factorise 6xy - 5x squared

Answer:

Step-by-step explanation:

Love these kinda problems.

Alr,

d/dx of lnx = 1/x

let 3x³ + 12x = t

dt/dx = 9x² + 12 ( d/dx of xⁿ = n[tex]x^{n-1}[/tex])

then, d/dx of ln t= 1/t x dt/dx  = 1/(3x³+12x) x (9x² + 12) = (3x² + 4)/(x³ + 4x)

Pls mark as brainliest if possible. Cheers

The geom_ jitter () method creates a scatter plot and then it adds a small amount of random noise to every point in the plot to make the points easier to find.

Therefore, the geom_jitter is shortcut that creates a scatterplot and add random variation in each point.

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The daily cost to heat a building at 10 degrees celsius is  $82.72

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

f(x)=6(1.3)^-x

Then, we have

x = 10

This implies that

f(-10) = 6(1.3)^-(-10)

Evaluate the expression

f(-10) = 82.72

This means that the cost to heat is $82.72

Also, the domain is all set of real numbers and the range is y > 0

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Complete question

During the winter if the low temperature outside is x Celsius,the daily cost to heat a building can be determined using the function f(x)=6(1.3)^-x.find and interpret the given function values and determine an appropriate domain for the function

f(10)

Answer:

Step-by-step explanation:

You want to know the amounts invested at each rate if twice as much is invested at 4.5% as at 3.5%, and the total earnings are $1875.

Let x represent the amount invested at 3.5%. Then 2x is the amount invested at 4.5%, and the total earnings are ...

  0.035x +0.045(2x) = 1875

  0.125x = 1875 . . . . . . . . . collect terms

  x = 15000 . . . . . . . . . divide by 0.125

  2x = 30000 . . . . . . . find the other value invested

The amount deposited at 3.5% is $15,000; the amount deposited at 4.5% is $30,000.

Answer:

6

Step-by-step explanation:

85 +12.5*x visits =155

12.5x≥70

x must be greater than 5.6 so she need to go 6 times & then she'll get her free ticket

Plot the given coordinates of the polygon in the coordinate plane and connect it with a smooth curve.

A two-dimensional geometric shape with a finite number of sides is called a polygon. A polygon's sides are constructed from segments of straight lines joined end to end.

A coordinate plane is a two-dimensional plane created by the intersection of two number lines. The x-axis, a horizontal number line, and the y-axis, a vertical number line, are two of these number lines.

Plot the points on the graph according to the given coordinates. Connect all the points. The polygon is triangle.

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Answer:

2 miles

Step-by-step explanation:

Distance = speed x time

= 10mph x 1/5

= 2 miles

√25  is the greatest value of the expressions .

What is an expression in maths ?

A number, a variable, or a mix of both plus certain operation symbols make up an expression. Two expressions are combined to form an equation, which is joined by the equal sign.

                         The combination of 8 and 3 is an example of a word. Example sentence: The result of adding 8 and 3 is 11. An expression in mathematics is made up of a mixture of variables, numbers, and functions (such as addition, subtraction, multiplication or division etc.) In some ways, phrases and expressions are comparable.

√25   = 5

√5  =   2.2360

√8  =   2.8284

√10 =    3.1622

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Answer: 96 Euros each month

Step-by-step explanation: 2400 * 0.2 = 480 -> 2400-480 = 1920(this is the amount of money needed to pay each month) 1920 / 20 = 96

Answer:

>4

Step-by-step explanation:

the answer of the question is >4

Answer:

A= 110 degrees AND B= 140 degrees.

Y= 112 degrees and X= 157 degrees.

Step-by-step explanation:

Triangle XYZ is an isocoles triangle, because it has two congruent sides. 70 degrees is a measurement of an angle opposite of one of those congruent sides, so angle YXZ is also 70 degrees. By the triangle angle sum theorem, we can say that the measurement of angle YZX is 40 degrees. So, for the first triangle, by the linear pairs theorem, we can find the two missing angles.

A= 110 degrees AND B=140 degrees.

For the triangle on the right, we can use the triangle angle sum theorem to say that angle BDC is 68 degrees. Then, we can say that by the by the linear pairs theorem that angle ADE is 112 degrees.  From there, we need to look at the 23 degree measurement on the lower right triangle. We can see that the angle steadily rises on that line and then we can take 180-23 by the linear pairs theorem to conclude than angle BEA is 157 degrees. This can be confirmed by looking at the two innermost angles in the top right triangle. If you take 180-23-112, you will get 45. If you add 45 to 112, you will get 157.

Y= 112 degrees and X= 157 degrees.

The time it takes until the deposit amounts to $6,000 is 2.6 years

From the question, we are to calculate how long it takes until the deposit amounts to $6000

From the compound interest formula, we have that

A = P(1 + r/n)^nt

Where A is the amount

P is the principal

r is the interest rate

n is the number of times compounded per year

and t is the time.

From the given information,

P = $5,000

r = 7%= 0.07

n = 12

t = ?

A = $6,000

Putting the parameters into the formula

A = P(1 + r/n)^nt

6000 = 5000(1 + 0.07/12)^(12×t)

6000/5000 = (1 + 0.0058333)^12t

1.2 = (1.0058333)^12t

Take log1.0058333 of both sides

31.346375 = 12t

31.346375/12 = t

t = 2.6 years

Hence, the time it takes is 2.6 years

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The graph that represents a geometric sequence is Graph A.

A geometric sequence is a sequence of numbers in which each term after the first is found by multiplying the preceding one by a fixed, non-zero number called the common ratio.

Examples of geometric sequences include:

2, 4, 8, 16, 32, ... (common ratio of 2)

1/3, 2/3, 4/3, 8/3, ... (common ratio of 2/3)

5, -25, 125, -625, ... (common ratio of -5)

Geometric sequences have the property that the ratio of any two consecutive terms is always the same, and the quotient of any two consecutive terms is the common ratio.

This is shown only in the first graph so Graph A shows the geometric sequence.

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Answer:

[tex] - 2 \sqrt{5} [/tex]

Step-by-step explanation:

[tex] \sqrt{20} - \sqrt{80} [/tex]

[tex]2 \sqrt{5} - 4 \sqrt{5} [/tex]

[tex](2 - 4) \sqrt{5} [/tex]

[tex] - 2 \sqrt{5} [/tex]

Answer: 844000

Step-by-step explanation:

843857 = 844000 because you round up

Answer:

0.65 and 13/20

Step-by-step explanation:

The two column proof showing that  ΔWXZ ≅ ΔYXZ is as shown below

From the given triangle, we see that;

Given: WX ≅ XY, XZ bisects WXY

Prove: ΔWXZ ≅ ΔYXZ

The two column proof for the above is as follows;

Statement 1;  WX ≅ XY, XZ bisects 2

Reason 1; Given

Statement 2: ∠WXZ ≅ YXZ

Reason 2; Angle bisector

Statement 3; XZ ≅ XZ

Reason 3: Reflexive property of congruence

Statement 4:  ΔWXZ  ≅ ΔYXZ

Reason 4:  SAS Congruence Postulate

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a. The explanatory variable is the new blood clot medication, and the confounding variable is the time period of 12 hours after the stroke begins.

b. The explanatory variable is the new software program, and the confounding variable is the 1-hour period after school

The confounding variable may invalidate the conclusions of the study because it is possible that the higher rate of total recovery is not due to the new medication, but rather due to the fact that the patients are being treated within the crucial 12-hour period after the stroke begins. To eliminate the effect of the confounding variable, the study could be conducted as a randomized controlled trial, where patients are randomly assigned to receive either the new medication or a placebo, and both groups are treated within the 12-hour period after the stroke begins.

In (b) the explanatory variable is the new software program, and the confounding variable is the 1-hour period after school. The confounding variable may invalidate the conclusions of the study because it is possible that the higher scores are not due to the software, but rather due to the fact that the students using the software were given more time to study and practice. To eliminate the effect of the confounding variable, the study could be conducted as a randomized controlled trial, where students are randomly assigned to use the software or not, and both groups are given the same amount of time to study and practice.

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Answer:

10

Step-by-step explanation:

The given series is a geometric series with the first term a = 8, and the common ratio r = 1/5. To find the sum of the series, we can use the formula for the sum of an infinite geometric series:

S = a / (1 - r)

So, in this case, the sum of the series is:

S = 8 / (1 - 1/5) = 8 / (4/5) = 8 * (5/4) = 40/4 = 10.

Therefore, the sum of the series is 10.

Answer:

10

Step-by-step explanation:

A geometric series is the sum of the terms of a geometric sequence.

[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Sum of an infinite geometric series}\\\\$S_{\infty}=\dfrac{a}{1-r}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $r$ is the common ratio.\\\end{minipage}}[/tex]

Given geometric series:

The ellipsis means to "continue in this pattern".  Therefore, find the sum to infinity of the given geometric series.

From inspection of the sequence, the first term is 8:

[tex]\implies a=8[/tex]

To find the common ratio, divide consecutive terms:

[tex]\implies r=\dfrac{a_2}{a_1}=\dfrac{1.6}{8}=0.2[/tex]

Substitute the found values of a and r into the geometric series formula:

[tex]\implies S_{\infty}=\dfrac{8}{1-0.2}=\dfrac{8}{0.8}=10[/tex]

Therefore, the sum of the given geometric series is 10.

Step-by-step explanation:

as always with % calculations :

first find what is 100% or 1%. everything else can be calculated from that.

in our case, we got 100% = 18.

therefore, 1% = 100%/100 = 18/100 = 0.18

how many % are 4 students ?

as many as the times 1% (0.18) fits into 4 :

4 / 0.18 = 22.22222222... %

so,

22.22222222... %

of the students passed.

therefore,

100 - 22.22222222... = 77.77777777... %

of the students did not pass.

The expression for the given word phrase is

46M + M² + 2 + 1/M²

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Number = M

Reciprocal of M = 1/M

Now,

46 x (M + 1/M)²

Step 1:

46M + M² + 2 + 1/M²

Thus,

The expression is 46M + M² + 2 + 1/M²

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well, the interest is going to be the increase factor on both cases, so we can simply check how much each will accumulate to in those 4 years

[tex]~~~~~~ \stackrel{\textit{\LARGE University Bank}}{\textit{Compound Interest Earned Amount}} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$4000\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &4 \end{cases}[/tex]

[tex]A = 4000\left(1+\frac{0.05}{4}\right)^{4\cdot 4} \implies A=4000(1.0125)^{16}\implies \boxed{A \approx 4879.56} \\\\[-0.35em] ~\dotfill[/tex]

[tex]~~~~~~ \stackrel{\textit{\LARGE Rosemont Savings Bank}}{\textit{Compound Interest Earned Amount}} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$4000\\ r=rate\to 5.5\%\to \frac{5.5}{100}\dotfill &0.055\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semiannually, thus two} \end{array}\dotfill &2\\ t=years\dotfill &4 \end{cases}[/tex]

[tex]A = 4000\left(1+\frac{0.055}{2}\right)^{2\cdot 4} \implies A=4000(1.0275)^8\implies \boxed{A \approx 4969.52} ~~ \textit{\LARGE \checkmark}[/tex]

The midpoint of f(x) over the interval [1, 2] is 4.8655

Generally, The point that represents the precise midway point between an interval's beginning and ending points is known as the midpoint of the interval. It may be determined by calculating the average of the two values that serve as endpoints.

For instance, the value 5 would represent the point that is exactly in the middle of the interval [3,7].

The midpoint of the interval [1, 2] is

(1 + 2) / 2

= 1.5.

To calculate the value of f(x) at x = 1.5, we need to substitute 1.5 for x in the function:

f(1.5) = 6 * ln(1.5^2)

= 6 * ln(2.25)

= 6 * 0.83

= 4.8655

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Answer:

B)  x + y ≤ 30,000

     x ≥ 8,000

     x ≥ 3y

Step-by-step explanation:

Definition of the variables:

If Tamara has $30,000 and part or all of which she wants to invest into a combination of corporate bonds and municipal bonds, then the sum of the investments in the two bonds will be less than or equal to $30,000:

If Tamara wants to invest no less than $8,000 into corporate bonds, then the amount invested in corporate bonds (x) will be greater than or equal to $8,000:

If Tamara wants to invest at least three times as much into corporate bonds than into municipal bonds, then the amount invested in corporate bonds (x) will be greater than or equal to 3 times the amount invested in municipal bonds (y):

a) The perimeter of a rectangle is the sum of all four sides. So to find the perimeter we can add these two sides together, and then double the result.

The simplified expression for the perimeter of the rectangle would be:

2(2n - 3 + 4)

This can also be written as:

2(2n + 1)

This expression represents the mathematical operation where the sum of 2n - 3 and 4 is calculated, then multiplied by 2 to find the perimeter of the rectangle.

b) If the perimeter of the rectangle is 26, we can use the expression for the perimeter that we found earlier to solve for the value of n.

