A student graphed f(x)=x and g(x)=1/2f(x)-3 on the same coordinate grid. Describe how the graphs of f and g are related. (Describe the transformations)

Answer: C

Step-by-step explanation:

First, we solve for y in the expression:

So, the y-intercept is (0, -4).

The error is that you are given the wrong y-intercept and the wrong x-intercept; they are swapped in the place of writting.

Answer:

3x - 21 = 3(x + 7).

Step-by-step explanation:

3x - 21 = 3(x + 7)

3x - 21 = 3x + 21

3x - 3x = 21 + 21

0 = 42

Since the two are not equal, this equation has no solution.

3x - 21 = 3(x - 7)

3x - 21 = 3x - 21

3x - 3x = -21 + 21

0 = 0

Since the two are equal, this equation has infinitely many solutions.

3x - 21 = x - 7

2x = 14

x = 7

This equation has one solution.

Since there is only one choice that makes sense, the answer won't be all of the choices.

The answer is A. 3x - 21 = 3(x + 7).

Hope this helps!

Step-by-step explanation:

There are six cards in the deck, and two of them are F's.

When drawing the first card, the probability of getting an F is 2/6, or 1/3.

After the first card is drawn, there are now five cards left in the deck, and one of them is an F. Therefore, the probability of drawing an F on the second draw without replacement is 1/5.

The probability of drawing an F on the first draw and then drawing an F on the second draw without replacement is the product of these two probabilities:

P(F, then F without replacement) = P(F on first draw) x P(F on second draw without replacement)

= (1/3) x (1/5)

= 1/15

Therefore, the probability of drawing an F, then drawing an F without the first replacing a card is 1/15.

Answer:

6

Step-by-step explanation:

The critical value  from the data for a two-tailed test with 10 independent variables and 96 observations would be ±2.306.

To determine the rejection or critical region for the given hypothesis, we need to calculate the critical value of the t-distribution. Since we are performing a test at the 0.05 level of significance, the critical value for a two-tailed test with 10 independent variables and 96 observations would be ±2.306. This means that if our calculated t-value falls outside this range, we would reject the null hypothesis and conclude that beta subscript 5 is significantly different from 0.

The t-value for beta subscript 5 can be calculated using the formula t = (b subscript 5 - 0) / (SE subscript b subscript 5), where b subscript 5 is the estimated coefficient for the fifth independent variable and SE subscript b subscript 5 is the standard error of the estimate for that coefficient. If the calculated t-value falls outside the critical region, we can reject the null hypothesis and conclude that there is a significant relationship between the fifth independent variable and the dependent variable.

In summary, to determine the rejection or critical region for the given hypothesis, we need to calculate the critical value of the t-distribution using the level of significance, number of independent variables, and number of observations. We can then use this critical value to determine if our calculated t-value falls within or outside the critical region, which will determine whether we reject or fail to reject the null hypothesis.
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Answer:

  0

Step-by-step explanation:

Multiplying the first equation by xy, we have ...

  x^2 +y^2 = -xy

Factoring the expression of interest, we have ...

  x^3 -y^3 = (x -y)(x^2 +xy +y^2)

Substituting for xy using the first expression we found, this is ...

  x^3 -y^3 = (x -y)(x^2 -(x^2 +y^2) +y^2) = (x -y)(0) = 0

The value of x^3 -y^3 is 0.

Answer: 6

Step-by-step explanation:

Answer: Hi the answer to your question would be

GCF = 12

for the values 12, 24, 36, 48, 60

Here is an explanation!

The factors of 12 are: 1, 2, 3, 4, 6, 12

The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24

The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36

The factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

The factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

Then the greatest common factor is 12.

Hope this helps Ihsan!

Answer:27777777777777/10000000000000

Step-by-step explanation:A decimal that keep repeating over and over again is called a repating decimal or irrational numbers as the classifying numbers that these.

Answer:

87.9990

Step-by-step explanation:

−2.7¯¯¯

Answer:

A and C are functions.

The domain is x and the range is y

Step-by-step explanation:

Each x - value can have only one y -value

Function= unique x-values

Y can be the same answer but the X has to be different

What I do understand of the quesetion, it should be "The change from Thursday to Friday represents a bigger  change in temperature."

The postfix expression of "7+5-3*2(6*7)/4" is "7 5 + 3 2 * 6 7 * 2 * - 4 /". Evaluating the postfix expression gives the result of the expression. The prefix expression for the given infix expression is "/ - + 7 5 * 3 * 2 ( * 6 7 ) 4".

To convert the infix expression "7+5-3*2(6*7)/4" into postfix expression, we follow the rules of operator precedence and associativity. The postfix expression is obtained by placing operators after their operands.

The postfix expression for the given infix expression is:

"7 5 + 3 2 * 6 7 * 2 * - 4 /"

To evaluate the postfix expression, we use a stack data structure. We scan the postfix expression from left to right and perform the corresponding operations.

Starting with an empty stack, we encounter the operands "7" and "5". We push them onto the stack. Then we encounter the operator "+", so we pop the last two operands from the stack (5 and 7), perform the addition operation (7 + 5 = 12), and push the result back onto the stack.

We continue this process for the remaining operators and operands in the postfix expression. Finally, after evaluating the entire expression, the result left on the stack is the final answer.

To convert the infix expression into prefix expression, we follow similar rules but scan the expression from right to left. The prefix expression is obtained by placing operators before their operands.

The prefix expression for the given infix expression is:

"/ - + 7 5 * 3 * 2 ( * 6 7 ) 4"

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The parametric equation of the line that passes through the points (5,2,7) and (8,–6,1) is \(\vec r= < 5,2,7 > +\lambda < 3,-8,-6 >\)

Also, the point (17,–30,31) does not lie on the line.

for given question,

We need to find the parametric equation of the line that passes through the points (5,2,7) and (8,–6,1)

Let \(\vec r_0= < 5,2,7 >\)

and

\(\vec v= < 8-5,-6-2,1-7 > \\\\\vec v= < 3,-8,-6 >\)

where vector v is the direction vector.

So, the equation of the line would be,

\(\vec r=\vec r_0+\lambda \vec v\\\\\vec r= < 5,2,7 > +\lambda < 3,-8,-6 >\)

Now we need to determine whether the point (17, -30, 31) is on the line.

Let \(< 17,-30,31 > = < 5,2,7 > +\lambda < 3,-8,-6 >\)

For first component,

⇒ 17 = 5 + 3λ

⇒ 3λ = 12

⇒ λ = 4

For the second component,

⇒ -30 = 2 - 8λ

⇒ -8λ = -32

⇒ λ = 4

For third component,

⇒ 31 = 7 - 6λ

⇒ -6λ = 24

⇒ λ = -4

since the values of the λ are not consistent, the point (17,–30,31) does not lie on the line.

Therefore, the parametric equation of the line that passes through the points (5,2,7) and (8,–6,1) is \(\vec r= < 5,2,7 > +\lambda < 3,-8,-6 >\)

Also, the point (17,–30,31) does not lie on the line.

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Answer:

6= 4k/9

Step-by-step explanation:

RLLY HOPE THIS HELPS QUICK ANSWER TRYING Q.8

Answer:

k = -6

p = 1

Step-by-step explanation:

You can start by distributing:

8k - 6 = 6k + 18 + 6k

Next, you can combine like terms on the right side:

8k - 6 = 12k + 18

Now, you can subtract 8k from both sides to combine the terms with k:

-6 = 4k + 18

And subtract 18 from both sides to isolate the k-term:

-24 = 4k

Lastly, divide by 4 to get k.

k = -6

You can start by distributing -8:

-8 - 32p + 7p = -25 - 8p

Then combine the like terms in the left side:

-25p - 8 = -25 - 8p

Next, add 25p to both sides to combine the p-terms:

- 8 = -25 + 17p

And add 25 to isolate p:

17 = 17p

Divide by 17 to get the answer:

p = 1

The mass of the gold bar of the trapezium shape and a density of 19.3g/cm³ is found to be 8.646 KG.

The volume of the trapezoidal prism will be determined first. V = BL, where B is the area of the trapezoidal face and L is the prism's length, is the formula for the volume of the prism.

We are aware that a trapezoid's area is equal to B = 1/2(6+10). (4)

B = 32 m²

When we enter the formula for volume, V = 32 x 14 V = 448 m³, we know that L is 14 cm.

Divide the mass by the volume to get the density, or D = M/V.

According to values,

19.3 = M/448

M = 8646.4 grams, which is equal to 8.646 grams.

The density is stated to be 19.3 kg/m³. Hence, the gold weighs 8.646 kilos.

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Complete question - The gold bar trapezium has cross-sectional area. Gold has a density of 19. 3 per cm3. Work out the mass of the gold bar. Give your answer in kilograms. The dimension of the trapezium are length = 14cm, parallel sides are 6cm and 10cm nd the height is 4cm.

A′(2, 1), B′(6, 1), and C′(2, 5) are the image's positions as a result of moving the triangular 6 units to the right.

The order of the numbers is always latitude first, semicolon after which is followed by longitude. For instance, New York City is located approximately at 40°N and 74°W in terms of latitude and longitude. The approximate coordinates for Sydney are 34°S and 150°E. When using a chart or globe, your longitude as well as latitude won't be precisely accurate.

To translate a point (x, y) to the right by 6 units, we add 6 to the x-coordinate.

So, the image of vertex A(-8, 1) would be A'(-8 + 6, 1) = A'(-2, 1).

Similarly, the image of vertex B(0, 1) would be B'(0 + 6, 1) = B'(6, 1).

And, the image of vertex C(-4, 5) would be C'(-4 + 6, 5) = C'(2, 5).

Therefore, the coordinates of the image after translating the triangle 6 units to the right are:

A′(−2, 1), B′(6, 1), C′(2, 5).

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" Horizontal stretch followed by a translation 1 unit right, so g(x) = (x − 1))." describes g(x) as a transformation of f(x) and identifies an equation for g(x). Option D

Generally, A horizontal stretch is a transformation that stretches the graph of a function horizontally by a factor of k, where k is a positive number. This can be represented by the equation g(x) = kf(x).

A translation is a transformation that moves the graph of a function horizontally or vertically without changing its shape. A translation 1 unit right can be represented by the equation g(x) = f(x - 1). Therefore, the equation for g(x) as a horizontal stretch followed by a translation 1 unit right would be g(x) = kf(x - 1).

The other statements do not accurately describe g(x) as a transformation of f(x) or provide the correct equation for g(x).

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Answer:

1066528471

Step-by-step explanation:

\(\frac{6,666,666*666,666}{1+2+3+4+5+6+5+4+3+2+1}\)  -  \(\frac{777,777*777,777}{1+2+3+4+5+6+5+4+3+2+1}\)

The lowest common multiple is 1+2+3+4+5+6+5+4+3+2+1, so that;

= \(\frac{(6,666,666*666,666)-(777,777*777,777)}{1+2+3+4+5+6+5+4+3+2+1}\)

= \(\frac{(444443955600)-(60493706170}{1+2+3+4+5+6+5+4+3+2+1}\)

= \(\frac{38395024940}{36}\)

= 1066528471

The solution to the given question is 1066528471.

Field extensions and polynomials are used to demonstrate why a regular 9-gon is not constructible using a compass and straight-edge but a regular 20-gon is.

A regular 9-gon is a polygon having nine equal-length sides that are linked to the other eight sides. Because the lengths of the 9-gon's sides are not constructible numbers, it is impossible to build a regular 9-gon with a compass and straight edges because generating a normal 9-gon necessitates the production of a cube root, which necessitates a field extension. A cube root, on the other hand, is not a constructible integer since the accompanying third-degree equation has no constructible solution.

A normal 20-gon, on the other hand, is constructible since it requires just a constructible integer, namely a fifth root. This is due to the fact that building a regular 20-gon necessitates the construction of a fifth root, which may be built via a field extension since the fifth-degree equation associated with it has a constructible solution.

In conclusion, a regular 9-gon cannot be built with a compass and straight-edge, however, a regular 20-gon can.

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Answer:

C

Step-by-step explanation:

-2^4-5(5)+2(-2-3)^2

16-25+2(25)

16-25+50

41

Answer:

7. x = 38°

8. y = 65°

9. 261° and 81°

Step-by-step explanation:

Finding x:

You can make an equality with (2x +5) and (3x +33) because the value of these angles are the same, so:

2x +5 = 3x -33

2x - 3x = -33 -5

-x = -38

x = 38°

Finding y:

You can find the value of y making another equally, but this time you have to sum (4y -1) with (3x - 33) or (2x +5) and equal it with 180°:

(4y -1)+(2x +5) = 180

4y -1 +2x +5 = 180

4y +2x +4 = 180

We know from the question 7 that x is 38°:

4y +2•(38) +4 = 180

4y - 76 +4 = 180

4y - 80 = 180

4y = 180 + 80

4y = 260

y = 260/4

y = 65

Finding the value of the angles:

You just have to put the value of x and y in their places and make the calculations:

4•65 +1 = 261°

3•(38) -33 = 81°

Answer:

3cm

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

second choice

Answer:

$130

Step-by-step explanation:

90 + (20 * 2) = 130

Answer:

√63 can be written as

√ 9 × 7 = √ 9 × √7 = 3 × √ 7

= 3√7

Hope this helps you

Answer: \(3\sqrt{7}\)

Step-by-step explanation:

Separate \(\sqrt{63}\) into \(\sqrt{7}\) and \(\sqrt{9}\).  Then simplify \(\sqrt{9}\) into 3.  Thus, the simplified version of \(\sqrt{63}\) is \(3\sqrt{7}\)

The expression represents the height of the, rectangular prism has a square base with edge length, which is 3 cm.

The expression represents the height of the rectangular prism with a square base of edge length and volume .

To make this more concrete, let's assume some values for and . Let's say that the edge length of the square base is 4 cm, and the volume of the rectangular prism is 48 cubic cm.

Using the formula for the volume of a rectangular prism, we can write:

Volume = Base Area x Height

Since the base of the rectangular prism is a square with edge length 4 cm, its area is:

Base Area = 4 x 4 = 16 square cm

Substituting the given values into the formula for volume, we get:

48 cubic cm = 16 square cm x Height

To solve for the height, we can isolate it on one side of the equation by dividing both sides by 16 square cm:

48 cubic cm ÷ 16 square cm = Height

3 cm = Height

Therefore, in this scenario, the expression represents the height of the rectangular prism, which is 3 cm.

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To evaluate the integral Σ(n=0) (n+1)x^n 5^n dx, we can first rewrite the series as a power series. Then, we integrate each term of the power series individually. The resulting integral will be the sum of the integrals of each term.

The given series can be written as Σ(n=0) (n+1)x^n 5^n. This can be expanded as (1+1)x^0 5^0 + (2+1)x^1 5^1 + (3+1)x^2 5^2 + ...

To integrate each term, we can treat x and 5 as constants. Integrating x^n with respect to x gives us (1/(n+1))x^(n+1). Multiplying by the constant (n+1) and 5^n gives us (n+1)x^(n+1) 5^n.

Therefore, integrating each term of the series individually gives us (1/(0+1))x^(0+1) 5^0 + (2/(1+1))x^(1+1) 5^1 + (3/(2+1))x^(2+1) 5^2 + ...

Simplifying each term, we have x^1 + 2x^2 5 + (3/2)x^3 5^2 + ...

The integral of the series is then x^2/2 + (2/3)x^3 5 + (3/8)x^4 5^2 + ... + C, where C is the constant of integration.

Therefore, the evaluated integral of the given series is x^2/2 + (2/3)x^3 5 + (3/8)x^4 5^2 + ... + C.

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In a school of 2000 students, the ratio of teachers to students is 3:80. This means there are 3 teachers for every 80 students.

Thus, 25 teachers joined the school.

Let the number of teachers be x and students be y.

Then, according to the given ratio, we have the equation:

\(\frac{x}{y}=\frac{3}{80}$$\)

Multiplying both sides by 80y, we get:

80x=3y

Thus, we know that there are 3/80 teachers per student.

Now let's consider the new ratio, which is 1:20.

This means there is 1 teacher for every 20 students.

We can set up another equation based on this ratio:

\(\frac{x+a}{y}= \frac{1}{20}$$\)

where a is the number of teachers who joined the school. Multiplying both sides by 20y, we get:

20(x+a)=y

Now we have two equations:

\(80x=3y\)

20(x+a)=y

We can solve for a by substituting y in the second equation with the expression we get from the first equation:

20(x+a)=80x/3

x+a=4x/3

a = x/3

Therefore, the number of teachers who joined the school is x/3.

We know that the initial ratio of teachers to students is 3:80.

So the initial number of teachers x can be calculated by:

\(\frac{x}{2000}=\frac{3}{80}$$\)

\(x=\frac{3}{80} \times 2000$$\)

x=75

Thus, the number of teachers who joined the school is:

a = x/3

= 75/3

=25

Therefore, 25 teachers joined the school.

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Answer:

180°

Step-by-step explanation:

In all triangles, the measure of its three angles always adds up to 180. Therefore, the m∠UWV is 180°.

:Done