Jose creates a scale drawing of a character from one of his comic books using a scale factor of 40%. Caroline wants to use Jose’s scale drawing to create the original-size image of the comic book character. What scale factor will Caroline need to use to draw the original-size image?

Final answer:

Elizabeth's speed in miles per hour is calculated using the formula for speed, which is distance divided by time. By setting up the proportion with the given numbers, it's determined that Elizabeth runs at a speed of 7.5 miles per hour.

Explanation:

To calculate Elizabeth's speed in miles per hour, we need to use the information that 3/4 mile is covered in 1/10 of an hour and then find out how many miles would be covered in one full hour. To do this, we set up a proportion where the distance (miles) is divided by the time(hours).

The formula for finding speed is:

Speed = Distance / Time

Using the given numbers:

Speed = (3/4) miles / (1/10) hour

By performing the division, we get:

Speed = (3/4) × (10/1) miles/hour

Speed = (30/4) miles/hour

Speed = 7.5 miles/hour

Therefore, Elizabeth runs at a speed of 7.5 miles per hour.

Final answer:

The statement that equations 'a + 4 = 8' and '4 - m = 2' have exactly one solution is always true, as these are linear equations with one variable. Such equations normally have a unique solution when they are not degenerate.

Explanation:

The statement 'Equations like a + 4 = 8 and 4 - m = 2 have exactly one solution' is always true. For the equation a + 4 = 8, there exists one and only one number a such that when you add 4 to it, you get 8.

Similarly, for 4 - m = 2, there is exactly one solution for m that makes the equation true. These are examples of linear equations with one variable, which have a unique solution assuming they are not degenerate (such as an equation like 0x = 0 which has infinitely many solutions).

In general, if a and b are two given numbers, there exists one and only one number x, and also one and only one number y, such that a+x=b, and y+ a = b respectively.

This principle follows from the property of numbers where there exists a definite number, called 0, such that for every number a, we have a + 0 = a and 0 + a = a. Equations are statements of truth, like √4=±2 which indicates a solution set of {-2, 2} for the equation x² = 4.

The original two-digit number is 86. We determined this through solving a system of equations where the sum of the digits is 14 and doubling the reversed number before adding it to the original number equals 222.

The student is given a mathematical problem involving a two-digit number. First, we are told that the sum of the digits of the number is 14. Let's assume that the number is made up of digits a and b, where a is the tens digit and b is the ones digit. Therefore, our number can be represented as 10a + b and the reversed number as 10b + a.

According to the given information:

Writing the second equation in standard form gives us 20b + 2a + 10a + b = 222, which simplifies to 21b + 12a = 222. Using the first equation, we can substitute the value of b as (14 - a) into the second equation, resulting in 21(14 - a) + 12a = 222. Solving for 'a' gives us a value of 8, and consequently, b equals 6. Therefore, the original number is 86.

The original number is 86.

To find the original number, let's assume the tens digit as 'x' and the units digit as 'y'. So, the original number can be written as 10x + y.

According to the question, we have two equations:

Equation 1: x + y = 14 (The sum of digits is 14)

Equation 2: (10y + x) + 2(10x + y) = 222 (Double the reversed number and add it to the original number is 222)

Simplifying Equation 2, we get: 12x + 21y = 222

We can now solve the system of equations by substituting the value of 'x' from Equation 1 into Equation 2:

12(14 - y) + 21y = 222

Simplifying further, we get:

168 - 12y + 21y = 222

Combining the 'y' terms, we get:

9y = 54

Dividing both sides by 9, we get:

y = 6

Substituting the value of 'y' into Equation 1, we get:

x + 6 = 14

Subtracting 6 from both sides, we get:

x = 8

Therefore, the original number is 10x + y = 10(8) + 6 = 86.

Say f(x) = y.

Consider option A.

[tex]y=\sqrt{x} -2[/tex]

[tex]y+2=\sqrt{x}[/tex]

Squaring, we get,

[tex](y+2)^{2} =x[/tex]

Clearly, the above equation represents a parabola (open right) with vertex at (0, -2).

We can easily notice that this function is graphed.

Answer:

yea

Step-by-step explanation:

Answer:

We cant see anything

Step-by-step explanation:

The length of RS is 64 units. Therefore, the correct answer is C. 64.

Since HJKL is similar to QRST, corresponding sides of the two figures are proportional.

Given that the scale factor applied to HJKL to create QRST is 8 to 7, this means that the ratio of corresponding sides of HJKL to QRST is 8:7.

Let's denote the length of RS as x.

According to the scale factor, the ratio of corresponding sides RS and HJ is 8:7. So, we can set up the following proportion:

[tex]\[\frac{RS}{HJ} = \frac{8}{7}\][/tex]

Given that HJ is 56 units (since 8 times the length of HJ), we can solve for RS:

[tex]\[x = \frac{8}{7} \times 56\][/tex]

[tex]\[x = \frac{448}{7}\][/tex]

[tex]\[x = 64\][/tex]

Therefore, RS is 64 units.

So, the correct answer is C. 64.

In this exercise we have to use the knowledge of division, that is, how much is left of a certain food that is found in terms of fraction, in this way we can say that:

[tex]3/8[/tex] left.

So to calculate this exercise, we have to use the total amount minus the amount eaten to find what's left, so we have to:

[tex]8/8-5/8=3/8[/tex]

See more about fraction at brainly.com/question/1301963

its d so i really hope this help