Jonah ran 1 Taps on Monday, 21 laps on Tuesday, and 6 laps on Wednesday.
How much farther did he run on Wednesday than on the other two days
combined? Show your work.

Answer:

x² +y² -10x -8y +21 = 0

Step-by-step explanation:

try desmos graph

Answer:

5.46

Step-by-step explanation:

precio original = x

0.7(1.3x) = x - 0.54

0.91x - x = -0.54

x = 6

6 + 30% de 6 = 7.8

7.8 - 30% de 7.8 = 5.46

Arturo compró por 6.

Aumentó 30% para 7.80.

Bajó 30% para 5.46.

6 - 5.46 = 0.54

Value of x would make these two solids similar when x is equal to 7.75.

When it comes to Euclidean geometry, two things are said to be similar if they have the same shape or the same shape as each other's mirror image. One can be created from the other more precisely by evenly scaling, possibly with the inclusion of further translation, rotation, and reflection. If two figures have the same shape, they are said to be comparable. In more formal terms, two figures are said to be comparable if their respective angles are congruent and their corresponding side length ratios are identical. The scale factor is the name given to this usual ratio.

Given

Two figures given

Value of x would make these two solids similar

D. X=7.75

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Increasing the area from 400 to 600 (50%) results in an increase in cost from 500 to 750 (50% increase), which shows that the cost is not proportional to the area.

In a situation where cost is proportional to area, the relationship between cost and area is said to be directly proportional. Direct proportionality means that if the value of one variable (in this case, area) is multiplied by a certain factor, then the other variable (in this case, cost) will also be multiplied by the same factor. The mathematical formula for direct proportionality is [tex]y = kx,[/tex] where y and x are the two variables, and k is the constant of proportionality. If the relationship between the variables is not proportional, then it is a non-proportional relationship.

The objects are proportional if increasing one quantity by a certain factor results in the other quantity increasing by the same factor. In this case, cost is proportional to area if doubling the area would double the cost. Based on the table, we can see that the cost is not proportional to the area since the cost does not increase by the same factor as the area. For example, increasing the area from 400 to 800 (double) results in an increase in cost from 500 to 1000 (also double). However, increasing the area from 400 to 600 (50%) results in an increase in cost from 500 to 750 (50% increase), which shows that the cost is not proportional to the area.

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The pairs of triangles that are congruent are;

A. Δ1 and Δ5

B. Δ1 and  Δ2

C. Δ2 and Δ3

D. Δ3 and Δ5

E. Δ1 and Δ3

F. Δ3 and Δ4

G. Δ1 and Δ4

H. Δ4 and Δ5

Congruent triangles are triangles that have all three sides  and all three angles on each triangle having the same length and the same measure.

The congruent angles are indicated by the number of markings

The angles in the figures are;

Angle with  one arc

Angles with two arcs marks

Angles with three arc marks

The congruent sides are indicated by one dash, and two dashes

Therefore;

Δ2 s congruent to Δ1 is congruent to Δ3 by  Angle-Side-Angle rule of congruency

Similarly, we have;

Δ3 is congruent to Δ4 by Angle-Side-Angle congruency postulate

Therefore;

Triangle Δ2 is congruent to Δ3  by Angle-Side-Angle congruency postulate

From the diagram, the one arc, two arcs, and three arc angles form a linear pair, therefore;

Therefore, Δ4 is congruent to Δ5

Δ1 is congruent to Δ4

Δ2 is congruent to Δ5, therefore; Δ3 is congruent to Δ5

Similarly;

Δ1 is congruent to Δ3

Δ1 is congruent to Δ2, therefore , therefore, Δ1 is congruent to Δ5

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Answer:

Step-by-step explanation:

To find 50% of 950, you can multiply 950 by 0.50. 50% is the same as 0.50.

The calculation is: 50% * 950 = 0.50 * 950 = <<50*.01*950=475>>475

So, 50% of 950 is 475.

Answer:

∠1+∠2≅∠3+∠4 cant be proven because sum of two obtuse angles is sure to be greater than sum of two acute angles of a triangle.

The three sticks will not form a triangle.

What is the triangle inequality theorem?

The triangle inequality theorem explains the connection between a triangle's three sides. This theorem states that for any triangle, the sum of the lengths of the first two sides is always greater than the length of the third side. In other terms, this theorem states that a straight line is always the shortest distance between any two places.

Given, Mr Hansen has three sticks that measure 5 inches, 10 inches and 17 inches

From the above definition of the Triangle inequality theorem,

Sum of two sides = 5 + 10 = 15 which is less than

the length of the third side = 17

So, the three sticks will not form a triangle.

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The value of missing coordinate d of the point (d, 7) in the line such that its slope is 1 / 3 is - 9.

In this problem we must determine the value of the missing coordinates of a point in a line such that its slope is 1 / 3. The slope of the line can be determined by means of the secant line formula:

m = Δy / Δx

Where:

If we know that (x₁, y₁) = (d, 7), (x₂, y₂) = (0, 10) and m = 1 / 3, then the missing coordinate is:

1 / 3 = (10 - 7) / (0 - d)

1 / 3 = - 3 / d

d = - 9

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The number of  chaperones that are needed is 128/15.

What is unitary method?

The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.

Given that the number of students in 8th grade is 400.

Four fifth of total number of students go for trip.

The number of student who goes for the trip is 400 × 4/5

                                                                                = 320.

To carry 75 students, we need 2 chaperones.

Apply unitary method:

To carry 1 student, we need 2/75 chaperones.

To carry 320 students, we need (2 ×320)/75  chaperones.

                                                  = (2 × 64)/15

                                                  = 128/15

                                                  = 8.533

                                                 = 9

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Answer:

7 5 15 22

step,by step explanation: yes

In the given argument and condition, (D) there are several observations, which strengthen the argument.

An argument is a statement or set of claims, known as premises, that seeks to evaluate the plausibility or acceptability of a conclusion.

The logical, dialectical, and rhetorical perspectives are the three basic areas of study for arguments.

Giving an argument entails offering a group of premises as justifications for believing the conclusion.

It's not always necessary to criticize or insult someone when making an argument.

Arguments can also be employed to back up the beliefs of others.

An example of an argument is as follows:

You should put in a lot of effort if you want to find a decent career.

So, in the given argument and condition, (D) there are several observations, which strengthen the argument.

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Complete question:
Consider the following argument:

Observation: Here in Nashville, the sun has risen every morning. Conclusion: The sun is going to rise in Nashville tomorrow.

a. The argument is weak because there is only one specific case.

b. The argument is strong because the premise includes scientific evidence.

c. The argument is weak because the observation does not consider other cities.

d. The argument is strong because there are a large number of observations.

Interior angles on the same side are supplementary, which means they add up to 180°. We can write the equation as follows and refer to the two angles as x° and (x + 20)°.

When two rays are linked at their ends, they create an angle in geometry. The sides or arms of the angle are what are known as these rays.

When two lines meet at a point, an angle is created.

An "angle" is the measurement of the "opening" between these two rays. It is symbolized by the character. The circularity or rotation of an angle is often measured in degrees and radians.

Angles are a common occurrence in daily life.

Angles are used by engineers and architects to create highways, structures, and sports venues.

According to our question-

x + x + 20 = 180

2x + 20 = 180

2x = 160

If x = 80, the angles are 80° and 80 + 20 = 100°, respectively.

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Answer:

5/8=25/40   7/10=28/40

Step-by-step explanation:

5/8<7/10

The required number of candles Marcella has in the starting is 56.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
As mentioned in the question,
She has some candles in the starting  before she starts collecting the candles, let x be the candle she had in the starting,
Now,
According to the question she is buying 13 candles every week, at the end of 8 weeks she has 160 candles,
So.
x + 13(8) = 160
x + 104 = 160
x = 160 - 104
x = 56

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The quadratic equation of the function C(t) is; C(t)= (x - 4)²

We are given the coordinates as;

When t = 2, C(t) = 4

When t = 3, C(t) = 1

When t = 4, C(t) = 0

When t = 5, C(t) = 1

When t = 6, C(t) = 4

The general formula formula for quadratic equation is;

y = ax² + bx + c

where c is y-intercept

We are given that x = 4, when y = 0. Thus, x = 4 is a root of the equation.

Put x = 2and y = 4  into the equation to get;

4a + 2b + c = 4    -----(1)

Put x = 3 and y = 1  into the equation to get;

9a + 3b + c = 1    -----(2)

Put x = 4 and y = 0  into the equation to get;

16a + 4b + c = 0    -----(3)

Using simultaneous equation solver gives;

a = 1, b = -8 and c = 16. Thus, our equation is;

y = x² - 8x + 16

By factorization;

y = x² - 4x - 4x + 16

y = x(x - 4) - 4(x - 4)

y = (x - 4)²

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Answer:

Triangle B

Step-by-step explanation:

The triangles have three pairs of congruent sides.

After using the Pythagorean theorem the missing length of c is √148

What is the Pythagorean theorem in plain English?

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse.

How may the Pythagorean Theorem be demonstrated the simplest way?

Angles CAB, AC'B, and AB'C must be equal in order for AC2 + AB2 to equal BC(CB' + BC'). Triangles ABC, AC'B, and AB'C are indeed comparable. Since AB/BC' = BC/AB and AC/CB' = BC/AC, we have the necessary identity right away. Theorem reduces to Pythagorean proposition and proof if angle A is correct.

Pythagorean Theorem: a²+b²=c²

so (12)^2+(2)^2 = 144+4 = 148

c²=148

c=√148

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Answer:

[tex]\huge\boxed{\sf d = 1.25\ m}[/tex]

Step-by-step explanation:

Work = W = 22 J

Force = F = 17.5 N

Distance = d = ?

W = Fd

Put the given data in the above formula.

22 = 17.5 (d)

Divide 17.5 to both sides

22/17.5 = d

1.25 m = d

[tex]\rule[225]{225}{2}[/tex]

The total ticket sales was $ 2298, and the theater was filled to capacity

Children: 158

Students: 158

Adults: 79

The amount of space occupied by a flat (2-D) surface or an object's shape is known as its area. Draw a square on a piece of paper using a pencil. A 2-D figure, that is. The term "Area" refers to the area that a shape occupies on paper. Now picture that your square is composed of smaller unit squares.

According to Study.com, area is a mathematical concept that is defined as the two-dimensional space occupied by an item. Area is used in many real-world contexts, including building, farming, architecture, science, and even determining how much carpet you'll need to cover your home's rooms.

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Answer: x=27/6

Step-by-step explanation:

-1 2/3 = -5/3

17/6 = -5/3 + x

x = 17/6 + 5/3

x = 17/6 + 10/6

x = 27/6

Amplitude is 5, midline is 3, period is π and the frequency is 2

We can describe the cosine function as y = Acos(B(x + C )+ D

where,

amplitude is A

Frequency is B

period is 2π/B

phase shift is C (positive is to the left)

vertical shift is D

Step 1:

Identify

5 cos(2x) + 3 → Acos(B(x + C )+ D

Hence

A = 5 = Amplitude

B = 2.C = 0. So,

Period = 2π / B

= 2π / 2 = π

Period = π

Frequency = B = 2

Vertical shift = D = 3

Step 2:

Midline

The equation of the midline of periodic function is the average of the maximum and minimum values of the function.

a) we have a maximum when

cos(2x) = 1

x =0, because (cos 0) = 1 Now, replace

y = 5 cos(2x) + 3

y = 5cos(2. 0 ) +3

= 5.1 + 3

= 8

So, the maximum is 8

b) we have a minimum when

cos(2x) = -1

x = π/2 , because

cos(2.π/2) = cos(π) = -1

Now, replace

y = 5cos(2.π/2) + 3

= 5. (-1) + 3

= -5+3

= -2

So, the midline is the average of 8 and -2

Midline = y = [8 + (-2)] / 2

= 6/2

y = 3

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LM is translated 5 units right and 2 units up to LM' as the graph shows the move in positive direction.

In elementary mathematics, the term "graph" designates a plot or a function graph. A graph is, in the language of mathematicians, a set of points and the connections between some subset of those points (which may be empty). In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.

Here,

As the graph indicates a move in the right direction, LM is translated 5 units right and 2 units up to LM'.

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[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

P = $1,500

r = 0.06

n = 365 times per year

t = varies

so:  [tex]A(t)=\$1500(1+\frac{0.06}{365})^{365t}=\$1500(1.00016438)^{365t}[/tex]

a) A(5) = [tex]\$1500(1.00016438)^{365*5} = \$2,024.73[/tex]

b) A(10) = [tex]\$1500(1.00016438)^{365*10} = \$2,733.01[/tex]

c) 18 months = 1.5 years, so:

   A(1.5) = [tex]\$1500(1.00016438)^{365*1.5} = \$1,641.25[/tex]

The length of the line segment GH is 34 units

The complete question is added at the end of this solution

From the question, we have the following parameters that can be used in our computation:

GH= 7z - 1

BC = 4z - 3

Also from the question, we understand that the line segment BC is half the line segment GH

This can be represented mathematically as follows

BC = 1/2 * GH

Substitute the known values in the above equation, so, we have the following representation

4z - 3 = 1/2(7z - 1)

Multiply through by 2

8z - 6 = 7z - 1

Collect the like terms

8z - 7z = 6 - 1

Evaluate the like terms

z = 5

Recall that

GH= 7z - 1

Substitute the known values in the above equation, so, we have the following representation

GH= 7 * 5 - 1

Evaluate

GH= 34

Hence, the length is 34 units

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Complete question

The line segment BC is half the line segment GH

If GH = 7z- 1 and BC=4z- 3,

What is GH?

There is a translation 6 units to the left and 5 units​ down, followed by a reflection across the​ x-axis is the description of the rigid motions which maps ΔEFG to Δ​MNO and he reflected the triangle across the wrong axis is the Alis error.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Given,

The coordinates of ΔEFG are ​E(6​,5​), ​F(9​,5​), and ​G(6​,10​).

The coordinates of ΔMNO are ​M(0​,0​), ​N(−3​,0​), and ​O(0​,5​)

A translation is a movement of the graph either horizontally parallel to the -axis or vertically parallel to the -axis

Reflections of graphs involve reflecting a graph over a specific line. Reflecting functions are functions whose graphs are reflections of each other.

There is a translation 6 units to the left and 5 units​ down, followed by a reflection across the​ x-axis is the description of the rigid motions which maps ΔEFG to Δ​MNO and he reflected the triangle across the wrong axis is the Alis error.

Hence, there is a translation 6 units to the left and 5 units​ down, followed by a reflection across the​ x-axis is the description of the rigid motions which maps ΔEFG to Δ​MNO and he reflected the triangle across the wrong axis is the Alis error.

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Initial size of bacteria is 313, population of bacteria after 5 hours is 3.346 ×10¹¹.

here growth means increases in the number of bacterial populations with respect to time. Generally, the rate of growth of bacteria is occurred exponentially. We use the following exponential equation to calculate the number of bacteria.

N= N° e∧(kt)

In the above equation, N and N° denotes the number of populations after t minutes and initial time respectively.

k is a constant of proportion

t is the time in minutes

as per given data, the number is doubled after 10 min

N=2N°, t=10

2N°=N° e∧(k10)

2= e∧(k10)

㏑2 = k10 [we took ㏑ in both side]

k= 0.0693

after t= 80 min, the population N= 80000

now using the equation, 80000=N° e∧(k80)

as k=0.0693, N°= 313

the initial number is 313'

after t=5 hours =300 min, the population will be

N= 313 e∧ (0.0693x300)

N = 3.346×10¹¹

hence, initial population is 313 and the number increase to 3.346×10¹¹ after 5 hours.

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