x = Company A

70 + .40x = Company B

If we set these two equations equal to each other, we find out when the price will be the same.

150 + .20x = 70 + .40x

If we solve for x, we find out how many miles must be driven in a day to make the rental cost the same. After that, Company A will be a better deal.

At 350 miles, the rental costs for company A and company B become the same. This result is found by setting the two cost functions equal to each other and solving for the number of miles.

To find when the rental costs from both companies are the same, you need to set the expenses equal to each other and solve for miles (m). The cost for company A can be represented as 130 + 0.30m (130 dollars for the daily rental and 0.30 dollars per mile) and the cost for company B is represented as 60 + 0.50m (60 dollars for the daily rental and 0.50 dollars per mile).

Upon setting the costs equal to each other: 130 + 0.30m = 60 + 0.50m, and simplifying, you'll get 0.20m = 70. Therefore, by dividing by 0.20, m = 350.

So, at 350 miles, the rental costs for both companies A and B are the same, with each charging the same amount for the truck rental.

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Answer: 68

Step-by-step explanation:

LM   +    MN     =   LN

x + 7  + 3x + 20 = 6x - 5

            4x + 27 = 6x - 5

           -4x         -4x      

                    27 = 2x - 5

                     +5        +5

                    32  = 2x

                    ÷2   ÷2    

                     16 = x

MN: 3x + 20

       3(16) + 20

         48   + 20

               68

This question is based on a principle in Mathematics called the Midpoint of a linelineline

Based on this question, the line = LNLN

To solve this question, we have the expression

LM + MN = LN

Step 1

We solve for x

Given that: LN= 6x-5 , LM= x + 7 , and MN= 3x + 20

Hence,

x + 7 + 3x + 20 = 6x - 5

Collect like terms

7 + 20 + 5 =6x - x - 3x

32 = 2x

Divide both sides by the coefficient of x = 2

32/2 = 2x/2

x = 16

The value of x = 16

Step 2

Find MN

Given that : MN= 3x + 20 and x = 16

We substitute 16 for x in MN

MN = 3(16) + 20

MN = 48 + 20

MN = 68

Therefore, the value of MN is 68.

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Answer:

the answer is 3x-5

Step-by-step explanation:

break the expression in to groups

3x^2 + 4x -15 =  (3x^2 -5x) + (9x-15)

factor out x from 3x^2 -5x: x(3x-5)

factor out 3 from 9x-15: 3(3x-5)

=x(3x-5) +3(3x-5)

factor out common terms

(x+3) (3x-5)

=((x+3) (3x-5)) / (x+3)

cancel the common factor x+3

=3x-5

The quotient for the expression is equal to 3x-5.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Break the expression into groups

3x² + 4x -15 =  (3x² -5x) + (9x-15)

Factor out x from 3x^2 -5x: x(3x-5)

Factor out 3 from 9x-15: 3(3x-5)

=x(3x-5) +3(3x-5)

Factor out common terms

(x+3) (3x-5)

=((x+3) (3x-5)) / (x+3)

Cancel the common factor x+3

=3x-5

Therefore, the quotient for the expression is equal to 3x-5.

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let x be the price before the discount

If you get 12% off, then you only pay the remaining 88% (since 88%+12% = 100%). This means if you take 88% of the original price (x), then you get the final price (132)

In terms of an equation, we have,

88% of (original price) = final price

(88/100)*(x) = 132

0.88*x = 132

0.88*x/0.88 = 132/0.88 <--- divided both sides by 0.88

x = 150

--------------------------------------------

Answer: The price without the discount is $150

The chance of winning is 1/9

Number 3: D

Number 4: C

one tip:

Example: 4 - (-3)

it instantly becomes positive because the negatives are close to each other as shown.

hope that helps :)

Since an integer is any whole (not fractional) number on the number line, all you have to do is move to the left however many units you're subtracting by from the point given. Say the problem is 3 - 7. This means we start at 3, and move to the left 7 units, which lands us at -4. However, if we had a problem like 12 - (- 2), the two negatives would cancel out, meaning we will move to the right 2 units on the number line, or 12 + 2, which is 14. Some other examples are:

-12 - 4, (you should get -16)

3 - 8, ( you should get -5)

16 - (- 3), ( you should get 19)

I hope these tips helped you out! I know that when I first had to subtract integers, using a number line really helped me out. Eventually, it'll just be a natural thing. :D

x= 5

Slove for x by simplifying both sides of the equation, then isolating the variable

Hey there!!

Given equation :

... 6 - 4x = 7x - 9x - 4

Combining like terms :

... 6 - 4x = - 2x - 4

Adding 4x on both sides :

... 6 = 2x - 4

Adding 4 on both sides :

... 2x = 10

Dividing by 2 on both sides :

... x = 5

Hence, the value of x is 5.

Hope my answer helps!!

The table is shown in figure.

Here,

Function is given as;

f (x) = x - 5

We have to complete the table.

What is Function?

A relation between a set of inputs having one output each, is called Function.

Now,

Function is given as;

f (x) = x - 5

Hence, after putting all the given values of x, we get;

Put x = -1,

Then, f (x) = -1 - 5 = - 6

Put x = 0

Then, f (x) = 0 - 5 = -5

Put x = 1

Then, f (x) = 1 - 5 = -4

Put x = 2

Then, f (x) = 2 - 5 = -3

Put x = 4

Then, f (x) = 4 - 5 = -1

Therefore, All values of f (x) are;

⇒ -6, -5, -4, -3, -1

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Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42

Factors of 28: 1, 2, 4, 7, 14, 28

Factors of 70: 1, 2, 5, 7, 10, 14, 35, 70

The greatest common factor of 42, 28, and 70 is 14.

[tex]\boxed{=14}[/tex]

Hope this helps!

And thank you for posting your question at here on brainly, and have a great day.

-Charlie

It is 128.1 pounds.....

Answer:

There is 127.91lbs in that many kilograms.

Step-by-step explanation:

In order to find this, you need to know the unit rate. There is 2.2lbs in every kilogram. Therefore, we can multiply the number of kilograms that we have by 2.2 to get the correct answer.

58.14*2.2 = 127.91

You must find the unit cost in dollars per gallon for each purchase by dividing the cost by the number of gallons.

Graven: $55.20 for 15 gallons

$55.20/(15 gal) = $3.68/gal

Project: $72.80 for 20 gallons

$72.80/(20 gal) = $3.64/gal

Answer: Project paid less per gallon.

yes it would be rational

Since repeated decimals are rational in nature, hence, 6.565656... is rational

Rational numbers are numbers that can be written as the ratio of two integers. For example:

All repeating decimals are also classified as rational numbers. For example:

The given decimal value 6.565656... is a repeating decimal. The three dots after the decimal values shows that the number is a repeating decimal.

Since repeated decimals are rational in nature, hence, 6.565656... is rational

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