A home improvement store sells bags of sand, which are labeled as
weighing 35 pounds. The equipment used to package the sand produces bags
with a weight that is within 8 ounces of the labeled weight.
a. Write an absolute value equation to represent the maximum and minimum
weight for the bags of sand.
b. Solve the equation and interpret the result.

Based on the calculation below, we have:

The tuition per year is $36,000; and

The amount of increase in the tuition each year is $1,000.

The tuition per year and the amount of increase in the tuition each year can be calculated as follows:

Number of semesters in a year = 2

Tuition per semester = $18,000

Amount of increase in the tuition each semester = $500

Therefore, we have:

Tuition per year = Number of semesters in a year * Tuition per semester = 2 * $18,000 = $36,000

Amount of increase in the tuition each year =  Number of semesters in a year * Amount of increase in the tuition each semester = 2 * $500 = $1,000

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Interior angles in triangles are all equal to 180 degrees. A triangle's angles are equal to the sum of the angles at each of its three vertices. The sides of the triangle are 35cm, 21cm, and 42cm.

Due to the fact that one outside angle of a triangle is equal to the sum of its other two angles, all of its angles add up to 180 degrees. In other words, the third angle must be added to the other two angles in the triangle (the ones that add up to generate the outer angle) to form a 180-degree angle.

The perimeter of the triangle = 98cm

The ratio of the 3 sides is 5: 3: 6

Take it as 5x, 3x, 6x

where, x is the scaling factor

5x + 3x + 6x = 98

simplifying the above variables, we get

14x = 98

x = 7

The sides of the triangle are

5x = 5 × 7 = 35 cm

3x = 3 × 7 = 21 cm

6x = 6 × 7 = 42 cm

Therefore, the sides of the triangle exists 35 cm, 21 cm and 42 cm.

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Answer:

No, they must sum up to give 360 degrees so it's not possible for them to be equal, if they are equal like 180 degrees each, there won't be a polygon formed!

The expression to represent the number of cousins that Anna has is c + 5.

We are given a statement that says:

Number of cousins that Simon has is equal to = c

Now, it is also given that Anna has 5 more cousins than Simon.

So, we have to write an expression to show the number of cousins that Anna has.

An expression is a combination of constants and variables to express something or a statement.

So, the expression will be made by adding 5 to c

So, we get the expression as:

The number of cousins that Anna has = c + 5

Therefore, we get that, the expression to represent the number of cousins that Anna has is c + 5.

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Answer:

m∠B = 26°

Step-by-step explanation:

∠A and ∠B being complementary means  m∠A + m∠B = 90°

4x + 24 + 3x - 4 = 90

7x + 20 = 90

 7x = 70

  x = 10

m∠B = (3•10 - 4)° = 26°

Answer:

m∠A = 46°

Step-by-step explanation:

The first number (a) is - 5 and the second number (b) is 4.

let the first number be a

let the second number be b

given,

On adding 3 times the first number and 4 times the second number we get 1

=> 3 a + 4 b = 1                -      eq 1

On adding 2 times the first number and 3 times the second number we get 2

=> 2 a + 3 b = 2              -      eq 2

To solve the obtained equations using elimination method

Multiplying eq 1 with 3 and eq 2 with 4, we get

9 a + 12 b = 3                 -    eq 3

8 a + 12 b = 8                -     eq 4

Subtract eq 4 from eq 3

=> a = - 5

On Substituting the value of a in either eq 1 or eq 2, we get

b = 16

Therefore, using the elimination method, we get the first number as - 5 and the second number as 4.

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Answer:

1 5/6 or 11/6

Step-by-step explanation:

2/3+3/4+5/12 = 11/6

Answer:

22/12

Step-by-step explanation:

Add all 2/3 + 3/4 +5/12

=take LCM of 3 , 4, 12

=

12/8 +9 + 5

= 22/12

Answer: [tex]525(2)^{n-1}[/tex]

Step-by-step explanation:

We can represent this as a geometric sequence with first term 525 and common ratio 2.

Answer:

2) (1/3)x + 15 = 45

Step-by-step explanation:

Given that,

→ Katelynn's commute takes 15 minutes more than 1/3 as many min as Petra's.

→ It takes Katelynn 45 minutes.

Then the equation will be,

→ (1/3) times + 15 = 45

→ (1/3)x + 15 = 45

Hence, option (2) is correct.

Answer: C. 7/9

Step-by-step explanation:

For the given situation, we can clearly say that the change in one quantity will also cause a change in the second quantity.

Correlation is a relationship between the values ​​of two variables. A scatter plot is a useful tool for displaying data about two variables as a series of points in the x and y plane and determining whether there is a correlation between the variables.

Causality means that one event causes another. Well-designed experiments can only determine causality. In such experiments, similar groups receive different treatments, and the results of each group are examined.

The collected data on the number of miles driven and fuel expenses. we found that number of miles driven tended to be lower when fuel expenses were high, and the number of miles driven tended to be higher when fuel expenses sales were high.

We do not conclude that more fuel expenses mean fewer miles driven. Likely, an Increased in fuel expenses and the number of miles driven may be caused by a third factor, car mileage. So, the present case is a case of negative correlation.

Negative correlation: y decreases as x increases.

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On simplifying the expression 13.8+ (-11.5) , we get 2.3 . And additions

13.8 + (-11.5) and (-13.8) +  11.5 are numbers will same value and opposite sign.

For adding a negative and a positive number, use the sign of the larger number and subtract.

For example: (–8) + 2 = -6

Given that we have to solve 13.8 + (-11.5) = 13.8-11.5 (we subtract smaller no from larger and will use the sign of lager number that is + here)

13.8+(-11.5) = 13.8-11.5 =2.3

13.8+(-11.5) simply means that 13.8 -11.5 which is subtraction of 11.5 from 13.8

but (-13.8) +  11.5 = -13.8 +11.5  =  -( 13.8 -11.5) [taking -1  common from the expression]

Therefore , -13.8 + 11.5 has same value as 13.8- 11.5 but opposite  in sign.

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Answer:

Positive Irrational Number

Step-by-step explanation:

The whole numbers are the numbers without fractions and it is a collection of positive integers and zero. Integers are the numbers that can be positive, negative or zero, but cannot be a fraction. All rational numbers can be expressed as a fraction whose denominator is non-zero. Whereas, pi cannot be expressed in the fraction of two integers and has no accurate decimal value, so pi is an irrational number.

Answer:

Step-by-step explanation:

8-3k-6 = 2-3k   (distribute -3 to (k+2))

-3k+2 = 2-3k  (8-6 is 2)

2 = 2   (subtract 3k from both sides)

2 = 2 means all real numbers

Answer:

0

Step-by-step explanation:

Distribute

8-3(k+2)=2-3k

8-3k+2=2-3k

subtract

8-6=2

2-3k+2=3k

rearrange

-3k+2=3k

I dont feel like typing the rest, watch khan academy

(ill take your email if you want to review on the weekend)

Answer:

i had this question before and the correct answer was "subtract 12r from both sides of the equation" im sorry if im wrong that was my correct answer when i had this question

Step-by-step explanation:

Answer:

4.92 ft

Step-by-step explanation:

The ladder is the hypotenuse of a right triangle

adjacent  leg / hypotenuse =  cos 75

cos 75 = adjacent leg / 19

19 cos 75 ° = adjacent leg = 4.92 ft

Answer:

11/61

Step-by-step explanation:

Cos is equal to Adjacent over hypotenuse

For angle B, the adjacent side is side BC which is 11 units long

the hypotenuse is 61

11/61

Answer:

at least two solution so c

 A parabola having vertex at the origin and focus at (2,0) is expressed by the following equation:

x = y²/8

  A parabolic function is one that has a quadratic variable, its shape is defined by the intersection of an inclined plane whose angle of inclination with respect to the axis of revolution of the cone is equal to that presented by its generatrix.

Since the vertex and the focal axis are on the same axis, we analyze that:

(y - 0)² = 4p(x - 0)

Focus

0 + p = 2

p = 0 + 2

p= 2

(y - 0)² = 4*2(x - 0)

(Y)² = 8(X)

x = y²/8

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Answer:

Not 100% sure. Hope it helps you

The length of the hypotenuse c is 6

The given parameters are

Legs = a and b

Hypotenuse = c

a = 2√3

c = 2b

Make b the subject in c = 2b

b = 1/2c

By Pythagoras theorem, we have:

c^2 = a^2 + b^2

This gives

c^2 = (2√3)^2 + (1/2c)^2

Evaluate the exponents

c^2 = 12 + 1/4c^2

Evaluate the like terms

1/3c^2 = 12

This gives

c^2 = 36

Take the square roots

c = 6

Hence, the length of the hypotenuse c is 6

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If we find the decimal values of 1/9,2/9 and so on then we will get 1/9=0.11,2/9=0.22,3/9=0.33,4/9=0.44,5/9=0.55,6/9=0.66,7/9=0.77,

8/9=0.88,9/9=1.

Given some values in which the denominator is 12 and we are required to find the values of numbers whose denominator is 9.

Decimal expansion is basically representation of a non-negative real number r is its expression as a sequence of symbols consisting of decimal digits traditionally written with a single separator.

1/9=0.11

2/9=0.22

3/9=0.33

4/9=0.44

5/9=0.55

6/9=0.66

7/9=0.77

8/9=0.88

9/9=1

Hence if we find the values of 1/9,2/9 and so on then we will get decimals of 1/9=0.11,2/9=0.22,3/9=0.33, 4/9=0.44,5/9=0.55,6/9=0.66, 7/9=0.77, 8/9=0.88,9/9=1.

