In the figure below, o ll k . Find the values of x and z .

The equation log328 is c.3/5 32 is 8.

The following examples illustrate how to express numbers raised to specific powers of their prime factors in order to write them in exponential form,

8 = 2 × 2 × 2 = 23. Therefore, the exponential form of 8 can be written as 2.... 72 = 2 2 2 3 3 = 23 32.... 121 = 112.

First, isolate the exponential expression. Step 2: Take the natural log from both sides. Step 3: Extract the x from the exponent using the properties of logs. Solve for x in step four.

The following examples illustrate how to express numbers raised to specific powers of their prime factors in order to write them in exponential form:

8 = 2 × 2 × 2 = 23. Therefore, the exponential form of 8 can be written as 2.... 72 = 2 2 2 3 3 = 23 32.... 121 = 112.              

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12 persons will fit in a 6 feet by 6 feet space.

As per the data given in the above question are as bellow,

12 persons can fit in a room that is 9 feet by 4 feet.

We have to find how many people can fit in a 6' by 6' room.

Solving further we get,

Surface area of a 9 x 4 ft. room is equal to 9 x 4.

Surface area of a 9 by 4 foot space is equal to 36 feet2.

So,

Surface area of a room measuring 6 by 6 feet is 6 x 6.

A 6 by 6 foot room's surface area is 36 feet2.

The two rooms' floor space is equal. hence, the population is equal.

12 persons will fit in a 6 feet by 6 feet space.

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Answer:

just put your mind to it fam

Step-by-step explanation:

Answer:

this is nonsense

Step-by-step explanation:

(4x³ + 23x² + 22x - 10) [tex](x + 2)^{-1}[/tex]

(4x³ + 23x² + 22x - 10) (1 / (x + 2))

(4x³ + 23x² + 22x - 10) / (x + 2)

4x² + 2x³ + 23x + 11.5x² + 22 + 11x - 10/x - 5

2x³ + 15.5x² + 44x - 10/x + 17 ??????

Answer:

3x - 5=-3

3x - 5+5=-3+5

3x=2

3x/3=2/3

x=2/3

Positive :D Hope this helped!!

Step-by-step explanation:

Answer:

x is positive.

Step-by-step explanation:

3x - 5= -3   ==> isolate x

3x = 2  ==> add 5 on both sides

x = 2/3  ==> divide 3 on both sides

Hence, x is positive.

Answer:

x= -18.6666666667

Step-by-step explanation:

[tex]3/4x+5=-9\\ \\3/4x=-9-5\\ \\3/4x=-14\\ \\x= -14 X \frac{4}{3}\\ \\x= \frac{-14 X4}{3}\\ \\x= \frac{-56}{3}\\\\x= -\frac{56}{3}\\\\x= -\frac{56}{3} = -18.6666666667[/tex]

Answer:

The expression. 7 plus the sum of a number x and 5 will be written as 7 + (x + 5).

Step-by-step explanation:

From the information given, the phrase is written as 7 plus the sum of a number x and 5. Therefore, the expression will be:= 7 + (x + 5).

Let's say x is 2. The the value will be:= 7 + (2 + 5)

= 7 + 7 = 14 

In conclusion, the correct option is 7 + (x + 5).

The factors of the given polynomial as calculated from the given data is found as , (x−1) and (x 2 +x+1) .

The equation given in the question is , x³ - 1 .

On solving this equation we will get the result as ,

x³  −1

=(x−1)(x 2 +x+1)

Therefore, the factors of the given equation is both (x−1) and (x 2 +x+1) .

A quadratic equation factored form is used to find the roots or solutions of the given equation.  Example , the factored form of x2 +5x+6 = 0, is  x^2 +5 x + 6 = 0 is= 0 (x-2)(x-3) = 0.

When the product of two terms is zero, it signifies that any of them might be zero.

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Answer:

X=4 or -6 and y= 6 or -4

(4,6),(-6-4)

Step-by-step explanation:

Xy=24 -------(i)

X=y-2 ---------(ii)

substitute (ii) into (i)

=> (y-2)y=24

y²-2y=24

y²-2y-24=0

(y-6)(y+4)=0

=> y= 6 or y=-4

when y=6;

X=6-2=4

when y=-4;

X= -4-2=-6

The height of the antenna on the roof of the local building is approximately 2 meters.

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a2 + b2 = c2.

here, we have,

The situation forms a right angle triangle.

Properties of a right angle triangle:

One of its angles is equals to 90 degrees

The sides of the triangles can be calculated using Pythagoras theorem.

Therefore, let's find the height of the building and the radio antenna from the eye point.

Using trigonometric ratios,

tan 35° = opposite / adjacent

tan 35° = x / 28

where

x = the height of the building and the radio antenna from the eye point.

x = 28 tan 35

x = 28 × 0.700207

x = 19.60581 meters

Let's find the height of the building from his eye point.

tan 32° = y / 28

where

y = height of the building from his eye point

y = 28× tan 32°

y = 28 × 0.6248693

y = 17.496341 meters

Height of the antenna

=  19.60581 -17.496341

=2.109469

hence, Height of the antenna ≈ 2 meters

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The likelihood that the first question will be true, given the  true and false quiz  is C. Equally likely and unlikely.

The likelihood that the first question will be true will be based on the probability that each question is true or false. This simply means that to solve the question, you need to look at the probability given of a question being true.

That probability is given as P ( true ) = 0. 5 which means that the probability of a question being true is 50%.

The probability is therefore equally likely or unlikely as 50 % is the median probability.

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Answer: C: Equally likely and unlikely.

Step-by-step explanation:

Answer: The opposite of a number is the number that, when added to it, equals zero. In this case, the opposite of -2/5 is 2/5. When you add -2/5 and 2/5, the result is 0.

Step-by-step explanation:

Answer: 2/5

Step-by-step explanation: If it’s negative you change it, if it’s positive you keep the number the same so in this question the fraction 2/5 is negative so the opposite of -2/5 is 2/5.

Answer:

No

Step-by-step explanation:

They did not get everyones imput

Answer: The measure of an angle is the same as the measure of its reference angle in the first or fourth quadrant. Since, m∠884° is in the 8th quadrant, we can use the reference angle in the first quadrant, which is m∠4°.

So, m∠1 = m∠4°

To find the measure of the angle m∠3, we can use the fact that angles in different quadrants that share a terminal side have measures that add up to 180°.

m∠3 = 180° - m∠1

m∠3 = 180° - m∠4°

m∠3 = 180° - 4° = 176°

Therefore, m∠1 = m∠4° and m∠3 = 176°.

Step-by-step explanation:

The result of this calculation is -20xyz. This answer can be verified by taking 5x, which is 5 times x, and -4xyz, which is -4 times xyz, and multiplying them together. This gives -20 times x times y times z, which is -20xyz.

The product of 5x and -4xyz is -20xyz.

-20xyz

5x * (-4xyz) = 5x * (-4) * xyz = -20xyz

Multiplying 5x and -4xyz together yields -20xyz. To calculate this, first take the 5x and multiply it by -4. Then take the answer and multiply it by xyz. The result of this calculation is -20xyz. This answer can be verified by taking 5x, which is 5 times x, and -4xyz, which is -4 times xyz, and multiplying them together. This gives -20 times x times y times z, which is -20xyz.

The product of 5x and -4xyz is -20xyz.

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The missing value in the ratio table will be calculated is 4.

Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).

The missing values in the ratio table will be calculated this:

1/2 = x / 8

The next thing to do after the above is to cross multiply in order to get the value of x. This will be:

2 × x = 1 × 8

2x = 8

Then, we have to divide through by 2.

x = 8 / 2

x = 4

Therefore, the value of x is 4.

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Complete question

Find the missing values in the ratio table.

1/2 : x/8

The table that shows a proportional relationship is Table D.

Please find attached the graph of Table D created with MS Excel

The variables x and y in a set of ordered pair (x, y), are proportionally related, when the ratios of the x and y values for of all data points in the set are equivalent, such that a proportional relationship can be expressed in the form; y = k·x

Where;

k = The constant of proportionality

Therefore; k = y/x

The ratio of the y-values to the corresponding x-values in the table that shows a proportional relationship is therefore a constant.

