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How tall is this tree?
The tree is
ft tall.
(Round to the nearest tenth.)

Answer:

The answer is The vertex of the graph of f(x) = |x – 3| + 6 is located at (3,6)

3

and

6

Step-by-step explanation:

Vertex of graph located at (3,6)

A mathematical object's vertex is a special point where two or more lines or edges typically meet. Angles, polygons, and graphs are the most common examples of vertices.

Given equation f(x) = |x - 3| +6

after simplifying there will be two equations they are

y = x - 3 + 6 = x +3...….(1)

and y = -(x-3) +6

y = 9 - x...…(2)      

substitute value of equation 2 in eq. 1

9 - x = x + 3

      x = 3 and

substitute value of x in eq. 1

y = x + 3 =3 + 3

y = 6

x = 3, y = 6

Hence the intersecting points of both equation are (3,6)

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Answer:

Last option:

(-13, -12, 9)

Step-by-step explanation:

Here you need to look at a number line.

(an infinite line with the zero in the middle, at the left we have the negative numbers which increase to the left, and at the right, we have the positive numbers that increase to the right)

for any two pair of numbers in the number line, the number at the right is larger than the number at the left.

So for example, -10 is at the left of -3

Then:

-10 < -3.

Then a set is ordered from least to greatest if:

first we have the largest negative numbers

then the smaller negative numbers

then the zero (if there is a zero)

then the smaller positive numbers

then the largest positive numbers.

The only set that meets this condition is the last one:

(-13, -12, 9)

Why the others not meet this condition?

in the first one we have -9 after 5, and we know that -9 < 5

in the second one we actually have an order from greatest to least.

in the third one we have -8 at the right of 12, and we know that -8 < 12

Answer:

AB = 28 , BC = 17.5 , X = 13.2

Step-by-step explanation:

since the figures are similar then the ratios of corresponding sides are in proportion, that is

\(\frac{AB}{PQ}\) = \(\frac{AD}{PS}\) ( substitute values )

\(\frac{AB}{8}\) = \(\frac{14}{4}\) ( cross- multiply )

4 AB = 8 × 14 = 112 ( divide both sides by 4 )

AB = 28

and

\(\frac{BC}{QR}\) = \(\frac{AD}{PS}\) ( substitute values )

\(\frac{BC}{5}\) = \(\frac{14}{4}\) ( cross- multiply )

4 BC = 5 × 14 = 70 ( divide both sides by 4 )

BC = 17.5

similarly for the 2 similar figures

\(\frac{x}{6}\) = \(\frac{11}{5}\) ( cross- multiply )

5x = 6 × 11 = 66 ( divide both sides by 5 )

x = 13.2

Answer:

\(\overline{AB}=28\)

\(\overline{BC}=17.5\)

\(x=13.2\)

Step-by-step explanation:

If quadrilateral PQRS is similar to quadrilateral ABCD, their corresponding sides are in the same ratio:

\(\overline{PQ} : \overline{AB} = \overline{QR} : \overline{BC} = \overline{RS} : \overline{CD} = \overline{SP}:\overline{DA}\)

From inspection of the two quadrilaterals, the given side lengths are:

\(\overline{PQ} = 8\)

\(\overline{QR} = 5\)

\(\overline{RS} = 6\)

\(\overline{SP} = 4\)

\(\overline{DA} = 14\)

Substitute these into the ratio equation:

\(8 : \overline{AB} = 5 : \overline{BC} = 6 : \overline{CD} = 4:14\)

Solve for AB:

\(8 : \overline{AB} = 4:14\)

   \(\dfrac{8}{\overline{AB}}= \dfrac{4}{14}\)

 \(8 \cdot 14=4 \cdot{\overline{AB}}\)

   \(\overline{AB}=\dfrac{8 \cdot 14}{4}\)

  \(\boxed{\overline{AB}=28}\)

Solve for BC:

\(5 : \overline{BC} = 4:14\)

  \(5 \cdot 14=4 \cdot \overline{BC}\)

    \(\overline{BC}=\dfrac{5 \cdot 14}{4}\)

   \(\boxed{\overline{BC}=17.5}\)

\(\hrulefill\)

Assuming the two figures are similar, their corresponding sides are in the same ratio. Therefore:

\(x:6=11:5\)

   \(\dfrac{x}{6}=\dfrac{11}{5}\)

   \(x=\dfrac{11 \cdot 6}{5}\)

   \(x=\dfrac{66}{5}\)

  \(\boxed{x=13.2}\)

Answer:

\(\begin{aligned}x &= 16\sqrt3 \\ &\approx 27.7\end{aligned}\)

Step-by-step explanation:

We can see that the longer leg (a) of a right triangle is half of the circle's radius. Since we are given the other two sides of the triangle (shorter leg and hypotenuse), we can solve for the length of the longer leg using the Pythagorean Theorem:

\(a^2 + b^2 = c^2\)

↓ plugging in the given values

\(a^2 + 2^2 = 14^2\)

↓ subtracting 2² from both sides

\(a^2 = 14^2 - 2^2\)

\(a^2 = 196 - 4\)

\(a^2 = 192\)

↓ taking the square root of both sides

\(a = \sqrt{192\)

↓ simplifying the square root

\(a = \sqrt{2^6 \cdot 3\)

\(a = 2^{\, 6 / 2} \cdot \sqrt3\)

\(a = 2^3\sqrt3\)

\(a = 8\sqrt3\)

Now, we can solve for the radius (x) using the fact that the longer leg of the triangle is half of it.

\(a = \dfrac{1}{2}x\)

↓ plugging in the a-value we solved for

\(8\sqrt3 = \dfrac{1}2x\)

↓ multiplying both sides by 2

\(\boxed{x = 16\sqrt3}\)

Answer: Un alambre de acero de 1.5 m se estira 2.0 mm con fuerza F. El diámetro del alambre de acero es 4.0 mm. El módulo de Young del acero es 2.0 x 1011 Nm-2. Determine la fuerza F aplicada sobre el alambre.

Step-by-step explanation:

Answer:

x=10

Step-by-step explanation:

easy

The test statistic when the a simple random sample has been selected from a normally distributed population is a) -2.24

The test statistic is a number derived from a statistical test that is used to determine whether your data could have occurred under the null hypothesis.

u = 30000

x = 22298

s = 14200

n = 17

Test statistic = = (x - u) / s / ✓n

x = mean

u = theoretical value

s = standard deviation

{n} = variable set size

= (x - u) / s / ✓n

= (22298 - 30000) / 14200 / ✓17

= -2.24

Test statistic = -2.24

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Answer:

Mean = 53.

Step-by-step explanation:

The median is the middle value so the 3 cards are

36, 46, x       where x is to be found.

The range is 41, so:

x - 36 = 41

x = 41 + 36

x = 77.

Therefore, the mean is

(36+46+77) / 3

= 159/3

= 53.

Answer: To make "w" the subject of the formula "P+aw=b", we need to isolate "w" on one side of the equation.

First, we can subtract "P" from both sides of the equation to get:

aw = b - P

Next, we can divide both sides of the equation by "a" to get:

w = (b - P) / a

Therefore, the solution is:

w = (b - P) / a

Step-by-step explanation:

The equivalent equation of  r sinθ = 10 in rectangular coordinates is y²  +   y⁴/x² - 100 = 0.

The rectangular coordinates is calculated from the polar equation as follows;

r sinθ = 10

the conversion from polar to rectangular coordinates;

r² = x² + y²

r = √(x² + y²) ----- (1)

y/x = tanθ  ------ (2)

r sinθ = 10

√(x² + y²)(y/x) = 10

(x² + y²)(y²/x²) = 100

y²  +   y⁴/x² = 100

y²  +   y⁴/x² - 100 = 0

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Answer:

a) See step by step explanation

b) z(s) = - 2.178

c)  z(c) = - 1.64

d) We reject H₀

e) The proportion of drivers has decreased

Step-by-step explanation:

We assume a survey with a random sample

Normality population

Size is big enough to use the approximation of binomial distribution to normal distribution

2019 sample:

sample size   n  = 963

drivers who admitted going more than 10 miles over the limit

x₁ =  315

p₁  =  315/963       p₁ = 32.71 %    or   p₁  = 0.3271   and  q₁ =  1 - 0.3271

q₁  =  0.6729

Hypothesis Test:

a) Null Hypothesis                    H₀                    p₁  =  36 %

Alternative Hypothesis        Hₐ                    p₁ <  36 %  or  p₁ < 0.36

b) To calculate z(s)  ;   z(s)  =  (  p₁  - 0.36 ) / √ (p₁*q₁)/n

z(s) =  (  0.3271 - 0.36 ) / √ ( 0.3271* 0.6729)/963

z(s) = - 0.0329 /  0.0151

z(s) = - 2.178

c) we will use a confidence interval of 95 %. Then significance level     α = 5 %    α = 0.05  As the alternative hypothesis indicates we are going to develop a one-tail test

From z- table we find  z(c) = - 1.64

d) Comparing z(s) and z(c)  |z(s)| > |z(c)|

Then z(s) is in the rejection region for H₀  we reject H₀

e) we can support that the proportion of drivers has decreased since 2002

Answer:6.05

Step-by-step explanation:

6 is the ones place. 0 is the tenths place. 5 is the hundredths place.

The two equations that can be most appropriately solved by using the zero product property are:

3x² - 6x = 0 and -(x - 1)(x + 9) = 0.

What is the quadratic equation?

The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.

The zero product property can be used to solve equations that can be factored into the product of two or more expressions, where one or more of those expressions is equal to zero.

Therefore, the two equations that can be solved using the zero product property are:

3x² - 6x = 0

This equation can be factored as:

3x(x - 2) = 0

Using the zero product property, we get:

3x = 0 or x - 2 = 0

Solving for x, we get:

x = 0 or x = 2

-(x - 1)(x + 9) = 0

This equation can be factored using the difference of squares:

-(x - 1)(x + 9) = -(x² - 1² - 9x + 1x) = -(x² - 8x - 9) = 0

Using the zero product property, we get:

x - 1 = 0 or x + 9 = 0

Solving for x, we get:

x = 1 or x = -9

Therefore, the two equations that can be most appropriately solved by using the zero product property are:

3x² - 6x = 0 and -(x - 1)(x + 9) = 0.

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None of the given answer options (-10, 10, 16, ¾/1) correspond to the correct slope of -1/2.

To find the slope of the red line given that it is perpendicular to the green line with a slope of 2, we can use the property that perpendicular lines have slopes that are negative reciprocals of each other.

The slope of the green line is 2. To find the slope of the red line, we take the negative reciprocal of 2. The negative reciprocal is obtained by taking the reciprocal (flipping the fraction) and changing the sign.

Reciprocal of 2: 1/2

Negative reciprocal: -1/2

Therefore, the slope of the red line is -1/2.

However, none of the given answer options (-10, 10, 16, ¾/1) correspond to the correct slope of -1/2.

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Answer:

-a/b

Step-by-step explanation:

ax+by=c

First get the equation in slope intercept form ( y= mx+b  where m is the slope and b is the y intercept)

Subtract ax from each side

ax+by -ax=-ax +c

by = -ax+c

Divide each side by b

by/b = -ax/b + c/b

y = -a/b * x + c/b

The slope is -a/b and the y intercept is c/b

We want the line parallel so it has the same slope, -a/b

Answer:-a/b

Step-by-step explanation:

The polynomial with the given zeros is:;

P(x) = (300/108)*x*(x + 1)*(x - 1)*(x - 3/2)

Remember that if a polynomial has the zeros a, b, c, and d, then we can write it as:

P(x) = K*(x - a)*(x - b)*(x - c)*(x - d)

Where K is a coefficient.