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The new cost function for downloading data is as follows:

C(x) = { 14.50x if 0 <= x < 2

           20.50x if 2 <= x < 5

           24.60x if x >= 5 }

Option D is correct.

Here, we have, the new cost function for downloading data based on the given conditions.

If 0 <= x < 2 gigabytes:

The original cost function is C(x) = 12x.

After raising the rate by $2.50, the new cost function for this range becomes C₁(x) = (12+ 2.50)x = 14.50x.

If x >= 2 gigabytes:

The original cost function is C(x) = 18x.

After raising the rate by $2.50, the new cost function for this range becomes C₂(x) = 18x + 2.50x = 20.50x.

If x >= 5 gigabytes (20% more):

The original cost function is C(x) = 18x.

After raising the rate by $2.50 and charging 20% more, the new cost function for this range becomes C₃(x) = [1.20 * (18+ 2.50)]x = 24.60x.

Now, we need to combine these functions to get a single function for the new rates:

For 0 <= x < 2 gigabytes: C(x) = C₁(x) = 14.50x

For 2 <= x < 5 gigabytes: C(x) = C₂(x) = 20.50x

For x >= 5 gigabytes: C(x) = C₃(x) = 24.60x

So, the new cost function for downloading data is as follows:

C(x) = { 14.50x if 0 <= x < 2

           20.50x if 2 <= x < 5

           24.60x if x >= 5 }

Option D is correct.

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Answer:

The midpoint of the line segment AB

is at (−1, 0).

Step-by-step explanation:

In a general sense the midpoint formula for a line segment whose endpoints are

[tex] \sf ( x_1 + x_2) (y_1 + y_2)[/tex]

would be the mean of the abscissa and the ordinate as seen in the formula below:

[tex] \sf \: (x_m, \: y_m) = ( \frac{x_1 + x_2}{2} , \frac{y_1 + y_2}{2} )[/tex]

When the line segment lies on one axis, then the there would be only one non-zero value in the ordered pair.

Assuming that the line segment AB

is in the x-axis, then the coordinates of the points would be:

[tex] \sf \: A(−2, 0)B(0,0)[/tex]

To get the midpoint, substitute the points above in the formula for the midpoint:

[tex] \sf \: (x_m, \: y_m) = ( \frac{x_1 + x_2}{2} , \frac{y_1 + y_2}{2} ) \\ \sf \: = ( \frac{ - 2 + 0}{2} ),0 \\ \sf \: = ( \frac{ - 2}{2} ), 0 \: \: \: \: \: \: \: \: \\ \sf \: ( - 1, 0)[/tex]

The midpoint of the line segment AB

is at (−1, 0).

Answer:

-20

Step-by-step explanation:

Answer:

[tex]{ \tt{area = \pi {r}^{2} }} \\ \\ { \tt{ = 3.14 \times {6}^{2} }} \\ \\ = 113.04 \: mm {}^{2} [/tex]

Answer:

A = 113.1 mm²

Step-by-step explanation:

Area of circle = πr²

A = 22/7(6mm)²

A = 22/7(36mm²)

A = 792mm²/7

A = 113.1 mm²

Therefore the area of the circle is 113.1mm².

Answer: y - 6 = -(1/2)(x+1)

Step-by-step explanation:

1. First step is to remember point slope form (a common way of expressing the equation for a line).

y - y1 = m(x - x1)

2. Next fill in the data we are given.

y - 6 = m(x -(-1)) ----> y - 6 = m(x + 1)

3. Next step is to find the value of the slope (m) using slope formula.

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

4. Fill in the data

m = (5 - 6) / (1 +1) = - 1 /2

5. Add the calculated slope to the point slope form.

y - 6 = -(1/2)(x+1)

Answer:

The answers are 45f - 42 and -42+45f

Step-by-step explanation:

-5(-9f + 7) - 7

45f (-35 -7)

45f -42

also

-42 + 45f

The slope-intercept form is y = 1/2x - 4 for line perpendicular to 4 x+2 y=7 through (4,-2) ,

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

In an equation, perpendicular lines have the opposite reciprocal slope. In other words, if a line's slope is a positive fraction, its reciprocal slope is negative.

Here given that  4 x+2 y=7

can also be written as

y = -2x + 7/2

Here -2 is the slope and 7/2 is the y-intercept

To find a perpendicular line to the following equation, use the opposite reciprocal slope and point, then solve using the point-slope formula.

y - y₁ = m(x - x₁)

We have, m = 1/2, x₁ = 4and y₁ = -2

y - (-2)= 1/2(x - 4)

y + 2= 1/2x - 2

y = 1/2x - 4

We have the slope-intercept form y = 1/2x - 4 of a line  perpendicular to  4 x+2 y=7 through (4,-2)

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