correct 19784065 to 2 significant figures​

A. Rachel have the amount of money left in her account after 9 trips, $112

B. Rachel can take a number of trips until her account is empty, 16 trips

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

For example, 3x+2y=0.

Types of equation

1. Linear Equation

2. Quadratic Equation

3. Cubic Equation

Given that,

Rachel spends amount of money in each trip = $16

Rachel has total money in beginning of a month = $256

Equation for a relation between number of trips and amount of money in account,

A(t)=256-16t

A.   Amount of money left in account after 9 trips

    A(9) = 256-16×9

    A(9) =  256 - 144

    A(9) =    112

B.   Number of trips she can do till her account becomes empty

      0 = 256 - 16t

      16t = 256

       t =  256/16

       t = 16

Hence, the results are respectively,   $112 and 16    

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The sine function graphed is given as follows:

y = 0.5sin(x - π/4).

The sine function for this problem is defined as follows:

y = Asin(Bx - C).

For which the parameters are given as follows:

The difference between the highest value and the lowest value is of 1, hence the amplitude of the function is givne as follows:

2A = 1

A = 1/2

A = 0.5.

The period of the function is of 2π, hence the parameter b is obtained as follows:

2π/B = 2π

B = 1.

The sine function, without phase shift, should pass through the origin, while the function here was shifted right π/4 units, hence the parameter C is given as follows:

C = π/4.

Hence the function is:

y = 0.5sin(x - π/4).

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Answer:

A line plot is the most appropriate way to visualize these data. The scale should be labeled starting at 14 and going up to 19, with increments of 1/8 pound. For example, the x-axis labels could be 14, 14⅛, 14¼, 14⅜, 14½, 14⅝, 14¾, 14⅞, 15, 15⅛ and so on up to 19.

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Answer:

y = -64

Step-by-step explanation:

y / -8 = 8

y = -64

Answer:

y= -64

Step-by-step explanation:

I don't understand the question but

y/-8 = 8

y = 8×-8

y = -64

Answer: Hi there! Your equation would be y = −4x + 8

Step-by-step explanation: I hope this helps!

A linear expression is in polynomials when it is expressed as the product of it's factor

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power. In other words, none of the exponents can be greater than 1. For example, x² is a variable raised to the second power, but x is a variable raised to the first power.

When two linear factors are expressed together the result forms a polynomial.

A polynomial is an expression in which the power of it's variable is higher than 1. quadratic expression is also an example of polynomial.

For example if an expression is given as (x+2)(x+3). The result of the expression will give x²+5x+6 which is a quadratic expression and a polynomial.

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The sentence that correctly places the slash between the subject and the predicate of the stated sentence is, Four groups / of four soldiers guarded / Pedro in jail. Correct answer: letter B.

Is important to consider the context in which the sentence is used. Depending on the situation, the answer may vary. For example, if the sentence is part of a larger dialogue about the strength of a prison guard, then more information about the security measures taken and the number of soldiers deployed to guard Peter would be relevant.

Alternatively, if the sentence is part of a discussion about the importance of loyalty and friendship, then information about the relationship between Peter and the soldiers would be important.

Which sentence correctly places the slash mark between the subject and predicate of the sentence? Four groups of four soldiers watched over Peter in jail.

A) Four groups / of four soldiers watched over Peter in jail.

B) Four groups of four soldiers / watched over Peter in jail.

C) Four groups of four soldiers watched / over Peter in jail.

D) Four groups of four soldiers watched over Peter/in jail.

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The German mark appreciated by 1.3% against the US dollar between 1970 and 1976.

This was due to strong economic growth in Germany and a decrease in inflation, which increased the purchasing power of the mark against the dollar. The appreciation of the mark against the dollar also helped to stimulate exports from Germany and reduce imports, creating a more balanced trade balance between the two countries.

The German mark appreciated by 1.3% against the US dollar due to strong economic growth and reduced inflation.

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Any three equations do not have any solution if all the determinants associated with the system of equations are equal to 0.

For a system of 3 linear equations

a₁x + b₁y + c₁z + d₁ = 0

a₂x + b₂y + c₂z + d₂ = 0

a₃x + b₃y + c₃z + d₃ = 0

We need to find some determinants that will help us determine the no. of solutions it can have.

We have,

 [tex]\Delta = \left[\begin{array}{ccc}a_1&b_1&c_1\\a_2&b_2&c_2\\a_3&b_3&c_3\end{array}\right][/tex]

[tex]\Delta_1 = \left[\begin{array}{ccc}d_1&b_1&c_1\\d_2&b_2&c_2\\d_3&b_3&c_3\end{array}\right][/tex]

[tex]\Delta_2 = \left[\begin{array}{ccc}a_1&d_1&c_1\\a_2&d_2&c_2\\a_3&d_3&c_3\end{array}\right][/tex]

[tex]\Delta_3 = \left[\begin{array}{ccc}a_1&b_1&d_1\\a_2&b_2&d_2\\a_3&b_3&d_3\end{array}\right][/tex]

Now first we need to check the value of Δ

If, Δ ≠ 0, then we can say that the system of equations is consistent and will give us a unique solution.

However, we are concerned with the case when Δ = 0.

If Δ = 0, then we need to find the values of Δ₁, Δ₂, and Δ₃.

If at least one of the three Δ₁, Δ₂, and Δ₃ is not equal to 0 then we say that the equation is consistent.

Now if,

Δ₁ = Δ₂ = Δ₃ = 0, then we need to do the following:-

We need to take any 2 equations and get the values of x and y in terms of z.

Now we need to substitute the value of x and y for these values in the third equation.

If the third equation is satisfied, we can say that they will have infinite solutions but if they don't, then we can say the given system of equations will have no solutions.

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One concept that I have learnt in geometry is the congruency of triangles.

We know that in geometry, the core of the study is the shapes. We have studied several shapes and the properties of the shapes and there are a lot of concepts that have been discussed.

One of the important concepts of geometry that we have discussed is the congruency of the triangles. There are several reasons why we can say that the triangles are congruent such as;

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The expression that represents the total cost of buying and shipping the baseball cards,

= 6(1.75) + 5(9.5) + 2(20.5) + 4

Combining objects and counting them as one big group is done through addition. In arithmetic, addition is the process of adding two or more integers together. Addends are the numbers that are added, and the sum refers to the outcome of the operation.

Given:

Jake is buying baseball cards for his brother in college.

The price of a card is based on its condition.

The table shows the total cost of x number of cards for each condition.

He buys 6 that are in fair condition, 5 that are in good condition, and 2 that are in excellent condition.

The shipping cost for the baseball cards is $4.00.

The expression that represents the total cost of buying and shipping the baseball cards,

= 6(1.75) + 5(9.5) + 2(20.5) + 4

= 10.5 + 47.5 + 41 + 4

= 103

Therefore, the total cost is $103.

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Answer: Quantity is the indefinite amount of any material item. It's a measurement of something.

Step-by-step explanation:

I hope this helps!

The enlarged size of the poster will be 13.5 inches.

A scale factor is defined as the ratio of the scale of a given original object to the scale of a new object that is its representation but of a different size (bigger or smaller).

The scale factor is defined as the proportion of the new image's size to that of the previous image.

Given that Alisha wants to enlarge a photograph to make into a poster for her room. The photograph is 6 inches tall. The poster will be created using a scale of 4.5 inches = 2 inches.

Scale factor = 4.5 / 2 = 2.25

The enlarged size of the poster will be calculated as:-

Size = 6 x 2.25

Size = 13.5 inches

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Emilia and her brother used the computer for 1.5 hours.

When Emilia and her brother need to use the family computer for their homework, they have agreed to share the computer equally. On this particular evening, they both needed the computer for 3 hours. To understand how much time each of them used the computer, we need to divide the total time by the number of users.

Dividing the total time of 3 hours by the number of users which is 2, we get 3 hours / 2 = 1.5 hours. This means each person, Emilia, and her brother, use the computer for 1.5 hours each.

It's important to note that this is possible because they both agreed to share the computer equally. If one of them needed more time than the other, they might have to work out a different arrangement.

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Answer:

4

Step-by-step explanation:

8x + 15 = 5.5x +25

so 2.5x =10

x=4

Answer:

#1) [tex]\frac{1}{7}[/tex]

#2) 4

Step-by-step explanation:

#1) 37x=9x+4

37x=9x+4

-9x

28x=4

28   28

answer: [tex]\frac{4}{28} = \frac{1}{7}[/tex]

#2) 2x+3=11

2x+3=11

        -3

2x= 8

2     2

answer: [tex]\frac{8}{2} =4[/tex]

Answer:

2.29 pounds.

Step-by-step explanation:

The following is the analysis for the response to this query:

There must be some relationship among both the volume and the weight.

According to the given label's information, one cup weighs 99 grams. Given that there are 99/453.6 pounds for every cup as well as you require 7*1 1/2 cups, multiplying 10.5 cups by 99/453.6 pounds for every cup results in 2.3 pounds. A pound (avoirdupois) is defined as 453.6 grammes.

Another way to write this would be:

7 (pecan pie) * 1.5 (cup/pecan pie) * 99 (gram/cup) * 0.0022 (pounds/gram) = 2.292 pounds

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The solution is the set of values for the two variables (x, y) that satisfy both equations.

To solve a system of two equations with two variables that are both quadratic (2nd degree), you can use the following steps:

Write the two equations in standard form, which is ax² + bx + c = 0 for each equation, where a, b, and c are coefficients.

Solve each equation separately for one variable by factoring or by using the quadratic formula.

Substitute the value of one variable from one equation into the other equation, and solve for the other variable.

Substitute the value of the other variable from the previous step back into one of the original equations to find the value of the first variable.

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Answer:

88 yards

Step-by-step explanation:

because the park is 11 inches wide in the drawling, and the scale of it is 1:8

so the actual width of the park is

[tex]11/1/8=11*8=88 yards[/tex]

11 divided by 1/8

Answer:

Hope it will help you...

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The area of an isosceles triangle with an equal side of 8 cm and each equal side of 5cm is 12cm².

[tex]Altitude =\sqrt{5^{2} -4^{2} }=3[/tex]

[tex]Area = 1/2(base)(height)[/tex]

[tex]Area = 1/2*8*3 = 12cm^{2}[/tex]

A triangle is a polygon with three edges and 3 vertices. The terminology for categorizing triangles is more than two thousand years vintage, having been defined on the first actual page of Euclid's elements.

In Euclidean geometry, any three factors, while non-collinear, decide a completely unique triangle and simultaneously, a unique plane (i.e. a -dimensional Euclidean space). In different words, there's best one plane that consists of that triangle, and every triangle is contained in some plane. If the entire geometry is only the Euclidean plane, there is the best one plane and all triangles are contained in it; however, in higher-dimensional Euclidean spaces, this is not real. this text is ready triangles in Euclidean geometry, and in particular, the Euclidean plane, except wherein otherwise stated.

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The solution for the logarithm, log2 x 2 is x=2log(2) or x=6.6438561

Given,

In an exponential equation, the variable is expressed as an exponent.

A logarithmic equation is one that uses the logarithm of an expression involving a variable.

Check to check if you can write both sides of an exponential equation as powers of the same number before you attempt to solve it.

Here,

Divide each term in

log(2)x=2

by log(2).

That is,

log(2) x log(2)=2log(2)

Simplify the left side.

log(2).

x=2log(2)

The result can be shown in multiple forms.

Exact Form:

x=2log(2)

Decimal Form:

x=6.6438561

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Answer :

Domain: Domain of a functions is defined as set of all values of x taken by the function, Which means all the values of x taken by the graph.

From the figure, we can see that all values of x taken from [-1, - 4]. So domain is [-1, - 4].

Range: Set of all values produce of by function, Which means all y's values taken by the graph.

