A single Rhinovirus is 2 × 10-8 meters long, and a single E. coli bacterium is 2 × 10-6 meters long. How many times larger is an E. coli bacterium than a Rhinovirus?

Answer:

x=y/4 + 4

Step-by-step explanation:

y=4x-16

-need to isolate x

add 16 to both sides.

y+16=4x

divide by 4 on both sides.

y/4 + 4 = x

Answer: [tex]y=\frac{1}{3}x+3[/tex]

Step-by-step explanation:

The equation of the line is Slope-intercept form is:

[tex]y=mx+b[/tex]

Where "m" is the slope and "b" the y-intercept.

The slopes of perpendicular lines are negative reciprocal.

Then, if the slope of the first line is -3, the slope of the other line must be:

[tex]m=\frac{1}{3}[/tex]

Substitute the point (3,4) into the equation and solve for b:

[tex]4=\frac{1}{3}(3)+b\\ 4-1=b\\b=3[/tex]

Then the equation of this line is:

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

ANSWER

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

EXPLANATION

We want to find the equation of a line which is perpendicular to another line with slope -3 and passes through (3,4).

Our line of interest is has a slope that is the negative reciprocal of -3

[tex]m = - \frac{1}{ - 3} = \frac{1}{3} [/tex]

The equation is given by

[tex]y-y_1=m(x-x_1)[/tex]

We substitute the point and slope to get:

[tex]y-4= \frac{1}{3} (x-3)[/tex]

Expand

[tex]y-4= \frac{1}{3} x-1[/tex]

[tex]y= \frac{1}{3} x-1 + 4[/tex]

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

Answer:

[tex]A(t)=A_{0}e^{\frac{ln(\frac{1}{2})}{22}t}[/tex]

Step-by-step explanation:

This half life exponential decay equation goes by the formula:

[tex]A(t)=A_{0}e^{kt}[/tex]

Where

[tex]k=\frac{ln(\frac{1}{2})}{Half-Life}[/tex]

Since half life is given as 22, we plug that into "Half-Life" in the formula for k and then plug in the formula for k into the exponential decay formula:

So,

[tex]k=\frac{ln(\frac{1}{2})}{Half-Life}\\k=\frac{ln(\frac{1}{2})}{22}[/tex]

Now

[tex]A(t)=A_{0}e^{\frac{ln(\frac{1}{2})}{22}t}[/tex]

third choice is correct.

Answer:

415

Step-by-step explanation:

the nth term of the sequence is -13 + 4n

the sequence is an arithmetic progression with nth term a + (n - 1)d

a = -9, d = a5- a4 = 7 -3 =4

nth = -9 + (n -1) 4

       = -9 + 4n -4

       = -13 + 4n

hence the 107th term; -13 + 4*107

                                      -13 + 428 = 415

X=3.6

See the attached photo

Without specific diagram or context, this answer is based on the relationship between tangent lines and circles. The angle between a tangent and a radius of a circle is always 90 degrees. Understanding this along with the Pythagorean theorem and trigonometric ratios will help solve for 'x'.

Based on the information provided, it seems the question is related to circular geometry, however, we need more specific information to solve your problem such as a diagram or more context. However, if we consider that we're dealing with a tangent and a radius of a circle, it's important to know that the angle between a tangent and a radius of a circle is always 90 degrees. So, if we have an angle opposite a 90-degree angle in a right triangle, we could use tangent properties, Pythagorean theorem, or trigonometric ratios to solve for 'x'

For example, in a right triangle, tangent of an angle is equal to the opposite side length divided by the adjacent side length (tan(θ) = opposite/adjacent). Also, the Pythagorean theorem tells us that the square of the hypotenuse (radius) is equal to the sum of the squares of the other two sides (c² = a² + b²).

Those concepts and formulas are key to understanding the intersection between lines and circles, and they should assist you in solving queries closely related to this problem.

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Answer:

Step-by-step explanation:

The sine of any acute angle is equal to the cosine of its complement. The cosine of any acute angle is equal to the sine of its complement. of any acute angle equals its cofunction of the angle's complement. Yes, there is a "relationship" regarding the tangent of the two acute angles (A and B) in a right triangle.

hope this helps u

Answer:

answer: 1

Step-by-step explanation:

using pemdas you would first go into the parenthesis and multiply 2 by 2 the subtract that from three giving you -1. then, you would multiply that by 1 and add that to 2.

Answer:

A

Step-by-step explanation:

6 3/4 + 9 1/2 = 65/4

26 2/5 - 65/4 = 203/20 or 10 3/20

Answer:

1 and 4

Step-by-step explanation:

[tex]\bf slope = m = \cfrac{rise}{run} \implies \cfrac{ f(x_2) - f(x_1)}{ x_2 - x_1}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array}\\\\[-0.35em] \rule{31em}{0.25pt}\\\\ h(x)= 2x^2\qquad 2\leqslant x \leqslant 4 \qquad \begin{cases} x_1=2\\ x_2=4 \end{cases}\implies \cfrac{h(4)-h(2)}{4-2} \\\\\\ \cfrac{2(4)^2~~-~~2(2)^2}{2}\implies \cfrac{32-8}{2}\implies \cfrac{24}{2}\implies 12[/tex]

Answer:

The center is (-3,2) and the radius is r=2

Step-by-step explanation:

The general equation of the given circle is

[tex]x^2+6x+y^2-4y=-9[/tex]

Add the square of half the coefficient of the linear terms to both sides of the equation to obtain;

[tex]x^2+6x+3^2+y^2-4y+(-2)^2=-9+3^2+(-2)^2[/tex]

[tex]x^2+6x+9+y^2-4y+4=-9+9+4[/tex]

[tex]x^2+6x+9+y^2-4y+4=4[/tex]

The quadratic trinomials in x and y on the left side of the equations are perfect squares.

We factor to obtain;

[tex](x+3)^2+(y-2)^2=4[/tex]

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

Comparing to:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

The center is (-3,2) and the radius is r=2

To complete the square and put the equation into graphing form, group x's and y's, add appropriate constants to each group, and rewrite. The circle's equation becomes (x + 3)² + (y - 2)² = 4, with the center at (-3, 2) and a radius of 2.

To complete the square for the equation x² + 6x + y² - 4y = -9 and convert it to graphing form, we need to group the x's and y's together and add the right constants to each group.

Now, the equation is in the graphing form of a circle ((x-h)² + (y-k)² = r²), where (h, k) is the center and r is the radius. Hence, the circle's center is at (-3, 2) and its radius is 2.

Answer:

210

Step-by-step explanation:

Divide 120 by 4 and get 30 and multiply 7 by 30 and you get 210

Final answer:

To dilute 120 cl of orange squash with a ratio of 7:4 (water to squash), you need 210 cl of water. The total mixture will be 330 cl (7+4 parts), of which 120 cl is the squash and the remainder is water.

Explanation:

The student is asking how much water is needed to dilute 120 cl of orange squash if the mixture ratio of water to orange squash is 7:4. To solve this, you need to work with ratios.

First, add the parts of the ratio together: 7 (water) + 4 (orange squash) = 11 parts in total. Now, find out how many parts of the total mixture the 120 cl of orange squash represents. Since the ratio of orange squash is 4 parts, this means that 120 cl is 4 parts of the total mixture.

We can then set up the proportion: 4 parts / 11 parts total = 120 cl / total mixture in cl. Solving for the total mixture gives us: 11 parts * 120 cl / 4 parts = 330 cl.

Finally, to find out how much water is needed, subtract the volume of orange squash from the total mixture volume: 330 cl - 120 cl = 210 cl of water.

The answer is -4/7 or in decimal it’s -0571429

Answer:

∠B

∠Y

Step-by-step explanation:

we know that

In the right triangle ABC

[tex]tan(B)=\frac{AC}{BC}[/tex] ----> opposite side to angle B divided by the adjacent side to angle B

substitute the values

[tex]tan(B)=\frac{3}{4}[/tex]

Remember that

If two triangles are similar, then the corresponding sides are proportional and the corresponding angles are congruent

so

∠A=∠W

∠B=∠Y

∠C=∠Z

therefore

[tex]tan(B)=tan(Y)[/tex]

Base on the fact that the triangle ABC and WYZ are similar, the angles whose tangent equals 3 / 4 are ∠B and ∠Y

Similar triangle are only different in sizes but are of the same shape.

Similar triangles, corresponding sides are always in the same ratio. Corresponding angles of similar triangles are always congruent. Therefore,

∠A = ∠W

∠B = ∠Y

∠C = ∠Z

Therefore, let's find all angles in the similar triangles whose tangent is equal to 3 / 4 .

tan ∅ = opposite / adjacent

Since,

tan B = 3 / 4

Then

tan Y = 3 / 4

Therefore,

The angles whose tangent equals 3 / 4 are ∠B and ∠Y

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Answer:

i think its C

Step-by-step explanation:

Final answer:

To solve the triangle with sides a=26, b=29, and angle A=58 degrees, apply the Law of Sines to find another angle, use the sum of angles to find the third angle, and then the Law of Cosines to find the remaining side, ensuring all conditions are satisfied for a valid triangle.

Explanation:

To find all solutions for a triangle given a=26, b=29, and A=58 degrees, we use the Law of Sines, which relates the lengths of sides to the sine of their opposite angles. Since sin A > sin a (opposite side to angle A) would result in no solution and considering the given values, we don't encounter this issue. Instead, we have:

sin B / b = sin A / a

Rearranging for B, we have:

B = sin⁻¹(sin A / a × b)

Plugging in our numbers:

B = sin⁻¹((sin 58°) / 26 × 29)

Once B is calculated, we can find angle C since the interior angles of a triangle sum to 180 degrees. Following that, we can use the Law of Cosines to find the third side, c. The process is:

After finding all angles and sides, verify the solution by checking if the interior angles sum to 180 degrees and the sides satisfy the Triangle Inequality Theorem.

For this case we have the following equation:

[tex]x + 1 = \frac {2} {x + 1}[/tex]

We must find the value of [tex]x + 1[/tex]:

Multiplying both sides of the equation by[tex]x + 1:[/tex]

[tex](x + 1) ^ 2 = 2[/tex]

Applying square root on both sides of the equation to eliminate the exponent:

[tex]x + 1 = \sqrt {2}[/tex]

Answer:

Option B

Answer: B

Step-by-step explanation:

it’s 321 because whether negative or positive it’s absolute value

1 minus 321 is -320. Since you’re finding the absolute value it’s 320

the answer is 40% hope this helps

Answer:

Aproximately 40% is the correct option)))

Answer:

x ≈ 78.7° (in degree)

x ≈ 1.4      (in radians)

Step-by-step explanation:

Given in the question an equation

tan(x) = 5

       x =  [tex]tan^{1}(5)[/tex]

       x = 78.69

       x ≈ 78.7°

In radian:

x ≈ 1.4

Answer:

The correct answer is x = 78.7°

Step-by-step explanation:

It is given that,

Tan x = 5

To find the value of x

If tan ∅ = x then ∅ = tan⁻¹ x =

Here  we have tan x = 5

x =  tan⁻¹ 5 = 78.69 ≈ 78.7°

Therefore the value of x = 78.7°

The correct answer is 78.7°

Answer: Option B

Step-by-step explanation:

By definition, the ratio is a comparison between two different things. It can be written in:

Odd notation

[tex]a:b[/tex]

Fractional notation

[tex]\frac{a}{b}[/tex]

Or in words:

[tex]a\ to\ b[/tex]

Given the ratio 3 to 4 and the ratio of 4 to 3, you can rewrite them the fractional form:

[tex]\frac{3}{4}\\\\\frac{4}{3}[/tex]

To know if these ratios are the same number, divide the numerator by the denominator of each one of them:

 [tex]\frac{3}{4}=0.75\\\\\frac{4}{3}=1.33[/tex]

Therefore, the ratio of 3 to 4 and the ratio of 4 to 3 ARE NOT the same number.

Answer:

1 centimeter = 10 millimeters  

Step-by-step explanation:

we have to find about how many millimeters are in a centimeter.

We know that  1 centimeter = 10 millimeters

or 10 millimeters  = 1 centimeter

divide both sides by 10

or \frac{10}{10} millimeters  = \frac{1}{10} centimeter

or 1 millimeters  = 0.1 centimeter

But we need millimeters  in centimeters so we should write :

final answer as 1 centimeter = 10 millimeters.

[tex]\boxed{x^2=4py}[/tex]

A parabola is the set of all points that lies on a plane and are equidistant from  a fixed line called the directrix and a fixed point called focus, that doesn't lies on the line. If the  vertex is at the origin and the directrix crosses the negative part of the y-axis, then the equation takes the following forms:

[tex]\boxed{x^2=4py}[/tex]

Where the focus lies on the axis [tex]p \units[/tex] (directed distance) from the vertex.

The representation of this problem is shown below. As you can see, the vertex lies on the origin while the directrix crosses the negative part of the y-axis.

Answer:

The actually answer is x(2) = 4y

Answer:

1800

Step-by-step explanation:

850*4=1800

Answer:

212.5 lb

Step-by-step explanation:

850 students × 4oz/student = 3400 oz

There are 16 ounces in a pound, so:

3400 oz × (1 lb / 16 oz) = 212.5 lb

For this case we have that the parts of a division are:

Dividend, divisor, quotient and remainder.

To make the division of polynomials, we must build a quotient that when multiplied by the divisor (and when the sign is changed), eliminate the terms of the dividend until reaching the remainder of the division.

It must be fulfilled that:

[tex]Dividend = Quotient * Divider + Remainder[/tex]

Then, if we look at the attached figure, the quotient is:

[tex]x ^ 2-2x-3[/tex]

Answer:

[tex]x ^ 2-2x-3[/tex]

Answer:

C:  f(x) = (x - 13)(x + 11)

Step-by-step explanation:

Please use " ^ " to indicate exponentiation:  y = x^2 – 2x – 143.

x^2 – 2x – 143 factors into (x - 13)(x + 11).  Note that -13x + 11x = -2x, which matches the middle term of the given function.

Thus, the zeros are {-11, 13}

Answer C is correct:  f(x) = (x - 13)(x + 11).

In factored form, the function is y = (x – 13)(x + 11), so the zeros of the function are x = 13 and x = –11. Option C is correct.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Given function,
y = x² – 2x – 143

y = x² -13x + 11x - 143
y = (x - 13)(x + 11)

Let,
y = 0
(x - 13)(x  + 11) = 0
Now,
zeros is given as,
x = 13 and x = -11

Thus, in factored form, the function is y = (x – 13)(x + 11), so the zeros of the function are x = 13 and x = –11. Option C is correct.

Learn more about simplification here:

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Answer:

pythagorean theorem

Step-by-step explanation:

a²+b²=c²

Pythagorean theorem

Answer: c is your answer

Step-by-step explanation:

We want to find a fraction a/b such that

[tex]\dfrac{9}{11}\leq\dfrac{a}{b}\leq\dfrac{11}{13}[/tex]

This is true if and only if

[tex]\dfrac{9b}{11}\leq a \leq\dfrac{11b}{13}[/tex]

We can choose a value for a only if the two extremes include at least one integer, i.e. if

[tex]\dfrac{11b}{13}-\dfrac{9b}{11}\geq 1[/tex]

Solving for b, we have [tex]b>35[/tex]

So, the smallest fraction is given for [tex]b=36[/tex]. We have

[tex]\dfrac{9}{11}\leq \dfrac{a}{36} \leq \dfrac{11}{13}[/tex]

Solving for a, we have a=30.

The fraction 30/36 can be simplified to 5/6. So, we have

[tex]\dfrac{9}{11}\leq \dfrac{5}{6} \leq \dfrac{11}{13}[/tex]

and this is the smallest possible denominator.

We want to find a fraction a/b such that

\dfrac{9}{11}\leq\dfrac{a}{b}\leq\dfrac{11}{13}

11

9

≤

b

a

≤

13

11

This is true if and only if

\dfrac{9b}{11}\leq a \leq\dfrac{11b}{13}

11

9b

≤a≤

13

11b

We can choose a value for a only if the two extremes include at least one integer, i.e. if

\dfrac{11b}{13}-\dfrac{9b}{11}\geq 1

13

11b

−

11

9b

≥1

Solving for b, we have b>35b>35

So, the smallest fraction is given for b=36b=36 . We have

\dfrac{9}{11}\leq \dfrac{a}{36} \leq \dfrac{11}{13}

11

9

≤

36

a

≤

13

11

Solving for a, we have a=30.

The fraction 30/36 can be simplified to 5/6. So, we have

\dfrac{9}{11}\leq \dfrac{5}{6} \leq \dfrac{11}{13}

11

9

≤

6

5

≤

13

11

and this is the smallest possible denominator.

Answer:

Lines RQ and SP are perpendicular to SR

Step-by-step explanation:

SR are parallel to PQ so that means that RQ and SP are perpendicular to SR

Answer:

The surface area of the figure is 96 + 64π ⇒ 1st answer

Step-by-step explanation:

* Lats revise how to find the surface area of the cylinder

- The surface area = lateral area + 2 × area of one base

- The lateral area = perimeter of the base × its height

* Lets solve the problem

- The figure is have cylinder

- Its diameter = 8 cm

∴ Its radius = 8 ÷ 2 = 4 cm

- Its height = 12 cm

∵ The perimeter of the semi-circle = πr

∴ The perimeter of the base = 4π cm

∵ The area of semi-circle = 1/2 πr²

∴ The area of the base = 1/2 × π × 4² = 8π cm²

* Now lets find the surface area of the half-cylinder

- SA = lateral area + 2 × area of one base + the rectangular face

∵ LA = perimeter of base × its height

∴ LA = 4π × 12 = 48π cm²

∵ The dimensions of the rectangular face are the diameter and the

   height of the cylinder

∴ The area of the rectangular face = 8 × 12 = 96 cm²

∵ The area of the two bases = 2 × 8π = 16π cm²

∴ SA = 48π + 16π + 96 = 64π + 96 cm²

* The surface area of the figure is 96 + 64π

Answer:

A

Step-by-step explanation:

edge 2021