What is the slope of the line in the graph?A. 1 B. 1/4C. 4 D. -4

Answer:

  a) x = 1 ± (3/7)√7

  b) (-∞, -5) ∪ [-2, 5) ∪ [6, ∞)

Step-by-step explanation:

You want solutions to the relations ...

We like to solve these in the form f(x) = 0. It helps avoid extraneous solutions.

  \(7+\dfrac{1}{x} -\dfrac{1}{x-2}=0\\\\\\\dfrac{7x+1}{x}-\dfrac{1}{x-2}=0\\\\\\\dfrac{(7x+1)(x-2)-x}{x(x-2)}=0\\\\\\ \dfrac{7x^2-14x-2}{x(x-2)}=0\)

The roots of the numerator quadratic are found by ...

  x² -2x -2/7 = 0 . . . . . divide by 7

  x² -2x +1 -9/7 = 0 . . . . add and subtract 1

  (x -1)² = 9/7 . . . . . . . . . . write as a square, add 9/7

  x -1 = ±√(9·7/49) = ±(3/7)√7 . . . . take the square root

  x = 1 ± (3/7)√7

Rational inequalities are best solved by identifying the roots of numerator and denominator. These tell you where the function changes sign. The end behavior of the rational function tells you what the signs are changing from.

  \(\dfrac{x^2-4x-12}{x^2-25}\ge 0\\\\\\\dfrac{(x+2)(x-6)}{(x+5)(x-5)}\ge0\)

This has a horizontal asymptote at y=1 for |x|→∞. It has vertical asymptotes at x=±5.

The sign changes occur at x ∈ {-5, -2, 5, 6}. The rational expression is positive (approaching +1) for x < -5 and for x > 6. It is negative in the adjacent intervals, so positive again for -2 < x < 5.

The inequality is satisfied for ...

Answer:

It is 7.56!

Other:

Brainliest? Thanks!

Answer:

A= 2 B= 1

Step-by-step explanation:

1/2 +3/2= 4/2 than divide 4/2 by 2 it will give you 2/1 so 2/1 equal 2 because 2 is bigger than 1

2/5 + 3/5 = 5/5 it is 1 because if you divide it by 5 you will get a whole number which is 1

Answer:

  (a)  twenty-eight ninths, square root of nineteen, cube root of eighty-eight

Step-by-step explanation:

When ordering a list of numbers by hand, it is convenient to convert them to the same form. Decimal equivalents are easily found using a calculator.

The attachment shows the ordering, least to greatest, to be ...

  \(\dfrac{28}{9}.\ \sqrt{19},\ \sqrt[3]{88}\)

__

Additional comment

We know that √19 > √16 = 4, and ∛88 > ∛64 = 4, so the fraction 28/9 will be the smallest. That leaves us to compare √19 and ∛88, both of which are near the same value between 4 and 5.

One way to do the comparison is to convert these to values that need to have the same root:

  √19 = 19^(1/2) = 19^(3/6) = sixthroot(19³)

  ∛88 = 88^(1/3) = 88^(2/6) = sixthroot(88²)

The roots will have the same ordering as 19³ and 88².

Of course, these values can be found easily using a calculator, as can the original roots. By hand, we might compute them as ...

  19³ = (20 -1)³ = 20³ -3(20²) +3(20) -1 = 8000 -1200 +60 -1 = 6859

  88² = (90 -2)² = 90² -2(2)(90) +2² = 8100 -360 +4 = 7744

Then the ordering is ...

  28/9 < 19³ < 88²   ⇒   28/9 < √19 < ∛88

Answer:

the ordering is

28/9 < 19³ < 88²   ⇒   28/9 < √19 < ∛88

Step-by-step explanation:

The decimal number that represents the expression (3 * 100) + (7 * 10) + (5 * 1) + (9 * 0.01) + (2 * 0.001) is; 375.092

We want to find the decimal that is equivalent to the expression (3 * 100) + (7 * 10) + (5 * 1) + (9 * 0.01) + (2 * 0.001).

Thus, we have;

(3 * 100) = 300

(7 * 10) = 70

(5 * 1) = 5

(9 * 0.01) = 0.09

(2 * 0.001) = 0.002

Thus, the given initial expression can now be written as;

300 + 70 + 5 + 0.09 + 0.002 = 375.092

Thus, the decimal number that represents the expression

(3 * 100) + (7 ** 10) + (5 * 1) + (9 * 0.01) + (2 * 0.001) is; 375.092

The complete question is;

What is a decimal that is equivalent to the expression (3 * 100) + (7 ** 10) + (5 * 1) + (9 * 0.01) + (2 * 0.001)?

