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Answer:

Step-by-step explanation:

presumably this is the answer and if you want the reasoning I could explain it in more detail if needed

Answer:

The limit of a sum is equal to the sum of the limits.

Step-by-step explanation:

The limits of a constant times a function is equal to the constant times the limit of the function.

Answer:

x^2 + 12x + 27

Step-by-step explanation:

x^2 + 9x + 3x + 27 =

= x^2 + 12x + 27

Answer:

1/14

Step-by-step explanation:

The ratio is 5:70. The fraction form of that is 5/70. To get the lowest terms, I divided both numbers by 5. So it is 1/14

On solving the provided question we can say that so SAS, the are congruent triangles

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

here,

we have to triangles

with angles as 30,60,90 and 60,60,90 respectively

and 2 sides of 7 cm each.

so SAS, the are congruent triangles

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The range, in centimetres (cm), of the following lengths is 20.5 cm

What is the range?

The difference between the lowest and highest numbers is referred to as the range. For instance, the range will be 10 - 2 = 8 if the given data set is 2, 5, 8, 10, and 3.

As a result, the range may alternatively be thought of as the distance between the highest and lowest observation. The range of observation is the name given to the outcome. Statistics' range reflects the variety of observations.

Given, 15 cm, 0.5 cm, 10.3 cm, 16.7 cm, 21 cm, 8.6 cm

So, the highest value of length = 21 cm

the lowest value of length = 0.5 cm

Then, range = the highest value - the lowest value

                    = 21 - 0.5 = 20.5 cm

Hence, the range, in centimetres (cm), of the following lengths is 20.5 cm

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Answer:

b = 5

Step-by-step explanation:

All quadratic equations are formed in the format of \(a^{2}\) + bx + c = 0

Using this formula, we can re-arrange the equation to fit the given format.

\(3x^{2}\) - 2 = -5x
\(3x^{2}\) + 5x - 2 = 0

5 is plugged in for "b" in this equation, therefore b = 5.

The scenarios that can be considered a seller-based discount are:

A. The offer by Wire and Cable

B. Carfna's Fine Foods

C. Mouser Electronics offer

E. Carchex Car Maintenance

A seller-based discount is a discount that is offered by a seller for the early purchase of a product. The goal of the seller in this case is to get cash as he or she is in an immediate need for cash.

The most outstanding example is that of Carchex Car Maintenance where an offer is made by the seller for the early purchase of products.

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Answer:

B.

Step-by-step explanation:

Answer:

dI/dt = 0.0001(2000 - I)I

I(0) = 20

\(I(t)=\frac{2000}{1+99e^{-0.2t}}\)

Step-by-step explanation:

It is given in the question that the rate of spread of the disease is proportional to the product of the non infected and the infected population.

Also given I(t) is the number of the infected individual at a time t.

\(\frac{dI}{dt}\propto \textup{ the product of the infected and the non infected populations}\)

Given total population is 2000. So the non infected population = 2000 - I.

\(\frac{dI}{dt}\propto (2000-I)I\\\frac{dI}{dt}=k (2000-I)I, \ \textup{ k is proportionality constant.}\\\textup{Since}\ k = 0.0001\\ \therefore \frac{dI}{dt}=0.0001 (2000-I)I\)

Now, I(0) is the number of infected persons at time t = 0.

So, I(0) = 1% of 2000

            = 20

Now, we have dI/dt = 0.0001(2000 - I)I  and  I(0) = 20

\(\frac{dI}{dt}=0.0001(2000-I)I\\\frac{dI}{(2000-I)I}=0.0001 dt\\\left ( \frac{1}{2000I}-\frac{1}{2000(I-2000)} \right )dI=0.0001dt\\\frac{dI}{2000I}-\frac{dI}{2000(I-2000)}=0.0001dt\\\textup{Integrating we get},\\\frac{lnI}{2000}-\frac{ln(I-2000)}{2000}=0.0001t+k \ \ \ (k \text{ is constant})\\ln\left ( \frac{I}{I-222} \right )=0.2t+2000k\)

\(\frac{I}{I-2000}=Ae^{0.2t}\\\frac{I-2000}{I}=Be^{-0.2t}\\\frac{2000}{I}=1-Be^{-0.2t}\\I(t)=\frac{2000}{1-Be^{-0.2t}}\textup{Now we have}, I(0)=20\\\frac{2000}{1-B}=20\\\frac{100}{1-B}=1\\B=-99\\ \therefore I(t)=\frac{2000}{1+99e^{-0.2t}}\)

The required expressions are presented below:

\(\frac{dI}{dt} = 0.0001\cdot I\cdot (2000-I)\) \(\blacksquare\)

\(I(0) = \frac{1}{100}\) \(\blacksquare\)

\(I(t) = \frac{20\cdot e^{\frac{t}{5} }}{1+20\cdot e^{\frac{t}{5} }}\) \(\blacksquare\)

After reading the statement, we obtain the following differential equation:

\(\frac{dI}{dt} = k\cdot I\cdot (n-I)\) (1)

Where:

Then, we solve the expression by variable separation and partial fraction integration:

\(\frac{1}{k} \int {\frac{dI}{I\cdot (n-I)} } = \int {dt}\)

\(\frac{1}{k\cdot n} \int {\frac{dl}{l} } + \frac{1}{kn}\int {\frac{dI}{n-I} } = \int {dt}\)

\(\frac{1}{k\cdot n} \cdot \ln |I| -\frac{1}{k\cdot n}\cdot \ln|n-I| = t + C\)

\(\frac{1}{k\cdot n}\cdot \ln \left|\frac{I}{n-I} \right| = C\cdot e^{k\cdot n \cdot t}\)

\(I(t) = \frac{n\cdot C\cdot e^{k\cdot n\cdot t}}{1+C\cdot e^{k\cdot n \cdot t}}\), where \(C = \frac{I_{o}}{n}\) (2, 3)

Note - Please notice that \(I_{o}\) is the initial infected population.

If we know that \(n = 2000\), \(k = 0.0001\) and \(I_{o} = 20\), then we have the following set of expressions:

\(\frac{dI}{dt} = 0.0001\cdot I\cdot (2000-I)\) \(\blacksquare\)

\(I(0) = \frac{1}{100}\) \(\blacksquare\)

\(I(t) = \frac{20\cdot e^{\frac{t}{5} }}{1+20\cdot e^{\frac{t}{5} }}\) \(\blacksquare\)

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Answer:

9. B. 32 millimeters

10. C. 7 inches

11. C. 56.24 millimeters

13. B. 14.13 square feet

Step-by-step explanation:

9. Radius of a circle or any circular shape = ½ of its diameter

Diameter of the disk = 64 millimeters

Radius of the disk = ½(64) = 32 millimeters

10. Width of the cooler = 6 in.

Length = 8 in.

Volume = 336 in.³

Height = ?

Formula for volume of a rectangular prism = L*W*H

Plug in the values

336 = 8*6*H

336 = 48*H

Divide both sides by 48

336/48 = H

H = 7 inches

11. A dime has a circular shape

The circumference of the dime = circumference of a circle = πd

Where,

d = 17.91 millimeters

π = 3.14

Plug in the values

C = 3.14 × 17.91 = 56.2374

≈ 56.24 millimeters (nearest hundredth)

12. Area of the top of the desk = area of semicircle = ½ × πr²

Where,

r = ½(6) = 3 ft

π = 3.14

Plug in the values

Area = ½ × 3.14 × 3² = ½ × 3.14 × 9

Area = 14.13 square feet

Answer:

B, (-1/3, 3)

Step-by-step explanation:

This is the correct answer :)

Answer:

B, (-1/3, 3)

Step-by-step explanation:

Answer:

hope it's helpful for you

The answer of the given question based on the graph is ,  The locations of A′ and B′ are A′ (0, 1) and B′ (1, 0); lines f and f′ are parallel.

A scale factor is a number that scales, or multiplies, a quantity by some factor. It is used in mathematics to describe the relationship between corresponding measurements of two similar figures, such as triangles or rectangles.

To dilate line f by scale factor of one half with center of dilation at origin, we  multiply coordinates of each point on line f by 1/2.

The equation of line f can be found by using the points A and B:

slope of line f = (0 - 2)/(2 - 0) = -1

y-intercept of line f = 2

Therefore, the equation of line f is y = -x + 2.

To find the coordinates of A' and B' after dilation, we can apply the dilation factor to each point:

A' = (0, 2)*1/2 =(0, 1)

B' = (2, 0)*1/2 =(1, 0)

So A' is located at (0, 1) and B' is located at (1, 0) after dilation.

Now let's analyze the relationship between lines f and f'. The dilation was centered at the origin, so the origin is a fixed point of the dilation. This means that the point where lines f and f' intersect must be the origin.

If we plug in x = 0 into the equation of line f, we get y = 2. This means that point A is located at (0, 2) and intersects with line f at y = 2. After dilation, point A' is located at (0, 1), which means that lines f and f' intersect at point A.

To determine the relationship between lines f and f', we can compare their equations. The equation of f' can be found by using the points A' and B':

slope of f' = (0 - 1)/(1 - 0) = -1

y-intercept of f' = 0

Therefore, the equation of f' is y = -x.

Comparing the equations of f and f', we can see that they have the same slope of -1, which means they are parallel. Therefore, the correct answer is: The locations of A′ and B′ are A′ (0, 1) and B′ (1, 0); lines f and f′ are parallel.

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a) Angle of line of sightFrom a point O in the school compound, Adeolu is 100 m away on a bearing N 35° E and Ibrahim is 80 m away on a bearing S 55° E. (a) How far apart are both boys? (b) (c) What is the bearing of Adeolu from point O, in three-figure bearings? What is the bearing of Ibrahim from point O, in three-figure bearings?The angle of the line of sight of Adeolu from the point O is given by:α = 90 - 35α = 55°.The angle of the line of sight of Ibrahim from the point O is given by:β = 90 - 55β = 35°.a) By using the Sine Rule, we can determine the distance between Adeolu and Ibrahim as follows:$

\frac{100}{sin55^{\circ}} = \frac{80}{sin35^{\circ}

100 sin 35° = 80 sin 55°=57.73 mT

herefore, both boys are 57.73 m apart. b) The bearing of Adeolu from the point O can be determined as follows:OAN is a right-angled triangle with α = 55° and OA = 100. Therefore, the sine function is used to determine the side opposite the angle in order to determine AN.

Thus:$$sin55^{\circ} = \frac{AN}{100}$$AN = 80.71 m.

To find the bearing, OAD is used as a reference angle. Since α = 55°, the bearing is 055°.

Therefore, the bearing of Adeolu from the point O is N55°E. c) Similarly, the bearing of Ibrahim from the point O can be determined as follows:OBS is a right-angled triangle with β = 35° and OB = 80. Therefore, the sine function is used to determine the side opposite the angle in order to determine BS.

Thus:$$sin35^{\circ} = \frac{BS}{80}$$BS = 46.40 m.

To find the bearing, OCD is used as a reference angle. Since β = 35°, the bearing is 035°.Therefore, the bearing of Ibrahim from the point O is S35°E. A boy walks 5 km due North and then 4 km due East. (a) Find the bearing of his current posi- tion from the starting point.

(b) How far is the boy now from the start- ing point?The boy's position is 5 km North and 4 km East from his starting position. The Pythagorean Theorem is used to determine the distance between the two points, which are joined to form a right-angled triangle. Thus

:$$c^2 = a^2 + b^2$$

where c is the hypotenuse, and a and b are the other two sides of the triangle. Therefore, the distance between the starting position and the boy's current position is:$$

c^2 = 5^2 + 4^2$$$$c^2 = 25 + 16$$$$c^2 = 41$$$$c = \sqrt{41} = 6.4 km$$

Therefore, the boy is 6.4 km from his starting point. (a) The bearing of the boy's current position from the starting point is given by the tangent function.

Thus:$$\tan{\theta} = \frac{opposite}{adjacent}$$$$\tan{\theta} = \frac{5}{4}$$$$\theta = \tan^{-1}{\left(\frac{5}{4}\right)}$$$$\theta = 51.34^{\circ}$$

Therefore, the bearing of the boy's current position from the starting point is N51°E.

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Answer:

4:10 hope this helps

Step-by-step explanation:

Therefore, **x < 7** is the inequality that may be utilized to find x

A mathematical statement known as an inequality compares two expressions using an inequality sign, such as (less than), > (greater than), or (less than or equal to).

For instance, the inequality x + 2 5 signifies that "x + 2 is less than 5".

Let x represent how many days the client paid for pet sitting.

$15 per day plus a $20 fixed service fee equals the total cost of pet sitting.

We are aware that the customer's purchase was under $125. Consequently, we can write:

20 + 15x < 125

Putting this disparity simply:

15x < 105

x < 7

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Answer:

C, F

Step-by-step explanation:

Dont have time rn

A. Yes, the two expressions in discuss as given in the task content are; equivalent expressions.

B. The two expressions when simplified to the fewest terms is; 5m - 10. Hence, the two expressions are equivalent expressions.

It follows from the task content that the two expressions given are to be compared and determined if they are equivalent expressions.

A. By evaluation; using the Distributive property; we have;

3(m - 2) + 2(m - 2) = 3m - 6 + 2m - 4 = 5m - 10.

Also; 5(m - 2) = 5m - 10.

Therefore, the two expressions are equivalent.

B. Since both expressions given can be written in fewest terms as; 5m - 10, the expressions are equivalent. Hence, the two expressions are said to be equivalent expressions.

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Answer:

216 inches

Step-by-step explanation:

72+72+36+36=216

The perimeter and area of the square are; 24√2 units and 12 units² respectively

Given the coordinates of the midpoints of the four sides of a square are S(-4,11), Q(2,5), U(-4,-1), A (-10,5)

But since we have the midpoints of all the sides, we can assume they're equidistant from one another since the figure is a square.

SQ = √(x₂ - x₁)² + (y₂ - y₁)²

SQ = √(2 - (-4)² + (5 - 11)²

SQ = 6√2

Let's find QU

QU = √(-4 - 2)² + (-1 - 5)²

QU = 6√2

Let's find UA ;

UA = √(-10 - (-4))² - (5 - (-1)²

UA = 6√2

And the distance AS = 6√2

The perimeter of the square = 4 (6√2)

Perimeter = 24√2 units

The area of the square = l²

Area of the square = (6√2)²

Area of square = 12 units²

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Answer:

37.9°

Step-by-step explanation:

ΔABC is similar to ΔPQR, so ∠R ≅ ∠C.

Given AB = 7 and AC = 9, we can find m∠C using tangent.

tan C = AB / AC

tan C = 7 / 9

m∠C = 37.9°

m∠R = 37.9°

Answer:

c = 85 in is the answer.

Step-by-step explanation:

a = 36 in

b = 77 in

c = ?

According to the Pythagoras theorem,

a² + b² = c²

36² + 77² = c²

1296 + 5929 = c²

7225 = c²

c = 85 in

∴ c = 85 in is the length of the missing leg.

Answer:

1/3 foot longer

Step-by-step explanation:

2/3-1/3=1/3

Answer:

x = 0 , x = 2

Step-by-step explanation:

3x² = 6x ( subtract 6x from both sides )

3x² - 6x = 0 ← factor out 3x from each term

3x(x - 2) = 0

equate each factor to zero and solve for x

3x = 0 ⇒ x = 0

x - 2 = 0 ( add 2 to both sides )

x = 2

solutions are x = 0 , x = 2

In order to solve for c we just have to remember one simple rule: what we do in one side of the equal "=" we should do it in the other side.

In this case:

2c + 7n + z = y

↓ substracting z both sides

2c + 7n + z - z = y - z

2c + 7n + 0 = y - z

2c + 7n = y - z

↓ substracting 7n both sides

2c + 7n - 7n = y - z - 7n

2c + 0 = y - z - 7n

2c = y - z - 7n

↓ dividing by 2 both sides

Then, we have the answer:

Answer:

See below.

Step-by-step explanation:

STEP 1:  If you write the given terms all with denominators of 16, they are 28/16, 25/16, 22/16, 19/16, __, ____, ____, 7/16, 4/16.

STEP 2: The terms decrease by 3/16 for each step.

RULE: Term 1 = 7/4 and term (n + 1) = term 'n' - 3/16

The operation for increasing by the same amount every step is addition.

The operation for decreasing by the same amount every step is subtraction.

STEP 3: The rule is that the terms decrease by 3/16 at each step.

So the next 3 terms after 19/16 will be 16/16, 13/16, and 10/16.

Reformat them and you have 1, 13/16, 5/8.

So now the completed sequence is 1&3/4, 1&9/16, 1&3/8, 1&3/16, 1, 13/16, 5/8, 7/16, 1/4.

Answer:

Step-by-step explanation:

Answer:

7/12. if you find a common denominator for the two, like 24 for example, 2/8 converts to 6/24 and 1/3 converts to 8/24. 6/24+8/24=14/24, and that reduced is 7/12.

Step-by-step explanation: