The time is takes an object to move a certain distance is inversely propotional to the speed that it's travelling at.
it takes a car 12 minutes to travel the length of a road if it goes at an average speed of 60mph

a) How long would it take the car to travel down the same road if it travelled at an average speed of 30mph
B) if it takes the car 36 minutes to drive down the road, what will it's average speed

Jada is planning a kayak trip. She finds an expression for the time, T(s), in hours it takes her to paddle 10 kilometers upstream in terms of s, the speed of the current in kilometers per hour. Jada gets if she allows s to take on any value between 0 and 7.5.

The domain of the function that represents Jada's trip is the set of input value the function can take

The appropriate domain is all real numbers except

x = 5.5

by looking at the graph, we can see that:

The x-value starts at negative infinity, and ends near 5.5

The x-value then continues near 5.5, and ends at positive infinity

This means that the input of the graph cannot be 5.5

Hence, an appropriate domain would be: x # 5.5

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The graph with the y-intercept of 1 and a slope of -2/3 is added as an attachment

Linear equations are equations whose slopes are constant average rates of change.

The given parameters are

A linear equation is represented as

y = slope * x + y-intercept i.e. y = mx + c

Substitute the known values in the above equation

So, we have the following equation

y = -2/3x + 1

Hence. the linear equation is y = -2/3x + 1

See attachment for the graph

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The number of kilograms that the crane is lifting, based on the maximum it can lift and the proportion being lifted is 160 kilos

The number of kilos that the crane is lifting can be found by the formula :

= Maximum kilogram capacity x Proportion of maximum being lifted

Maximum kilogram capacity = 224 kg

Proportion of maximum being lifted = 5 / 7

The kilos being lifted by the crane is therefore :

= 224 x 5/7

= 1, 120 / 7

= 160 kilos

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The total number of cattle Frank currently owned could be C)350

The problem is asking multiples of 7.

Multiples of 7 come into play after working the the percentage as follows

Frank sold 30%, the percentage left is

= 100% - 30%

= 70%

= 0.7

The multiple of 7 that is a number 7 will divide without remainder here is 350 and this is the correct answer.

= 350 / 0.7

= 500

This means Frank had 500 cattle sold

0.3 * 500 = 150

currently having

= 500 * 0.7 = 350

= 500 - 150 = 350

Remember that a cattle will always be in whole number

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Answer:

22. 2 (-4) = -8

23. (2(-4) + 11) = (-8 + 11) = 3

24. -3 (5 (-4) = -3 (-20) = 60

Answer:

  22.  8

  23.  3

  24.  -60

Step-by-step explanation:

You want the values of the given absolute value expressions when x = -4.

The absolute value function changes the sign to positive, if it isn't already.

  2|-4| = 2(4) = 8

  |2(-4) +11| = |-8 +11| = |3| = 3

  -3|5(-4)| = -3|-20| = -3(20) = -60

The missing values are:

m∠1 = 36°

m∠2 = 122°

m∠3 = 122°

m∠4 = 38°

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

The figure has two triangles.

58° and m∠3 is a straight angle.

58 + m∠3 = 180

m∠3 = 180 - 58

m∠3 = 122

Now,

m∠3 + m∠4 + 20 = 180

122 + m∠4 + 20 = 180

m∠4 = 180 - 122 - 20

m∠4 = 180 - 142

m∠4 = 38

m∠3 and m2 are opposite angles.

Opposite angles are equal.

m∠3 = m∠2 = 122

Now,

m∠1 + m∠2 + 22 = 180

m∠1 + 122 + 22 = 180

m∠1 = 180 - 144

m∠1 = 36

Thus,

The missing values are:

m∠1 = 36°

m∠2 = 122°

m∠3 = 122°

m∠4 = 38°

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The standard form of the given fractions are;

(i)  −45/30

(ii)  16/−36

(iii)  −3/−15

(iv)  68/−119

A fraction is said to be in standard form when both the numerator and denominator are co-prime numbers. Thus;

1) −45/30; Divide both numerator and denominator by 15 to get;

(−45 ÷ 15)/30

=  -3/2.

(2)  16/−36; Divide both numerator and denominator by 4 to get;

(16 ÷ 4)/(−36 ÷ 4)

= -4/9

(iii)  −3/−15; Divide both numerator and denominator by -3 to get;

(-3 ÷ 4)/(−15 ÷ 4)

1/5

(iv)  68/−119; Divide both numerator and denominator by 19 to get; -4/7

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Complete question is;

Reduce each of the following rational numbers in standard form:

(i)  −45/30

(ii)  16/−36

(iii)  −3/−15

(iv)  68/−119

​

Given equation 2x + 4y = 4 has infinitely many solutions.

We have been given an equation 2x + 4y = 4

We need to find the number of solutions.

Above equation is a linear equation with two variables.

We know that, a linear equation in two variables has infinitely many solutions.

For any value real value of x we can find corresponding value of y.

Since x can takes infinitely many inputs the output would be infinitely many.

Therefore, given equation 2x + 4y = 4 has infinitely many solutions.

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Patrick is vegetarian and Thelma is non vegetarian.

What are vegetarian?

The practice of not eating any meat is known as vegetarianism. It might also mean avoiding eating any leftovers from animal slaughter. There are several reasons to embrace a vegetarian diet. Due to their respect for sentient animal life, many people refrain from eating meat.

Main Body:

As Thelma ordered Turkey sandwich with extra mustard and turkey is an animal , which makes her non vegetarian so it is obvious that Patrick is a vegetarian and Thelma is non vegetarian.

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Quadratic equation that passes through the points (-4,2) and (1,2) and a form a graph of horizontal line y =2.

Graph is attached.

As given in the question,

Quadratic equation passes through the points (-4,2) and (1,2)

(x₁, y₁) =(-4,2)

(x₂ ,y₂) = (1,2)

(y-y₁)/ (x-x₁) = (y₂ -y₁)/(x₂ -x₁)

⇒(y-2)/(x +4) =(2-2)/)1+4)

⇒ (y-2)/(x+4) =0

⇒y -2 =0

⇒y =2

Quadratic equation formed from the given points (-4,2) and (1,2) is y =2.

which represents the horizontal line and does not have any vertex.

Graph of the quadratic equation y =2 is attached.

Therefore, quadratic equation that passes through the points (-4,2) and (1,2) and a form a graph of horizontal line y =2.

Graph is attached.

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A total of 2587 students attended the collage

From the question, the given parameters are:

The above parameters implies that

Number of students that attended = 56% x Total number of students

Represent the total number of students with x

So, we have the following representation

Number of students that attended = 56% * x

Where

x = 4620

So, we have

Number of students that attended = 56% x 4620

Evaluate the products

Number of students that attended  = 2587.2

Approximate

Number of students that attended = 2587

Hence, 2587 of the students attended the collage

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Answer:

G LCM (least common multiple) of 3, 9, and 12. After doing that, find the number that is between 61 and 107.

Step-by-step explanation:

Least common multiple (lcm) is where g finds out the number that can be divided by all the numbers (3, 9, and 12 in this case) and still come out with a whole number.

The greatest temperature in Africa occur is 367 feet.

The collection of positive and negative integers is known as an integer. Integers, like whole numbers, do not include the fractional portion.

Given:

The greatest temperature ever recorded in the United States occurred at an elevation of 178 feet below sea level.

Using integers we represent it as (-178) feet.

and, greatest temperature ever recorded in Africa 545 feet greater than in the United States

= -178 + 545

= 367 feet.

Hence, The greatest temperature in Africa occur is 367 feet.

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The price for 7 bags of trail mix and 4 bananas is  15.45  dollars.

The expression for x trail bag and y bananas is 1.35x + 1.50y.

In maths, an expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division etc.)

Therefore, the cost of a bag of trail mix at the corner store is 1.35 dollars  and the cost of a banana is 1.5 dollars.

The cost for 7 bags of trail mix and 4 bananas can be computed as follows;

let

x = bags of trail mix

y = number of banana

Therefore,

1.35x + 1.50y

1.35(7) + 1.50(4) = 9.45 + 6 = 15.45

Therefore, let's find the expression for x trail bag and y bananas.

Hence,

1.35x + 1.50y

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Answer:

if the selling price of the radio is Arya 4321 and loss e79 find the cost price of the radio

Answer:

LCM = 42

Step-by-step explanation:

There are many ways to do this.

Listing Multiples:

Find and list multiples of each number until the first common multiple is found. This is the lowest common multiple.

Multiples of 14:

14, 28, 42, 56, 70

Multiples of 21:

21, 42, 63, 84

Therefore,

LCM(14, 21) = 42

Prime Factorization:

List all prime factors for each number.

Prime Factorization of 14 is:

2 x 7  =>  21 x 71

Prime Factorization of 21 is:

3 x 7  =>  31 x 71

For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.

The new superset list is

2, 3, 7

Multiply these factors together to find the LCM.

LCM = 2 x 3 x 7 = 42

In exponential form:

LCM = 21 x 31 x 71 = 42

LCM = 42

Therefore,

LCM(14, 21) = 42

Cake / Ladder:

Divide your numbers by prime numbers as long as both numbers are evenly divisible by that prime.

Cake / Ladder

7 14 21

2       3

When there are no more primes that evenly divide into both numbers you are done.

The LCM is the product of the numbers in the L shape, left column and bottom row.

LCM = 7 x 2 x 3

LCM = 42

Therefore,

LCM(14, 21) = 42

Division Method:

Write your numbers in the top row.

Divide your numbers by prime numbers as long as at least one of your numbers is evenly divisible by a prime number.

Division Table

2 14 21

3 7 21

7 7 7

1       1

Bring down any numbers that are not evenly divisible by the prime number.

When the last row of results is all 1's you are done.

Find the product of the prime numbers in the first column to get the LCM:

LCM = 2 x 3 x 7

LCM = 42

Therefore,

LCM(14, 21) = 42

GCF Method:

LCM(14,21) = (14 × 21) / GCF(14,21)

= (14 × 21) / 7

= 294 / 7

= 42

Therefore,

LCM(14, 21) = 42

Venn Diagram:

Inside circle 14: 2

In between circles: 7

Inside circle 21: 3

Then, use prime factorization.

Find the set of prime factors for each number.

Prime Factorization Set for 14 is:

2, 7

Prime Factorization Set for 21 is:

3, 7

Identify the intersections of prime numbers and put them into the Venn Diagram where their circles intersect. Remove the numbers from the original sets.

14 ∩ 21

7

With the remaining prime numbers in each set, if any, put them into their respective circles, not in intersections.

14

2

21

3

Find the union of the sets in the Venn Diagram. This is the superset of all of the prime numbers in the diagram.

14 ∪ 21

The new superset list is

2, 3, 7

Multiply these factors together to find the LCM.

LCM = 2 x 3 x 7 = 42

LCM = 42

Therefore,

LCM(14, 21) = 42

Answer:

-2/3 or -0.6666

Step-by-step explanation:

-3x + 6 = 4 -6x

Let's move the x to one side

-3x +6x=4-6

Combine like terms

3x = -2

Divide both sides by 3

-2/3=x

or -0.666666

There is a total of 2152 yes votes

From the question, the statement is given as

The ratio of yes votes to no votes was 4 to 7

Mathematically, this can be represented as

Ratio = 4 : 7

Alternatively, we have

Yes : No = 4 : 7

Express the ratio as fraction

Yes = Yes/Yes + No

So, we have

Yes = 4/4 + 7

Evaluate the sum

Yes = 4/11

From the question, we have

Total votes = 5918

So, we have

Yes = 4/11 * 5918

Evaluate

Yes = 2152

Hence, the number of yes votes is 2152

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Answer:

50.24

Step-by-step explanation:

so u subtract the distanse not 9-4 u have to find a porportional ratio it was 100 - 50 or something add u get 50.24

tbh i didnt knw i just searched it up and im only in 6th grade so im not the the smartest in the world

i have no clue what the second on is so good luck with that

The percent of error concerning Alton's estimated attendance and actual attendance at the band concert is 30%.

The percent of error is a measure showing how big an error is between the estimate and actual results.

The smaller the percent of error the closer the estimate is to the actual observations, and vice versa.

Actual Observed Value = 200

Expected Value = 260

Percentage of error = (Expected Value - Observed Value) ÷ Actual Value

= (260 - 200)/200

= 60/200

= 0.3

= 30%

Thus, we can conclude that Alton made a 30% error in his estimate of attendance at the band concert.

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The original price of desk bought by kevin is $780.

What is original price?

