Two of the angles in a triangle measure 56° and 28°. What must be the measure of the third angle?

Answer:

The row with x = 2 and y = 4 is incorrect. The y value should be y = 3 when x = 2.

==============================================================

Explanation:

Fractions can be a bit of a pain, so I'm going to be converting to decimal form to help with the computation; however, I will convert the y value results to mix number form so that it matches what the table shows.

Keep in mind that 3/4 = 0.75 when you use a calculator or long division. So a number like 2.75 means 2 & 3/4 (two and three quarters)

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Let's check the first row. Plug in x = 0 and it leads to...

y = (3/4)*x^2

y = (3/4)*0^2

y = (3/4)*0

y = 0.75*0

y = 0

This shows us that row 1 is correct. When x = 0, y = 0 leading to (x,y) = (0,0).

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Repeat the same basic outline of steps, but now use x = 2

y = (3/4)*x^2

y = (3/4)*2^2

y = (3/4)*4

y = 0.75*4

y = 3

So instead of 4, the proper y value is y = 3 when x = 2. This means row 2 is the answer (the row that has the incorrect values).

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For the sake of completeness, let's see if the third row is correct or not. Plug in x = 3

y = (3/4)*x^2

y = (3/4)*3^2

y = (3/4)*9

y = 0.75*9

y = 6.75

y = 6 & 3/4

We see that x = 3 points to y = 6 & 3/4, so we have the correct values in this row. We can cross this off the list of choices.

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Finally, let's check x = 5

y = (3/4)*x^2

y = (3/4)*5^2

y = (3/4)*25

y = 0.75*25

y = 18.75

y = 18 & 3/4

We get the proper y value. So we can also cross this off the list.

Answer:

Her son mowed more and 7/20 need to be mowed

Step-by-step explanation:

1/4 x 5 = 5/20 - Mrs Tran

2/5 x 4 = 8/20 - her son

20/20 - 13/20 = 7/20 needs to be finished

Answer:

5.) Proportionality is 3/1 or 3 simplified

6.) Proportionality is 1/6

Step-by-step explanation:

You would take the first column (or in this case row (pens and packs) and place the 2nd row under it in fraction form.

That would be your proportion

Then you would (in place of numbers) use letters to symbolize in the equation

Then create an equation to figure out how to get the correct numbers.

Answer:

slope is -4 or in a fraction, -4/1

Step-by-step explanation:

When you have 2 points, you can find the slope by subtracting them by each other. You must do 8 - 0 which is 8, then -2 - 0 which is -2. Then you get 8/-2. Once simplified, you get -4, and you know if the number is alone, there is always a 1 under it so you get -4/1.

Hello!

Step-by-step explanation:

[tex]Slope=\frac{Y_2-Y_1}{X_2-X_1}=\frac{RISE}{RUN}[/tex]

[tex]\frac{8-0}{(-2)-0}=\frac{8}{-2}=-4[/tex]

Slope is -4

Final answer is -4

*The answer must have a negative sign.*

I hope this helps you!

Have a nice day! :)

-Charlie

:D

Answer: C

Step-by-step explanation: The equation is y = x/7. For every 7 numbers that x increases, y increases by 1.

42.9

"74% of 58" translates to ...

... 74/100 × 58 = 42.92

Rounded to the nearest tenth, this is 42.9.

_____

Comment on translation

In this context, "of" means "times." Of course, % means /100, so ...

... 74% = 74/100 = 0.74

[tex]\frac{8x-2}{42}=\frac{63}{49}\\\frac{8x-2}{42}=\frac{9}{7}\\7(8x-2)=9\cdot42\ /:7\\8x-2=9\cdot6\\8x-2=54\\8x=54+2\\8x=56\ /:8\\x=7[/tex]

The water used will be greater than 1600000 thousands of gallons for the fixed amount to be less expensive.

The users can either pay 77 cents per thousand gallons, or pay a fixed amount of $1,232,000 for unlimited water usage for one year.

Therefore,

77 cents = 0.77 dollars

Hence,

The user can pay 0.77 per thousand gallons.

He can pay a fixed amount of $1,232,000 .

Therefore, the amount of water the company will use for the fixed amount to be less expensive is as follows;

let

x = amount of water use in thousand gallons

Using inequalities,

0.77x ≥ 1,232,000

x ≥ 1,232,000 / 0.77

x ≥ 1600000

Therefore, the water used will be greater than 1600000 thousands of gallons for the fixed amount to be less expensive.

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Answer:

Step-by-step explanation:

the answer is

t=5c+35

t=10c

i just did this problem and got it right.

To represent the scenario of two training programs with different costs, we can use the equations t = c + 35 and t = 5c.

In this scenario, we have two different training programs at a pet store. The first program charges a $35 membership fee and $5 for each class.

The second program does not have a membership fee, but charges $10 for each class. We want to find out for how many classes the total cost will be the same for both programs.

To create the system of equations, we can use the variable c to represent the number of classes and t to represent the total cost. The equations that represent the scenario are:

t = c + 35

t = 5c

On the graph, the solution to the system of equations is the point of intersection (the point where the lines meet)

So the solution is (-4, 3)

Answer:

The solution for the system is [tex](-4,3)[/tex], that is, [tex]x=-4[/tex] and [tex]y=3[/tex].

Step-by-step explanation:

The solution of a system of equations can be find by using different methods, one of them is the graphic method, which is the one aplied to this problem.

When we use the graphic method to solve a system of equations, the interception point of both line represents the solution of such system.

Therefore, in this case, the solution for the system is [tex](-4,3)[/tex], that is, [tex]x=-4[/tex] and [tex]y=3[/tex].

The answer explains how to calculate the SUTA and FUTA amounts owed by Roger Ratkin for the first 12 weeks for his employees' wages.

State Unemployment Tax Act (SUTA) and Federal Unemployment Tax Act (FUTA)

[tex]p\%=\dfrac{p}{100}\\\\40\%=\dfrac{40}{100}=\dfrac{4}{10}=0.4;\ 60\%=\dfrac{60}{100}=\dfrac{6}{10}=0.6;\ 55\%=\dfrac{55}{100}=0.55\\\\\left\{\begin{array}{ccc}x+y=5&\to x=5-y\\0.4x+0.6y=0.55\cdot5\end{array}\right\\\\\text{Use substitution method}\\\\0.4(5-y)+0.6y=2.75\qquad\text{use distributive property}\\\\(0.4)(5)+(0.4)(-y)+0.6y=2.75\\\\2-0.4y+0.6y=2.75\qquad\text{subtract 2 from both sides}\\\\0.2y=0.75\qquad\text{multiply both sides by 5}\\\\\boxed{y=3.75}[/tex]

[tex]\text{Put the value of y to the first equation}\\\\x=5-3.75\\\\\boxed{x=1.25}\\\\Answer:\ x=1.25\ and\ y=3.75.[/tex]

Answer:

c. The number of packages of corn purchased.

Step-by-step explanation:

We have been given that a store sells four 1 1/8-pound ears of corn in a package for $3.59. The expression [tex]3.59p[/tex] represents the cost of the corn for a number of packages.

Since the cost of each package of corn is $3.59 and [tex]3.59p[/tex] represents the cost of 'p' packages of the corn. So 'p' represents the number of packages of corn purchased.

Upon looking at our given choices, we can see that option C is the correct choice.

Answer:

Domain: all real numbers

Step-by-step explanation:

The domain of a function is the set of values that x can be replaced with.

In this function, x can be replaced by any real number, so the domain of the function is all real numbers.

Here we need to find the domain of the given function.

We will see that the domain is the set of all real numbers.

The first thing we need to do is to define the domain of a function.

For a given function f(x), we define the domain as the set of possible inputs that we can use on the function.

Usually, we start by defining the domain as the set of all real numbers and then remove from the domain the numbers that cause "a problem" with our function.

Where these "problems" are undefined operations, like the logarithm of a negative number or a zero in a denominator.

Particularly, in our function: f(x) = (1/2)^x

We do not have a denominator that can become zero nor a function that has problems with some given values of x (the exponent of a number can be any real number).

Concluding, because there is no problem with any real value,  we can see that the domain is the set of all real numbers.

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Answer:

x = 2.696, x = -0.696

Step-by-step explanation:

We are given the following function of x and we are to find the zeros for the given quadratic function:

[tex]f(x)= 8x^2-16x-15[/tex]

To find its zeros, we will use the quadratic formula:

[tex]x=\frac{-b+-\sqrt{b^2-4ac} }{2a}[/tex]

Substituting the values in the formula where [tex]a=8[/tex], [tex]b=-16[/tex] and [tex]c=-15[/tex].

[tex]x=\frac{-(-16)+-\sqrt{(-16)^2-4(8)(-15)} }{2(8)}[/tex]

[tex]x=\frac{16+-\sqrt{736} }{16}[/tex]

[tex]x=\frac{16+27.13}{16}[/tex] , [tex]x=\frac{16-27.13}{16}[/tex]

[tex]x = 2.696[/tex] , [tex]x=-0.696[/tex]

Therefore, the solutions are 2.696 and -0.696.

Answer: c on edge

Step-by-step explanation:

x=1-square root 23/8 and x=1+square root 7

The population decreased 96.8%.

Initial value = 100,000

Final value = 3,200

The percentage decrease is

= (Final value - initial value) * 100% /initial value

= [tex]\frac{\left(3200-100000\right)}{100000}\cdot100 \%[/tex]

= −96.8%

Negative sign because of decrease.

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Answer: n=42

Step-by-step explanation: Lets suppose n is a number. Since the numbers are consecutive, they would be:

n

n+1

n+2

If the sum is 129, then an equation would be

n+n+1+n+2=129

3n=126

n=42

So, the smallest number would be 42

Answer:

A: 1 Minute

Step-by-step explanation:

Buses start running at 7 and run every eight minutes. This means that:

Bus 1: 7:00 AM

Bus 2: 7:08 AM

Bus 3: 7:16 AM

Bus 4: 7:24 AM

Bus 5: 7:32 AM

Bus 6: 7:40 AM

Bus 7: 7:48 AM

Bus 8: 7:56 AM

Bus 9: 8:04 AM

Bus 10: 8:12 AM

Bus 11: 8:20 AM

The waiting time of the bus is 7 minutes,

To calculate the waiting time, we need to break down the time difference between your arrival (8:19 am) and the next bus arrival (scheduled to come every 8 minutes). Let's start by determining the time between 8:19 am and the next scheduled bus at 8:20 am. This is only 1 minute of waiting time.

However, you want to know how long you'll have to wait until the next bus after 8:20 am, which means we need to consider the remaining time until the next 8-minute interval. From 8:20 am to 8:24 am, the bus does not arrive yet, resulting in an additional 4 minutes of waiting time

=> (8:24 am - 8:20 am = 4 minutes).

Now, we have reached the second 8-minute interval from 8:24 am to 8:28 am. As you arrived at 8:19 am, you will have to wait for 5 more minutes

=> (8:28 am - 8:19 am = 7 minutes)

to catch the bus.

So, the Main Answer: c: 7 minutes.

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Answer:

50 mi

Step-by-step explanation:

Two hours after leaving port,

The triangle formed by their tracks and the line joining their current positions is a right-angled triangle.

According to Pythagoras,

        a² + b² = c²

   30² + 40² = c²

900 + 1600 = c²

            2500 = c²

     √(2500) = c

                    c = 50 mi

The boats will be separated by 50 mi two hours after leaving port.

The problem requires setting up a system of two equations: one representing the total number of tickets sold (c + a = 150) and the other representing the total revenue from ticket sales (7.75c + 10.25a = 1470). Solving this system will yield the number of adult and child tickets sold.

To determine how many adult tickets, a, and child tickets, c, were sold by the Grand Prix Cinema, we need to establish a system of equations based on the given information:

These two equations can be used simultaneously to solve for the variables a (adult tickets) and c (child tickets). This problem is an example of a linear system of equations that can be solved by various methods such as substitution, elimination, or matrix operations.

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The hypothesis of the conditional statement given is a quadrilateral has 4 right angles.

This is the 'If' part of the 'If P then Q' structure of a conditional statement.

In a conditional statement in logic, the statement is usually given in the form 'If P then Q'. Here, 'P' is called the Hypothesis, and 'Q' is the Conclusion. In the statement 'If a quadrilateral has 4 right angles, then the quadrilateral is a rectangle', the Hypothesis (P) is a quadrilateral has 4 right angles. So, to answer your question, the hypothesis of this conditional statement is that a quadrilateral has 4 right angles.

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Answer:

percent error = 15%

Step-by-step explanation:

The following question is missing: What is the percent error?

percent error = (measure error/ actual weight)*100

where:

measure error = incorrect weight - correct weight  = 11.5 - 10 = 1.5 pounds

percent error = (1.5/10)*100 = 15%

Answer:

  =36.36 percent

Step-by-step explanation:

First we need to determine what you saved

11-7 = 4

You saved 4 dollars

Percentage of savings = savings /original price * 100

                                      = 4/11 * 100

                                       =36.36 percent

You saved $4.00 using an RX savings card on a prescription that originally cost $11.00. To find how much you saved in percentage terms, you divide the amount saved by the original cost and multiply by 100. In this case, you saved approximately 36.36%.

You are asking about the percentage savings when using a free RX savings card. To get the savings percentage, you first need to know how much money you saved. In your case, you would have paid $11.00, but you only paid $7.00 with the RX savings card. That means you saved $11.00 - $7.00 = $4.00.

Next, to find the savings as a percentage, you divide the amount saved by the original cost, then multiply by 100 to get a percentage. Here's the calculation:

Savings Percentage = ($4.00 / $11.00) * 100

Doing the division first (4 ÷ 11 = 0.3636), then multiplying by 100, you saved approximately 36.36% with your RX savings card.

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Answer:

Without math, how would we know how to count seconds minutes, etc.?

Math is extremely important for knowing how to do simple things like cooking, you need to know for how much time to put something in the oven or microwave or stove. Those are just the basics. There is a lot more stuff out there that math is used for.

If you want to get a job, you have to know about math. Without math, you will be unable to get a job. Every single job you can get requires math. Even working in a grocery store, you need math. Whether we like it or not, you will have to learn math or you'll end up homeless and without a job.

Answer:

5x+30-2x+9

Step-by-step explanation:

first you have to do the ''distributive property'' then you will get 5x+30-2x+9

Question

Write an expression equivalent to the one below

5(x + 6)-2x + 9

Answer:

Step-by-step explanation:

5(x + 6)-2x + 9 =

5x + 30 - 2x + 9 =

3x + 39

----------------------------

2x + 10 + 29 + x =

3x + 39

For both questions, you essentially use the equation r = d/t

a. 34/7 = about 4.86 dollars per hour

b. 4/10 = 0.40 dollars per pound.

[tex]a,\ b-the\ length\ of\ sides\\\\(1)\qquad4a+4b=40\qquad\text{divide both sides by 4}\\\\a+b=10\to a=10-b\\\\(2)\qquad a^2+b^2=58\\\\\text{Substitute}\ (1)\ \text{to}\ (2):\\\\(10-b)^2+b^2=58\qquad\text{Use}\ (x-y)^2=x^2-2xy+y^2\\\\10^2-2(10)(b)+b^2+b^2=58\\\\100-20b+2b^2=58\qquad\text{subtract 58 from both sides}\\\\42-20b+2b^2=0\\\\2b^2-20b+42=0\qquad\text{divide both sides by 2}\\\\b^2-10b+21=0\\\\b^2-7b-3b+21=0\\\\b(b-7)-3(b-7)=0\\\\(b-7)(b-3)=0\iff b-7=0\ \vee\ b-3=0\\\\\boxed{b=7\ \vee\ b=3}[/tex]

[tex]\text{Put the values of b to }\ (1):\\\\for\ b=7\to a=10-7=3\\\\for\ b=3\to a=10-3=7\\\\Answer:\ \boxed{7cm\ and\ 3cm.}[/tex]

The sides of the squares will be 3 and 7.

A square is a geometrical figure in which we have four sides each side must be equal and the angle between two adjacent sides must be 90 degrees.

Area of square = Side²

The perimeter of the square = 4× side

Length of diagonal of square = √(2) × side

Let's say the side of the first square is a while the second is b

Now,

the sum of the perimeter of two squares is 40cm

4a + 4b = 40

a + b = 10

Now,

The Sum of the area is 58cm²

So,

a² + b² = 58

By substituting,

a² + (10 - a)² = 58

a² - 10a + 21 = 0

a² - 7a - 3a + 21 =0

a(a - 7) - 3(a - 7) = 0

(a-3)(a - 7) = 0

a = 3 ,7

Corresponding to 3 and 7

b = 10 - 3 = 7 and b = 10 - 7 = 3.

Hence "The sides of the squares will be 3 and 7".

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