What is the equation of a line that passes through the point (2, −10) and is parallel to 14x+2y=6?

Answer:

Step-by-step explanation:

m= [ -3-(-3)] ÷ [-8-7} = 0

Therefore, the slope of the line is 0.

Now use the slope and either of the two points to find the y-intercept.

y= mx+b

-3= (0)(7)+b

b=-3

Write the equation in slope intercept form as:

y= mx+b

y= (0)x-3

y= -3

Hence, the equation of the line is y= -3.

The correct statement regarding the algebra will be:

A. Leena consumed 1,500 calories at dinner.

B. The equation StartFraction 2 Over 3 EndFraction left-parenthesis x plus 400 plus 350 right-parenthesis equals x.(x + 400 + 350) = x can be used to model the situation.

Calories consumed at dinner = x

x = 2/3 of daily calorie

Hence, the fraction of calories consumed during breakfast and lunch can be calculated thus :

1 - 2/3 = 1/3

Let the total amount of calories consumed per day = c

1/3 × c = 750

c/3 = 750

c = 750 × 2 = 2250 calories

Calories consumed at dinner = (2250 - (750)) = 1500 calories

Therefore, the correct options are A and B.

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If you have applied for two jobs a and b and the probability that you get an offer for the job a is 0.25 and the probability of being offered job b is 0.20, then the probability that you will be offered both jobs is 0.05.

Probability is a term used in mathematics that is concerned with the numerical illustration of the possibility of an event to take place. Its value is between 0 and 1 where 0 illustrates the impossibility of the event to take place while 1 illustrates the certainty of an event to take place.

As the probability of both the jobs are not dependent on each other, the probability that both jobs will be offered can be calculated by the formula;

P(A∩B) = P(A) × P(B)

Here, P(A∩B) represents the probability of both the events to take place together

As P(A) is equal to 0.25

P(B) is equal to 0.20

P(A∩B) = (0.25)(0.20)

P(A∩B) = 0.05

Therefore, 0.05 is the probability that both jobs will be offered.

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The function y = 5x demonstrates exponential growth.

The exponential function is a fundamental mathematical function with the following formula:

f(x) = aˣ

Here,

So,

Given function: y = 5x

If we put x = 1 as follows:

Then, if we put x = 2 as follows:

We see that 10 > 5.

Therefore, the function y = 5x demonstrates exponential growth.

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Answer: 1.2 tons

Step-by-step explanation:

Answer:  1,777

Step-by-step explanation:

Volume is a three-dimensional quantity that is used to measure the capacity of a solid shape. If oil flows through a pipe at a rate of 40m³/s then it takes 50mins to fill a tank of volume 1.2x10⁵m³

Volume is a three-dimensional quantity that is used to measure the capacity of a solid shape. It means the amount of three-dimensional space a closed figure can occupy is measured by its volume.

Given that Oil flows through a pipe at a rate of 40m³/s.

Volume of the tank is 1.2x10⁵m³

volume =Rate *time

Time=Volume/ Rate

Time= 1.2*10⁵m³ / 40m³=3000seconds

We need to convert time in seconds to minutes

We know that 1 hr = 60 mins.

So divide 3000 sec by 60

3000/60= 50 minutes.

Therefore 50 min it will take to fill a tank of volume 1.2x10⁵m³.

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The numeric values for the function are given as follows:

A. f(a) = 9a - 9.

B. f(a + h) = 9a + 9h - 9.

C. f(a + h) - f(a) = 9h.

D. (f(a + h) - f(a))/h = 9.

To find the numeric value of a function, we replace each instance of the variable by the desired value.

For this problem, the function is given by:

f(x) = 9x - 9.

At x = a, the numeric value is given by:

f(a) = 9(a) - 9 = 9a - 9.

Hence:

f(a) = 9a - 9.

At x = a + h, the numeric value is given by:

f(a + h) = 9(a + h) - 9 = 9a + 9h - 9.

Hence:

f(a + h) = 9a + 9h - 9.

Subtracting these values, we have that:

f(a + h) - f(a) = 9a + 9h - 9 - 9a + 9 = 9h.

Hence:

f(a + h) - f(a) = 9h.

Dividing by h, we have that:

(f(a + h) - f(a))/h = 9h/h = 9.

Hence:

(f(a + h) - f(a))/h = 9.

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Solution: the number of miles in the taxi ride.= 180 miles

Miles : A unit of length equal to exactly 1.609344 kilometers.

Also equal to 1,760 yards or 5,280 feet.

The average walking speed is 3 miles per hour (so it takes about 20 minutes to walk 1 mile).

The taxi company charged a pick-up fee of $4.60

The taxi company charged $0.50 per mile.

The total fare was $13.60

The total fare = pick-up charged + traveling charged

the number of miles in the taxi ride = m

$13.60= $4.60 +  m x $.50

$13.60-$4.60 = $.50m

9 =.50 m

9 /.50 = m

900/5 = m

180 = m

the number of miles in the taxi ride.= 180 miles

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Step-by-step explanation:

the perimeter is the sum of all sides.

it is clearly a symmetric figure.

I assume the sqrt(36) is the whole baseline (incl. the left and right x).

so, we have

sqrt(8) + 2x = sqrt(36) = 6

1/2 × sqrt(8) + x = 3

sqrt(1/4 × 8) + x = 3

sqrt(2) + x = 3

x = 3 - sqrt(2)

to get the inclined sides we use Pythagoras

c² = a² + b²

c being the Hypotenuse, a and b being the legs of the right-angled triangle.

so,

side² = sqrt(8)² + (3 - sqrt(2))² = 8 + (9 - 6×sqrt(2) + 2) =

= 19 - 6×sqrt(2)

each inclined side is

sqrt(19 - 6×sqrt(2))

so, as perimeter we get

6 + sqrt(8) + 2×sqrt(19 - 6×sqrt(2)) =

= 15.3137085...

Answer:

50.28 m²

Step-by-step explanation:

Area of a circle = pi r²

= 22/7 × 4 × 4

= 50.28 m²

Answer:

x=11

Step-by-step explanation:

3x=2+31

3x=33

divide both sides by the coefficient of x

x=11

Answer:

Dunno

Step-by-step explanation:

The fractions 16/20, 12/15, and 8/10 are equivalent fractions to 4/5.

When writing equivalent fractions, the numerator and denominator should be multiplied or divided by the same number. This is the reason why when these fractions are simplified, they are reduced to the same value.

Let us understand the two ways in which we can make equivalent fractions:

Now, Divide the denominator or numerator by the same number or multiply the denominator and the numerator by the same number.

So, the equivalent fractions for 4/5 are:

(4/5) × (2/2) = (4 × 2) / (5 × 2) = 8/10

(4/5) × (3/3) = (4 × 3) / (5 × 3) = 12/15

(4/5) × (4/4) = (4 × 4) / (5 × 4) = 16/20

After simplifying, 16/20, 12/15, and 8/10 equal 4/5, indicating that they are identical in nature.

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log (24) is each expression as a single logarithm.

A logarithm is defined simply.

Each of the properties of exponential functions has an analog for

logarithmic functions.

logb(x)+logb(y)= logb(xy)

Use this properties

log 8+log 3  = log ( 8 * 3 )

log 8+log 3  = log (24)

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We get that an equation to represent this relationship the relation of increase in radius with respect to time as R = r + 16 t where t is the time and r is the initial radius.

We are given that, the wave travels at a rate of 16 feet / sec when George jumps off a tire swing in the circular pond.

So, this means that the radius of the wave increases by 16 feet in every second.

Now, let the initial radius be r and the radius after t seconds be R.

So, the equation will become:

R = r + 16 t

where 16 t represents the increase in radius in t seconds.

Therefore, we get that an equation to represent this relationship the relation of increase in radius with respect to time as R = r + 16 t where t is the time and r is the initial radius.

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Answer:

[tex]\boldsymbol{\boxed{f(-4) = -1}}[/tex]

Step-by-step explanation:

[tex]\displaystyle f(x) = \left \{ {{x + 3, x < -1} \atop {-4x -2,x \geq 1}} \right.[/tex]

[tex]-4 < -1 \Longrightarrow f(-4) = -4 + 3 =-1[/tex]

[tex]\boxed{f(-4) = -1}[/tex]

Answer:Eric cause 5/12 is greater

Step-by-step explanation:

If an angle is acute, then its supplement is an obtuse angle (true).

An acute angle is an angle that has a measurement that is below 90 degrees (right angle).

The measurement of an obtuse angle is less than 180 degrees but more than angle 90 degrees (right angle).

The supplement of an angle is the measure of that angle subtracted from 180 degrees.

For example, if an acute angle measures 30°, therefore:

The complement of 30° = 90 - 30 = 60°. 60° is also an acute angle.

The supplement of 30° = 180 - 30 = 150°. 150° is an obtuse angle.

Therefore, we can conclude that: if an angle is acute, then its supplement is an obtuse angle (true).

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By solving the percent application, the result is 45% of 120 is 54 and 81 is 75% of 108.

(A) 45% of 120

Multiply 45/100 with 120 =(45/100) x 120 = (45 x120) / 100 = 54.

(B) 81 is 75%

Formula = Number x 100/Percent

             = 81 x 100/ 75 = 108

Following shows the steps on how to derive this formula and find out 75% of what number is 81. Then take 100% of that figure. Setup the equation

81/75% = Y/100%

Solve for Y

Using cross multiplication of two fractions, we get

75Y = 81 x 100

75Y = 8100

Y = 8100

100 = 108

Hence, by solving the percent application, the result is 45% of 120 is 54 and 81 is 75% of 108.

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For graph number 13:

We can see that the domain is: {-3, 3} the range is: R: {-4, 2} this is not a function

For a relation that maps elements x into elements y, we define the domain as the set of the inputs and the range as the set of the outputs. And we say that the relation is a function if each input is mapped into, at most, one output.

If you look at the graph 13 you can see several points, which are of the form (x, y) and are:(-3, 2), (3, 2), (-3, -4), (4, -4)And it makes a little square.

Then you can see that the inputs are -3 and 3, so the domain is:

{-3, 3}

And the outputs are 2 and -4, then the range is:

R: {-4, 2}

And this is not a function, because for example, output 3 is being mapped into two different values.

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Part A: Expression to represent the total amount of juice left in the jar : (0.25 +0.30 + 0.75) - 0.20

Part B: Simplifying above expression using properties of addition and subtraction gives that total amount of juice left is  1.1 liter.

An expression is a group of terms consisting of numbers and mathematical operators ( +, -,*,/) and "=" is not there.

Given that a  jar contains 0.25 liter of apple juice, 0.30 liter of grape juice, 0.75 liter of pineapple. Melissa then drank 0.20 liter of the mixture.

Therefore, total juice in the jar before Melissa drank it = quantity of (apple juice + grape juice + pineapple juice ) = (0.25+ 0.30+0.75) liters

After Melissa drank 0.20 liter juice left = total  juice before - 0.20

Thus, Expression to represent the total amount of juice left in the jar is: (0.25 +0.30 + 0.75) - 0.20

And it can be solved as (0.25 +0.30 + 0.75) - 0.20 = (0.55+0.75)-0.20

                                                                                   = 1.30-0.20 = 1.1 liter

Thus, after simplifying expression we get that the left juice in the jar is 1.1 liter.

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The result of simplifying each number (32)⁻⁴/₅ using the exponent rules is 1/16

To solve this exercise we have to resolve algebraic operations following the exponent rules.

(32)⁻⁴/₅

Base= 32

Exponent= -4/5

As we have a negative exponent, you have to pass the exponent to the denominator:

1/(32)⁴/₅

As we have a fractional exponent, you must convert the exponent to root:

1/[tex]\sqrt[5]{}[/tex](32)⁴

1/[tex]\sqrt[5]{}[/tex]1048576

1/16

In mathematics an exponent is the number of time that a number, called (base) is multiplied by itself. It is also called, power or index.

Example: 3² = 3*3 = 9

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Frequency refers to the number of times an event or a value occurs. A frequency table is a table that lists items and shows the number of times the items occur(C)

Answer:

198299    -    Hundreds

2040949    -    Millions

94.542    -    Hundredths

5848    =    5800

1.83    =    2

459900    =    460000

0.07234    =    0.07

Answer:

8/9×7/4×(-5/8)=8/9×(-5/8)×7/4

Step-by-step explanation:

first equation

The algebraic expression that describes how much Samantha earns after h hours if she makes $14.55 an hour is x = $14.55h, where x is the amount of money she earns and h is the number of hours she works.

An algebraic expression is the combination of numbers and variables in expressing and solving a particular mathematical question.

If Samantha makes $14.55 an hour, and h is the number of hours she works, then the algebraic expression to demonstrate how much she earns is:

x = $14.55h

where x = amount of money she earns

h = number of hours she works

Another real life situation:

A piggy bank contains $25, and $1.50 is added each day. The algebraic expression to demonstrate how much money the piggy bank contains is:

m = $25 + $1.50(d)

where m = amount the piggy bank contains after d days

d = number of days

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By applying the distributive property, the equivalent expression to 3v - (7.9w - 9.3) is: 3v - 7.9w + 9.3.

Two expressions are equivalent if they both have equal values when simplified or evaluated.

To apply the distributive property, the term or operation sign outside the parentheses is used to multiply each of the terms that are within the parentheses.

Given the expression, 3v - (7.9w - 9.3)

Apply the distributive property to find an equivalent expression

3v - (7.9w - 9.3) = 3v -(7.9w) - (-9.3)

3v - (7.9w - 9.3) = 3v - 7.9w + 9.3

Therefore, by applying the distributive property, the sign "-" is distributed to get the equivalent expression to 3v - (7.9w - 9.3, which is: 3v - 7.9w + 9.3.

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Answer:

1/2,187

1/367

3^-7

Step-by-step explanation:

I hope this helped, have an amazing day! :D

Answer:

36

Step-by-step explanation:

3=3

9=3*3 = 3^2

12=2*2*3 = 2^2*3

lcm = 2^2*3^3

      = 4*9

therefore lcm= 36

Answer:

36

Step-by-step explanation:

[tex]\bold{3} \times \bold{12} = 36\\\bold{9} \times 4 = 36[/tex]

The expression represented by 21 increased by twice Gail's height is 21 + 2g

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

21 increased by twice Gail's height

Where

g represents Gail's height

So, we have

21 increased by twice Gail's height ⇒ 21 increased by twice g

Twice means 2*

So, we have

21 increased by twice Gail's height ⇒ 21 increased by 2g

increased by means +

So, we have

21 increased by twice Gail's height ⇒ 21 + 2g

Hence, the expression represented by 21 increased by twice Gail's height is 21 + 2g

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