There were some pencils in a pencil box. Zoe added 7 more pencils to the pencil box. Now there are 24 pencils in the box. How many pencils were in the box to start with?

Using the Mean Value Theorem, we can determine the possible values for f(2) which is D) 1

To find the possible values for f(2), we can use the Mean Value Theorem. Taking into consideration the mean value theorem, the value of the function f'(x) has to have the value equal to the average slope between the two points at at least one point between the two given values.

Since f(0) = -5 and f'(x) is less than or equal to 3 for all x, we know that f(2) must lie between -5 and -5 + 3(2) = 1.

Therefore, 1 is not a possible value for f(2), making the correct answer choice D) 1.

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It is -1/2x + 2...she just didnt add the negative sign

The equation of line will be -

y = [tex]-\frac{1}{2} x[/tex] + 2

We have a graph as shown in the figure.

We have to find out the equation of this straight line in the graph.

The general form of a equation of a straight line is -

y = mx + c

where -

m - slope of line

c - the y - intercept

We have -

The y intercept of the straight line as = (0, 2)

The x intercept of the straight line as = (4, 0)

The slope of the line will be m = [tex]\frac{2 - 0}{0 - 4}[/tex] = - [tex]\frac{1}{2}[/tex]

The y-intercept is at (0, 2) , therefore the value of c = 2.

Substituting the values in the general equation of line we get -

y = mx + c

y = [tex]-\frac{1}{2} x[/tex] + 2

Hence, the equation of line will be -

y = [tex]-\frac{1}{2} x[/tex] + 2

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Answer:

G (-6,-8) H(-2,-2) F(0,-4)

Step-by-step explanation:

So really you add an negitive symbol to each number then its reflected acroos the x axis

To find all possible values for θ if 0° < θ < 360° and tanθ = -1, we need to determine in which quadrants the tangent function is negative and then find the specific angles in those quadrants where the tangent equals -1.

The tangent function is negative in the second and fourth quadrants. Since tan(45°) = 1, we are looking for angles where the reference angle is 45° and the tangent is negative.

In the second quadrant, the angle that meets these criteria is 180° - 45° = 135°.

In the fourth quadrant, the angle that meets these criteria is 360° - 45° = 315°.

Therefore, the correct values for θ are:

c. 135°

e. 315°

The correct answer is [tex]135^{0}[/tex], [tex]225^{0}[/tex]

To find all possible values of θ if 0° < θ < 360° and tan θ = -1, we need to consider the values of θ in the different quadrants where the tangent function is negative.

In the first quadrant (0° < θ < 90°), the tangent function is positive, so there are no solutions in this range.

In the second quadrant (90° < θ < 180°), the tangent function is negative, and tan(135°) = -1.

In the third quadrant (180° < θ < 270°), the tangent function is also negative, and tan(225°) = -1.

In the fourth quadrant (270° < θ < 360°), the tangent function is positive, so there are no solutions in this range.

Therefore, the possible values of θ satisfying the given conditions are:

[tex]\theta = 135^\circ and \theta = 225^\circ[/tex]

Analyzing the given options:

a. [tex]-225^\circ[/tex] is not a solution, as it lies outside the given range of 0° < θ < 360°.

b. [tex]-45^\circ[/tex] is not a solution, as the tangent function is positive in the fourth quadrant.

c. [tex]135^\circ[/tex] is a solution, as tan(135°) = -1.

d. [tex]225^\circ[/tex] is a solution, as tan(225°) = -1.

e. [tex]315^\circ[/tex] is not a solution, as the tangent function is positive in the fourth quadrant.

Therefore, the correct options are c. 135° and d. 225°.

The area of the figure that is made up of a triangle and a semicircle is 23.137 units².

The area of a triangle is half the product of its base and its height.

[tex]Area \triangle = \dfrac{1}{2}\times base \times height[/tex]

In order to solve the problem, we will divide the given figure into two parts such that the first one will be a right-angled triangle while the second one is a semi-circle as shown below.

As we can see in the ΔABC, the height of the triangle is 3 units, while the length of the base of the triangle is 6 units. therefore, the area of the triangle can be written as,

[tex]\begin{aligned}\triangle ABC &= \dfrac{1}{2} \times height \times base\\\\&= \dfrac{1}{2} \times BC \times AB\\\\& = 0.5 \times 3 \times 6\\\\& = 9\rm\ unit^2 \end{aligned}[/tex]

Now, if we look at the semi-circle we will find that the diameter(BC) of the semi-circle is 3 units, therefore, the area of the semi-circle can be written as,

[tex]\begin{aligned}\text{Area of Semi-circle} &= \dfrac{\pi}{2}d^2\\\\ &= \dfrac{\pi}{2}(3)^2\\\\&= 14.137\rm\ units^2 \end{aligned}[/tex]

Further, in order to get the total area of the figure, simply add the two areas, therefore,

The area of the figure = Area of triangle + Area of the semi-circle

                                     = 9 + 14.137

                                     = 23.137 units²

Hence, the area of the figure that is made up of a triangle and a semicircle is 23.137 units².

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Answer:

B

Luis’s, because he flipped the inequality sign when he subtracted

Step-by-step explanation:

got it right on Edge

please mark as Brainliest

(P.S. Luis is my first name)

Answer:

Just did it

The answer is 3

Step-by-step explanation:

The correct properties of equality used to solve the equation given x = 8 are Given, Substitution Property, Subtraction Property of Equality, Division Property of Equality, and Symmetric Property of Equality.

The student has shared the steps of solving an equation and is asking for the correct sequence of properties used to solve it:

The correct properties of equality should be applied as follows:

A ratio shows us the number of times a number contains another number. The correct option is C.

A ratio shows us the number of times a number contains another number.

The complete answer is mentioned in the below image.

The ratio of the hypotenuse to the given side is,

Ratio = (6√2)/ 6 = √2 : 1

Hence, the correct option is C.

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Answer: B

Step-by-step explanation: EDGE 2022

The correct answer is (d). If d represents the number of dimes and q the number of quarters, the total number of coins would be d+q, which is given as 40 in the prompt: d+q=40

Since each dime is worth ten cents and each quarter worth twenty-five cents, their total value would be 0.10d+0.25q which would total 5.80.: 0.10d+0.25q=5.80        I HOPE THIS HELPS YOU

To solve the inequality -4.9x + 1.3 > 11.1, subtract 1.3 from both sides and then divide by -4.9, flipping the inequality sign to get x < -2. The solution set is x < -2.

To solve the inequality -4.9x + 1.3 > 11.1, follow these steps:

The solution set for the inequality is x < -2.

Answer:

Option B. 4

Step-by-step explanation:

By the table mentioned by you in the comments that the correct table is

x(miles)   2        5        8     12

y(cost)   8.5   15.25    22    31

As we know that the standard equation of a linear function is represented as

y = mx + c

For the points (2, 8.5) and (5, 15.25)

[tex]Slope(m)=\frac{15.25-8.5}{5-2}=\frac{6.75}{3}=2.25[/tex]

y = 2.25x + c

This function passes through (2, 8.5)

8.5 = 2.25×2 + c

c = 8.5 - 4.5 = 4

Therefore, y- intercept of the function will be option B. 4.

The y-intercept of this line is (4). Therefore, the estimated y-intercept of the function represented by the given data is 4.

To find the y-intercept of the function from the provided table, we look for the point where (x = 0), which represents the cost when no miles are traveled.

However, in the given table, there is no entry for \(x = 0\), which means we don't have a direct value for the y-intercept from the given data.

To estimate the y-intercept, we can use the concept of linear interpolation.

We can assume that the relationship between miles traveled and cost is linear, so we can find the slope of the line passing through two consecutive points and use it to estimate the cost when (x = 0).

Using the points (2, 8.5) and (5, 15.25) from the table:

[tex]\[ \text{Slope} = \frac{{15.25 - 8.5}}{{5 - 2}} = \frac{6.75}{3} = 2.25 \][/tex]

Now, we can use the slope and one of the points to find the y-intercept using the point-slope form of the equation of a line: [tex]\(y - y_1 = m(x - x_1)\).[/tex] Let's use the point (2, 8.5):

y - 8.5 = 2.25(x - 2)

y - 8.5 = 2.25x - 4.5

y = 2.25x + 4

The y-intercept of this line is (4). Therefore, the estimated y-intercept of the function represented by the given data is [tex]\(\boxed{4.00}\)[/tex].

Complete question:

By the table mentioned by you in the comments that the correct table is

x(miles)   2        5        8     12

y(cost)   8.5   15.25    22    31
In the table below, x represents miles traveled and y represents the cost to travel by train.

What is the y-intercept of this function?

2.25

4.00

6.50

17.13

Corresponding angles : 1 & 5 , 2 & 6 , 4 & 7 , 3 & 8 .

Alternate interior angles : 4 & 6 , 3 & 5

Alternate exterior angles : 1 &8 , 2 & 7

Consecutive interior angles : 4 & 5, 3 & 6

By using the above definitions,

Corresponding angles : 1 & 5 , 2 & 6 , 4 & 7 , 3 & 8 .

Alternate interior angles : 4 & 6 , 3 & 5

Alternate exterior angles : 1 &8 , 2 & 7

Consecutive interior angles : 4 & 5, 3 & 6