Fran graphs the equations y = 2x2 – 2 and y = –0.5x + 4. Her graph is shown below.

Which value is an approximate solution of 2x2 – 2 = –0.5x + 4?

Answer: The functions all have the same slope

Step-by-step explanation:

just took the assessment and I got it right.

Joey must work 26 weeks until he has enough to purchase the car.

An equation is a mathematical statement formed when two algebraic expressions are equated using an equal sign.

The equations are useful in determination of unknown parameters.

Joey wants to buy a used car,

The cost of the car is $2500.

The money he has saved is $1200

The money he makes by walking a dog is $50 per week.

Let w represent the number of weeks.

The equation for the condition can be written as:

The cost of the car is equated with the money he has and the money he earned in w weeks by dog walking.

2500 = 1200 + 50w

To determine the number of weeks he has to work to buy the car, the equation has to be solved for w,

50w = 2500 - 1200

50w = 1300

w = 1300 / 50

w = 26 weeks.

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Answer:

Option D) [tex]\displaystyle\frac{50}{8} < 6\frac{2}{5} < 6.45 < \frac{26}{4}[/tex]

Step-by-step explanation:

We are given the following information in the question:

We are given a set of numbers:

[tex]\displaystyle\frac{26}{4}, 6.45, 6\frac{2}{5}, \frac{50}{8}[/tex]

First, we write all the numbers in decimal form.

[tex]\displaystyle\frac{26}{4} = 6.5\\\\6\frac{2}{5} = \frac{32}{5} = 6.4\\\\\frac{50}{8} = 6.25[/tex]

Hence, the given numbers are:

6.5, 6,45, 6.4, 6.25

Arranging in order of least to greatest:

[tex]6.25 < 6.4 < 6.45 < 6.5[/tex]

Thus,

[tex]\displaystyle\frac{50}{8} < 6\frac{2}{5} < 6.45 < \frac{26}{4}[/tex]

Option D is the correct option.

Final answer:

The future value of a rare postage stamp that cost $5000 and increases by 11% annually over 10 years is calculated using the compound interest formula V = P(1 + r)[tex]x^{n}[/tex], where P is the principal amount, r is the annual rate, and n is the number of years.

Explanation:

Calculating the Future Value of a Rare Postage Stamp

The value of a rare postage stamp, originally purchased for $5000, that has been increasing in value by 11% annually for 10 years can be calculated using the formula for compound interest: V = P(1 + r)[tex]x^{n}[/tex], where:

P = $5000,

n = 10 years.

Plugging these values into the formula, we get:

V = $5000(1 + 0.11) [tex]x^{10}[/tex]

Performing the calculations gives us the future value of the stamp after 10 years.

By setting up a system of equations, we find that 375 adult tickets were sold for the school play.

To solve this problem, we need to set up a system of equations using the information provided:

Let's define the following variables:

According to the problem:

Now we substitute the second equation into the first:

So, 375 adult tickets were sold.

To subtract 19 from 33 using a tape diagram, draw a rectangle labeled 33, mark off a section labeled 19, and the unshaded difference represents the result, which is 14.

To create a tape diagram to show the subtraction of 33-19, we start by drawing a long rectangle to represent the number 33. We then mark off the length that represents the number 19 on the same tape, indicating the part we want to subtract. Lastly, the remaining part of the tape diagram represents the difference between the two numbers.

The final result is the length of the unshaded part of the tape diagram, which shows the difference when you subtract 19 from 33.

The correct option is [tex]\boxed{\text{\bf option C}}[/tex] i.e., the length is [tex]6\text{ cm}[/tex] and breadth is [tex]7\text{ cm}[/tex].

Further explanation:

The perimeter of arectangle is calculated as follows:

[tex]\boxed{\text{Perimeter}=2\cdot (l+b)}[/tex]

Here, [tex]l[/tex] is the length and [tex]b[/tex] is the breadth of the rectangle.

Given:

The length of the rectangle is [tex]5\text{ cm}[/tex] less than twice its breadth and the perimeter of the rectangle is [tex]26\text{ cm}[/tex].

Calculation:

Step 1:

First we write the dimensions in the form of variable [tex]x[/tex].

Consider [tex]x[/tex] as the breadth of the rectangle and [tex]y[/tex] as the length of the rectangle.

As per the question the length is [tex]5\text{ cm}[/tex] less than twice its breadth.

Therefore, the length can be expressed in the form of the equation as follows:

[tex]\boxed{y=2x-5}[/tex]  …… (1)

Step 2:

Now, we have to calculate the dimensions of the rectangle.

So, substitute [tex]l=2x-5[/tex] and [tex]b=x[/tex] in the formula of the perimeter of the rectangle to obtain the value of [tex]x[/tex].

[tex]\begin{aligned}\text{Perimeter}&=2\cdot (l+b)\\26&=2\cdot (2x-5+x)\\26&=2\cdot (3x-5)\\26&=6x-10\\6x&=26+10\\6x&=36\\x&=6\end{aligned}[/tex]  

Therefore, the breadth of the rectangle is [tex]6\text{ cm}[/tex].

Now, substitute [tex]x=5[/tex] in the equation (1) to obtain the value of the length.

[tex]\begin{aligned}l&=2x-5\\&=(2\cdot 6)-5\\&=12-5\\&=7\end{aligned}[/tex]

Therefore, the length of the rectangle is [tex]7\text{ cm}[/tex].

Thus, the correct option is [tex]\boxed{\text{\bf option C}}[/tex] i.e., the length is [tex]6\text{ cm}[/tex] and breadth is [tex]7\text{ cm}[/tex].

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Answer details:

Grade: Junior school

Subject: Mathematics

Topic: Area and Perimeter  

Keywords: Length, breadth, perimeter, area, side, dimensions, rectangle, shapes, figure, triangle, square, equation, variable, constant, twice, area, mensuration.

Answer:

She is incorrect because 2.81 × 10^4 is around 30,000 so the units must be smaller than feet. She most likely measured in inches.

To calculate the total cost, multiply the price of each item by the number purchased then add those totals together. In this case, purchasing two hot dogs and one candy bar costs $5.00.

To find the total cost of purchasing two hot dogs and one candy bar, you would simply multiply the cost of each item by the number of that item you are buying, and then add all these costs together. So, if a hot dog is $2.00 and you want to buy two, this costs $2.00 * 2 = $4.00. A candy bar is $1.00 each, and if you want to buy one, this costs $1.00 * 1 = $1.00. So, the total cost would be the cost of the hot dogs plus the cost of the candy bar, which is $4.00 + $1.00 = $5.00. Therefore, the total cost of two hot dogs and one candy bar is $5.00.

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Answer:

2x + 1 = 67

Let the smaller integer be x.

The next larger consecutive integer is 1 more than x, so it's x + 1.

x + x + 1 = 67

2x + 1 = 67

The correct options are B. An angle that measures 65 is an acute angle. and C. An acute angle measures less than 90 degrees.

To determine the truth of each statement, let's analyze each option:

A. An angle that measures 180 degrees is a reflex angle.

This statement is false. An angle that measures exactly 180 degrees is a straight angle, not a reflex angle. A reflex angle is greater than 180 degrees but less than 360 degrees.

B. An angle that measures 65 degrees is an acute angle.

This statement is true. An acute angle is an angle that measures less than 90 degrees. Since 65 degrees is less than 90 degrees, it is indeed an acute angle.

C. An acute angle measures less than 90 degrees.

This statement is true. By definition, an acute angle is any angle whose measure is less than 90 degrees.

D. An angle that measures 300 degrees is an obtuse angle.

This statement is false. An obtuse angle is an angle that measures more than 90 degrees but less than 180 degrees. Since 300 degrees is greater than 180 degrees, it is not an obtuse angle but rather a reflex angle.

The conversion factor to convert cups to liters is 0.237. When converting from cups to liters, multiply the number of cups by 0.237.

According to the conversion table provided, the conversion factor to convert cups to liters is 0.237. That means for every 1 cup, it equals approximately 0.237 liters. To convert from cups to liters, you simply multiply the number of cups by this conversion factor, 0.237.

For example, to find out how many liters is 2 cups, you do the multiplication: 2 cups * 0.237 = 0.474 liters.

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The complete question is given below:

Given : A table showing conversions for common units of capacity.

                              Units of  capacity  

Customary System Units                             Metric System Units

        1 gallon                                                           3.79 liters

        1 quart                                                            0.95 liters

         1 pint                                                              0.473 liters

         1 cup                                                              0.237 liters

What is the conversion factor to convert cups to liters?

The conversion factor to convert cups to liters, according to the given table, is that 1 cup equals 0.237 liters. To convert any amount of cups to liters, multiply the number of cups by 0.237.

The table in your question provides the conversion factors for common units of capacity, including the conversion of cups to liters in both the Customary and Metric systems.

According to the table, 1 cup is equivalent to 0.237 liters. This means that to convert any given number of cups to liters, you multiply the number of cups by 0.237.

For example, to convert 5 cups into liters, you would perform the following calculation: 5 cups × 0.237 = 1.185 liters. This conversion factor is useful in everyday scenarios such as cooking or reading a recipe that uses different measurement systems.

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Measure of angle is equals to 39degrees as per given conditions of supplement and complement angles.

" Angle is defined as when two rays meet at one endpoint known as vertex."

According to the question,

'x' represents the measure of an angle

Measure of its supplement angle = 180 - x

Measure of its complement angle= 90 - x

As  per given condition of angle we get,

[tex]180 - x = 2(90 - x) +39\\\\\implies 180-x= 180 -2x +39\\\\\implies 2x-x = 39\\\\\implies x=39degrees[/tex]

Hence, measure of angle is equals to 39degrees as per given conditions of supplement and complement angles.

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