Let
x--------> the amount you have left to spend
y--------> the cost of a shirt you want
z------> the amount of the gift card
we know that
[tex] x+y \leq z [/tex] --------> equation [tex] 1 [/tex]
[tex] y=\$ 15 [/tex] --------> equation [tex] 2 [/tex]
[tex] z=\$ 60 [/tex] --------> equation [tex] 3 [/tex]
Substitute the equation [tex] 2 [/tex] and equation [tex] 3 in the equation [tex] 1 [/tex] [/tex]
[tex] x+y \leq z [/tex]
[tex] x+15 \leq 60 [/tex]
therefore
the answer is the option
x+15 is less than or equal to 60
Julia wrote 14 letters to friends each month for y months in a row. Write an expression to show how many total letters she wrote.
The expression representing the total number of letters that Julia wrote after 'y' months is '14y', as she writes 14 letters each month.
Explanation:This is a mathematics problem related to writing algebraic expressions. In this case, Julia has written 14 letters each month for 'y' months. Hence, the expression to determine the total number of letters Julia has written is '14y'. Let's break this down:
Julia writes 14 letters each month. This is a constant, represented by the number 14. The time period over which she continues this action is variable, represented by 'y'. So, for every month 'y', she writes 14 letters. We multiply 14 (letters per month) by 'y' (number of months) to get the total number of letters, hence the expression 14y.Learn more about Algebraic Expression here:
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The expression to show how many total letters Julia wrote is 14y.
Explanation:To find the total number of letters Julia wrote, we need to multiply the number of letters she wrote each month (14) by the number of months she wrote letters (y). So, the expression to show how many total letters she wrote is 14y.
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write 42.5% as a fraction in simplest form
The fraction of 42.5% in its simplest form is 17/40.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
42.5%
= 42.5/100
= 425/1000
= 85/200
= 17/40
Thus,
The fraction is 17/40.
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42.5% can be expressed as the fraction 17/40 in simplest form.
To express 42.5% as a fraction in the simplest form, we need to convert the percentage to a fraction with the numerator and denominator in their simplest form. Here's the step-by-step process:
Recognize that a percentage is a fraction out of 100. In this case, 42.5% can be written as 42.5/100.
Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor. In this case, the greatest common divisor of 42.5 and 100 is 2. Dividing both the numerator and denominator by 2 gives us 21.25/50.
Continue simplifying the fraction by dividing both the numerator and denominator by any common factors. In this case, we can divide both by 25: 21.25/50 = 0.85/2.
Finally, express the fraction in simplest form by dividing both the numerator and denominator by their greatest common divisor, which is 5 in this case: 0.85/2 = 17/40.
Therefore, 42.5% can be expressed as the fraction 17/40 in simplest form.
This means that 42.5% is equivalent to 17 parts out of 40 parts.
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If Y is between X and Z, then X, Y, and Z are collinear?
A) Always true
B) Sometimes true
C) Never true ...?
Yes, its always true that if Y is between X and Z, then X, Y and Z are collinear.
Here,
Given that;
Y is between X and Z.
We have to find X, Y and Z are collinear.
What is Collinear points?
Two or more points are Collinear points if they are lie in one straight line.
Now,
Y is between X and Z.
Clearly, XZ is a line and Y is lie in between X and Z.
So, X, Y and Z are Collinear points.
Therefore, its always true that if Y is between X and Z, then X, Y and Z are Collinear.
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Sarah's craft project uses pieces of yarn that are 1/8 yard long. She has a piece of yarn that is 3 yards long. How many 1/8 yard pieces can she cut and still have 1 1/4 yards left?
When rewriting y = 2x + 1 in function notation, what do you replace with f(x)?
