Triangle STU is a right triangle.
Write an equation that relates the lengths of sides s, t, and u? (5 points)

Logarithmic Functions

In mathematics, the logarithmic function is an inverse function to exponentiation

Domain and range of logarithmic functions

We know that is defined only when >0. So the domain is the set of all positive real numbers. We can see that can be either a positive or negative real number (or) it can be zero as well. Thus,  can take the value of any real number.

Note:

The domain of function = is >0 (or) (0,∞).

The range of any log function is the set of all real numbers ().

Logarithmic graph

We know that exponentials and functions are inversely proportional to each other, and so their graphs are symmetric concerning the line =. Also, note that =0 when =0 as =(1)=0 for any . Thus, all such functions have an -intercept of (1,0).  A logarithmic function doesn’t have a -intercept as 0 is not defined.

Properties of logarithmic graph

>0 and ≠1.

The logarithmic graph increases when >1 and decreases when 0<<1.

The domain is obtained by setting the argument of the function greater than 0.

The range is the set of all real numbers.

Graphing logarithmic functions

Before plotting the log function, just have an idea of whether you get an increasing curve or decreasing curve as the answer. If the >1 then the curve is increasing, and if 0<<1, then the curve is decreasing.

Here are the steps for graphing logarithmic functions:

Find the domain and range.

Find the vertical asymptote by setting the argument equal to 0. Note that a  function doesn’t have any horizontal asymptote.

Substitute some value that makes the argument equal to 1 and use the property (1)=0. This gives us the -intercept.

Substitute some value that makes the argument equal to the base and use the property ()=1 This would give us a point on the graph.

Connect the two points (from the last two steps) and extend the curve on both sides relative to the vertical asymptote.

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Answer:

2^2×5×13

Step-by-step explanation:

its simple using only prime numbers to divide the answer of 52×5

Answer:

5x∧52

Step-by-step explanation:

Answer:

supplementary angles

Step-by-step explanation:

for instance, 50 + 130 = 180.

3.) x = 15.25 or 15 1/4 ( not sure if you'll need to round your answer )

4.) x =6

5.) x = 10

6.) x = 9

Explanation:

1.) write your equation down 8x + 9 = 131

2.) Subtract +9 from 131. you'll get 122

3.) divide 8x and 122.

4.) Then there's your answer 15.25

you'll do the same thing throughout each equation. write down your equation but with the 22x and 23x you're going to subtract 22x from 23x. and you'll get 1x then continue on the same way as with the last equation.

Answer:

3.975 square inches

Step-by-step explanation:

Step 1

We find the length of the triangle

We solve using Pythagoras Theorem

Diagonal² = Length² + Width²

Diagonal = 4 inches

Width = 3 inches

Length² = Diagonal² - Width²

Length = √Diagonal² - Width²

Length = √4² - 3²

Length = √16 - 9

Length = √(7)

Length = 2.6457513111 inches

Length = 2.65 inches

Step 2

Area of Triangle = 1/2 × Base × Height

Base = Length = 2.65 inches

Height = Width = 3 inches

=1/2 × 2.65 inches × 3 inches

= 3.975 square inches

Therefore, the area of one of the triangles that are formed is 3.975 square inches

The temperature of the city of Puerto Rico in Fahrenheit will be 104 Fahrenheit.

Unit modification is the process of converting the measurement of a given amount between various units, often by multiplicative constants that alter the value of the calculated quantity without altering its impacts.

A temperature C, in degrees Celsius, is the same as a temperature of (9/5)C + 32, in degrees Fahrenheit.

The hottest temperature ever recorded in Puerto Rico was 40 degrees Celsius.

Convert the temperature from Celcius to Fahrenheit. Then we have

⇒ (9/5)C + 32

⇒ (9/5) x 40 + 32

⇒ 9 x 8 + 32

⇒ 72 + 32

⇒ 104 F

The temperature of the city of Puerto Rico in Fahrenheit will be 104 Fahrenheit.

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Step-by-step explanation:

u vector components:

x-comp = 8 - (-17) = 25

x-comp = -11 - 4 = -15

Therefore, we can write vector u as

u = 25i - 15j

v = 14i - 4j

u - v = 11i - 11j

Therefore,

2(u - v) = 22i - 22j

Answer:

first you subtract 5 from both sides

your left with 3x=11

divide by 3 on both sides

x=3.666 repeating

Step-by-step explanation:

The number of machines to minimize the unit cost is 110 and minimum cost is 10,389 .

What is Quadratic Equation?

Quadratic equation can be defined as the equation which is in the form of ax^2 +bx +x = 0.

where a,b,c are constants.

Given ,

The standard form of a quadratic is given by:

ax^2 + bx + c

So for our function, we can say,

a = 0.1

b = -22

c = 11599

We can find the vertex (x-coordinate where minimum value occurs) by the formula -b/2a

So,

= -(-22) / 2*0.1

=22/0.2

= 110

Plugging this value into original function would give us the minimum (unit cost):

C(x) = 0.1 x ^2 - 22x +11599

C(x) = 0.1(110*110) - 22(110)+11599

C(x) = 110(11-22) + 11,599

C(x) = -11(110) + 11599

C(x) = -1210 + 11599

C(x) = 10,389

Hence , The number of machines to minimize the unit cost is 110 and minimum cost is 10,389 .

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The volume of the composite solid round to the nearest tenth is 83.7 inches³.

Volume of a three dimensional shape is the space occupied by the shape.

There are 2 hemispheres and a cylinder in the given composite solid.

Volume of hemisphere =  [tex]\frac{2}{3}[/tex] π r³, where r is the radius.

Volume of the cylinder = π r² h, where r is the radius and h is the height.

Here r = 2 inches and

h = 8 - 4 = 4 inches

Volume of hemisphere = [tex]\frac{2}{3}[/tex] π × 2³

                                      = [tex]\frac{16}{3}[/tex] π

There are two hemispheres.

Volume of two hemispheres = 2 × [tex]\frac{16}{3}[/tex] π =  [tex]\frac{32}{3}[/tex] π

Volume of the cylinder = π r² h

                                      = π × 2² × 4

                                      = 16 π

Volume of the composite Solid = [tex]\frac{32}{3}[/tex] π + 16 π

                                                    = [tex]\frac{80}{3}[/tex] π

                                                    = 83.7 inches³

Hence the volume of the composite solid is 83.7 inches³.

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A graph of quadrilateral ABCD whose vertices are A (0, 0) B(5, 0), C(3, 2) and D (0, 2) is shown in the image attached below.

In Geometry, there are different types of quadrilateral and these include the following:

Next, we would use an online graphing calculator to construct (plot) quadrilateral ABCD on a cartesian coordinate based on the given vertices. Also, you should enter the value for each vertices of quadrilateral ABCD on the x-coordinate and y-coordinate respectively as shown in the table.

By critically observing the graph of quadrilateral ABCD, we can reasonably infer and logically deduce that it represents a trapezium.

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The complete maze pattern is shown below.

Given is an exponent maze.

We can complete the maze as -

START HERE →→ 3³ → → 9 →→ 1³ →→ 1 →→ 9² →→ 81 →→ 4³ →→ 64 →→ 2⁵ →→ 32 →→ 11² →→ 121 →→ 8² →→ 64 →→ 15³ →→ 3375 →→ 13² →→ 169 →→ 2⁴ →→ 16 →→ 10² →→ 100 →→ 2³ →→ 8 →→ 6⁴ →→ 1296 →→ 12² →→ 144 →→ 3³ →→ 27 →→ YOU MADE IT.

Therefore, the complete maze pattern is shown above.

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The stem plot for the given data is 3 4 5 6.

A stem and leaf plot, also known as a stem and leaf diagram, is a technique to arrange data such that it is simple to see how frequently certain sorts of values occur. It is a graph that displays ordered numerical data. A stem and a leaf are divided into each piece of data.

Arranging the given data in ascending order,

30, 34, 34, 35, 35, 36, 39, 39, 40, 40, 41, 42, 42, 43, 43, 43, 44, 46, 46, 48, 49, 49, 50, 52, 53, 58, 59, 61, 66, 68

The stem plot = 3 4 5 6

Calculated Statistics:

Minimum:30

Maximum:68

Range:38

Count:30

Sum:1365

Mean:45.5

Median:43

Mode:43

Standard Deviation:9.616

Variance:92.47

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The two step equations are used to represent the equations and solve real life problems .

What is Two Step Equations ?

The Equations that can be solved in exactly two steps are called as Two Step Equations .

We can use the two-step equations to represent and solve real-world problems by translating the problem into an algebraic equation, and solving equation, and then interpreting the solution of equation.

An example of the two step equation is : If a rental car costs $40 plus extra 10 cents for every mile driven, then how many miles can be driven for $50 ?

Translating The problem into equation we get  [tex]40 + 0.1m = 50[/tex] where m is  number of miles driven.

Step(i) we Subtract 20 from both sides

we get , [tex]0.1m = 10[/tex].

Step(ii) We Divide both sides by 0.1 ;

we get , [tex]m = 100[/tex].

Therefore , the problem to find the number of miles is solved in exactly two steps .

The given question is incomplete , the complete question is

What is the two step equation used for ?

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Answer:

[tex]y=0[/tex]

Step-by-step explanation:

[tex]y+25=25 \\ \\ y=25-25 \\ \\ y=0[/tex]

Answer:

[tex] \sf \: y = 0[/tex]

Step-by-step explanation:

Given equation,

→ y + 25 = 625 ÷ 25

Now the value of y will be,

→ y + 25 = 625 ÷ 25

→ y + 25 = 25

→ y = 25 - 25

→ [ y = 0 ]

Hence, the value of y is 0.

Answer: Is this completing a a square?

Step-by-step explanation:

Answer:

Step-by-step explanation:

The perfect square identity is:

Apply to the given equation to complete the square:

Required number is 9/4

Answer:

A box and whisker plot is a way of summarizing a set of data measured on an interval scale. It is often used in explanatory data analysis. ... In a box and whisker plot: the ends of the box are the upper and lower quartiles, so the box spans the interquartile range. the median is marked by a vertical line inside the box.

Step One: The first step to creating a box and whisker plot is to arrange the values in the data set from least to greatest.

Step Two: Identify the upper and lower extremes (the highest and lowest values in the data set).

The lower extreme is the smallest value, Which in this case is 31

The upper extreme is the highest value which is62

Step Three: Identify the median, or middle, of the data set.

Which is 50 in this case

Step Four: Identify the upper and lower quartiles.

To find the lower quartile and the upper quartile, start by splitting the data set at the median into lower and upper regions.

The upper quartile is the median of the upper region and the lower quartile is the median of the lower region.

Step-by-step explanation:

Also, your answer is C.

Answer:

Since your diameter is 8,

half of that is 4.

We are going to find the area now of both the bottom and the top.

4^4 = 16

16 x 3.14 = 50.24

Now we multiply by two since there are two circles  (bottom and top) we only got one circle's area.

50.24 x 2 = 100.48

Now we need to find the round curved area.

In order to do that we need to find the circumference them multiply by the height:

2 x 3.14 x 4 = 25.12(circumference)

25.12 x 19Height) = 477.28

Now we need to add both the areas(surface area):

477.28 + 100.48 = 577.76 yard2 is your answer.

Answer:

I think it should be x-360

Step-by-step explanation:

general angle is counter clock wise and and reference angle is clockwise!

ONLY FOR 4th QUADRANT

Answer:

1 ) 597

2 ) 346

Step-by-step explanation:

1 )

A.P : - 15, - 7, 1, ...

Here,

a = - 15

d = - 7 - ( - 15 )

= - 7 + 15

d = 8

65th term is t65.

t65 = a + ( 65 - 1 )d

= a + 64 d

= - 15 + 64 ( 8 )

= - 15 + 512

t65 = 597

Therefore,

65th term = 597

2 )

A.P = 3, 10, 17, 24, ...

Here,

a = 3

d = 10 - 3 = 7

50th term is t50.

t50 = a + ( 50 - 1 )d

= a + 49d

= 3 + 49 ( 7 )

= 3 + 343

t50 = 346

Therefore,

50th term = 346

Answer:

65ᵗʰ Term of the sequence is 479

50ᵗʰ Term of the sequence is 346

Step-by-step explanation:

Here,

First Term = a₁ = 3

Second Term = a₂ = 10

Third Term = a₃ = 17

Now,

Common Difference (d)

d = a₂ - a₁ = (-7) - (-15) = -7 + 15 = 8

d = a₃ - a₂ = 1 - (-7) = 1 + 7 = 8

Here, Common Difference is same everywhere

Now, For 65ᵗʰ term, n = 65

aₙ = a + (n - 1)d

a₆₅ = (-15) + (65 - 1) × 8

a₆₅ = (-15) + 64 × 8

a₆₅ = (-15) + 512

a₆₅ = 479

Thus, 65ᵗʰ Term of the sequence is 479

Here,

First Term = a₁ = -15

Second Term = a₂ = -7

Third Term = a₃ = 1

Now,

Common Difference (d)

d = a₂ - a₁ = 10 - 3 = 7

d = a₃ - a₂ = 17 - 10 = 7

Here, Common Difference is same everywhere

Now, For 50ᵗʰ term, n = 50

aₙ = a + (n - 1)d

a₅₀ = 3 + (50 - 1) × 7

a₅₀ = 3 + 49 × 7

a₅₀ = 3 + 343

a₅₀ = 346

Thus, 50ᵗʰ Term of the sequence is 346

-TheUnknownScientist

Answer: x<-2 or -2>x<1 or x>1

(-infinity,-2) U (-2,1) U (1,infinity)

Step-by-step explanation:

Therefore, the slope of the line passing through the points (-8, 5) and (7,0) is -1/3.

The slope of the line passing through the points (-8, 5) and (7,0) can be found by using the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept.

To find the slope (m), we can use the formula:

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

where (x1, y1) and (x2, y2) are the coordinates of the two points.

So, using the coordinates (-8, 5) and (7,0), we have:

m = (0 - 5) / (7 - (-8)) = -5 / 15 = -1/3

Therefore, the slope of the line passing through the points (-8, 5) and (7,0) is -1/3.

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The degree of the given polynomial is 2 because the highest exponent is 2 present in terms 2x^2 or 5y^2.

First, try to understand what is polynomial.

Algebraic expressions called polynomials include coefficients and variables. Indeterminates are another name for variables. For polynomial expressions, we can do mathematical operations like addition, subtraction, multiplication, and positive integer exponents but not division by variables. x^2+ 3x - 5 is an illustration of a polynomial with a single variable. There are three terms in this example: x^2, 3x, and -5.

The word "polynomial" is derived from the Greek words "poly" and "nominal," which combined translate to "many phrases."

Now let's talk about the degree of the polynomial.

The highest exponent of a monomial contained within a polynomial is referred to as the polynomial's degree. As a result, a polynomial equation with one variable having the biggest exponent is referred to as a polynomial degree.

The terms of a given polynomial is 2x^2, 3xy, 5y^2, and 2 Highest exponent is 2 in 2x^2 or 5y^2.

So the degree of the polynomial is 2.

The given Question is an incomplete complete question here.

[tex]2x^2 + 3xy + 5y^2 +2[/tex].

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Answer:

Step-by-step explanation:

7

Answer:

61.03

Step-by-step explanation:

c=a2+b2=352+502≈61.03278

Answer:

Answer:

Foci: (±5, 0)

Vertex: ( ±4 , 0)

Eccentricity: e = 5/4

Step-by-step explanation:

Hyperbola:

Write the equation of hyperbola in the form,

\boxed{\dfrac{x^2}{a^2}-\dfrac{y^2}{b^2}=1}

a

2

x

2

−

b

2

y

2

=1

9x² - 16y² = 144

Divide the entire equation by 144,

\begin{gathered}\sf \dfrac{9x^2}{144}-\dfrac{16y^2}{144}=\dfrac{144}{144}\\\\\\ \dfrac{x^2}{16}-\dfrac{y^2}{9}=1\\\\\\\dfrac{x^2}{4^2}-\dfrac{y^2}{3^2}=1\end{gathered}

144

9x

2

−

144

16y

2

=

144

144

16

x

2

−

9

y

2

=1

4

2

x

2

−

3

2

y

2

=1

a = 4 and b =3

Eccentricity: e

\boxed{e=\sqrt{1+\dfrac{b^2}{a^2}}}

e=

1+

a

2

b

2

\begin{gathered}\sf = \sqrt{1+\dfrac{9}{16}}\\\\=\sqrt{\dfrac{16}{16}+\dfrac{9}{16}}\\\\=\sqrt{\dfrac{25}{16}}=\sqrt{\dfrac{5*5}{4*4}}\\\\\\=\dfrac{5}{4}\end{gathered}

=

1+

16

9

=

16

16

+

16

9

=

16

25

=

4∗4

5∗5

=

4

5

Foci:

(ae, 0) & (-ae , 0)

\begin{gathered}\sf \left(4*\dfrac{5}{4},0 \right) \ ; \ \left( -4*\dfrac{5}{4},0 \right)\\\\\\(5, 0) \ ; \ (-5,0)\end{gathered}

(4∗

4

5

,0) ; (−4∗

4

5

,0)

(5,0) ; (−5,0)

Vertex of hyperbola:

The vertex of the hyperbola is a point where the hyperbola cuts the axis. (-a , 0) ; (a , 0)

Vertex : (-4 , 0) ; (4 , 0)

Answer:

Probability of one hit in 4 in a row = 42% = 42/100

Probability of 4 hits in a row = 3.1% = 31/1000

Step-by-step explanation:

Since all throws are independent events;

If 4 hits in a row

You can make a fraction and square by the amount of hits so if the questions asking 4/4 hits see below or change to the amount of hits you need.

(42/100)^4 = 0.03111696

This is 3.1%

42/100^1 stays 42% = 42/`100

42/100^2 becomes 17.64% = 441/2500

42/100^3 becomes  7.4% = 37/500

The probability that the baseball player will get a hit in 4 at-bats in a row is 0.0313 or about 3.13%.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

Example:

The probability of getting a head in tossing a coin.

P(H) = 1/2

We have,

Assuming each at bat is independent of the others.

The probability of getting a hit in any one at bat = 0.42

The probability of not getting a hit = 0.58.

The probability of getting a hit in 4 at bats in a row is the product of the probabilities of getting a hit in each of the 4 at bats.

= P(hit in 4 at bats)

= 0.42 × 0.42 × 0.42 × 0.42

= 0.0313

Therefore,

The probability that the baseball player will get a hit in 4 at-bats in a row is 0.0313 or about 3.13%.

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The park should be expanded based on the information as the majority want the expansion.

From the information, on the small town surveyed 250 adults, 180 of whom were parents, about whether a park should be expanded.

Also, the results showed that 150 of the adults who were parents and 40 of the adults who were not parents thought the park should be expanded.

Based on the above the number of people that wants the expansion will be:

= (150 + 40) / 250 × 100

= 190 / 250 × 100

= 76%

It should be expanded.

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Answer: Breadth? Did you mean width? If so, the answer is 128cm

Step-by-step explanation:

Area = Width x Length

8x16=128