What is FG?
pls help this is hard

Answer:

Step-by-step explanation:

y=kx+b

b=3

(1,5)

1*k+3=5

k=2

so, 2x+3=y

Answer:

12 minutes

Step-by-step explanation:

To estimate the time for a trip that is 6 miles long, we need to solve for x in the equation y = 0.467x + 0.417, where y represents the distance in miles.

First, we substitute the value of y, which is 6:

6 = 0.467x + 0.417

Next, we subtract 0.417 from both sides:

5.583 = 0.467x

Finally, we divide both sides by 0.467:

x = 12

So, the estimated time for a trip that is 6 miles long is 12 minutes.

Answer:

=3y - x =0

Step-by-step explanation:

[tex] \frac{y - y1}{x - x1} = m[/tex]

Therefore the gradient ( m ) is not given

from the question point =(-9,-3) and (-12,-4).

Gradient (m) =

[tex] \frac{y2 - y1}{x2 - x1} \\ = \frac{ - 4 - ( - 3)}{ - 12 - ( - 9)} \\ = \frac{ - 4 + 3}{ - 12 + 9} \\ = \frac{ - 1}{ - 3} \\ = \frac{1}{3} [/tex]

therefore m = 1/3.

The equation

[tex] = \frac{y - y1}{x - x1} = m \\ \frac{y - ( - 3)}{x - ( - 9)} = \frac{1}{3} \\ \frac{y + 3}{x + 9} = \frac{1}{3} \\ 3(y + 3) = 1(x + 9) \\ 3y + 9 = x + 9 \\ 3y = x + 9 - 9 \\ 3y = x + 0 \\ 3y - x = 0[/tex]

therefore the equation of the line = 3y-x=0

There will be enough water for all the guests.

Measurement is the method of comparing the properties of a quantity or object using a standard quantity.

Measurement is essential to determine the quantity of any object.

Total number of bottles = 24

Capacity of each bottle = 12 oz

Total capacity of the 24 water bottles = 12 × 24 = 288 oz

Now we have,

8 ounces = 1 cup

288 ounces = 288 / 8 = 36 cups

So there are 36 cups of water in total.

Number of guests = 30

If each guest drinks one cup of water, there will be 36 - 30 = 6 cups of water remaining.

Hence there will be enough water for the guests with 6 cups of water remaining.

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Your question is incomplete. Probably the correct question is as follows.

Before a party, Ashley bought a tray of 24 water bottles, each bottle has a capacity of 12 oz. There are 30 guests. If each guest drinks I cup of water, is there enough water for all the guests?

The crane's shadow is 45 meters long when the crane is 24 meters tall.

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent. Triangle resemblance is indicated here by the symbol "≅"

Let the shadow cast by the crane be x.

The triangle formed by the tower and by the crane are similar.

Using the rule of similar triangles we have:

16/24 = 30/x

16x = (30)(24)

x = 45

Hence, the crane's shadow is 45 meters long.

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Answer:

AAS

Step-by-step explanation:

[tex]\overline{PR} \cong \overline{PR}[/tex] by the reflexive property.

Answer:

Step-by-step explanation:

2.75 x 8 = 22

Check the picture below.

[tex]\begin{array}{llll} f(x)~from\\\\ x_1 ~~ to ~~ x_2 \end{array}~\hfill slope = m \implies \cfrac{ \stackrel{rise}{f(x_2) - f(x_1)}}{ \underset{run}{x_2 - x_1}}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array} \\\\[-0.35em] ~\dotfill\\\\ f(x) \qquad \begin{cases} x_1=-4\\ x_2=-3 \end{cases}\implies \cfrac{f(-3)-f(-4)}{-3 - (-4)}\implies \cfrac{[-6]~~ - ~~[-4]}{-3+4} \\\\\\ \cfrac{-6~~ + ~~4}{1}\implies \text{\LARGE -2}[/tex]

Answer:

-2

[tex]\hrulefill[/tex]

Step-by-step explanation:

The average rate of change of a function f(x) on the interval a ≤ x ≤ b can be calculated using the formula:

[tex]\boxed{\textsf{Average rate of change}=\dfrac{f(b)-f(a)}{b-a}}[/tex]

The given interval is -4 ≤ x ≤ -3, so:

From observation of the given graph, the values of f(a) and f(b) are:

[tex]f(a)=f(-4)=-4[/tex]

[tex]f(b)=f(-3)=-6[/tex]

Substitute the values of a, b, f(a) and f(b) into the formula to calculate the average rate of change of the function f(x) on the interval -4 ≤ x ≤ -3:

[tex]\begin{aligned}\textsf{Average rate of change}&=\dfrac{f(-3)-f(-4)}{-3-(-4)}\\\\&=\dfrac{-6-(-4)}{-3-(-4)}\\\\&=\dfrac{-6+4}{-3+4}\\\\&=\dfrac{-2}{1}\\\\&=-2\end{aligned}[/tex]

Therefore, the average rate of change of the function f(x) on the given interval is -2.

The surface area is changing at a rate of approximately 2.94 square meters per second when the volume is 36 cubic meters and the balloon is being inflated at 3 cubic meters per second.

Volume of a sphere in terms of its radius = V = (4/3)π[tex]r^3\\[/tex]     .......(1)

Differentiating on both sides,                       [tex]\frac{dV}{dt}[/tex] = 4π[tex]r^{2}[/tex][tex]\frac{dr}{dt}[/tex]      .......(2)      

r = radius of the sphere.

Spherical balloon is being inflated at a rate of 3 cubic meters per second.

[tex]\frac{dV}{dt}[/tex] = 3 [tex]m^3/sec[/tex]

Volume is 36 cubic meters.

V = 36 [tex]m^3[/tex]

From equation (1), [tex]r^3[/tex] = [tex]\frac{3V}{4\pi }[/tex]

                              [tex]r^3[/tex] = [tex]\frac{3*36}{4*\pi }[/tex]

                              [tex]r^3\\[/tex] = [tex]8.59^1^/^3[/tex]

                               r = 2.04 meters

Substituting this in equation (2),  [tex]\frac{dr}{dt}[/tex]  =   [tex]\frac{dV}{dt}[/tex] / 4π[tex]r^{2}[/tex]

                                                     [tex]\frac{dr}{dt}[/tex]  =   3/(4π[tex]2.04^{2}[/tex])

                                                     [tex]\frac{dr}{dt}[/tex]  =   0.05737 m/sec

Now, surface area of sphere = A = 4π[tex]r^{2}[/tex]

Differentiating on both sides,

Rate of change of surface area  [tex]\frac{dA}{dt}[/tex] = [tex]8\pi r\frac{dr}{dt}[/tex]

                                                       = 8* 3.14* 2.04* 0.05737

                                                       = 2.94 [tex]m^2/sec\\[/tex]

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The surface area of the triangular prism is 62 square units.

The area is the area occupied by a two-dimensional flat surface. It has a square unit of measurement. The surface area of a three-dimensional object is the space taken up by its outer surface.

For each three-dimensional geometrical shape, surface area and volume are determined. The area or region that an object's surface occupies is known as its surface area. Volume, on the other hand, refers to how much room an object has.

The side length of each of the three squares is 4 units.

The area of each would be:

4² = 16 sq. units.  

For the three squares we have:

16(3) = 48 sq. units.

The area of each triangle is 7 sq. units.

This means together the area of the two triangles is 2(7) = 14 sq. units.

The surface area of the prism is:

14 + 48 = 62 sq. units.

Hence, the surface area of the triangular prism is 62 square units.

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Calories were burned for each minute of jogging is 10 calories and for each minute of cycling is 10 calories.

Two or more algebraic equations that share variables, such as x and y, are referred to be simultaneous equations.

When the equations are solved simultaneously, they are known as simultaneous equations.

Jogging be considered as x

Cycling be considered as y

Shelly spent 40 minutes jogging and 22 minutes cycling, and burned 620 calories to write this in equation we get,

40x + 22y = 620

Shelly swapped times,

22 minutes of jogging and 40 minutes of cycling and burned the same number of calories,

22x + 40y = 620

By multiplying two equation we get,

multiply equation 1 by 22 and equation 2 by 40 we get,

880x + 484y = 13640

880x + 1600y = 24800

Now subtracting equation 1 from 2 we get,

1116y = 11160

y = 11160/1116

y = 10

Therefore, putting value of y in equation 1 we get,

880x + 484(10) = 13640

880x = 13640 - 4840

x = 8800/880

x = 10

Therefore, calories were burned for each minute of jogging is 10 calories and for each minute of cycling is 10 calories.

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Answer: 3/17 or 17.64%

Step-by-step explanation:

Just add everything (adds up to 17), then you put the color frequency number as the numerator of the fraction, then have the added up number as the denominator.

Answer:

The height of an equilateral triangle can be found using the Pythagorean theorem by treating it as a 30-60-90 triangle. In a 30-60-90 triangle, the ratio of the side lengths is 1:√3:2. In this case, the side length of 3 cm is the shorter leg, so the height (the longer leg) is 3√3 cm. Rounding to 1 decimal place, the height is approximately 5.1 cm.

The average change in weight calculated by the researcher for the sample of 25 freshmen is an example of a statistic.

A statistic is a numerical summary of a sample that is used to make inferences about a population. In this case, the sample is the 25 freshmen, and the population could be all freshmen entering college.

The average change in weight is a statistic because it summarizes the data collected from the sample, and is used to make conclusions about the population.

It represents the typical or average amount of weight gained or lost by the freshmen in the sample during their first semester in college.

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The shapes with the same areas are (c) A and B

The complete question is added as an attachment

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

Figures A, B and C

For the figures A, B and C to have the same area, the number of boxes on the shapes must be the same

Using the above as a guide, we have the following:

By comparison, we have

A and B = 16 square units

Hence, the shapes A and B have the same area

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Answer:

7n - 4

Step-by-step explanation:

The expression 24a+(-26b)-13a+12b is equivalent to 11a-14b.

What is algebraic expression ?

An algebraic expression is a combination of variables, numbers, and mathematical operations, such as addition, subtraction, multiplication, and division. It can be used to represent a mathematical relationship or formula and can be simplified or evaluated using algebraic rules.

Examples of algebraic expressions include "3x + 4y", "2a^2 - 5b", and "(x + 3)(x - 2)".

Given expression ,

24a+(-26b)-13a+12b

= 24a - 13a +12 b - 26b

= 11a - 14b

Therefore, The expression 24a+(-26b)-13a+12b is equivalent to 11a-14b.

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The degree of the term with the greatest degree is called the degree of the polynomial.

Here, it is necessary to remember that, by the definition, we can find the "Degree of a polynomial" by identifying the greatest degree of its terms.

The "Leading term" of a polynomial is defined mostly as the term with the highest power of the variable of the polynomial.

The numbers located in front to the variable (those numbers that multiply the variable) are called "Coefficients". The coefficient of the Leading term is known as the "Leading coefficient."

For example, given the following polynomial:

18x² + 2x - 6

You can identify that, in this case:

degree of the polynomial: 2

leading term: 18x²

leading coefficient: 18

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The value of the shortest of the three side lengths is 3 inches.

A triangle is a three-sided polygon that consists of three edges and three vertices.

The lengths of the three sides of a triangle (in inches) are consecutive integers.

The three sides are x, x+1 and x+2 which are consecutive.

We know that perimeter of a triangle is the sum of the three sides of a triangle.

Add the three Consecutive sides to find the perimeter.

Perimeter of triangle=x+x+1+x+2

The perimeter of triangle is 27 inhces.

27=3x+3

Substitute 3 from both sides

24=3x

Divide by 3 on both sides

8=x

Hence, the value of the shortest of the three side lengths is 3 inches.

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Answer:104

Step-by-step explanation:

If 1/2 d=52,

d/2=52

Multiply both sides by 2.

Thus, d=52×2= 104.

Hope this helps! :)

Events Q and R are not mutually exclusive, thus we are given two probabilities, P(Q) = 0.41 and P(R) = 0.44.

Therefore,

Events Q and R are not mutually exclusive, thus we are given two probabilities, P(Q) = 0.41 and P(R) = 0.44.. In this instance, the likelihood of Q and R is equal to P(Q) × P(R), which is 0.1804. The solution to this issue is this.

The complete question is:

Suppose Q and R are independent events. Find the probability of Q and R when P(Q)=0.41 Ans P(R)=0.44.

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Mary  age  is ( x -1 ) years old now.  4 years ago=  ( x -1 )-4 =0,  x=4+1=5,

now he is x -1 =5-1=4,  4 years ago=5-4=1 year,  iii) (3*8/3+8)=16 year old

Will he be 8 years from now  .now she is 4  year old now.

if he is x year old . he will be 8 years from now=(3x+8)=0

x=- 8/3. now his age is (3x+8) =(3*8/3+8)=16

A time of human existence, defined in years starting at birth, that is typically characterized by a certain stage or degree of mental or physical development and involves the potential for legal responsibility. the discretionary age. the legal drinking age. The legal drinking age was increased by the state from 18 to 21. Age is a notion that describes a person's age at a specific period. It is described as the measurement of the amount of time that has passed between the date of the live birth to a particular point in time, typically the date the data was collected. Age range, according to the Longman Dictionary of Contemporary English, is the term for a group of people who fall between two certain ages.

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In given lines, y = -1/4 x + 7 represents a transversal line.

A transversal is a line that, at two different locations, cuts through two lines in the same plane. Various types of angles in pairs, including successive internal angles, corresponding angles, and alternate angles, are produced by a transversal intersection with two lines.      

Here we have

y = 1/6x - 3  ---- (1)    

y = -1/4 x + 7 ---- (2)  

y = 1/6x - 9 ---- (3)        

Here given lines are in y = mx + c form

The slope of the line (1) is 1/6

The slope of the line (2) is -1/4

The slope of the line (3) is 1/6

As we can see that line (1) and line (3) have the same slope,

Hence, Lines (1) and (3) are two parallel lines

where Line (2) is transversal which cuts the given two parallel lines  

Therefore,

In given lines, y = -1/4 x + 7 represents a transversal line.

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It is not always possible for the hunter to ensure that the distance between her and the rabbit is at most 100 after $10⁹$ rounds. The distance between the hunter and the rabbit can increase by a factor of 2 in each round, making it impossible for the hunter to catch the rabbit in some scenarios.

It is not always possible for the hunter to ensure that the distance between her and the rabbit is at most 100 after $10⁹$ rounds, regardless of how the rabbit moves or what points are reported by the tracking device. This is because the distance between the hunter and the rabbit can increase by a factor of 2 in each round, which means that after $10⁹$ rounds, the distance between them could be as much as $2⁽¹⁰⁾⁹$ times the initial distance. This value could be much larger than 100, making it impossible for the hunter to catch the rabbit. Therefore, there are scenarios in which the hunter cannot catch the rabbit within $10⁹$ rounds.

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The given statement about the disjunction is true.

A compound statement with two distinct statements (disjuncts) connected by the wedge symbol (v) is called Disjunction.

Given is the statement -

(S~T) v (~U.W)

The given statement about the disjunction is true.

Therefore, the given statement about the disjunction is true.

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Answer:

median = 95

Step-by-step explanation:

the median is indicated by the line inside the box.

each interval on the number line is 5 units.

median = 75 + 4 units = 75 + 20 = 95

Answer:

Step-by-step explanation: A congruence statement expresses that two figures have the same size and shape. Here's how you can write a congruence statement step by step:

Write the two figures you want to compare. For example, you could write "Triangle ABC" and "Triangle DEF".

Use the symbol "≅" to indicate congruence. Place the symbol between the two figures, like this: "Triangle ABC ≅ Triangle DEF".

Label the corresponding parts of the two figures to show that they are congruent. For example, you could write "AB = DE", "BC = EF", and "AC = DF".

The final congruence statement would look like this: "Triangle ABC ≅ Triangle DEF, with AB = DE, BC = EF, and AC = DF". This statement says that Triangle ABC is congruent to Triangle DEF, and that the lengths of their corresponding sides are equal.

Answer:

Any line except a vertical line represents a linear function.

Step-by-step explanation:

Any "diagonal" line is a linear function. Even a horizontal line represents a linear function. Only a vertical line does NOT represent a linear function.

Step-by-step explanation:

an inscribed angle has its vertex on the circle, and the sides of the angle are two chords of the circle.

the inscribed angle is half the size of the arc angle (the angle at the center of the circle) of the arc that the two sides cut out of the circle.

110° is the arc angle (at the center of the circle) of the arc GJ.

for the inscribed angle GFJ the vertex is F, and the angle there is half of the arc angle :

angle GFJ = 110/2 = 55°

the second problem is the opposite "direction".

we have the inscribed angle FJH = 36°.

and we want the arc angle FH.

now, since the inscribed angle is half of the arc angle, the arc angle is twice the inscribed angle :

arc angle FH = 36×2 = 72°