13) jimmy paid $2 for a sandwich. he now has $20. with how much money did he start?

i.  The position vector of X is 2b - a.

ii.  The position vector of Y is (3b + c)/4.

iii.  The ratio XY : Y Z is \(|(2b - a) - ((3b + c)/4)|/|((3b + c)/4) - (a + c)/2|\). Simplifying this expression will give us the final ratio.

i. To find the position vector x of point X, we can use the concept of vector addition. Since AB : BX = 2 : 1, we can express AB as a vector from A to B, which is given by (b - a). To find BX, we can use the fact that BX is twice as long as AB, so BX = 2 * (b - a). Adding this to the vector AB will give us the position vector of X: x = a + 2 * (b - a) = 2b - a.

ii. Similar to the previous part, we can express BC as a vector from B to C, which is given by (c - b). Since BY : YC = 1 : 3, we can find BY by dividing the vector BC into four equal parts and taking one part, so BY = (1/4) * (c - b). Adding this to the vector BY will give us the position vector of Y: y = b + (1/4) * (c - b) = (3b + c)/4.

iii. Z is the midpoint of AC, so we can find Z by taking the average of the vectors a and c: z = (a + c)/2. The ratio XY : YZ can be calculated by finding the lengths of the vectors XY and YZ and taking their ratio. Since XY = |x - y| and YZ = |y - z|, we have XY : YZ = |x - y|/|y - z|. Plugging in the values of x, y, and z we found earlier, we get XY : YZ =\(|(2b - a) - ((3b + c)/4)|/|((3b + c)/4) - (a + c)/2|\).

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After answering the presented question, we can conclude that As a radius result, a titanium sphere with a radius of 11 cm would weigh roughly 25.1 kg (rounded to 1 decimal place).

In more modern parlance, the length of a circle or sphere is the same as its radius in classical geometry, which is one of the line segments from its centre to its circumference. The term was derived from the Latin word radius, which also refers to the spokes of a waggon wheel. The radius of a circle is the distance between its centre and any point on its periphery. It is usually denoted by "R" or "r." A radius is a line segment with one endpoint in the centre and one on the circle's circumference. The radius of a circle matches its diameter. The diameter of a circle is the segment that passes through its centre and has ends on the circle.

The formula for the volume of a sphere of radius "r" is:

V = (4/3)πr³

Substituting the specified radius value (r = 11 cm), we get:

V = (4/3)π(11)³ \sV = 5575.279 cm³

Now we must compute the weight of the titanium sphere, which can be found by multiplying its volume by its density:

Density = Volume Weight

Weight = 25121.811974 g Weight = 5575.279 cm3 4.506 g/cm3

When we divide 1000 by 1000 to convert grammes to kilogrammes, we get:

The weight is 25.121811974 kg.

As a result, a titanium sphere with a radius of 11 cm would weigh roughly 25.1 kg (rounded to 1 decimal place).

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Solution :-

As we know that,

Therefore ,

>> m = -2 - (-3) / -1 - (-8)

>> m = -2 + 3 / -1 + 8

>> m = 1 / 7

We have that the data are:

(x₁ = -8, y₁ = -3) and (x₂ = -1, y₂ = -2)

The slope is equal to the change in and with respect to change in X, or what rises when moving forward.

\(\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{m=\frac{Change \ in \ y}{Change \ in \ x} \ \longmapsto \ \ m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} } \end{gathered}$}}\)

The change in X is equal to the subtraction in the X coordinate (also called advance), and the change in and is equal to the subtraction in the coordinate and (also called elevation).

Introduce the values of x and y In the equation to find the slope.

\(\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{m=\frac{-2-(-3)}{-1-(-8) } } \end{gathered}$}}\)

\(\boxed{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{m=\frac{1}{7} } \end{gathered}$}}}\)

Answer:

7, 2, -3, -8

Step-by-step explanation:

y = -5x + 2  Substitute in -1 for x

y = -5(-1) + 2

y = 5 + 2

y = 7

y = -5x + 2  Substitute in 0 for x

y = -5(0) + 2

y = 0 + 2

y = 2

y = -5 + 2 substitutes in 1 for x

y = -5(1) + 2

y = -5 + 2

y = -3

y = -5x + 2  Substitute in 2 for x

y = -5(2) + 2

y = -10 + 2

y = -8

Helping in the name of Jesus.

Answer:

Multiplicar el divisor por la unidad seguida de tantos ceros como cifras decimales queramos eliminar (3,6 x 10 = 36).

Multiplicar el dividendo por el mismo número que hayamos multiplicado el divisor (278 x 10 = 2780).

Answer:

블랙핑크

Step-by-step explanation:

Answer:

v=16w

Step-by-step explanation:

v=16w

8=16(1/2)

8=8✔

Answer: q=13

Step-by-step explanation:

add the separate the q, add 4 to the 9= 13

13=q

The total length of the metallic rod used for the diagonal is

The wooden frame is a parallelogram and the diagonals of a parallelogram bisects each other.

Using this property we set the equation

(2y - 1) ft = 9 ft

2y - 1 = 9

2y = 10

diving through by 2

y = 5

hence the first diagonal is 18 feet and the second diagonal is solved below

(y + 3) ft

= 5 + 3

= 8 ft

length of the diagonal

= 18 + 16

= 34 feet

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There were 5 1/4 bags of popcorn left after eating 4 bags.

To find out how much popcorn was left after eating 4 bags, we need to subtract the amount eaten from the total amount Brianna made.

Brianna made 9 1/4 bags of popcorn, which can be represented as a mixed number. To perform calculations, let's convert it to an improper fraction:

9 1/4 = (4 * 9 + 1) / 4 = 37/4

Now, let's subtract the 4 bags eaten from the total:

37/4 - 4

To subtract fractions, we need a common denominator. The common denominator of 4 and 1 is 4. Therefore, we can rewrite the expression as:

37/4 - 4/1

Now, let's find a common denominator and subtract the fractions:

37/4 - 16/4 = (37 - 16) / 4 = 21/4

The result is 21/4, which is an improper fraction. Let's convert it back to a mixed number:

21/4 = 5 1/4

Therefore, there were 5 1/4 bags of popcorn left after eating 4 bags.

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The value of f'(x) is \(f'(1) = 1.303\), and the estimate should be less than f'(x)

The equation of the function is given as:

\(f(x) = 3\log(x)\)

To estimate f'(1), we set x = 1 and a number close to 1 (for instance x = 1.0001).

Next, we compute the average rate of change of this interval.

So, we have:

\(f'(1) = \frac{f(1.0001) - f(1)}{1.0001 -1}\)

\(f'(1) = \frac{f(1.0001) - f(1)}{0.0001}\)

Calculate f(1.0001) and f(1)

\(f(1.0001) = 3*log(1.0001) =0.00013028183\)

\(f(1.0001) = 3*log(1) =0\)

So, we have:

\(f'(1) = \frac{0.00013028183 - 0}{0.0001}\)

\(f'(1) = \frac{0.00013028183}{0.0001}\)

\(f'(1) = 1.3028183\)

Approximate

\(f'(1) = 1.303\)

From the graph of f(x) (see attachment), we have that:

The graph of function f(x) is concave down

This means that, the estimate should be less than f'(x)

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The value of the missing data point is 10. Option C

The data set has 8 data points, and the median is given as 12. The median is the middle value when the data points are arranged in ascending or descending order.

Let's arrange the data set in ascending order:

6, 8, ?, 8, 14, 15, 16, 18

Since the median is 12, it should be the fourth data point when arranged in ascending order. Therefore, the missing data point must be the fourth value in the sorted data set.

From the given options, the only whole number that could fit as the fourth value in the data set is 10.

Thus, the value of the missing data point is C. 10.

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The following tests will be the most appropriate is X^2 test for proportions.

Given :

The director of a training program wanted to know if a one week orientation would change the perception of potential clients who would perceive the program as being good.

He collected information on the number of clients who would rate the program as being good before and after the orientation .

What is X^2 test ?

It tests whether two populations come from the same distribution by determining whether the two populations have the same proportions as each other.

This test is also called as Chi - square test .

