Someone please help me with this question

Answer:

slope is 4

Step-by-step explanation:

Slope is rise/run

for every 4 units it rises it runs 1 unit

4/1=4

We conclude that the exponential function is:

f(x) = -1*(2)ˣ

Here we know that we have an exponential function of the form:

f(x) = a*b^x

And we know two points on the function, that are:

f(1) = -2 = a*b^1 = a*b

f(2) = -4 = a*b^2

Then we have a system of equations to solve, which is:

-2 = a*b

-4 = a*b^2

From the first equation we can solve:

-2/a = b

Replacing that in the other equation we can get:

-4 = a*(-2/a)^2 = 4/a

a = 4/-4 = -1

Now that we know the value of a, we can get the value of b:

-2/a = b

-2/-1 = 2 = b

In this way, we conclude that the exponential function is:

[tex]f(x) = -1*(2)^x[/tex]

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Using a trigonometric identity, and considering that the angle is in the fourth quadrant, the tangent of the angle is given as follows:

tan(theta) = -1/4

The following identity is used to relate the measures, considering an angle [tex]\theta[/tex]:

[tex]\sin^2{\theta} + \cos^2{\theta} = 1[/tex]

For this problem, the sine is given as follows:

[tex]\sin{\theta} = -\frac{1}{\sqrt{17}}[/tex]

Then the cosine, which we need to find the tangent, is found as follows:

[tex]\sin^2{\theta} + \cos^2{\theta} = 1[/tex]

[tex]\left(-\frac{1}{\sqrt{17}}\right)^2 + \cos^2{\theta} = 1[/tex]

[tex]\frac{1}{17} + \cos^2{\theta} = 1[/tex]

[tex]\cos^2{\theta} = \frac{16}{17}[/tex]

[tex]\cos{\theta} = \pm \sqrt{\frac{16}{17}}[/tex]

Since the angle is in the fourth quadrant, the cosine is positive, hence:

[tex]\cos{\theta} = \frac{4}{\sqrt{17}}[/tex]

It is the sine of the angle divided by the cosine of the angle, hence:

[tex]\tan{\theta} = \frac{\sin{\theta}}{\cos{\theta}} = \frac{-\frac{1}{\sqrt{17}}}{\frac{4}{\sqrt{17}}} = -\frac{1}{4}[/tex]

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[tex]\bold{Answer:} \small\boxed{21e-42}[/tex]

Step-by-step explanation:

 [tex]To\ solve\ : \ 9e-6(-2e+7)[/tex]

we first must use the distributive property. You can think about solving this like this:

[tex]=9e-(6)(-2e+7)[/tex]

Notice how we are not distributing -6, but only 6. Now we can solve normally:

[tex]=9e-(-12e+42)[/tex]

Now we distribute the '-' sign to the terms in parenthesis.

[tex]=9e+12e-42[/tex]

[tex]\longrightarrow \large\boxed{21e-42}[/tex]

The decimal form is 15.08 rounded.

The given geometric sequence has the common ratio, r = -2/3, and the value of the 4th term, a₄ = -8/3.

A geometric sequence is a special series where every term is the product of the previous term and a common ratio.

The first term of a geometric sequence is represented as a, the common ratio as r, and the n-th term as aₙ, which is calculated as, aₙ = a.rⁿ⁻¹.

In the question, we are asked to find the common ratio and the 4th term of the geometric sequence, 9, -6, 4, ........

The first term of the sequence, a = 9.

The second term of the sequence, a₂ = -6.

By the formula of the n-th term, aₙ = a.rⁿ⁻¹, we can show that:

a₂ = a.r²⁻¹.

Substituting the values, we get:

-6 = 9(r²⁻¹),

or, r²⁻¹ = -6/9,

or, r = -2/3.

Thus, the common ratio of the given geometric sequence is -2/3.

The 4th term can be calculated using the formula of the n-th term, aₙ = a.rⁿ⁻¹ as:

a₄ = a.r⁴⁻¹ = a.r³.

Substituting the values, we get:

a₄ = 9(-2/3)³,

or, a₄ = 9.(-8/27),

or, a₄ = -8/3.

Thus, the 4th term of the given geometric sequence is -8/3.

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The value of x in the equation (43/7 ÷ x + 32/9) ÷ 25/6 = 4/3 is 43/14

The equation is given as:

(43/7 ÷ x + 32/9) ÷ 25/6 = 4/3

Rewrite as a product

(43/7 ÷ x + 32/9) x 6/25 = 4/3

Multiply both sides of the equation by 25/6

(43/7 ÷ x + 32/9)= 4/3 x 25/6

Evaluate the product

(43/7 ÷ x + 32/9)= 50/9

Rewrite the equation as:

43/7x + 32/9= 50/9

Subtract 32/9 from both sides

43/7x = 2

Multiply both sides by 7x

14x = 43

Divide by 14

x =43/14

Hence, the value of x in the equation (43/7 ÷ x + 32/9) ÷ 25/6 = 4/3 is 43/14

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The total number of eggs needed for b batches is n = 3b

The total number of eggs needed for 6 batches is 18.

Multiplication is one of the basic mathematical operation that is used to determine the product of two or more numbers. The sign used to denote multiplication is x. Other mathematical operations include addition, subtraction and division.

In order to determine the total number of eggs needed, multiply the number of eggs needed for one batch by the total number of batches.

Total eggs needed = eggs needed for one batch x total number of batches

n = 3 x b

n = 3b

6 x 3 = 18

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The statements which are correct about the equation of circle [tex]x^{2} +y^{2}-2x-8=0[/tex] are 1) The radius of the circle is 3 units,2) The center of the circle lies on the x axis,5) The radius of this circle is the same the radius of the circle whose equation is [tex]x^{2} +y^{2} =9[/tex].

Given the equation of circle be [tex]x^{2} +y^{2}-2x-8=0[/tex].

We are required to find the appropriate statements related to the equation [tex]x^{2} +y^{2}-2x-8=0[/tex].

[tex]x^{2} +y^{2}-2x-8=0[/tex] can be written as under:

[tex]x^{2} +y^{2} -2x+1-9=0[/tex]

[tex]x^{2} +1^{2}-2x+y^{2} -9=0[/tex]

[tex](x-1)^{2}+y^{2}[/tex]-9=0

[tex](x-1)^{2} +y^{2} =9[/tex]

[tex](x-1)^{2}+y^{2} =3^{2}[/tex]

Equation of a circle usually in the form [tex]x^{2} +y^{2} =a^{2}[/tex] in which a is radius.

From the comparison of both the equations we get that radius is 3 units.

From the equation point will be (1,0). It is on the x axis.

Hence the statements which are correct about the equation of circle [tex]x^{2} +y^{2}-2x-8=0[/tex] are 1) The radius of the circle is 3 units,2) The center of the circle lies on the x axis,5) The radius of this circle is the same the radius of the circle whose equation is [tex]x^{2} +y^{2} =9[/tex].

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Answer: 1,2,5 on edge

Step-by-step explanation:
see above ans for work

We conclude that the width of the rectangular garden is 80 feet.

Let's define the variables:

The perimeter of a rectangle of length L and width W is given by the simple formula:

P = 2*(L + W)

The perimeter is equal to 400ft, then:

400ft = 2*(L + W)

And we know that the length is 120ft, then:

L = 120ft.

Replacing the length in the perimeter equation we get:

400ft = 2*(120ft + W)

Now we can solve this linear equation for W.

400ft/2 = 120ft + W

200ft = 120ft + W

200ft - 120ft = W

80ft = W

We conclude that the width of the rectangular garden is 80 feet.

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sorry its a little messy!! not good at drawing with a finger haha. all you need to do is follow pedmas and isolate, knowing that a right angle=90°. hope this helps!<3<3

Answer: [tex]\Large\boxed{x=12}[/tex]

Step-by-step explanation:

Given information

∠1 = x + 42°

∠2 = 3x°

Total Angle = 90° (Right Angle)

Derived formula from the given information

∠1 + ∠2 = Total Angle

Substitute values into the given formula

(x + 42) + (3x) = (90)

Combine like terms

x + 3x + 42 = 90

4x + 42 = 90

Subtract 42 on both sides

4x + 42 - 42 = 90 - 42

4x = 48

Divide 4 on both sides

4x / 4 = 48 / 4

[tex]\Large\boxed{x=12}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

The possible values of y are 9n where n is an integer greater than 0 equal to 0

The statement is given as;

y is a multiple of 9

The above means that

The number y can be divided by 9 without remainder

The numbers in this category are:

Numbers = 9, 18, 27, 36, 45......

This can be rewritten as:

Numbers = 9n where n is an integer greater than 0 equal to 0

Hence, the possible values of y are 9n where n is an integer greater than 0 equal to 0

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Step-by-step explanation:

1 meter = 1000 mm

the area of 1.6 m² means the side length of the square is

sqrt(1.6) = 1.264911064... m = 1,264.911064... mm

to create a square out of the rectangular pattern he needs to put e.g. 42 patterns along the 45 mm side and stack 45 patterns on top of the 42 mm side.

the minimum number of needed patterns we get via the last common multiple (LCM) of 42 and 45.

for this we use the prime factorization :

45 ÷ 2 no

45 ÷ 3 = 15

15 ÷ 3 = 5

5 ÷ 3 no

5 ÷ 5 = 1

45 = 3² × 5¹

42 ÷ 2 = 21

21 ÷ 2 no

21 ÷ 3 = 7

7 ÷ 3 no

7 ÷ 5 no

7 ÷ 7 = 1

42 = 2¹ × 3¹ × 7¹

the LCM is the product of the longest streaks of each used prime factor.

LCM(42, 45) = 2¹ × 3² × 5¹ × 7¹ = 2×9×5×7 = 630

(i) he needs 210 patterns to form the smallest square.

this will be

14×45 mm on one side = 630 mm

15×42 mm on the other side = 630 mm

14×15 = 210 patterns.

(ii)

the limit per side length is as established

1,264.911064... mm

starting with the minimum of 630 mm how often can we add 42 mm in one direction and 45 mm in the other, and keep a 15 : 14 ratio between these numbers ?

and we need integer numbers, as we cannot use parts of the patterns (only full patterns).

45 × x <= 1264

x <= 1264/45 = 28.08888888... = integer 28

42 × y <= 1264

y <= 1264/42 = 30.0952381... = integer 30

30/28 = 15/14

so, the ratio is maintained for these numbers.

that means as maximum we can put

30×28 = 840 patterns as square inside the max. allowed area.

the dimensions of this max. square are therefore

30×42 = 1260 mm

28×45 = 1260 mm

the area of this square is then

1260mm × 1260 mm = 1,587,600 mm² = 1.5876 m²

The probability of occurrence for the events A, B and C is; 1/4.

For the first event A in which case, there's no odd number on the first two rolls, the possible events are; EEE and EEO. Consequently, the required probability is;

Event A = 2/8 = 1/4.

For the event B in which case, there's an even number on both the first and last rolls; the possible events are; EEE and EOE. Consequently, the required probability is;

Event B = 2/8 = 1/4.

For the event C in which case, there's an odd number on each of the first two rolls; the possible events are; OOO and OOE. Consequently, the required probability is;

Event C = 2/8 = 1/4.

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Let the function be (3x+15)/(6-x) then the value of x exists at -5.

Given: Rational Expression (3x+15)/(6-x)

To find the value of x when given a rational expression equivalent to 0.

To estimate the value of x, convey the variable to the left side and convey all the remaining values to the right side. Simplify the values to estimate the result.

Consider, (3x+15)/(6-x) = 0

3x + 15 = 0(6-x)

3x + 15 = 0

Subtract 15 from both sides of the equation, e get

3x + 15 - 15 = 0 - 15

simplifying the above equation, we get

3x = 0 - 15

3x = -15

Divide both sides by 3, then we get

x/3 = -15/3

x = -5

Therefore, the value of x exists at -5.

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Answer:

0.6 km/hr

Step-by-step explanation:

Speed downstream: 13/5= 2.6 km/hr

Speed upstream: 7/5= 1.4 km/hr

Therefore, Velocity of current is: 1/2 (2.6-1.4) km/hr = 1/2(1.2) km/hr

Answer:4 1/12.

Step-by-step explanation: First, you add 3 and a half with a quarter. A half equals two quarters so it equals 3 and 3/4.  Then, you add 3 3/4 with 1/3. A common denominator here is 12. 3/4 times 3/3 = 9/12. 1/3 times 4/4 = 4/12. 9+4 = 13. The answer is more than one so we carry and get 4 and 1/12.

If four books are 100%, then 3 books are how much percent of total books?

[tex]\frac{3}{4}[/tex] × 100 = 3 × 25 = 75%

Hope it helps!

The answer is 75%.

To find the percentage, divide the number of given books by total books and multiply by 100%.

Assuming you mean

[tex]\displaystyle \sum_{i=0}^n {}_nC_{i}[/tex]

where

[tex]{}_n C_i = \dbinom ni = \dfrac{n!}{i! (n-i)!}[/tex]

we have by the binomial theorem

[tex]\displaystyle (1 + 1)^n = \sum_{i=0}^n {}_nC_{i} \cdot 1^i \cdot 1^{n-i}[/tex]

so that the given sum has a value of [tex]\boxed{2^n}[/tex].

40+1 in dollars per hour

Answer:

2400

Step-by-step explanation:

40 = 2^3 * 5

120 = 2^5 * 5

150 = 2 * 3 * 5^2

LCM = 2^5 * 3 * 5^2

Answer:  0

Step-by-step explanation:

Answer:  10

Step-by-step explanation: 800/80 = 10

Answer: -6

Step-by-step explanation:

[tex]x+3y=-5\\\\3y=-x-5\\\\y=-\frac{1}{3}x-\frac{5}{3}[/tex]

So, since parallel lines have the same slope, the slope of the line we need to find is -1/3.

Substituting into point-slope form, the equation is

[tex]y-2=-\frac{1}{3}(x+7)\\[/tex]

Converting to the required form,

[tex]y-2=-\frac{1}[3}x-\frac{7}{3}\\\\\frac{1}{3}x+y=-\frac{1}{3}\\\\-3x-9y=3[/tex]

So, B-A is equal to -6.

If [tex]$&f(x)=\frac{19}{x^{2}} \\[/tex] then the inverse function exists  [tex]$&f^{-1}(x)=\sqrt{\frac{19}{x}}[/tex].

An inverse function in mathematics exists function which "reverses" the another function.

Let f(x) = y, then the inverse function, [tex]$x=f^{-1}(y)$[/tex]

[tex]$&f(x)=\frac{19}{x^{2}} \\[/tex]

[tex]$&y=\frac{19}{x^{2}} \\[/tex]

[tex]$&x^{2}=\frac{19}{y} \\[/tex]

simplifying the equation, we get

[tex]$&x=\sqrt{\frac{19}{y}} \\[/tex]

[tex]$&x^{-1}=f^{-1}(y)=\sqrt{\frac{19}{y}} \\[/tex]

[tex]$&f^{-1}(y)=\sqrt{\frac{19}{y}},[/tex]  then [tex]$&f^{-1}(x)=\sqrt{\frac{19}{x}}[/tex].

If [tex]$&f(x)=\frac{19}{x^{2}} \\[/tex] then the inverse function exists  [tex]$&f^{-1}(x)=\sqrt{\frac{19}{x}}[/tex].

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Answer:

[tex]\lim_{x\rightarrow +\infty } x-1+\frac{1+ln^{2}x}{x} = + \infty[/tex]

[tex]\lim_{x\rightarrow 0 } x-1+\frac{1+ln^{2}x}{x} = + \infty[/tex]

Step-by-step explanation:

[tex]\lim_{x\rightarrow +\infty } x-1+\frac{1+ln^{2}x}{x}[/tex]

[tex]= [\lim_{x\rightarrow +\infty } (x-1)]+[ \lim_{x\rightarrow +\infty } (\frac{1+ln^{2}x}{x})][/tex]

=          +∞             +          0

= +∞

[tex]\lim_{x\rightarrow +\infty } x-1+\frac{1+ln^{2}x}{x}[/tex]

[tex]= [\lim_{x\rightarrow 0 } (x-1)]+[ \lim_{x\rightarrow 0 } (\frac{1+ln^{2}x}{x})][/tex]

=            -1             +      +∞  

= +∞  

Answer:

Square Pyramid

Step-by-step explanation:

Thats what a Square Pyramid is

After half of the men go away, the provisions will last for another 16 days.

First, we know that the garrison has provisions for 10 days.

2 days after that, the garrison has provisions for another 8 days. Here we know that the number of men on the garrison is reduced to its half. Then, the time that the provisions in the garrison will last is multiplied by 2.

So we just need to solve the product:

2*8 days = 16 days.

After half of the men go away, the provisions will last for another 16 days.

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Answer: 34.3 megabytes

Step-by-step explanation:

To find how many megabytes have been downloaded you must multiply 13.3% by 258. 13.3% can be written as the decimal 0.133

Now let's multiply

[tex]258[/tex]×[tex]0.133[/tex]=34.314

Rounded to the nearest tenth that is 34.3

Answer:

Step-by-step explanation: