Start with the top figure. Which transformation was used to create the pattern?
translation
rotation
reflection
glide reflection

The statement that describes the type of solutions of the specified  equation is the third option C.;

C. The equation has two valid solutions and no extraneous solutions

A solution to an equation are values of the variables of the equation that make the equation true.

The possible equation obtained from a similar question on the website can be presented as follows;

4/(3·x + 1) = x/(2·x + 10)

The above equation expressions can be combined into a quadratic equation as follows;

4 × (2·x + 10) = x × (3·x + 1)

8·x + 40 = 3·x² + x

3·x² + x - 8·x - 40 = 0

3·x² - 7·x - 40 = 0

3·x² - 15·x + 8·x - 40 = 0

3·x·(x - 5) + 8·(x - 5) = 0

(3·x + 8)·(x - 5) = 0

x = -8/3 and x = 5

Therefore, the equation has two valid solutions and no extraneous solutions

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The polynomial function in factored form with roots x = 7, x = -10, and x = 3, each with a multiplicity of 1, is  [tex]f(x) = x^3 - 76x + 210.[/tex]

To write a polynomial function in factored form with the given roots, we can use the factored form equation:

f(x) = (x - r1)(x - r2)(x - r3)...

Where r1, r2, r3 represent the roots of the polynomial.

Given the roots x = 7, x = -10, and x = 3, we can write the factored form equation as:

f(x) = (x - 7)(x + 10)(x - 3)

Expanding this equation will give us the polynomial function in factored form:

[tex]f(x) = (x - 7)(x + 10)(x - 3)[/tex]

[tex]= (x^2 - 7x + 10x - 70)(x - 3)[/tex]

[tex]= (x^2 + 3x - 70)(x - 3)[/tex]

[tex]= x^3 - 3x^2 + 3x^2 - 9x - 70x + 210[/tex]

[tex]= x^3 - 76x + 210[/tex]

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The circumference of the circle with the measure of diameter as 28 cm is 87.92 cm.

Given a circle.

Also given that,

Diameter of the circle = 28 cm

We know that, radius of a circle is half the measure of the diameter of the circle.

Radius of the circle = 28 / 2 = 14 cm

The formula to find the circumference of the circle is,

Circumference = 2 πr

Here r is the radius of the circle.

Substituting the given,

Circumference = 2 π (14)

                         = 28π

                         = 28 × 3.14

                         = 87.92 cm

Hence the circumference is 87.92 cm.

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There are a fixed number of trials is not a condition for a geometric setting

In a geometric setting, we are dealing with a sequence of independent trials, where each trial can result in either a success or a failure.

The key concept in a geometric setting is the number of trials needed until the first success occurs.

The trials are independent  is essential in a geometric setting.

It means that the outcome of one trial does not affect the outcome of subsequent trials.

The probability of success is the same for each trial is also crucial in a geometric setting.

It implies that the probability of achieving a success does not change from trial to trial.

There are a fixed number of trials is not specific to a geometric setting.

The variable of interest is the number of trials required to reach the first success is fundamental to a geometric setting.

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Using the formula for two events not mutually exclusive, the probability of ordering either one is given as 0.8.

Since we assume that the events are not mutually exclusive, this implies that the occurrence of event B is not affected by the probability of occurrence of event A.

Then, the probability of ordering either one is the sum of their individual probabilities minus the probability of ordering both.

The probability formula is:

p (chocolate or vanilla) = p (chocolate) + p (vanilla) - p (chocolate and vanilla)

p (chocolate) = 0.6

p (vanilla) = 0.5

p (chocolate or vanilla) = 0.6 + 0.5 - 0.6 * 0.5

= 1.1 - 0.3

= 0.8

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UIF at 1% of the basic salary is R234.

The actual dimension of the kitchen on the floor is 0.036 meters.

2.2.1. UIF stands for Unemployment Insurance Fund.

2.2.2. To calculate UIF at 1% of the basic salary, we multiply the basic salary by 1%:

UIF = 1% of Basic Salary

= 1/100 x Basic Salary

Given that the Basic Salary is R23,400, we can calculate UIF:

UIF = 1/100 x 23,400

= 234

Therefore, UIF at 1% of the basic salary is R234.

2.2.3. One benefit of contributing UIF by the employee is that it provides financial protection against unemployment. If an employee becomes unemployed, they may be eligible to receive UIF benefits, which can provide temporary financial support during the period of unemployment.

2.2.4. Unfortunately, the values of B and C are not provided in the given information. If you provide the values, I can assist you with determining them.

3.1.1. The scale used is 1:100.

3.1.2. If the dimension (length) of the kitchen on the plan is 3.6 cm, to determine the actual dimension in meters, we need to scale it up by the scale factor:

Scale factor = 1/100 (since it's a 1:100 scale)

Actual dimension = Dimension on the plan x Scale factor

= 3.6 cm x (1/100)

= 0.036 meters

Therefore, the actual dimension of the kitchen on the floor is 0.036 meters.

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The length of side m is, 5.1 inches.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

In ΔMNO,

⇒ o = 8 inches, m ∠M = 28° and m ∠O = 48°.

Now, Let the length of side m = x

So, By sine rule, we get;

[tex]\rightarrow \sf \dfrac{sin \ M}{m} = \dfrac{Sin \ O}{o}[/tex]

Substitute all the values, we get;

[tex]\sf \rightarrow \dfrac{sin \ 28^\circ}{x} = \dfrac{sin \ 48^\circ}{8}[/tex]

[tex]\sf \rightarrow \dfrac{0.47}{x} = \dfrac{0.74}{8}[/tex]

[tex]\sf \rightarrow x=\dfrac{ 0.47 \times 8}{0.74}[/tex]

[tex]\sf x = 5.08\thickapprox 5.1 \ inches[/tex]

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Answer:

To find the sum of (-2.1x + 3.7) and (5 + 4.9x), we need to add the like terms (terms with the same variable and exponent). In this case, the x term is the like term. Therefore:

(-2.1x + 3.7) + (5 + 4.9x) = -2.1x + 4.9x + 3.7 + 5

Combining like terms, we get:

(-2.1x + 4.9x) + (3.7 + 5) = 2.8x + 8.7

Therefore, the sum of (-2.1x + 3.7) and (5 + 4.9x) is 2.8x + 8.7.

So, the answer is: 2.8x+8.7.

Step-by-step explanation:

Solution 2:

The correct answer is 2.8x+8.7.

Here's the solution:

(-2.1x +3.7) + (5 + 4.9x) =

-2.1x + 3.7 + 5 + 4.9x =

-2.1x + 4.9x + 3.7 + 5 =

2.8x + 8.7: answer

The four iterates of the function f(z) = z² + 2 + 2t are:

To find the first four iterates of the function f(z) = z² + 2 + 2t with an initial value of z0 = -1 + 2t, we will substitute the initial value into the function repeatedly.

Substitute z0 into the function:

f(z0) = (-1 + 2t)^2 + 2 + 2t

Simplify the expression:

f(z0) = 1 - 4t + 4t² + 2 + 2t

f(z0) = 4t² - 2t + 3

This is the first iterate of the function.

Substitute the first iterate into the function:

f(f(z0)) = f(4t² - 2t + 3)

Simplify the expression:

f(f(z0)) = (4t² - 2t + 3)² + 2 + 2t

f(f(z0)) = 16t⁴ - 16t² + 40t² - 12t + 14

This is the second iterate of the function.

Repeat the process for the third and fourth iterates:

f(f(f(z0))) = (16t⁴ - 16t³ + 40t² - 12t + 14)² + 2 + 2t

f(f(f(z0))) = 256t⁸ - 512t⁷ + 768t⁶ - 768t⁵ + 560t⁴ - 288t³ + 88t² - 16t + 18

and, f(f(f(f(z0)))) = (256t⁸ - 512t⁷ + 768t⁶ - 768t⁵ + 560t⁴ - 288t³ + 88t² - 16t + 18)² + 2 + 2t

f(f(f(f(z0)))) = 65536t¹⁶ - 262144t¹⁵ + 557056t¹⁴ - 787456t¹³ + 801216t¹² - 623616t¹¹ + 378752t¹⁰ - 185536t⁹ + 72432t⁸ - 21856t⁷ + 4916t⁶ - 800t⁵ + 84t⁴ - 4t³ + 2t² + 2t + 2

These are the first four iterates of the function f(z) = z² + 2 + 2t with the initial value of z0 = -1 + 2t.

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Answer:

c) y=-x^2/4 - 2x - 7

Step-by-step explanation:

When A plug is removed from a trough to drain the water, The appropriate form of the expression is 10(x - 1)² - 3. Option D

The appropriate form of the expression that would reveal the time, in minutes, when the trough is empty is: 10(x - 1)² - 3.

This expression represents the volume of the trough after the plug is removed, with x representing the time in minutes. When the volume of the trough is equal to zero, it means the trough is empty.

Therefore, setting the expression equal to zero and solving for x will give us the time when the trough is empty.

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The bisector of angle RQP is angle PQT and angle RQT, both angles are equal and their sum is equal to angle RQP.

Angle bisector or a bisector angle is a type of angle obtained after dividing the initial angle into two equal parts.

The bisected angle can be obtained using a pair of compass and a pencil attached to it.

To bisect the given angle RQP; we will take the following steps;

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Hello !

Answer:

[tex]\boxed{\sf (3x + 4)(x - 1)=3x^2+x-4}[/tex]

Step-by-step explanation:

We will have to use the distributive property to expand this expression.

Let's remember :

[tex]\sf (a+b)(c+d)=ab+ad+bc+bd)[/tex]

Let's apply this property to our expression :

[tex]\sf (3x + 4)(x -1)\\=3x\times x+3x\times(-1)+4\times x+4\times(-1)[/tex]

Now let's calculate and combine like terms :

[tex]\sf 3x^2-3x+4x-4\\\boxed{\sf =3x^2+x-4}[/tex]

Have a nice day ;)

The measure of segment HI is given as follows:

HI = 7.

The measure of segment HI for this problem are obtained considering the triangle midsegment theorem, which states that the length of the midsegment of the triangle is equals to half the length of the base, hence the base has the length that is twice the midsegment.

The lengths are given as follows:

Hence the value of x is obtained as follows:

EF = 2HI

-21 + 5x = 2(-9x + 70)

-21 + 5x = -18x + 140

23x = 161

x = 7.

Hence the length HI is given as follows:

HI = -9(7) + 70

HI = 7.

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Answer:

6 hours

Step-by-step explanation:

So therefore,

4 roofers= 1 hour

1 roofer= 9 * 4

= 36 hours

6 roofers= 36/6=6 hours

Answer:

tan T = 12/5

sin A = 12/13

sec Z = 97/65

m<H = 54.5°

Step-by-step explanation:

In general:

sin A = opp/hyp

cos A = adj/hyp

tan A = opp/adj

sec A = 1/cos A = hyp/adj

tan T = 48/20

tan T = 12/5

AB = √(100 + 576)

AB = 26

sin A = 24/26

sin A = 12/13

XZ = √(72² + 65²)

XZ = 97

sec Z = 97/65

tan H = 7/5

H = tan^-1 7/5

m<H = 54.5°

Answer:

x = 93

Step-by-step explanation:

the adjacent angle to x ( on the right side) and 48° are alternate angles and are congruent.

the 3 angles lying on line m sum to 180° , that is

39 + x + 48 = 180

x + 87 = 180 ( subtract 87 from both sides )

x = 93

Answer: [tex]x\approx 6.2[/tex]

Step-by-step explanation:

Detailed explanation is attached below.

[tex]x-9z^5+4z+11+2z^5+14=-5z^5-3z+25\\x=2z^5-7z[/tex]

Therefore, it's [tex]2z^5-7z[/tex].

10-10=69.420!!!!!!!!!!

Sorry for bad handwriting

if i was helpful Brainliests my answer ^_^

hello

the answer is:

1)

Sin 28° = x/19 ----> x = 8.91 or 9

2)

tan 41° = x/32 ----> x = 27.8 or 28

3)

Cos 21° = x/26 ----> x = 24.2 or 24

4)

Cos 55° = 8/x ----> x = 13.9 or 14

5)

Sin 33° = 15/x ----> 27.57 or 28

6)

Cos 43° = 36/x ----> x = 49.2 or 49

7)

tan 72° = 25/x ----> x = 8.12 or 8

8)

Cos 64° = x/11 ----> x = 4.81 or 5

The concentration of the mixture made by mixing 6 fl. oz. of a 20% alcohol solution and 4 fl. oz. of a 5% alcohol solution will be; 14%

Consider that x represents the concentration of the mixture, hence:

(6 x 20%) + (4 x 5%) = x (4 + 6)

1.2 + 0.2 = 10x

x = 0.14 = 14%

The concentration of the mixture is made by mixing 6 fl. oz. of a 20% alcohol solution and

Thus 4 fl. oz. of a 5% alcohol solution = 14%

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Answer:

Step-by-step explanation:

He had 1 cups .

He used 1/4th cup to make cookies .

Now , he is left with ( 1 - 1/4 ) cups .

                                = 3/4 cups

The statement is not true because random sampling does not eliminate all potential sources of bias and variability in the sample selection process.

Other factors and variables that influence study outcomes include sampling bias, sample size, sampling frame, selection methods, population heterogeneity, and study design and execution.

The statement that random sampling guarantees a representative sample of the population is not entirely true.

While random sampling is a valuable method to increase the likelihood of obtaining a representative sample, it does not provide an absolute guarantee.

There are several factors and variables that can influence the outcomes of studies, even with random sampling.

Sampling Bias: Despite random sampling, certain biases can still occur. For example, non-response bias can arise if selected individuals choose not to participate or are unavailable, which can lead to a non-representative sample.

Sample Size: The size of the sample plays a crucial role in its representativeness.

If the sample size is too small, it may not accurately reflect the diversity and characteristics of the population, leading to biased results.

Sampling Frame: The sampling frame refers to the list or method used to identify potential participants.

If the sampling frame is incomplete or inaccurate, the resulting sample may not be representative of the entire population.

Selection Methods: Random sampling is just one method of selecting a sample. Other sampling methods, such as stratified sampling or convenience sampling, may introduce additional biases and affect the representativeness of the sample.

Population Heterogeneity: The variability and diversity within the population can impact the representativeness of the sample.

If the population is highly heterogeneous, it may be challenging to capture all its characteristics accurately.

Study Design and Execution:

The design and execution of the study, including survey questions, data collection methods, and potential confounding variables, can influence the outcomes and introduce biases.

While random sampling is a valuable tool, researchers must consider and address these factors and variables to enhance the representativeness and reliability of their study results. It is essential to employ rigorous methodologies and employ statistical techniques to account for potential biases and limitations.

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The final transformed graphs are 1) f'(x) = (1/2)|x + 1| + 3, 2) f'(x) = -√x + 1 and 3) f'(x) = -√x - 2.

1. Break down the transformations step by step.

Start with the function f(x) = |x|.

a. Shrink vertically by a factor of 1/2: Multiply the function by 1/2.

g(x) = (1/2)|x|.

b. Shift to the left 1 unit: Replace x with (x + 1).

h(x) = (1/2)|x + 1|.

c. Shift upward 3 units: Add 3 to the function.

f'(x) = (1/2)|x + 1| + 3.

Therefore, the equation for the final transformed graph is f'(x) = (1/2)|x + 1| + 3.

2. Start with the function f(x) = √x.

a. Reflect in the x-axis: Multiply the function by -1.

g(x) = -√x.

b. Shift 1 unit upward: Add 1 to the function.

f'(x) = -√x + 1.

Therefore, the equation for the final transformed graph is f'(x) = -√x + 1.

3. Start with the function f(x) = √x.

a. Reflect in the y-axis: Multiply the function by -1.

g(x) = -√x.

b. Shift 2 units down: Subtract 2 from the function.

f'(x) = -√x - 2.

Therefore, the equation for the final transformed graph is f'(x) = -√x - 2.

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the answer is of the inequality is x>8

The time needed before the doctor administers the medication again is given as follows:

d) 22.2 hours.

The exponential function giving the amount of the medicine in the patient's bloodstream after t hours is given as follows:

[tex]A(t) = 500(0.93)^t[/tex]

The medication will be applied when the amount is given as follows:

A(t) = 100.

Hence the time needed is obtained solving the exponential function as follows:

[tex]100 = 500(0.93)^t[/tex]

[tex](0.93)^t = \frac{100}{500}[/tex]

[tex](0.93)^t = 0.2[/tex]

The logarithm of base 10 is the inverse of the exponential, hence:

[tex]t = \frac{\log{0.2}}{\log{0.93}}[/tex]

t = 22.2 hours.

Which is the time needed before the doctor administers the medication again.

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The correct option is: (x + 3)² = 17; x equals negative 3 plus or minus the square root of 17(x = -3 ± √17) by completing the square

The completing the square method require we move constant term to the right hand side of the equation, divide the middle term and add its square to both sides of the equation as follows:

For the equation;

x² + 6x - 8 = 0

add 8 to both sides

x² + 6x = 8

divide 6 by 2 and add the square of the result to both sides

x² + 6x + 3² = 8 + 3²

by factorization;

(x + 3)² = 8 + 9

(x + 3)² = 17

x + 3 = ± √17 {take square root of both sides}

x = -3 ± √17

Therefore, by completing the square we the equation to be (x + 3)² = 17 and the solution for the value of x = -3 ± √17

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