Davis has $5.40 in his bank account on his fourth birthday. If his parents add $0.40 to his bank account every week, when will he have enough to buy the new Smokin' Derby race car set which retails for $24.99

Answer: We can use the Squeeze theorem to find the limit.

We know that:

x^2 + y^2 >= 0 for all (x, y)

Also,

|3xy| <= 3|x||y| <= 3x^2 + 3y^2

So,

|3xy/(x^2 + y^2)| <= 3(x^2 + y^2)/(x^2 + y^2) = 3

As we approach (x, y) = (0, 0), x^2 + y^2 becomes arbitrarily close to 0, so the right-hand side of the inequality becomes arbitrarily close to 3, and the left-hand side becomes arbitrarily close to 0.

Therefore,

lim[(x,y)->(0,0)] (3xy/(x^2+y^2)) = 0

Hence, by the sandwich theorem, we can say that the limit of the function is 0.

Step-by-step explanation:

The slope of this line is equal to 8/3.

The two additional points on the line are (-1, 13/3) and (1, 29/3).

Mathematically, the slope-intercept form of a line can be calculated by using this equation:

y = mx + c

Where:

Next, we would determine the slope of the data points as follows;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Slope, m = (7 - (-1))/(0 - (-3))

Slope, m = 8/3

At point (0, 7), an equation of this line can be calculated in slope-intercept form as follows:

Note: The y-intercept is equal to 7.

y = mx + c

y = 8x/3 + 7

For the additional points, when x = 1 we have:

y = 8(1)/3 + 7

y = 8/3 + 7

y = 29/3

When x = -1, the value of y is given by;

y = 8(-1)/3 + 7

y = -8/3 + 7

y = 13/3

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Answer:

52

Step-by-step explanation:

RTQ is 52 because if PTR is a right angle, right angles equal 90 degrees. So if PTQ is 38 degrees, we subtract 38 from 90 to get RTQ. 90-38 equals 52.

Answer:

52 degrees

Step-by-step explanation:

right angle = 90

90-38=52

So RTQ = 52 degrees

Answer:13/5

Step-by-step explanation:The answer would be 13/5 because that is the trigonometric ratio.

The 1st table is proportional and the 2nd table is not proportional.

The equation y = 3x is proportional and the equation y = 2x + 1 is not proportional.

The 1st graph is not proportional and the 2nd graph is proportional.

A proportional relationship is a type of mathematical relationship in which two variables are directly proportional to each other. This means that as one variable increases, the other also increases in a consistent ratio.

The equation for a proportional relationship is typically written as y = kx, where y and x are the variables and k is a constant ratio of proportionality. In other words, y is always k times x.

From the 1st table, let's the ratios of pencils to students (k). That:

k = 3/1 = 3

k = 6/2 = 3

k = 9/3 = 3

12/4 = 3

Thus, this is proportional.

From the 2nd table, the ratios y to x are not the same. Thus, this is not proportional.

The equation y = 3x is proportional.

The equation y = 2x + 1 is not proportional.

The 1st graph is not proportional because it does not start from the origin.
The 2nd graph is proportional because it starts from the origin.

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The sum of numbers 4 and - 9 is, - 5.

And, A weather station is a collection of instruments that measure atmospheric conditions to help study the weather and climate of a specific location.

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

Given that;

The numbers are,

⇒ 4 and - 9

Now, Sum of the numbers 4 and - 9 as;

⇒ 4 + (-9)

⇒ 4 - 9

⇒ - 5

Thus, The sum of numbers 4 and - 9 is, - 5.

And,  A weather station is a collection of instruments that measure atmospheric conditions to help study the weather and climate of a specific location.

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The equivalent expression to the given expression; 30 / 100 is; 3 / 10.

It follows from the task content that the equivalent expression to the given fraction 30 / 100 is to be determined.

Since the given expression is; 30 / 100.

It follows that the greatest common factor to the numerator and denominator is 10.

Hence, by dividing the numerator and denominator each by 10; the resulting equivalent fraction is; 3 / 10.

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The inequality that we can write is:

x - 2.45 ≥ 4.6

And the solution is x ≥ 7.05

Here we want to write in mathematic form the following sentence:

"2.45 less than a number x is greater than or equal to 4.6 "

First, "2.45 less than a number x...."

Is written as the difference:

x - 2.45

And that is greater or equal to 4.6, then we will have an inequality, and it will be:

x - 2.45 ≥ 4.6

We can solve that for x by adding 2.45 in both sides, so we will get:

x ≥ 4.6 + 2.45

x ≥ 7.05

That is the inequality solved.

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The inequality 2.45 less than a number x is greater than or equal to 4.6 as an equation is

[tex] x \: \geqslant 6.95[/tex]

An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size.

The question can be expressed mathematically as:

x - 2.4

[tex] \geqslant [/tex]

4.5

By solving the above inequality,

We have x

[tex] \geqslant [/tex]

4.5 + 2.5

Hence, the inequality gives us

[tex]x \: \geqslant 6.95[/tex]

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The rectangular bin has a depth of 20 feet.

A cuboid is a three-dimensional shape with rectangles on all sides. A cuboid has six faces, eight vertices, and twelve edges. All of the angles formed at a cuboid's vertices are right angles. The opposing edges are perpendicular to each other.

For the given situation,

A rectangular bin is in the shape of a cuboid.

Volume of the rectangular bin, V = 1200 cubic feet

Length of the rectangular bin ,l = 10 feet

Width of the rectangular bin,w = 6 feet

Let the height of the rectangular bin be h.

The formula of volume of cuboid is

[tex]v=lwh[/tex]

Now substitute the above values,

⇒ 1200= (10)(6)h

⇒ [tex]h=\frac{1200}{60}[/tex]

⇒ h= 20

Hence we can conclude that the rectangular bin is 20 feet deep.

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The depth of the box is found through the volume formula for a rectangular prism, which involves multiplying the length, width and depth. Knowing the volume when half-filled, and the length and width, we can calculate the box is 10 feet deep.

This problem deals with the concept of volume in mathematics. First, the formula for the volume of a rectangular prism (or a box) is length multiplied by width multiplied by height. In this case, we know that the box is half filled with grain and that the total volume of that grain is 200 cubic feet. So, if the box was filled completely, it would have a volume of twice that, or 400 cubic feet.

Now we know that the box's volume is 400 cubic feet and its length is 8 feet and width is 5 feet. So to find the height (which is what we're calling 'depth' in this case), we can use our volume formula. We divide the total volume by the product of the length and width (400/40) to find the height or depth, resulting in a depth of 10 feet.

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Quotient of x⁴ - 13x² + 36 ÷ x-3 = x³+3x²-4x-12

Factored form of x⁴ - 13x² + 36 = (x+3)(x+2)(x-2)(x-3)

Zeros of  x⁴ - 13x² + 36 = -3, -2, 2, 3

A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division (No division operation by a variable).

Given,

f(x) = x⁴ - 13x² + 36 and its factor (x-3)

Using synthetic division

x⁴ - 13x² + 36 ÷ (x-3) = x³+3x²-4x-12

Quotient = x³+3x²-4x-12

= (x³+3x²)-(4x-12)

= x²(x + 3) - 4 (x + 3)

= (x+3)(x² - 4)

= (x+3)(x+2)(x-2)

x⁴ - 13x² + 36 = (x³+3x²-4x-12) (x-3)

Factored form

x⁴ - 13x² + 36 = (x+3)(x+2)(x-2)(x-3)

By factors, zeros are:

x+3 ⇒ x = -3

x+2 ⇒ x = -2

x-2 ⇒ x = 2

x-3 ⇒ x = 3

Hence, x³+3x²-4x-12 is the quotient of x⁴ - 13x² + 36 ÷ x-3 .

(x+3)(x+2)(x-2)(x-3) is the factored form of x⁴ - 13x² + 36.

x⁴ - 13x² + 36 has zeros = -3, -2, 2, 3

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230p – 1010 = 650p – 400 – p and 2.3p – 10.1 = 6.49p – 4 are the equations after rewriting their properties have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p.

As with other words like "equal," "equality," and "equate," the word "equa" at the start of the equation will sound familiar to you. Making things balance out is the theme of all these words. A statement of two quantities' equality is expressed by an equation.

You might still attempt to make the two sides equal even if the equation is not mathematical but rather, say, interpersonal. It might be simpler for two people to decide to remain together for a while if marriage is removed from the picture, for instance.

Given the equation 2.3p – 10.1 = 6.5p – 4 – 0.01p

When multiplied by 100, it becomes

230p – 1010 = 650p – 400 – p

And 6.5p - 0.01p = 6.49p

So, 2.3p – 10.1 = 6.49p – 4

Thus, 230p – 1010 = 650p – 400 – p and 2.3p – 10.1 = 6.49p – 4 are the equations after rewriting their properties have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p.

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Answer:

Sophia's airplane flew 8.6 + 2.2 = 10.8 yards.

Franco threw his airplane 1.5 times as far as Sophia's airplane, which means that Franco's airplane flew 1.5 * 10.8 = 16.2 yards.

Therefore, Franco's paper airplane flew 16.2 yards.

Answer:

Franco went 16.2 yards

Step-by-step explanation:

8.6 + 2.2 = 10.8

10.8 x 1.5 = 16.2

Answer:

-----------------------------------------

To find the remaining credit plug in the value of x = 30 into equation and calculate:

In mathematics, the value for x is 9.38 in Example 1 and 11.40 in Example 2.

What are the value signifies?

The value in mathematics refers to the numerical representation of a quantity or concept. It represents the numerical magnitude of a mathematical expression, equation, or quantity.

For example, in the expression 2 + 3 = 5, the value of 2, 3, and 5 all represent specific numerical magnitudes. The value of a variable, such as x or y, can change depending on the context or equation it is used in, but it still represents a specific numerical value.

Values can be represented in different forms, such as integers, fractions, decimals, or real numbers, and they are used to perform mathematical operations and solve mathematical problems.

a) Example 1

AB  is a diameter

PQ is a chord

AO = 13

AO is perpendicular to PQ (2AP=AQ)

In Δ APO

[tex](AO)^2 =(AP)^2+ (PO)^2[/tex]

[tex](13)^2 = (9)^2 + X^2[/tex]

[tex]169 = 81 +X^2[/tex]

X^2 = 169-81

X^2 = 88

X = √88

X = 9.38

As a consequence, 9.38 is equal to x.

b) Example 2

LM = 18

KN = 7

LK = ?

LN = 9

In Δ LKN:

[tex]X^2 = (KN)^2 + (LN)^2[/tex]

[tex]X^2 = (7)^2 + (9)^2[/tex]

X^2 = 49 + 81

X^2 = 130

X =√ 130

X = 11.40

As a consequence, 11.40 is equal to x.

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The algebraic fraction which is equivalent to the given expression in which case, the denominator is 24a³b² as required is; 15b³ / 24a³b².

As evident in the task content; the given algebraic expression whose equivalent is to be determined is; 5b / 8a³.

However, to determine an equivalent expression whose denominator is; 24a³b²; one must determine the quotient of 24a³b² and 8a³.

= 24a³b² / 8a³.

= 3b²

On this note, it follows that the numerator and denominator of the given algebraic fraction can each be multiplied by 3b² in order to determine the equivalent expression.

= ( 5b • 3b² ) / ( 8a³ • 3b² )

= 15b³ / 24a³b².

Ultimately, thee required equivalent algebraic fraction is; 15b³ / 24a³b².

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Since George can build a laptop twice as fast as Kurt and working together takes them 3 hours, an equation which you would use to determine how long it will take Kurt working alone is: D. 1/t + 1/2t = 1/3.

In order to determine the amount of time it would take Kurt working alone, we would have to assign variables to the amount of time taken by George to build a laptop and the amount of time taken by Kurt to build a laptop, and then translate the word problem into an algebraic equation (expression) as follows;

Since George can build a laptop twice as fast as Kurt, an equation which models this situation is given by;

g = 2t     .....equation 1.

Next, we would write an algebraic equation (expression) that models the combined work rate;

1/c = 1/t + 1/g     .....equation 2.

Substituting equation 1 into equation 2, we have the following:

1/3 = 1/t + 1/2t

1/t + 1/2t = 1/3.

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Answer:

IT is 245 pounds

Step-by-step explanation:

The solution is: 0.1225 tons  is 245 pounds.

Here, we have,

given that,

245 pounds

we need to find the value in ton

we know that,

1 pound = 1/2000 ton

             = 0.0005 ton

let, 245 pounds = x ton

so, we get,

1 pound = 0.0005 ton

245 pounds = 0.0005 * 245  tons

                    = 0.1225 tons

so, x = 0.1225 tons

Hence, The solution is: 0.1225 tons  is 245 pounds.

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The correction of the three capitalization that where wrongly written in the given statement are

The capitalization of a word is defined as the use of capital letters for the first word of a sentence and for all proper nouns.

The sentence, ' Darnell is Writing an Article about an early Period of art history' contains proper nouns such as art and history which should be in capital letters.

The word 'written' should be in a small letter because it didn't start the sentence.

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Answer:

1:3 5/9

18/18=1 64/18=3 5/9

Answer:

4. So Adrian can buy 3 more cd's at the sale price.

5. 36 km every week.

Step-by-step explanation:

Adrian has enough money to buy 3 cd's at $16 each. If the cd's are on a sale and are sold at a discount price of $12, he can buy more cd's because the price is cheaper. To find out how many more cd's he can buy, you can subtract the original cost of the cd's from the sale price of the cd's and then divide that amount by the sale price of the cd's.

3 cd's x $16 = $48

$48 - $12 = $36

$36 / $12 = 3

Rehman and his father jog to the park 3 km away from their house and back every evening except Sundays, so they jog a total of 6 km per day. To find out how many kilometres they jog per week, you need to multiply the distance they jog per day by the number of days they jog in a week (7 days - 1 Sunday).

6 km/day x 6 days/week = 36 km/week

So Rehman and his father jog 36 km every week.

Jonathan deposited $847 in his saving account.

This bank deposit slip is the record of the total amount that a person is depositing into a bank account. It includes the details of the items being deposited, that is, the number of checks and notes or coins of each type in the form of cash.

Given,

Amount in checks = $40 + $50 + $35 = $125

8 fifty-dollar bills = 8 × $50 =$400

12 twenty-dollar bills = 12 × $20 = $240

12 ten-dollar bills = 12 × $10 = $120

8 five- dollar bills = 8 × $5 = $40

22 1-dollar bills = 22 × $1 = $22

Subtotal = $125 + $400 + $240 + $120 + $40 + $22 = $947

Less cash = $100

Total = $947 - $100

Total = $847

Hence, $847 is the total deposited amount by Jonathan.

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The given expression (3p)³ without exponents is 27×p×p×p.

Exponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself.

The given exponential expression is (3p)³.

Here, (3p)³=3p×3p×3p

= 27×p×p×p

Therefore, the given expression (3p)³ without exponents is 27×p×p×p.

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Using the rate of the exponential growth to calculate the exponential function, the number of subscribers after 10 years is 3446

An exponential function is a function in which the variable appears in an exponent. It is of the form f(x) = aˣ, where a is a constant and x is the independent variable. The graph of an exponential function is a curve that increases or decreases at an increasing rate.

To solve this problem, we have to find the rate and then calculate the number subscribers after 10 years.

In a given exponential function;

A = P(1 + x)ⁿ

Since this is an exponential growth, we can calculate the rate as;

1 year = 250 subscriber

2 years = 3 * 250

rate = (250 / 750) * 100

rate = 30%

We can substitute the values into the formula and solve

A = 250(1 + 0.3)¹⁰

A = 3446.46

They are expected to have 3446 subscribers after 10 years

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Answer: 4

Step-by-step explanation: Amplitude has to do with how high and low the function goes according to the midline. The midline for this function is at -3. The maximum point is 1, and the minimum point is -7. The function goes up 4 units and down 4 units

Answer:

Amplitude = 4

Step-by-step explanation:

The amplitude of a sinusoidal function is the height (vertical distance) from the midline to the peak (or trough).

To calculate the amplitude, simply divide the vertical distance between the maximum and minimum y-values by 2.

From inspection of the given graph:

Therefore:

[tex]\implies \sf Amplitude = \dfrac{1-(-7)}{2}=\dfrac{8}{2}=4[/tex]

Answer:

x(8 + 3x)

Step-by-step explanation:

8x + 3x^2

Find what is common between the two coefficients, which is x.

So place x as the multiplier:

x(8 + 3x) = will give you the same result (8x + 3x^2).

Hope you understood :)

The number of seniors that are on academic watch than freshman will be 868.

A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.

In this case, since there are there are 2435 seniors and 1567 freshmen on academic watch. The number of seniors that are on academic watch than freshman will be:

= 2435 - 1567

= 868

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Complete question

In a school, there are 2435 seniors and 12567 freshmen on academic watch. How many more seniors are on academic watch than freshman

Answer:

c.

Step-by-step explanation:

that is easy.

a matrix multiplied by a constant is multiplying every element in the matrix by that constant.

and subtracting a matrix from another is subtracting the elements on each position.

it is a simile as that.

for that reason I only need to look at the first, top left element to determine the correct answer :

-1×2 - 4×7 = -2 - 28 = -30

so, c. is the right answer.

the calculation in full :

2A =

-2 18 4

20 -20 4

-10 12 -10

4B =

28 -4 -4

24 -16 -12

-40 40 -28

so, 2A - 4B =

-30 22 8

-4 -4 16

30 -28 18

Answer:

Step-by-step explanation:

Yes, Monica is correct. When dealing with simple interest, the amount of interest earned is determined by the principal amount, the interest rate, and the time the money is invested. Since Monica and Paul both have different principal amounts and interest rates, the amount of interest each of them earns in one year will be different. Monica's account has a higher interest rate of 3.4%, so she will earn more interest in one year compared to Paul's account, which has a lower interest rate of 2.6%.

Based on the graph of this quadratic function with vertex (-1, -4), the domain and the range are as follows;

Domain = {-3, 0.5}.

Range = {-4, ∞}.

In Mathematics, the horizontal extent of any graph of a function represents all domain values and they are read and written from smaller to larger numerical values, and from the left of a graph to the right.

Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

Note: The vertex of any quadratic function represents the minimum of the given function.

By critically observing the graph shown in the image attached below, we can reasonably and logically deduce the following:

Domain = -3 < x < 0.5 or [-3, 0.5].

Range = -4 < y < ∞ or [-4, ∞].

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