simplfy 4x(2x-3) distributive property

Final answer:

The inequality that represents this situation is: 500 - 40w < 30, where w represents the number of weeks that have passed.

Explanation:

The situation can be represented by the inequality:

500 - 40w < 30

where w represents the number of weeks that have passed.

This inequality states that the amount of money remaining in Kayla's account (500 - 40w) must be less than $30 for her to have to pay a penalty. If Kayla's account falls below $30, she would have to pay a penalty because she does not have enough money to cover her regular expenses.

For example, if we substitute w = 10 into the inequality, we get 500 - (40 × 10) < 30, which simplifies to 100 < 30. Since 100 is not less than 30, Kayla would not have to pay a penalty.

well first do -6-2 which is -8 so next you would multiply -8 and 3 which is -24 then add 1 that makes it -23 then multiply that by 3 then you get -2+(-69) which is -71 so then you add -71 and 14 then you get -57 hope this helped :3

Answer:

x+1 is greater than or equal to -7

Step-by-step explanation:

x is the first integer and x+1 is the next (consecutive) integer.

At least stands for greater than or equal to

x+x+1 is greater than or equal to -15

Subtract 1 from each side

2x is greater than or equal to -16

x is greater than or equal to -8

This means

x+1 is greater than or equal to -7

The smallest values of the integers are: x+1 ≥ -7

Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign. It shows the relationship of equality between the expression written on the left side with the expression written on the right side. In every equation in math, we have, L.H.S = R.H.S (left hand side = right hand side).

Parts of an Equation

There are different parts of an equation which include coefficients, variables, operators, constants, terms, expressions, and an equal to sign. When we write an equation, it is mandatory to have an "=" sign, and terms on both sides. Both sides should be equal to each other. An equation doesn't need to have multiple terms on either of the sides, having variables, and operators. An equation can be formed without these as well, for example, 5 + 10 = 15. This is an arithmetic equation with no variables. As opposed to this, an equation with variables is an algebraic equation.

let the consecutive integers are x  and x+1.

So,

x+ (X+ 1)= -15

2x + 1 =-15

2x= -16

x= -8

Hence, x+1 ≥ -7

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Final answer:

The difference between the product of 26.22 and 3.09 and the sum of 3.507, 2.08, 11.5, and 16.712 is 47.2208.

Explanation:

The difference between the product and the sum can be found by first calculating the product of 26.22 and 3.09 and then calculating the sum of 3.507, 2.08, 11.5, and 16.712. Once both of these values are calculated, subtract the sum from the product to find the difference.

To calculate the product of 26.22 and 3.09, you would multiply these two numbers:

26.22 × 3.09 = 81.0198

To calculate the sum of 3.507, 2.08, 11.5, and 16.712, you would add these numbers together:

3.507 + 2.08 + 11.5 + 16.712 = 33.799

Finally, to find the difference, subtract the sum from the product:

81.0198 - 33.799 = 47.2208

The difference between the product of 26.22 and 3.09 and the sum of 3.507, 2.08, 11.5, and 16.712 is 47.2208.

To convert hours to minutes, multiply the number of hours by 60. When adding or subtracting time, work with like units first and simplify when needed. For conversion, it's also helpful to understand that 60 minutes equals 1 hour for fractional time units.

Converting units of time such as hours to minutes involves understanding the relationship between these units. In this case, the conversion factor between hours and minutes is that 1 hour is equivalent to 60 minutes.

Therefore, to convert hours into minutes, you would multiply the number of hours by 60.

Here's an example on how to convert 5 hours to minutes:
5 hours = 5 × 60 minutes = 300 minutes.

In this context, let's look at a smaller unit to larger unit conversion example:
120 seconds = 120 ÷ 60 = 2 minutes. Dividing the number of seconds by 60 converts seconds to minutes.

Now, let's consider another example by converting a larger unit to a smaller unit:
4 hours = 4 × 60 minutes = 240 minutes. Multiplying the number of hours by 60 converts hours to minutes.

Adding measures of time involves combining like units first, as in the example of adding 1 hour 55 minutes to 45 minutes, resulting in 1 hour 100 minutes. This can be simplified by recognizing that 60 minutes is equivalent to 1 hour, resulting in a total of 2 hours.

