Determine the domain and range of the function f(x) = 23/108²x.
O {x all real numbers}; {yl y >0}
O x all real numbers}; {yl y ≥ 0}
O {xx>0}: {yl all real numbers}
O x x ≥ 0}; {yl all real numbers}

Answer: x-intercept: 5/4

y-intercept: -5/3

Step-by-step explanation:

We can find the y-intercept by looking at the y = mx + b form, the y-intercept would be b in that form:

4x = 3y + 5

y = 4/3x - 5/3

Next, we plug x into that equation:

We can graph it, or find it mathematically:

Set 4/3x = 5/3

4/3x * 3/4 = 5/3 * 3/4

x = 5/4

Answer:

[tex]y - ( - 9)) = \frac{1}{5} (x - ( - 1))[/tex]

[tex]y + 9 = \frac{1}{5} (x + 1)[/tex]

Using the definition of a midpoint and collinear points, the proof that shows that B is the midpoint of AC is explained below.

If three points are on a straight line, they are defined as being collinear points. That is, three points, A, B, and C are collinear points if they are on a straight line, and B is in the middle of points A and b.

When a segment is divided into two equal halves, the point that lies in the middle of the segment where the segment is cut into halves is called the midpoint of the line segment.

The proof that shows that B is the midpoint of line segment AC is shown below:

Statements                                  Reasons                                        

a. A, B, and C are collinear        a. Given

AB = BD, BD = BC                        

b. AB = BC                                   b. Substitution

c. AB ≅ BC                                   c. Definition of congruency

d. B is the midpoint                    d. AB ≅ BC

Thus, the proof above explains how point B is the midpoint of line segment AC in the image given.

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Answer:

7

Step-by-step explanation:

A(3,2) is the element located at row 3, column 2 and that is 7

Answer: 7

Step-by-step explanation:

A₃₂ - the first index is a line, the second index is the column

Their intersection is this number

This number is 7

Using proportions, it is found that:

A proportion is a fraction of a total amount, and the measures in the context of a problem are found using basic arithmetic operations such as multiplication and division.

One application of proportions is for ratio problems, as fractions are built from the ratios to find the equivalent amounts.

Caleb noticed that for every 10 orders of cheese pizza there were 7 orders of pepperoni pizza, 5 orders of sausage pizza and 8 orders of mushroom pizza, hence the fraction of Pepperoni pizzas out of the total is given by:

Pepperoni = 7/(10 + 7 + 5 + 8) = 7/30 of the total.

If 35 pepperoni pizzas were ordered, the total number is found as follows:

7x/30 = 35

7x = 30 x 35

x = 30 x 5

x = 150 pizzas.

2 out of every 25 pizzas were burned, hence the number of burned pizzas is given by:

2/25 x 150 = 2 x 6 = 12 pizzas.

The cheese fraction is given by:

10/30.

Hence, out of 360 pizzas, the number is given by:

10/30 x 360 = 10 x 12 = 120 cheese pizzas

The mushroom fraction is given by:

8/30.

Hence, out of 360 pizzas, the number is given by:

8/30 x 360 = 8 x 12 = 96 mushroom pizzas

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The values of x that will make this expression equal to 0 are -1 and 9

Given the expression;

(x-9)(x+1)

Let's take the following steps to determine the values

First, expand the bracket, we get;

x² + x - 9x - 9

x² + x - 9x - 9

equate the expression to zero, we have;

x² + x - 9x - 9 = 0

add or subtract the like terms, we get;

x² - 8x - 9 = 0

Factorize the values

x² - 9x + x - 9 = 0

Factor out the common terms in the equation, we get;

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

The equation are;

x + 1 = 0 and x - 9 = 0

Then,

x + 1 = 0

x = -1

x - 9 = 0

x = 9

Thus, the values are - 1 and 9

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The value of the product -8/9 . 5/6 is -20/27. Option C

A fraction can simply be defined as the part of a whole set or element.

The several types of fractions are listed as;

Examples of proper fractions: 3/4, 5/6

Examples of improper fractions: 4/3 , 8/7

Examples of mixed fractions:  2 1/2 , 3 4/5

Examples of simple fractions: 1/2 , 1/3

Given the expression:

-8/9 . 5/6

To determine the product of the fractions, we need to follow the steps

Multiply the numerators

-40/ 9 × 6

Now, multiply the denominators

-40/57

Reduce to simplest forms by using the divisor 2, we have;

-20/ 27

Hence, the value is -20/27

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The statements that are true if the given pairs of triangles are congruent are:

1. ∠A ≅ ∠T; AC ≅ QT; ∠C ≅ ∠Q; ∠ABC ≅ ∠QRT

2. ∠ATF ≅ ∠LYZ; FT ≅ YL

3. B

4. ∠TAW ≅ ∠ERS; AW ≅ ER; WT ≅ SE

5. ∠GER ≅ ∠WAC; GE ≅ AC; AW ≅ ER; RE ≅ WA

If two triangles are congruent to each other, every part of the triangles that corresponds to each other will have congruent or equal measures.

1. Triangle ABC and TRQ are congruent to each other, therefore, the statements that are true are:

2. Triangle FAT and LZY are congruent to each other, therefore, the statements that are true are:

3. Two triangles are congruent if and only if their corresponding parts are congruent, therefore, the answer is: B.

4. Triangle WAT and ERS are congruent to each other, therefore, the statements that are true are:

5. Triangle GRE and CWA are congruent to each other, therefore, the statements that are true are:

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If the lengths of a certain species of crocodiles are normally distributed with a mean of 12.5 ft and a standard deviation of 2.1 ft. the probability that a randomly selected crocodile is more than 12 feet long is  0.5941.

Given :

Mean = 12.5 ft

Standard deviation = 2 .1 ft

Randomly selected crocodile = 12 ft

Hence,

First find Z value, Z = (12 – 12.5) / 2.1

Z =  - 0.5 / 2. 1

Z = - 0.238

Using Z table, we will get the probability :

Probability =  1 – 0.4059

Probability = 0.5941

Therefore we can conclude that the probability is 0.5941.

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Seasonality is a data pattern that repeats itself after a period of weeks, days, months, or quarters.

The progressive upward or downward movement of the data over time is referred to as a trend. Trend movement may be explained by shifts in income, population, age distribution, or cultural perspectives.

Data patterns called cycles appear every few years. They play a significant role in short-term company analysis and planning and are typically linked to the business cycle. Because they might be influenced by worldwide unrest or political events, business cycles are challenging to predict.

Data "blips" are caused by chance and uncommon circumstances and are known as random fluctuations. They exhibit no clear pattern, making prediction impossible.

Seasonality is a recurring trend in data that occurs every few days, weeks, months, or quarters. Six typical seasonality patterns exist.

Hence, the correct option is (d) seasonality.

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$ 807.76    is the balance after 3 years by compound interest.

What is compound interest with example?

Given

Principal , P = $675

Rate , r = 6% = 0.06

Time = t years

n = 12             (compounded monthly)

(a)

Balance after t years is given as,

A = P(1 + r/n)nt

A = 675(1 + 0.06/12)12t

A = 675(1.005)12t

Balance after t years =  675(1.005)12t              

(b)

Balance after 3 years =  675(1.005)12*3

= 675(1.005)36

= 675*1.19668

=807.7593 \approx 807.76

Balance after 3 years = $ 807.76          

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The perimeter is 70[tex]cm^{2}[/tex]. and x is 7

The complete circumference of a shape is referred to as its perimeter. It is the length of any geometric shape with a two-dimensional boundary or outline. Depending on their proportions, multiple figures can have equal perimeters. Think of a triangle built of an L-length wire as an example. If the length of each side is the same, the same wire can be used to create a square. Look at the illustration below, which shows the bounds of a rectangular park.

Given that :The perimeter is 70[tex]cm^{2}[/tex]. The sides are 3x-1, 3x, 4x+ 1.

3x -1 + 3x + 4x + 1 = 70

10x = 70

x = 7

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Algebric equations which has the same solution as 4 - 2(x - 5) = (x - 19)/4 are all equations which has a solution of 55/9.

The equation given is,

4 - (2x-5) = (x - 19)/4

16 - 4(2x - 5) = (x - 19)

16 - 8x + 20 = x - 19

All terms having a variable x is taken to one side and the numerical values are kept on the other side.

16 + 20 + 19 = x + 8x

9x = 55

x = 55/9

Therefore, equation which has the same solution as 4 - 2(x - 5) = (x - 19)/4 are all equations which has a solution of 55/9.

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An additional strategy for splitting polynomials is synthetic division. If you are dividing by a polynomial of degree 1, it is a shortcut for long division that only functions in that situation.

The divisor often takes the shape of (x a). Contrary to long division, you are solely concerned with the polynomials' coefficients in synthetic division.

Another method for dividing a polynomial by the binomial x - c, where c is a constant, is synthetic division.

Setting up the synthetic division is the first step.

Bring the leading coefficient down to the bottom row in step two.

Step 3: Divide c by the amount that was just entered in the bottom row.

Add the column you made in step 3 in step 4.

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Answer:

£72.00

Step-by-step explanation:

60*20% (0.20) = 12
60 (original price) + 12 = 72
therefore, the original price of the bag was £72.00

Answer:

6 m

Step-by-step explanation:

First I want you to understand that distance = speed × time.Consider:

speed= 250. 300.

minutes= let it be x. x-1

distance= 250× x. 300(x-1)

=250x. 300x-300

Since distance remains the same ,250x=300x-300

hence. -50x=-300.

x= 6

The length of the race was 1500 meters.

What is Speed?

Speed is defined as the rate of change of distance travelled per unit time.

Given is an athlete who ran at a speed of 250 m/min. However, on the day of the race, he increased his average speed to 300 m/min and finished the race one minute faster than he had during training.

Assume that the length of the race is (x) meters. Suppose that the runner takes (t) minutes to to complete the race in training. Therefore, we can write -

x = 250t

During the race -

x = 300(t - 1)

Equating both, we get -

250t = 300(t - 1)

250t = 300t - 300

300 = 50t

t = 6 min

Then, the length of the race will be -  

x = 250 x 6 = 1500 meters

Therefore, the length of the race was 1500 meters.

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to get the slope of any straight line, we simply need two points off of it, let's use the ones from the picture below.

[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{-4})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{4}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{4}-\stackrel{y1}{(-4)}}}{\underset{run} {\underset{x_2}{0}-\underset{x_1}{(-3)}}} \implies \cfrac{4 +4}{0 +3}\implies {\Large \begin{array}{llll} \cfrac{8}{3} \end{array}}[/tex]

Answer:   M = -8/3

Step-by-step explanation:

Using proportions, it is found that:

a. The scale of the model is of 9:900.

b. The scale factor used was of 100.

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the context of a situation using operations such as multiplication and division to find the unit rates.

The concept of proportion is followed in scale problems, as scale is the proportion of the drawn distance by the actual distance, as follows:

Scale = Drawn distance : Actual distance.

For the building, in this problem, we have that:

Applying it's formula, the scale is given by:

9 : 900

The ratio between the actual height and the drawn height is the scale factor, hence:

Scale factor = 900/9 = 100.

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Answer:

9

Step-by-step explanation:

2x3=6 (2+2+2=6)

3x3=9 (3+3+3=9)

Answer:

ans is 9 bro

Step-by-step explanation:

the question does not have a solution.

a) graphing - the parabola never crosses the x-axis. When y = 0, what does x equal? none.

b) cannot factor/properly solve for zeros.

Since TV and WY are parallel lines, the angles which are adjacent angles include the following: C. <VUX and <WXZ.

Parallel lines can be defined as two (2) lines that are always the same (equal) distance apart and never meet.

The vertical angles theorem is also referred to as vertically opposite angles theorem and it states that two (2) opposite vertical angles that are formed whenever two (2) lines intersect each other are always congruent, which simply means being equal to each other.

In Geometry, when two (2) parallel lines are cut by a transversal, the vertical angle and its adjacent angle that are formed are supplementary angles, which makes:

<VUX and <WXZ.

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Complete Question:

TV and WY are parallel lines. Which angles are adjacent angles?

<VUX and <TUX.

<VUX and <VUX.

<VUX and <WXZ.

<VUX and <YXZ.

Answer:

Option 1, 4

Step-by-step explanation:

[tex]\frac{108}{8}=\frac{27}{4}=6.75 \\ \\ 169<170<196 \implies 13<\sqrt{170}<14 \\ \\ \therefore \frac{108}{8}<\sqrt{170}[/tex]

I WILL USE THE REASONS CORRESPONDING ANGLES AND ANGLES ON THE STRAIGHT LINE. SINCE THE DIAGRAM LACKS FULL LABELLING THAT MAKES ME UNABLE TO EXPLAIN MORE USING DEMONSTRATION

[tex]3x - 3 + (4x - 6) = 180 \\ 3x + 4x - 3 - 6 =180 \\ 7x - 9 = 180 \\ 7x = 180 + 9 \\ 7x = 189 \\ \frac{7x}{7} = \frac{189}{7} \\ x = 27[/tex]

ATTACHED IS THE SOLUTION x=27°

Answer:

x = 27

Step-by-step explanation:

3x - 3 and 4x - 6 are same- side exterior angles and sum to 180° , that is

3x - 3 + 4x - 6 = 180

7x - 9 = 180 ( add 9 to both sides )

7x = 189 ( divide both sides by 7 )

x = 27

From the given dot plot, it is found that:

1. Farm 1 has mean of 8 inches and standard deviation of 1.15 inches, while Farm 2 has a mean of 8 inches but a standard deviation of 2.31 inches.

2. The lower standard deviation tells that the heights of the trees in Farm 1 are more uniform than in Farm 2.

A dot plot shows the number of times that each observation appears in a data-set.

Hence, at farm 1, the measures are given as follows:

6, 7, 7, 8, 8, 8, 9, 9, 10.

The mean is given by:

M = (6 + 2 x 7 + 3 x 8 + 2 x 9 + 10)/9 = 8 inches.

The standard deviation is given by:

S = sqrt[((6-8)² + 2 x (7-8)² + 3 x (8-8)² + 2 x (9-8)² + (10-8)²)/9] = 1.15 inches.

For Farm 2, the measures are given as follows:

4, 6, 6, 8, 8, 8, 10, 10, 12.

Hence the mean and the standard deviation are given, respectively, by:

Farm 1 trees' heights have a lower standard deviation than Farm 2 trees' heights, hence they have more uniform trees.

The problem is missing and is given by the image at the end of the answer.

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The sum of exterior angles of a regular octagon

=360°

Each exterior angle of a regular octagon

=360°/8

=45°

Each interior angle of a regular octagon

=180°-45°=135°

Hope it helps you : )

The factorization of the trinomial -x² - 2x + 48 gives the expression -1(x + 8)(x - 6)

An equation is an expression that shows the relationship between two or more numbers and variables.

Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.

Given the polynomial:

-x² - 2x + 48

Factorizing:

-1(x² + 2x - 48)

= -1[x² + 8x - 6x - 48]

= -1[x(x + 8) -6(x + 8)]

= -1(x + 8)(x - 6)

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The expression represents a polynomial with  two terms. The constant term is 1 ; leading terms is 7X^4 and leading coefficient is 7

Algebraic expressions that are made up of variables and coefficients are called Polynomials. Variables may be called indeterminates. Arithmetic operations such as addition, subtraction, multiplication can be performed for polynomial expressions but not division. As can be noticed, Polynomial is made up of two terms that are  Poly meaning “many” and nominal meaning “terms.”.

Term with the highest degree is the leading term of a polynomial therefore 7X^4

Coefficient of the leading term is the leading coefficient of a polynomial therefore 7

The expression has only two terms separated by "+" therefore two terms.

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