The ratio of the number of text messages sent by Diego to the number of text messages sent by his sister is 3 to 4. Diego sent 18 text messages. How many more text messages did his sister send?​

Answer: passes a horizontal AND vertical line test✅; no repeating x values✅

Step-by-step explanation:

To pass a line test, the function must pass BOTH the horizontal and vertical line test. If it only passes one but not the other, is it NOT a function.

Lastly, it can be a function if it has repeating y values.

Answer: We have f(x)=3x⁵+6x²-5 and g(x)= 2x⁴+7x²-x+16

                        (f-g)(x)= 3x⁵-2x⁴-x²+x-21

Step-by-step explanation:

Here we have,

Given : f(x)=3x⁵+6x²-5 and g(x)= 2x⁴+7x²-x+16

We know,

(f-g)(x)= f(x)-g(x)

= (3x⁵+6x²-5 ) - ( 2x⁴+7x²-x+16)

On subtracting g(x) from f(x) we get,

(f-g)(x)= (3x⁵+6x²-5  - 2x⁴-7x²+x-16)

On simplify,

 (f-g)(x) =3x⁵-2x⁴-x²+x-21

Hence,

(f-g)(x) = f(x) - g(x) = 3x⁵-2x⁴-x²+x-21

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Answer:(-5,-28)

Step-by-step explanation:

Hi

Answer:

D

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = \(\frac{1}{2}\) x + 3 ← is in slope- intercept form

with slope m = \(\frac{1}{2}\)

• Parallel lines have equal slopes , then

y = \(\frac{1}{2}\) x + c ← is the partial equation

to find c substitute (2, - 4 ) into the partial equation

- 4 = \(\frac{1}{2}\) (2) + c = 1 + c ( subtract 1 from both sides )

- 5 = c

y = \(\frac{1}{2}\) x - 5 ← equation of parallel line

The total time taken for the entire journey is 2.8 hours.

To calculate the total time taken for the entire journey, we can use the formula:

Time = Distance / Speed

For the first part of the journey, the car travels a distance of 112 km at an average speed of 70 km/h. Using the formula, the time taken for this part is:

Time1 = 112 km / 70 km/h = 1.6 hours

For the second part of the journey, the car travels a further distance of 60 km at an average speed of 50 km/h. Again, using the formula, the time taken for this part is:

Time2 = 60 km / 50 km/h = 1.2 hours

To find the total time for the entire journey, we sum up the times for both parts:

Total Time = Time1 + Time2 = 1.6 hours + 1.2 hours = 2.8 hours

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Answer:

Step-by-step explanation:

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To divide the 1/4 of a pound into two equal parts, it is necessary to divide 1/4 by 2, as follow:

(1/4)/2

if 2 is written as 2/1, the previous quotient can be written as a product:

(1/4) (1/2) = 1/8

Now, to write a general expression that takes into account the number of siblings, you name the number of siblings as x. Thus, you have:

(1/4)/(x) = 1/(4x)

Answer:

10 years

Hence, it will take 10 years for the sum of money to double itself with the rate of 10% per annum simple interest. Note: While solving questions related to principal interest, it is important to keep in mind that simple interest calculated from the formula, Simple Interest (I) = P × R × t 100, doesn’t represent the total amount of money.

Step-by-step explanation:

Answer: 17/20

Step-by-step explanation:

85% to 85/100

Then divide 85/100 by 5

17/20

The m<3 is approximately equal to 85.39 degrees.

The sum of the measures of the angles of a triangle is 180 degrees. So, we have:

m<1 + m<2 + m<3 = 180

So, (3x + 12) + (3x + 18) + (7x + 10) = 180

Simplifying and solving for x, we get:

13x + 40 = 180

13x = 140

x = 10.77

Now, we can find m<3 by substituting x in the expression for m<3:

m<3 = 7x + 10

m<3 = 7(10.77) + 10

m<3 = 85.39

Therefore, m<3 is approximately equal to 85.39 degrees.

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Line (1) to line (2)

Commutative property of addition

Because

Line (2) to Line (3)

Distributive Property.

Because

Answer: I’m

Step-by-step explanation: I’d not knkw

Answer:

a = 5

Step-by-step explanation:

Topic: Pythagorean Theorem

In this problem, we need to solve for a missing side in a right triangle using the Pythagorean theorem.

Formula: \(a^2 + b^2 = c^2\)

Parts:

Step 1: Plug in information

We want to use the info we have and plug in the values for the variables

"a" is unknown, so we can leave it like that

"b" is the second-longest and it is a leg. In this case, it is 12

"c" is the hypotenuse and the longest side. This has a value of 13

We can use this to rewrite the equation

a² + 12² = 13²

Step 2: Solve for a

We want all terms with "a" on one side, and we want "a" alone, no exponents, nothing.

a² + 12² = 13²

a² = 13² - 12²

a = √(13² - 12²)

Step 3: Solve for a

The rest is the same, just solving the equations. Remember, square rooting and squaring are not distributive to adding and subtracting. This means that √(13² - 12²) is not 13 - 12.

a = √(13² - 12²)

a = √(169 - 144)

a = √(25)

a = 5

-Chetan K

Answer:

The length of a is 5.

Step-by-step explanation:

Solution :

Here, we have given that the two sides of triangle are 12 and 13.

Finding the third side of triangle by pythagorean theorem formula :

\({\longrightarrow{\pmb{\sf{{(c)}^{2} = {(a)}^{2} + {(b)}^{2}}}}}\)

Substituting all the given values in the formula to find the third side of triangle :

\(\begin{gathered}\quad{\longrightarrow{\sf{{(c)}^{2} = {(a)}^{2} + {(b)}^{2}}}}\\\\\quad{\longrightarrow{\sf{{(13)}^{2} = {(a)}^{2} + {(12)}^{2}}}}\\\\\quad{\longrightarrow{\sf{{(13 \times 13)} = {(a)}^{2} + {(12 \times 12)}}}}\\\\\quad{\longrightarrow{\sf{(169)= {(a)}^{2} + (144)}}}\\\\\quad{\longrightarrow{\sf{169 = {(a)}^{2} + 144}}}\\\\\quad{\longrightarrow{\sf{{(a)}^{2} = 169 - 144}}}\\\\\quad{\longrightarrow{\sf{{(a)}^{2} = 25 }}}\\\\\quad{\longrightarrow{\sf{a= \sqrt{25}}}}\\\\\quad{\longrightarrow{\sf{a= \sqrt{5 \times 5}}}}\\\\\quad{\longrightarrow{\sf{a= 5}}}\\\\ \qquad\star{\underline{\boxed{\frak{\red{a= 5}}}}}\end{gathered}\)

Hence, the length of a is 5.

\(\rule{300}{2.5}\)

To find the distance between Basti and Cian, we can use the law of sines in triangle ABC. The law of sines states that the ratio of the length of a side to the sine of the opposite angle is constant for all sides and their corresponding angles in a triangle.

Let's label the distance between Basti and Cian as "x". We know that the measure of angle ABC is 50 degrees and the measure of angle BAC is 60 degrees. We also know that Ali is exactly 150 ft away from Basti.

Using the law of sines, we can set up the following equation:

sin(50°) / 150 = sin(60°) / x

To solve for "x", we can rearrange the equation:

x = (150 * sin(60°)) / sin(50°)

Using a calculator, we can evaluate the expression:

x ≈ (150 * 0.866) / 0.766

x ≈ 168.4 ft

Therefore, the distance between Basti and Cian is approximately 168.4 ft.

Answer:

reeee whenever it was happy bday ily by :)

Computing the total number of counters in the class as 1,108, the mean number of counters that the 46 children have is 24.

The mean refers to the average value.

The average is the quotient of the total value divided by the number of items in the data set.

The number of boys in the class = 26

The number of girls in the class = 20

The total number of boys and girls in the class = 46

The mean number of counters that the boys have = 28

The total number of counters that the boys have = 728 (28 x 26)

The mean number of counters that the girls have =19

The total number of counters that the girls have = 380 (19 x 20)

The total number of counters that the class has = 1,108 (728 + 380)

The average or mean number of counters in the class = 24 (1,108 ÷ 46)

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The theorem states that if a set of vectors {v1, ..., vp} in R^n has more vectors than entries in each vector (p > n), then the set is linearly dependent, so it is free variable and a nontrivial solution.

This means that there exists a nontrivial solution to the equation Ax = 0, where A is the matrix formed by the vectors v1, ..., vp.

The proof involves showing that the corresponding matrix A has more variables than equations, resulting in a free variable and a nontrivial solution for Ax = 0. Figure 3 illustrates this theorem and shows that the columns of the matrix A are linearly dependent when p > n. Figure 3 is a visualization of this theorem using a 5 x 3 matrix.

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--The given question is incomplete, the complete question is given

" If a set contains more vectors than there are entries in each vector, then the set is linearly dependent: That is_ any set V1 , Vp} in R" is linearly dependent if p > n. FIGURE 3 p > n . the columns are linearly dependent: PROOF Let A = [V1 Then A is n X p, and the equation Ax corre - sponds t0 a system of n equations in p unknowns. If p > n, there are more variables than equations_ So there must be a free variable. Hence Ax 0 has a nontrivial solution and the columns of A are linearly dependent. See Figure 3 for a matrix version of this theorem matric version is P= n[*]5 x 3 matrix "--

On solving the provided question, we can say that the range of this data will be as follows, range = {2,3 U (-3,7)}

The variable's range is obtained by finding its largest observed value (maximum) and subtracting its smallest observed value (minimum). Variational bounds or possible range: various steel prices; various styles; The extent or magnitude of a procedure or action: insight. the maximum or expected range of a weapon's projectile. The range of a list or set is the number between the minimum and maximum. Prior to identifying the region, align all the numbers. Remove (remove) the lowest number from the highest number next. The list's range is provided in the solution.The solution provides the list's range.

the range of this data will be as follows,

range = {2,3 U (-3,7)}

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The option that best describes the dispersion of the data is: "The data has a range of 5, which is a narrow dispersion. This means that most students have taken a similar number of flights." Thus, option C is correct.

The variable's range is obtained by finding its largest observed value (maximum) and subtracting its smallest observed value (minimum). Variational bounds or possible range: various steel prices; various styles; The extent or magnitude of a procedure or action: insight. the maximum or expected range of a weapon's projectile. The range of a list or set is the number between the minimum and maximum. Prior to identifying the region, align all the numbers.

In the case presented, the range is the difference between the maximum value and the minimum value of the data. The range describes the breadth of the data and how much they vary from the minimum value to the maximum value. Therefore, the range indicates the dispersion of the data.

The statement indicates that the range is 5, which means that the most flights made by students is 5. Since the data has a narrow dispersion, we can conclude that most students have taken a similar number of flights, implying that most students have flown an amount close to the maximum number observed.

Therefore, the option that best describes the dispersion of the data is: "The data has a range of 5, which is a narrow dispersion. This means that most students have taken a similar number of flights."

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if Judy took $30 with her to spend on popcorn and drinks for herself and her friends at the movie theater. The price for each bag of popcorn was $5. The price of each drink was half the price of a bag of popcorn.Graph the piecewise function and Graph the step function over the interval. you need to solve for how many freinds she has.

Answer:

54

Step-by-step explanation:

ratio is 7:9

7=42

9=?

9×42÷7

Answer:

0.000000010

Step-by-step explanation:

Answer:

\(P(Woman) = \frac{23}{106}\)

Step-by-step explanation:

Given

\(Women = 23\)

\(Men = 83\)

Required

\(P(Woman)\)

This is calculated as the number of women divided by the population of the class

i.e.

\(P(Woman) = \frac{Women}{Women + Men}\)

So, we have:

\(P(Woman) = \frac{23}{23+83}\)

\(P(Woman) = \frac{23}{106}\)

The reason that the point (3, 5) is not a solution to the given inequality is given below.

We are given that;

y > 2x + 1

Now,

The inequality y > 2x + 1 can be graphed by first graphing the boundary line y = 2x + 1. Since the inequality is strict (y >), we draw a dashed line to indicate that points on the line are not solutions to the inequality. Then, we shade the region above the line to indicate all points that satisfy the inequality.

If we have (3,5) as a point, we can see that it lies on the boundary line

y = 2x + 1.

Since the inequality is strict (y >), points on this line are not solutions to the inequality

Therefore, by the inequality the answer will be given above.

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Julio accidentally put in an extra 1/10 cup of sugar.

To calculate the number of extra cups of sugar that Julio put in, we need to find the difference between what the recipe called for (3/10 cups) and what he actually added (4/10 cups).

The difference can be calculated as follows:

Actual amount - Required amount = Extra amount

= 4/10 - 3/10

= 1/10

Therefore, Julio accidentally put in an extra 1/10 cup of sugar.

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The dimensions of the room are approximately 5.87 meters by 7.63 meters.

Let's assume the width of the room is "x" meters.

According to the problem, the length of the room is 1.3 times the width, so the length would be 1.3x meters.

The perimeter of a rectangle is calculated by adding the lengths of all four sides. In this case, the perimeter is given as 27 meters.

Perimeter = 2(length + width)

Substituting the values we know:

27 = 2(1.3x + x)

Simplifying:

27 = 2(2.3x)

27 = 4.6x

Dividing both sides by 4.6:

x = 27 / 4.6

x ≈ 5.87

The width of the room is approximately 5.87 meters.

To find the length, we can multiply the width by 1.3:

Length = 1.3 * 5.87 ≈ 7.63

The length of the room is approximately 7.63 meters.

Therefore, the dimensions of the room are approximately 5.87 meters by 7.63 meters.

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Answer:

96Consider the arithmetic sequence with a first term of 11 and sixth term of 21. What is the

sum of these first six terms?

The required sum of the first 6th term of an arithmetic progression is 96. Option D is correct.

Given that,
Consider the arithmetic sequence with the first term of 11 and the sixth term of 21. To determine the sum of these first six terms.

Arithmetic progression is the series of numbers that have common differences between adjacent values

Geometric progression is a sequence of series whose ratio with adjacent values remains the same.

Here,
First term a = 11
6th term = a + 5d
21 = 11 + 5d
5d = 10
d = 2
Now,
sum of the six terms, = 6 / 2{11 + 21}
                                   = 3 (32)
                                   = 96

Thus, the required sum of the first 6th term of an arithmetic progression is 96. Option D is correct.

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