Analyzing the Table C, we get;

The points are; (2, 1), (4, 3), (6, 5), (8, 7)
x/y for each data point is therefore;

1/2 ≠ 3/4 ≠ 5/6 ≠ 7/8

Table C does not show a proportional relationship

The coordinate points in Table D are; (2, 1), (6, 3), (8, 4), (10, 5)

The ratio, x/y at each point in the table are therefore;

1/2 = 3/6 = 4/8 = 5/10 = 1/2

The ratio, x/y at each point in the table is constant, therefore, Table D ahows a proportional relationship.

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Penelope would have to pay 11.80 for a mug with her own name on it. the fixed cost would be 5.40 and cost per letter would be 0.80.

Total cost = Fixed cost + (no. of letters*cost per letter)

let us take the fixed cost as x and cost per letter as y

so for alexander,

12.60 = x + 9y (eq 1)

for lucia,

9.40 = x + 5y (eq 2)

equating eq1 and eq 2

12.60 - 9y = 9.40 - 5y

12.60 - 9.40 = - 5y + 9y

4y = 3.20

y = 0.80

x = 9.40 - 5y

= 9.40 - 4 = 5.40

therefore, the cost for penelopes mug will be,

= 5.40 + (8*0.80)

= 5.40 + 6.40 = 11.80

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The quotient when (x³ + 8) is divided by   (x+2) is (x² - 2x + 4)

A polynomial is an equation that solely uses the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminates. x² + 4x + 7 is an illustration of a polynomial with a single indeterminate x.

An algebraic expression known as a polynomial requires that all of its exponents be whole numbers. Any polynomial must have variable exponents that are non-negative integers. Although a polynomial contains variables and constants, we are unable to divide a polynomial by a variable.

The degree of a polynomial is the highest or biggest exponent of the variable in the polynomial. Using Descartes' Rule of Signs, the degree is used to calculate the greatest number of polynomial problem solutions.

The polynomials are (x³ + 8) and (x+2)

                         dividing  (x³ + 8) by  (x+2) we get,

                                     x + 2 ) x³ + 8 ( x² - 2x + 4

                                              - x³ - 2x²

                                                    -2x² + 8

                                                     2x² +4x

                                                              4x + 8

                                                             -4x - 8

                                                                  0

The quotient when (x³ + 8) is divided by   (x+2) is (x² - 2x + 4)

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The speed of the ball as it left the bat is 121.904 ft/s.

Here I attached the answer

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Answer:

x=-3

Step-by-step explanation: 5x+6=2x-3

Answer:

x = -3

Step-by-step explanation:

5x + 6 = 2x - 3

Subtract 2x + 6 on both sides,

5x + 6 - (2x+6) = (2x-3) - (2x + 6)

3x = -9

x = -3

From the ratio test, r=1/3. The series converges.

We must calculate the ratio between two successive phrases in order to perform the ratio test:

The nth term is n / 3n.

The (n + 1)th term is (n + 1) / 3n + 1.

The ratio test:  lim |   [ (n + 1) / 3n + 1 ]  /  [  n / 3n ]   |

                =    lim |    [ (n + 1) / n ]  ·  [ 3n  / 3n + 1 ]   |

                =    lim |    [ (n + 1) / n ]  ·  [  1/3  ]   |

                =   (1/3) · lim |  (n + 1) / n  |

                =   (1/3) · lim |  ( n/n ) + (1/n)  |

                =   (1/3) · lim |  1 + (1/n)  |

                =   (1/3) · [ lim | 1 | + lim | 1/n |

                =   (1/3) · [ 1 + 0 |

According to the ratio test, the series converges if this ratio is between -1 and 1 (excluded). This sequence thus comes together.

                =   (1/3)   <---  converges

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The full question:

A series is given by 1/3^1+2/3^2+3/3^3+4/3^4+5/3^5+...

Francine correctly applies the ratio test to determine whether the series converges or diverges.

Which statement reflects Francine's conclusion?

From the ratio test, r = 3. The series converges.

From the ratio test, r=1/3. The series diverges.

From the ratio test, r = 3. The series diverges.

From the ratio test, r=1/3. The series converges.

Answer:

From the ratio test, r=13. The series converges.

Step-by-step explanation:

I took the Test

The probability that at least one psychologist is chosen is 5/9 and the probability that exactly three psychologists are chosen is 16.3.

Total number of Attendants in a certain conference are 54

There are 24 psychiatrists and 30 psychologists

Total number of attendants = 24 + 30= 54.

Therefore total number of cases is 54

1 ) Since there are 30 psychologists, the number of favorable outcomes is 30.

So P ( 30 psychologists) =Number of favorable cases/ Total number of cases

= 30/54

= 5/9.

So probability of at least one psychologist is 5/9.

2 ) If we have to choose 3  psychologist favorable outcomes are

= 30/54 x 29/53 x 28/52

= 1015/6201

= 16.3

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

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So, the midpoint is at a ratio of 1/2 of the way from the first point to the second point on both x and y axis.

The ratio used to find the midpoint of a line segment is 1:1 or 1/2:1/2.

To find the midpoint of a line segment, we need to average the x-coordinates and the y-coordinates of the two given points.

The x-coordinate of the midpoint = (x1 + x2)/2

The y-coordinate of the midpoint = (y1 + y2)/2

So we can say that the midpoint is at a ratio of 1/2 of the way from the first point to the second point on both x and y axis.

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Second box required more material to make.

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

The first box has a base that measures 8 inches by 10.5 inches with a height of 6.25 inches

8=length, 10.5=width and height=10.5

SA=2(8 ×6.25+8 × 10.5+6.25 × 10.5)

SA=2(50+84+65.625)

SA=2(199.625)

SA=399.25

For second box

9=length, 5.5=width and height=11.75

SA=2(9 ×5.5+9 ×11.75+5.5 ×11.75)

SA=2(49.5+105.75+64.625)

SA=2(219.875)

SA=439.75

Hence, second box required more material to make.

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The volume of the picnic basket is 1920in^3.

If the prism is such that if we slice it horizontally at any height smaller or equal to its original height, the cross section is same as its base, then its volume is:

[tex]V = B \times h[/tex]

where h is the height of that prism and B is the area of the base of that prism.

Given;

The height of the basket is 8 inches

The bottom of the basket has an area of 240 square inches.

Now,

V=B x h

V= 8 x 240

V= 1920

Therefore, the volume will be 1920in^3

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We choose any number at random from 1 -5 . total number of favourable outcomes = 5. Therefore, probabilty of each outcome = 1/5 .

If we pick a number at random between 1 and 5, the total number of favorable outcomes is 5. As a result, the probability of each scenario is 1/5. P (X) = n/N, where n is the number of favorable outcomes and N denotes the total number of potential outcomes.

A random variable in probability is a real-valued function whose domain is the sample space of the random experiment. It indicates that each random experiment outcome is connected with a single real number, and the single real number may change depending on the random experiment outcomes.

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A recent national survey of 1,000 married couples found that approximately 5% of husbands and 6% of wives admitted to having physically attacked their partner in the past year.

This is a concerning statistic, demonstrating the prevalence of domestic violence in marriages across the United States. It is important that couples learn how to recognize and address any forms of violence in their relationships.

It is also critical that communities and society as a whole recognize the seriousness of domestic violence and take the necessary steps to provide support and resources to help affected individuals and families.

This statistic that shows that 5% or husbands and 6% of wives were admitted due to violence is particularly concerning given the long-term implications of domestic violence in relationships.

To help address this issue, it is important to understand the root cause of these acts of violence and provide appropriate interventions to couples in need.

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Answer:

The answer is 48.6667 or 48 2/3

Step-by-step explanation:

Answer:

We know that the total age of both kids is 36

we also know that Ahmed is 4 years older than Tamir.

To find the answer we will first divide 36 by 2

36/2 = 18

Now we will subtract 4 from 18 and we get 14

lastly, subtract 14 from 36

36 - 14 is 22

Hence, Ahmed is 22 while Tamir is 14

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