For the given equation find the value a, b, and c, determine the direction in which the parabola opens and determine the y-intercept. Decide which table best illustrates these values for the equation:
y=x^2-6x

Answer:

7). y = 140

8). x = 9

Step-by-step explanation:

Question (7).

All-right pencil factory will produce the graphite pencils, table formed will represent a linear graph.

Three points on the graph are (12, 42) and (18, 63), (40, y)

Slope of the line passing through these points = \(\frac{y_2-y_1}{x_2-x_1}\)

m = \(\frac{63-42}{18-12}\) = \(\frac{y-42}{40-12}\)

\(\frac{21}{6}\) = \(\frac{y-42}{40-12}\)

3.5 = \(\frac{y-42}{40-12}\)

98 = y - 42

y = 140

Question (8),

If a bicyclist rides at a constant rate, table formed will represent a linear graph.

Slope of a line passing through three points (2, 25), (5, 62.5) and (x, 112.5) given in the table,

m = \(\frac{y_2-y_1}{x_2-x_1}\)

\(\frac{62.5-25}{5-2}=\frac{112.5-62.5}{x-5}\)

\(\frac{37.5}{3}=\frac{50}{x-5}\)

37.5x - 187.5 = 150

37.5x = 337.5

x = 9

Answer:

it is right triangle so we have trigonometric ratio: tan(54)=3/x and from that we have x=3/tan(54)

The following answers are obtained from HW, which it shows answers to.

Answer:

A. The Queen can state, "All the inscriptions are false."If the Queen can state this, in which of the trunks are the treasures hidden?

False, Cannot be determined

(b) The Queen can state, "Exactly one of the inscriptions is true."If the Queen can state this, in which of the trunks are the treasures hidden?

True, Trunk 1 and 3

(c) The Queen can state, "Exactly two of the inscriptions are true."If the Queen can state this, in which of the trunks are the treasures hidden?

True, Cannot be determined

d) The Queen can state, "All the three inscriptions are true."If the Queen can state this, in which of the trunks are the treasures hidden?

False, Cannot be determined

The correct statement is: g(x) is translated up 5 units compared to f(x).

The correct answer is A.

The correct answer is A.

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Answer:

(1/x + 1/y)k is the answer :)

Answer:

250

Step-by-step explanation:

(f/g)(-5) is equal to 1/4, and the value -1 is not in the domain of f/g.

To find (f/g)(-5), we need to substitute -5 into the functions f(x) and g(x) and then divide f(-5) by g(-5).

Given:

f(x) = (4+x)(6+x)

g(x) = 1+x

Substituting -5 into the functions:

f(-5) = (4+(-5))(6+(-5)) = (-1)(1) = -1

g(-5) = 1+(-5) = -4

Now, we can calculate (f/g)(-5):

(f/g)(-5) = f(-5) / g(-5) = -1 / -4 = 1/4

Therefore, (f/g)(-5) equals 1/4.

Now let's determine the values that are not in the domain of f/g. The values that are not in the domain of f/g are the values that make the denominator g(x) equal to zero. In this case, the denominator is g(x) = 1+x.

To find the values that make the denominator zero, we solve the equation:

1 + x = 0

Subtracting 1 from both sides, we get:

x = -1

So, the value x = -1 is not in the domain of f/g because it would make the denominator equal to zero.

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Answer:

Statement 1 is correct.

Step-by-step explanation:

Inverse sign is only defined from -90° to 90° therefore statement 2 is false.

The correct statements are;

The x-intercept of f(x) and the y-intercept of f–1(x) are reciprocals of each other.

The point of intersection of the two functions indicates that the functions are inverses.

Option C and D

To accurately compare a function and its inverse based on the graphs, we have to know the following;

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The linear equation in standard form is g + s + b=104, the relationship between silver to bronze medals is g = s  and the solution is g=46, s=29, b=29

(a) Since the United States won 104 gold (g), silver s, and bronze (b) medals in the 2012 Summer Olympics.

This means the sum of gold (g), silver s, and bronze (b) medals is equal to 104. Thus, the linear equation in standard form is:

g + s + b = 104

(b) Since the United States won 46 gold medals and the same number each of silver and bronze medals. This implies:

g = 46

s = b

Thus, the relationship between the number of silver to bronze medals is s = b

(c) To solve the linear equation, substitute g = 46 and s = b into the equation g + s + b = 104:

g + s + b = 104

46 + b + b = 104

46 + 2b = 104

2b = 104 -46

2b = 58

b = 58/2

b = 29

Also, s = 29        (Remember: s = b)

Thus, g = 46, s =29, b = 29

Therefore, the United States won 46 gold (g), 29 silver (s), and 29 bronze (b) medals in the 2012 Summer Olympics. Select options a., d. and e. for a., b., and c. respectively

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A²+B²= C²

31²+ 21²= z²

961+441 = z²

1402= z²

z= 37.443290454

Answer:

The correct answer is Integer ;)

A. The distribution of the time spent is X ~ N(41, 19²)

B. The distribution of the sample mean is x-bar ~ N(41, (19²)/17)

C. The distribution of the total study time is X_total ~ N(17 × 41, 17 × 19²)

D. The probability is 0.3168

E. The probability is 0.6837

F. The probability is 0.6368

G. The least total time that a group of 17 students can study and still receive a sticker for "Great dedication" is approximately 350.3618 minutes.

To answer these questions, use the properties of the normal distribution. Given the mean and standard deviation provided, calculate the required probabilities and values.

a) The distribution of the time spent studying by a single student is given by:

X ~ N(41, 19²)

b) The distribution of the sample mean for a sample size of 17 students is given by:

x-bar ~ N(41, (19²)/17)

c) The distribution of the total study time for 17 students is given by:

X_total ~ N(17 × 41, 17 × 19²)

d) To find the probability that a randomly selected student's time is between 37 and 43 minutes, use the normal distribution:

P(37 ≤ X ≤ 43) = P((37 - 41) / 19 ≤ Z ≤ (43 - 41) / 19)

Using standard normal distribution tables or a calculator, find the corresponding probabilities for Z = -0.2105 and Z = 0.1053:

P(37 ≤ X ≤ 43) ≈ P(-0.2105 ≤ Z ≤ 0.1053) ≈ 0.3168

e) To find the probability that the average time studying for the 17 students is between 37 and 43 minutes, use the distribution of the sample mean:

P(37 ≤ x-bar ≤ 43) = P((37 - 41) / (19 / √(17)) ≤ Z ≤ (43 - 41) / (19 / √(17)))

Again, using standard normal distribution tables or a calculator, find the corresponding probabilities for Z = -0.8292 and Z = 0.8292:

P(37 ≤ x-bar ≤ 43) ≈ P(-0.8292 ≤ Z ≤ 0.8292) ≈ 0.6837

f) To find the probability that the randomly selected 17 students will have a total study time less than 731 minutes, use the distribution of the total study time:

P(X_total < 731) = P((X_total - (17 × 41)) / (√(17) × 19) < (731 - (17 * 41)) / (√(17) × 19))

Again, using standard normal distribution tables or a calculator, find the corresponding probability for Z ≈ 0.3503:

P(X_total < 731) ≈ P(Z < 0.3503) ≈ 0.6368

g) Yes, the assumption of normality is necessary for parts e) and f) since we are using the properties of the normal distribution.

h) To find the least total time that a group of 17 students can study and still receive a sticker for "Great dedication," find the cutoff point where the top 15% of the distribution lies.

Using the inverse normal distribution (also known as the Z-score or percent-point function), we can find the Z-score corresponding to the top 15% of the distribution. The Z-score for the top 15% is approximately 1.0364.

Now, solve for the least total time using the formula for the total study time:

X_total = (Z × √(17) × 19) + (17 × 41)

Substituting Z = 1.0364, we can calculate:

X_total ≈ (1.0364 × √(17) × 19) + (17 × 41) ≈ 350.3618

Therefore, the least total time that a group of 17 students can study and still receive a sticker for "Great dedication" is approximately 350.3618 minutes.

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Answer:

x < -3 or x > 2

Step-by-step explanation:

x² + x - 6 > 0

Convert the inequality to an equation.

x² + x - 6 = 0

Factor using the AC method and get:

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

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

x - 2 = 0

x = 2

x + 3 = 0

x = -3

So, the solution is x < -3 or x > 2

The depth of the aquarium is approximately 4 feet when rounded to the nearest whole number (since 3.64 is closer to 4 than it is to 3 when rounded to the nearest whole number).

To calculate the depth of the aquarium, we need to use the formula for volume of a rectangular prism,

which is V = lwh where V is the volume, l is the length, w is the width, and h is the height (or depth, in this case).

Given that the aquarium holds 11.35 cubic feet of water, the volume of the aquarium can be represented by V = 11.35 cubic feet.We are also given that the length of the aquarium is 2.6 feet and the width is 1.1 feet.

Substituting these values into the formula for volume,

we get:11.35 = 2.6 × 1.1 × h

Simplifying this expression:

11.35 = 2.86h

Dividing both sides by 2.6 × 1.1,

we get:h ≈ 3.64 feet (rounded to two decimal places)

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The value of x in the quadratic equation is -0.12 or 3.12.

The value of x in the quadratic equation is calculated as follows;

h(x) = -16x² + 48x + 6

Using formula method, the value of x is calculated as;

x = (-b ± √(b² - 4ac)) / 2a

Where;

a = -16, b = 48, c = 6

x = (-48 ± √(48² - 4(-16)(6))) / 2(-16)

x = (-48 ± √(2304 + 384)) / (-32)

x = (-48 ± √(2688)) / (-32)

x = (-48 ± 51.85) / (-32)

x = (-48 + 51.85)/(-32)  = - 0.12

or

x = (-48 - 51.85)/(-32) = 3.12

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It should be noted that the addition of the variables give in the expression will be 11✓2.

It should be noted that the information is incomplete. Therefore, an overview will be given. In this case, let a = ✓2, b = ✓8 and c = ✓128.

This can be illustrated as:

= a + b + c

= ✓2 + ✓8 + ✓128

= ✓2 + 2✓2 + 8✓2

= 11✓2

Therefore, it should be noted that the should be noted that the addition of the variables give in the expression will be 11✓2

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Answer:

421.4 miles

Step-by-step explanation:

Numner of miles= ($270.79-$17.95)/86 cents

= $252.84/$0.60

=421.4 miles

The limits of the function for this problem are given as follows:

In this problem, we are given the graph of the function, hence the limit is given by the value of the function as the function approaches x = a, not the actual numeric value of the function at x = a.

At x = -2, we have that:

As the lateral limits are equal, lim x -> -2 f(x) = 3.

At x = 1, we have that:

As the lateral limits are different, the lim x -> 1 f(x) does not exist.

At x = 4, we have that:

As the lateral limits are equal, lim x -> 4 f(x) = -3.

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Answer:

The days will it take the store to make $50,000 in a whole number are:

Step-by-step explanation:

Remember that x represents the number of days, so, you must replace different values in the formula until you obtain a value of $50,000, in this form:

So, I'll show you that the value that you need is 30 in a whole number.

I know that the value exceeds the amount of $50,000, but if you use just a day before:

How you can see, if you use 29 days, the value doesn't reach $50,000, by this reason, you must use 30 days to reach it.

Check the picture below.

