Identify the constant of proportionality in the equation. 3y = 15x

Answer:

Estimate is 150 and actual product is 138.

Step-by-step explanation:

To estimate products, we round the numbers to nearest unit place, 10th, 100th, 1000th, and so on.

Given are the numbers 3 and 46.

We can round 46 ≈ 50.

So Estimation would be 3 x 46 ≈ 3 x 50

3 times 5 is 15 and we can add zeros after it.  

So estimation is 3 x 46 ≈ 150.

Now actual product would be...

3 times 6 is 18, so we note down 8 and 1 goes to carry over 4.

3 times 4 is 12 and carry 1 will be added in it, so 12 + 1 = 13.

It means the actual product is 3 x 48 = 138.

The answers to all the parts are -

Equation : (1/2)n + n = 90

Apples picked up by Nate : 60

Apples picked up Laura : = 30

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have Nate and Laura picked apples. Laura picked 1/2 as many as Nate picked. Together they picked 90 apples.

Let [n] stand for the number Nate picked. Then, the number of apples picked up by Laura will be (1/2)n. Then, we can write -

Equation : (1/2)n + n = 90

1.5n = 90

n = (90/1.5)

n = 60

Apples picked up by Nate : 60

Apples picked up Laura : 60/2 = 30

Therefore, the answers to all the parts are -

Equation : (1/2)n + n = 90

Apples picked up by Nate : 60

Apples picked up Laura : = 30

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Answer:

- c = 9

Step-by-step explanation:

given c = - 9 ← multiply both sides by - 1

c × - 1 = - 9 × - 1 ⇒ - c = 9

Answer:

SSS - Two triangles have to have 3 congruent pairs of sides.

ASA - Two triangles have to have 2 congruent pairs of angles with an included congruent pair of sides.

SAS - Two triangles have to have 2 congruent pairs of sides with an included congruent pair of angles.

AAS - Two triangles have to have 2 pairs of congruent angles with a non-included congruent pair of sides.

Answer:

6. d.

8. see below

Step-by-step explanation:

6.

A large pizza costs $4.25 more than a medium pizza.

L = $4.25 + M

4 large & 6 medium cost $99.50.

4L + 6m = $99.50

Answer d.

8.

A large river runs right through a city called Chestnutville. There are many bridges and tunnels connecting the two sides of the river. The total number of bridges and tunnels is 15. The number of tunnels is 3 more than twice the number of bridges. How many bridges, b, are there in Chestnutville, and how many tunnels, t, are there in Chestnutville?

Answer:

50 C = 122 F

Step-by-step explanation:

50°C × 9/5 +32

Answer:

50°C = 122°F.

Step-by-step explanation:

Given  : The formula to convert F° to C° is [tex]C = \frac{5}{9}( f - 32)[/tex].

To find :  Convert 50°C to °F

Solution : We have given

[tex]C = \frac{5}{9}( f - 32)[/tex].

On multiplying by 9 both sides.

[tex]9 C = 5( f - 32)[/tex].

On dividing both sides by 5

[tex]\frac{9C}{5} =( f - 32)[/tex].

On adding both sides by 32

[tex]\frac{9C}{5}+ 32 = f[/tex].

Then plug C = 50°

[tex]\frac{9 * 50 }{5}+ 32 = f[/tex].

[tex]\frac{450}{5}+ 32 = f[/tex].

[tex] 90+ 32 = f[/tex].

[tex] 122°= f[/tex].

Therefore,  50°C = 122°F.

Answer:

2693.45

Step-by-step explanation:

step 1 - 2615*3%=78.45

step 2 - 2615+78.45=2693.45

Answer:

5 is the initial value

Step-by-step explanation:

From the table we can see that the values of y are increasing by 4

Lets use two points and find out slope

[tex]slope = \frac{y_2-y_1}{x_2-x_1}[/tex]

we use points (0,5) (1,9)

[tex]slope = \frac{9-5}{1-0}=4[/tex]

slope m= 5

Now we use y=mx+b equation

m= slope and b= y intercept, plug in (0,5)  and find out b

y=4x+b

5= 4(0) +b

so b= 5

b=5 is the initial value of the function

Answer:

5 is the initial value

Step-by-step explanation:

From the table we can see that the values of y are increasing by 4

Lets use two points and find out slope

formula of slope

slope=m=[tex]\frac{y2-y1}{x2-x1}[/tex]

putting points (0,5) (1,9) in equation of slope

m=[tex]\frac{9-5}{1-0}[/tex]

slope m= 4

we know y=mx+b

m= slope and b= y intercept, plug in (0,5)  and find out b

b=?

x=0

m=4

y=5

putting these values in y=mx+b

y=4x+b

5= 4(0) +b

so b= 5

b=5 is the initial value of the function

Answer:

260 in economy

100 in business

Step-by-step explanation:

ok so out of 18 seats 13 are economy and 5 are business and since 18 times 20 is 360 we multiply each of these by 20 so 13 times 20 is 260 20 times 5 is 100 there you go

Answer:

y = 0 and z = 5

Step-by-step explanation:

the denominator of the expression cannot equal zero as this would make the expression undefined Equating the denominator to zero and solving gives the values that y and z cannot be

solve y(z - 5) = 0

equate each factor to zero and solve

y = 0 ← excluded value

z - 5 = 0 ⇒ z = 5 ← excluded value

Answer:

[tex]x^{\circ}=56^{\circ};[/tex]

The exterior angle has measure [tex]116^{\circ}.[/tex]

Step-by-step explanation:

Angle QRP and angle with measure of (2x+4)° are supplementary, then

[tex]m\angle QRP+(2x+4)^{\circ}=180^{\circ},\\ \\m\angle QRP=180^{\circ}-(2x+4)^{\circ}.[/tex]

The sum of the measures of all interior angles of the triangle is equal to 180°, then

[tex]m\angle PQR+m\angle QRP+m\angle RPQ=180^{\circ},\\ \\x^{\circ}+180^{\circ}-(2x+4)^{\circ}+60^{\circ}=180^{\circ},\\ \\x^{\circ}-2x^{\circ}=-60^{\circ}+4^{\circ},\\ \\-x^{\circ}=-56^{\circ},\\ \\x^{\circ}=56^{\circ}.[/tex]

The exterior angle has measure

[tex](2\cdot 56+4)^{\circ}=116^{\circ}.[/tex]

Answer:

x=56 and the exterior angle is 116

Step-by-step explanation:

We will call the unknown angle in the triangle y.  Angle y and the angle (2x +4) form a straight line so they make 180 degrees.

y + 2x+4 =180

Solve for y by subtracting 2x+4 from each side.

y + 2x+4 - (2x+4) =180 - (2x+4)

y = 180-2x-4

y = 176-2x

The three angles of a triangle add to 180 degrees

x+ y+ 60 = 180

x+ (176-2x)+60 = 180

Combine like terms

-x +236=180

Subtract 236 from each side

-x+236-236 = 180-236

-x = -56

Multiply each side by -1

-1*-x = -56*-1

x=56

The exterior angle is 2x+4.  Substitute x=56 into the equation.

2(56)+4

112+4

116

Answer:

C  PLEASE GIVE BRAINLIEST

Step-by-step explanation:

4.20 ÷ 60 = 0.07

sales tax is 7% and this is your constant of variation

The answer is 0.07 hope this helps you ! :)

Answer:

Whats the question?

Step-by-step explanation:

Answer:

5 mililmiters = 0,005 meters = 0,000005 kilometers

2 kilometers = 2000 meters

Step-by-step explanation:

km  / hectometer / decameter / meter / dcm / centimeter / milimeter

1000 m /     100  m   /    10   m     <     1  >    0,1 m/    0,01  m     /  0,0001 m

1 meter = 0,  1 decimeters / 0, 01 centimeters /0, 000 1 millimeters

1 meter = 10 decameters / 100 hectometers / 1000 kilometers

so 5 millimeters = 0,005 meters = 0, 000 005 kilometers

so  2 km = 2 000 meters  = 2 000 000 millimeters

the reference unit of measure is the meter.

Answer:

313

Step-by-step explanation:

Quotient - Division

5,008 ÷ 16 = 313

Hope this helps you! And btw, you can use a calulator. :D

Answer:

313

Step-by-step explanation:

5,008/16 equals 313

Answer:

b. 3 4/6 cant equal 3 2/3

Step-by-step explanation:

Answer:

A - $2240

Step-by-step explanation:

120(12) + 800 =

1440 + 800 = 2240

Answer:

0

Step-by-step explanation:

while rounding the fraction to half,it is to remember that

anything less than 1/4 can be rounded to zero.

anything equal or 1/4 or greater and less than 3/4 can be rounded to 1/2.

anything greater than 3/4 and less than 1 can be rounded to one.

so,1/9<1/4

the value is 0.

Final answer:

The fraction 1/9, when rounded off to the nearest 1/2, is closest to 0, so it rounds down to 0.

Explanation:

To round the fraction 1/9 to the nearest 1/2, you must decide which multiple of 1/2 (0, 1/2, or 1) it is closest to. Since 1/9 is less than 1/2, the first decision is whether it's closer to 0 or to 1/2. Since 1/9 is much smaller than 1/2, it makes sense to round it down to 0. Therefore, when rounding 1/9 to the nearest 1/2, the answer is 0.

Answer: x < 3

Step-by-step explanation:

NOTE: [tex]\sqrt{(x+5)^2} = |x + 5|[/tex]

Rewrite the equation:

| x + 5 | < | x + 1 |

Remember that absolute value makes the "inside" value positive, so we need to solve for 2 case of x + 5 (inside is positive or negative) and 2 cases of x + 1.

± (x + 5) < ± (x + 1)

Case 1: +  +

x + 5 < x + 1

    5 < 1

  FALSE

Case 2: - -

-(x + 5) < -(x + 1)

 x + 5 > x + 1   divided both sides by -1

      5 > 1

     TRUE so this works when both "insides" are negative

⇒   x + 5 < 0     and      x + 1 < 0

          x < -5     and           x < -1

since it has to satisfy both, x < -5

Case 3: + -

x + 5 < -(x + 1)

x + 5 < -x - 1     distributed -1 on right side

2x + 5 < -1

2x       < -6

 x       < -3

Case 4: - +

-(x + 5) < x + 1

-x - 5 < x + 1     distributed -1 on left side

   -5 < 2x + 1

   -6 < 2x

   -3 < x

     x > -3

This is a contradiction of Case 3 so need to choose a test point.

TEST POINTS (I choose -6, -4, and -2)

 | -6 + 5 | < | -6 + 1 |

 |    -1     | < |    -5   |

          1   <   5

        TRUE so x < -5 is valid

 | -4 + 5 | < | -4 + 1 |

 |     1     | < |    -3   |

          1   <   3

        TRUE so x < -3 is valid

 | -2 + 5 | < | -2 + 1 |

 |     3     | < |    -1   |

          3   <   1

        FALSE so x > 3 is NOT valid

Note that x < -3 includes all the values of x < -5, so x < -3 is the answer.

*******************************************************************************

This is a faster way to solve it. Thank you @proner26 !

| x + 5 | < | x + 1 |

(| x + 5 |)² < (| x + 1 |)²

x² + 10x + 25 < x² + 2x + 1

       10x + 25 <       2x + 1

        8x + 25 <                1

        8x         <             -24

          x         <              -3

Answer: x < -3

Answer:

Function 2 has a greater rate of change

Step-by-step explanation:

Function 1:

Number of Weeks (x)               1     2      3     4

Amount Remaining (dollars) (y) 40   36    32   28

We can find the slope by using

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

  = (40-36)/ (1-2)

  = 4/-1

 = -4

Function 2:

y = −5x + 40

Using y = mx+b

The slope is -5

Function 2 has a greater rate of change

Answer:

Function 2, because Steve spends $5 each week and Ada spends $4 each week

Step-by-step explanation:

I took the test

Answer:

The annual percentage yield is 6.609%

Step-by-step explanation:

Let's assume

amount invested=$1

so, P=1

APR of 6.4% compounded daily

so, r=6.4%=0.064

n=365

t=1

now, we can use formula

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

now, we ca plug values

[tex]A=1(1+\frac{0.064}{365})^{365\times 1}[/tex]

we get

[tex]A=1.06609[/tex]

now, we can find APY

[tex]APY=\frac{A-P}{P}\times 100[/tex]

now, we can plug values

[tex]APY=\frac{1.06609-1}{1}\times 100[/tex]

we get

APY is 6.609%

Answer:

The annual percentage yield is 6.609%.

Step-by-step explanation:

The annual percentage yield is calculated by:

APY = [tex](1+\frac{r}{n} )^{n} -1[/tex]

where r is the percentage rate and n refers to the number of times compounded.

So, r = [tex]\frac{6.4}{100}[/tex] = 0.064

Since the APR is compounded daily,

n = 365

Now,

APY = [tex](1+\frac{0.064}{365} )^{365} -1[/tex]

= 6.609% approximately

Answer:

2.04

Step-by-step explanation:

Answer:

a) There is no solution

Step-by-step explanation:

Answer:

These fractions are not equivalent.

Step-by-step explanation:

To tell whether the fractions are equivalent, get a common denominator.

The common denominator is 10

1/2 *5/5 = 5/10

2/5 *2/2 = 4/10

5/10 ≠4/10

These fractions are not equivalent.

Substitute y = 2x - 4 to x + 2y = 12:

x + 2(2x - 4) = 12    use distributive property

x + (2)(2x) + (2)(-4) = 12

x + 4x - 8 = 12     add 8 to both sides

5x = 20    divide both sides by 5

x = 4

Put the value of x to the first equation:

y = 2(4) - 4

y = 8 - 4

y = 4

Answer:

x=4, y=4

Step-by-step explanation:

y=2x-4;

x+2y=12

We can use substitution since the first equation is solved for y

Where ever you see y in the second equation, replace it with 2x-4

x + 2(2x-4) = 12

Distribute the 2

x+4x-8 = 12

Combine like terms

5x-8=12

Add 8 to each side

5x-8+8=12+8

5x=20

Divide by 5

5x/5 = 20/5

x =4

We still need to solve for y

y = 2x-4

We know x =4

y = 2(4) -4

y = 8-4

y=4

Answer:

Tony

Step-by-step explanation:

Tony:

3 Packs = 12 dollars

1 Pencil Box = 7 dollars

Mario:

4 Binders = 24 dollars

-6.

12+7= 19

24-6=18

Tony spent more money.

Answer:

1/12

Step-by-step explanation:

subtract the two :)

This is true.  The slope of the perpendicular line is equal to the negative reciprocal.  This means that you "flip" the fraction and multiply by negative 1.  Since the reciprocal is also the multiplicative inverse (something you multiply by a number to get 1), and the signs are different (one is positive, one is negative) it equals -1.

Hope this helps!

The statement is true that the product of the slopes of perpendicular lines, excluding vertical lines, always equals -1. This is a basic rule in geometry, where two lines are perpendicular if their slopes multiply to -1.

The statement that 'the product of the slopes of perpendicular lines (excluding vertical lines) always equals -1' is true.

In the coordinate system, two lines are perpendicular if the product of their slopes is -1. This is because the slope is a measure of the steepness of a line. Imagine you have two lines with slopes m1 and m2. If these lines are perpendicular to each other, then m1 * m2 = -1.

For example, if one line has a slope of 2 (m1 = 2), the line perpendicular to it will have a slope of -1/2 (since 2 * -1/2 = -1).

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