Sarah opens a new checking account. She deposits $211 to start initially. If sarah is able to deposit her allowance for 16 weeks straight, she will have $355. How much does Sarah receive for an allowance every week?​

The polynomial identities and proofs are mathematical statements that show that two algebraic expressions are equal. They can be used to simplify equations or to prove certain properties of polynomials.

For example, to prove x^2 + 2x + 1 = (x + 1)^2, you can factor the left side and expand the right side. This will show that x^2 + 2x + 1 = x^2 + 2x + 1 and thus the two polynomials are equal.

x^2 + 2x + 1

= (x + 1) (x + 1)

= x^2 + 2x + x + 1

= x^2 + 3x + 1

= (x + 1)^2

To prove that x^2 + 2x + 1 = (x + 1)^2, we first factor the left side x^2 + 2x + 1 and expand the right side (x + 1)^2. This will give us two equations: x^2 + 2x + 1 and x^2 + 3x + 1. From here, we can observe that both equations are identical, and thus the two polynomials are equal. This can be further verified by noting that the left side is the result of squaring x + 1, and the right side is the square of x + 1. Therefore, x^2 + 2x + 1 is equal to (x + 1)^2.

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Answer:

the answer 446600 ,nice to be of help to u

Latoya swims 7 kilometers per hour if there were no currents.

Latoya's speed without the current can be calculated by adding the speed she swam against the current (S-c) to the speed of the current (c). Since she swam the same distance at the same time in both cases, we know that (S-c) * t = S * t. Therefore, S = (S-c) + c. We know that the rate of the current is c = 2 Km/h and she swam 5 Km against the current, so (S-c) = 5 Km/t and S * t = 15 Km.

By substituting the values, we get S = (5 + 2) Km/t = 7 Km/t.

Complete question :

Latoya swam 5 kilometers against the current in the same amount of time it took her to swim 15 kilometers with the current. The rate of the current was 2 kilometers per hour. How fast would Latoya swim if there were no currents?

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The three numbers which are in the ratio 1:2:3 and whose sum of the cubes is 4500 are 5, 10, and 15.

As given in the question,

Let us consider three number which are in the ratio 1: 2 : 3 be,

y, 2y , and 3y.

As per given condition:

Sum of their cubes = 4500

⇒x³ + (2x)³ + (3x)³ = 4500

⇒ x³ ( 1 + 8 + 27 ) = 4500

⇒36x³ = 4500

⇒ x³ = 4500/36

⇒x³ = 125

⇒ x = ∛125

⇒ x = 5

⇒2x = 10

⇒3x = 15

Therefore, three numbers which are in the given ratio are given by 5, 10, 15.

The above question is incomplete, the complete question is :

Three numbers are in the ratio 1:2:3 and the sum of their cubes is 4500. Find the numbers.

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Answer:

-8

Step-by-step explanation:

Suppose we have a linear system that consists of 5 equations with 3 variables, then the maximum number of pivot columns is 3. In this case, the solution exists and unique.

A pivot is defined as the position of the leading entry in a matrix. For example in the matrix below:

1 0 *

0 1 *

0 0 0

The pivot positions are the ones with bold entries.

If we have a system of 5 equations with 3 variables, then the maximum pivot columns is 3.

 0 1 * | *

 0 0 0 | 1

 0 0 0 | 0

 0 0 0 |0

       The last column is an augmented column

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The angle-side connection theorem states that angle E in triangle DEF is equal to angle F.

Since a triangle has three sides and three vertices, it is a polygon. It is a fundamental geometric shape. Triangle ABC is the moniker given to a triangle that has vertices A, B, and C. When the three points are not collinear, a singular plane and triangle are found in Euclidean geometry. A triangle is a polygon if it has three sides and three corners. The points where the three sides meet are known as the triangle's corners.

given

The length of every triangle side is proportional to the size of the angles that are directly across from them, according to the angle-side relationship theorem.

Thus,

Angle F = (61 + 58)/180 (sum of triangle)

F = 61 degree angle

Since mE = 61 degrees, F and E are therefore congruent to one another.

It follows that the sides that are perpendicular to each angle will also be parallel to one another.