The perimeter of the rectangle is:

2(2n + 1) = 26

So if we divide both sides of the equation by 2, we get:

2n + 1 = 13

then if we subtract 1 from both sides

2n = 12

then if we divide by 2

n = 6

So the value of n is 6.

I hope this helps :)

Answer:

a. [tex]P = 4n + 2[/tex]

b. [tex]n = 6[/tex]

Step-by-step explanation:

a. The formula for the perimeter of a rectangle was:

[tex]P = 2L + 2W[/tex]

Given that the length was 2n-3 and the width was 4, substitute the values its formula:

[tex]P = 2L + 2W\\P = 2(2n-3) + 2(4)\\P = 4n - 6 + 8\\P = 4n + 2[/tex]

b. Since the perimeter of the rectangle was already indicated, we will just sunstitute it to the expression that we get from a.

[tex]P = 4n + 2\\26 = 4n + 2\\26 - 2 = 4n\\24 = 4n\\6 = n[/tex]

The alternate interior angles are the angles that are formed inside the two parallel lines, when it is intersected by a transversal, and are equal to its alternate pairs.

Alternate interior angles are the angles formed when a transversal intersects two coplanar lines. They lie on the inner side of the parallel lines but on the opposite sides of the transversal. The transversal crosses through the two lines which are Coplanar at separate points.

Alternate angles are shaped by the two parallel lines crossed by a transversal. Consider the given figure, EF and GH are the two parallel lines. If two parallel lines are cut by a transversal, then the alternate angles are equal.

In order to understand alternate interior angles, one must first picture a set of parallel lines, and then a line intersecting them. The intersecting line is called a transversal, and all the angles formed between the parallel lines are the interior angles.

At the point of intersection of transversal and two lines we have:

∠3 + ∠4 = 180 .........(1)

∠6 + ∠8 = 180 ...........(2)

We know that angle 4 and angle 8 are equal:

Thus, using 1 and 2 we have:

∠3 = ∠6

Hence, ∠3 and ∠6 are congruent.

Now, using the alternate interior angle we know that:

∠3 = ∠6

Also, we have:

∠5 + ∠6 = 180 (Straight line)

Substituting the value of ∠6 = ∠3 we have:

∠5 + ∠3 = 180

Thus, the two angles are supplementary.

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The values are;

1. 35/3 days - Direct proportion

2. 4254 - Direct proportion

3. 120 teachers - Indirect proportion

Proportion can be described as an equation that has two ratios set equal to each other.

It is also seen as a mathematical comparison of numbers, terms, or variables.

The different types of proportion are;

From the information given, we have;

1. If 3 men completes the project in 7 days

Then 5 men would finish it in x days

cross multiply

x = 5(7)/3

x = 35/3 days

2. If 25kg of rice cost 1130

Then 100kg would cost x

cross mutiply

x = 1130(100)/25

x =  4,254

3. If there are 90 teachers = 1500 students

Then x teachers = 2000 students

x = 2000(90)/1500

x = 120 teachers

Hence, the values are 35/3 days, 4, 254 and 120 teachers.

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Side AC in the triangle is 3.6 and side BC in the triangle is 1.7

The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.

To find side AC :

4/sin90 = AC / sin64.3

AC × sin90 = sin 64.3 × 4

AC = 0.9 ×4

AC = 3.6 ( nearest tenth)

To find side BC:

using Pythagoras theorem

4² = 3.6² + (BC)²

16 = 12.96 +(BC)²

(BC)² = 16 - 12.96

(BC)² = 3.04

BC = √ 3.04

BC = 1.7( nearest tenth)

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Answer:

Question 4:

Question 5:

Question 6:

Step-by-step explanation:

Given vertices of the pre-image:

If the pre-image is reflected in the line x = -1, the transformation rule is:

Therefore the vertices of the image are:

Given vertices of the pre-image:

If the pre-image is rotated 180° about the origin, the transformation rule is:

Therefore the vertices of the image are:

Given vertices of the pre-image:

If the pre-image is rotated 270° about the origin, the transformation rule is:

If the direction of a rotation is not specified, then it is counterclockwise.

Therefore the vertices of the image are: