DE≅AE ,BA∥CE , CB∥DA and m∠C=65∘

Answer:

To expand (x + 4)², we can use the formula for squaring a binomial: (a + b)² = a² + 2ab + b². In this case, a = x and b = 4.

So,

(x + 4)² = x² + 2(x)(4) + 4²

= x² + 8x + 16

Thus, (x+4)² when expanded and simplified gives x² + 8x + 16.

Step-by-step explanation:

Answer:

x²n+ 8x + 16

Step-by-step explanation:

(x + 4)²

= (x + 4)(x + 4)

each term in the second factor is multiplied by each term in the first factor, that is

x(x + 4) + 4(x + 4) ← distribute parenthesis

= x² + 4x + 4x + 16 ← collect like terms

= x² + 8x + 16

The interval which shows the height of the rocket decreasing is 1. 75 seconds - 5 seconds.

The interval that the height of the rocket would be decreasing in would be between the time that the rocket takes to reach its highest extent and then the time that the rocket reaches the ground once more.

The time that the rocket reaches the highest extent is 1. 75 seconds and the time it reaches the ground is 5 seconds.

The interval for the decreasing height is therefore 1. 75 seconds to 5 seconds.

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Answer:

32x^2y*1/4xy

Step-by-step explanation:

Answer:

9k+6+4k+5=180°

13k=180-11=169°

k=13°

The price of carrots per ounce is $0.24 .

Ounce is an unit of mass in the Imperial System. It is widely used throughout the world and is one of the oldest units of measurement to still exist. The unit ounce is derived from uncia, a unit of measurement in roman times.

The ounce(abbreviated oz) is equal to approximately 28.35 grams and 16 ounces make up a pound.

Now it is given that a 2-pound bag of carrots cost $7.68 .

Therefore price per pound of carrots=$7.68÷2

Price per pound=$ 3.84 .

Now we know that 16 ounces make up a pound.

Price of carrots per ounce=  $3.84 ÷16

Price per ounce=  $ 0.24

Therefore the price of carrots per ounce is $0.24

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Let's translate the argument into symbolic form using the following symbols:

B: Brazil has a huge foreign debt.

A: Argentina has a huge foreign debt.

The argument can be represented as follows:

B → (B ∨ A)

To determine the validity of the argument, we can construct a truth table for the expression (B → (B ∨ A)). The truth table will include all possible combinations of truth values for B and A, and we will evaluate the truth value of the entire expression for each combination.

The truth table for the argument is as follows:

B A B ∨ A B → (B ∨ A)

T T T T

T F T T

F T T T

F F F T

As we can see from the truth table, regardless of the truth values of B and A, the expression B → (B ∨ A) always evaluates to true. Therefore, the argument is valid because the conclusion is always true when the premise is true.

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Answer:

38.7°

Step-by-step explanation:

∆ = Tan-1(opposite/ Adjacent)

=Tan-1(8/10)

= 38.66°

= 38.7° to n nearest tenth

If the first inequality is written as:

3x ≤ -12

Then the correct option is D.

If it is written as it is in the problem, then neither of the graphs is the correct option.

Here we have the inequalities:

3x ≤ 12

2x + 3 > 11

(notice that in all the options, the first inequality has a negative sign, while in the two given inequalities there are no negative sign. This means that you will never get the correct answer if you use the given information, as the problem is incorrectly written).

First, we need to isolate x on both inequalities, we will get:

3x ≤ 12

x ≤ 12/3

x ≤ 4

(As you can see, because we don't have the negative sign, this inequality is different to all the ones in the options).

And for the other:

2x + 3 > 11

2x > 11 - 3

x > 8/2

x > 4

So neither of the options is actually correct.

If we instead write the first inequality as:

3x ≤ -12

We would solve this as:

x ≤ -4

And in that case, our two inequalities are:

x ≤ -4

x > 4

So the correct graph is graph D.

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Answer:

180

Step-by-step explanation:

a^2 + b^2 = c^2

(18^2)+(80^2)=6724

square root of 6724 is 82

82+18+80 = 180

Positive mean deviation means that the data values are on average greater than the mean, while negative mean deviation means that the data values are on average lower than the mean. This provides insight into the distribution of the data and can help identify outliers or trends in the data.

Mean deviation is a measure of dispersion that indicates how much a set of data values varies from the mean value of the data set. A positive mean deviation indicates that the data values are larger than the mean value, while a negative mean deviation indicates that the data values are smaller than the mean value.

In other words, a positive mean deviation indicates that the data set tends to be higher than the average, while a negative mean deviation indicates that the data set tends to be lower than the average.

Therefore, the sign of the mean deviation reflects the direction of deviation of the data values from the mean value, whether above or below it, and it provides important information about the distribution of the data set.

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Answer:

slope= -3

Step-by-step explanation:

the slope formula is \(\frac{y_{2} -y_{1} }{x_{2} -x_{1} }\)

plug in your numbers: \(\frac{(-2)-(-5)}{(-4)-(-3)}\)

solve:\(\frac{3}{-1}\)

simplify: -3

Answer:

a. standard deviation

Step-by-step explanation:

Standard deviation measures the variation (how spread out the data is from the mean) of a data set.  

Answer:

this is the answer okkkkkkkkkkkkkkkk

Answer:

81 and 324

Step-by-step explanation:

total units->3+12=15

1u=405÷15=27

3u=27×3=81

12u=27×12=324

Answer: 3m + 28

 ———————

    4  

A: The domain, range and x-intercept of the function g(x) is x>3, [-∞ < f(x) < ∞] and (19,0) respectively.

B: The vertical asymptote for g(x) is x=3.

C: The interval where the graph of g(x) is positive x=3 and the end-behaviour is not deduced.

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

The given function is g(x)=-log_4(x-3)+2.

The domain of a function is the set of input or argument values for which the function is real and defined.

The domain of the function is x>3.

The set of values of the dependent variable for which a function is defined is the range.

The range of the function is -∞ < f(x) < ∞.

Plug y=0 into the equation and solve the resulting equation 0=−ln(x−3)/ln(4)+2 for x.

The x-intercept is obtained as (19,0).

Line y=L is a horizontal asymptote of the function y=f(x), if either limx→∞f(x)=L or limx→−∞f(x)=L, and L is finite.

Calculate the limits:

limx→∞(−ln(x−3)/ln(4)+2)=−∞

limx→−∞(−ln(x−3)/ln(4)+2)=−∞

Thus, there are no horizontal asymptotes.

In the graph it can be seen that the line is starting to curve at x=3 so the vertical asymptotes is x=3 and at this point the graph is positive.

Since, the function g(x) is not a polynomial end behaviour cannot be deduced.

Therefore, the range, domain, x-intercept and asymptotes are found.

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Answer:

Answer is below

Step-by-step explanation:

To solve this, you can set up an equation. Make the length of the shortest side x, so the 2 sides double the length will equal 2x. Since they all equal the perimeter of 36, do x + 2x + 2x =36. These values all represent the sides(2 longer, one short). Combine like terms to get 5x=36 then divide by 5 to find the value of x. x=7.2in meaning the shorter side is 7.2 inches while the longer sides are both 14.4 inches each since they are double in size.

Answer:

D:X+2X+2X=36

Step-by-step explanation:

X+X=EQUAL AND DOUBLE THE SHORTEST SIDE

2[X+X]+[X]=36

Answer:

SSS

Step-by-step explanation:

We can see that 2 sides are equal already, and because they share a side, that side is also equal. So, side side side.

Answer:

  L

Step-by-step explanation:

You want to know how to express 50 in Roman numerals.

The symbols used to form Roman numerals are I, V, X, L, C, D, M. They have values 1, 5, 10, 50, 100, 500, 1000.

The symbol L is used to express the value 50 in Roman numerals.

The number 50 will be written as 'L' in roman numerals.

What are roman numerals?

The ancient number system known as roman numerals is still widely used today. To express the fixed positive numbers in roman numerals, alphabets are utilised. These roman numerals, which stand for 1, 2, 3, 4, 5, 6, 7, 8, and 9, respectively, are I, II, III, IV, V, VI, VII, VIII, IX, and X.

We are given number 50 which is to be resented in roman numerals.

The number is not represented by five Xs rather there is a special alphabet denoted for representing 50 which is 'L'.

Hence, the number 50 will be written as 'L' in roman numerals.

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X is a connected set but not a path-connected set. X={x,0xe[0,1}U{1/nyneN,ye{0,1]}U{0,1}.

To prove that X is connected, let us assume that X can be divided into two disjoint non-empty open sets A and B. Since X is the union of different points, any point in X will be in either A or B. Let us take an arbitrary point p in A. Since A is open, there is an open ball centered at p that is contained in A. Because B is disjoint from A, it follows that every point in this ball is also in A. By a similar argument, any point in B must have a ball centered at that point that is entirely contained in B. Thus, X must be either in A or B and hence, cannot be divided into two disjoint non-empty open sets. However, X is not path-connected since there is no path between points in [0,1] x {0} and {1} x {1}. Thus, it is connected but not path-connected.

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Answer:

f(- 1) = 3

Step-by-step explanation:

To evaluate f(- 1), substitute x = - 1 into f(x) , that is

f(- 1) = (- 1)² - 2(- 1) = 1 + 2 = 3

Answer:

Below

Step-by-step explanation:

Losing 27 % of value each year means it retains 73% each year

  we need to multiply 20 000 x  .73 x .73 x .73     ....  .73     (twelve times )

                  or   re-written as   20 000 * .73^12 = value =$ 458.04

Answer:

67.5

Step-by-step explanation:

what i did is i subtracted

180-45=135

so both sides is equal to 135

both sides are = so divide

135 divided by 2 = 67.5

hope this helps

Answer:

100 times smaller

Step-by-step explanation

48.6 / 0.486 = 100

1) \(\overline{AB} \cong \overline{CD}\), \(\overline{AD} \cong \overline{CB}\), \(\overline{AX} \perp \overline{BD}\), \(\overline{CY} \perp\overline{BD}\) (given)

2) \(\overline{BD} \cong \overline{BD}\) (reflexive property)

3) \(\triangle ABD \cong \triangle ACDB\) (SSS)

4) \(\angle ADB \cong \angle CBY\) (CPCTC)

5) \(\angle CYB\) and \(\angle AXD\) are right angles (perpendicular lines form right angles)

6) \(\triangle CYB\) and \(\triangle AXD\) are right triangles (a triangle with a right angle is a right triangle)

7) \(\triangle AXD \cong \triangle CYB\) (HA)

8) \(\overline{AX} \cong \overline{CY}\) (CPCTC)

A line is the shortest distance between two points. The value of x from the given parameters is 3

A line is defined as the shortest distance between two points. Given the following parameters

TU = 1 - x,

UB = 4x + 17,

TB = -3x

According to the addition postulate;

TU + UB = TB

Substitute the given parameters to have:

1 - x + 4x + 17 = -3x

Collect the like terms to have:

1+3x+17 = -3x

3x+3x = -1-17

Simplify

6x = -18

Divide both sides by 6

6x/6 = -18/6

x = -18/6

x = -3

Hence the value of x from the given parameters is 3

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The probability that the T-shirt John picks is dark blue is 2/3.

To find the probability that John picks a dark blue T-shirt, we'll need to consider the total number of blue T-shirts and the number of dark blue T-shirts.
Determine the total number of blue T-shirts.
John has 2 dark blue and 1 light blue T-shirt, so he has a total of 2 + 1 = 3 blue T-shirts.
Determine the number of dark blue T-shirts.
John has 2 dark blue T-shirts.
Calculate the probability.
The probability that John picks a dark blue T-shirt is the number of dark blue T-shirts divided by the total number of blue T-shirts.
Probability = (Number of dark blue T-shirts) / (Total number of blue T-shirts) = 2 / 3.

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The solution is, area of this diagram is (2x^2 + 9x + 8) unit^2 and perimeter of this diagram is 6x + 18 unit.

We have,

Area of a rectangle (A) is the product of its length (l) and width (w). Basically, the formula for area is equal to the product of length and breadth of the rectangle. Whereas when we speak about the perimeter of a rectangle, it is equal to the sum of all its four sides. Hence, we can say, the region enclosed by the perimeter of the rectangle is its area.

and, we know that,

perimeter of rectangle = 2 ( l + w)

here, we have,

from the given diagram, we get,

length = 2 + x

width = 2x + 7

so, perimeter is:

2( 2 + x + 2x + 7 )

=2 ( 3x + 9 )

=6x + 18 unit

now, area = area of upper part + area of lower part

so, we have,

area of upper part = 2*(x+4) unit^2

area of lower part = x*( 2x+7)

                             =2x^2 + 7x unit^2

so, we get,

area = [2(x+4) +2x^2 + 7x ] unit^2

       = (2x^2 + 9x + 8) unit^2

Hence, area of this diagram is (2x^2 + 9x + 8) unit^2 and perimeter of this diagram is 6x + 18 unit.

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1)  The number of gallons of soapy water that are in Elianni's bucket are; 1.5 gallons

2) The number of more quarts that it can hold is; 14 more quarts

Elianni puts 12 pints of soapy water in the bucket to wash her blue Hondi. From conversion factors, we know that;

1 pint = 1/8 gallon

Thus;

12 pints = 12 * (1/8)

12 pints =  (12/8) gallons

= 3/2 = 1.5 gallons.

Due to the fact that the bucket is 5 gallon capacity, It can hold:

5 - 1.5 = 3.5 gallons more.

But from conversion factors, we know that;

1 gallon = 4 quarts.

Thus;

3.5 gallons = 3.5 * 4

= 14 quarts more.

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Answer:

1) 4·(n + 9) = 4·n + 4·9; Distributive Property

2) (6·7)·m = 6·(7·n); Associative Property of Multiplication

3) b · 1 = b; Multiplicative Identity Property

4) a + (-a) = 0; Additive Inverse Property

Step-by-step explanation:

1) The given equation and the properties that justifies the equation are;

4·(n + 9) = 4·n + 4·9

The above equation can be written as follows;

4 × (n + 9) = 4 × n + 4 × 9

Therefore, the common factor, 4 is distributed across the to the two terms inside the parenthesis, which gives the property as distributive property

2) (6·7)·m = 6·(7·n)

The above equation gives the association of the product of the  first two terms on the left multiplied by the third term being equal to the product of the first term and the association of the product of the last two terms on the right of the term on the right hand side of the equation

Therefore, we have associative property of multiplication

3) b · 1 = b

The value of the product of any variable and 1 is the value of the variable

Therefore, we have the multiplicative identity property

4) a + (-a) = 0

The sum of a variable (or number) and the negative (or opposite) of the variable (or number) is 0

Therefore, we have the additive inverse property