\(\textit{perimeter of a rectangle}\\\\ P=2(L+w) ~~ \begin{cases} L=length\\ w=width\\[-0.5em] \hrulefill\\ P=88\\ L=w+8 \end{cases}\implies 88=2( ~~(w+8)+w ~~ ) \\\\\\ 88=2(2w+8)\implies 88=4(w+4)\implies \cfrac{88}{4}=w+4 \\\\\\ 44=w+4\implies \boxed{40=w}\hspace{5em}\stackrel{w+8}{\boxed{L=48}}\)

Answer:

y-4x-7.

HOPE ITS HELPSS

Answer:

To solve this expression, we need to follow the order of operations (PEMDAS) which stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

The expression is:

1234 - 4566 / 45.44 + 67 * 755.34

First, we need to perform the division operation since it comes before addition and multiplication.

4566 / 45.44 = 100.50

Now, we can substitute that into the expression:

1234 - 100.50 + 67 * 755.34

Next, we need to perform the multiplication operation:

67 * 755.34 = 50,548.78

Now, we can substitute that into the expression:

1234 - 100.50 + 50,548.78

Next, we can perform the addition and subtraction operations:

1234 + 50,448.28 = 51,682.28

Therefore, the result of the expression is 51,682.28.

The monthly income of the first person is $600.

Given that, the average monthly income of three persons is RS 3,600.

The income of the first is 1/5 of the combined income of the other two.

Here, Let income of the first be A, let income of the second be B and let Income of the third be C.

A+B+C=3600 -----(i)

Income for the first person = 1/5(B+C) -----(ii)

Substitute equation (ii) in equation (i), we get

(B+C)/5 +B+C =3600

B+C+5B+5C=3600×5

6B+6C=18000

6(B+C)=18000

B+C=3000 ------(iii)

Substitute (iii) in equation (i), we get

A=$600

Therefore, the monthly income of the first person is $600.

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The following sets of side dimensions could be combined to create a right triangle 6, 8, 13 is √3, √13, 4.

In the triangle, there are three angles: two acute angles and one 90-degree angle. The hypotenuse, perpendicular, and base are the terms used to describe the sides of a right-angled triangle.

The next choice shows the triangle's side length:

The point is,

The hypotenuse square of a right-angled triangle is equal to the sum of its squares on its other two sides, according to Pythagoras' Theorem.

Using Pythagoras' Theorem.

Use the formula:

a² + b² = c²

For 4, 8, 11

4, 8, 11

4² + 8² = 16 + 64 = 80

11² = 121

80 is not equal to 121 it cann ot form a right triangle

For 6, 8, 13

6² + 8² = 36 + 64 = 100

13² = 169

100 is equal to 169 - 69 can form a right triangle

For √3, √5, 8

(√3)² + (√5)² = 3 + 5 = 8

8² = 64

8 is equal to 64 cannot form a right triangle

For √3, √13, 4

(√3)² + (√13)² = 3 + 13 = 16

4² = 16

16 is equal to 16 can form a right triangle

In order to create a right triangle, one may utilise the following set of side measurements √3, √13 and 4 form a triangle.

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The price for 7 bags of trail mix and 4 bananas is  15.45  dollars.

The expression for x trail bag and y bananas is 1.35x + 1.50y.

In maths, an expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division etc.)

Therefore, the cost of a bag of trail mix at the corner store is 1.35 dollars  and the cost of a banana is 1.5 dollars.

The cost for 7 bags of trail mix and 4 bananas can be computed as follows;

let

x = bags of trail mix

y = number of banana

Therefore,

1.35x + 1.50y

1.35(7) + 1.50(4) = 9.45 + 6 = 15.45

Therefore, let's find the expression for x trail bag and y bananas.

Hence,

1.35x + 1.50y

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Answer:

2

Step-by-step explanation:

1+1=2

Answer:

200000×2

=R400 000 and minus 50000

=300000

Answer: 5% increase

Step-by-step explanation:

To get to 22 from 17 you would have to add 5 to get 22. 17+5=22.