Here the zeros are 0, -1, 1, 3/2

Then we can write:

P(x) =K*(x - 0)*(x + 1)*(x - 1)*(x - 3/2)

P(x) =K*x*(x + 1)*(x - 1)*(x - 3/2)

We also know that when x = -3, P(x) = 300

Then we can write:

300 = K*(-3)*(-3 + 1)*(-3 - 1)*(-3 - 3/2)

300 = K*(-3)*(-2)*(-4)*(-9/2)

300 = K*108

300/108 = K

Then the polynomial is:

P(x) = (300/108)*x*(x + 1)*(x - 1)*(x - 3/2)

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Given the circle shown in the exercise, you can identify that:

By definition:

In this case, you know that:

The exercise does not provide the measure of the Arc DE, but you know that there are 360 degrees in a circle and you know that the other Arc of the circle is:

Then, you can set up that:

Simplifying, you get that:

Knowing the expression that represents the Tangent chord angle and the expression that represents the Intercept Arc, you can substitute them into the formula, in order to find the value of "x":

Solving for "x", you get:

Therefore, the answer is: Option C.

Answer:

70%

Step-by-step explanation:

50/10 is 5 (which is 10%). 5 x 7 is 35 (or 70%)

The area of the circle circumscribed about the right triangle with legs 6 and 8 is approximately 78.54 square units.

To find the area of the circle circumscribed about a right triangle, we can use the fact that the diameter of the circle is equal to the hypotenuse of the right triangle. In this case, the legs of the right triangle are given as 6 and 8.

Using the Pythagorean theorem, we can find the length of the hypotenuse:

\(c^2 = a^2 + b^2\)

where c is the length of the hypotenuse, and a and b are the lengths of the legs.

Substituting the values:

\(c^2 = 6^2 + 8^2\)

\(c^2 = 36 + 64\\ c^2 = 100\)

Taking the square root of both sides:

\(c = \sqrt{100} \\ c = 10\)

Therefore, the length of the hypotenuse is 10 units.

Since the diameter of the circumscribed circle is equal to the hypotenuse, the radius of the circle is half the length of the hypotenuse, which is 10/2 = 5 units.

Now we can calculate the area of the circle using the formula:

Area = π \(r^2\)

where r is the radius of the circle.

Area = π \(5^2\)

Area = π × 25

Area = 78.54 square units

Hence, the area of the circle circumscribed about the right triangle with legs 6 and 8 is approximately 78.54 square units.

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Andre needs average 6 cups of yellow paint if he uses 8 cups of blue paint to make the same shade of green. Andre needs 10 cups of blue paint if she uses 15 cups of yellow paint to make the same shade of green.

To make the same shade of green, the amount of yellow and blue paint needed is determined by their respective ratios. If Andre is using 8 cups of blue paint, he will need 6 cups of yellow paint for the same shade of green. This is because the ratio of blue to yellow paint is 8:6, or 1.3333:1. This means that for everyis needed. When using 15 cups of yellow paint, the amount of blue paint needed to make the same shade of green is 10 cups. This is because the ratio of yellow to blue paint is 15:10, or 1.5:1. This means that for every 1.5 cups of yellow paint, 1 cup of blue paint is needed. Therefore, if Andre wants to achieve the same shade of green, he will need 6 cups of yellow paint if he uses 8 cups of blue paint, and 10 cups of blue paint if he uses 15 cups of yellow paint.

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Answer:

4x^2 - 12x + 9

Explanation:

(2x - 3)^2

(2x - 3)(2x - 3)

2x(2x - 3) -3 (2x - 3)

4x^2 - 6x - 3 (2x - 3)

4x^2 - 6x - 6x + 9

4x^2 - 12x + 9

Answer:

  8

Step-by-step explanation:

You want to know the measure of segment XY if ∆XYZ ≅ ∆MNL and MN = 8.

Segment XY is named using the first two vertices listed in the name of ∆XYZ. That means the segment is the same length as the one named by the first two vertices listed in the name of congruent ∆MNL, segment MN.

Segment MN is given as 8 units long. Segment XY is congruent, so is also 8 units long.

  XY = 8 units

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The mean of the test is 20.

To determine the mean of the test, we need to use the information provided about the scores falling above the mean in terms of standard deviations.

Let's denote the mean of the test as μ, and the standard deviation as σ.

We are given that a score of 29 falls three standard deviations above the mean, so we can write this as:

29 = μ + 3σ

Similarly, we are told that a score of 23 falls one standard deviation above the mean, which can be expressed as:

23 = μ + σ

Now we have a system of two equations with two variables (μ and σ). We can solve this system of equations to find the values of μ and σ.

From the second equation, we can isolate μ:

μ = 23 - σ

Substituting this value into the first equation, we have:

29 = (23 - σ) + 3σ

Simplifying the equation, we get:

29 = 23 + 2σ

2σ = 29 - 23

2σ = 6

σ = 3

Substituting the value of σ back into the second equation, we find:

μ = 23 - 3

μ = 20

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Answer:

B

Step-by-step explanation:

The reference angles of -320 is 40 degrees and the reference angle of 19π/12 is 5π/12

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

Angle = -320

The reference angle is caculated as

Reference = 360 + Angle

So, we have

Reference = 360 - 320

Evaluate

Reference = 40

For the other angle, we have

θ = 19π/12

The above angle is in the fourth quadrant

So, we subtract it from 2π to calculate the reference angle

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

Reference angle = 2π - 19π/12

Evaluate the difference

Reference angle = 5π/12

Hence, the reference angle is 5π/12

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The area of​ RSTU is 144 cm² which is equal to the area of JKLM.

The area of the square is defined as the product of the length and width.

Given square JKLM and t(-6,4) t (1,5)

We have to determine the area of​ RSTU.

The given translation doesn't change the shape or dimensions, therefore the area will remain the same.

Here Side of (JKLM)​ = Side of RSTU

So the area of​ RSTU = the area of​ JKLM

The area of​ RSTU = (length of JM)²

The area of​ RSTU = (12cm)²

The area of​ RSTU = 144 cm²

Thus, the area of​ RSTU is 144 cm² which is equal to the area of JKLM.

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The question seems to be incomplete the correct question has been attached in file

The answer is C.

\(f(x) =\frac{12}{x} -18 \\g(x) = \frac{12}{x-8}\)

Step by step ex[planation:

To solve for the inverse of the first function

Replace f(x) or g(x) with y, switch x and y, solve for y and replace it with f⁻¹(x)

Here , the option C is correct because:

f(x)=18/x-9

y=18/x-9

x=18/y-9

x+9=18/y

y(x+9)=18

y=18/(x+9)

f⁻¹(x)=18/(x+9)

So , the correct, the answer is C

Option (A) represents the function and its inverse of a function option (A) is correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a function and inverse of a function shown in the picture.

Checking for option (A):

\(\rm f(x) = \dfrac{x}{4}+10 \ \ \ and \ \ \ g(x) = 4x -10\)

Taking f(x):

\(\rm f(x) = \dfrac{x}{4}+10\)

To find the inverse of a function interchange the x and y variables:

f(x) → x

x  → g(x)

\(\rm x = \dfrac{g(x)}{4}+10\)

Solving:

4x = g(x) + 10

g(x) = 4x - 10

Similarly, we can find the inverse of a function.

Thus, option (A) represents the function and its inverse of a function option (A) is correct.

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