Subtraction of time units might require 'borrowing' from a larger unit, such as borrowing 60 minutes from an hour, to facilitate the subtraction process.

Hence, for 5 hours 10 minutes minus 30 minutes, we adjust it to 4 hours 70 minutes and then subtract, resulting in 4 hours 40 minutes.

Answer:

Givens:

To know if the have enough flour, we just need to sum both amounts, but before that, we need to transform all mixed numbers into fractions

[tex]2\frac{1}{3}= \frac{7}{3}[/tex]

[tex]1\frac{3}{4}=\frac{7}{4}[/tex]

Now, we sum

[tex]\frac{7}{3}+\frac{7}{4}=\frac{28+21}{12}=\frac{49}{12}\approx 4.08[/tex]

Therefore, the just have enough flour to do their recipes, because they need 4.08 c of flour approximately, and they have 4 c of flour.

Final answer:

Eliza and Jamie do not have enough flour for both of their recipes for a school bake sale. After adding the required amounts, they are short by 1/12 cup since they need 4 1/12 cups and have only 4 cups of flour.

Explanation:

Eliza needs 2 1/3 cups of flour for her recipe and Jamie needs 1 3/4 cups for hers. To determine if they have enough flour, we must add these two amounts together:

Since they have exactly 4 cups of flour, Eliza and Jamie do not have enough flour; they are short by 1/12 cup for both recipes combined.

When considering the total amount of flour needed for a recipe, it's important to make sure the sum does not exceed the available amount. In Eliza and Jamie's case, they will need to acquire more flour to meet the requirements of both their recipes for the bake sale.

For this problem, an important thing to note is how the question says that 'the temperature dropped', meaning that it went down.

This means that the 2 degrees is actually negative.

Then you multiply the change in degrees by hours past:

(−2)×6=−12

Final Answer:

−12∘F

we have that

[tex]f(x)\\g(x)=f(x+2)[/tex]

we know that

the rule of the translation of f(x) to g(x) is equal to

[tex](x,y)----> (x-2,y)[/tex]

that means

the graph of g(x) is the graph of f(x) translated [tex]2[/tex] units left

therefore

the answer is the option

the graph of g(x) is the graph of f(x) translated [tex]2[/tex] units left

Step-by-step explanation:

a little late on this answer

The area of a right isosceles triangle with legs each measuring 8 feet is calculated using the formula A = (base x height) / 2, resulting in an area of 32 square feet.

The question you've asked is about finding the area of a right isosceles triangle when one leg is known. In a right isosceles triangle, both legs are of equal length. Since one leg is given as 8 feet, the other leg is also 8 feet. The formula for the area of a right triangle is A = (base x height) / 2.

In this case, the base and height are the same, which are the lengths of the legs of the triangle, so the formula becomes A = (8 feet x 8 feet) / 2. Performing the calculation, we find that A = 64 feet2 / 2, which simplifies to A = 32 feet2. Therefore, the area of the triangle is 32 square feet.

There are four terms because they are separated by addition or subtraction symbols: 8x, 6, 2xy, and z.

It is defined as the combination of constants and variables with mathematical operators.

It is given that the expression is,

8x + 6 + 2xy + z

The representation of number patterns can be done using algebraic expressions. If we know the values of each variable in an algebraic expression, we can find the value of the expression.

When one or more quantities in the real world are unknown or have a variable value, you can describe the situation using a variable expression.

In order to create a variable expression for a situation in reality: Establish a variable to represent the quantity that is unknown in the situation by identifying the unknown quantity.

Thus, there are four terms because they are separated by addition or subtraction symbols: 8x, 6, 2xy, and z.

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Final answer:

The expression 8x + 6 + 2xy + z is made up of four terms: 8x, 6, 2xy, and z.

Explanation:

The expression 8x + 6 + 2xy + z consists of four separate terms. In algebra, terms are the parts of an expression separated by addition or subtraction signs. The terms in this expression are as follows:

Identifying terms is essential for simplifying expressions and performing operations such as addition and subtraction of like terms in algebra.