Mary saw two poison dart frogs. One was 7/8 inch long and the other was 5/8 inch long. How much longer was one than the other?

Keith live 480 miles far way from the mountains.

The distance between two locations is represented by the length of the line linking them. If the two points are on the same horizontal or vertical line, subtracting the various coordinates will show how far apart they are.

Consider the provided information.

Keith drove to the mountains last weekend. The trip took 12 hours because of the high traffic on the way there.

Let the distance is D and average rate or speed is x miles.

Distance = speed × time

Substitute the respective values.

D = x  * 12

D= 12x

When Keith drove home, there was no traffic and the trip only took  

hours. The average rate was  8 miles per hour faster on the trip home,

The average rate or speed during return is x+20 miles.

Substitute the respective values in the above formula.

D = (x+20) ×8

D= 8x+160

Equate both the equations.

8x+160 = 12x

4x= 160

x=160/4

=40

Substitute the value of x in D= 12x

D=12(40)

D= 480

Hence, Keith live 480 miles far way from the mountains.

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Answer:

The ball reaches 14 ft in 0.75 seconds

Step-by-step explanation:

[tex]h(t) = -16t^2+24t+5\\h'(t) = -32t+24\\[/tex]

The highest point occurs when the derivative is equal to 0, because the tangent line is horizontal at that point

[tex]-32t + 24 = 0\\24 = 32t\\t = \frac{24}{32}=\frac{3}{4}=0.75s\\[/tex]

plug t back into h(t) to get height

[tex]h(0.75) = -16(0.75)^2+24(0.75)+5\\=(-16)(9/16)+23\\=-9 + 23\\= 14 ft[/tex]

Note: If you are not familiar with the concept of derivatives yet, you can find the time of the highest point using the equation [tex]t =-\frac{b}{2a}[/tex] where [tex]h(t) = at^2 + bt + c[/tex]

the anwser is 14 degrees for angle 1

The ball may rise up to a height of 20 feet. and it will strike the ground in 1 second.

Height is the vertical measurement from an object's top to its base. On sometimes, it has the designation "altitude."

The vertex at point (h,k) of a parabola, y = ax2 + bx + c, is first determined using the equation h = -b / 2a, and then that point is entered into the equation to determine k.

Let's now solve for h in this issue. We know that a = -16, b = 32, and c = 4 in the equation y = -16t2 + 32t + 4.

h = -b/2a

h = -(32) / 2(-16) (-16)

1 second is equal to h = -32/-32.

This means the the ball will reach it's maximum height after 1 seconds. But the problem is asking is for what that height is. So for our final step, let's plug in t=1 to our equation:

y = -16t^2 + 32t + 4

y = -16*(1)^2 + 32*(1)+ 4

y = -16 + 36

y = 20 feet

which means that the final answer is that the maximum height of the ball is 20  feet. and it will take 1sec to hit the ground.

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Using the Pythagorean Theorem for the right angled triangles and observing the given figure, The value of x can't be solved because the hypotenuse must be the longest side of the right angled triangle which is violated in this question.

A triangle is a three-sided polygon with three vertices. The triangle's internal angle, which is 180 degrees, is constructed. It implies that the internal angles of a triangle add up to 180 degrees.

The required formula is:

[tex]h^{2}=p^{2}+b^{2}[/tex]

In the triangle, Hypotenuse is not the biggest side. So, We can't solve for the value of x.

[tex]10^{2} = 15^{2}+x^{2}[/tex]

[tex]x=\sqrt{10^{2}-15^{2}}[/tex]

which yields a negative number inside square root which is not possible to solve.

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The expression for the given variable is -276

What is variable?

A variable is anything that can take on any one of a number of values. A variable is a symbol. A variable is something that can change in an experiment.An amount that can fluctuate depending on the mathematical issue is referred to as a variable. The generic letters x, y, and z are often employed in mathematical expressions and equations. A variable, then, is a symbol denoting a number whose value is unknown. In this case, x + 5 Equals 10. "X" in this case is a variable.

[tex]\sqrt[3]{6 \times 288}-288[/tex]

[tex]\sqrt[3]{6 \times 288}=12[/tex]

[tex]=12-288[/tex]

[tex]Subtract the numbers: $12-288=-276$$$=-276$$[/tex]

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Answer:

2. C

3. BCEF

4. C

Step-by-step explanation:

2. In a function, the x value cannot have two y values (for example: if the points are (1,2) and (1,3) then that is not a function).

In this question, none of the x values repeat with multiple y values, so it is a function. the answer is C.

It is not D, because not all straight lines are functions. If the straight line is vertical, then there is only one x value and it has infinitely many values for y. So, not all straight lines are necessarily functions.

3. Range is the y values. The points are (3,4), (-2,3), (7,1), (2, 1/2)

Here, the y values are 4, 3, 1, and 1/2

Choices B,C,E,F are the answers.

4. If the domain is x[tex]\geq[/tex]0, then 0 is the lowest we can plug into x.

y=2(0)+6

y=6

So, the answer is C. y[tex]\geq[/tex]6

You were on the right track :)

Answer:

y = 5x - 2

Step-by-step explanation:

y-8 = 5(x-2)

y-8 = 5x - 10

y = 5x - 10 + 8

y = 5x -2

The total years taken to double the money according to Compounding will be  12.5 years.

What is compound interest?

Compound interest is that the interest on savings calculated on each the initial principal and therefore the accumulated interest from previous periods.

Main body:

Given :

rate = 6%

amount = $2500

Total amount = $5000

Compounded semi -anually,so formula becomes,

Total amount = amount (1+r/200)^2t

T = A[tex](1+r/200)^{2t[/tex]

5000 = 2500 (1+3/100)^2t

2 =(1+ 0.03)^2t

2 =(1.003)^2t

taking log on both sides

log 2 = 2t *log 1.03

0.3/0.012 = 2t

t = 12.5 years

Hence the time taken to double the money is 12.5 years.

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Answer:1235160000 beats

Step-by-step explanation:

There are 525600 minutes in a year

47*525600= 24703200

24703200*50= 1235160000

a. Acceleration of the system (a) = 6.125 m/s^2

b. The tension in the rope (T) = 110.25

What is the definition of acceleration ?

Acceleration  defines that the rate at which velocity changes with time, in terms of both speed and direction.

For 30 kg mass

m . g - T = m . a

30 x 9.8  - T = 30. a   ⇒  (1)

For 10 kg mass

T - m base 2 g Sin θ = m base 2 a

T - 10 x 9.8 Sin 30° = 10 x a         ⇒  (2)

a. Adding equation (1) and (2)

    294 - 49 = 30 a + 10 a

    245 = 40 a

     a = 245/40

     a = 6.125 m/s^2

  Therefore, acceleration = 6.125 m/s^2

b. Sub a value in equation (1) we get,

    T = 110.25

   Therefore , tension in the role = 110.25

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Answer: Based on the information you provided, it seems that the correct answer is "left 6 units, down 1 unit." This translation will map the graph of the function f(x) = x² onto the graph of the function g(x) = x² - 6x + 6.

To understand why this is the case, it helps to understand what the different parts of the function g(x) represent. The term x² represents the original function f(x) = x², the term -6x represents a horizontal translation of the graph of f(x) by 6 units to the left, and the constant term 6 represents a vertical translation of the graph of f(x) by 1 unit downward. Together, these transformations map the graph of f(x) onto the graph of g(x).

Note that if we were to apply the other translations you listed, they would not produce the correct graph. For example, if we were to apply a translation of "right 3 units, down 3 units," this would produce a graph that is shifted 3 units to the right and 3 units down, which is not the same as the graph of g(x). Similarly, if we were to apply a translation of "right 6 units, down 1 unit," this would produce a graph that is shifted 6 units to the right and 1 unit down, which is also not the same as the graph of g(x).

Answer:

(-8, -10)

Step-by-step explanation:

(-4 + x)/2 = -6

-4 + x = -12

x = -8

(4 + y)/2 = -3

4 + y = -6

y = -10

Answer: (-8, -10)

Answer:

[tex]2\sqrt{281}[/tex] inches

Step-by-step explanation:

Using the 3D Pythagorean theorem, the diagonal has length [tex]\sqrt{32^2+6^2+8^2}=2\sqrt{281}[/tex] inches.

Answer:

60

Step-by-step explanation:

The markup from cost to sale price is $135.

What is the cost price?

Cost price, for instance, equals selling price plus profit ( when selling price and profit are given ) Cost is equal to Selling price plus Loss ( when selling price and loss is given ).

Cost price = 100 Selling Price + 100 + Profit (where the Selling Price and Profit Percentage are supplied)

Given the selling price of the item = $650

The cost = $450

Therefore,

10% × $650 = $585

$585-$450=$135

Hence,  the markup from cost to sale price is $135.

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Complete question:

The selling price of an item is ​$650 It is marked down by 10%, but this sale price is still marked up from the cost of ​$450.Find the markup from cost to sale price.

Therefore, the equation that best fits these facts as the answer to this problem is y=661-0.1x.

The term "scatter plot" refers to a particular sort of graph in which the x- and y-axes are used to represent the values of two variables, with the dots that arise indicating any association between the data.

Given the correlation between the data at this moment and the graph provided in the question, y=661-0.1x is an equation that best captures the scatterplot's line of best fit.

y=661-0.1x is the equation whose solution best fits this data.

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The linear regression equation in this problem is given as follows:

y = 4.774x + 39.474.

Then the estimates are given as follows:

a) x = 3 hours: 53.8.

b) x = 4.5 hours: 61.

c) x = 13 hours: 101.5.

d) x = 1.5 hours: 46.6

The linear regression equation is obtained inserting the points of the table into a linear regression calculator.

From the table in this problem, the points are given as follows:

(0,39), (1,45), (2,52), (4, 49), (5, 61), (5,72).

Inserting these points into a calculator, the equation is given as follows:

y = 4.774x + 39.474.

Then the estimates are obtained with the numeric values, as follows:

a) x = 3 hours: y = 4.774(3) + 39.474 = 53.8.

b) x = 4.5 hours: y = 4.774(4.5) + 39.474 = 61.

c) x = 13 hours: y = 4.774(13) + 39.474 = 101.5.

d) x = 1.5 hours: y = 4.774(1.5) + 39.474 = 46.6.

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Answer:

explain m ore

Step-by-step explanation:

y = -1.893x + 31.901

Detailed explanation:

We are given the following values in a table:

x  y

2  30

5  19

7  20

12  9

16  2

It is now abundantly evident from the set of values that when x increases, the y-value decreases, indicating a negative connection.

Therefore, the line of best fit will have a negative slope.

Consequently, a scatter plot is used to display the data values.

As can be seen, the line of best fit equation

y = -1.893x + 31.901T

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Answer:

Line t:  y = 1/9x + 8

Step-by-step explanation:

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

The formula for finding the slope the line perpendicular to line s is:

[tex]m_{2}=-\frac{1}{m_{1} }[/tex], where m2 is the slope of the line we don't know (in this case, line t) and m1 is the slope of the line we're given (in this case, line s).

Currently line s is in point-slope form or

[tex](y-y_{1})=m(x-x_{1})[/tex].  Since m is the slope, we know that the slope of line s is -9.

By plugging in -9 for m1 in our equation, we have:

[tex]m_{2}=-\frac{1}{-9}\\ m_{2}=-\frac{1}{9}[/tex]

Since we know -1/9 is the slope of line t, we can plug this in for m and (9,9) for x and y in the slope-intercept equation to find b:

[tex]9=1/9(9)+b\\9=1+b\\8=b[/tex]

Thus, the equation of line t in slope intercept form is y = 1/9x + 8

The second place player must earn 0.0467 points per game in each of the next three games to take the lead in this category.

What is PPG Statistics?

First, calculate the PPG earned by the current leader of the season.

The total points earned by the current leader amount to 2112 and he had participated in a total of 77 games.

The following formula can be used to determine the PPG earned by the current leader per game,

PPG = Total Points / Total Games

[tex]\implies PPG=\frac{2112}{77}\\ \implies PPG = 27.42[/tex]  -----(1)

Now, calculate the PPG of the player who is ranked in the second place for the season.

The total number of points earned by the second place player is 2020 and he played a total of 74 games.

The second place player earned the following points per game,

PPG = Total Points / Total Games

[tex]\implies PPG=\frac{2020}{74}\\ \implies PPG = 27.29[/tex]  ---(2)

The difference in score with the leading team can be found by subtracting (2) from (1),

[tex]\implies 27.42-27.29=0.13[/tex]

So, to be the leading player, the second place player must obtain a lead of 0.14 points per game in the next three games if the current player plays no more games.

In such a situation, the total PPG of the player should be 27.43 and the number of games to be played is 3.

So, the number of points required to take lead can be calculated as,

PPG = Total Points / Total Games

[tex]\implies 27.43=P/3[/tex]

So, the Total Points required, [tex]P=27.43 \times 3 =82.29[/tex]

And, the PPG required by the second place player to score in each of the next three games is calculated as,

[tex]\frac{0.14}{3}=0.0467[/tex]

Therefore, the second place player must earn 0.0467 points per game in each of the next three games to take the lead in this category.

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The area of the given figure is 48 [tex]ft^{2}[/tex].

Area is a measurement of the space inside a two-dimensional shape. It is determined by multiplying the length and width of the shape together. Area is most commonly measured in square units, such as square feet, square meters, or square kilometers. When measuring curved shapes, the area is determined by measuring the space inside the shape and applying a mathematical formula to calculate the total area. Area is an important concept in mathematics and is used to measure surface area, volume, length, and other measurements. It can also be used to compare the sizes of different shapes.

Firstly, to calculate the area assume the figure as two separate rectangles. Think that you a drawing an imaginary line in the gap between the two 4-ft segments to make a line of 12ft in length.

To solve, multiply to find individual areas then add together to get the total area.

Given: The first rectangle is 5ft by 4ft.

We know, the area of a rectangle = Base × Height

[tex]4ft[/tex] × [tex]3ft[/tex] = [tex]12ft^{2}[/tex] .....(1)

The next rectangle is 12 by 3ft, as you have to add the missing length in the middle to accurately calculate the length of the line.

[tex]12ft[/tex] × [tex]3ft[/tex] = [tex]36ft^{2}[/tex] .....(2)

Adding (1) and (2) we get,

[tex]12ft^{2} +36ft^{2}[/tex] = [tex]48ft^{2}[/tex]

Hence, the area is [tex]48ft^{2}[/tex].

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Hence, we get the curve, [tex]$$\mathrm{y}(\mathrm{x})=\left[-\frac{3}{4 \mathrm{x}^4}+7 \ln (\mathrm{x})-\mathrm{x}\right]+\frac{23}{4}$$[/tex].

What is  slope of function ?

Algebra. Finding the rate at which the value of y (the dependent variable) changes in relation to x is what this process entails. The slope itself identifies the line's slope and direction.

Given the slope of function is,

[tex]$$\begin{aligned}\frac{\mathrm{dy}}{\mathrm{dx}} & =\frac{3}{\mathrm{x}^5}+\frac{7}{\mathrm{x}}-1 \\\Rightarrow \mathrm{dy} & =\left(\frac{3}{\mathrm{x}^5}+\frac{7}{\mathrm{x}}-1\right) \mathrm{dx}\end{aligned}$$[/tex]

Taking integration both side, we get

[tex]$$\begin{aligned}\int \mathrm{dy} & =\int\left(\frac{3}{\mathrm{x}^5}+\frac{7}{\mathrm{x}}-1\right) \mathrm{dx} \\\Rightarrow \mathrm{y} & =3 \int \mathrm{x}^{-5} \mathrm{dx}+7 \int \frac{1}{\mathrm{x}} \mathrm{dx}-\int \mathrm{dx} \\& =\left[3 \cdot \frac{\mathrm{x}^{-5+1}}{-5+1}+7 \ln (\mathrm{x})-\mathrm{x}\right]+\mathrm{c} \\& =\left[-\frac{3}{4 \mathrm{x}^4}+7 \ln (\mathrm{x})-\mathrm{x}\right]+\mathrm{c}\end{aligned}$$[/tex]

( where, [tex]$\mathrm{c}=$[/tex] constant)

Now. given that the curve is passing through point (1,4). So, putting $x=1$ and, y=4 into the curve,

[tex]$$\begin{aligned}\mathrm{y} & =\left[-\frac{3}{4 \mathrm{x}^4}+7 \ln (\mathrm{x})-\mathrm{x}\right]+\mathrm{c} \\\Rightarrow 4 & =\left[-\frac{3}{4}+7 \ln 1-1\right]+\mathrm{c} \\\Rightarrow 4 & =-\frac{7}{4}+\mathrm{c} \\\Rightarrow \mathrm{c} & =\frac{23}{4}\end{aligned}$$[/tex]

Therefore,

[tex]$$\mathrm{y}(\mathrm{x})=\left[-\frac{3}{4 \mathrm{x}^4}+7 \ln (\mathrm{x})-\mathrm{x}\right]+\frac{23}{4}$$[/tex]

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The number of days it will take the bacteria to multiply to 10,000,000 colonies will be 39,493.

Let a be the initial value and x be the power of the exponent function and b be the increasing factor.

The exponent is given as

y = a(b)ˣ

There were 700 provinces of microbes on day 1 of refined. With a development pace of 2.3. Then the equation is given as,

[tex]\rm A = 700 \times (2.3)^{t - 1}[/tex]

Then the number of days it will take the bacteria to multiply to 10,000,000 colonies will be given as,

[tex]\rm 10,000,000 = 700 \times (2.3)^{t - 1}\\[/tex]

Take log on both sides, then we have

(t - 1) × log 2.3 = 14,285.71

t - 1 = 39,492.99

t ≈ 39,493 days

The number of days it will take the bacteria to multiply to 10,000,000 colonies will be 39,493.

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The coordinates of the intersection with the x-axis are (-2,0), and (4, 0) and the maximum point is (1,9).

What are the coordinates of the axis?

A Cartesian coordinate system in a plane is a system of coordinates that uniquely identifies each point by a pair of numerical coordinates. These numerical coordinates are the signed distances from two fixed perpendicular oriented lines to the point, measured in the same unit of length.

We have,

The graph shows the sketch of y=f(x).

The graph passes through the points (-2,0), (0,8), (4, 0), and (1,9).

The coordinates of the intersection with the x-axis are

(-2,0), and (4, 0).

The maximum point is (1,9).

Hence, the coordinates of the intersection with the x-axis are

(-2,0), and (4, 0) and the maximum point is (1,9).

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The equations will be 20x and 500w.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

In this case, when offered a job in sales where you can choose to either make a salary $500 (constant) every week or commission of $20 per sale. This will be:

Let the sales be x

The equation will be:

= 20 × x

= 20x.

The second equation will be:

= 500 × w

where w = number of weeks.

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