What is the common difference in the sequence below? 9, 2, -5, -12, ......
Select one:
a. -5
b. -6
c. -8
d. -7

- tan = opposite/ adjacent

- tan 64 = x(the height of the ladder)/ 9ft

- 2.050= x/9ft

-x= 9ft * 2.050

- x= 18.45ft  = 18.5 ft= 19 ft

so x or the unkown height is 19 ft

Answer:

cannot understand the language man

but please follow

Answer:

80b-11

Step-by-step explanation:

14b + 1 - 6(2 - 11b)

Distribute

14b+1-12+66b

Combine like terms

80b-11

Answer:

80b - 11

Step-by-step explanation:

what is the problem ?

just multiply it out and combine terms.

14b + 1 - 6(2 - 11b) = 14b + 1 - 12 + 66b = 80b - 11

Answer:

The zeros are x=4, -2

Step-by-step explanation:

Its zeros can be found by setting the function to zero. The values of x that represent the set equation are the zeroes of the function. To find the zeros of a function, find the values of x where f(x) = 0.

Hope this helped!!!!

x = 20

y = 7

x + 3y = 41 ...equation 1

x = 2y + 6​ ....equation 2

Using the blob method: This is another word for substitution method

Using substitution method:

Substitute x in equation 2 in equation 1

(2y + 6) + 3y = 41

2y + 6 + 3y = 41

5y + 6 = 41

5y = 41 - 6

5y = 35

y = 35/5

y = 7

Substitute for y in equation 2:

x = 2(7) + 6

x = 14 + 6

x = 20

Answer:

Step-by-step explanation:

\( \frac{8 {x}^{4} }{16 {x}^{7} } \)

Reduce the fraction with 8

\( \frac{ {x}^{4} }{2 {x}^{7} } \)

Simplify the expression

\( \frac{1}{2 {x}^{3} } \)

Hope this helps...

Good luck on your assignment...

The relative change in price from 1993 to 2016 is 57.02%, which means that the price increased by 57.02%.

The real difference between two numbers is referred to as an absolute change. The absolute difference in temperature, for instance, is 5 degrees Celsius if the temperature rises from 20 to 25 degrees Celsius.

On the other hand, relative change expresses the difference between two values as a percentage of the starting point. Regardless of the values' dimensionality, it enables us to compare changes across various settings.

The relative change is given by:

Relative Change = (New Value - Old Value) / Old Value * 100%

Substituting the values we have:

Relative Change = (435 - 277) / 277 * 100%

Relative Change = 158 / 277 * 100%

Relative Change = 57.02%

Therefore, the relative change in price from 1993 to 2016 is 57.02%, which means that the price increased by 57.02%.

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The exact area of the inscribed circle is 12π square units.

A circle is a geometric shape consisting of all the points in a plane that are equidistant from a given point called the center of the circle. The distance between the center and any point on the circle is called the radius of the circle.

The radius of the inscribed circle is also the distance from the center of the hexagon to each of its sides. To find this distance, we can divide the hexagon into six equilateral triangles, each with side length 2 units. The height of each triangle is √3 times the side length, or 2√3 units. The distance from the center of the hexagon to each side is equal to this height, or 2√3 units.

Therefore, the radius of the inscribed circle is 2√3 units. The area of the circle is given by the formula A = πr², where r is the radius. Substituting in the value of the radius, we get:

A = π(2√3)² = 12π

So the exact area of the inscribed circle is 12π square units.

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Answer:

1/2 mi

Step-by-step explanation:

Fairfax to Greenwood is equal to one mile

Now think of it as an equation and substitute 1/2 for fairfax and x for greenwood

1/2 + x = 1

This means that x = 1/2

Because of this from Arcadia to Greenwood it is 1/2 mi

The probability that all 4 computers with the critical file fail in this incident

P(x=4)=0.00085

This is further explained below.

Generally,  is  mathematically given as

\($H \rightarrow(n, m)$\)

p.d.F. of Hyper Geometric distribution

given, $N=39, n=4, M=8, x=4$

\(\begin{aligned}P(x=4) &=\frac{8}{4} \frac{39}{39} \\&=\frac{70 \times 1}{82251}\end{aligned}$$\)

\(\begin{aligned}&P(x=4)=8.5106 \times 10^{-4} \\&P(x=4)=0.00085\end{aligned}\)

In conclusion, P(x=4)=0.00085

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Answer:

$125

Step-by-step explanation:

$315-$190=125

Using the Central Limit Theorem, it is found that Jackson has 8 guinea pigs.

It states that the sampling distribution of sample means of size n has standard error \(s = \frac{\sigma}{\sqrt{n}}\), in which \(\sigma\) is the standard deviation of the population.

In this problem, we have that \(s = 0.2227, \sigma = 0.63\), hence we solve for n to find the number of guinea pigs that he has.

\(s = \frac{\sigma}{\sqrt{n}}\)

\(0.2227 = \frac{0.63}{\sqrt{n}}\)

\(0.2227\sqrt{n} = 0.63\)

\(\sqrt{n} = \frac{0.63}{0.2227}\)

\((\sqrt{n})^2 = \left(\frac{0.63}{0.2227}\right)^2\)

\(n = 8\)

Jackson has 8 guinea pigs.

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Answer:

108 x 25²  divided by 2⁶ x 5² is equal to \(42\frac{3}{16}\)

Step-by-step explanation:

Given;

108 x 25²  divided by 2⁶ x 5²

The expression is simplified as follows;

\(\frac{108\times 25^2}{2^6 \times 5^2} = \frac{108\times 625}{64\times25} =\frac{675}{16} = 42\frac{3}{16}\)

Therefore, 108 x 25²  divided by 2⁶ x 5² is equal to \(42\frac{3}{16}\)

Answer:

Step-by-step explanation:

\(y=(\frac{1}{g} )x\)

Constant up a proportionally is  \(\frac{1}{g}\).

is 750.000 is your answer.

The conclusion about the composite function is that  if g(3) = 5 and f(5) = 20, then (f ∘ g)(3) = 20

The definition of the composite function is given as

(f ∘ g)(x) = f(g(x))

The above means that

We start by calculating g(x)

Here, we have

g(3) = 5

Substitute g(3) = 5 in (f ∘ g)(x) = f(g(x))

So, we have

(f ∘ g)(3) = f(g(3))

So, we have

(f ∘ g)(3) = f(5)

From the question, we have

f(5) = 20

This means that

So, we have

(f ∘ g)(3) = 20

Hence, the conclusion about the composite function is that if g(3) = 5 and f(5) = 20, then (f ∘ g)(3) = 20

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\(\large\underline{\sf{Solution-}}\)

Given that:

\(\sf p(y) = 2y^3+my^2+11y+m+3 \)

We are also given that, p(y) is divisible by 2y - 1.

So, 2y - 1 is a factor of p(y).

\(\sf\longmapsto 2y-1=0\)

\(\sf\longmapsto y=\dfrac{1}{2}\)

So, 1/2 is a zero of p(y).

\(\sf\longmapsto p(1/2) =0 \)

\(\sf\longmapsto p(y) = 2y^3+my^2+11y+m+3 \)

\(\sf\longmapsto p\left(\dfrac{1}{2}\right) = 2\left(\dfrac{1}{2}\right)^3+m\left(\dfrac{1}{2}\right)^2+11\left(\dfrac{1}{2}\right)+m+3 \)

So,

\(\sf\longmapsto p\left(\dfrac{1}{2}\right) = 2\left(\dfrac{1}{8}\right)+m\left(\dfrac{1}{4}\right)+11\left(\dfrac{1}{2}\right)+m+3 \)

\(\sf\longmapsto p\left(\dfrac{1}{2}\right) = \dfrac{1}{4}+\dfrac{m}{4}+\dfrac{11}{2}+m+3 \)

\(\sf\longmapsto p\left(\dfrac{1}{2}\right) =\dfrac{1}{4}+\dfrac{m}{4}+\dfrac{22}{4}+\dfrac{4m}{4}+\dfrac{12}{4} \)

\(\sf\longmapsto 0 =\dfrac{1+m+22+4m+12}{4} \)

\(\sf\longmapsto 0 =\dfrac{5m+35}{4}\)

\(\sf\longmapsto 5(m+7)=4\times0\)

\(\sf\longmapsto 5(m+7)=0\)

\(\sf\longmapsto m+7=0\)

\(\longmapsto\bf m=-7\)

Therefore, the value of m is -7.

During the exponential phase, e.coli bacteria in a culture increase in number at a rate proportional to the current population. If growth rate is 1.9% per minute and the current population is 172.0 million, the population 7.2 minutes from now can be calculated using the following formula:

P(t) = P ₀e^(rt)where ,P₀ = initial population r = growth rate (as a decimal) andt = time (in minutes)Substituting the given values, P₀ = 172.0 million r = 1.9% per minute = 0.019 per minute (as a decimal)t = 7.2 minutes

The population after 7.2 minutes will be:P(7.2) = 172.0 million * e^(0.019*7.2)≈ 234.0 million (rounded to the nearest tenth)Therefore, the population of e.coli bacteria 7.2 minutes from now will be approximately 234.0 million.

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Answer: why do we even need math

Step-by-step explanation:

The tip of the minute hand on a clock travels a distance of 4π inches in 15 minutes.

The distance traveled by the tip of a minute hand on a clock can be calculated using the circumference formula.

The circumference of a circle is given by the formula:

C = 2πr C is the circumference, π is pi (approximately 3.14159) and r is the radius.

The distance from the center of the clock to the tip of the minute hand is the radius is 8 centimeters.

The circumference of the circle traced by the tip of the minute hand is:

\(\text{C} = 2\pi \text{r}\)

\(= 2\pi (8)\)

\(= 16\pi \ \text{centimeters}\)

Since the minute hand travels the full circumference of the circle in 60 minutes, in 15 minutes it will cover 15/60 = 1/4 of the circumference.

The distance traveled by the tip of the minute hand in 15 minutes is:

\(\text{Distance} = \huge \text(\dfrac{1}{4}\huge \text) \times C\)

\(= \huge \text(\dfrac{1}{4}\huge \text) \times (16\pi)\)

\(= 4\pi \ \text{centimeters}\)

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Answer:

4π cm ≈ 12.6 cm

Step-by-step explanation:

The clock can be modelled as a circle, where the radius (r) is equal to the length of the minute hand:  r = 8 cm.

A clock face is divided into 12 equal sectors (numbered 1 to 12).

It takes 60 minutes for the minute hand to complete one revolution of the clock. Therefore, each sector represents the passing of 5 minutes.

This means that 15 minutes equals 3 sectors, which is a quarter of the circle.

To find the distance the tip of the minute hand travels in 15 minutes, we need to find a quarter of the circumference of a circle with radius 8 cm.

The formula for the circumference of the circle is C = 2πr, where r is the radius. Therefore, the equation to find the distance the tip of the minute hand travelled in 15 minutes is:

\(\sf Distance=\dfrac{2 \cdot \pi \cdot 8}{4}\)

Simplifying, we get:

\(\sf Distance=\dfrac{16 \cdot \pi}{4}\)

\(\sf Distance=4 \pi\)

Therefore, the minute hand will travel 4π cm or approximately 12.6 cm (to the nearest tenth) in 15 minutes.

Answer:

D : Obtuse

Step-by-step explanation:

A right angle is 90 degrees.

An acute and obtuse angle are found by looking at the angle between the sides being looked at.

If the angle is GREATER i.e. Angle > 90 , then it is obtuse.

If the angle is LESS THAN i.e. Angle < 90 , then it is acute.

This angle is apparently greater than 90 degrees and therefore is obtuse.

Answer:

I think the answer would be -8

Answer:

hrhry is g eggrhrhr dgdgeg evehrg dhheg hrhr

when the scale factor is 1, we have:

(side length of side opposite ∠A) / (length of hypotenuse) = sin A

When the scale factor is 1, the ratio of the side length of the side opposite ∠A to the length of the hypotenuse remains the same as in the original triangle. In a right triangle, the side opposite ∠A is referred to as the "opposite" side, and the hypotenuse is the longest side.

The ratio of the side length of the side opposite ∠A to the length of the hypotenuse is commonly known as the sine of angle A (sin A). So, when the scale factor is 1, the ratio of the side length of the side opposite ∠A to the length of the hypotenuse is equal to sin A.

In mathematical terms, when the scale factor is 1, we have:

(side length of side opposite ∠A) / (length of hypotenuse) = sin A

It's important to note that this ratio holds true for any right triangle, regardless of its size or dimensions, as long as the angle A remains the same.

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Answer:

25 and 18

Step-by-step explanation:

Let's say that the first number is x and the second one is y.

First, the difference between them is 7, so x-y=7

Next, the sum of their squares is 949, so x²+y² = 949

We have

x-y=7

x²+y²=949

One thing we can do to solve this problem is to solve for x in the first equation, plug that into the second equation, and go from there

Adding y to both sides in the first equation, we have

x = 7 + y

Plugging that into the second equation for x, we have

(7+y)²+ y² = 949

expand

(7+y)(7+y) + y² = 949

49 + y² + 7y + 7y + y² = 949

combine like terms

2y² +14y + 49 = 949

subtract 949 from both sides to put this in the form of a quadratic equation

2y² + 14y - 900 = 0

divide both sides by 2

y² + 7y - 450 = 0

To factor this, we want to find 2 numbers that add up to 7 and multiply to -450.

The factors of 450 are as follows:

1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, and 450.

Note that we want to find two numbers with a difference of 7, as one will have to be negative for the multiplication to end up at -450. Two numbers that stand out are 18 and 25. To make them add up to 7, 18 can be negative. We therefore have

y² + 25y - 18y - 450 = 0

y(y+25) - 18(y+25) = 0

(y-18)(y+25) = 0

Solving for 0,

y-18 = 0

add 18 to both sides

y=18

y+25 = 0

subtract 25 from both sides

y= -25

As the question states "two positive integers", this means that y must be positive, so y = 18. We know x-y=7, so

x-18 = 7

add 18 to both sides to isolate x

x = 25

The numerical value of side lengths x and y are 2 units.

The figure in the image is a right triangle which has one of its interior angle at 90 degrees.

Angle θ = 45 degree

Opposite to angle θ = x

Adjacent to angle θ = y

Hypotenuse = 2√2

To solve for side x and side y, we use the trigonometric ratio.

Note that:

Sine = opposite / hypotenuse

Cosine = adjacent / hypotenuse

Solve for x:

Sine = opposite / hypotenuse

Plug in the values:

sin( 45 ) = x / 2√2

Cross multiply:

x = sin( 45 ) × 2√2

x = 2

Next, we solve for side y:

Cosine = adjacent / hypotenuse

Plug in the values:

cos( 45 ) = y /  2√2

Cross multiply:

y = cos( 45 ) × 2√2

y = 2

Therefore, the value of y is 2.

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The ratios of ounces of water and fruits for different servings are:

1 serving = 3/4

2 servings = 6/8

3 servings = 9/12

4 servings = 12/16

5 servings = 15/20

A ratio is an ordered pair of numbers a and b.

It is written as:

a / b

where b does not equal 0.

A proportion is an equation in which two ratios are set equal to each other.

We have,

In one serving:

= 3/4

The ratio of ounces of water to the ounces of fruit is 3/4.

In every number of servings, the ratios must be in proportion so,

We have the following cases:

2 servings:

= 3x2 / 4x2

= 6/8

3 servings:

= 3x3 / 4x3

= 9/12

4 servings:

= 3x4 / 4x4

= 12/16

5 servings:

= 3x5 / 4x5

= 15 / 20

Thus the ratios of ounces of water and fruits for different servings are:

1 serving = 3/4

2 servings = 6/8

3 servings = 9/12

4 servings = 12/16

5 servings = 15/20

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