From the graph, we can see that between - 2 to - 4 all values are taken by graph Hence, Range is given as [-2,-4].

Answer:

Step-by-step explanation:

The speed of a point on the wheel rim is 35000π cm/s (2500 rev/min and 14cm diameter).

what is circumference ?

Circumference is the distance around the edge of a circle. It can be calculated using the formula: C = 2πr, where C is the circumference and r is the radius of the circle.

To express the speed of a point on the rim of the wheel in centimeters per second, we first need to find the circumference of the wheel using the diameter. The circumference can be found using the formula: C = 2πr, where C is the circumference and r is the radius of the wheel.

Since the diameter is 14cm, the radius of the wheel is 14/2 = 7cm.

Therefore, the circumference of the wheel is: C = 2π(7) = 14π cm

Next, we need to find the distance traveled by a point on the rim of the wheel in one revolution. This distance is equal to the circumference of the wheel.

So, the distance traveled by a point on the rim of the wheel in one revolution is: 14π cm

To find the speed in centimeters per second, we need to multiply the distance traveled in one revolution by the number of revolutions per minute.

The wheel rotate 2500 revolution per minute.

The speed of a point on the wheel rim is 35000π cm/s (2500 rev/min and 14cm diameter).

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Circumference is the distance around the edge of a circle. It can be calculated using the formula: C = 2πr, where C is the circumference and r is the radius of the circle.

We must first determine the circumference of the wheel using the diameter in order to describe the speed of a point on the rim of the wheel in centimeters per second. The formula C = 2r, where C is the circle and r is the radius of the wheel, can be used to determine the circumference.

Since the diameter is 14cm, the radius of the wheel is 14/2 = 7cm.

Therefore, the circumference of the wheel is: C = 2π(7) = 14π cm

The Cartesian product of A(1, 2) and B(a, b) is the set A × B, i.e., {(1, a), (1, b), (2, a), (2, b)}.

Given sets are:

A(1, 2)

B(a, b)

A × B = {1, 2} × {a, b}

         = {(1, a), (1, b), (2, a), (2, b)}

The Cartesian product, which consists of all ordered pairs of items with the first element coming from the first set and the second element coming from the second set, and so on, is a set created from two or more given sets. Once more, an ordered pair set results from the Cartesian product of sets.

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Answer: it mean 7-9.

Step-by-step explanation:

7 is smaller than 9, so the answer is going to be negative. I like to do

7-9

Is basically just 9-7, just put a negative label

So 7-9 can be solved as 9-7=2 slap on a negative sign and -2! Hope this helps!

To write 10 more than a number, we use the mathematical operation of addition and the notation 10 + Number = N+10.

To write 10 more than a number, we need to use the mathematical operation of addition. Addition is the process of combining two or more numbers to find the total or sum.

In this case, we are given the number 5 and we are asked to find the number that is 3 more than it. To do this, we can use the mathematical notation: 10 + Number = N+10.

This notation means that we are adding 10 to a number, which results in N+10. The "+" symbol is the addition operator and it is used to indicate that we are performing an addition operation. The "=" symbol is used to indicate that the result of the addition is N+10.

Another way to write 10 more than a number is to use the phrase "10 plus a number". This phrase indicates that we are adding 10 to a number to get N+10.

Therefore, In short, to write 10 more than a number, we use the mathematical operation of addition and the notation 10 + Number = N+10. This means that we are adding 10 to a number, resulting in N+10. It can also be written as "10 plus N", indicating the same operation.

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[tex]x~~ : ~~(x+5)~~ = ~~4~~ : ~~5\qquad \implies \qquad \cfrac{x}{x+5}=\cfrac{4}{5} \\\\\\ 5x=4x+20 \implies x=20[/tex]

Answer:

1/9880

Step-by-step explanation:

Number of Combinations

[tex]\displaystyle C(40,3)=\frac{40!}{3!(40-3)!}=\frac{40!}{3!\cdot37!}=\frac{40*39*38}{3*2*1}=40*13*19=9880[/tex]

Thus, the probability of guessing that exact combination on the first try is 1/9880.