5. Claire is buying a new bicycle for $295. If the
sales tax is 4.75%, what will she pay in total?

When constructing a triangle with given side lengths, the possible range for the third side can be determined by adding and subtracting the lengths of the existing sides. Side lengths of 4, 10, and 14 inches are not possible choices for the third side length.

The third side of a triangle must be less than the sum but greater than the difference of the other two sides. Given sides of 6 inches and 8 inches:

Therefore, the lengths of the sides 4, 10, and 14 inches are not possible.

A. Inverse

Basically, inverse Property of Addition states that if you add any number added to its opposite the result will be equal zero. So, here we have the following equation:

[tex]x + 12 = 47[/tex]

Adding -12 to both sides we get:

[tex]x + 12 - 12= 47-12 \\ \\ \\ But \ 12+(-12)=0 \\ \\ \\ So: \\ \\ x + 0= 35 \\ \\ Finally: \\ \\ \boxed{x=35}[/tex]

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Answer:

A. Inverse

Step-by-step explanation:

The given equation is [tex]x+12=47[/tex]

To solve this equation, we use the inverse property of addition.

We add the additive inverse of 12 to both sides to get:

[tex]x+12-12=47-12[/tex]

We then simplify to obtain:

[tex]x+0=35[/tex]

This gives us  x=35.

The correct answer is A

Number of adults = 264

Number of children= 127

Step-by-step explanation:

Let the number of adults be......x

Let the number of children be.....y

The total number of people that used the public swimming pool is given as 391. This means

x+y=391

The total cost per the receipt is : $752.75

This means, 2.25 x+ 1.25 y = 752.75

The two equations are;

x+y=391  ...........(i)

2.25 x+ 1.25 y = 752.75...........(ii)

Making the x variable equal to eliminate x

2.25x + 2.25 y = 879.75

2.25x + 1.25 y = 752.75

Apply subtraction as

1.00 y = 127.00

y=127

Use the value of y in equation (i)

x+y=391

x+127=391

x=391-127=264

Number of adults = 264

Number of children= 127

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Answer: - 0.2727

Step-by-step explanation:

Answer:

Fred is 31 years old and Natalie is 14 years old.

Step-by-step explanation:

Given:

If you add Natalie's age and Fred's age, the result is 45.

If you add Fred's age to 3 times Natalie's age, the result is 73.

Now, to find the age of Fred and Natalie.

Let the age of Fred be [tex]x.[/tex]

And the age of Natalie be [tex]y.[/tex]

As, given If you add Natalie's age and Fred's age, the result is 45.

[tex]x+y=45[/tex]    ......(1)

Now, if you add Fred's age to 3 times Natalie's age, the result is 73.

[tex]x+3y=73[/tex]   ......(2)

So, to solve the equations by using elimination method.

Now, subtracting both the equations (1) and (2):

[tex]x+y-(x+3y)=45-73[/tex]

[tex]x+y-x-3y=-28[/tex]

[tex]-2y=-28[/tex]

Dividing both sides by -2 we get:

[tex]y=14.[/tex]

Natalie's age = 14 years.

Now, to get the age of Fred by substituting the value of [tex]y[/tex] in equation (1):

[tex]x+y=45\\\\x+14=45[/tex]

Subtracting both sides by 14 we get:

[tex]x=31.[/tex]

Fred age = 31 years.

Therefore, Fred is 31 years old and Natalie is 14 years old.

Answer:

Apply the distributive property.

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Step-by-step explanation:

Answer:

The absolute value of 13 is (-13)

Step-by-step explanation:

It just is lol

Answer: 13

Explanation: The absolute value of an integer it its distance from zero on a number line. Since 13 is 13 units from zero, the absolute value of 13 is 13.

To represent the absolute value of a number, we use a vertical bar on either side of the number so we say that |13| = 13.

I have drawn a number line and also showed you in the image attached.

[tex]\frac{1}{7} -3(\frac{3}{7}h -\frac{2}{7}) = \frac{7-9h}{7}[/tex]

Solution:

Given expression is:

[tex]\frac{1}{7} -3(\frac{3}{7}h -\frac{2}{7})[/tex]

We have to combine the like terms

From given expression,

[tex]\frac{1}{7} -3(\frac{3}{7}h -\frac{2}{7})[/tex]

By distributive property,

The distributive property lets you multiply a sum by multiplying each addend separately and then add the products.

a(b + c) = ab + bc

Therefore,

Solve for brackets using distributive property

[tex]\frac{1}{7} - (3 \times \frac{3}{7}h) + (3 \times \frac{2}{7})\\\\\frac{1}{7} - \frac{9h}{7} + \frac{6}{7}[/tex]

Add 1/7 and 6/7

[tex]\frac{1}{7} + \frac{6}{7} -\frac{9h}{7}\\\\\frac{1+6}{7} -\frac{9h}{7}\\\\Simplify\\\\\frac{7}{7}-\frac{9h}{7}\\\\1-\frac{9h}{7}\\\\Simplify\\\\\frac{7-9h}{7}[/tex]

Thus the equivalent expression is found

The given values for x and y are not related to a specific equation or line, so we cannot determine the x-intercept.

The x-intercept represents the point at which a line crosses the x-axis. To find the x-intercept, we need to determine the value of x when y is equal to zero. In this case, the given values for x and y are not related to a specific equation or line, so we cannot determine the x-intercept.

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Answer:

86.666666 or 0.01153846153

Answer:

0.0115

Step-by-step explanation:

Answer:

[tex]Final\ grade=79.5[/tex]

Step-by-step explanation:

[tex]Homework\ grade=92\\\\quiz\ grade=68\\\\Test\ grade=81\\\\Final\ Grade=10\%\ of\ homework\ grade+20\%\ of\ quizzes\ grade+70\%\ of\ test\ grade\\\\Final\ Grade=\frac{10}{100}\times 92+\frac{20}{100}\times 68+\frac{70}{100}\times 81\\\\Final\ grade=0.1\times 92+0.2\times 68+0.7\times 81\\\\Final\ grade=9.2+13.6+56.7\\\\Final\ grade=79.5[/tex]

Final answer:

The final grade, calculated by weighting the individual grades for homework, quizzes, and tests, and then applying standard rounding rules, would be a rounded grade of 80.

Explanation:

To calculate the final grade based on the given weights, multiply each individual grade by its respective percentage and then add the results together. Here's a step-by-step calculation:

Homework: 92 (weight 10%) -> 92 x 0.10 = 9.2

Quizzes: 68 (weight 20%) -> 68 x 0.20 = 13.6

Tests: 81 (weight 70%) -> 81 x 0.70 = 56.7

Add these results together to get the final grade:

9.2 (Homework) + 13.6 (Quizzes) + 56.7 (Tests) = 79.5

Using standard rules for rounding, 79.5 would be rounded to 80, which is typically a 'B' grade.

Answer:

look at the picture shown

Answer:

the function that would represent a reflection of the function y = f(x) = [tex]\frac{3}{8} \times 4^x[/tex] would be a function where x is negative, that is to say the required function which is a reflection across the y axis is given by

[tex]y = f(x) = \frac{3}{8} \times 4^{-x}[/tex]

Step-by-step explanation:

the function that would represent a reflection of the function y = f(x) = [tex]\frac{3}{8} \times 4^x[/tex] would be a function where x is negative, that is to say the required function which is a reflection across the y axis is given by

[tex]y = f(x) = \frac{3}{8} \times 4^{-x}[/tex]

Answer:

g(x) = 3/8(4)^–x

Answer:

Judy

Step-by-step explanation:

Answer:

Andy had 3 apples, and his mom surprised him with x apples. His mom told him that he had 8 apples in total. As he counted the apples he found out his mom gave him 5 apples By subtracting 8 and 3.

Step-by-step explanation:

Answer:

Step-by-step explanation:

1/2x-33/2=1/2(x-33)

The process of factoring 1/2 out of the equation 1/2x - 33/2 involves dividing each term in the expression by 1/2. This process yields the result x - 33.

To factor 1/2 out of the expression 1/2x - 33/2, you perform the factoring by dividing every term in the expression by 1/2. In mathematics, factoring is a crucial concept and is widely used in simplifying expressions, solving quadratic equations, and multiple other scenarios. So, the factoring works as follows:

Hence, when you factor 1/2 out of 1/2x - 33/2, the result is x - 33.

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Answer:

£28+£16(each half hour)

£28+£48= £76

Answer:

there is no table :)

Step-by-Step Explanation:

y = 1/4x +1

X        Y

4        2

8        3

12       4

Answer:

Anya spend the most money

The inequality is:

[tex]70+6x\geq 150[/tex]

You must do more than 14 sales to get at least $ 150

Solution:

Given that,

As a salesperson you are paid $70 per week plus $6 per sale

Let "x" be the number of sales

This week you want your pay to be at least $150

We have to frame a inequality to represent the number of sales you need to make to achieve your goal

This week he must earn at least $ 150

Thus, he can spend $ 150 or more then 150 also

So we have to use "greater than or equal to" symbol

From given,

[tex]70 + 6(\text{number of sales})\geq 150[/tex]

[tex]70+6x\geq 150[/tex]

Thus the inequality is found

Solve the inequality

[tex]70+6x\geq 150\\\\Subtract\ 70\ from\ both\ sides\\\\6x\geq 150-70\\\\6x\geq 80\\\\Divide\ both\ sides\ by\ 6\\\\x\geq 13.3\\\\Thus\ approximately\ we\ get\\\\x\geq 14[/tex]

So he must do more than 14 sales to get at least $ 150

Any decimal number that lies between 0.15 and 0.7 meets the criteria, such as 0.6, 0.20 or 0.30. In mathematics, there can be infinite possibilities between these values as you can always add more digits after the decimal point.

In mathematics, a decimal number greater than 0.15 and less than 0.7 could be any number that falls within these two boundaries.  For example, 0.6 is a decimal number that would meet these criteria. Alternatively, a number like 0.20 or 0.30 would also satisfy the conditions specified in the question.

Remember, a decimal between two numbers can have infinite possibilities. That's because you can always add more digits after the decimal point (for example, 0.601, 0.602, 0.603, ..., and so on).

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Step-by-step explanation:

[tex] \frac{1}{4} \: log_4 16 \\ \\ = \frac{1}{4} \: log_4 {4}^{2} \\ \\ = \frac{1}{4} \times 2\: log_4 {4} \\ \\ = \frac{1}{4} \times 2\: \times 1 \\ \\ = \frac{1}{2} \\ \\ \huge \blue{ \boxed{\therefore \: \frac{1}{4} \: log_4 16= \frac{1}{2} }}\\ [/tex]

Answer:

22

Step-by-step explanation: