what is the difference between the longest and the shortest pencil​

Answer is A because it’s moved 2 to the right which makes it x-2 and it’s moved 1 down so -1 and it needs to be -x because it’s facing down so the answer is A

Answer:

Option A. f(x) = -(x - 1)² - 1

Step-by-step explanation:

After the transformation of g(x) = x², vertex of the red parabola f(x) is (2, -1).

Therefore, equation of the parabola in the vertex form will be

f(x) = (x - 2)² - 1

Since opening of the parabola is downwards so the function will be

f(x) = - (x - 2)² - 1

This function matches with option A.

[tex]7\frac{4}{5} = \frac{28}{5}[/tex]

because 7 x 4 = 28

[tex]4\frac{7}{5} = \frac{28}{5}[/tex]

because 4 x 7 = 28

This means that

[tex]7\frac{4}{5} = [tex]4\frac{7}{5}[/tex]

[tex]6\frac{12}{5} = \frac{72}{5}[/tex]

because 6 x 12 = 72

This means

[tex]7\frac{4}{5} = [tex]6\frac{12}{5}[/tex]

Answer:

[tex]\large\boxed{The\ vertex:\ (-5,\ 49)}[/tex]

Step-by-step explanation:

[tex]f(x)=ax^2+bx+c\\\\\text{The vertex}\ (h,\ k),\ \text{where}\ h=\dfrac{-b}{2a}\ \text{and}\ k=f(h).\\\\\text{We have:}\ y=-x^2-10x+24\to f(x)=-x^2-10x+24\\\\a=-1,\ b=-10,\ c=24.\\\\\text{Substitute:}\\\\h=\dfrac{-(-10)}{2(-1)}=\dfrac{10}{-2}=-5\\\\k=f(-5)=-(-5)^2-10(-5)+24=-25+50+24=49[/tex]

Answer:

1024πcm²

Step-by-step explanation:

The surface area of a sphere is found using the following formula:n A=4πr². r is the radius while A is the surface area.

in the sphere the radius is 16 cm thus:

A=4×π×16²

=1024π cm²

Answer:

The correct answer is third option 1024π

Step-by-step explanation:

Formula:-

Surface area of sphere = 4πr²

Where r is the radius of sphere

To find the surface area of sphere

Here r = 16

Surface area =  4πr²

  = 4 * π *16²

  = 4 * π * 16 * 16 = 1024π

Therefore surface area of sphere = 1024π

The correct answer is third option 1024π

Answer:

x = 5

Step-by-step explanation:

In this problem, the angles are vertical, which mean that they are congruent.

So we can set them equal to each other and solve.

13x + 19 = 84

Subtract 19 from both sides.

13x = 65

Divide each side by 13

x = 5

Answer:

8

Step-by-step explanation:

200 divided by 25 is 8

Step-by-step explanation:

Area of a trapezoid is 1/2h(b1+b2)

So let's substitute.

1/2*17*(15+27)

1/2*17*42

Answer is 357 cm squared

40+20=72-12 is how you rewrite it

To correctly rewrite the equation 4(10+5)=6(12-2) using the distributive property, we apply the property to each term inside the parentheses. The equation can be correctly rewritten as 60=60.

To correctly rewrite the equation 4(10+5)=6(12-2) using the distributive property, we apply the property to each term inside the parentheses. Starting with the left side, we have 4(10+5). Using the distributive property, this becomes 4(10) + 4(5) = 40 + 20 = 60. Now, let's apply the distributive property to the right side of the equation. We have 6(12-2), which becomes 6(12) - 6(2) = 72 - 12 = 60. Therefore, the equation 4(10+5)=6(12-2) can be correctly rewritten as 60=60 using the distributive property.

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Answer:

48.4512

product means the answer so just multiply.

Answer:

it is 48.4512

Step-by-step explanation:

so what i like to do is first step: dont worry about the decimals at the moment so the equation would be 824 x 588. then it is 484,512. Third step is count how many numbers is behind the decimals. There are 4 so move 4 spaces to the left which we get 48.4512. Hope this helps!

Answer:

[tex] 0.25 [/tex]

Step-by-step explanation:

We are given the following verbal expression and we are to first translate it and then evaluate it:

'6- the square root of 25 divided by 4'

[tex] \frac { 6 - \sqrt { 25 } } { 4 } [/tex]

Taking the square root first to get:

[tex] \frac { 6 - 5 } { 4 } [/tex]

[tex] \frac { 1 } { 4 } [/tex]

[tex] 0.25 [/tex]

Answer:

.25

Step-by-step explanation:

ANSWER

[tex]y \leqslant - 2x - 2[/tex]

EXPLANATION

The boundary line passes through (-2,2) and (0,-2).

The slope of this line is

[tex]m = \frac{ - 2 - 2}{0 - - 2} [/tex]

[tex]m = \frac{ - 4}{2} = - 2[/tex]

The y-intercept is , c=-2.

The slope-intercept form of this line is given by;

[tex]y = mx + c[/tex]

We substitute values to obtain;

[tex]y = - 2x - 2[/tex]

Since the lower half-plane is shaded the required inequality is

[tex]y \leqslant - 2x - 2[/tex]

Answer:

1 3/8 ft.

Step-by-step explanation:

The cabinet's center will be at the same place as the wall's center. The wall's center is at its 3 1/8 ft mark. The cabinet's center will also be at the wall's 3 1/8 mark. This means that both sides of the cabinet is 1 3/4 around the center line (if my wording is vague, look at the image). So, we have to find 3 1/8 - 1 3/4, which is 1 3/8 ft.

Subtraction is one of the most basic mathematical operations. The end of the cabinet is 1.375 feet far from the edge of the wall.

Subtraction is a mathematical operation that reflects the removal of things from a collection. The negative symbol represents subtraction.

The centre of the cabinet will lie at half the width of the cabinet, therefore, the centre of the cabinet will be at,

[tex]\text{Centre of the cabinet}= \dfrac{3\frac{1}{2}}{2}[/tex]

                                  [tex]\rm = \dfrac{\frac{(3 \times 2)+1}{2}}{2}\\\\=\dfrac{7}{2 \times 2} = \dfrac{7}{4} = 1.75\ feet[/tex]

Since Bobby wants the cabinet to be at the centre of the wall horizontally, we need to find the centre point of the wall as well, and then align both the centres together, therefore, the centre of the wall is at,

[tex]\text{Centre of the wall} = \dfrac{6\frac{1}{4}}{2}[/tex]

                            [tex]\rm = \dfrac{\frac{(6 \times 4)+1}{4}}{2}\\\\=\dfrac{25}{2 \times 4} = \dfrac{25}{8} = 3.125\ feet[/tex]

Now, the length between the end of the cabinet from the edge of the wall is the difference between the half the length of the wall and half the length of the cabinet, therefore, the length can be written as,

[tex]\rm Length = \text{Centre of the Wall} - \text{Centre of the Cabinet}\\[/tex]

            [tex]\rm = 3.125 - 1.75\\\\= 1.375\ feet[/tex]

Hence,  the end of the cabinet is 1.375 feet far from the edge of the wall.

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Answer:

y=-5/2x-19/2

Step-by-step explanation:

The vertex of the quadratic equation is (-7,8).

Isolate the variable y for the equation 2x-5y=7

You get y = 2/5x-7/5

The slope we have to find is the inverse of the current slope.

So the slope for the final equation is -5/2.

Then use point slope form to get y - 8 = -5/2 * (x+7)

Then convert it into slope intercept form to get y - 8 = -5/2x - 35/2

Then add 8 to each side to get y=-5/2x-19/2

Answer:

b

Step-by-step explanation:

The true statement is B. A rhombus is a parallelogram. This is true because rhombuses have parallel opposite sides, defining them as parallelograms. The other statements are false due to specific conditions not met by all parallelograms, rhombuses, or trapezoids.

The true statement among the options provided is B. A rhombus is a parallelogram. This is because all rhombuses have opposite sides that are parallel to each other, which is a defining property of parallelograms. Not all parallelograms are squares because a square is a special type of parallelogram where all sides are equal in length and all angles are right angles - a condition not required for a general parallelogram.

Similarly, not all rhombuses are squares since rhombuses do not require all angles to be right angles. Lastly, a trapezoid typically has only one pair of parallel sides, not two, which differentiates it from parallelograms.

To illustrate why a rhombus is a parallelogram, we can consider A1 Constructibility of parallelograms: Given any three points P, Q, and R, there exists a point S such that quadrilateral PQRS is a parallelogram. In a rhombus, all four sides are of equal length - satisfying the conditions of a parallelogram, which requires only that opposite sides be parallel and of equal length.

When it comes to the diagonals of a rhombus being perpendicular, we use the concept of the scalar or dot product of vectors. The diagonals bisect each other at right angles because the dot product of the vectors representing the diagonals equals zero, indicating that they are perpendicular to each other. This fact further underscores the relationship between rhombuses and parallelograms and their distinct geometric properties.

Answer:

option A is the correct choice

Step-by-step explanation:

The trigonometric equation you are using has a general form

y = A* tan w*(x - r)

Where

A is the amplitude of the function

w is the frequency rad/s

r  is the phase shift

In your case

A = 2

B = w = 3

r = pi/2

y = 2* tan 3*(x - pi/2)

Answer:

y=1/5

Step-by-step explanation:

6x-5y=5

3x+5y=4

we are now going to multiply the second equation by -6

6x-5y=5

-2(3x+5y=4)

so it becomes

6x-5y=5

-6x-10y=-8

the 6 can cancels out so it becomes  -15y=-3

divide both sides by -15

y=1/5

The X coordinate is X = 1

See the image

Answer:

Normally it would be 40 and anything over 80 hours in a two-week time frame would be considered OT

Step-by-step explanation:

Answer:

a. y÷x=5 , b. y=60 because x is increased by 2 times  so y should be increased by 2 times

Step-by-step explanation:

Answer:

0.00487

Step-by-step explanation:

You move the decimal place back 3 places because it’s 10 to the -3

Answer:

0.00487

Step-by-step explanation:

When you have a negative power, you move the decimal point to the left. In this case, move the decimal three places left.

A complete probability model provides a framework for calculating the likelihood of events within an experiment or a process. When we talk about a complete probability model, we are referring to a comprehensive description that includes all necessary components to understand and predict outcomes within a probability space.

Let's look at each option and determine which one correctly describes a complete probability model:

A. A list of all possible outcomes in the sample space and their probabilities.
- **This option is correct because a complete probability model does indeed require a list of all possible outcomes (the sample space) and the probability associated with each outcome.** Every outcome must be accounted for, and the sum of the probabilities of all individual outcomes must equal 1. This is because the sample space encompasses every possible outcome that could occur, and their associated probabilities reflect the likelihood of each of these outcomes.

B. The actual outcomes of a trial.
- This option is incorrect because the actual outcomes of a trial are observational results from a single execution of the probability experiment and do not represent a comprehensive model. A complete probability model is theoretical and does not depend on individual trial results, even though it can predict the distribution of those results over many trials.

C. The number of trials conducted.
- This option is incorrect. The number of trials refers to the experimental aspect of probability where an experiment or process is repeated multiple times. It does not provide a model of the entire probability space, only empirical data based on these repetitions.

D. The difference between the theoretical and experimental probabilities of all outcomes.
- This option is incorrect as it refers to the concept of variance between what is expected theoretically and what is observed in practice. While this can be a useful measure for understanding how closely an experiment follows its theoretical predictions, it is not a description of a complete probability model itself.

Given the options, the correct answer is:
A. A list of all possible outcomes in the sample space and their probabilities.

This is the definition of a complete probability model as it provides the necessary information to fully describe the probability of events within a given context.

Answer:

Step-by-step explanation:

The equation of a circle in a standard form:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

(h, k) - center

r - radius

We have the equation:

[tex]x^2-16x+y^2=36\\\\x^2-2(x)(8)+y^2=36\qquad\text{add}\ 8^2\ \text{to both sides}\\\\\underbrace{x^2-2(x)(8)+8^2}_{(*)}+y^2=36+8^2\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2\qquad(*)\\\\(x-8)^2+(y-0)^2=36+64\\\\(x-8)^2+(y-0)^2=100\\\\(x-8)^2+(y-0)^2=10^2\\\\\text{Therefore}\\\\center:(8,\ 0)\\radius:10[/tex]

Kash to Gary is 8 miles

Gary to Joan is 5 miles

Use the Pythagorean theorem to calculate the distance from Joan to Kash:

x = √8^2 + 5^2

x = √64+25

x = √89

x = 9.4

Total distance = 5 + 8 + 9.4 = 22.4 miles.

Rounded to nearest mile = 22 miles.

Answer:22 miles

Step-by-step explanation:

Got it right on a quiz

Answer:

A=75 cm

Step-by-step explanation:

The formula of the area of a triangle is A=bh/2.

A=(15)(10)/2.

A=150/2

A=75 cm is your answer.

Answer:

A=75 cm

Step-by-step explanation:

A=bh/2 is the formula for the area of a triangle

1) Multiply 15 the base and the height 10 first

A=(15)(10)

A= 150 cm

2) divide 150cm by 2

A=150/2

A=75 cm is your answer.

Hopes this helps My friend!

The solution to the equation j/3 = 4.5 is j = 13.5

From the question, we have the following parameters that can be used in our computation:

j/3 = 4.5

Multiply both sides of the equation by 3

So, we have

3 * j/3 = 4.5 * 3

Evaluate the products

This gives

j = 13.5

Hence, the solution to the equation is 13.5

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To find which binomial is a factor of the polynomial x^2 - x - 6, one needs to factor the polynomial and find its roots. The factored form of the polynomial is (x -2)(x +3), indicating that the roots are x = 2 and x = -3. Consequently, the correct answer is (X - 2).

The question is asking us to identify which of the listed binomials is a factor of the polynomial x^2 - x - 6. A factor of a polynomial is a polynomial which divides the original polynomial exactly. To find the factors of the polynomial x2 - x - 6, we have to solve the equation for it equal to zero, x2 - x - 6 = 0. This is a quadratic equation, and we can find its roots via factoring. The factored form of the polynomial is (x - 2) (x + 3). From the factored form, we see that the roots or zeros of the polynomial are x = 2 and x = -3. Hence, the answer is (X - 2).

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[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{}{ h},\stackrel{}{ k})\qquad \qquad radius=\stackrel{}{ r} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ (x-\stackrel{h}{3})^2+(y-\stackrel{k}{7})^2=9\implies (x-\stackrel{h}{3})^2+(y-\stackrel{k}{7})^2=\stackrel{r}{3^2}~\hfill \begin{cases} center~(3,7)\\ radius=3 \end{cases}[/tex]

Final answer:

The radius of the circle with the equation (x − 3)² + (y − 7)² = 9 is found by taking the square root of 9, which is 3. Therefore, the correct answer is A) 3.

Explanation:

The question asks to find the radius of a circle given its equation. The standard form of the equation of a circle is (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius. Comparing this with the given equation (x − 3)² + (y − 7)² = 9, we see that the value of r² is 9.

Therefore, the radius r of the circle is the square root of 9, which is 3.

Hence, the correct answer is A) 3.

The answer is 120 because 13 times 8 equals 104, and all you have to do is find the base edge length of the triangle which is found by subtracting 13 from the 17 and getting 4 for the triangle base length, multiplying it by the height (8) which you get 32, dividing it by two to get 16, add 104 and there's your answer.

Answer:

4 inches long each i think im not completely sure

Step-by-step explanation:

Rectangle has its adjacent sides perpendicular to each other. The lengths of the sides of the considered rectangle are: 5 inches and 12 inches.

Its the sum of length of the sides used to made the given figure.

For a rectangle, as the rectangle has two of its sides equal to its length, and rest two are equal to its width, thus,

perimeter of rectangle = twice of (width + length)

If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:

[tex]|AC|^2 = |AB|^2 + |BC|^2[/tex]  

where |AB| = length of line segment AB.

In a rectangle, its adjacent sides are perpendicular to each other(making 90 degrees with each other), thus, when its diagonal is drawn, we can use Pythagoras theorem to relate its length, width and length of the diagonals (both of diagonals of a rectangle are of same length).

Thus,  using Pythagoras theorem, we get:

[tex](|Diagonal|)^2 = |Length|^2 + |Width|^2[/tex]

Suppose its length and width are L and W, then we get two equations:

Perimeter = 2(L + W) = 34 inches

Diagonal² = 13² = 169 = L² + W²

From the first equation, getting L in terms of W, we get:

[tex]L = 17 - W[/tex]

Putting this value in second equation, we get:

[tex]L^2 + W^2 = 169\\(17-W)^2 + W^2 = 169\\289 + W^2 + W^2 -34W = 169\\2W^2 -34W + 120 = 0\\W^2 - 17W + 60 = 0\\W^2 -12W - 5W + 60 = 0 \\W(W - 12) - 5(W - 12) = 0\\\\(W-5)(W-12) = 0\\W = 5, 12[/tex](in inches)

Thus, we get L= 17-W = 12 or 5,

Thus, dimensions of the considered rectangle are 5 inches and 12 inches.

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Answer:

[tex]\boxed{\bold{\left(x+7\right)\left(x+1\right)\left(x-1\right)=0}}[/tex]

Step-by-step explanation:

Factor [tex]\bold{x^3+7x^2-x-7}[/tex]

[tex]\bold{\left(x+7\right)\left(x^2-1\right)}[/tex]

Factor [tex]\bold{0}[/tex]

[tex]\bold{0}[/tex]

Rewrite Equation

[tex]\bold{\left(x+7\right)\left(x+1\right)\left(x-1\right)=0}[/tex]

[tex] {x}^{3} + 7 {x}^{2} - x - 7 = 0 \\ \Leftrightarrow {x}^{2} (x + 7) - (x + 7) = 0 \\ \Leftrightarrow ( {x}^{2} - 1)(x + 7) = 0 \\ \Leftrightarrow (x - 1)(x + 1)(x + 7) = 0 \\ \Leftrightarrow x = - 7 \: \vee \: x = - 1 \: \vee \: x = 1[/tex]