Select the reason that best supports statement 5 in the given proof.
A.Substitution
B. Multiplication
C. Addition property of equality
D.Transitive property

Answer:

um what

Step-by-step explanation:

Answer:

Y=70

Step-by-step explanation:To find Y add 57 + 13. To check your answer do 70-13=57.

Answer:

\( 9\frac{1}{3} \)

The value of the expression is 16x(x+1) / 10x² -14x -12

In mathematics, an algebraic expression is an expression built up from constant algebraic numbers, variables, and the algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number)

The given expression is

16/(x-2)  ÷ 4/(x+1) + 6/x

Simplify this to have

16 / (x-2) ÷ (10x + 6) / (x+1)(x)

this implies that 16/(x-2) * (x+1)(x)/(10x +6)

16(x² + x)/(x-2)(10x+6)

Therefore the value of the expression is

16x(x+1) / 10x² -14x -12

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The 2 : 5 scaled version of the deck Sam plans to build and the dimensions of the original deck indicates;

Part A; Base length of the new deck = 7.2 feet

Height of the new deck = 2.8 feet

Part B; The area of the original deck is 63 square feet

The area of the new deck is 10.08 square feet

Part C; The ratio of the areas is the square of the scale factor

A scale factor is a number or factor that is used to enlarge or reduce the dimensions a shape or size of a figure.

The base length of the triangular deck = 18 feet

The height of the triangular deck = 7 feet

The scale factor for the scaled version Sam intends to build = 2 : 5

Part A; The dimensions of the new deck are;

Base length of the new deck using the the 2 : 5 ratio is; (2/5) × 18 = 7.2 feet

The height of the new deck = (2/5) × 7 = 2.8 feet

Part B; The area of the original deck = (1/2) × 18 × 7 = 63 square feet

Area of the new dec = (1/2) × 7.2 × 2.8 = 10.08 square feet

Part C; The ratio of the areas is; 10.08/63

Ratio of the area = 10.08/63 = 4/25 = 4 : 25

The scale factor is; 2 : 5

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B

Step-by-step explanation:

20³ = 20 x 20 x 20. That is equal to 400 x 20 = 8000

=8000

Answer:

----------------------

There are various combinations of coins.

In total there are:

Answer:

1742 hours

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Single light:

Mean of 1700 hours and standard deviation of 400 hours, which means that \(\mu = 1700, \sigma = 400\)

Sample of 64:

This means that \(n = 64, s = \frac{400}{\sqrt{64}} = 50\)

The probability is 0.20 that the sample mean lifetime is more than how many hours?

This is the 100 - 20 = 80th percentile, which is X when Z has a pvalue of 0.8. So X when Z = 0.84

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem

\(Z = \frac{X - \mu}{s}\)

\(0.84 = \frac{X - 1700}{50}\)

\(X - 1700 = 50*0.84\)

\(X = 1700 + 50*0.84\)

\(X = 1742\)

Answer:

to solve the equation you first need to bring it to factors and by doing that you first need to let the equation equal 0 hence you need to minus 2 on both sides of the equation therefore

x^2 + 10x + 25 - 2 =2 - 2

therefore

x^2 + 10x +23 = 0

now since the equation cannot be factored, we use the formula.

x= \(\frac{-b +- \sqrt{b^{2}-4ac } }{2a}\)

where

a=1

b=10

c=23

note we use the coefficients only.

therefore x = \(\frac{-10 -+ \sqrt{10^{2}-4(1)(23) } }{2(1)}\)

=\(\frac{-10-+\sqrt{100-92} }{2}\)

=\(\frac{-10-+\sqrt{8} }{2}\)

then we form two equations according to negative and positive symbols

x=\(\frac{-10+\sqrt{8} }{2} or x =\frac{-10-\sqrt{8} }{2}\)

therefore x = \(-5+\sqrt{2}\)   or x=\(-5-\sqrt{2}\)

Answer:

I think its C

Step-by-step explanation:

Answer:

Step-by-step explanation:

3250 : 156 = y : 40

y = 3250 × 40 : 156

y = 833.(3)                                    3 repeating

--------------------------

check

3250 : 156 = 833.(3) : 40

20,83333333333333 = 20,83333333333333

the answer is good

Answer:

A)

\(f'(x) = \left\{ \begin{array}{lIl} \frac{1}{2} & \quad x >2 \\ 0& \quad x =2\\1&\quad x<2 \end{array} \right.\)

B) Continuous but not differentiable.

Step-by-step explanation:

So we have the piecewise function:

\(f(x) = \left\{ \begin{array}{lIl} \frac{1}{2}x+5 & \quad x >2 \\ 6& \quad x =2\\x +4&\quad x<2 \end{array} \right.\)

A)

To write the differentiated piecewise function, let's differentiate each equation separately. Thus:

1)

\(\frac{d}{dx}[\frac{1}{2}x+5}]\)

Expand:

\(\frac{d}{dx}[\frac{1}{2}x]+\frac{d}{dx}[5]\)

The derivative of a linear equation is just the slope. The derivative of a constant is 0. Thus:

\(\frac{d}{dx}[\frac{1}{2}x+5}]=\frac{1}{2}\)

2)

\(\frac{d}{dx}[6]\)

Again, the derivative of a constant is 0. Thus:

\(\frac{d}{dx}[6]=0\)

3)

We have:

\(\frac{d}{dx}[x+4]\)

Expand:

\(\frac{d}{dx}[x]+\frac{d}{dx}[4]\)

Simplify:

\(=1\)

Now, let's substitute our original equations for the differentiated equations. The inequalities will stay the same. Therefore:

\(f'(x) = \left\{ \begin{array}{lIl} \frac{1}{2} & \quad x >2 \\ 0& \quad x =2\\1&\quad x<2 \end{array} \right.\)

B)

For a function to be differentiable at a point, the function must be a) continuous at that point, and b) the left and right hand derivatives must be equivalent.

Let's first determine if the function is continuous at the point. Remember that a function is continuous at a point if and only if:

\(\lim_{x \to n^-} f(n)= \lim_{x \to n^+}f(n)=f(n)\)

Let's find the left hand limit of f(x) at it approaches 2.

\(\lim_{x \to 2^-}f(x)\)

Since it's coming from the left, let's use the third equation:

\(\lim_{x \to 2^-}f(x)\\=\lim_{x \to 2^-}(x+4)\)

Direct substitution:

\(=(2+4)=6\)

So:

\(\lim_{x \to 2^-}f(x)=6\)

Now, let's find the right-hand limit:

\(\lim_{x \to 2^+}f(x)\)

Since we're coming from the right, let's use the first equation:

\(\lim_{x \to 2^+}(\frac{1}{2}x+5)\)

Direct substitution:

\((\frac{1}{2}(2)+5)\)

Multiply and add:

\(=6\)

So, both the left and right hand limits are equivalent. Now, find the limit at x=2.  

From the piecewise function, we can see that the value of f(2) is 6.

Therefore, the function is continuous at x=2.

Now, let's determine differentiability at x=2.

For a function to be differentiable at a point, both the right hand and left hand derivatives must be equivalent.

So, let's find the derivative of the function as x approahces 2 from the left and from the right.

From the differentiated piecewise function, we can see that as x approaches 2 from the left, the derivative is 1.

As x approaches 2 from the right, the derivative is 1/2.

Therefore, the right and left hand derivatives are not the same.

Thus, the function is continuous but not differentiable.

Answer:

Step-by-step explanation:

You want to know the number of pounds of each of Earl Gray and Orange Pekoe tea to make 600 pounds of mix that is valued at $4.50 per pound, if Earl Gray costs $5 per pound and Orange Pekoe costs $3 per pound.

Let x represent the number of pounds of Earl Gray tea in the mix. Then the value of the mix is ...

  5x +3(600 -x) = 4.50(600)

Simplifying, we have ...

  2x +1800 = 2700

  2x = 900 . . . . . . . . . subtract 1800

  x = 450 . . . . . . . . . divide by 2

  600 -x = 150 . . . find pounds of Orange Pekoe

The blend will consist of 450 pounds of Earl Gray, and 150 pounds of Orange Pekoe tea.

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Answer:

Step-by-step explanation:

x > 36

Answer:

.

Step-by-step explanation:

.

By using the properties of parallel lines, it can be inferred that -

Corrosponding angle goes in the place of first question mark and substitution property of equality goes in the place of second question mark.

What are parallel lines?

Two lines are said to be parallel if on extending them indefinitely, they will never intersect

Transversal is a line that intersects two or more parallel lines

For the first question mark

\(\angle ASR \cong \angle AVU\) [Corrosponding angle]

For the second question mark

\(m\angle AVU = 90^{\circ}\) [Substitution property of equality]

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The similar shapes EFGH and JKLM have the measurement of angle Z equal to 65°, the length x = 27.5 and the length of y = 12

Similar shapes are two or more shapes that have the same shape, but different sizes. In other words, they have the same angles, but their sides are proportional to each other. When two shapes are similar, one can be obtained from the other by uniformly scaling (enlarging or reducing) the shape.

Given that the shape EFGH is a smaller shape of JKLM, and they are similar, then:

the measure of angle Z is equal to 65°

the side EF corresponds to JK and side FG corresponds to KL, so:

8/20 = 11/x

x = (11 × 20)/8 {cross multiplication}

x = 27.5

the side EF corresponds to JK and EH corresponds to JM, so:

8/20 = y/30

y = (30 × 8)/20 {cross multiplication}

y = 12

Therefore, the similar shapes EFGH and JKLM have the measurement of angle Z equal to 65°, the length x = 27.5 and the length of y = 12

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Answer:

Absolute value is the distance from 0 all negative numbers become positive and positive stays positive.

Step-by-step explanation:

Answer: B. Completely Randomized Design

Step-by-step explanation:

A completely randomized design is an experimental design such that treatments are assigned at random completely in order for each experimental unit to have same chance of receiving treatment.

In this scenario, since all the dogs are randomly assigned treatment by picking a card without taking into consideration other factors, then we can infer that thus is a completely randomized design.

Triangle ADC also has a right angle at D, making it a right-angled triangle.

The exact value of x be 2.25.

The hypotenuse's square is equal to the sum of its two other side squares of a right-angled triangle, according to the Pythagoras theorem.

Triangle ADB exists even a right-angled triangle with right-angle at D.

Therefore, Base of Triangle ADB = BD = 4,

Height of Triangle ADB = AD = 3,

Hypotenuse of Triangle ADB = AB

Using the Pythagoras Theorem, we get,

\($\left[(A D)^2+(B D)^2\right]=(A B)^2$\)

substitute the values in the above equation, we get

or,\($(A B)^2=\left[(3)^2+(4)^2\right]$\)

simplifying the equation, we get

or, \($(A B)^2=[9+16]$\)

or, \($(A B)^2=25$\)

or, \($\sqrt{(A B)^2}=\sqrt{25}$\)

or, AB = 25

Triangle ADC is also a right-angled triangle with right-angle at D.

Therefore, Base of Triangle ADC = DC = x

Height of Triangle ADC = AD = 3,

And, Hypotenuse of Triangle ADC = AC

Using the Pythagoras Theorem, we get,

\(& {\left[(D C)^2+(A D)^2\right]=(A C)^2} \\\)

simplifying the equation, we get

\(& \text { or },(A C)^2=\left[(3)^2+(x)^2\right] \\\)

\(& \text { or },(A C)^2=\left[9+x^2\right]\)

Triangle ABC is also a right-angled triangle with right-angle at A. Therefore, Base of Triangle ABC = AC,

Height of Triangle ABC = AB = 5,

And, Hypotenuse of Triangle ABC =  BC = (4 + x)

Using the Pythagoras Theorem, we get,

\(& {\left[(A C)^2+(A B)^2\right]=(B C)^2} \\\)

\(& \text { or, }(B C)^2=\left[(A C)^2+(A B)^2\right] \\\)

substitute the values in the above equation, we get

\(& \text { or, }(4+x)^2=\left[\left(9+x^2\right)+(5)^2\right] \\\)

simplifying the equation, we get

\(& \text { or, }\left[4^2+(2 \times 4 \times x)+x^2\right]=\left[9+x^2+25\right] \\\)

\(& \text { or, }\left[16+8 x+x^2\right]=\left[(9+25)+x^2\right] \\\)

\(& \text { or, }\left[16+8 x+x^2\right]=\left[34+x^2\right] \\\)

\(& \text { or, }\left[16+8 x+x^2\right]-\left[34+x^2\right]=0 \\\)

\(& \text { or, },(16-34)+8 x+\left(x^2-x^2\right)=0 \\\)

8x - 18 = 0

8x = 18

\(& \text { or, } x=\frac{18}{8} \\\)

\(& \text { or, } x=\frac{9 \times 2}{4 \times 2} \\\)

\(& \text { or, } x=\frac{9}{4} \\\)

Therefore, the value of x be 2.25.

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Answer:

3

Step-by-step explanation:

Explanation:

Anything parallel to Ax+By = C is of the form Ax+By = D, where C and D are different values.

The given equation is 3x+y = 3. Anything parallel to this is 3x+y = D

Plug (x,y) = (1,-7) into that second equation to compute D

3x+y = D

D = 3x+y

D = 3(1)+(-7)

D = 3-7

D = -4

Therefore, our answer is 3x+y = -4

If you wanted to solve for y, then you'd get y = -3x-4. Both parallel lines have a slope of -3 but different y intercepts.

Step-by-step explanation:

The transformation y = sin(2x) affects the graph of y = sin(x) by compressing it horizontally.

The function y = sin(2x) has a coefficient of 2 in front of the x variable. This means that for every x value in the original function, the transformed function will have half the x value.

To see the effect of this transformation, let's compare the graphs of y = sin(x) and y = sin(2x) by plotting some points:

For y = sin(x):

x = 0, y = 0

x = π/2, y = 1

x = π, y = 0

x = 3π/2, y = -1

x = 2π, y = 0

For y = sin(2x):

x = 0, y = 0

x = π/2, y = 0

x = π, y = 0

x = 3π/2, y = 0

x = 2π, y = 0

As you can see, the y-values of the transformed function remain the same as the original function at every x-value, while the x-values of the transformed function are compressed by a factor of 2. This means that the graph of y = sin(2x) appears narrower or more "squeezed" horizontally compared to y = sin(x).

Therefore, the correct statement is: It is compressed horizontally.

Answer:

  y = 2x

Step-by-step explanation:

You want the simplified form of y = |x -5| +|x +5| if x > 5.

The graph of the whole function will have turning points where the absolute value expressions are 0:

  x -5 = 0   ⇒   x = 5

  x +5 = 0   ⇒   x = -5

For values of x > 5, we are concerned with that portion of the graph that is to the right of both of these turning points. Hence, both absolute value expressions are positive and unchanged by the absolute value bars.

  y = (x -5) +(x +5) . . . . . . if x > 5

  y = 2x . . . . . . . . . . . . . . collect terms

The simplified function is y = 2x.

__

Additional comment

The attached graph shows y=2x and the given function for x > 5. They are identical. (The y=2x graph is shown dotted, so you can see the red graph of the given function.)

Answer:

19

Step-by-step explanation:

tan35=x/20

20tan35=x

x=14.0041507641942

x+5=19.0041507641942

The nearest foot is 19

The Binary search tree for the given words using alphabetical order is given below .

What is a Binary Search Tree ?

A binary search tree(BST) can be defined as a binary tree in which each child is either left or right child. A vertex cannot have more than 1 left child and cannot have more than 1 right child.

the words given are : banana, peach, apple, pear, coconut, mango, and papaya .

Banana is the first word , and then the tree's root are assigned .

Peach will be the next word on tree . According to the alphabetical order , peach comes after banana, so it must be right offspring of banana.

Apple will be the next word on list. Apple should be left child of banana because in the alphabetical order it comes after banana .

Pear will be the next word on the list. According to the alphabetical order , pear comes after banana, hence,  pear must be to right of banana.

Therefore , the binary search tree is shown below .

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Answer:

Step-by-step explanation:

f(0) = 4

f(x)=0   when x = 0.75

f(x) =5  when x =3

A{ x ∈ R ║ 3≤x}

Answer:

I believe the answer is A

Step-by-step explanation:

I say it's A because the volume is double like it told us. Compared to the new box it's twice as long as the old boxes.

I hope this helps! ~~~~

The volume of the new box is 8 times the volume of the old box.

The correct answer is option (D).

The volume of a rectangular box with length L, width W and height H is,

V = L × W × H

Given: -

Let \(l,w,h\) represents the length, width and height of the old rectangular boxes.

Let \(V_o\) represents the volume of the old rectangular box.

⇒ \(V_o=l\times w \times h\)

The length, width and height of the new boxes are all twice as long as those of the old boxes.

This means the length, width and height of the new boxes would be \(2l,2w,2h\).

Let \(V_n\) represents the volume of the new rectangular box.

So, the volume of the new rectangular box would be,

⇒ \(V_n=2l \times 2w \times 2h\)

⇒ \(V_n = 8 \times l \times w \times h\)

⇒ \(V_n=8 \times V_o\)

This means, the volume of the new box is 8 times the volume of the old box.

Hence, option (D) is the correct answer.

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