The angle-side connection theorem states that angle E in triangle DEF is equal to angle F, which also implies that the sides that are opposite one other are congruent.

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The triangles are similar triangles. and the scale factor of triangle UVW to triangle XYZ is 7

What is triangle ?

triangle can be defined in which it contains three sides , three angles and the sum of three angles is always is 180 degrees.

How to determine the scale factor

From the given figure, we have the following corresponding side lengths:

UW = 2

XZ= 14

The scale factor of UVW to XYZ is then calculated using:

Scale factor = XZ/UW

Substitute known values

Scale factor = 14/2

Divide

Scale factor = 7

Hence, the scale factor of triangle UVW to triangle XYZ is 7

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Answer:Acute Angle

Step-by-step explanation:

What is a 15 degree angle called? Acute Angle – Acute Angle An acute angle is an angle that is more than 0° but less than 90°. Common examples of acute angles include: 15°, 30°, 45°, 60°, etc.

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If the value of a car is $21000 and it loses 8% of its value every year , then the approximate monthly decrease in value is $140   .

The value of the car is given as = $21000 ;

the percent decrease in the value of car is = 8% every year ;

So , in 1 year the value of car decreased is = [tex]0.08\times 21000[/tex]

= [tex]1680[/tex]  .

So , in 1 year value of car decreased by $1680 ;

to find the monthly decrease , we divide the value by 12 ;

the monthly decrease is = [tex]\frac{1680}{12}[/tex] = $140 .

Therefore , The Approximate monthly decrease in the value of car is $140 .

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According to the ratio presented, he spends 32 minutes on his science homework.

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

Given, The ratio Tim spends on math homework to science homework is 5 to 4.

thus,

(time on math)/ (time on Science) = 5/4

Since he spends 40 minutes on math homework,

From equation 1

Time spent on science = 4/5 * (time on math)

Time spent on science = 4/5 * 40

Time spent on science = 32

therefore, 32 minutes he spends on science homework as per the given ratio.

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[tex]\it 13x+9x=20x+12 \Rightarrow 22x=20x+12\bigg|_{-20x} \Rightarrow \ 2x=12 \Rightarrow x=6[/tex]

After taking the common, the factored form of [tex]27x^3-64[/tex] is [tex](3x-4)(9x^2+12x+16)[/tex].

In the given question, we have to find the factored form of [tex]27x^3-64[/tex].

The following is how we factor the GCF out of a polynomial:

(1) Determine the polynomial's GCF for each term.

(2) Present each term as the GCF and another factor's product.

(3) To factor out the GCF, use the distributive property.

To solve this question we use the formula [tex](a^3-b^3) = (a-b)(a^2+ab+b^2)[/tex]

We can write [tex]27x^3-64[/tex] as

[tex]27x^3-64[/tex] = [tex](3x)^3-(4)^3[/tex]

[tex]27x^3-64[/tex] = [tex](3x-4)((3x)^2+3x\cdot4+(4)^2)[/tex]

[tex]27x^3-64[/tex] = [tex](3x-4)(9x^2+12x+16)[/tex]

Hence, the factor form of [tex]27x^3-64[/tex] is [tex](3x-4)(9x^2+12x+16)[/tex].

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The complete question is:

What is the factored form of [tex]27x^3-64[/tex]?

The unique solution system is given by the intersection of two lines .

When the line intersects at a point the value of the function becomes zero and also intersecting lines meet at only one point.

Hence this type of system have a unique solution.

The condition of the unique solution is

a1/a2[tex]\neq[/tex]b1/b2

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7x is equal to 7 times x, so the answer is 7 times whatever x is.  if x is equal to 6, then 7x would be equal to 7 multiplied by 6, which is 42. Therefore, the product of 7x is 7 times whatever x is.

7x is an expression that is asking for the product of 7 and x. The product is the result of multiplying two or more numbers together. Therefore, 7x is equal to 7 times whatever x is.

7x is an expression used to calculate the product of 7 and x. The product is the result of multiplying two or more numbers together, so 7x is equal to 7 multiplied by whatever x is. It is important to remember that the product of two or more numbers is the answer you get after multiplying them together. For example, if x is equal to 6, then 7x would be equal to 7 multiplied by 6, which is 42. Therefore, the product of 7x is 7 times whatever x is.

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Answer:

Option D

Step-by-step explanation:

As per your question, cos θ = 3/10

tanθ = √(sec²θ - 1) = √((1/cos²θ) - 1)

Put the value of cos θ, √(1/(9/100) - 1 = √(100/9 - 1) = ±√91/9 = -√91/3 (tan θ is negative in the third quadrant.)

So, option D is the correct answer.

Answer: C- Opposite sides are parallel. (Same distance apart)

Hope this helps :)

To find out how many people watching the parade are adults, we can subtract the number of children from the total number of people.

524 people - 178 children = 346 adults

So, 346 people watching the parade are adults.

Answer:

To find out how many people watching the parade are adults, we have to subtract the number of children from the total number of people.

Total number of people watching the parade: 524

Number of children watching the parade: 178

524 - 178 = 346

Therefore, 346 people watching the parade are adults.

The relative frequency for the fourth class, 240 - 259 is 22.

The number of times a specific value for a variable (data item) has been seen to occur in relation to the overall number of values for that variable is referred to as the relative frequency. By dividing the absolute frequency by all possible values of the variable, the relative frequency is derived.

To calculate the relative frequency,

Divide the frequency by the total number of data values to obtain the relative frequency. Add all of the earlier relative frequencies to the relative frequency for the current row to obtain the cumulative relative frequency.

Below you can see a distribution table to compare the relative frequencies of other class of students to better understand it.

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The coordinates of point J' are J'(-12,8)

A dilation is a transformation that changes the size of a figure but not its shape.

In a dilation with respect to the origin, a point (x, y) is transformed to a point (kx, ky) where k is a scale factor.

In this case, the point J (-3, 2) is transformed under a dilation of 4 with respect to the origin.

So the image point J' is (kx, ky) = (-3*4, 2*4) = (-12, 8)

So the image point of J(-3,2) under a dilation of 4 with respect to the origin is J'(-12,8)

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Complete question

The triangle JKL is dilated by a scale factor of 4 with the center of dilation at the origin.

What are the coordinates of point J' if J = (-3, 2)?

The k represents a vertical shift (how far up, or down, the graph has shifted from y = 0).

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Note that if a tomato has a mass of 100 grams and the mass of the ant is 4.0x10⁻³gram, then the mass of the tomato is 25,000 times greater than the mass of the ant.

The expression for finding the extent to which the Mass of the tomato is greater than that of the ant is given as follows:

100/4.0x10⁻³

= [100 x 10³] / 4.0x10⁻³ x 10³

= 100,000/4

= 25,000

Therefore, the tomato is 25,000 times the mass of the ant.

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Answer:yes 2.5* 10-2

Step-by-step explanation:

The SSS (Side-Side-Side) similarity theorem states that if three sides of one triangle are equal to the three corresponding sides of another triangle, then the triangles are similar.

To prove this theorem, one would have to use the Triangle Proportionality Theorem. This theorem states that the ratio of any two sides of a triangle is equal to the ratio of the corresponding sides of a similar triangle. Therefore, if the ratio of the corresponding sides of the two triangles is equal, then the triangles must be similar. To prove the SSS theorem, one would have to show that the ratio of the corresponding sides of the two triangles is equal.

The SSS (Side-Side-Side) similarity theorem states that if three sides of one triangle are equal to the three corresponding sides of another triangle, then the triangles are similar.

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Let length of the rectangle be l

Let witdth of the rectangle be b.

Perimeter = 2*(l+b)

Given

2*(l+b) = 52. ------------(1)

Now length is an odd integer. Let it be represented as

l = 2k+1 , where k is a positive integer

Given width of the rectangle is the 3 times next consecutive odd integer( next in reference to l = 2k+1)

So b = 3*(2k+3), where k is a positive , integer

From (1) we get

2[2k+1 + 3*(2k+3)] = 52

2[2k+1 + 6k +9] = 52

2[8k +10] = 52

4[4k +5] = 52

4k + 5 = 13

4k = 8

k = 2

so length (l) = 2k +1 = 2*2 + 1 =5 cm

width b = 3(2k +3) = 3(2*2+3) = 21 cm

Negative, positive, zero, and undefined are the 4 types of slopes on the graph.

the 4 types of slopes, include:

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Answer:

Option B) 803.84in²

Step-by-step explanation:

We know the formula to find the area of a circle is listed as,

[tex]A = \pi r^{2}[/tex]

But over here the diameter is only given

that means we have to find the radius which is,

[tex]r = \frac{32}{2}[/tex]

[tex]r = 16in[/tex]

Now we can find the area of a circle which is,

[tex]A = 3.14X(16)^{2}[/tex]

[tex]A = 803.84in^{2}[/tex]

Hence , Option B) is the correct answer

The value k = 6 satisfies both equations Kx + 3y − (K − 3) = 0 and 12x + Ky − K = 0.

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

An equation that depicts a straight line on a graph is said to be linear. The "line" in the name of the equation will help you remember this. Regular Form. Standard forms for linear equations look like this: Ax + By = C.

A linear equation has the form y = mx + b in the slope-intercept notation. X and Y are the variables in the equation. The values m and b represent the line's slope (m) and the value of y when x is 0. (b).

Given

Kx + 3y −(K − 3) = 0

Comparing with [tex]$a_1 x+b_1 y+c 1=0$[/tex]

[tex]$$\therefore \mathrm{a}_1=\mathrm{k}, \mathrm{b}_1=3, \mathrm{c}=-(\mathrm{k}-3)$$[/tex]

12x + ky - k = 0

Comparing with [tex]$a_1 x+b_1 y+c 1=0$[/tex]

[tex]$$\therefore a_1=12, b_1=k, c=-k$$[/tex]

Since equation has infinite number of solutions

So, [tex]$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$[/tex]

substitute the values in the above equation, we get

[tex]$\frac{\mathrm{k}}{12}=\frac{3}{\mathrm{k}}=\frac{\mathrm{k}-3}{\mathrm{k}}$$[/tex]

simplifying the equation, we get

[tex]$\frac{\mathrm{k}}{12}=\frac{3}{\mathrm{k}}$$[/tex]

[tex]$$\mathrm{k}^2=12 \times 3$$[/tex]

[tex]$$\mathrm{k}^2=36$$[/tex]

[tex]$$\mathrm{k}=\pm 6$$[/tex]

[tex]$\frac{3}{\mathrm{k}}=\frac{\mathrm{k}-3}{\mathrm{k}}$$[/tex]

simplifying the equation, we get

[tex]$$3 \mathrm{k}=\mathrm{k}(\mathrm{k}-3)$$[/tex]

[tex]$$\mathrm{k}=\pm 6$$[/tex]

[tex]$\frac{3}{k}=\frac{k-3}{k}$$[/tex]

[tex]$$3 \mathrm{k}=\mathrm{k}(\mathrm{k}-3)$$[/tex]

simplifying the equation, we get

[tex]$$3 k=k^2-3 k$$[/tex]

[tex]$$\mathrm{k}^2-3 \mathrm{k}-3 \mathrm{k}=0$$[/tex]

[tex]$$k^2-6 k=0$$[/tex]

[tex]$$\mathrm{k}(\mathrm{k}-6)=0$$[/tex]

k = 0, 6

Therefore, k = 6 satisfies both equations.

The complete question is:

For what value of K will the following pair of linear equations have infinitely many solutions?

Kx + 3y −(K − 3) = 0

12x + Ky − K = 0

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Common logarithmic functions are defined as logarithms with base 10 and natural logarithmic functions as those with base e. The common log function is primarily utilized.

The log's value can be expressed in either base 10 or base e. While the value of [tex]log_e 10[/tex] or ln(10) is 2.302585, the value of [tex]log_{10} 10[/tex] is 1. In general, there are two types of logarithmic functions, namely:

1. Frequently Used Logarithmic Function

2. Natural Logarithmic Function

If [tex]log_{a}b[/tex] = x, then axe = b is the definition of the logarithmic function.

Where x is a number's logarithm, "b," and "a" is the base of the log function, which might be either the value "e" or "10." Any positive number, other than 1, should be used as the variable "a," which should not be equal to 1.

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