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A geometric series is one in which there is a constant between two successive numbers in the series.

When there is a constant between the two successive numbers in the series then it is called a geometric series. In other words, every next term is multiplied by that constant term to form a geometric progression.

The sequence in which every next number is the addition of the constant quantity in the series is termed the arithmetic progression

Suppose the series is given as

2,4,8,16,32,64.........

The common difference is defined as the ratio of the next term to the previous term.

From the above series, the common ratio is calculated as,

Common ratio = 4 / 2

Common ratio = 2

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The length of AC is equal to 5 units.

Given:

From the figure :

ΔABC is a right angled triangle with sides:

AB = 3 and BC = 4

Right angled triangle:

A right-angled triangle is a type of triangle that has one of its angles equal to 90 degrees.

The other two angles sum up to 90 degrees. The sides that include the right angle are perpendicular and the base of the triangle.

The third side is called the hypotenuse, which is the longest side of all three sides.

we know that,

According to pythagorean theorem:

\(AB^2+BC^2 = AC^2\)

3^2 + 4^2 = AC^2

9 + 16 = AC^2

AC^2 = 25

AC = \(\sqrt{25}\)

AC = 5 units.

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Full question:

is in the image uploaded

7) The  probability that the two numbers have an even sum is: 0.5

8) The probability that the two are even is: 0.25

7) We want to find the probability that the two numbers have an even sum.

The only combinations that produces an even sum are:

(1, 3), (3, 1), (1, 1), (2, 2), (2, 4), (4, 2), (4, 4), (3, 3)

The other combinations of numbers are:

(1, 2), (1, 4), (2, 1), (4, 1), (2, 3), (3, 2), (3, 4), (4, 3)

Thus, we have a total of 16 combinations and the  probability that the two numbers have an even sum is:

P(two numbers with even sum) = 8/16 = 0.5

8) The probability that the two are even is:

4/16 = 1/4

= 0.25

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The probability that four batteries connected in series will have a combined voltage of 60.8 or more volts is approximately 0.0228 or 2.28%.

To find the probability that four batteries connected in series will have a combined voltage of 60.8 or more volts, we need to use the concept of the Central Limit Theorem.

In this case, we know that the mean voltage of a single battery is 15 volts and the standard deviation is 0.2 volts. When batteries are connected in series, their voltages add up.

The combined voltage of four batteries connected in series is the sum of their individual voltages. The mean of the combined voltage will be 4 times the mean of a single battery, which is 4 * 15 = 60 volts.

The standard deviation of the combined voltage will be the square root of the sum of the variances of the individual batteries. Since the batteries are connected in series, the variance of the combined voltage will be 4 times the variance of a single battery, which is 4 * (0.2)^2 = 0.16.

Now, we need to calculate the probability that the combined voltage of four batteries is 60.8 or more volts. We can use a standard normal distribution to calculate this probability.

First, we need to standardize the value of 60.8 using the formula:

Z = (X - μ) / σ

Where X is the value we want to standardize, μ is the mean, and σ is the standard deviation.

In this case, the standardized value is:

Z = (60.8 - 60) / sqrt(0.16)

Z = 0.8 / 0.4

Z = 2

Next, we can use a standard normal distribution table or calculator to find the probability associated with a Z-score of 2. The probability of obtaining a Z-score of 2 or more is approximately 0.0228.

Therefore, the probability that four batteries connected in series will have a combined voltage of 60.8 or more volts is approximately 0.0228 or 2.28%.

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Step-by-step explanation:

The given equation is :

2x+7y=11

We need to tell the point (-5,3) lies on the graph of the above equation of not.

Put x = -5 and y = 3 in the LHS of the above equation.

LHS = 2x+7y

= 2(-5)+7(3)

= -10 +21

= 11

It means, when we put  x = -5 and y = 3 in the above equation, we get 11. Hence, (-5,3) lies on the graph of the equation.

Answer:

50,000+30,000+13852=93,852

9514 1404 393

Answer:

  {2.96, 12.66}

Step-by-step explanation:

A graph shows the rocket will be 600 feet up after 2.96 seconds, and again at 12.66 seconds.

__

You can solve the equation h = 600 to find the times.

  -16t^2 +250t = 600

  -16(t^2 -15.625t) = 600

  -16(t^2 -15.625t +7.8125²) = 600 -16(7.8125²)

  -16(t -7.8125)² = -376.5625

  t -7.8125 = √(376.5625/16) ≈ ±4.8513

  t = 7.8125 ± 4.8513 ≈ {2.9612, 12.6638}

The rocket will be 600 ft above the ground 2.96 and 12.66 seconds after launch.

Answer:

a, t = (p - 4)/5

b. t =√(a + 4)

c. t = d/(5-f)

Step-by-step explanation:

a. p = 5t + 4

To make t the subject of the equation, subtract 4 from both sides

p - 4 = 5t + 4 - 4

p - 4 = 5t

Divide both sides by 5

(p - 4)/5 = t

t = (p - 4)/5

b. a = t2 - 4

to make t the subject, add 4 to both sides

a + 4 = t2 - 4 + 4

a + 4 = t2

find the root of both sides

t =√(a + 4)

c. d = t(5 – f)

to make t the subject, divide both sides by 5 - f

d/(5-f) = t(5 – f)/(5 – f)

t = d/(5-f)

Answer:

167.67 divided by 8.1 = 20.7

(a) The algebraic expression, -5x - 2 + 5x + 2 is simplified as 0.

(b) The algebraic expression, 5x -2  - (5x + 2) is simplified as -4.

The given algebraic expression is simplified by adding similar terms together, as it will make the expression to be in simplest form.

The given algebraic expressions are;

-5x - 2 + 5x + 2

5x -2  - (5x + 2)

The first algebraic expression is simplified as follows;

-5x - 2 + 5x + 2

collect similar terms;

(-5x + 5x) + (-2 + 2)

= 0 + 0

= 0

The second algebraic expression is simplified as follows;

5x - 2 - (5x + 2)

= 5x - 2 - 5x - 2

collect similar terms;

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

= 0 - 4

= - 4

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Answer:

To find the radius of the circle inscribed in an isosceles triangle, we can use the following formula:

r = (a/2) * cot(π/n)

where r is the radius of the inscribed circle, a is the length of one of the equal sides of the isosceles triangle, and n is the number of sides of the polygon inscribed in the circle.

In this case, we have an isosceles triangle with two sides of 5cm and one side of 6cm. Since the triangle is isosceles, the angle opposite the 6cm side is bisected by the altitude and therefore, the two smaller angles are congruent. Let x be the measure of one of these angles. Using the Law of Cosines, we can solve for x:

6^2 = 5^2 + 5^2 - 2(5)(5)cos(x)

36 = 50 - 50cos(x)

cos(x) = (50 - 36)/50

cos(x) = 0.28

x = cos^-1(0.28) ≈ 73.7°

Since the isosceles triangle has two equal sides of length 5cm, we can divide the triangle into two congruent right triangles by drawing an altitude from the vertex opposite the 6cm side to the midpoint of the 6cm side. The length of this altitude can be found using the Pythagorean theorem:

(5/2)^2 + h^2 = 5^2

25/4 + h^2 = 25

h^2 = 75/4

h = sqrt(75)/2 = (5/2)sqrt(3)

Now we can find the radius of the inscribed circle using the formula:

r = (a/2) * cot(π/n)

where a = 5cm and n = 3 (since the circle is inscribed in a triangle, which is a 3-sided polygon). We can also use the fact that the distance from the center of the circle to the midpoint of each side of the triangle is equal to the radius of the circle. Therefore, the radius of the circle is equal to the altitude of the triangle from the vertex opposite the 6cm side:

r = (5/2) * cot(π/3) = (5/2) * sqrt(3) ≈ 2.89 cm

Therefore, the radius of the circle inscribed in the isosceles triangle with sides 5cm, 5cm, and 6cm is approximately 2.89 cm.

Answer:

d. 9x^2 + 25x + 14

Step-by-step explanation:

Formula of area of a rectangle is L * W;

L being length

W being width

x + 2 is our W

9x + 7 is our L, thus;

(x+2)(9x+7)

[9x^2 + 25x + 14]

The calculated ratio for the sine the angle A has its value to be 8/17

The ratio for sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right triangle.

This ratio is commonly denoted as sin(θ), where θ is the angle of interest.

Mathematically, we can express this as:

sin(θ) = opposite / hypotenuse

Using the above, we have

opposite = 8

hypotenuse = 17

So, we have

sin(A) = 8/17

Hence, the ratio is 8/17

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(9) The slope of a line perpendicular to the line, f(x) = 0.75x + 6 is - 4/3.

(10) The slope of a line parallel to this line, y = 10 -8x is -8.

The slope of a line perpendicular to the line is the negative reciprocal of the slope of the line equation.

Question 9.

f(x) = 0.75x + 6

where;

The slope of a line perpendicular to this line = -1/0.75 = -100/75 = -4/3

Question 10.

For the equation of another line, y = 10 - 8x

The slope of a line parallel to this line is equal to the slope of this line and it is calculated as follows;

y = 10 - 8x

where;

slope of a line parallel to the line = -8

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The absolute value function as a piecewise function f(x) = |- x² - 8x - 7| is

f(x) = { - (x² + 8x + 7) , x ≤ -7 or x ≥ -1    

        { x² + 8x + 7 , -7 < x < -1

What is meant by absolute value?

Absolute value is a mathematical function that gives the distance of a number from zero on a number line. It is denoted by two vertical bars enclosing the number and always returns a non-negative value.

What is meant by piecewise function?

A piecewise function is a function that is defined by different expressions or rules on different parts or intervals of its domain. The domain is divided into pieces, and each piece has its own expression or rule.

According to the given information

When x² + 8x + 7 ≥ 0, we have:

f(x) = |-(x² + 8x + 7)| = -(x² + 8x + 7)

When x² + 8x + 7 < 0, we have:

f(x) = |x² + 8x + 7| = x² + 8x + 7

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Answer:

\( \frac{\pi}{4} = 45° \\ \\ \frac{\pi}{6} = 30°\)

\(( \cos( \frac{\pi}{4} ) + \sin( \frac{\pi}{6} ) ) ^{2} \\ \\ \\ {( \cos(45°) + \sin(30°) ) }^{2} \\ \\ \\ ( \frac{1}{ \sqrt{2} } + \frac{1}{2} ) ^{2} \\ \\ \\ (( \frac{1}{ \sqrt{2}} \times \frac{ \sqrt{2} }{ \sqrt{2}} ) + \frac{1}{2} )^{2} \\ \\ ( \frac{ \sqrt{2} }{2} + \frac{1}{2} )^{2} \\ \\ {( \frac{ \sqrt{2} + 1}{2} })^{2} \\ \\ \frac{( \sqrt{2} + 1)( \sqrt{2} + 1)}{ {2}^{2} } \\ \\ \\ \frac{2 + \sqrt{2} + \sqrt{2} + 1}{4} \\ \\ \\ = \frac{3 + 2 \sqrt{2} }{4} \\ \\ \\ = \frac{3 + 2(1.414)}{4} \\ \\ = \frac{3 + 2.828}{4} \\ \\ = \frac{5.828}{4} \\ \\ = 1.457\)

I hope I helped you^_^

Answer:

x<-12 or x>16

Step-by-step explanation:

Answer:

|x - 2| + 3 > 17

|x - 2| > 14

x - 2 < -14 or x - 2 > 14

x < -12 or x > 16

Answer:

720 (If you are counting 10% of 820, not 10% of 100)

Y = 800(1 - 0.1)

Y = 800(0.9)

Y = 720

Answer: \(720\)

Step-by-step explanation:

\(800-10%\)%

\(Y = 800(0.9)\)

Answer:

65000 is the right answer, hope it helps ^w^

To support her discussion, it would be best for Alex to use Graph A for her presentation. Alex should use this graph for her presentation because the number of faulty products appears to decrease less on this graph.

In Mathematics and Geometry, a steeper slope simply means that the slope of a line is bigger than the slope of another line. This ultimately implies that, a graph with a steeper slope has a greater (faster) rate of change in comparison with another graph.

In order to determine an equation with a declining line, we would have to determine the slope of each line graphically and then taking note of the line with a negative rate of change (slope) because it indicates a decreasing function.

In this context, we can reasonably infer and logically deduce that Graph A is more suited for Alex's presentation because the number of faulty products appears to decrease less on it.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

x^2 - 22

Step-by-step explanation:

Answer:

x^2 - 13x + 22

Step-by-step explanation:

( x - 2 ) ( x - 11)

Start off with the first variable which is the “x”

Then multiply it by the variables in the other binomial

x * x = x^2

x * - 11 = -11x

Then take the -2 and do the same thing

-2 * x = -2x

-2 * -11 = 22

Now the the formula that you would have is: x^2 - 11x - 2x + 22

Simplify and your answer is:

x^2 - 13x + 22

Reflex angle

Step-by-step explanation:

Reflex angle is more then 180 and less then 360

Answer:

yes buddy ans is reflex angle

Answer:

the dimensions are 3 sq in x 12 sq in

Step-by-step explanation:

12 divided by 3 is four (like the question said four times the width)

and then 3 times 12 is 36 sq in

sq in = square inches