Answer:
You replace y with f(x)
Step-by-step explanation:
- Function is a relation between two sets of numbers, with every element
in the first set has only one corresponding element in the second set
- The first set is called the domain of the function (input)
- The second set is called the range of the function (output)
- If the first set is set X and the second set is set of Y, then each value
of x has only one value of y and x is the input and y is the output
- Function notation is the way to write a function f(x) = y, where f(x)
represents the values of y
∵ y = 2x + 1
∵ f(x) = y
- Replace y by f(x)
∴ f(x) = 2x + 1
* You replace y with f(x)
Answer:
That is what I got off of USA Test Prep
Step-by-step explanation:
For function notation you are saying that you have a relation that is a function of another variable. To correctly rewrite using function notation you replace y with f(x).
The sum of three consecutive integers is 303. If n is the smallest of the three, which equation represents this situation?
Answer:
The correct equation is 3n + 3 = 303
Correct value of n is 100
Step-by-step explanation:
The sum of three consecutive integers is 303.
Consecutive integer is next number of previous one.
Let n be smallest integer.
Next two integer: n+1, n+2
Sum of n, n+1 and n+2 is 303
Therefore,
n + n + 1 + n + 2 = 303
3n + 3 = 303
3n = 300
n = 100
Hence, The correct equation is 3n + 3 = 303
what is the difference between all real numbers and no solution how do you know when these situations occur
The difference between 'all real numbers' and 'no solution' is that the former means any real number satisfies the equation while the latter means no real number satisfies it. These concepts are essential in understanding and solving mathematical problems, which is a skill developed through practice.
Explanation:The difference between 'all real numbers' and 'no solution' in mathematical equations is significant. When an equation has all real numbers as its solution, it means that any real number can be substituted for the variable and the equation would still hold true. This situation typically occurs when both sides of the equation are identical after simplification. For example, if we simplify an equation and end up with a statement like 5 = 5, it implies that all real numbers are solutions since the statement is always true, regardless of the value of the variable.
On the other hand, 'no solution' means that there are no real numbers that satisfy the equation, often arising when a statement is made that is logically false after simplification, such as 0 = 5. Identifying knowns and unknowns and checking if an answer is reasonable are part of the problem-solving process, where we also look for unreasonable results that might suggest 'no solution'.
The occurrence of these situations during problem solving reflects the complexity of real-world problems, where we must determine which information is relevant and sort out the possible from the impossible. This discernment can be developed through consistent practice in evaluating and solving various types of problems. In some cases, particularly in systems of equations, if the number of unknowns is larger than the number of equations, it may indicate that there could be infinite solutions or no unique solution.
The hypotenuse of a right triangle has endpoints A(4, 1) and B(–1, –2).
At which points could the vertex of the right angle in the triangle be located? Check all that apply.
(–1, 1)
(4, –2)
(1, 1)
(2, –2)
(4, –1)
(–1, 4)
Answer:
(–1, 1)
(4, –2)
Step-by-step explanation:
Let
(x,y) ----> the coordinates of point C
Applying the Pythagoras Theorem
[tex](-1-4)^2+(-2-1)^2=(x-4)^2+(y-1)^2+(x+1)^2+(y+2)^2[/tex]
step 1
Find the possibles values of x
[tex](-1-4)^2=(x-4)^2+(x+1)^2\\\\25=x^{2}-8x+16+x^{2}+2x+1\\\\2x^{2}-6x-8=0[/tex]
Simplify
[tex]x^{2}-3x-4=0[/tex]
Solve the quadratic equation
[tex]x^{2}-3x-4=(x+1)(x-4)[/tex]
The values of x are
x=-1 and x=4
step 2
Find the possibles values of y
[tex](-2-1)^2=((y-1)^2+(y+2)^2\\\\9=y^{2}-2y+1+y^{2}+4y+4\\\\2y^{2}+2y-4=0[/tex]
Simplify
[tex]y^{2}+y-2=0[/tex]
Solve the quadratic equation
[tex]y^{2}+y-2=(y+2)(y-1)[/tex]
The values of y are
y=-2, y=1
therefore
The possibles coordinates of point C are
(-1,1),(4,-2)
Answer:
(–1, 1)
(4, –2)
Step-by-step explanation:
Given that the hypotenuse of a right triangle has endpoints A(4, 1) and B(–1, –2), then two triangles can be formed (see figure attached).
The vertex of the right angle in each triangle are on points (-1, 1) and (4, -2), as can be seen in the figure.
you can buy an 8 pack of paper towels for $7.92 or 12 pack for $11.64, which is a better buy?
Why do we use scientific notation, and what are the parts of an expression written in scientific notation?
You need to know how to use it propeller to also use it at all
If v=5, what is the value of 3v 9?
find the derivative of y=(2x-7)^3
To find the derivative of y=(2x-7)^3, use the power rule and chain rule. Differentiate each term individually and apply the chain rule. Add all the terms together to get the derivative.
Explanation:To find the derivative of y=(2x-7)^3, we can use the chain rule. First, we can rewrite the equation using the power rule: y = (2x - 7)(2x - 7)(2x - 7). Next, we differentiate each term individually using the power rule and then apply the chain rule. The derivative of the first term will be 2(2x - 7)(2), the derivative of the second term will be 2(2x - 7)(2), and the derivative of the third term will be 2(2x - 7)(2). Finally, we add all these terms together to get the derivative of the original equation.
The difference of two numbers is more than 12,and one of the numbers is 3
Inequality for the other number x > 15.
What is inequality?An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The most frequent application is to size-compare two numbers on a number line.
Given,
Difference of two numbers is greater than 12
One number is 3
Let the other number be x
Then, inequality becomes
x - 3 > 12
Adding 3 on both sides
x > 12 + 3
x > 15
Hence, x>15 represents the other number so that difference of two numbers is greater than 12.
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What is the solution of the system?
Use the substitution method.
{y−2x=8
{16+4x=2y
The only solution is (24, 0)
The only solution is (1, 10)
There is no solution.
There are an infinite number of solutions.
mary has $500 in her savings account and she buy a pair of shoes every week for $125 write a function
need answers............
It took morry 2 and 5/6 hours to drive to the beach. it took jason twice as long. about how long did it take jason to drive to the beach?
What is 1,019.7 rounded to the nearest whole number?
How many square feet of outdoor carpet will we need for this hole
Answer:
The actual answer is 36. If I am wrong i am sorry
Step-by-step explanation:
Answer:
36 square ft
Step-by-step explanation:
Write a real- world problem that you can solve by writing an equation. the answer to the problem must be 6.
The number of fish (F) in a fish tank increases when the number of plants (P) increases. Write the correct equation for this scenario and solve for the number of fish when the number of plants is 3.
What are the different mathematical relationships in data?
Chris is calculating his deductions for his tax return. He is filing singly. He can claim $1,813 from property taxes, $1,513 from medical expenses, and $761 from state income tax. The standard deduction for a single filer is $5,700. How does the standard deduction compare to Chris’s deductions? a. Chris’s deductions are $1,437 better than the standard deduction. b. Chris’s deductions are $4,087 better than the standard deduction. c. The standard deduction is $1,613 better than Chris’s deductions. d. The standard deduction is $664 better than Chris’s deductions.
Answer:
(C)
Step-by-step explanation:
Chris's deductions for tax return = claim from property taxes +claim from medical expenses+claim form state income tax
= $1813+$1513+$761
= $4087
Standard deductions = $5700
Difference between standard deduction and Chris's deductions = 5700-408
= $1613
Hence standard deductions is better than Chris's deductions by $1613
Therefore, option (C) is correct.
Let h(x)=2x+5h(x)=2x+5h, left parenthesis, x, right parenthesis, equals, 2, x, plus, 5 and g(x)=8-3xg(x)=8−3xg, left parenthesis, x, right parenthesis, equals, 8, minus, 3, x. What is the value of h(g(1.5))h(g(1.5))h, left parenthesis, g, left parenthesis, 1, point, 5, right parenthesis, right parenthesis?
The question is asking for the value of h(g(1.5)) using given functions h(x) and g(x). First, find g(1.5) by substituting 1.5 into g(x) to get 3.5. Then, substitute 3.5 into h(x) to get the final answer of 12.
Explanation:Firstly, identify the functions h(x) and g(x) given to you. h(x) =
2x+5
and g(x)=
8-3x
. The question requires you to find h(g(1.5)). This means that you need to plug g(1.5) into h(x).
Start by calculating g(1.5). In the function g(x), replace x with 1.5. g(1.5) = 8 - 3*1.5 = 3.5.
Now, substitute the value obtained, which is 3.5, into h(x). So, h(g(1.5)) turns into h(3.5) = 2*3.5 + 5 = 12. Therefore, the value of h(g(1.5)) is
12
.
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To calculate the composite function h(g(1.5)), first calculate the value of g(1.5) which is 3.5, then substitute this value into the function h(x) to get the answer, which is 12.
Explanation:The question is asking us to find the value of h(g(1.5)). This means we need to first find the value of g(1.5) and then substitute that value into the function h(x).
So, let's first determine g(1.5). We know that g(x)=8-3x. Substituting 1.5 in place of x in g(x), we get: g(1.5) = 8 - 3*(1.5) = 8 - 4.5 = 3.5.
Next, to find h(g(1.5)), we substitute the value of g(1.5) which is 3.5 into h(x) to get: h(3.5) = 2*(3.5) + 5 = 7 + 5 = 12. Thus, the value of h(g(1.5)) is 12.
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There are 6 female goldfish for every 10 male goldfish in the aquarium. there are 216 female goldfish in the aquarium. how many male goldfish are in the aquarium?
If there are 6 female goldfish for every 10 male goldfish in the aquarium and if there are 216 female goldfish in the aquarium then there are 360 male goldfish in the aquarium.
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Let us use a proportion to represent the relationship between the number of female and male goldfish in the aquarium
6 female goldfish / 10 male goldfish = 216 female goldfish / x male goldfish
We know that there are 216 female goldfish in the aquarium, so we can substitute that value into the equation:
6 / 10 = 216 / x
Let us solve for x by cross-multiply:
6x = 10 × 216
6x = 2160
Divide both sides by 6
x = 360
Therefore, there are 360 male goldfish in the aquarium.
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Choose the best verbal statement for the following inequality: m > 13
How do you write 9.76*10^-2 in standard form?
From 2006 to 2010, the population of a town declined to 22,000. The population is expected to continue to decline at a rate of 2.8% each year. What will the population be in 2040? Round to the nearest whole number. Enter your answer in the box.
actually i just took the test and it said the answer was 9384
How many solutions does this equation have?
Would the placement of the parentheses affect the value of an expression when only multiplication is used? Explain.
Yes, the placement of parentheses can affect the value of an expression even when only multiplication is used. This is because parentheses can change the grouping of factors, which can in turn change the order of operations.
The order of operations is a set of rules that dictate the order in which operations should be performed in an expression. When there are no parentheses, the order of operations is as follows:
Exponents
Multiplication and division (from left to right)
Addition and subtraction (from left to right)
However, when there are parentheses, the operations inside the parentheses are performed first. This means that the order of operations is not always followed strictly from left to right.
For example, consider the following expression:
3 * 2 * 4
According to the order of operations, this expression should be evaluated as follows:
3 * 2 = 6
6 * 4 = 24
However, if we add parentheses to the expression, we can change the value:
(3 * 2) * 4
In this case, the parentheses tell us to evaluate the expression inside the parentheses first. So, we have:
(3 * 2) = 6
6 * 4 = 24
Therefore, the value of the expression is different depending on the placement of the parentheses.
This is because the parentheses change the grouping of factors. In the first expression, the factors are grouped as (3)(2)(4). In the second expression, the factors are grouped as ((3)(2))(4). This change in grouping changes the order in which the operations are performed, which can in turn change the value of the expression.