For each function, determine whether y varies directly with x . If so, what is the constant of variation?
a. 5 x+3 y=0

Step-by-step explanation:

10^2=100x8 =800

800=8x100

10^2 =100.The reason is, you are basically doing 10x10=100x8=800.

Answer: (x-2)(x+7)

Step-by-step explanation:

Answer: (x+7)(x-2)

Step-by-step explanation:

[tex]x^2+5x-14=\\x^2+7x-2x-14=\\x(x+7)-2(x+7)=\\(x+7)(x-2)[/tex]

Determining the best path involves the evaluation of multiple paths to the same destination network and selecting the optimum or shortest path.

How is the best route to a network determined?

7 types of routing protocols -

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Answer:

Step-by-step explanation:

Let,  

For English = x min.

For Biology= (x+30) min.

For Math= 3(x+30) min.

2 hours= 2*60 = 120 min.

Now,  x+(x+30)+3(x+30)=120

Or, x=  0 min.

For English = 0 min.

For Biology= 30 min.

For Math= 90 min

Ahmad spent 159 minutes for the scooter ride

Ahmad paid $3 fee to start the scooter ride

She also paid 11 cents per minutes of the ride

The total bill at the end of the ride is $20.49

The first step is to convert 11 cents to dollars

= 11/100

= 0.11

Therefore the number of minutes can be calculated as follows

20.49 = 0.11x + 3

collect the like terms

20.49 - 3 = 0.11x

17.49 = 0.11x

x= 17.49/0.11

x= 159

Hence Ahmad spent 159 minutes for the scooter ride

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Albert drove 5 miles farther than Tom if their speed were 50mi/h and 65 mi/hr.

Distance is the size or extent of the displacement between two places. Remember that the travel distance between two points is not the same as their distance from one another. The distance traveled is the total distance traveled to get from one place to another. Distance traveled is not a vector.

Tom's distance is calculated as

Put D= D₁, r = 50 miles per hour, and t = 2.5 hours in the distance formula

D₁ = (50 mi/h)·(2.5 h)

D₁ = 125 mi

Albert's distance is calculated as

Put D= D₂, r = 65 miles per hour, and t = 2 hours in the distance formula

D₂ = (65 mi/h)·(2 h)

D₂ = 130 mi

Comparing both the distances

Albert drove 130 -125 = 5 miles farther than Tom.

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Answer:

8cm

Step-by-step explanation:

Given-;

BC(base)=6cm

AC(hypotenuse)=10cm

To Find-:

AB(Perpendicular)=?

Solution-:

As we know that

Pythagoras Theorem=>H²=P²+B²

By using it

=>10²=P²+6²

=>100=P²+36

=>100-36=P²

=>64=P²

Therefore, the height of AB is 8cm.

Answer:        0= negative 6

Step-by-step explanation:

Answer:

1+4×1

1+4

5

I think this is the correct answer if it isn't pls notify me

Experimenters show a link between adult-onset diabetes and obesity is most likely a causal relationship. Option C is correct.

A causal relationship exists when one variable in a data set directly affects another variable.

As a result, one thing triggers another to happen. A causal link is also known as cause and effect.

According to studies and experiments, there is a clear causal link between adult-onset diabetes and obesity. A causal relationship demonstrates that one occurrence is the cause and the other is the outcome.

Researchers have found what is most likely a causal association between adult-onset diabetes and obesity.

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Answer:

D

Step-by-step explanation:

5[tex]\sqrt{2}[/tex] + [tex]\sqrt{2}[/tex] + 3[tex]\sqrt{2}[/tex] ← factor out [tex]\sqrt{2}[/tex] from each term

= [tex]\sqrt{2}[/tex] (5 + 1 + 3)

= 9[tex]\sqrt{2}[/tex]

Answer:

0.6508

Step-by-step explanation:

The standard normal distribution has a mean μ= 1 and standard deviation σ = 0

The area under the normal curve for any z value say Z i.e. P(z ≤ Z) can be read off from the Standard Normal Tables or just use a statistical calculator

Using a calculator is best
I see the lower z score as - 2.61 and the upper z score as 0.4

P(-2.61 ≤ z ≤ 0.4) = P(0.4) - P(-2.61)

P(z ≤ 0.4) = 0.65542

P(z ≤ -2.6) = 0.0045271

P(z ≤ 0.4) - P(z ≤ -2.6)  = 0.65542 - 0.0045271  = 0.6507588 = 0.6508 rounded to 4 decimal places

(Note: some calculators are able to directly compute the area between two z values)

5:9 is degrees Celsius and the second element is its equivalent in degrees Fahrenheit.

What does a temperature in Fahrenheit mean?

F = (9/5)C+32

F = C x 9/5 + 32

C = (F - 32) x 5/9

The above equations could easily be derived by the following relationships:

Freezing Point = 0C or 32F and Boiling Point = 100C or 212F

Range from freezing point to boiling point = 100C or 180F,

i.e. C : F = 100:180 = 5:9

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Answer:

-31

Step-by-step explanation:

You use pemdas which is

parathesis

exponents

multiply or divide, use in order

then add or subtract, use in order

(-8)+(-3)+(-4)(7)÷14+9(-2)

multiply first

-4*7=-28

(-8)+(-3)+(-28)÷14+9(-2)

Divide next

-28÷14=-2

(-8)+(-3)+(-2)+9(-2)

multiply again

9*(-2)=-18

(-8)+(-3)+(-2)+(-18)

now add

-8+(-3)=-11

(-11)+(-2)+(-18)

add again

-11+(-2)=-13

(-13)+(-18)

add for the last time

-13+(-18)=-31

Answer:

its equivilant

Step-by-step explanation:

Equivalent expressions are:

[tex]2^{3t}.2^t[/tex] / 4 and [tex]8^{t}.2^t[/tex] / [tex]2^{0.5}.8^{0.5}[/tex].

Options B and C are the correct answer.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Solve each expression.

[tex]16^{t-0.5}[/tex]

= [tex]2^{4t - 2}[/tex]

Now,

1)

[tex]2^{3t}.2^t[/tex] / 16

= [tex]2^{4t}[/tex] / [tex]2^4[/tex]

= [tex]2^{4t - 4}[/tex]

2)

[tex]2^{3t}.2^t[/tex] / 4

= [tex]2^{4t}[/tex] / [tex]2^2[/tex]

= [tex]2^{4t - 2}[/tex]

3)

[tex]8^{t}.2^t[/tex] / [tex]2^{0.5}.8^{0.5}[/tex]

= [tex]2^{3t + t}[/tex] / [tex]2^{0.5 + 1.5}[/tex]

= [tex]2^{4t}[/tex] / [tex]2^2[/tex]

= [tex]2^{4t - 2}[/tex]

Thus,

Equivalent expressions are:

[tex]2^{3t}.2^t[/tex] / 4 and [tex]8^{t}.2^t[/tex] / [tex]2^{0.5}.8^{0.5}[/tex].

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Answer: width is 49

Step-by-step explanation: 84-35= 49

The number of times that (4 x 10⁴) is higher than (1.25 x 10²) is 3.2 × 10².

It should be noted that the information is to find the number of times that (4 x 10⁴) is higher than (1.25 x 10²).

This will be calculated by dividing the values we have.

= (4 × 10⁴) / (1.25 × 10²)

= 3.2 × 10²

In conclusion, the number of times that (4 x 10⁴) is higher than (1.25 x 10²) is 3.2 × 10².

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The initial velocity of the runner was 2 m/s, and the runner stopped after 8 seconds. Therefore, option (b) is correct.

The velocity of an object helps to calculate the speed of the object in a particular direction. A velocity-time graphs shows the speed and direction of an object that travels over a specific period of time. They are also known as speed-time graphs too.

The vertical axis represents the velocity of an object and horizontal axis represents the time taken to cover particular distance with the speed.

Here, the ordered pairs given in the question are (0,2), (6,8) going through one line segment and for other line segment it is (6,8) and (8,0) respectively. We have to conclude various statement that matches best for the ordered pairs given to us. Let's proceed to solve this.

For (0,2), this ordered pair conclude that: At t = 0 sec, the initial velocity of the runner was 2m/s respectively.

Similarly, for (6,8) this represents that at t = 6 sec the velocity of the runner reaches at maximum. i.e., 6m/s and acceleration is 1 m/s² also from this ordered pair for another line segment a state of deceleration begins which ultimately reduces the acceleration of an object.

For (8,0), this ordered pair represents that at t = 8 sec the velocity of the object which is the final velocity it become 0 m/s i.e., the runner stopped.

From all the ordered pair we have concluded that option (b) is correct which says that the initial velocity of the runner was 2 m/s, and the runner stopped after 8 seconds.

Hence, option (b) is correct.

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The given sequence is geometric, with the common ratio = 2.

Given: 1, 2, 4, 8, ...

=> 2⁰, 2¹, 2², 2³, ...

We can see that the quotient of each two consecutive terms is 2, in the given sequence, following the necessary condition for a sequence to be geometric.

Thus, The given sequence is geometric, with the common ratio = 2.

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The required value of constant of variation, k does not exist for which x and y vary directly.

What is the constant of proportion?

A constant of proportion is illustrated as the ratio which relates two given quantities with each other in the relationship of proportion. Constant of proportion is also called constant variation, rate of change, and constant ratio.

Solving for the value of constant of variation

When a quantity varies directly with others, then we have a relation, y = kx, where k is the constant of the proportion      —-- 1

Given relation is y = 4x - 3

Comparing with equation 1, we get, that y does not vary directly with x

Hence, the required value of constant of variation does not exist.

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The value of given expression 100−20.2×4.5 is 9.1 .

We have given an expression 100−20.2×4.5  .

Using BODMAS we will first solve the multiplication term than the subtraction term .

We will do multiplication operation which is given by

20.2 ×  4.5  = 90.9

Now , we will subtract 90.9 from 100 , we get

100 - 90.9 = 9.1

Hence , the value is 9.1

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Answer:

2x²-10x+3=0

Step-by-step explanation:

2x²+1 - 5(2x)+2=0

2x²+1 - 10x+2=0

Combine like terms.

2x²+1 - 10x+2=0

2x²-10x+3=0

Hope this helps!

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Have a great day!

Answer:

5/12

Step-by-step explanation:

Answer:

24 is the least common factor of 5/8 - 5/12.

Answer:

Step-by-step explanation:

2 2/3

The inequality to model this situation is given by x>60 .

Inequality is defined as the relationship between a variable and a constant or two variables which can be written in the form of an equation using the notations < , > , ≤ or ≥ .

Let us consider the number of bags of lettuce bought be x.

Therefore amount needed to buy x bags from Val's veggies is :

250 + 1.5 x

And the amount needed to buy x bags from Sally's Salads is :

100 + 4 x

Now it is given that Val's Veggies need to be cheaper than Sally 's.

a) Therefore we will write an inequality and solve it for x:

∴ 250 + 1.5 x < 100 + 4 x

moving the variables and constants together

or, 1.5 x - 4 x < 100 - 250

or, - 2.5x < -150

or, x > 60

b) Therefore from the inequality we can conclude more than 60 bags of lettuce needs to be purchased for Val's cost to be cheaper.

c) Set notation: {x ∈ Z | x>60}

interval notation : x∈(60.∞)

Therefore from the inequality , the number of bags to be purchased must be more than 60.

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The measure of the angle ADB is 65 degrees

The angles are given as

Angle ADB = (7x + 2) degrees

Angle CDB = (3x - 2) degrees

The angles are complementary angles

This means that they add up to 90 degrees

So, we have:

ADB + CDB = 90

This gives

7x + 2 + 3x - 2 = 90

Evaluate

10x = 90

Divide by 10

x = 9

Substitute x = 9 in Angle ADB = (7x + 2) degrees

Angle ADB = (7 x 9 + 2) degrees

Evaluate

Angle ADB = 65 degrees

Hence, the measure of the angle ADB is 65 degrees

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The given rational and irrational numbers can be ordered from least to greatest as follows; -2 3/5 < 10/3 < 3 7/8 < 3.9 < √20.

It follows from the task content that the numbers given are rational and irrational numbers.

To order the numbers, they should be converted to decimal numbers as follows;

-2 3/5 = -2.6

√20 = 4.47

3.9 = 3.9

10/3 = 3.33

3 7/8 = 3.875

Hence, the order from least to greatest is; -2 3/5 < 10/3 < 3 7/8 < 3.9 < √20.

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the number of pennies that Ella has in all is 500 pennies.

Number of stickers = 50

Cost of each sticker = 10 pennies

Now, we need to find the total pennies Ella has.

We will use multiplication to find the same.

So, by using the operation of multiplication, we get that:

Number of pennies = 10 × 50 pennies.

Number of pennies = 500 pennies.

Therefore, we get that, the number of pennies that Ella has in all is 500 pennies.

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The value of x is 9 and the measure of AB is 27.

A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.

We need to Find x and AB if B is between A and C,

Given that AB=3x, BC=14, and AC=41.

AB + BC = AC

3x+14=41

3x=27

X=9

Now substitute to find the AB;

AB=3(9)

AB =27

Therefore the value of x is 9 and the measure of AB is 27.

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