To calculate the initial worth of a reduced or sale item, you wish to grasp the sale worth and also the discount proportion. The calculations embody an easy formula that divides the sale worth by the results of one minus the discount in proportion form.

Main body:

Let the original price of desk be x.

After sale price of desk - $280.80

According to question, 36% of original price is what kevin bought it for.

So the equation formed is,

⇒36% of x = 280.80

⇒0.36*x = 280.80

⇒x = 280.80/ 0.36

⇒x = $780

Hence the original price of desk is $780.

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The measure of an obtuse angle is greater than 90° but less than 180°

An obtuse angle is a type of angle that is always larger than 90° but less than 180°. In other words, it lies between 90° and 180°.

An angle is the space between two intersecting lines or surfaces at or close to the point where they meet.

Angles are mostly measured in degrees. But it can also be measured in radian. Examples of obtuse angle are 91°, 100°, 150° e.t.c

Other examples of angles are acute angle, reflex angle , right angle.

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If a claim will be made against such a policy and an average claim of $4900. the insurance company should make on average off of each policy holder is $683.5.

Using this formula to find the amount

Amount = [Percentage claim × ( Base price - Average claim)] + [(1 - percentage claim) × Base price]

Let plug in the formula

Amount = [0.085 × ($1,100 - $4,900)] + [(1-0.085) × $1,100]

Amount = [0.085 ×  (- $3,800)] + [(0.915 × $1,100]

Amount = -$325+ $1,006.5

Amount = $683.5

Therefore the insurance company will make the amount of $683.5.

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The solution of the equation given as 1/3a² + a=0 is a = 3

From the question, we have the following equation that can be used in our computation:

1/3a^2+a=0

Rewrite the equation properly

So, we have

1/3a² + a=0

Multiply through the above equation by 3

So, we have the following equation

3 * (1/3a² + a) =0 * 3

Evaluate the products

So, the equation becomes

a² + 3a = 0

Next, we divide through the equation by the variable a

This gives

a + 3 = 0

Subtract 3 from both sides of the equation

i.e. Add -3 to both sides of the equation

a = -3

The above equation cannot be solved further.

So, we leave it like that and stop solving

Hence, the solution to the equation is a = -3

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The independent variable x is the hour of work.

The dependent variable y is the total money Ethan earn per visit.

The y-intercept is 25.

The slope is 22.

Ethan charges a one time fee of 25 dollars. For each visit Ethan earns 22 dollars for each hour of work.

Ethan repairs household appliances like dishwashers and refrigerators. For each visit, he charges 25 plus 22 per hour of work.

A linear equation that expresses the total amount of money Ethan earns per visit is y = 25 + 22x.

Using slope intercept equation,

y = mx + b

where

y = 25 + 22x

The independent variable x is the hour of work.

The dependent variable y is the total money Ethan earn per visit.  

The y-intercept is the value of y when x = 0. Therefore, the y-intercept is 25.

The slope is the change in the dependent variable with respect to the change in the independent variable. The slope is 22.

Ethan charges a one time fee of 25 dollars. For each visit Ethan earns 22 dollars for each hour of work.

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Answer:

245.57

Step-by-step explanation:

[tex]P\left(1+0.05)^{10}=400 \\ \\ P=\frac{400}{(1.05)^{10}} \\ \\ P \approx 245.57[/tex]

The function y = 4 is a straight line and not an exponential function.

Given, a function y = 4

now, we have to test the function is exponential or not

As, the function is a straight line graph i.e. y = 4.

Now, the function y = 4 is a straight line graph which is parallel to the x-axis.

So, the function y = 4 is not an exponential function

Hence, the function y = 4 is a straight line and not an exponential function.

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The value of x in 7-3(2x-1)= 2x+26 is -4

Linear equation is is a mathematical statement, which has an equal sign (=) between the algebraic expression. Linear equations are the equations of degree 1. It is the equation for the straight line. The solutions of linear equations will generate values, which when substituted for the unknown values, make the equation true. In the case of one variable, there is only one solution. For example, the equation x + 3= 0 has only one solution as x = -3.

To find x in 7-3(2x-1)= 2x+26 ,we solve the parentheses first which will give

7- 6x+3= 2x+26

collect the like terms

-6x-2x=26-3-7

-8x= 16

divide both side by -8

-8x/-8= 16/-8

therefore x= -2

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