Ettwice is three times as old as mavis. the sum of their age is 60. how old each ​

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies a=\sqrt{c^2 - o^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{18}\\ a=\stackrel{adjacent}{x}\\ o=\stackrel{opposite}{12} \end{cases} \\\\\\ x=\sqrt{ 18^2 - 12^2}\implies x=\sqrt{ 324 - 144 } \implies x=\sqrt{ 180 }\implies x\approx 13.4\)

The missing side of a right-angled triangle, assuming it to be the hypotenuse with other sides as 12 and 18, can be calculated using the Pythagorean theorem. The square root of the sum of 12^2 and 18^2 gives the length of the hypotenuse, which is approximately 21.6 when rounded to the nearest tenth.

This question relates to the Pythagorean theorem which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as: a² + b² = c².

Assuming that the missing side in your question (x) is the hypotenuse and the other two sides are 12 and 18, you can calculate it using the aforementioned theorem. Therefore, you find x by calculating the square root of (12² + 18²), or √(144 + 324) which equals to √468. This value, rounded to the nearest tenth, is 21.6.

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Slope = change in y / change in x

Use the two pints shown on the graph.

Slope = ( 0- -2) / ( -6 -2)

Slope = 2/-8

Slope = -1/4

answer: slope = -1/4

Slope

Answer:

B Is correct

Step-by-step explanation:

Solve the solution set and divide to get the points and whether to fill them in or not.

-5 filled in, and 5 open circle

The graph of the solution set can be seen in option B.

The solution set is the set representing all solutions for an equation. It is also the roots that obey a quadratic equation or an inequality.

From the given equation, we have:

\(\mathbf{\dfrac{x^2+9x+20}{x^2-x-20}\ge 0}\)

Let's factor out the quadratic equation, we have:

\(\mathbf{\dfrac{(x+4)(x+5)}{(x+4)(x-5)}\ge 0}\)

By identifying the intervals;

x ≤ -5 or x > 5

The representation of these intervals on a graduated scale on a number line can be seen in the image attached below.

Therefore, we can conclude that the correct graph that show the solution set to the given equation can be seen in Option B.

Solution

The final answer

Option C

The maximum value of the original data set is 109.

To determine the maximum value of the original data set from the given stemplot, we need to look at the rightmost digits in each stem and identify the highest value.

Looking at the stemplot:

O 10 | 0 0 8 9 8 9 0 0 0

0 20 | 5 4 7 9 6

0 30 | 1 4 6 7 7 9 7

0 40 | 0 0 2 5 5 7 7 9 9 8

0 50 | 1 2 2 2 3 4 5 5 7 8 9 9

0 60 | 0 0 0 3 3 3 3 6 8

The rightmost digits in each stem represent the original data values. We can see that the highest value occurs in the stem "10" with a rightmost digit of "9".

Therefore, the maximum value of the original data set is 109.

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The statements supported by the data in the table are:

The mean number of cars sold in a month is the same at both dealerships.

The total number of cars sold is the same at both dealerships.

The data for Admiral Autos shows greater variability.

To determine which statements are supported by the data in the table, let's analyze the given information:

The mean number of cars sold in a month is the same at both dealerships.

To calculate the mean, we need to find the average number of cars sold each month at each dealership.

For Admiral Autos:

(4 + 19 + 15 + 10 + 17) / 5 = 65 / 5 = 13

For Countywide Cars:

(9 + 17 + 14 + 10 + 15) / 5 = 65 / 5 = 13

Since both dealerships have an average of 13 cars sold per month, the statement is supported.

The median number of cars sold in a month is the same at both dealerships.

To find the median, we arrange the numbers in ascending order and select the middle value.

For Admiral Autos: 4, 10, 15, 17, 19

Median = 15

For Countywide Cars: 9, 10, 14, 15, 17

Median = 14

Since the medians are different (15 for Admiral Autos and 14 for Countywide Cars), the statement is not supported.

The total number of cars sold is the same at both dealerships.

To find the total number of cars sold, we sum up the values for each dealership.

For Admiral Autos: 4 + 19 + 15 + 10 + 17 = 65

For Countywide Cars: 9 + 17 + 14 + 10 + 15 = 65

Since both dealerships sold a total of 65 cars, the statement is supported.

The range of the number of cars sold is the same for both dealerships.

The range is determined by subtracting the lowest value from the highest value.

For Admiral Autos: 19 - 4 = 15

For Countywide Cars: 17 - 9 = 8

Since the ranges are different (15 for Admiral Autos and 8 for Countywide Cars), the statement is not supported.

The data for Admiral Autos shows greater variability.

To determine the variability, we can look at the range or consider the differences between each data point and the mean.

As we saw earlier, the range for Admiral Autos is 15, while for Countywide Cars, it is 8. Additionally, the data points for Admiral Autos are more spread out, with larger differences from the mean compared to Countywide Cars. Therefore, the statement is supported.

Based on the analysis, the statements supported by the data are:

The mean number of cars sold in a month is the same at both dealerships.

The total number of cars sold is the same at both dealerships.

The data for Admiral Autos shows greater variability.

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Step-by-step explanation:

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The total length of the centre circle and the two goal semi circles to be repainted is 56.22 meters.

Given:

Court lines are 50 mm wide.

Court paint covers 7 m² per litre of paint.

The centre circle is a complete circle, so the circumference is given by the formula: Circumference = 2πr

Radius of the entire circle = 9 m / 2 = 4.5 m

Radius of the centre circle = 4.5 m - 0.05 m (converted 50 mm to meters) = 4.45 m

Circumference of the centre circle = 2π(4.45 m) = 27.94 m

Next, let's calculate the circumference of the semicircles:

The semicircles are half circles, so the circumference is given by the formula: Circumference = πr

The radius (r) of the semicircles is the same as the radius of the entire circle, which is 4.5 m.

Circumference of a semicircle = π(4.5 m) = 14.14 m

Total length = Circumference of the centre circle + 2 x Circumference of a semicircle

Total length = 27.94 m + 2(14.14 m)

Total length = 56.22 m

Therefore, the total length of the centre circle and the two goal semi circles to be repainted is 56.22 meters.

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Answer:

-4

Step-by-step explanation:

2t=-1-7

t=-8/2

t=-4

i am not sure also

Answer:

See below.

Step-by-step explanation:

We have:

Given:

\(-5(r+3)<12-10r+3r\)

Step 1: Combining Like Terms (on the right):

\(-5(r+3)<12-7r\)

Step 2: Distributive Property (distribute the -5 on the left):

\(-5r-15<12-7r\)

Step 3: Addition Property of Equality (add 7r to both sides):

\(2r-15<12\)

Step 4: Addition Property of Equality (add 15 to both sides):

\(2r<27\)

Step 5: Division Property of Equality (divide both sides by 2):

\(r<13.5\)

And we're done!

Answer:

Step 1: Combining Like Terms

Step 2: Distributive Property  

Step 3: Addition Property of Equality

Step 4: Addition Property of Equality

Step 5: Division Property of Equality  

The growth rate function indicates that the number of years The Iron Man's net worth will reach the net worth of T'Challa is about 87 years

The growth rate is the rate of growth of a function with regards to the input variable.

T'Challa's net worth in the Marvel comics = 80 trillion (8 × 10¹³) Dollars

The Iron Man's net worth = 20 billion (2 × 10¹⁰) Dollars

The growth rate per annum of The Iron Man's net worth = 10% per annum

The number of years it will take to reach T'Challa can therefore, be found as follows;;

(2 × 10¹⁰) × (1 + 0.1)ˣ = (8 × 10¹³)

(1 + 0.1)ˣ = (8 × 10¹³)/(2 × 10¹⁰)

x·ln(1 + 0.1) = ln((8 × 10¹³)/(2 × 10¹⁰))

x = (ln((8 × 10¹³)/(2 × 10¹⁰)))/(ln(1 + 0.1)) ≈ 87 years

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This represents the distance that Mr. Stein drove, given that Mr. Smith drove x miles. The value of x must be between 0 and 140, since Mr. Smith cannot drive more than 140 miles and less than 0 miles.

An algebraic expression is a combination of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. It can be simplified, evaluated, or manipulated using algebraic rules and properties.

Let x be the number of miles Mr. Smith drove. Then, the number of miles Mr. Stein drove is \(140 - x\)  , since they drove a total of 140 miles and Mr. Smith already drove x miles.

the algebraic expression for how many miles Mr. Stein drove is:

\(140 - x\)

Therefore, This represents the distance that Mr. Stein drove, given that Mr. Smith drove x miles. The value of x must be between 0 and 140, since Mr. Smith cannot drive more than 140 miles and less than 0 miles.

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Answer:

La abscisa x del centro de masa está en reposo (velocidades opuestas)

Vx = 0

La ordenada del centro de masa es:

y = h + Vo sen(α) t + Vo sen(α) t = h + 2 Vo sen(α) t

La velocidad es la derivada de y respecto del tiempo:

Vy = 2 Vo sen(α)

b) Momento lineal (p = m V)

En el eje x: px = 0 (momento lineal)

En el eje y: py = 2 m Vy = 4 m Vo sen(α)

dame corazon y 5 estrellas

Step-by-step explanation:

Answer:

True

False

True

Step-by-step explanation:

Interior angles are supplementary

Corresponding angles makes mangle2 and mangle6 the same deg

mangle1 = mangle5 (corresponding angles)

mangle5 = mangle8 (vertically opposite angles)

A transformation is applied to the input vector v by the function f. This transformation might include extending, rotating, or reflecting the vector in a certain way, depending on the precise shape of the function.

We may enter certain fixed vectors into the function, c, and watch as f transforms them to better understand its behavior (c). It may also be helpful to see the modified vectors as images or diagrams to have a better understanding of how the function behaves.

The term "vector" is used informally to describe constituents of particular vector spaces or some values that cannot be described by a single integer.

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Based on mathematical operations, the lowest amount that Annabel can pay for pencils is $15.20

The lowest amount that Annabel can pay for pencils can be determined using the mathematical operations of multiplication and division.

Multiplication and division are two of the four basic mathematical operations, including addition and subtraction.

If Annabel chooses to purchase the first pencil at 30p each, she would pay £22.80 (£0.30 x 76).

If Annabel chooses to purchase the second pencil class of a pack of 10 pencils for £2, she would pay £15.20 [£2 x (76 ÷ 10)].

Pencils for sale

30p each

Pack of 10 pencils for £2

Thus, if Annabel wants to buy the pencils, she can either pay £15.20 or £22.80, but using mathematical operations, the lowest amount she can pay is £15.20.

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Answer:

A. 42½ units

Step-by-step explanation:

the volume = 5×2×4¼ = 10×4¼ = 42½

Answer:

x = 16°

Step-by-step explanation:

What we know:

∠JML = 47°

∠JKL = (7x + 21)°

∠JML is an inscribed angle

∠JKL is an inscribed angle

Inscribed angles are half of the value of their intercepted arc

So if m∠JML = 47° then mArc JL is double that or 94°

And ∠JKL is intercepted by Arc JML which is the rest of the circle not intercepted by ∠JML so

mArc JL + Arc JML = 360°

94 + Arc JML = 360

Subtract 94 from both sides to isolate Arc JML

Arc JML = 266°

So if Arc JML = 266° then it's intercepted inscribed angle is half of that.

Arc JML ÷ 2 = ∠JKL

266 ÷ 2 = ∠JKL

133 °= ∠JKL

Now we can use this value and set it equal to the expression to find the value of x

(7x + 21) = 133

Subtract 21 from both sides to isolate the x

7x = 112

Divide both sides by 7

x = 16

Answer:   10°

__________________________________________________________

We are given:

Sin(6θ)  = Cos(3θ)

Solving for θ:

Simplifying Cos(3θ):

We know that:  

Cos(θ) = Sin(90-θ)

So, we can say that:

Cos(3θ) = Sin(90 - 3θ)

Finding the value of θ:

Sin(6θ) = Cos(3θ)

Sin(6θ) = Sin(90 - 3θ)                             [Since Cos(3θ) = Sin(90 - 3θ)]

6θ = 90 - 3θ                                            [If Sin(θ) = Sin(A) ; θ = A]

9θ = 90                                                   [adding 3θ on both sides]

θ = 10°                                                     [dividing both sides by 9]

Answer:

48s + 48

Step-by-step explanation:

Answer:

This is called absolute sign | | or something near to that...

Any number inside the | | will always be positive in the output. For example |3|= 3 and also |-3|= 3

|-x| = x (notice that)

That's the bottom line and the idea of this equation

You will substitute with the value of function g(x) in the function f(g(x)) = x

The value of g(x) is known as it states g(x) = -x

So when substituting it's going to be like that

f(-x) = -x (right)?

But notice they told you that

f(x) = |x| so as we stated earlier if it's

Anything inside the | | is always positive

So f(-x) = x ###

Why?

Because when we substitute

|-x| =x

Step-by-step explanation:

Log(x²+8)=log 10+ log x

Log(x²+8)=log(10×x)

x²+8=10x

x² - 10x + 8=0

x is approximately to - 1 and - 8✅

The solutions to the given equation are x = -1 and x = 8.

Option A is the correct answer.

Solutions are the values of an equation where the values are substituted in the variables of the equation and make the equality in the equation true.

We also find the solution in a system of equations using the substitution or elimination method.

Example:

2x + 4 = 8

The solution is x = 2.

We have,

Using logarithmic properties, we can simplify the given equation:

logs(x² + 8) = 1 + log g(x)

logs(x² + 8) - log g(x) = 1

log[(x² + 8)/g(x)] = 1

(x² + 8)/g(x) = 10

x² + 8 = 10g(x)

Now we can solve for x by substituting the given answer options and solving for g(x):

For x = -2 and x = -4:

x = -2:

(-2)² + 8 = 12, which is not equal to 10 g(x) for any value of g(x).

So x = -2 is not a solution.

x = -4:

(-4)² + 8 = 24, which is also not equal to 10g(x) for any value of g(x).

So x = -4 is not a solution.

For x = -1 and x = 8:

x = -1:

(-1)² + 8 = 9, which is equal to 10g(x) when g(x) = 0.9.

So x = -1 is a solution.

x = 8:

(8)² + 8 = 72, which is equal to 10g(x) when g(x) = 7.2.

So x = 8 is a solution.

For x = 1 and x = -8:

x = 1:

(1)² + 8 = 9, which is equal to 10g(x) when g(x) = 0.9.

So x = 1 is a solution.

x = -8:

(-8)² + 8 = 56, which is not equal to 10g(x) for any value of g(x).

So x = -8 is not a solution.

Therefore,

The solutions to the given equation are x = -1 and x = 8.

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The only possible value of "a" that satisfies the given equations is a = 5.

The possible values of "a" that satisfy the given equations, let's solve the system of equations:

a + ab = 250 ---(1)

a - ab = -240 ---(2)

We can solve this system by using the method of substitution. Rearranging equation (2), we get:

a = ab - 240 ---(3)

Substituting equation (3) into equation (1), we have:

(ab - 240) + ab = 250

2ab - 240 = 250

2ab = 250 + 240

2ab = 490

ab = 490/2

ab = 245

Now we have the value of "ab."

We can substitute this back into equation (3) to solve for "a":

a = (245) - 240

a = 5

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ANSWER:

Point in original figure (2, -3)

Point in final figure (-3, -2)

STEP-BY-STEP EXPLANATION:

The first thing is to determine the original point of the figure on the graph, which would be:

The rule for 270° counterclockwise rotation is as follows:

We apply it in this case, and the new point would be:

We represent the result on the graph, as follows

Answer:

C

Step-by-step explanation:

The value of x is 8.77

a. The secant slope through (-2,4) and (0,0) is -2.

b. The secant slope through (-1.5,2.25) and (-0.5,0.25) is -2.

The estimated slope of the tangent line to f(x) = x^2 at x = -1 is approximately -2.

To estimate the slope of the tangent line to the function f(x) = x^2 at x = -1, we can find the slopes of the secant lines through different pairs of points.

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

The coordinates of the two points are (-2, 4) and (0, 0). We can calculate the slope of the secant line passing through these points using the formula:

msec = (y2 - y1) / (x2 - x1)

Plugging in the values, we get:

msec = (0 - 4) / (0 - (-2))

= -4 / 2

= -2

So, the slope of the secant line passing through (-2, 4) and (0, 0) is -2.

b. (-1.5, 2.25) and (-0.5, 0.25):

The coordinates of the two points are (-1.5, 2.25) and (-0.5, 0.25). Using the slope formula, we can calculate the slope of the secant line passing through these points:

msec = (0.25 - 2.25) / (-0.5 - (-1.5))

= (-2) / (1)

= -2

So, the slope of the secant line passing through (-1.5, 2.25) and (-0.5, 0.25) is -2.

By finding the slopes of the secant lines, we have estimated the rate of change of the function f(x) = x^2 at x = -1. The slope of the tangent line at this point will be very close to these secant slopes, particularly as the two points used to calculate the secant lines get closer together.

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