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A certain kind of bacteria multiplies at a rate of 150 percent per hour. When a person’s blood has 45,000,000 of these bacteria, the person will fall sick. Let’s suppose 100 such bacteria entered a person’s blood. How many hours will it take for the person to become sick? Arrange the steps in the right order to show how to find the number of hours it will take for the person to fall sick.

Answer:

A dilation preserves angle measures.

A dilation alters the length of line segments by the same proportion.

Step-by-step explanation:

A dilatation is a transformation that alters a figure's size while maintaining its shape and orientation. Each linear measure of the figure, such as a side length, is multiplied by the scale factor of a dilatation. A dilation is a transformation where all line segments' lengths are altered uniformly. While a dilatation can alter a figure's size, it cannot alter a figure's form. Dilations are not isometries as the figure's size changes.

From unit conversion, it is found the following results:

6km ≈ 3.73 mi

2.5 L≈ 0.66 gal

90 lb ≈ 40.82 kg

Units of measurement are part of our daily lives. There are different units for area, length, volume, mass, and others.  Because of this, it is important to know converting them.

For solving this question you need some information as:

1 km = 0.621371 mi ( unit for length and distance)

1 L = 0.2641722 gallons (unit for volume)

1 lb = 0.453592 kg (unit for mass)

Therefore,

           1 km --------  0.621371 mi

           6 km --------  x mi

           x= 6* 0.621371

           x=3.73 mi

Thus, 6km ≈ 3.73 mi.

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The 3 steps to solve the algebra equation have each sub step as explained and written below.

We are given the algebraic equation;

2x + 5 = 4x - 1

Step 1; After adding 1 to both sides, we have;

2x + 5 + 1 = 4x - 1 + 1

2x + 6 = 4x

Step 2; We subtract 3x from both sides to get;

2x - 2x + 6 = 4x - 2x

2x = 6

Step 3; Divide both sides by 3 to get;

2x/2 = 6/2

x = 3

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Answer:

X=-12

Step-by-step explanation:

Subtract -5/2 on both sides:

X/3+5/2-5/2=-3/2-5/2

X/3=-8/2

X/3=-4

Multiply both sides by 3:

X/3*3=-4*3

X=-12

Answer:

x = -12

Step-by-step explanation:

To solve for x, we always want to isolate x {isolate = getting it by itself}

So, for the equation: X/3 + 5/2 = -3/2

we should first get x on its own side:

[tex]\frac{x}{3}+\frac{5}{2}=-\frac{3}{2}[/tex]

   [tex]-\frac{5}{2}[/tex]     [tex]-\frac{5}{2}[/tex]      {subtract 5/2 from both sides} {-3/2 - 5/2 = -8/2}

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

×3     ×3            {multiply both sides by 3 to find "1"x}

x = -12

check:

-12/3 + 5/2 = -3/2

-4 + 5/2  = -3/2

(5/2 = 2 [tex]\frac{1}{2}[/tex]  ;   2 [tex]\frac{1}{2}[/tex] - 4 = -1 [tex]\frac{1}{2}[/tex])

-1 [tex]\frac{1}{2}[/tex] = -3/2      {3/2 = 1 [tex]\frac{1}{2}[/tex]}

-1 [tex]\frac{1}{2}[/tex] = -1 [tex]\frac{1}{2}[/tex]

{TRUE}

so, x = -12

hope this helps!!

Step-by-step explanation:

1&$)&(5$6$5*-_+_7&'+&-^€=%

The molar heat of fusion for substance X , given the data is 775.6 cal/mol

Mole = mass / molar mass

Mole = (326 / 58.45) moles

Q = n × ΔHf

4325.8 = (326 / 58.45) × ΔHf

4325.8 = (326 × ΔHf ) / 58.45

Cross multiply

326 × ΔHf = 4325.8 × 58.45

Divide both sides by 326

ΔHf = (4325.8 × 58.45) / 326

ΔHf = 775.6 cal/mol

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The property of each given rational number operation are respectively; Commutative Property; Closure Property; Associative Property; Closure Property; Distributive Property

The main properties of rational numbers are:

a) The property used here is commutative property which says that;

a + b = b + a.

This tallies with the operation used on the rational numbers.

b) The property used here is called Closure Property. This is because for two rational numbers say a and b, the results of addition, subtraction and multiplication operations gives a rational number.

c) The property used here is called associative property because it states that; a * (b * c) = (a * b) * c.

d) The property used here is called Closure Property. This is because for two rational numbers say a and b, the results of addition, subtraction and multiplication operations gives a rational number.

e)  The property used here is called distributive property because it states that; a * (b * c) = (ab * ac)

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The cost price of the product will be 25000.

From the information given, the cost price is 25000. The loss is 10%. This will be:

= 25000 - (10% × 25000)

= 25000 - 2500

= 22500

The tax is 13%. This will be:

= 22500 + (13% × 22500)

= 22500 + 2925

= 25425

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Answer:

I think the answer is B

Step-by-step explanation:

Answer:

1/6

Step-by-step explanation:

the total carrot is 1/1 and fluffy ate 1/2 of it . this means half has been eaten and it is left with half so now 1/2 -1/3 ( carrot left in the morning - the carrot left now ) this will be 1/6

Answer:

D.) x - 4

Step-by-step explanation:

This is a graph of an exponential/quadratic function. There general structure looks like this:

ax² + bx + c

Generally, when finding the zeros these functions, you are told to factor the equation. Once you have factored the equation, you can set the factors equal to zero to find the points where the function touches the x-intercept.

That being said, you can determine the factors without having the entire equation by identifying the zeros on the function. On this graph, there is a zero at (4,0). This means that one of the factors must have been "x - 4". You can check your work by setting the factor equal to zero.

x - 4 = 0

x = 4

Answer:

  28.2

Step-by-step explanation:

The perimeter of a plane figure is the sum of the lengths of its sides. Those lengths and their sum can be found a number of different ways.

__

The values computed by the graphing program in the attachment add up to 28.2 units.

__

The length of each side of the triangle can be computed using the distance formula or the Pythagorean theorem. For a given "rise" and "run", the length of a line segment is ...

  d = √(rise^2 +run^2)

  HI = √((-4)^2 +10^2) = √116 ≈ 10.770

  IJ = √(1^2 +12^2) = √145 ≈ 12.042

  JH = √(5^2 +2^2) = √29 ≈ 5.385

The perimeter is the total of the lengths of the sides:

  P = HI +IJ +JH = 10.770 +12.042 +5.385 = 28.197

To the nearest tenth, the perimeter is 28.2 units.

The value of the logarithmic function log₄7 = 1.404, when the values of the logarithmic functions log₄3 = 0.792 and log₄21 = 2.196.

We are given the logarithmic functions:

log₄3 = 0.792 ,,, (i), and log₄21 = 2.196 ... (ii),

and we are asked to find the value of the logarithmic function log₄7.

On subtracting (i) from (ii), we get:

log₄21 - log₄3 = 2.196 - 0.792.

Using the quotient law of logarithms, according to which:

logₓa - logₓb = logₓ(a/b), we can write the above equation as:

log₄(21/3) = 1.404,

or, log₄7 = 1.404.

Therefore, the value of the logarithmic function log₄7 = 1.404, when the values of the logarithmic functions log₄3 = 0.792 and log₄21 = 2.196.

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Answer:

A.

1.404

Step-by-step explanation:

Answer:

115.2 in^2

Step-by-step explanation:

total surface area Stot = 113.2 in2

lateral surface area Slat = 103.2 in2

top surface area Stop = 6 in2

bottom surface area Sbot = 6 in2

Answer:

C [tex]\sqrt{5}[/tex]

Step-by-step explanation:

Use pythagorean theorem.

[tex]x^{2}[/tex] +[tex]\sqrt{7} ^{2}[/tex] = (2[tex]\sqrt{3}) ^{2}[/tex]    

[tex]x^{2}[/tex] + 7 = 12   Subtract 7 from both sides

[tex]x^{2}[/tex] = 5           Take the square root of both sides to solve

x = [tex]\sqrt{5}[/tex]

Answer:

20 Players

Step-by-step explanation:

Total Amount of Money: $2412.50

First the team rented us a bus for $1072.50

Subtract the bus from the total

$2412.50 - $1072.50 = $1340

Total Amount of Money after bus: $1340

From there we need to find the max number of players that can go.

The budget cost for each player is $67.

So we divide the remaining money by $67 to find the number of players that can go.

$1340/$67 = 20 Players.

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Hope this helps!

Step-by-step explanation:

I am not sure what your problem here is.

you understand the inequality signs ?

anyway, to get

6×f(-2) + 3×g(1)

we can calculate every part of the expression separately, and then combine all the results into one final result.

f(-2)

we look at the definition.

into what category is -2 falling ? the one with x<-2, or the one with x>=-2 ?

is -2 < -2 ? no.

is -2 >= -2 ? yes, because -2 = -2. therefore, it is also >= -2.

so, we have to use

1/3 x³

for x = -2 that is

1/3 × (-2)³ = 1/3 × -8 = -8/3

g(1)

again, we look at the definition.

into what category is 1 falling ? the one with x > 2 ? or the one with x <= 1 ?

is 1 > 2 ? no.

is 1 <= 1 ? yes, because 1=1. therefore it is also <= 1.

so we have to use

2×|x - 1| + 3

for x = 1 we get

2×0 + 3 = 3

6×f(-2) = 6 × -8/3 = 2× -8 = -16

3×g(1) = 3× 3 = 9

and so in total we get

6×f(-2) + 3×g(1) = -16 + 9 = -7

Answer:

89

Step-by-step explanation:

Answer:

D: 6.5, 3

C: 23.5, 9

I think

Answer:

C (23.5, 9)

D (6.5, 3)

Answer:

B) the lines never intersect

Step-by-step explanation:

okay essentially, syllogism is formatted in a repetitive way

it's something like:

if "a" are "b"

and "b" are "c"

then "a" are "c"

(a = b

b = c

logically, c = a)

(idea, thing related to idea, conclusion relating the two)

hope this helps!!

Answer:

the lines never intersect

Step-by-step explanation:

Syllogisms are connected by a shared statement that connects a hypothesis to a different conclusion.

Answer: 8

Step-by-step explanation:

We know that scale factor = (image)/(preimage).

Substituting in what we have,

[tex]5=\frac{R'S'}{RS}\\\\5=\frac{40}{RS}\\\\RS=\boxed{8}[/tex]

Answer:

Step-by-step explanation:

We know that r's't' was formed by a scale factor of 5.

This means rst was multiplied by 5 to create r's't'.

Dividing the sides of r's't' by 5 will give us the sides of the

pre-image.  If r's' = 40 - dividing 40 by 5 = 8.

So rs is 8.

The new coordinates of C is (-5,2), (-5,5) (-7,3) (-7,5)

The correct question is

Shape R is reflected in x axis and is translated by (-3, 0) , What will be the coordinates of the new figure

The figure is attached with the answer.

When  a figure is reflected along any axis , the coordinate of the axis on which it is reflected remains the same while the other coordinate vis the additive inverse of the given coordinate

It is given that the coordinate point of R

(-2 ,-2) , (-2,-5) (-4,-3) (-4,-5)

When it is reflected along x axis the new coordinates are

(-2 , 2), (-2,5) (-4,3) (-4,5)

and when translated by -3,0

(-5,2), (-5,5) (-7,3) (-7,5)

Therefore the new coordinates of C is (-5,2), (-5,5) (-7,3) (-7,5)

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Answer:

x is 90°

y is 56°

Step-by-step explanation:

Concepts used :

The angle subtended by a diameter inside the circle is always 90° .

Sum of interior angles of a triangle is 180°.

Here x is the angle subtended by the diameter of the circle therefore ,

x is 90°.

let the end points of diameter  as A , B

and the point where the it subtends the 90° angle be C

using interior angle property on the triangle  ΔABC

90° + 62° + ∠A = 180°

152° + ∠A = 180°

∠A = 180° - 152°

∠A  =  28°

now let he midpoint of diameter as D

as the sides DC and DA are radius of circle  and therefore equal

so using isosceles triangle property which states that angle opposite to equal sides are equal

so the angle ∠ACD = 28°

now using exterior angle property on ΔADC

y = 56°

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Answer:

Symmetric property

[tex]3(8 - 4x) < 6(x - 5) \\ 24 - 12x < 6x - 30 \\ 24 + 30 < 6x + 12x \\ 54 < 18x \\ \frac{54}{18} < \frac{18x}{18} \\ x > 3[/tex]

Solution : ] 3 , + ♾️ [

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I am assuming you meant to write b(x) = x-4.

[tex](b \circ a)(x)=b(a(x))=b(3x+1)=(3x+1)-4=\boxed{3x-3}[/tex]

Since this is a linear function, the domain is all real numbers.

The volume of the cone is V = 381.15 cu.cm

The curved surface area of the cone is given by

A = πrl

The slant height given in the question is

l = 10.5 cm

A = 115.5 sq.cm

radius = ?

Height = ?

Volume = ?

Using the Curved Surface Area Formula

115.5 = π * r * 10.5

taking π = 22/7

r = 3.5 cm

The slant height is given by

[tex]\rm l = \sqrt{ r^2 + h^2}[/tex]

Therefore the height is

[tex]\rm h = \sqrt{ 10.5^2 -3.5^2}[/tex]

h = 9.9 cm

The volume of the cone is

V = π r²h

V = (22/7) * 3.5 * 3.5 * 9.9

V = 381.15 cu.cm

The volume of the cone is V = 381.15 cu.cm

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