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Answer:

1/3 divided by 4

Step-by-step explanation:

Because you start off with 1/3 and then you split it into 4, 1/12's and 4*1/12 is equal to 1/3

So the answer is 1/3 divided by 4

Answer: \(f^{-1} (x)=x^{2} -7\)

Step-by-step explanation:

To find the inverse of a function replace f(x) with x and the original x with y

\(f(x)=\sqrt{x+7} \\x=\sqrt{y+7}\)

Now we can solve for y

Square both sides so we can cancel out the root

\(x=\sqrt{y+7}\\x^{2} =\sqrt{y+7}^{2} \\x^{2} =y+7\)

Now subtract 7 from both sides

\(x^{2} =y+7\\x^{2} -7=y+7-7\\x^{2} -7=y\)

Now replace y with the inverse of f(x), \(f^{-1} (x)\)

f⁻¹=x²+7

Hope it helps.

Do comment if you have any query.

Answer:5y-3x

Step-by-step explanation: distributive

Step-by-step explanation:

the answer either maybe somebody could help

Answer:

6 year's old

Step-by-step explanation:

Grandma is G and Robin is R

G=7R

G+12=3(R+12)

G+12=3R+36

7R+12=3R+36

7R-3R=36-12

4R=24

R=6

Robin is 6 years old

The correct graph of the inequality -0.4x - 2 < - 1.2 is option 2.

Equation containing a relational operator and a linear expression is known as a linear inequality. In a coordinate plane or space, regions that satisfy a linear inequality are defined. A linear inequality defines a half-plane in two dimensions, which, depending on the inequality, can be either above or below a line. A linear inequality defines a half-space in three dimensions, which, depending on the inequality, is either above or below a plane. The goal of optimization problems is to determine the maximum or minimum value of a linear function under a set of constraints, which are typically represented by linear inequalities.

The given inequality is -0.4x - 2 < - 1.2.

-0.4x - 2 < - 1.2

Adding 2 on both sides of the equation we have:

-0.4x < -1.2 + 2

-0.4x < 0.8

-x < 2

x > -2

Hence, the correct graph of the inequality is option 2.

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Using the given formula v² = v₀² + 64h, and plugging the values of v₀ and v, we find the vertical height of drop of roller coaster is 75.53  feet.

The given equation is: v² = v₀² + 64h

Given that given final velocity is  v = 70 ft/s  and initial velocities is v₀ = 8 ft/s.

Substitute the given values into the equation

(70 ft/s)² = (8 ft/s)² + 64h

Simplifying and solving for h

4900 ft^2/s² = 64h + 64 ft²/s²

4836 ft^2/s² = 64h

h = (4836 ft²/s²)/64

h = 75.53 feet (rounded to two decimal places)

Therefore, the vertical drop height is approximately 75.53 feet.

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

" ROLLER COASTERS The velocity of a roller coaster as it moves down a hill is v = v , where is the

v^2 = v₀^2 + 64h

v₀ =0 and h is the vertical drop in feet. If v = 70 feet per second and initial velocity v₀ = 8 feet per second, find h. "--

the length of side a is 91 ft (rounded to the nearest whole foot) and the length of side b is 132 ft (rounded to the nearest whole foot). The area of the triangle is approximately 6007 sq ft.

Given: The hypotenuse of the right triangle,

c = 159 ft; angle A = 34°

We know that, in a right-angled triangle:

\($$\sin\theta=\frac{\text{opposite}}\)

\({\text{hypotenuse}}$$$$\cos\theta=\frac{\text{adjacent}}\)

\({\text{hypotenuse}}$$\)

We know the value of the hypotenuse and angle A. Using trigonometric ratios, we can find the length of sides in the right triangle.We will use the following formulas:

\($$\sin\theta=\frac{\text{opposite}}\)

\({\text{hypotenuse}}$$$$\cos\theta=\frac{\text{adjacent}}\)

\({\text{hypotenuse}}$$$$\tan\theta=\frac{\text{opposite}}\)

\({\text{adjacent}}$$\) Length of side a is:

\($$\begin{aligned} \sin A &=\frac{a}{c}\\ a &=c \sin A\\ &= 159\sin 34°\\ &= 91.4 \text{ ft} \end{aligned}$$Length of side b is:$$\begin{aligned} \cos A &=\frac{b}{c}\\ b &=c \cos A\\ &= 159\cos 34°\\ &= 131.5 \text{ ft} \end{aligned}$$\)

Now, we have the values of all sides of the right triangle. We can calculate the area of the triangle by using the formula for the area of a right triangle:

\($$\text{Area} = \frac{1}{2}ab$$\)

Putting the values of a and b:

\($$\begin{aligned} \text{Area} &=\frac{1}{2}ab\\ &=\frac{1}{2}(91.4)(131.5)\\ &= 6006.55 \approx 6007 \text{ sq ft}\end{aligned}$$\)

Therefore, the length of side a is 91 ft (rounded to the nearest whole foot) and the length of side b is 132 ft (rounded to the nearest whole foot). The area of the triangle is approximately 6007 sq ft.

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The domain of the quadratic function in this problem is given as follows:

All real values.

The domain of a function is the set of all the possible input values that can be assumed by the function.

On the graph, the domain of the function is given by the values of x of the function.

A quadratic function has no restrictions on the domain, hence it is defined by all the real values.

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The value of 0.045 × 2.05 / 0.0025 in standard form is 3.69 × 10.

To perform the calculation and express the answer in standard form, follow these steps:

Multiply 0.045 by 2.05:

0.045 × 2.05 = 0.09225

Divide the result by 0.0025:

0.09225 / 0.0025

= 36.9

Convert the answer to standard form by writing it as a decimal multiplied by a power of 10:

36.9 = 3.69 × 10

Therefore, the value of 0.045 × 2.05 / 0.0025 in standard form is 3.69 × 10.

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Answer:

350

Step-by-step explanation:

525/15=35

35x10=350

The solution of the system of equation is the point where the 2 lines cross each other.

By looking at the graph, we can see that they cross each other at (-3,-8)

Correct option: 2

Answer: 14 1/7

Step-by-step explanation:

Answer:

Given that the vertices of quadrilateral PQRS are P(6,3), Q(4,2), R(2,4) and S(4,5) and the quadrilateral is dilated with a scale factor of 2, about the origin.

Now, let's find the new vertices of the dilated image:

Vertex P is dilated by a scale factor of 2, its new coordinates will be (2 × 6, 2 × 3) = (12, 6). Therefore, the new vertex P' is at (12, 6).

Vertex Q is dilated by a scale factor of 2, its new coordinates will be (2 × 4, 2 × 2) = (8, 4). Therefore, the new vertex Q' is at (8, 4).

Vertex R is dilated by a scale factor of 2, its new coordinates will be (2 × 2, 2 × 4) = (4, 8). Therefore, the new vertex R' is at (4, 8).

Vertex S is dilated by a scale factor of 2, its new coordinates will be (2 × 4, 2 × 5) = (8, 10). Therefore, the new vertex S' is at (8, 10).

Therefore, the coordinates of the vertices of the final image are P’(12, 6), Q’(8, 4), R’(4, 8), and S’(8, 10).So, the correct option is D. P’(12, 6), Q’(8, 4), R’(4, 8), and S’(8, 10).

Step-by-step explanation:

Hope this helps you!! Have a good day/night!!

The new area would be 40 square inches. When a scale factor dilates a polygon, the area is multiplied by the square of the scale factor. If the original area is 10 square inches and the scale factor is 4, the new area would be 10 x 4^2 = 10 x 16 = 40 square inches.

The required piecewise linear relations are f(x) = 4 if [0, 2), and f(x) = -2x + 8 if [2, 4).

A piecewise-defined function (also known as a piecewise function or a hybrid function) is a function defined by multiple sub-functions, each of which applies to a different interval of the main function's domain (a sub-domain).

The graph is given in the question, as shown

f(x) = 2x + 4 if [-2, 0]

This the sub-function define between the interval [-2, 0].

f(x) = 4 if [0, 2)

This the sub-function define between the interval [0, 2).

f(x) = -2x + 8 if [2, 4)

This the sub-function define between the interval [2, 4).

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Answer:

X=0,y=-5

x=4,y=-1

Step-by-step explanation:

Replace all occurrences of y with x^2-3x-5

(x^2-3x-5)+5=x

x^2-3x=x

X^2-4x=0

so :x=0,4

enter the value of x in the equation then find y

y=-5,-1